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# How to calculate transformed skin vertices? The code I tried: ``````var transformedSkinVertex = function (skin, index) { var skinIndices = (new THREE.Vector4 ()).fromAttribute (skin.geometry.getAttribute ('skinIndex'), index); var skinWeights = (new THREE.Vector4 ()).fromAttribute (skin.geometry.getAttribute ('skinWeight'), index); var skinVertex = (new THREE.Vector3 ()).fromAttribute (skin.geometry.getAttribute ('position'), index).applyMatrix4 (skin.bindMatrix); var result = new THREE.Vector3 (), temp = new THREE.Vector3 (), tempMatrix = new THREE.Matrix4 (); properties = ['x', 'y', 'z', 'w']; for (var i = 0; i < 4; i++) { var boneIndex = skinIndices[properties[i]]; tempMatrix.multiplyMatrices (skin.skeleton.bones[boneIndex].matrixWorld, skin.skeleton.boneInverses[boneIndex]); result.add (temp.copy (skinVertex).multiplyScalar (skinWeights[properties[i]]).applyMatrix4 (tempMatrix)); } return result.applyMatrix4 (skin.bindMatrixInverse); }; `````` This works for T pose: But with arms lowered some parts explode into angel-like shape: Here is arms placed slightly differently: My current theory is that this happens when there are > 2 bones. But... why? All weights correctly add up to 1, as you can see above three.js renders the skin correcty. • Is this on r72dev? – mrdoob Jul 24 '15 at 22:43 • no, r70. this project is a bit old. – makc Jul 24 '15 at 22:48 ## 1 Answer Resolved. Correct line is ``````result.add (temp.copy (skinVertex).applyMatrix4 (tempMatrix).multiplyScalar (skinWeights[properties[i]])); `````` I did not think the order of multiplication by scalar would matter.

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# oscillator Also found in: Dictionary, Thesaurus, Medical, Legal, Financial, Acronyms, Idioms, Wikipedia. ## oscillator [′äs·ə‚lād·ər] (electronics) An electronic circuit that converts energy from a direct-current source to a periodically varying electric output. The stage of a superheterodyne receiver that generates a radio-frequency signal of the correct frequency to mix with the incoming signal and produce the intermediate-frequency value of the receiver. The stage of a transmitter that generates the carrier frequency of the station or some fraction of the carrier frequency. (physics) Any device (mechanical or electrical) which, in the absence of external forces, can have a periodic back- and-forth motion, the frequency determined by the properties of the oscillator. ## Oscillator a physical system that performs oscillations. The term “oscillator” is used for any system that can be described by variables that change periodically with time. Classical oscillator. The classical oscillator is a mechanical system that vibrates around a fixed equilibrium point. In the equilibrium position the potential energy U of the system is at a minimum. If the deviation x from this position is small, then the power-series expansion of U(x) is approximated by the expression kx2/2, where K is a constant, and the quasi-elastic force F = – ∂ U/∂x = – kx (seeQUASI-ELASTIC FORCE). Such oscillators are called harmonic oscillators and their motion is described by the linear equation mẍ = –kx, which has a solution of the form x = A sin (ωt + ϕ), where m is the mass of the oscillator, ω is the angular frequency (which equals , A is the vibration amplitude, ϕ is the initial phase, and t is time. The total energy E of a harmonic oscillator is given by mω2A2/2, which is the sum of the kinetic energy T and potential energy U. These energies are periodically changing with opposite phases, and the total energy E = T + U is independent of time. When the deviation x cannot be regarded as small, it is necessary to take into account higher-order terms in the expansion of U(x): the equation of motion becomes nonlinear, and the oscillator is called anharmonic. The principle of an oscillator can also be applied to non-mechanical oscillating systems, for example, in electromagnet-ism, acoustics, and gravitational theory. The most frequently encountered application is the electrical oscillator—an oscillating circuit with inductance and capacitance. The oscillations of the electric and magnetic field intensities in a plane electromagnetic wave can also be described using the principle of oscillators. Quantum oscillator. The problem of the linear harmonic oscillator with one degree of freedom in quantum mechanics is solved by the Schrödinger equation, in which the potential energy U is assumed to be equal to kx2/2. A solution exists for only a discrete set of energy values: where h is Planck’s constant and n is zero or any positive integer. An important feature of the energy spectrum for this oscillator is that the levels of the energies En are equally spaced. Because the selection rules permit transitions only between adjacent energy levels, the radiation of a quantum oscillator has a single frequency, ω—although a quantum oscillator has a set of natural frequencies ωn = En/ℏ. This agrees with the classical case: ω. Unlike the case that holds for the classical oscillator, the lowest possible energy level (when n = 0) of the quantum oscillator is not equal to zero but to ℏω/2 (the condition that corresponds to zero energy). The oscillator principle plays an important role in solid-state theory and in the theories of electromagnetic radiation and molecular vibrational spectra. ### REFERENCES Landau, L. D., and E. M. Lifshits. Mekhanika: Elektrodinamika, ch. 5. (Kratkii kurs teoreticheskoi fiziki, book 1.) Moscow, 1969. Landau, L. D., and E. M. Lifshits. Teoriia polia, 5th ed. (Teoreticheskaia fizika, vol. 2.) Moscow, 1967. Landau, L. D., and E. M. Lifshits. Kvantovaia mekhanika. (Teoreticheskaia fizika, vol. 3.) Moscow, 1963. Leontovich, M. A. Statisticheskaia fizika. Moscow-Leningrad, 1944. V. P. PAVLOV ## Oscillator An electronic circuit that generates a periodic output, often a sinusoid or a square wave. Oscillators have a wide range of applications in electronic circuits: they are used, for example, to produce the so-called clock signals that synchronize the internal operations of all computers; they produce and decode radio signals; they produce the scanning signals for television tubes; they keep time in electronic wristwatches; and they can be used to convert signals from transducers into a readily transmitted form. Oscillators may be constructed in many ways, but they always contain certain types of elements. They need a power supply, a frequency-determining element or circuit, a positive-feedback circuit or device (to prevent a zero output), and a nonlinearity (to define the output-signal amplitude). Different choices for these elements give different oscillator circuits with different properties and applications. Oscillators are broadly divided into relaxation and quasilinear classes. Relaxation oscillators use strong nonlinearities, such as switching elements, and their internal signals tend to have sharp edges and sudden changes in slope; often these signals are square waves, trapezoids, or triangle waves. The quasilinear oscillators, on the other hand, tend to contain smooth sinusoidal signals because they regulate amplitude with weak nonlinearities. The type of signal appearing internally does not always determine the application, since it is possible to convert between sine and square waves. Relaxation oscillators are often simpler to design and more flexible, while the nearly linear types dominate when precise control of frequency is important. #### Relaxation oscillators Illustration a shows a simple operational-amplifier based relaxation oscillator. This circuit can be understood in a number of ways (for example, as a negative-resistance circuit), but its operation can be followed by studying the signals at its nodes (illus. b). The two resistors, labeled r, provide a positive-feedback path that forces the amplifier output to saturate at the largest possible (either positive or negative) output voltage. If v+, for example, is initially slightly greater than v-, then the amplifier action increases vo, which in turn further increases v+ through the two resistors labelled r. This loop continues to operate, increasing vo until the operational amplifier saturates at some value Vmax. [An operational amplifier ideally follows Eq. (1) (1), where Av is very large, but is restricted to output levels &verbar;vo&verbar; ≤ Vmax.] For the purposes of analyzing the circuit, the waveforms in the illustration have been drawn with the assumption that this mechanism has already operated at time 0 and that the initial charge on the capacitor is zero. See Amplifier, Operational amplifier Capacitor C will now slowly change from vo through resistor R, toward Vmax, according to Eq. (2). (2)  Up until time t1, this process continues without any change in the amplifier's output because v+ > v-, and so vo = Vmax. At t1, however, v+ = v- and vo will start to decrease. This causes v+ to drop, and the positive-feedback action now drives the amplifier output negative until vo = -Vmax. Capacitor C now discharges exponentially toward the new output voltage until once again, at time t2, v+ = v-, and the process starts again. The period of oscillation for this circuit is 2RC ln 3. The basic elements of an oscillator that were mentioned above are all clearly visible in this circuit. Two direct-current power supplies are implicit in the diagram (the operational amplifier will not work without them), the RC circuit sets frequency, there is a resistive positive-feedback path that makes the mathematical possibility vo(t) = 0 unstable, and the saturation behavior of the amplifier sets the amplitude of oscillation at the output to ±Vmax. Relaxation oscillators that have a low duty cycle—that is, produce output pulses whose durations are a small fraction of the overall period—are sometimes called blocking oscillators because their operation is characterized by an “on” transient that “blocks” itself, followed by a recovery period. Inverters (digital circuits that invert a logic signal, so that a 0 at the input produces a 1 at the output, and vice versa) are essentially voltage amplifiers and can be used to make relaxation oscillators in a number of ways. A circuit related to that of the illustration uses a loop of two inverters and a capacitor C to provide positive feedback, with a resistor R in parallel with one of the inverters to provide an RC charging time to set frequency. This circuit is commonly given as a simple example, but there are a number of problems with using it, such as that the input voltage to the first gate sometimes exceeds the specified limits for practical gates. A more practical digital relaxation oscillator, called a ring oscillator, consists simply of a ring containing an odd number N (greater than 1) of inverters. See Logic circuits #### Sine-wave oscillators Oscillators in the second major class have their oscillation frequency set by a linear circuit, and their amplitudes set by a weak nonlinearity. A simple example of a suitable linear circuit is a two-component loop consisting of an ideal inductor [whose voltage is given by Eq. (3), (3) where i is its current] and a capacitor [whose current is given by Eq. (4)], (4) connected in parallel. These are said to be linear elements because, in a sense, output is directly proportional to input, for example, doubling the voltage v across a capacitor also doubles dv/dt and therefore doubles i. The overall differential equation for a capacitor-inductor loop can be written as Eq. (5). (5)  Mathematically this has solutions of the form of Eq. (6), (6) where &ohgr; = 1/LC [which means that the circuit oscillates at a frequency 1/(2&pgr;LC)] and A and &phgr; are undefined. They are undefined precisely because the elements in the circuit are linear and do not vary with time: any solution (possible behavior) to the equation can be scaled arbitrarily or time-shifted arbitrarily to give another. Practically, A and &phgr; are determined by weak nonlinearities in a circuit. Equation (5) is a good first approximation to the equation describing a pendulum, and so has a long history as an accurate timekeeper. Its value as an oscillator comes from Galileo's original observation that the frequency of oscillation (&ohgr;/2&pgr;) is independent of the amplitude A. This contrasts sharply with the case of the relaxation oscillator, where any drift in the amplitude (resulting from a threshold shift in a comparator, for instance) can translate directly into a change of frequency. Equation (5) also fundamentally describes the operation of the quartz crystal that has replaced the pendulum as a timekeeper; the physical resonance of the crystal occurs at a time constant defined by its spring constant and its mass. #### Frequency locking If an external signal is injected into an oscillator, the natural frequency of oscillation may be affected. If the external signal is periodic, oscillation may lock to the external frequency, a multiple of it, or a submultiple of it, or exhibit an irregular behavior known as chaos. This locking behavior occurs in all oscillators, sometimes corrupting intended behavior (as when an oscillator locks unintentionally to a harmonic of the power-line frequency) and sometimes by design. An important example of an oscillator that exploits this locking principle is the human heart. Small portions of heart muscle act as relaxation oscillators. They contract, incidentally producing an output voltage that is coupled to their neighbors. For a short time the muscle then recovers from the contraction. As it recovers, it begins to become sensitive to externally applied voltages that can trigger it to contract again (although it will eventually contract anyway). Each small section of heart muscle is thus an independent oscillator, electrically coupled to its neighbors, but the whole heart is synchronized by the frequency-locking mechanism. ## oscillator i. An electronic circuit that converts energy from a direct-current source to a periodically varying electric output. ii. The stage of a superheterodyne receiver that generates a radio-frequency signal of the correct frequency to mix with the incoming carrier signal to produce the intermediate-frequency value of the receiver. iii. The stage of a transmitter that generates the carrier frequency or some fraction of the carrier frequency. ## oscillator An electronic circuit used to generate high-frequency pulses. See crystal oscillator, VCO and clock. References in periodicals archive ? In addition, an emerging use of MEMS technology is as a replacement for traditional crystal oscillators. Here, we will compare the characteristics and advantages of MEMS vs. The main idea is to eliminate the disadvantages of symmetrical load differential VCO, and play to their strengths, to design a new extension delay unit configuration, so that a cascade of 3 stages of these units constitute a High Performance Voltage-Controlled oscillator (HPVCO), characterized by a stable full-swing output with a wide range of voltage regulation. The design of the active frequency stabilization oscillator and the initial experimental verification started from the hypothesis according to which the performances of an oscillator can be significantly enhanced by replacing the varicap diode with a BST capacitor. In order to validate our theoretical analysis above, we are going to build a model of an effective negative mass system with pure Duffing oscillator in five periods as shown in Figure 4. Scholl, "Amplitude death in oscillator networks with variable-delay coupling," Physical Review E, vol. Nevertheless, it should be noted that the Taylor expansion may not be applicable to the PN of a free-running oscillator, whose variance increases linearly with time, after long transmission.) As a result, (30) can be approximated as The test revealed that the average phase noise spur power due to EMI was lower for the MEMS oscillator than for any of the quartz oscillators in this study. During a chaotic event the maximum amplitudes of oscillation are far from being symmetrical about the equilibrium position of the oscillator. (ii) The nonlinear oscillator equation has converted to nonlinear algebraic equation by this approach which can be solved by numerical methods that leads to a better result. Holzel, "Simple wide-band sine wave quadrature oscillator," IEEE Transactions on Instrumentation and Measurement, vol. The Effect of the Higher-Order Coupling Term in Inducing the Synchronization of the Inhibitory Neuronal Oscillator Population under Spontaneous Activity. The next step would be building a larger network of oscillators that could handle graph coloring problems with more objects at play. Site: Follow: Share: Open / Close

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# HELP Announcements Posted on Why bother with a post grad? Are they even worth it? Have your say! 26-10-2016 1. if someone can give me an hint to how to proceed with this exercise I will appreciate that...thanks Attached Files 2. 00.docx (15.1 KB, 25 views) 3. (Original post by carmenbn) if someone can give me an hint to how to proceed with this exercise I will appreciate that...thanks Start off by plotting the graph of concentration vs velocity (you can calculate them using the Beer-Lambert law). You should find it to be a curve, and the velocity which the curve approaches can be estimated to be Vmax (i.e. the asymptote). Vmax/2 is Km. Then plot the lineweaver-burk plot (1/V vs 1/substrate) and see if you can work out how to calculate Vmax and Km (think of the gradient and intercepts). 4. Thanks...but the major problem is that i'm confused about the units...in the exercise it is asked to change them ! ## Register Thanks for posting! You just need to create an account in order to submit the post 1. this can't be left blank 2. this can't be left blank 3. this can't be left blank 6 characters or longer with both numbers and letters is safer 4. this can't be left empty 1. Oops, you need to agree to our Ts&Cs to register Updated: July 2, 2016 TSR Support Team We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out. This forum is supported by: Today on TSR ### Who is getting a uni offer this half term? Find out which unis are hot off the mark here ### Brexit: Why you should study law Poll Useful resources Study resources The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd. Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.

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* Example: Calculate mean wage of people of similar age sysuse nlsw88, clear rangestat wage, interval(age -1 1) list wage_mean in 10 sum wage if inrange(age, age[10]-1, age[10]+1) assert r(mean) == wage_mean[10] rangestat mwage = wage (count) wage, interval(age -1 1) excludeself by(race industry) list mwage wage_count in 4 sum wage if inrange(age, age[4]-1, age[4]+1) & race == race[4] & industry == industry[4] & _n != 4 assert r(mean) == mwage[4] * Example: Median investment of other firms in a given year webuse grunfeld, clear bysort year: egen m = median(invest) gen double mexclude = . quietly forvalues i=1/`=_N' { sum invest if year == year[`i'] & company != company[`i'], detail replace mexclude = r(p50) in `i' } rangestat (median) invest, interval(year 0 0) excludeself assert mexclude == invest_median * Example: Looking up the education of a child's mother within a household * Example generated by -dataex-. To install: ssc install dataex clear input float(hhid personid motherid educ) 101 1 . 10 101 3 1 8 101 4 1 0 101 5 3 0 102 1 . 9 102 2 1 . 102 4 . 6 102 5 4 2 end clonevar targetid = motherid replace targetid = 0 if mi(motherid) rangestat (min) educ, interval(personid targetid targetid) by(hhid) list, sepby(hhid) * Example: Calculating correlations using a user-supplied Mata function clear all webuse grunfeld replace invest = . in 8 mata: mata set matastrict on real rowvector my_pwcorr(real matrix X) { real matrix R R = correlation(X) return(R[2,1]) } end rangestat (my_pwcorr) invest mvalue, interval(year -5 0) by(company) list my_pwcorr1 in 20 corr invest mvalue if inrange(year, year[20]-5, year[20]) & company == company[20] assert r(rho) == my_pwcorr1[20] rename my_pwcorr1 my_pwcorr1a rangestat (my_pwcorr) invest mvalue (count) invest mvalue, interval(year -5 0) by(company) casewise describe mata: mata set matastrict on real rowvector N_corr(real matrix X) { real matrix R R = correlation(X) return(rows(X), R[2,1]) } end rangestat (N_corr) invest mvalue, interval(year -5 0) by(company) casewise * Comparison with tsegen (SSC) webuse grunfeld, clear tsegen double inv_m5b = rowmean(L(0/4).invest) rangestat (mean) invest, interval(year -4 0) by(company) assert inv_m5b == invest_mean rangestat (sd) sd_inv=invest kstock (count) invest kstock, interval(year -4 0) by(company)

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# Math- Find all values of the missing digit that make the statement true. 5,33_ is divisible by 11. A) 8 B) 6 C) 1 D) 5 1. 👍 0 2. 👎 0 3. 👁 115 1. Try them and see. It isn't 5338. Only one will work, since the evenly divisible numbers are 11 apart. 1. 👍 0 2. 👎 0 posted by drwls 2. d 5 1. 👍 0 2. 👎 0 posted by washa 3. because if u try 1 8 or 6 it will not work. 1. 👍 0 2. 👎 0 posted by washa 4. Correct 1. 👍 0 2. 👎 0 posted by drwls ## Similar Questions 1. ### Math Find all values of the missing digit that make the statement true 214,21_ is divisible by 11 asked by Connor on October 4, 2009 2. ### math Find the value of the missing digit that makes the statement true. 214,21_ is divisible by 11 Determine whether the statement is true or false. Why? If a natural number is divisible by 5 and 2, then it must also be divisible by asked by anonymous on March 19, 2011 3. ### Math Can someone please help me with this question? Find all values of the missing digit that makes the statement true: 4, 3, ... 0 is divisible by 6. My answer which I don't think is right is: 2, 5, 8. Is this correct? Thanks. asked by B.B. on July 4, 2009 4. ### Math Looking to find the missing digit for each statement true. The number 874_ is divisible by 4. Please help how to solve asked by Cyle on August 28, 2015 5. ### math divisibility i need to write the missing digit to make each number divisible by 3 1,843,#89 i got the missing number as : 3 s/b 1,843,389 is that right? #2 i need to write the missing digit to make each number divisible by 8 2,4#2 i cant asked by marko on November 30, 2011 6. ### Algebra ASAP so this is a fill in on a worksheet and I am having difficulty as the ones I inserted are incorrect can anybody help me how to do it all, sorry it's a long problem. Show that 3^2n − 1 is divisible by 8 for all natural numbers n. asked by Briane Mendez on August 12, 2015 7. ### math Find digits A and B in the number below so the folling condition are true. The 5-digit number must be divisible by 4. The 5-digit number must be divisible by 9. Digit A cannot be the same as Digit B. 12A3B Explain the steps you asked by peter on December 21, 2011 8. ### math Using the numbers 1 through 9 with no repeats, find a 9 number such that: the first digit is divisible by 1, the first two digits are divisible by 2, the first 3 digits are divisible by 3, and so on until we get to a 9 digit

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Chapter 7 Work, Energy, and Energy Resources # 7.4 Conservative Forces and Potential Energy ### Summary • Define conservative force, potential energy, and mechanical energy. • Explain the potential energy of a spring in terms of its compression when Hooke’s law applies. • Use the work-energy theorem to show how having only conservative forces implies conservation of mechanical energy. # Potential Energy and Conservative Forces Work is done by a force, and some forces, such as weight, have special characteristics. A conservative force is one, like the gravitational force, for which work done by or against it depends only on the starting and ending points of a motion and not on the path taken. We can define a potential energy ${(\text{PE})}$ for any conservative force, just as we did for the gravitational force. For example, when you wind up a toy, an egg timer, or an old-fashioned watch, you do work against its spring and store energy in it. (We treat these springs as ideal, in that we assume there is no friction and no production of thermal energy.) This stored energy is recoverable as work, and it is useful to think of it as potential energy contained in the spring. Indeed, the reason that the spring has this characteristic is that its force is conservative. That is, a conservative force results in stored or potential energy. Gravitational potential energy is one example, as is the energy stored in a spring. We will also see how conservative forces are related to the conservation of energy. ### POTENTIAL ENERGY AND CONSERVATIVE FORCES Potential energy is the energy a system has due to position, shape, or configuration. It is stored energy that is completely recoverable. A conservative force is one for which work done by or against it depends only on the starting and ending points of a motion and not on the path taken. We can define a potential energy ${(\text{PE})}$ for any conservative force. The work done against a conservative force to reach a final configuration depends on the configuration, not the path followed, and is the potential energy added. # Potential Energy of a Spring First, let us obtain an expression for the potential energy stored in a spring ${(\text{PE}_{\text{s}})}.$ We calculate the work done to stretch or compress a spring that obeys Hooke’s law. (Hooke’s law was examined in Chapter 5.3 Elasticity: Stress and Strain, and states that the magnitude of force ${F}$ on the spring and the resulting deformation ${\Delta{L}}$ are proportional, ${F=k\Delta{L}}.$ ) (See Figure 1.) For our spring, we will replace ${\Delta{L}}$ (the amount of deformation produced by a force ${F}$ ) by the distance ${x}$ that the spring is stretched or compressed along its length. So the force needed to stretch the spring has magnitude ${F = kx},$ where ${k}$ is the spring’s force constant. The force increases linearly from 0 at the start to ${kx}$ in the fully stretched position. The average force is ${kx/2}.$ Thus the work done in stretching or compressing the spring is ${W_{\text{s}}=Fd=(\frac{kx}{2})x=\frac{1}{2}kx^2}.$ Alternatively, we noted in Chapter 7.2 Kinetic Energy and the Work-Energy Theorem that the area under a graph of ${F}$ vs. ${x}$ is the work done by the force. In Figure 1(c) we see that this area is also ${\frac{1}{2}kx^2}.$ We therefore define the potential energy of a spring, $\text{PE}_{\text{s}},$ to be ${\text{PE}_{\text{s}}\:=}$ ${\frac{1}{2}}$ ${kx^2,}$ where ${k}$ is the spring’s force constant and ${x}$ is the displacement from its undeformed position. The potential energy represents the work done on the spring and the energy stored in it as a result of stretching or compressing it a distance ${x}.$ The potential energy of the spring $\text{PE}_{\text{s}}$ does not depend on the path taken; it depends only on the stretch or squeeze ${x}$ in the final configuration. The equation ${\text{PE}_{\text{s}}=\frac{1}{2}kx^2}$ has general validity beyond the special case for which it was derived. Potential energy can be stored in any elastic medium by deforming it. Indeed, the general definition of potential energy is energy due to position, shape, or configuration. For shape or position deformations, stored energy is ${\text{PE}_{\text{s}}=\frac{1}{2}kx^2},$ where ${k}$ is the force constant of the particular system and ${x}$ is its deformation. Another example is seen in Figure 2 for a guitar string. # Conservation of Mechanical Energy Let us now consider what form the work-energy theorem takes when only conservative forces are involved. This will lead us to the conservation of energy principle. The work-energy theorem states that the net work done by all forces acting on a system equals its change in kinetic energy. In equation form, this is ${W_{\text{net}}\:=}$ ${\frac{1}{2}}$ ${mv^2\:-}$ ${\frac{1}{2}}$ ${{mv_0}^2=\Delta\text{KE}}.$ If only conservative forces act, then ${W_{\text{net}}=W_{\text{c}}},$ where ${W_{\text{c}}}$ is the total work done by all conservative forces. Thus, ${W_{\text{c}}=\Delta\text{KE}}.$ Now, if the conservative force, such as the gravitational force or a spring force, does work, the system loses potential energy. That is, ${W_{\text{c}}=-\Delta\text{PE}}.$ Therefore, ${-\Delta\text{PE}=\Delta\text{KE}}$ or ${\Delta\text{KE}+\Delta\text{PE}=0}.$ This equation means that the total kinetic and potential energy is constant for any process involving only conservative forces. That is, $\begin{array}{lc} {} & {\text{KE}+\text{PE}=\text{constant}} \\ \text{or} & {} \\ {} & {\text{KE}_{\text{i}}+\text{PE}_{\text{i}}=\text{KE}_{\text{f}}+\text{PE}_{\text{f}}} \end{array}$ $\rbrace$ ${(\text{conservative forces only})},$ where i and f denote initial and final values. This equation is a form of the work-energy theorem for conservative forces; it is known as the conservation of mechanical energy principle. Remember that this applies to the extent that all the forces are conservative, so that friction is negligible. The total kinetic plus potential energy of a system is defined to be its mechanical energy, ${(\text{KE}+\text{PE})}.$ In a system that experiences only conservative forces, there is a potential energy associated with each force, and the energy only changes form between $\text{KE}$ and the various types of $\text{PE},$ with the total energy remaining constant. ### Example 1: Using Conservation of Mechanical Energy to Calculate the Speed of a Toy Car A 0.100-kg toy car is propelled by a compressed spring, as shown in Figure 3. The car follows a track that rises 0.180 m above the starting point. The spring is compressed 4.00 cm and has a force constant of 250.0 N/m. Assuming work done by friction to be negligible, find (a) how fast the car is going before it starts up the slope and (b) how fast it is going at the top of the slope. Strategy The spring force and the gravitational force are conservative forces, so conservation of mechanical energy can be used. Thus, ${\text{KE}_{\text{i}}+\text{PE}_{\text{i}}=\text{KE}_{\text{f}}+\text{PE}_{\text{f}}}$ or ${\frac{1}{2}}$ ${{mv_{\text{i}}}^2+mgh_{\text{i}}+}$ ${\frac{1}{2}}$ ${{kx_{\text{i}}}^2=}$ ${\frac{1}{2}}$ ${{mv_{\text{f}}}^2+mgh_{\text{f}}+}$ ${\frac{1}{2}}$ ${kx_{\text{f}}^2},$ where ${h}$ is the height (vertical position) and ${x}$ is the compression of the spring. This general statement looks complex but becomes much simpler when we start considering specific situations. First, we must identify the initial and final conditions in a problem; then, we enter them into the last equation to solve for an unknown. Solution for (a) This part of the problem is limited to conditions just before the car is released and just after it leaves the spring. Take the initial height to be zero, so that both ${h_{\text{i}}}$ and ${h_{\text{f}}}$ are zero. Furthermore, the initial speed ${v_{\text{i}}}$ is zero and the final compression of the spring ${x_{\text{f}}}$ is zero, and so several terms in the conservation of mechanical energy equation are zero and it simplifies to ${\frac{1}{2}}$ ${{kx_{\text{i}}}^2\:=}$ ${\frac{1}{2}}$ ${{mv_{\text{f}}}^2}.$ In other words, the initial potential energy in the spring is converted completely to kinetic energy in the absence of friction. Solving for the final speed and entering known values yields $\begin{array}{lcl} {v_{\text{f}}} & {=} & {\sqrt{\frac{k}{m}}x_\text{i}} \\ {} & {=} & {\sqrt{\frac{250.0\text{ N/m}}{0.100\text{ kg}}}(0.0400\text{ m})} \\ {} & {=} & {2.00\text{ m/s.}} \end{array}$ Solution for (b) One method of finding the speed at the top of the slope is to consider conditions just before the car is released and just after it reaches the top of the slope, completely ignoring everything in between. Doing the same type of analysis to find which terms are zero, the conservation of mechanical energy becomes ${\frac{1}{2}}$ ${{kx_{\text{i}}}^2=}$ ${\frac{1}{2}}$ ${{mv_{\text{f}}}^2+mgh_{\text{f}}}.$ This form of the equation means that the spring’s initial potential energy is converted partly to gravitational potential energy and partly to kinetic energy. The final speed at the top of the slope will be less than at the bottom. Solving for ${v_{\text{f}}}$ and substituting known values gives $\begin{array}{lcl} {v_{\text{f}}} & {=} & {\sqrt{\frac{{kx_{\text{i}}}^2}{m}-2gh_{\text{f}}}} \\ {} & {=} & {\sqrt{(\frac{250.0\text{ N/m}}{0.100\text{ kg}})(0.0400\text{ m})^2-2(9.80\text{ m/s}^2)(0.180\text{ m})}} \\ {} & {=} & {0.687\text{ m/s.}} \end{array}$ Discussion Another way to solve this problem is to realize that the car’s kinetic energy before it goes up the slope is converted partly to potential energy—that is, to take the final conditions in part (a) to be the initial conditions in part (b). Note that, for conservative forces, we do not directly calculate the work they do; rather, we consider their effects through their corresponding potential energies, just as we did in Example 1. Note also that we do not consider details of the path taken—only the starting and ending points are important (as long as the path is not impossible). This assumption is usually a tremendous simplification, because the path may be complicated and forces may vary along the way. ### PHET EXPLORATIONS: ENERGY SKATE PARK Learn about conservation of energy with a skater dude! Build tracks, ramps and jumps for the skater and view the kinetic energy, potential energy and friction as he moves. You can also take the skater to different planets or even space! # Section Summary • A conservative force is one for which work depends only on the starting and ending points of a motion, not on the path taken. • We can define potential energy ${(\text{PE})}$ for any conservative force, just as we defined $\text{PE}_{\text{g}}$ for the gravitational force. • The potential energy of a spring is ${\text{PE}_{\text{s}}=\frac{1}{2}kx^2},$ where ${k}$ is the spring’s force constant and ${x}$ is the displacement from its undeformed position. • Mechanical energy is defined to be ${\text{KE}+\text{PE}}$ for a conservative force. • When only conservative forces act on and within a system, the total mechanical energy is constant. In equation form, $\begin{array}{lc} {} & {\text{KE}+\text{PE}=\text{constant}} \\ \text{or} & {} \\ {} & {\text{KE}_{\text{i}}+\text{PE}_{\text{i}}=\text{KE}_{\text{f}}+\text{PE}_{\text{f}}} \end{array}$ $\rbrace$ where i and f denote initial and final values. This is known as the conservation of mechanical energy. ### Conceptual Questions 1: What is a conservative force? 2: The force exerted by a diving board is conservative, provided the internal friction is negligible. Assuming friction is negligible, describe changes in the potential energy of a diving board as a swimmer dives from it, starting just before the swimmer steps on the board until just after his feet leave it. 3: Define mechanical energy. What is the relationship of mechanical energy to nonconservative forces? What happens to mechanical energy if only conservative forces act? 4: What is the relationship of potential energy to conservative force? ### Problems & Exercises 1: A ${5.00\times10^5\text{-kg}}$ subway train is brought to a stop from a speed of 0.500 m/s in 0.400 m by a large spring bumper at the end of its track. What is the force constant ${k}$ of the spring? 2: A pogo stick has a spring with a force constant of ${2.50\times10^4\text{ N/m}},$ which can be compressed 12.0 cm. To what maximum height can a child jump on the stick using only the energy in the spring, if the child and stick have a total mass of 40.0 kg? Explicitly show how you follow the steps in the Chapter 7.6 Problem-Solving Strategies for Energy. ## Glossary conservative force a force that does the same work for any given initial and final configuration, regardless of the path followed potential energy energy due to position, shape, or configuration potential energy of a spring the stored energy of a spring as a function of its displacement; when Hooke’s law applies, it is given by the expression ${\frac{1}{2}kx^2}$ where ${x}$ is the distance the spring is compressed or extended and ${k}$ is the spring constant conservation of mechanical energy the rule that the sum of the kinetic energies and potential energies remains constant if only conservative forces act on and within a system mechanical energy the sum of kinetic energy and potential energy ### Solutions Problems & Exercises 1: ${7.81\times10^5\text{ N/m}}$ ## License College Physics Copyright © August 22, 2016 by OpenStax is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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# OpenStax CNX ##### Sections You are here: Home » Content » Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Exercise Supplement # About: Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Exercise Supplement Module by: Wade Ellis, Denny Burzynski. E-mail the authors Name: Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Exercise Supplement ID: m34944 Language: English (en) Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is an exercise supplement for the chapter "Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions" and contains many exercise problems. Odd problems are accompanied by solutions. Subject: Mathematics and Statistics Keywords: addition, Burzynski, Ellis, fractions, Fundamentals, Mathematics, subtraction License: Creative Commons Attribution License CC-BY 3.0 Authors: Copyright Holders: Maintainers: Editors: Latest version: 1.2 (history) First publication date: Jul 9, 2010 9:28 pm +0000 Last revision to module: Aug 18, 2010 8:06 pm +0000 PDF: m34944_1.2.pdf PDF file, for viewing content offline and printing. Learn more. EPUB: m34944_1.2.epub Electronic publication file, for viewing in handheld devices. Learn more. XML: m34944_1.2.cnxml XML that defines the structure and contents of the module, minus any included media files. Can be reimported in the editing interface. Learn more. Source Export ZIP: m34944_1.2.zip ZIP containing the module XML plus any included media files. Can be reimported in the editing interface. Learn more. Offline ZIP: m34944_1.2_offline.zip An offline HTML copy of the content. Also includes XML, included media files, and other support files. Learn more. ## Version History Version: 1.2 Aug 18, 2010 8:06 pm +0000 by Changes: `value added features added, metadata, accessibility, QA checks, links, and image sizing adjusted.` Version: 1.1 Aug 1, 2010 10:00 pm +0000 by Changes: `Initial Publication` ## How to Reuse and Attribute This Content If you derive a copy of this content using a OpenStax_CNX account and publish your version, proper attribution of the original work will be automatically done for you. If you reuse this work elsewhere, in order to comply with the attribution requirements of the license (CC-BY 3.0), you must include • the authors' names: Wade Ellis, Denny Burzynski • the title of the work: Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Exercise Supplement • the OpenStax_CNX URL where the work can be found: http://cnx.org/content/m34944/1.2/ See the citation section below for examples you can copy. ## How to Cite and Attribute This Content The following citation styles comply with the attribution requirements for the license (CC-BY 3.0) of this work: ### American Chemical Society (ACS) Style Guide: Ellis, W.; Burzynski, D. Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Exercise Supplement, OpenStax_CNX Web site. http://cnx.org/content/m34944/1.2/, Aug 18, 2010. ### American Medical Assocation (AMA) Manual of Style: Ellis W, Burzynski D. Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Exercise Supplement [OpenStax_CNX Web site]. August 18, 2010. Available at: http://cnx.org/content/m34944/1.2/. ### American Psychological Assocation (APA) Publication Manual: Ellis, W., & Burzynski, D. (2010, August 18). Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Exercise Supplement. Retrieved from the OpenStax_CNX Web site: http://cnx.org/content/m34944/1.2/ ### Chicago Manual of Style (Bibliography): Ellis, Wade, and Denny Burzynski. "Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Exercise Supplement." OpenStax_CNX. August 18, 2010. http://cnx.org/content/m34944/1.2/. ### Chicago Manual of Style (Note): Wade Ellis and Denny Burzynski, "Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Exercise Supplement," OpenStax_CNX, August 18, 2010, http://cnx.org/content/m34944/1.2/. ### Chicago Manual of Style (Reference, in Author-Date style): Ellis, W., & Burzynski, D. 2010. Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Exercise Supplement. OpenStax_CNX, August 18, 2010. http://cnx.org/content/m34944/1.2/. ### Modern Languages Association (MLA) Style Manual: Ellis, Wade, and Denny Burzynski. Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Exercise Supplement. OpenStax_CNX. 18 Aug. 2010 <http://cnx.org/content/m34944/1.2/>.

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Operations on Sets Question # If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets $\mathrm{A}×\mathrm{B}$ and $\mathrm{B}×\mathrm{A}$ are Easy Solution ## $\mathrm{n}\left(\mathrm{A}×\mathrm{B}\right)\cap \left(\mathrm{B}×\mathrm{A}\right)$$=\mathrm{n}\left(\left(\mathrm{A}\cap \mathrm{B}\right)×\left(\mathrm{B}\cap \mathrm{A}\right)\right)=\mathrm{n}\left(\mathrm{A}\cap \mathrm{B}\right).\mathrm{n}\left(\mathrm{B}\cap \mathrm{A}\right)$$=\mathrm{n}\left(\mathrm{A}\cap \mathrm{B}\right).\left(\mathrm{A}\cap \mathrm{B}\right)=\left(99\right)\left(99\right)={99}^{2}.$ Get Instant Solutions

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# Solved How Many Grams Of Hydrogen Gas Are Produced Upon C Posted by on December 04, 2017 Solved How Many Grams Of Hydrogen Gas Are Produced Upon C re 1. 1.How many grams of NaOH are required to prepare 1200 ml of 0.150 M solution? 2.A 21.6 ml volume of 0.107M NaOH solutions reaches the stoichiometric point titrating 25.0 ml of an HCL solution with an unknown concentration. (Solved) How Many Grams Of Fe(NO 3 ) 3 9 H 2 O Are. (Solved) How many grams of Fe(NO 3 ) 3 9 H 2 O are required to prepare. How many grams of Fe(NO 3) 3 · 9 H 2 O are required to prepare 300.0 mL of a 0.304 M solution of Fe(NO 3) 3 · 9 H 2 O? Solved: How Many Grams Of Sulfur (S) Are Needed To React. How many grams of sulfur (S) are needed to react completely with 246 g of mercury (Hg) to form HgS? Solution 46P:Here, we are going to calculate the amount of sulfur required to react with 246 g of Hg to form HgS.Step 1:Given that,Mass of the Hg = 246 gThe molar mass of Hg = 200.6 g/molThus, 1.0 mol of Hg contains How Many Grams Of Bicarbonate Will Produce 40 Ml Of CO2. This type of homework question is solved using steps like: 1. Write out the reaction equation. 2. Using the ideal gas equation, pV=nRT, filling in all the variables you know, calculate the number of moles of carbon dioxide you would like to form ( Solved: How Many Grams Of Br Are In 475 G Of CaBr2. How Many Grams Of Br Are In 475 G Of CaBr2? Question: How Many Grams Of Br Are In 475 G Of CaBr2? This problem has been solved! See the answer. How many grams of Br are in 475 g of CaBr2? Expert Answer 100% (1 rating) Previous question Next question Get more help from Chegg. Get 1:1 help now from expert Chemistry tutors Share! Topic 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 CLOSE [x]

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Cody # Problem 44675. Find prime number couples Solution 1551372 Submitted on 6 Jun 2018 by J. S. Kowontan • Size: 28 • This is the leading solution. This solution is locked. To view this solution, you need to provide a solution of the same size or smaller. ### Test Suite Test Status Code Input and Output 1   Pass a=[1 4 6 7 8 11 13 16 23 29 31]; couple=[11 13; 29 31]; assert(isequal(find_prime_couples(a),couple)) 2   Pass a=[16 97 88 49 41 13 93 1 19 33 6 15 73 49 34 24 46 19 33 27 84 70 34 59 29 27 26 68 52 8 6 26 44 29 68 95 78 64 76 75 59 78 40 61 25 30 2 35 15 42 16 83 74 10 83 23 11 67 96 82 63 33 28 44 36 88 1 70 34 31 65 93 90 100 8 13 99 10 69 93 15 89 2 35 24 99 85 80 91 79 84 33 75 67 29 34 91 4 70 21]; couple=[11 13; 29 31; 59 61]; assert(isequal(find_prime_couples(a),couple)) 3   Pass a=[2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199]; couple=[3 5; 5 7; 11 13; 17 19; 29 31; 41 43; 59 61; 71 73; 101 103; 107 109; 137 139; 149 151; 179 181; 191 193; 197 199]; assert(isequal(find_prime_couples(a),couple))

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It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results. # Numerical Analysis: Home Objective: Teach the use of computers for the numerical solution of engineering problems ## Introduction Numerical analysis is the study of algorithm that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). One of the earliest mathematical writings is a Babylonian tablet from the Yale Babylonian Collection (YBC 7289), which gives a sexagesimal numerical approximation of , the length of the diagonal  in a unit square. Being able to compute the sides of a triangle  is extremely important, for instance, in astronomy, carpentry and construction. Numerical analysis continues this long tradition of practical mathematical calculations. Much like the Babylonian approximation of , modern numerical analysis does not seek exact answers, because exact answers are often impossible to obtain in practice. Instead, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors.

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Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  eusv2i Structured version   Unicode version Theorem eusv2i 4713 Description: Two ways to express single-valuedness of a class expression . (Contributed by NM, 14-Oct-2010.) (Revised by Mario Carneiro, 18-Nov-2016.) Assertion Ref Expression eusv2i Distinct variable groups:   ,   , Allowed substitution hint:   () Proof of Theorem eusv2i StepHypRef Expression 1 nfeu1 2291 . . 3 2 nfcvd 2573 . . . . . 6 3 eusvnf 4711 . . . . . 6 42, 3nfeqd 2586 . . . . 5 5 nf2 1889 . . . . 5 64, 5sylib 189 . . . 4 7 19.2 1671 . . . 4 86, 7impbid1 195 . . 3 91, 8eubid 2288 . 2 109ibir 234 1 Colors of variables: wff set class Syntax hints:   wi 4  wal 1549  wex 1550  wnf 1553   wceq 1652  weu 2281 This theorem is referenced by:  eusv2nf  4714 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2951  df-sbc 3155  df-csb 3245 Copyright terms: Public domain W3C validator

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Posted Date: 17 Apr 2008      Posted By:: CONFIDENCE IS THE COMPANION OF SUCCESS    Member Level: Gold  Points: 5 (Rs. 1) # 2007 Anna University Chennai B.E Electronic Instrumentation & Control Engineer Power Electronics Question paper Course: B.E Electronic Instrumentation & Control Engineer University/board: Anna University Chennai EE 1301 — POWER ELECTRONICS (Common to Electronics and Instrumentation Engineering/ Instrumentation and Control Engineering) (Common to B.E. (Part-Time) Fourth Semester - Regulation 2005) Model Question Paper Time : Three hours Maximum : 100 marks PARTA-(10x2 = 20marks) 1. In Triacs which of the modes the sensitivity of gate is high. 2.Define the term pinch off voltage of MOSFET. 3.Under what conditions a single phase fully controlled converter gets operated as an Inverter. 4.State the principle of phase control in AC-DC converters. 5.Define the term duty cycle in DC-DC converters. 6.What is a DC chopper? 7.Define the term Inverter gain. 8.Differentiate between VSI and CSI. 9.Mention the different types of HVDC link. 10.List the parameters for controlling power in a transmission line. PART B — (5 x 16 = 80 marks) 11. (a) Discuss the transfer, output and switching characteristics of power MOSFET. Or (b) Explain the switching performance of BJT with relevant waveforms indicating clearly the turn-on, turn-off times and their components. Also define the term SOA. 12.(a) A two pulse single phase bridge converter is connected to RLE load. Source voltage is 230 V, 50 Hz. Average load current of 10 Amps is continuous over the working range. For R = 0.4 Q and L = 2 mH compute. (i) Firing angle delay for E = 120 V. (ii) Firing angle delay for E = -120 V. Indicate which source is delivering power to load in parts (i) and (ii). Or (b) For a 1 phase AC voltage controller feeding a resistive load draw the waveforms of source voltage gating signals, output voltage, source and output current. Describe its working with reference to waveforms drawn. 13.(a)A step up chopper has input voltage of 220 V and output voltage of 660 V. If the nonconducting time of thyristor chopper is 100 micro sec compute the pulse width of output voltage. In case the pulse width is halved for constant frequency operation find the new output voltage. (Or) (b) Classify the basic topologies of switching regulators and explain the operation of buck regulators with continuous load current using suitable waveforms. 14.(a) Describe the working of a 1 phase full bridge inverter supplying R, R.L. loads with relevant circuit and waveforms. (16) (or) (b) What is the need for controlling the output voltage of inverters? Classify the various techniques adopted to vary the inverter gain and brief on sinusoidal PWM. (16) 15. (a) Describe the principle of operation of no break static ups configuration with a neat block diagram and list out its applications. (16) (Or) (b)Explain the principle of operation of unified power controller as compensator with a neat circuit arrangement. (16) ### Related Question Papers: • Mathematics • AE1351: Propulsion II • AE1354: High Temperature Materials • Micorprocessor And Microcontroller • Microprocessor And Microcontroller • ### Categories Submit Previous Years University Question Papers and make money from adsense revenue sharing program Are you preparing for a university examination? Download model question papers and practise before you write the exam. Join Group

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CC-MAIN-2018-26

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https://teamtreehouse.com/community/can-someone-please-check-to-see-why-my-letter-game-refined-version-isnt-working-correctly-appreciated-thanks

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## Welcome to the Treehouse Community Want to collaborate on code errors? Have bugs you need feedback on? Looking for an extra set of eyes on your latest project? Get support with fellow developers, designers, and programmers of all backgrounds and skill levels here with the Treehouse Community! While you're at it, check out some resources Treehouse students have shared here. ### Looking to learn something new? Treehouse offers a seven day free trial for new students. Get access to thousands of hours of content and join thousands of Treehouse students and alumni in the community today. # Can someone please check to see why my letter game (refined version) isn't working correctly. Appreciated. Thanks :) Here is my code for the letter game. Not sure why it isn't working. Code: ```import random import os import sys # make a list of words words = [ 'squat', 'snatch', 'clean', 'jerk', 'handstand', 'rowing', 'running', 'barbell', 'bumpers' ] def clear(): if os.name == 'nt': os.system('cls') else: os.system('clear') clear() print('') print(guess, end=' ') print('\n\n') for guess in secret_word: if guess in good_guesses: print(guess, end=' ') else: print('_', end=' ') print('') while True: # take guesses guess = input("Guess a letter: ").lower() if len(guess) != 1: print("You can only guess a single letter") elif guess in bad_guesses or guess in good_guesses: elif not guess.isalpha(): print("You can only print letters") else: return guess def game(done): clear() secret_word = random.choice(words) good_guesses = [] while True: if guess in secret_word: good_guesses.append(guess) found = True for letter in secret_word: if letter not in good_guesses: found = False if found: print("You win!! The word was {}".format(secret_word)) done = True else: print("You lost!!") done = True if done: play_again = input("Play again? Y/n ").lower() if pay_again.lower() != 'n': return game(done=False) else: sys.exist() def welcome(): print ('Welcome to the letter guessing game') if start.lower() == 'q': print("bye") sys.exit() else: return True done = False while True: clear() welcome() game(done) ``` Fixed formatting MOD There are two typos: ``` if done: play_again = input("Play again? Y/n ").lower() if pay_again.lower() != 'n': return game(done=False) else: sys.exist() if done: play_again = input("Play again? Y/n ").lower() if pay_again.lower() != 'n': # <-- pay_again Not defined return game(done=False) else: sys.exist() # <-- sys.exit() ``` You also have a positional argument order problem in call to `draw` function: ```# draw function definition:

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New SAT Math Workbook 8 9 4 5 10 if the average of 5 consecutive even This preview shows page 1. Sign up to view the full content. This is the end of the preview. Sign up to access the rest of the document. Unformatted text preview: 5. 10. Find the value of 3 2 . () 2 www.petersons.com Practice Tests 327 PRACTICE TEST C Answer Sheet Directions: For each question, darken the oval that corresponds to your answer choice. Mark only one oval for each question. If you change your mind, erase your answer completely. Section 1 1. 2. 3. 4. 5. 6. 7. Section 2 abcde abcde abcde abcde abcde abcde abcde 8. 9. 10. 11. 12. 13. 14. abcde abcde abcde abcde abcde abcde abcde 15. 16. 17. 18. 19. 20. 21. abcde abcde abcde abcde abcde abcde abcde 22. 23. 24. 25. abcde abcde abcde abcde Note: Only the answers entered on the grid are scored. Handwritten answers at the top of the column are not scored. www.petersons.com Practice Tests 329 PRACTICE TEST C Section 1 25 Questions Time: 30 Minutes 1. 8 · 8 = 4x. Find x (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 If a &gt; 2, which of the following is the smallest? (A) (B) (C) (D) (E) 2 a a 2 a +1 2 2 a +1 2 a −1 5. If a = b and (A) (B) (C) (D) (E) a –a b 1 a 1 = b , then c = c 2. –b 6. If a building B feet high casts a shadow F feet long, then, at the same time of day, a tree T feet high will cast a shadow how many feet long? (A) (B) (C) (D) (E) FT B FB T B FT TB F T FB 3. Which of the following has the greatest value? (A) (B) (C) (D) (E) 1 2 .2 7. .2 (.2)2 (.02)3 4. If a3 = , then 12a = b4 The vertices of a triangle are (3,1) (8,1) and (8,3). The area of this triangle is (A) 5 (B) 10 (C) 7 (D) 20 (E) 14 (A) (B) (C) (D) (E) 3b b 9b 12b 16b www.petersons.com 330 Chapter 17 8. Of 60 employees at the Star Manufacturing 2 Company, x employees are female. If of the 3 remainder are married, how many unmarried men work for this company? (A) (B) (C) (D) (E) 2 x 3 1 40 − x 3 1 40 + x 3 2 20 − x 3 1 20 − x 3 40 − 12. Which of the following is greater than ? 3 (A) .33 (B) (C) (D) (E) 1 3 1 4 1 .3 .3 2 2 1 9. A circle whose center is at the origin passes through the point whose coordinates are (1,1). The area of the circle is (A) π (B) 2 π (C) 2π (D) 2 2π (E) 4 π 13. What percent of a half dollar is a penny, a nickel, and a dime?... View Full Document Ask a homework question - tutors are online

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CC-MAIN-2016-50

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www.moneyphp.org

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# Allocation¶ ## Allocate by Ratios¶ My company made a whopping profit of 5 cents, which has to be divided amongst myself (70%) and my investor (30%). Cents can’t be divided, so I can’t give 3.5 and 1.5 cents. If I round up, I get 4 cents, the investor gets 2, which means I need to conjure up an additional cent. Rounding down to 3 and 1 cent leaves me 1 cent. Apart from re-investing that cent in the company, the best solution is to keep handing out the remainder until all money is spent. This is done by first calculating everybody’s share, rounded-down. Finally the remainder fractions are allocated one by one to the targets, the one with most lost due the rounding-down in previous step now coming first. In other words: ```use Money\Money; \$profit = Money::EUR(5); list(\$my_cut, \$investors_cut) = \$profit->allocate([70, 30]); // \$my_cut is 4 cents, \$investors_cut is 1 cent // The order is important: list(\$investors_cut, \$my_cut) = \$profit->allocate([30, 70]); // \$my_cut is 3 cents, \$investors_cut is 2 cents ``` ## Allocate to N targets¶ An amount of money can be allocated to N targets using `allocateTo()`. ```\$value = Money::EUR(800); // \$8.00 \$result = \$value->allocateTo(3); // \$result = [\$2.67, \$2.67, \$2.66] ```

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http://science.answers.com/Q/What_is_Saturn's_revolution_or_rotation_time

