uuid
stringlengths
36
36
subject
stringclasses
6 values
has_image
bool
2 classes
image
stringclasses
160 values
problem_statement
stringlengths
32
784
golden_answer
stringlengths
7
1.13k
b750bd34-f50c-493d-b569-d3bc6ab886f1
integral_calc
true
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
Let $Q$ be the region bounded by the graph of $x=\frac{ 2 }{ 1-y }$, the line $x=-1$, and the line $y=\frac{ 5 }{ 4 }$, as shown in the figure above. Write, but do not evaluate, an integral expression that can be used to find the volume of the solid generated when $Q$ is revolved about the line $x=-1$.
$V$ = $\int_{\frac{5}{4}}^3\left(\pi\cdot\left(\frac{2}{1-y}+1\right)^2\right)dy$
b75b8718-0c2d-4333-9d47-a9a7a16878ae
precalculus_review
false
null
Find all the solutions of the equation $1 + \left(\sin(x) - \cos(x)\right) \cdot \sin\left(\frac{ \pi }{ 4 }\right) = 2 \cdot \left(\cos\left(\frac{ 5 }{ 2 } \cdot x\right)\right)^2$ which satisfy the condition $\sin(6 \cdot x) < 0$.
The final answer: $x=\frac{5\cdot\pi}{16}+\pi\cdot k$
b775a64a-639f-497b-b064-ba7db40ab3ca
sequences_series
false
null
Using the series expansion for the function $(1+x)^m$, calculate approximately $\sqrt[3]{7}$ with an accuracy of 0.0001.
The final answer: $1.9129$
b78a35bf-86eb-4ed0-8899-09518687eaeb
algebra
false
null
Use the values of $f(x)$ listed in the table below to solve the equation $f^{-1}(x) = 5$ for $x$. | $x$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | $f(x)$ | $8$ | $0$ | $7$ | $4$ | $2$ | $6$ | $5$ | $3$ | $9$ | To find the solution, we need to find the value of $x$ such that $f(x) = 5$.
The solution is $x$ = $5$
b78b640e-2077-4261-8d0d-6af62d82047e
integral_calc
false
null
Compute the integral: $$ \int \sin(3 \cdot x)^6 \cdot \cos(3 \cdot x)^2 \, dx $$
Answer is: $\frac{1}{32}\cdot x-\frac{1}{32}\cdot\frac{1}{12}\cdot\sin(12\cdot x)-\frac{1}{8}\cdot\frac{1}{6}\cdot\frac{1}{3}\cdot\sin(6\cdot x)^3+\frac{1}{128}\cdot x-\frac{1}{128}\cdot\frac{1}{24}\cdot\sin(24\cdot x)+C$
b7a0b462-28e2-47c0-be0c-1c233c09fe99
precalculus_review
false
null
Simplify the expression $\tan(x)^2 + \sin(x) \cdot \csc(x)$ by writing it in terms of sines and cosines, then simplify. The final answer does not have to be in terms of sine and cosine only.
$\tan(x)^2 + \sin(x) \cdot \csc(x)$ = $\sec(x)^2$
b7a66b26-e0ab-4533-a404-db2f9afeb3b0
sequences_series
false
null
Suppose that $\lim_{n \to \infty}\left(\left|\frac{ a_{n+1} }{ a_{n} }\right|\right)=p$. For which values of $p$ must $\sum_{n=1}^\infty\left(2^n \cdot a_{n}\right)$ converge?
$|p|$ < $\frac{1}{2}$
b800fdc0-a9c8-47b9-b98f-9c4ec5811709
multivariable_calculus
false
null
Find the equation of an ellipse with the following conditions: 1. The ellipse is tangent to the y-axis at $(0,3)$. 2. The ellipse intersects the x-axis at $(3,0)$ and $(7,0)$. 3. The axes of the ellipse are parallel to the cartesian axes.
The final answer: $\frac{(x-5)^2}{25}+\frac{7\cdot(y-3)^2}{75}=1$
b82a9cc4-bafb-4dff-b474-ea2287346a3d
differential_calc
true
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
Find values of $a$ and $b$, making function continuous and differentiable at $x=1$. The graph is shown.
The $a$ and $b$ values are: $a=-4$, $b=2$
b84018c9-fd9f-4ef5-917a-9ed1849998ea
differential_calc
false
null
For the function $y = (4 - x)^3 \cdot (x + 1)^2$ specify the points where local maxima and minima of $y$ occur. 1. The point(s) where local maxima occur 2. The point(s) where local minima occur
1. The point(s) where local maxima occur: $P(1,108)$ 2. The point(s) where local minima occur: $P(-1,0)$
b887d056-ce73-4520-a35b-d59f1198f8a3
differential_calc
false
null
Compute the limit: $$ \lim_{x \to 4}\left(\frac{ x }{ x-4 }-\frac{ 1 }{ \ln\left(\frac{ x }{ 4 }\right) }\right) $$
$\lim_{x \to 4}\left(\frac{ x }{ x-4 }-\frac{ 1 }{ \ln\left(\frac{ x }{ 4 }\right) }\right)$ = $\frac{1}{2}$
b8a1a55a-f36b-4033-9813-55d603b2edd9
integral_calc
false
null
Compute the integral: $$ \int \frac{ -2 }{ e^{3 \cdot x} + \sqrt{1 + e^{6 \cdot x}} } \, dx $$
$\int \frac{ -2 }{ e^{3 \cdot x} + \sqrt{1 + e^{6 \cdot x}} } \, dx$ = $C-\frac{1}{3}\cdot\left(\frac{2}{e^{3\cdot x}+\sqrt{1+e^{6\cdot x}}}+2\cdot\ln\left(\frac{e^{3\cdot x}+\sqrt{1+e^{6\cdot x}}-1}{1+e^{3\cdot x}+\sqrt{1+e^{6\cdot x}}}\right)\right)$
b8e659f6-36d7-4648-9a18-b9a397fa9c13
multivariable_calculus
false
null
Evaluate the iterated integral: $$ \int_{e}^{e^2} \int_{\ln(u)}^2 \left(v + \ln(u)\right) \, dv \, du $$
$\int_{e}^{e^2} \int_{\ln(u)}^2 \left(v + \ln(u)\right) \, dv \, du$ = $e^2-\frac{e}{2}$
b9549494-f051-4d1b-891b-874e88c55728
precalculus_review
false
null
Find the product $C=\left(-\frac{ 2 }{ 3 }-\frac{ 1 }{ 2 } \cdot i\right) \cdot \left(\frac{ 1 }{ 5 }+\frac{ 4 }{ 5 } \cdot i\right)$.
The final answer: $C=\frac{4}{15}-\frac{19}{30}\cdot i$
b95c92b9-de56-4e8a-8b1a-c7cd1d375bf5
sequences_series
false
null
Find the Taylor series for $f(x) = \frac{ x }{ (1+x)^2 }$, centered at $x=0$. Write out the sum of the first four non-zero terms, followed by dots.
The final answer: $x-2\cdot x^2+3\cdot x^3-4\cdot x^4+\cdots$
b9ac8e90-d4b9-4750-906c-54109d1396d7
algebra
false
null
You inherit one hundred thousand dollars. You invest it all in three accounts for one year. The first account pays $4\%$ compounded annually, the second account pays $3\%$ compounded annually, and the third account pays $2\%$ compounded annually. After one year, you earn $\$3650$ in interest. If you invest five times the money in the account that pays $4\%$ compared to $3\%$, how much did you invest in each account?
The first account investment: $75000$ The second account investment: $15000$ The third account investment: $10000$
b9ba91e6-fd9d-4131-9c7d-ba92a0947e30
differential_calc
false
null
Given $y = 3 \cdot x^5 + 20 \cdot x^4 + 40 \cdot x^3 + 100$ find where the function is 1. concave up, 2. concave down, and 3. point(s) of inflection.
1. Concave up: $(0,\infty)$ 2. Concave down: $(-\infty,-2)$, $(-2,0)$ 3. Point(s) of Inflection: $P(0,100)$
b9cdefb2-0696-45ba-a3d0-d4804c70d4f0
integral_calc
false
null
Calculate the integral: $$ \int_{-\sqrt{2}}^{\sqrt{2}} \frac{ 2 \cdot x^7+3 \cdot x^6-10 \cdot x^5-7 \cdot x^3-12 \cdot x^2+x+1 }{ x^2+2 } \, dx $$
$\int_{-\sqrt{2}}^{\sqrt{2}} \frac{ 2 \cdot x^7+3 \cdot x^6-10 \cdot x^5-7 \cdot x^3-12 \cdot x^2+x+1 }{ x^2+2 } \, dx$ = $\frac{5\cdot\pi-64}{10\cdot\sqrt{2}}$
b9fdcdf9-caa8-482e-b135-c2073d4e0c25
differential_calc
false
null
Make full curve sketching of $y = \sqrt[3]{x^2 - \frac{ x^3 }{ 8 }}$. 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) $(-1\cdot\infty,\infty)$ 2. Vertical asymptotes None 3. Horizontal asymptotes None 4. Slant asymptotes $y=-\frac{1}{2}\cdot x+\frac{4}{3}$ 5. Intervals where the function is increasing $\left(0,\frac{16}{3}\right)$ 6. Intervals where the function is decreasing $(-\infty,0)$, $\left(\frac{16}{3},8\right)$, $(8,\infty)$ 7. Intervals where the function is concave up $(8,\infty)$ 8. Intervals where the function is concave down $(-\infty,0)$, $(0,8)$ 9. Points of inflection $P(8,0)$
ba021e0e-5fd6-428c-91e4-fcd26bec895f
differential_calc
false
null
Consider a bank investment: The initial investment is $\$10000$. After $25$ years, the investment has tripled to $\$30000$. Use Newton’s method to determine the interest rate if the interest was compounded annually.
$4.492$%
ba6d988a-5f01-4dfe-a6c1-f85fb7f22f01
precalculus_review
false
null
Simplify the expression $\sin(x) \cdot \left(\csc(x)-\sin(x)\right)$ by writing it in terms of sines and cosines, then simplify. The final answer does not have to be in terms of sine and cosine only.
$\sin(x) \cdot \left(\csc(x)-\sin(x)\right)$ = $\cos(x)^2$
baea3a26-3788-4b32-b19e-931a1c4bed1d
sequences_series
false
null
Find the Fourier series of the function $\psi(x) = 2 \cdot e^{-2 \cdot x}$ in the interval $(-\pi, \pi)$.
The Fourier series is: $2\cdot e^{-2\cdot x}=\frac{\left(e^{2\cdot\pi}-e^{-2\cdot\pi}\right)}{\pi}\cdot\left(\frac{1}{2}+\sum_{n=1}^\infty\left(\frac{2\cdot(-1)^n\cdot\left(2\cdot\cos(n\cdot x)+n\cdot\sin(n\cdot x)\right)}{4+n^2}\right)\right)$
bba192e9-a029-4393-a68e-e42c6444ae52
differential_calc
false
null
Evaluate the limit: $$ \lim_{x \to 0}\left(\frac{ \ln\left(1+x+x^2\right)+\ln\left(1-x+x^2\right) }{ x^2 }\right) $$
$\lim_{x \to 0}\left(\frac{ \ln\left(1+x+x^2\right)+\ln\left(1-x+x^2\right) }{ x^2 }\right)$ = $1$
bbe52c80-dc6a-4752-8fa2-e540fdd12adb
algebra
false
null
Use the Rational Zero Theorem to find the real solution(s) of the equation: $x^4 + 2 \cdot x^3 - 4 \cdot x^2 - 10 \cdot x - 5 = 0$
By the Rational Zero Theorem, possible rational zeros of the function are: $1$, $-1$, $5$, $-5$ $x$ = $\sqrt{5}$, $-\sqrt{5}$, $-1$
bc1290d0-681b-468e-b494-3a277399c84f
sequences_series
false
null
Find the interval of convergence of the series $\sum_{n=1}^\infty \frac{ 3 \cdot x^n }{ n \cdot 7^n }$. (Use interval notation)
The final answer: $[-7,7)$
bc24c3db-73a9-4f4d-84c9-58dcebd518f9
algebra
false
null
Solve the following equations: 1. $8 s - (8 + 6 s) = 20$ 2. $34 = 2 x + 8 (x + 3)$ 3. $3 (x + 9) = 60$ 4. $2 (m - 8) = 12$ 5. $35 = 22 x - 12 x + 5$ 6. $6 (b + 8) = 54$ 7. $99 = 33 x + 3 (3 x + 5)$
The solutions to the given equations are: 1. $s=14$ 2. $x=1$ 3. $x=11$ 4. $m=14$ 5. $x=3$ 6. $b=1$ 7. $x=2$
bc3c0d6d-ed63-46d2-9537-1d1c3ad95d1c
multivariable_calculus
false
null
Evaluate the triple integral $\int_{0}^1{\int_{1}^2{\int_{z}^{z+1}{(y+1) d x} d y} d z}$ by using the transformation $u = x - z$, $v = 3 \cdot y$, and $w = \frac{ z }{ 2 }$.
