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9d959d14-7b9a-4159-a162-048d3b44d728
integral_calc
false
null
Solve the integral: $$ \int \frac{ -8 \cdot \cos(-4 \cdot x)^3 }{ 5 \cdot \sin(-4 \cdot x)^9 } \, dx $$
$\int \frac{ -8 \cdot \cos(-4 \cdot x)^3 }{ 5 \cdot \sin(-4 \cdot x)^9 } \, dx$ = $C-\frac{2}{5}\cdot\left(\frac{1}{3}\cdot\left(\cot(4\cdot x)\right)^6+\frac{1}{4}\cdot\left(\cot(4\cdot x)\right)^4+\frac{1}{8}\cdot\left(\cot(4\cdot x)\right)^8\right)$
9d9a08e8-cb1b-4e73-bdb1-5c8f16ce0448
algebra
false
null
Find the zeros of the polynomial function with complex roots: $f(x) = 2 \cdot x^3 - 2 \cdot x^2 + 5 \cdot x - 5$.
$x$ = $1$, $i\cdot\sqrt{\frac{5}{2}}$, $-i\cdot\sqrt{\frac{5}{2}}$
9d9a2009-a680-4c90-b633-7abf18e2f9e0
differential_calc
false
null
Calculate the integral: $$ \int \frac{ 1 }{ \sqrt[4]{(x-1)^3 \cdot (x+2)^5} } \, dx $$
$\int \frac{ 1 }{ \sqrt[4]{(x-1)^3 \cdot (x+2)^5} } \, dx$ = $\frac{4}{3}\cdot\sqrt[4]{\frac{x-1}{x+2}}+C$
9e0bf1a0-877c-4582-bfb0-0f1dd3945485
sequences_series
false
null
For a sequence with the general term $x_{n} = \frac{ 3 \cdot n - 5 }{ 9 \cdot n + 4 }$, it is known that $\lim_{n \to \infty} \left(x_{n}\right) = \frac{ 1 }{ 3 }$. Find the number of points $x_{n}$ lying outside the open interval $\left(\frac{ 1 }{ 3 } - \frac{ 1 }{ 1000 }, \frac{ 1 }{ 3 } + \frac{ 1 }{ 1000 }\right)$.
The final answer: $703$
9e33d4d5-111e-40d8-947f-1e6745799fb6
algebra
false
null
Find two consecutive even numbers whose product is $624$. Use the method of factoring, the square root principle, or the Quadratic Formula.
The final answer: $24$, $26$, $-24$, $-26$
9e64c3be-6d67-467d-ba24-30c5fb0b90dc
integral_calc
true
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
Let $S$ be the region bounded by the graphs of $y = -\sin(\pi \cdot x)$ and $y = -x^3 + 4 \cdot x$, as shown in the figure above. Find the area of $S$.
The area of $S$ is $4$ units².
9e8c6804-bff6-4a53-9a3d-aafd24edb916
multivariable_calculus
false
null
Evaluate the integral $\int_{0}^1 \int_{x^3}^{x^2} (x+y) \, dy \, dx$ by reversing the order of integration.
The integral corresponding to the reversed order of integration: $\int_0^1\int_{\sqrt{y}}^{\sqrt[3]{y}}(x+y)dxdy$ The value of the given integral: $\frac{11}{140}$
9eaefe5e-2a89-4c91-8807-8a51a4682bd8
sequences_series
false
null
Find the Fourier series of the function $f(x) = \frac{ -1 }{ 2 } \cdot x$ in the interval $[-2,2]$.
The Fourier series is: $\sum_{n=1}^\infty\left(\frac{2\cdot(-1)^n}{\pi\cdot n}\cdot\sin\left(\frac{\pi\cdot n\cdot x}{2}\right)\right)$
9ed2cf0b-2cab-4481-8a1f-d82d0592618b
multivariable_calculus
false
null
Find the moment of inertia of one arch of the cycloid $x = 3 \cdot a \cdot \left(\frac{ t }{ 2 } - \sin\left(\frac{ t }{ 2 }\right)\right)$, $y = 3 \cdot a \cdot \left(1 - \cos\left(\frac{ t }{ 2 }\right)\right)$ relative to the x-axis.
Moment of Inertia: $\frac{1152}{5}\cdot a^3$
9eedef68-3b7f-472b-80eb-594924624379
precalculus_review
false
null
Find zeros of $f(x) = 2 \cdot x^4 - 13 \cdot x^3 + 24 \cdot x^2 - 13 \cdot x + 2$.
The final answer: $x_1=2+\sqrt{3}$, $x_2=2-\sqrt{3}$, $x_3=2$, $x_4=\frac{1}{2}$
9eee7969-14e8-4e46-af9e-f5abe22824c9
sequences_series
false
null
Let $P_{n}(x)$ be the n-th order Taylor polynomial of $f(x) = \cos(x)$ about $a = 0$. Find the minimum $n$ such that the approximation $f(x) \approx P_{n}(x)$ is accurate to within $0.00001$ for every value of $x$ satisfying $|x| \le 0.1$.
The final answer: $n=3$
9f291789-5366-4314-8c23-34f9d11ce96d
integral_calc
false
null
Compute the volume of the solid formed by rotating about the x-axis the area bounded by the axes and the parabola $x^{\frac{ 1 }{ 2 }}+y^{\frac{ 1 }{ 2 }}=3^{\frac{ 1 }{ 2 }}$.
Volume = $\pi\cdot\frac{9}{5}$
9f754564-1291-4160-9cb2-349689537534
differential_calc
false
null
Solve to four decimal places using Newton's method: $x^3 + (x + 1)^3 = 10^3$. Choose any initial guess $x_0$ that is not the exact root.
$x$ ≈ $x=7.4055$
a05cd0c6-c878-437a-8b28-5137e7036859
integral_calc
false
null
Compute the integral: $$ \int \frac{ 3 }{ 4 \cdot x^2 \cdot \sqrt{5 \cdot x^2-2 \cdot x+1} } \, dx $$
Answer is: $\frac{3}{4}\cdot\left(C-\sqrt{5+\frac{1}{x}^2-\frac{1\cdot2}{x}}-\ln\left(\left|\frac{1}{x}+\sqrt{5+\frac{1}{x}^2-\frac{1\cdot2}{x}}-1\right|\right)\right)$
a0840748-bc14-4a3b-b024-7db40ab0ae4a
differential_calc
false
null
Use implicit differentiation to find an equation of the tangent line to the curve $x^4 - x^3 \cdot y^2 - y^3 \cdot x + 5 \cdot y^4 = 17$ at the point $P(-2,-1)$.
The line tangent to the curve $x^4 - x^3 \cdot y^2 - y^3 \cdot x + 5 \cdot y^4 = 17$ at the point $(-2,-1)$ is: $y+1=-\frac{43}{30}\cdot(x+2)$
a0aa7803-36b6-4822-a264-43c4b180b36f
differential_calc
true
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
Given $m(x) = g(x)^2$, find $m'(-2)$ using the table below:
$m'(-2)$ = $-418$
a112f370-d3c2-4094-b750-8d9886059273
multivariable_calculus
true
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
Use the midpoint rule with $m=2$, $n=2$ to estimate $\int \int f(x,y) \, dx \, dy$, where the values of the function $f$ on $R = [8,10] \times [9,11]$ are given in the following table:
$\int \int f(x,y) \, dx \, dy$ is approximately: $21.3$
a14e11ca-bae3-4aa2-9e08-d7b73a0e3f5a
integral_calc
false
null
Calculate the integral: $$ \int_{-\sqrt{2}}^{\sqrt{2}} \frac{ 23 \cdot x^7+7 \cdot x^6-130 \cdot x^5-72 \cdot x^3-112 \cdot x^2+4 \cdot x+7 }{ x^2+4 } \, dx $$
$\int_{-\sqrt{2}}^{\sqrt{2}} \frac{ 23 \cdot x^7+7 \cdot x^6-130 \cdot x^5-72 \cdot x^3-112 \cdot x^2+4 \cdot x+7 }{ x^2+4 } \, dx$ = $7\cdot\arctan\left(\frac{1}{\sqrt{2}}\right)-\frac{392\cdot\sqrt{2}}{15}$
a1cfa2ef-8b1f-409b-bffe-7e18847ddd71
multivariable_calculus
false
null
Find the first derivative $y_{x}'$ of the function: $$ x = \arcsin\left(\frac{ t }{ \sqrt{1+t^2} }\right), \quad y = \arccos\left(\frac{ 1 }{ \sqrt{1+t^2} }\right), \quad t \ge 0 $$
$y_{x}'$ = $1$
a20500e2-a8d0-47d3-a626-99e954939c82
multivariable_calculus
true
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
The graph of the polar rectangular region $D$ is given. Express the region $D$ in polar coordinates.
1. The interval of $r$ is $[3,5]$ 2. The interval of $\theta$ is $\left[\frac{\pi}{4},\frac{5}{4}\cdot\pi\right]$
a2102909-944e-4b02-bcfb-74f3d7ebf95b
integral_calc
false
null
Compute the integral: $$ 3 \cdot \int x^{-8} \cdot \left(9+x^2\right)^{\frac{ 1 }{ 2 }} \, dx $$
$3 \cdot \int x^{-8} \cdot \left(9+x^2\right)^{\frac{ 1 }{ 2 }} \, dx$ = $C+\frac{2}{1215}\cdot\left(1+\frac{9}{x^2}\right)^2\cdot\sqrt{1+\frac{9}{x^2}}-\frac{1}{729}\cdot\left(1+\frac{9}{x^2}\right)\cdot\sqrt{1+\frac{9}{x^2}}-\frac{1}{1701}\cdot\left(1+\frac{9}{x^2}\right)^3\cdot\sqrt{1+\frac{9}{x^2}}$
a2746873-77c8-49fc-97b9-98a814c7f0f1
algebra
false
null
Perform the indicated operation and express the result as a simplified complex number: $$ \frac{ 4+5 \cdot i }{ 4-5 \cdot i } $$
The final answer: $-\frac{9}{41}+\frac{40}{41}\cdoti$
a29dedad-3c66-4fb6-a142-1d724cd3f3f0
sequences_series
false
null
For which $p$ does the series $\sum_{n=1}^\infty \left(\frac{ p^{n^2} }{ 2^n }\right)$ converge?
Converges for : $p\le1$ (leave empty, if the series diverges for any $p$).
a328709a-3973-45ce-ac0c-956e736146fb
precalculus_review
false
null
A rental car company rents cars for a flat fee of $\$20$ and an hourly charge of $\$10.25$. Therefore, the total cost $C$ to rent a car is a function of the hours $t$ the car is rented plus the flat fee. 1. Write the formula for the function that models this situation. 2. Find the total cost to rent a car for 2 days and 7 hours. 3. Determine how long the car was rented if the bill is $\$432.73$. (Round to 2 decimal places)
1. The formula for the function is $C(t)$ = $10.25\cdot t+20$ 2. The total cost to rent a car is $ $583.75$ 3. The time of car rental in hours is $40.27$
a3940e7d-d8a4-47f5-a5b8-fd8850fea3e8
differential_calc
false
null
For the function $r = \frac{ 1 }{ 2 } \cdot \arctan\left(\frac{ 3 }{ \beta }\right) + \arccot\left(3 \cdot \cot\left(\beta\right)\right)$, find the derivative $r'(0)$ and $r'(2 \cdot \pi)$. Submit as your final answer: 1. $r'(0)$ 2. $r'(2 \cdot \pi)$
1. $r'(0)$ = $\frac{1}{6}$ 2. $r'(2 \cdot \pi)$ = $\frac{9+8\cdot\pi^2}{54+24\cdot\pi^2}$
a3b43f93-43b4-4b70-90f5-548457398733
multivariable_calculus
false
null
Find the tangential and normal components of acceleration if $\vec{r}(t) = \left\langle 6 \cdot t, 3 \cdot t^2, 2 \cdot t^3 \right\rangle$
$a_{T}$ = $\frac{12\cdot t^3+6\cdot t}{\sqrt{t^4+t^2+1}}$ ; $a_{N}$ = $\frac{6\cdot\sqrt{t^4+4\cdot t^2+1}}{\sqrt{t^4+t^2+1}}$
a3bd66e6-c94c-4f2f-8571-02904921c0b1
differential_calc
false
null
Find $\frac{ d y }{d x}$, given $y=\tan(2 \cdot v)$ and $v=\arctan(2 \cdot x-1)$.
The final answer: $\frac{dy}{dx}=\frac{2\cdot x^2-2\cdot x+1}{2\cdot\left(x-x^2\right)^2}$
a3d65618-5fb7-4674-96dd-b23aa1ecfe58
algebra
false
null
A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is proportional to her velocity, and the constant of proportionality is $0.24$. It can be shown that the downward velocity of the sky diver at time $t$ is given by $$ v(t) = 180 \cdot \left(1 - e^{-0.24 \cdot t}\right) $$ where $t$ is measured in seconds and $v(t)$ is measured in feet per second. 1. Find the initial velocity of the sky diver. 2. Find the velocity after $4$ seconds (round your answer to one decimal place). 3. The maximum velocity of a falling object with wind resistance is called its terminal velocity. Find the terminal velocity of this sky diver. (round your answer to the nearest whole number).
1. The initial velocity of the sky diver is $0$. 2. The velocity after $4$ seconds is $111.1$. 3. The terminal velocity of the sky diver is $180$.
a3d66c89-c806-451b-8a24-006d0d179cf7
algebra
false
null
Determine the point(s) where the line $y = m \cdot x$ intersects the circle $x^2 + y^2 = 4$.
The final answer: $P\left(\sqrt{\frac{4}{1+m^2}},\sqrt{\frac{4\cdot m^2}{1+m^2}}\right)$, $P\left(-\sqrt{\frac{4}{1+m^2}},-\sqrt{\frac{4\cdot m^2}{1+m^2}}\right)$
a4a45e5a-b4ee-43fd-813e-09deaedcad2b
multivariable_calculus
true
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
Find the area of the region $D$:
The area is $1$
a4e37a73-6d8c-4d88-b69a-73d95d6eb24c
multivariable_calculus
false
null
Let $z = e^{1 - x \cdot y}$, $x = t^{\frac{ 1 }{ 3 }}$, $y = t^3$. Find $\frac{ d z }{ d t }$.
$\frac{ d z }{ d t }$ = $\frac{-(10\cdot e)}{3}\cdot e^{-t^3\cdot\sqrt[3]{t}}\cdot t^2\cdot\sqrt[3]{t}$
a5188065-d6c7-41b1-875b-d6511217d604
algebra
false
null
Consider the equation $25 + 8x + x^2 + y^2 - 10y = 0$. 1. Complete the square to write the equation in the standard form of a circle. 2. Identify the center and the radius of the circle. *Note: The standard form of a circle is $(x-a)^2 + (y-b)^2 = r^2$.*
1. Standard form: $(x+4)^2+(y-5)^2=16$ 2. Center $(a,b) = $ $P\left(-4,\ 5\right)$ 3. Radius $r = $ $4$
a5621a7e-3e22-421b-9363-cae4747d5c39
algebra
false
null
To convert from $x$ degrees Celsius to $y$ degrees Fahrenheit, we use the formula $f(x) = \frac{ 9 }{ 5 } \cdot x + 32$. Find the inverse function, if it exists. If it doesn't exist, write $\text{None}$.
Inverse function: $g(x)=\frac{5}{9}\cdot(x-32)$
a674c2d7-a34b-478c-a2db-568882e13a76
integral_calc
false
null
The chain of length $200$ rises up, winding on the winch. Compute the work of the weight force when lifting the chain, neglecting the size of the winch, if the running meter of the chain weighs $50$ kg.
$W$ = $-1000000$
a6a2e299-2748-478f-b471-75c40da9448b
algebra
false
null
Rewrite the quadratic expression $2 + z - 6 \cdot z^2$ by completing the square.
$2 + z - 6 \cdot z^2$ = $-6\cdot\left(z-\frac{1}{12}\right)^2+\frac{49}{24}$
a6d4ebc2-4ce7-401f-bafd-bb7e50fe8ee7
differential_calc
true
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
Use the graph of the function $y = f(x)$ shown here to find $\lim_{x \to 0} \left(f(x)\right)$, if possible. Estimate when necessary.
$\lim_{x \to 0} \left(f(x)\right)$ = None
a747b4a2-1af3-4522-83ed-b5d654c1b27d
sequences_series
false
null
Compute $\lim_{x \to 0}\left(\frac{ \cos(x)+2 }{ x^3 \cdot \sin(x) }-\frac{ 3 }{ x^4 }\right)$. Use the expansion of the function in the Taylor series.
The final answer: $\frac{1}{60}$
a77b8f2c-9d90-4790-8e66-137b7346b88c
integral_calc
false
null
Compute the integral: $$ \int \frac{ -\sin(2 \cdot x)^4 }{ \cos(2 \cdot x) } \, dx $$
$\int \frac{ -\sin(2 \cdot x)^4 }{ \cos(2 \cdot x) } \, dx$ = $\frac{1}{2}\cdot\left(C+\frac{1}{3}\cdot\left(\sin(2\cdot x)\right)^3+\sin(2\cdot x)-\frac{1}{2}\cdot\ln\left(\frac{\left|1+\sin(2\cdot x)\right|}{\left|\sin(2\cdot x)-1\right|}\right)\right)$
a80b7fea-f3d2-4cee-a773-0468cbb62864
integral_calc
true
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
Evaluate the integral of the functions graphed using the formula for areas of triangles, and subtracting the areas below the $x$-axis:
The final answer: $6$
a84a369a-f932-4e1b-81d4-3ba80b0674d9
integral_calc
false
null
Compute the integral: $$ \int \frac{ \sin(x)^2 \cdot \cos(x) }{ \sin(x) + \cos(x) } \, dx $$
$\int \frac{ \sin(x)^2 \cdot \cos(x) }{ \sin(x) + \cos(x) } \, dx$ = $C+\frac{1}{4}\cdot\left(\ln\left(1+\tan(x)\right)+\ln\left(\left|\cos(x)\right|\right)\right)-\frac{1}{4}\cdot\left(1+\tan(x)\right)\cdot\left(\cos(x)\right)^2$
a8f0eaa3-b9da-4124-8a5f-fb474f6d858d
differential_calc
false
null
Compute the limit: $$ \lim_{x \to 3} \left( \frac{ x }{ x-3 } - \frac{ 1 }{ \ln\left( \frac{ x }{ 3 } \right) } \right) $$
$\lim_{x \to 3} \left( \frac{ x }{ x-3 } - \frac{ 1 }{ \ln\left( \frac{ x }{ 3 } \right) } \right)$ = $\frac{1}{2}$
a8f44f48-ca13-4087-8c8f-a3a62866f729
differential_calc
false
null
Compute the derivative of the function $y = \sqrt[4]{\frac{ x^5 \cdot \left(5 \cdot x^2+1\right) }{ \sqrt[3]{2+3 \cdot x} }}$ by taking the natural log of both sides of the equation.
Derivative: $y'=\frac{50\cdot x^3+35\cdot x^2+14\cdot x+10}{30\cdot x^4+20\cdot x^3+12\cdot x^2+8\cdot x}\cdot\sqrt[4]{\frac{x^5\cdot\left(5\cdot x^2+1\right)}{\sqrt[3]{2+3\cdot x}}}$
a9032c60-861d-40cc-9d18-5703fc391b80
integral_calc
true
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
The data in the following table are used to estimate the average power output produced by Peter Sagan for each of the last $18$ sec of Stage $1$ of the $2012$ Tour de France. Average Power Output: Estimate the net energy used in kilojoules (kJ), noting that $1 \cdot W = 1 \cdot \frac{ J }{ s }$ and the average power output by Sagan during this time interval.
$17$ kJ.
a91364ec-3bee-4ace-a8e8-c9d004878f3f
sequences_series
false
null
Compute $\lim_{x \to 0}\left(\frac{ 3 \cdot \cos(x)+6 }{ 4 \cdot x^3 \cdot \sin(x) }-\frac{ 9 }{ 4 \cdot x^4 }\right)$. Use the expansion of the function in the Taylor series.
The final answer: $\frac{1}{80}$
a91e763c-994d-43f5-bee0-b4348dcf9e16
precalculus_review
false
null
Solve $2 \cdot z = |z| + 2 \cdot i$.
The final answer: $z=\frac{1}{\sqrt{3}}+i$
a92b0179-4b43-4f1b-844d-303642f4a04f
multivariable_calculus
false
null
Find $f(x,y) = e^{x^2} + \sqrt{y}$ at $P(0.1,9.1)$. Find the linear approximation for this function.
The final answer: 1. $f\left(x_{0},y_{0}\right)$: $4.02667079$ 2. $L(x,y)$: $4+\frac{1}{6}\cdot(y-9)$
a9475aa9-2408-495d-8644-3b969183c644
differential_calc
false
null
Compute the derivative of the implicit function: $$ 2 \cdot y^4 - \frac{ 3 \cdot x + 3 \cdot y }{ 2 \cdot x - 2 \cdot y } = 0 $$
$y'$: $y'=-\frac{y^2}{2\cdot\left(x^2-y^2\right)-x\cdot y}$
a984873a-826c-47e9-827c-626afd748f10
sequences_series
true