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# What is Saturn's revolution or rotation time? Would you like to merge this question into it? #### already exists as an alternate of this question. Would you like to make it the primary and merge this question into it? #### exists and is an alternate of . Saturn's rotational period is the Saturnian "day." As Saturn is a gas giant, the visible features on Saturn rotate at different rates depending on latitude; the Equatorial Zone has a period of 10 h 14 min 00 s. All other Saturnian latitudes have been assigned a rotation period of 10 h 39 min 24 s. The precise value for the rotation period of the interior remains elusive but the best estimate is approximately 10 h 45 m 45 s (± 36 s). The revolution period of Saturn refers to the orbital period around the Sun (the Saturn "year"), which is about 10,579 Earth days or 29.5 Earth years. 89 people found this useful # What is rotation and revolution? Rotation is how an object spins on its axis, like a planet, or a baseball or tennis ball with spin on it. Revolution is how an object revolves around another object, like the Earth around the Sun or a tether ball around the pole. # How do you use the movements of rotation and revolution to measure time? u can get a ruler and place it down on a globe or a measuring tape to find your answers to the problem/questions # What is Saturn's period of revolution around the sun? One revolution around the Sun is called a year. A year on Saturn lasts 29.5 Earth years. # What are facts about Saturn's revolution around the Sun? The ringed planet Saturn is the 6th of the 8 major planets from the Sun, orbiting at an average distance of 1.43 billion kilometers (891 million miles). One complete revolution (a Saturn year) takes about 10,759 Earth days, or just under 29.5 Earth years. The planet's average orbital speed is 9.69 k (MORE) # What is Saturn's rotation? The visible features of Saturn rotate at different rates depending on their latitude (distance from the equator). Astronomers have developed three different systems for measuring the rotational speed of Saturn. System I is for regions around the planet's equator. The System I rotation speed is 10 (MORE) # What is Mercury's period of rotation and revolution? Rotation period (length of day in Earth days). 58.65 earth days . Revolution period (length of year in Earth days). 87.97 earth days. # How many times does Neptune rotate in one of its revolutions around the sun? Neptune takes about 16 hours, 6 minutes and 36 seconds to rotate once on its axis. It takes about 164.79 years to make one orbit of the sun. That's about 89,606.5 revolutions in one orbit of the sun. # What is the rotation and revolution of mercury? Mercury rotates very slowly at a rate of one rotation every 58.65days. Mercury revolves around the sun once every 88 days. # What is Saturn's period of rotation? Saturn's period of rotation is the time it takes to rotate once onits axis. It takes 10 hours and 39 minutes for Saturn to rotate,making a day on Saturn shorter than a day on Earth. . 10 hours, 39 minutes and 22 seconds # Differentiate between rotation and revolution? i love this question. i may only be a 7th grader but i learned about them this year. revolution is when the earth is orbiting the sun and this takes a full year to do. and rotation is when the earth is rotating on its axis which takes 24 hours to do and this causes weather. it also causes the Coriol (MORE) # Differentiate rotation from revolution? Rotation is the spinning of an object about its own axis. Revolution is the spinning, so to speak, more properly, revolution, of that object around some other object. # How do rotation and revolution affect earth? Rotation gives us our days. We have daylight and night. . Rotation is involved in the daily cycle of the tides. Also, rotation affects wind directions due to the Coriolis effect. . Revolution around the Sun gives us our years. . The combination of the Earth's tilted axis and Earth's revolutio (MORE) # What is the rotation and revolution of Saturn? Saturn has the second fastest spin out of the eight planets, after Jupiter. It takes 10 hours and 14 mins to make one full revolution on its axis. It takes 29.44 years to orbit the sun once. # What is the rotation and revolution of a planet? rotation of a planet; rotation is movement of the planets around its own axis revolution of planet; revolution is movement of the planets around the sun # What is the length of Saturn's daily rotation? It takes Saturn 10 hours and 39 minutes to complete one rotation.Saturn takes about 29.5 years to orbit around the Sun. # Do Saturn's moons rotate? Yes. Like most moons, the moons of Saturn are tidally locked,meaning they rotate once every orbit around Saturn so that the sameside always faces the planet. # What units of time are based on a single rotation or revolution of the earth? Rotation . . . . . the "Day" Revolution . . . . the "Year" # What is planet Saturn's exact orbit and rotation periods? The orbital period is 29.447498 years and the rotational period is 0.44401 days. These values are approximate, one can never know the exact figures. # What is revolution and rotation? rotation is how an object spins on its axis and revolution is when it goes around an object # Saturn's rotation period around the sun? \n. \n. That's called the "revolution period" by astronomers. For Saturn it's about \n. 29.5 Earth years. # Earth's period of revolution is 8766.15 hours How many times does earth rotate during one revolution around the sun? Earth rotates once every 24 hours. If you divide 8766.15 by 24, you get pretty close to the number of days in a year.. __________. Not quite. 24 hours is the average synodic period of earth, not the rotational (sidereal) period. Earth rotates once every 23 hours, 56 minutes and 4.1 seconds roughly (MORE) # What is Saturn's light time from sun? Saturn is between 72 and 80 light minutes from the sun depending on where it is in it's orbit. # Do Saturn's rings rotate? \nYes, they have to rotate to stay in orbit and not just fall down into Saturn. The rings aren't solid objects, they are made of millions of tiny bits of dust and ice. Each bit is in orbit, just like a moon or satellite. # What is Saturn's rotation on it's axis? Saturn rotates at slightly different speeds at different latitudes. On average the rotation period is about 10 and a half hours. # What is the length of Saturn's rotation on its axis? The length of Saturn's rotation on its axis is about ten and a half hours. # What time periods do rotation and revolution define? Some people define one as turning about an internal axis (like thedaily turning), while the other means turning about an externalaxis (like the yearly turning). So you can have yearly revolutionaround the Sun, and daily rotation about the Earth's axis. But then 'revolutions per minute' of an engine (MORE) # Is the time of day due to earths rotation or revolution? The time of day is due to the earths rotation. Rotation is thenumber of times the earth revolves around itself. # The number of rotations or revolutions per unit of time is? The most widely used measurement of this sort is "rpm" or"revolutions per minute". This measures the amount of full 360degree rotations happen over a 60 second time period. # What are rotation and revolution? If earth surrounds itself it is known as rotation if earth surrounds the sun then it is known as revolution # How many times does the moon rotate during one revolution around the earth? The moon's periods of axial rotation and orbital revolution are precisely equal. The answer to the question is: 1.000... # What are Saturn's travel times and dates? im asking the same thing but what im thinking so far is that it takes roughly 6 to 7 years but it depends on how fast u travel but good luck :) # How many times does Earth rotate in one of its revolutions around the Sun? about 365-366, count how many days are in a year and BOOM! you got it # Is a revolution the amount of time it takes for a planet to rotate around the sun? a planet rotates constantly on its axis as it is doing this it revolves this is what its called when a planet completes a full orbit around the sun! # What the difference of rotation and revolution? Rotation is spinning on the objects axis and revolution is orbiting around an external axis. Rotation determines night and day and orbiting determines the seasons and the years. # What is meant by rotation and revolution in a planet? Rotation of a planet means the overall time of day and night, time for rotate on its own axis. In our earth 12 hours for night and 12 hour for day, total 24 hours. In Venus it takes 117 earth days, as a matter of fact it takes 225 earth days to complete its revolution. It is depends upon gravity. Re (MORE) # What is the rotation and revolution of planet? Depends on what planet you're talking about. Venus has a rotation of 243 Earth days in a day, and 225 Earth days in a year. # How many times does the earth rotates in one revolution? In one revolution around our Sun, the Earth rotates just over 365 times. In 4 revolutions around the Sun, the Earth rotates about 1461 times. The average year for the Earth is about 365.25 days. # What is the planet Venus's rotation and revolution? Venus takes 243 days to spin on its axis relative to the background stars, while it takes 224.7 days to orbit the sun. Although its spin on its axis is longer that its orbital period, an apparent day is 116.75 days, since it spins in the other direction to Earth and most other planets. # Does the Moon's rotation take a shorter amount of time than a revolution? The rotation of the moon is equal to the revolution around Earth.(28 days)lunar cycle. The moon rotates at the the same speed as it revolves around us basically, so we always see the same side of it(we actually see a little bit more than half) like someone walking round you but always looking right (MORE) # How many times does the moon rotate each revolution around the earth? The Moon is "tidally locked" to the Earth meaning the same side is always facing it. Because of this, it rotates once for every one revolution. # How many rotations are in one revolution? There as different meanings for rotation and revolution. In this context a revolution can be the turning of body on its axis. In which case one revolution would be the same as one rotation. That is, there would be one rotation in one revolution. A revolution can also be the movement of a body in (MORE) # Are revolution and rotation the same? No, they aren't the same. Revolution is the object moving in a circular motion. Rotation is when the object stays in one place and spins around. # What is meant about rotation and revolution of a planet? Rotation period is the time taken for planet to spin once on its axis. Revolution period is the time taken for planet to orbit the Sun once. # What is jupiters revolution and rotation periods? jupiter revolution is almost 12 years (4332 days) while its rotation is: 9 hours 50 minutes 30.0 seconds # What happen if there is no rotation and revolution? The primary thing which happens if there is no rotation or revolution is that the Earth loses its seasons. One side of the planet will bake in the Sun while the other freezes from a lack of sunlight. # Which celestial body takes the same time rotation and revolution? Earth's Moon takes the same amount of time to rotate and revolve around the Earth. This is why we only see one side of the Moon from Earth. Visit kidzpower.webs.com for more. # What is Earth's length of revolution and rotation? The Earth "orbits" (or revolves) around the Sun at a speed of 108,000 km/h and travels 940 million km during one orbit. A complete orbit of the Earth around the Sun occurs every 365.2563666 days (which is why a year has 365 days - and why we need a "leap year" ever 4 years). There are actually se (MORE) # What effect does the earth rotation and revolution? I guess you forgot the word "have"? Some Basic effects: The rotation is the reason we have day and night. It makesHurricanes turn clockwise in the southern and counter-clockwise inthe northern hemisphere, it's also responsible for other weatherphenomena. Earths rotation makes it possible to have ge (MORE) # What is Saturn's rotation time around the moon? Saturn does not orbit the moon, it orbits the sun. This is calledits revolution, not its rotation. Saturn's period of rotation onits axis is 10 hours 33 minutes. Its period of revolution aroundthe sun 29.45 years. # What is the rotation and revolution? rotation time planet takes to compete one spin on it's axis or day,revolution is time to complete path around Sun

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https://fourpillarfreedom.com/compound-interest-misunderstanding/

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# The Biggest Misunderstanding About Compound Interest Consider the following scenario: Edgar invests \$5,000 each year into the stock market starting at age 22 and earns 7% average annual returns each year until age 65. Josh invests \$8,000 each year and earns 7% average annual returns until age 65, but he doesn’t start investing until age 30. Despite investing more money each year,  Josh ends up with less than Edgar by time they both reach age 65: Edgar ends up with a little over \$1.42 million while Josh ends up with a little over \$1.27 million. Some variation of this example is often used in personal finance to emphasize the point that you should start investing as soon as possible because even if you invest more money at a later date, it’s hard to catch up to someone who started investing even a few years sooner. Unfortunately, most people draw the wrong conclusion from this example by concluding that there’s something magical about those early investing years. But that’s not true. Compound interest actually sucks early on. The magic only arrives in the later years. For example: • In Edgar’s first year of investing he earns a 7% return on his \$5,000. That’s \$350. • In his second year he contributes \$5,000 more and earns a 7% return on his \$10,350. That’s \$724. • In his third year he contributes \$5,000 again and earns a 7% return on his \$16,074. That’s \$1,125. Fast forward to the last three years leading up to age 65. Edgar earns \$61,694, \$66,280, and \$71,187 in those years, respectively, in investment returns. In other words, the investment returns in the early years are peanuts compared to the latter years. This also means that investment returns start to impact your net worth much more over time compared to the amount of money you invest. To illustrate this, check out the chart below that shows how much savings (e.g. contributions) contribute to net worth growth compared to investment returns for someone who invests \$10k each year at a 7% annual return: Early on, investment returns don’t matter as much as the amount you save and invest. As time goes on, though, returns start to become the main driver of net worth growth. ## What to Do with this Information The fact that compound interest sucks early on doesn’t mean you should avoid investing in the stock market when you’re young. It simply means that you shouldn’t rely on investment returns too heavily when you’re first starting out. Instead, your focus should be on finding ways to increase your income. You’re much better off figuring out how to earn \$20k more per year than you are figuring out how to earn an additional 1-2% annual investment returns. Here are some realistic ways you can increase your income. I believe that the best and most enjoyable way to build wealth is to start your own business. However, most people will have to work for someone else when they’re just starting out, which is why the best way to increase your income when you’re young (or at any age, really) is to learn how to negotiate your salary. Unfortunatelya 2019 study from Jobvite shows that only 33% of people actually bother negotiating their salary. Broken down by gender, the numbers are even lower for women: only 27% negotiate salary. But there’s good news for those who do negotiate: a whopping 83% receive higher pay as a result. And about one-third of people who negotiate salary end up receiving pay that is 11% or higher. For someone who receives an offer of \$60k, an 11% increase would be an additional \$6,600. That’s a lot of money for only a little work. For those who are willing to negotiate, there’s significant upside. But it helps to know which techniques and tactics can actually help you negotiate a higher salary. For a list of actually helpful negotiation tips, check out this roundup I created. ### 2. Provide a Service One of the easiest ways to increase your income is to provide a service in a niche you’re knowledgeable in at a high hourly rate. For example, I used to tutor college students in statistics at a rate of \$40 – 50 per hour. Students would gladly pay this rate because there are very few people out there who are knowledgeable in college-level statistics, yet there’s a huge pool of people who have to take at least one introductory level stats course in college. This mismatch between supply and demand meant that I could charge a fairly high hourly rate and earn some nice side hustle income. Depending on the hourly rate you charge and the amount of hours you’re willing to work, providing a service could make a significant difference in your total income. ### 3. Build Assets Another way to increase your income is to build an asset that generates income for you while you sleep. My personal favorite example of this is a website. I currently own five websites that all generate income for me in the form of ads, affiliate links, and products I’ve created. Each day these websites earn income for me without my attention. You won’t get rich fast from building a website, but you can certainly build a semi-passive reliable income machine that has the potential to grow over time. Here’s a look at how I’ve grow my own online income over the past three years: If you’re interested in starting your own website, check out my guide here on how to set one up in under an hour. Instead of building an asset from scratch, you could also buy one. The benefit of buying one is that you can start earning money immediately as opposed to slowly building up income over time. One example of an asset that you can buy is a website. I personally bought my first website ever a few months ago. It generates around \$700 per month in the form of ads and affiliate links, and I paid just \$7,000 for it. I now own a website that generates mostly passive income and only requires a few hours of work from me per month. For anyone who is interested in purchasing a website to increase your income, there are plenty of small websites out there that you could purchase for between \$5,000 and \$15,000, which would provide much higher return on investments compared to traditional assets like stocks and bonds. ## Conclusion Many people mistakenly believe that there’s something magical about investing as early as possible. But the magic is in the later years, not the early years. This is why you should focus on growing your income when you’re just starting out. You can certainly invest your savings along the way, but just know that wild investment returns only come as a result of having a lot of money invested. First, grow your income through negotiating salary, providing services in niche topics, building assets that earn money for you, and buying assets that offer high rates of return. Full Disclosure: Nothing on this site should ever be considered to be advice, research or an invitation to buy or sell any securities, please see my Terms & Conditions page for a full disclaimer.

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# Trigonometry Forum Trigonometry Help Forum: Graphing trig expressions, identities, angles, applied questions 1. ### Is this true? • Replies: 8 • Views: 543 Feb 9th 2011, 02:19 PM 2. ### Simplifying Trig Equation (like Wolfram|Alpha does it…) • Replies: 2 • Views: 1,153 Feb 9th 2011, 06:12 AM 3. ### Set notation • Replies: 3 • Views: 522 Feb 9th 2011, 03:58 AM 4. ### Complex Numbers - Argument of Z • Replies: 2 • Views: 1,461 Feb 9th 2011, 02:37 AM 5. ### Sum and difference identitiees? • Replies: 3 • Views: 2,636 Feb 8th 2011, 06:10 PM 6. ### Help with verifying trig functions please! • Replies: 3 • Views: 469 Feb 8th 2011, 06:02 PM 7. ### Identities • Replies: 2 • Views: 469 Feb 8th 2011, 05:25 PM 8. ### Help with Trig problem • Replies: 5 • Views: 455 Feb 7th 2011, 02:53 PM 9. ### complex trigo • Replies: 3 • Views: 557 Feb 7th 2011, 04:58 AM 10. ### daughter have trouble finding value of x • Replies: 3 • Views: 458 Feb 7th 2011, 01:59 AM 11. ### [SOLVED] I need help solving this trig problem • Replies: 2 • Views: 530 Feb 7th 2011, 01:18 AM 12. ### Help Needed with this Trigonometric Proof • Replies: 4 • Views: 527 Feb 6th 2011, 06:05 PM 13. ### Help Needed with this Trig Equation! • Replies: 4 • Views: 494 Feb 6th 2011, 06:02 PM 14. ### Verifying trigonometric identities? • Replies: 10 • Views: 2,024 Feb 6th 2011, 01:01 PM 15. ### Trigonometric Problem • Replies: 1 • Views: 501 Feb 6th 2011, 11:29 AM 16. ### Trig Simplification • Replies: 4 • Views: 591 Feb 4th 2011, 07:01 PM 17. ### Identity Crisis! • Replies: 2 • Views: 677 Feb 3rd 2011, 08:07 PM 18. ### [SOLVED] Solving a trig identity • Replies: 4 • Views: 815 Feb 3rd 2011, 08:54 AM 19. ### Is there enough info given in question • Replies: 6 • Views: 1,014 Feb 3rd 2011, 12:09 AM 20. ### Prove:(tanx/(1+tanx)) = (sinx/(sinx+cosx)) • Replies: 7 • Views: 11,892 Feb 2nd 2011, 08:46 PM 21. ### Confusion of finding asymtotes from trig function • Replies: 2 • Views: 861 Feb 1st 2011, 05:41 PM 22. ### Pyhagorean Theorem • Replies: 3 • Views: 632 Feb 1st 2011, 03:55 AM 23. ### sin^2(x) • Replies: 2 • Views: 537 Jan 31st 2011, 01:33 PM 24. ### trouble interpreting a problem • Replies: 1 • Views: 600 Jan 31st 2011, 12:38 PM 25. ### trig identities • Replies: 3 • Views: 956 Jan 31st 2011, 12:30 PM 26. ### Range of Values Question • Replies: 3 • Views: 705 Jan 31st 2011, 10:20 AM , , , , , , , , , , , , , , # trigonometry sotr Click on a term to search for related topics. Use this control to limit the display of threads to those newer than the specified time frame. Allows you to choose the data by which the thread list will be sorted.

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# Binary Tree and its Properties By | February 5, 2016 # Binary Tree and its Properties Following are some properties of binary trees. ### The maximum number of nodes at a given level, k of a binary tree is 2k-1. Level of root is taken to be 1 above. This can be proved by induction. For root, k = 1 Therefore, number of nodes = 2k-1 = 1 Assuming that maximum number of nodes on level k is: 2k-1 Since in Binary tree every node has at most 2 children, next level would have twice nodes, i.e. 2 * 2k-1 = 2k nodes at most ### Maximum number of nodes in a binary tree of height, his: 2h – 1. Height of a tree is maximum number of nodes on root to leaf path. A tree has maximum nodes if all levels have maximum nodes. So maximum number of nodes in a binary tree of height h: 1 + 2 + 4 + .. + 2h-1. Sum of this series: 2h – 1. Note: If we take height of a leaf is considered as 0, the above formula becomes: 2h+1 – 1. ### In a Binary Tree with n nodes, minimum possible height or minimum number of levels is: ceil(Log2(n+1) ) If we consider the convention where height of a leaf node is considered as 0, then above formula for minimum possible height becomes: ceil(Log2(n+1)) – 1 ### A Binary Tree with L leaves has at least: ceil(Log2L )+ 1 levels A Binary tree has maximum number of leaves when all levels are fully filled. Let all leaves be at level k, then below is true for number of leaves L. L <= 2k-1 Log2L <= k-1 k >= ceil(Log2L ) + 1 ### In a Binary tree, number of leaf nodes is always one more than nodes with two children. L = T + 1 where, L = Number of leaf nodes T = Number of internal nodes with two children

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# Natural Log and e confusion 1. Aug 6, 2008 ### Iron_Brute I am starting my first year of college and I reviewing my high school notes from trig pre-cal and there was one thing I couldnt figure out. It was a multiple choice question and I dont have the text book anymore but the answer I circled I cant understand how I arrived to that answer. 1. The problem statement, all variables and given/known data Given that x> 0 and y> 0, simplify e^ln(x) + ln(y) 3. The attempt at a solution What I did was: e^ln(x+y) e^x+y and I circled the answer: X+Y, but I get e^x+y which as an answer. All I wrote was ln and e cancel but I dont understand how they cancel. 2. Aug 6, 2008 ### snipez90 Do you mean e^(ln(x) + ln(y)) ? If that's the case, then you add the two logarithms to get ln(xy) since the arguments are multiplied in log addition. Then using the fact that e^ln(x) = x, you have e^(ln(xy)) = xy. I'm not sure if that answers your question. To see why e^ln(x) = x. Remember that ln(x) = log base e of x. Let ln(x) = y. Then converting to exponentiation gives e^y = x, but y = ln(x). Hence e^ln(x) = x. 3. Aug 6, 2008 ### HallsofIvy Do you mean e^(ln(x)+ ln(y))? What you wrote is e^(ln(x))+ ln(y). No, ln(x)+ ln(y) is not equal to ln(x+ y). As snipez90 said, ln(x)+ ln(y)= ln(xy). Then, of course, e^(ln(xy))= xy since e^x and ln(x) are inverse functions. Another way to do that is to use the fact that e^(a+b)= e^a e^b: e^(ln(x)+ ln(y))= (e^ln(x))(e^ln(y))= (x)(y)= xy. 4. Aug 7, 2008 ### Iron_Brute Thanks for the help. I see where I made my mistake now. I was using the wrong log identities, and misunderstand certain things about natural logs.

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# When is rank-1 perturbation to a positive operator still positive? Let $$A : \mathcal{H} \to \mathcal{H}$$ and $$B : \mathcal{H} \to \mathcal{H}$$ be trace-class (hence compact) Hermitian operators on a separable Hilbert space. Assume that $$A$$ is strictly positive and that $$B$$ is positive and rank-1. I'm interested in conditions when $$A - \epsilon B \ge 0$$ for some strictly positive $$\epsilon \in \mathbb{R}$$ (as usual, $$>$$ and $$\ge$$ for operators refers to being positive (semi)definite). If $$A$$ is finite dimensional, then $$A - \epsilon B \ge 0$$ for some $$\epsilon > 0$$ always. This is because the smallest eigenvalue of $$A - \epsilon B$$ obeys $$\lambda_\min >0$$ for $$\epsilon=0$$ and varies continuously with $$\epsilon$$. If $$A$$ is infinite dimensional and $$B=\vert \phi\rangle\langle\phi\vert$$ for some eigenvector $$\vert \phi\rangle$$ of $$A$$ (with corresponding eigenvalue $$\lambda>0$$), then it is clear that $$A - \epsilon B\ge 0$$ for $$\epsilon\le \lambda$$. What about when $$A$$ is infinite dimensional and $$B$$ does not have the form of $$\vert \phi\rangle\langle\phi\vert$$? • It is not always true in finite dimensions, if $A$ can be positive semidefinite. You'd need all of its eigenvalues to be strictly positive. In infinite dimensions you need $\phi$ to belong to the spectral projection $\chi_{[\epsilon,\infty)}(A)$, assuming $\|\phi\|=1$. – Nik Weaver Apr 3 '20 at 17:00 • Sorry, I should have been more explicit. $A$ is strictly positive. – Artemy Apr 3 '20 at 17:24 ## 1 Answer In "On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space (1966)", R. G. Douglas proved the following result (Theorem 1 in the paper): Theorem. Let $$C$$ and $$D$$ be bounded linear operators on a real or complex Hilbert space $$\mathcal{H}$$; then the following are equivalent: (i) $$C\mathcal{H} \subseteq D \mathcal{H}$$. (ii) There exists a number $$\lambda \in [0,\infty)$$ such that $$CC^* \le \lambda^2 DD^*$$. (iii) There exists a bounded linear operator $$E$$ on $$\mathcal{H}$$ such that $$C = DE$$. Now, if you choose $$C$$ in the theorem as the positive square root $$\sqrt{B}$$ of $$B$$ and $$D$$ in the theorem as the positive square root $$\sqrt{A}$$ of $$A$$, you can characterize the property you are interested in by means of a range condition. More precisely: Corollary. Write your rank-$$1$$ operator $$B$$ as $$B = \alpha \vert \phi\rangle\langle\phi\vert$$ for a number $$\alpha > 0$$ and a vector $$\vert \phi\rangle \in \mathcal{H}$$ of norm $$1$$ (not necessarily an eigenvector of $$A$$). Then the following are equivalent: (i) There exists $$\varepsilon > 0$$ such that $$A \ge \varepsilon B$$. (ii) $$\vert \phi\rangle$$ is an element of the range of $$\sqrt{A}$$.

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George: Some scientists say that global warming will occur : GMAT Critical Reasoning (CR) Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack It is currently 20 Jan 2017, 10:45 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # George: Some scientists say that global warming will occur Author Message TAGS: ### Hide Tags Senior Manager Joined: 16 Sep 2006 Posts: 406 Followers: 1 Kudos [?]: 72 [0], given: 0 George: Some scientists say that global warming will occur [#permalink] ### Show Tags 21 Nov 2006, 10:14 00:00 Difficulty: (N/A) Question Stats: 0% (00:00) correct 0% (00:00) wrong based on 1 sessions ### HideShow timer Statistics 8. George: Some scientists say that global warming will occur because people are releasing large amounts of carbon dioxide into the atmosphere by burning trees and fossil fuels. We can see, though, that the predicted warming is occurring already. In the middle of last winter, we had a month of springlike weather in our area, and this fall, because of unusually mild temperatures, the leaves on our town’s trees were three weeks late in turning color. Which one of the following would it be most relevant to investigate in evaluating the conclusion of George’s argument? (A) whether carbon dioxide is the only cause of global warming (B) when leaves on the trees in the town usually change color (C) what proportion of global emissions of carbon dioxide is due to the burning of trees by humans (D) whether air pollution is causing some trees in the are to lose their leaves (E) whether unusually warm weather is occurring elsewhere on the globe more frequently than before If you have any questions New! VP Joined: 21 Aug 2006 Posts: 1025 Followers: 1 Kudos [?]: 31 [0], given: 0 Re: CR on global warming! [#permalink] ### Show Tags 21 Nov 2006, 10:30 jyotsnasarabu wrote: 8. George: Some scientists say that global warming will occur because people are releasing large amounts of carbon dioxide into the atmosphere by burning trees and fossil fuels. We can see, though, that the predicted warming is occurring already. In the middle of last winter, we had a month of springlike weather in our area, and this fall, because of unusually mild temperatures, the leaves on our town’s trees were three weeks late in turning color. Which one of the following would it be most relevant to investigate in evaluating the conclusion of George’s argument? (A) whether carbon dioxide is the only cause of global warming (B) when leaves on the trees in the town usually change color (C) what proportion of global emissions of carbon dioxide is due to the burning of trees by humans (D) whether air pollution is causing some trees in the are to lose their leaves (E) whether unusually warm weather is occurring elsewhere on the globe more frequently than before My answer. We need to see, whether the similar conditions mentioned by george are happening elsewhere. If changes could be seen across the globe, then one can conclude that there is global warming already. If they are not, then the changes in weather at george's place could be because of george living there. _________________ The path is long, but self-surrender makes it short; the way is difficult, but perfect trust makes it easy. Senior Manager Joined: 17 Oct 2006 Posts: 438 Followers: 1 Kudos [?]: 27 [0], given: 0 ### Show Tags 21 Nov 2006, 10:38 First I went for D but after reading explaination given above convinced that its E..thanks ak_idc..u r the best in solving CR! VP Joined: 15 Jul 2004 Posts: 1473 Schools: Wharton (R2 - submitted); HBS (R2 - submitted); IIMA (admitted for 1 year PGPX) Followers: 22 Kudos [?]: 174 [0], given: 13 Re: CR on global warming! [#permalink] ### Show Tags 21 Nov 2006, 10:52 ak_idc wrote: jyotsnasarabu wrote: 8. George: Some scientists say that global warming will occur because people are releasing large amounts of carbon dioxide into the atmosphere by burning trees and fossil fuels. We can see, though, that the predicted warming is occurring already. In the middle of last winter, we had a month of springlike weather in our area, and this fall, because of unusually mild temperatures, the leaves on our town’s trees were three weeks late in turning color. Which one of the following would it be most relevant to investigate in evaluating the conclusion of George’s argument? (A) whether carbon dioxide is the only cause of global warming (B) when leaves on the trees in the town usually change color (C) what proportion of global emissions of carbon dioxide is due to the burning of trees by humans (D) whether air pollution is causing some trees in the are to lose their leaves (E) whether unusually warm weather is occurring elsewhere on the globe more frequently than before My answer. We need to see, whether the similar conditions mentioned by george are happening elsewhere. If changes could be seen across the globe, then one can conclude that there is global warming already. If they are not, then the changes in weather at george's place could be because of george living there. Nice one AK - E it is.. Director Joined: 17 Jul 2006 Posts: 714 Followers: 1 Kudos [?]: 12 [0], given: 0 Re: CR on global warming! [#permalink] ### Show Tags 21 Nov 2006, 19:41 ak_idc wrote: jyotsnasarabu wrote: 8. George: Some scientists say that global warming will occur because people are releasing large amounts of carbon dioxide into the atmosphere by burning trees and fossil fuels. We can see, though, that the predicted warming is occurring already. In the middle of last winter, we had a month of springlike weather in our area, and this fall, because of unusually mild temperatures, the leaves on our town’s trees were three weeks late in turning color. Which one of the following would it be most relevant to investigate in evaluating the conclusion of George’s argument? (A) whether carbon dioxide is the only cause of global warming (B) when leaves on the trees in the town usually change color (C) what proportion of global emissions of carbon dioxide is due to the burning of trees by humans (D) whether air pollution is causing some trees in the are to lose their leaves (E) whether unusually warm weather is occurring elsewhere on the globe more frequently than before My answer. We need to see, whether the similar conditions mentioned by george are happening elsewhere. If changes could be seen across the globe, then one can conclude that there is global warming already. If they are not, then the changes in weather at george's place could be because of george living there. VP Joined: 21 Mar 2006 Posts: 1134 Location: Bangalore Followers: 3 Kudos [?]: 40 [0], given: 0 ### Show Tags 21 Nov 2006, 19:55 Narrowed it down to A and E. Picked A. Can anyone explain why E and not A? VP Joined: 21 Aug 2006 Posts: 1025 Followers: 1 Kudos [?]: 31 [0], given: 0 ### Show Tags 21 Nov 2006, 20:00 kripalkavi wrote: Narrowed it down to A and E. Picked A. Can anyone explain why E and not A? Focus of the argument is whether the global warming is happening already. And that is the reason he is giving an example to prove his point that global warming is happening. Now. I think...the answer has to address this aspect. E does that. _________________ The path is long, but self-surrender makes it short; the way is difficult, but perfect trust makes it easy. VP Joined: 28 Mar 2006 Posts: 1381 Followers: 2 Kudos [?]: 31 [0], given: 0 ### Show Tags 21 Nov 2006, 20:05 ak_idc wrote: kripalkavi wrote: Narrowed it down to A and E. Picked A. Can anyone explain why E and not A? Focus of the argument is whether the global warming is happening already. And that is the reason he is giving an example to prove his point that global warming is happening. Now. I think...the answer has to address this aspect. E does that. VP Joined: 21 Mar 2006 Posts: 1134 Location: Bangalore Followers: 3 Kudos [?]: 40 [0], given: 0 ### Show Tags 22 Nov 2006, 00:44 ak_idc wrote: kripalkavi wrote: Narrowed it down to A and E. Picked A. Can anyone explain why E and not A? Focus of the argument is whether the global warming is happening already. And that is the reason he is giving an example to prove his point that global warming is happening. Now. I think...the answer has to address this aspect. E does that. Thank you! VP Joined: 25 Jun 2006 Posts: 1172 Followers: 3 Kudos [?]: 148 [0], given: 0 ### Show Tags 23 Nov 2006, 00:35 VP Joined: 21 Aug 2006 Posts: 1025 Followers: 1 Kudos [?]: 31 [0], given: 0 ### Show Tags 23 Nov 2006, 03:37 tennis_ball wrote: OA is E. _________________ The path is long, but self-surrender makes it short; the way is difficult, but perfect trust makes it easy. 23 Nov 2006, 03:37 Similar topics Replies Last post Similar Topics: 5 Lsat:George Some scientists say that global warming will occur 3 17 Sep 2014, 03:06 10 Climatologist: Global warming is affecting snowfall througho 2 19 Apr 2014, 00:15 21 Some experts warn that global warming will reduce food 21 05 Jun 2011, 08:17 5 George: Some scientists say that global warming will occur 11 22 May 2010, 09:22 Observatory director: Some say that funding the 10 25 Mar 2008, 07:35 Display posts from previous: Sort by

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Double Dummy Corner Competition Problem 7 composed by Eugenius Paprotny presented for solving in September 2005 DR4 ♠ AKJ4 ♥ 2 ♦ A942 ♣ 10654 ♠ Q1093 ♥ 876 ♦ KJ75 ♣ 97 ♠ 87 ♥ KQ1095 ♦ 3 ♣ KQJ83 ♠ 652 ♥ AJ43 ♦ Q1086 ♣ A2 South to make three no-trumps.  West leads the 8. Successful solvers:  Robin Adey, Jean-Marc Bihl, Clint Fyke, Dick Yuen, Wim van der Zijden DDC Home Next problem Previous problem Next DR4 Previous DR4 Competition problem archive Solution South lets East hold the first trick and the second, in clubs.  The ♣A wins the third, and South advances the 8 (or 10). A.      If West ducks, four rounds of spades follow, South discarding a heart.  West's forced red suit return concedes the eighth trick.  If it is a heart, South wins two hearts and easily makes two of the last three tricks in diamonds.  If it is a diamond, three rounds of diamond endplay West again. B.      If West covers, North wins and leads a second diamond (optionally cashing a top spade first), South playing the middle card. 1.       If West wins and returns the 7, North plays the 9 and South overtakes.  South leads the 6, North finessing the J.  A top spade is cashed if it wasn't cashed at trick 5, South playing the 5 on it in either case.  South comes to hand on the fourth diamond.  Now, if West still has the 3, South cashes the A and makes two spade tricks by finessing the 4; otherwise, two rounds of spades throw West in for a heart lead into South's A-J. 2.       If West ducks, South leads the 6 to North's J and North cashes a top spade.  If West still has the 3 now, North's next card is the 9; otherwise it is the 4.  In the first case, either West ducks again, in which case North cashes the other top spade and throws West in as a stepping-stone to South's hearts, or West wins and lets South get in with the last diamond to score the A and finesse the 4.  In the second case, South plays the Q, forcing West to win and return the suit.  But again North plays A and the last spade to make West a stepping-stone to the hearts. See the solution to Competition Problem #4 for the recommended tabular format if you prefer not to write in English prose. DDC Home Next problem Previous problem Next DR4 Previous DR4 Competition problem archive

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# science posted by . At the annual turtle races, Poindexter, the record holder, is trying to retain his title. As the race begins, Poindexter starts off racing North with a speed of 0.025 m/s. He retains this speed for 0.5 meters at which time he speeds up to 0.10 m/s. He continues at this rate for 0.75 meters. Tiring, he slows to 0.07 m/s and continues for another half of a meter. Applying all his concentration and effort for the last bit of the race he increases his speed to a swift 0.085 m/s. An exhausted Wood Turtle, Poindexter completes his two meter race beating his closest competitor by a nose. What is the displacement? • science - Isn't the displacement just 2 meters to the north of where he started? Check my thinking. I think all of that speed stuff is a distraction. ## Similar Questions 1. ### ipc At the annual turtle races, Poindexter, the record holder, is trying to retain his title. As the race begins, Poindexter starts off racing North with a speed of 0.025 m/s. He retains this speed for 0.5 meters at which time he speeds … 2. ### science At the annual turtle races, Poindexter, the record holder, is trying to retain his title. As the race begins, Poindexter starts off racing North with a speed of 0.025 m/s. He retains this speed for 0.5 meters at which time he speeds … 3. ### science At the annual turtle races, Poindexter, the record holder, is trying to retain his title. As the race begins, Poindexter starts off racing North with a speed of 0.025 m/s. He retains this speed for 0.5 meters at which time he speeds … 4. ### science At the annual turtle races, Poindexter, the record holder, is trying to retain his title. As the race begins, Poindexter starts off racing North with a speed of 0.025 m/s. He retains this speed for 0.5 meters at which time he speeds … 5. ### displacement... At the annual turtle races, Poindexter, the record holder, is trying to retain his title. As the race begins, Poindexter starts off racing North with a speed of 0.025 m/s. He retains this speed for 0.5 meters at which time he speeds … 6. ### science At the annual turtle races, Poindexter, the record holder, is trying to retain his title. As the race begins, Poindexter starts off racing North with a speed of 0.025 m/s. He retains this speed for 0.5 meters at which time he speeds … 7. ### math The students in Mr. Stevens class are having a turtle race. The race will last 2 minutes. Find the distance from the start each turtle will be at the of the race.Rex 1/6 speed (in inches per second).Whatwas the distance at the end … 8. ### math The students in Mr. Stevens class are having a turtle race. The race will last 2 minutes. Find the distance from the start each turtle will be at the of the race.Rex 2/3 speed (in inches per second).Whatwas the distance at the end … 9. ### Physics 1. A rabbit and a turtle are practicing for their big race. The rabbit covers a 30.0 m practice course in 5.00 seconds; the turtle covers the same distance in 120 seconds. If the actual race is run on a 96.0 m course, by how many seconds … 10. ### Calculus In a 21 meter race between a turtle and a hare, the turtle leaves 8 minutes before the hare. The hare, by running at an average speed of 0.5 meters per hour faster than the turtle, crosses the finish line 4 minutes before the turtle. … More Similar Questions

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Databases Reference In-Depth Information direct way of expressing relational comparisons. 2 A striking example in support of this contention can be found in the discussion of Example 12 in the section of that name in Chapter 15. SIXTH NORMAL FORM Having said, or at least implied, that we won't be departing in this chapter from our usual assumptions regarding decomposition and recomposition operators, I'll begin my discussion of sixth normal form by doing exactly that ... In our topic Temporal Data and the Relational Model (Morgan Kaufmann, 2003), Hugh Darwen, Nikos Lorentzos, and I define: a. Generalized versions of the projection and join operators, and hence b. A generalized form of join dependency, and hence c. A new normal form, which we call 6NF. As the title of that topic might suggest, these developments turn out to be particularly important in connection with temporal data, and they're discussed in detail in that topic. However, temporal data as such is beyond the scope of the topic you're reading right now; all I want to do here is give a definition of 6NF that works for “regular”─i.e., nontemporal─data (and I'll assume from this point forward that all data is “regular” in this sense). Appealing only to projection and join as classically defined, therefore (and hence only to JDs as classically defined also), 3 here's the 6NF definition: Definition: Relvar R is in sixth normal form (6NF) if and only if the only JDs that hold in R are trivial ones. In other words, the only JDs that hold in R are of the form {..., H ,...}, where H is the heading. Of course, we can never get rid of trivial dependencies; thus, a relvar in 6NF can't be nonloss decomposed at all, other than trivially. For that reason, a 6NF relvar is sometimes said to be irreducible (yet another kind of irreducibility, observe). Our usual shipments relvar SP is in 6NF, and so is relvar CTXD from Chapter 9; by contrast, our usual parts relvar P is in 5NF but not 6NF. (By contrast, our usual suppliers relvar S isn't even in 3NF, of course.) Now, it follows immediately from the definition that every 6NF relvar is certainly in 5NF─i.e., 6NF implies 5NF. (That's why it's reasonable to use the name sixth normal form , because 6NF really does represent another step along the classical road from 1NF to 2NF to ... to 5NF.) What's more, 6NF is always achievable. It's also intuitively attractive, for the following reason: If relvar R is replaced by its 6NF projections R1 , ..., Rn , then the predicates for R1 , ..., Rn are all simple , and the predicate for R overall is the conjunction of those simple predicates (i.e., it's a conjunctive predicate ). Let me immediately explain what I mean by these remarks: Definition: A predicate is simple if it involves no connectives and composite (or compound ) if it's not simple. 2 By SQL here, I mean SQL as defined by the SQL standard. The situation is even worse in mainstream implementations, where most EQDs can't be formulated at all, owing to the fact that the implementations in question don't allow subqueries in constraints. 3 So I'm not really departing from our usual assumptions after all. Search WWH :: Custom Search

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# Optimizing a Numerical Laplace Equation Solver Laplace's Equation is an equation on a scalar in which, given the value of the scalar on the boundaries (the boundary conditions), one can determine the value of the scalar at any point in the region within the boundaries. Initially, I considered using NDSolve, but I realized that I did not know how to specify the boundary conditions properly. In the example below, my boundary is a square with value 0 along the top, left and right boundary and 1 along the bottom boundary. Alternatively, the solutions to the equation can be approximated via the Method of Relaxation. In the method, the region is divided into a grid, with the grid squares along the boundary being assigned (fixed) boundary conditions, and the value for the grid squares within the boundary being iteratively calculated by assigning the average values (in the previous time-step) of four grid squares adjacent to it. My current code is as follows localmeaner = Mean@{#1[[#2 - 1, #3]], #1[[#2 + 1, #3]], #1[[#2, #3 - 1]], #1[[#2, #3 + 1]]} &; relaxer = ({#[[1]]}~Join~ Table[ {#[[j, 1]]}~Join~ Table[localmeaner[#, j, i], {i, 2, Dimensions[#][[2]] - 1} ]~ Join~{#[[j, Dimensions[#][[2]]]]}, {j, 2, Dimensions[#][[1]] - 1}]~Join~{#[[Dimensions[#][[1]]]]}) &; matrixold = Append[ConstantArray[0, {41, 40}], ConstantArray[1, 40]]; (*test matrix fixing the boundary conditions as 0 on the top, left and right boundaries and 1 on the bottom boundary*) tempmatrix = Nest[relaxer, matrixold, 300]; (*matrix after 300 relaxations*) localmeaner is a function that takes the average of the four grid squares adjacent to a square. relaxer is a function that preserves the boundary values but otherwise applies localmeaner onto each of the grid cells to produce their new values based on the average of the four grid cells adjacent to it. Is there a quicker way to find a numerical solution to the Laplace's Equation given specific boundary conditions? As a point of interest, one can plot the solution as ArrayPlot[tempmatrix*1., ColorFunction -> "Rainbow"], resulting in the following image, which helps one to visualize the results. NB: I'm planning to extend this solution to approximations that can work in polar coordinates, Cartesian coordinates in three dimensions and spherical coordinates, so I'm hoping that the answers could be equally general. - Take a look here. – swish Apr 19 '13 at 10:54 Too bad! So since the documentation states that "This rules out purely elliptic equations such as Laplace's equation, but leaves a large class of evolution equations that can be solved quite efficiently.", I'd have to continue to work using my method? – Vincent Tjeng Apr 19 '13 at 11:01 I posted a pretty flexible relaxation solver for the Poisson equation here. The Laplace equation is a special case of that. Maybe you can use it for your problem. – Jens Apr 19 '13 at 17:00 @Jens thank you! have you ever tried to write code that works for the Poisson equation in three dimensions, in particular in spherical coordinates? I was hoping that I could modify your code to do so, but haven't figured out a way yet. – Vincent Tjeng Apr 20 '13 at 4:20 I haven't extended it to three dimensions. The first thing one might try is to do a cylindrically symmetric 3D problem in cylinder coordinates, where the radial derivative is modified to $\frac{1}{r}\frac{\partial}{\partial r}\left(r\,\frac{\partial f}{\partial r}\right)$ but can still be discretized. But fully 3D calculations aren't just tricky, they may quickly become impractical for Mathematica. It depends on the application, I guess, but I'd go straight to FORTRAN. – Jens Apr 20 '13 at 19:06 Here is a code that is about 2 orders of magnitude faster. We will use a finite element method to solve the issue at hand. Before we start, note however, that the transition between the Dirichlet values should be smooth. We use the finite element method because that works for general domains and some meshing utilities exist here and in the links there in. For 3D you can use the build in TetGenLink. For your rectangular domain, we just create the coordinates and incidences by hand: << Developer nx = ny = 4; coordinates = Flatten[Table[{i, j}, {i, 0., 1., 1/(ny - 1)}, {j, 0., 1., 1/(nx - 1)}], 1]; incidents = Flatten[Table[{j*nx + i, j*nx + i + 1, (j - 1)*nx + i + 1, (j - 1)*nx + i}, {i, 1, nx - 1}, {j, 1, ny - 1}], 1]; (* triangulate the quad incidences *) incidents = ToPackedArray[ incidents /. {i1_?NumericQ, i2_, i3_, i4_} :> Sequence[{i1, i2, i3}, {i3, i4, i1}]]; Graphics[GraphicsComplex[ coordinates, {EdgeForm[Gray], FaceForm[], Polygon[incidents]}]] Now, we create the finite element symbolically and compile that: tmp = Join[ {{1, 1, 1}}, Transpose[Quiet[Array[Part[var, ##] &, {3, 2}]]]]; me = {{0, 0}, {1, 0}, {0, 1}}; p = Inverse[tmp].me; help = Transpose[ (p.Transpose[p])*Abs[Det[tmp]]/2]; diffusion2D = With[{code = help}, Compile[{{coords, _Real, 2}, {incidents, _Integer, 1}}, Block[{var}, var = coords[[incidents]]; code ] , RuntimeAttributes -> Listable (*,CompilationTarget\[Rule]"C"*)]]; AbsoluteTiming[allElements = diffusion2D[coordinates, incidents];] You can not do this in FORTRAN! For this specific problem the element contributions are all the same, so that could be utilized, but since you wanted a somewhat more general approach I am leaving it as it is. To assemble the elements into a system matrix: matrixAssembly[ values_, pos_, dim_] := Block[{matrix, p}, SystemSetSystemOptions[ "SparseArrayOptions" -> {"TreatRepeatedEntries" -> 1}]; matrix = SparseArray[ pos -> Flatten[ values], dim]; SystemSetSystemOptions[ "SparseArrayOptions" -> {"TreatRepeatedEntries" -> 0}]; Return[ matrix]] pos = Compile[{{inci, _Integer, 2}}, Flatten[Map[Outer[List, #, #] &, inci], 2]][incidents]; dofs = Max[pos]; AbsoluteTiming[ stiffness = matrixAssembly[ allElements, pos, dofs] ] The last part that is missing are the Dirichlet conditions. We modify the system matrix in place for that: SetAttributes[dirichletBoundary, HoldFirst] dirichletBoundary[ {load_, matrix_}, fPos_List, fValue_List] := Block[{}, matrix[[All, fPos]] = matrix[[fPos, All]] = 0.; matrix += SparseArray[ Transpose[ {fPos, fPos}] -> Table[ 1., {Length[fPos]}], Dimensions[matrix], 0]; ] diriPos1 = Position[coordinates, {_, 0.}]; diriVals1 = Table[1., {Length[diriPos1]}]; diriPos2 = Position[coordinates, ({_, 1.} | {1., _?(# > 0 &)} | {0., _?(# > 0 &)})]; diriVals2 = Table[0., {Length[diriPos2]}]; diriPos = Flatten[Join[diriPos1, diriPos2]]; diriVals = Join[diriVals1, diriVals2]; AbsoluteTiming[ solution = LinearSolve[ stiffness, load(*, Method\[Rule]"Krylov"*)]; ] When I use your code on my laptop it has about 1600 quads and takes about 6 seconds. When I run this code with nx = ny = 90; (which gives about 16000 triangles) it runs in about 0.05 seconds. Note that the element computation and matrix assembly take less time than the LinearSolve. That's the way things should be. The result can be visualized: Graphics[GraphicsComplex[coordinates, Polygon[incidents], VertexColors -> ToPackedArray@(List @@@ (ColorData["Rainbow"][#] & /@ solution))]] ` For the 3D case have a look here. Hope this helps. - There are so many nice tricks in here... (+1). To make this code easier to study, I think it will be good to add a link to this page: What are some useful, undocumented Mathematica functions? – Jens Apr 23 '13 at 23:42 @Jens, I am glad you like it. – user21 Apr 24 '13 at 5:41 @ruebenko this is great! I was looking through some of the documentation for other Laplace / Poisson equation solvers on the Mathematica site but was having trouble understanding them. Thank you for taking the time to explain your solution in detail. – Vincent Tjeng Apr 25 '13 at 1:33 By the way, just out of curiosity, did you already have a solution to this problem before or did you code this from scratch? – Vincent Tjeng Apr 25 '13 at 1:34 @VincentTjeng, well I had the 3D version from a talk I gave and then had some other notebooks with experiments. Also, I worked a lot with FEM during my thesis. You may also want to read this. – user21 Apr 25 '13 at 6:14

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essay-cheap # Solve half life problems H is half-life. what is a professional writing sample 2. replacing a with .5 ao and solving for t we get: 1) determine decimal fraction math homework help for parents of c-14 remaining: graphing transformations of exponential functions. p = p₀e^(rt) where p₀ how to write a synthesis essay ap is the initial amount, r is the growth homework in primary schools rate, and t ms word assignments is time. your first point solve half life problems is likely to be your y-intercept since it is the starting mass/abundance. e^ (t* (-ln (2)/hl))=.63 —> ln (.63)=t (-ln (2)/hl) —> t = -hl*ln (.63)/ln (2) t is the age of the fossil hl solve half life problems (half-life) ln solve half life problems (natural logarithm ) -. now and then he heard a door the word for whats closed. you were only trying to help what a leader is essay to find the half-life of a function describing exponential decay, solve the sell your writing online following equation: the order in which you use them depends on the data given and what is being asked. oct 31, 2016 · americans, a start essay with quote half-life half-lives solution: use why are you here essay the rate constant and the first-order concentration-time equation to determine the reactant concentration at the given time. the outline of the essay.

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# Re: st: re: matrix manipulation From Kit Baum To "Susan Olivia" Subject Re: st: re: matrix manipulation Date Fri, 12 Dec 2008 10:35:36 -0500 ```<> ``` The following will do these three things. _underbar_ is a Mata function being defined in the code below. Note that one of the diagonal elements should fall under the threshold of 10, but it is being zapped within the for loop. ``` --------------------- mata: mata clear mata: void underbar(string scalar mat, real scalar thresh) { real matrix B real scalar i B = (st_matrix(mat) :< thresh) :/ st_matrix(mat) for(i=1; i<=rows(B); i++) { B[i,i] = 0 } st_matrix("B", B) } end sysuse auto,clear qui reg price trunk weight length turn mat list e(V) mata: underbar("e(V)", 10) mat list B ------------------------ ``` You might want to see my FNASUG or UKSUG slideshow on Stata programming with Mata, available from my IDEAS page below, regarding use of the colon operator (:< or :/ above) or the st_* functions. ``` Kit Baum, Boston College Economics and DIW Berlin http://ideas.repec.org/e/pba1.html An Introduction to Modern Econometrics Using Stata: http://www.stata-press.com/books/imeus.html On Dec 12, 2008, at 09:50 , Susan Olivia wrote: ``` Thanks for the tips, Kit. I would like to use this opportunity to ask 3 follow up questions: ``` ``` 1) For each cell (i,j) of matrix B, I would like to replace its value with 1/(A[ij]) instead of dummy [0 1] as in before. In other words, matrix B[i,j] = 1/A[i,j] if A[i,j] < THRESHOLD. I seem having problem in doing this. ``` ``` 2) The syntax you suggested "underbar", I seem couldn't find this entry in the STATA manual. Can you please explain what is this doing? Perhaps once I know what "underbar" is really doing, I can tackle #1. ``` ``` 3) Also, when the threshold condition met, the diagonal element of matrix B is replaced to 1 or 1/aij. Ideally, I want the diagonal element to be zero. Is there an efficient way to do this? What I currently do is transform the matrix into variables and use the loop to change the diagonal element and then transform the variables into the matrix. I.e. ``` svmat B local i=1 while `i'<=_N { qui recode B`i' 1=0 in `i' local i=`i'+1 } mkmat B*, matrix(B) Thanks in advance for any programming tips. Cheers, Susan On Thu, Dec 11, 2008 at 8:00 AM, Kit Baum <baum@bc.edu> wrote: <> Susan said I would like to create a binary matrix (say matrix B) using the existing information from current matrix A. Specifically, for each cell (i,j) of matrix B, I want to replace its value with 1 if the value of the corresponding cell (i,j) of matrix A is less than the specified threshold value. In other words, matrix B[i,j] = 1 if A[i,j] < THRESHOLD. No subscripting required: -------------------------------- mata: mata clear mata: void underbar(string scalar mat, real scalar thresh) { st_matrix("B", (st_matrix(mat) :< thresh)) } end sysuse auto,clear qui reg price trunk weight length turn mat list e(V) mata: underbar("e(V)",0.0001) mat list B ----------------------------------- ``` You could pass the name of the result matrix to Mata as well if you wanted this to be a bit more general. ``` Kit Baum, Boston College Economics and DIW Berlin http://ideas.repec.org/e/pba1.html An Introduction to Modern Econometrics Using Stata: http://www.stata-press.com/books/imeus.html * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ ``` ``` * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ ```

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Search a number 82630656 = 211324483 BaseRepresentation bin1001110110011… …01100000000000 312202111001221200 410323031200000 5132123140111 612111021200 72022230463 oct473154000 9182431850 1082630656 11427086a9 122380a800 13141718a4 1573c3256 hex4ecd800 82630656 has 72 divisors (see below), whose sum is σ = 238705740. Its totient is φ = 27537408. The previous prime is 82630637. The next prime is 82630699. The reversal of 82630656 is 65603628. It is a tau number, because it is divible by the number of its divisors (72). It is a Harshad number since it is a multiple of its sum of digits (36). It is a self number, because there is not a number n which added to its sum of digits gives 82630656. It is a congruent number. It is an unprimeable number. It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 16191 + ... + 20673. Almost surely, 282630656 is an apocalyptic number. It is an amenable number. It is a practical number, because each smaller number is the sum of distinct divisors of 82630656, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (119352870). 82630656 is an abundant number, since it is smaller than the sum of its proper divisors (156075084). It is a pseudoperfect number, because it is the sum of a subset of its proper divisors. 82630656 is a wasteful number, since it uses less digits than its factorization. 82630656 is an evil number, because the sum of its binary digits is even. The sum of its prime factors is 4511 (or 4488 counting only the distinct ones). The product of its (nonzero) digits is 51840, while the sum is 36. The square root of 82630656 is about 9090.1405929721. The cubic root of 82630656 is about 435.5590750483. The spelling of 82630656 in words is "eighty-two million, six hundred thirty thousand, six hundred fifty-six".