$I$ = $\frac{5}{2}$
bc5b6d16-0655-4241-850e-6c54cc736d93
sequences_series
false
null
Consider the function $y = \left| \cos(2 \cdot x) \right|$. 1. Find the Fourier series of the function. 2. Using this decomposition, calculate the sum of the series $\sum_{n=1}^\infty\frac{ (-1)^n }{ 4 \cdot n^2-1 }$. 3. Using this decomposition, calculate the sum of the series $\sum_{n=1}^\infty\frac{ 1 }{ 4 \cdot n^2-1 }$.
1. The Fourier series is $\frac{2}{\pi}-\frac{4}{\pi}\cdot\sum_{n=1}^\infty\left(\frac{(-1)^n}{\left(4\cdot n^2-1\right)}\cdot\cos(4\cdot n\cdot x)\right)$ 2. The sum of the series $\sum_{n=1}^\infty\frac{ (-1)^n }{ 4 \cdot n^2-1 }$ is $\frac{(2-\pi)}{4}$ 3. The sum of the series $\sum_{n=1}^\infty\frac{ 1 }{ 4 \cdot n^2-1 }$ is $\frac{1}{2}$
bcc5b742-cc7b-42d6-98eb-9db904ab8078
multivariable_calculus
false
null
Evaluate $\int\int\int_{E}{\left(x^3+y^3+z^3\right) d V}$, where $E$ is the region defined by: $$ E = \left\{(x,y,z) | 0 \le x \le 2, 0 \le y \le 2 \cdot x, 0 \le z \le 4-x-y\right\} $$
$I$ = $\frac{112}{5}$
be0450d9-d002-494c-b831-25492d662296
sequences_series
false
null
Use the substitution $(b+x)^r = (b+a)^r \cdot \left(1 + \frac{ x-a }{ b+a } \right)^r$ in the binomial expansion to find the Taylor series of the function $\sqrt{x^2+2}$ with the center $a=0$.
$\sqrt{x^2+2}$ = $\sum_{n=0}^\infty\left(2^{\frac{1}{2}-n}\cdot C_{\frac{1}{2}}^n\cdot x^{2\cdot n}\right)$
be5b328d-cd61-45c8-97bf-93d2e3f5c525
algebra
false
null
Find the solution to the following inequality and express it in interval notation: $$8 (x-9) (x+5) (x-3) > 0$$
The solution set to the inequality is $\left(-5,\ 3\right)\cup\left(9,\ \infty\right)$
be642fd8-0fc8-450f-867d-eea4c7765a27
differential_calc
false
null
For what values of $a$, $b$, and $c$ does the curve $y = a \cdot x^4 + b \cdot x^3 + c \cdot x^2 + e \cdot x + f$ have points of inflection?
The final answer: $3\cdot b^2-8\cdot a\cdot c>0$
be8194d4-6693-48d6-a382-70e25ddc9b86
precalculus_review
false
null
Simplify the expression $\left(1+\tan\left(\theta\right)\right)^2-2 \cdot \tan\left(\theta\right)$ by writing it in terms of sines and cosines, then simplify. The final answer does not have to be in terms of sine and cosine only.
$\left(1+\tan\left(\theta\right)\right)^2-2 \cdot \tan\left(\theta\right)$ = $\sec\left(\theta\right)^2$
bea9777f-c66e-48e1-b32b-f2795b3f8c4f
integral_calc
false
null
Compute the integral: $$ \int \frac{ -12 }{ \sin(6 \cdot x)^6 } \, dx $$
$\int \frac{ -12 }{ \sin(6 \cdot x)^6 } \, dx$ = $C+2\cdot\cot(6\cdot x)+\frac{2}{5}\cdot\left(\cot(6\cdot x)\right)^5+\frac{4}{3}\cdot\left(\cot(6\cdot x)\right)^3$
bf49a8b7-ff89-4c97-86c5-94549ff3ce80
sequences_series
true
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
Find the Fourier series expansion of the function $f(x) = \begin{cases} -x, & -\pi < x \le 0 \\ \frac{ x^2 }{ \pi }, & 0 < x \le \pi \end{cases}$ with the period $2 \cdot \pi$ on the interval $[-\pi,\pi]$.
The Fourier series is: $f(x)=\frac{5\cdot\pi}{12}+\sum_{n=1}^\infty\left(\frac{(-1)^n\cdot3-1}{\pi\cdot n^2}\cdot\cos(n\cdot x)+\left(\frac{2}{\pi^2\cdot n^3}\cdot\left((-1)^n-1\right)\right)\cdot\sin(n\cdot x)\right)$
bf6ce9fb-0a58-4dab-8385-8e9e64099565
precalculus_review
false
null
Calculate $E = \frac{ 1 }{ \sin(10) } - \frac{ \sqrt{3} }{ \cos(10) }$.
The final answer: $E=4$
bf760c7e-8f0f-4e8f-8add-9a1541343d1a
multivariable_calculus
false
null
Find the equations of the planes below: 1. The plane through $P(2,2,1)$ perpendicular to the vector $\left\langle 1,0,-1 \right\rangle$ 2. The plane containing the line $\left\langle x,y,z \right\rangle = t \cdot \left\langle 1,2,3 \right\rangle$ and through the point $P(2,1,-1)$ 3. The plane containing the points $P(2,0,3)$, $P(0,4,1)$, $P(-1,3,3)$
1. $x-z=1$ 2. $-5\cdot x+7\cdot y-3\cdot z=0$ 3. $x+y+z=5$
bfd92140-56a4-4cd9-a0d4-c99aef34eb24
algebra
false
null
Use the Remainder Theorem to find the remainder when dividing $5 \cdot x^5 - 4 \cdot x^4 + 3 \cdot x^3 - 2 \cdot x^2 + x - 1$ by $x + 6$.
The remainder is $-44791$
bff02121-9696-4fd4-9951-072d213b75f0
differential_calc
false
null
Evaluate $\lim_{x \to 0^{+}} \left( \left( \frac{ \tan(x) }{ x } \right)^{\frac{ 1 }{ x^2 }} \right)$ using l'Hospital's Rule.
$\lim_{x \to 0^{+}} \left( \left( \frac{ \tan(x) }{ x } \right)^{\frac{ 1 }{ x^2 }} \right)$ = $e^{\frac{1}{3}}$
c1776c95-1585-4f95-8a20-535567d00fae
multivariable_calculus
false
null
Evaluate $\int\int\int_{E}{z \, dV}$, where $E$ is the region defined by: $$ E = \left\{ (x,y,z) \mid -y \le x \le y, \, 0 \le y \le 1, \, 0 \le z \le 1-x^4-y^4 \right\} $$
$I$ = $\frac{113}{450}$
c1c7b5c8-ba37-4871-9cc7-79a575e299a1
integral_calc
false
null
Calculate the integral: $$ \int \frac{ 3 \cdot x + 4 }{ \left( x^2 + 1 \cdot x + 7 \right)^2 } \, dx $$
$\int \frac{ 3 \cdot x + 4 }{ \left( x^2 + 1 \cdot x + 7 \right)^2 } \, dx$ = $\frac{\frac{5}{27}\cdot x-\frac{38}{27}}{\frac{27}{4}+\left(x+\frac{1}{2}\right)^2}+\frac{30\cdot\sqrt{3}}{729}\cdot\arctan\left(\sqrt{\frac{4}{27}}\cdot\left(x+\frac{1}{2}\right)\right)+C$
c1fc8501-1c68-469f-a8b9-22b27702d1c8
algebra
false
null
Use Descartes’ Rule of Signs to determine the possible number of positive and negative real zeros of the following polynomial: $p(x) = 2 \cdot x^3 - x^2 + 7 \cdot x - 1$
The number of positive zeros: $1$, $3$ The number of negative zeros: $0$
c221a7ed-a23f-41f3-89c0-2b6faf6228de
precalculus_review
false
null
Solve the trigonometric equation $\sec(x)^2 - 2 \cdot \sec(x) + 1 = 0$ on the interval $[-2 \cdot \pi, 2 \cdot \pi]$.
$x$ = $-2\cdot\pi$, $2\cdot\pi$, $0$
c251e922-18a0-40d3-a506-3a4d6f32a485
algebra
false
null
Write an expression for a rational function with the given characteristics: 1. vertical asymptotes $x=-5$ and $x=5$, 2. x-intercepts at $P(2,0)$ and $P(-1,0)$, 3. y-intercept at $P(0,4)$.
The rational function satisfying the given conditions is $f(x)=\frac{50\cdot(x-2)\cdot(x+1)}{(x+5)\cdot(x-5)}$
c2a16bfe-a68f-49e2-a46b-b76210e6995a
differential_calc
false
null
Make full curve sketching of $y = \arcsin\left(\frac{ 2-5 \cdot x^2 }{ 2+5 \cdot x^2 }\right)$. 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) $(-1\cdot\infty,\infty)$ 2. Vertical asymptotes None 3. Horizontal asymptotes $y=-\frac{\pi}{2}$ 4. Slant asymptotes None 5. Intervals where the function is increasing $(-\infty,0)$, $(0,\infty)$ 6. Intervals where the function is decreasing $(-\infty,0)$, $(0,\infty)$ 7. Intervals where the function is concave up $(-\infty,0)$ 8. Intervals where the function is concave down None 9. Points of inflection None
c2c64c79-64e8-4c01-8d35-17ac590004cd
differential_calc
false
null
For the function $y = x \cdot \sqrt[3]{2 \cdot x - \frac{ 4 }{ 3 }}$ determine the intervals, where the function is concave up and concave down and points of inflection. Submit as your final answer: 1. Interval(s) where the function is concave up 2. Interval(s) where the function is concave down 3. Point(s) of inflection
1. Interval(s) where the function is concave up: $\left(-\infty,\frac{2}{3}\right)$, $(1,\infty)$ 2. Interval(s) where the function is concave down: $\left(\frac{2}{3},1\right)$ 3. Point(s) of inflection: $P\left(\frac{2}{3},0\right)$, $P\left(1,\sqrt[3]{\frac{2}{3}}\right)$
c2d80e7a-26ff-46c4-a9ac-1d3f772e77ab
precalculus_review
false
null
Solve $\left(\sin(x)\right)^{10} + \left(\cos(x)\right)^{10} = \frac{ 29 }{ 16 } \cdot \left(\cos(2 \cdot x)\right)^4$.
The final answer: $x=\frac{\pi}{8}+\frac{\pi\cdot k}{4}$
c3062353-e56a-4397-bc22-1ea7e9e7fc72
differential_calc
false
null
Where is the parabola $y = x^2$ closest to the point $(2,0)$?
The final answer: $P(0.8351,0.6974)$
c37c3f43-24ad-4906-a400-c14ace455f14
multivariable_calculus
false
null
Use Lagrange multipliers to find the maximum volume of a rectangular box that can be inscribed in the ellipsoid $\frac{ x^2 }{ 9 } + \frac{ y^2 }{ 25 } + \frac{ z^2 }{ 4 } = 1$.