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xcXPC1TEiSDA0Ntdvt58+fb21t/fzzz9Vqtaen55o1a/z8/BiGsVqtzc3NgYGBFouFYZgdO3bs3LmTIAiFQuHYCdHr9UajES8aWJblg8RxnJeXF76Lv9IR/h9/9DgYjs244//BwcE4Hi0tLbW1tSEhITixPF9f3+bmZnxktslk+svvwGKx4K24YWFhTU1NM2fO1Ol0lZWVAQEBHYa/paXllltucRyERNP0mTNn5s+fHxAQ8PPPP48cOdJisRgMhvDw8MbGxjZdnsLCwtDQ0G6dwUyj0dhsNpqm+Sl6vd7LywshpNVq/fz8WlpaHK9DgwsjSRJ/nt7e3h1ejhF/4G36WZ2QyWSO82n/xDZfRF8gSbK32s/ly5e/8847YWFhgYGBo0aNGjduXFhYWHh4ePsLQJeUlLS2tgYGBuLPvEP/81m0/+128kHTNN3JF0AQhEwmo2nabDYrFAr8u8ETcagYhjEYDCqVSqPRGI1GnU7HsqzdbrdYLF5eXhaLxdvb++WXX37++ef5WfEzd3d3N5vN+EKAZrNZq9UihGw2m8FgGDRoUFNT06lTp0iSTEhIoCjq5MmT7u7uzc3NFEW1KbK4uNhoNBqNxuzs7KSkJL4jeu7cOQ8Pj7CwsLKysosXLyKEVCrV3Xff3eYrvHr1KkmSERERjhPtdrvNZrt06dLIkSMRQleuXMnNzcV3Pfroo1OmTEEIHT16lC8mISHh1KlT+MMJDQ3dvn17eXk5vgu/tebmZvzzpSiK/0b4D5m/GiKeiB/AcRxJkvgu/uvDxXf4dTtOJEkS50GlUul0ujadBW9vb5VKNWDAgKqqqtzcXB8fn/bbCxQKhZ+fX0VFha+vb21treNdLi4u7a/gqFAoRowYceLECX6Kh4eHY/usVCrnzp17+vRpfgpe6l27do2fIpPJkpKSCIKwWCw+Pj47duyIj48vKioaMWIE6pqcnJz09PTPPvssLi7O3d3d39//3Llz1dXVCKH777/fbrfjT0mn0ykUijZL/DY/jMLCwhEjRvAjVUiSlMvlgYGBI0eOVCgUXl5eU6ZMGTZsWGtr68aNG7Ozs9PS0saOHftnhXV1OScwhmFUKtX69etTUlL69IX69O03NDQ8//zzmZmZAwcOLC8vz8rKSk5Obr8O77iG73gXXnI1NjaazeZff/3Vx8fHz8/vypUr4eHhNputubl58ODBBw8eLCkpGThwYFhYmEwmCwsLu3jxotlsvuOOO3JycmiaHjFixG+//dba2jpmzBiVStXU1FRTU+Pt7a1UKgsKCnAn6NixYzRNJyYmFhQU8L/purq6CxcuOL4XnU7H/xYrKysPHToUFRWVmJiIp5SXl5eVlbm7u8fFxREEQVFUUVGRUqkMCwsrKSlxXD42NTVRFIVXXtRqteP5Yvz9/XEq8KehUqmsVitFUZcvX+Y/GTwrmUwWFBRUX1/Pz5kgCJqmfX19jUYjRVFyubzNVg+WZZVKpVqtbm5u5jiOYZjg4OCmpiaFQmEymWiaxo2HXC4PCgqqrq6madrV1bWpqUmr1VIUZbPZSJLU6/UhISGNjY0WiyUgIECpVFZWViYlJTmmlOO4LVu28B3M9hyr8vT0jImJeeyxxyIiIvB31PbBko2ot7f35cuX/f39xa6lJxiGsdvtAwcOrKmpCQoKys3NjY+PT01Nfe2113r9tbqy+e0v54Aceqdtpnf4KgaDITo6Oj09HfcLEEIsy+Jg8J1S3Fry7TkP97863HjWYZeNZVm+RWIYBq9hRUZGDhgwgKIox5lfvHhx+PDhFoulpKQEry07MhgMCCE/Pz+aphsbGysqKuLj42maxtnesWPHk08+uWrVqhkzZri4uFgsFqvVKpfL8/Ly+Hbew8Nj7969dXV1hw4d8vT0TElJyczMrKurw/O/7bbbTp8+jbs8DQ0N9fX1nX/sbd44QRCpqanLli1r+21ykkTTdHh4uNlsbn+XzWbDmxMl6/r164899tj999+PEHJ1dd25c2dTU1NwcHBWVpbYpfWahoYGHx+fzZs3i/LqLMv2+jw/+ugj3Ph3/qIsy7IsyzAMfxP/7zidZdl33333z5abBEEolUqVSuXi4jJmzJixY8dGRERMmzbt2WefNRqN7V9XopcAlslk+/fvb3PBXLvdvmHDhoULF3733XcPPvigWLV17tSpU1OnTuWXrPPnz58yZQruWfXWJj7pqKysFOV1+2JX3OTJk1988cXc3NykpKROXtTxL/qj9WvzmJycnA0bNnB/dAfUavWgQYNiYmLq6+sTExO1Wu1TTz3l7u6O/tgPhzvYbWbFk0pEbTbbtm3bCgoKOI7btWsXx3E6ne7ee++NjIwcMmSITCY7ffr0ihUr8vPzaZrGb09qCgsLv/zyy/T09MbGRjwlPDz8tddew9uW8XayDp9IUVRBQUF5ebmrq6vjVivpGzJkSIfTaZpuv/VS4vDK5LFjx/4sol3HMMzgwYMHDBjw4IMPJiQkeHh4OO4daJ/Dv9iS3Osdhh44e/bs0KFD25Tu4uKiVCrx7xsvYzw8PB588MHjx4+LXW8HDh065OPj0+YtfPPNN/jelpaWiIiIjz76qP0T8/PzIyIi+IXotGnTampqhK29G4qKitasWZOamnrLLbfI5fIJEyYsXbp0r4N33nln+vTpoaGhhYWFYhfbPWazedq0aTt27OiVueHubq/MSvyI0jQdHR3t6uq6bNmyI0eOvP766wihuLi4ysrKioqKsrIyPJjhySefrKio6IuVkBtks9mefPLJ9hviRo0aZbPZ8GMMBoNer9+4cWOb51ZWVg4ePDghISEtLe3zzz+fPXu2XC5/4IEHJLiyzTDM7NmzNRoNSZJqtVqj0bi7uysUCrlcTvwvuVweFRXV2toqdsndhjc+iV1FW+L3RkiSjI6OfvPNN2fMmGEwGP7+979rNJp169YFBgYihOrr6/38/Jqbm7/66iu1Wi12sW1dunTp6aefzsvL4/53O6Snp+f333/fZpyQ4348hFBZWdmUKVMsFsuJEyfc3d3xxsympqbNmzczDCO1YWhLlixZu3btwIEDIyMjv/jiC71er1arq6qqaJo+duyY49uPjY0dPny4AIMNep1EO+cCLxJaWlq+++67goICx41X/NJr0aJFcrl8586d/Oay5557jiCIF198UYINS35+fodX9SUI4pNPPnFcHuNWdO/evY5P//DDDwmCWLt2LT+FYZgxY8bgvQKCvYuuaGpq8vX11el0p0+fpijq2rVrjz/++J49e/iv6eTJk7NmzSooKJBgKyQuvAfVcQrDMFVVVV2fg9AR/eCDD3B3yN/ff+LEiSkpKY2Njfy9gYGBeFcVvvnzzz8TBJGUlOT4GOk4derUnDlzPD0920Q0OTm5zQIFR3Tr1q38lNLS0uDg4MTERMcO4YYNG2QyWUpKitR+6Hv27CFJMiMjA+9XmDp1qouLy+HDh/l73d3d3dzcpLmZQFwpKSmjR4/mdx/W1tZOmzYtLi6u602O0BEtKyv717/+lZaWlpqaOnTo0OHDh1dUVOC7Dh8+7OLi8tRTT+HqS0pKvLy8oqKi8DX/JIhhmLVr17bpkXp5eRUVFbV5JI5oeno6vsmy7DPPPCOTyRw3TjQ3Nw8fPlytVuPB3JJC0/SWLVvwPsNDhw6RJDl9+nSr1cpx3LFjx/DotrNnz4pdphTNmjVLpVJdvHgR9zXwUJw33nij60thETYX8ft57Xa7YxsyefJkT09Pg8GAb86aNQsh9Oabb0qtSeFt27bN8Ug9hBBJkvjYnTaPxBE9cOAAvtnS0hISEjJp0iQ88hP7+OOPCYJ49913Jft+OY5rbm4ePXq0Tqerra3lOK6srEyv1wcHB1+7dk3s0iQqMzOTIIhHHnlk2bJleD//6tWr8X7yLhJ/iy524MABgiDuvfde/AOladrT0zMgIECav1eWZVevXs1vEYmMjNyzZ49Op5s+fXqHq5FtInry5EmCIH744Qf+AbgHcfvttzuGVoI2btwok8kWL16Mv5cnnngCIfTll19K82uSgtLSUtzPwrsPlyxZ0t2tKuJHlGXZq1evBgYGBgQE8LsEaZqWyWT333+/BL97lmVXrVrFDzDw9fX9/fffy8rKxowZU19f3+FT2kS0urqaIIglS5bgm+Xl5fhAhx9//FGg99AjNpstKirK09Ozurqa47jLly+TJDl27FipbdySFLxegBAKCAj46aefOhlg+GdEi+jKlStnzZo1a9asBx54wNXVlSTJ1NRUfgGDI/rAAw9IMKL/+c9/+K3zgwYNunjxIp7eSantO7oJCQmurq6rVq169913g4KCEEKxsbF8J1+aFi9eTBDEF198wXGc3W4fP368QqGAVdBOnDt3jj8OZO3atT37MYsW0VWrVvE/dK1Wu3r1aseFMU3Ter1+5syZkoooTdOrV6/m208vL68jR4505YltIspx3PXr10eOHCmTyfDRsI8++miHxwxIx5EjR1Qq1YQJE3BXHDehcXFx/PAM4Mhms6Wnp2s0GvwVEwTR40MORNtXO3v27Ojo6F27do0dO3bIkCGhoaGOo+dkMllhYSEeFidWhW3QNL148eJPPvkEH6Do7e2dm5vb/oinDlEU5XhIOkLI39//6NGjubm5+fn50dHRY8eOleDADKvVunDhwvj4+MOHD+/Zs8fNzW3FihV4CfXrr79yHKfVap1oRLFgTCbT9OnTs7OzEUIvvfSS2WyOiYmZPHlyD2fXq8uObpNUI9kJu93+5Zdf8vtXPDw89u/f3/WnFxQUEATxwQcf9F2FfcFoNPLno/L09MzPz+fvWr58OUEQL730krN8g0Jas2YN3ji0dOlShmHmzZun0+kc94p3i8ijzKTTSHZu1apVCxcuxIeqBAYG7tixY/z48d2dyZ8d6SJZ7u7ur7zyyj333DN+/Phvv/321ltv5e+KjY2NjIxsf/ADQAgdPnwYIfTBBx8sWrSIJMn4+HiTyfT888+bzeaezK5XFx/9EF4K8j/EqKiokpKS7s6k/egiZ8HvxG4/HTbk/pmioqKTJ0/yH5rZbF65cuUXX3zRg825nBSG0UsZx3Effvjh6tWrOY5DCEVGRh4+fBhvgO3ufBBCnZzMRrI6OXWAMw6UF0ZERITjSec0Gs28efN6PDdpHU4hKTRNz5kz5/XXX8fbh5KSknqWT4RQfn5+Q0MDXBkN9AC0oh2rra2dMmXKmTNncAOYnJy8adOmHl/AAvd5rly5go+wA6DroBXtQH19/dSpU/l8Tpw4MSMj40YuMBMSEoKccHMRkAJoRdsyGAzjx48/d+4cQoggiAkTJmzdulWCOy3BTQJa0f9RX18/d+7c8+fP45vJycnbtm1zdXUVtypwM4NW9L+KiooeeeSR06dPcxxHEMQTTzyxevXqbl0iBYBeBxH9f/X19RMnTsSnFyII4u2333711Vd7a3QbrIWCHoOIIoSQ0WicOnUqn88333wzLS2tF8fN7N69u7dmBW42sC6Kzpw5k5iYmJeXhxAiSfLee+/F56fuxZcYOnRoL84N3FRu6ohyHHfs2LFJkybhSxvL5fLly5dnZmb2+kV48TB6/mLKAHTdzdvR5TguOzv7gQceMBqNCCGCIB566KF//vOffTEufNiwYQih/ndNFyCAm7cVzcjImD59Os4nQig5ORkfQ9QXrzVgwACCIDo86S4AnbsZI8px3I4dO2bOnIkvBa3VapcsWbJly5YbGT/UOTzKV2onmAdO4Wbs6K5fv/6ZZ57x8/NraGhACG3evHnixIl9etwjPodlbW0t9HVBd91cy3WO49avXz9r1iyKoiorKxUKRVZWVl/nEyF09epVBK0o6JGb6Edjt9vT09Nnz56NL3UeHBycmZk5efJkAc4bwLIsQRBhYWF9/UKg/7lZOroURT3++ONZWVl4oE9YWNiePXsGDx4sWAEcx126dCkuLk6wVwT9w00RUYqi5syZg8+SiBCKjo4+cOCAwIdu4nVRIV8R9A/9P6IMwyxbtmzNmjU4n0FBQQcPHgwICBC7LgC6pJ+vi+J84ms3IYSGDRt26tQpUfJJEMSAAQOEf13g7PpzK8px3Pz587/++mu8fSg2NvbIkSPu7u7CV3LXXXchhOC4cNAD/bYVpWl60aJFq1atwvkMCQnJyMgQJZ8IIYqi8IXeRHl14NT6ZytK0/T8+fO//fZbvP5566237tu3z8fHR6x6jh8/PnXqVDirJeiBfhhRq9X69NNPZ2Rk4HyGhIRkZ2eLO6yH47jKykp8MgcRywDOqL91dO12+4IFC/h8jh49Ojc3VwrD7rKzs/EhbwB0S7+KKL64w3fffYfzedttt23YsKFnJ6fuC1arVewSgPPpPx1dm83WZv3z8OHDGo1G7LoQQsjDw4PjOIPBIHYhwPn0k1aUZdm0tDS+/ZwyZcquXbskkk/0x6muAeiB/tCK1tXVpaam/vDDDzift99++/r16729vcWu678uXrwodgnAWTl9K8px3Isvvsjnc9KkSTk5OZLKJ/rjymhwQWvQA84d0ZaWltdee43Pp4eHx9dff913J0+4ESRJjho1SuwqgPNx4ojabLa5c+cuW7YMj7+NiYk5c+aMlNf6YKco6AFnXRelKGrWrFkbN27E7ae/v//x48fh/F2g/3HKVtRgMDz00EN8Pn18fI4cOSLxfHIcV1NTI3YVwPk4X0TNZvOcOXO2b9/OH/95/PjxqKgosev6CxzHXb58WewqgPNxsojW1dU9+uijmZmZOJ/x8fE5OTkRERFi19UluGYAusWZ1kWNRmNycvLJkyfxb33YsGHZ2dlarVbsuv6aTqcjCELKm7KAZDlNK3r+/Pm77777xIkT/Pjb7du3O0U+EUIEQRAEER4eLnYhwPk4Ryt65syZ8ePH4zNTI4SmTp2alZUlzf2fHWpsbBS7BOCsnKAVPX/+/OTJk/l8xsfHb9q0yYnyiWAtFNwAqUe0tLR0woQJ/OktR40atWXLFumMjwegr0m6o2s0GpOSkvh8hoWFbd68WfpnAGJZlmEYGJELeoXkIlpZWblr166rV6/i66/wu/vDw8PXrl0rhXyWlJQcOHDg9OnTBoNh0KBB06ZN8/LyioiIUCgUDMMUFhYuXry4pKQkJydHp9Php/z222/Q1wU9I62I7t69+5FHHmlubm7zg/bz8zt06FBoaKhYhWEMw3z//fcLFy40m818hUuXLpXL5X5+fuHh4XV1dcXFxXa7/Z577nFsRaOjo2GALugZCa2LNjc3P/HEE3K5fPbs2QcPHhwxYgSeHhoaumPHDtHziRDKycl59tlnPT09X3755a1bt27fvl2tVt99990zZsyQy+U5OTmXLl1ydXV9//33d+/e3WaF2cvLS6yygXPjJCMrK0smk3322Wcsy3Icd+XKFbzbc926dXiK6LKzswcOHHj8+HFcz6ZNmxQKxa5du1iWPXHihFwuJwhi586d7at9/fXXExISGIYRo2rg3CQU0U8//VStVpeVleGbBoPBx8cnPDwc9yqlgGVZi8WC/9+0aZNarV6+fDlN0y0tLbGxsQqF4quvvqIoin+8xWIxmUw7duzQ6XQjR45sbW0tLCzctGlTRkZGRkaGyWQS6X0AZyKhiO7du1culy9ZsoRhmLq6urS0NIIg7rrrLrvdLlZJLMu2trbidWNHZrN50KBBISEhJpOJZdmUlBS1Wv3NN9/w7ef27dtvueWW8PBwhULh6uqKOyx6vZ4kSeIPgYGBjY2Ngr8n4GQkFFGKooKCglQqlZ+fn4eHB0mSGo0Gj8gVns1m+/e//z18+HC9Xh8VFTVz5swXXnihtrYW37tv3z6SJH/88UeO4woLC93d3SdNmuTYj6Vpuqamxmg01tTUXL161cXFJSYmJj09PT09/R//+Ider/f19V24cGFLS4so7w44EQlFlOO4CxcujB07ViaTyWSyoUOHZmRkiLUWevTo0fbXd1i7di3HcTRNjxo1Sq1WNzU1cRy3YMECpVJ58ODBTuY2efLkhx9+mP2D2Wy22+0SWcEGEietnS6xsbH79+/Hp4RWqVQi7v1PTExcsGDBnj17YmNjZ86cabfbz5w589BDDyGEfvrppxMnTjz99NNarZbjuH379sXFxY0bN66TuanVanyYC971AqOjQDeIvYyQLrYj77//vpubm1KpzMvL4ziuublZqVS++uqrnTeJgYGBL730EjSboAek1YpKCj/YwGKxfP75501NTcXFxVu3brXZbE899VR8fDxCaPfu3RRFhYeHdzIygeM4o9FIUZRAdYP+BSL61/Ly8l577TV8nkGO4x5++OGvvvoKZzImJkav1/v5+f3lTOB4NNAzENG/lpiY+Oyzzx46dEir1S5YsCAlJUWpVOK7hg4dWlNT0/ngPoIgNBqNWFcfBs6O4GB4dxewLEtRFEmSPduCdd9997m6um7YsAFG6oLugla0S0iSVKlUPX66TCaDSwCDnpHQMPr+DdZFQc9ARAWCW1GxqwDOByIqhKampsbGRrvdLnYhwPlARPscx3G5ubksy548eVLsWoDzgYgKh6ZpsUsAzgciCoCkQUT7HEEQ9913n4+Pj6+vr9i1AOcDQxeEQNM0RVFqtVrsQoDzgYgCIGnQ0QVA0iCiAEgaRBQASfs/RIJB9/X/vLEAAAAASUVORK5CYII=
Find the Fourier series expansion of the function $f(x) = \begin{cases} x, & -\pi \le x < 0 \\ \pi, & 0 \le x \le \pi \end{cases}$ with the period $2 \cdot \pi$ on the interval $[-\pi, \pi]$.
The Fourier series is: $f(x)=\frac{\pi}{4}+\sum_{n=1}^\infty\left(\frac{1+(-1)^{n+1}}{\pi\cdot n^2}\cdot\cos(n\cdot x)+\frac{(-1)^{n+1}\cdot2+1}{n}\cdot\sin(n\cdot x)\right)$
a9c9f912-3c8e-4269-b099-4025c1d4eabb
integral_calc
false
null
Compute the integral: $$ \int \frac{ 2 \cdot x+\sqrt{x-2} }{ \sqrt[4]{x-2}+\sqrt[4]{(x-2)^3} } \, dx $$
$\int \frac{ 2 \cdot x+\sqrt{x-2} }{ \sqrt[4]{x-2}+\sqrt[4]{(x-2)^3} } \, dx$ = $C+20\cdot\sqrt[4]{x-2}+\frac{8\cdot1}{5}\cdot\sqrt[4]{x-2}^5-20\cdot\arctan\left(\sqrt[4]{x-2}\right)-\frac{1\cdot4}{3}\cdot\sqrt[4]{x-2}^3$
a9dffc8e-7ced-4002-b02a-9baebbe9603d
precalculus_review
false
null
Solve $\sqrt{3 \cdot x^2+5 \cdot x+8}-\sqrt{3 \cdot x^2+5 \cdot x+1}=1$.
The final answer: $x=-\frac{8}{3} \lor x=1$
aa1d7802-dd5b-476c-b14f-4a42e7c3e978
algebra
false
null
Find the zeros of the polynomial function with complex roots: $f(x) = 2 \cdot x^3 + 4 \cdot x^2 + 3 \cdot x + 6$.
$x$ = $-i\cdot\sqrt{\frac{3}{2}}$, $i\cdot\sqrt{\frac{3}{2}}$, $-2$
aaa1aca4-7a50-4e00-8119-c633ec60663a
differential_calc
false
null
For the function $y = \frac{ x }{ x^2 - 1 }$ find the derivative $y^{(n)}$.
The General Form of the Derivative of $y = \frac{ x }{ x^2 - 1 }$: $y^{(n)}=\frac{1}{2}\cdot(-1)^n\cdot\left(n!\right)\cdot\left((x+1)^{-(n+1)}+(x-1)^{-(n+1)}\right)$
aaf96d92-2e6d-4d51-9302-ebdab0643835
integral_calc
false
null
Compute the integral: $$ \int \frac{ 4 \cdot x-\sqrt[3]{36 \cdot x^2}-\sqrt[6]{6 \cdot x} }{ x \cdot \left(1+\sqrt[3]{6 \cdot x}\right) } \, dx $$
$\int \frac{ 4 \cdot x-\sqrt[3]{36 \cdot x^2}-\sqrt[6]{6 \cdot x} }{ x \cdot \left(1+\sqrt[3]{6 \cdot x}\right) } \, dx$ = $C+5\cdot\ln\left(\left|1+\sqrt[6]{6\cdot x}^2\right|\right)+\sqrt[6]{6\cdot x}^4-5\cdot\sqrt[6]{6\cdot x}^2-6\cdot\arctan\left(\sqrt[6]{6\cdot x}\right)$
ab489b92-5b36-40ad-9a82-491fad3195f7
differential_calc
false
null
Given $y = 3 \cdot x^5 + 10 \cdot x^4 - 20$, find where the function is 1. concave up, 2. concave down, and 3. point(s) of inflection.
1. Concave up: $(-2,0)$, $(0,\infty)$ 2. Concave down: $(-\infty,-2)$ 3. Point(s) of Inflection: $P(-2,44)$
ab60fd32-4edd-4d98-9274-20131190ef32
integral_calc
false
null
Compute the integral: $$ \int \frac{ x^3 }{ \sqrt{x^2+x+1} } \, dx $$
$\int \frac{ x^3 }{ \sqrt{x^2+x+1} } \, dx$ = $\left(\frac{1}{3}\cdot x^2-\frac{5}{12}\cdot x-\frac{1}{24}\right)\cdot\sqrt{x^2+x+1}+\frac{7}{16}\cdot\ln\left(\left|x+\frac{1}{2}+\sqrt{x^2+x+1}\right|\right)+C$
ab849658-cfda-452a-9ade-f2e14d96048a
integral_calc
false
null
Compute the integral: $$ \int \frac{ -3 }{ e^{4 \cdot x} + \sqrt{1 + e^{8 \cdot x}} } \, dx $$
$\int \frac{ -3 }{ e^{4 \cdot x} + \sqrt{1 + e^{8 \cdot x}} } \, dx$ = $C-\frac{1}{4}\cdot\left(\frac{3}{e^{4\cdot x}+\sqrt{1+e^{8\cdot x}}}+3\cdot\ln\left(\frac{e^{4\cdot x}+\sqrt{1+e^{8\cdot x}}-1}{1+e^{4\cdot x}+\sqrt{1+e^{8\cdot x}}}\right)\right)$
aba7e397-b652-4286-99f3-01d44606e733
sequences_series
false
null
Since $1 + x^3 + x^6 + \cdots + x^{3 \cdot n} + \cdots = \frac{ 1 }{ 1 - x^3 }$, when $|x| < 1$, then find the sum of the series: $$ \sum_{n=1}^\infty \left(3 \cdot n \cdot x^{3 \cdot n-1}\right) $$
The final answer: $\frac{3\cdot x^2}{\left(1-x^3\right)^2}$
ac4b6e12-42b6-4dbe-a5fd-4258b6db282b
differential_calc
false
null
Find the derivative of $y = x \cdot \sin(x) + 2 \cdot x \cdot \cos(x) - 2 \cdot \sin(x) + \ln(\sin(x)) + c^2$.
The final answer: $y'=\frac{\left(\sin(x)\right)^2+x\cdot\sin(x)\cdot\cos(x)-2\cdot x\cdot\left(\sin(x)\right)^2-\cos(x)}{\sin(x)}$
ac5571b3-1a5f-4cb5-b874-0ec90e7dc14b
algebra
false
null
Evaluate the expression $\frac{ (3+i)^2 }{ (1+2 \cdot i)^2 }$ and write the result as a simplified complex number.
$\frac{ (3+i)^2 }{ (1+2 \cdot i)^2 }$ = $-2\cdoti$
ace5f20b-07ce-4e6f-ac92-1de254bede66
precalculus_review
false
null
Use properties of logarithms to write the expression as a sum, difference, and/or product of logarithms: $$ \log_{4}\left(\frac{ \sqrt[3]{x \cdot y} }{ 64 }\right) $$
$\log_{4}\left(\frac{ \sqrt[3]{x \cdot y} }{ 64 }\right)$ = $-3+\frac{1}{3}\cdot\log_4(x)+\frac{1}{3}\cdot\log_4(y)$
ad240384-461f-42ca-bfb9-6227380f6674
precalculus_review
false
null
Find the domain of the function $f(x) = \arccos\left(\frac{ 3 }{ 4+2 \cdot \sin(x) }\right)$
The final answer: $-\frac{\pi}{6}+2\cdot k\cdot\pi\le x\le\frac{7\cdot\pi}{6}+2\cdot k\cdot\pi$
ad9dc540-5423-4bf8-86c4-a43e8a8dcdc7
sequences_series
false
null
Given that $\frac{ 1 }{ 1-x } = \sum_{n=0}^\infty x^n$, use term-by-term differentiation or integration to find a power series for the function $f(x) = \ln\left(1+x^2\right)$ centered at $x=0$.
$\ln\left(1+x^2\right)$ = $\sum_{n=0}^\infty\left((-1)^n\cdot\frac{x^{2\cdot n}}{n+1}\cdot x^2\right)$
ae0786f8-f333-4c38-acea-8be761157570
differential_calc
false
null
Find the derivative of the function: $y = -3 \cdot x^{\sqrt[3]{2 \cdot x}}$
$\frac{ d y }{d x}$ = $-\left(\frac{3\cdot\sqrt[3]{2}}{x^{\frac{2}{3}}}+\frac{\sqrt[3]{2}\cdot\ln(x)}{x^{\frac{2}{3}}}\right)\cdot x^{\sqrt[3]{2}\cdot\sqrt[3]{x}}$
ae2e969d-3eb4-4b7d-aeb1-9816a02b2670
integral_calc
true