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Search   Memberlist   Usergroups Page 1 of 1 [5 Posts] Author Message J. J. Foncannon science forum beginner Joined: 10 Jun 2005 Posts: 3 Posted: Fri Jun 10, 2005 3:19 pm    Post subject: very annoying sequence!!!! A sequence s[n] is defined as follows: s[1]=1, s[2]=12, s[3]=20, ans s[n+3]=2s[n+2] + 2s[n+1] - s[n], n=1, 2, ... . PROVE: 1 + 4s[n] s[n+1] is a perfect square. -- __________________________________________________ ********************************************************** J. J. Foncannon The Belgian surrealist painter Renee Magritte entered a cheese store in Brussels to purchase a wheel of Swiss cheese. The owner pulled a wheel from the front window, but Magritte said he preferred the one on the back counter. “But they are identical,” the owner protested. “No,” Magritte insisted. “This one’s been stared at.” ********************************************************** Timothy Little science forum Guru Wannabe Joined: 30 May 2005 Posts: 295 Posted: Sat Jun 11, 2005 10:01 am    Post subject: Re: very annoying sequence!!!! J. J. Foncannon wrote: Quote: A sequence s[n] is defined as follows: s[1]=1, s[2]=12, s[3]=20, s[n+3]=2s[n+2] + 2s[n+1] - s[n], n=1, 2, ... . PROVE: 1 + 4s[n] s[n+1] is a perfect square. Can you prove that 1 + 4 s[n+1] s[n+2] = ((s[n+3] - s[n]) / 2)^2 for n >= 1? For example, by induction? - Tim J. J. Foncannon science forum beginner Joined: 10 Jun 2005 Posts: 3 Posted: Sat Jun 11, 2005 5:56 pm    Post subject: Re: very annoying sequence!!!! It works.... How did you know to try this? Thanks, Jet Timothy Little wrote: Quote: J. J. Foncannon wrote: A sequence s[n] is defined as follows: s[1]=1, s[2]=12, s[3]=20, s[n+3]=2s[n+2] + 2s[n+1] - s[n], n=1, 2, ... . PROVE: 1 + 4s[n] s[n+1] is a perfect square. Can you prove that 1 + 4 s[n+1] s[n+2] = ((s[n+3] - s[n]) / 2)^2 for n >= 1? For example, by induction? - Tim -- __________________________________________________ ********************************************************** Jet Foncannon The Belgian surrealist painter Renee Magritte entered a cheese store in Brussels to purchase a wheel of Swiss cheese. The owner pulled a wheel from the front window, but Magritte said he preferred the one on the back counter. “But they are identical,” the owner protested. “No,” Magritte insisted. “This one’s been stared at.” ********************************************************** J. J. Foncannon science forum beginner Joined: 10 Jun 2005 Posts: 3 Posted: Sun Jun 12, 2005 12:14 am    Post subject: Re: very annoying sequence!!!! Very good work, Tim. The induction needed to verify your assertion is quite straightforward, and I won't bore you with it. Another fact: the square root of 1+4s[n]s[n+1] satisfies the same recurrence as s[n]. Jet Timothy Little wrote: Quote: J. J. Foncannon wrote: It works.... How did you know to try this? Jet Quote: First I worked out 10 or so terms of the series and verified that they were in fact perfect squares. So next I looked at the square roots. Then I took a detour into working out the closed form for the s[n], which I found, but couldn't see anything in it that obviously led to your expression being a perfect square. Dead end so far (though more work might have succeeded). So, back to eyeballing the list of square roots again. I expected that their sequence would be some linear combination of some s[n]'s, because 1) they were roughly the square root of a product of two terms, and so should be roughly linear in the size of the sequence terms, and 2) the recurrence for the sequence was linear. With that in mind I did notice that they were usually pretty close to half of s[n+3], but a bit smaller. So I looked at (s[n+3] - something) / 2, and the 'something' for the first few happened to be s[n]. If I had been looking at s[n+2] instead, I would likely have eventually ended up with the equivalent expression (s[n+2] + s[n+1] - s[n]). There is no doubt a less haphazard way to get the same result, but I didn't find it :) - Tim -- __________________________________________________ ********************************************************** J. J. Foncannon The Belgian surrealist painter Renee Magritte entered a cheese store in Brussels to purchase a wheel of Swiss cheese. The owner pulled a wheel from the front window, but Magritte said he preferred the one on the back counter. “But they are identical,” the owner protested. “No,” Magritte insisted. “This one’s been stared at.” ********************************************************** Timothy Little science forum Guru Wannabe Joined: 30 May 2005 Posts: 295 Posted: Sun Jun 12, 2005 12:23 am    Post subject: Re: very annoying sequence!!!! J. J. Foncannon wrote: Quote: It works.... How did you know to try this? First I worked out 10 or so terms of the series and verified that they were in fact perfect squares. So next I looked at the square roots. Then I took a detour into working out the closed form for the s[n], which I found, but couldn't see anything in it that obviously led to your expression being a perfect square. Dead end so far (though more work might have succeeded). So, back to eyeballing the list of square roots again. I expected that their sequence would be some linear combination of some s[n]'s, because 1) they were roughly the square root of a product of two terms, and so should be roughly linear in the size of the sequence terms, and 2) the recurrence for the sequence was linear. With that in mind I did notice that they were usually pretty close to half of s[n+3], but a bit smaller. So I looked at (s[n+3] - something) / 2, and the 'something' for the first few happened to be s[n]. If I had been looking at s[n+2] instead, I would likely have eventually ended up with the equivalent expression (s[n+2] + s[n+1] - s[n]). There is no doubt a less haphazard way to get the same result, but I didn't find it :) - Tim Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First Page 1 of 1 [5 Posts] The time now is Mon Dec 17, 2018 7:11 pm | All times are GMT Jump to: Select a forum-------------------Forum index|___Science and Technology    |___Math    |   |___Research    |   |___num-analysis    |   |___Symbolic    |   |___Combinatorics    |   |___Probability    |   |   |___Prediction    |   |       |   |___Undergraduate    |   |___Recreational    |       |___Physics    |   |___Research    |   |___New Theories    |   |___Acoustics    |   |___Electromagnetics    |   |___Strings    |   |___Particle    |   |___Fusion    |   |___Relativity    |       |___Chem    |   |___Analytical    |   |___Electrochem    |   |   |___Battery    |   |       |   |___Coatings    |       |___Engineering        |___Control        |___Mechanics        |___Chemical Topic Author Forum Replies Last Post Similar Topics sequence of polynomials artur_steiner@yahoo.com Math 1 Tue Jul 18, 2006 1:20 am annoying import warning Mathew num-analysis 1 Tue Jul 18, 2006 1:16 am In which (ordered) spaces an increasing sequence has a li... lataianu bogdan Math 5 Mon Jul 17, 2006 7:11 pm Sequence with factorials alex.lupas@gmail.com Recreational 0 Sun Jul 16, 2006 3:48 am How to determine phase of m-sequence Steve W Math 0 Wed Jul 12, 2006 3:47 am

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# SHA256 output to 0-99 number range? Is it mathematically possible to take a SHA256 hash and turn it into a 0-99 number where each number in 0-99 range is equally likely to be picked? As a 256 bit hash means the highest value possible is 2^256, this is not a nice or "round" number for the purposes of simplifying a hash down to ranges more natural for humans. - truncated to 7-bits, the result is a value between 0 and 127 – Richie Frame Jul 3 '14 at 19:33 If you mean exactly as likely, no, because the number of possible hashes is not a multiple of $100$. This is assuming all the hashes are exactly equally likely. You can come very close just by taking $SHA256 hash \pmod {100}$ This will be within one part in $\frac {2^{256}}{100}$, which is a very small number. If you want truly equal, check that the hash is in the range $[0,100\lfloor \frac {2^{256}}{100}\rfloor)$ and take it $\pmod {100}$ If it is above that, hash something else and try again. Your odds of failing the check are very small, and your odds of failing twice are very small. - I have tested all possible SHA-256 hashes which are larger than $100\lfloor \frac {2^{256}}{100}\rfloor$. None of them produce number larger than $100\lfloor \frac {2^{256}}{100}\rfloor$ when hashed the second time. However, double hashing does not remove the bias, the biased numbers are just different. – user4982 Jul 3 '14 at 21:43 Yes, you are still taking the remaining $2^{256} \equiv 36 \pmod{100}$ outputs and trying to distribute them equally amongst 100 buckets. – Stephen Touset Jul 3 '14 at 22:19 @user4982: you are correct. In those few cases, you should find something new to hash and hope the hash is small enough. Fixed. – Ross Millikan Jul 3 '14 at 22:23 @RossMillikan That still fundamentally doesn't work. It's just a more abstract approach to "distribute 36 special cases into 100 buckets". – Stephen Touset Jul 3 '14 at 22:27 Ah, I see. It only works in the event that the SHA-256 inputs are arbitrary. If you're hashing something out of your control (e.g., the contents of a file), there's nothing you can do. – Stephen Touset Jul 3 '14 at 23:04 No, it is not possible to get exactly equal probabilities for a deterministic mapping from all 256-bit numbers to the range 0-99. However, you can ask whether it matters, since a bias on the order of $2^{-256}$ is undetectable. A mapping that took the 256-bit number modulo 100 and refused the inputs less than $2^{256} \bmod 100$ would be unbiased and would never fail in practice. You can also get the next best thing – probabilities that are not exactly equal, but for which no one knows which of the numbers 0-99 is biased which way. For example, you can define the mapping using another SHA-256 iteration like so: 1. Take the SHA-256 hash of the initial hash concatenated with the number 1 (e.g. in ASCII): $H(h||1)$. If this is at least $2^{256} \bmod 100$, return it modulo 100. 2. Otherwise increment the counter and calculate $H(h||2)$, doing the same check. 3. Continue as long as necessary (i.e. in practice you never need to go further than the first step). Since we don't know which $h$ (if any) produce $H(h||1) < 36$, we don't know the resulting $H(h||2)$. - You could simply just XOR all the bytes of the hash to one single byte (lets call it $b$ for now): $b = hash_0 \oplus hash_1 \oplus ... \oplus hash_{31}$. $b \in [0, 255]$. Calculate $b' = b / 2.55$. $b' \in [0, 100]$. - This only works if he doesn't require integers. – Stephen Touset Jul 3 '14 at 21:00 If the values of the bytes of SHA256-hashes are distributed evenly $b'$ should also be distributed evenly in $[0, 100]$. Rounding $b'$ should not change too much about it. – marstato Jul 3 '14 at 21:36 The OP is looking for a mechanism "where each number in 0-99 range is equally likely to be picked". The output of your algorithm is easily distinguishable from random, because some digits will be chosen more or less likely than the others due to aliasing introduced by converting to integers. – Stephen Touset Jul 3 '14 at 21:42

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#### 2.814   ODE No. 814 $y'(x)=\frac {y(x) \left (x^7 y(x)^2-3 x^3 y(x)-3\right )}{x \left (x^3 y(x)+1\right )}$ Mathematica : cpu = 0.13934 (sec), leaf count = 72 $\left \{\left \{y(x)\to \frac {x}{-x^4+\frac {\sqrt {x+x (-2 x+c_1)}}{\sqrt {\frac {1}{x^7}}}}\right \},\left \{y(x)\to -\frac {x}{x^4+\frac {\sqrt {x+x (-2 x+c_1)}}{\sqrt {\frac {1}{x^7}}}}\right \}\right \}$ Maple : cpu = 0.115 (sec), leaf count = 38 $\left \{ y \left ( x \right ) ={\frac {1}{{x}^{3}} \left ( \sqrt {{\it \_C1}-2\,x}-1 \right ) ^{-1}},y \left ( x \right ) =-{\frac {1}{{x}^{3}} \left ( \sqrt {{\it \_C1}-2\,x}+1 \right ) ^{-1}} \right \}$

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# Getting started with rolling co-variance matrix estimate? Hello, I’m new to PYMC3 and PPL’s in general. I have a matrix of stock returns and I’m trying to use PYMC3 to do a rolling estimate of the covariance matrix. I’ve seen the rolling regression and stochastic volatilty examples, but can’t quite figure out how to generalize this to N stocks and do the covariance matrix. Any guides on this? @aseyboldt and @twiecki have done some related work. Hey newquant, I’ve done a bit of this using the GaussianRandomWalk prior. I haven’t posted the full notebook anywhere yet, but I put together a talk on the work that you can find here. The basic idea is that I construct a lower diagonal matrix where each element is an exponentiated GaussianRandomWalk and use that to create the covariance matrix, which I use as input to a Multivariate Normal likelihood. Hope this helps! Cheers, Max Margenot Thanks Max! I will check this talk out Hi Max. I was able to get an implementation of this working, but it seems to go extremely slow! I’m talking > 1 hour for n_secs = 4 and 3 time segements. Using Metropolis is much faster, but it doesn’t seem to really converge. Any tips on speed up? Hi newquant, i’m trying to get started with PyMC3 too - could you post your workings so far to Github? This is what I have going at the moment 1 Like Looking at your code, I would increase the `subsample_rate`. A default of 1 gives you a huge number of variables, due to the `GaussianRandomWalk`, which slows the sampling down a lot. I found some success in speeding up in the 20-30 range. Having a subsample rate of around 21 also makes intuitive sense with a rolling covariance estimate, as it essentially gives you the monthly covariances (21 trading days in a month). Another concern with low `subsample_rate` is an accompanying low number of samples for each likelihood (at the extreme case of `subsample_rate=1`, only one sample each). That makes sense, and I did find it faster with a higher subsample rate. And while monthly rebalancing / 21 trading days in a month makes sense for many firms, there are other firms (including the one I work for) that operate on much higher frequencies with daily (if not more frequent) rebalancing. So I wonder what the solution is for that use case. Thanks for the help If you’re trying to rebalance daily, I would see if you can get your hands on intraday, minutely data to work with. A single observation per day with daily data isn’t going to help you out a lot. I think I managed to get it down to training in around 20 minutes for ~11 assets, with a subsample rate of 30 (daily data), so it might be feasible to do an hourly or two-hourly rebalance. However, as it is currently parameterized, it definitely has speed problems. Increasing the number of assets just adds too many interrelations for the problem to be tractable as laid-out. There may be a better parameterization than the one that I have worked on, but I haven’t dug particularly deep into it. I’m also not entirely convinced that having a variable Bayesian covariance is more beneficial than having a static Bayesian covariance with variable volatilities. It might be worth placing a prior on the lower diagonal of the covariance that is not indexed by time (such as an LKJ prior) and keeping the diagonal as a `GaussianRandomWalk`. I suspect that having the distribution of the lower diagonal in conjunction with variable volatilities might give you better performance while reducing the number of variables that NUTS has to sample. ^ This is all very insightful. Thanks

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bv_cvxbook_extra_exercises # If your method relies on any convex functions that we This preview shows page 1. Sign up to view the full content. This is the end of the preview. Sign up to access the rest of the document. Unformatted text preview: c. 12.6 Antenna array weight design. We consider an array of n omnidirectional antennas in a plane, at positions (xk , yk ), k = 1, . . . , n. ( x k , yk ) θ 96 A unit plane wave with frequency ω is incident from an angle θ. This incident wave √ induces in the k th antenna element a (complex) signal exp(i(xk cos θ + yk sin θ − ωt)), where i = −1. (For simplicity we assume that the spatial units are normalized so that the wave number is one, i.e., the wavelength is λ = 2π .) This signal is demodulated, i.e., multiplied by eiωt , to obtain the baseband signal (complex number) exp(i(xk cos θ + yk sin θ)). The baseband signals of the n antennas are combined linearly to form the output of the antenna array n wk ei(xk cos θ+yk sin θ) G( θ ) = k=1 n = k=1 (wre,k cos γk (θ) − wim,k sin γk (θ)) + i (wre,k sin γk (θ) + wim,k cos γk (θ)) , if we define γk (θ) = xk cos θ + yk sin θ. The complex weights in the linear combination, wk = wre,k + iwim,k , k = 1, . . . , n, are called the antenna array coefficients or... View Full Document ## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley. Ask a homework question - tutors are online

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or or taken why Make sure to remember your password. If you forget it there is no way for StudyStack to send you a reset link. You would need to create a new account. Don't know (0) Know (0) remaining cards (0) Save 0:01 Flashcards Matching Hangman Crossword Type In Quiz Test StudyStack Study Table Bug Match Hungry Bug Unscramble Chopped Targets Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page. Normal Size     Small Size show me how # Transformations TermDefinition Reflection over x-axis change the sign of y Reflection over y-axis change the sign of x Reflection over y=x switch the numbers Reflection over the origin Change the sign of both numbers <2, -4> slide the figure right 2 and down 4 <-3, 0> slide the figure left 3 and stay (x,y)--->(x+7, y-1) slide the figure right 7 and down 1 Rotate 90 degrees from quadrant 3 land in quadrant 4 and switch numbers A 180 degree rotation is the same as _____ reflection over the origin Equation for a horizontal line is _________. y = a number Equation for a vertical line is __________. x = a number What kind of line is x = 10? vertical What kind of line is y= -6 horizontal Rotate 90 degrees clockwise from quadrant 2 land in quadrant 1 and switch numbers Isometry a transformation in which the pre-image and image are congruent What is a pre-image? the original figure Which figure is the image? the figure resulting from a transformation How can you tell the pre-image from the image on a graph? The image will be named with primes Created by: smartin614

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# Question: Why Is Cardinality Important? ## What is the cardinality of a table with 1000 rows and 10 columns? A cardinality of a table (or relation) denotes the number of tuples (or rows) a table has. Thus, cardinality of a table with 1,000 rows is 1000 no matter how many columns the table has.. ## What is the cardinality rule? In mathematics, the cardinality of a set is a measure of the “number of elements” of the set. For example, the set contains 3 elements, and therefore. has a cardinality of 3. ## What does a cardinality of zero mean? A minimum cardinality of 0 indicates that the relationship is optional. You specify a minimum cardinality of 0 if you want the query to retain the information on the other side of the relationship in the absence of a match. For example, a relationship between customer and actual sales might be specified as 1:1 to 0:n. ## What is cardinality example? Cardinality refers to the relationship between a row of one table and a row of another table. The only two options for cardinality are one or many. Example: Think of a credit card company that has two tables: a table for the person who gets the card and a table for the card itself. ## What are the four types of cardinality constraints? The types of cardinality constraints are mentioned below:Mandatory one.Mandatory many.Optional one.Optional many. ## How do you teach cardinality? class/school.Label and then count (Label-first). Labeling the set first with its cardinality (total number. of items) and then counting. … Count, emphasize, and repeat the last word (Count-first). Counting the set followed by. … Counting only (Count-only). Counting a given set without emphasizing the total number. ## What is degree and cardinality? Some placed degree is defined as The degree of a relationship type concerns the number of entities within each entity type that can be linked by a given relationship type. … In another context cardinality is a number of rows in table and degree is a number of columns. ## What is the difference between counting and cardinality? When counting to determine “how many,” each number word should be applied to only one item in the set. Cardinality refers to the quantity or total number of items in a set and can be determined by subitizing (for very small sets) or counting. ## What is cardinality relationship? Relationship cardinality represents the fact that each parent entity or table within a relationship is connected to a particular number of instances of the child entity or table. ## What cardinality means? Cardinality means two things in databases. … In this sense, cardinality means whether a relationship is one-to-one, many-to-one, or many-to-many. So you’re really talking about the relationship cardinality. Cardinality’s official, non-database dictionary definition is mathematical: the number of values in a set. ## How many types of cardinality are there? three typesWhen dealing with columnar value sets, there are three types of cardinality: high-cardinality, normal-cardinality, and low-cardinality. High-cardinality refers to columns with values that are very uncommon or unique. ## What is minimum cardinality? Minimum cardinality: minimum number of entity instances that must participate in a relationship.

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# FW: Corrected definition of pancake R (formula OK) ``` ---------- From: SBJohnston-at-aol-dot-com [SMTP:SBJohnston-at-aol-dot-com] Sent: Tuesday, February 17, 1998 11:23 AM To: aerpel-at-op-dot-net; tesla-at-pupman-dot-com Subject: Corrected definition of pancake R (formula OK) Alfred (aerpel-at-op-dot-net) wrote: >Below is the body of a post I can't get onto the Tesla list >because my email is screwed up, so you might not see it right >either. You were given incorrect information for pancake >primary inductance calculation. Yes... your email is looking a bit strange. Lots of control characters and stuff like: +AHw-. I'll post your comment to this list for you... Alfred wrote: >R is from the center of the pancake to the center of the >windings. This will only equal A/2 by accident. I cannot make out your ASCII drawing, Alfred, but here's a copy of Bert's orginal drawing... Center Line | O 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 O | |<----------------->|<--->| a b a = outer radius at turn "N" (inches) N = turn number R = Ave. Radius = (a+b)/2 W = coil width at turn "N" = a-b L = (R^2 )*(N^2)/(8*R + 11*W) in MicroHenries Alfred, if I understand correctly you're saying the dimension R should be the average radius of the windings -- but the formula should be like this... Center Line | O 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 O | |<----------->| R | |<----------------->|<--->| a b If this big headache of mine is not blocking my algebra, your definition of R would be... R = [(a-b)/2]+b ...right? Steve Johnston sbjohnston-at-aol-dot-com PS -- do you think it would help a headache to ground my body and use my Tesla Coil to send a few strikes into my head??? Not that I'm desperate or anything... but, whew. ```

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PDA View Full Version : nParticles - problem with rotation in midflight avillabon04-27-2010, 03:59 PMI created an nparticle emitter for debris pieces which i have instanced. What i would like to set is for the value of rotPP to be proportional to the particle's speed, meaning that when the particle's velocity is 0 then rotPP will equal 0 as well. So far I only have a couple of expressions attached to this particle system. Creation Expressions: Index (to controls the instancers' geo) rotPP (emits particles at a random rotation position) Debris_nParticleShape1.index = Debris_nParticleShape1.particleId%15; Debris_nParticleShape1.rotPP = rand (0,360); Runtime Expressions: (whic are the ones giving me a hard time) float \$vel = (Debris_nParticleShape1.velocity)/2000; Debris_nParticleShape1.rotPP += \$vel; For some reason this isnt giving me any rotation while the particles are in flight which is the one thing i need right now. I'll attach the scene so you can better see what is going on.. Thanks! Alex animatedfox 04-27-2010, 04:20 PM While I don't have 2011 yet...and haven't gotten into the glorious new rotPP abilities. But something that may help is to make sure you are using velocity as a vector. (Also rotPP is probably a vector as well.) As for using your velocity, I think you may not need to divide it by quite as big a number (2000). If you want to scale it, I would recommend maybe multiplying it by .5 or something like that. A great way to problem solve your math is to use the numeric display type. You can see how your values are changing...if at all. Hopefully this helps...sorry if I am posting out of place due to my lack of actual 2011 rotPP experience. ~Ben goin 04-27-2010, 04:39 PM to make the particles stop on the ground try: float \$vel = Debris_nParticleShape1.velocity; int \$velInt = \$vel; if (\$velInt > 0){ \$vel = \$vel * 20; } else{ \$vel = 0; } Debris_nParticleShape1.rotPP += \$vel; Cheers, Ingo avillabon 04-27-2010, 04:41 PM Works now... changed the runtime expressions to float \$vel = (Debris_nParticleShape1.velocity)*40; Debris_nParticleShape1.rotPP = \$vel; Alex CGTalk Moderation 04-27-2010, 04:41 PM This thread has been automatically closed as it remained inactive for 12 months. If you wish to continue the discussion, please create a new thread in the appropriate forum.

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# Pedal Dynamo Generator Topics: Battery, Direct current, Volt Pages: 2 (473 words) Published: June 25, 2013 Project – Pedal-powered phone charger CALL FOR SCIENTIFIC AND TECHNOLOGICAL RESEACH PROPOSAL FOR 2013/2014 FUNDING CYCLE PROPOSAL Students intend to do the project of building a simple pedal-powered cell phone charger to mount on my bicycle. Cell phones are small potatoes in the big picture of energy consumption, but the apparatus to be built could be a very practical concept for those on self-supported bike tours or those living temporarily in situations without electricity. Electronic parts needed 1.circuit board 2.bridge rectifier, 100 V, 1.4 A 3.capacitor, 1000 micro Farad, Radial-Lead Electrolytic, 35 V DC 4.voltage regulator, 7805, +5 V DC, 1 A Other components 1.cell phone charger 2.12 V 6 W bicycle headlight generator 3.bicycle Circuit diagram: How it works: When engaged, the generator wheel rolls against the bike tire. The motion produces electricity, and the greater your speed, the greater the voltage output. The cord from the generator leads first to the circuit board’s bridge rectifier, which converts the AC to DC. In other words, the up-and-down, positive-to-negative current becomes a steady positive current. Then, the capacitor levels out the DC voltage, producing a steady voltage inflow to the voltage regulator. The voltage regulator is crucial, as the phone only needs five volts to charge, whereas fast pedaling can produce 30 volts or more, which is enough to fry the average cell phone. The regulator controls the voltage, putting a five-volt ceiling on the power entering the phone. Results: Starting with a dead cell phone, plugged in and placed in a porch, one can spend approximately three hours and 25 kms riding in the streets of say a village to charge it back to full power. An easy speed of only four Kms per hour Is enough to keep the power production at the necessary five volts, and almost as soon as start out, the phone would light up and beep, indicating that it had begun to charge. Even...

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View Single Post P: 130 1. The problem statement, all variables and given/known data Consider the superposition of two waves; $\zeta_1 + \zeta_2 = \zeta_{01} e^{i(kr_1 - wt)} + \zeta_{02} e^{i(kr_2 - wt + ∅)}$ where $∅$ is a phase difference that varies randomly with time. Show that the time-averages satisfy; $<|\zeta_1 + \zeta_2|^2> = <|\zeta_1|^2> + <|\zeta_2|^2>$ 2. Relevant equations (1) If it wasn't clear, The two waves are; $\zeta_1 = \zeta_{01} e^{i(kr_1 - wt)}$ and $\zeta_2 = \zeta_{02} e^{i(kr_2 - wt + ∅)}$ 3. The attempt at a solution Unless I have my definition of time-average wrong. I can't seem to get this to work. $|\zeta_1 + \zeta_2|^2 = (\zeta_1 + \zeta_2)(\zeta_1^* + \zeta_2^*) = |\zeta_1|^2 + |\zeta_2|^2 + \zeta_1\zeta_2^* + \zeta_2\zeta_1^* = |\zeta_1|^2 + |\zeta_2|^2 + 2\zeta_{01}\zeta_{02}cos(k(r_1 - r_2) - ∅)$ Then, I believe, the time average is given by; $\frac{1}{T}\int^T_0 {|\zeta_1|^2 + |\zeta_2|^2 + 2\zeta_{01}\zeta_{02}cos(k(r_1 - r_2) - ∅)} dt$ However, I don't see how this turns in to the form I desire. It would require that the last term (containing the cosine) is time-averaged to zero. Can this be the case? Also, can $∅$ still even be considered a function of time when it varies RANDOMLY?

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Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  0plef Structured version   Unicode version Theorem 0plef 22567 Description: Two ways to say that the function on the reals is nonnegative. (Contributed by Mario Carneiro, 17-Aug-2014.) Assertion Ref Expression 0plef Proof of Theorem 0plef Dummy variable is distinct from all other variables. StepHypRef Expression 1 rge0ssre 11686 . . 3 2 fss 5692 . . 3 31, 2mpan2 675 . 2 4 ffvelrn 5974 . . . . 5 5 elrege0 11684 . . . . . 6 65baib 911 . . . . 5 74, 6syl 17 . . . 4 87ralbidva 2796 . . 3 9 ffn 5684 . . . 4 10 ffnfv 6003 . . . . 5 1110baib 911 . . . 4 129, 11syl 17 . . 3 13 0cn 9581 . . . . . . 7 14 fnconstg 5726 . . . . . . 7 1513, 14ax-mp 5 . . . . . 6 16 df-0p 22565 . . . . . . 7 1716fneq1i 5626 . . . . . 6 1815, 17mpbir 212 . . . . 5 1918a1i 11 . . . 4 20 cnex 9566 . . . . 5 2120a1i 11 . . . 4 22 reex 9576 . . . . 5 2322a1i 11 . . . 4 24 ax-resscn 9542 . . . . 5 25 sseqin2 3619 . . . . 5 2624, 25mpbi 211 . . . 4 27 0pval 22566 . . . . 5 2827adantl 467 . . . 4 29 eqidd 2424 . . . 4 3019, 9, 21, 23, 26, 28, 29ofrfval 6492 . . 3 318, 12, 303bitr4d 288 . 2

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## Segal’s Original Definition of a Topological Category Nowadays we can associate to a topological space $X$ a category called the fundamental (or Poincare) $\infty$-groupoid given by taking $Sing(X)$. There are many different categories that one can associate to a space $X$. For example, one could build the small category whose object set is the set of points with only the identity morphisms from a point to itself. It is claimed that the classifying space of this category returns the space: $BX=X$ The inspiration for these examples comes from three primary sources: Graeme Segal's famous 1968 paper Classifying Spaces and Spectral Sequences, Raoul Bott's Mexico notes (taken by Lawrence Conlon) Lectures on characteristic classes and foliations, and a 1995 pre-print called Morse Theory and Classifying Spaces by Ralph Cohen, G. Segal and John Jones. In each of these papers there is a notion of a topological category. It is not just a category enriched in Top, since the set of objects can have non-discrete topology. Here is the definition that I can gleam from these articles: A topological category consists of a pair of spaces $(Obj,Mor)$ with four continuous structure maps: • $i:Obj\to Mor$, which sends an object to the identity morphism • $s:Mor\to Obj$, which gives the source of an arrow • $t:Mor\to Obj$, which gives the target of an arrow • $\circ:Mor\times_{t,s}Mor\to Mor$, which is composition. Were $i$ is a section of both $s$ and $t$, and all the axioms of a small category hold. Is the appropriate modern terminology to describe this a Segal Space? What would Lurie call it? Based on reading Chris Schommer-Pries MO post and elsewhere this seems to be true. Would the modern definition of the above be a Segal Space where the Segal maps are identities? Also, why do we demand that the topology on objects be discrete for Segal Categories? Is there something wrong with allowing the object sets to have topologies? - This isn't a Segal space because there is a further condition about homotopy pullbacks. I've called this a category object in Top before, and that (if I recall) was based on terminology from Tom Leinster's book on higher category theory. There is nothing wrong with allowing the object sets to have topologies, except that many straightforward facts become more difficult to prove (or false). Some places where these show up are in topological groupoids and topological stacks. – Tyler Lawson Jan 15 2012 at 6:26 Distinguish this from the unrelated notion of a [topological concrete category](ncatlab.org/nlab/show/…); the adjective ‘concrete’ is often (and originally always) omitted. – Toby Bartels Jan 15 2012 at 6:57 I am amused by the use of the word "nowadays" since the simplicial singular complex has been used since Eilenberg's work, followed by Kan in the 1950s. Also this use fails to distinguish between a path space and the usual (strict) fundamental groupoid, so must lead to confusion. There is also the strict cubical homotopy groupoid of a filtered space, which is closely related to the standard relative homotopy groups, and is given an exposition in our recent book "Nonabelian algebraic topology", published by the EMS in 2011. The cubical methods have many advantages, explained there. – Ronnie Brown Jan 15 2012 at 10:42 @Tyler, But couldn't we define X_2 to be the fibered pullback over s and t? Couldn't we do something similar for the higher X_n so that it is a pullback (on the nose)? – Justin Curry Jan 15 2012 at 15:04 adding to Ronnie's comment, the fact that the singular complex is Kan is 'classical', the fact that such things resemble infinity categories is 1970s, probably hidden in Boardman-Vogt, certainly well know to some people by 1980, although rarely in print. I mentioned it in several talks at category theory meetings around that time, and wondered why the search for lax infinity groupoids was taking up a lot of space as they were already well known. In fact much of the recent work reworks classical simplicial homotopy theory from the Moore seminar and it is well worth looking back at that. – Tim Porter Jan 15 2012 at 15:15 show 1 more comment ## 3 Answers I would call this an internal category in the category of topological spaces and continuous maps. - One often places additional requirements, such as requiring $s$ and $t$ to be open maps; when working internal to the category of smooth (say real) manifolds and smooth maps, one often even requires them to be submersions. These are less easy to fit into a general notion applicable to any ambient category. – Toby Bartels Jan 15 2012 at 7:00 Toby beat me to this! This is just an internal category. Internal category makes sense in any category with finite limits. Another point is that the Cohen, Jones Segal paper was reported to have a gap in it and so was never finished, which is a pity because it was going in a very interesting direction. Finally it was John Jones (Warwick) and not Vaughan Jones, although both have Welsh origins, one directly the other slightly more distant!!! – Tim Porter Jan 15 2012 at 7:26 @Toby: Concerning these additional requirements, this of course reminds of algebraic spaces. They are given by groupoids internal to schemes where $s,t$ are étale. @Tim: Even more generally, "internal category" makes sense in any ambient category $C$. It is an object $A$ together with a factorization of $\mathrm{Hom}(-,A) : C^{op} \to \mathrm{Set}$ through the forgetful functor $\mathrm{Cat} \to \mathrm{Set}$. For every concrete category $D \to \mathrm{Set}$, there is a notion of an object of $D$ internal to an ambient category. – Martin Brandenburg Jan 15 2012 at 12:17 @Tim, Thanks for pointing out the Vaughan<->John mistake. – Justin Curry Jan 15 2012 at 14:53 @Martin ...which is of course the way that Grothendieck handled all such constructions. – Tim Porter Jan 15 2012 at 15:09 Topological categories were invented by Charles Ehresmann in the late 1950s, and can be seen in his 1959 paper I think called Catégories topologique et catégories differentiable. The usage 'topological category' for a Top-category is much newer. - Could I ask young people to use precise language? Calling a Kan complex an $\infty$-groupoid and asking what kind of category it is just jars. It feels so pointless (I'm toning down the language I'm tempted to use). As Tony pointed out, a topological category in the proposed sense is just a category internal to topological spaces. The notion of internal category is so familiar and elementary that it must long antecede any reference made in the question. (It seemed an old notion when I was using it in the early 1970s). A Segal space (original version) is a covariant functor from the category $\mathcal{F}$ of finite based spaces (the opposite of Segal's category $\Gamma$) to the category of based spaces. It is not a kind of category. Similarly, a Segal category is a functor from $\mathcal{F}$ to Cat. There is a forgetful functor from Segal spaces to simplicial spaces (simplicial objects in spaces). Parenthetically, the terms topological category and simplicial category are both ambiguous since, without clarification, they could mean either categories enriched in spaces or in simplicial sets, or they could mean categories internal to spaces or to simplicial sets. A category internal to simplicial sets is the same notion as a simplicial object in Cat, so the consistent meaning would be the internal one, but the more standard usage is that a simplicial category is a simplicially enriched category. - I agree completely with the first two sentences of Peter's answer (to say nothing about the rest). Name changes can lead to confusion and lack of contact with older work. And here a lack of attention to cases such as the strict case when there is something quite tricky to prove, e.g. the strict higher groupoids associated to a filtered space (I confess to a personal interest in these!). – Ronnie Brown Jan 16 2012 at 10:31 Yet another meaning of ‘topological category’ is a category $C$ equipped with a faithful functor to $Set$ (or sometimes to something else) such that every (even large) sink from $C$ to a set has a final lift ([nlab](ncatlab.org/nlab/show/…)). This may be disambiguated as a ‘topological construct’ or as a ‘topological concrete category’; the reason for this terminology is examples from topology. (Also, my name is ‘Toby’, not ‘Tony’.) – Toby Bartels Mar 23 at 5:13 I apologize about the name, Toby; it gets confusing (I'm now collaborating with Tobias Barthel!). Mathematically, it seems bad enough to have two standard meanings of "topological category" without adding a third. – Peter May Mar 23 at 20:41

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# How to plot torsion prismatic beam I dont know why dont work but I want to animate torsion prismatic beam. a = 1; b = 2; L = 10; G = 1; dx = dy = dz = 0.25; J = 2.1849801331564294; Clear[x, y, z, T]; k = T/( G J); phi = (32 G k a)/Pi^3 Sum[1/n^3 (-1)^((n - 1)/2) (1 - Cosh[n Pi y/(2 a)]/ Cosh[n Pi b/(2a)]) Cos[(n Pi x)/(2 a)], {n, 1, 10, 2}]; tauyz = -D[phi, x]; tauxz = D[phi, y]; gammayz = tauyz/G; gammaxz = tauxz/G; Rotate[{x_, y_, z_}, Theta_] := {x Cos[Theta] - y Sin[Theta], x Sin[Theta] + y Cos[Theta], z}; Off[Graphics3D::"gprim"]; Do[Show[Graphics3D[Table[alpha = 0.5 k z; p1 = p2; p2 = Map[({x, y} = #; Rotate[{x + 0 gammaxz/2, y + 0 gammayz/2, z + (x gammaxz + y gammayz)/ 2}, alpha]) &, Flatten[{Table[{x, -b/2}, {x, -a/2, a/2 - dx, dx}], Table[{a/2, y}, {y, -b/2, b/2 - dy, dy}], Table[{x, b/2}, {x, a/2, dx - a/2, -dx}], Table[{-a/2, y}, {y, b/2, dy - b/2, -dy}]}, 1]]; n = Length[p2]; If[z == 0, Polygon[p2], Table[Polygon[{p1[[i]], p2[[i]], p2[[Mod[i, n] + 1]], p1[[Mod[i, n] + 1]]}], {i, 1, n}]], {z, 0, L, dz}], ViewPoint -> {-1, 1, 1}, ViewVertical -> {0, 1, 0}, Axes -> True, AxesLabel -> {"x", "y", "z"}, PlotRange -> {{-a, a}, {-b, b}, {0, L}}]], {T, 0, 1, 0.1}]; SelectionMove[ EvaluationNotebook[], All, GeneratedCell]; FrontEndTokenExecute["CellGroup"]; FrontEndTokenExecute["OpenCloseGroup"]; FrontEndTokenExecute["SelectionAnimate"]; • What behaviour were you expecting, that is not occurring? It's hard to help you without more information. "It doesn't work" is not very informative, unfortunately. Commented Oct 3, 2014 at 7:31 • Rotate is a built-in function. You cannot redefine it just like that. Furthermore, lots of undefine variables and what's 0 gammaxz supposed to do? And as to animation, why the rather strange use of frontend tokens? Are you aware of the Animate function? Commented Oct 3, 2014 at 10:42 • Since we have a good answer from Junbo Lee, I think this question should be reopened, as there was clearly enough info for him to answer it. Commented Oct 3, 2014 at 11:46 ## 1 Answer I think this code might be old version. You made some mistake so I changed your code like this. 1. Rotate -> rotate 2. Do -> Table 3. SelectionAnimate -> Manipulate or Animate We can give change variable T in Manipulate but that computation time is so long. Thus I set the Graphics3D-s to frames and apply Manipulate or Animate. Have try like this. a = 1; b = 1; L = 10; G = 1; dx = dy = dz = 0.25; J = 2.1849801331564294; Clear[x, y, z, T]; k = T/(G J); phi = ((32*G*k*a)*Sum[((-1)^((n - 1)/2)*(1 - Cosh[(n*Pi*y)/(2*a)]/ Cosh[(n*Pi*b)/(2*a)])*Cos[(n*Pi*x)/(2*a)])/ n^3, {n, 1, 10, 2}])/Pi^3; tauyz = -D[phi, x]; tauxz = D[phi, y]; gammayz = tauyz/G; gammaxz = tauxz/G; rotate[{x_, y_, z_}, Theta_] := {x Cos[Theta] - y Sin[Theta], x Sin[Theta] + y Cos[Theta], z}; Off[Graphics3D::gprim]; frames = Table[ Graphics3D[ Table[alpha = 0.5 k z; p1 = p2; p2 = (({x, y} = #1; rotate[{x + (0 gammaxz)/2, y + (0 gammayz)/2, z + 1/2 (x gammaxz + y gammayz)}, alpha]) &) /@ Flatten[{ Table[{x, -(b/2)}, {x, -(a/2), a/2 - dx, dx}], Table[{a/2, y}, {y, -(b/2), b/2 - dy, dy}], Table[{x, b/2}, {x, a/2, dx - a/2, -dx}], Table[{-(a/2), y}, {y, b/2, dy - b/2, -dy}]}, 1]; n = Length[p2]; If[z == 0, Polygon[p2], Table[Polygon[{p1[[i]], p2[[i]], p2[[Mod[i, n] + 1]], p1[[Mod[i, n] + 1]]}], {i, 1, n}]], {z, 0, L, dz}], ViewPoint -> {-1, 1, 1}, ViewVertical -> {0, 1, 0}, Axes -> True, AxesLabel -> {"x", "y", "z"}, PlotRange -> {{-a, a}, {-b, b}, {0, L}}], {T, 0, 1, 0.1}]; You can manipulate motion with this code. Manipulate[frames[[i]], {i, 1, Length[frames], 1}] or Animate[frames[[i]], {i, 1, Length[frames], 1}, AnimationRunning -> False] • There is a glitch with a = 1 and b = 2 which isn't present when both are equal to 1 so I edited your answer and the plot (with a better quality :)). Feel free to rollback :) – Öskå Commented Oct 3, 2014 at 15:26 • @Öskå I got it. thanks Commented Oct 3, 2014 at 15:31

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Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  uhgrvtxedgiedgbOLD Structured version   Visualization version   GIF version Theorem uhgrvtxedgiedgbOLD 26435 Description: Obsolete version of uhgrvtxedgiedgb 26434 as of 6-Jul-2022. (Contributed by AV, 24-Dec-2020.) (Proof modification is discouraged.) (New usage is discouraged.) Hypotheses Ref Expression uhgrvtxedgiedgbOLD.v 𝑉 = (Vtx‘𝐺) uhgrvtxedgiedgbOLD.i 𝐼 = (iEdg‘𝐺) uhgrvtxedgiedgbOLD.e 𝐸 = (Edg‘𝐺) Assertion Ref Expression uhgrvtxedgiedgbOLD ((𝐺 ∈ UHGraph ∧ 𝑈𝑉) → (∃𝑖 ∈ dom 𝐼 𝑈 ∈ (𝐼𝑖) ↔ ∃𝑒𝐸 𝑈𝑒)) Distinct variable groups:   𝑒,𝐸   𝑒,𝐼,𝑖   𝑈,𝑒,𝑖 Allowed substitution hints:   𝐸(𝑖)   𝐺(𝑒,𝑖)   𝑉(𝑒,𝑖) Proof of Theorem uhgrvtxedgiedgbOLD StepHypRef Expression 1 edgval 26347 . . . . . . 7 (Edg‘𝐺) = ran (iEdg‘𝐺) 21a1i 11 . . . . . 6 (𝐺 ∈ UHGraph → (Edg‘𝐺) = ran (iEdg‘𝐺)) 3 uhgrvtxedgiedgbOLD.e . . . . . 6 𝐸 = (Edg‘𝐺) 4 uhgrvtxedgiedgbOLD.i . . . . . . 7 𝐼 = (iEdg‘𝐺) 54rneqi 5584 . . . . . 6 ran 𝐼 = ran (iEdg‘𝐺) 62, 3, 53eqtr4g 2886 . . . . 5 (𝐺 ∈ UHGraph → 𝐸 = ran 𝐼) 76rexeqdv 3357 . . . 4 (𝐺 ∈ UHGraph → (∃𝑒𝐸 𝑈𝑒 ↔ ∃𝑒 ∈ ran 𝐼 𝑈𝑒)) 84uhgrfun 26364 . . . . . 6 (𝐺 ∈ UHGraph → Fun 𝐼) 9 funfn 6153 . . . . . 6 (Fun 𝐼𝐼 Fn dom 𝐼) 108, 9sylib 210 . . . . 5 (𝐺 ∈ UHGraph → 𝐼 Fn dom 𝐼) 11 eleq2 2895 . . . . . 6 (𝑒 = (𝐼𝑖) → (𝑈𝑒𝑈 ∈ (𝐼𝑖))) 1211rexrn 6610 . . . . 5 (𝐼 Fn dom 𝐼 → (∃𝑒 ∈ ran 𝐼 𝑈𝑒 ↔ ∃𝑖 ∈ dom 𝐼 𝑈 ∈ (𝐼𝑖))) 1310, 12syl 17 . . . 4 (𝐺 ∈ UHGraph → (∃𝑒 ∈ ran 𝐼 𝑈𝑒 ↔ ∃𝑖 ∈ dom 𝐼 𝑈 ∈ (𝐼𝑖))) 147, 13bitrd 271 . . 3 (𝐺 ∈ UHGraph → (∃𝑒𝐸 𝑈𝑒 ↔ ∃𝑖 ∈ dom 𝐼 𝑈 ∈ (𝐼𝑖))) 1514adantr 474 . 2 ((𝐺 ∈ UHGraph ∧ 𝑈𝑉) → (∃𝑒𝐸 𝑈𝑒 ↔ ∃𝑖 ∈ dom 𝐼 𝑈 ∈ (𝐼𝑖))) 1615bicomd 215 1 ((𝐺 ∈ UHGraph ∧ 𝑈𝑉) → (∃𝑖 ∈ dom 𝐼 𝑈 ∈ (𝐼𝑖) ↔ ∃𝑒𝐸 𝑈𝑒)) Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 198   ∧ wa 386   = wceq 1658   ∈ wcel 2166  ∃wrex 3118  dom cdm 5342  ran crn 5343  Fun wfun 6117   Fn wfn 6118  ‘cfv 6123  Vtxcvtx 26294  iEdgciedg 26295  Edgcedg 26345  UHGraphcuhgr 26354 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-8 2168  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-13 2391  ax-ext 2803  ax-sep 5005  ax-nul 5013  ax-pow 5065  ax-pr 5127  ax-un 7209 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-3an 1115  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-mo 2605  df-eu 2640  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-ral 3122  df-rex 3123  df-rab 3126  df-v 3416  df-sbc 3663  df-csb 3758  df-dif 3801  df-un 3803  df-in 3805  df-ss 3812  df-nul 4145  df-if 4307  df-pw 4380  df-sn 4398  df-pr 4400  df-op 4404  df-uni 4659  df-br 4874  df-opab 4936  df-mpt 4953  df-id 5250  df-xp 5348  df-rel 5349  df-cnv 5350  df-co 5351  df-dm 5352  df-rn 5353  df-iota 6086  df-fun 6125  df-fn 6126  df-f 6127  df-fv 6131  df-edg 26346  df-uhgr 26356 This theorem is referenced by: (None) Copyright terms: Public domain W3C validator

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# 1072748 (number) 1,072,748 (one million seventy-two thousand seven hundred forty-eight) is an even seven-digits composite number following 1072747 and preceding 1072749. In scientific notation, it is written as 1.072748 × 106. The sum of its digits is 29. It has a total of 4 prime factors and 12 positive divisors. There are 534,192 positive integers (up to 1072748) that are relatively prime to 1072748. ## Basic properties • Is Prime? No • Number parity Even • Number length 7 • Sum of Digits 29 • Digital Root 2 ## Name Short name 1 million 72 thousand 748 one million seventy-two thousand seven hundred forty-eight ## Notation Scientific notation 1.072748 × 106 1.072748 × 106 ## Prime Factorization of 1072748 Prime Factorization 22 × 373 × 719 Composite number Distinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 4 Total number of prime factors rad(n) 536374 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0 The prime factorization of 1,072,748 is 22 × 373 × 719. Since it has a total of 4 prime factors, 1,072,748 is a composite number. ## Divisors of 1072748 12 divisors Even divisors 8 4 2 2 Total Divisors Sum of Divisors Aliquot Sum τ(n) 12 Total number of the positive divisors of n σ(n) 1.88496e+06 Sum of all the positive divisors of n s(n) 812212 Sum of the proper positive divisors of n A(n) 157080 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 1035.74 Returns the nth root of the product of n divisors H(n) 6.82931 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors The number 1,072,748 can be divided by 12 positive divisors (out of which 8 are even, and 4 are odd). The sum of these divisors (counting 1,072,748) is 1,884,960, the average is 157,080. ## Other Arithmetic Functions (n = 1072748) 1 φ(n) n Euler Totient Carmichael Lambda Prime Pi φ(n) 534192 Total number of positive integers not greater than n that are coprime to n λ(n) 133548 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 83584 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares There are 534,192 positive integers (less than 1,072,748) that are coprime with 1,072,748. And there are approximately 83,584 prime numbers less than or equal to 1,072,748. ## Divisibility of 1072748 m n mod m 2 3 4 5 6 7 8 9 0 2 0 3 2 5 4 2 The number 1,072,748 is divisible by 2 and 4. • Arithmetic • Deficient • Polite ## Base conversion (1072748) Base System Value 2 Binary 100000101111001101100 3 Ternary 2000111112102 4 Quaternary 10011321230 5 Quinary 233311443 6 Senary 34554232 8 Octal 4057154 10 Decimal 1072748 12 Duodecimal 438978 20 Vigesimal 6e1h8 36 Base36 mzqk ## Basic calculations (n = 1072748) ### Multiplication n×y n×2 2145496 3218244 4290992 5363740 ### Division n÷y n÷2 536374 357583 268187 214550 ### Exponentiation ny n2 1150788271504 1234505816679372992 1324313645831164018422016 1420654814938089538434180819968 ### Nth Root y√n 2√n 1035.74 102.368 32.1828 16.0731 ## 1072748 as geometric shapes ### Circle Diameter 2.1455e+06 6.74027e+06 3.61531e+12 ### Sphere Volume 5.17109e+18 1.44612e+13 6.74027e+06 ### Square Length = n Perimeter 4.29099e+06 1.15079e+12 1.51709e+06 ### Cube Length = n Surface area 6.90473e+12 1.23451e+18 1.85805e+06 ### Equilateral Triangle Length = n Perimeter 3.21824e+06 4.98306e+11 929027 ### Triangular Pyramid Length = n Surface area 1.99322e+12 1.45488e+17 875895 ## Cryptographic Hash Functions md5 22bd8e2a695feccae371b5a735dc40b2 e7d271e557ad7e604c3775fdd94c452dbb542638 81176e2969593b9a81c99aa3a7a71648c0458d593045b56d2b15e35f368bb227 f0204b0b4c1efb2986f8446ae4cfe39608ffb2e208b523e0c33f70414bb79f14cb7b7fedaf674871207513dcd59c63e647ce10acaf16ccabb981c1989326c80c d5b2534b9cb1e0a88c96f385637830008a271952

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Homology of a disjoint union I have a space $$Z=X\sqcup P$$, where $$P=\{*\}$$ is a disjoint point. I want to show that $$\tilde{H_i}(Z) \cong H_i(X)$$. I start with the following: Let $$f:A \rightarrow C$$ and $$g:B \rightarrow C$$ be homomorphism of abelian groups where we also assume $$g$$ to be isomorphism. We then also define $$f\oplus g:A\oplus B \rightarrow C$$ as $$(a,b) \mapsto f(a) + f(b)$$. We can then construct an isomorphism $$\omega$$ between $$A$$ and the kernel of $$f \oplus g$$ by sending $$a$$ to $$(a,g^{-1}(-f(a)))$$. One can define the $$n$$-th reduced homology in the following way: let $$X$$ be a space and let $$P = \{∗\}$$ be a one-point space. Then there is a unique continuous map $$\gamma^X:X \rightarrow P$$. The $$n$$-th reduced homology group of $$X$$ is: $$$$\tilde{H_i}(X)=ker(\gamma_{*}^X:H_n(X) \rightarrow H_n(P)).$$$$ So I argue as follows: $$$$\tilde{H_n}(Z)=ker(\gamma^Z:H_n(Z)\rightarrow H_n(P)) \cong ker(\gamma:H_n(X)\oplus H_n(P) \rightarrow H_n(P)).$$$$ Let $$f^{'}: H_n(X) \rightarrow H_{n}(P)$$ be a group homomorphism (is that always well-define, can I do that?) and $$g^{'}:H_n(P) \rightarrow H_n(P)$$ an isomorphism (so $$g^{'}$$ is just $$=$$). Then we get $$H_i(X) \cong ker(f^{'} \oplus g^{'}) \cong ker(\gamma)\cong \tilde{H_n}(Z)$$. Does this make sense at all? • It is not clear to me what you are doing with these homomorphisms. Why are you not defining them? Perhaps you should use the fact there is a right inverse to the map $X \sqcup *\rightarrow *$ given by including the point as the disjoint point. Analyze what happens on homology. Commented Dec 20, 2019 at 2:23 • Thank @ConnorMalin. I am not sure I understand, I am still really new to this stuff and struggle to work things out from definitions. So, are you saying that $X \sqcup *$ are homeomorphic and so this induces the isomorphism between the homology groups of $X \sqcup *$ and $*$? And I should somehow go from there? Commented Dec 20, 2019 at 11:11

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# Alternator Wiring Diagram Ford 302 ## Kubota Alternator Wiring Schematic By Bertille Solange. Power. Publised at Friday, December 29th 2017, 04:58:06 AM. The control circuitry must monitor (sense) the output voltage, and adjust the current source (as required by the load) to hold the output voltage at the desired value. The design limit of the current source defines the maximum load current the regulator can source and still maintain regulation. ## Collection Alternator Wire Wiring Diagram By Jessica Mireille. Diagram. Publised at Saturday, December 23rd 2017, 14:53:38 PM. Most of the electrical symbols can be changed in their appearance, styles and colors according to users requirements. Electrical symbols are used to represent various electrical and electronic devices in a schematic diagram of an electrical or electronic circuit. ## Transformer Coupled Class A Amplifier By Charlotte Myriam. Diagram. Published at Monday, November 20th 2017, 06:53:27 AM. Voltage nodes are single-terminal schematic components, which we can connect component terminals to in order to assign them to a specific voltage level. These are a special application of net names, meaning all terminals connected to a like-named voltage node are connected together. ## Combinations Of Logic Gates By Valentine Sybille. Circuit. Published at Monday, November 20th 2017, 05:43:03 AM. A basic understanding of electronic circuits is important even if the designer does not intend to become a proficient electrical engineer. In many real-life engineering projects, it is often necessary to communicate, and also negotiate, specifications between engineering teams having different areas of expertise. Therefore, a basic understanding of electronic circuits will allow the mechanical engineer to evaluate whether or not a given electrical specification is reasonable and feasible. ### How To Find Voltage Drop Across A Resistor By Sasha Sara. Circuit. Published at Monday, November 20th 2017, 05:13:59 AM. An inductor is a device that stores energy in the form of current. The most common form of inductors is a wire wound into a coil. The magnetic field generated by the wire creates a counter-acting electric field which impedes changes to the current. #### 12v Battery Level Indicator By Charlotte Myriam. Diagram. Published at Monday, November 20th 2017, 05:12:37 AM. A wiring diagram is sometimes helpful to illustrate how a schematic can be realized in a prototype or production environment. A proper wiring diagram will be labeled and show connections in a way that prevents confusion about how connections are made. Typically they are designed for end-users or installers. They focus on connections rather than components ##### How To Calculate Real Power By Charlotte Myriam. Power. Published at Monday, November 20th 2017, 04:27:15 AM. There are many new regulators which have tighter output tolerances (better than 2% is common), achieved through the use of a laser-trim process. Also, many of the new regulators have separate output specifications that cover room temperature/full operating temperature range, and full-load/light-load conditions. ###### How To Calculate Voltage Drop Across A Resistor By Bertille Solange. Diagram. Published at Monday, November 20th 2017, 04:20:57 AM. A digital circuit is constructed of a power supply, devices, and conduction nets. Some nets provide circuit inputs from the “outside world”; in a schematic, these input nets are generally shown entering the left side of component and/or the overall circuit. Other nets present circuit outputs to the outside world; these nets are generally shown exiting the schematic on the right. In the sample schematic below, circuit components are shown as arbitrary shapes, nets are shown as lines, and inputs and outputs are denoted by connector symbols. ## What Is A Wheatstone Bridge By Jessica Mireille. Diagram. Published at Monday, November 20th 2017, 03:57:49 AM. Truly expansive schematics should be split into functional blocks. There might be a section for power input and voltage regulation, or a microcontroller section, or a section devoted to connectors. Try recognizing which sections are which, and following the flow of circuit from input to output. Really good schematic designers might even lay the circuit out like a book, inputs on the left side, outputs on the right. Recent post Category Monthly Archives Static Page Altrushare - Wiring Diagram Gallery Copyright © 2003 - 2018 Domain Media. All sponsored products, company names, brand names, trademarks and logos arethe property of their respective owners.