The final answer: $\frac{80}{\sqrt{3}}$
c38d8b60-f7e8-433d-ac1c-3d3adc457a9b
sequences_series
false
null
Give the first six terms of the sequence and then give the $n$th term. 1. $a_{1} = 1$ 2. $a_{2} = 3$ $a_{n+1} = 3 \cdot a_{n} - 2 \cdot n - 1$ for $n \ge 2$
$a_{1}$ = $1$ , $a_{2}$ = $3$ , $a_{3}$ = $4$ , $a_{4}$ = $5$ , $a_{5}$ = $6$ , $a_{6}$ = $7$ $a_{n}$ = $n+1$ for $n \ge 2$
c3b0d303-3a1c-431d-9b8e-84e4d9d8a53e
differential_calc
false
null
Given $g(x) = \frac{ 1 }{ 3 } \cdot (a+b) \cdot x^3 + \frac{ 1 }{ 2 } \cdot (a+b+c) \cdot x^2 - (a+b+c+d) \cdot x + a \cdot b \cdot c \cdot d$, simplify the derivative of $g(x)$ if $x^2 + x = a + b$.
The final answer: $g'(x)=(a+b)^2+c\cdot x-(a+b+c+d)$
c47c3a9b-3f0f-4752-b421-b9a8a197b1e9
multivariable_calculus
true
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lz58695557Bg4c+Oc//7nBCZRdVOxYAcBpG7xNHDlNpVLFxcW8rQ89+AABoYE2aN5i7/emTd+nS6eCIoQEGdMlMWR+CM0mTXWI5csz1dXVRpOUyvf9jxd8yo+yL75YyA/VLxcuXbthk3A9pdxmRcW6qMRREGRgtAJJYdNlpe3ati4tKtp338577r5Hx05tu3bbK9BIObCA1ihwQIBCPoIFSAJZEEEJQMJn61hACQAQMIIg2GYmghBkrZAOgFRB+vXX3yhMN3gSC7t4xo4dC+Dmm29uHHV0JpMpKyvjZqsNJ0+JK05+97vflZeX33rrrTt2FfXXyMav7/tlZWUTJ05EzEHZcCCi2267DcA111xTJ3NmB66F9RKRk9d13ai4T8Mh0oaPGzdOSnndddc1jiJNa11SUvLOO++kUim+RDmMxlw0ZcqUoUOHcvvLIAj4yBx00EGHHnro0KFDTzjhhJwyt6G3kuNZnNsAoKCggHM5HMepqqriQX0YhvnrwMJqT0lPybDqm0N7dwpNLlgucxKkGuR/kHtT4qJlpwJH1vDRMYfuBUBbKHmEAAwhNHAdVFRh5cpvN5aXr16z7tv1G75avWbdpvLlK1etXvPtkrUbvq4Og0A7sz43ZHXgO4r22K1F2zatD+iyb4e27dq12WvfjnuVFsNTcABFIEBJ9iVbCKkEDBBqWAFXQUAJASKWsluyJJVjLaSUQTYsTBc0tPuMg+CI+emiC6VB18snGrWTuHdgg1W+ySNZj+u6mzdv5qSgHbL8rSHKPE6lUplMhkeCbNQ36HrZKONDyoiSoHbI8rl7I9tZHJSLAnQ7ZPlbQzwXkaPKfGU2wno5iBRlRrCRV0dcDKBVq1ZDhgwZNGjQD3/4w5YtW7IzCvmnZmNYoPvtt18QBPPnz+/evTtPnD9/vtb6yCOP5I/RHa516Loyn0xkFaAUNm0uL21WSiDA2pwNKgFIUgCkgLXsUBecX8mZRFKJMDRKqZTMTUkpwbtbWISyfXZXzu4W+3AMyCeMu+0h6t3twovOXbZq/eLlK9et3zhz1hwpxOeffrb66283biz/7NMvrQ7IGCVRWlLQpVOHdm1b9+h+QLcD92vdqpknISC1BQGOhONAcIDJwhGQQoEgJARJE2rlOtFeNLTvLIqoRmPMiFIbB3VStnfU/nIAJ55YxaOtRot7MFhBxS6phl6ptZb9dLzLUcLlDlk+mzVsdSLPzjvQ5bI1ROVLAESJlY1QzaSOFc97GuXyCCE6duz4xz/+8ZhjjmndunWU7xMdebb5nEYwlZVSxxxzjOu67777bq9evXjM/vLLLwM49NBDM5mM67ocRHIcx3VT/NzJZnVRYak1EALNS0qDQHueAwgZ18tz4pE1koXxVkghYEkIpaSAJc9REAhDI6V0pCALSwRopVTKAQALEQRB2kulBI7tdyCks08ZWhe3HNa9pQVw9hCWOi1avLG6Ojt/wSeLFi1Zu2793I8/W7exatOChTPmL3r6lcmB0V461a5du27de3bp2HroId13a5ZqXgIJwEIKCBEpoCRZKMeBhTG4dfxtxpBSDXuB8hPVGDN8+PD4x0aoWnTrrbeyb4sHaDt2FB8Z0WwSEtGAAQMaQdnOoTB+P2bMmGw2m06nG+F4WmuPPPJIY0xN4YgdyjKpVCoq3BWxMzd8bFBEUjCt9ZAhQ4io0fK7tNbjx4+PtoHHMVF6Utu2bc8999xUKsWOZqVUJpPhETPbqhwmbaRUztNOO23KlCnPPPPM4MGDp06dOmLEiFGjRt177738XOWnqDFGSmUs+FKUwiMbEEGIWGWlSB5E+QevDaAESNgwlK4LCwgBKUCSrBX557M1kOy2zCs3+VtrjFQKRBCKrBbS4cIj2gSO8ghS59kvMJAKAKpCrFodLF6+cvGylXPnL1i0bOWm8gpDVltIk3V0RauWzdq2bdtln3179eze/cCue+7huQKCIq9ojltzT4Et8Qnl6pXEkU++EjU2OLZSiGoLC6w5yzZGYQ3oCY3WGGfMHW4hRnVqGmLhW0OUBRjxZuO4lXkH4+vasbscvxN5vxrhwRBPyY0eCY2WzRn3KUWZrPH3LGyKT2TwkSGiRqrGVFVVNWLEiKlTpzLNH3XUUX/72988z4u75+ocMiEU0b8T2axNNJTLMLfaSEdFTzMm4nxhylzyFl8cbEQAsrq6srCwmMgQCSkRBJqfw0JKIhhjpSMBhAYyn0/PvobNlVi4eMmcOXO+WLJsweJlq9Zu8LNhYWEJtAwCvdcerfbft8tBvbof1Ktr1/3THmAN0goKMDpwVP5hG3PyWlgJa6xRUgnAkoUVUinYqKyfgFDakIHgK9wSpIAAdBik3JwTR0rHhFo5jtFaOQ6EDfyMl0qRtYasozxAaq2VckA5OrWGlMqNjqMBcuMUiIzfNvGiR1F9oCgUGd3Y8Uz/KD+nvo0WmRg8czRY4+VH7+vM36A7Gx3h+sXJ+G90BOI0jdh1G93/8d/GM9nr70XjFKziTYpfM1GYqM6GRf5xAPGqtaj9lOIhdvzJEQW7sKNr7kUXPHvYee2vv/76vHnzWrZseemll/Jsd999d2Vl5f777994xUQqKio2b968ePHiNm3adOrUKaq5idjFFP/h/x5w4BuPVSbIn8V4EQHKV5NkazxyKsWHaUJQxNGBH3qpVGS4WWstcZ5Pbo0hkAG+qcKixatnzl4w86N5ixYvz1QHvF4TZIoLnG4HdBrQ/6C+B/Xo2KFVsQdr4CpoDb7YjIWSELDaBl6uVCiB8q4oIhgNpawlAqRyDUAEKWAIIP4tSZA1RggSUoIcHYaO60JAh77jurmPkHVuJ2tgyTrOFqr2NoKFFd3/bI9Et1Z9omQvUPz+jKuv63C9tdb3fVY4Rh493il2YzF50ZZKaTQCoq3NP8WBvHciSompU28NsUpX0XZG1y2HlSKbjsG3QOMMjWMmC3GcmjtNIHa7IVbStE45Tr434wuJjG7+lk8Qn77I/KpTFuR/Qdz6jhhp+vTpQ4cOtdauXr26ZcuW559//tNPP921a9f333+/kQoqR0/LIAgib0udb+v85H8n0BozWwi+5vjeYCNFa51Op+PcHbe2YptkI1dAfqLMZDLpdDraZm0o74oWrBYILTQgJLLAZ19+s+DTRZ8vWjJr9vzly1d6XkpAVVVlysrKuuyz76F9D+7Rbb9DDtrDBQTAf8nalJQCMIZ460JtALiuAnTWzxakUtYYIpJSCemw3U2EMLReSlptpOIifSEcTxvtKM8Pdcr1QAhDOA6Ichml2milhNZBKsUNqMHFqKqrq5VSdaiqQcH3W6Rejk/nieyEirNbZLygdr1hPu8cTY5iaFGlMo6WxFdRp8pnIyC6ttnYyT1iYx7qaAsj6q+oqCgpKUG92p31Kzpz9JxDC1GMq3H2Mbrd4kZ9fGJEnciTlM2Xs0PtAld8HHjvOPAdfcULrG+k78BdiL8JgmDYsGHTp08/++yz+/fvf8kll3Tt2nXGjBnpdLoxCDSyAeORrPqbWwf/I4HWGQfFVxeGYfxRHJ8nulhrnpZkcvOk08hduynUtppryuMRYAwgIAApIcClR8L837Xr8fEnCz/85+wF87/4es232WzG9YRS5Ejq3aPrgP6H9uy6/wH7tnQBY5Dig0Q5PylLSRXHywDAhkHgup4NQ6lcw+mSnmeCQHkeYGEthLCChHAsWSmcmo3M7bhNpaQly6WWw8B3PQ9QWtfktzRO8dA6iEQtzCw8MTrgfEfliicoVWc8jto3bZT+FPdI8Gz8FLT5ngjxQWIj+ODiFjG2FBHiKXxxxm3SCJxEEDeXeAfZMqi/xkbzEcdHLUyI8TrQDE7q4+cBIzoC/PN4peo4qxJRNpuNHhh1Hjb/O+JRrEjm4brutGnTjjzySD7mJSUl8+fP33333RuDQNkQiHLO6nj9sXVdy/9IoPHhwOrVq5csWZLJZIqKitLpdDab9TyvX79+0dBv9uzZr776ahiGp556as+ePeM30pJFiydPnvzNt2v322+/U045hRced+JQPjMaIj/ctzzshhVkYVhtZWAFHAP4Gp4DAaxYGX78+Wcfzvlw+j9nrF9XoWRaIkWkWjRv2ffgXof27XNw73333h0CMBopBSUgiRAK4cBoKBcA1n67dtHCz3p271bUrBBkEYZwU7BiQ3nl3199Y/mqr9q2bXv00cP32nMP5DVeQuD551/8/LPPdtutxTHHHNOmzd559rE6DD/7fNHLL7+czWZ//OMf77PPPmys1XnkNAQoX0nXcZy4O2zDhg0sgGvZsiXyd9fHH3+8YcMGkUcmkznwwAP33ntvHggHQfDGG2988sknxcXFxx9/fMeOHSnWqmH+/Pkvv/yyEOLUU0/df//9efp39cCYNWvWyy+/rLXu16/fcccdx5erEMJ13U2bNr300kurVq1q1arV6aefXlxczKUkmO5ffvnl2bNn77333scff/yee+4ZGdoA5syZ8+qrrxpjjj/++IMPPpitUeavxmx2xOv6+OOP//rXv3qe17NnzxNPPDFynnz55ZfffvttVI7a87w99tiD9Y58pb3++uv/+te/dtttt6OPPrpLly7IGzrW2s8///y5554johEjRvTo0YN2aE2ACBEpRybwKaec8uabb4ZhOGvWrD59+vA+5giu4RAEAb+pqqpiBxblnSO5nPE86nwEdsC28dr79+8PIF5Zevjw4ZlMhoiMMeeddx6AXr16sUz1wgsvjLZwwoQJEmLvvVodccQRnuftt99+FRUVvAtRLfSa7SciSzYk0kSGPxORsRRYylrKBpQNSWsiTeQbCjT5RJVE5USfrql+YfInP7np4Z7DLupyxPn7D7yw+7BLDhh8zlFn/uqux1+ft2LzJqJKogxRSGQt+ZoyAU1+7/3mzVsIYPLb/yBdSbZaV60nG8ydM6ugsLhsj737HDqgWdkeZS32nDvvk6wfBqFZv3HDQYf0gcBh/Q7u2KktBCZMeMKakKwmS+edcy6Anj179urVC8D555/Ph+h/PxH/Pnh1fJCnT5/evHlzAO+9917uIOflzXVwyy238Azl5eW9e/dWSvXr169Vq1aO4/zpT38ioiAIjDHnn3++67q9evU68MADhRDnnHMO/0prHRXHa7Td7N+/vxCib9++AwcOBHDooYdu2LCB93HWrFktW7ZMp9NDhw4tKCgoKSn56KOP+Kvy8vIePXqkUqkhQ4a0bt0awCOPPBIdsfPOO08pdeCBB/bs2VMIMWrUqOgq9X2/EfYrujvCMBwyZAhfToMHD3Ycp2vXrps2bSKi6CHB547p7ze/+Q0fFt5BAAMGDGjfvj2fQb5brbXnnHOOEOLAAw/s1auX67rnn38+1+7cUdvPsUq+HuKM9Oc//zmKQD722GPRGhucQDk+U2fKFmerM/1/J9Dq6mq+G4cOHXrEEUfUX7Ux5t133wUwYcIEItJaP/PMMwDefPNNItq8eXNxcfHZZ5/LP5o//+Pddtvjhhtuin5rrSUyRMZabUxorSYylsiS0TbUJmspIAqJQqOz1vhEhizZiF4NBVmqqjJMqZU++UQZon9+tureCa/98Jxrux15Tsd+Z+535EX7Druw6wmXn//rZ/7yz1XfEG0gWmdozG9/V9Ks+VU/u7wA4p/vTSFNFJLRlM3SgMHH9jp4wDfrqzXRuvWbe/Y4+LBDj+Ctvu76X7bcrdn8BR8RZS1lzjn3zOKS9ObNm7TW778/A5BPPDGBd/CRRx4BMGXKFL52GxpReZtsNstTbrzxxqKioquuuspxnLfffpun84XLjBllCUcgojFjxhQWFs6ePZsXctZZZ7Vo0aKiooKIuIz3hAkT2Op54oknAEycOJGIfN9vZAK97777hBBs7BPR3LlzAVx55ZW8FwMHDuzRo0dlZSURVVVVcQEL/uq6664rKSmZO3cuE+LIkSNbtWq1Zs0ayhf+ePLJJ/lA/fWvf+UzaK3l49Y4z0I+kvfcc4/jOM8//zyvd+bMmUqpyy+/nOeJP/N4/kwmw3t0ww03lJSULFiwgO2tiy66qEWLFuvWrSOit956C8ATTzxhjAnDcMKECQAmTZq0Y7e/Phe9+eabAFq0aPGrX/1KKdWmTRvebGNMgxNodJVT7DnPp7OO+Vnnh/8jgUZGLhEdccQRo0aNovzNFp9hxIgRXbt2jTbJGNOzZ88f/ehHRHTXXXdJKTduLCci3w+NoSuv/HlRUUl8+yPezDEpBZqyhjKWAqKAbGBNSEaTpdwrNyNZnTdRLZEla3JvQyKfqIqokmjxRnpx2pKfjHuy94lXdRhyQaejLmk75Nx2g884d/Tvn3p35ikX/XzB4tVvTp4hRMHEt6daQ1pToGnux0uBor88+6omCjWRpddffU0Bc+fMIjLNSgquuvKn2mSMzRIFm8rXQeD3v78nDMMRI07q0aMX7xefpp49ex533HHUiEYonxQ+TVdcccWKFSveffdd13WnTJkSHXbf94UQjz/+OOXvvfgPS0pKfvGLX0TP7I0bNwK4++67rbUnn3xyjx494lda9+7deVwZLYQLPzfCnj766KOjR4/m98yhgwcPHjBgABEtWLBACPHSSy9R/si/8MILAObPn2+MKSsr++Uvf8k/McZs2rQJwF133UVEJ510Ere8jXand+/eJ554In9snCdEdHgfe+yx6667Lv7VwIED+/fvT/lY2aOPPsrT2RbhUxaGYWlp6VVXXUV5k3ndunUA7r333jAMTzrppO7du8fX1aNHj5NPPnmLNtl/h/jFwAd/1qxZLVq08Dxv5syZWusOHTpIKfnyo0bIhY8qlSKWPsXWe9z7ucPd21G0imMRnTt3Rqx9SOTq+uijj4YNGxZtm5Sya9eu//rXv8Iw/PTTT9u0acN+bs9zAPTo0aO6unrJkiWdOnVCrlZxLb2LgFA5kRPr5WVuryg2DSBwzicIsKKm3z3/UgIeYIG9SrHH4R2PPqIjYdTni9e9+cbEKdP/uXotTZ340QdT5hrQleP+2LrNXlTatrqkZbWEAhzgww/edt3g0D4HKgLBAnb//doL4PNPPm5e0qyiInNQn8OUSHOOVrNmLTt26jRz9iwSdt6C2ezriBzWffr0YaOGGquKKAfcWd1yzz33hGH4+eef86WMfOMzDhDtu+++8SY2fGZXrFhRUVHB/gcAYRg2b968ffv28+bNE0L885//HDZsWPxK692796RJk1g1FY9yUMPHW84++2y+RKWUrEtZuHDh8OHDtdazZs0iooMOOog5QkrJezRnzpyWLVtu3Lixe/fu0aaWlpa2b99+/vz5PMOQIUOYTTi00r1796lTp/LuOI3S0TrShJ177rk61kOQiJYtWzZ8+PBI1cv+B6Yhme9Wsnz58srKSn7OsTO0efPm++6770cffaSU+uijj6L8b3aJ9u3b9/XXX9+BJ4uPEkfntNbz588/6qijNm3a9OCDDx500EEARo4cOX78+PHjx59wwgktWrRovG7ajY+ItWfMmDF37tyuXbuy5+Wss87KZDLs41i3bl3btm1Z5MTlqQ888MBFixa5rrto0aJOnTpxqqXvh0Ro3749ES1fvnwb68y3HJE5Pqx3ZinXmTlHqvneTbGuy/wipAQKBFyCR+jVebdrLzvjtb/e89yER6//5VWdO7QnoqUrv54646POfY+44/7HHn5u0pJ1fgZY9W15qKlj505kIaSEoE777KMcfPLJJytWfZ1OFbZp0yEILAhSKGOw5x6t1qxZq5RaumxZp307aR3wpQOgZcuWXEKtEeIqrFNhOUR0/7uu26xZM/7IdooQ4r333nMc57777tt33325dOOYMWM4mrR06VIAe+21F8/PZLH33nsvWbIkCIJ169Z17NiRd40ZuXPnzmvXrqVYMJPtoEaIVkdJk7yu+++/f+3atVdccYXjOIsXL/Y8b/fddwfgOE4QBJ06deIL8pNPPvE8r23bto7jbN68mZUD++yzz+LFi4lo6dKle++9N5MRx3A6d+68YsUKVvxwDktD7xfTN//lJxNPvPvuu7/66qtLLrnEdd2JEydaa1999dUOHTo4jrPHHnvcfvvtfAF8/fXXxhi28ky+dPFee+21Zs0aIcTXX3/dpk0bk68MaYxp1arV2rVrd2DtO77qorXvvvvuzzzzzD//+c8LL7yQZ7jqqqumT59+//338yXaeI2YGxn8oONr1Fr71ltv3XXXXfvvv/+yZcsuv/zyzz777N133+UayY7jcDQwnU7z3cUiDBaRGAsAqZRLhHQ6zXHSbazXQOatNZuT2ItYL2WCAKTIEaZAvh6fsJAGsAQOkUghmIsdyTmgBBCsRqc2cvfdep52Yu/1lfjgn3Nffv2tGTPnr9uYffDxl+6+7+le3farLl+PglY+4CgoAuASHF/DLWiWyeqMHwShdlPSElinX1hYuLm8UkDBwnVTjpMTcADYc889Ubshc8OBzY1I9cIs4Ps+N3vgKcw1LE1dunTp6NGj99577w8//HD8+PGLFy/+85//zIsqKioCwGfKdd2SkhLWXfDfuHKInYMiX1gejWhrR+K5MAyffvrpK6644pFHHunVqxcHMQCwxCqeds0TeYMBNGvWDAA/+FOpFE9U+aYDXGooKhjKpNAIUfgoTstbxVLCv/3tbzfeeOOf/vSnPn36RNK0KVOm3HLLLZ07d3777bevu+66Tz/9dMKECZEylG1zYwxXbquoqND5tlpRBoHIJwvtwAcDqzKQNxr23HNPtpSRf+iWlZUddthhUZnwXZZAWUQWFSGNFHNE1Llz54EDB77yyitnn312ZHtGrWaqq6t5YlVVVfPmzTmnk6R0HFlRUSGE2J4auZZRnysQlTdoBIFEzd/cHOB2zRZCCxgFCRiCAhwBa4islVIJAK6L0OjmaYeAvYpx9BG9yorTf/vDvZeNvX3j5qoPZnw0Z978opS3f98Bp59/3VFHDvzBUUfu0cJVQkAUCbfYKSiBUF5xsSEYiyAIigu8bDZIp9PWIpUqrN6cZY+H53nGmA0bNvBhaZw8ziifhIvfIM+VSilOW2A55OGHH84byZR65JFHWmu5ZR6X86msrOSLm7mYMwJ4Layxj/NIHW9SfbllA4GvImvtqFGjJk6c+Pjjj59zzjnMqpw1hHzRCuTHxZFVjtqtgLlgJS+Wj0xEwVFqOdcwbJwqXOwfS6fTLAC65JJLXnrppXvuuWfUqFFsMg8aNIidjCz1HzhwYGFh4Q033HDzzTfziJ7PV+RUEUJwqWPecWbPqqoqrgseVfPcgdvPxzbaQg4rRQaWzLf5QuP0RPquwIZ9Npt1XTfSGxtjBgwYIIRYuHBhGIb77LPPkiVLWOGUzWaVUuvXr2dDoEuXLlzF3fMc5UhtzbfffmNMeOCBB8acO/neyfmXyrf6dGoPzMG2pqj1lwTIATmsundBKVAByAUpZH1BIShUykrHWGMMkdZwpSMMdMZIg+YpuNkNUpSPOHyfR2+7dPa7j/32hp/26daxOqj+9Otv73n6tX4nnP3zmx/801Nvo3jPvToesFubjlDegi++MAJCoaDA87VZs+br3r0PMqFt27r9mq+/iYtLVq1a1aVLFx5FNvTJ4jE4Z57w2isqKgAUFRWxTgV5duPBAQ9+2TIdNGiQEGL58uXt2rXTWq9Zs4Zn4J+sWrWqR48eQRB07Nhx2bJllG/tx94YdmfXKRixRaXUjkU2m62qqjrkkEPee++9KVOmnH766VprZtX27dsXFhYuWbKEz0UYhkuWLHEcp1u3buxuWrJkSWSwSykXLVrUt2/fbDbbrl27b7/9lo+eUiqbzS5fvrxnz57Mp42mAI2s4Orq6uHDh7/00kuTJk26+OKLc4yTb8SSq6fpOGEY9u/fXym1du3a9u3bA1i6dGnkRwqCYNGiRay7bN269fLly3nhRUVFUspvvvnmwAMP3LHnK14kgTfY8zzOTYhufHaJWGt3WQKNhvBCiBkzZixfvpyzCBzH4btozz33dF23d+/e77//PgDO3/B9/7XXXjvggAOklEOHDl26dOkXX34BQButpHrrrbfatWu3xx57bOta5FOZ71kfTa1pPx/7i1zCkKUc2TqAC0rBpoRXDLjQlvih5wiphHJBBFikU8oREASdLRdhdQH8FLQXZk46tv+Nv/zZilkz9uvc4YD9u6QLi6Z+OPueB5/oetDhH83/YtXaTS3ad3n/oznVGr5FdWDWfPPtkiXLenTv6nmyf7/D3pn4FvJXttZ6+vTphx9+eHV1dSPkUEdGBDcsIKKSkpIgCCorK6NiphwVXbZs2UsvvcSXL28q31TNmzdv165dhw4duEo8X+vLli1btmxZv379PM8bMGDApEmTmHYBCCHefvvtgQMH8u0n8q1h0fBFWgGk0+lLLrkklUotWLBgv/32S6fTUSD4sMMOq66unj59ejSEnzp1qjGmT58+HTt27Ny5M+8g254rV65cuXJljx49PM877rjj3njjDe41wqt45513+vTpw/vVOJY1Szh4Xb/4xS9Wr1792Wef9enThxU4PM/atWufe+45AKy4dF33yy+/5Adbp06d2rZtO3ny5Gw26zhOJpP55ptvvv766wMOOCAIgmOPPZbPIPIemL///e/du3ffgc8GyudcGGM43ylifABshLLZm0sI+u+C/Y0A7AghPRGtWbOmsLDw+OOPLy8vJyJr7ciRI6WUCxYsoLw28LHHHiMiY8x9992nlJo0aZLWury8vEWLFj+57KeV1VWW6KNZMyFwy5jRfFnnlm7rvXIypVrf6+jLWj8xZA0LRYlMrW8sGVPzE2ut1gELSwM/Q5asNpnqSiIzdcpkAUyZMiUItDY5FVT/YT/cr/fhqzbpL9YG4x57a49DTuk4cFSnAT/uMvjM9occ3+6gY96bt7KKKEt0wklnpgtKNmzYQGTee+etAlc+9ujDvJm/+c1vpJSsYG8EZQ+vgtU5vu9HgrNp06YJIaZNm8ZaTiJ64403XNcdN24cEVVUVGzYsKFHjx6tW7fmAzV27NiSkpIPP/yQlzZixIjS0tJ169Zprd977z0Ajz76qLXW9/3f/e53UsqJEyfyiqLoRx3ZcgPh8ccfB8B61To6cGPMUUcd1bNnT26yVl5e3qFDBxYAaa1vuummli1bzpw5k9nnuOOOa968Oed3sEzyqaeeIiLucYK8TLK+cLBBYa19+OGHAfBdFmmDeDPefPPNoqKim27KSarXrl170EEHderUiZu7/eY3vyksLJw3bx5/+8Mf/jDSgU6aNElK+eCDD/KOPPDAA47jcHPfHbXlddIN4h95L/ICcAqCIJPJ7MoEGklBn3zySQAtW7YcMGBAhw4dkFfOs0T87LPPFkL06NGDxSLRea2srHz66ach0KFTxyHDhkJg8NAh2tamkq0RaE4WWvubmp8YsoaMIRvG5s9RbZ1X/odMtQHL8qdOmewooSREbsQhIVzHLfADqw3NnrOgeVnLkpLSw4cegxYdi/ft9+zUL2+87/khZ1x9wMAz9h9werfBZ5x03g37H/rDwpb7PP/a5HzylD3nnFEAunU7sFevXlLKW265RWtNlnfF1NlUG9vCes+G+A5vcdoWEA/gTps2rY5poPKly4nozDPPFEK0atVq2LBhJSUlpaWlCxYs4K/WrVvXrVs313UHDhzYpk2bsrKyl19+ORIjsxuud+/ePXr0cBznxhtvzB1cYyLebBy95KBBg6JdcxwnXleJiD788MPS0tKysrLBgwen0+mOHTsuWrSID86mTZs4Ueeoo45q165dixYt/v73v0f3+bnnngugd+/erLkZP348xXITGgd8MIcNGxa5niPjNyq4d/rpp0sp27dvP2jQIJYcRLkPq1ev5gH74MGD27dvX1ZWxgMOPkGjRo0SQvTq1YsPAktNd+wDPhLSR5dEtPa4ujyXI0uNFXb8T/E/5sLb2oUhFi1aNHHixK+++mq33XYbMWJE+/bt2VDnQMSCBQueffbZdDp99NFHH3zwwdFCiGjFihUvv/zyhg0bevXq9aMf/ajOwv9L1FQfsXXc0NsskFwTKV67dt2yZcu4C1BeGCBTqdTBBx/MRZXWrVv36quvrlixok271iee9KPi0pYADPDBzGWvvzl54jvvcTX+4sLU8CMHH3/cMb267+kACvh0/rzXX33JhDjllP/resCBQgLGgGxOCkAEJUNjpfJMTN6qAAWAbFR7P6fGyjt8I8gtKLuAeufrm2++Wbp0KeeSlZSUVFZWshuBM8pYEvjWW2+FYdi+fftTTz2VgwyUL9Lz5ptvLliwwHXdM888s02bNvEVzZ0795VXXpFSHnfccXyjfieYOXNmlP4ULw3B/lwA69ate+utt7744osuXbr88Ic/5JRWDmsEQfD222/PnDmzWbNmJ510Utu2beORsVmzZr355pucC9+7d2/ki2LwEW6cgXx1dfXSpUvZIRsFrFm5NXjwYBbGzJkz5x//+Ifv+127dh04cGAU7Gbn28svvzxv3rwWLVoce+yx++yzT3zhs2fPfv311621J554YqT5/a6wyxJoneIuiNXljVchjMT2UQEYxGrbiFhVK5uvLsOhjMa5EOuDYlXOkLfLTKzMlc1XLbLWSgnSGeE4xsisJiflBQZQqKjGpKnzXnv9rXnz5pEURLT33nsdd+zRPzhq6J4tnWIXWkMCaQfWkGLtlQmstdLziAApLWRorZBS5DlRxuo8AYi6CFDt47Tto2ZipUjj1Yb4bHKtkIhq+U28qQbbCzLfO8TG6kjGy4CxyqJ+YbDGR3x/qV5tHZuvEYV8dgPli4RFO0VbUq2yDchKSdbn8fQtzrxjEbctdKxWNINvtKiiUB1hQPysIXYBUKysHE/hcXSd6trfCXZZAo3ARMMmd6Qd4dbeqHeObb6yMvKXQrzYYmMWs9ka2J8d32bK51ZFJlgUYCHANzAEJeDGcqQswQho4ItFa1/5xzuTp/1r+VffwEl5bnrIoAEn/+gHfbuXgZAWABlPqCAMPNcLAut5Ofmq0YFSnFYluVUVASZvJOcp1easT7ZJI1t767dwPIYTPynRPcm+UZZGIh/wrUMKFCvVHtdIIlYo8384Aw2L6AiY2kWR47sZXbTRI5PyIieeUp8lo3kaYfsp36YtPj3+vEdMIRRVEeThYDRDnBa3JsCqXyWv8bErE6ipXXIR+ZrYW9T6mXrFz+OnJ2rXx+Zq/Ex/J4iCqvym/jM/x6QELXKN7BWgw9B1BEDQGm6KIEMgY+BbTHl/4cuvvTnjo9lSpbLZ6v06733yiceOOH5QsxS0QYHKCVoVoDV5XDeaLPkZ4RVAAEKSyBEo5dhTq7j1yYot/rwlAo1MKuR930LUdBaJ+1viP9GxDqMRm/DDI/60iyyy+AHcsQLs/xTRtc0nK/ooa7fei7ouAvB9P0oEqO9Eiv8qEks6+Q69iEncGwFbuz6RzyCof7shFvPYoqshEj9xdkz9ZTb0Tm0RuzKBRj/ngVL84RaNjJDXzUYfo7wUFStgHs353fImYhLFOm4EEyv7GJ/ZkJVSKiGNMUrIqDgzEXxt3ZQMKeemNMCqb/Vfn3/ljbcmrd9YaUk4jjNixA9O/MHQA/Zp7hAKBKwxaaVgYUI4bp4Kc55cS0Ak44pd/qKeInaruxYfm/PEiAfjg1YO5sZHpjbW1CFOvvzki1wxbAd952ZLHcQH72ZLDYLiF15cEovYRR5RT31ijQ5CIwzh2eyIM2A0QqqzbZwnFleP8a+i41DH31JnRSbfs36LFnejYZclULOluve2duHxOohfx1S7MwHqPSq/w3NWH3UGuTZfZd1xJKzJ5UIRQbAv2HqeJIHQQMpc09NQQ0oYARLwgXcmf/nkX5799IulylMQuk/P/Y87avCI4X0dgEIUuJCEbMYWFMioyykAptHYdkUp/zI+x9YOXLQXkYkRVWLfRhZN1F9MxHo8MCJLtr7VRnm533fOpPVdn4y4exSx1KPtbjPlFSyRMyr6VSNct1tcRXTkOYodJUREN2OdEGL9MxUtqv6O/K8R3f8NuyyBMiJ3dXTDICaIYaKJBxOibhD8MK8TheBxn4j1mWh8UEzgBSC6x+o7uYhICILWOatTCggnJEuQEDnHaBgYRTadckFAGMDxjAZcBAIaWPhVxZ8m/O2Nt96XTpHWtrS4YNTpJ/34lMNLU0gLuAC0D8Xc6EAIwIm3Ua2bhQUAUFsh0PipiW6PePSARwl19jEa10f8Elmsday2qORSPDz4HSLaNVu7oyJfbKjtLgQQ9UPk/a0zKmfXcBRzq+MbjVbaaFwTvz636HOoM4SP/nLPNJ4n3tMlvu/xVWzN7m407LIEGjdMUO/81QkHUaxrRR3bJP5IjN43jj9+a6h/y9UPL+T21xKiYyihjSblkJAWlkAKKucbzWaclAsroTVcj3L9SJAFLFCexZ+fnfHqPyZ+s+5bYXxBVccfM3jk6Sft26FlCnBQo2aKJ/dvDf/OUYtUEBRrBhPf2egURKc1oow6Ifi4ByBOynVG/d8h4hZond2p2za1noujvrlnY92St0Y9DY0616eNtchG/pEfBZGilNwo/y3+qOMl1DHGTaxxWZ0HbeNDRFVP6ogDtsgjyJ+8uXPnWms5Qys6TwAWLFjw4osvAuDSp4j14F61atWf//znTCbDRV7rHAv+GL/0RT5usLUxToJ/C7liJbnST1RjC1oAIkdonMgPCJCwFpCQNe2cBbSEAf4+8aNnn//7l8tWZANjrO198EGnn3Ly8H4dJMEVEBaehDWhVAAQQgg4FiALR0IRyEJEOoAECXYJCCKKujXxUz3yQEWkGWlBwjAMguCiiy7629/+dthhh02fPj0yoQGcffbZEyZM6NmzJ4B58+aNGjXqySefZDZ8/PHHzzvvvH333Xe33XabOXPmPvvsM3nyZK6WhnoSh9yW5VtjNmXRSRMH1XZPCgDQW5rMJVE49MPEKnNMSznyDU0oXFcD8xeu/9vLb77xznvflpc3L91tt+YtL7/kosH92jZLIw0Iq6UkYwKpXAvHQlpuomdBGkIQHJEQaIJdBzae2R3Llq3fgioMw+XLl7dv3/4HP/hB9+7djz766CiH1/f9yZMne57HSeVE9Nhjj3meN3nyZCJat25dcXHxBRdcwF999NFHu+22G3dEiVqzsTaTk6D5TfPmzaNUDdtYOby7GCyRT+QTcbJmbpI1ZMOaVyyLNJeJqin/VU2ePlnK+tbPN8L77Bvzmycn9jjup/scfUXLfucc9KOr//jC+ys3UtbwyQrJhjbIWG3IUk3fk+Q0Jti1kPMz1gl3sk2ayWS46Eg08V//+tecOXMuv/zyQYMGGWOmT58eOe+PP/74VatWzZ49O/JK9OnTp02bNi+//PJDDz102WWXrV+/vrS0lMV3l1122V//+lfudhLvIh3ROuXzSSKW/w4DbTsvInG7zCdc1uSKks1bgjkZfG42DgNJze8IABQgjSWQVEpoi+oAqTQssK4SL735z+f//tpXK5frbPVupcUXnnPWUUMOb71HgWugiGtBWwhpjZGOomT4nmDXguQ6z5FWjuXiqVQqDMOCggJOXmSvaCqVGjBgwOWXX85mI8/PNWuttZ988knv3r3ZH8xasN69e3/yySdKqRkzZrRr166srEwIwYGdww8/fP369cuWLUO+/DvTJRe84prbkcuVhWDf4THaecGk6TIF8oici5AKm28+IpnSBEERBIF4VjhcllRACoQCvpJaKGMAIVGchkNIW7QuxE9POfSNJ8f9dszPe/XuUYmi2x56bthpV9xwx7NLviXjCBDCyipAS0eUZ6rCLSX7J0iw80KySJXrEiEvNo5SVpHvtcBlboMg4PrEUXYE+yillEuXLuWqDVwVHECbNm2WLl0ahuGqVau4VhVzYlVVFXetWbFiBW9EJFWJlwePzM8oby/BfwFB+Vct609S7pVntHyOkEVODZp3jOY8pKEJCWSMNsZySpIwWgntoKpY+Ecf0evxB26++7fjDu17iBXixdcnnnDGuTfe/uTCrzaLZiVVoQxIpguKGn/3EyRoUDhSyurq6nvvvbe6uprTpIqLi7mbCsvKunTp8qMf/YjzwSOhT2VlZfPmzaPhP5d8Z09ltGiWiTD9cbYPO1uLi4v5fVQlgVk4lUr5vi+l5LoeiCWEJfhvYfNj8hwPii1agDUJRTYvhZc1HAoHgKdSAJQ0PDCAsNaxxhohlJKyUGjPOsN7tDiixwUff3HSE888P+X9f/75zcnPTZp2RL+DR5124kFdW6WQdxMkSLCrwNFaFxYW9u3bV0rJCqwonYO9n6WlpZy7yiTI3xYVFVVXV8dlrnE/AIO9AVEVmbiwmdvUCCG4lE5UvOP6669fsGBBeXl5aWmpEGLo0KH88+7du997773fxfHZNfDv8JbNx99JAoC1sZ9wRlFeh2TJWkghhRRKWrKAUIJgMkq6wqre+7XoMeai5Rsv+v2DT7039YPJ0z+cNm1a397dLzjr//r16RQiUk4B23GJxoYdJLcxa/yhkDxvEzQmcsNt7o0eB8eYokhOVFdK5Ttb8aCeiDKZTGFhYdu2bZcvX862JNuky5Yt6969u5SyVatW06ZNi6qNCSFWr15tjOnVq1e84py19qyzztq8eXMmkykrK5s4ceKYMWM4T7Zly5aNfmR2DTBNxShrqwRTQ5ci97n2FAGheFFW5F3SApBCcmhIOQKAJ40LxwBdynDHNSPXXjjyvgcffnfKtLnzPr141s2HHdLngrPO6NurlSCA4EmQgRK5dFJj86ml1rJgHLQd6ifwfPw+X1XvPztECRL899hqtk88sMPsGW8EOGjQIMdxWKXEiXQ/+clP3n33XW7MzWP5jh07Dh8+/MEHH3z66afPP//8RYsWtW3bll2rF1xwweTJk7nBerTYCL7vO45TXFxcXV2NvCA0Gcs3TUQ1lXN8l+s4KgFpgBAwwMq1+OOjT732xltuKgUTdD+gy08vOq9vz9ZcwlkRrIXMJzIJyckzWkiSQuZL4W2lhlOeXiNj9btPLUrwfcJWH+9SSt/3AXiex0HweMmiqAIKR8k9zzvrrLOWLVv2yCOPcCT9gQce+Oabb3784x+7rjtixIjmzZvfeuutbIQuWrToySefPPfcc6Mglc2XyDf5ZrZKqWw2G4/FN/iRSLBDQLlqTzoIBQEaDrBHGcZdN/KNl58eNvjwDNGCpSsv++XYUZfePmPWV76FIUhhSGcEtCDYIBQkpHJJeAYOhAMhmZFjsa/cS8DyS5FVZBVsEuZP0KjYmkA0DMOofRKXUwzDkBu5RNn+7NPk9l5EdN555ymlevfuffDBBwshfvWrX0VLmzBhAoC99tpr6NChAAYMGBBfV7xnS/SeDU/W1f97mtYE3wFqNzuKS/Q1f1vlU7WmSkMVROVE89bRpbc9ue/Qc/YbdG73oWdff+fTX3xV4fNCgpB8n9vpaW39wGZCW6eTUp0mffleTIZsSCYgE+Rk/wkSNAq2M4QHUF1dXVhYyG7K2bNnb968WQiRTqfLy8sBeJ7XoUMH7soSBMGcOXO4zeGxxx7bt29f5NVImUxm8+bNL7300rffftuzZ88TTjhBCOH7vlIqCkNFvgIistZyUL4plHtIsA3UtHcCciNpyg0XqqqqC9JFrJ8HwXDFUAkNLP668tE/P/vqW+8HoSgubDZswKE/Pf//2u8pUgCZjLJCqBQgkBNUQfCaRK7gfd1cVAKgQQYAhJtPuU+QoMGxVQKN12AHwOFyjhHx0D6yQylf7IPyZmM2m2XZU/1mDMhroSJw9eyoHQXypWhYkx8vz9UwRyDB/4TaBIo6HAoLEAGSiITjUGihpBYwEtXAyvV4+Inn//7aRCWl0JUnHjfs7NNP2L9dCwdwCAACP/RSLkTd1dS5ZAVzK0WF9RpoXxMkqIttlYxj2orKEbKAiWoXTxOx4t51Cn/E1fhsV0a9olgHWr/EFjcw4GVGNcfiPeAS7CSwYRC4ngcdgk+c1lAOICFkYCElIKABH1i8auNtd943a+5S5ZWUNis+bvig8888ardi2IwuTjuABsC0mMsyzRmktqaBiHAMoAEBuEkUPkEjYvsEyu+jirao11wlKkIcL3+3tVKGdcp0RtlHqF2wjgNTvG1JQaYmjVgYvg6CIOu5bq4FkxQQEtaSSkHAaigFogBSZuEEwIcL1j34yF8+/nQhYItTZuRpJ54/8pg04CEX2K8dZ2d704AkhCDhhIAGZD5vNUGCxsEuW1A5QWOg7li67rT6jtG8g9LmipAC3I1OAyEw5+M1Y267a/nKtU4q3ax50WWXnnfi0G5RLr8DwFghLUAgkNbCTUFI30CpnH3qJRZogkZE0yWphEB3AhBinYy3XJRe1nGP1lR0FrBOzr8poAVljZHK8YFX35z79HOvfLlkJWB7HtD5Jxee3a93GxdIAwi1cABrWd6kjVWOBJAJjKekUolaOEGjoumSVEKgOwFqCJRpUkYEWie4FKPREEBUoyRajBUICSFICpEllJfb11+bOuGvL67PVGf9yqGHHTz62iv3LnMKFIQFBIy2kIIgpIQUAGkgH4VP8u0TNBaaLkklBLoTICLQqLRorN59neqfErGEpXysPDrBxkCpHPPy36oMMhb3P/H3F155JazeXODgnB+fftYZJ5cWwRWQIidgImsFhVASFMIQ3IKEQBM0GpouSSUEunOgXhApOmf189ijWlBRJ3oAClqCbBAopwBWghAY+Ja8QhECAlj6VebBRye8+c4kxy0oLi4+/5wzf/yjfh6QIkhYkIHRcBRBCZEEkBI0KpouSSUEurOgtqVZJ+lW1p2V/4tomG8FjIIFoDOh4xXz4gwBjiVYax1NIIWPPl3/6zvuXf7Vaq2DPVuWjbn2qsMPaq+rtKdsOu0EQeB4KSJSiYo+QSOi6ZJUQqA7BShmadbE3GslCvF8taJMucyi2PCfiLKBn04Vhjr0HBeEIJPxCgpAIInAQEtYgRdfn/WnJ5/+eu06x3F69ug+5saft2kBk0VpGsL4Usl8xD5BgsZA0yWphEB3CmyHQInLKwEiV9MzR6D8j7VNQgIIjZWODG3gSikgJAGkYPOyT6ZRwAKry/HSa5P++MgTUFJo++PTTrrk7BEtCiFCpHOSYstVmkS0DTUftqJbrckTrYOaMFcS309QH02XpBIC3VmwJXKpLWTaIv3U04vmJ1jBtFVDdZYgo/gSO09XrAl+/du75s39ONS2efMWl/3kp0cddWBaogAIshWpdAkAGKOEzFfYyzW8JwFL0H6QTjsivjHC5ok+vrUcFpO1HxIJEuTQdEkqIdAEyPtJ859kPEyvgX/NXnnHXb9ftmq1UOmevQ7+ycXn9NgvnQKC0Ba6UgEga4JAuSnkWpEgtPDyoSZrwliKsK292kh/lRBogq2i6ZJUQqAJ6oMvCAMYwNdwHFSHeOzxV/72wkvVmTBVUHTs8cf99KITW3og3xa6AsKwi8DPVqfS6fxiHEvQ2riu2ortXFdBQIBIXKsJ6qHpklRCoAm2BgICA6EQFRRZu5F+d8/v33h7ikw3T6fTN1x16Q+P6u5EefGklcg7AAxZKKlcY4Ssx5954rSAFHUVBdtpzZTge4imS1IJgSYAttJIXoAAXxtj4XqKgEwAz8P8T74aM/bO5V+v86EOPvTgn1x8Trd9iz2NQsdanRWwjqMAUBgKtwBwQ20dp6arEmr7P2slodZsRsKhCWrQdEkqIdAEwJYINBYuJ8hqP0ilPACZ0HquBPD7h1596a0pX2/c5DjywvNGjjp5QJGLQgEFSyZgq5O0Fk6KSAih4vn7dTJQ8waszX3HrZ4TAk2QR9MlqYRAEwBbtEAthNVh6LhuEGjP80JjHeXwcN4P4bj4am142933T/xglnSLWrRocdvYGw7uUlSsYLOB60A5jrGhyrk0Vb7bEi+6FvIEipwRmhBogtpouiSVEGiCWsipmmp0pmStkNJoqxwHgLZGSdcAfmBdT2rgrfcX3/vgE0tXrRVExw7t//NLz2m7e66EidWh58DaUEq3TsAddZWtW67alyABtltQGfnOcURkjHEch0smR5WVufFcVCM5KqjMb+pMZMT7fAAIw9BxnPq9ixMCTYCttQypNYeMieQtgbQFhGI/6Tcb7F9eeP3hCX9DqlmqIH3R2aePPKWvZ1EgIQGjA0dJkIGUOcEUCSm53+d2tiNBAmy7L7wxhtsiaa2jDkgRuCld1KXDcRx+H7VI4oVYa7mefFSjXmvNc0ZfMepUnk8INEE0rM7bgzH2pJioqFYpE26BLQFIghWoyGLJ6oprx9+9cNlqY8IBhx103eUXddzbsT4KU5DGCml9P8sXp1Qucv0X0kiQYHvYFkmxScitkJDv/saNjNiuFEJIKePN4HgKAO6HzIbnFhuBIGaKRt3oEgs0QRxsFMby6msuIVFnvnwGURAShPaUJNLGWOU6gMsNP/784uQHn3pxQ3m1p7zzR51x8Y8HFii4BK2N4+Tac1VXVxYWFtaQdj6FP7FAE2wRWyWpbfc4isiOf86je/4qPvCPELVCCoKgTmc67tbJrTrjo/uEQBNwI2QLm6fOegQa5zUCkG+DTCFymUcgCGMJMlWlsXqjHvubP0yfMbu4uLhrxw6/vPLS7vs3k4DV4MLMjoCAtcZIvoBjBFrTYDlBgjy2RaDW2og9lVJSSrZGIzLNZrOu60ZmZjQDAH4T+QEARG04eU5uJ1ffdK3ZsoRAE+QYMJ8d/2/kAlkCEchqCK2EEJIIEpAWDsvvlcKbk+aMuf2eTVnH9dQlZ596wcjhLPmUgLDwJKwxSgmQzZXNj6XqJwSaII5tkRQ7JSOrkDmRbdLq6urCwkLEgkXW2mhED4CJMhrFR8TKtif3+ETM71l/mJ8QaAIA+foh2yXQXGumMAydqM8rLMgYCylloI3reJLH+K7YkMVNtz/69qT3FIXdDuhy/bW/3LdTSRpwAEFwBf82avcUqyPVcDuaYCfEVq/IKMKTzWb5YyqVWrdu3ZgxYzp16lRWVlZcXHzBBResXbsWABPlggULRowYwX7SESNGLFiwQCkVhiGAMAzPP/9813ULCwt79uz5xhtvVFdX8w95hvo94hMkyEOC+IUtvHIMyy+tnFxLEV8bDUnClcIVUCnHs8YSACkIaJbGbdef/9j943fbc69Zny6+4LKr77jnr+urUB0CAr7m9kq8druVSncJEmzPBxp9ZDv0xBNPnD59+kUXXXTMMccsX778Jz/5yf777z9z5kxrbUVFRatWrQ444ICbb74ZwNixYz/77LPVq1eXlpYS0aBBg+bPn3///fe3bNny4YcffvHFF6dPn37IIYdwr/n68SUkFmiCHDgLaOu2Z0wZCkAb7SiH4Jg8AZKBI0EWQoAkLBDmDQcNfFOJ2+9+/L333tM66NB279vG3NR1n+Yu4OaC/rGeo3mxPbZlh9ZpSJpgV0cQBKzxpDzCMOQ3/FWEZcuWARg9ejTPo7V++umnAcycOZOIxowZ06xZsw0bNvDIfdOmTc2aNRs9erTWeurUqQCmTJnCXxHREUccMXjwYF6p1po9APxtNA/ySqlsNksJvuew253D1H6Rzb/qLyn+0paqDb04+YtDR1ze5vAf73fkeXc8+eZGIp/IN3wtGmOM1gFRSBRqMpkwsERkyRoyAZGJ1mSIQqLAUtZSsMW1J9jFIFnpSXlOBMAjd62167pBEACw1mqt27dvT0SXXXYZACmlUqpVq1ZKqYqKCgATJ0485JBDysrKeLmlpaWHHHLIxIkTlVKTJ08G0L9/fyGE1tpae/TRR0+ZMoXj9VLKMAz5KwAc+o/IHQA7Xhv7wZKgSWH73h1Z+wWRf9VfUvylgLTA8AFdnn/q3uOPGhb6/iNP/uXsi2+Zt2iDlsInhCSFlEopS1wXX7qOqzV838BCsvaECCKqDAVAAWqLa0+wi0EGQaCUUkq5rsuJRvwF06jneWEYsluTnZUtWrTwfZ8H3RMmTHBdd/DgwQA++OCDww8/nGcWQoRh2L9//w8++EBrPWXKlMGDB/PCWW/fv39/ADNmzGDqdF23uro6kkmx60BKyVNYA9D4hybBLg8CAoGKUBcptC7GPTee99Bvx3oqvWDh2jN+cvOdj08JBDIhABgdBDoAlJ/RiqBEmEpboTSMT9AQGggJhjgERY6IPLYJdmlIz/OIyBjD/MjkFYYhM2nElUxnWmshBMfT//SnP02YMOHZZ5/l2TgKH6lBWWxPRI7jBEHAQfmIBzlYr7XmCD6AwsJCtnMpn93EC2RDuPGPS4LvD9KeIxAKCl3CwL6d3vr7gwP7H5b1zYRnXjh51E0bMggActKuW6zDMJ12kMv0NBAGDiAtCQKkgBJwRE10K8GuD4eIhBBHHnkkB3OYxTzPY/2mUqpLly733Xcf8qF2FoFef/31d95556OPPnr88cdXVFSUlJQgT5rRnDzMR96VyXzKa2HS9DyP30dxpE8++WTjxo1SSg79T58+nZNEi4uL+/Tp8x0epgS7JASstKGSyhIJKKGggBYp3Df+7LfeH3jL+N8uXbPhuDN/ds5pJ11w5pASCUe60FVkjEgVWpJZHaTcFAABKUjV8GbS/eN7A4dNvDfffNN13TrR8Hh8nP2kjuNks9kLL7zwpZdeeuutt4YMGZLNZktKSji9nZ2YyAfQiSiVSjEDRgTKC2SebdasGYBsNltQUMA/fOqpp2bNmhWGYUlJiZTyxhtvVEplMpl+/folBJqgIeBIVZ2pLihoZoEw8FNeKiUgDI49vON+T9w/5o77Z839+NGn/vbxxx//+rqf7dVcKpUiZIWQBMd1lYEBpAuVa9WUAyufnKSX5y4PQUSZTKagoIDH1DxejhcBYa07S9/DMDzqqKPWrVv3l7/8pVu3brwInmHYsGFhGE6dOpV/q5QaNGhQUVHRG2+8MW7cuJtvvtn3fRbPA7j55pt/85vfbN68mVmbI0ts9nJtJy5fwplOqKepSpBgR8EYow05ngNAwmrtu44EZMY3KpWuBp5+dur9Dz6WyYat9trj+p//bHC/TimFwGillAthARewGkrmR+45yRM3D0XSp37XhrTWptNpZihmTLYT+b3v+5yMxMH6a6+9dt68eVOmTOnWrRvrjQA4jqO1Pu644z744IMNGzZwEGn16tXTpk0bPnw4gGOPPVYIMWnSpEwmA8Ba+9RTTx199NEcXmfD1vM8Dmcxe0Yr5a1M2DNBA4EgHc8hQyALItdxAQljCzzlEYosLvi/gU889LtevQ5cs37TlTePu+Xux1dXgZTDAlTrG0EQlE8FVVHsn0kzUeDv4tiqWD1Ksowy35cvX96xY8fBgwcfdthhqVSK89mllEceeeThhx++YcOGLl26tGnT5te//nUQBOPGjSsvL581a1ZZWZm19sgjj/zoo4/uv//+1q1bP/TQQ88///z8+fO7dOnCVie7SpNydgkaGdGwW0VMFyn2CbAGpOG4gZDrfDz6wjsPPvKUsKJT271/O/6GA9oXFfEo3QLSQtgQMFY6UloLTwI6hBIQMrFAd2Fsp6ByZAYGQfDpp59eeeWVxpiCgoLKysp0Os3+zZEjR55//vkA5s+ff9NNN/39738HcOKJJ951112dO3dmfly/fv3VV1/90ksvZTKZtm3bPvbYY3379mXXZ5QXXyclKSHQBI0AgkVNbacYewKgELCwFEonVM7aEJ8uWX/NDb/euG5jyvo/v/SCUacOKXSgCCAyIoSQBpBwuA6UJG6onPhBd2Vs3wLl90IIpVRUqo4VSHVG1uxLjX4blV9CrJ4TzxlZnfEaInUK1ycEmqDhYXMll4SkfM2SvA7JwIZwPAgQpAYsEADrDW68+Y8zps5IOe4hPQ+4bewvWjaDIFBoUx4AQzCAMFZCuEJAJYGkXRrbyoVHPh+Jp/BYPl4FmYNFUfQpXn4pKgDKAfr6g3SudBexKjNpJIRCQqAJGgGEPIGCRJ5AAS5NYrSG8gSkECCrpbC+thk3bYG/vDDjmb88v/qrNbu3bH7zdVcPObyTx6ny1ocwBECms1rCoDCV8OeujO2QFNMch3Qi85DTh6LS9NHMlK/BHA38KV/aLrJGo7ymeAl6nlgn3Sgh0ASNAXZ+iuivzVdxBiCNJSUVuDyoNRAIrdDK0cCcL76943cPL1r8tV9ZPfKMEb/82QkpwBUAbBga6bpcssRNDNBdGtsiqfj4mg1PzlbiHnAAeCAfae95tmhsHnErh/Vzuff1Ci/FpycV6RM0NuKXWC6fHQTpa+M4rshPlgIIA0iCI0NjfOGSVCFw1wOv/e2vL3mO6tJpz9+MvbH93ike7QsJx9F+mE27hUkQaRfGdoJIUSpRnZTKOu2M4jPzmD1OiNlslpOOWCLK7tT6Y3YkBJqgcRErT1e3DF2unx0bolHfTy4/agwctzq0wpUhMHHG52PH31FVbZs1az7uphv69dmtUCANIKiEqyBcCAcJdlFsn0AjzyZTXtSig2Kd4OJ8WsecjKbEeyXVrwEaxalqtiwh0AQNDG64hBrXZ75JMvcFIQgBY61yZM2VGBjpKdJauFKDDFQW+HqD/cW1v/5y8Uqd9U8+/tgbrj7NNSj28gr7Wk1DgahncqzGPbfPAyASc3WnQtMlqYRAEzQC/uNGHbV8ptZAGsACGcKEpyc+/tjTfmj227fzjTde26VzgQIKCQIhhDXWSOkG1kjpOPGaI7kyz5YQCkDCTTh0J0LTJamEQBM0ReRZD6gxHg1ggBCYN/+ra28Ys7kqcNIFF1x00ekjepcACH0rrOu4vglTyg1CnXLTNZVHcgKAXOqnhEoIdCdC0yWphEATNEXUuyRZ/2QADfgaocWVPx/98acLvVTJMUcP+9WVp3IBCAF4gCDobKWTLmTlKWpUU0hiTTsjmi5JJQSaoOkh3yWJauJC3C+ejVD+OiDc/bsJzz//d+l6HTt3+P29vy4rQlpABkh5ABBkqrzCAvZ7CjApOznDNhE97VRouiSVEGiCpoeozVytwDoBBsaQFcL1iZQQBEz94Itbxv92U+AS0d2jf3nUgH0cgszH+xV0zpolkWPPiEATDt150HRJKiHQBE0SdYbbuZ6ghiyE9LV2nLQGFFDt49vNdPn1ty9f8bUKKs4765RLzv+h1pAEz4ErrOB6d6RyOfgJge6EaLoklRBogqaImtx2mx+1I59DLwEZGKuU9APjeopbKN88fsJrk6ZqYw4/tNddt17RzIUXI+DcED6xQHdONF2SSgg0QVNETeiHx+CayTDU1nUKAAQhua4IrVFSGEgCQuDFtz+9894/VlZubrvXbnffemO3fcpEXnyaK18CJD7QnRFNl6QSAk3QFFGTvWTzRihbk/mReMw+5bZzBhDAJ4vKr/jF6A3lvlfgXnXFRSOO7uoCHnQYZFyvUEEFWZNKqZw0qnYLhqQjQ5NF0yWphEATNEXE0j9BEY2yEzM/Lhc5xyhxUTxr0rJQEzZlceW19/1z3sfWhiedOPiGq0emc7WcrQmRdh0igCBlLqMP+UoUCZosmi5JJQSaoEkjrqhHTSESADV8KqyBLwHACQKlPKmBux9645kXXq4IggP36/DIfbcUOygg40hYKGPhAIp/HcuKTizQJoumS1IJgSZokshHjai2NZojUJ6kYtaoD1g/MJ5XDKAygPLwxpQvfnPPAxs2VzQrUE88/Ic2u6WLXV4oZC4bvxYSAm2ySAYICRL8+7C5VxRKqomb176VIrrTgBYpr9ACPuB5cIDjBu13363X9OrUtqLCnHj6pRP/ubQKAEA2I0Fa66hDONuhCXs2WTRdKy+xQBM0PeScm/FMpJi9WHsIj/wwX2st4RvtctMPE3oqRcDacoy54+F3ps+wMKeffNy1l/1fgcgVYI5KnXH5x8QT2mTRdEkqIdAETRFUEyPKT5LczqMerIAMfet6HJ232oaarKNSvhGOEhYgwhNP/+NPjz+tSXY/6JBbR1+xm