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q4cKE++eQTfffdd8rLy1NMTIz69eunIUOGqFWrVlaXCQDwIQQQAPByYWFhGj16tEaPHm11KQAAcA4IAAAAAPMQQAAAAACYhgACAAAAwDQEEAAAAACmIYAAAAAAMA0BBAAAAIBpCCAAAAAATEMAAQAAAGAaAggAAAAA0xBAAAAAAJiGAAIAAADANAQQAAAAAKYhgAAAAAAwDQEEAAAAgGkIIAAAAABMQwABAAAAYBoCCAAAAADTEEAAAAAAmIYAAgAAAMA0BBAAAAAApiGAAAAAADANAQQAAACAaQggAAAAAExDAAEAAABgGgIIAAAAANMQQAAAAACYhgACAAAAwDQEEAAAAACmIYAAAAAAMA0BBAAAAIBpCCAAAAAATEMAAQAAAGAaAggAAAAA0xBAAAAAAJiGAAIAAADANAQQAAAAAKYhgAAAAAAwDQEEAAAAgGkIIAAAAABMQwABAAAAYBoCCAAAAADTEEAAAAAAmIYAAgAAAMA0BBAAAAAApiGAAAAAADANAQQAAACAaQggAAAAAExDAAEAAABgGgIIAAAAANMQQAAAAACYhgACAAAAwDQEEAAAAACmIYAAgJc7deqU5s+fr759+yosLEwOh0PXXHONRo4cqbS0NJWXl1tdIgDAhxBAAMCLpaWlqXv37hoxYoSWLl2qvLw8SVJmZqbefPNN3XLLLZo8ebLy8/MtrhQA4CsIIADgpXbu3Klx48YpIyNDvXv31nfffaeSkhIZhqGcnBy9+OKLCg0N1fTp0/Xaa6+ptLTU6pIBAD6AAAIAXsgwDH3xxRdav369evbsqbfeeks33nij/Pz8JEmNGjXShAkTNGvWLEnSggULlJmZaWXJAAAfQQABAC904sQJrVixQpI0aNAgXXbZZU77OBwO9evXT7feequ2bdumn376yewyAQA+iAACAF4oNzdXwcHBioyMVFRUVJX7BQQEKCAgQJI4BAsAYAo/qwsAANS8tm3b6sMPPzzvfqdOndKJEyckqeLwLAAAahMTEADwUYZhaPny5Vq/fr2ioqLUoUMHq0sCAPgAAggA+Kjt27dr/vz5kqS77rpLV111lcUVAQB8AQEEAHxQVlaWHn/8ca1fv15du3bVo48+WnEuCAAAtYkAAgA+ZufOnRo1apQWL16s6Ohovfrqq2rTpo3VZQEAfARnHAKAD9m4caMeeeQRrV+/XtHR0ZozZ466dOlidVkAAB/il5ycbHUNlaxZs8bqEmyN/rhHf6qHPrnnDf1p3769OnfurKCgIElnTzhfunSpRo8eraysLHXt2lXz5s1T+/btK7YfOHBA6enpysnJcfvY6enpKigoqPiz3X6P2IU3PI9qE/2pHvrkHv1xz6794RAsAPAyV199ta699tqK8FFaWqo5c+Zo0KBBysrK0sCBA/Xhhx9WCh/Z2dn6/vvvzxs+AAC4VH6jRo2yugaX7FqXXdAf9+hP9dAn97yhP6WlpZo1a5aefPJJSdKTTz6pSZMmKTQ0tGIfh8Ohli1basCAAdV6zLy8PKWmpkqSYmJivKJPtYn+uEd/qoc+uUd/3LNbfzgHBAC81H+Gj9DQUE2bNk2jRo3ialcAAEsRQADAS61YsULTpk2TJP3lL3/R6NGjuds5AMBy/CYCAC905MgRzZkzR3l5eerZs6fat2+vdevWuf2eiIgIRUVFmVQhAMBXEUAAwAulp6fr888/lyStXLlSK1euPO/3TJkyRZMnT67t0gAAPo6rYAGAF8rIyLC6BAAAXGICAgBeaPLkyUwzAAC2xAQEAAAAgGkIIAAAAABMQwABAAAAYBoCCAAAAADTEEAAAAAAmIYAAgAAAMA0BBAAAAAApiGAAAAAADANAQQAAACAaQggAAAAAExDAAEAAABgGgIIAAAAANMQQAAAAACYhgACAAAAwDQEEAAAAACmIYAAAAAAMA0BBAAAAIBpCCAAAAAATEMAAQAAAGAaAggAAAAA0xBAAAAAAJiGAAIAAADANAQQAAAAAKYhgAAAAAAwDQEEAAAAgGkIIAAAAABMQwABAAAAYBoCCAAAAADTEEAAAAAAmIYAAgAAAMA0BBAAAAAApiGAAAAAADANAQQAAACAaQggAAAAAExDAAEAAABgGgIIAAAAANMQQAAAAACYhgACAAAAwDQEEAAAAACmIYAAAAAAMA0BBAAAAIBpCCAAAAAATEMAAQAAAGAaAggAAAAA0xBAAAAAAJiGAAIAAADANAQQAAAAAKYhgAAAAAAwDQEEAAAAgGkIIAAAAABMQwABAAAAYBoCCAAAAADTEEAAwMfk5ubq/vvvV58+fXT8+HGrywEA+BgCCAD4kNLSUiUnJ+ujjz6yuhQAgI/ys7oAAIA5ioqK9Oqrr2ratGlWlwIA8GEEEADwAUePHtUzzzyjpKQkq0sBAPg42xyCdezYMS1fvlzLli3T3r17debMGatLAgCPV1RUpEWLFik2NlZJSUmKjIzUoEGDrC4LAODDLA8gKSkpuueee9SpUycNHTpUy5Yt0+uvv66OHTvq4Ycf1s8//2x1iQDgsT7++GPFxcXp4MGDeuKJJ7R27VrdfffdVpcFAPBhlh6C1adPH/34448utxUUFGjZsmVatmyZnn32WY0YMcLk6gDA8/n7+2vKlCkaOnSoWrVqZXU5AABYF0ASEhKqDB//7a9//au6dOmi66+/vparAgDvMnDgQKtLAACgEksOwVq+fLm+/PLLC/qexMREnThxonYKAgAAAGAKSyYgs2fPrnJbeXm56tRxzkW//vqrZs+ercmTJ9dmaQB8TH5+vo4fP67jx4+rsLBQkrR7925J0rfffitJcjgcatCggRo3bqyIiAjLagUAwBtYEkC2bt3qtHb69GkVFhaqrKxMfn5+qlu3rgIDA8/7fQBQHVlZWdqxY4e2bNmiZcuWVYQOV1fcKygokCS99957Lh8rLCxMjRs3VqtWrdSnTx9dffXVioqKUsOGDWvzrwAAgFfwS05ONvUHHj58WEePHnVaLygoUHl5uQzDUElJiU6cOKGgoCD5+f1fRlq3bp3Mrtdu1qxZY3UJtkZ/qsfb+7Rr1y798ssvOnLkiA4fPqwjR46opKSk2t9fXFzsdntBQYEOHTqkn3/+WUuWLKlYDw4OVkREhFq0aKEmTZqobdu2atGixUX/PS5GvXr1FBUVpfLycu3evVuFhYVq1KiRYmNj1bx58yq/78yZM9qwYUO1PuhJT0+vCGnp6ek+/7pcFW//d3ap6E/10Cf36I97du2P6ROQ/Px8pzXDMFReXu60XlhYWCmE5OXl1Xp9ADxLaWmp9u7dqz179lT8r1Xy8/O1Z8+eSjUEBgbqyiuvVNu2bdW2bVtddtlltVpDSUmJtmzZUqs/AwCAS+E3atQoU3/g8ePHXR7WUFpaqqKioor/djgcks5+KtegQQMFBgYqKipKZtdrV/TBPfpTPZ7cpy+++ELvv/++Vq1aVWm9fv36NfYzauqx9u7dq7179+qbb75RcHCw7rnnHj300EPq0qVLjTx+TQgMDFS3bt3UrVu38+6bl5en1NRUSVJMTIxHP4/MQH/coz/VQ5/coz/u2a0/pk9AGjdurNatWysrK6vSekhIiEpLS1VaWur0PSdPnpQk/fa3vzWlRgD2tG3bNr377rv69NNPderUqRp73CZNmqhx48Zq1KiRHA6H9u7dK0n6zW9+I+nsByRHjx5VTk7OJf/c/Px8vf/++3r//ffVrl07PfDAAxo4cKCaNGlyyX8PAAA8gSUnoffu3VtvvPFG5UL8/NSwYUPl5OS4PBzr5MmTCg0NNatEADZx6tQpLVy4UB9//LG2bdt2UY/RsGFDRUZG6uqrr1a7du10zTXXKCIiQk2aNFGjRo2c9j93TkNVnxgdPnxYx44d06+//qrt27crMzNTmZmZF1zfzp07NXXqVE2dOlW33nqr4uLi1K9fvwv/CwIA4EEsCSBPPvmkUwCRzoaQoKAgFRYWyjCMStuCg4O1YMEC3XLLLfyCBnxAVlaWkpOT9f7777u8UpU7HTp0UNeuXdWtWzdde+21atq0aY3WFhERoYiICLVv31533nlnpW179+7VqlWrtHLlSq1bt67ata9atUqrVq3SFVdcoeHDhysuLk7BwcE1WjcAAHZgSQAJDAzUvHnzlJCQ4LStTp06CgoKUlFRkcrKyirWQ0JCZBiGEhISNG/ePEII4KUyMjL08ssv6+uvv67291xxxRW6++67FR0drZtvvlkhISG1WKF7v/nNb/Sb3/xGw4YNkyStXLlSK1eu1PLly7Vv377zfv/+/fv1zDPPaObMmYqPj9ef/vQnl1MaAAA8lSV3Qpek3/3ud5o3b57LX6x16tRRw4YNVbduXdWrV6/Sjb/OhZB//etfZpYLoJadPHlSzzzzjO65555qhY+IiAiNGDFCX3zxhdavX6+nnnpKd9xxh6Xhw5WePXtqypQp+vbbb7Vjxw49//zzuv7668/7fadPn9bcuXPVq1cvffDBBy4PTQUAwBNZFkCksyFk2bJlGjNmjPr27avWrVtLklq0aKGBAwdq3LhxiomJcfo+QgjgXV5//XVFR0crOTn5vPfreOCBB/SPf/xDmzZt0pQpU2x1JanzCQkJ0eDBg7V48WKtWrVKI0eOVOPGjd1+z6FDhzR+/Hjddttt+uabb0yqFACA2mPJIVj/qUWLFvrLX/5S8d//ffLnjh07lJCQoB07dlT6vvLy8orDse666y7zCgZQYz7++GPNmDFDBw8edLtfw4YNNWzYMD388MM1fj6HVa6++mo9++yzevbZZ7Vu3Tq98sor+vbbb6vcf8eOHRo8eLC6deumv/71r2rfvv1F/+y4uDjFxcVd9PcDAHApLJ2AVMfVV1+tefPm6eqrr3badi6EMAkBPMuWLVt0yy23aOzYsW7DR7t27TRz5kxt3bpVjz/+uNeEj//WrVs3ffzxx/riiy90++23u9133bp1uuOOO5SUlGRSdQAA1CzbBxDp/CEkMTFRS5YssaAyABdq9uzZ6tOnj9sTsps0aaLZs2dr9erVeuihh8wrzmJdunTRu+++q6+++koPPPCA232fe+459e3b96IvTQwAgFU8IoBI7kNIWVmZEhISCCGAjR06dEi///3v9be//a3KfYKDg/Xkk0/qu+++0+9//3sTq7OXjh076qWXXtKyZct0ww03VLlfRkaGevXqpWnTpplYHQAAl8ZjAohECAE81UcffaTu3bsrLS2tyn2GDRum7777TmPHjlVgYKCJ1dlX+/bt9fnnn2vWrFluDz+bM2eOYmJitHv3bhOrAwDg4nhUAJEIIYAnKSws1KhRo/TYY4/p9OnTLvdp06aNvv76a02bNo37XVThwQcf1Lp16/TYY49Vuc8vv/yifv36ad26dSZWBgDAhfO4ACKdP4QkJiZq6dKlFlQG4JyDBw/qd7/7nb788ssq90lMTNTKlSvVoUMHEyvzTKGhoXriiSe0evXqKq+AderUKd1///166623TK4OAIDq88gAIrkPIaWlpUpISCCEABbZsGGD7rjjjipPkG7Tpo2+/PJLPf300woICDC5Os/Wrl07LVmyRH/+859Vt25dl/s89dRTGjdunEpLS02uDgCA8/PYACIRQgA7+t///V/dc889ys3Ndbl92LBhWrlypTp37mxyZd7Dz89PEydO1Geffeby9U+SPvzwQ9133306cOCAydUBAOCeRwcQqXoh5KuvvrKgMsD3/OMf/9D48eNdbqtXr56mT5+uadOmMfWoIZ07d9ayZct03333udy+YcMG9enTR7t27TK5MgAAqubxAUQihAB2kJKSokcffVTl5eVO21q2bKkvvvhCDz/8sPmFebl69erptdde09NPP+1y+/Hjx3XfffcRQgAAtuEVAURyH0JKSkoIIUAtWrBggSZOnOhyW2xsrFasWKFrr73W5Kp8S2Jioj788EOFhoY6bTt27JgGDBhACAEA2ILXBBCJEAJY4ZVXXtH/+3//z+W2+Ph4ffjhhwoLCzO5Kt8UGxurL7/8UiEhIU7bjh8/rnvvvZd7hQAALOdVAUSqXgj5+uuvLagM8D6zZ8/WCy+84HJbfHx8ldtQe9q1a6fPPvtM4eHhTttycnLUv39/bd682fzCAAD4N68LIBIhBDDD4sWLNWPGDJfbhg4dSviwUFRUlL744gtFREQ4bcvJyVF8fLz2799vQWUAAHhpAJHch5Di4mJCCHAJNm7cqEcffVSGYTht+9Of/qS//e1vFlSF//Sb3/xGX3zxhVq3bu207VwIycvLs6AyAICv89oAIhFCgNqwf/9+DR06VEVFRU7bnnjiiSrPB4H5Lr/8cv3zn/9Uy5Ytnbbt3LlTw4cPt6AqAICv8+oAIlUvhCxbtsyCygDPk5eXpwceeEA5OTlO2+644w6NHTvWgqrgTkREhFJSUlyemL5u3To98sgjFlQFAPBlXh9AJEIIUBNOnz6t4cOHa+/evU7bOnXqpHnz5snhcFhQGc7nmmuu0dtvv+1y26effqoFCxaYXBEAwJf5RACR3IeQoqIiQghwHhMmTNC6deuc1lu0aKGFCxcqMDDQgqpQXV27dtU777zjMiQ+88wzXJ4XAGAanwkgEiEEuFiffvqpvvjiC6f1kJAQffDBBy4v+Qr76d27t6ZPn+60XlRUpNGjR1tQEQDAF/lUAJHOH0ISExO1fPlyCyoD7OnAgQN64oknXG6bP3++2rVrZ3JFuBRDhw7VQw895LT+008/adq0aRZUBADwNT4XQCT3IeTMmTNKSEgghACSysvLlZiYqNOnTzttmzZtmmJjYy2oCpfqmWee0RVXXOG0npSUpLS0NAsqAgD4Ep8MIBIhBKiO2bNna+PGjU7rPXr00LBhwyyoCDUhJCREb731lurVq1dp3TAMjRkzhvuDAABqlc8GEKl6IeSbb76xoDLAevv379fzzz/vtB4eHq6///3vFlSEmtS+fXs988wzTuuHDx92eZ4IAAA1xacDiEQIAary9NNPu1x/5ZVX1LRpU5OrQW0YNmyY+vTp47S+YMEC/fjjjxZUBADwBT4fQCT3IaSwsJAQAp+zatUqffXVV07rDz/8sG6//XYLKkJteeWVV1xexezJJ5+0oBoAgC8ggPwbIQQ4q6SkRP/v//0/p/WWLVu6PGQHni0sLEzjx493Wt+0aZMWLlxoQUUAAG9HAPkP1QkhK1assKAywDxz585VVlaW0/qUKVPk7+9vQUWobUOHDlVUVJTT+tSpU3Xq1CkLKgIAeDMCyH8hhMCXHTt2TC+//LLTerdu3XTXXXdZUBHMULduXb3wwgtO66dOneKEdABAjSOAuOAuhBQUFBBC4LWSk5N15swZp3VXb07hXbp06aJBgwY5rb/77rs6fPiwBRUBALwVAaQKhBD4mlOnTuntt992Wh8zZozatGljfkEw3eTJkxUWFua0zmWXAQA1iQDiRnVCyMqVKy2oDKh5b7zxhvLz853WR4wYYUE1sEJ4eLjLG0y+/fbbOnr0qAUVAQC8EQHkPAgh8AX5+fl64403nNYfeughNW/e3IKKYJWRI0c63SFdkubNm2dBNQAAb0QAqQZ3ISQ/P58QAo/39ttvO13tqE6dOho3bpxFFcEq4eHhGjx4sNP6W2+9xRWxAAA1ggBSTYQQeDNX537cd999uuyyyyyoBlZ79NFHndbOnDmj9957z4JqAADehgByAc4XQhITE7Vq1SrzCwMuwerVq5Wdne20PnbsWAuqgR00b95cDz30kNP6+++/b0E1AABvQwC5QO5CyOnTp5WQkEAIgUdZtGiR01rfvn111VVXWVAN7OKxxx5zWtuzZ482btxoQTUAAG9CALkIhBB4i5ycHC1dutRp3dWn3/AtV1xxhWJjY53WP/roIwuqAQB4EwLIRSKEwBt8+OGHKikpqbQWERGhnj17WlQR7OT+++93WvvnP/+p8vJyC6oBAHgLAsglOF8ISUxM1OrVqy2oDKieDz74wGktPj5ederw0gCpX79+ql+/fqW1U6dOafv27RZVBADwBrzLuETuQkheXp4SEhIIIbClY8eOaefOnU7rDzzwgAXVwI4CAwPVv39/p3XOAwEAXAoCSA0ghMATbdu2zWmtR48eXHoXlQwaNMhpbe/evTIMw4JqAADegABSQ6oTQtasWWNBZYBrW7dudVrr3bu3BZXAzm666SY1btzYab24uNiCagAA3oAAUoMIIfAUZ86c0d69e53W77rrLguqgd3dcccdTmtFRUUWVAIA8AYEkBrmLoScOnWKEAJbyMzMdLqS0TXXXKOIiAiLKoKduboqGgEEAHCxCCC1gBACu+PwK1yI2267zWmtvLxcpaWlFlQDAPB0BJBaUp0QsnbtWgsqA6R9+/Y5rXXr1s38QuARgoODFR0d7bT+3/eQAQCgOgggtYgQAjs6fvy4cnNzndavu+4684uBx3B1V3QCCADgYhBAapm7EHLy5ElCCEz3ww8/OK1FRkYqJCTEgmrgKTp16uS0RgABAFwMAogJCCGwk02bNjmtdenSxYJK4ElcBZCysjLOAwEAXDACiEmqE0LWrVtnQWXwNa4CyI033mhBJfAkTZo0cbpJpWEY+vXXXy2qCADgqQggJiKEwA52797ttHb99ddbUAk8javzhLKzs80vBADg0QggJnMXQk6cOEEIQa1z9Yl169atLagEnsbVYVg5OTkWVAIA8GQEEAsQQmAVV9OP5s2bKyAgwIJq4Gnatm3rtObqimoAALhDALHI+UJIYmKiUlNTLagM3szV/T9cvakEXGnTpo3T2okTJ0yvAwDg2QggFnIXQnJzc5WQkEAIQY3KyspyWnP1phJw5corr3RaYwICALhQBBCLEUJgpl9++cVpjQkIqisgIEBNmzattGYYhg4fPmxRRQAAT0QAsQFCCMzi6oThFi1aWFAJPFWTJk2c1o4cOWJBJQAAT0UAsYnzhZDExER9++23FlQGb3L69GmnNe6AjgvRuHFjp7Vjx45ZUAkAwFMRQGzEXQjJyclRQkKCy6sYAdXlKoDUr1/fgkrgqRo2bOi05up5BQBAVQggNnO+EJKSkkIIwUVjAoJLFRgY6LR25swZCyoBAHgqAogNuQsh+fn5WrhwIYdj4aLk5+errKxMRUVFKi8vlyQFBwdbXBU8SVBQkNMaAQQAcCH8Zs2aZXUNlaSnp0uS8vLyLK7EetHR0dq/f7+OHj1asVZcXKyioiL9/ve/18CBA7mD9X/h+eNeRkaGTp06Jensc6mkpEQpKSkKDQ21uDJ74XlUtU2bNqmgoKAiwBYUFOiLL77gRHQXeB65R3+qhz65R3/cs2t/HC1atDCsLuI/FRQUSOK49HNKS0t18uRJlZaWOm2rU6eOGjRoIH9/fwsqsyeeP1XLz8+vCB/nOBwORUREyOFwWFSVPfE8qtrJkycr+nNOYGCgGjVqZFFF9sXzyD36Uz30yT36455d+8MhWDbn5+enBg0ayM/Pz2lbeXm5Tp48qeLiYgsqgyfJz8+v8kRhwgcuhKvXopKSkoqJCAAA5+M3YcIEq2uo5NyoKCYmxuJK7OXo0aP6+OOPdeDAAUmqNPXw9/fXH/7wBw7HEs8fV1avXq3Vq1crJCREZ86cUUlJScW26Oho/eEPf7CwOnvieeTexIkTKwKHw+FQUFCQbrrpJvXo0cPiyuyF55F79Kd66JN79Mc9u/bHYRiGrQ7BSk5OliSNGjXK4krsZ8eOHbr77rt1+PBhpxOHmzRponnz5tnuCWY2nj+VzZo1Sy+99FLFf5eXl6uwsFDFxcW67bbb9OWXX1pYnX3xPHLvnnvu0eLFi2UYhoKCgtSwYUM1a9ZMS5YsUfPmza0uzzZ4HrlHf6qHPrlHf9yza384BMuDXH311YqPj1dERITTtmPHjikhIaEi6QL/HT6ks+cNBQcHq1+/frrnnnssqgyerkePHnI4HHI4HBWHZB05ckQLFy60uDIAgCcggHiYiIgIxcfHu7xELyEE57gKH+eMHz9ed9xxh8kVwdu4unxzSkqKDh06ZEE1AABPQgDxQBEREVXeJ+RcCFm/fr0FlcEOzhc+7HbeFzxTcHCw0wUMjhw5opSUFIsqAgB4CgKIh3J3s0JCiO8ifMBMTEEAABeDAOLB3IWQo0ePEkJ8DOEDZnMVQI4ePcoUBADgFgHEwxFCIBE+YB1Xl95lCgIAcMd2l+G16x0b7eKnn37SNddc43QzsB07dighIUGZmZlOx2U3a9ZM8+bN00033WRmqZYoLS11eaM0b3ax4aOsrEx169atzdI81unTpxUSEmJ1GbY1a9YszZo1S5I0YcIEl8+/cePG6X/+53/MLs1WysvLVacOn/NVxRdfry9WcXFxpft/4f/88ssvuuKKK7ipbhXs+r7adq+M9evXt12T7KRt27YuX7DPTUIiIyOdth05ckQJCQn67rvvzCjRUr72y+xSJh+Ej6q5OrQIVXP1PEtJSVF2drYF1dgH4cM9X3u9vhSEj6q1bNmS8OGGXd9X8+roYdw9idwdjuVLIcRXcNhV7eGX2YUZN26cU884FwSAGQiynsnSAHLw4EH17Nmz4oZWVX316dNHx48ft7JUWzEMQ4sWLVJYWJgSExNVWFhYsc0XQ4hhGNq2bZsmTJiga665Rg6HQ9dcc40ee+wxZWRkyGZHGdaICw0fpaWlWrVqlR5++GG1adNGDodDjRs31t13361FixYpPz/fjLI9Sm5uru6//36veP0pKirS0qVLdf/996tx48ZyOByKiYnRrFmzdPTo0Ut+fIfDofHjxzutMwWRPvvsM4WFhXGTxn/jtej88vPztWjRIvXt21dhYWEKCwtT3759NX/+fPpThfz8fD3yyCNyOBw+/2+trKxMkyZNOu97a4fDodTUVOsKNSy0YcMGo0WLFoYkt1933nmncezYMStLtZWtW7canTp1MiQZCQkJRkFBgdM+mZmZxq233mq0bNnS6ev66683vvvuOwsqr3klJSXGm2++aYSGhrp87oSGhhpTp0512SNPNXPmTJf/v7Zs2dKYOXOm0/5HjhwxBg8e7PbfWO/evY0dO3ZY8Lexp5KSEmPGjBle8fpz+vRp47HHHqvy//vo6Ghjw4YNF/SYM2fONFq0aGG0aNGi4jlXXl5uXHbZZU7PyRdeeKE2/loeYevWrUZ0dLQhyUhJSbG6HMvxWnR++/btM/r161dlf7p27Wps3LjR6jJtpby83HjvvfcqeuTr/9ZOnDhh/OEPfzjve2tJxrp16yyr09IJyIEDB5Sdna3Y2Fh9+eWXWrlypcuvZ555hhNC/y03N1d//etflZGR4XY/d5OQw4cPKyEhQd9//31tlWmaxYsXa9y4cZKkKVOmKCcnR4Zh6OTJk3r99ddVr149TZ48WcnJyV4xCbnQyUdhYaGmTJmi9957T61bt9Z7772n06dPyzAMFRUVacmSJerUqZO+/vprPf744zp8+LAZfw1bKyoq0ksvvaRp06ZZXcolKy0t1WuvvaZXX31VkZGR+vzzz1VUVKSysjJlZGRowIABWr9+vR5//HEdOHDgkn6Ww+HgXJD/8PPPP2vkyJFchfDfeC06v9zcXD3++ONavHixunbtqrS0NJWUlFT695qamqqxY8dq3759VpdrGxs3btRTTz1ldRm2ceLECR08eFChoaGaO3dule+tV65c6fK8YdNYFn0Mw5g+fbohyRg3bpxRVFRkZSkeobS01HjhhRcqpdeqJiDnePMkJCcnxxgwYIAhyZg0aZJRUlJSaXt5ebmRnJxsSDJuv/124+DBgxZVWjMudPJhGIaxfv16o0WLFkZoaKjx1VdfudwnIyPDiIqKMiQZb775Zm3+FWzvyJEjxpgxY7xmAvvTTz8ZUVFRVf7/f+jQIaN///6GJGPWrFlGeXl5tR7X1QTEMJiCGIZhlJWVGV9++aURGRlZ6Xnk65/K8lp0fp988okhyYiKijIyMjKctv/6669Gz549fbY/rhw5cqTifQD/1s5KS0szQkNDjVtuucXYt2+f1eVUybIJSEFBgfbs2SNJioyM5AoP1bBu3TrNmTNH/fv318MPP1yt7/HmScjWrVu1fPlytWvXToMGDXI6Ec3hcCg6Olrt2rXT+vXrlZWVZVGll+5iTzj/5ptvlJ2drXvvvVc333yzy33at2+ve++9V5L0ww8/6MyZMzVSsycpKirSokWLFBsbq6SkJEVGRmrQoEFWl3VJDMPQV199pW3btlX5/39ERISGDBkiSVqyZMkl37vD3RTk4MGDl/TYnmDfvn0aNmyYfve73ykzM1P33XefOnXqZHVZtsBrkXuFhYX6+uuvJUn33nuv2rdv77RP8+bNFRMTI8n3+uNKaWmp3nrrLX366acaO3asYmNjrS7JFnbs2KG8vDxdeeWVCg8Pt7qcKlkWQE6cOKFdu3YpNDSUF+hqOHTokF588UVJZ68407Zt22p/7/lCSGJiojZs2FBjtZrF4XCoX79+uv7663XFFVdUrJeXl1f8uaSkpOKeDvXq1bOizEt2seHjzJkzKigoUExMjNq2bVvpMMY1a9bo9OnTks5ejjcoKEjS2ZPXDC84VO1Cffzxx4qLi9PBgwf1xBNPaO3atbr77rutLuuSnDp1SmlpaZKk66+/XqGhoS73++1vf6uOHTvWWEj/85//7HRFrGPHjnn9FbGOHz+uxMREvfvuu7rxxhu1bNkyzZ07V82bN7e6NMtV9VqUk5OjNWvWVOzny69FZWVlatWqlWJjY3X99ddXukz6uT6UlZVVhI6AgACfv8zzmjVr9Oqrr6p///4aNWqULS81a7aysjJt375dkhQVFVXl674dWPbszc7OVmZmpjp27Kji4mI999xz6ty5sxwOh9q0aaMRI0YoLS2t0ptJX1VaWqrZs2dr8eLFeuSRR9StW7cLfgx3IeTQoUNKSEjwuBByyy236P3339eHH36oRo0aVayfe1EuLS3VkiVLlJ2drfbt26tly5ZWlXrRLuVSu4GBgZo6darS0tL0zDPPVHpTePnll1e8WBcVFenYsWOSzr4B8MVL0Pr7+2vKlCn66aefNGPGDDVt2tTqki7ZueOAJalDhw5V7te0aVO1bNlSeXl52r179yX/XF+egrRr105LlizR2rVrdfvtt/v8G8RzqnotKi8v1+WXX16xny+/FoWEhGjSpElas2aNBg4cWGnbuT7s3r1bK1askHR2WuTLR44cOHBAzz33nPz9/fX4448T9P/t9OnT2rlzpySpVatWLq+mZperzVn26rhr1y5lZ2fr22+/VY8ePTR58mRt2rRJkpSVlaX58+frlltu0eTJk23RKCstXrxYs2fP1sCBAzVixIiLvoGcN4YQV0pLS/Xjjz9q7Nixmjx5slq3bq2nnnpKLVq0sLq0C1Kb9/lo3bp1xZujzMxMLVu2TJLUuXNnBQYGXvTjeqqBAwdq8uTJatWqldWl1JiTJ09WXGLX3SeDQUFBFRPEc4fFXipXU5Djx4979RSkcePGmj17tvr06aOAgACry/EIYWFhat26dcV/81rkWm5urlJSUvTggw8qIyNDY8aM0QMPPGB1WZYpKirSyy+/rJUrV2rcuHG65ZZbrC7JNo4ePaq9e/dKkuLj4xUXF6elS5cqLy9PeXl5Wrp0qeLi4nTfffdVBBWrWBZAduzYUfHnIUOGaMuWLRVXe9i9e3fFlY2mT5+u1157TaWlpVaVaqlt27bpb3/7my6//HI99dRTlT7pvxjVCSEbN268pJ9hleLiYo0fP1716tXTtddeq9dff109e/bUJ598ou7du1td3gVxFT4Mw5BhGDVyk8FzITY/P1/z5s3Ttm3b1LVrV/Xq1euSHhf2kZeXp507d6pTp05q0qRJlfs5HI6L/lDD3WP66hQE1efv789rkRsbN25Uy5YtFR4ersGDBysjI0PPP/+8XnjhBQUHB1tdniUMw9Ann3yi5ORkDRkyRMOGDfOpSdn5HD58uOI93I033qgvv/yy4mpzOTk5mj9/vlq3bm2Lq81ZEkDOnDmj4uJixcTEaMyYMUpKSlLHjh3l5+enOnXqqG3btnrhhRc0Y8YMSdLrr7+uzZs3W1GqpfLz8/Xaa69p/fr1mjRpkjp27Fgjj+utIaS0tFR5eXmV1s5dxvl8ly22k6omH+fe1NXUHc4LCws1c+ZMJSUlKTQ0VI8//rjatGlTI48NPPbYY06HIHn7FAQXh9ci1/Lz850uYf38888rOTm50g2Ifcn27dv197//XW3bttWTTz6psLAwq0uylWPHjqlnz57q2rWrFixYoH79+lWE1UaNGumPf/yjFixYoNatW+uzzz7TBx98YNm5VpYEkP88HnTOnDkuk7yfn5/i4uIUGxurrKwsLV261KdOSDMMQ59++qmSkpI0ZswYDRgwoEZTvrsQkp2d7ZEhJDAwUC+99JLKy8tVVFSk1atXq3fv3vryyy917733WnvHz2qqzcOu/lN+fr6ee+45PfPMMwoNDdXLL7+sfv361chjA9LZc7Gqujv6pd5zBN6D16Kq3XjjjSoqKlJ5ebmys7M1Y8YMlZSUaPz48Zo4caLPhZD8/Hy9/PLL2rp1qyZOnKhrrrnG6pJsp3///lqxYoXWrVunqKgol/t07dq14iqPS5cu1fHjx80ssYKtz5Br1qyZbrjhBklnzwvxpX9s526sEx0drUcffbRWxq3eFkLq1Kmj0NBQORwO+fv7q3v37hWfAGRlZenNN9+09flEZoWPnJwcjRs3TtOnT6/4hT906FCnyxgDl4opCNzhtci9oKAg+fv7y+FwqHnz5po4caKSkpIkSQsWLNC3335rcYXmMQxDb775pt544w0NHjxY/fv359Cri+Tn56euXbtKOnsy/7kLP5itRgNIYWGhEhMT5XA4XH4lJiaeN0Rs2LCh4jJz/v7+Fec87N+/3ysCSGZmpq677roqe7Rw4UIdPXpU06dPV05Ojv785z9XmWJrQnVCyA8//FBrP9+V1NTUKvvjcDguaJLRvHlzDRgwQJK0adMm/frrr7VV9iW50PAxderUKvvTp0+fKj/RyMrK0pAhQ/TGG28oPDxcc+fO1bBhw7zuF35NvBZ5usaNG6tjx47KyMhw+wvGMAyVlZVJUo0/D+rUqVPluSBMQXybr7wW1SSHw6FevXrp9ttvV15enk8FkG+//VYvv/yyoqOj9ec//9lnz4G5GLt379aqVasqrTVu3FiS9OOPP/reBKS0tFS5ubkqLi6utH7kyBGXN9dp1qyZz1xybseOHfr000+Vl5enBx980OUbqKefflqSNG/ePNWvX78ivFwMO4aQi3X69OmKK0Ccc25Me743YlYxa/KRlpam/v37a/HixYqMjNQnn3yiBx98kEuFeqmgoKCKa8AXFBRUuV9hYaH2798vSbVyFbCxY8c6PcdycnKYgvgwXosuzP79+ysuxNOwYUNdeeWVks5+eu3tH6Scs2LFCmVlZWn9+vW6+uqrnd4TNWnSRF999ZWks1d/cjgcuu6665SZmWlx5eYyDEMnT56suM+XdPaiM1W992nXrp1l9wqp0X/tQUFBmjt3bsXVev77a+7cuQoKClJ6errCw8MVHh6u1atXOz3GuaBRUFCgX375RZLUpEkTr7i0YWRkpDZv3lxlj+Li4iypy10IOXjwoKkhpGvXrlX2xzAMde3aVcXFxZo6daq6d++u//mf/6kIsoZhON3L4Nynuy1atLDdZR0vNnxMnjy5yv4sXbq04tONc1avXl1xCcfevXvrn//8p2699VavHWFX97XIm4WHh1e8UXF3ed2jR4/q4MGDCg0Nrdi/JjEFwX/ytdei6tqyZYt+97vfqXPnzk6HPu/du1clJSWSKk8s69evX+NXsIPnys3N1d13362GDRtq+vTpFc+T4ODgSjcillTxPqlp06Zq0KCB6bVKFk1AWrVqpS5dukiS1q5dW9EkSerWrVvFNev37t1bcbhNt27dfGYCcr434IZhaMqUKZKkhIQEFRQU1Eh4sVMIOR9/f3+FhIRo7dq12rhxY0W6Dw0NrXTJXcMwKu5tEhkZaat7gZg1+Vi9erWGDh2qrKwsDR48WAsWLODkPR8QEhKi6667TpKUnp5e5flPW7du1Y8//qjo6OhK92SoSUxBIPFa5E6DBg2Um5urTZs2Od2P6+abb674wOTw4cP68ccfJZ39neYr74vcfehmGIaOHTumO++8U9LZDzcMw9DmzZsVGRlpceXmCQsL07XXXitJ+v7773XkyBFJZw+3uu222yr2y8/P18qVKyVJN9xwg2U3cbQkgERERCg2NlaS9Pnnn1e6J0i9evUknW1QUlKStm3bpnvuueei7v6NC3e+EJKYmFhxw0irxcbGqnXr1lq1apU++uijiquk/ecL8k8//aR3331XktS7d29FRERYUut/Myt8HDhwQM8++6yysrLUv39/vfjii9wx1kc4HA51795drVu31ieffKI1a9Y4XUnw0KFDeuuttyRJffv2rbXnhrspiF3Py0LN4rXIvebNm+vmm2+WJL333nvat29fxbZz74uKioqUkpKi9evXq1OnTrr11lstqBR2VbduXfXq1UuhoaFavny5vvnmGxmGoTp16lS8LzIMQ5999pk++eQTtWjRQr///e8tO7rIkgBSt25dDR48WNHR0crIyNDQoUO1bNkylZaWqry8XDt37tTIkSOVlJSk1q1ba/z48WrWrJkVpfokdyHkwIEDSkhIsEUIue666zR69GhJZz8dmTVrlnJzcyWdDbD/+Mc/NHDgQGVkZKh///764x//aItxtVnho6ysTO+++65WrlypZs2aqW/fvtq2bZtWrVpV5Vd6erqKiopq5OfDeuf+jeTl5Wn06NFauHChCgsLVV5eri1btmjMmDFavHixevbsqUGDBtXqYTBMQXwXr0XnFxAQoOHDhys6OlqpqalKSEjQ999/X/G+aM+ePRo7dqyefvpphYaGauLEiS5/R8O33XLLLRo6dKiks1chfOWVV3Tq1ClJZw/RmjVrlhITE5WXl6fHHnvM2rvIGxbauHGj0bVrV0OSy6/IyEjjH//4h1FeXm5lmbY0ZcoUQ5KRkJBgFBQU1MrPyMzMNG699VajZcuWTl833nij8cMPP9TKz70QBQUFxtSpU43Q0NAqn0cDBgww9u3bZ3WphmEYxsyZM132s2XLlsbMmTNr9Gft27fPuOWWW6rsi6uvO++80zh27FiN1uGpUlJSvKInp0+fNh577LEq/z+Pjo42NmzYcEGPOXPmTKNFixZGixYtLuh5+/LLLzs97zt06GDs37//Qv9aHuHYsWPGnXfeaUgyUlJSrC7HMrwWVd/53heFh4cb77zzjlFSUmJ1qbbCv7X/c/z4cWPMmDFVPodCQ0ONp556yjh9+rSldVp6yYnOnTvrq6++0ptvvqk+ffpUnInfo0cPzZw5UytXrqzxG/Ch+jxhEhIUFKRJkyZp1apVGjFiRMXxnq1bt9b999+vJUuW6P3336+1Y9svhFmTj3N+/fVXn7pMI1wLDg7W888/ryVLlmjgwIEKDw+XJEVHR2vmzJn64osvKs7Jq21jx451mkIyBfF+vBZVX+fOnfWvf/1LSUlJFYfTSFJMTIymTp2qTZs2ca8UuBUeHq7Zs2dr1apVGjp0aMX7n8jISI0dO1arVq3Ss88+a/mljB2G4UO3F8dF2bFjhxISEiqdq3PO5Zdfrnnz5lWc7ArXzA4fQG2aNWuWZs2aJUmaMGHCBT1/X3nlFb344ouV1ho1aqSlS5fq8ssvr9E6AQD2xEW3cV7uJiG//vqrEhIStHnzZvML8xCED+D//OlPf3KaguTm5jIFAQAfQgBBtRBCLg7hA6isbt26VV4R69wNEQEA3s12AWTjxo365ptvrC7DtpKTk5WcnGzJz/aEELJlyxZt2bLF0hrOsXP4sPJ55AnoT+169NFHfWIKwvPIPfpTPVu2bFFGRobVZdgWzyP3tmzZYvn5uq7YMoD8952sYR/nCyGJiYmWvlCmp6crPT3dsp9/jp3DB2C1qqYgCxcuZAoC/Jf09HStX7/e6jLgodLT0/X9999bXYYT2wUQ2J+7ELJ//34lJCT49Kc1hA/g/HxlCgIAcEYAwUUhhLhG+ACqh3NBAMB3EUBw0aoTQuxyPoYZCB/AhXE1BTlx4gRTEADwcgQQXBJCyFmED+DCMQUBAN9EAMElcxdCfvnlF68PIYQP4OI9+uijTnd1ZgoCAN6NAIIa4ashhPABXJq6detq/PjxTutMQQDAexFAUGOqE0J+/PFHCyqrHYQPoGZUNQV57733LKoIAFCbCCCoUb4SQggfQM3hXBAA8C0EENQ4dyEkKyvL40MI4QOoeWPGjHGagpw8eZIpCAB4IQIIaoW3hhDCB1A7/Pz8mIIAgI8ggKDWnC+EJCYm6qeffrKgsotD+ABqF1MQAPANBBDUKnchZN++fUpISPCIEEL4AGofUxAA8A0EENQ6Tw8hhA/APFVNQd59912LKgIA1DQCCEzhqSGE8AGYiykIAHg/AghMc74QkpiYqJ9//tmCylwjfADWcDUFOXXqFFMQAPASBBCYyl0I2bt3rxISEmwRQggfgHWYggCAdyOAwHR2DyGED8B6Y8aMUb169SqtMQUBAO9AAIEl7BpCCB+APTAFAQDvRQCBZc4XQhITE7V161bT6iF8APYyevRol1OQBQsWWFQRAKAmEEBgKXchZM+ePUpISDAlhBA+APthCgIA3okAAstZHUIIH4B9uZqC5OXlMQUBAA9GAIEtVCeEbNu2rcZ/LuEDsDemIADgfQggsA2zQwjhA/AMiYmJTEEAwIsQQGAr7kLI7t27ayyEED7gy3Jzc3X//ferT58+On78uNXlnFe9evWYggCAFyGAwHZqO4QQPuDLSktLlZycrI8++sjqUi5IVVOQd955x5qCAAAXjQACW6pOCNm+ffsFPy7hA76sqKhIL730kqZNm2Z1KReMKQgAeA8CCGyrpkMI4QO+7OjRoxo/fryeeOIJ5eXlWV3ORUlMTJS/v3+ltdOnTzMFAQAPQwCBrbkLIbt27ap2CCF8wFcVFRVp0aJFio2NVVJSkiIjIzVo0CCry7ooTEEAwDsQQGB7lxpCCB/wZR9//LHi4uJ08OBBPfHEE1q7dq3uvvtuq8u6aAkJCUxBAMDDEUDgEc4XQhITE5WZmem0jfABX+fv768pU6bop59+0owZM9S0aVOrS7okTEEAwPMRQOAx3IWQnTt3KiEhQYcPH65YI3wA0sCBAzV58mS1atXK6lJqTFVTkLffftuiigAAF4IAAo9yvhCSkpKiw4cPEz4AL1bVFGThwoVMQQDAAxBA4HHchZDDhw9r9uzZeuGFF1x+L+ED8A5MQQDAcxFA4JGqCiFFRUU6fvy4Tpw4odLS0krbCB+A9+BcEADwXAQQeKz/DiHFxcUqLi6WJJWVlen06dMV+xI+AO8zatQopylIfn4+UxAAsDm/5ORkq2uoZM2aNVaXYGv0x9ltt92mgwcPKisrS4ZhVKyfOXNGeXl5uvPOOxUaGiq7PdetxPPIPbv156abblKHDh3k5+enzMxMDRo0SBkZGS73TUlJUVxcnCTp119/1bp161S3bl3FxsaqefPmVf6MM2fOaMOGDdq6det560lPT1dBQUHFn638txUTE6MlS5ZUWpszZ44CAgLUqFEji6o6y27PI7uhP9VDn9yjP+7ZtT9MQODxIiIiFB8fr/Dw8ErrDodDd955p+644w6LKgNQ27p376569epVWisqKlJqaqpFFQEAzsdv1KhRVtfgkl3rsgv646x79+4aOHCgjh8/rtDQUHXv3l0fffSR1WXZGs8j9+zYn8jISG3evLla+15++eV64IEHqrVvYGCgunXrpm7dup1337y8vIo3+DExMZb3qby8XNOnT6+0tn37ds2ZM0dXXHGFRVX9H6v7Y3f0p3rok3v0xz279YcJCLxGjx499Nxzz2ns2LE6ceKEPv/8c6tLAmCCkSNHKiAgoNJafn6+3nrrLYsqAgC4QwCB14mKirK6BAAm8vf354pYAOBBCCAAAI/nagpSUFDAFAQAbIgAAgDweExBAMBzEEAAAF6BKQgAeAYCCAD4mLi4OBmGoaVLl6px48ZWl1NjmIIAgGcggAAAvEZVU5D58+dbVBEA4L8RQAAAXoMpCADYHwEEAOBVRowYocDAwEprhYWFTEEAwCYIIAAArxIQEKDx48c7rTMFAQB7IIAAALwOUxAAsC8CCADA6wQEBHAuCADYFAEEAOCVhg8f7nIK8uabb1pUEQBAIoAAALwUUxAAsCcCCADAa7magpw5c4YpCABYiAACAPBaTEEAwH4IIAAAr8YUBADshQACAPBqTEEAwF4IIAAArzd8+HAFBQVVWjtz5ozeeOMNiyoCAN9FAAEAeD3ujg4A9kEAAQD4BFdTkKKiIqYgAGAyAggAwCdwLggA2AMBBADgM4YNG8YUBAAsRgABAPiMwMBApiAAYDECCADAp1Q1BUlOTraoIgDwLQQQAIBPYQoCANYigAAAfI6rKUhxcTFTEAAwAQEEAOBzmIIAgHUIIAAAnzRs2DDVr1+/0hpTEACofQQQAIBPCgwM5O7oAGABAggAwGdVNQWZN2+eRRUBgPcjgAAAfFZV54IsXLiQKQgA1BICCADApz388MNMQQDARAQQAIBP44pYAGAuAggAwOcNHTrUaQpSUlLCFAQAagEBBADg84KCgpiCAIBJCCAAAKjqKcjcuXMtqggAvBMBBAAAVT0F4YpYAFCzCCAAAPzb0KFDFRwcXGmNKQgA1CwCCAAA/xYUFMTd0QGglhFAAAD4D66mIKWlpUxBAKCGEEAAAPgPXBELAGoXAQQAgP8yZMgQpiAAUEsIIAAA/BemIABQewggAAC4UNUU5PXXX7eoIgDwDgQQAABcYAoCALWDAAIAQBVcTUHKysqYggDAJSCAAABQBaYgAFDzCCAAALgxePBghYSEVFpjCgIAF48AAgCAG/Xr1+fu6ABQgwggAACcR1VTkKSkJIsqAgDPRQABAOA86tevz7kgAFBDCCAAAFRDfHy80xSkvLycKQgAXCACCAAA1cAUBABqBgEEAIBqYgoCAJeOAAIAQDUxBQGAS0cAAQDgAlQ1BZkzZ45FFQGAZyGAAABwAZiCAMClIYAAgJc7deqU5s+fr759+yosLEwOh0PXXHONRo4cqbS0NJWXl1tdoseJj49XaGhopTXDMJiCAEA1EEAAwIulpaWpe/fuGjFihJYuXaq8vDxJUmZmpt58803dcsstmjx5svLz8y2u1LNwd3QAuHgEEADwUjt37tS4ceOUkZGh3r1767vvvlNJSYkMw1BOTo5efPFFhYaGavr06XrttddUWlpqdckeJS4ujikIAFwEAggAeCHDMPTFF19o/fr16tmzp9566y3deOON8vPzkyQ1atRIEyZM0KxZsyRJCxYsUGZmppUle5zg4GCmIABwEQggAOCFTpw4oRUrVkiSBg0apMsuu8xpH4fDoX79+unWW2/Vtm3b9NNPP5ldpseragry2muvWVQRANgfAQQAvFBubq6Cg4MVGRmpqKioKvcLCAhQQECAJHEI1kUIDg7WuHHjnNZTUlKUm5trQUUAYH8EEADwQm3bttWHH36o7du3q3v37lXud+rUKZ04cUKSKg7PwoVxdUUsSVq5cqUF1QCA/RFAAMBHGYah5cuXa/369YqKilKHDh2sLskjVTUFWb9+PVMQAHCBAAIAPmr79u2aP3++JOmuu+7SVVddZXFFnquq+4IwBQEAZwQQAPBBWVlZevzxx7V+/Xp17dpVjz76aMW5ILhwVU1B0tPTuSIWAPwXAggA+JidO3dq1KhRWrx4saKjo/Xqq6+qTZs2Vpfl8eLj4xUWFua0Pnv2bAuqAQD78ktOTra6hkrWrFljdQm2Rn/coz/VQ5/cs1t/brrpJnXo0OGCTxI/ceKE/P39Vb9+/Yq1jRs36pFHHtH69esVHR2tOXPmqEuXLpKk8vJy7du3T2lpaW7vjJ6enq6CgoKKP9vt94iVunTpoi+//FKSVFxcLElKTk5W48aN1ahRIytLsx27/TuzK/rkHv1xz679YQICAB4kMzNT1113nRwOh8uvhQsXVuwbFhZWET4Mw9CSJUv0+9//vuKwq/nz51eED8MwdPDgQf3www9uwwfci46OVlBQkNP6uXuyAAAkv1GjRlldg0t2rcsu6I979Kd66JN7nt6fOnXOfsZUWlqquXPnatKkScrLy9PAgQP18ssvV7o5ocPh0OWXX64//OEP533cvLw8paamSpJiYmI8vk81zd/fX1OmTKn47+DgYP3000968803dcUVV1hYmT3x/Kke+uQe/XHPbv1hAgIAHiQyMlKbN2+WYRguv+Li4irtX1paqlmzZulPf/qT8vLy9OSTT2r+/Pku74yOmhEXF8e5IADgBgEEALzUufDx5JNPKjQ0VH//+9/1zDPPuLxpHmpOSEiI/vznPzutL1y4kCtiAYAIIADgtVasWKFp06ZJkv7yl79o9OjRXGrXJHFxcS7PBfn73/9uQTUAYC8XdkkVAIBHOHLkiObMmaO8vDz17NlT7du317p169x+T0REhKKiokyq0LuFhISoV69eFVfEOmfRokUaO3Ys54IA8GkEEADwQunp6fr8888lSStXrqzWHbmnTJmiyZMn13ZpPiM6OlrffPON0/rf//53vfjiixZUBAD2wCFYAOCFMjIyrC7B5wUEBKhXr15O64sWLeJcEAA+jQACAF5o8uTJVV4pq6ovph81Lzo6Wg0aNHBa51wQAL6MAAIAQC0JCAjQ2LFjndaZggDwZQQQAABqUXx8PFMQAPgPBBAAAGpRSEgIUxAA+A8EEAAAallVU5BXX33VgmoAwFoEEAAAallVU5D333+fKQgAn0MAAQDABExBAOAsAggAACZgCgIAZxFAAAAwSVxcHFMQAD6PAAIAgElCQ0P1pz/9yWmdKQgAX0IAAQDARPHx8WrYsKHT+iuvvGJ6LQBgBQIIAAAmCg0N1aOPPuq0/sEHHzAFAeATCCAAAJiMKQgAX0YAAQDAZExBAPgyAggAABZgCgLAVxFAAACwAFMQAL6KAAIAgEWqmoK8/PLL5hcDACYhgAAAYJGqpiAffvghUxAAXosAAgCAhZiCAPA1BBAAACzEFASAryGAAABgsbi4ODVq1MhpnSkIAG9EAAEAwGJhYWF65JFHnNaZggDwRgQQAABsoKopyEsvvWRBNQBQewggAADYQFhYmMaMGeO0/r//+79MQQB4FQIIAAA2ER8fzxQEgNcjgAAAYBNMQQD4AgIIAAA2whQEgLcjgAAAYCNMQQB4OwIIAAA2wxQEgDcjgAAAYDNMQQB4MwIIAAA2FB8fr/DwcKd1piAAPB0BBAAAGwoLC9Po0aOd1pmCAPB0BBAAAGwqLi6OKQgAr0MAAQDApho0aMAUBIDXIYAAAGBjTEEAeBsCCAAANtagQQMlJiY6rTMFAeCpCCAAANgcV8QC4E0IIAAA2BxTEADehAACAIAHYAoCwFsQQAAA8ABMQQB4CwIIAAAegikIAG9AAAEAwEMwBQHgDQggAAB4kPj4eDVu3NhpnSkIAE9BAAEAwIM0aNBACQkJTutMQQB4CgIIAAAehikIAE9GAAEAwMMwBQHgyQggAAB4oLi4OKYgADwSAQQAAA/UsGFDjRo1ymmdKQgAuyOAAADgoTgXBIAnIoAAAOChmIIA8EQEEAAAPBhTEACehgACAIAHYwoCwNMQQAAA8HDx8fFq0qSJ0zpTEAB2RAABAC+Xn5+vRYsWqW/fvgoLC1NYWJj69u2r+fPnKz8/3+ryUAMaNmyokSNHOq0zBQFgRwQQAPBiWVlZGjRokOLi4rR06VLl5eUpLy9PS5cu1YgRI3TnnXfqhx9+sLpM1ACmIAA8BQEEALxUbm6uHn/8cS1evFhdu3ZVWlqaSkpKVFZWpoyMDA0YMECpqakaO3as9u3bZ3W5uERMQQB4CgIIAHiplStX6qOPPlJUVJSSkpIUExMjPz8/1alTR9dee61mz56tnj17KjU1Vd98843V5aIGMAUB4AkIIADghQoLC/X1119Lku699161b9/eaZ/mzZsrJiZGkvTDDz/ozJkzptaImscUBIAnIIAAgBcqKytTq1atFBsbq+uvv15169Z1uc+50BEQEKA6dfiV4A3i4uKYggCwNX7bAIAXCgkJ0aRJk7RmzRoNHDjQ5T67d+/WihUrJEnt27eXv7+/mSWiljRq1IgpCABbI4AAgI/Jzc1VSkqKHnzwQWVkZGjMmDF64IEHrC4LNYgpCAA7I4AAgI/YuHGjWrZsqfDwcA0ePFgZGRl6/vnn9cILLyg4ONjq8lCDGjVqpBEjRjitMwUBYAcEEADwEfn5+crOzq609vzzzys5OVmFhYUWVYXaEh8fr6ZNmzqtMwUBYDUCCAD4iBtvvFFFRUUqLy9Xdna2ZsyYoZKSEo0fP14TJ04khHiZRo0aafjw4U7rTEEAWI0AAgA+IigoSP7+/nI4HGrevLkmTpyopKQkSdKCBQv07bffWlwhahpTEAB25JecnGx1DZWsWbPG6hJsjf64R3+qhz65Z7f+3HTTTerQoYP8/PyUmZmpQYMGKSMjw+W+KSkpiouLq9bjOhwO9erVS7fffruWL1+ub7/9Vr169ZIk5eTkaN26dTp06JDT96Wnp6ugoKDiz3b7PWIXdnkeRUVFOd3p/u2331bz5s3VqFEja4qSffpjd/TJPfrjnl37wwQEAHxEWVmZDh06pP3796u0tFTS2RvXXXnllZKkAwcOVByGVa9ePS7L6yWio6MVGhrqtL5s2TILqgEAyW/UqFFW1+CSXeuyC/rjHv2pHvrknh37ExkZqc2bN593vy1btmjSpEk6ePCg3njjDXXp0kV169ZV8+bNK+1nGIbKysokSfXr16+4YWFoaKj69Onj8rHz8vKUmpoqSYqJibFln+zEDv2pW7euZsyYUWlt27Zt6tu3r6644gqLqjrLDv3xBPTJPfrjnt36wwQEALxQgwYNlJubq02bNmnDhg1V7nf48GH9+OOPks6GG6Ye3olzQQDYCQEEALxQ8+bNdfPNN0uS3nvvPadzACSpqKhIKSkpWr9+vTp16qRbb73V3CJhGq6IBcBOCCAA4IUCAgI0fPhwRUdHKzU1VQkJCfr+++9VWlqq8vJy7dmzR2PHjtXTTz+t0NBQTZw4UVdffbXVZaMWxcXFMQUBYAsEEADwUlFRUUpKSlLXrl319ddf66abblK9evVUt25dXXnllUpOTlZ4eLhmz56t+++/Xw6Hw+qSUYvCw8OZggCwBQIIAHixzp0761//+peSkpLUq1eviqshxcTEaOrUqdq0aZOGDh0qPz8/iyuFGeLi4tSsWTOndaYgAMxEAAEALxcWFqbRo0dr+fLlOnXqlAzDUFpamp566im1atXK6vJgovDwcA0bNsxpnSkIADMRQAAA8CHx8fFMQQBYigACAIAPYQoCwGoEEAAAfAxTEABWIoAAAOBjmIIAsBIBBAAAH8QUBIBVCCAAAPggpiAArEIAAQDARzEFAWAFAggAAD6KKQgAKxBAAADwYfHx8YqIiHBaZwoCoLYQQAAA8GHh4eF6+OGHndaZggCoLQQQAAB8XFxcHFMQAKYhgAAA4OMaN26soUOHOq0zBQFQGwggAACAc0EAmIYAAgAAmIIAMA0BBAAASGIKAsAcBBAAACCJKQgAcxBAAABABaYgAGobAQQAAFRgCgKgthFAAABAJfHx8WrevLnTOlMQADWBAAIAACpp3LixhgwZ4rTOFARATSCAAAAAJ0xBANQWAggAAHDCFARAbSGAAAAAl+Li4piCAKhxBBAAAOBSkyZNmIIAqHEEEAAAUCWmIABqGgEEAABUqUmTJho8eLDTOlMQABeLAAIAANziilgAahIBBAAAuMUUBEBNIoAAAIDzio+PV4sWLZzWmYIAuFAEEAAAcF5NmjRRfHy80zpTEAAXigACAACqhSkIgJpAAAEAANXCFARATSCAAACAamMKAuBSEUAAAEC1MQUBcKkIIAAA4ILExcUxBQFw0QggAADggjRt2pQpCICLRgABAAAXjCkIgItFAAEAABesadOmiouLc1pnCgLgfAggAADgonBFLAAXgwACAAAuClMQABeDAAIAAC5afHy8mjdv7rTOFARAVQggAADgonFFLAAXigACAAAuCVMQABeCAAIAAC4JUxAAF4IAAgAALhlTEADVRQABAACXjCkIgOoigAAAgBrBFARAdRBAAABAjWAKAqA6CCAAAKDGxMXFMQUB4BYBBAAA1JhmzZpxd3QAbhFAAABAjeJcEADuEEAAAECNYgoCwB0CCAD4oNWrV6tNmzbq06ePjh8/bnU58ELx8fGKiIhwWmcKAoAAAgA+5tChQ3rxxReVlZVldSnwYs2aNeOKWABcIoAAgA8pKirSzJkztXjxYqtLgQ9gCgLAFQIIAPiQTz/9VMnJyVaXAR/hbgqSm5trQUUA7MDP6gIAAObYtm2bXnnlFf32t79V165d+RQapoiPj1dKSooOHz5caX3ZsmW6//77LaoKnmz79u3auHGjdu7cqaVLl6pevXrKzc3V1Vdfrb59+yowMNDqEnEeBBAA8AH5+fl6+eWXtXXrVs2dO1fl5eVWlwQfcW4KMmvWrErrGzZs0B133GFRVfBUaWlpGjNmjI4cOSLp7GubJO3Zs0eSdPPNN2vq1KmKioqyrEacH4dgAYCXMwxDixYt0htvvKGhQ4dqwIABcjgcVpcFH1LVuSDLli2zoBp4qlmzZukPf/hDRfhwJS0tTbfffrtT4IW9EEAAwMtt3LhR06ZNU9euXTVhwgQFBQVZXRJ8TFXngmzYsIErYqFaPvjggws6bPSll15SWlpaLVaES0EAAQAvdvjwYT333HPKycnR008/rTZt2lhdEnxUXFwcV8TCRfn555/17LPPXvD3TZs2rRaqQU3gHBAA8FKlpaV655139Nlnn2nq1Km67bbbrC4JPiwiIqLiXBDDMFRcXKzy8nK9+eabKi4uVmhoqNUl2lJGRoak/zvHwRdt375dv/76q8ttJSUlcjgcqlevnvz9/Stt27Rpk/bu3avf/OY3ZpSJC0AAAQAvtWbNGr366qvq37+/Ro4cKT8/XvJhrbi4OKWkpGj79u06c+aMpLNBecGCBQoLC7O4OnsqKCiQ9H9BxBedPn26og9VycnJUZMmTZxe5wgg9uRnt+vBr1mzxuoSbI3+uEd/qoc+uWe3/tx0003q0KHDBQWIffv26emnn5a/v7/GjRvn8tAXd06ePKnU1FSXnzqmp6dXvBlIT0/nviJVsNvzyC5at26tzZs3V/x3eXm5iouLz/sG01cVFxdbXYLlzoVVVwzDkCQ5HA6dPn1a9erVq7R9/vz52rVrV63WZ2d2fR3iHBAA8CCZmZm67rrr5HA4XH4tXLhQhYWFmjVrllJTU/XII4+oW7duVpcNVIiOjladOrz9QPVdylX7AgICarAS1BS/UaNGWV2DS3atyy7oj3v0p3rok3ue2p9ffvlFa9eulSRNnDhREydOrHLfr776Sk2aNJEkTZkyRZMnT5YkNWjQQHfddZfL78nLy1NqaqokKSYmxmP7ZBb642zjxo369NNPVV5erjp16qhBgwZOn1yjsvr161tdgmUMw9Dp06ddbjsXTurWrauwsDCncDty5EjdfPPNtV6j3dntdYgDggHAg0RGRlY6fMWVzMxMc4oBLtJHH32kIUOGKCcnR507d9ZVV11ldUm2tXLlSklSz549La7EOps2bdI777zjctu5Q9RchQ9JXPnPpgggAOBlqhNSFi5cqPj4eN15551auHChGjdubE5xwL+dOzTQbp/M2s258x+GDBlicSXWGTBggDZu3Kjdu3c7bTt3Doir8HH77berRYsWtV4fLhwHYQIAAMC2QkNDNWXKlAv+vr/+9a+1UA1qAgEEAAAAtnbrrbdq/Pjx1d5//Pjxatu2bS1WhEtBAAEAAIDtTZgwQatWrdKtt95a5T4PPvigNm/erAkTJphXGC4Y54AAAADAI7Rr104LFy7U7t27tWvXLi1YsED+/v764x//qKuuukotW7a0ukRUAwEEAHxQXFyc4uLirC4DAC7KlVdeqSuvvFJZWVmSpO7du1tcES4Eh2ABAAAAMA0BBAAAAIBpCCAAAAAATEMAAQAAAGAaAggAAAAA0xBAAAAAAJiGAAIAAADANAQQAAAAAKYhgAAAAAAwDQEEAAAAgGkIIAAAAABMQwABAAAAYBoCCAAAAADTEEAAAAAAmIYAAgAAAMA0BBAAAAAApiGAAAAAADANAQQAAACAaQggAAAAAExDAAEAAABgGgIIAAAAANMQQAAAAACYhgACAAAAwDQEEAAAAACmIYAAAAAAMA0BBAAAAIBpCCAAAAAATEMAAQAAAGAaAggAAAAA0xBAAAAAAJiGAAIAAADANAQQAAAAAKYhgAAAAAAwDQEEAAAAgGkIIAAAAABMQwABAAAAYBoCCAAAAADTEEAAAAAAmIYAAgAAAMA0BBAAAAAApiGAAAAAADANAQQAAACAaQggAAAAAExDAAEAAABgGgIIAAAAANMQQAAAAACYhgACAAAAwDQEEAAAAACmIYAAAAAAMA0BBAAAAIBpCCAAAAAATEMAAQAvdvDgQfXs2VMOh8PtV58+fXT8+HGrywUA+AACCAB4sezsbGVmZlpdBgAAFfysLgAAUHsOHDig7OxsxcbG6oknnlBwcLDL/QIDAxUSEmJydQAAX0QAAQAv9vPPP0uSbrjhBt1xxx3y9/e3uCIAgK/jECwA8FIFBQXas2ePJCkyMpLwAQCwBQIIAHipEydOaNeuXQoNDVWnTp2sLgcAAEkEEADwWudOQO/YsaOKi4v13HPPqXPnznI4HGrTpo1GjBihtLQ0lZeXW10qAMCHcA4IAHipXbt2KTs7W9nZ2erRo0elbVlZWZo/f77mz5+vSZMmadKkSVWeoA4AQE1iAgIAXmrHjh0Vfx4yZIi2bNmikpISlZWVaffu3Ro3bpwkafr06XrttddUWlpqVakAAB9CAAEAL3TmzBkVFxcrJiZGY8aMUVJSkjp27Cg/Pz/VqVNHbdu21QsvvKAZM2ZIkl5//XVt3rzZ2qIBAD6BAAIAXigwMFBTp05VWlqa5syZ4/LwKj8/P8XFxSk2NlZZWVlaunSpDMOwoFoAgC/xS05OtrqGStasWWN1CbZGf9yjP9VDn9yzW39uuukmdejQQX5+NX/aXrNmzXTDDTdo7dq1ysrKUmFhoerXr6/Tp08rLS1Ne/fudfqe9PR0FRQUVPzZbr9H7MJuzyO7oT/VQ5/coz/u2bU/TEAAwINkZmbquuuuk8PhcPm1cOHCKr+3tLRUP/zwgzZs2KAzZ85Ikvz9/dWoUSNJ0v79+1VYWChJqlu3LvcNAQDUCr9Ro0ZZXYNLdq3LLuiPe/SneuiTe57en9LSUuXl5Sk4OFj+/v7y8/NT586dq9y/WbNmFaEjKChIPXr0cLp6liTl5eUpNTVVkhQTE+Pxfapt9Mc9+lM99Mk9+uOe3frDBAQAPEhkZKQ2b94swzBcfsXFxUk6e2hUeHi4wsPDtXr16iofr6CgQL/88oskqUmTJgoICDDl7wEA8F0EEADwQq1atVKXLl0kSWvXrlVZWZnL/fbu3VsxzejWrRuHXQEAah0BBAC8UEREhGJjYyVJn3/+eaV7gpyTn5+vpKQkbdu2Tffcc4+6detmdpkAAB9EAAEAL1S3bl0NHjxY0dHRysjI0NChQ7Vs2TKVlpaqvLxcO3fu1MiRI5WUlKTWrVtr/PjxatasmdVlAwB8QM1f0xEAYAvt2rVTUlKSxo4dq9TUVPXu3dtpn8jISP3tb39T9+7dLagQAOCLCCAA4MU6d+6sr776Sh988IE+/vhjpaamKi8vTz169NDdd9+thx56SC1atLC6TACADyGAAICXCw4O1vDhwzV8+HCrSwEAgHNAAAAAAJiHAAIAAADANAQQAAAAAKYhgAAAAAAwDQEEAAAAgGkIIAAAAABMQwABAAAAYBoCCAAAAADTEEAAAAAAmIYAAgAAAMA0BBAAAAAApiGAAAAAADANAQQAAACAaQggAAAAAExDAAEAAABgGgIIAAAAANMQQAAAAACYhgACAAAAwDQEEAAAAACmIYAAAAAAMA0BBAAAAIBpCCAAAAAATEMAAQAAAGAaAggAAAAA0xBAAAAAAJiGAAIAAADANAQQAAAAAKYhgAAAAAAwzf8HoZF5KZjMU3EAAAAASUVORK5CYII=
Graph of $f$: The function $g$ is defined as $g(x) = 2 \cdot x^2 + \int_{-1}^{x^2} f(t) \, dt$ on $[-2,1]$. The graph of $f$ consists of four line segments and a semi-circle, and is shown above. What is the absolute maximum of $g$ on the interval $[-2,1]$?
The absolute maximum of $g$ on the interval $[-2,1]$ is $1+\frac{ \pi }{ 4 }$.
ae7253eb-638d-404d-8764-16d3eca93f52
integral_calc
false
null
Compute the integral: $$ \int \frac{ 1 }{ \left(\cos(2 \cdot x)\right)^3 } \, dx $$
$\int \frac{ 1 }{ \left(\cos(2 \cdot x)\right)^3 } \, dx$ = $C+\frac{\sin(2\cdot x)}{4\cdot\left(\cos(2\cdot x)\right)^2}+\frac{1}{4}\cdot\ln\left(\left|\tan\left(\frac{1}{2}\cdot\left(2\cdot x+\frac{\pi}{2}\right)\right)\right|\right)$
aee39c3c-776c-45db-a4b1-78f279287461
integral_calc
false
null
Compute the volume of the solid formed by rotating about the x-axis the area bounded by the axes and the parabola $x^{\frac{ 1 }{ 2 }}+y^{\frac{ 1 }{ 2 }}=2^{\frac{ 1 }{ 2 }}$.
Volume = $\frac{8\cdot\pi}{15}$
af144f31-5706-4ad7-84ab-94a14799bbb6
precalculus_review
false
null
Find all values of $x$ that satisfy the following equation: $$ \left|\left(x^4-4\right)-\left(x^2+2\right)\right|=\left|x^4-4\right|-\left|x^2+2\right| $$
The final answer: $|x|\ge\sqrt{3}$
af573af8-742d-47e3-9086-1c954a95c86b
multivariable_calculus
false
null
Use the method of Lagrange multipliers to find the maximum and minimum values of the function $f(x,y,z) = x + y + z$ subject to the constraint $\frac{ 1 }{ x }+\frac{ 1 }{ y }+\frac{ 1 }{ z }=1$.
Minimum: $1$ Maximum: $9$
af740483-5226-4f0a-b027-4762d47d868b
differential_calc
true
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
Use the graph of the function $y = g(x)$ shown here to find $\lim_{x \to 0^{+}}\left(g(x)\right)$, if possible. Estimate when necessary.
$\lim_{x \to 0^{+}}\left(g(x)\right)$ = $0$
af865556-4ec7-4cd3-8fff-592c30074325
integral_calc
true
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
Let $R$ be the shaded region bounded by the graphs of $y=\frac{ 1 }{ x+2 }$ and $y=-\frac{ 1 }{ 2 } \cdot x+3$, as shown above. Find the volume of the solid generated when $R$ is rotated about the vertical line $x=-3$.