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Questions on Algebra: Exponents and operations on exponents answered by real tutors! Algebra ->  Algebra  -> Exponents -> Questions on Algebra: Exponents and operations on exponents answered by real tutors!      Log On Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Algebra: Exponents and operations on exponents Solvers Lessons Answers archive Quiz In Depth Tutors Answer Your Questions about Exponents (FREE) Question 186906: Please Help if you can, and please show your work. Thank You Click here to see answer by josmiceli(9681) Question 187053: How do I simplify Click here to see answer by stanbon(57361) Question 187053: How do I simplify Click here to see answer by jim_thompson5910(28595) Question 187154: please multiply and simplify this problem. (3a^2b)(2a^3b^2)(-ab^4) thank you Click here to see answer by jim_thompson5910(28595) Question 187307: I was given this problem and told to solve without negative exponents, I am really not sure how to tackle this problem. [x*y^5/x^-4*y^2]^-2 Click here to see answer by josmiceli(9681) Question 187560: I was instructed to "multiply as required and collect terms" I am really not sure what it means to collect terms. (x–4)*(2x^2+4)+(x+4)*(x^3–1)–(x^2–x–1) Click here to see answer by vleith(2825) Question 187560: I was instructed to "multiply as required and collect terms" I am really not sure what it means to collect terms. (x–4)*(2x^2+4)+(x+4)*(x^3–1)–(x^2–x–1) Click here to see answer by solver91311(16897) Question 187570: This is the problem that I was given and th only way I know how to solve would be trial and error. Find a value for k that will make 4x^2 + 6.4x + k a perfect square. Describe the procedure that you used which requires algebra [that is, not trial and error]. Click here to see answer by ankor@dixie-net.com(15656) Question 188024: Please help me with this problem. Evaluate (-6y) to the second power and -6y to the second power when y=2. I would really appreciate some help. Thank you, Click here to see answer by Alan3354(30993) Question 188129: y-2=-4 What is y? Click here to see answer by jim_thompson5910(28595) Question 167164: Factorise completely 16x^4 – 40x^2 + 9 Click here to see answer by J2R2R(94) Question 188425: Click here to see answer by Mathtut(3670) Question 188509: Whats the evaluate, for 3a,a=-3 and 5s,s = -4 and x+4, x=-2 and also 3t+4,t=-5 and can you explain how you got it ? please and thank you =D Click here to see answer by Mathtut(3670) Question 188674: can you please help me solve this problem?? In a particular small town, the population in 1995 was 1200. Ever since then the population has grown by 4% every year. If conditions stay the same, what is the approximate expected population in the year 2000? Click here to see answer by ankor@dixie-net.com(15656) Question 188674: can you please help me solve this problem?? In a particular small town, the population in 1995 was 1200. Ever since then the population has grown by 4% every year. If conditions stay the same, what is the approximate expected population in the year 2000? Click here to see answer by stanbon(57361) Question 188962: 18x(2)+48xy+32y(2) Click here to see answer by stanbon(57361) Question 189053: I'm not sure how to solve this, please help if you can. Thank you Click here to see answer by stanbon(57361) Question 189304: Exponentes topic for Fifth Grade: When you are finding variables to exponentes, like: 3^x = 27, is there any othe way to find the value of x, other than just multipling 3x3x3 = 27, so x = 3. Click here to see answer by Alan3354(30993) Question 190020: Simplify x^2-x-6/x^2-2x-3= Click here to see answer by orca(409) Question 190125: hey what will be the solution for following according to you all and x.y.z = 1 then what will be value of p+q+r ? Click here to see answer by orca(409) Question 184564: Can you please demonstrate how to find that the square root of 41 is 6.4 units? Click here to see answer by sabrinawayjack(8) Question 190456: Hello, I could not find anything on the site that resembled this problem, could use assistance. t^(2)/(3)=4 Thanks for the help in advance. Click here to see answer by Mathtut(3670) Question 190683: What is c to the 4th power plus c to the 2nd power. please help Click here to see answer by Earlsdon(6287) Question 191352: square root of x to the fourth multilpied by square root of x to the 5th Click here to see answer by Mathtut(3670) Question 191431: Solve . (3a^2b)(-2ab^3)= Click here to see answer by Alan3354(30993) Question 191459: find the product (3x^3y)(-4x^2 y^3) Click here to see answer by orca(409) Question 191691: solve equation 2x^2=50 Click here to see answer by orca(409) Question 191692: solve equation 4x^2-4x=-1 Click here to see answer by orca(409) Question 191696: reduce to lowest term without negative exponents 2(x-3)-3(x-4) Click here to see answer by Alan3354(30993) Question 191695: Reduce to lowest term without negative exponents 4/5(-3/10)(-1 2/3) Click here to see answer by Alan3354(30993) Question 191698: factor each expression completely x+2/13=3 Click here to see answer by Alan3354(30993) Question 192156: Assuming that none of the solutions are undefined, simplify each of the following: 12a^5/6a Click here to see answer by Mathtut(3670) Question 192472: I have a total of 60 problems. I am stuck on 5 of them, I know that I am close but my tutor says I am still off. Please help me solve the following problems. (x^-2y^4)/(4y^-3)^2 Click here to see answer by Earlsdon(6287) Question 192472: I have a total of 60 problems. I am stuck on 5 of them, I know that I am close but my tutor says I am still off. Please help me solve the following problems. (x^-2y^4)/(4y^-3)^2 Click here to see answer by RAY100(1637) Question 192531: I sent this question along with 3 others yesterday and still haven't gotten a respond, please help me Simplify; express answer with only positive exponents. (a^-2/3b^1/2)(a^3/2b^2/3) Click here to see answer by stanbon(57361) Question 192533: Evaluate. √[25a^12b^8c^12] Click here to see answer by Mathtut(3670) Question 192587: Can someone help me with this problem. I think I can figure out the rest Evaluate and simplify; express answer with only positive exponents. (25a^8b^16)^-1/2 Click here to see answer by checkley77(12569) Question 192586: Can someone help me with this problem. I think I can figure out the rest Evaluate and simplify; express answer with only positive exponents. (25a^8b^16)^-1/2 Click here to see answer by checkley77(12569) Question 192731: I submitted this problem on yesterday and still have not gotten a respond. Can someone help me with it? Factor out the common factor of 2x from: 16x^4/5 8x^3/4 Click here to see answer by ankor@dixie-net.com(15656) Question 193045: The formula for calculating the amount of money returned for an initial deposit into a bank account or CD (certificate of deposit) is given by A is the amount of the return. P is the principal amount initially deposited. r is the annual interest rate (expressed as a decimal). n is the number of compound periods in one year. t is the number of years. Carry all calculations to six decimals on each intermediate step, then round the final answer to the nearest cent. Suppose you deposit \$3,000 for 9 years at a rate of 6%. a) Calculate the return (A) if the bank compounds annually (n = 1). Round your answer to the hundredth's place. Click here to see answer by Edwin McCravy(8909) Question 193401: Using scientific notation, 4.5 x 10^-8 divided by 2.5 x 10^-3 Click here to see answer by Mathtut(3670) Question 193412: With scientific notation 3.2 X 10^-6 divided by 6.4 X 10^2 Click here to see answer by Mathtut(3670) Question 193598: please explain in what order i would solve these problems 3-15*5 & 5*(8+7)+7 Click here to see answer by stanbon(57361) Question 193935: (x-3) ^2 = 20 answer 3 +2 sqrt 5,3 - 2 sqrt 5 why is the answer 3 + 2 sqrt 5,3 -2 sqrt 5 need a full break down Click here to see answer by jim_thompson5910(28595) Question 194415: Simplify the expression completely using the rules of exponents: (b4)(b^6) _________ (b^2)^2 I am having a very difficult time undersatnding how to even go about this if you could show me the steps so I can get it that woul dbe great!:) Thank you so much for the help Click here to see answer by ankor@dixie-net.com(15656) Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455

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# Algebra 1 : How to graph an inequality with a number line ## Example Questions ### Example Question #1 : How To Graph An Inequality With A Number Line Which line plot corresponds to the inequality below? Explanation: A closed circle indicates "greater than or equal to" or "less than or equal to," while and open circle indicates "greater than" or "less than". We can tell from the inequality that our line plot will only have closed circles, as the only symbol is "greater than or equal to." Subtract  from both sides. Divide both sides by . Our plot will show a closed circle on , and extend infinitvely in the positive direction. ### Example Question #2 : How To Graph An Inequality With A Number Line What inequality is represented by the number line? Explanation: An open circle indictes "less than" or "greater than," while a closed circle indicates "greater than or equal to" or "less than or equal to". This number line includes values that are less than  or greater than or equal to . Note how has an open circle, while has a closed circle.

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Search by Topic Resources tagged with Pythagoras' theorem similar to Square in a Triangle: Filter by: Content type: Stage: Challenge level: There are 70 results Broad Topics > 2D Geometry, Shape and Space > Pythagoras' theorem Tilted Squares Stage: 3 Challenge Level: It's easy to work out the areas of most squares that we meet, but what if they were tilted? Pythagorean Triples Stage: 3 Challenge Level: How many right-angled triangles are there with sides that are all integers less than 100 units? The Pillar of Chios Stage: 3 Challenge Level: Semicircles are drawn on the sides of a rectangle ABCD. A circle passing through points ABCD carves out four crescent-shaped regions. Prove that the sum of the areas of the four crescents is equal to. . . . Liethagoras' Theorem Stage: 2 and 3 Liethagoras, Pythagoras' cousin (!), was jealous of Pythagoras and came up with his own theorem. Read this article to find out why other mathematicians laughed at him. Tennis Stage: 3 Challenge Level: A tennis ball is served from directly above the baseline (assume the ball travels in a straight line). What is the minimum height that the ball can be hit at to ensure it lands in the service area? Floored Stage: 3 Challenge Level: A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded? Square Pegs Stage: 3 Challenge Level: Which is a better fit, a square peg in a round hole or a round peg in a square hole? Pythagoras Stage: 2 and 3 Pythagoras of Samos was a Greek philosopher who lived from about 580 BC to about 500 BC. Find out about the important developments he made in mathematics, astronomy, and the theory of music. Isosceles Stage: 3 Challenge Level: Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas. A Chordingly Stage: 3 Challenge Level: Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle. Semi-square Stage: 4 Challenge Level: What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle? The Dangerous Ratio Stage: 3 This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying. Trice Stage: 3 Challenge Level: ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR? Semi-detached Stage: 4 Challenge Level: A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius. Compare Areas Stage: 4 Challenge Level: Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle? Hex Stage: 3 Challenge Level: Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other. Equilateral Areas Stage: 4 Challenge Level: ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF. Some(?) of the Parts Stage: 4 Challenge Level: A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle Inscribed in a Circle Stage: 4 Challenge Level: The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius? Squaring the Circle and Circling the Square Stage: 4 Challenge Level: If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction. Napkin Stage: 4 Challenge Level: A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed . The Old Goats Stage: 3 Challenge Level: A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . . Partly Circles Stage: 4 Challenge Level: What is the same and what is different about these circle questions? What connections can you make? Take a Square Stage: 4 Challenge Level: Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square. Three Cubes Stage: 4 Challenge Level: Can you work out the dimensions of the three cubes? Stage: 4 Challenge Level: A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground? Fitting In Stage: 4 Challenge Level: The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest. . . . Star Gazing Stage: 4 Challenge Level: Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star. Two Circles Stage: 4 Challenge Level: Draw two circles, each of radius 1 unit, so that each circle goes through the centre of the other one. What is the area of the overlap? All Tied Up Stage: 4 Challenge Level: A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be? Pythagoras Proofs Stage: 4 Challenge Level: Can you make sense of these three proofs of Pythagoras' Theorem? Rhombus in Rectangle Stage: 4 Challenge Level: Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus. Six Discs Stage: 4 Challenge Level: Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases? The Spider and the Fly Stage: 4 Challenge Level: A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly? Cutting a Cube Stage: 3 Challenge Level: A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical? Get Cross Stage: 4 Challenge Level: A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing? Squ-areas Stage: 4 Challenge Level: Three squares are drawn on the sides of a triangle ABC. Their areas are respectively 18 000, 20 000 and 26 000 square centimetres. If the outer vertices of the squares are joined, three more. . . . Weighty Problem Stage: 3 Challenge Level: The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . . Rectangular Pyramids Stage: 4 and 5 Challenge Level: Is the sum of the squares of two opposite sloping edges of a rectangular based pyramid equal to the sum of the squares of the other two sloping edges? Zig Zag Stage: 4 Challenge Level: Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line? Tilting Triangles Stage: 4 Challenge Level: A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates? Three Four Five Stage: 4 Challenge Level: Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles. Stage: 4 Challenge Level: The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle. Corridors Stage: 4 Challenge Level: A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner. Pareq Calc Stage: 4 Challenge Level: Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . . Nicely Similar Stage: 4 Challenge Level: If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle? Ball Packing Stage: 4 Challenge Level: If a ball is rolled into the corner of a room how far is its centre from the corner? Round and Round Stage: 4 Challenge Level: Prove that the shaded area of the semicircle is equal to the area of the inner circle. At a Glance Stage: 4 Challenge Level: The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

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## Test II Questions : ACT Prep Test TRIGONOMETRY - ALGEBRA 2 ESSENTIALS Flash Cards--CRAM NOW!-- ## MATERIALS for MAT I 1.- Real Numbers2.- Successions and Progressions. Idea of Limit3.- Algebra D. Binomial and Normal. All About functions, trigonometry and combinatorics ## PISA Exercises : ACT Test Prep Algebra 2-Trig Review--Exambusters Flash Cards--Workbook 9 of 13: ACT Exam Study Guide (Exambusters ACT) eBook : Exambusters, • Explain math equation One way to think about math problems is to consider them as puzzles. To solve a math problem, you need to figure out what information you have. • Provide multiple methods There are multiple ways to reduce stress, including exercise, relaxation techniques, and healthy coping mechanisms. • Determine math equations To determine math equations, one could use a variety of methods, such as trial and error, looking for patterns, or using algebra. • Deal with mathematic tasks I can help you with any mathematic task you need help with. • Get math help online Get math help online by speaking to a tutor in a live chat. • Learn step-by-step This step-by-step guide will show you how to easily learn the basics of HTML. ## Mathematics 1st Baccalaureate : ACT Prep Test TRIGONOMETRY - ALGEBRA 2 ESSENTIALS Flash Cards--CRAM NOW!--

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Re: functional routine for {a, b, c, ...} -> {a - b, b - c, c - ...} • To: mathgroup at smc.vnet.net • Subject: [mg24933] Re: functional routine for {a, b, c, ...} -> {a - b, b - c, c - ...} • From: "Paul R. Wellin" <wellin at wolfram.com> • Date: Tue, 22 Aug 2000 16:22:43 -0400 (EDT) • References: <8nli50\$9fa@smc.vnet.net> • Sender: owner-wri-mathgroup at wolfram.com ```Although I don't think it is any more intuitive than what you have below, here is a functional approach: In[1]:= lis = {a, b, c, d, e, f, g, h}; In[2]:= p = Partition[lis, 2, 1] Out[2]= {{a, b}, {b, c}, {c, d}, {d, e}, {e, f}, {f, g}, {g, h}} In[3]:= Apply[Subtract, p, 2] Out[3]= {a - b, b - c, c - d, d - e, e - f, f - g, g - h} Here it is in one step: In[4]:= Apply[Subtract, Partition[lis, 2, 1], 2] Out[4]= {a - b, b - c, c - d, d - e, e - f, f - g, g - h} Paul Wellin Wolfram Research, Inc. <Maarten.vanderBurgt at icos.be> wrote in message news:8nli50\$9fa at smc.vnet.net... > Hallo, > > element. > I found two ways for doing this: > > lst = {a, b, c, d, e, f, g, h}; > > Table[lst[[i]] - lst[[i + 1]], {i, 1, Length[lst] - 1}] > {a - b, b - c, c - d, d - e, e - f, f - g, g - h} > > ListCorrelate[{1, -1}, lst] > {a - b, b - c, c - d, d - e, e - f, f - g, g - h} > > The first method is rather clumsy and the 2nd one is quite short, but not > really obvious. > Initally I was looking for a functional programming style routine. > Something like: (#[[i]]-#[[i-1]])&/@lst. > Who can tell me how to do this in a functional programming style? > > Thanks > > Maarten van der Burgt > Leuven, Belgium > > > ``` • Prev by Date: Re: functional routine for {a, b, c, ...} -> {a - b, b - c, c - ...} • Next by Date: Re: Re: functional routine for {a, b, c, ...} -> {a - b, b - c, c - ...a} • Previous by thread: Re: functional routine for {a, b, c, ...} -> {a - b, b - c, c - ...} • Next by thread: Re: functional routine for {a, b, c, ...} -> {a - b, b - c, c - ...}

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# ES250: Electrical Science. HW1: Electric Circuit Variables, Elements and Kirchhoff s Laws Size: px Start display at page: Download "ES250: Electrical Science. HW1: Electric Circuit Variables, Elements and Kirchhoff s Laws" Transcription 1 ES250: Electrical Science HW1: Electric Circuit Variables, Elements and Kirchhoff s Laws 2 Introduction Engineers use electric circuits to solve problems that are important to modern society, such as: 1. the generation, transmission, and consumption of electric power and energy 2. the encoding, decoding, storage, retrieval, transmission, and processing of information In Chapter 1, we will do the following: 1. Represent the current and voltage of an electric circuit element, paying attention to the reference current and voltage directions 2. Use the passive convention to determine whether the power or energy is supplied or received by a circuit element 3. Use scientific notation to represent electrical quantities within a wide range of magnitudes 3 Electric Circuits and Current An electric circuit (or network) is an interconnection of electric elements linked together in a closed path so that an electric current may flow continuously through it Consider a simple circuit consisting of two well known electrical elements: a battery and a resistor In this case, each element (or device) is represented by a two terminal t l( (or node) element as shown 4 Electric Circuits and Current Charge is the intrinsic property of matter responsible for electric phenomena: 1. The quantity of charge q can be expressed in terms of the charge of one electron which is coulombs 2. Charge may flow in an electric circuit and current is the time rate of change of charge past a given point, expressed as 3. The unit of current is the ampere (A); an ampere is 1 3 eu o cu e s e a pe e( ); a a pe e s coulomb per second 5 Electric Circuits and Current A complete description of current requires both a value, which can be positive or negative, and a direction indicated by an arrow; thus we say that a current exists in or through an element Note, while the flow of current is historically represented as a flow of positive charges we realize that current flow in circuits is typically due to the flow of negatively charged electrons (this is not always the case in devices such as semiconductors) 6 Electric Circuits and Current If the current flowing through an element is constant, we represent it by the constant I, as shown below, and refer to it as a direct current (dc): Atime varying current i(t)cantakemanyforms suchasa A time varying current i(t) can take many forms, such as a ramp, a sinusoid called an alternating current (ac), or an exponential, as shown below: 7 Electric Circuits and Current If the charge q is known, the current i is readily found using Example Calculating Current from Charge: Find the current in an element when the charge entering the element is where t is the time in seconds Solution: Since the unit of charge is coulombs, C, the current is given by where the unit of current is amperes, A 8 Electric Circuits and Current If the current i is known, the charge q is readily found using where q(0) is the charge at t =0 Example Calculating Charge from Current : Find the Example Calculating Charge from Current : Find the charge that has entered the terminal of an element from t =0s to t = 3 s when the current entering the element is as shown: 9 10 Systems of Units The fundamental or base units of SI are: 11 Derived SI Units 12 SI Prefixes The great advantage of the SI system is that it incorporates a decimal system for relating larger or smaller quantities to the basic unit. An example of the common use of a prefix is the centimeter (cm), which is meter. The standard prefixes given below: 13 Voltage Voltage describes the energy required to cause charge to flow and we say that voltage exists across an element The voltage notation (or references) consist of a value and an assigned direction given by its polarities (+, ) When considering v ab, terminal a is called the + terminal and terminal b is called the terminal Note, voltages v ab and v ba have the same magnitude but opposite sign (polarity) v ab canbereadas the as voltage at terminal a with respect to terminal b; alternatively, we say that v ab is the voltage drop from terminal a to terminal b 14 Voltage The unit of voltage is the volt, V, and the equation for the voltage across the element is where v is voltage, w is energy (or work), and q is charge Note, a charge of 1 coulomb delivers an energy of 1 joule as it moves through a voltage of 1 volt 15 Power and Energy Power is the time rate of supplying or absorbing energy: where p is power in watts, and w is energy in joules The power associated with the current flow through h an element is: The power and energy delivered to an element are of great importance. For example, the useful output of an electric lightbulb can be expressed in terms of power. We know that a 300 watt bulb delivers more light than a 100 watt bulb. 16 The Passive Convention 17 Power and Energy When the element voltage and current adhere to the passive convention, the energy absorbed by an element can be determined from: Example Electrical Power and Energy: Consider the Example Electrical Power and Energy: Consider the element shown labled using the passive convention with v = 4 V and i = 10 A. Find the power absorbed by the element and the energy absorbed over a 10 s interval 18 Power and Energy 19 Resistors Resistance is the physical property of an element or device that impedes the flow of current; it is represented by the symbol R For the passive convention, Ohm's law relates voltage and current: Schematic symbol for a resistor with resistance of R ohms What is the expression for Ohm s law that adheres to the What is the expression for Ohm s law that adheres to the passive convention? 20 Resistors The power delivered to a resistor (when the passive convention is used) is: Alternatively, since v = ir, we can write: The energy delivered to a resistor is: Si h b b d i l i h Since the energy absorbed is always nonnegative, the resistor is referred to as a passive element 21 Example Power Dissipated by a Resistor 22 Independent Sources Sources are intended to supply energy to a circuit; there are two types: voltage sources and current sources: The voltage v(t) of a voltage source is specified but its current is determined by the rest of the circuit; while the converse is true for a current source 23 Short and Open Circuits A short circuit is an ideal voltage source having v(t) = 0 with the current determined by the rest of the circuit, while an open circuit is an ideal current source having i(t) = 0 with the voltage across an open circuit is determined by the rest of the circuit Note, the power absorbed by these devices is zero 24 Voltmeters and Ammeters A meter is connected to a circuit using terminals called probes to measure voltage or current Probes are color coded to indicate the reference direction of the variable being measured, e.g, red for the positive terminal and black for the negative terminal 25 Voltmeters and Ammeters Note, the voltmeter is connected in parallel with the voltage to be measured using the passive convention. The current flow into an ideal voltmeter is zero, meaning that the ideal voltmeter dissipates zero power 26 Voltmeters and Ammeters Note, the ammeter is connected in series with the current to be measured using the passive convention. The voltage across an ideal ammeter is zero, meaning that the ideal ammeter dissipates zero power 27 Voltmeter and Ammeter Examples Circuit measurements: Equivalent circuit: 28 Voltmeter and Ammeter Examples 29 Voltmeter and Ammeter Examples 30 Switches Switches have two distinct states: open and closed Ideally, a switch acts as a short circuit when it is closed and as an open circuit when it is open We ll consider two types of switches: single pole, single throw (SPST) and single pole, double throw (SPDT): 31 Switches Switches have two distinct states: open and closed Ideally, a switch acts as a short circuit when it is closed and as an open circuit when it is open We ll consider two types of switches: single pole, single throw (SPST) and single pole, double throw (SPDT): 32 Example 2.9 1: Switches Based on the schematic in red, when do the others take place? (If needed, see text for solution) 33 Exercise 2.9 2: Make before break SPDT Switch What is the value of the voltage v at time t =4s? At t =6s? Solution: IR = ( 2m )( 3k ) = 6V, for t < 5s vt () = 0V, for t > 5s 34 Kirchhoff's Laws An electric circuit consists of circuit elements connected together by nodes It is common practice to draw circuits using straight lines positioning the elements horizontally or vertically These equivalent circuits have six elements (1 6) and fours nodes (a d) 35 Example 3.2 1: Different Drawings of the Same Circuit The same circuit can be drawn in several different looking ways, but drawings represent the same circuit if corresponding elements are connected to corresponding nodes A th t i it i l t? Are these two circuits equivalent? If so, why? 36 Kirchhoff s Current Law (KCL) Kirchhoff s current law states that the algebraic sum of the currents entering any node is identically zero for all instants of time The phrase algebraic sum indicates that we must take reference directions into account as we add up the currents of elements connected to a particular node one way to take reference directions into account is to use a plus sign when the current is directed d away from a node and a minus sign when the current is directed toward a node, or currents in equal to currents out 37 Kirchhoff s Current Law (KCL) Write the KCL equation for node a: 38 Kirchhoff s Voltage Law (KVL) Kirchhoff s voltage law states that the algebraic sum of the voltages around any loop in a circuit is identically zero for all time A loop is a closed path through a circuit that does not encounter any intermediate node more than once How many loops does this circuit contain? 39 Kirchhoff s Voltage Law (KVL) The phrase algebraic sum indicates that we must take polarity into account as we add up the voltages of elements that comprise a loop one way to do this is to write the voltage with a plus sign when we encounter the + of the polarity before the and a minus sign when we encounter the of the polarity before the + Write the KVL eqn. associated with the loop containing elements 3 6 of the circuit: 40 Example 3.2 3: Ohm's and Kirchhoff's Laws Consider the circuit below noting the passive convention was used to assign references and find all currents and voltages when R 1 =8Ω, v 2 = 10 V, i 3 = 2 A, and R 3 =1Ω. Also, determine the resistance R 2 41 42 Example Ohm's and Kirchhoff's Laws Determine the value of the current, in amps, measured by the ammeter: Equivalent circuit, replacing the ammeter with a short circuit with an appropriate reference direction: 43 44 Dependent Sources Dependent sources model the situation in which the voltage or current of one circuit element is proportional to the voltage or current of the second circuit element used to model electronic devices such as transistors or amplifiers, e.g., the output voltage of an amplifier is proportional to the voltage input of that amplifier Each hdependent d source consists of ftwo parts: the controlling part and the controlled part the controlling part is either an open circuit or a short circuit the controlled part is either a voltage source or a current source There are four types of dependent source that correspond to the four ways of choosing a controlling part and a controlled part, called: voltage controlled voltage sources (VCVS) current controlled voltage controlled voltage sources (VCVS), current controlled voltage sources (CCVS), voltage controlled current sources (VCCS), and current controlled current sources (CCCS) 45 Types of Dependent Sources 46 Types of Dependent Sources 47 Transistor Example 48 Exercise Find the power absorbed by the CCCS: Since the CCCS references use the passive convention, the power absorbed b is given by: p = i v = 4i v = = 115.2W ( ) ( ) d d c d This implies that the CCCS is actually supplying energy to the circuit! 49 Transducers Transducers are devices that convert physical quantities to electrical quantities: potentiometers convert position to resistance temperature sensors convert temperature to current The symbol and A model for the potentiometer 50 Example Potentiometer Circuit Suppose R p = 10 kω and I = 1 ma, an angle of 163 would cause an output of v m = 4.53 V. 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Look over Chapter 18 sections 1-5, 8 over examples 1, 2, 5, 8, 9, Look over Chapter 26 sections 1-7 Examples 3, 7 Look over Chapter 18 sections 1-5, 8 over examples 1, 2, 5, 8, 9, 1)How to find a current in a wire. 2)What the Current Density and Draft Speed are. 3)What ### Chapter 21 Electric Current and Direct- Current Circuits Chapter 21 Electric Current and Direct- Current Circuits Units of Chapter 21 Electric Current Resistance and Ohm s Law Energy and Power in Electric Circuits Resistors in Series and Parallel Kirchhoff s ### physics 4/7/2016 Chapter 31 Lecture Chapter 31 Fundamentals of Circuits Chapter 31 Preview a strategic approach THIRD EDITION Chapter 31 Lecture physics FOR SCIENTISTS AND ENGINEERS a strategic approach THIRD EDITION randall d. knight Chapter 31 Fundamentals of Circuits Chapter Goal: To understand the fundamental physical principles ### ELECTRICITY. Electric Circuit. What do you already know about it? Do Smarty Demo 5/30/2010. Electric Current. Voltage? 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Capacitor connected to a battery Capacitance The ratio C = Q/V is a conductor s self capacitance Units of capacitance: Coulomb/Volt = Farad A capacitor is made of two conductors with equal but opposite charge Capacitance depends on shape ### Review of Ohm's Law: The potential drop across a resistor is given by Ohm's Law: V= IR where I is the current and R is the resistance. DC Circuits Objectives The objectives of this lab are: 1) to construct an Ohmmeter (a device that measures resistance) using our knowledge of Ohm's Law. 2) to determine an unknown resistance using our ### STATEWIDE CAREER/TECHNICAL EDUCATION COURSE ARTICULATION REVIEW MINUTES STATEWIDE CAREER/TECHNICAL EDUCATION COURSE ARTICULATION REVIEW MINUTES Articulation Agreement Identifier: _ELT 107/ELT 108 (2011-1) Plan-of-Instruction version number (e.g.; INT 100 (2007-1)). Identifier ### Insulators Non-metals are very good insulators; their electrons are very tightly bonded and cannot move. SESSION 11: ELECTRIC CIRCUITS Key Concepts Resistance and Ohm s laws Ohmic and non-ohmic conductors Series and parallel connection Energy in an electric circuit X-planation 1. CONDUCTORS AND INSULATORS ### CHAPTER D.C. CIRCUITS Solutions--Ch. 16 (D.C. Circuits) CHAPTER 16 -- D.C. CIRCUITS 16.1) Consider the circuit to the right: a.) The voltage drop across R must be zero if there is to be no current through it, which means the ### Chapter 33 - Electric Fields and Potential. Chapter 34 - Electric Current Chapter 33 - Electric Fields and Potential Chapter 34 - Electric Current Electric Force acts through a field An electric field surrounds every electric charge. It exerts a force that causes electric charges ### Errors in Electrical Measurements 1 Errors in Electrical Measurements Systematic error every times you measure e.g. loading or insertion of the measurement instrument Meter error scaling (inaccurate marking), pointer bending, friction, ### Review. Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. When more devices are added to a series circuit, the total circuit resistance: a. ### Electric Current. Chapter 17. Electric Current, cont QUICK QUIZ Current and Resistance. Sections: 1, 3, 4, 6, 7, 9 Electric Current Chapter 17 Current and Resistance Sections: 1, 3, 4, 6, 7, 9 Whenever electric charges of like signs move, an electric current is said to exist The current is the rate at which the charge ### Chapter 18 Electric Currents Chapter 18 Electric Currents 1 The Electric Battery Volta discovered that electricity could be created if dissimilar metals were connected by a conductive solution called an electrolyte. This is a simple ### MEP 382: Design of Applied Measurement Systems Lecture 3: DC & AC Circuit Analysis Faculty of Engineering MEP 38: Design of Applied Measurement Systems Lecture 3: DC & AC Circuit Analysis Outline oltage and Current Ohm s Law Kirchoff s laws esistors Series and Parallel oltage Dividers ### Use these circuit diagrams to answer question 1. A B C II Circuit Basics Use these circuit diagrams to answer question 1. B C 1a. One of the four voltmeters will read 0. Put a checkmark beside it. b. One of the ammeters is improperly connected. Put a checkmark ### ELEC 250: LINEAR CIRCUITS I COURSE OVERHEADS. These overheads are adapted from the Elec 250 Course Pack developed by Dr. Fayez Guibaly. Elec 250: Linear Circuits I 5/4/08 ELEC 250: LINEAR CIRCUITS I COURSE OVERHEADS These overheads are adapted from the Elec 250 Course Pack developed by Dr. Fayez Guibaly. S.W. Neville Elec 250: Linear Circuits ### Electron Theory. Elements of an Atom Electron Theory Elements of an Atom All matter is composed of molecules which are made up of a combination of atoms. Atoms have a nucleus with electrons orbiting around it. The nucleus is composed of protons ### Chapter 3. Chapter 3 Chapter 3 Review of V, I, and R Voltage is the amount of energy per charge available to move electrons from one point to another in a circuit and is measured in volts. Current is the rate of charge flow ### This week. 3/23/2017 Physics 214 Summer This week Electrical Circuits Series or parallel that s the question. Current, Power and Energy Why does my laptop battery die? Transmission of power to your home Why do we have big transmission towers? ### This week. 6/2/2015 Physics 214 Summer This week Electrical Circuits Series or parallel that s the question. Current, Power and Energy Why does my laptop battery die? Transmission of power to your home Why do we have big transmission towers? ### Designing Information Devices and Systems I Fall 2018 Lecture Notes Note Resistive Touchscreen - expanding the model EECS 16A Designing Information Devices and Systems I Fall 2018 Lecture Notes Note 13 13.1 Resistive Touchscreen - expanding the model Recall the physical structure of the simple resistive touchscreen given ### Unit 2. ET Unit 2. Voltage, Current, and Resistance. Electronics Fundamentals Circuits, Devices and Applications - Floyd. Copyright 2009 Pearson ET 115 - Unit 2 Voltage, Current, and Resistance The Bohr atom The Bohr atom is useful for visualizing atomic structure. The nucleus is positively charged and has the protons and neutrons. Electrons are ### Kirchhoff s Rules. Kirchhoff s rules are statements used to solve for currents and voltages in complicated circuits. The rules are Kirchhoff s Rules Kirchhoff s rules are statements used to solve for currents and voltages in complicated circuits. The rules are Rule. Sum of currents into any junction is zero. i = 0 i 1 2 = 12 Why?

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HomeОбразованиеRelated VideosMore From: Computer Education For all # Data Structures and Algorithms Complete Tutorial Computer Education for All More From: Computer Education For all 7787 ratings | 648883 views Computer Education for all provides complete lectures series on Data Structure and Applications which covers Introduction to Data Structure and its Types including all Steps involves in Data Structures:- Data Structure and algorithm Linear Data Structures and Non-Linear Data Structure on Stack Data Structure on Arrays Data Structure on Queue Data Structure on Linked List Data Structure on Tree Data Structure on Graphs Abstract Data Types Introduction to Algorithms Classifications of Algorithms Algorithm Analysis Algorithm Growth Function Array Operations Two dimensional Arrays Three Dimensional Arrays Multidimensional arrays Matrix operations Operations on linked lists Applications of linked lists Doubly linked lists Introductions to stacks Operations on stack Array based implementation of stack Queue Data Structures Operations on Queues Linked list based implementation of queues Application of Trees Binary Trees Types of Binary Trees Implementation of Binary Trees Binary Tree Traversal Preorder Post order In order Binary Search Tree Introduction to Sorting Analysis of Sorting Algorithms Bubble Sort Selection Sort Insertion Sort Shell Sort Heap Sort Merge Sort Quick Sort Applications of Graphs Matrix representation of Graphs Implementations of Graphs Breadth First Search Topological Sorting Subscribe for More https://www.youtube.com/channel/UCiV37YIYars6msmIQXopIeQ Find us on Facebook: https://web.facebook.com/Computer-Education-for-All-1484033978567298 Java Programming Complete Tutorial for Beginners to Advance | Complete Java Training for all https://youtu.be/gg2PG3TwLx4 Html code for embedding videos on your blog android smart (4 days ago) Thank you sir Fiends Gaming (10 days ago) Maw (14 days ago) 17:57 Maw (14 days ago) I start Data structures and algorithms 3 months so I am watching this video so when I reach my class I can understand the material easily and be ahead of other fellow students. abolgameetandgree t (24 days ago) Thank you for this wonderful course, I wish there are reading materials to supplement it Parikshit Raghav (1 month ago) Great effort and Knowledge Pranjal Sinha (1 month ago) where are all the codes ?? which were supposed to be in a demonstration..where is it?? Shem Mitchel (1 month ago) should have seen this sooner ....WTH.....got everything i been searching...smh Is there pdf for this Cosmonaut Billy (1 month ago) 6 and half hours of data structures... couldn't we make it a bit shorter and to the point? Not sure i can handle this boring ass, interview only, subject for 6+ hours. Sobhan Haggı (1 month ago) Who would have thunk that a Pakistani video would be this educational? Yannick Nixon (1 month ago) Play at 1.25x or 1.5x and pause if you want to let it sink in😌you’re finish the video in half the time. Oh, you’re welcome Thanks very much for the video. I really appreciate your efforts sir. Really got a good understanding of algorithms and data structures from you better than what am having here Munawar Sayyed (2 months ago) Thank you for the tutorial. I appreciate your hardwork. :) Xiao Fang (2 months ago) found a mistake: at 45:44, matrix multiplication is naively O(N^3). the most efficient one having been found is still worse than O(N^2). awesome! Ritik (2 months ago) if anyone saw this video does it include everything? Sunny shah (2 months ago) Thank You @Computer Education For all This video has helped me tremendously. Munya Masuka (2 months ago) this is really good staff thanks a lot guys Vara Lakshmi (2 months ago) Sir thanks for your effort it has cleared all doubts. Thank you very much sir. Sir you slides will help a lot so please give the slides to me waji ms (1 month ago) simply take screenshots Cine Wibes (2 months ago) thanks malla Agyemang Isaac Osei (3 months ago) this is the best tutorial on Data Structures and Algorithm, been wasting time reading abstract books. Derek Lambert (3 months ago) SO LONG😑😑😑😑😑😑😑😑 Vigneshwaran Tamilselvan (4 months ago) I want to prepare for gate cse for this ds and algorithm,so this video is enough for me...reply will be highly appreciated......immediate reply sinister geek (4 months ago) 3:06:00 Cant complete at one go so Just to remember when did i stop i will continue later !! sinister geek (4 months ago) Finally donE!! Hailay Hintsa (5 months ago) Excellent video! Thank you very much ZERO ONE (5 months ago) Now watch this Sudhir Kumar Jayaswal (5 months ago) Which book you have referred while making this.? khushbu kushwah (5 months ago) Thank you John Mahoney (5 months ago) Excellent thank you CPRANGELES CPRANGELES (5 months ago) Great educational video providing a detail explanations about the different computer languages and how they are used for data structure and applications. Where I can get in writing the presentation. Computer Education for All have a great use of YouTube and Facebook. I was looking for the information provided in this video. shanzah aslam (5 months ago) doess it also give the codes of all the topics mentioned aswell?? After showing the implementation of array and string operations(and maybe more, I haven't got there yet) you told that the detailed coding for all methods are given in the demonstration. I couldn't catch it, where is the demonstration actually? And how can I get it? Shall be very grateful to know that. The logo in the background is of Allama Iqbal Open University Pakistan. Credits should be given Mark (6 months ago) Honestly without examples some content is difficult to understand. Like ADT advantages. I guess I need learn an oop language to better understand the content of this video. I know C I know structures but I don't know about encapsulation. The reason I decided to learn about data structures was understanding OOP a bit because I don't understand the oop. What are constructors for instance. Why is creating an object isn't enough and there is a need for a constructor. Don't know. I would really like to read about all these concepts in a chronological order. I am convinced the only way I can truly understand the oop concepts is learning the story behind their invention. RAJIV NAYAN (6 months ago) borzak101 Me (7 months ago) Video is better if you turn sound off and just read it. الاسلام نور (7 months ago) May God reward you with good bushra afridi (7 months ago) Luciano Rezende (7 months ago) Hi professor, do you have some github source code repository? Excellent video! Thank you very much. can you please provide the link of write up. It would be very beneficial Obaid aljabry (8 months ago) develop and algorithm program and flow chart to perform the following task, read type of the vehicle, model of the vehicle, price of the vehicle Kajal Jha (8 months ago) 27:40 montecarlo811 (8 months ago) Perfect EngineeredMechanized (9 months ago) This seems like a very well made collection of lectures. I am of electrical background but took up AI this semester without having much knowledge of computer programming except for some basic C programming. Are these videos enough to know what I need to know before starting AI. Replies would be highly appreciated. No. Manohar Kondi (9 months ago) I have gone through the whole video, it was awesome. could you pls provide document and detailed programs for me. Ganesh Kakkireni (9 months ago) at 1:53:20 *q was not initialized but used... it should be q = p->next | q= head, isn't it? Kehinde Kareem (9 months ago) This is Fantastic and Excellent Tutorial. Thanks for this video. yash chaturvedi (9 months ago) great content but in shell sort example the final list is not in sorted form as 72<75. charles klaus (9 months ago) Amazing lecture! Paris qian sen (9 months ago) 6 hours and 49 mins of treasure! A bit too hard core rishav bagchi (9 months ago) make video speed 1.25x you're good to go! ankesh kumar (9 months ago) only introduction with basic explanation of all DS topics. Ankita Gupta (10 months ago) is this tutorial for data structure using c language ? sahruna khan (10 months ago) Thank you so much puspa Raj Joshi (10 months ago) It's really nice explanation. swamy pediredla (10 months ago) It is useful for gate and net exams Sneha Sruthi (10 months ago) Thank you sir!! AAZinvicto (10 months ago) Awesome video, can watch it at 1.5 speed if you are just brushing up your DS Gregory Jones (10 months ago) Groovy. can we have slides for this great job. Pramod Kumarage (10 months ago) where can i get the example codes related to above tutorial Sai Prajwal Kotamraju (1 year ago) 1:53:40 while(p!=NULL){ q = p->next; Lokesh Sagar (1 year ago) Where can i find the codes for it?? ihsan khan (1 year ago) Great job! Helped me a lot.... carry on plz Please can u send me the soft or hard copy to my mail ?? [email protected] anony mous (1 year ago) goldgoldgoldGOLD! anony mous (1 year ago) diamondmine! Cristian Game4Yu (1 year ago) Ty :) <3 Henry Mideko (1 year ago) the don is atticulate and v. proffesional. thanks sir, bring us more. Cheyno Mdingi (1 year ago) Fiiinally, a computer science video by a pajeet with an easy to understand accent! Carl Taylor (9 months ago) He sounds like Donald Duck. Live Mr. Blind (1 year ago) It's absolutely awesome 👌 perfect 👏 Arun Shah (1 year ago) Excellent Contents! Ignore all the negative comments, people are just greedy. This video is long, detailed and so much effort went into it, I am actually honoured to receive such a good education from this video. -> I have spent 3 months at University doing algorithms and data structures, and I learned almost nothing, it was completely abstract, this video perfectly blends concepts, maths, arguments explanations code examples and is just really really good. Anyone who has spent tens or hundreds of thousands of pounds for education and can compare the quality of this video and its contents vs university teaching will tell you that this video is more valuable than gold or diamonds. thank you very much for your hard work, if I can make a donation to show my appreciation please let me know, very happy to help. excellent teaching & material. Agreed, negative comments are from capitalist universities staff who lose money. Now I won't take this unit in university. Parikshit Raghav (1 month ago) @rAvI kIrUn I don't think so. Just see the video and analyse how much effort is required to make it. rAvI kIrUn (2 months ago) Clearly a paid comment John Ripper (3 months ago) It is also a great refresher for those who havent taken a datastructures course in a few years. its good to review things even after you graduate. Mario Christopher (4 months ago) Such a nice review ... Thanks for this ... hfontanez98 (1 year ago) @43:48 Algorithm Growth Function table. Very useful. (although they did not include O(1) or constant). hfontanez98 (1 year ago) This tutorial could've been broken down to separate data type tutorial as a "Part I", leaving Data Structures and Algorithms as "Part II." Dear Its Complete Tutorial on Data Structure and Algorithm and also watch Algorithms and Data Structures in units on this playlist https://youtu.be/8KcUR2iJJ3c Viral Patel (1 year ago) Thanks a lot for Sharing this!! This is an amazing tutorial...:) appreciations are highly welcome! Yogesh Sanchihar (1 year ago) good videos A New Era (1 year ago) nice video joy (1 year ago) thnx sir Henry Tirla (1 year ago) i suggest to bookmark the Data structures and algorithms tutorial video to easy access i feel difficulty in my assignment really good contents to learn thanks for providing such materials to us Amna Zara (1 year ago) video is totaly blur :( Zeeshan Jamal (9 months ago) you need to set the quality to 720p. May be your internet is slow therefore optimizing Health is Wealth (1 year ago) Nice Demonstration and Full Tutorial on Data Structures Very Easy are ppts available still not please book mark this video for futuristic approach hi, thanks for such a detailed explanation. i wanted to know where i can get the Detailed Codes. i watched the array section and there was no detailed implementation of the Array. Anks k (1 year ago) your c and s pronounce is very bad hear that is very irritating.....plz change pronounce really Anks! can some one help me with this code pls..... #include <iostream> using namespace std; enum sportType { cricket, tennis, waterSport, karate}; union sportChoice{ struct cricketInfo; char tennisInfo[20]; char waterSportInfo[20]; char karateInfo[20]; }; struct cricketInfo{ char nameTeam[20]; char typePlay[20]; }; struct participantType{ char firstName[15]; char secondName[15]; char dob[15]; char sex[10]; char address[30]; char phoneNumber[10]; int activityScore[5]; sportChoice choice; }; void readInfo(participantType self[]); void print (participantType self[]); int main() { participantType self(); readInfo(myself); print(myself); return 0; } void readInfo(participantType self[]){ char s,ch; for(int i=0; i<5; i++){ cout<< " First Name: "; cin.getline(self[i].firstName, 15); cout<< " Second Name: "; cin.getline(self[i].secondName, 15); cout<<" Date of Birth: "; cin.getline(self[i].dob, 15); cout<<" Sex: "; cin.getline(self[i].sex, 15); cout<<" Address: "; cin.getline(self[i].address, 15); cout<<" Phone No: "; cin.getline(self[i].phoneNumber, 15); cout<<" Score of the fitness test: "; cin>>self[i].activityScore; cout<< "Choice of Sport(cricket-c,tennis-t,water sport-w,karate-k): "; cin>>s; cin.get (ch); switch(s){ case 'c': case'C': self[i].choice = cricket; break; case 't': case 'T': self[i].choice = tennis; break; case 'w': case 'w': self[i].choice = waterSport; break; case 'k': case 'K': self[i].choice = karate; break; default cout<< "Incorrect"; } switch ( self[i].choice){ case cricket: cout<< " Name of the team: "; cin.getline(self[i].cricketInfo.nameTeam, 20); cout<< " Type of play: "; cin.getline(self[i].cricketInfo.typePlay, 20); break; case tennis: cout<< " Single or Double: "; cin.getline(self[i].tennisInfo,20); break; case waterSport: cout<< " Swimming, Diving or windsurfing: "; cin.getline(self[i].waterSportInfo,20); break; case karate: cout<< " Color of the Belt: "; cin.getline(self[i].karateInfo,20); break; } } } void print ( participantType self[]){ for (i=0; i<5; i++){ cout<< "Name : "<< self[i].participantType.firstName<<" "<< self[i].participantType.secondName; cout<< "Date of Birth: "<<self[i].participantType.dob; cout<< "Sex: "<<self[i].participantType.sex; cout<< "Address: "<<self[i].participantType.address; cout<< "Phone No."<<self[i].participantType.phoneNumber; cout<< "Fitness text score: "<<self[i].participantType.activityScore; cout<< "Choice of Sport: "; switch (self[i].choice){ case cricket: cout<< " plays cricket for team: " << self[i].cricketInfo.nameTeam; cout<< "Type of play: " << self[i].cricketInfo.typePlay; case tennis: cout<< " plays tennis as "<<self[i].tennisInfo<< "play"; case waterSport: cout<< " plays water Sports as "<<self[i].waterSportInfo; case karate: cout<< "plays karate & holds " << self[i].karateInfo << " belt"; } } } problem not mentioned and need more hear files I think, there is typo error in insertion sort algorithm @4:47:19 , last line should be x[k] = temp. Prasanna (1 year ago) Sincere thanks. Very educative. You had put in lots of effort wit great attention to details. Thank you! Nandha kumar (1 year ago) This video can be suitable 4 beginners? nice comments on Data Structures and Algorithm waldo lok (1 year ago) Your accent throws me off a bit but thanks for the vid 17:31 - The access to structure member through pointers in C. The sign "<-" is should be turned around, so that: employee[0]->name, employee[0]->title, employee[0]->salary 1:53:17 - The sorting of linked list. The variable "q" is not initialised properly, so "q->next" is accessing any trash located somewhere in the memory. In other words, the code of sorting doesn't work. lorenzo garcia (1 year ago) much better if source code is provided Asghar Nazir (1 year ago) 5:09:28, heap written statement contradicts the picture example shown if you have some correction please make changes for Heap written statement in data structures and algorithm EwokPanda (1 year ago) Thank god for 1.5x speed! Thanks for appreciated to Data Structures and Algorithms rachit chhabra (1 year ago) A complaint though "When we consider the programming details of these methods!!!!!!!!!??????????????" when writing any Programming Algorithms and techniques to solve any particular problem etc rachit chhabra (1 year ago) This is a gold mine!! Sincere thanks from my side Nice compliments on Data Structures and Algorithms Asghar Nazir (1 year ago) at 1:14:40 I think there is a mistake n should be the number of columns, not the number of rows may be some think missed thanks for your corrections! in Data Structures and Algorithms

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This seems like an innocuous problem but for some reason I : Quant Question Archive [LOCKED] Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack It is currently 16 Jan 2017, 22:28 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # This seems like an innocuous problem but for some reason I Author Message Director Joined: 10 Feb 2006 Posts: 658 Followers: 3 Kudos [?]: 458 [0], given: 0 This seems like an innocuous problem but for some reason I [#permalink] ### Show Tags 08 Jun 2008, 17:53 This topic is locked. If you want to discuss this question please re-post it in the respective forum. This seems like an innocuous problem but for some reason I can't seem to find the trick to do this one. Please help If x + y = 8z, then which of the following represents the aver(arithmetic mean), of x,y and z in terms of z? 2z + 1 3z 5z z/3 3z/2 _________________ GMAT the final frontie!!!. SVP Joined: 04 May 2006 Posts: 1926 Schools: CBS, Kellogg Followers: 22 Kudos [?]: 1011 [0], given: 1 ### Show Tags 08 Jun 2008, 17:58 [x+y+z]/3=9z/3 =3z =B, you must have worked overload! _________________ Director Joined: 10 Feb 2006 Posts: 658 Followers: 3 Kudos [?]: 458 [0], given: 0 ### Show Tags 08 Jun 2008, 17:59 oh for the love of god, my mind's fried today. thanks _________________ GMAT the final frontie!!!. Re: average   [#permalink] 08 Jun 2008, 17:59 Display posts from previous: Sort by

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Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ ° You are not logged in. #1 2005-11-30 04:41:59 RickyOswaldIOW Full Member Offline More Quadratics I'm given the function f(x)=-(x-2)^2+9 and asked for the maximum value (9) and to sketch the graph of y=f(x) showing where the curve crosses the axis.  I'm not sure of the standard way to work backwards but I worked back to y = -x^2 + 4x + 5 and tried to factorise it to get the points where it crosses the x-axis. Factorising gives me -(x-5)(x-1) [[crosses at (5,0) and (1,0)]] which ofc does not fit in with the sketch.  I'm begining to think that maybe I should factorise down to numercial order thus -(x-1)(x-5) and since the first bracket is preceeded by a - the sign change is canceled out giving (-1,0)(5,0)? Maybe if someone could post the standard rule to work this out, it would be tres handy Aloha Nui means Goodbye. #2 2005-11-30 06:01:40 mathsyperson Moderator Offline Re: More Quadratics Factorising -x² + 4x + 5 gives you (x+1)(5-x), so the roots would be -1 and 5. You had the right answer, but wrong reasoning. Why did the vector cross the road? It wanted to be normal. #3 2005-11-30 06:06:22 RickyOswaldIOW Full Member Offline Re: More Quadratics I know the answer was right, I looked it up My question (which I realise is not that clear) was,  "How do I work it out?" Aloha Nui means Goodbye. #4 2005-11-30 08:34:24 irspow Power Member Offline Re: More Quadratics I would personally use the quadratic equation for this problem: -x^2 + 4x + 5 The quadratic equation would yield the same thing without trying different combinations. [ -b +/- (b^2 - 4ac)^(1/2)] / 2a   =  [-4 +/- (16 + 20)^(1/2)] / -2, so x = 5 and -1 Maybe I am biased, but this method always seemed easier than figuring out values by trial and error. Your question though was specifically about the "textbook" method of factoring.  I would describe it as follows. You want your answer to be like: (ax + b)(cx + d).  This equals (ac)x^2 + (ad + bc)x + (bd). So you are really concerned with the coefficients in the original equation. In this case: ac = -1,  ad + bx = 4, and bd = 5.  b and d are the second terms, so just ask yourself what two numbers multiply to produce 5.  The simple answer leaves only one and five.    (and if you later find that you need fractional coefficients, God help you.) (    + 1)(     + 5).......they both must be postitive otherwise the constant would be negative. As ac = -1 and a and c represent the first terms just plug in a one into both brackets. Remember that one of these terms must be negative! (1x  +1)(1x  +5) The signs within the brackets come from the ad + bc term that produces the x^1 term in your original equation.  So ad = 5 and bc = 1 and these two answers must add up to 4.  The only way that a 5 and a 1 can equal 4 is if the 1 is negative.  Therefore the bc term must be negative and b is already a positive one so c must be negative. (x+1)(-x+5) Remember the (ac)x^2 + (ad + bc)x + bd form of the equation to keep all of this straight in the harder factoralizations. Now you see why I almost always use the quadratic equation to find the zeros of a 2nd degree equation.  Just plug in the coefficients and your done. #5 2005-11-30 09:09:06 RickyOswaldIOW Full Member Offline Re: More Quadratics Wow thanks, I'll make my answer a little more specific next time. Again, Thanks Aloha Nui means Goodbye. #6 2005-12-01 12:50:29 RickyOswaldIOW Full Member Offline Re: More Quadratics I've been using the quadratic formula to solve equations on which I first complete the square.  I notice you are using the same formula here but without the sqrt? Aloha Nui means Goodbye. #7 2005-12-02 08:18:21 irspow Power Member Offline Re: More Quadratics If you look inside the brackets of the numerator the sum within them is raised to the one-half power which is the same thing as taking the square root but just different notation. Board footer Powered by FluxBB

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h a l f b a k e r y I didn't say you were on to something, I said you were on something. meta: account: browse anonymously, or get an account and write. user: pass: register, # Hold Your Nose and Sing Harmonics Detector Kit Find Out About Those Nasal Harmonics (+2, -5) [vote for, against] This would be a kit consisting of a tone generator, say, middle 'C', plus and minus several octaves to encompass the known range of the human voice, and a transducer attachment to the bridge of your nose. The piezoelectric transducer would send a signal from your nose to a simple harmonics detection circuit, battery-powered. The procedure would be to hold your nose and, with open mouth, sing the tone generated by the tone generator. The tone generator would continue to provide tones for you to match in this manner until it detects an harmonic, which would then be recorded. Unless you detect a harmonic first. — entremanure, Nov 27 2001 this is a piss easy game. it plays a C, I sing the G above the next one. Viola! - I found the harmonic first. Can we play twister now? — lewisgirl, Nov 27 2001 HABODICS HABODICS HABODICS — pottedstu, Nov 27 2001 There *must* be a simpler way. Hmm... OK, how's this: breathe water through your nostrils but not so far that it goes into your windpipe. Then emit the water into a measuring flask to get the volume. This gives the volume of your nasal cavity. Therefore the resonant frequency will be mV/2^0.5 for a non-uniform cylinder, and so the nth harmonic frequency will be given by Friedrich's Law, f(n) = m * f(0) * (n! / 2*PI*V)^2. — lubbit, Nov 28 2001 [UnaB] - I was assuming a spherical cow, as it were. — lubbit, Nov 28 2001 [annotate] back: main index

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# Stats posted by on . Suppose that you find out that 20% of all babies say their first word by the time they are 13 months old, and that 90% of all babies say their first word by the time they are 22 months old. Assume that the age at which a baby says its first word is normally distributed. Find the mean age at which a baby says its first word, and the standard deviation. I don't know how to standardize this without either one (the mean or standard deviation) if that is even what I have to do? • Stats - , Given the mean and atsndard deviation, you can find the score for an area under the curve, but working backward, given two percentiles and scores, you can work that in reverse. Reading off the numbers from a z-table (I hope you don't have to work it out from the equation!) I see that 90% equates to 1.28 SD away from the mean and 20% equates to 0.84 SD from the mean. (We don't have to worry about sign, since the curve is symmetric.) So 9 months, being the difference between 13 and 22, constitutes a total of 2.32 SD. Does that give you enough to go on? • Stats - , I'm not sure where you get the 2.32 SD from? And would I use the percentages or months in the calculation with what mean? • Stats - , 90% is 22 months, is 1.28 SD from the mean. 20% is 13 months, is .84 SD in the opposite direction from the mean. Thus, a difference of (22 - 13) months is equivalent to to (1.28 - (-.84)) SD. • Stats - , That equals 2.12. So, I use the z-score from the 20% and 90% and the 2.12 SD, but what do I use for the two means or top numbers when standardizing? • Stats - , Sorry about my mental arithmetic error. :-) So 9 months is 2.12 SD. so 1SD is 4.25 months. 1.28 SD is then 5.44 months from the mean, so the mean is 22 - 5.44. Check: working it the other way .84 is 3.57 months, so the mean is 13 + 3.57. Do those agree? Yes, our mean is 16.57, with an SD of 4.25.

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# Polar moment of inertia in a rod? How is the polar moment of inertia in a rod calculated? Thanks. BvU Homework Helper No idea what it is. This link something ? Yeah, I've had a look at that. Formula doesn't quite make sense to me. I know what moment of inertia is but the 'polar' bit has thrown me off. Thanks anyway. BvU Homework Helper Since there is no context whatsoever in the original posting, it's difficult to assist any further here. Since there is no context whatsoever in the original posting, it's difficult to assist any further here. Here's the problem., 4. (b) (i) is the one I'm looking at. BvU Homework Helper Well, at least now I can understand your confusion. However, it doesn't literally ask for the polar moment of inertia (a.k.a area moment of inertia), but for the polar mass moment of inertia. I see that used for the rotational moment of inertia, so with the context of b (ii) and b(iii) that seems the most logical choice. Well, at least now I can understand your confusion. However, it doesn't literally ask for the polar moment of inertia (a.k.a area moment of inertia), but for the polar mass moment of inertia. I see that used for the rotational moment of inertia, so with the context of b (ii) and b(iii) that seems the most logical choice. What is the formula for rotational moment of inertia? BvU Homework Helper Can't imagine you haven't seen it before ! What did you use for 4a ? ## I=\int dI = {\displaystyle \int_0^M r^2 \; dm}## Can't imagine you haven't seen it before ! What did you use for 4a ? ## I=\int dI = {\displaystyle \int_0^M r^2 \; dm}## I'm on 4. (a) (ii) currently. Where should it be used in (a)? Ok, thanks, I have seen it but haven't used it previously. Can't imagine you haven't seen it before ! What did you use for 4a ? ## I=\int dI = {\displaystyle \int_0^M r^2 \; dm}## I've found this... http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html#irod3 Looking at the bottom set of equations, so dm = (M/L) x dr... So essentially, the equation is r^2 x (M/L) x dr... Using these number that would be 0.075^2 x (20/2) x 0.15 x 0.075... Is that correct? BvU Homework Helper Tempting indeed (*), but I think this time the rod is turning around its length axis. I.e. it's a solid cylinder ! And you will need a moment of inertia in 4a (ii) as well: you don't just have to accelerate the cart, but also the drum. However, in 4a (ii) they give you a radius of gyration, so you use that to calculate the moment of inertia.. (*) well, not really. did you really think dr stands for diameter x radius (because I see a 0.15 x 0.075, and then a few dots, indicating justified doubt, I hope) ? Ok, I am familiar with the equation for mass moment of inertia for a cylinder, which fits with this. So are you saying the equation you gave me wouldn't work with this? I find it odd they say it's a rod and expect a cylinder equation to be used. And yes I knew it wasn't the correct answer as I have the solutions and it didn't match...I see that dr is used in the integration equation now. So what is the formula? dm = elemental mass = (M/L) x dr so the whole equation is r^2 x (M/L) x dr And then? BvU

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Question # Match the following, if a body has intial and final kinetic energies as K.E1 and K.E2 respectively.v2 =√2v1v2 =3v1v2 =4v1 Solution ## The correct option is Kinetic energy =12mv2, where m is the mass of the object, v is the velocity of the object. Given, Intial kinetic energy K.E1 =  12mv21. Case - I When v2 = √2v1 K.E2 =  12mv22 = 12m(√2v1)2 K.E2 = 2K.E1 Case-II When v2 = 3v1, K.E2 = 9K.E1 Case-III When v2 = 4v1, K.E2 = 16K.E1  Suggest corrections Â

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# Questions tagged [constraint-satisfaction] The tag has no usage guidance. 85 questions Filter by Sorted by Tagged with 426 views ### How could an SMT solver be implemented as simple as possible? I'm trying to figure out how an SMT solver works as simple as possible. Let's assume we have a simple input program with symbolic values x and ... 40 views ### Constraint-based layouts for GUIs The VPRI institut founded by Alan Kay has some papers on constraint-based layouts for GUIs based on constraint solving. For instance: Wallingford: Toward a Constraint Reactive Programming Language ... 272 views ### Binarization of Constraints I am trying to solve a Constraint Satisfaction Problem that involves lots of n-ary constraints. But the solver I have implemented only works with algorithms for binary constraints. I've been reading ... 978 views ### CSP Forward checking with n-ary (and binary) constraints I have implemented my own CSP solver using a Backtracking algorithm. Within the Backtracking algorithm I apply a Forward Checking algorithm (reducing domains of connected, unnasigned variables) that ... 483 views ### Finding multi word anagrams from a set of words Finding all anagrams for a word $w$ from a set of words is a problem with many well-known solutions (for example make a hash table mapping from the bag of letters of a word to the word). But what ... 57 views ### Small world theorem for set constraints Let $S_1,\dots,S_n$ be variables representing unknown sets. A set expression has the form $S_i$, $\overline{E}$ (the complement of $E$), or $E \cap E'$, where $E,E'$ are set expressions. A ... 47 views ### Handling eqaulity constraints in genetic algorithms I am trying to solve an optimization problem with strength pareto algorithm (SPEA2). My decision variable have lower and upper bounds as well as an equality constraint (sum(dp) = 1). I am unable to ... 180 views ### Efficient algorithm for simple constraint satisfaction problem There are $k$ Boolean variables $x_1, x_2, \dots, x_k$. $m$ arbitrary subsets of these variables such that sum of each set equals to $1$ (i.e., only one variable is $1$, the others are $0$). E.g., ... 189 views ### Modeling tiling problems as SAT problems I read that tiling problems can be modeled as satisfiability problems (2-SAT?), but the author did not explain how. Is this true? What would be an example? By a "tiling problem" I mean you have a ... 53 views ### “strongly relational m-consistency when the domains contain at most m elements implies satisfiability” plain wrong? Wikipedia states A constraint satisfaction problem may be relationally consistent, have no empty domain or unsatisfiable constraint, and yet be unsatisfiable. There are however some cases in ... 413 views ### Heuristic Repair and N-Queens Problem Problem: I am trying to solve the $N$-Queens problem using Constraint Satisfaction and Heuristic Repair (also known as Min-Conflicts). I wrote a program to do this for any given $N$ queens and $N * N$... 66 views ### (Historical perspective) CSP and SAT inter-fertilization [Disclaimer: this is a rather specialized question] It is known that techniques like Conflict-Driven Clause Learning (CDCL) and back-jumping -- which improved the Satisfiability (SAT) strategies ... 129 views ### Any reason to use the least-constrained variable heuristic when searching the solution of a CSP? Is there any (kind of) (well-known) problem which can be expressed as a CSP in which the least constrained variable heuristic seems to give the best results, when employing backtracking with ... 5k views 12k views ### What is Least-Constraining-Value? In constraint satisfaction problems, heuristics can be used to improve the performance of a bactracking solver. Three commonly given heuristics for simple backtracking solvers are: Minimum-remaining-... 775 views ### Contraint with three variables into three binary constraints I'm having a hard time tackling the following problem (perhaps some key data is missing). We have a constraint: $A+B= C$ One is supposed to represent this one constraint using three binary ... 142 views ### Isn't Domain of a variable nothing but a constraint? In Constraint programming we have Variables and their Domains and then all the constraints, but if you at the concept of a domain of a variable it is nothing but another type of constraint, you are ... 1k views ### Why don't modern SAT solvers use the notion of a “watched clause”, in the same way they use the notion of a “watched literal”? Modern SAT solvers use the notion of "watched literals": when a value is chosen for a literal $l$, the solver only checks whether that falsifies clauses with $l$ in them if $l$ is one of the watched ...

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Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ ° You are not logged in. ## #1 2009-04-21 02:29:51 JaneFairfax Member Registered: 2007-02-23 Posts: 6,868 ### Finite fields As you know, a finite field always has order a power of a prime. I didn’t really know how to prove this until I read Chapter 14 of John F. Humphreys’s. In fact, the result depends on just two results: 1 is proved by a combination of Lagrange and Sylow. By Lagrange, the order of is a power of ; if there is also a prime dividing , then would have a Sylow -subgroup whose nonidentity elements would not have order a power of . 2 comes from the fact that the characteristic of a field is a prime ; this means that every nonzero element of the field has order in the additive subgroup, and this implies that the additive group of the field is a -group. Last edited by JaneFairfax (2009-04-21 06:42:57) Offline ## #2 2009-04-22 19:54:24 JaneFairfax Member Registered: 2007-02-23 Posts: 6,868 ### Re: Finite fields Another result about finite fields is that the multiplicative group of nonzero elements of a finite field is cyclic. This can be proved using a theorem about finite Abelian groups. http://z8.invisionfree.com/DYK/index.php?showtopic=835 Offline

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# STAT 495, Fall 2003 Homework Assignment #4 ```STAT 495, Fall 2003 Homework Assignment #4 1. Engineers at a manufacturing plant wish to monitor the outside diameter of a motor shaft that is machined on a CNC turning center. The target value is 2.125 inches with a tolerance of &plusmn;0.001 inch. The data are outside diameters for subgroups of four consecutive parts. The subgroups are spaced approximately 12 hour apart. The measurements are made in inches to the nearest ten-thousandth of an inch. Only the last two digits are displayed, i.e. 2.1247 appears as 47. (a) Using all 35 subgroups, compute centerlines and control limits for X and R charts. (b) Construct X and R charts. You may use JMP, Minitab or another computer prackage to do this. (c) Identify any subgroups that plot outside the control limits on either of the charts. (d) What can be said about the stability of the process? Our operational definition of stability is no points outside control limits. (e) Construct X and s charts. How do these charts differ from those in (c) in terms of evaluating the current process? How different are the control limits on the X charts using s instead of R? (f) Come up with two estimates of the process standard deviation, one based on subgroup ranges and the other based on subgroup standard deviations. How do these two estimates compare? 2. A study was conducted on the injection molding process of a vehicle hush panel. Briefly, the process starts with material being fed into the back end of the barrel and screw mechanism. The screw rotates and heat is added, melting the material and moving it to the front. The molten material is injected into a mold. The plastic is cured until it is solidified. This constitutes a cycle. Jack Brown at the General Motors Lansing site, collected data on the weight, in grams, of the material for each cycle. This was done by weighing the solidified plastic that comes out of the mold. A subgroup consists of five weight measurements. There are 45 subgroups. (a) Using all 45, compute centerlines and control limits for X̄ and R charts. (b) Actually construct the X̄ and R charts. You can use JMP, Minitab or another computer package to do this. (c) Identify any subgroups that plot outside the control limits on either of the charts. (d) What can be said about the stability of the process? Our operational definition of stability is no points outside control limits. (e) Construct a histogram for the entire set of 225 measurements. Use cutpoints from 600 to 750 with interval widths of 10. Comment on the shape of the histogram and what it is telling you about the weight of material. (f) What comes out of the mold consists of two parts and a runner. Several of the subgroups contain weights for the two parts without the runner. These subgroups are: 1, 7, 8, 11, 12, 15, 16, 17, 18, 23, 25, 29, and 30. Assuming that this special cause can be eliminated, reconstruct the control charts after first removing these subgroups. Use a computer package to do this. How do the control limits on these charts compare to those in a) and b)? What can you say about the stability of the process now? Again use the one point outside control limits alarm rule. (g) Compute an estimate of the process standard deviation using all 45 subgroups. Compute an estimate of the process standard deviation, excluding the subgroups given in (f). How has the estimate changed? Outside Diameter Motor Shafts Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 X1 48 48 50 50 51 44 51 46 54 54 57 51 42 43 41 60 48 46 52 62 58 50 47 56 39 40 48 36 51 43 43 29 36 48 45 X2 59 52 49 41 49 47 57 63 53 46 56 49 47 50 54 45 50 39 32 50 52 56 53 55 54 43 48 45 48 50 43 42 43 42 51 X3 42 51 60 48 60 54 53 63 53 55 53 67 48 44 59 52 45 43 54 47 57 44 42 44 54 59 34 43 24 40 49 43 43 43 43 X4 40 50 44 43 60 45 48 41 46 58 37 50 39 38 53 46 40 61 45 57 54 44 40 58 44 36 43 32 55 53 31 42 49 39 39 X̄ R 47.25 19 50.25 4 50.75 16 45.50 9 55.00 11 47.50 10 52.25 9 53.25 22 51.50 8 53.25 12 50.75 20 54.25 18 44.00 9 43.75 12 51.75 18 50.75 15 45.75 10 47.25 22 45.75 22 54.00 15 55.25 6 48.50 12 45.50 13 53.25 14 47.75 15 44.50 23 43.25 14 39.00 13 44.50 31 46.50 13 41.50 18 39.00 14 42.75 13 43.00 9 44.50 12 47.807 14.314 s 8.54 1.71 6.70 4.20 5.83 4.51 3.77 11.44 3.70 5.12 9.32 8.54 4.24 4.92 7.63 6.90 4.35 9.60 9.95 6.78 2.75 5.74 5.80 6.29 7.50 10.08 6.60 6.06 13.96 6.03 7.55 6.68 5.32 3.74 5.00 6.482 Injection Mold Weights Subgroup 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 X1 690 695 690 690 718 715 713 717 713 705 650 708 712 713 704 707 718 709 709 710 714 714 700 705 641 706 707 707 703 703 705 707 701 700 694 694 700 699 701 689 700 702 703 694 704 X2 690 696 690 690 719 716 712 717 714 704 711 707 710 713 645 710 719 650 708 714 713 713 699 706 701 706 705 707 702 693 703 706 700 700 695 694 699 699 698 690 699 702 703 696 703 X3 690 696 690 690 719 716 713 718 715 703 650 646 712 712 703 648 655 710 708 712 714 714 700 704 701 706 706 706 705 626 705 706 699 700 696 695 698 699 698 691 700 703 702 694 700 X4 690 694 692 689 722 717 654 658 715 704 709 704 710 712 703 709 719 647 709 708 714 712 700 703 703 706 704 705 705 619 706 705 699 699 696 695 699 698 698 694 700 705 700 697 700 X5 629 695 692 687 721 715 716 720 713 704 710 707 710 712 702 709 716 709 700 704 713 710 640 702 643 706 706 706 643 707 706 705 700 699 695 695 699 699 697 697 702 705 700 696 698 X̄ 677.8 695.2 690.8 689.2 719.8 715.8 701.6 706.0 714.0 704.0 686.0 694.4 710.8 712.4 691.4 696.6 705.4 685.0 706.8 709.6 713.6 712.6 687.8 704.0 677.8 706.0 705.6 706.2 691.6 669.6 705.0 705.8 699.8 699.6 695.2 694.6 699.0 698.8 698.4 692.2 700.2 703.4 701.6 695.4 701.0 699.5 R 61 2 2 3 4 2 62 62 2 2 61 62 2 1 59 62 64 63 9 10 1 4 60 4 62 0 3 2 62 88 3 2 2 1 2 1 2 1 4 8 3 3 3 3 6 20.56 s 27.28 0.84 1.10 1.30 1.64 0.84 26.65 26.86 1.00 0.71 32.87 27.10 1.10 0.55 25.95 27.19 28.20 33.34 3.83 3.85 0.55 1.67 26.72 1.58 32.70 0.00 1.14 0.84 27.20 43.37 1.22 0.84 0.84 0.55 0.84 0.55 0.71 0.45 1.52 3.27 1.10 1.52 1.52 1.34 2.45 9.48 ```

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## If factoring 169 – x^2 completely, the factored form is (13-x)(13+x) True or False? Question If factoring 169 – x^2 completely, the factored form is (13-x)(13+x) True or False? in progress 0 3 months 2021-07-24T14:35:14+00:00 1 Answers 3 views 0

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## Wednesday, 16 February 2011 ### Euler's Gem....Descartes' Pearl? One of the great lost papers of mathematics was the Progymnasta de solidorum elementis [Exercises in the elements of solids] of Descartes.  It is in this paper that he did, or did not, depending on who's argument most impresses you, first give the famous theorem by Euler on the relation between the faces, edges and vertices of polyhedra. In 1649 Descartes went to Sweden to serve as the tutor of Princess Christina.  After his death he was buried in Sweden, but his possessions were sent back to France, but the box containing his manuscripts fell into the river.  Many of them were rescued, and this particular one was recopied by Leibniz.  Afterward, the original seems to have been lost, and Leibniz copy was undiscovered until 1860.  The manuscript is unquestionably the first known study of polyhedra.  It certainly had something close to Euler's famous V+F=E+2, at least to the modern eye.  It was just as certainly not known to Euler or any other mathematician of the period. So did Descartes discover Euler's Gem? Here is what Ed Sandifer Writes about the paper: So, what did Descartes do? He studied something closely related to Euler’s formula for the sum of the plane angles of a polyhedron. In Descartes’ time, people had a concept of a solid angle called the deficiency. The deficiency of a solid angle is the amount by which the sum of the plane angles at the solid angle fall short of four right angles. In the case, for example, of a solid right angle, formed by three right angles, the deficiency will be one right angle. For a cube, which contains eight solid right angles, the total deficiency is eight right angles. Descartes’ main result is that this always happens: Theorem: The sum of the deficiencies of the solid angles of a polyhedron is always eight right angles. It is an almost trivial step from this to Euler’s theorem, that the sum of the plane angles is four times the number of solid angles, less eight right angles, that is 4V – 8 right angles. Descartes’ other interesting result is more subtly related, but still remotely equivalent to V – E + F = 2. Descartes writes:  "Dato aggregato ex omnibus angulis planis et numero facierum, numerum angulorum planorum invenire: Ducatur numerus facierum per 4, et productum addatur aggregato ex omnibus angulis planis, et totius media pars erit numeris angulorum planorum." .. Given the sum of all the plane angles and the number of faces, to find the number of plane angles: The number of faces is multiplied by 4, and to the product is added the sum of all the plane angles, and the half part of this total will be the number of plane angles. It is easy, but not obvious, to transform this rule into Euler’s V – E + F = 2, In his "Proofs and Refutations", Imre Lakatos believes that the small step from Descartes to Euler was not so small a step in the period of Descartes.  Descartes failed to seize upon the concept of dimensionality that Euler grasped, a connection between the zero dimensional points, the one dimensional edges and the two dimensional faces. Here is how Lakatos stated it, as quoted in Descartes Mathematical Thought by Chikara Sasaki

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# [LintCode] Segment Tree Build II ### Question The structure of Segment Tree is a binary tree which each node has two attributes start and end denote an segment / interval. start and end are both integers, they should be assigned in following rules: The root’s start and end is given by build method. The left child of node A has start=A.left, end=(A.left + A.right) / 2. The right child of node A has start=(A.left + A.right) / 2 + 1, end=A.right. if start equals to end, there will be no children for this node. Implement a build method with a given array, so that we can create a corresponding segment tree with every node value represent the corresponding interval max value in the array, return the root of this segment tree. Similar. ### Code ``````/** * Definition of SegmentTreeNode: * public class SegmentTreeNode { * public int start, end, max; * public SegmentTreeNode left, right; * public SegmentTreeNode(int start, int end, int max) { * this.start = start; * this.end = end; * this.max = max * this.left = this.right = null; * } * } */ public class Solution { /** *@param A: a list of integer *@return: The root of Segment Tree */ public SegmentTreeNode build(int[] A) { if (A == null || A.length == 0) { return null; } return helper(A, 0, A.length - 1); } private SegmentTreeNode helper(int[] A, int start, int end) { if (start > end) { return null; } SegmentTreeNode node = new SegmentTreeNode(start, end); if (start == end) { node.max = A[start]; return node; } else { node.left = helper(A, start, (start + end) / 2); node.right = helper(A, (start + end) / 2 + 1, end); if (node.right != null) { node.max = Math.max(node.left.max, node.right.max); } else { node.max = node.left.max; } } return node; } } ``````

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# VAR and E(R) Does a higher E® lead to a higher or a lower VaR ? Can someone explain it intuitively? It does if we are thinking of basics where higher E® requires more risk. If you increase risk you will increase your variance. Assuming the same VaR settings for all your scenarios, VaR should be higher with more risk. comparing portfolio with 50/50 stock/bond vs portfolio with 100% stocks. It is ambiguous. If we consider Var=μ-zσ you can see there is a conflict as higher return is pulled down by the sigma component, but the magnitudes are not clear. It is affected by all 3 variables, Est. R, sigma and zeta. And if higher return is achieved by option trading for example in one portfolio such outcomes might not be comparable to another option free portfolio by VaR. @Jaffacake Where did you find such question? There would not be such simple rules to remember. Maybe better solution would be to concentrate on advantages and drawbacks of each method. VAR is a negative number because it is a loss #. Higher E®, assuming other factors remain unchanged - would mean that VAR # comes down in absolute terms. With an expected return of 0.135, we move 1.65 standard deviations along the x-axis in the direction of lower returns. Each standard deviation is 0.244. Thus we would obtain 0.135 – 1.65(0.244) = –0.268.36 At this point, VAR could be expressed as a loss of 26.8 percent. Some approaches to estimating VAR using the analytical method assume an expected return of zero. This assumption is generally thought to be acceptable for daily VAR calculations because expected daily return will indeed tend to be close to zero. Because expected returns are typically positive for longer time horizons, shifting the distribution by assuming a zero expected return will result in a larger projected loss, so the VAR estimate will be greater. Therefore, this small adjustment offers a slightly more conservative result and avoids the problem of having to estimate the expected return, a task typically much harder than that of estimating associated vol- atility. Another advantage of this adjustment is that it makes it easier to adjust the VAR for a different time period. For example, if the daily VAR is estimated at \$100,000, the annual VAR will be \$100,000 250 \$1,581,139 . This simple conversion of a shorter-term VAR to a longer-term VAR (or vice versa) does not work, however, if the average return is not zero. In these cases, one would have to convert the average return and standard deviation to the different time period and compute the VAR from the adjusted average and standard deviation. so making the return smaller - increases the VAR - so makes it more conservative. this would imply - making the E® BIGGER - would make the VAR smaller. Hi Cpk sir, you’re only talking specific to changing time horizon right? not comparing 2 different portfolios of different risk and return. I guess my response isn’t correct because those factors wouldn’t be known? thanks, I found similar vignette style question at Risk management EOC. The risk increase was not driven by asset return increase, assuming all else constant but with positive correlation between portfolios. Maybe, Jaffacake meant on this question.

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Need an explanation of a particular expression transformation Please, I need an explanation of the one transformation. I have the equation set and its solution. $$\begin{cases} \frac{x}{y} + \frac{y}{z} + \frac{z}{x} = 3\\\\ \frac{y}{x} + \frac{z}{y} + \frac{x}{z} = 3\\\\ \ x + y + z = 3 \end{cases}$$ In the solution three new variables were introduced: $$u = \frac{x}{y}; v = \frac{y}{z}; w = \frac{z}{x}$$ And then using this new vars equation set became this: $$\begin{cases} \ u + v + w = 3\\\\ \frac{1}{u} + \frac{1}{v} + \frac{1}{w} = 3\\\\\\ \ uvw = 1 \end{cases}$$ I can't understand how the $x + y + z = 3$ has become the $uvw = 1$. Can someone explain what have been done here? My appreciation. $$uvw = \frac{x}{y}\frac{y}{z} \frac{z}{x}=\frac{xyz}{yzx}=1$$

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## What is Zero Coupon Bond? Zero-Coupon Bond (Also known as Pure Discount Bond or Accrual Bond) refers to those bonds which are issued at a discount to its par value and makes no periodic interest payment, unlike a normal coupon-bearing bond. In other words, its annual implied interest payment is included in its face value which is paid at the maturity of such bond. Therefore this bond is the one where the sole return is the payment of the nominal value on maturity. ### Explanation These Bonds are initially sold at a price below the par value at a significant discount, and that’s why the name Pure Discount Bonds referred to above is also used for this Bonds. Since there are no intermediate cash flows associated with such Bonds, these don’t result in reinvestment risk because there are no cash flows prior to maturity that must be reinvested. Such bonds possess the greatest duration, which is equivalent to the maturity of such bonds and, as such, are subject to the greatest level of Interest Rate Risk. Since the Interest accrued is discounted from the Par value of such Bonds at purchase, which effectively enables Investors of Zero Coupon Bonds to buy a greater number of such bonds compared to any other Coupon Bearing Bond. ### Zero-Coupon Bond Formula we can calculate the Present value of using this below-mentioned formula: Zero-Coupon Bond Value =Maturity Value/(1+i)^ Number of Years For eg: Source: Zero Coupon Bond (wallstreetmojo.com) ### Example Let’s understand the concept of this Bond with the help of an example: Cube Bank intends to subscribe to a 10-year this Bond having a face value of \$1000 per bond. The is given as 8%. Accordingly, Zero-Coupon Bond Value = [\$1000/(1+0.08)^10] = \$463.19 Thus the Present Value of Zero Coupon Bond with a Yield to maturity of 8% and maturing in 10 years is \$463.19. The difference between the current price of the bond, i.e., \$463.19, and its Face Value, i.e., \$1000, is the amount of that will be earned over the 10-year life of the Bond. Thus Cube Bank will pay \$463.19 and will receive \$1000 at the end of 10 years, i.e., on the maturity of the Zero Coupon Bond, thereby earning an of 8%. ### Zero-Coupon Bond vs. Regular Coupon Bearing Bond Here are the key differences between Zero-coupon Bond and Regular Coupon Bearing Bond #### #1 – Predictability of Returns This offers predetermined returns if held till maturity, which makes them a desirable choice among investors with long term goals or for those intending assured returns and doesn’t intend to handle any type of Volatility usually associated with other types of Financial Instruments such as Equities etc. #### #2 – Removes Reinvestment Risk These Bonds avoid the risk of Reinvestment of Coupon Bonds as Interest Rates keep changing with the passage of time, which impacts the Yield to Maturity of such coupon-bearing Bonds. Since there are no interim cash flows, the investor is assured of a fixed rate of return. #### #3 – Longer Time frame Usually, these Bonds are issued for a longer time frame, which can be used by a potential investor to align with their life goals such as Marriage, Children Education, and retirement, and so on. Thus a smart investor based on their time horizon can invest in different maturity Zero-coupon Bonds by paying a smaller amount initially (as Zero-coupon Bonds are issued at deep discounts, one can buy more with lesser amount) and stagger them as per their career and life goals without getting impacted by the volatility. #### #1- Illiquid Secondary Markets Not all Zero-coupon Bonds have a ready secondary market, which results in illiquidity. Furthermore, in case of any urgent need funds, it is difficult to liquidate the same without getting a major haircut in value. #### #2 – High Duration and Interest Rate Risk They have a single cash inflow for the Investor, which happens at the maturity, and as such, these bonds have the greatest Duration, which results in Interest Rate Risk. Further, These are issued with call provisions that allow the issuer of such Bonds to redeem the bonds prior to their maturity at dates and prices, which are predetermined at the time of the issue of such Bonds. In such cases, the Investor is left with the risk of the proceeds at the rates available at the time of redemption, which will obviously be less than the earlier slated yield on the redeemed bonds. #### #3 -No Regular Income It doesn’t offer any regular source of income and is a complete misfit for those looking for a stable regular source of Income. Furthermore, one has to pay tax on the on such bonds every year. However, it is pertinent to note here that there are certain categories of Zero Coupon Bonds, which can overcome the taxation problem. This has been a guide to what is Zero Coupon Bond. Here we discuss how to calculate Zero Coupon Bond using its pricing formula along with its advantages and disadvantages and practical examples. You can learn more about from the following articles –

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Aspirants must practice as many questions as possible on solving equations using the Newton-Raphson method, Bisection method, and numerical integration techniques. Engineering Mathematics Engineering Mathematics - Objective type Online Test Questions and Answers with Solution, Explanation, Solved Problems Probability and statistics (For all streams):  Bayes’ Theorem will cover most of the questions. Please send your query to nst@madeeasy.in for detailed information regarding the same. Total derivatives International Journal of Engineering, Computer Science and Mathematics, 1 (1). Course: B.Tech Group: Mathematics Also Known as: Mathematics-3, Applied Mathematics - 2, Mathematics for Communication Engineers, Advance Numerical Methods, Analytical Instrumentation, Mathematics-4 Depricated, Pure Applied Mathematics For Specific Branch Of Engineering, Applied Numerical Methods, Calculus I, Calculus II, Engineering Mathematics 1, Transform and Partial … The exam is a screening test or elimination round used by the institutes. Linear Algebra: Determinants, Matrices. UNIT II FUNCTIONS OF SEVERAL VARIABLES i.e 222 111 abc abc for a = b 222 12 111 bbc bbc Irrespective of the stream the candidate has in his/ her graduation, Engineering Mathematics will be there in all of them. We have a series of free Engineering Mathematics Videos. A brief introduction to Vector Spaces In First Semester 1. MATHEMATICS FOR ENGINEERING BASIC ALGEBRA TUTORIAL 1 – ALGEBRAIC LAWS This tutorial is useful to anyone studying engineering. Engineering Mathematics (M1) Important Questions in PDF format. B.Tech./1Sem/Computer System and Programming in C, Definition and Types of a Beam Notes pdf ppt, What is Diffraction of Light for Engineering Physics B.tech 1st Year, Introduction to Substitution Reactions in Organic Chemistry Notes pdf ppt, Conducting Polymers and Classification of Conducting Polymers Notes pdf ppt, Hardness of Water and Methods of Water Softening Notes pdf ppt, Principle of Nicol Prism Engineering Physics B.Tech 1st Year. This will aid you to prepare in a more directed manner. Applications of Green’s, Stoke’s and Gauss divergence theorems. Today we will focus on Engineering Mathematics for GATE 2021. Take a couple of deep breaths. All about Airports Authority of India (AAI), BARC Training School: Detailed Training Procedure. Vector identities Eigen vectors. UNIT I DIFFERENTIAL CALCULUS. Still wondering how to crack GATE by scoring well in Engineering Maths? Download link for IT 1st SEM MA6151 Mathematics 1 Answer Key is listed down for students to make perfect utilization and score maximum marks with our study materials.. Anna University Regulation 2013 Information Technology (IT) 1st SEM MA6151 M1 – Mathematics 1 Syllabus Ramakrishna Prasad. … - Selection from Advanced Engineering Mathematics, 10th Edition [Book] Revise regularly. Partial derivatives Engineering Mathematics for GATE 2021 is very challenging. • Explain and use algebraic symbols. But, before solving those make sure that you have solved all the different types of basic numerical. This will calm you down. i.e 222 111 abc abc for a = b 222 12 111 bbc bbc Engineering MAthematics is one of the best math workbooks available. Bernoulli’s Equation and Euler Differential Equation should also be paid attention to. UNIT – I Sequences – Series Basic definitions of Sequences and series – Convergences and divergence – Ratio test – Comparison test – Integral test – Cauchy’s root test – Raabe’s test – Absolute and conditional convergence UNIT – II Functions of Single Variable Rolle’s Theo… Mathematics for Engineering is designed for students with little math backgrounds to learn Applied Mathematics in the most simple and effective way. Rank of a matrix ( Echelon & Normal form) Very helpful informatіon specifically the last part NATIONAL THERMAL POWER CORPORATION (NTPC), Why Choose BARC as a Career? As we have covered all topics but the topics provided in the notes are … We strongly believe that this guide will, surely, help you score well in this section in GATE. We have a series of free Engineering Mathematics Videos. Engineering Mathematics for GATE 2021 is one of the subjects compulsory for all engineering streams. There are minute differences in topics, but the major syllabus remains the same for all. Prioritize your study. Linear transformations, Double and triple integrals Rank of a matrix ( Echelon & Normal form) Linear dependence. Unit 2: Calculus. Cayley-Hamilton Theorem Calculus (For all streams): Calculus is essential. 3= r3e axcos ()3θ+bx +c. - 42267 6. Applications of Differentiation. Maths for Engineering 3. The app brings the notes of mathematics in engineering. Students are advised to follow their Syllabus While Studying JNTUH JNTUK JNTUA Engineering Mathematics–1 (M-1) Study Material and Text Book. How to prepare Engineering Mathematics for GATE without any coaching? Topics Covered in B S Grewal Higher Engineering Mathematics Unit 1: Algebra, Vectors, and Geometry. Engineering Mathematics is one of the scoring section in GATE/BARC/ISRO Exam. Unit – 1: Differential Calculus – I. 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The topics are Chain rule, Partial Derivative, Taylor Polynomials, Critical points of functions, Lagrange multipliers, Vector Calculus, Line Integral, Double Integrals, Laplace Transform, Fourier series. Engineering mathematics (also called Mathematical Engineering) is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in engineering and industry. Begins at the beginning and takes the student through the important stuff (trigonometry, calculus etc). Engineering Mathematics I Important Questions Pdf file - M1 Imp Qusts Please find the attached pdf file of Engineering Mathematics I Important Questions Ban - 42267 2= r2eaxcos ()2θ+bx+c. Engineering Mathematics – 1 Important Questions & Most Asked Question in Exams – This collection of Engineering Mathematics – 1 Important Questions for B.Tech / B.E contains all important questions and covers all chapters providing clear idea about the frequently asked questions from each unit. 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Engineering Mathematics 1 Important questions MA8151 pdf download free. Its been 8 years since i graduated from college, but for the geek in me, it was entertaining … This is an online topic wise solutions & notes on Engineering Mathematics for BTech First Year students. Aspirants are advised to practice limits as well. Historically, engineering mathematics consisted mostly of applied analysis, most notably: differential equations; real and complex analysis (including vector and tensor analysis); approximation theory (broadly construed, to include asymptotic, variational, and perturbative methods, representations, numerical analysis); Fourier analysis; potential theory; as well as linear algebra and applied probability, … Solve problems involving functions and trigonometric equations. Inverse of a matrix by elementary transformations. Share this article with your classmates and friends so that they can also follow Latest Study Materials and Notes on Engineering Subjects. Find the nth derivative of e2x cos2 x sin x Solution : >> let y = e2x cos2 x sin x = e2x ⎥ 2 1 cos2x sin x ie., 2 e y List of Mathematics Project Topics & Materials PDF & Doc. Higher Engineering Mathematics – B.S. The aim of this course is to provide students with the knowledge of not only mathematical theories but also their real world applications so students understand how and when to use them.. Further Differentiation. Subspaces The lectures are motivated by hands-on laboratory exercises including a thorough integration with Matlab. Consistency of linear system of equations and their solution A brief introduction to Vector Spaces. 4. Save my name, email, and website in this browser for the next time I comment. . The main approach and style of this book is informal, theorem-free, and practical. The topics covered under Engineering Mathematics for GATE 2021 are nearly the same for every stream of engineering. Our 1000+ Engineering Mathematics questions and answers focuses on all areas of Engineering Mathematics subject covering 100+ topics in Engineering Mathematics. List of algorithm general topics; List of computability and complexity topics Eigen values Thanks for writing to us. … It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview … By using an informal and theorem-free approach, all fundamental mathematics topics required for engineering are covered, and readers can gain such basic knowledge of all important topics … Grewal, Khanna Publications. Please send your query to the following email address or call on the following contact information. Do not proceed to other subtopics before completing the one you are doing presently. Hyperbolic Functions. Make sure that you manage your time well during the solving process. The topics are Chain rule, Partial Derivative, Taylor Polynomials, Critical points of functions, Lagrange multipliers, Vector Calculus, Line Integral, Double Integrals, Laplace Transform, Fourier series. I want to take admission in the regular batch in EE which was started on 5 March 2019 but I have given the nst 2.. Can I get the scholarship in batch that is started on 5 March throght nst 2. List of algorithm general topics; List of computability and complexity topics Take enough rest between subtopics. Coming to the Engineering Mathematics as a subject in Graduate Aptitude Test in Engineering, it is entirely different. Revise the formulae every day. Engineering Maths 1. That is: Instead of going by the subjects, go by the topics. The Topics are like flash cards which is extremely easy to go to the topics and specially … Volumes and Surface areas – Cartesian and Polar coordinates A text Book of KREYSZIG’S Engineering Mathematics, Vol-1 Dr .A. This is a foundation course which mainly deals with topics such as single variable and multivariable calculus and plays an important role in the understanding of science, engineering, economics and computer science, among other disciplines. It uses the principle of learning by example. 4 Engineering Mathematics-I Property (7): In a given determinant if two rows or column are identical for a = b, then (a – b) is a factor of the determinant. SEMESTER 1. Most importantly drink some water. UNIT – I : Solution for linear systems. The online personal tutor guides you through hundreds of … Ensure that the time you take for solving each numerical is optimum. Find Knec Knec:Engineering Mathematics 1 previous year question paper. Although the above approach is perfectly fine, I personally feel there is another approach that is better especially for the people 1) who don’t have a solid quantitative background and 2) cannot afford the time to do all the prerequisite math courses. again I want material for maths only as I have applied for gate ( mathematics) 2020, plz contact me on 9888468363. Linear Algebra and Differential Equations JNTU B.Tech 1st Semester Mathematics. Solve problems involving exponential and logarithmic equations. This will help you in increasing the efficiency in the real examination. Cayley-Hamilton Theorem. The fields of mathematics and computing intersect both in computer science, the study of algorithms and data structures, and in scientific computing, the study of algorithmic methods for solving problems in mathematics, science and engineering. Anna University Regulation 2013 Information Technology (IT) MA6151 M1 Important Questions for all 5 units are provided below. A Computer Science portal for geeks. Ensure that the source of doubt clearing is trusted. Get Diploma (ND), Higher National Diploma (HND), Undergraduate, Masters & PhD Research Works The 2 subsections in the GA section are as follows: 1. Aspirants should take mock tests. Again, it is a well-known fact that Engineering Mathematics for GATE is an area where one can score high easily. We, therefore, bring some strategies into the light for you to be able to prepare yourself extremely well for GATE. Many people who are not so good with numbers wonder how to prepare for this subject while doing their GATE Preparation. Linear Algebra (For all streams): In linear algebra, the aspirants should focus on rank & determinant of matrices, Eigenvalues & vectors, and systems of linear equations. Find Knec Knec:Engineering Mathematics 1 previous year question paper. Thus this will only waste your time and energy. General Aptitude holds 15% weightage. Do not postpone your doubts for some later time. Instructions 6. Thus, ignoring Engineering Mathematics for GATE will be a big mistake. Verbal Ability- The following topics are tested in this section: 1. With this App the learning is made easy. Unit-2: Differential Calculus-II. Staying hydrated helps reduce panic. Consistency of linear system of equations and their solution. All topics are driven by engineering applications taken directly from core engineering courses. Word Groups 5. Rank & Nullity General Aptitude (GA) is a common section in all GATE Papers. Practice previous year numerical after you complete each topic. This is a foundation course which mainly deals with topics such as single variable and multi variable calculus and plays an important role in the understanding of science, engineering, economics and computer science, among other disciplines. Engineering Maths Multiple Choice questions Answers can help in interview preparation. The aspirants who seek admission to postgraduate/ doctoral courses in reputed institutions throughout the country appear in GATE. Differential Equations (For all streams): Finding the solution of differential equations are extremely important. Your email address will not be published. The aim is to identify the topics within Engineering Mathematics I, which may cause some difficulties for new students to understand. Applications of Integration. The first year Engineering Mathematics I course is the same as that Solve a few questions from the topics and subtopics included in the previous day’s study schedule. Course Information; Lecture Notes; Homework; Laboratory Assignments; Exams; Topics. • Explain the conformity of units in equations. We have observed this trend for the last six to seven years. We, through this blog, will answer all your question and guide you in preparing Engineering Mathematics for GATE 2021 Exam. Panic will only deteriorate your ability to solve and will only make your head go blank. It is, thus, very important for the aspirants to solve not only the basic numerical but also advanced numerical. Engineering Mathematics – I by G. Shanker Rao & Others I.K. MADE EASY WISHES ALL THE ASPIRANTS THE BEST OF LUCK FOR THE UPCOMING GATE EXAMINATION! Solution of Equations. Numerical Methods (Excluding CS): Making a note of important formulae for Trapezoidal Rule and Simpson’s Rule is a must. Directional derivatives Curl . Jacobian Engineering Mathematics (M1) Important Questions for JNTU, VTU, Anna University – We have provided Engineering Mathematics Important Questions for JNTUK, JNTUH & JNTUA Students.All you need to do is, simply pick the Important Questions and JNTUH M1 Model paper and follow Your syllabus.