The volume of the solid is $292.097$ units³.
afb51ba2-1ec2-4e8b-b6ca-eee46a61357f
differential_calc
false
null
Make full curve sketching of $y = \frac{ 1 }{ 2 } \cdot \ln\left(\left|\frac{ x-4 }{ x+4 }\right|\right)$. Submit as your final answer: 1. The domain (in interval notation) 2. Vertical asymptotes 3. Horizontal asymptotes 4. Slant asymptotes 5. Intervals where the function is increasing 6. Intervals where the function is decreasing 7. Intervals where the function is concave up 8. Intervals where the function is concave down 9. Points of inflection
1. The domain (in interval notation) $(-\infty,-4)\cup(-4,4)\cup(4,\infty)$ 2. Vertical asymptotes $x=-4$, $x=4$ 3. Horizontal asymptotes $y=0$ 4. Slant asymptotes None 5. Intervals where the function is increasing $(-\infty,-4)$, $(-4,0)$ 6. Intervals where the function is decreasing $(-4,4)$ 7. Intervals where the function is concave up $(4,\infty)$, $(-\infty,-4)$ 8. Intervals where the function is concave down $(0,4)$, $(4,\infty)$ 9. Points of inflection $P(0,0)$
afc947d1-b4ea-4c8e-9540-0fc72f85b060
algebra
false
null
Solve the following equation for $x$: $3 \cdot x - (x - 4) = 10 + 5 \cdot (2 \cdot x + 2)$
$x$ = $-2$
afd775c9-9303-4cfc-a781-3399caf2e0b1
differential_calc
true
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
Use the following figure to find the indicated derivatives, if they exist (enter 'undefined' in case, if the derivative doesn't exist): Let $h(x) = f(x) \cdot g(x)$. Find: 1. $h'(1)$ 2. $h'(3)$ 3. $h'(4)$
1. $h'(1)$ = $2$ 2. $h'(3)$ = None 3. $h'(4)$ = $2.5$
afeb0054-83bd-4632-a3f9-8cf9685452d7
multivariable_calculus
false
null
The integral has been converted to polar coordinates. Verify that the identity is true and choose the easiest way to evaluate the integral, in rectangular or polar coordinates: $$ \int_{0}^1 \int_{x^2}^x \frac{ y }{ \sqrt{x^2+y^2} } \, dy \, dx = \int_{0}^{\frac{ \pi }{ 4 }} \int_{0}^{\sec(\varphi) \cdot \tan(\varphi)} r \cdot \sin(\varphi) \, dr \, d\varphi $$
$I$ = $\frac{1}{6}\cdot\left(2-\sqrt{2}\right)$
b031545d-ffe2-41b9-ae2f-5c5e1b989168
differential_calc
false
null
The position function of a ball dropped from the top of a $200$-meter tall building is given by $s(t) = 200 - 4.9 \cdot t^2$, where position $s$ is measured in meters and time $t$ is measured in seconds. Compute the average velocity of the ball over the given time intervals. Round your answer to eight significant digits: 1. $[4.99,5]$ 2. $[5,5.01]$ 3. $[4.999,5]$ 4. $[5,5.001]$
1. $-48.951000$ m/sec. 2. $-49.049000$ m/sec. 3. $-48.995100$ m/sec. 4. $-49.004900$ m/sec.
b04b5d6e-8250-4931-b2cd-f93c3b884ea5
differential_calc
true
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
Using the graph, find each limit: 1. $\lim_{x \to -1}\left(f(x)\right)$ 2. $\lim_{x \to 1}\left(f(x)\right)$ 3. $\lim_{x \to 0^{+}}\left(f(x)\right)$ 4. $\lim_{x \to 2}\left(f(x)\right)$
1. $\lim_{x \to -1}\left(f(x)\right)$ = None 2. $\lim_{x \to 1}\left(f(x)\right)$ = $1$ 3. $\lim_{x \to 0^{+}}\left(f(x)\right)$ = $0$ 4. $\lim_{x \to 2}\left(f(x)\right)$ = None
b0d28b67-d169-4f97-9f81-a001177c77df
algebra
true
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
Use the graph to write an equation for the function:
$f(x)$ = $-8\cdot\frac{(x-3)}{(x+3)\cdot(x-4)}$
b0f6581a-bda8-4027-96db-3dfb44273449
multivariable_calculus
false
null
Calculate the second-order partial derivatives. (Treat $A$,$B$,$C$,$D$ as constants.) $$ f(x,y) = \frac{ A \cdot x + B \cdot y }{ C \cdot x + D \cdot y } $$
$f_{xx}(x,y)$ = $\frac{2\cdot C\cdot(B\cdot C-A\cdot D)\cdot y}{(C\cdot x+D\cdot y)^3}$ $f_{xy}(x,y)$ = $f_{yx}(x,y)$ = $\frac{-(B\cdot C-A\cdot D)\cdot(C\cdot x-D\cdot y)}{(C\cdot x+D\cdot y)^3}$ $f_{yy}(x,y)$ = $-2\cdot D\cdot\frac{B\cdot C\cdot x-A\cdot D\cdot x}{(C\cdot x+D\cdot y)^3}$
b1cbb170-d4d2-4f07-81f3-ee4094350ade
integral_calc
false
null
Compute the integral: $$ \int \frac{ 3 \cdot x+\sqrt[3]{9 \cdot x^2}+\sqrt[6]{3 \cdot x} }{ x \cdot \left(4+\sqrt[3]{3 \cdot x}\right) } \, dx $$
$\int \frac{ 3 \cdot x+\sqrt[3]{9 \cdot x^2}+\sqrt[6]{3 \cdot x} }{ x \cdot \left(4+\sqrt[3]{3 \cdot x}\right) } \, dx$ = $C+3\cdot\arctan\left(\frac{\sqrt[6]{3}}{2}\cdot\sqrt[6]{x}\right)+36\cdot\ln\left(\left|4+\sqrt[3]{3}\cdot\sqrt[3]{x}\right|\right)+\frac{\left(3\cdot3^{\frac{2}{3}}\right)}{2}\cdot x^{\frac{2}{3}}-9\cdot\sqrt[3]{3}\cdot\sqrt[3]{x}$
b1d83dc5-da1a-4559-b8f4-c8a0ac9c7e7d
multivariable_calculus
false
null
The integral has been converted to polar coordinates. Verify that the identity is true and choose the easiest way to evaluate the integral, in rectangular or polar coordinates. $$ \int_{0}^1 \int_{x^2}^x \frac{ 1 }{ \sqrt{x^2+y^2} } \, dy \, dx = \int_{0}^{\frac{ \pi }{ 4 }} \int_{0}^{\tan(\varphi) \cdot \sec(\varphi)} 1 \, dr \, d \varphi $$
$I$ = $\sqrt{2}-1$
b26a668e-b0d8-497f-be3e-9e980702227d
integral_calc
true
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
The region bounded by the parabola $y^2 = 2 \cdot p \cdot x$ and the line AB is revolved about the Y-axis. The line AB passes through the focus of the parabola and is perpendicular to the X-axis. Find the volume of this solid of revolution using integration with respect to $y$. Use $p = 6$.
Volume: $\frac{432}{5}\cdot\pi$
b27a2ed1-91ab-4864-b50e-4aebf48d87b1
differential_calc
false
null
Consider a wire 4 ft long cut into two pieces. One piece forms a circle with radius $r$ and the other forms a square of side $x$. Choose $x$ to maximize the sum of their areas.
$x$ = $0$
b27c8456-96d3-4d5b-891a-f756b95ca624
integral_calc
true
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8/v7p06WJDRenj8QEkPDxcffr0sYzv27dPc+fOtaEiAAAAwD4TJ07UsWPHLOMDBgxQ9uzZbagofTw+gEhS3bp1U9zDePjw4Tp//rwNFQEAAADud+zYMU2cONEy/vTTT6tmzZo2VJR+XhFAJGns2LEKCgoyjV2+fJkF6QAAAPAbnTt3VlxcnGksJCREo0ePtqmi9POaABIREaHGjRtbxj/55BNt3brVhooAAAAA9/n888/1448/WsZbtWqlokWL2lBRxnhNAJFuJL78+fNbxrt27cqCdAAAAPisa9eupXiyeaFChdS+fXv3F3QHvCqAZM+eXQMHDrSMHzx4UPPnz7ehIgAAACDzjRw5UmfOnLGMDx06VHfddZcNFWWcVwUQSapRo4YqV65sGR81apT+/vtvGyoCAAAAMs/hw4c1bdo0y/gLL7ygF1980YaK7ozXBRBJGjx4sGVB+oULFzRy5EibKgIAAAAyR0pTr+666y4NHz7chmrunFcGkNKlS+v999+3jM+dO1cHDhxwf0EAAABAJvjmm2+0adMmy3jHjh1VqFAhGyq6c14ZQKQbC9Jz5sxpGe/Ro4cN1QAAAACulZiYqN69e1vG7733XjVv3tyGilzDawNIzpw51a1bN8v4Tz/9pHXr1tlQEQAAAOA6c+bM0dGjRy3jffv29bqF5868NoBIUv369VW6dGnLeN++fS0HtAAAAADe4u+//9aoUaMs44899pheffVVGypyHa8OIEFBQSkuvvnzzz9T3CkAAAAA8AbDhg3T5cuXTWMBAQEaMWKETRW5jlcHEEmqVKmS/vOf/1jGx48fr7/++suGigAAAICMO3jwoBYuXGgZf/vtt/Xggw/aUJFreX0AkaSBAwcqJCTENHb16lUNHjzYpooAAACAjOnevbuSk5NNY1mzZlXPnj1tqsi1fCKApLYTwPLly7V9+3YbKgIAAADSb926dfrpp58s4x07dtTdd99tQ0Wu5xMBRJLat2+f4v8pKe2UBQAAAHia+Ph49e3b1zJ+7733qmnTpjZUlDl8JoBkzZo1xf/D9uzZo48//tiGigAAAIC0mzFjhv7880/LeErLDbyZzwQQSXrjjTdSXJgzePBgyy4CAAAAgKc4d+6cxo4daxlPbcMlb+ZTAURSiluTnTt3TuPGjbOhGgAAAOD2Bg8erKtXr5rGAgICUjxywtv5XAB57LHHVKdOHcv4rFmzUjxJEgAAALDTnj17tHTpUst43bp1Uzx029v5XACRpF69eilr1qymsdQW9QAAAAB26tatm2Xb3ezZs/vsZko+GUAKFCigdu3aWcbXr1+vTZs22VARAAAAYLVy5coUj43wpW13b+aTAUSSmjdvrnvvvdcy3r17d8XHx9tQEQAAAPCPuLg49e/f3zJerFgxNW7c2P0FuYnPBpC77rpLAwYMsIwfPXpUc+bMsaEiAAAA4B+TJk3SX3/9ZRnv37+/T227ezOfDSCS9PLLL6tSpUqW8TFjxujcuXM2VAQAAABIf/31lyZMmGAZr1Spkl588UUbKnIfnw4gkjR8+HAFBASYxi5fvqxhw4bZVBEAAAD83cCBAxUXF2caCwoK8sltd2/m8wGkdOnSeu+99yzjS5Ys0YEDB2yoCAAAAP5s+/btWrFihWW8fv36Prnt7s18PoBINxaeZ8+e3TSWlJSkXr162VQRAAAA/FVK2+v68ra7N/OLAJIzZ84U/w/dvHmzNmzYYENFAAAA8EfLli3Tnj17LONdu3ZVzpw5bajI/fwigEhS48aNVaxYMcv44MGD3V8MAAAA/M61a9c0ZMgQy3ixYsXUpEkTGyqyh98EEEkpbst74MABRUZG2lANAAAA/MnkyZN15swZy/igQYNsqMY+fhVAqlWrpn/961+W8ZEjR+rq1as2VAQAAAB/EB0drSlTpljGq1Spoueff96GiuzjVwFESjlhRkdHa9KkSTZUAwAAAH8wYsSIFD/wHjhwoA3V2MvvAkhERITefPNNy/iUKVNSPIkSAAAAuBNHjhzR4sWLLePvvvuuX2y7ezO/CyCS1KNHD4WGhprGrl+/7hcHvwAAAMC9+vTpo6SkJNNY1qxZ1b17d5sqspdfBpACBQqoZcuWlvFly5ZxOCEAAABcZvPmzfrmm28s4y1btlTevHltqMh+fhlAJKl169aW/9M5nBAAAACuktrvlnnz5k3xw3B/4bcBJLW2F4cTAgAAwBU++eSTFGfXdOvWTVmzZrWhIs/gtwFEkt5++2098MADlvG+ffta5ukBAAAAaXX9+nUNGzbMMn7//ffrnXfesaEiz+HXASQwMDDF0yiPHDmiRYsW2VARAAAAfMH06dNT3GF14MCBCgz061/B/TuASNK//vUvVa1a1TLO4YQAAADIiIsXL2r8+PGW8X/9619+d+hgSvw+gEg3Die8OYlGR0dr4sSJNlUEAAAAb5XaoYMpzbzxRwQQ3ZiLV7duXcv41KlTOZwQAAAAaXbkyBFFRkZaxuvUqZPi2mN/RAD5f126dLHsRsDhhAAAAEiPAQMGKDEx0TQWGhrKUQ9OCCD/L2/evGrXrp1lnMMJAQAAkBa//PKLvvrqK8v4Bx98oAIFCthQkWcigDhp1qyZ5S8HhxMCAAAgLXr27GkZy5Url9q0aWNDNZ6LAOIkNDRUvXv3toxzOCEAAABu5dNPP9Xu3bst4126dFGOHDlsqMhzEUBuUrt2bZUrV84yzuGEAAAASEl8fLwGDRpkGS9cuLDee+89GyrybASQFAwdOtQyxuGEAAAASMnMmTNT3Dm1f//+CgoKsqEiz0YASUGFChVUvXp1yziHEwIAAMBZaocOVqhQQf/5z39sqMjzEUBSMWDAAEtijY6O1qRJk2yqCAAAAJ5mzJgxunTpkmU8pRk1uIEAkorChQurYcOGlvEpU6ZwOCEAAAB04sQJzZs3zzJeo0aNFNcU4wYCyC107txZ4eHhpjEOJwQAAIAkDRw40HLooCT16dPHhmq8BwHkFsLDw9WhQwfL+LJly7Rv3z4bKgIAAIAn+OWXX/T5559bxps2bap7773Xhoq8BwHkNho1aqTChQubxpKSkpjXBwAA4MdSOnQwR44c6tSpkw3VeBcCyG2EhISkeDjhhg0btG3bNhsqAgAAgJ1WrVqV4qGDHTp04NDBNCCApMGrr76qiIgIyzjz+wAAAPxLfHy8hgwZYhkvXLiwGjdubENF3ocAkkYDBgywjO3atUtffPGFDdUAAADADnPmzNGJEycs4z179lRISIgNFXkfAkgaVa5cWVWqVLGMDx48WElJSTZUBAAAAHeKiYnRuHHjLOPlypVTzZo1bajIOxFA0qFfv36WsaioKC1dutSGagAAAOBOU6ZMUUxMjGWczYnShwCSDhEREapRo4ZlfOTIkbp+/boNFQEAAMAdzpw5owkTJljGq1evrgoVKthQkfcigKRTz549FRQUZBo7ffq0Zs+ebVNFAAAAyGwpTb0KDAxUr169bKjGuxFA0qlIkSKqW7euZXz8+PG6dOmSDRUBAAAgMx0/flyRkZGW8TfeeEMlSpSwoSLvRgDJgE6dOik0NNQ0dunSJU2cONGmigAAAJBZhg0bpsTERNNYSEiIunbtalNF3o0AkgH58uVTs2bNLOMzZ87U2bNnbagIAAAAmWHfvn1auXKlZfz9999XwYIFbajI+xFAMqhVq1aWky6vX7+uUaNG2VQRAAAAXG3QoEGWsbCwMHXo0MGGanwDASSDcuTIkeJfvMWLF+v48eM2VAQAAABX2rp1qzZu3GgZb9GihXLlyuX2enwFAeQONG7cWPfcc49pLDExMcWkDAAAAO+S0hlwuXLlUosWLWyoxncQQO5ASEiIunXrZhn//PPPtWvXLhsqAgAAgCusW7dOv/76q2W8Y8eOCgsLs6Ei30EAuUNvvPGGihcvbhnv06ePDdUAAADgTiUlJaV4unnBggXVoEEDGyryLQSQOxQYGKjevXtbxrdt25binEEAAAB4tqVLl+rw4cOW8e7duyskJMSGinwLAcQFqlevrocfftgyzloQAAAA7xIfH5/irqYlSpRQ7dq1bajI9xBAXCSlsLFv3z599tln7i8GAAAAGTJ79mydOnXKMt6nTx8FBvKrsyvwv6KLVKxYUc8//7xlfPjw4ZaTMwEAAOB5YmJiNGHCBMv4I488ohdffNGGinwTAcSFevbsaUnGx48f14IFC2yqCAAAAGk1depUXbx40TI+YMAA9xfjwwggLhQREaFatWpZxkeNGqXY2FgbKgIAAEBanD17VtOmTbOMV61aVU888YQNFfkuAoiL9erVy7I7wsWLF1P8Cw0AAADPMG7cOF2/ft0y3qtXLxuq8W0EEBe755579N5771nGp0yZkmJLDwAAAPY6fvy4Fi5caBl/7bXXFBERYUNFvo0Akgk6depkOSEzNjZWY8eOtakiAAAApCalTYOCgoLUvXt3myrybQSQTJArVy61aNHCMj5//nydPn3ahooAAACQktSOTahfv76KFCni/oL8AAEkk7Ro0UK5cuUyjcXHx2vIkCH2FAQAAACLwYMHW8ZCQ0PVoUMHG6rxDwSQTBIWFqZOnTpZxlesWKF9+/bZUBEAAACcbd26Vd9++61lvFmzZsqXL58NFfkHAkgmeu+993TPPfeYxpKSkjR06FCbKgIAAIBDv379LGPh4eFq2bKlDdX4hy1bthBAMlNISIh69+5tGd+wYYN++uknGyoCAACAJH355Zf69ddfLePt2rVTeHi4DRX5nuTkZG3evFmjR49W7dq1de+996pOnToKtrswX/f6669r8uTJlmlXAwcO1Nq1a22qCgAAwH8lJSWluPYjX758atSokQ0V+YakpCRt2bJFmzdv1pYtW/Tzzz+neD8CiBv07NlT9evXN43t3LlTX331lV588UWbqgIAAPBPy5Yt0+HDhy3jXbt2VWhoqA0VeafExERT4Ni6dWuaHkcAcYPnn39ejz76qHbu3GkaHzx4MAEEAADAjeLj4zVy5EjLeJEiRfT222/bUJH3SEhIMMLGli1btG3btgw9DwHETfr166datWqZxg4dOqTPPvtMr732mj1FAQAA+Jk5c+bo1KlTlvHevXsrKCjIhoo8V3x8vClw/O9//7vj58yRIwcBxF2efPJJPfPMM/ruu+9M4yNGjNCrr77KX3gAAIBMFhsbq/Hjx1vGIyIi9N///teGijxLXFycKXD88ssvd/ycefLk0WOPPWb6IoC4Ud++ffX888+bxo4dO6YlS5aobt26NlUFAADgHyZNmqSLFy9axvv37+/2WjzBtWvXjLCxZcsWbd++/Y6fM1++fKpQoYIpcNy8roYA4kYRERGqXr26vvjiC9P4yJEj9eabbyokJMSmygAAAHzb2bNnNWPGDMv4E088oX//+982VOR+V69eNQWOHTt23PFz3nPPPapYsaIpcAQG3vqkDwKIm/Xs2dMSQM6ePau5c+eqadOmNlUFAADg2z788EPFxsZaxgcMGGBDNe4RGxtrChw3b4iUEffee6+efPJJI2w88sgj6X4OAoiblSxZUrVq1dKKFStM4xMnTlS9evUUFhZmU2UAAAC+6Y8//tDcuXMt46+88kqGfoH2VFeuXDEFjpQOWkyvIkWKqFKlSkbgePDBB+/4OQkgNujatatWrVqlxMREY+zcuXOaMWOG2rdvb19hAAAAPmjcuHGWscDAQHXv3t2Galzn8uXLpsCxa9euO37O+++/X0899ZSxjqN06dIuqNSMAGKDokWL6s0339TixYtN49OmTVOjRo0UHh5uU2UAAAC+5dixY1q6dKll/K233lKJEiVsqCjjLl26ZAocu3fvvuPnLFmypJ566ik9/vjjeuyxx1S8eHEXVHprBBCbdO7cWZ988oni4+ONsZiYGE2cOFG9evWysTIAAADfMWbMGNOsE0kKCQlRp06dbKoo7WJiYkyB47fffrvj5yxTpowqVaqkJ554Qo899pgKFy7sgkrThwBik4IFC6pevXqW+YizZs1S06ZNlS9fPpsqAwAA8A3Hjh3Tp59+ahmvV6+eChUqZENFtxYdHa2tW7fq559/1pYtW7Rnz547fs4HH3xQlSpVMtZx3HPPPS6o9M4QQGzUvn17LVq0SNevXzfGrl+/rg8//FBDhgyxsTIAAADvN2zYMCUlJZnGQkND1a5dO5sqMjty5Ii2bt1qfEVFRd3xcz788MOqVKmSnnrqKT322GPKmzevCyp1LQKIjfLly6fGjRtrypQppvHIyEi1bt1aBQsWtKkyAAAA73bo0CGtWrXKMt6gQQPlz5/fhoqkXbt2GWHj559/VnR09B0/Z/ny5fXUU0+pUqVKevzxx5UzZ04XVJq5CCA2a9u2rebNm2falzo+Pl4jR45McccGAAAA3N7w4cMtY+7sfsTHx5u6Gz///LNp1ktGPf7440bgeOKJJ7zyCAcCiM3Cw8PVokULjRkzxjS+bNkytWrVSiVLlrSpMgAAAO+0d+9erV271jL+wQcfKHfu3JlyzfPnz5vChisO/ZOkJ5980ggcTz75pO666y6XPK+dCCAeoEWLFpo5c6ZiYmKMsaSkJI0cOVIzZsywsTIAAADvM2LECMtYWFiYWrdu7bJrHDt2zBQ4Dh8+fMfPeddddxlB48knn1SlSpUUEBDggmo9CwHEA4SFhalt27YaPHiwaXzNmjXat2+fIiIibKoMAADAu+zdu1dff/21Zbx58+Z3dNbab7/9ZoSNrVu36syZM3dSpiQpV65cRth48skn9eijj97xc3oDAoiHaNy4saZPn66zZ8+axocMGaLIyEibqgIAAPAuN3+gK92Y8t60adM0P0diYqKpu7F161ZdvXr1jmsrWLCgKXA88MADd/yc3ogA4iEci6J69+5tGv/mm2+0c+dOv0nEAAAAGbVjxw5t3LjRMt6iRYtbdj8uXrxoChvbt293ST3Fixc3Tamy49A/T0QA8SD169fX5MmTderUKdP4gAEDtGLFCpuqAgAA8A5Dhw61jOXOnVsffPCBaezEiROmwPH777+75PoPPfSQqcPhiWdweAICiAcJCQlR586d1alTJ9P4zz//rG+//VbPPfecTZUBAAB4tp9++kk//vijZbxVq1Y6evSoETa2bt2q06dPu+SaFStWNAWObNmyueR5fR0BxMO8+eabmjBhgo4dO2YaHzx4MAEEAAAgFYMGDTJux8fHKy4uTgEBARo3bpyGDBlyx88fGhpq7EzlCBy+uEOVOxBAPExQUJC6du2qVq1amcb37dunzz//XK+88opNlQEAAHiemJgYzZw5U99//73i4+MVHx9v/FmOHDlMhz2nR+7cuU3djUceecRVJfs9AogHqlWrlsaNG6dDhw6ZxkeMGKH//Oc/CgwMtKkyAAAAe/3xxx+mE8YPHDigc+fOKSEhwXS/wMBAZc2aNc3PW6hQIVPgKF26tKtLx/8jgHionj17qlGjRqaxQ4cO6ZNPPtGbb75pU1UAAADutW/fPlPgOHnypOnPr1+/bgkfkpQtW7ZbTpEqUaKEaUrVfffd5/LakTICiIeqXr26IiIitG/fPtP4iBEjVKtWLYWEhNhUGQAAQOZITEzUtm3btHXrVm3btk3btm3TpUuXUr1/cnJyin8eGBiosLAw01i5cuVMHY67777b5fUjbQggHqxPnz569913TWOnTp1SZGSkGjZsaFNVAAAArhEdHW0EjW3btt32/I3k5GQlJycrKSlJycnJpu6Hc7cje/bseuKJJ0yB4+ZAAvsQQDzYs88+q0cffVQ7d+40jX/44Yd69913FRoaak9hAAAAGXDo0CFTd+PIkSOp3tcRNpy/buZ8Ovldd92lkJAQFSlSRDt37lRQUFCmvAbcOQKIh+vXr59q1aplGjt79qxmz56tli1b2lQVAADA7Tl3N7Zu3aqLFy+met+0BA6H8PBw5c2bV3v27FFwcLBCQ0ONTXr69+9P+PBwBBAP9+STT+rZZ5/Vxo0bTeMTJkzQ+++/TzsRAAB4hIsXL1rWb9yK81SqW4UNScqXL58eeugh4+u+++5T48aNlSVLFgUEBBjho2TJkpYPbuF5CCBeoE+fPpYAEhMTo8mTJ6tLly72FAUAAPzakSNHTB2O33//PdX7pqe7IUmlSpVS2bJlVbZsWUVERChfvnymP9+wYYNOnTolSabjCTp37sxxBV6AAOIFIiIiVL16dX3xxRem8enTp6tJkybKnTu3TZUBAAB/sWPHDlOHIzo6OtX7OgeNpKSkWz5vjhw5FBERYYSNsmXLKjg49V9Rk5KSFBkZKUmW7keNGjUy8MrgbgQQL9GzZ09LAImNjdX48ePVv39/e4oCAAA+6fLly6apVNu2bUvxrA0H56lUt+tuFC5c2NTdKFy4cLpqW79+fYrdj169eqXreWAfAoiXKFmypF577TV99tlnpvG5c+eqVatWltYkAABAWp04ccK0WHz//v2p3jc906mCg4NNYaNs2bLKnj17hutMSkrSwoULJZm7H2XLltVLL72U4eeFexFAvEi3bt20evVqJSYmGmPx8fEaNWqURo4caWNlAADAm+zevdvU4Th9+nSq97357I1byZcvnylwlCpVyqV1r1u3TmfPnpVk7n707NnTpddB5iKAeJGiRYvqzTff1OLFi03jixcvVqtWrVS0aFGbKgMAAJ7q6tWrlu1wr1+/nuJ907tYvHTp0qbuRt68eTPjJUiSEhIS9NFHH0kydz/Kly+vqlWrZtp14XoEEC/TuXNnSwBJTEzUqFGjNGnSJJuqAgAAnuLUqVOmxeK//fZbqvdN72Lxm6dTufO8jbVr1+r8+fOSzN2PHj16uK0GuAYBxMsULFhQDRs21Ny5c03jn332mdq3b6+SJUvaVBkAALDD3r17TR2OP/74I9X7pnex+IMPPmiEjfvuu8/VpadZXFyclixZIsnc/ahUqZIqV65sW13IGAKIF+rYsaMWL16sa9euGWNJSUkaPXq0pk2bZmNlAAAgM8XHx1sO+7ty5UqK903PdKqQkBBFRESYAke2bNky62Wk25o1a+h++BACiBe6++671bhxY02ePNk0vmrVKnXu3JkuCAAAPuLPP//U9u3b9csvv2jbtm3auXNnqvdN72Jx57Dhyb87pNb9qFKliipWrGhnacggAoiXatOmjebOnavY2FjT+LBhwzR79mybqgIAABmVkJBghA3Hf//6668U75uRxeLOgePuu+/OjJeQKVasWKGYmBhJ5u5Ht27d7CoJd4gA4qXCw8PVrFkzjRs3zjS+bt067d27V2XLlrWpMgAAkBZHjx41BY5du3alet+MLhZ3fDn/4u5Nrl27pqVLl0oydz+qVaum8uXL21ka7gABxIs1a9ZMs2fPNj4VcBgxYoTmz59vU1UAAOBmV69eNXU2tm/fbqxpuFl6uxtFihQxhY177703M16CLZYvX26scaH74TsIIF7M0QUZNWqUafzrr7+mCwIAgI1+//13U+BI68nit+tuhISEWLobYWFhri7fI1y5ckXLli2TZO5+vPzyy/yO4+UIIF6uWbNmmj59uqULMmTIEOOwHgAAkHn+/vtvU2dj+/btunTpUqr3T89WuIUKFVKZMmUUERGhiIgIlShRwtXle6xPPvnE2PHTufvRvXt3u0qCixBAvFxYWJhat26toUOHmsa//fZb7dixg/mRAAC42J49e0yB4/Dhw6neNz3TqbJmzaoyZcqYvsLDwzPjJXi8mJgYrVixQpK5+1GzZk2P3rELaUMA8QEffPCBpk6dqgsXLpjGhw8fro8//timqgAA8H7R0dGmzsYvv/yi69evp3r/9HQ3ihQpooiICKPDUbRoUVeX77WWLVtmdD8cp60HBgbS/fARBBAfEBoaqrZt22rAgAGm8e+//54uCAAA6bBz505T4Dh+/Hiq901PdyNHjhymzkZERISyZs2aGS/B68XExGjlypWSbnQ/AgICJEm1a9cmpPkIAoiPeP/99zV16lSdOXPGND5o0CB9+umnNlUF+J/9+/dr//79eu2111zyfPHx8Zo6dareffdd5c2b1yXPCeCGkydPmjob27dvv+UicOdD/m7X3ShRooQRNMqUKeNTO1NltsWLFysuLk7SP92PoKAgdr7yIQQQH+HogvTu3ds0/tNPP+mHH35Q5cqVbaoM8B9btmxR7dq11axZM5cFkICAAH399deaP3++PvvsMxUuXNglzwv4m8TERMtUqtOnT6d6//R0N3Lnzm3qbJQpU0YhISGZ8TJ83vnz57V69WpJN6ZcObofb7/9tgoVKmRnaXAhAogPqV+/viZMmGDpggwbNkyff/65TVUB3uevv/7S2rVr9fXXX2vjxo169tlnVaNGDb399tupPubHH3/UG2+8oYoVK6pnz54uqyU4OFizZs1StWrV9Nprr2nFihUqUqSIy54f8FXHjh0zdTZ+/fXXW97feRvc23U3HnjgASNolClTRgUKFHBl6X5t8eLFSkhIkPTPzlchISHq0KGDnWXBxQggPiQkJEQdO3a0LNDasWOHvvvuOz3zzDM2VQZ4j19++UXvvPOOsmTJonr16qlOnTpq3bq1Nm7cqIIFC6b47+iHH37Qm2++qbx582rGjBku/+SzQIECmj17tmrWrKlatWrp008/ZR404OTq1auWqVTnzp1L9f7p6W7ky5fP1NkoU6aM8ak8XOvs2bNat26dJHP3o169enQ/fAwBxMfUrVtXEyZM0MmTJ03jI0eOJIAAt7FmzRo1bdpUefPm1apVq1SsWDGtWbPG+PONGzda/h0dPHhQb775piRpxowZmfZJaMWKFdW3b18NHDhQr7/+ujZt2qRs2bJlyrUAT3fo0CHTIX/79u275f3T2t0ICgoyBY2IiAjlyZPH1eUjFR999JGl+xEaGqp27drZWRYyAQHExwQFBalz587q2LGjaXzHjh3asGGDnn/+eZsqAzzbt99+q6ZNm0qSPvzwQxUrVkyS9Mgjj6h06dIKCgoygoZDUlKSunTpIkmqUqWKKlWqlKk1NmjQQGPHjtWpU6c0ZswY9e3bN1OvB3iCCxcuaMeOHdqxY4cROG51yF96uhsFCxY0BY5SpUplxktAGpw9e1ZfffWVJHP3o0GDBsqfP7+dpSETEEB80BtvvKHx48fr2LFjpvFhw4YRQIAUxMTEGJ+wVa1aVVWrVjX+rHDhwtq4cWOKj/v444+1bds2SVKrVq0yvc6sWbOqbdu2Gjp0qKZNm6ZatWqpXLlymX5dwF0SExONsLFz507t2LHD8l52s7TuTJUlSxbLQnF/PeTPEy1YsMDYgYzuh+8jgPigoKAgderUSW3btjWN7927V19++aVeeuklmyoDPNPMmTMVHR0t6caW1mkRHR2tfv36SZLKlSvntp3m6tevr6FDh0qSOnfurHXr1hlv1oC3OXjwoBE0duzYod27d9/y/unpbhQpUsQUOBxdTXieU6dOacOGDZLM3Y8mTZood+7cdpaGTEIA8VGvv/66xowZY/nkaMiQIQQQwMlff/2lMWPGSJKyZ8+e5rVSa9as0eXLlyXd6Dq6a1Fqzpw5VatWLa1YsUK7d+/Wzp079dhjj7nl2sCd+Ouvv4yg4ehwXLlyJdX7pydsZM+e3bJQPCwsLDNeBjLB/PnzLd2PsLAwtWnTxs6ykIkIID4qMDBQ3bt3V4sWLUzjhw4d0ueff65XXnnFpsoAz/Lhhx8at19//fU072C1du1a4/bjjz/u6rJu6cknn9SKFSskSRs2bCCAwONcvXrVEjZOnTp1y8c4T6O63Ta4xYsXNwWO++67z5Xlw41OnDihTZs2STJ3P5o3b84UOR9GAPFhNWvW1JgxY3To0CHT+IgRIwgggKRly5Zp/vz5xvcvvvhimh538eJF/fDDD8b3Dz74YLquGxcXp7vuuivDf+4ceFauXGkshAfs8ttvv5nWbRw4cOCW909PdyNv3rx64IEHjK8yZcrc8t8HvEtKaz/Cw8ONTUHgmwggPq5bt2764IMPTGOHDh3SypUrVbNmTZuqAuzz22+/acaMGTp06JB27txp+rMVK1Zo3bp1evfdd1W+fPlUn+O7774zblepUuWWXZOrV69qw4YNOnDggPbu3Wt8Erx69WpVqFDBdN+VK1eqT58+io6OVs2aNTV16tQUn7N06dLG7aioKB05ckT333//rV424DLHjx83rdvYsWOHsXVqStITNrJmzWoEjdKlS6tMmTJsg+vDoqKi9P3330sydz9atGhB98PHEUB83CuvvKKyZctq7969pvHhw4fr1VdfZfEq/M6vv/6a6q5WjmDx7rvv3vI5Dh8+bNx+6KGHbnnfa9euKTIyUtu3bzfWjEhS69attWHDBmOeer9+/TRz5kzjz1euXKmuXbumGCyCg4NVsWJFYwcuAggyy8WLF01hY+fOnS474E+SSpUqZYSNBx54QEWKFHH1S4AHW7BggXHb8ftI7ty5LR+cwvcQQPxAt27d1KBBA9PYsWPHtGLFCtWuXdumqgB71K1bV3Xr1pV0I2g4wsiQIUPUsGHDND2HY8cs6cai8FvJnTu3lixZoqSkJG3evNk4S+TYsWNat26dateurXHjxmnmzJkqXry4pBufCj755JO3nNeeK1cu4/bZs2fTVDdwK8nJyZZ1G0eOHLntY5wP+buVggULmqZSPfDAA3wI5seioqL0008/STJ3P1q1asUGAn6AAOIHqlWrlmIXZPTo0apVqxZvAPBL169fN3VCKlasmObHOv/Cf7sA4hAYGKjKlSurbdu2mjBhgqQbC9nvu+8+jRo1Sg0aNNCQIUMUGBh42zUgkkzTUm71iTSQmkOHDpnWbfz666+3vH96uhs5cuRQmTJlTNOpmFIDZ3PmzDFuO3c/GjdubFdJcCMCiJ/o1auX8amvw7Fjx7Rs2TK99dZbNlUF2Md5/Uf27NkVERGR5seeOXPGuO3ciUiLt99+2wgg69at07Zt21SlShUNGjTIeBNOywJb5+ueP38+XTXA/5w5c8aybsN5SuDN0hM2AgMDjcXhjqlUBQsWzIyXAR9x4MAB/e9//5Nk7n506NBBoaGhdpYGNyGA+InnnntO5cuX144dO0zjo0aNUp06dRQUFGRTZYA9tmzZYtz+97//na5/A84BJHv27Om6brFixVSwYEFjS9Lo6GiNGjVKwcHp+3Hs/Gny1atX0/VY+LZr165Z1m38+eeft3yM8zSq263bKFKkiGkaVcmSJV1ZPvzA3LlzjduOD17y589vmS4O30UA8SM9evQw5p87nDx5UkuWLLF0RwBf57yTVXpPMXeenxwfH5/ua1etWlUfffSRJKlRo0YqXLhwup/D+bq3m3sP37Z3715T2Ni3b98t75+e7sbdd99t7EblCBxZsmRx9UuAH3EcoCpZux9pPYcJ3o8A4kcqV66sSpUqGYu+HMaNG6c333yTf/jwG7Gxsfr555+N7ytVqpSuxxcoUMD4Je/ixYvpvv5TTz1lBJDjx4+n+/GSdOHCBeN2vnz5MvQc8D5//PGHad3Gjh07FBcXl+r90xM2QkNDTWdtlC5dWnnz5s2MlwE/NmvWLOO2o/tRqFAh1atXz66SYAMCiJ/p06eP5RDCkydPatGiRbQ+4Td++eUX43b27NlN52qkRYECBYzbf//9d7qvHxUVZdxev369EhIS0j0FyzmA3H333emuAZ4vOjpav/76q3799Vft2rVLO3bsMO3AlpL0nCZeokQJ01SqokWLurJ8wGL79u3GIZXO3Y/OnTszFdzPEED8TPny5fXvf//bOPjHYdy4cXr33XfpgsAvOHcBn3vuuXS/8Tl/KhwTE5Oux/75558aO3asaWz//v23PU/kZs6dFwKI97t48aIRNByh4+TJk7d8THq2wL3nnntMh/s98MAD/MIHt5s/f75x2/H3r2jRonrjjTfsKgk2IYD4oe7du1sCyJkzZ7Rw4UI1atTIpqoA9/n222+N21WrVk334/Pnz2/cvt3i3pv17t1bRYsWVenSpfX1119Lkv73v/+lO4AcO3YsxXrg+a5cuWKEDMfX7abipXcLXMduVI7pVGyBC7tt3brV6H44h1+6H/6JAOKHypcvr6pVq+qbb74xjU+YMEF169ZlCzz4tJiYGNMWvP/+97/T/RxPPfWUcXvTpk1pftzKlSv15ZdfavHixYqKijICyE8//aT3339fknTq1Cnt2bNHL7zwQqrPEx0dbQogDz/8cDpfAdzl+vXrpmlUv/76qw4fPnzLx6QnbAQEBFgO9ytUqJCrXwZwx+bNmyfpxt9Zx9qPkiVLqlatWjZWBbsQQPxUz549LQHkzJkzmjdvnpo1a2ZTVUDm27p1q3G7dOnSGfpl7cEHH1TevHkVHR2tU6dO6fTp07rnnntu+ZiTJ0+qS5cuevvtt/XMM8+YDhL85ptvlJSUpPj4eDVu3FhFihS5ZQBx3k771VdfZVciD5GYmGiZRuX4xDc16QkbklS4cGHT4X7pXb8E2GHz5s3G2jfnw487d+7MYch+igDip8qWLauXXnpJX375pWl8woQJev/99+mCwGc5r/+oXr16hp4jICBAr7/+umbMmCHpxqL2mzd3WLlypaZPn66XX35Z//3vf/X+++8rR44c6tevnyQpIiJC2bNn1+XLl3X58mWtWrVKGzduVGxsrEaPHn3L6zuHqP/85z8Zeg24c7t37zZNo9qzZ88t75/esHHPPfeoVKlSRtAoWbKkaQtowFs4zv24uftRo0YNO8uCjQggfqxXr16WAHLhwgXNnj1bLVu2tKkqIHOtX7/euP3f//43w89TvXp1I4B8//33lgDSp08fRUdHa+fOnRo6dKgk6auvvlLOnDklScHBwapatapWrVolSWrZsqWyZ8+ur7/++raHGzqmbknSs88+m+HXgLTbt2+fpbtxqwCR3rCRL18+lSpVyggcpUqVUo4cOVz9MgC327Rpk06cOCHJ3P3o2bOnXSXBAxBA/FjJkiX13//+V2vWrDGNT548We+//z6ftMHnnDlzRgcPHpQklStXLt0Lv51VqlTJ6CIuWLBAnTp1Mp3H8dRTT2n16tWSbuyaNXv2bMv1mjRpYgSQvHnzavr06bfdCvWHH34wXkOPHj2UK1euDL8GpOz33383BY1ff/31lgdOpjds5M6d2xQ0Spcuzf+P8ElJSUlauHChJHP3o2zZshnuQMM3EED8XNeuXbV27VrTFo4XLlzQzJkz1a5dOxsrA1zPefqVKw69GjJkiNFFdIQQh8mTJ+vtt99WQkKCnnrqqRS7Go8//rg2bNigw4cP64UXXkjTWo4pU6ZIurF+pXnz5nf8Gvzd0aNHTUFj165dio2NTfX+6Q0bjh2pHGGjVKlSHO4Hv7Fx40a6H0gRAcTPOeZgfvbZZ6bxqVOn6oMPPqALAp/i2H43e/bseu211+74+QoVKqQhQ4aoV69emj59upo1a2YEjeDgYD333HO3fY6IiAhFRESk6Xq//fabNm7cKEkaPXo05/ak0x9//GGZRnW7c1zSc7BfWFiYKWiULl3adGgl4E9S6344duKEfyOAQN26ddOqVatMXZCYmBhNnTrV9Iku4M2uXr2qzz//XJI0aNAgl82vr1+/vn766SetXr1affr00bhx41zyvDe7evWq8e+xZ8+eevzxxzPlOr7i9OnTlmlU58+fv+Vj0nOwX2hoqCloZHRHNcBXrV+/XqdOnZJk7n706NHDrpLgQQggUNGiRVWnTh0tXbrUNO7ognCAFXzB2rVrdfnyZZUrV0516tRx2fMGBwdr0qRJkqSPP/5YjzzyiHGmhyv16NFDu3fvVo8ePdS6dWuXP783O3funGUa1V9//XXLx6RnKlVQUJBpvUapUqVUpEgRV78MwGek1v2oVKmSKleubGdp8BAEEEi6sRZk+fLlSkxMNMZiY2M1bdo0de3a1cbKgPQ5fvy4evfurb///luTJ0/Wfffdp0uXLhk7UY0cOdLlp+6GhIRo0qRJCggIUM+ePfXggw+qYsWKLnv+uXPnaunSperVq5datWrlsuf1Rn///bdlGtXtTqNP77qNm3ejKl68uCtfAuDzvvjiC509e1aSufvRp08fu0qChyGAQNKNuexvvfWWFi1aZBqfMWOGmjdvThcEXmPhwoXGVru//vqrcuTIoXfeeUenTp3S0qVL9cgjj2TKdR0hJFeuXBo1apSlo5hRV69e1bBhwzRkyBA1bNjQJc/pLS5fvmw5a8P5BPiUpDds3H///ZZF4gAyLiEhQZGRkZLM3Y8qVaqofPnydpYGD0IAgaFjx45atmyZabvJ2NhYTZw4Ub169bKxMiDtnDsPa9euVYcOHZQjRw4tXbo001v/wcHBGj58+C23bE2vrFmzas+ePT6/4PzixYvavXu36evIkSO3fEx6w0aRIkUsi8Rd3Q0D/N3atWuN9VbO3Y9u3brZVRI8EAEEhkKFCundd9/V/PnzTeOzZs1Sy5YtlTt3bpsqA9LuxRdf1BdffKHPP/9cycnJGjNmjF566SXdddddbqvB1WHB18LHuXPnjJCxa9cu7d6929iqMzXpDRv33nuvZZG4O/8OAP4oLi5OS5YskWTufrzwwgt0P2BCAIFJhw4dtGjRItMnuNevX9fEiRPVt29fGysD0u7hhx/Www8/bHcZ0I3DHx0hw/F18uTJWz4mvWGjQIEClkXibCEOuN+aNWtS7H50797drpLgoQggMMmfP7/ee+89zZ492zQ+d+5cNW/eXPnz57epMgCe7uTJk6agsWvXLp05c+aWj0lv2MibN68paJQqVYo1aoAHSK378fLLL6ts2bJ2lgYPRACBRceOHRUZGanr168bY44uyKBBg2ysDICnSExMVEJCgr755htt375du3fv1rlz5275mPSGjbvvvlslS5ZUyZIljcDBVFDAM3322WfGwZ50P3A7Acm3eweAXxo0aJCmTp1qGgsJCdG2bdvoggB+5siRI6bOxsaNGxUdHS1JypYtm3H6u0N6g4Z0o/tasmRJlSpVyggduXLlyoyXA8DFrl27prp16+rKlSsKCAhQcPCNz7dr1qxp+V0CkAggSMWFCxdUsWJFxcbGmsbff/994zwFAL7n0KFDlgXily9fNt3n8uXLunLliqQbASQsLCxdYaNQoUJGyHB8uepkegDut2jRIi1YsEDSjYM7AwMDFRgYqB9//FFFixa1uTp4IqZgIUW5c+dW48aNNXHiRNP4Rx99pNatW6tQoUI2VQbAVQ4cOGBZIH716tVU739zyEhOTlZiYqLpANObFS5c2BI2WCAO+I4rV65o+fLlksxrP2rXrk34QKrogCBVMTExeuyxxyxdkHr16mnkyJE2VQUgI/bs2WPpbNzqvJJbTaOKjY01gkrWrFmNQHH//fdbwgZb3wK+bcGCBcYhxo7uR1BQkH7++Wc+rESqCCC4pdGjR2vs2LGmMX6wAJ4rOTnZFDIcX0lJSbd8THrWbMTGxio+Pl5BQUGqUqWKGjRooJIlS5oWngLwfVeuXFHdunV17do109qPd999V6NHj7a5OngyAghuKTY2Vo899pixs4XDW2+9pXHjxtlUFQBJSkhIsASN33777ZaPSW/YCA4OtnQ1tmzZosjISEk3OqL16tVz2WsC4D3mzJmjpUuXSrrxsyIgIEAhISHasmULH1LillgDglsKCwtTixYtNGLECNP4J598ovbt2zO/E3CTa9euWaZQ7d+//5aPSW/YCA0NtYSNYsWKWe63ZcuWO3kpAHxATEyMPvvsM0k3tt0NCAiQJNWtW5fwgdsigOC2PvjgA82YMUMXLlwwxhITEzVmzBhNmDDBxsoA33TlyhVLZ+P333+/5WPSGzbCwsIsYaNw4cKufBkAfNiSJUsUFxcn6Z9zP0JCQtS+fXsbq4K3IIDgtsLCwtSqVSsNHjzYNP7pp5+qU6dOdEGAO/Dnn39qz5492rt3r/bs2aM9e/bo2LFjt3xMesNGjhw5jJDhOGejYMGCrnwZAPzI+fPntWbNGknm7kfDhg05KwxpQgBBmjRu3FiTJ082dUGSkpI0fPhwDhkC0iA5OdkIGI6wsXfvXv3999+3fMzN297eLmzkzp3b0tngFwIArpRS9yM0NFTt2rWzsyx4EQII0sTxg6V///6m8ZUrV6pTp04qWbKkPYUBHuj8+fOWoLFv375bPiYjp4fny5fPEjby5MnjqpcBABbnz5/X2rVrJZm7H02aNFHu3LntLA1ehACCNGvYsKGmTJmiM2fOmMZHjhypGTNm2FQVYK/Dhw+bpk/t3btXp0+fvuVjMhI27rnnHkvYyJkzp6teBgCkSWRkpBISEiT90/0ICwtTmzZt7CwLXoYAgjQLCQlRu3bt1KtXL9P4mjVrdOjQIbog8GlXr161dDX27Nmj69ev3/JxGQkb9913n0qUKGFas5EtWzZXvRQAyJCzZ8/qiy++kGTufjRr1kzh4eF2lgYvQwBButSrV0/jx4+3dEGGDh2qOXPm2FQV4FonT560BI0jR47c8jEZCRpBQUEqUaKESpQooeLFixu3OT0cgCdauHChcaipo/sRHh6uZs2a2VkWvBABBOkSEhKizp07q2vXrqbxL774Qnv37lXZsmVtqgzImJuDxp49e3Tx4sVbPiYjYSNHjhyWsMEOcgC8xalTp7R+/XpJ5u5H8+bN6X4g3QggSLd33nlHH374oU6ePGkaHzRokBYvXmxTVcCtXbx4McVdqG4nI2GjQIECRthwBI58+fK54mUAgC1S6n7kzp1bTZs2tbMseCkCCNItKChIXbt2tRw29N133+l///ufHn/8cXsKA/7fkSNHLEHj5sCckoyEjfvvv9/S2WC9BgBfcuLECX3zzTeSzN2P1q1bKywszM7S4KUIIMiQOnXqaNy4cZYD04YOHapPP/3Upqrgb65fv26ZPrV3715dvXr1lo/LSNDImjWraZ2GI3A43ogBwFctXLjQuO3c/WjUqJFdJcHLEUCQIYGBgerWrZtatmxpGv/pp5/0ww8/qHLlyjZVBl91+vRpS1fj8OHDt31cRsJGnjx5LEGjUKFCrngZAOBVTpw4oU2bNkkydz86dOig0NBQO0uDFyOAIMNee+01jR07VocOHTKNDxs2TJ9//rlNVcEX7Nu3z7I4/Pz587d9XEbCRuHChS2dDc7XAIAb5s6da9x2dD/y58+vBg0a2FUSfAABBHeke/fuatKkiWlsx44d+uabb1S1alWbqoK3uHjxovbt22eZRnW74OAcLtIaNoKDgy3b3RYvXpwtbwEgFVFRUdq8ebMka/cjJCTEztLg5QgguCMvv/yyypYta9lNaOjQoQQQmPz+++/au3ev0d3Yu3evTp06ddvHZaSrER4ebgkbRYoUccXLAAC/MW/ePOO2o/tRqFAh1atXz6aK4CsIILhj3bp1s7Ri9+7dqy+++ELVq1e3qSrY5cKFC0bIcA4bCQkJt31sRsLGPffcYwkbefPmdcVLAQC/deDAAW3dulWSufvRqVMnBQUF2VkafAABBHesWrVqKl++vHbs2GEaHzp0KAHExx08eNAUMvbt25dpXQ1JRshwDhtsAQkArjd//nzjtqP7UbRoUb355pt2lQQfQgCBS3Tr1k1vv/22aezQoUNatWqVatSoYVNVcJULFy6YQobjdmJi4m0fm9Etb28+W6NEiRKueCkAgNs4cOCAtm/fLsnc/ejcuTPdD7gEAQQuUaVKlRS7IMOGDdN///tf49MTeL4DBw5YuhqnT5++7eMy2tXIly+f5TC/ggUL3unLAABk0KxZs4zbzt2PWrVq2VUSfAwBBC7Tp08fvf7666axY8eO6dNPP1WdOnVsqgqpOX/+vKWjsW/fvkzragQFBal48eK6//77jf/ef//9ypEjhyteDgDABXbu3Kndu3dLMnc/evTowYeJcBkCCFymUqVK+ve//63vv//eND5mzBjVqlWLtq2NDhw4YJlC9ddff932cRntauTNm9cIGI6wwS5UAOD5Ujr3o2TJkkynhksRQOBS3bp1swSQY8eOaenSpXrnnXdsqsp/nDt3LsWuRlJS0m0fm5GwERgYaOpqFC9eXMWKFVN4eLgrXg4AwI22bdumAwcOSDJ3P3r16mVnWfBBBBC41GOPPaYXXnhB69evN42PGTNGderU4eAiF9q/f7+lq3HmzJnbPi6jXY27777bCBiOsEFXAwB8h3P3wzFroWzZsnrppZfsKgk+igACl+vevbslgJw8eVKRkZFq2LChTVV5r+joaEtHY+/evWkKDhntajhPnXL8l64GAPiuzZs3KyoqSpJMU6bpfiAzEEDgcmXLltV//vMfrVu3zjQ+fvx4vfvuuwoNDbWpMs+X0gF+Z8+eve3jMtrVyJMnj2lBePHixVW0aNE7fRkAAC/j6H4EBAQYaz/Kly+v5557zs6y4KMIIMgUPXr0sASQM2fOaP78+WratKlNVXmOs2fPptjVSIuMhI2AgABL0ChevDhdDQCAvvvuO504cUKSTDtd9enTx66S4OMIIMgUJUuWVM2aNbVy5UrT+Pjx49WgQQO/6YIkJCRo37592r9/v7FmY9++fZna1cidO7cRMByBo1ixYnf4SgAAvigpKUnz5s2TZO5+VK5cWZUqVbKxMvgyAggyTffu3bV69WrTDkwXLlzQzJkz1bp1axsryxxHjhzR/v37TYHj8OHDt32cI1hkpKtx85kaxYsXV86cOe/4tQAA/MOGDRt06tQpSebuR48ePewqCX6AAIJMU7RoUdWpU0dLly41jU+aNEmNGjVSWFiYTZXdmTNnzhgBwzlwxMXF3faxd9LVuHlhOF0NAMCdSEpK0oIFCySZux9Vq1ZV+fLl7SwNPo4AgkzVtWtXLV++3HS6dkxMjKZOnapOnTrZWNntXblyxRQ0HF/nz5+/7WNTChlpDRs3n6lRvHhx5cqV605eCgAAFl988YUxJdi5+9GzZ0+7SoKfIIAgUxUqVEjvvPOOIiMjTeNTp07VBx984DGLoFMKGo4FebeS0elT0o2uhvOZGo5pVAAAZLaEhATjvdm5+1G9enWVLVvWztLgBwggyHTt27fXxx9/rPj4eGMsNjZWU6ZMUffu3d1ayx9//GFao+H4SouMTp8KCQlRsWLFVLRoURUrVswIGrlz576TlwIAQIatXbvW6OjT/YC7EUCQ6QoVKqR69eqZTliVpFmzZqlZs2aZ8ov4hQsXLGs09u/frytXrtz2sRmdPhUQEKCiRYsaX47QUahQoTt+PQAAuEpcXJyWLFkiydz9qFmzpkqWLGlnafATBBC4Rbt27bRo0SJdv37dGIuNjdXEiRPVt2/fDD9vXFxcigvCz5w5c9vH3sn0qXvvvdcIGI6wUaRIkQy/DgAA3GXVqlWW7kdgYKDbZyXAfxFA4Bb58+dXw4YNNW3aNNP43Llz1bx5c+XPn/+2z3H48GHL1KmoqKg0XT+j06cKFChgChmO0BEUFJSmxwMA4EmuXbtm7E7p3P2oU6eOihYtamdp8CMEELhNmzZttGDBAsXGxhpj169f1/jx4zVkyBBj7PTp0ykuCndeQ5KajE6fypMnjyVkFC1aVFmyZMnAKwUAwDOtWLFCMTExkv7pfgQFBalr1652lgU/QwCB2+TOnVtNmjTRhAkTJN0IBgkJCZo+fbouX76sP/74Q/v379fFixdv+1wZnT4VHh5uWp/huJ09e/Y7em0AAHi6K1eu6JNPPpFk7n688847rFeEWxFAkOmSk5ONLsbVq1d1+fJlXbt2zXRC+pw5c1Ldkjcj06eyZs1q2nnKETbYeQoA4K+WL19ubMbiCB8hISHq3LmznWXBDxFA4FLHjx+3LAo/ePCg6T4BAQGm8CFJV69eVVhYmAIDA9M1fcp5i1vnr7SsKQEAwF9cuXJFn376qSRz96N+/fq8Z8LtCCDIkKNHj+rgwYP6/fffdfDgQeP21atXb/vYbNmyKTY21hQukpOTdenSpVSnQrHFLQAAGbdkyRJdu3ZN0j/dj9DQULVt29bOsuCnCCC4pUOHDpmChuO/aVkQnpqAgABly5ZNly9flvRPl+P69evKmjWrihQpwha3AAC4SExMjFauXCnJ3P1o3Lgx3Q/YggACJSUlmboYzv9N63a16RUWFqa4uDhJN3bfCAwMVFBQkJ599llOYQUAwIUWLVpkvOc6wkdYWJhatWplZ1nwYwQQPxIXF5fitKnDhw9n6nULFCigBx54QGXKlNEDDzxgfEVGRqp///6SpISEBCUnJ2vTpk2qX7++ChcunKk1AQDgD86fP681a9ZIMnc/mjZtysYssA0BxAfFxsamGDSOHTuWqdfNkyePKWA4QkfOnDlTvH+DBg00ZcoUnTlzRoGBgUpMTJR043DCOzkdHQAA3PDRRx8pISFB0j/dj/DwcDVv3tzOsuDnCCBeLCYmJsVpU3/++WemXjdPnjwqXbq0SpcurQceeMD47913352u5wkNDVW7du3Uq1cvBQYGKikpScnJydq8ebOioqJUvHjxTHoFAAD4vrNnz2rdunWSzN2P5s2bp7r1PeAOBBAvcP78+RSDxl9//ZWp182dO7cpZDhu582b12XXqFevniZPnqyTJ0+auiDz5s3TwIEDXXYdAAD8zcKFC41t7x3hI3fu3GratKmdZQEEEE9y5syZFIPGuXPnMvW6uXLlsoSM0qVLK1++fJl6XenGOR4dO3ZU586dTV2QrVu36sCBA3rggQcyvQYAAHzNqVOntH79eknm7kfr1q0VFhZmZ2kAAcQOJ0+etKzPOHjwoP7+++9MvW7OnDlNU6YcgcPuLfjeeustTZw4UceOHVNQUJAxV3XevHkaNmyYrbUBAOCNFixYYHQ/goKCJEn58+dXo0aN7CwLkEQAyVTHjx9PMWhcuXIlU6+bM2dOSzejdOnSKlCgQKZeN6OCgoLUqVMntW3bVgEBAQoICFBycrJ27Nih3bt3q1y5cnaXCACA1zhx4oS+++47STemXgUEBEiS2rZtq9DQUDtLAyQRQFwiKirKMm3q4MGDun79eqZeNzw8PMU1Gp4aNG7l9ddf15gxYyxdkFmzZmn8+PE2VwcAgPeYP3++Ze1H/vz5Vb9+fTvLAgwEkHRIaX3GwYMHjYXTmSVHjhyWHadKly6te+65J1Ov606BgYHq0aOHmjdvbsxVTUpK0oEDB7R9+3Y99thjdpcIAIDHi4qK0g8//CDJ3P3o3LmzQkJC7CwNMBBAbhIbG6vff/9dhw4dsvw3s2XPnj3FxeAFCxbM9Gt7gho1amj06NE6dOiQEUCkG5/kEEAAALi9+fPnG7cd3Y9ChQrpnXfesaskwMJvA0h0dLQRLpyDxsmTJzP92tmyZUtxMXihQoUy/dqermfPnmrUqJGlC/Lzzz/rySeftLs8AAA8luP9UjJ3P7p162YsRAc8gc8HkOPHj1uCxuHDh3X+/PlMv3a2bNlSPLCPoJG66tWrq2zZstq7d6+lC0IAAQAgdSl1P4oWLaratWvbVRKQIp8IIImJiZbpUocOHVJUVJRiY2Mz/fphYWEpLga/9957M/3avqhnz56qV6+eqQsSFRWlH3/8UU8//bTd5QEA4HEcayYlc/ejR48eRhgBPIVXBZBLly6Zgsbhw4d1+PBhRUVFGZ+UZ6asWbOmuBj8vvvuy/Rr+5OqVauqfPny2rFjh6kLMm/ePAIIAAApmDVrlnHbEThKliypGjVq2FUSkCqPDCB//fWXqZsRFRWlqKgonThxwi3Xz58/v0qWLGn5oqPhPj169NCbb75p6oKcOHFCGzdu1LPPPmt3eQAAeAzHuVmSufvRs2dPO8sCUmVrADly5IgRNBwhIyoqSmfPnnXL9UuUKJFi0AgPD3fL9ZG6ypUrq1KlSvrpp58sa0GqVKlCOxkAgP83b94847bj/bFs2bKqXr26TRUBt5bpASQuLs60+Ns5aFy6dCmzL6/s2bOnGDJKlixpfEIAz9SnTx+98sorCggIUFBQkBITE3Xq1CmtX79eL774ot3lAQBgu61bt+rAgQOSpKCgILof8AouCyAXL140dTKcw0Z8fLyrLpOqggULphgyfOmwPn9Tvnx5Pfvss9q4caMCAwONAx8XLlyoF154gS4IAMDvObofjinL0o33z6pVq9pYFXBr6Q4gJ0+etHQyDh8+rGPHjmVGfSaBgYGpdjOyZcuW6deH+/Xu3VsbN26UJKMLcvbsWX3xxRd6+eWX7S0OAAAb/fjjj4qKipIk04dyffr0saskIE1SDSA3hwzH1+nTpzO9qJw5c6YYMooXL57p14ZnKVu2rKpVq6avv/7aWAuSnJysyMhIvfjiiwoO9sh9FAAAyHQpdT+efvppVapUycaqgNsL3rNnT4pB4+LFi5l+8fvuuy/FoJEvX75Mvza8R7du3fT1119LkjEV6/z581q7di3bCwIA/NLGjRuN3UGdux+s/YA3CM7sxbwhISGpTpvKkiVLpl4bvqFs2bL673//qzVr1pi6IEuWLFH16tV111132V0iAABuk5SUZJx67tz9cJyjBXg6l81fyZMnT4oho2jRoq66BPxY165dtXbtWiUlJZm6IKtWrVKdOnXsLg8AALdZv369Tp06JYnuB7xTugNI0aJFUwwaefLkyYz6AEk3TnN97bXX9Omnn5q6IEuXLtV///tfumkAAL+QkJCgBQsWSDJ3P6pXr66yZcvaWRqQZikGkCxZsqQ6bSokJMTdNQKSpM6dO+vTTz+V9M9akJiYGH322Wd6++23ba4OAIDMt3btWkVHR0sydz+6du1qV0lAugU/9dRTlpBx33332V0XYFGsWDG98847Wrx4saUL8sorryhHjhx2lwgAQKa5du2aFi9eLMnc/ahRo4bKlCljZ2lAugR/8skndtcApFmnTp20dOlSJSYmGl2Q2NhYLV26VI0bN7a7PAAAMs2KFSt04cIFSf90P4KCglj7Aa/DUdLwKoUKFVKDBg0k3fjhGxAQIElauXKl8UMZAABfc+XKFTk+NA4MDDQCyJtvvqkiRYrYWRqQbgQQeJ3OnTsrLCxM0j+fAMXFxSkyMtLOsgAAyDSLFy/WlStXJP3z3hcSEqLOnTvbWRaQIQQQeJ1cuXKpadOmksyfAq1bt06nT5+2szQAAFzuwoULWrVqlSRz979hw4YqWLCgnaUBGUIAgVdq3ry5wsPDJf3zSZDzwUwAAPiKBQsWKC4uTtI/73lhYWFq3769jVUBGUcAgVcKDw9X27ZtJZl3Avn222915MgRO0sDAMBlTp8+rS+//FKSufvRokUL5cqVy8bKgIwjgMBrNW7cWPny5ZNk3gt93rx5NlUEAIBrzZkzR0lJSZL+ea/LlSuXWrRoYWdZwB0hgMBrhYaGqkuXLpLMXZCff/5ZBw8etLM0AADu2JEjR7Rp0yZJ5u5Hu3btjM1YAG9EAIFXe+edd4ztB527INOnT7erJAAAXGLmzJnGbcd7XL58+dSoUSO7SgJcggACrxYUFKQePXpIMndB9uzZo//97392lgYAQIbt2bNH27dvl2TufnTr1k0hISF2lgbcMQIIvF7NmjUVEREhydwFmT17tl0lAQBwR5w7+Y73tiJFiuitt96yqyTAZQgg8Am9evWSZO6COM+dBQDAW2zevNlYy+jc/ejZs6eCgoLsLA1wCQIIfELVqlX1xBNPSDJ3QZx3DwEAwNMlJSVpzpw5xveOwBEREaEaNWrYVRbgUgQQ+IwBAwZIMndBnPdPBwDA061fv15//PGHJJm6Hb1797arJMDlCCDwGY888oiqVasmydwFWbBggRISEuwqCwCANElISNCCBQskmT9Me+KJJ/Tcc8/ZWRrgUgQQ+JTu3btLuvGD2/HJ0YULF7Ry5Uo7ywIA4LbWrFmj6OhoSeYP0hwdfsBXEEDgUyIiIlSrVi1J5oV7S5Ys0bVr1+wsDQCAVF27dk0fffSRJHP344UXXtAjjzxiZ2mAyxFA4HO6detmdD8cP8AvXbqkZcuW2VkWAACp+uSTT3Tp0iVJ5u6H46wrwJcQQOBzihQponr16kkyd0GWL19u/HAHAMBTXLp0SZ988okkc/fjtddeM865AnwJAQQ+qWPHjgoNDZX0zydJ165d06JFi+wsCwAAi8WLFxvThB3vWUFBQca6RsDXEEDgk/Lly6cmTZpIMndBVq9ebSzwAwDAbtHR0Vq1apUkc/fj3XffVZEiRewsDcg0BBD4rDZt2ig8PFzSP58oOW9xCACA3Zy3ine8V4WGhqpz5852lgVkKgIIfFZ4eLhatWol6cYPdccPdudDngAAsMsff/yh9evXSzK/TzVu3Fj58uWzszQgUxFA4NOaNm1q/BB3/GBPSkrS/Pnz7SwLAADNnTtXSUlJkv55jwoPD1fbtm3tLAvIdAQQ+LTQ0FB16NBBknlu7ffff68jR47YWRoAwI8dPHhQP/74oyTzWsXmzZsb04cBX0UAgc+rX7++sZDPeW/1mTNn2lUSAMDPTZ8+3bjteG/KlSuXmjZtaldJgNsQQODzgoKC1KVLF0nmLsj27du1Z88eO0sDAPihHTt2GO8/zt2PTp06KSwszM7SALcggMAv1KpVSyVKlJBk7oI4fwIFAIA7zJgxw7jteE8qWLCg3nvvPbtKAtyKAAK/EBgYqL59+0oyd0EOHjyon376yc7SAAB+5IcffjDWIDp3P7p27aqQkBA7SwPchgACv1GtWjU98sgjkm5My3L80J81a5axCwkAAJklKSlJ8+bNk3Tjw7CgoCBJUokSJfTGG2/YWBngXgQQ+JUBAwYYtx1dkD/++EPffvutXSUBAPzE119/bZxD5TwduEePHqbvAV/H33b4lSeeeELPPfecJHPre+HChXaWBQDwA473GuepwA8//LBefvllO8sC3I4AAr/Tu3dv47bjDeD06dNatWqVXSUBAHzc8uXLFR0dLcnc/ejVq5ddJQG2IYDA70RERKhGjRqSzF2Qjz76SHFxcXaWBgDwQVeuXNGiRYskmbsflStX1r///W87SwNsQQCBX+rZs6ex+M/xRvD3339rxYoVdpYFAPBBS5Ys0ZUrVySZux99+vSxqyTAVgQQ+KUiRYro7bfflnTjzcDxhvDxxx/r0qVLdpYGAPAh586d08qVKyWZux81atRQuXLl7CwNsA0BBH6ra9euCg0NlfTPJ1KxsbFGmxwAgDs1f/58Y3qv470mJCSEtR/wawQQ+K18+fKpcePGksyfSq1YsUKnT5+2szQAgA84evSovvrqK0nmbnuDBg1UuHBhO0sDbEUAgV9r166dcuTIIck8L3fu3Ll2lQQA8BFz5swxbjveY8LCwtSxY0e7SgI8AgEEfi1HjhzGG4FzF+S7777ToUOH7CwNAODF9u7dq61bt0oy77jYpk0b5cqVy8bKAPsRQOD3GjVqZLTCnbsgU6ZMsaskAICXc34Pcby35M2bV82bN7erJMBjEEDg90JCQtSjRw9J5i6I86dXAACk1aZNm4wuunP3o3v37sbmJ4A/I4AAkl577TVjO8SgoCDjzWL69OlKSkqyszQAgBdJSkrS7Nmzje8dH2oVL17c2P4d8HcEEOD/DRkyxLjteMP4888/9fXXX9tVEgDAy6xZs0Z//fWXJHP3o1+/fqZpvoA/418C8P8ef/xxvfDCC5LMbxpz58419nAHACA1165d08KFC43vHYHj8ccfV7Vq1ewqC/A4BBDASf/+/Y03DMd/L168qOXLl9tZFgDACyxdulSXLl2SZJ7O69xhB0AAAUyKFy+ut956S5K5C/Lxxx8bbyoAANzs4sWL+uSTTySZNzT573//a6wxBHADAQS4SY8ePYxdShxvIDe31QEAcLZgwQJjuq7jvSMoKEh9+vSxsyzAIxFAgJvkzZtXLVq0kHTjTcTxRuK8sBAAAIc///xTX3zxhSRz9+O9994zzpkC8A8CCJCC1q1bGyfVOt5IkpKSNGvWLBurAgB4otmzZxtbtjveM8LCwtSlSxc7ywI8FgEESEFYWJi6du0qyfxp1vfff28cLgUAwKFDh7R582ZJ5veLVq1aGR9kATAjgACpqF+/vtE6d967fcqUKXaVBADwMM7vCUFBQZJuTOVt1qyZXSUBHo8AAqQiKChI/fr1k2T+VGvv3r3asmWLnaUBADzAli1btHfvXknmnRO7dOmisLAwO0sDPBoBBLiFl19+WY8//rgk857us2bNMub7AgD8z83rAh0fUhUvXlzvvvuuXWUBXoEAAtyG8wFSjjcY5x1PAAD+58svv9Sff/4pydz96N27tzEVC0DKCCDAbZQrV04vv/yyJPObzIIFC3Tt2jU7SwMA2CAuLk7z58+XdGOKriNwPP7446pevbqdpQFegQACpEG/fv2MNxhHF8T51FsAgP9Yvny5Ll68KMm8SYlzxxxA6gggQBoULlxY7733niTz4YSffPKJ8SYEAPB9ly5d0scffyzJvEHJf/7zH5UrV87O0gCvQQAB0sh5VxPHG861a9e0cOFCO8sCALhRZGSkMf3W8V4QFBSkXr162VkW4FUIIEAa5cqVS61bt5Zk/tRr3bp1xkJEAIDv+uuvv/T5559LMnfD69atq+LFi9tZGuBVCCBAOrRo0UJ58+aV9M8nX0lJSZo9e7adZQEA3GD27NlKSEiQ9M97QFhYmDp37mxnWYDXIYAA6RAaGqoePXpIMu98snnzZuMwKgCA79m3b582bdokybwjovMHUwDShgACpNM777yj0qVLSzK/Cc2cOdPOsgAAmWjKlCnGbUf3I2/evGrRooVdJQFeiwACZEDv3r2N2443on379umHH36wqyQAQCbZsGGDfv/9d0k3Fpw7Pnjq2rWrsTkJgLQjgAAZ8MILL+hf//qXJHMXZM6cOXaWBQDIBI51fs4bkJQtW1b16tWzsyzAaxFAgAzq16+fcduxFuTkyZNatmyZXSUBAFwsMjJS58+fl2Q+dHDQoEF2lQR4PQIIkEHlypXT66+/Lsn8qdiiRYs4nBAAfMD58+cVGRkpyfxz/qWXXtJTTz1lZ2mAVyOAAHegT58+uuuuuyT988nY1atXNW/ePBurAgC4gvMW645Od0hICN0P4A4RQIA7UKBAgRQPJ/zyyy8VFRVlZ2kAgDtw+PBhbdiwQZJ5rV+jRo1033332Vka4PUIIMAdatWqlQoUKCDpn91RkpOTNWHCBJsrAwBk1KRJk4zbjg+XcubMqY4dO9pVEuAzCCDAHcqaNat69eplfO94o9q/f79xaBUAwHts2rRJ+/btk2TufnTv3l05cuSwszTAJxBAABeoU6eOHnroIUnmN6tZs2YpPj7eztIAAOkQHx+vWbNmSboxtdax9qN06dJsuwu4CAEEcJFhw4YZtx1dkDNnzuiTTz6xqyQAQDp9+umnOnPmjCTztrvDhg0zwog32r9/vz777DOXPV98fLwmTJig6Oholz0n/AcBBHCRChUq6LXXXpNk7oIsWbLE2EMeAOC5/v77by1atEiSeWORF154wau33d2yZYuqVq2qX3/91WXPGRAQoK+//lovvfSSTpw44bLnhX8ggAAu1K9fP2NbXscnZdevXzdt5QgA8Exz587V9evXJf3T/QgKCtLAgQPtLOuO/Pjjj6pdu7YqVqyonj17uux5g4ODjWnGr732mo4fP+6y54bvI4AALpTatrwbNmxgW14A8GDHjx/Xl19+KelG+HD8/G7YsKGKFStmY2UZ98MPP+iNN95Q3rx5NWPGDIWEhLj0+QsUKKDZs2fr1KlTqlWrlo4dO+bS54fvIoAALua8La/z/GG25QUAzzVp0iQlJydLMm+726VLFzvLyrCDBw/qzTfflCTNmDHDeF9ytYoVK6pv3746deqUXn/9dV25ciVTrgPfQgABXMx5W17nHVT279+vb775xs7SAAAp2LJli3bt2iXJvIavS5cuXrntblJSkhGcqlSpokqVKmXq9Ro0aKDs2bPr1KlTGjNmTKZeC76BAAJkgltty+uYXwwAsF9CQoKmTp0qyfyhUbFixdSgQQM7S8uwjz/+WNu2bZN0oyuf2bJmzaq2bdtKkqZNm6bdu3dn+jXh3QggQCZJaVve8+fP6+OPP7arJADATVatWpXitruDBw/2ym13o6Oj1a9fP0lSuXLlVLlyZbdct379+sbtzp07KykpyS3XhXcigACZ5OZteR1vbMuWLWNbXgDwAJcvX1ZkZKQk88YhzzzzjKpWrWpnaRm2Zs0aXb58WZL0xhtvGB34zJYzZ07VqlVLkrR7927t3LnTLdeFdyKAAJnIeVtexxtbfHy8pk2bZmdZAABJCxYsUGxsrKR/tk4PCgoydbC9zdq1a43bjz/+uFuv/eSTTxq3N2zY4NZrw7sQQIBMVKBAAWP+rfOna5s2bdL+/fvtLA0A/NrJkye1Zs0aSea1eu+9957HbbubkJCga9eu3fZ+Fy9e1A8//GB8/+CDD6brOnFxcXf0586BZ+XKlem6NvwLAQTIZK1bt051W17Hlo8AAPeaMmWKsU7B8bM5R44c6tq1q51lSZKuXbumWbNmqVmzZqpcubKKFCmi4sWLq1ChQmrcuLGxY9fNvvvuO+N2lSpVbnnux9WrV7VmzRqNGTNGjRs3VoUKFVSsWDH98ssvlvuuXLlSDz/8sIoVK6YWLVqk+pylS5c2bkdFRenIkSNpebnwQwQQIJNlzZpVvXv3lmTeYSUqKkpff/21naUBgF/avn27/ve//0m6MeXKedvdnDlz2lmavvzySz399NPq27evVq9erZo1a2r+/Plq2bKlsmfPrnXr1ql69eoqVKiQ6WvUqFE6fPiw8TyOnRhTc+3aNUVGRmr69Olat26dTp06JenGh2aOaWnSjanELVq0UHR0tKQbYSS1YBEcHKyKFSsa3xNAkBoCCOAGtWvXTnFb3tmzZ7MtLwC4UUJCgiZOnCjJPDW2WLFiatiwoZ2lafny5WrYsKERBpYuXaouXbqoWrVq6t27t1F3Sh566CEjJEi6bZDKnTu3lixZov3792vp0qXG+LFjx7Ru3TpJ0rhx4zRz5kwVL15cxYsXl3Rjncd9992X6vPmypXLuH327Nlb1gD/RQAB3CSlbXn//vtvffTRR3aVBAB+Z8WKFcYv+M7TYgcMGGDrtru//fab2rRpY6rn5i10n332WdP3DRs21BdffKEvvvhCzz33nOkX/rR2cgIDA1W5cmXjHA/pxkL2n3/+WaNGjVKDBg20adMm/fDDDzp69KhWrFhxy6ldefLkMW6fO3cuTTXA/xBAADdJbVvepUuX6vTp0zZWBgD+4fz588aHPs4/h6tUqaJq1arZWZqxHbAkZc+eXe+++67lPqGhocqbN6/pfg8//LAefvhhZcmSxTjPRDJ3ItLi7bffNm6vW7dOH3zwgapUqaJBgwYZ/zs5dnW8FefrsuU8UkMAAdwopW15JWnGjBl2lQQAfmPGjBnGblKOn8EhISEaMWKEnWUpOTlZn376qfF9zZo1lS1bNsv9Ll68aJpmFRYWZvpz5wCSPXv2dNVQrFgxFSxY0Pg+Ojpao0aNUnBwcLqeJzw83Lh99erVdD0W/oMAArhRatvybt68mUObACAT7d27Vxs3bpRkXovXpEkTFS1a1MbKbpwP5Tg8UJJKlCiR4v0c2wY73DxFyzmQxMfHp7sO58MXGzVqpMKFC6f7OZyvy2noSA0BBHAz5215nXdfGT9+vBISEuwsDQB8UlJSksaNGyfJ/OFPgQIF1LlzZztLk3RjapNz9yGlX9yTk5M1a9Ys4/ty5crpkUceMd3H8d4i3eiWpNdTTz1l3D5+/Hi6Hy9JFy5cMG7ny5cvQ88B30cAAdzMeVte6Z9pAKdOndKKFSvsKgsAfNbq1at14sQJSebuR9++fZU1a1Y7SzO89957xu2lS5daOgl9+/bVwYMHJd2YXjV79mzL9CjnAPL333+nu4aoqCjj9vr16zP0oZhzALn77rvT/Xj4BwIIYIPatWvr0UcflWR+M4yMjGTRHgC4UExMjObPny/J3P2oWLGiatWqZWdpJi1bttQLL7wgSTp48KDeeecdfffdd1q5cqXef/99zZ49W9KNBfNfffVVilvhOi9Qj4mJSdf1//zzT40dO9Y0tn///vS+DFPnhQCC1BBAAJuMGTPG2PLR8d/r169r+vTpdpYFAD5l5syZxsF6jvARFBSkMWPG2FmWRUhIiObNm6eRI0cqe/bs2rx5s9555x21aNFCf/75p5o3b66PPvpIixcvVrFixVJ8jvz58xu3//zzz3Rdv3fv3ipatKhpNzDHYY3pcezYsRTrAZwRQACbREREGC1350/lvvvuO+3du9fO0gDAJxw8eFBff/21JPO2u++//75KlixpZ2kpunDhgvbs2aPLly+ratWqWrx4sY4fP64NGzaob9++eu6554yOeUqc13Bs2rQpzddduXKlvvzySw0fPtx01shPP/1k3D516pTWr19/y+eJjo42BZCHH344zTXAvxBAABv16NHDOLTJeVvecePGsXsIANyB5ORkY+G59M/P2Dx58qhbt252lZWqq1ev6sUXX9T8+fPVtm1bRUZG6plnnknXNrgPPvigMQ3r1KlTaTpj6uTJk+rSpYvefvttPfPMM3r88ceNP/vmm2+UlJSk69evq3Hjxvrkk09u+Vw7duwwbr/66qvKkiVLmmuHfyGAADbKnj27+vTpI+lGF8QxFevEiRNauXKlnaUBgFf7/PPPdeTIEUnmtXZ9+vRJ9xkZ7rB8+XLjhPaVK1dqxowZ+u2339K1EDwgIECvv/668f0vv/xiuc/KlSv18ssva9KkSTp69Kjeffdd5ciRQ/369ZN0ozvv+N/n8uXLWrVqlbp166bY2FiNHj36ltffunWrcfs///lPmuuG/yGAADZ76623UlyQvnDhwnQvIgQASFeuXNHcuXMlmT/cefTRR/XWW2/ZWVqqnEPRsWPH1L9/f7344osqUqSI3n33XU2aNEn79u277fNUr17duP39999b/rxPnz7auXOnhg4dqn/96186ePCg5s+fr5w5c0qSgoODTeeBtGzZUmvXrtX8+fNvG9wc090kmaZyATcjgAAeYMyYMUbwcEwTiI2N5YR0AMiAWbNm6cqVK5L++ZkaEBDgcQvPHeLj403b195s48aNGjp0qJ5//nk99dRTWr16dar3rVSpkl566SVJ0oIFC3T27FnTnzuvE8mbN69Wrlyphx56yHSfJk2amO4zf/782x7W+MMPPxjbBPfo0UO5cuW65f3h3wgggAdwXpDuvFBy/fr1xg90AMDtHTlyRF988YUk88/T+vXrKyIiws7SUrRz505Vq1ZNvXr1Uu3atfXtt99q6tSpeu+991L8pf/YsWNq1qyZFi5cmOpzDhkyxLi9YMEC059NnjxZH330kebPn6/NmzerYsWKlsc//vjj2rBhg2bMmKGtW7eaQktqpkyZIkkqXbq0mjdvftv7w78FJCcnJ9tdBIAbe7Y/8cQTiomJUXJysjHv9/7779eUKVNuufMJ4E6RkZGKjIyUJNWrV0/16tWzuSLgH23btjU+uAkODlZAQIDCw8O1detWhYeH21yd2a5du4wpU71791bLli0t9zlz5oy2b9+u7777zjjPRJKKFi2qLVu2pPrcc+fOVa9evZQ9e3Zt3749U9e9/Pbbb3rxxRclSatWrTItZAdSQgcE8BDh4eHq27evJPO2vEeOHNGaNWvsLA0AvMKXX35phA/nNXW9e/f2uPAhSV26dJF0Y5pT06ZNU7xP/vz5Vb16dQ0bNkzbtm0zxp23u01J/fr19eqrr+ry5cvGZieZ4erVq+rUqZMkqWfPnoQPpAkBBPAg7777rrEgPSgoyHjznDdvnjGfGQBgFRsba5wW7rzwPCIiQnXr1rWztBSdOXNGu3fvliQ9/fTTadpu99577zV2l3K8V6QmODhYkyZN0quvvqqPP/5Y8+bNu9OSU9SjRw/t3r1bPXr0UOvWrTPlGvA9BBDAw6S0IP3KlSuaOXOmnWUBgEebN2+esXOg87lKzj9TPUnu3LmNMzt+/PFHnTx58raP+eWXX7Ru3TpJUqtWrW57/5CQEE2aNEk1atRQz549TR0UV5g7d66WLl2qXr16qU2bNi59bvg2AgjgYZw/rXNeQOk8tQAA8I8jR44YO0M5/9x8++23b9spsEtISIjat28v6cYJ4tWrV9fEiRN16tQp00G08fHx2rJli3r16qVXX31VktSpUye98sorab7OpEmT9N5772nUqFEuq//q1asaNmyYhgwZkqYwBDhjETrggViQDk/GInR4mpQWnmfPnl0//fST8uTJY3N1t/bDDz+oe/fuioqKMo3nzZtX165d0+XLl42x2rVrq127dipZsmSGrhUfH6+QkJA7qjcznw/+4/YTDgG4XXh4uHr37q2uXbsac5kTExN15MgRffXVV8Ye7wDg7/73v/8Z4cN57VyPHj08PnxIUuXKlfXdd9/pyJEjOnHihP744w8dP35csbGxKlKkiIoXL66iRYuqSJEiypIlyx1dy9VhgfCBjCKAAB6qbt26mjt3rvbt26fAwEAlJSUpOTlZM2bMUOXKlZUtWza7SwQAW129elVjx46VZN49sGTJksbZSt4gKChIJUuWzHBnA/A2rAEBPNTNp/Y6L0jPrN1MAMCbzJ8/X+fPn5ckY9cr6cbCc+fvAXgWAgjgwR599NEUF6SvXr3aMl8YAPzJ4cOH9dlnn0kyn/nx9ttvp3i6NwDPQQABPFyfPn2MA7Sct5b88MMPbaoIAOyVnJxs/Ax0PvMjd+7c6t+/v32FAUgTAgjg4cLDw9WjRw9J5jfagwcP6qeffrKzNACwxerVq/X7779LMn8wM3DgQI888RyAGQEE8AINGjRQ2bJlJZmnGowdO9Y4eAsA/MG5c+c0Z84cSeapqU8//bRq165tZ2kA0ogAAniJESNGGLcdXZCYmBhNnz7drpIAwO2mTJmia9euSTJ3P0aPHm1XSQDSiQACeIkKFSqoadOmkszbTW7YsEHbt2+3szQAcItffvlFP/74oyRzN7hz584qWrSonaUBSAcCCOBFunfvroIFC0oyH7g1duxYxcXF2VkaAGSquLg4jRs3TpJ5PVyJEiXUtm1bO0sDkE4EEMCLZMmSxTh0S/pn+kF0dDRngwDwafPmzVN0dLQk646AwcGcqwx4EwII4GWeeeYZvfrqq5LMCzA/++wzHTp0yM7SACBTHD161HTmh+Pn3ltvvaUKFSrYWBmAjCCAAF5o8ODBypYtm6R/PglMSkrSqFGjlJSUZGdpAOBSycnJGjNmjPGzzfEzL3fu3BowYICdpQHIIAII4IXy5cunvn37SjIvSD927Jg++eQTO0sDAJdyPvPDee1b3759OfMD8FIEEMBL1a9f35h64PymvHDhQp0+fdrO0gDAJc6fP6+5c+dKMn/YUqFCBb311lt2lgbgDhBAAC82fvx4Y/Gl4405Pj7etFAdALzV1KlTdfXqVUn/nH8UHBysDz/80MaqANwpAgjgxYoXL67WrVtLMi/M3LVrl7766is7SwOAO/LLL7/o+++/l2Q+86Nt27YqUaKEnaUBuEMEEMDLtW/fXkWKFJFkfpOePn26Lly4YGdpAJAhqZ35UaRIEc78AHwAAQTwcnfddZfpjdrRBbly5YqmTp1qZ2kAkCELFy5M8cyPsWPH6q677rKrLAAuQgABfMBTTz1lLMh0noq1adMmbd++3c7SACBdjh49quXLl0sy/zyrU6eO/vWvf9lZGgAXIYAAPqJ///66++67JVk/MXQs4gQATxYXF6e+ffsqKSnJ1NENDw9X//797S0OgMsQQAAfkTNnTuNQLuc509HR0cY2lgDgyebMmaMzZ85IMq9pGzBggPLkyWNnaQBciAAC+JDXX39dTz31lCTzm/fq1au1b98+O0sDgFs6cOCAVq5cKck89YozPwDfQwABfMy4ceOMRZqOLkhycrJGjx6txMREO0sDgBTFxcVpxIgRSk5OlvTPNNIsWbKwmQbggwgggI8pUqSIunbtKsm8K9aff/6pzz//3M7SACBF8+fP18mTJyXd+ODE0b3t2bOn7rvvPjtLA5AJCCCAD2rZsqXKli0ryfxmPmXKFJ04ccLO0gDAZP/+/cauV84fmjz++ONq0qSJnaUByCQEEMBHjRs3zggejqlYkjRs2DAlJSXZVRYAGBISEjRy5Ejje8fPqpCQEE2YMMGusgBkMgII4KPKlSunVq1aSTJ/qhgVFaVly5bZWRoASJIWLFhgTL1y3jije/fuKlasmI2VAchMBBDAh3Xp0kWlSpWSZJ6KtXDhQh0/ftzO0gD4uaioKH3yySeSzFuHly9fXk2bNrWzNACZjAAC+LCQkBBNnTrV6H44/puQkKDhw4czFQuALRITE00/gxw/m0JCQjR58mTTtFEAvocAAvi4smXLqm3btpLMe+tHRUVpyZIldpYGwE999NFHRhfW+edSp06dmHoF+AECCOAHOnbsaEzFcrzRS+ZfAgDAHaKiovTxxx9LMq9Pe/DBB411awB8GwEE8APBwcGaOnWqgoODTXOtHdMgOKAQgDvc/DPHsfA8ODiYqVeAHyGAAH6CqVgA7LZkyZIUp161a9dOpUuXtrM0AG5EAAH8SPv27VOcirVo0SKmYgHIVMePH9eiRYskmXe9Kl26tNq1a2dnaQDcjAAC+BGmYgGwQ1JSkmXqlXRje/DJkycrODjYzvIAuBkBBPAzZcuWNT5tvHkqluPTSQBwpWXLlikqKkqS+edO69at9eCDD9pZGgAbEEAAP9SuXTuVLVtWkvn04SVLlhi/JACAK5w8eVILFy6UZJ161alTJztLA2ATAgjgh4KDgzVx4kRJ5m0wExMTNWrUKDtLA+Bjpk2bpoSEBEnmtWcTJkxg6hXgpwgggJ+KiIhQ165dJZmnRBw5ckQLFiywszQAPmLp0qXaunWrJPPPmVatWunhhx+2szQANiKAAH6sffv2xi8BQUFBxlSsRYsW6dChQ3aWBsDLHT16VHPmzJFknnpVtGhR9erVy87SANiMAAL4uYkTJxrTIJynR4wcOZJdsQBkSEJCggYPHmx873zA4MCBA+0oCYAHIYAAfq5UqVLq0qWLJPMUiePHj+uzzz6zsTIA3mrOnDn6448/JJk3uqhXr56qVatmZ2kAPAABBIDatGmT4lSsmTNnav/+/XaWBsDL7Ny5U59++qkk89SrYsWKqX///jZWBsBTEEAASJImT55s3HaeLjF8+HBdu3bNjpIAeJkrV66YdtJz/lkyZcoUhYWF2VEWAA9DAAEgSSpRooQaN24sybw17+nTpzVlyhQ7SwPgJSZOnKhz585JMk+96tatmx599FEbKwPgSQggAAx9+/ZVmTJlJJmnYn311Vf6+eef7SwNgIfbtGmTNm7cKMk89apChQpq06aNjZUB8DQEEACGkJAQzZo1S6GhoZLM0ydGjRql8+fP21UaAA92/vx5ffjhh8b3jp8dOXLk0PTp00077AEAPxEAmBQvXtxYKOr8Kebly5c1fPhwJScn21gdAE80fPhwxcbGSjJ3T4cNG6ZChQrZWRoAD0QAAWDRoEEDvfDCC5LM87h37dql5cuX21kaAA+zYsUK7dq1S5J5K+9XX31Vr7/+up2lAfBQBBAAKZo4caLy588vyTwVa968eTpy5IhdZQHwIH/88Ydmz54tybx5RaFChTR69Gg7SwPgwQggAFKUM2dOTZs2TQEBAaapWAkJCRoyZIji4uJsrhCAnRITEzVkyBAlJCRI+qdbGhAQoOnTpytHjhw2VwjAUxFAAKSqUqVKatGihSTz1Io//vhDs2bNsrM0ADabP3++0Q11/vnQunVrVahQwc7SAHg4AgiAW+revbseeughSebFpatWrdL27dvtLA2ATfbt26dly5ZJMm9WUa5cOXXp0sXO0gB4AQIIgFsKDg7WjBkzlDVrVknm9SCjR4/W33//bVdpAGxw/fp1TZo0ydgRz/lnwrRp0xQcHGxXaQC8BAEEwG0VK1ZMw4cPl2T+tPP8+fMaO3asnaUBcLMPP/xQhw8flmTuio4aNUr333+/naUB8BIEEABp8sYbb+iVV16RZJ7v/fPPP2vNmjV2lgbATdauXatvv/1WkvnnQLVq1VS3bl07SwPgRQggANJs7NixxqFizp98zpgxQwcPHrSzNACZ7OjRo5o2bZokcyc0LCxMgwYNsrM0AF6GAAIgzXLkyKEZM2YYn3o6fgGJi4tTv379FBMTY2d5ADJJbGys+vXrZ2y/7bzuY+zYsSpSpIhdpQHwQgQQAOny2GOPqUOHDpLMn4JeuHBBQ4cOtbM0AJlk7Nix+uuvvySZu5/169dXjRo17CwNgBcigABIt06dOql8+fKSzPPAd+7cqUWLFtlZGgAXW7NmjX744QdJ5n/vZcuW1YgRI+wsDYCXIoAAyJDRo0crJCREkvkT0cjISP366692lgbARaKiokzrPhzhI3v27Jo7d66dpQHwYgQQABkSERGhIUOGGN87pmIlJSVpyJAhunDhgl2lAXCB2NhYDRgwQAkJCZJudD8cHzRMnDhRhQsXtrM8AF6MAAIgw+rVq6fatWtLMq8HiYmJ0aBBg5SUlGRneQDuwKhRo0zrPhzdj4YNG+qll16yszQAXo4AAuCOjBkzRqVKlZJknh++d+9eRUZG2lkagAz67LPPtGXLFknWdR/9+/e3sTIAvoAAAuCO3HXXXZo/f76yZcsmyTxNY/HixawHAbzMwYMHNXPmTEnmzqZj3Ydj7RcAZBQBBMAdK1asmKZMmSLJ/AtLcnIy60EAL3LlyhUNGDBAiYmJksznfbDuA4CrEEAAuES1atX0wQcfSGI9COCthg0bpnPnzkky7273wQcfsO4DgMsQQAC4zIABA1ShQgVJ1vUgCxYssLM0ALexfv16/e9//5Nk/vdbvnx5DRgwwM7SAPgYAggAl5o5c6by5MkjyfwJ6pIlS7Rt2zY7SwOQin379mn06NGSboQPRwczPDxcM2bMsLM0AD6IAALApe655x7NmDHDCB7OIWT48OHG9A4AnuH8+fPGzlbOhw1K0tSpU3XvvffaVBkAX0UAAeBy//rXv9S5c2dJ5vUgV65c0aBBg+wsDcBN+vbtq7///luS+QOD9u3b67nnnrOzNAA+igACIFN06NBBzz77rCRzCNm/f7969uxpY2UAHEaMGKFDhw5JMoeP6tWrq2vXrnaWBsCHEUAAZBrn6RvOi1q3b9/OonTAZp9++qm+/fZbSeZ/nw888IAmTZpkZ2kAfBwBBECmyZkzp2bPnm0cXOb8CeuiRYu0efNmO8sD/NbOnTs1a9YsSeYOZXh4uObNm6ewsDA7ywPg4wggADLVww8/rA8//ND43jmEjBgxQkeOHLGpMsA/nTx50jibxzl8SNKsWbNUtGhRG6sD4A8IIAAyXa1atdS2bVtJ5l12rl+/rr59++rSpUt2lgf4jatXr6pv3766cuWKJPMHAgMGDFDlypXtLA+AnyCAAHCLbt266cUXX5RkPmfg7Nmz6t+/PyelA5ksOTlZQ4cO1R9//CHJHD5q1KihDz74wM7yAPgRAggAtwgICNC0adNUunRpSeZFr3v27NG0adPsLA/weQsWLDAOA3X+9/fQQw9pwoQJdpYGwM8QQAC4TZYsWbRo0SLdfffdksyfwK5atUpff/21neUBPmvz5s1avHixJHMH8u6779bChQt111132VkeAD9DAAHgVoUKFdLChQtT3Blr/PjxOnDggJ3lAT7n6NGjGj58uCTzjlchISFasGCBChQoYGd5APwQAQSA2z366KMaNWqUJPMvRAkJCerfv7/Onz9vZ3mAz7h06ZLGjBmjuLg4STLteDVmzBiVL1/ertIA+DECCABbvPnmm2rWrJkkcwi5cOGC+vfvb2NlgO/o37+/fv/9d0nmbuMHH3ygOnXq2FkaAD9GAAFgmz59+ujpp5+WZF4Ue/DgQQ0dOtTO0gCvlpycrIEDB2rPnj2SboQPx7+vJ554Qn379rWzPAB+jgACwDaBgYGaM2eOSpYsKcn8Ce2mTZs0e/ZsO8sDvNbcuXO1efNmSeZwnytXLk2aNMk0FQsA3I0AAsBWOXLkUGRkpHLkyCFJCg4ONkLIsmXL9PHHH9tZHuB1vv76ay1dulSSecerkJAQLVy4UPfdd5+d5QEAAQSA/YoUKaK5c+ca3wcHBxu3586dq2+++caOsgCvs23bNo0ZM0aSeW2VJE2dOlUVKlSwqzQAMBBAAHiEf/3rXxo0aJDxvXMIGTlypHbs2GFHWYDXiIqK0pAhQ4zvncNHv3799PLLL9tRFgBYEEAAeIyGDRvqxRdflGT99HbAgAE6cuSIXaUBHu3cuXPq1auXrl27Jsm8nqpevXrGjnMA4AkIIAA8RmBgoGbOnKknnnjC+N6xePbatWvq2bOnzp07Z2eJgMeJjY1V9+7ddeHCBUnmHa+ef/554xBCAPAUBBAAHiUkJESRkZEqU6aMJPMvUxcuXFD37t11+fJlO0sEPEZCQoL69eunEydOSDL/eylXrpxmzpxpfA8AnoKfSgA8Tvbs2bV06VIVLlxYknk6yYkTJ9SnTx/jZGfAn40YMUK7d++WZA4fBQsW1KJFi5QlSxY7ywOAFBFAAHikvHnz6uOPP1bu3Lklmbfn3bdvn4YPH66kpCQ7SwRsk5SUpL59++r777+XZJ6umCNHDn388ce6++677SwRAFJFAAHgsYoVK6alS5cqW7ZskswhZPPmzZo6daqd5QG2GT16tLZu3SrJfNaHJM2fP9843BMAPBEBBIBHe/DBB/XRRx8pJCREknl73tWrV2vZsmV2lQbYYvz48cbZODfvFjdt2jRVqlTJrtIAIE0IIAA83hNPPKEpU6YY3zvCiCTNnj1bCxYssKMswO1mzpypdevWGd87B/IRI0aoRo0adpQFAOlCAAHgFV555RXjhGfJHEIWLVqkxYsX21EW4DZLlizR8uXLje+d/w0MGTJE9evXt6MsAEg3AggAr/HOO++oY8eOxvfOv4DNnz9fq1atsqMsINOtW7dO8+bNM753/rvfvn17NWzY0IaqACBjCCAAvErnzp1Nv2w5/yI2ZcoUrVmzxo6ygEzz9ddfa/z48cb3ztOuGjdurK5du9pRFgBkGAEEgNcZMmSIKYQ4/0I2efJkbdiwwY6yAJfbvHmzxo0bZ3zvvBNcnTp1NHDgQLtKA4AMI4AA8EpDhgxR3bp1Jd3YCcgRQpKTkzVmzBht2rTJzvKAO7Zjxw4NGTLEOO/GOXxUr15dH374ofE9AHgTAggArzVq1CjVqVNHkjmEJCUlaejQofrxxx/tLA/IsIMHD2rYsGFKTEyUZA4fzz//vObMmWMcPAgA3oafXgC82oQJE/Tqq69KMocQSRo0aJBxWBvgLX777Td169ZNMTExkszho1KlSpo1a5ad5QHAHSOAAPB6kydP1vPPPy/JGkIGDhyoHTt22FUakC47d+5Uz549dfXqVUnm8PHwww/ro48+UmhoqJ0lAsAdI4AA8HrBwcFauHChnnvuOUnmEJKQkKB+/frpyJEjdpYI3NbPP/+s7t27Ky4uTpI5fJQtW1Yff/yxsmbNameJAOASBBAAPmPOnDmqVKmSJHMIiYuLU6dOnbR37147ywNStWXLFtOOVs7h48knn9SqVauUM2dOu8oDAJcigADwGaGhoYqMjFSFChUk3QghjnNCYmNj1bFjR23evNnOEgGL9evXa8CAASkuOK9SpYoWL16ssLAwO0sEAJcigADwKWFhYVqyZIkefvhhY8z5sMLBgwdr3bp1dpQGWHz11VcaM2aM8b1z+KhataoWLlyoLFmy2FUeAGQKAggAn5MtWzYtXbpUVapUMcYcISQpKUnjx4/XokWL7CoPkCStWLFCY8eOVXJysiRz+KhZs6YiIyNN4RkAfAUBBIBPCg8P15IlS/Sf//zHGHP+ZW7BggWaMmWKHaUBWrdunaZPn2587xw+3njjDU2dOtWu0gAg0xFAAPi0mTNn6vXXXze+dw4hq1at0qBBg5SQkGBHafBTc+bM0fjx443vncPH22+/rQ8//NCmygDAPQggAHxaYGCgJk2apEaNGhljISEhxi98P/74o/r06aNr167ZVSL8yPDhw7V06VJJ/+zU5vi72KJFC40dO9b4HgB8FQEEgF8YPHiwOnbsaHwfHByswMAbPwJ37Nihzp0721Ua/EBsbKy6du2qjRs3SrKGj06dOqlPnz42VggA7kMAAeA3OnfubDprISgoyAghhw4dUtOmTfXXX3/ZVR581Pnz59WpUyft2rVLkvmMGklq0KCBOnXqZFd5AOB2BBAAfqVJkyYaN26c8X1QUJCCgoIkScePH1ebNm3022+/2VUefMzx48fVtm1bHTlyRJI1fHTr1k3Dhg2zqzwAsAUBBIDfeeuttzR9+nTjF8HAwEAjhMTExKhbt2765ptv7CwRPmDXrl1q3769oqOjJd34e+b4OxcUFKRJkyapXbt2dpYIALYggADwS6+++qoWLVqk3LlzSzKHkMTERI0cOVKzZ8+2s0R4sWXLlqlr166KjY2VZO60ZcuWTR999JFpdzYA8CcEEAB+q3Llylq7dq2KFi0qyRxCpBu/RPbo0UNXr161q0R4mWvXrqlfv36m8Oq81ih//vxas2aN6ZBMAPA3BBAAfq1o0aL64osv9MQTT0j6Z5qMY3eiHTt2qEOHDjp79qydZcILnDlzRu3atdPPP/8s6Z/1Ho7wUapUKa1du1YPPPCAnWUCgO0IIAD8Xs6cOfXZZ5+pVq1akqy/OB49elStWrXS8ePH7SwTHmznzp1q0aKFjh07JskaZCtWrKjVq1erUKFCdpYJAB6BAAIA/2/y5MmmRcHOU2diYmLUtGlTrV271q7y4KGWLl2q7t2768qVK5KsU/nq1aunlStXKjw83K4SAcCjEEAAwEm3bt304YcfGt87Lx6WpAkTJmj48OGsC4EkadSoUZozZ47xvfPfl6xZs2rKlCkaOXKkXeUBgEcigADATd58800tX75cOXLkkGSdTrNx40a1atVKR48etbFK2On48eNq1aqVNmzYIMk6ba9YsWJau3atXnvtNRurBADPRAABgBQ89dRT+vzzz1W8eHFJ1l8wT548qebNmzMlyw8tW7ZMTZs21eHDhyVZA2q1atX05ZdfstgcAFJBAAGAVJQsWVI//PCD6tevb4wxJct/nT9/Xj169LBssev896FHjx6aP3++0T0DAFgRQADgNkaMGKGpU6cqW7ZsklKfkuU48Rq+5+eff1bz5s21Y8cOSTc6Ys6bFOTOnVtLly5VmzZt7CwTALwCAQQA0qBmzZr66quvVKZMGUkpT8lq1KiRli9fbmeZyARTpkxRv379FBMTI8kaPsqUKaP169ercuXKdpYJAF6DAAIAaXT//ffrm2++SXFKVkBAgOLi4jRz5ky1bdtWR44csbFSuMKJEyfUokULrVq1yhi7ufv18ssva/ny5SpYsKBdZQKA1yGAAEA6OaZkZc2aVdI/5z44PhE/ePCgWrRoYdqeFd7lq6++Ups2bYwg6eh4OdZ7ZM+eXRMnTtSsWbOUO3duO0sFAK9DAAGADKhZs6bWr1+vxx57TNI/03KcFyQvXbpUjRo10q5du+wqE+kUFRWlDh06aOzYsbp27Zoka9ejcuXK+u6771S7dm07SwUAr0UAAYAMuv/++7VmzRoNHDhQoaGh0v+1d7+hWZb9H8c/TrdIC8RNTSW0pBBBMRIyetAfqAQxelYON6EsSEELyYLsUU+i/FM9ECwZFCvCIMNsiMsKxcJUCAqnJEVSU1zOTJ25kfs9+N1bzj93d6XH1F4vuBhc18X4XlwwzveO8zjPnH2w2tramsWLF/e5uSGXno6OjqxcuTLz5s1LS0tLkrNXPZLkhRdeyJo1a5xyBfAPCBCAf2ju3LnZvHlzn9WQMw9cN2zYkLq6unz22Wf9NCXn88knn2Tu3Ll99noMHDiwT0hOmTIlW7duzaOPPtpfYwJcMQQIwAVw/fXXZ/369Xn++ed7n+tZDenZG9LW1pYXX3wxTz31VL799tv+GpX/OHz4cBYvXpyXXnop7e3tSc7+zpKktrY2TU1NueGGG/prVIArigABuICeeOKJfP7555k8eXKSvntDev6b3tLSkgULFuTll1/uPfClnF9++SUrV65MfX197/6cc31P48ePz/vvv5+lS5f257gAVxwBAnCBjRs3Lk1NTVmyZEmqqqqSnP2f9e7u7mzatCmPPPJI3nnnnXR2dvbnyP8KR48eTUNDQ+bMmZN169alq6srydnfzeDBg/Pcc8/l008/zbRp0/pzZIArkgABuAgqKioyb968bN++PQ8//HDv8z17C3oOdn/77be89dZbefLJJ7Nx48b+GveKduLEiTQ2Nqauri5r1qzJyZMnk/wRHqfv1ZkxY0a2bNmS+fPnZ9CgQf01MsAVTYAAXETDhw/P8uXL8/HHH+e2225L8sfpPqdvcv7uu++yfPny1NXVpampqT9HvqI0Nzenrq4ujY2NvZfVPdfpVmPHjs3bb7+dN954wxWuAC4yAQJQwMSJE7N27dqsWrUqY8aMSdL3alk9B8JtbW157bXXUltbm7Vr1zo162/o6OjImjVrMmvWrCxbtizHjh1L0jf8elagampqsmLFinzxxRe5++67+3NsgH8NAQJQ0MyZM7N9+/Y8++yzfe6kfmaItLe3Z9WqVamvr8/GjRvT0dHRn2NfFtrb2/P666+ntrY2DQ0NOXz4cJJzh8fVV1+dZ555Jl9++WUeeuih/hwb4F9nQHd3d3d/DwHwb7R///4sWLAgW7du7fP8qVOncurUqZz+57mqqip33nln7rvvvkyaNKn0qH00NjamsbExSTJ79uzMnj27X+f59ddfs3r16rP20AwYMCAVFRV9LqmbJHV1dXn66adTU1NTckwA/sMOO4B+MmrUqLz33nvZuXNnXnnllWzatClJeg+au7u7e2Oks7Mzzc3NaW5uzpgxYzJ9+vTce++9GTp0aP9+iH7S0dGRLVu2pLm5Od98802f1yoqKnrj43T3339/lixZkvHjx5ccFYAzWAEBuER8/fXXWbFiRTZs2NDn+dND5EwPPPBAbrnlltx66629l/y92PpzBWT79u1pbm7O5s2bz3qtJ9x6TmPrUVtbm/nz57uRIMAlwgoIwCVi0qRJaWhoyJ49e/Lqq6/mgw8+SNL3qk1nnp61bt26rFu3LlVVVZk6dWruuOOO3H777Rk8eHA/fpIL66uvvsquXbuyfv36s27ceL7TrK655prMmTMnjz32WEaMGFFyXAD+hBUQgEvUoUOH0tjYmDfffDMHDhzo81rPqkh3d3fO9Wd86tSpefDBBzNu3LgLvtfhYq+AHDlyJNu2bcu2bduyc+fO3svnnu58p1mNHDkyjz/+eOrr6zNkyJALOhcAF4YVEIBLVHV1dRYuXJiFCxfmww8/TENDQ7Zt25bkj1WR5Nyb1nfs2JEdO3YkSUaPHp0pU6ZkypQpmTx58iW3b+TYsWPZtWtX9u7dm5aWlmzfvv2c7ztfdCTJPffck1mzZmXGjBkXe1wA/iEBAnAZmDlzZmbOnJldu3Zl9erVeffdd3tfO/0UpJ4QOX2/SGtra1pbW3tvcDhhwoRMnTo1lZWVGTt2bK677rqMGzeu6OdpamrK7t27s3v37uzbt++c7xkwYEDv41zRMXLkyNTW1mb27NluHghwGREgAJeRiRMnZvny5b13V//oo4+yYcOGHDlyJEl6D9QHDhx43tO0eg78zzRy5MhMmzYt1157bQYNGpSampqMGDEiNTU1GT169HlnOnnyZI4cOZKjR4/m+PHjvc//+OOP2b17d9ra2nLw4MG0tbX96Y0Ve1Y5eh7nctddd6W+vj7Tp0//r78LgEvTgKVLl9oDAnCZ+/7777Nnz560tLTk6NGj53xPT4Sc+fOv6urqSldXV5KksrIylZWVf+v39ATGf4uNJBk8eHBuuumm3HzzzRk/fnyxq30BcHEMGDVqlAABuIJ0dnbmxIkT6erqyu+//37Bf//pKyp/Fg9/V2VlZa666qpUVVX97cAB4NLkFCyAK0xVVVXvKsGpU6d6Vyx6HpfaxQ8rKip6V1J6HhcjagC4NAxatGhRf88AQCEnTpzI3r17097enp9//jk///xz2tvbe0+p+l90dnbm5MmTSdK7SvG/qq6uTnV1dWpqalJTU5MxY8Zk+PDhf/lzAHD5ch8QALJ///788MMPOXDgQFpbW/PTTz+ltbU1Bw8ezL59+3Lo0KHe9x4/fjzHjh1L8v83/BsyZEiqq6szbNiwDBs2LEOHDs2wYcNSXV2doUOHZsKECRk3blxuvPHG/vp4AFxCBAgAf8myZcuybNmyJMmiRYtiJR2Av+LsC6sDAABcJAIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKAYAQIAABQjQAAAgGIECAAAUIwAAQAAihEgAABAMQIEAAAoRoAAAADFCBAAAKCY/wOY2YnCvBGB0gAAAABJRU5ErkJggg==
Let $R$ be the region enclosed by the graphs of $f(x) = 1 - \cos(3 \cdot x)$ and $g(x) = e^{0.3 \cdot x}$, as shown in the figure above. Find the volume of the solid generated when $R$ is revolved about the $x$-axis.
The volume of the solid is $2.655$ units³.
b27efb6c-ef58-438a-9b61-007ea74acd47
multivariable_calculus
true
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
Two children are playing with a ball. The girl throws the ball to the boy. The ball travels in the air, moves $3$ ft to the right, and falls $5$ ft away from the girl (see the following figure). If the plane that contains the trajectory of the ball is perpendicular to the ground, find its equation.
The equation of the plane: $3\cdot y-5\cdot x=0$ (If it is not perpendicular, just click submit.)
b28ab25c-39a1-415e-8c6c-5a8cef4b18f1
algebra
false
null
Solve the following equations: 1. $\frac{ 2 }{ 3 } (6 x+18)=20$ 2. $\frac{ 6 }{ 5 } (10 z+15)=-6$ 3. $\frac{ 3 z }{ 8 }-4=5$ 4. $\frac{ 1 }{ 2 } x+\frac{ 3 }{ 4 }=-\frac{ 7 }{ 8 }$ 5. $3\frac{1}{4} p+4 \left(\frac{ 3 }{ 4 } p-12\right)=-79.25$ 6. $3\frac{1}{2} w-2 \left(\frac{ 5 }{ 6 } w+2\right)=-\frac{ 1 }{ 3 }$
The solutions to the given equations are: 1. $x=2$ 2. $z=-2$ 3. $z=24$ 4. $x=-\frac{ 13 }{ 4 }$ 5. $p=-5$ 6. $w=2$
b2e51a16-da23-4146-b609-b4083ae88786
precalculus_review
false
null
Use the Rational Zero Theorem to find all real zeros of the following polynomial: $p(x) = 2 \cdot x^3 - 5 \cdot x^2 + 9 \cdot x - 9$
The real zeros are $\frac{3}{2}$
b2f618b5-8496-4cb1-9cfa-bb7ec9d0cd99
precalculus_review
false
null
1. Find the inverse function of $f(x) = \sqrt[3]{x-4}$ 2. Find the domain of the inverse function 3. Find the range of the inverse function
1. The inverse function is: $x^3+4$ 2. The domain of the inverse function is: $(-\infty,\infty)$ 3. The range of the inverse function is: $(-\infty,\infty)$
b3072b54-bb84-41dd-b303-7dd7249ba64d
integral_calc
true
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
The region $R$ is the region in the first and second quadrants bounded by the graphs of $y = 5 \cdot \cos\left(\frac{ x^2 }{ 4 }\right)$ and $y = 2 + \sqrt[3]{x}$, as shown in the diagram above. Find the volume of the solid generated from rotating region $R$ about the horizontal line $y = -2$.
The volume of the solid is $336.509$ units³.
b318ad71-d185-4390-acca-0699ca019773
precalculus_review
false
null
Find zeros of $f(x) = \sin(x) + \sin(2 \cdot x) + 2 \cdot \sin(x) \cdot \sin(2 \cdot x) - 2 \cdot \cos(x) - \cos(2 \cdot x)$.
The final answer: $x_1=-\frac{\pi}{2}+2\cdot\pi\cdot n$, $x_2=-\frac{2\cdot\pi}{3}+2\cdot\pi\cdot n$, $x_3=\frac{2\cdot\pi}{3}+2\cdot\pi\cdot n$, $x_4=(-1)^n\cdot\frac{\pi}{6}+\pi\cdot n$
b3573d9a-dceb-44bb-bd9a-009f13c4cc13
integral_calc
false
null
Compute the integral: $$ \int \frac{ \tan(2 \cdot x) }{ \sqrt{\sin(2 \cdot x)^4+\cos(2 \cdot x)^4} } \, dx $$
$\int \frac{ \tan(2 \cdot x) }{ \sqrt{\sin(2 \cdot x)^4+\cos(2 \cdot x)^4} } \, dx$ = $C+\frac{1}{4}\cdot\ln\left(\sqrt{1+\tan(2\cdot x)^4}+\tan(2\cdot x)^2\right)$
b39f8c2e-5c3c-474e-a7e1-adce52e0feaf
differential_calc
true
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
The graph of the function $f$ is shown above. What are all values of $x$ at which $f$ has a jump discontinuity? [Image_0]
The function $f$ has a jump discontinuity at $x$ = $-2$
b3ccc40f-c39b-46f5-8e7a-93f91b06f532
multivariable_calculus
false
null
Let $u(x,y,z) = x \cdot y + y \cdot z + x \cdot z$, where $x = r \cdot \cos(\theta)$, $y = r \cdot \sin(\theta)$, and $z = r \cdot \theta$. Evaluate $\frac{\partial w}{\partial r}(r,\theta)$ and $\frac{\partial w}{\partial \theta}(r,\theta)$ for $r = 1$, $\theta = \frac{ 3 \cdot \pi }{ 2 }$, where $w(r,\theta) = u(x(r,\theta),y(r,\theta),z(r,\theta))$.
The final answer: $\frac{\partial w}{\partial r}(1,\frac{ 3 \cdot \pi }{ 2 })$ is equal to $-3\cdot\pi$ . $\frac{\partial w}{\partial \theta}(1,\frac{ 3 \cdot \pi }{ 2 })$ is equal to $\frac{3\cdot\pi}{2}-2$ .
b3f1345e-4df9-4e1e-b9f5-f0b644753869
sequences_series
false
null
Find the Fourier series of the function $u = \left| \frac{ \sin\left( \frac{ x }{ 2 } \right) }{ 2 } \right|$ in the interval $[-2 \cdot \pi,2 \cdot \pi]$.
The Fourier series is: $\frac{1}{\pi}+\sum_{k=1}^\infty\left(-\frac{2}{\pi\cdot\left(4\cdot k^2-1\right)}\cdot\cos(k\cdot x)\right)$
b414e258-7f9a-4c2a-aad3-5529aead66c2
sequences_series
false
null
Find the Fourier series of the function $\psi(x) = e^{-x}$ in the interval $(-2 \cdot \pi, 2 \cdot \pi)$.
The Fourier series is: $e^{-x}=\frac{\left(e^{2\cdot\pi}-e^{-2\cdot\pi}\right)}{\pi}\cdot\left(\frac{1}{4}+\sum_{n=1}^\infty\left(\frac{(-1)^n}{4+n^2}\cdot\left(2\cdot\cos\left(\frac{n}{2}\cdot x\right)+n\cdot\sin\left(\frac{n}{2}\cdot x\right)\right)\right)\right)$
b46190d9-ebed-4e4b-b32e-6167579d4c2b
differential_calc
false
null
If it takes $6$ years for an exponentially growing quantity to triple in size, then by what percentage does it increase every year? Round your answer to two decimal places, and omit the % sign.
The final answer: $20.09$
b4947d95-c61d-4939-9adb-119988a7c1c1
precalculus_review
false
null
1. Find the inverse function of $f(x) = x^2 - 4$, for $x \ge 0$. 2. Find the domain of the inverse function. 3. Find the range of the inverse function.
1. The inverse function is: $\sqrt{x+4}$ 2. The domain of the inverse function is: $x\ge-4$ 3. The range of the inverse function is: $y\ge0$
b55f6e2f-3e64-466f-9524-b9bcc1986c46
differential_calc
true
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
The graph of the function $f(x)$ is shown below. Determine the interval(s) where $\frac{ d f }{d x}>0$.
The final answer: $(1,4)$
b5c10639-0db9-4bd6-8b11-e245dac06e15
integral_calc
false
null
Solve the integral: $$ \int \frac{ 4 \cdot \cos(6 \cdot x)^3 }{ 9 \cdot \sin(6 \cdot x)^9 } \, dx $$
$\int \frac{ 4 \cdot \cos(6 \cdot x)^3 }{ 9 \cdot \sin(6 \cdot x)^9 } \, dx$ = $C-\frac{2}{27}\cdot\left(\frac{1}{3}\cdot\left(\cot(6\cdot x)\right)^6+\frac{1}{4}\cdot\left(\cot(6\cdot x)\right)^4+\frac{1}{8}\cdot\left(\cot(6\cdot x)\right)^8\right)$
b6943d35-373f-44b1-8886-587ed5656553
integral_calc
false
null
$\int \frac{ 7+2 \cdot x-4 \cdot x^2 }{ 2 \cdot x^2+x-3 } \, dx$
$\int \frac{ 7+2 \cdot x-4 \cdot x^2 }{ 2 \cdot x^2+x-3 } \, dx$ = $-2\cdot x+\ln\left(\left|2\cdot x^2+x-3\right|\right)+C$
b726f1ca-7edd-47ed-918f-b9fc63c3a1d9
integral_calc
false
null
Solve the integral: $$ \int \left(\frac{ x+1 }{ x-1 }\right)^{\frac{ 3 }{ 2 }} \, dx $$
$\int \left(\frac{ x+1 }{ x-1 }\right)^{\frac{ 3 }{ 2 }} \, dx$ = $C+\sqrt{\frac{x+1}{x-1}}\cdot(x-5)-3\cdot\ln\left(\left|\frac{\sqrt{x-1}-\sqrt{x+1}}{\sqrt{x-1}+\sqrt{x+1}}\right|\right)$