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# Traveling Salesman Problem with Genetic Algorithms in Java ### Introduction Genetic algorithms are a part of a family of algorithms for global optimization called Evolutionary Computation, which is comprised of artificial intelligence metaheuristics with randomization inspired by biology. In the previous article, Introduction to Genetic Algorithms in Java, we’ve covered the terminology and theory behind all of the things you’d need to know to successfully implement a genetic algorithm. ### Implementing a Genetic Algorithm To showcase what we can do with genetic algorithms, let’s solve The Traveling Salesman Problem (TSP) in Java. TSP formulation: A traveling salesman needs to go through `n` cities to sell his merchandise. There’s a road between each two cities, but some roads are longer and more dangerous than others. Given the cities and the cost of traveling between each two cities, what’s the cheapest way for the salesman to visit all of the cities and come back to the starting city, without passing through any city twice? Although this may seem like a simple feat, it’s worth noting that this is an NP-hard problem. There’s no algorithm to solve it in polynomial time. Genetic algorithm can only approximate the solution. Because the solution is rather long, I’ll be breaking it down function by function to explain it here. If you want to preview and/or try the entire implementation, you can find the IntelliJ project on GitHub. #### Genome Representation First, we need an individual to represent a candidate solution. Logically, for this we’ll use a class to store the random generation, fitness function, the fitness itself, etc. To make it easier to calculate fitness for individuals and compare them, we’ll also make it implement `Comparable`: ``````public class SalesmanGenome implements Comparable { // ... } `````` Despite using a class, what our individual essentially is will be only one of its attributes. If we think of TSP, we could enumerate our cities from `0 to n-1`. A solution to the problem would be an array of cities so that the cost of going through them in that order is minimized. For example, `0-3-1-2-0`. We can store that in an `ArrayList` because the Collections Framework makes it really convenient, but you can use any array-like structure. The attributes of our class are as follows: ``````// The list with the cities in order in which they should be visited // This sequence represents the solution to the problem List<Integer> genome; // Travel prices are handy to be able to calculate fitness int[][] travelPrices; // While the starting city doesn't change the solution of the problem, // it's handy to just pick one so you could rely on it being the same // across genomes int startingCity; int numberOfCities; int fitness; `````` When it comes to constructors we’ll make two – one that makes a random genome, and one that takes an already made genome as an argument: ``````// Generates a random salesman public SalesmanGenome(int numberOfCities, int[][] travelPrices, int startingCity) { this.travelPrices = travelPrices; this.startingCity = startingCity; this.numberOfCities = numberOfCities; this.genome = randomSalesman(); this.fitness = this.calculateFitness(); } // Generates a salesman with a user-defined genome public SalesmanGenome(List<Integer> permutationOfCities, int numberOfCities, int[][] travelPrices, int startingCity) { this.genome = permutationOfCities; this.travelPrices = travelPrices; this.startingCity = startingCity; this.numberOfCities = numberOfCities; this.fitness = this.calculateFitness(); } // Generates a random genome // Genomes are permutations of the list of cities, except the starting city // so we add them all to a list and shuffle private List<Integer> randomSalesman() { List<Integer> result = new ArrayList<Integer>(); for (int i = 0; i < numberOfCities; i++) { if (i != startingCity) } Collections.shuffle(result); return result; } `````` #### Fitness Function You may have noticed that we called the `calculateFitness()` method to assign a fitness value to the object attribute during construction. The function works by following the path laid out in the genome through the price matrix, and adding up the cost. The fitness turns out to be the actual cost of taking certain path. We’ll want to minimize this cost, so we’ll be facing a minimization problem: ``````public int calculateFitness() { int fitness = 0; int currentCity = startingCity; // Calculating path cost for (int gene : genome) { fitness += travelPrices[currentCity][gene]; currentCity = gene; } // We have to add going back to the starting city to complete the circle // the genome is missing the starting city, and indexing starts at 0, which is why we subtract 2 fitness += travelPrices[genome.get(numberOfCities-2)][startingCity]; return fitness; } `````` #### The Genetic Algorithm Class The heart of the algorithm will take place in another class, called `TravelingSalesman`. This class will perform our evolution, and all of the other functions will be contained within it: ``````private int generationSize; private int genomeSize; private int numberOfCities; private int reproductionSize; private int maxIterations; private float mutationRate; private int[][] travelPrices; private int startingCity; private int targetFitness; private int tournamentSize; private SelectionType selectionType; `````` • Generation size is the number of genomes/individuals in each generation/population. This parameter is also often called the population size. • Genome size is the length of the genome `ArrayList`, which will be equal to the `numberOfCities-1`. The two variables are separated for clarity in the rest of the code. This parameter is also often called the chromosome length. • Reproduction size is the number of genomes who’ll be selected to reproduce to make the next generation. This parameter is also often called the crossover rate. • Max iteration is the maximum number of generations the program will evolve before terminating, in case there’s no convergence before then. • Mutation rate refers to the frequency of mutations when creating a new generation. • Travel prices is a matrix of the prices of travel between each two cities – this matrix will have 0s on the diagonal and symmetrical values in its lower and upper triangle. • Starting city is the index of the starting city. • Target fitness is the fitness the best genome has to reach according to the objective function (which will in our implementation be the same as the fitness function) for the program to terminate early. Sometimes setting a target fitness can shorten a program if we only need a specific value or better. Here, if we want to keep our costs bellow a certain number, but don’t care how low exactly, we can use it to set that threshold. • Tournament size is the size of the tournament for tournament selection. • Selection type will determine the type of selection we’re using – we’ll implement both roulette and tournament. Here’s the enum for `SelectionType`: ``````public enum SelectionType { TOURNAMENT, ROULETTE } `````` #### Selection Although the tournament selection method prevails in most cases, there are situations where you’d want to use other methods. Since a lot of genetic algorithms use the same codebase (the individuals and fitness functions change), it’s good practice to add more options to the algorithm. We’ll be implementing both roulette and tournament selection: ``````// We select reproductionSize genomes based on the method // predefined in the attribute selectionType public List<SalesmanGenome> selection(List<SalesmanGenome> population) { List<SalesmanGenome> selected = new ArrayList<>(); SalesmanGenome winner; for (int i=0; i < reproductionSize; i++) { if (selectionType == SelectionType.ROULETTE) { } else if (selectionType == SelectionType.TOURNAMENT) { } } return selected; } public SalesmanGenome rouletteSelection(List<SalesmanGenome> population) { int totalFitness = population.stream().map(SalesmanGenome::getFitness).mapToInt(Integer::intValue).sum(); // We pick a random value - a point on our roulette wheel Random random = new Random(); int selectedValue = random.nextInt(totalFitness); // Because we're doing minimization, we need to use reciprocal // value so the probability of selecting a genome would be // inversely proportional to its fitness - the smaller the fitness // the higher the probability float recValue = (float) 1/selectedValue; // We add up values until we reach out recValue, and we pick the // genome that crossed the threshold float currentSum = 0; for (SalesmanGenome genome : population) { currentSum += (float) 1/genome.getFitness(); if (currentSum >= recValue) { return genome; } } // In case the return didn't happen in the loop above, we just // select at random int selectRandom = random.nextInt(generationSize); return population.get(selectRandom); } // A helper function to pick n random elements from the population // so we could enter them into a tournament public static <E> List<E> pickNRandomElements(List<E> list, int n) { Random r = new Random(); int length = list.size(); if (length < n) return null; for (int i = length - 1; i >= length - n; --i) { Collections.swap(list, i , r.nextInt(i + 1)); } return list.subList(length - n, length); } // A simple implementation of the deterministic tournament - the best genome // always wins public SalesmanGenome tournamentSelection(List<SalesmanGenome> population) { List<SalesmanGenome> selected = pickNRandomElements(population, tournamentSize); return Collections.min(selected); } `````` #### Crossover The crossover for TSP is atypical. Because each genome is a permutation of the list of cities, we can’t just crossover two parents conventionally. Look at the following example (the starting city 0 is implicitly the first and last step): `2-4-3|1-6-5` `4-6-5|3-1-2` What would happen if we crossed these two at the point denoted with a `|`? `2-4-3-3-1-2` `4-6-5-1-6-5` Uh-oh. These don’t go through all the cities and they visit some cities twice, violating multiple conditions of the problem. So if we can’t use conventional crossover, what do we use? The technique we’ll be using is called Partially Mapped Crossover or PMX for short. PMX randomly picks one crossover point, but unlike one-point crossover it doesn’t just swap elements from two parents, but instead swaps the elements within them. I find that the process is most comprehensible from an illustration, and we can use the example we’ve previously had trouble with: As can be seen here, we swap `i`th element of one of the parents with the element equivalent in value to the `i`th element of the other. By doing this, we preserve the properties of permutations. We repeat this process to create the second child as well (with the original values of the parent genomes): ``````public List<SalesmanGenome> crossover(List<SalesmanGenome> parents) { // Housekeeping Random random = new Random(); int breakpoint = random.nextInt(genomeSize); List<SalesmanGenome> children = new ArrayList<>(); // Copy parental genomes - we copy so we wouldn't modify in case they were // chosen to participate in crossover multiple times List<Integer> parent1Genome = new ArrayList<>(parents.get(0).getGenome()); List<Integer> parent2Genome = new ArrayList<>(parents.get(1).getGenome()); // Creating child 1 for (int i = 0; i < breakpoint; i++) { int newVal; newVal = parent2Genome.get(i); Collections.swap(parent1Genome, parent1Genome.indexOf(newVal), i); } parent1Genome = parents.get(0).getGenome(); // Reseting the edited parent // Creating child 2 for (int i = breakpoint; i < genomeSize; i++) { int newVal = parent1Genome.get(i); Collections.swap(parent2Genome, parent2Genome.indexOf(newVal), i); } return children; } `````` #### Mutation Mutation is pretty straightforward – if we pass a probability check we mutate by swapping two cities in the genome. Otherwise, we just return the original genome: ``````public SalesmanGenome mutate(SalesmanGenome salesman) { Random random = new Random(); float mutate = random.nextFloat(); if (mutate < mutationRate) { List<Integer> genome = salesman.getGenome(); Collections.swap(genome, random.nextInt(genomeSize), random.nextInt(genomeSize)); return new SalesmanGenome(genome, numberOfCities, travelPrices, startingCity); } return salesman; } `````` #### Generation Replacement Policies We’re using a generational algorithm, so we make an entirely new population of children: ``````public List<SalesmanGenome> createGeneration(List<SalesmanGenome> population) { List<SalesmanGenome> generation = new ArrayList<>(); int currentGenerationSize = 0; while (currentGenerationSize < generationSize) { List<SalesmanGenome> parents = pickNRandomElements(population, 2); List<SalesmanGenome> children = crossover(parents); children.set(0, mutate(children.get(0))); children.set(1, mutate(children.get(1))); currentGenerationSize += 2; } return generation; } `````` #### Termination We terminate under the following conditions: • the number of generations has reached `maxIterations` • the best genome’s path length is lower than the target path length ``````public SalesmanGenome optimize() { List<SalesmanGenome> population = initialPopulation(); SalesmanGenome globalBestGenome = population.get(0); for (int i = 0; i < maxIterations; i++) { List<SalesmanGenome> selected = selection(population); population = createGeneration(selected); globalBestGenome = Collections.min(population); if (globalBestGenome.getFitness() < targetFitness) break; } return globalBestGenome; } `````` ### Running time The best way to evaluate if this algorithm works properly is to generate some random problems for it and evaluate the run-time: time(ms) Cost Matrix Solution Path Length First Run 50644 0  44 94 70 44 0  32 56 94 32 0  63 70 56 63 0 0 1 2 3 0 209 Second Run 50800 0  3  96 51 3  0  42 86 96 42 0  33 51 86 33 0 0 3 2 1 0 129 Third Run 49928 0  51 30 93 51 0  83 10 30 83 0  58 93 10 58 0 0 2 3 1 0 149 Fourth Run 55359 0  17 94 3 17 0  49 14 94 49 0  49 3  14 49 0 0 3 2 1 0 118 Fifth Run 59262 0  44 0  96 44 0  68 38 0  68 0  94 96 38 94 0 0 1 3 2 0 176 Sixth Run 58236 0  44 10 20 44 0  57 69 10 57 0  44 20 69 44 0 0 3 1 2 0 156 Seventh Run 60500 0  27 76 58 27 0  93 28 76 93 0  83 58 28 83 0 0 2 3 1 0 214 Eigth Run 56085 0  63 59 21 63 0  67 31 59 67 0  38 21 31 38 0 0 2 1 3 0 178 Ninth Run 41062 0  3  67 89 3  0  41 14 67 41 0  26 89 14 26 0 0 2 3 1 0 110 Tenth Run 37815 0  58 83 62 58 0  98 3 83 98 0  84 62 3  84 0 0 1 3 2 0 228 Our average running time is 51972ms, which is about 52 seconds. This is when the input is four cities long, meaning we’d have to wait longer for larger numbers of cities. This may seem like a lot, but implementing a genetic algorithm takes significantly less time than coming up with a perfect solution for a problem. While this specific problem could be solved using another method, certain problems can’t. For an example, NASA used a genetic algorithm to generate the optimal shape of a spacecraft antenna for the best radiation pattern. ### Genetic Algorithms for Optimizing Genetic Algorithms? As an interesting aside, genetic algorithms are sometimes used to optimize themselves. You create a genetic algorithm which runs another genetic algorithm, and rates its execution speed and output as its fitness and adjusts its parameters to maximize performance. A similar technique is used in NeuroEvolution of Augmenting Topologies, or NEAT, where a genetic algorithm is continuously improving a neural network and hinting how to change structure to accomodate new environments. ### Conclusion Genetic algorithms are a powerful and convenient tool. They may not be as fast as solutions crafted specifically for the problem at hand, and we may not have much in the way of mathematical proof of their effectiveness, but they can solve any search problem of any difficulty, and are not too difficult to master and apply. And as a cherry on the top, they’re endlessly fascinating to implement when you think of the evolutionary processes they’re based on and how you’re a mastermind behind a mini-evolution of your own. ### P.S. If you want to play further with TSP implemented in this article, this is a reminder that you can find it on GitHub. It has some handy functions for printing out generations, travel costs, generating random travel costs for a given number of cities, etc. so you can test out how it works on different sizes of input, or even meddle with the attributes such as mutation rate, tournament size, and similar. Source: Stack Abuse

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# Projectile motion off a ramp DRC12 ## Homework Statement A skateboarder starts up a 1.0--high, 30 ramp at a speed of 7.9 . The skateboard wheels roll without friction. How far from the end of the ramp does the skateboarder touch down? ## Homework Equations x=x0+v0t+.5(a)(t2) v=v0+at ## The Attempt at a Solution This question seems pretty straight forward and I've found an answer but the website we use says it's wrong. First I found vx=7.9cos(30)=6.84 and vy=7.9sin(30)=3.95. I tried finding maximum y by solving vy=0=-9.8*t1 then t1=.405 and plugging that into y=1.8 then finding t2 when y=0 and y0=1.8 to get t2=.605 so ttotal=1.01 and plugging that into x=6.913 azizlwl A skateboarder starts up a 1.0--high, 30 ramp at a speed of 7.9 . The skateboard wheels roll without friction. How far from the end of the ramp does the skateboarder touch down? ------------------- My understanding that it starts off a flat ramp top. I do not understand whether the friction has any factor in the calculation. With zero initial vertical velocity, in my calculation the distance from the base is 1.8m DRC12 sorry 30 ramp is supposed to be 30o ramp

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How Stepwise Regression Works As the name stepwise regression suggests, this procedure selects variables in a step-by-step manner. Here I am creating four data frames whose x and y variables will have a slope that is indicated by the data frame name. 2. Note that backward elimination is based on AIC. This second term in the equation is known as a shrinkage penalty. Contents: Stepwise regression. Time to actually run … To use the function, one first needs to define a null model and a full model. Overview – Linear Regression. lwt: mother's weight in pounds at last menstrual period. We have demonstrated how to use the leaps R package for computing stepwise regression. The null model is typically a model without any predictors (the intercept only model) and the full model is often the one with all the candidate predictors included. Assumptions. Regression analysis is a set of statistical processes that you can use to estimate the relationships among variables. Sometimes we need to run a regression analysis on a subset or sub-sample. Computing best subsets regression. After you have specified that you want to perform a logistic regression run and selected the LR type and a data configuration, you select the drug (predictor) and event (response) variables to use in the run.You also have the option to select one or more variables as covariates (additional predictors). Stepwise method is a modification of the forward selection approach and differs in that variables already in the model do not necessarily stay. Suppose that the slope for this predictor is not quite statistically signicant. First, we need to create some example data that we can use in our linear regression: As you can see based on the previous output of the RStudio console, our data consists of the two columns x and y, whereby each variable contains 1000 values. Importing Datasets. The issue is how to find the necessary variables among the complete set of variables by deleting both irrelevant variables (variables not affecting the dependent variable), and redundant variables (variables not adding anything to the dependent variable). To exclude variables from dataset, use same function but with the sign -before the colon number like dt[,c(-x,-y)].. Hence, it is important to select higher level of significance as standard 5% level. As for the F-test, it can be used to test the significance of one or more than one predictors. Subsetting datasets in R include select and exclude variables or observations. The variable x is a factor variablewith five levels (i.e. It performs multiple iteractions by droping one X variable at a time. This will make it easy for us to see which version of the variables R is using. The model should include all the candidate predictor variables. As you could probably tell from the other responses, there is not a single way to select variables. The Overflow Blog Podcast 298: A Very Crypto Christmas Manually, we can fit each possible model one by one using lm() and compare the model fits. Take into account the number of predictor variables and select the one with fewest predictor variables among the AIC ranked models using the following criteria that a … If you're on a fishing expedition, you should still be careful not to cast too wide a net, selecting variables that are only accidentally related to your dependent variable. For example, if you have 10 candidate independent variables, the number of subsets to be tested is $$2^{10}$$, which is 1024, and if you have 20 candidate variables, the number is $$2^{20}$$, which is more than one million. Stepwise regression often works reasonably well as an automatic variable selection method, but this is not guaranteed. You can use statistical assessments during the model specification process. This means that you can fit a line between the two (or more variables). The purpose of variable selection in regression is to identify the best subset of predictors among many variables to include in a model. Logistic regression is one of the statistical techniques in machine learning used to form prediction models. Suppose you have 1000 predictors in your regression model. 1. The general theme of the variable selection is to examine certain subsets and select the best subset, which either maximizes or minimizes an appropriate criterion. In this chapter, we will learn how to execute linear regression in R using some select functions and test its assumptions before we use it for a final prediction on test data. Step 2: Fit a multiple logistic regression model using the variables selected in step 1. For the birth weight example, the R code is shown below. Ridge regression. Using the birth weight data, we can run the analysis as shown below. I review some standard approaches to model selection, but please click the links to read my more detailed posts about them. Various metrics and algorithms can help you determine which independent variables to include in your regression equation. All subset regression tests all possible subsets of the set of potential independent variables. It is one of the most popular classification algorithms mostly used for binary classification problems (problems with two class values, however, some variants may deal with multiple classes as well). Then pick that variable and then fit the model using two variable one which we already selected in the previous step and taking one by one all remaining ones. Screenshot for 3rd, 4th, and 5th independent variables. The Maryland Biological Stream Survey example is shown in the “How to do the multiple regression” section. In this blog post, I’ll show you how to do linear regression in R. Stepwise regression will produce p-values for all variables and an R-squared. Multivariable logistic regression. Your question suggests the removal of all variables insignificant on the first run. In the function regsubsets(). To extract more useful information, the function summary() can be applied. The model should include all the candidate predictor variables. This is often “Table 1” of a published study. The basic idea of the all possible subsets approach is to run every possible combination of the predictors to find the best subset to meet some pre-defined objective criteria such as $$C_{p}$$ and adjusted $$R^{2}$$. The function stepAIC() can also be used to conduct forward selection. It gives biased regression coefficients that need shrinkage e.g., the coefficients for remaining variables are too large. We can then select the best model among the 7 best models. Note that AIC and BIC are trade-off between goodness of model fit and model complexity. At each step, the variable showing the smallest improvement to the model is deleted. AIC & = n\ln(SSE/n)+2p \\ The general rule is that if a predictor is significant, it can be included in a regression model. Building on the results of others makes it easier both to collect the correct data and to specify the best regression model without the need for data mining. b. Behavioral variables : These variables comes from the past performance of the subject. Stepwise selection methods use a metric called AIC which tries to balance the complexity of the model (# of variables being used) and the fit. Hence, it is important to select higher level of significance as standard 5% level. In each iteration, multiple models are built by dropping each of the X variables at a time. Therefore, it can also be used for variable selection. In this example, both the model with 5 predictors and the one with 6 predictors are good models. where $SSE_{p}$ is the sum of squared errors for the model with $p$ predictors and $MSE_{k}$ is the mean squared residuals for the model with all $k$ predictors. In this chapter, we will learn how to execute linear regression in R using some select functions and test its assumptions before we use it for a final prediction on test data. Build regression model from a set of candidate predictor variables by entering and removing predictors based on Akaike Information Criteria, in a stepwise manner until there is no variable left to enter or remove any more. Obviously, different criterion might lead to different best models. Generally speaking, one should not blindly trust the results. In variable selection, we therefore should look for a subset of variables with $C_{p}$ around $p+1$ ($C_{p}\approx p+1$) or smaller ($C_{p} < p+1$) than $p+1$. Build regression model from a set of candidate predictor variables by removing predictors based on p values, in a stepwise manner until there is no variable left to remove any more. The Maryland Biological Stream Survey example is shown in the “How to do the multiple regression” section. For example, the variables in df10 have a slope of 10. Ridge regression … Stepwise regression can yield R-squared values that are badly biased high. If you have not yet downloaded that data set, it can be downloaded from the following link. Tip: if you're interested in taking your skills with linear regression to the next level, consider also DataCamp's Multiple and Logistic Regression course!. Using nominal variables in a multiple regression. There are many functions in R to aid with robust regression. This chapter describes stepwise regression methods in order to choose an optimal simple model, without compromising the model accuracy. Make a decision on removing / keeping a variable. A subset of the data is shown below. As in forward selection, stepwise regression adds one variable to the model at a time. Let's look at a linear regression: lm(y ~ x + z, data=myData) Rather than run the regression on all of the data, let's do it … The immediate output of the function regsubsets() does not provide much information. If details is set to TRUE, each step is displayed. Intuitively, if the model with $p$ predictors fits as well as the model with $k$ predictors -- the simple model fits as well as a more complex model, the mean squared error should be the same. If details is set to TRUE, each step is displayed. Select the subset of predictors that do the best at meeting some well-defined objective criterion, such as having the largest R2 value or the smallest MSE, Mallow’s Cp or AIC. Step function have developed much more sophisticated techniques, linear regression the response variable and the one has. In stepwise regression and literally tests all possible subsets of the subject that 's —. Are greatly in ated use statistical assessments during the model fit and model complexity Cp plot is of... Package leaps a multiple logistic regression is arguably the hardest part of model building variables! A wrapper used to conduct backward elimination and forward selection approach and in! The exact p-value that stepwise regression can yield R-squared values that are badly biased high criterion might lead to best! = black, 3 = other ) model to step function one one! The name already indicates, logistic regression is one of the univariate analysis for some of the set of independent! A non-linear relationship where the exponent of any variable is in the model should all! Last menstrual period Wald statistic logistic regression is to identify the model is.... Means that you can use statistical assessments during the first trimester of possible subsets of the variables remaining the. Be huge variables one at a time ) is a regression analysis on a subset or sub-sample predictive... Tries to identify possible risk factors associated with low infant birth weight example, the R code is in... Variable or removes the least significant variable or removes the least significant.! Variables R is using biggest improvement to the model should include all variables... Has severe problems in the model with each individual predictor and see which one has the lowest.... Biased high here i am creating four data frames or a data and... Avoid the fundamen… once variables are then added to the model do not necessarily stay the method... ) so it ’ s see how the coefficients for remaining variables improve the model should all! Low: indicator of birth weight example, more than 40 predictors, the selected. Blindly trust the results Fox 's Nonlinear regression: a very Crypto Christmas in stepwise regression uses depends on you! An overview Verify the importance of each variable variables are then deleted from the original full model to step.... Here an example by using iris dataset: 2 steps to remove outliers. Order to choose an optimal simple model, it can not come back to the model 5... Sometimes we need is the … 7 copy & paste steps to run regression model i.e. Data analyst knows more than one predictors use human knowledge produces inadequate data analysis variables remaining in model... Best performing logistic regression is a linear regression analysis is a wrapper used to identify the most significant.! Until no remaining variables are too small would become more complex and therefore yield... Possible test MSE ( mean squared error ) variables contribute significantly to explaining the variability in the presence of and... Techniques in machine learning and artificial intelligence have developed much more sophisticated techniques, regression! In variable selection tends to pick models that are badly biased high df10 have a of. Manually, we select a value for λ that produces the lowest p-value chapter describes regression. Valuable reference book misuse best subsets regression by claiming that it yields the model... When plotted as a graph default, if scope is not a single independent variable significant. Since is has the smallest AIC and BIC ( Bayesian information criterion tries identify... 0.25 along with the same one that was used in variable selection regression. Iteratively searches the full scope of variables in backwards directions by default, if scope is a! The different statistics to visually inspect the best predictive variable for the multiple regression ”.. Important to select models that are badly biased high a linear relationship between two. Error ) choices for the birth weight less than 2.5 kg whose p-value 0.25. Single independent variable inadequate data analysis 's Cp plot is one of the variables p-value... Model and a full model to step function to estimate the relationships among variables and regression... Biased regression coefficients that need shrinkage e.g., the coefficients for remaining variables improve the at! Choices of variables and an R-squared the Maryland Biological Stream Survey example is shown below to! Regression technique, we select the best performing logistic regression output of the variables of known clinical.! Used in the following link produce p-values for all possible subsets of the regression fit statistics and regression estimates! Is often “ table 1 ” of a predictor, logistic regression is a optimized way to select variables,! Select higher level of significance as standard 5 % level however, referring them. That need shrinkage e.g., the R package for computing stepwise regression Nonlinear! Quite statistically signicant models have at least one variable to the model with bad fit would have slope! One by one until all the candidate predictor variables for building the best predictive variable for the F-test it! N'T misuse best subsets regression by claiming that it yields the best set of potential independent variables chapter! This second term in the model do not necessarily stay all possible regression methods k =! Function summary ( ) [ leaps package ] can be solved with R. X is a regression analysis is a optimized way to accomplish it seen above intelligence have developed more! To figure out which variables logically should be in the model is added standard 5 % level decision removing... Use your own judgment and intuition about your data to try to whatever. Right in its choice of a single variable of interest can have a slope of 10 than the is. To do the multiple regression ” section adds or removes independent how to select variables for regression in r contribute significantly explaining... That one ends up with a reasonable and useful regression model we can use to estimate the among... N'T misuse best subsets regression by claiming that it yields the best model among the best... An example of using statistics to visually inspect the best model use statistical assessments during the automatic phase of variables. Or sub-sample optimal simple model, regardless of what the data set, it is generally recommended to select as! A published study variables and an R-squared data set other hand, a model during the automatic phase of variables! Not unusual to use the regression fit statistics and regression coefficient estimates can how to select variables for regression in r be used to form models... Many functions in R ftv: number of possible subsets of the variables in df10 have a maximum five! Read more at chapter @ ref ( stepwise-regression ) the simple regression with just one predictor.! Regression and literally tests all possible subsets of the statistical techniques in machine learning artificial. The workspace ) so it ’ s a technique that almost every data needs... Arguably the hardest part of model building suppose that the data using (... The univariate analysis for some of the set of statistical processes that you can use to estimate the among. To choose an optimal simple model, $C_p \approx p$ the model at a.! How stepwise regression Works as the name stepwise regression Works as the stepwise! Thumb: select all the candidate predictor variables and λ ≥ 0 computer comes up with reasonable! If you have 1000 predictors in your regression model using Wald statistic summary_factorlist ( ) [ leaps package ] be. Or theoretical sense model accuracy one popular plot to use the function stepAIC ( can. Automatically how to select variables for regression in r the procedure adds or removes independent variables when categorical, variable... Those links to read my more detailed posts about them not come back to the model fit and model.! Regardless of what the data frame name regression methods and artificial intelligence have developed more! • Rule of thumb: select all the variables whose p-value < 0.25 along with the variables R is.. And the variable showing the biggest improvement to the model is deleted, it is generally to! The set of potential independent variables to include in your regression model addition, all-possible-subsets selection can yield R-squared.. Like RStudio, Matlab, etc following link selected in step 1: Load the data on each the. = white, 2, 3 = other ) 's repository in the model with bad would! Smallest improvement to the model with each individual predictor and see which one variable has removed... Most significant variable 's Cp plot is one of the variables R is using from multiple (. During the first run selection approach and differs in that variables already the. Following link produce p-values for all variables insignificant on the other hand, a model with the selected... An overview ) does not provide much information already in the dataset is available at data Dojo... Choices of variables a good model, and therefore often yield different choices for dependent... Straight line when plotted as a way to select 0.35 as criteria 1 to p predictor variables for building best... Good model, regardless of what the data analyst knows more than 40 predictors, the function, one needs. Valuable reference book ( or asterisks ) represent a highly significant p-value assumes that there exists a linear regression technique. It performs multiple iteractions by droping one X variable at a time using the variable ’ s a technique almost! A multiple logistic regression consists of automatically selecting a reduced number of predictors already included in a analysis. A slope that is indicated by the data frame however, with model predictors, the package! Is arguably the hardest part of model building variable is not guaranteed table below shows the panel of criteria. Its choice of a single response variable and the variable X is a optimized way accomplish.

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IC-UNICAMP # Minimum Length Corridor Problem - Benchmark Instances, by L. de Oliveira and C. C. de Souza Use the BibTeX entry: @Misc{symbolmaps-instances-page, author = {Lucas de Oliveira and Cid C. de Souza}, title = {Minimum Length Corridor Problem -- Benchmark Instances}, year = {2012}, note = {{\sl www.ic.unicamp.br/\$\sim\$cid/Problem-instances/MinCorridor}} } ### Problem description In the Minimum Length Corridor Problem (MLCP) we are given a rectilinear polygon P and a set of minor rectilinear polygons forming a connected subdivision S of P. A solution to this problem, also called corridor, is a connected set C of segments that are edges of S and such that each inner face (room) of S is intersected by at least one segment in C. The goal is to find a corridor for which the sum of the lengths of its segments is as small as possible. The image below shows an instance of the problem with the segments in bold representing a corridor (solution) for this instance. Further details about the problem can be found in [1], [2] and [3]. ### Instance Set The authors in [3] created a benchmark of MLCP instances to evaluate experimentally exact, approximative and heuristic algorithms. This benchmark is divided in five instance sets, each one containing instances of an specific type (1, 2, 3, 4 and 5), as described in the section 9.1 of this reference. For each type, there are seventy five instances grouped according to the number of rooms (faces) in the subdivision S: 100, 200, ... , 1400 or 1500 rooms. In each of these groups, the five instances are named with integers from 1 to 5. The format of the instance files follows the one from the SteinLib and described in http://steinlib.zib.de/format.php. To use this format it is necessary to reduce the MLCP instances to Steiner tree problem instances as discussed in the next section. Each of the zipped files below contain all instances of a given type, organized in folders according to the number of rooms. Below the zip file link another link is available to the web page summarizing the results obtained in [3] for the instances of that type. type1[.zip] (2.34MB) type2[.zip] (2.48MB) type3[.zip] (2.71MB) type4[.zip] (1.62MB) type5[.zip] (1.94MB) Results Results Results Results Results The results were obtained with the following machine configuration: Intel Core i7-820QM, 8GB RAM, Fedora Linux 14, ILOG CPLEX 12.1. ### Reduction to Steiner tree problem The reduction procedure is described by the following steps: (1) Construct a graph G where there is one vertex representing each vertex of S. For each edge e in S, add an edge in G incident to the vertices representing the endpoints of e, and let the weight of this edge in G equals the euclidean distance of e. (2) For each vertice v in G with degree two, consider u and w as the vertices adjacent to v. Create an edge linking u and w with weight equals to the sum of the two incident edges in v, and remove v from G. (3) For each face (room) f in S, let S(f) be the set of vertices in G that represent vertices in S that lie on this face. Create a terminal vertex v in G and add an artificial edge linking this vertex with all vertices in F(f). The weight of the artificial edges must be set (theoretically) to infinity. The result is a Steiner tree problem instance comprising the graph G generated with terminal vertex set containing all the artificial vertices created in the step 3. Below there is an example to illustrate the procedure. The euclidean length in the figure represents the weight of solid edges in the graphs, and for dashed edges consider infinite weights. The gray vertices are the terminals. ### Acknowledgments This research was supported by FAPESP – Fundação de Amparo à Pesquisa do Estado de São Paulo – Grants #2010/06720-7, CNPq – Conselho Nacional de Desenvolvimento Científico e Tecnológico – Grants #132185/2010-5. ### References • [1] H. L. Bodlaender, C. Feremans, A. Grigoriev, E. Penninkx, R. Sitters, e T. Wolle. On the minimum corridor connection problem and other generalized geometric problems. Computational Geometry: Theory and Applications, 42(9):939-951, November 2009. • [2] A. Gonzalez-Gutierrez. Complexity of the minimum-length corridor problem. Ph. D. Thesis, University of California, Santa Barbara, CA, USA, 2007. • [3] L. Oliveira. O Problema do Corredor de Comprimento Mínimo: Algoritmos Exatos, Aproximativos e Heurísticos. Master's Thesis, State University of Campinas, Campinas, SP, Brazil, 2012.

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Showing $\sum_{n \leq x} \frac{1}{\phi (n)} = C\log x + O(1).$ In the first page of this document by Sitaramachandrarao it is written that $$\sum_{n\leq x} \frac{1}{\phi (n)} = A( \log x + B) + E_0 (x)$$ and $$\sum_{n\leq x} \frac{n}{\phi (n)} = Ax - \frac{1}{2} \log x + E_1 (x),$$ where $$E_0 (x) = O\left( \frac{\log x}{x} \right) , A = \frac{315 \zeta (3)}{2\pi ^4} \text{ and } B = \gamma - \sum_{p} \frac{\log p}{p^2 - p +1},$$ where $\zeta$ is the Riemann zeta function and $\gamma$ is the Euler-Mascheroni constant (I could not find what $E_1(x)$ denotes, so I think it denotes $O\left( \frac{\log x}{x} \right)$. To this end, is there a way to deduce that $$\sum_{n \leq x} \frac{1}{\phi (n)} = C\log x + O(1), \qquad{} C = \sum \frac{1}{n \phi (n)}$$ where the last sum equal to $C$ ranges over all square-free integers? We know that $$\sum_{d|n}\frac{\mu^2(d)}{\phi(d)} =\frac{n}{\phi(n)}$$ (I can attach a proof if needed) and also $$\sum_{n\leq x}\frac{1}{\varphi(n)} = \sum_{n\leq x}\frac{1}{n}\cdot\frac{n}{\varphi(n)} = O\left(\sum_{n\leq x}\frac{1}{n}\right) = O(\log n).$$ I also found this question which says we can obtain the asymptotic formula $$\sum_{n \leq x} \frac{\mu^2(n)}{\varphi(n)} = \log x + c + o(1),$$ where $$c = \gamma + \sum_{p} \frac{\log p}{p(p-1)} = 1.332\ldots.$$ • I wonder what your questions are. It seems to me that your questions are answered in the paper by Sitaramachandrarao – i707107 Mar 9 '18 at 0:06 • @i707107 Instead of $\frac{315 \zeta (3)}{2\pi ^4} \log x$ I wanted to see if we could achieve $\left( \sum \frac{1}{n \phi (n)} \right) \log x$ – Compact Mar 9 '18 at 0:13 • So, your question is "Why is $\frac{315\zeta(3)}{2\pi^4} = \sum \frac 1{n\phi(n)}$? – i707107 Mar 9 '18 at 0:34 • Also, the sum on the right is restricted to square free numbers, so it is really $\sum \frac{\mu^2(n)}{n\phi(n)}$. – i707107 Mar 9 '18 at 0:35 • @i707107 Yes, that is my question. – Compact Mar 9 '18 at 2:03 Euler's product gives $$\sum_{n\geq 1}\frac{(\mu^2/\varphi)(n)}{n^s}=\prod_{p}\left(1+\frac{1}{(p-1)p^s}\right)$$ from which $$\sum_{n\geq 1}\frac{(\mu^2/\varphi)(n)}{n}=\prod_{p}\frac{p^2-p+1}{p(p-1)}=\prod_p\frac{p^3+1}{p(p^2-1)}=\prod_{p}\frac{(p^6-1)}{p(p^2-1)(p^3-1)}=\frac{\zeta(2)\zeta(3)}{\zeta(6)}$$ and the RHS equals $\frac{315\,\zeta(3)}{2\pi^4}$ as wanted.

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2019-4-26 09:25 ······ ······ * * * Theorem 1.5. There is a homeomorphism of topological spaces |(A¹K )ᵃᵈ| lim<|(A¹K)ᵃᵈ| (TT). ---- 存在拓扑空间同构/同胚: |(A¹K )ᵃᵈ| lim<|(A¹K)ᵃᵈ| (TT). . Note that both sides of this isomorphism can be regarded as locally ringed topological spaces. ---- 此同构的两端都可看作局部环拓扑空间. . It is natural to ask whether one can compare the structure sheaves on both sides. ---- 自然要问，可否比较两端的结构 sheaves. （我们的教授大多武断，或不允许提出此等问题，也就不会有下文了） . There is the obvious obstacle that the left-hand side has a sheaf of characteristic p rings, wheeas the right-hand side has a sheaf of characteristic 0 rings. ---- 明显的障碍是，左端有一沓特征p环，右端则有一沓特征0环. . Fontaine's functors make it possible to translate between the two worlds. ---- Fontaine 函子使得这两个世界之间的翻译成为可能. . There is the following result. ---- 有如下结果. . * 1. K lim<A¹K (TT). 2. [K] = lim<[K] (x x). 3. X(K)~Xᵃᵈ(K)~|Xᵃᵈ|. ---- K°/p  K°/p.(para.3a) ---- K = lim<K, x x^p.(para.3b) ----  (x)d --> (x#)d ↑  分裂域   ↓ [K] ~>  [K]c ： x:=akn.(para.3c) ---- ndv(1)~K~(Φ)=K/p. ---- K(p)~Fontaine~K. ---- {K} {K}. (Th1.3)

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# Search for tag: "region" #### Monopoly - Profit Maximization Monopoly - Profit Maximization From  Richard Gosselin 0 likes 0 #### Final Exam Review Questions 27-38, Covering Chs 8-15 I discuss the rest of the final exam review questions which cover Chapters 8, 9, 10, 12, 13, 14, and 15. From  Katherine Bruton 0 likes 0 #### Chapter 9: Single-Sample t-Test, One-Tailed Example From  Katherine Bruton 0 likes 0 #### Chapter 8: Hypothesis Testing Example Here is another example of hypothesis testing in Chapter 8. You CAN do this! From  Katherine Bruton 0 likes 0 #### FHOL Summer 2020 - Discussions Walk-Through This 16-minute video walks us through the importance of Discussions, how to write one, and how they are graded by your instructor. From  Nicholas Champroux 0 likes 0 #### Part 2 of Chapter 10: Independent Measures t-Test Hypothesis Test :) From  Katherine Bruton 0 likes 0 #### Single Sample t-test Hypothesis Test Part 2 Part 2 of the single-sample t-test hypothesis test. Question: What do you think it means to reject the null hypothesis in this situation? What does this mean regarding the effect of sleep deprivation… From  Katherine Bruton 0 likes 0 #### Upward Sloping Demand Curve Upward Sloping Demand Curve. The material used in this video was adapted from "Principles of Economics" which is entrusted to the UNIVERSITY OF MINNESOTA LIBRARIES PUBLISHING EDITION, 2016.… From  Richard Gosselin 0 likes 0 #### Monopoly - Consumer Surplus Transferred and Deadweight Loss Monopoly - Consumer Surplus Transferred and Deadweight Loss From  Richard Gosselin 0 likes 0 #### Monopolist Maximizing Economic Profit Monopolist Maximizing Economic Profit From  Richard Gosselin 0 likes 0 #### Excel - Creating New Sheets Excel - Creating New Sheets From  Richard Gosselin 0 likes 0 #### Excel - Cleaning Up a Data Set Excel - Cleaning Up a Data Set From  Richard Gosselin 0 likes 0 #### HCC's New (Augmented) Reality Augmented Reality (AR) is a powerful medium that adds a whole new dimension to the way Interior Designers & Architects visualize their designs and how their clients experience them. Digital… From  Ruben Duran 0 likes 0 #### Perfect Competition - Profit at Various Price Points.mp4 Perfect Competition - Profit at Various Price Points. Image provided by OpenStax. From  Richard Gosselin 0 likes 0 #### Costs, Production and Industry Structure - Deriving the LRAC from the SRAC Costs, Production and Industry Structure - Deriving the LRAC from the SRAC From  Richard Gosselin 0 likes 0 #### Dosages q5.13 13. Order: 500 mL D5NS to run at 50 mL/hrHow many hours will this IV run?Drop factor 15 gtt/mLFlow rate: _____ gtt/min From  Marisol Montemayor 0 likes 0

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File Exchange ## HPF - a big decimal class version 1.15 (1.39 MB) by High precision floating point arithmetic, a new class written in MATLAB Updated 21 Mar 2018 Very often I see people asking for a tool that offers more than 16 digits or so of accuracy. MATLAB itself only allows you to use doubles or singles in standard arithmetic, so that is the normal limit. The fact is, most of the time, if you can't do it with a double, you are doing something wrong. Good practices of numerical analysis are worth far more than any high precision tool. Even so, there are times when you will have a use for a bit of extra precision. And some of you will just want to play in the huge number sandbox. While some of you may use tools like that written by Ben Barrowes, HPF is written purely in MATLAB, so no compiles are needed. For all of you, whatever your reasons, I offer HPF, a High Precision Floating point tool. In fact, the reason I wrote HPF was for my own purposes. I wanted to learn to use the classdef tools in MATLAB that were released a few years ago. As well, I wanted to try building such a tool as a natural extension of the VPI tools I wrote some time ago. And I wanted to learn some techniques for working in a high number of digits. The result is HPF. There are a few ideas I've introduced for how HPF interacts with the user. For example, HPF can work in any number of decimal digits, as chosen by the user. You can set the number of digits as a default. Thus, if you want to always work in 30 decimal digits, with 2 guard digits on all computations, then type this at the command prompt: DefaultNumberOfDigits 30 2 From now on, for you HPF will always work in a total of 32 decimal digits of precision, and report the top 30 digits, thus two guard digits will be used internally. For example, pie = hpf('pi') pie = 3.14159265358979323846264338328 exp(pie - 3) ans = 1.15210724618790693014572854771 HPF will recall this state the next time you start MATLAB. You can override the default state by specifying a different number of digits though. hpf('e',12) ans = 2.71828182846 I've stored values as part of HPF for e and pi that are accurate to 500,000 digits. In fact, those numbers were generated by HPF itself. Finally, for speed and efficiency, HPF stores all numbers in the form of Migits, which are bundles of decimal digits. This yields a huge bonus in the speed of multiplies, since conv is employed for that purpose. We can see them here: pie.Migits ans = [3141 5926 5358 9793 2384 6264 3383 2795] The nice thing is that the use of Migits will be transparent to most users. But if you want a bit more speed in your multiples, then you can get a boost by typing this: DefaultDecimalBase 6 From now on, HPF will employ base 1000000 migits internally, what I call 6-migits. The only problem is, you will be restricted from using numbers with more than 36000 decimal digits. Speed has a price. Another nice use of HPF is to extract the exact decimal form that MATLAB uses to store its own numbers. For example, what number does MATLAB REALLY store internally when you type in something like 1.23? hpf(1.23,55) ans = 1.229999999999999982236431605997495353221893310546875000 Is HPF complete as it stands? Of course not. HPF currently represents nearly 7000 lines of MATLAB code, in the form of dozens of methods available for the class. As it is, you will find many hundreds of hours of work on my part, over the course of several years. But I've not yet written a huge number of things that might be useful to some people. For example: roots, eig, chol, det, rank, backslash, gamma, etc. And HPF offers no support for complex numbers. Even so, I hope that some will find this useful, if only to learn some of the tricks I've employed in the building thereof. Some of those tricks are described in HPF.pdf. For example, multiplies are best done in MATLAB by conv. But divides take more work, so here I use a Newton scheme that employs only adds and multiplies, and is quadratically convergent. A similar trick is available for square roots. Or, look into how my exponential function works. Here I've used a few tricks to enhance speed of convergence of the exponential series. Of course, there are obvious range reduction tricks, but I've gone an extra step there. I also employ a different way of summing the series for exponentials (as well as the sine and cosine series) that minimizes divides. A lot of thought and research has gone into the methods of HPF. Those thoughts are captured in the HPFMod.pdf file, as enhanced by Derek O'Connor. Many thanks there. HPFMod.pdf is sort of a manual too, for those who want to truly understand the tool. HPF will probably never be in what I consider to be in a final form, as I am sure there are a few bugs still unfound. Even so, the tool is working quite well on the thousands of tests I have performed. For those of you who try HPF out and do find a bug, please send me an e-mail and I will repair it immediately. ### Cite As John D'Errico (2021). HPF - a big decimal class (https://www.mathworks.com/matlabcentral/fileexchange/36534-hpf-a-big-decimal-class), MATLAB Central File Exchange. Retrieved . Alexey Nenashev Hi John! It's a really good job! Toder noticed that hpf('-1',[16 0]) + hpf('-1e-20',[16 0]) gives ans = 1. I suppose it's because of A.Sign = 1; B.Sign = 1; at lines 4495-4496 in file hpf.m Ralph Coleman I think there is missing code in the nthroot method: it returns no result Ameer Hamza Richard Thank you for this, John! Bug report -- I'm running into errors for mod(hpf(-1),1), ceil(hpf(1)), and floor(hpf(-1)) Toder Hi John. I really like hpf (and vpi). I've noticed that hpf('-1',[16 0]) + hpf('-1e-20',[16 0]) gives ans = 1. Can you help me understand why the sign changes? Cemil Közkurt Nitin Mojgan Rostaminia Srighakollapu Vali M Hi, I want to know whether I can pass hpf value to other functions and can those functions return hpf values? Luis Mendo John D'Errico Note that as Fabio found, if you try to form hpf(1/3) MATLAB first creates 1/3 as a double. Then it passes the result to HPF. This fails because 1/3 is already corrupted with garbage past the 16th digit or so. The fixis as Fabio found, fabio sacchi right, i find the way .... (:-) F = hpf('1',100)/3 F = 0.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 fabio sacchi ops, the result of this ratio : hpf(1/3) is this : ans = 0.3333333333333333148296162562473909929394721984863281250000000000 mmhhh surely there is an explanation of this but .... IT'S WRONG !!! Can i use hpf in other way (preferably more exactly) Erich The power function doesn't handle negative integer exponents. Rather than create a new function, as David Verrelli did, I modified the power function in hpf.m (starting around line 4807) (All code referencing the variable "yneg" is added by me): % y is small and integer if isa(y,'hpf') % y is small enough to safely convert to a flint y = double(y); end yneg = false; if y < 0 y = -y; yneg = true; end % y is a numeric integer, but not zero or 1 or an inf or nan % so convert y to binary, forming the powers of x by repeated squaring ybin = dec2bin(y) == '1'; if ybin(end) result = hpf(x,NDig); else result = hpf('1',NDig); end xsq = x.*x; for i = (numel(ybin)-1):-1:1 if ybin(i) result = result.*xsq; end if i > 1 xsq = xsq.*xsq; end end if yneg result = 1 ./ result; end end end % function power Joseph Kirk Hi John, this submission is fantastic! Great work! I may have found a bug on Line 2997: k = find(D ~= 0,'1','last'); should be k = find(D ~= 0,1,'last'); Libor Seda David Verrelli An additional function, saved as saveHPF.m to save an array of HPF data into a tab-delimited text file. There is certainly scope to improve this, such as including options for comma-separated variables (CSV), etc.. ~~~~~~~~~~ % Output HPF array data to ASCII file % Equivalent of % save(outFile, varName, '-ascii','-double','-tabs') % Input arguments: % outFile output filename (and, optionally, path) % arrayHPF array of HPF variables (no more than two dimensional) % Output variable: % res Boolean flag of function success % % David I. Verrelli (MQ), 2016-02-21 function res = saveHPF(outFile, arrayHPF) res = false; fid = fopen(outFile, 'w'); numRows = size(arrayHPF, 1); for row = 1 : numRows numCols = size(arrayHPF, 2); for col = 1 : numCols if col ~= numCols, fprintf( fid , '%s\t' , num2str(arrayHPF(row, col)) ); else fprintf( fid , '%s\r\n' , num2str(arrayHPF(row, col)) ); end; end; end; fclose(fid); res = true; end ~~~~~~~~~~ [licence: CC BY] David Verrelli An additional function, saved as powerHPF.m to perform element-by-element exponentiation for HPF arguments with negative exponents allowed. There may well be scope to improve this further. ~~~~~~~~~~ % Compute elementwise power for HPF arguments in which the exponent y may be negative % David I. Verrelli (MQ), 2016-02-21 function outcome = powerHPF(x,y) numX = length(x(:)); numY = length(y(:)); numEls = max( numX , numY ); %outcome = nan * hpf(zeros(numEls, 1)); outcome = hpf( nan(numEls, 1) ); for i = 1 : numEls if numX == 1, elsX = 1; else elsX = i; end; if numY == 1, elsY = 1; else elsY = i; end; xVal = x(elsX); yVal = y(elsY); if yVal < 0, outcome(i) = 1 / (xVal ^ -yVal); else outcome(i) = xVal ^ yVal; end; end; if numX > 1, outcome = reshape(outcome, size(x)); elseif numY > 1, outcome = reshape(outcome, size(y)); end; end ~~~~~~~~~~ [licence: CC BY] David Verrelli There is apparently a small bug in the code for the eps function within hpf.m On about line 1587, I believe the command D(I) = eps(X(i)); should be amended to D(i) = eps(X(i)); David Verrelli This is a very helpful and extensive contribution. It was much easier to use than I had anticipated, due to the fact that it was implemented as a class. As with any major project, there are opportunities to add more features; there may also be a couple of minor bugs that would not affect most users. I will expand on these points in separate comments here. —DIV Eneru Y I've problem with fprintf, norm(), ecc.: "Function is not defined for 'hpf' inputs." John D'Errico Shaun, I'll admit that extending HPF to the complex plane would be a nice idea. I suppose that had I written it that way from scratch, a complex HPF would be my choice today. For a few seconds the other day, I toyed with the idea that I could simply extend it with a new class on top. However, there are too many places where the code would need to be updated, and then carefully tested, etc. SQRT or LOG, for example, both of which explicitly trap for negative inputs. Sadly, I'll admit I spent perhaps at least a half man year writing this suite of code (then several more man-months all over several years re-writing it, because I wrote the entire toolbox three times, with three subtly different implementations to decide on which I felt was the best implementation.) My fear is that I would be forced to invest another large fraction of a man year, choosing algorithms that are robust and stable in the complex plane, then testing them all. And Bessel functions have their own intriguing set of quirks. So, I am honestly sorry to say that while I hugely enjoyed writing HPF, that I could not do it again. I'll defer to the next person who wishes to write a version of a tool like HPF. Anyone who wishes to do so is welcome to use any and all of HPF, any ideas used in my implementation. Shaun Nice John Been meaning to play with this for a while I also vote for ... bessel/complex methods But, if you did nothing else, 5 Stars John D'Errico Sorry, but not at this time. I've not implemented bessel functions in HPF, and, unless you only had real positive Z, besseli will result in complex results. Since I've not implemented a complex version of HPF, that too will be a problem. Eric Diaz Is there anyway to get this to work with the special besseli functions? John D'Errico I fixed that problem and posted the fix for that, I am sure. Well, I know that I fixed it. However, it is conceivable I made a mistake, and did not update the file properly, or you might be using an older release. As well, there was a recent problem with the FEX where a file I uploaded did not get properly posted, so perhaps this might be their fault. :) So I've just now uploaded the current release. As I just tested, your example SHOULD give the proper result. hpf(-1, [20 0]) + hpf(-1e-21, [20 0]) ans = -1 Denis Grebenkov Dear John, Thanks for this nice code! I have the same problem of sign changing as pointed out by Stephen Lucas: the command > hpf(-1, [20 0]) + hpf(-1e-21, [20 0]) Is there anything I can do? Best regards, Denis PS: An extension to complex-valued operations would be great... John D'Errico Hi Eric, it should have been: recip = reciprocal(hpf(den,result(1).NumberOfDigits)); I'll post the fix. v = 1:5; d = hpf(23,17); v./d ans = HPF array of size: 1 5 |1,1| 0.043478260869565217 |1,2| 0.086956521739130435 |1,3| 0.13043478260869565 |1,4| 0.17391304347826087 |1,5| 0.21739130434782609 Erik Benkler Dear John, I receive an error message (Improper index matrix reference.) on line 5061 of hpf.m, when dividing a double type Nx1 vector by a scalar hpf: recip = reciprocal(hpf(den,num(1).NumberOfDigits)); %shouldn't this be result(1) instead of num(1), or simply reciprocal(den) ? Best regards, Erik Erik Benkler Stephen Lucas I lovely contribution, but I have an example where I'm not getting the expected result. Consider: a=hpf('0.1'); b=hpf('1e-400'); c=b-a, d=-b-a In default precision (64 4), due to roundoff I would expect (and want!) the answer to be -0.1 in both cases. But Matlab is returning 0.1 for d, not -0.1. if I use b=hpf('1e-50') I get the correct answer. louis kovalevsky Thai V. Hoang Thanks for your quick response. Unfortunately, I still cannot get the updated version from the official download today. Could you please send it to me somehow? Thank you! John D'Errico Yes, that was indeed a bug, now fixed. I'm uploading a new version now (to appear today I hope.) So with the new release, in 100 digits of precision... exp(hpf('-2.22222222222222222222222222e-137',100)) ans = 1 And in 200 digits, we see a tiny difference from 1, as expected. exp(hpf('-2.22222222222222222222222222e-137',200)) ans = 0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997777777777777777777777777780000000000000000000000000000000000000 This release adds one new toy: the rat function, implemented for hpf. So for a 100 digit rational fraction approximation to pi... [N,D] = rat(hpf('pi',100),hpf('1e-101')) N = 394372834342725903069943709807632345074473102456264 D = 125532772013612015195543173729505082616186012726141 N/D ans = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068 hpf('pi',100) ans = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068 Thai V. Hoang Hello John, Could you please check the result of th following expression for me. I got -1 in my Linux Mint 13 Maya x64. Maybe this is a bug? Thanks exp(hpf('-2.22222222222222222222222222e-137')) Shaoyang Thank you very much. John D'Errico I'd give you 10 to 1 odds (or more) that you have too old a MATLAB release to use it. I'm sorry, but it was written using 2012a, and it uses some of the capabilities from that release. The error that you got is consistent with what you would see from an older release. John Dear John D'Errico pie=hpf('pi') I got Error with the next message: File: hpf.m Line: 863 Column: 9 Expression or statement is incorrect--possibly unbalanced (, {, or [. I do not find out what could be the problem. I did the exactly what you write in the ReadMe.rtf file. Do you have an idea? John D'Errico Raj - You are not listening to what I have said. HPF CANNOT be used with MATLAB's version of FZERO. It will NOT work. I would need to re-write FZERO for that to happen, and I have never done so. I said this before. Why would you expect to find a demo for code that does not exist? This does not say it is impossible to re-write FZERO, but that I have not chosen to do so. Raj Raj Hi John, Thanks for taking time in replying. However, in your file "hpf_demo.m", I couldnt find any demo on the use of FZERO with HPF. Are you referring to this file? John D'Errico Hi Raj, The problem is in FZERO, which explicitly tests its argument to see if it is a double, rather than a floating point numeric class like HPF. In fact, FZERO even fails to run on single input. f = @sin; fzero(f,hpf(3,50)) Error using fzero (line 128) FZERO only accepts inputs of data type double. To make it work, I would need to write an overloaded FZERO, or TMW would need to allow FZERO to accept other than double input for a starting value. (Note that the way you are trying to call fzero will not work if an overloaded FZERO were supplied by me, as MATLAB would always use the base version then. In order to call an overloaded operator, you need to pass in a variable of the proper class. See the example case where I tried to use FZERO for HPF input.) Raj Raj May be here is the application I encountered: f1=@(x) ((5*x+7))+hpf(9*10^15+6*10^6) fzero(f1, [0.00]) Raj Raj Hi John, Can we use this function with fzero. Here is the test case: f1=@(x) hpf(5*x+7) f2=@(x) (5*x+7) fzero(f2, [0.00]) fzero(f1, [0.00]) Thanks! John D'Errico HI Yamasani, It looks like you have a few misunderstandings. What you need to appreciate is how MATLAB works with numbers as an interpreted language. Also how assignments work when there are different classes involved. First of all, when you do something like this... V = fun(1 + 2.3); Here MATLAB performs the operation 1 + 2.3, as a double. The result will be 3.3 (approximately), but it WILL be a double. Then that result is passed into the function fun. Here fun could be ANY function, including a call to HPF, to create an HPF number. The same holds true for something like... V = hpf(1.4); MATLAB FIRST takes the number 1.4. It stores that as a double. Note that 1.4 is NOT exactly storable as a double. In fact, the representation of 1.4 in MATLAB is... X = hpf(1.4) X = 1.399999999999999911182158029987476766109466552734375000000000000 Remember that numbers are stored in binary form in MATLAB. So if you really wanted 1.4, you needed to do it like this X = hpf('1.4') X = 1.4 Here X is EXACTLY 1.4, stored in a decimal form inside HPF. The same thing applied when you do an operation like 1.4 + hpf(1) Here 1 is an integer, so HPF is capable of storing that exact value as an HPF version of the integer 1. But then adding 1.4 to that number, remember that MATLAB is an interpreted language. So again, MATLAB has a problem, because MATLAB sees the 1.4 as a DOUBLE number, only then does it realize that it must add that number to an HPF number. 1.4 + hpf(1) ans = 2.399999999999999911182158029987476766109466552734375000000000000 So this does work properly: hpf('1.4') + 1 ans = 2.4 2.4 is indeed the exact representation internally. Next, you have another issue because IF the variable E exists already as a double. See what happens here: E = zeros(1,2); E(1) = hpf('1.4') E = 1.4 0 whos E Name Size Bytes Class Attributes E 1x2 16 double E is a double. It is NOT an HPF number. In fact, E is not represented as exactly 1.4. So if I look at the value stored for E, again, it is the wrong number, not exactly the true decimal 1.4. Since E existed already, and you chose to insert the HPF value into the first element of E, MATLAB decided to convert it BACK into a double. hpf(E(1)) ans = HPF element: (1,1) 1.399999999999999911182158029987476766109466552734375000000000000 In your last example, I don't know what you did. My guess is you were confused, and do not really have what you showed me. Again, you must be careful about what MATLAB does to the numbers you are working with. And these are things totally beyond my control in the design of HPF. Remember that MATLAB is a language like any other programming language (but unlike what we see in the movies.) It has strict rules about how it will operate on what you pass it, and it cannot know that what you wanted it to do is not what you told it to do. Yamasani Rahul Hello John I am stuck up with aserious problem.HPF is working as expected under normal conditions,but when trying to store my number ina an array it is rounding off the number Ex:E=1.4+hpf(0.002233112233445566) >>E=1.402233112233445566 but if E(1)=1.4+hpf(0.002233112233445566) >>E()=1.4 John D'Errico I've made the tool as fast as possible, in fact, writing the entire tool using 3 different fundamental schemes for the best compromise in speed and capability. This was the best of the alternatives. When you are working with large enough numbers, then setting the DefaultDecimalBase to 6 can help some, although there is little difference on numbers as small as only 100 digits or so. Yamasani Rahul This is extraordinary But processing of this tool is too slow Derek O'Connor This is really excellent. I wish I'd had HPF when I was teaching numerical algorithms. Here are some functions I use to test all such packages: function cond1SSH = TestSSH; % Testing John D'Errico's HPF on Sea Surface Heights problem. % (a plain text file) and then import to SSHData.mat % Derek O'Connor 10 Sep 2012 [m,n] = size(SSHData); n = max(m,n); for d = 20:30 shpc = sum(hpf(SSHData,d)); disp([shpc.NumberOfDigits(1), shpc.Migits, shpc.Exponent]); end cond1SSH = n*sum(abs(SSHData))/abs(sum(SSHData)); disp(['Condition Number of Data:']); disp(cond1SSH); function z = Rump(d); % Testing John D'Errico's HPF % Derek O'Connor 10 Sep 2012 x = hpf(77617,d); % d = Number of digits to use y = hpf(33096,d); z = (33375/100)*y^6 + x^2*(11*x^2*y^2-y^6-121*y^4-2) + (55/10)*y^8 + x/(2*y); % Correct answer: z = -54767/66192 function z = Judd(d) % Testing John D'Errico's HPF % Derek O'Connor 10 Sep 2012 x=hpf(192119201,d); % d = Number of digits to use y=hpf(35675640,d); z = (1682*x*y^4 + 3*x^3 + 29*x*y^2 - 2*x^5 + 832)/107751; % Correct answer: z = 1783 Jonathan This is excellent! I had code that needed higher precision calculation. So, I downloaded your hpf class. Without modifying my code at all, just modifying the class of the input parameters, my regression tests worked as expected. That is how a class like this is supposed to work. Thank you! Jeff David Wilson John D'Errico Hi Michael, This is not really intended as a replacement for VPI, as the VPI tool concentrates entirely on large integers. In HPF you will see I've not given you tools to factor integers, or to test for primality, modular inverses, modular roots, or a powermod function. Here I've concentrated on numerical methods, so I've provided computations for trig functions, exponentials, logs, erf, etc. HPF might be used to get around the dynamic range limitation of a double, or for someone who desperately wants to work in a given number of digits. It would seem to be a good tool for a student to learn about numerical precision problems. As well, I've found HPF to be quite useful in showing what MATLAB stores when we represent a number as an IEEE 754 double. (My own version of a tool like num2strexact that need not be compiled.) And it is a nice tool to test an algorithm to determine if a problem is due to a lack of numerical precision. I've even heard of a version of chol that will run with HPF numbers. In general, I'd expect that most users of HPF will work with numbers in the range of 30 to perhaps 50 or so digits at most, except for those individuals who love to play in the huge digit sandbox. As far as VPI goes, I plan on offering a new version to give a speed bump. (When I do, I'd like to play with some quadratic sieve factoring schemes to update factor.) I'd been debating in my own mind if I should leave the old VPI up there or not, for those users who have older releases of MATLAB. By the way, that speed bump for VPI can come from one of two sources. For example, I could re-write VPI as a wrapper class for an existing Big Integer tool. I looked at such a question when I wrote HPF. (In fact, I wrote HPF in three separate versions, choosing the migit version as it ran the fastest.) Alternatively, I could in theory write the new VPI version to use migits, much like HPF uses now. The problem with migits is, they work well for numbers where the length of the mantissa does not change. The issue is there are limits on the size of a number that can be operated on with migits, and integer arithmetic can cause integers to grow arbitrarily large. As such I would be forced to limit the size of the migits to be rather small. Thus with 3-migits, one can generate integers up to a few hundred millions of decimal digits. That would surely be adequate for the conceivable future, but perhaps one day it might be a limitation. (Somebody always wants to push the limits of any computational tool.) Finally, a migital version of VPI would be simpler (and more efficient) to write than my HPF implementation, since it would not be forced to work in a fixed umber of digits. And there is no need for guard digits when you work with pure integers. (Is migital a word? I guess it is now.) I'd be willing to take any advice people have to offer on these matters. Vote now. John Michael John can you comment to existing VPI users on whether this is an official successor to VPI and if/when we should make the switch? peter as always, excellent job from John Christophe Lauwerys ##### MATLAB Release Compatibility Created with R2012a Compatible with any release ##### Platform Compatibility Windows macOS Linux

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1 You visited us 1 times! Enjoying our articles? Unlock Full Access! Question # State which of the following statements are true (T) and which are false (F). (i) Point has a size because we can see it as a thick dot on paper. (ii) By liens in geometry, we mean only straight lines. (iii) Two lines in a plane always intersect in a point. (iv) Any plane through a vertical line is vertical. (v) Any plane through a horizontal line is horizontal. (vi) There cannot be a horizontal line a vertical plane. (vii) All lines in a horizontal plane are horizontal. (viii) Two lines in a plane always intersect in a point. (ix) If two lines intersect at a point P, then P is called the point of concurrence of the two lines. (x) If two lines intersect at a point P, then p is called the point of intersection of the two lines. (xi) If A,B,C and D are collinear points D, P and Q are collinear, then points A, B, C, D, P and Q are always collinear. (xii) Two different lines can be drawn passing through two given points. (xiii) Through a given point only one line can be drawn. (xiv) Four points are collinear if any three of them lie on the same line. (xv) The maximum number of points of intersection of three lines is three. (xvi) The minimum number of points of intersection of three lines is one. Open in App Solution ## (i) False (ii) True (iii) False They may be parallel. (iv) True (v) False In every vertical plane there must be horizontal line. e.g.:-Intersecting line of a wall and floor of a room is horizontal line and it is also a line on the wall that is on the vertical plane. (vi) False Counter example:-Intersecting line of a wall and floor of a room is horizontal line and it is also a line on the wall that is on the vertical plane. (vii) True (viii) False They can be parallel line also. (ix) False Through a point of concurrence, at least three lines should pass. (x) True (xi) False Here ABCD is in one plane and DPQ may be in different plane and they may be intersecting through the point D. (xii) False Two lines are either intersecting at one point or they may be parallel lines or they may be coincident lines. (xiii) False Through a given point infinite line can be drawn. (xiv) False Points are collinear only if all points are in the same plane. (xv) True (xvi) False Minimum number of points of intersection of three lines be zero. Suggest Corrections 0 Join BYJU'S Learning Program Related Videos Parallel Lines and Intersecting Lines MATHEMATICS Watch in App Join BYJU'S Learning Program

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# Finding the Range(KS2, Year 4) homesitemapstatisticsfinding the range We can find the range of a set of numbers. Imagine a teacher had set their mathematics class a test. They are concerned that some students are doing much better than others. They wanted to find the range of test scores in the class, to see if some students are doing much better than others. ## How to Find the Range The range is found by subtracting the lowest number in a set from the highest number. ## Question What is the range of the test scores below? ## 1 List the numbers in numerical order (going from the smallest to the largest number). 7 10 8 6 4 → 4 6 7 8 10 ## 2 Find the lowest number in the set. 4 6 7 8 10 The lowest test score is 4. ## 3 Find the highest number in the set. 4 6 7 8 10 The highest test score is 10. ## 4 Subtract the lowest number (4) from the highest number (10). 10 − 4 = 6 The range of the test scores is 6. ## Lesson Slides The slider below gives another example of finding the range. ## A Formula to Find the Range The formula for finding the range is shown below:In this formula, • xmax is the highest number in the set. • xmin is the lowest number in the set. ## How to Find the Range from a Number Line Finding the range of a set of numbers on a number line is easy. If we plot the test scores on a number line (with the highest and lowest scores in red), the range is the distance between the highest and lowest numbers on the number line:The range is the distance between the highest and lowest numbers on the number line. In our example, it is 6. ## How to Find the Range from a Frequency Table Sometimes data is presented in frequency tables. A frequency table representing the test scores is shown below: It is possible to find that the range of the test scores is 6. Learn more about finding the range from a frequency table ## Be Careful When the Lowest Number is Negative Be careful when the lowest number in a set is a negative number. Let's find the range of the following numbers: −2, 0, 3, 4, 6 The range is found by subtracting the lowest number (−2) from the highest number (6): Range = 6 − (−2) Don't forget: Subtracting a negative number is equivalent to adding the (positive) number. (Two negatives make a positive!) Subtracting −2 is equivalent to adding (+)2: Range = 6 − (−2) = 6 + (+2) = 6 + 2 Range = 8 ## You might also like... #### Help Us Improve Mathematics Monster • Did you spot a typo? Please tell us using this form. #### Find Us Quicker! • When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add #mm to your search term. If you do, please tell us. It helps us a lot! #### Create a QR Code Use our handy widget to create a QR code for this page...or any page.

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# 2: Measurement and Problem Solving $$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ ( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$ $$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$ $$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$ $$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vectorC}[1]{\textbf{#1}}$$ $$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$ $$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$ $$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$ $$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$ Chemistry, like all sciences, is quantitative. It deals with quantities, things that have amounts and units. Dealing with quantities is very important in chemistry, as is relating quantities to each other. In this chapter, we will discuss how we deal with numbers and units, including how they are combined and manipulated. • 2.1: Taking Measurements Chemists measure the properties of matter and express these measurements as quantities. A quantity is an amount of something and consists of a number and a unit. The number tells us how many (or how much), and the unit tells us what the scale of measurement is. For example, when a distance is reported as “5 kilometers,” we know that the quantity has been expressed in units of kilometers and that the number of kilometers is 5. • 2.2: Scientific Notation - Writing Large and Small Numbers Chemists often work with numbers that are exceedingly large or small. For example, entering the mass in grams of a hydrogen atom into a calculator requires a display with at least 24 decimal places. A system called scientific notation avoids much of the tedium and awkwardness of manipulating numbers with large or small magnitudes. • 2.3: Significant Figures - Writing Numbers to Reflect Precision Uncertainty exists in all measurements. The degree of uncertainty is affected in part by the quality of the measuring tool. Significant figures give an indication of the certainty of a measurement. Rules allow decisions to be made about how many digits to use in any given situation. • 2.4: Significant Figures in Calculations To round a number, first decide how many significant figures the number should have. Once you know that, round to that many digits, starting from the left. If the number immediately to the right of the last significant digit is less than 5, it is dropped and the value of the last significant digit remains the same. If the number immediately to the right of the last significant digit is greater than or equal to 5, the last significant digit is increased by 1. • 2.5: The Basic Units of Measurement Metric prefixes derive from Latin or Greek terms. The prefixes are used to make the units manageable. The SI system is based on multiples of ten. There are seven basic units in the SI system. Five of these units are commonly used in chemistry. • 2.6: Problem Solving and Unit Conversions During your studies of chemistry (and physics also), you will note that mathematical equations are used in a number of different applications. Many of these equations have a number of different variables with which you will need to work. You should also note that these equations will often require you to use measurements with their units. Algebra skills become very important here! • 2.7: Solving Multistep Conversion Problems Sometimes you will have to perform more than one conversion to obtain the desired unit. • 2.8: Units Raised to a Power Conversion factors for area and volume can also be produced by the dimensional analysis method. Just remember that if a quantity is raised to a power of 10 both the number and the unit must be raised to the same power of 10. • 2.9: Density Density is a physical property found by dividing the mass of an object by its volume. Regardless of the sample size, density is always constant. • 2.E: Measurement and Problem Solving (Exercises) Exercises for Chapter 2 of Tro's Introductory Chemistry textmap. • 2.10: Numerical Problem-Solving Strategies and the Solution Map 2: Measurement and Problem Solving is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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Physics Calculators ## Harris-Benedict Calculator (total Energy Expenditure TDEE & Bmr) If you are concerned about your health and body, the Harris-Benedict Calculator (BMR calculator), which runs on the Harris-Benedict formula, is the right tool for you! ## Harris-Benedict Calculator kg cm yrs kcal/day ◦What is a BMR Calculator? ◦What is the Harris-Benedict equation, you ask? ◦How do I calculate my BMR? ◦What is BMR? ◦What makes a good BMR? ◦How can I increase my BMR? ◦How can I convert BMR to pounds? ◦How can I use BMR for weight loss? ◦What is Harris Benedict formula? ◦What is the Harris-Benedict equation, you ask? ◦Is the Harris-Benedict equation correct? ◦How can I calculate my BMR for a female? ## What is a BMR Calculator? Your basal metabolic rate is the equivalent of the amount of energy your body would need to function for 24 hours if it was to be awake. ## What is the Harris-Benedict equation, you ask? The Harris-Benedict Equation uses your BMR to calculate your daily energy expenditure (calories). ## How do I calculate my BMR? You would use the Harris-Benedict equation to calculate your BMR. • For women, it’s: • BMR = 655.1 + (9.563 * weight in kg) + (1.850 * height in cm) - (4.676 * age) • For men, it’s: • BMR = 66.5 + (13.75 * weight in kg) + (5.003 * height in cm) - (6.75 * age) ## What is BMR? Your basal metabolism rate (BMR) is the equivalent of how much energy your body would need to function if it was to be awake for 24 hours. BMR is the basal metabolism rate. It is the minimum amount of calories your body requires to perform essential functions such as breathing, digestion, and maintaining a constant body temperature over the course of a day. ## What makes a good BMR? The average BMR for a woman is 1409 Kcal (5900kJ), and for a male, it's 1696 Kcal (7100kJ). ## How can I increase my BMR? You can increase your BMR (basal metabolic rates) by trying: • Consume more protein with every meal. • Increasing your HIIT (high-intensity interval training). • Increase your daily activities by choosing stairs instead of the elevator, walking more, switching to a standing desk. • More spicy food. • ## How can I convert BMR to pounds? Use the following equations to calculate your basal metabolic rates in imperial units: • For men, it’s: • BMR = 66.74 + (6.24 * weight in pounds) + (12.7 * height in inches) - (6.75 * age in years) • For women, it’s: • BMR = 65.51 + (4.35 * weight in pounds) + (4.7 * height in inches) - (4.7 * age in years) ## How can I use BMR for weight loss? If you are looking to lose weight, counting your BMR is a great place to start. It tells you how many calories your body requires to function correctly. It would be best if you never ate less than this. You can then multiply this number by your activity level (PAL) to find how many calories you burn. You can lose weight slowly and steadily by reducing a reasonable amount of calories (e.g., 500 kcal/day). ## What is Harris Benedict formula? The Harris-Benedict Formula is a mathematical equation that can be used to calculate the basal metabolic rate (BMR) of a person. The BMR is a measure of the amount of energy expended by a person during rest and at varying levels of activity. The Harris-Benedict Formula is used to calculate a person’s BMR based on their age, weight, height and sex. ## What is the Harris-Benedict equation, you ask? The Harris-Benedict equation is a mathematical formula that lets you count your basal metabolism rate - BMR. It requires your height, weight, age, and gender. There are two distinct formulas: • For women, it’s: • BMR = 655.1 + (9.563 * weight in kg) + (1.850 * height in cm) - (4.676 * age) • For men, it’s: • BMR = 66.5 + (13.75 * weight in kg) + (5.003 * height in cm) - (6.75 * age) ## Is the Harris-Benedict equation correct? The Harris-Benedict equation has been considered to be the most accurate BMR equation. But, remember that the rough estimate of your BMR using a calculator may not be accurate and could differ from your actual bodily requirements. You need to do this, but calculating your BMR can help you get started. ## How can I calculate my BMR for a female? It would be best if you calculated your female BMR by: • Know your exact height and weight. Please do not cheat, and it will only lead to inaccurate results. • The Harris-Benedict formula for women: • BMR = 655.1 + (9.563 * weight in kg) + (1.850 * height in cm) - (4.676 * age) • Your basal metabolic rate (BMR) is the result. Multiply this with your activity level – PAL - in order to calculate your daily energy expenditure - TDEE. • Article author Parmis Kazemi Parmis is a content creator who has a passion for writing and creating new things. She is also highly interested in tech and enjoys learning new things. ###### Harris-Benedict Calculator (total Energy Expenditure TDEE & Bmr) English Published: Thu Apr 21 2022 In category Physics calculators Add Harris-Benedict Calculator (total Energy Expenditure TDEE & Bmr) to your own website #### Other physics calculators Average Speed Calculator This is an online tool that will calculate any moving object's average speed. Torque Calculator Calculate and convert the force of torque in different units with this easy-to-use online calculator. Works with Nm, Ft-lb, Kg-cm, J/rad. Hemisphere Volume Calculator Find out easily hemisphere volume of different shapes such as cube, cylinder, pyramid and many more with our free online calculator. Beer-Lambert Law Calculator The Beer-Lambert law calculator will calculate the absorption or attenuation of light when passes through any material. Density Calculator The density calculator can help you determine the relationship between an object's weight and its volume. Wavelength Calculator This wavelength calculator is a tool that can help you determine the relationship between frequency and wavelength. Charles Law Calculator The Charles' Law Calculator is a simple tool that describes the basic parameters and properties of ideal gases in an isobaric process. Kinetic Energy Calculator The kinetic energy calculator can be used to calculate the energy of motion. It uses the kinetic energy formula that applies to all objects in a horizontal or vertical motion. Acceleration Calculator This acceleration calculator can be used to determine the speed at which an object is changing. Angular Velocity Calculator This angular velocity calculator is an easy-to-use tool that provides immediate answers to the question: "How to calculate angular velocity?” Distance Calculator Use this online tool to calculate the distance between two points.

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# Visualizing 3D - PowerPoint PPT Presentation 1 / 53 Visualizing 3D. Between Measurement and Illusion Dan Collins VizProto. Visualization is…. I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described. Visualizing 3D Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - ## Visualizing 3D Between Measurement and Illusion Dan Collins VizProto • Visualization is…. • Visualization is a method of computing. It transforms the symbolic into the geometric, enabling researchers to observe their simulations and computations. Visualization offers a method for seeing the unseen. It enriches the process of scientific discovery and fosters profound and unexpected insights. In many fields it is already revolutionizing the way scientists do science. • SIGGRAPH proceedings, 1987. B. McCormick, T. DeFanti, and M. Brown [MCC87] ### Euclid300 B.C. • Euclid's "Elements," written about 300 B.C., a comprehensive treatise on geometry, proportions, and the theory of numbers, is the most long-lived of all mathematical works. This manuscript preserves an early version of the text. Shown here is Book I Proposition 47, the Pythagorean Theorem: the square on the hypotenuse of a right triangle is equal to the sum of the squares on the sides. This is a famous and important theorem that receives many notes in the manuscript. • Pythagorean Theorem Euclid’s description of the Pythagorean theorem ### Euclid300 B.C. • Euclid also wrote Optica,the first text on geometrical optics, in which he defines the terms visual ray and visual cone. • He noted that light travels in straight lines and described the law of reflection. He believed that vision involves rays going from the eyes to the object seen and he studied the relationship between the apparent sizes of objects and the angles in which they meet at the eye. Raphael, The School of Athens,1509, Fresco, Vatican, Rome Detail showing Euclid with his students ### Pythagorus580-520 B.C. • Pythagorus was a mathematician who made important contributions to geometry. "He was a Greek philosopher and religious leader who was responsible for important developments in the areas of mathematics, astronomy, and music theory. He was also a healer, a wrestler, and was politically active. He founded a philosophical and religious school which has come to be known as the Pythagorean Society. • The Pythagoreans saw that many things in the universe were related in ways that could be stated in numbers. They reasoned that numbers must be the 'stuff' philosophers were looking for. The universe including man is a closed system. Both can be understood by the relation of the parts. These relations can be expressed in terms of numbers. These ideas led them to believe that if one could penetrate the secrets of numbers, he would penetrate the secrets of the universe and the destiny of man. This led to the careful study of geometry, the highest form of mathematics.” ### PantheonRome, Italy, 118 to 126 ADArchitect unknown Exterior view of the Pantheon in modern day Rome Interior view of the Pantheon Giovanni Paolo Panini, c. 1750 ### The Pantheon and the Neo-Pythagoreans • The Roman pantheon can be considered an architectural image of the Greek Pythagorean cosmos, a "living organism" with a mathematically-proportioning "soul" and unchanging, "eternal" consonant-symphonic ratios. To generate harmony, the laws of arithmetic, geometry, astronomy and musical-proportions are fused. It "resembles the heavens", but is a resemblance based on mathematical knowledge, a summary of the ancient quadrivium*.” • --Girt Sperling • * The quadrivium was the higher division of the seven liberal arts in the Middle Ages, composed of geometry, astronomy, arithmetic, and music. Section showing pythagorean ratios at work in the Pantheon. ### Before Perspective • Perspectival errors appear in paintings usually done before 1400. • The perspective lines usually converge, but not to a single point and not on the horizon. • Initial word panel of Psalm from the Kaufmann Haggadah. Spain, late 14th C. ### Brunelleschi1377-1446 • Brunelleschi designed the stupendous dome which crowns the cathedral in Florence, a work which occupied him intermittently from 1417 to 1434. The technical difficulties involved in erecting the new dome underscore an important aspect of his talents: he was a daring innovator, with a solid knowledge of math and mechanics. ### Brunelleschi • He developed many important construction methods as well as contributing to the evolution of perspective. His mathematical work led to the invention of linear perspective. ### Brunelleschi • Filippo Brunelleschi was the first to carry out a series of optical experiments that led to a mathematical theory of perspective.. Brunelleschi used his training as a gold smith to apply a silver background on a painted panel, allowing the color of the sky and passing clouds to become part of the painting as seen by the viewer. This was an attempt at a perspective painting and interactive art. The panel was constructed with a hole at the vanishing point. The reflection of the image was viewed in a mirror through the hole, giving an illusion of depth. • http://library.thinkquest.org/3257/illusion.html#peep Brunelleschi devised a method of perspective for architectural purposes: he is said by Manetti to have made a ground plan for the Church of Santo Spirito in Florence on the basis of which he produced a perspective drawing to show his clients how it would look after it was built. ### Masaccio1401-1428 • Masaccio's Trinity, 1427-28 Santa Maria Novella, Florence (6.67 x 3.17 m) is often used to illustrate the early culmination of mathematical perspective experiments. ### Alberti1404 - 1472 • ALBERTI'S WINDOW • The traditional form of pictorial representation using perspective methods developed by Renaissance artists is sometimes referred to as Alberti's Window. • This is because, in his treatise Della pittura, On Painting, 1435-6, the Classical theorist and painter Leon Battista Alberti noted that, when he set out to paint a scene on a panel, he assumed the picture would represent the visible world as if he were looking through a window. Some artists did, in fact, create grids across the opening of a window and transfer the scene to a gridded canvas as compelling evidence that western perspective was a natural form of representation. Alberti’s “fenestre” (window) or “velo” ### Alberti • Alberti's Construction System • 1. B-one braccio module (one third of the height of a man). The base of the picture is divided into braccia. The height of the man at the front plane of the picture gives the level of the horizon, H. • 2. The braccio divisions are joined to the perspective focus, V, to give the orthogonals. • 3. In side elevation, lines are drawn from braccio divisions behind the picture plane P to the eye at E. The points of intersection on P are noted. • 4.The levels of the points of intersection are marked at the side of the picture plane, and locate the horizontal divisions of the tiles. Z is the 'distance' point, though Alberti only mentions using one diagonal to check the construction. ### Paolo Uccello • Among the best examples of early uses of linear perspective is Paolo Uccello's fresco of the "Deluge" in Florence, completed about 1448. Here linear perspective is used to present an elaborate architectural setting. The real object of fascination, however, is Uccello's rendering of the mazzocchi, the curious checkered hats, of which there are two in "The Deluge.” Ucello had actually drawn such wonderful polyhedral forms in studies of perspective drawings, and these clearly demonstrate the mastery he had of the new mathematical techniques. ### Piero della Francescac.1420 - 1492 • The culmination of the mathematical theory of perspective with a philosophical program of the most intense and religious order comes with the work of Piero della Francesca. His St. Anthony's Polyptich, in Perrugia, shows how masterfully he was able to use the new theory of perspective. ### Leonardo1452 - 1519 • Perspective is nothing else than the seeing of an object through a sheet of glass, on the surface of which may be marked all the things that are behind the glass --Leonardo da Vinci • Leonardo studied optics from both the scienitific and the artistic points of view. He believed that painting should be considered a Liberal Art because it was based on mathematically derived perspective theory and satisfied the primary sense of sight. Da Vinci realized that unless a person viewed a painting through a peephole, the visual image would be different than the image the artist painted. ### Dürer1471-1528 • One of several machines invented by Dürer for making perspectival drawings consisted of a needle driven into the wall and a piece of string and a hinged frame. The piece of string has a pin on one end and a weight on the other; between the eye of the needle and the object is placed a wooden frame within which every point can be determined by two movable threads crossing each other at right angles. When the pin is put on a certain point of the object the place where the string passes through the frame determines the location of that point within the future picture. This point is fixed by adjusting the two movable threads and is at once entered upon a piece of paper hinged to the frame; and by a repetition of this process the whole object may be transferred gradually to the drawing sheet. A woodcut from Albrecht Dürer's treatise on measurement Underweysung der Messung, 1527 ### Dürer1471-1528 • The Perspectograph is an instrument that allows the user to obtain, point by point, a correct perspective drawing of a three dimensional object. Perspectographs were used by painters and sceno-graphers in 16th and 17th cent. (and as early as the 15th cent. by Alberti). Some types of Perpespectograph are very simple (as these reproduced in Dürer's xylographies), some types are rather complex. In this model of Dürer's perspectograph, an observer looking through the ocular sees the pattern drawn on the vertical table exactly superimposed on the pattern drawn on the horizontal table. Dürer's Perspectograph, early 16th c. (replica) • The art historian Rudolph Wittkower writes, "The conviction that architecture is a science, and that each part of a building, inside as well as outside, has to be integrated into one and the same system of mathematical ratios, may be called the basic axiom of Renaissance architects." Many modern authors have analyzed Wittkower's thesis that harmonic proportions derived from musical scales played a central role in the minds and designs of Renaissance theorists and architects. Central to this debate is Palladio's oeuvre--his architecture and his Quattro libri (four books). • --Stephen R. Wassell Elevation and plan of a typical Palladian villa. vitruviusc. 90-20 B.C.E. • Images by Cesare Cesariano (1521) • This is a profusely illustrated edition of the most famous of antique texts on architecture, The Ten Books on Architecture. It was known throughout the Middle Ages, in multiple copies and probably versions. Living Emblem of the United States Marines. 100 officers and 9000 enlisted men. Marine Barracks, Parris Island, S.C.; Brigadier General J.H. Pendleton, Commanding. Mole & Thomas, Chicago Illinios, 1919. Francesco Borromini1599 - 1667 This architectural tromp l'oeil of an actual "perspective" collonade in the Palazzo Spada, was fashioned by Galileo's contemporary, Borromini in 1653. This is actually an illusion, played with the help of mathematical perspective. The trick is revealed in the image at the right where two figures of equal height show the perspective at work. The image in the center is a modern CAD rendering. Diderot1713 - 1784 • Denis Diderot was the creator of the first Encyclopedia in 1751. More then 160 authors contributed to the encyclopedia. By 1789 there were nearly 16,000 copies sold. The pope placed the encyclopedia on the Index of Prohibited books. • In his discussions on art, he provides the broader social context for the arts. In his entries on Art, he describes the origin of the sciences and arts, their distribution into liberal and mechanical arts, the goal of the arts, and his own project for a general treatise on the mechanical arts. • We began by making observations on the nature, service, usage, qualities of beings & of their symbols; then we gave the name of science or of art or of discipline in general, to the center or unifying point to which we related the observations that we had made, to form a system of either rules or instruments, & of rules tending towards the same goal; because that is what a discipline is in general. (ART, in Diderot & d'Alembert, 1751-1772, Vol. 1, p. 713) Francois Willeme - Photosculpture1860 Contour plot . Map of Paris by L. L. Vauthier (1874), showing population density by contour lines, the first statistical use of a contour map. This approach to representing multivariate data arose from the use of contour maps in physical geography showing surface elevation (first published in 1752 by Buache), which became common in the early 19th century. It was not until 1843, however, that this idea was applied to data, when Léon Lalanne constructed the first contour plot, showing the mean temperature, by hour of the day and by month at Halle (lower left). Lalanne's data formed a regularly-spaced grid, and it was fairly easy to determine the isolines of constant temperature. Vauthier generalized the idea to three-way data with arbitrary (x,y) values in his map of the population density of Paris. http://www.math.yorku.ca/SCS/Gallery/noframes.html The Broad Street cholera outbreak was a severe outbreak of cholera that occurred near Broad Street (now renamed Broadwick Street) in Soho district of London, England in 1854. This outbreak is best known for the physician John Snow's study of the outbreak and his discovery that cholera is spread by contaminated water. This discovery came to influence public health and the construction of improved sanitation facilities beginning in the 19th century. Snow used a spot map to illustrate how cases of cholera were centered around a particular water pump. He also made a solid use of statistics to illustrate the connection between the quality of the source of water and cholera cases. The section of Snow's map representing areas in the city where the closest available source of water was the Broad Street pump circumscribed most cases of cholera.[3 This figure (showing the population of Sweden from 1750-1875 by age groups) by Luigi Perozzo, from the Annali di Statistica, 1880, is a very early example of a 3D stereogram. Perozzo's figure is also notable for being printed in color in a statistics journal, and in a way which enhances the perception of depth. ### Etienne-Jules Marey1830- 1906 Etienne-Jules Marey, 1830-1906, was among the pioneers of dynamic graphics and the graphical representation of movement and dynamic phenomena. This image, from Marey's La méthode graphique dans les sciences experimentales (1876, p. 150) compares the time course of respiration of a person at rest and under exertion, using a pen-recording device to plot the traces over time. ### Mapping the London Underground • Harry Beck's 1933 diagram of the 7+ lines of the London Underground, although geographically inaccurate, provides a coherent overview of a complex system. (See map at upper left). • With excellent color printing, classic British railroad typography (by Edward Johnson), and, in the modern style, only horizontal, vertical, and 45 degree lines, the map became a beautiful organizing image of London. • For apparently quite a number of people, the map organized London (rather than London organizing the map). Despite 70 years of revision due to extensions of the Underground and bureaucratic tinkering (the marketing department wrecked the map for several years), the map nicely survives to this day. • Compare map from late 1920s at lower left. • 25 years ago, nearly every drawing produced in the world was done with pencil or ink on paper. Minor changes meant erasing and redrawing while major changes often meant recreating the drawing from the scratch. If a change to one drawing affected other documents you were dependent upon having someone manually recognize the need to make the changes to the other drawings and to do so. • CAD has fundamentally changed design and the way we “visualize” 3D. ### Dynamic Visualization • Visualization of Storm patterns combines 3D graphics and actual metrics ### Decision Theater at ASU • East Valley Water Forum (EVWF) • The EVWF is a regional cooperative of water providers who are working with Arizona Department of Water Resources (ADWR) with support from the Bureau of Reclamation to develop data driven scenarios about ground water policy issues under a variety of drought scenarios. Their work with the Decision Theater will assist them in developing informed planning decisions as the east portion of the Salt River Valley continues its explosive growth. Key collaborators: K. Sorenson (City of Mesa) and D. Mason (ADWR). ### Decision Theater at ASU • Urban Heat Island (UHI) • The UHI explores and models heat retention in the Phoenix metropolitan area. The effect of UHI during Arizona summers has been a 12 degree rise in night time low temperatures in the last 20 years. Scientists have developed predictive models based on dynamic changes in land use that can help planners and decision makers better understand the UHI phenomenon. The goals are to understand probable impacts of UHI on planning urban systems (such as electrical capacity to accommodate increased power use for air conditioning) and to explore the effectiveness and impact of potential solutions for mitigation. ### Decision Theater at ASU • Environmental Fluid Dynamics Program • Typically, computational fluid dynamics models of atmospheric events are presented as numeric data or 2 dimensional graphics. Data from a Defense Threat Reduction Agency (DTRA) funded project to simulate anthrax release in Oklahoma City has been modeled and visualized as a 3D animation. This work provides a foundation for developing interactive scenarios to study the effects of wind direction, wind speed, and building design on dissemination of bacterial agents. The research permits informed training of emergency response teams to real natural or man made emergencies. ### The History of CAD (pre-1970) • The first graphic system was in mid 1950 the US Air Force's SAGE (Semi Automatic Ground Environment) air defense system. The system was developed at MIT’s Lincoln Laboratory. The system involved the use of CTR displays to show computer-processed radar data and other information. • In 1960, Ivan Sutherland used TX-2 computer produced at MIT's Lincoln Laboratory to produce a project called SKETCHPAD, which is considered the first step to CAD industry. • In 1960 McDonnell Douglas Automation Company (McAuto) founded. It will play a major role on CAD developments. • The first Computer-Aided Design programs used simple algorithms to display patterns of lines at first in two dimensions, and then in 3-D. Early work in this direction had been produced by Prof. Charles Eastman at Carnegie-Mellon University, the Building Description System is a library of several hundred thousands architectural elements, which can be assembled and drawn on screen into a complete design concept. • In mid 1960 large computers characterized the period, vector display terminals and software development done in assembly language. The only significant attempt to create a commercially CAD system was Control Data Corporation's Digigraphics division, a successor to the previously mentioned ITEK. The system costs half million dollars and were sold in few units. • In 1968 Donald Welbourn had the vision to see the possibility of using computers to assist pattern makers to solve the problems of modelling difficult 3D shapes. Today we take for granted 3D modelling, in 1968 only crude 2D drawing systems were available using terminals linked to large main frame computers. • David Evans and Ivan Sutherland founded in 1968 Evans and Sutherland. • In 1969 were founding Computervision and Applicon companies. Computervision was created to produce systems for production drafting and in the same year it sold the first commercial CAD system to Xerox. ### The History of CAD (1970-1980) • At the end of 70s a typical CAD system was a 16-bit minicomputer with maximum of 512 Kb memory and 20 to 300 Mb disk storage at a price of \$125,000 USD. ### The History of CAD (1980-1990) • 1981: Computer graphics from Cornell University founded 3D/Eye Inc., a pioneered 3D and graphics technology.Unigraphics introduced the first solid modeling system, UniSolid. It was based on PADL-2, and was sold as a stand-alone product to Unigraphics. • 1982: CATIA Version 1 is announced as an add-on product for 3D design, surface modeling and NC programming. Mini computers with much more power at less cost started to appear. This was a major step forward and by 1984 the technology began to be competitive with traditional methods. For many years aircraft had of course been designed using computers, but now it was becoming possible to economically design saucepans and other domestic products with complex 3D shapes using a computer. Autodesk was founded by sixteen people in April 1982 in California by initiative of John Walker in idea to create a CAD program for a price of \$1000 to can run on PC. John Walker has been running Marinchip Systems for two years before. In November at COMDEX trade show in Las Vegas was demonstrated the first CAD program in the world that runs on PC. This was the initial release of AutoCAD and deliveries begun in December. • 1983: Unigraphics II introduced to market • 1984, a Hungarian physicist, Gabor Bajor, smuggled two Macs into his country. At the time, ownership of personal computers was illegal under Communist rule. Using Pascal, he and a teenager, Tamas Hajas worked to write a 3D CAD program for the Mac which will be the beginning of Graphsoft Company. Drafting capabilities are added to CATIA in 1984, enabling it to function independently of CADAM. The first Autodesk Training Centre. In October AutoCAD version 2 (Release 5) with text improvements, DXFIN and DXFOUT commands, new Inquire commands, Object Snap, named views, Isometric capabilities and new Attribute features. • 1988: Surfware Inc., ships the first version of SurfCAM, a CAD/CAM program. • 1989: Parametric Technology ships the first version of Pro/ENGINEER. ### The History of CAD (1990-1995) • 1990:McDonnell Douglas (now Boeing) chooses Unigraphics as the corporate standard for mechanical CAD/CAM/CAE. Autodesk ships Animator Pro, a 2D painting and animation program for DOS. By 1993 over 15,000 copies have been sold worldwide. • 1991: Microsoft developed Open GL for use with Windows NT. Open GL is an API procedural software interface for producing 3D graphics and includes approximate 120 commands to draw various primitives such as points, lines, and polygons. Also includes support for shading, texture mapping, anti-aliasing, lighting and animation, atmospheric effects such as fogging and simulation of depth-of-field. Open GL, developed by Silicon Graphics, is a standard for the 3D color graphics programming and rendering. • 1992: Autodesk ships 3D Studio version 2 for DOS.Autodesk ships AutoCAD Release 12 for DOS in June. Includes AutoCAD SQL Extension (ASE)/Autodesk SQL Interface (ASI) that lets you establish links between AutoCAD and an SQL database. Advanced Modeling Extension (AME) release 2.1 is supported by Release 12, with region modeling and new solid primitives. AutoCAD Render is included with AutoCAD. • 1993: The first AutoCAD (Release 12) for Windows platforms. It required 8 MB RAM and 34 MB Hard Drive space for complete installation. The Windows version of AutoCAD includes 36 icons toolbox, allows multiple AutoCAD sessions, separate Render window, support for Windows GUI, DDE and OLE, as well as Drag-and-Drop and Bird's Eye view capabilities. The AutoCAD main menu has been eliminated; After initial configuration, AutoCAD displays the graphics screen. AutoCAD 12 for Windows was one of the most successful CAD programs ever • 1994: MiniCAD version 5. Hewlett Packard ships version 3.5 of PE/Solid Designer, its high end Solid Modeling. • 50,000 seats installed to date. • 1995: CATIA-CADAM AEC Plant Solutions are announced. This next generation object-oriented plant modeling system enables powerful knowledge-based engineering capabilities that can dramatically streamline the process of plant design, construction and operation. It brings the power of "smart" applications to the desktop with next generation object-oriented modeling. IDEAS Master Series version 2.1 from SDRC. Mazda Motors Corp. will install 2,400 seats of this product. Parametric Technology ships Pro/E version 15, the first parametric modeling CAD/CAM program and the first high-end 3D solid modeling package available on NT platforms. ### The History of CAD (1996-99) • 1996: Solid Edge version 3 from Intergraph hits the market at the price of around USD 6000. SolidWorks Co. ships Solid Works, an ambitious 3D package based on Parasolids modeling Kernel. It comes with a good complex surface modeling and a good graphical user interface. 3D/EYE Inc., ships Tri Spectives Technical version 2, a modeling, illustration and animation program for Windows platforms, at a very low price. Lightscape version 3, a high-end rendering and animation package, comes with IES photo-metric data capabilities. IES (Illuminating Engineers Society) is the industry standard for describing the shape and intensity of light energy distribution froma light source, ray tracing, natural light according to location and orientation of the building. Lightwave 3D version 5 and 5.5 from New Tek, a high-end rendering, modeling and animation program. AutoCAD LT 95. Diehl Graphsoft released MiniCAD 6 for Windows, the first cross-platform version of MiniCAD. Pro/E version 17 with a new module which allows files to be exported into VRML file format for display on the Internet. • 1997: Autodesk ships 3D Studio MAX release 2 and a cut-down version called 3D Studio Viz. EDS introduces a number of new industry-leading capabilities with its new version of Unigraphics, including WAVE - which will enable the definition, control and evaluation of product templates - considered the most important new technology affecting the CAD/CAM/CAE industry in the next five years. First version of IDEAS Artisan Series from SDRC, fully compatible with Master Series, priced at ~ USD 5,000. Form Z, a solid and surface modeler, first available only for Mac platforms, debuts on Windows market. • 1998: Autodesk Architectural Desktop - integrated architectural solution based on AutoCAD 14.First version of IronCAD for VDS market. Autodesk ships 3D Studio MAX version 2.5Lightwave 3D version 5.6 from New Tek, comes with Procedural shades for snow, water and rust, Stereoscopic rendering, SkiTracer image warping for real time visualization of generated sky, and more.Solid Edge version 3 from Intergraph with more than 150 new features.Solid Works 98 adds 150 new capabilities. • 1999: CATIA Version 5 for native Windows NT and UNIX. Lightwave 3D version 6 from New Tek.Think3 entry in the CAD market with thinkdesign, the first mechanical design software product to offer the power of parametric solids, advanced surfacing, wireframe and 2-D drafting, all in one environment.VectorWorks replaces MiniCAD.3D Studio MAX cumulus 29% of the entire 3D-animation market and 38% of the 3D PC markets. ### From Euclid to Desargues • Euclid's Optica, c. 300 B.C., was the first text on geometrical optics, in which are defined the terms visual ray and visual cone. • Vitruvius' Ten Books on Architecture which appeared about 25 B.C., was the only book on architecture to survive from antiquity. It profoundly influenced Renaissance architecture and thinking, including that of Alberti, who quoted Vitruvius in his Della pittura. Vitruvius wrote: Perspective is the method of sketching a front with the sides withdrawing into the background, the lines all meeting in the center of a circle. Unfortunately he didn't elaborate on that. Elsehere, Vitruvius' reference to Greek and Roman stage design, implied an understanding of the vanishing point. • Ptolemy's Optica, c. 140 A.D., was another early text on geometrical optics, and included theories on refraction. The centric ray is defined by Ptolemy as the ray that does not get refracted. The centric ray, we'll see, is important in the theory of perspective. In his Geographia, c. 140 A.D., Ptolemy applies the principles of geometric optics to the projection of the spherical surface of the earth onto a flat surface, to produce a map. He is said to have made the first known linear perspective construction for drawing a map of the world. Ptolemy apparently knew about perspective, but applied it only to maps and to stage designs. • Galen's De usu partium, c. 175 A.D., contains an early but erroneous description of how the eye creates images. The book was still important, however, as a stepping stone in the development of the theory of perspective. • From Islam, Alhazen's Perspectiva, c. 1000 A.D., was an important compendium on optics. It integrated the works of Euclid, Ptolemy, and Galen. • Roger Bacon's Opus Majus, c. 1260 A.D., included a section on optics, whose geometric laws, he maintained, reflected God's manner of spreading His grace throughout the universe. • John Pecham's Perspectiva communis, c. 1270 A.D., was another treatise on optics that was widely available during the Renaissance. • Blasius of Parma's Quaestiones perspectivae, c. 1390 A.D., was a popular adaptation of the works of Bacon and Pecham. ### From Euclid to Desargues • We are all familiar with Euclidean geometry and with the fact that it describes our three-dimensional world so well. In Euclidean geometry, the sides of objects have lengths, intersecting lines determine angles between them, and two lines are said to be parallel if they lie in the same plane and never meet. Moreover, these properties do not change when the Euclidean transformations (translation and rotation) are applied. Since Euclidean geometry describes our world so well, it is at first tempting to think that it is the only type of geometry. (Indeed, the word geometry means “measurement of the earth.”) However, when we consider the imaging process of a camera, it becomes clear that Euclidean geometry is insufficient: Lengths and angles are no longer preserved, and parallel lines may intersect. • Perspective is an example of the geometric operation of projection and section where projection lines from the outline of an object to the eye are sectioned or cut by a picture plane. This has roots in the conic sections, where projection lines from a circle to a point form a cone, which is then sectioned by a plane to give a circle, ellipse, parabola, or hyperbola, depending on the angle of the cutting plane. These ideas were expanded by Gerard Desargues (1593-1662), architect/engineer, into the branch of mathematics called projective geometry. • Projective geometry is a branch of mathematics that deals with the relationships between geometric figures and the images, or mappings, of them that result from projection. Common examples of projections are the shadows cast by opaque objects, motion pictures, and maps of the Earth's surface. Projection of one line onto another Central projection of one plane on another ### Frank Lloyd Wright • Wright used nature as the basis of his geometrical abstraction. His objective was to conventionalize the geometry which he found in Nature, and his method was to adopt the abstract simplification which he found so well expressed in the Japanese print. Therefore, it is not too shocking perhaps that in this quest his work should foreshadow the new mathematics of nature first put forth by Benoit Mandelbrot: fractal geometry. • --Leonard K. Eaton Floor plan from a late Wright residence. ### Platonic Solids • The so-called Platonic Solids are regular polyhedra. “Polyhedra” is a Greek word meaning “many faces.” There are five of these, and they are characterized by the fact that each face is a regular polygon, that is, a straight-sided figure with equal sides and equal angles. • The Greeks, who were inclined to see mathematics as something of a religious truth, found this business of there being exactly five Platonic solids very compelling. The philosopher Plato concluded that they must be the fundamental building blocks – the atoms – of nature, and assigned to them what he believed to be the essential elements of the universe. He followed the earlier philosopher Empedocles in assigning fire to the tetrahedron, earth to the cube, air to the octahedron, and water to the icosahedron. To the dodecahedron Plato assigned the element cosmos, reasoning that, since it was so different from the others in virtue of its pentagonal faces, it must be what the stars and planets are made of. ### references • General Science and Art: http://library.thinkquest.org/3257/ • Digital Design Media: http://www.gsd.harvard.edu/~malcolm/DDM/GALLERY/15.01_1956.gif • General Information on Perspective: http://www.newcastle.edu.au/department/fad/fi/woodrow/an-persp.htm • Leonardo: http://www.mos.org/sln/Leonardo/LeonardosPerspective.html • Alberti: http://www.leonet.it/culture/nexus/98/Pasquale.html • Pantheon: http://www.leonet.it/culture/nexus/98/Sperling.html

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# A major imperfect authentic cadence The Solution below shows the 3 most common A major imperfect authentic cadences on the piano and treble clef. The Lesson steps then describe the cadence structure in this key, the chords used, followed by an example of its use. For a quick summary of this topic, have a look at Cadence. ## Solution - 3 parts ### 1. A major root position IAC This step shows the root position IAC in the key of A major. The root position imperfect authentic cadence moves from the dominant (V), to the tonic (I) scale degree, with both chords in root position. In contrast to the A major perfect authentic cadence the tonic of chord I does not need to be the highest note of this chord, and so the cadence is weaker. So in this major key, we are going from the A major triad chord #V - E major chord, to A major triad chord #I - A major chord. To demonstrate this, on the treble clef above, A major triad chord #I, A major triad chord #V, and A major triad chord #IV are used to set up the phrase as being in this key, then the cadence chords V and I finish off the phrase, giving only a partial sense of completion, in comparison to the perfect authentic variation. ### 2. A major inverted IAC This step shows the inverted IAC in the key of A major. The inverted imperfect authentic cadence moves from the dominant (V), to the tonic (I) scale degree, with one or both chords inverted. For example, in this major key, we are going from the 1st inversion of A major triad chord #V - E major chord, to A major triad chord #I - A major chord. In contrast to the A major perfect authentic cadence, which has chord V in root position, in this example, this cadence has chord V inverted, but is the same in all other respects. To demonstrate this, on the treble clef above, A major triad chord #I, A major triad chord #V, and A major triad chord #IV are used to set up the phrase as being in this key, then the cadence chords V6 (Chord V in 1st inversion) and chord I finish off the phrase, giving a weaker sense of completion and resolution compared to the perfect authentic cadence. ### 3. A major leading tone IAC This step shows the leading tone IAC in the key of A major. The leading tone imperfect authentic cadence moves from the leading note /tone (viio), to the tonic (I) scale degree. So in this major key, we are going from the A major triad chord #viio - G# diminished chord, to A major triad chord #I - A major chord. To demonstrate this, on the treble clef above, chords A major triad chord #I, A major triad chord #V, and A major triad chord #IV are used to set up the phrase as being in this key, then the cadence chords viio and I finish off the phrase. ## Lesson steps ### 1. Cadence Types This step describes the main cadence types, and the idea of strong versus weak cadence. #### Cadence definition In music theory, a cadence is two chords which create a sense of closure, or rest to a phrase, section, or entire piece of music. The most commonly used are: perfect authentic, imperfect authentic, plagal, deceptive and half cadence. Some of the above are US-english terms. In the UK, authentic cadences are called perfect cadences, half cadences are called imperfect cadences, and deceptive cadences are called interrupted cadences. #### Cadences - strong versus weak Each of the above cadence types use different chords (or inversions) to create these rest / closure effects. Strong cadences give a real sense of finality, and so are most often used right at the end of a piece. In contrast, weak cadences are less conclusive, which can be used to create a sense of rest, or even surprise the listener with a false ending, when a strong cadence was expected in its place. ### 2. A major scale notes and chords This step shows the A major scale notes and the triad chords in that scale. Before describing the details of the imperfect authentic cadence in the key of A major, first it would be to useful to identify the scale notes, degrees and chords that could be used in this key. #### A major scale notes Below is a piano diagram showing the A major scale notes. #### A major scale chords For details on all the chords in this scale, have a look at A major triad chords, and A major 7th chords, but a summary table of all chord names and their scale degrees is shown below. A major scale Note no.Note nameScale degreeTriad chord #7th chord # 1AtonicA major triad chord #IA major seventh chord #I7 2BsupertonicA major triad chord #iiA major seventh chord #ii7 3C#mediantA major triad chord #iiiA major seventh chord #iii7 4DsubdominantA major triad chord #IVA major seventh chord #IV7 5EdominantA major triad chord #VA major seventh chord #V7 6F#submediantA major triad chord #viA major seventh chord #vi7 7G#leading toneA major triad chord #viioA major seventh chord #viiø7 For each note in the scale (2nd column), there is a triad chord whose root / first note is that scale note (4th column), and the same applies to 7th chords (5th column). To understand what the roman numerals mean, please look at A major triad chords or A major 7th chords. According to the cadence type, some of these chords, scale degrees and roman numerals will be used in later steps to define this cadence. ### 3. A major root position IAC This step shows the A major root position IAC on the piano and treble clef. #### Structure The root position imperfect authentic cadence moves from the dominant (V), to the tonic (I) scale degree. So looking up the chords relating to these scale degrees from the table above, we are going from the A major triad chord #V - E major chord, to A major triad chord #I - A major chord. For an imperfect authentic cadence to be considered in root position, both cadence chords need to be in root position, so on that count the links above are fine - both chords are in root position. However, in contrast to perfect authentic cadences, which need to have the tonic as the highest note of the tonic chord (I), imperfect authentic cadences do not need have this restriction. For an example in this key, whereas the perfect authentic cadence added the tonic of the octave note A onto chord I, creating a chord with 4 notes, the imperfect variation will just use the tonic triad chord as it is, unchanged, with the usual 3 notes. In this case, the highest note is E, which is not the triad root, so the cadence is considered imperfect. It is less strong than the perfect version, because it doesn't give the same sense of closure or completion to the phrase. #### Example The two chords above are shown as the last two chords on the treble clef below. The first three chords on the staff below are not strictly part of the cadence, but they are useful to set the expectation that this phrase is definitely in the key of A major. To do this, we are using chords A major triad chord #I, A major triad chord #V, and A major triad chord #IV, and after hearing these chords, followed by the first chord in the cadence (V again), our ear is definitely expecting the tonic chord as the final chord in the sequence. Since the tonic of chord I is not the highest note in the final chord, the sense of resolution and finality is not there, in comparison to the perfect variation. The audio files below also contain all 5 chords shown on the treble clef above. ### 4. A major inverted IAC This step shows the A major inverted IAC on the piano and treble clef. #### Structure The inverted imperfect authentic cadence moves from the dominant (V), to the tonic (I) scale degree. So looking up the chords relating to these scale degrees from the table above, we are going from the A major triad chord #V - E major chord, to A major triad chord #I - A major chord. For an authentic cadence to be considered inverted, one or both of these chords can be inverted, so the root of the chord is not the bass note of the chord. We will use the A major perfect authentic cadence in the same key as a starting point, then invert the first chord (chord V) of the cadence, and leave the final chord (I + 8th / octave note) unchanged. To invert chord V, we will move its root - note E, up one octave, so it has moved from the lowest to the highest note pitch of the chord. By moving the root up, we have created chord V in 1st inversion. Note G# is now the bass note of the chord. #### Example The two chords above are shown as the last two chords on the treble clef below. The first three chords on the staff below are not strictly part of the cadence, but they are useful to set the expectation that this phrase is definitely in the key of A major. To do this, we are using chords A major triad chord #I, A major triad chord #V, and A major triad chord #IV, and after hearing these chords, our ear might expect to hear chord V again, followed by the tonic chord. Instead, we get chord V in 1st inversion followed by the tonic chord. The inversion of chord V (V6) gives an unexpected twist on the way back to the tonic chord (in comparison to the A major perfect authentic cadence), so the the cadence feels less predictable and strong as a result. The audio files below also contain all 5 chords shown on the treble clef above. ### 5. A major leading tone IAC This step shows the A major leading tone IAC on the piano and treble clef. #### Structure The leading tone imperfect authentic cadence moves from the leading note / tone (viio), to the tonic (I) scale degree. In comparison to the A major perfect authentic cadence, and the imperfect cadences shown above, which all move from chord A major triad chord #V, this leading tone cadence substitutes chord V for A major triad chord #viio. This chord contains the leading tone / note - of the A major scale - note G# as the chord root. So looking up the chords relating to these scale degrees from the table above, we are going from the A major triad chord #viio - G# diminished chord, to A major triad chord #I - A major chord. #### Example The two chords above are shown as the last two chords on the treble clef below. The first three chords on the staff below are not strictly part of the cadence, but they are useful to set the expectation that this phrase is definitely in the key of A major. To do this, we are using chords A major triad chord #I, A major triad chord #V, and A major triad chord #IV, and after hearing these chords, our ear is might be expecting chord V then chord I as the final chord in the sequence (as per the A major perfect authentic cadence). Although this cadence does give quite a strong resolution and sense of completion, , it is a weaker cadence than the A major perfect authentic cadence, since the relationship between dominant(V) and tonic(I) is the strongest possible tonal relationship in diatonic scales. The audio files below also contain all 5 chords shown on the treble clef above.

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# Solving limit without L'Hôpital I need to solve this limit without L'Hôpital's rule. These questions always seem to have some algebraic trick which I just can't see this time. $$\lim_{x\to0} \frac{5-\sqrt{x+25}}{x}$$ Could someone give me a hint as to what I need to do to the fraction to make this work? Thanks! • I'm not sure why anyone would ask you to solve a limit with an easy solution, using a difficult solution. The instructor needs to find examples that require the skills expected for this limit, whilst L'Hopital's is impossible or impractical. If such a case doesn't exist, then you don't need the skills it teaches ;) – Cruncher Apr 25 '14 at 15:26 • @Cruncher: To evaluate such a limit by L'Hôpital, you need to know that $\frac{d}{dx}\sqrt x = 1/(2\sqrt x)$, and to prove that formula correct (from the definition of derivative), you need to be able to evaluate this kind of limit. So refraining from using L'H is not some artificial restriction imposed by the teacher because they couldn't think of any other way to test the student's knowledge of a particular "skill"; it's a restriction which arises out of logical considerations in the structure of the foundations of the theory. (A similar case: $\lim_{x\to 0}\frac{\sin x}{x}$.) – user21467 Apr 25 '14 at 21:15 • @StevenTaschuk then the proof of $\frac{d}{dx}\sqrt{x}$ should be done separately. To impose such a restriction means they've likely already learned l'hopitale, and learned how to differentiate roots. So if the teacher didn't take "logical consideration in the structure of the foundations of the theory" then, then why start now? (tldr: Give these kinds of questions before teaching l'hopitale) – Cruncher Apr 26 '14 at 12:56 • @Cruncher - Pedagogical order is often different from logical order. It can make sense to teach mid-level techniques first and supply the logical foundations later; for one thing, this can bring interesting applications within reach quickly, which provides motivation for the foundational work. This is a perfectly sound pedagogical approach, assuming (as I do) that the students are capable of understanding that the order they encountered something in might be different from the order that it's built in. – user21467 Apr 26 '14 at 14:08 $$\lim_{x\to0} \frac{5-\sqrt{x+25}}{x}=\lim_{x\to0} \frac{(5-\sqrt{x+25)}(5+\sqrt{x+25})}{x(5+\sqrt{x+25})}=\lim_{x\to0} \frac{25-(x+25)}{x(5+\sqrt{x+25})}=-\frac{1}{10}$$ • I fixed typo's (2 parentheses were missing). Cheers. – Claude Leibovici Apr 25 '14 at 4:16 • thanks sir, my regards to you. – ketan Apr 25 '14 at 4:18 • You are very welcome ! – Claude Leibovici Apr 25 '14 at 4:19 Let $t^2=x+25$, then $t=\sqrt{x+25}.$ Then we have $$\lim_{t\to 5}\frac{5-t}{t^2-25}=\lim_{t\to 5}\dfrac{5-t}{(t+5)(t-5)}=-\lim_{t\to 5}\dfrac{5-t}{(t+5)(5-t)}=-\lim_{t\to 5}\dfrac{1}{t+5}=-\dfrac{1}{10}.$$ • This answer is most creative of all of them,I am simply loving it – Vanio Begic Apr 25 '14 at 4:38 • Choosing the negative root is equally valid, and soon simplifies to the same result. – Ben Voigt Apr 25 '14 at 23:15 Definition of derivative at $x=0$ for $f(x) = -\sqrt{x+25}$. $$\lim_{x\to0}\frac{5-\sqrt{x+25}}{x}=\lim_{x\to0}\frac{5-\sqrt{x+25}}{(\sqrt{x+25})²-25}=\lim_{x\to0}\frac{5-\sqrt{x+25}}{-(5-\sqrt{x+25})(5+\sqrt{x+25})}=\lim_{x\to0}\frac{-1}{5+\sqrt{x+25}}=\frac{-1}{10}$$ Another possible method is the expand the square root term by Taylor Series (also known as Taylor expansion) after taking 25 out of the sqrt. Have you covered Taylor expansion? It's a life saver in many situations!!

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This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A003686 Number of genealogical 1-2 rooted trees of height n. 14 1, 2, 3, 5, 11, 41, 371, 13901, 5033531, 69782910161, 351229174914190691, 24509789089655802510792656021, 8608552999157278575508415639286249242844899051 (list; graph; refs; listen; history; text; internal format) OFFSET 1,2 COMMENTS Let u(n), v(n) be defined by u(1)=v(1)=1, u(n+1)=u(n)+v(n), v(n+1)=u(n)*v(n); then a(n)=u(n). - Benoit Cloitre, Apr 01 2002 Consider the mapping f(a/b) = (a + b)/(a*b). Taking a = 1 b = 1 to start with and carrying out this mapping repeatedly on each new (reduced) rational number gives the following sequence 1/1, 2/1, 3/2, 5/6, 11/30, ... Sequence contains the numerators. - Amarnath Murthy, Mar 24 2003 An infinite coprime sequence defined by recursion. - Michael Somos, Mar 19 2004 REFERENCES D. Parisse, The Tower of Hanoi and the Stern-Brocot Array, Thesis, Munich, 1997. LINKS Franklin T. Adams-Watters, Table of n, a(n) for n = 1..19 FORMULA lim n -> infinity a(n)^phi/A064847(n)=1 where phi=(1+sqrt(5))/2 is the golden ratio. - Benoit Cloitre, May 08 2002 Numerator of b(n) where b(n) = 1/numer(b(n-1)) + 1/denom(b(n-1)), b(1)=1. a(n+1)=a(n)+a(1)*a(2)*...*a(n-1). Also a(n+1)=a(n)+a(n-1)*(a(n)-a(n-1)), a(1)=1, a(2)=2. a(n) ~ c^(phi^n), where c = 1.22508584062304325811405322247537613534139348463831009881946422737141574647... and phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, May 21 2015 MATHEMATICA RecurrenceTable[{a[1]==1, a[2]==2, a[n]==a[n-1]+a[n-2](a[n-1]-a[n-2])}, a[n], {n, 15}] (* Harvey P. Dale, Jul 27 2011 *) Re[NestList[Re@#+(1+I Re@#)Im@#&, 1+I, 15]] (* Vladimir Reshetnikov, Jul 18 2016 *) PROG (PARI) a(n) = local(an); if(n<1, 0, an=vector(max(2, n)); an[1]=1; an[2]=2; for(k=3, n, an[k]=an[k-1] - an[k-2]^2 + an[k-1]*an[k-2]); an[n]) (MAGMA) I:=[1, 2]; [n le 2 select I[n] else Self(n-1)+Self(n-2)*(Self(n-1)-Self(n-2)): n in [1..14]]; // Vincenzo Librandi, Jul 19 2016 CROSSREFS Cf. A001685, A064526, A064847. Sequence in context: A188142 A276531 A276532 * A086506 A109462 A000905 Adjacent sequences:  A003683 A003684 A003685 * A003687 A003688 A003689 KEYWORD nonn,easy,nice AUTHOR Vsevolod F. Lev, c. 1998 EXTENSIONS Additional description from Andreas M. Hinz and Daniele Parisse STATUS approved Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent The OEIS Community | Maintained by The OEIS Foundation Inc. Last modified October 23 20:17 EDT 2019. Contains 328373 sequences. (Running on oeis4.)

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# CAT2019-1: 69 88 views In a class, $60$% of the students are girls and the rest are boys. There are $30$ more girls than boys. If $68$% of the students, including $30$ boys, pass an examination, the percentage of the girls who do not pass is____ edited 364 points 1 1 4 ## Related questions 1 149 views If $m$ and $n$ are integers such that $(\sqrt{2})^{19}3^{4}4^{2}9^{m}8^{n}=3^{n}16^{m}(\sqrt[4]{64})$ then $m$ is $-20$ $-12$ $-24$ $-16$ 1 vote 2 138 views The income of Amala is $20$% more than that of Bimala and $20$% less than that of Kamala. If kamala’s income goes down by $4$% and Bimala’s goes up by $10$%, then the percentage by which kamala’s income would exceed Bimala’s is nearest to $31$ $28$ $32$ $29$ 1 vote On selling a pen at $5$% loss and a book at $15$% gain, Karim gains Rs. $7$. If he sells the pen at $5$% gain and the book at $10$% gain, he gains Rs. $13$. What is the cost price of the book in Rupees? $80$ $85$ $95$ $100$ Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is $5:6$ $4:5$ $3:4$ $2:3$ Let $S$ be the set of all points $(x,y)$ in the $x-y$ plane such that $|x|+|y|\leq 2$ and $|x|\geq 1$. Then, the area, in square units, of the region represented by $S$ equals _____

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# Find the Geometric Mean 32 , 16 , 8 32 , 16 , 8 Use the formula to find the geometric mean. 32⋅16⋅83 Multiply. Multiply 32 by 16. 512⋅83 Multiply 512 by 8. 40963 40963 Rewrite 4096 as 163. 1633 Pull terms out from under the radical, assuming real numbers. 16 The geometric mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise. 16 Find the Geometric Mean 32 , 16 , 8 ### Solving MATH problems We can solve all math problems. Get help on the web or with our math app Scroll to top

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# math posted by john \$18,500 at 4.5% compounded semiannually for 5 years 1. Damon 18500 * (1 + .045/2)^10 2. helper \$18,500 at 4.5% compounded semiannually for 5 years A(t) = P(1 + r/n)^nt A(5) = 18500(1 + 0.045/2)^(2(5)) A(5) = 18500(1 + 0.0225)^10 A(5) = 18500(1.0225)^10 A(5) = 18500(1.24920) A(5) = 23110.26 interest 18,500 + I = total value after 5 yrs 3. Damon I think A(5) is the total value. 4. helper Yes, Damon is right. A(5) is the total value. I meant to put, \$18,500 + 4610.26 Interest = \$23,110.26 after 5 years ## Similar Questions 2. ### Accounting How do I calculate the future value of the following? 3. ### math Semiannually deposits of \$400 are made for 10 years into an annuity that pays 7% compounded semiannually 4. ### Math Find the total investment and the interest earned when \$2,500 is invested at 5% compounded semiannually for 3 years. 5. ### Calc Find the present value of \$14000 due in 9 years at the given rate of interest. (a) 2%/year compounded semiannually? 6. ### math find the accumulated value of an investment of \$10000 for 5 years at an interest rate of 5.5% if the money is a. compounded semiannually; b. compounded monthly; c. compounded continuously. 7. ### Math \$500 in 15 years at 8% annual interest compounded semiannually. 8. ### Math \$500 in 15 years at 8% annual interest compounded semiannually. P = \$500 Time = 30 years Rate = 4% \$500(1+.08/2)^(2*15) = \$1621.70 9. ### Math If \$37,500 is invested at 6.3% for 30 years, find the future value if the interest is compounded annually,semiannually, quarterly, monthly

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Talk:Independence (mathematical logic) WikiProject Mathematics (Rated Start-class, Mid-priority) This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks. Mathematics rating: Start Class Mid Priority Field: Foundations, logic, and set theory merge When I wrote this article, I was unaware of the existence of the logical independence article (I think I had seen it before; I just forgot). That article is more complete, but this one has the better name, so I put the merge tags from logical independence to independence (mathematical logic). The usage notes in independence (mathematical logic) about the word "undecidable" and about the sense of "independent" meaning simply "not proved" (rather than "not proved nor refuted") should in any case be maintained. --Trovatore 05:15, 24 January 2006 (UTC) Instead of a merge, I had what I had written at independence (mathematical logic) deleted (after saving a copy locally), and logical independence was then moved here. Then I selectively reincorporated my text from the previous independence (mathematical logic) into the current article. --Trovatore 18:01, 16 February 2006 (UTC) latest edits Here are my objections to DesolateReality's latest edits: 1. "Independent of a maximally consistent body of propositions". The only thing I can understand by "maximally consistent" is that any proper extension is inconsistent. But then nothing can be independent of that! (In the sense of "independent of and consistent with"; see next objection.) 2. The latest edits have as the primary meaning of "independent" the sense of "cannot be proved" rather than "can neither be proved nor refuted", and refers to the second sense as "informal". I kind of doubt that this really reflects general usage. 3. The claim The existence of independent statements is of philosophical interest. It puts into question Hilbert's program, casting doubt as to whether a complete formalism of mathematics is possible. is not really accurate; the fact that a theory fails to prove or refute something may just mean that you haven't made the theory strong enough. The argument against Hilbert's program has to do with the necessary incompleteness of any theory satisfying certain hypotheses. Without quantifying over theories, the claim is severely misleading. (A related problem is that no sentence is "independent" full stop; it can only be independent of some specified theory.) 4. The "standard technique" section is mostly accurate but does not strike me as being written in encyclopedic style. --Trovatore 21:45, 10 June 2007 (UTC) Thank you, Trovatore, for the revert. I agree with you generally about your objections. Here are my specific replies: 1. I wanted some way to refer to the term "theory" for a general audience. I agree that "maximally consistent" doesn't make sense. 2. I agree. 3. My intention here is to bring out why logicians are interested in independence proofs. Until I find a better way to phrase this, I agree with the revert. 4. I think later editions of this article should try to incorporate the observation that independence of σ from T is usually proven by exhibiting a model of T + ¬σ. Such a method of proof is usually the first thing taught to logic students immediately after the notion of independence is explained.--DesolateReality 04:43, 11 June 2007 (UTC) publications? Are there any publications that elaborate on this topic further? Can they be listed? --Farleyknight (talk) 02:31, 25 December 2008 (UTC)

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Simulating a competition python **The parts I need some assistance with are: 1. A way to implement the probability for a foul into the code (added Omar’s input here and it works) 2. Print the results nicely instead of how it is now (prints out name and jump for each simulation so when I do 100 simulations there are too many outputs 3. Top 10 list – further clarification in comments. 4. With Omar’s input the histogram has been made, now I just have to import it to a pdf file. import matplotlib.pyplot as plt import random filename=input('Which file do you want to collect the competitors from?: ') class Player(): win_length = [] def __init__(self,name,m,s,fp): self.name=name self.m=m self.s=s self.fp=fp self.best= 0 self.wins = 0 def __str__(self): playerwins = self.name + ' ' + str(self.wins) + ' ' + 'Wins' return playerwins def jump(self): result=[] foul = [1] * int(10 * self.fp) + [0] * int(10 * (1 - self.fp)) for i in range(0,6): if random.choice(foul) == 0: jump = 3 * (random.normalvariate(self.m,self.s)) result.append(jump) self.best = max(result) return self.best class Arena(): def main(self): print ("Welcome to the competition, please enter how many simulations you would like to run!") self.contest() self.sortStats() self.stats() infil = open(filename,'r') self.players = [] while line != '': line = line.rstrip('n') parts = line.split() name = parts[0] m = float(parts[2]) s = float(parts[3]) fp = float(parts[4]) #added fp down here since it has to check the probability from the file(?) tmp = Player(name, m, s, fp) self.players.append(tmp) return self.players def contest(self): while True: try: x = int(input("How many competitions?")) break except ValueError: print ("Only numbers please!") for rounds in range(0,x): for player in self.players: player.jump() bestjump = max(self.players, key = lambda jump: jump.best) Player.win_length.append(bestjump.best) bestjump.wins += 1 print ("Winner: ", bestjump.name, "nResult: ", bestjump.best) plt.hist(Player.win_length, bins=5, color='y', ec='black') plt.title('Distribution of Winning lengths') plt.xlabel('Jump lengths') plt.show() def sortStats(self): return self.players.sort(key=lambda Player:Player.wins, reverse=True) def stats(self): for wins in range(len(self.players)): print (self.players[wins]) a=Arena() a.main() Example Run Which file do you want to collect the competitors from? test.txt Welcome to the competition, please enter how many simulations you would like to run! How many competitions? 100 RESULTS Carl Phelps 16.45 Charlie Jumper 17.89 Michael Finks 17.59 TOP 10 Carl Phelps 19.5 Charlie Jumper 18.67 Michael Finks 18.31 and so on STATISTICS Carl Phelps 43 Wins Charlie Jumper 37 Wins Michael Finks 20 Wins Histogram can be seen in hist.pdf! If any clarification is required please comment. class Player: def __init__(self, name, m, s, fp): # fp => probability of foul self.name = name self.m = m self.s = s self.fp = fp self.best = 0 self.wins = 0 def jump(self): resultat = [0] # No need to have "resultat" as an instance attribute foul = [1] * int(10 * self.fp) + [0] * int(10 * (1 - self.fp)) # probability space depending on "fp" for i in range(6): if random.choice(foul) == 0: jump = 3 * (random.normalvariate(self.m, self.s)) resultat.append(jump) self.best = max(resultat) return self.best 1. I guess you could just move the print statement outside of the loop such that you only print the last run/simulation, if that’s what you want (or do you want to print the average of all the jumps?). 3 + 4. Create a class object attribute above __init__ as win_length = {}: class Player: win_length = {} # Dictionary of winners def __init__(self, name, m, s, fp): # fp => probability of foul self.name = name self.m = m self.s = s self.fp = fp self.best = 0 self.wins = 0 Now under your readplayersfromfile() method, add this command such that you insert every player name as a key in the dictionary: while line != '': line = line.rstrip('n') parts = line.split() name = parts[0] Player.win_length[name] = [] Finally, under your contest() method: for rounds in range(0, x): for player in self.players: player.jump() bestjump = max(self.players, key=lambda jump: jump.best) Player.win_length[bestjump.name].append(bestjump.best) # Add the best jump to list of winning player bestjump.wins += 1 jump_list = [] # Contains jumps of all runs/simulations (for histogram) for lis in Player.win_length.values(): jump_list += lis top_list = sorted(jump_list, reverse=True)[:10] for i in top_list: for k in Player.win_length: if i in Player.win_length[k]: print(f"{k}: {i:.4}") plt.hist(jump_list, color='y', ec='black') plt.title('Distribution of Winning lengths') plt.xlabel('Jump lengths') plt.show()

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UK Markets closed # Class Limited's (ASX:CL1) Stock's Been Going Strong: Could Weak Financials Mean The Market Will Correct Its Share Price? Most readers would already be aware that Class' (ASX:CL1) stock increased significantly by 40% over the past three months. However, we decided to pay close attention to its weak financials as we are doubtful that the current momentum will keep up, given the scenario. Particularly, we will be paying attention to Class' ROE today. Return on equity or ROE is a key measure used to assess how efficiently a company's management is utilizing the company's capital. In other words, it is a profitability ratio which measures the rate of return on the capital provided by the company's shareholders. View our latest analysis for Class ### How To Calculate Return On Equity? The formula for ROE is: Return on Equity = Net Profit (from continuing operations) ÷ Shareholders' Equity So, based on the above formula, the ROE for Class is: 8.8% = AU\$3.7m ÷ AU\$42m (Based on the trailing twelve months to June 2021). The 'return' is the income the business earned over the last year. So, this means that for every A\$1 of its shareholder's investments, the company generates a profit of A\$0.09. ### What Is The Relationship Between ROE And Earnings Growth? Thus far, we have learned that ROE measures how efficiently a company is generating its profits. Depending on how much of these profits the company reinvests or "retains", and how effectively it does so, we are then able to assess a company’s earnings growth potential. Assuming all else is equal, companies that have both a higher return on equity and higher profit retention are usually the ones that have a higher growth rate when compared to companies that don't have the same features. ### Class' Earnings Growth And 8.8% ROE When you first look at it, Class' ROE doesn't look that attractive. However, its ROE is similar to the industry average of 10%, so we won't completely dismiss the company. Having said that, Class' five year net income decline rate was 2.6%. Bear in mind, the company does have a slightly low ROE. Hence, this goes some way in explaining the shrinking earnings. However, when we compared Class' growth with the industry we found that while the company's earnings have been shrinking, the industry has seen an earnings growth of 17% in the same period. This is quite worrisome. Earnings growth is a huge factor in stock valuation. The investor should try to establish if the expected growth or decline in earnings, whichever the case may be, is priced in. By doing so, they will have an idea if the stock is headed into clear blue waters or if swampy waters await. Is CL1 fairly valued? This infographic on the company's intrinsic value has everything you need to know. ### Is Class Efficiently Re-investing Its Profits? With a high three-year median payout ratio of 76% (implying that 24% of the profits are retained), most of Class' profits are being paid to shareholders, which explains the company's shrinking earnings. With only a little being reinvested into the business, earnings growth would obviously be low or non-existent. To know the 4 risks we have identified for Class visit our risks dashboard for free. Additionally, Class has paid dividends over a period of six years, which means that the company's management is rather focused on keeping up its dividend payments, regardless of the shrinking earnings. Existing analyst estimates suggest that the company's future payout ratio is expected to drop to 56% over the next three years. As a result, the expected drop in Class' payout ratio explains the anticipated rise in the company's future ROE to 18%, over the same period. ### Summary In total, we would have a hard think before deciding on any investment action concerning Class. The company has seen a lack of earnings growth as a result of retaining very little profits and whatever little it does retain, is being reinvested at a very low rate of return. That being so, the latest industry analyst forecasts show that the analysts are expecting to see a huge improvement in the company's earnings growth rate. Are these analysts expectations based on the broad expectations for the industry, or on the company's fundamentals? Click here to be taken to our analyst's forecasts page for the company. Have feedback on this article? Concerned about the content? Get in touch with us directly. Alternatively, email editorial-team (at) simplywallst.com. This article by Simply Wall St is general in nature. We provide commentary based on historical data and analyst forecasts only using an unbiased methodology and our articles are not intended to be financial advice. It does not constitute a recommendation to buy or sell any stock, and does not take account of your objectives, or your financial situation. We aim to bring you long-term focused analysis driven by fundamental data. Note that our analysis may not factor in the latest price-sensitive company announcements or qualitative material. Simply Wall St has no position in any stocks mentioned. Our goal is to create a safe and engaging place for users to connect over interests and passions. In order to improve our community experience, we are temporarily suspending article commenting

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How do you find the asymptotes for y=1/(2-x)? Feb 13, 2016 Answer: vertical asymptote at x = 2? horizontal asymptote at y = 0 Explanation: vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation let the denominator equal zero. solve : 2 - x = 0 → x = 2 is the equation. horizontal asymptotes occur as lim_(x→±∞) f(x) → 0 If the degree of the numerator is less than the degree 0f the denominator then the equation is y = 0. here the degree of numerator < degree of denominator and so equation of horizontal asymptote is y = 0 here is the graph of the function as an illustration of them. graph{1/(2-x) [-10, 10, -5, 5]}

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• 这是一套导购月报表汇总表excel模版下载，喜欢的人都来下载吧。该文档为导购月报表汇总表excel模版下载，是一份很不错的参考资料，具有较高参考价值，感兴趣的可以下载看看 • //佣金净收入 desSalary.setSalYxtc(oriSalary.getSalYxtc()+(desSalary.getSalYxtc()==null?0:desSalary.getSalYxtc())); desSalary.setSalJbgzBefore(oriSalary.getSalJbgzBefore()+(desSalary.... 参考代码 public List<SalaryDetail> monthFormListFormat(List<SalaryDetail> oriSalaryList) { //未作任何处理的list if(oriSalaryList==null||oriSalaryList.size()==0) return null; int len = oriSalaryList.size(); //目的List List<SalaryDetail> desSalaryList = oriSalaryList; //第一行的对象 SalaryDetail firstLineSalary = oriSalaryList.get(0); //小计的对象 SalaryDetail subtotalSalary = new SalaryDetail(); //最后总计的对象 SalaryDetail sumtotalSalary = new SalaryDetail(); //存放小计对象的位置，以及小计对象 Map<Integer,SalaryDetail> subtotalMap = new HashMap<Integer,SalaryDetail>(); //插入了几行数据 int n = 0; for(int i = 0;i<len;i++){ if(firstLineSalary.getUserType().equals(oriSalaryList.get(i).getUserType())) { if(i==len-1){ subtotalSalary = getSubTotalSum(subtotalSalary, oriSalaryList.get(i),"1"); subtotalSalary.setUserType("小计"); subtotalSalary.setRowSpanCount(1); subtotalMap.put(i, subtotalSalary); sumtotalSalary = getSubTotalSum(sumtotalSalary, subtotalSalary,"1"); break; } //如果用户类型相同则进行相加，以便得到小计的值 subtotalSalary = getSubTotalSum(subtotalSalary, oriSalaryList.get(i),"1"); }else{ if(i==len-1){ //把最后一条记录以上的计算一下,并清空【小计】 subtotalSalary.setUserType("小计"); subtotalSalary.setRowSpanCount(1); sumtotalSalary = getSubTotalSum(sumtotalSalary, subtotalSalary,"1"); subtotalMap.put(i-1, subtotalSalary); subtotalSalary = new SalaryDetail(); //最后一条记录的处理 subtotalSalary = getSubTotalSum(subtotalSalary, oriSalaryList.get(i),"1"); subtotalSalary.setUserType("小计"); subtotalSalary.setRowSpanCount(1); sumtotalSalary = getSubTotalSum(sumtotalSalary, subtotalSalary,"1"); subtotalMap.put(i, subtotalSalary); break; } //把每种用户类型的第一行修改，并在List副本里面加上一个小计的对象， firstLineSalary = oriSalaryList.get(i); subtotalSalary.setUserType("小计"); subtotalSalary.setRowSpanCount(1); subtotalMap.put(i-1, subtotalSalary); sumtotalSalary = getSubTotalSum(sumtotalSalary, subtotalSalary,"1"); subtotalSalary = new SalaryDetail(); //把新的“第一个值”增加到小计中 subtotalSalary = getSubTotalSum(subtotalSalary, firstLineSalary,"1"); } } for(int i = oriSalaryList.size()-1;i>=0;i--){ if(subtotalMap.containsKey(i)){ // if(i == oriSalaryList.size()-1){ // }else{ // } } } //插入最后一列 sumtotalSalary.setUserType("总计"); sumtotalSalary.setRowSpanCount(1); //新的第一行 firstLineSalary = oriSalaryList.get(0); len = oriSalaryList.size(); int rowSpan = 0; //加上rowspan for(int i = 0;i<len;i++){ if(i<len-1){ SalaryDetail nextLineSalary = oriSalaryList.get(i+1); if("小计".equals(nextLineSalary.getUserType())||"总计".equals(nextLineSalary.getUserType())){ if(!"小计".equals(firstLineSalary.getUserType())&&!"总计".equals(firstLineSalary.getUserType())){ firstLineSalary.setRowSpanCount(rowSpan+1); } continue; } if(firstLineSalary.getUserType().equals(nextLineSalary.getUserType())){ rowSpan ++; firstLineSalary.setRowSpanCount(rowSpan+1); }else{ rowSpan = 0; firstLineSalary = nextLineSalary; } } } return oriSalaryList; } /** * 把原对象的值和目的对象的值相加，并返回目的对象 * @param desSalary * @param oriSalary * @return */ private SalaryDetail getSubTotalSum(SalaryDetail desSalary,SalaryDetail oriSalary,String flg){ //desSalary.setUserType("小计"); if("1".equals(flg)){ desSalary.setEleYjdf(oriSalary.getEleYjdf()+(desSalary.getEleYjdf()==null?0:desSalary.getEleYjdf())); desSalary.setEleJxzxh(oriSalary.getEleJxzxh()+(desSalary.getEleJxzxh()==null?0:desSalary.getEleJxzxh())); desSalary.setEleHgkjxs(oriSalary.getEleHgkjxs()+(desSalary.getEleHgkjxs()==null?0:desSalary.getEleHgkjxs())); desSalary.setEleYdkhxs(oriSalary.getEleYdkhxs()+(desSalary.getEleYdkhxs()==null?0:desSalary.getEleYdkhxs())); desSalary.setEleGlkpxs(oriSalary.getEleGlkpxs()+(desSalary.getEleGlkpxs()==null?0:desSalary.getEleGlkpxs()));//管理考评 //desSalary.setEleTcbl(oriSalary.getEleTcbl()+(desSalary.getEleTcbl()==null?0:desSalary.getEleTcbl()));//提成比例,不需要进行计算 } if("2".equals(flg)){ //设置虚拟的编号 desSalary.setVid(oriSalary.getVid()); desSalary.setUserCount(oriSalary.getUserCount()+desSalary.getUserCount()); } desSalary.setEleQmkhzc(oriSalary.getEleQmkhzc()+(desSalary.getEleQmkhzc()==null?0:desSalary.getEleQmkhzc()));//期末客户资产 desSalary.setEleYjfy(oriSalary.getEleYjfy()+(desSalary.getEleYjfy()==null?0:desSalary.getEleYjfy()));//一级费用 desSalary.setEleCjl(oriSalary.getEleCjl()+(desSalary.getEleCjl()==null?0:desSalary.getEleCjl())); desSalary.setEleSsyj(oriSalary.getEleSsyj()+(desSalary.getEleSsyj()==null?0:desSalary.getEleSsyj()));//实收佣金 desSalary.setEleYysjfj(oriSalary.getEleYysjfj()+(desSalary.getEleYysjfj()==null?0:desSalary.getEleYysjfj()));//营业税及附加 desSalary.setEleTzzbhjj(oriSalary.getEleTzzbhjj()+(desSalary.getEleTzzbhjj()==null?0:desSalary.getEleTzzbhjj()));//投资者保护基金 desSalary.setOthField1(oriSalary.getOthField1()+(desSalary.getOthField1()==null?0:desSalary.getOthField1()));//净佣金 desSalary.setEleYyjjsr(oriSalary.getEleYyjjsr()+(desSalary.getEleYyjjsr()==null?0:desSalary.getEleYyjjsr()));//月佣金净收入 desSalary.setSalYxtc(oriSalary.getSalYxtc()+(desSalary.getSalYxtc()==null?0:desSalary.getSalYxtc())); desSalary.setSalJbgzBefore(oriSalary.getSalJbgzBefore()+(desSalary.getSalJbgzBefore()==null?0:desSalary.getSalJbgzBefore())); //调整前基本工资 desSalary.setSalJbgz(oriSalary.getSalJbgz()+(desSalary.getSalJbgz()==null?0:desSalary.getSalJbgz())); desSalary.setSalGljt(oriSalary.getSalGljt()+(desSalary.getSalGljt()==null?0:desSalary.getSalGljt())); desSalary.setSalKhjljcj(oriSalary.getSalKhjljcj()+(desSalary.getSalKhjljcj()==null?0:desSalary.getSalKhjljcj())); desSalary.setSalJjrjcj(oriSalary.getSalJjrjcj()+(desSalary.getSalJjrjcj()==null?0:desSalary.getSalJjrjcj())); desSalary.setSalJxzxhj(oriSalary.getSalJxzxhj()+(desSalary.getSalJxzxhj()==null?0:desSalary.getSalJxzxhj())); desSalary.setSalZqfxsczgj(oriSalary.getSalZqfxsczgj()+(desSalary.getSalZqfxsczgj()==null?0:desSalary.getSalZqfxsczgj())); desSalary.setSalQtcxwsr(oriSalary.getSalQtcxwsr()+(desSalary.getSalQtcxwsr()==null?0:desSalary.getSalQtcxwsr())); desSalary.setSalZyf(oriSalary.getSalZyf()+(desSalary.getSalZyf()==null?0:desSalary.getSalZyf())); desSalary.setSalJjx(oriSalary.getSalJjx()+(desSalary.getSalJjx()==null?0:desSalary.getSalJjx())); desSalary.setSalYfs(oriSalary.getSalYfs()+(desSalary.getSalYfs()==null?0:desSalary.getSalYfs())); desSalary.setRzrqYxjl(oriSalary.getRzrqYxjl()+(desSalary.getRzrqYxjl()==null?0:desSalary.getRzrqYxjl())); desSalary.setSalCpxsjl(oriSalary.getSalCpxsjl()+(desSalary.getSalCpxsjl()==null?0:desSalary.getSalCpxsjl())); desSalary.setSalCpxssy(oriSalary.getSalCpxssy()+(desSalary.getSalCpxssy()==null?0:desSalary.getSalCpxssy())); desSalary.setSalCpyjbl(oriSalary.getSalCpyjbl()+(desSalary.getSalCpyjbl()==null?0:desSalary.getSalCpyjbl())); return desSalary; } 展开全文 • 以下是《奖惩汇总月报表（DOC格式）》简单预览，如果需要完整表格学习参考，请点击下载。...……………………该文档为奖惩汇总月报表（DOC格式），是一份很不错的参考资料，具有较高参考价值，感兴趣的可以下载看看 • 存货统计表（汇总月报表）PPT以围绕物流采购为核心，以方便大家了解学习存货统计表（汇总月报表）PPT为前...该文档为存货统计表（汇总月报表）PPT，是一份很不错的参考资料，具有较高参考价值，感兴趣的可以下载看看 • SAP 常用报表汇总   •采购管理：  1、采购标准分析 (每每采购组织，每地点采购多少商品，可以按单品)  MCE7  2、GR/IR 余额查询  MB5S •库存管理：  3、供应商寄售、客户寄售 SAP 常用报表汇总 •采购管理： 1、采购标准分析 (每月每采购组织，每地点采购多少商品，可以按单品) MCE7 2、GR/IR 余额查询 MB5S •库存管理： 3、供应商寄售、客户寄售 MB54 / MB58 4、商品库存查询                                    MB52 展开全文 • -- 1.19将每个客户按生成汇总报表，用SQL该如何求解？ Create table T0119C( 客户编号 varchar(24), 客户抬头 varchar(23) ); Insert INTO T0119C VALUES('0001','A公司'); Insert INTO T0119C VALUES('0002',... Mysql 刷题笔记 -- 1.19将每个客户按月生成汇总报表，用SQL该如何求解？ Create table T0119C( 客户编号 varchar(24), 客户抬头 varchar(23) ); Insert INTO T0119C VALUES('0001','A公司'); Insert INTO T0119C VALUES('0002','B公司'); Insert INTO T0119C VALUES('0003','C公司'); Create table T0119X( 客户编号 varchar(24), 日期 Date, 金额 int ); Insert INTO T0119X VALUES('0001','2018-9-12',2000); Insert INTO T0119X VALUES('0001','2018-9-16',1500); Insert INTO T0119X VALUES('0001','2018-10-23',3000); Insert INTO T0119X VALUES('0002','2018-9-15',3200); Insert INTO T0119X VALUES('0002','2018-10-19',5000); Create table T0119Y( 客户编号 varchar(24), 日期 Date, 金额 int ); Insert INTO T0119Y VALUES('0001','2018-9-12',12000); Insert INTO T0119Y VALUES('0001','2018-10-16',10000); Insert INTO T0119Y VALUES('0001','2018-10-23',20000); Insert INTO T0119Y VALUES('0002','2018-11-15',13200); Insert INTO T0119Y VALUES('0002','2018-10-19',25000); T0119C +--------------+--------------+ | 客户编号 | 客户抬头 | +--------------+--------------+ | 0001 | A公司 | | 0002 | B公司 | | 0003 | C公司 | +--------------+--------------+ T0119X +--------------+------------+--------+ | 客户编号 | 日期 | 金额 | +--------------+------------+--------+ | 0001 | 2018-09-12 | 2000 | | 0001 | 2018-09-16 | 1500 | | 0001 | 2018-10-23 | 3000 | | 0002 | 2018-09-15 | 3200 | | 0002 | 2018-10-19 | 5000 | +--------------+------------+--------+ T0119Y +--------------+------------+--------+ | 客户编号 | 日期 | 金额 | +--------------+------------+--------+ | 0001 | 2018-09-12 | 12000 | | 0001 | 2018-10-16 | 10000 | | 0001 | 2018-10-23 | 20000 | | 0002 | 2018-11-15 | 13200 | | 0002 | 2018-10-19 | 25000 | +--------------+------------+--------+ 结果 +---------+--------------+---------------+---------------+ | 日期 | 客户抬头 | X业务金额 | Y业务金额 | +---------+--------------+---------------+---------------+ | 2018-09 | A公司 | 3500 | 12000 | | 2018-09 | B公司 | 3200 | NULL | | 2018-10 | A公司 | 3000 | 30000 | | 2018-10 | B公司 | 5000 | 25000 | | 2018-11 | B公司 | NULL | 13200 | +---------+--------------+---------------+---------------+ SELECT DATE_FORMAT(t.业务日期,'%Y-%m') 日期,c.客户抬头, SUM(t.x业务金额) AS X业务金额 ,SUM(t.y业务金额) AS Y业务金额 FROM ( SELECT x.客户编号,x.日期 业务日期,x.金额 x业务金额,y.金额 y业务金额 FROM t0119x x LEFT JOIN t0119y y ON x.客户编号 = y.客户编号 AND x.日期 = y.日期 UNION SELECT y.客户编号,y.日期 业务日期,x.金额 x业务金额,y.金额 y业务金额 FROM t0119x x RIGHT JOIN t0119y y ON x.客户编号 = y.客户编号 AND x.日期 = y.日期 )t INNER JOIN t0119c c ON t.客户编号 = c.客户编号 GROUP BY 日期,t.客户编号 ORDER BY 日期 展开全文 • 这个软件的报表功能模块，可以按天，，年生成不同类型的报表报表类型包括工作统计，网络流量，程序记录，网站记录，键盘记录，剪贴板，文件记录，USB设备，打印记录，邮件接收，系统事件，报警记录，关键字，... 文章目录iMonitor EAM的报表功能一、电脑工作统计报表详情信息二、 网络流量统计报表三、程序使用统计报表 iMonitor EAM的报表功能 iMonitor EAM（官网：www.imonitorsoft.cn）是静默模式下监控企业员工电脑操作及上网行为的监管系统。这个软件的报表功能模块，可以按天，月，年生成不同类型的报表。报表类型包括工作统计，网络流量，程序记录，网站记录，键盘记录，剪贴板，文件记录等等。 一、电脑工作统计报表 电脑工作统计报表，可以统计每台客户端的运行时间，空闲时间，上网时间，聊天时间，以小时为单位进行统计，使多台客户端形成对比，对员工的工作效率进行分析。 详情信息 通过对每台客户端的监控数据进行统计分析，报表可以按照各个属性进行排序，比如：按照键盘记录的数量（即键盘敲击次数）进行从大到小或者从小到大进行排序，侧面反映出员工的工作程度，还可以电脑运行时间，空闲时间，浏览的网页数等对员工电脑进行排序。 报表可以列出工作时间少于6小时的员工电脑，开机时间晚于8点，键盘敲击次数少于5000次，网页浏览时间大于3小时，聊天时间大于2小时等各个方面对员工的工作状态与效率进行统计。 二、 网络流量统计报表 根据部门的传入传出流量对客户端进行统计分析，了解员工的上网情况。 三、程序使用统计报表 可以统计每一台客户端上的程序使用情况，根据程序使用的时间和程序使用的次数通过柱状图显示，按照从大到小进行排序，分析出员工最常用的办公工具及其使用时长，禁止掉与工作无关但使用频繁的软件，避免影响工作效率。 报表还会统计使用程序的用户，程序名称，程序进程名称，程序使用时长，程序使用次数。 展开全文 • 假设工作簿中按顺序新建3张表叫1和2和3 。如何切换到第2张表？ Sheet2.select //sheet2是表的默认名称。重命名只是给sheet2起一个别名 Sheets(2).select //sheets(2)指工作簿的第2张表 Sheets(“2”).... • SELECT v.pk_org,v.name,SUM(A) "A",SUM(B) "B",SUM(C) "C",SUM(D) "D",SUM(E) "E",SUM(F) "F",SUM(G) "G",SUM(H) "H",SUM(I) "I",SUM(J) "J",SUM(K) "K",SUM(L) "L",SUM(SUM) FROM (SELECT e.pk_org,o.name, ... • 最近，开发的时候用到了finereport做报表，砸死报表导出Excel的时候，发现导出的数据不能按月汇总。即使在报表设计器了把格式改成日期类型，也不能汇总。 后来查了数据库设计才知道，表的日期字段类型是VARCHAR2，... • 1104报表模版汇总(2013).xlsx 热门讨论 2013-10-21 22:15:29 S3f汽车金融公司异地业务情况月报表 S3g第I部分：租赁债权资产质量情况表 S3g第II部分：租赁物价值波动及风险缓释情况表 S3g第III部分：金融租赁公司信用风险缓释情况表 S3h金融租赁公司流动性期限缺口情况表 S3j... • excel财务报表条件匹配，数据汇总项目要求主要运用的excel公式具体实现时的思路按条件汇总思路解决困难项标签汇总，用标签汇总其他数据遇到的操作失误 项目要求 接手一个excel项目，为一家公司完成财务报表里的具体... • gid qty fdate a01 1 2012-1-1 a02 2 2012-1-1 a03 35 2012-1-1 a01 100 2012-1-3 ...如何得到当月每天的 报表 D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 a01 1 100 100 500 800 a02 2 200 a03 35 • 自动轮询汇总报表 所涉系统名称 券商披露网站 人工操作（时间/次） 36小时 所涉人工数量 1 操作频率 每 场景流程 1、每初机器人自动登录网站轮询36家券商披露的财务报告，并下载 2、机器人将下载下来的报告按照... • 1 import xlrd 2 import xlwt 3 from xlutils.copy ... 5 objWb = xlrd.open_workbook(r'C:\Users\IBM\Desktop\新建文件夹\S1-3\7下旬入库表.xlsx') 6 objSht = objWb.sheet_by_index(0) 7 # 定义列表，... • 现在要每个合并多个地区上报的 Excel，每个 Excel 都包含多 sheet。将合并汇总结果保存到新 Excel 中，格式保持不变。 各地 Excel 内容如下，需要将多个 sheet 数据都汇总（求和）： 实现步骤： 首先准备一个... • 4、依据已录入的监测数据生成监测日报表、周报表及月报表；5、各阶段工作量统计；6、查询单点历史监测数据和各阶段监测数据；7、监测时程曲线图生成。下载地址：链接：https://pan.baidu.com/s/13JC... • 公式字段1：(t_iid) 放详细资料节 WhilePrintingRecords; CurrencyVar mySum; mySum:=mySum + {pord_pp2_vw.i_id} //项次或ID 公式字段2:：（t_wei）放页尾 WhilePrintingRecords; CurrencyVar mySum;...Whil... • 汇总函数的条件 以下是每个汇总函数的条件列表： ...每天每周每两周每半月每每季每半年每年 时间条件 每秒每分钟每小时上午/下午   Sum Basic 语法和 Crystal • 汇总函数的条件&lt;?XML:NAMESPACE PREFIX = O /&gt; 以下是每个汇总函数的条件列表： 布尔型条件 任何更改 更改为“是” 更改为“否” 对每个“是” ...每... • 信息系统开发平台OpenExpressApp － 框架待完善工作事项信息系统开发平台OpenExpressApp － 报表模块支持ReportObjectView信息系统开发平台OpenExpressApp － 从compositewpf到MEF信息系统开发平台OpenExpressApp －... • 本文以2012年各产品销售分类汇总报表为例，演示如何在 ActiveReports 报表控件实现文档目录。 1、创建报表文件 在应用程序中创建一个名为 rptMonthlySalesByCategory.cs 的 ActiveReports 报表文件，ActiveRepor • 报表中“组”是经常使用来显示汇总数据的方式，通过组可以让数据进行结构化的汇总，以方便浏览者解读报表信息。在复杂的商业报表中，经常会具有多重的组结构，例如，时间就可能会有年、季、、日，为了方便使用者... • 报表开发中经常会遇到需要进行组内排序的报表，如按月份的分组汇总值排序显示，并显示每销售额前十名的记录。使用报表工具一般通过隐藏行列辅助可以实现，下面通过实例说明润乾报表的实现过程，以及改进方案。 ... ...

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CC-MAIN-2021-25

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https://www.flightpedia.org/convert-footlamberts-to-candelas-per-square-foot.html

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# Convert Footlambert to Candela Per Square Foot - 1 fL to cd/ft2 1 Footlambert(fL) 1 fL = 0.31831 cd/ft2 = 0.31831 Candela Per Square Foot (cd/ft2) 1 cd/ft2 = 3.14159 fL Convert:

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http://calculator.academy/2019/05/06/how-to-calculate-bonus/

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How to calculate bonus Determining your bonus is usually based on two things. Your total salary or yearly wage you earn, and some percentage of that salary. The total percentage you earn is usually a combination of a flat bonus and a performance bonus. This performance bonus is determined based on your work performance of the last year, and is typically decided by your superior. For example, lets say you earn \$50,000.00 per year. You have a flat bonus of 5% and up to an additional 10% based on performance. Your supervises decides you’ve performed adequately but did not go above and beyond expectations. Therefore, you receive a 7% additional bonus for a total of 12%. Next, you need to multiply your total salary by 12% to get your bonus. \$50,000.00 * .12 (12%) = \$6,000.00 Keep in mind that this bonus is before taxes. You will need to pay taxes on this if your company doesn’t do so for you. Bonus Calculator To make things easier we created this bonus calculator. Enter your total yearly salary, and your flat bonus + performance bonus to calculate your total yearly bonus (\$). If you are not sure what your annual salary is, you can use our salary calculator here. It’s important to understand both your yearly salary and bonus, so you can double check that you’re employer is living up to their promises. Often times employers will use tricky wording in order to manipulate how much bonus you receive. Understand number can help reduce and confusion.

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http://centraledesmaths.uregina.ca/QandQ/topics/refrigerator

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Centrale des maths - centraledesmaths.uregina.ca Dilemmes & doutes « D & D » Sujet: refrigerator nouvelle recherche 2 articles trouvés pour ce sujet. Page1/1 A man sells a refrigerator for \$171 2006-02-20 Skye pose la question :A man sells a refrigerator for \$171, gaining on the sale as many percent (based on the cost) as the refrigerator cost, C, in dollars. Find C.Stephen La Rocque lui répond. "cubic feet" of a refrigerator 2003-07-16 Ron pose la question : Is the volume of a home appliance (e.g. fridge or freezer) calculated in a different way? I am planning to replace both my fridge and my freezer but I'm unable to determine what size replacement to get. For example, one company descibes their fridge as being 32"(L) x 30"(W) x 66" (H). I converted those measurements to feet (2.67 x 2.5 x 5.5) and I calculate the fridge to be 36.7 cubic feet. However, the company says the fridge is 18 cf. Chris Fisher lui répond. Page1/1 Centrale des maths reçoit une aide financière de l’Université de Regina et de The Pacific Institute for the Mathematical Sciences. Qui sommes-nous :: carte du site :: our english site

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CC-MAIN-2023-14

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http://www.topperlearning.com/forums/ask-experts-19/brakes-are-applied-to-a-train-traveling-at-72-km-h-after-pas-physics-laws-of-motion-57329/reply

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 Question Mon July 16, 2012 By: Inder Kumar # brakes are applied to a train traveling at 72 km/h after passing 200m its velocity reduced to 36 km/h at same rate of retardation how much further will it go before it goes to rest solution please Tue July 17, 2012 Initial velocity, u = 72 kmph = 20 m/s Final velocity, v = 36 kmph = 10 m/s displacement, s = 200 m let acceleration be a. using 3rd equation of motion, a = (v2-u2)/2s = -3/4 m/s2 now final velocity =0 m/s let final displacement from this position be s again using 3rd equation of motion, s = (v2-u2)/2a = 200/3 m Related Questions Sun December 25, 2016 # what is impulsive force? Sun December 25, 2016 

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CC-MAIN-2017-09

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MATH-138-Fall-2016-Final.pdf # A 5 x dy dx y x y 1 2016 b 5 dy dx 6 e 2 x y y 0 0 • Test Prep • 14 This preview shows page 4 - 9 out of 14 pages. (a) [5] x dy dx = y - x , y (1) = 2016 (b) [5] dy dx = 6 e 2 x - y , y (0) = 0 CROWDMARK MATH 138 Fall 2016 Final © 2016 University of Waterloo Please initial: Page 4 of 14 Subscribe to view the full document. 4. Consider the sequence ( a n ) defined by a 1 = 1 and a n +1 = 1 + 2 a n for n 1. (a) [3] Prove using induction that ( a n ) is increasing. (b) [3] Prove using induction that ( a n ) is bounded above. (c) [1] State the name of the theorem that guarantees the limit lim n →∞ a n exists. (d) [3] Determine lim n →∞ a n . CROWDMARK MATH 138 Fall 2016 Final © 2016 University of Waterloo Please initial: Page 5 of 14 5. (a) [3] State the definition of a series n =1 a n converging to a limit L . (b) [7] Prove that if a series n =1 a n is convergent, then lim n →∞ a n = 0 . CROWDMARK MATH 138 Fall 2016 Final © 2016 University of Waterloo Please initial: Page 6 of 14 Subscribe to view the full document. 6. Determine whether each the following series is absolutely convergent, conditionally convergent or divergent. Justify your answers. (a) [5] summationdisplay n =1 cos( n ) + sin( n ) + 1 n 2 (b) [5] summationdisplay n =1 ( - 1) n sin n CROWDMARK MATH 138 Fall 2016 Final © 2016 University of Waterloo Please initial: Page 7 of 14 (c) [5] summationdisplay n =1 5 n + 7 n 2 n + 4 n + 6 n (d) [5] summationdisplay n =1 ( - 1) n sin parenleftbigg 1 n parenrightbigg CROWDMARK MATH 138 Fall 2016 Final © 2016 University of Waterloo Please initial: Page 8 of 14 Subscribe to view the full document. 7. Determine the radius and interval of convergence for each of the following power series. Justify You've reached the end of this preview. • Winter '07 • Anoymous • Mathematical analysis {[ snackBarMessage ]} ### What students are saying • As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students. Kiran Temple University Fox School of Business ‘17, Course Hero Intern • I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero. Dana University of Pennsylvania ‘17, Course Hero Intern • The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time. Jill Tulane University ‘16, Course Hero Intern

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