4tmqfzvreWCuYkR2mTRdEkqIdAETRG5wXvc4ykASVvwhlkAgiQAo61UVkgKrRYyZSFtzuMJX+ONdz68496H1mWobetWf7j9+tYtCkuLlCBYS0pxtXJylIitvWb5ALbiiKtbIjpBQ2BbXTm5sHz09Mtms+l0GrUr1XM15Xhh+agPUrSceLf3+EJ4bBIVbPZ9P5VKRXMmBJqgaePfYihinXy+21I0kSAIivJTv1i8/uprb1y9dmO6qGz0TdcMOrRDSkLkc+clAANH8gIspAzCrOc5yFdoRo5UZY2BTDbmW6ixkRM7dsdiOyQVFYqPurczAwZBIKV0HIdbGUezRaXm+Q1TLbeP54r0XM0+ouA6TeHjQ5WEQBPsAqhNWxGHkiUSwtEkLUFIBBrG4sKf3TDr05XS9X552XlnnNTfBRwgCG3KlRLIKe0BP/BTKRewoQ4dx7WQkkvZ19wuFrD5DCeREGjDYTt94ev03uCP1dXVhYWFyPNgnPUiZox3fuclRF2RAXB/Otd1Izs02oyEQBPsStgKgYJH/RYINJQDX0NJBBJj7njmtbfeFWSPPXLgr687Nw0oawBD5EDJ0EBIKLJSxpdfu0cIo64uNRnFNwi21Reeh+dRRzmW9W7cuPG1115btmxZGIannnpqjx49uGcc893HH3/8/PPPAzjllFO6devGQ3trbTabLS8vf/bZZ9evX3/wwQefcMIJ8XUx20acm9uyhEAT7PyoR6A1MIYgFCQyPnmpXHa9D0x44f0HHnoi9INuHfZ+5Pe37dEMoJAgIB0LhNqkHCVio7daa4pD2HqTkDDpDgZtBVprbgofn/jRRx916NChWbNmRxxxRMeOHQHcd999/JW1duTIka7rdu3atWvXrq7rjhw50lobhiERPf300wBatWo1fPhwAD169NiwYYPv+1prIvJ9P2LqaF3b2LYECXYWWCJb88nkXpb8TDaaQRNVh1TpmyxROdE6ohdmrOg74ur9h1581JnXz1u83rdEFGarNhAF1uqsH1oiP7DW5ldga5ZdM6XWSsP8y1CCHYftkBTzGhFlMpmqqqrhw4e3bdu2oqKCJx5//PEANmzYQERTp04VQjz88MP81cMPPyyEmDp1KhFt3LixsLDw7LPPJqIgCObPn19WVnbTTTcREdMr5akzIdAEuxi2QKB5gjOhJqJsNtCGNJFvbEiUJcoQbbQ0+ePyQWeO7jzogq7Dz5m64KtKTURhJrORKMhkA82L3SJv2i1yaEgUJAS6w7EdktJa+74ffbzhhhveeecdnh6G4fTp04UQ7733HhGddNJJBxxwABH5vs8/OeCAA0466aQwDO+55x4AGzduJCI2aS+//PLmzZvzeybN+tZuQqAJdgFYMjZmeMYNRqspW53h2UKjQxNoa6wlSxQYqiL6ylC/H9+w/3FXdxx64YQ3ZlZa0tYnqrYUZvzsVg1PG+PPHIcmBNpQ2Lr8gr+W0vM8ytPc+PHjhw0bBkAppZRasmQJEbVu3RrAzJkz+/XrR0Se5/FP+vXrN3PmTMdxZs+e3aFDh+bNm/MCiah3796bNm1auXKl1prD9Em6RYJdEXUk9zEICIlUOm21ITJKWkcKYUMBCG1coZWxaeCVP48fMniAIXnTbfeO+91TvvAqA2EhU17KmJgoNffK9fisBeIyUbLeFwl2ABzkvdE8WgfA8RymsygLgoPyPMPSpUtXrFgxadKk++67b+zYsR06dACwYsWKfffdl8NN/MPWrVuvWLGCv2rTpg2vKJVKCSE6deokhFi0aFHbtm2Rj7xTPppfRzqaIMEuAmaw2tEeqRSEzaXTKwWjoSRpk3IcCRjgpitP7Ni2xQOPPP3sm+9/uyk77roLlUVaQjnQOnAcB7AgAoSlkCCkcLSxjqp9B0Wm0hZqlST47+GEYeh53i233OI4Dis3IyZ1HCebzXbu3Pncc89Np9MsmAfw1FNP3XrrrdbaU0899YwzzmCyE0Jks1mKxc2NMayZr6io2HPPPQFEQUN2fRYXF0spWUnKqqYwDAG4rssyfp6IpBpNgp0VsqZa6L8Z/pYSgA7hOnChpaEWjnvuaQOatWg5Ztyd706dWb6h4ve//vluzWC1STmShYBCCgsjBQQo1L7rpLa4aMAm7Llj4TAx9e/fn9ktDEMhBAs2pZSu65aWlkYWIhPZLbfccv311y9duvT666/v16/fokWLSktLiUgpxQuhWPKSMaZly5abNm2KbFgicl1XSlleXm6MKSgoYHG+1vqaa66ZM2dOGIYlJSUAhg8frpTKZDL9+vW76667vsvjlCDBfwVRnze3ZIdGsNZI6brpnKkhrO9K3UwUnDH8wG6d7r/857fMm//FaWf//IE//Lpd67QEpAKAbJhxHGEFSUghLafh1xTci0gzMT93NAQR1cmhjMCuT04xYk5kWowEaJs2bSorK7v99tuvueaazp07Dxky5OGHH84tV4hLLrnkgw8+mD9//tlnn/3OO+989dVXUXrSM888M2rUqPXr17do0SKS1gOYP3/+hg0bpJTZbPboo4+eNm0aZzEVFxf36dOn8Y5KggQNjbqi9/xkAyElgMD3vZSAIFhNcAPrkYN5i4Jxt9+5cPGilGufefL+tq2KUgAIUoAoVALZoKrIKxCQgIt4q6Xcihpp574/kABSqRTnWdoYALAp6jg5K/Xjjz8+9NBDp02bxmEfrXVpaSkArbUxpl+/fq+++mo8Kf6VV17p3bs3gEGDBq1Zs2bx4sUcZ1dK/eMf/2jXrh3/PMq411p379590KBBAwcOPOqoowAcccQRAwcOHDhwYMKeCXYt1Ar75DOFJCCFkEYDIvTS1gproEgUCXgpIG3RrYP32IPXd95nD3LViaec98ZbC0w+vSkkR1sq8IqqMhlA1I1ciSgfP8GOhGS3I6cASSmZAZnRmFWRT8fcf//9ly5d+tOf/rS6utrzPMdx2N4cOHAggIsvvnjTpk0PPvggACHEPffcs2HDhlGjRmUymR//+McFBQW33Xab67pCiLlz57744ovnnnsurzQMQ/bjMFNz5hJvDBE5jsNbmCDBroJtspiAMWGukhMcY4UOYXyu/WSLHKRh//j724cNGui6RTePv/Mvz32oCRpwpID0DKGooFiHYa1Wybm3Nkns2/EgoiAIor9EFKUPUV62SUSZTIaIXn755aKior322uuwww7jAPo555zDQSff9y+44AIAPXv2ZIPxV7/6VaSWeuKJJwC0bdt2wIABAAYOHBj9Ki6qiitDAUTfxgX2CRLsTKitpKecMjS0FFoyWxK/h0Sh1joMjdU1P89ms5Yo1FYTZYk2GLps/BM9hl/cY8h51/z6zxtDqjTkEwXWaB0QhWRNjT40r9y3iQh0R0OEYRhphiif/84eycg3yk5PIjLGVFVVPf/886tWrRJCnHDCCb169UJeeJTNZpcsWfLXv/5VCHHyySf36NGDF8sxohUrVvz973/fuHFjt27dfvSjHyEmV4qXbqJ8ACrKhd+aizZBgp0A9YogEew2QvOhqXaVa62ruOunARRBkoEMwiDtegC0hRYIBV56ffZvbr3Ldd0fHHfUFT/7caELTyCloMNagXgSsPk1qi1tUqzIqYxPQOI13R6absGOpJhIgl0XduuqpnzTOtRiujjpUb6YswZef2feTWNvtyLdqVOHxx64pVkBFKAAY+FISMCStlZL5QWBcF3hRKsQeXGoyLd4goWQALhMVL49XsKh20LTJamEQBMk2DYMsDnEwqXlP7/mlk2bN3fq0ObhB8cWuyADTyEMw7TrAlZbLYXjCGk1uMYkgNoMns+YEuDKoRbSADIh0O2h6ZJUQqAJEmwbBtBA1mDZsm8vvvyqNZtFuqDoxWce3LMULVxonZFOytcaVhW6CjAAQWypNmjNED73yebnkQmBbhNJ+nmCBDsrJBBmUaBwQOfdJzz6xz49D7TWnj7yopWrqwNAOqnQhCnHK/AUWcAaWAPUxOejV07kRJIH9QKQsBI2Yc/toulaeYkFmiDBdkGAH0K40ISMjwt/et1nS9cVlhRedunppx7TzzPWhZHSJR0IR8JaKI9vqvodnWJcmTSk+3eRHJ0ECXZuuC4cIC1QLOzj9992UI/9yzdXjr/zwefemmmUFMo1JhCO1NogVmEkPpLP9WmKvstVHrGJ8H67SAg0QYKdFQRUhyEB2vcVIe3KFNFD91z9ox8OJiocfdtDz741qwpQjgdAqhRBUn68LqJuc/mSJzY+ok/w76HpDpOTIXyCBNsGASFgrU4LCW0hHUhogUrg5tufe+PdKRZVZ570g19ccqpryHWEYB1orSqlNQ07bd2xfP1gfYK6aLoklRBoggTbBsEaWAEochDZlgQtEAAPTHj7/sdfkJ5z1NCDxl9zXhHgEBwBHWYcxwUIRBBC+4GTLiBIxChTAAmB/jtouiSVEGiCBNuDJRgBAG7NNAIIAUErPP36gl//7n6rzInHDLv+0tNbpqEslLSwBiDkdKHShlp6BVSbMvMcmhDottB0SSoh0AQJtgcLCiFgkCJAUS3vJY/lX5204Ppxv0+nCob263bdlRe1KoUDhNlsOuXkFJ9hCDcFoaIEJJHIP/9tNF2SSgg0QYLtwcIaSGgoC6kAFasB6utAuF418Owrcx945PHKqo0H7tfh/t+O3a0ELkDaIqx2XScXQnIcgpMQ6H+KpktSCYEmSLAdEHKlRQGDnERJ5cbhujr0U26RISjgy5WVZ1z6i03V2T5d9/3t2BtatYACUoAgDbKQAhBbItBkCL8dJEcnQYKdFgIQEuTkW3vUTA91WOh6wmoPkFp32Kv4/rt/W1ZaOnPeZ9eOv/vrchgga0FQOghBYktUkIhAt4+ma+UlFmiCBP8uYuXn8nWbrAkyyvVAFjJlgMBi4Sp9xk9/sbGi8qCune+57bpWzZAChNVSApD1fKBJFH77SI5OggQ7MeqZGDb3IlJuCiaElEFoAKQFOu7l/Om+37RsXrjg408u+umvvlhRUW1ghUNwCLCxkvUCnBqPGju0bv484ibq99bSabpWXmKBJkjwn4HqhH4igpMECIIR8IE1m82Fl924avWG4gL3gd/9tmfnQmGhJAgmYwJPpVxIYZAvKxIn0HyKZ02HJRbhy3oi/O8LEgs0QYJdBXXZK0rUhECuw3IKtnUz9fhDt+3Tsc3myuzFP/vlvz5epyUCgKAKlSsQ5rol22gh9d7kDRuCBbjc/fcUTdfKSyzQBAl2LFgqHxpIhU3VOO+no5euXuul3XvvvrVXp2JHa2XCVMqxZLU2nltoNDi2nwvK12k0L+Jd6uT3zfZkJBZoggTfFwhAElIKHqF5Cg/cM3rvPVpUZLKXXvmrz5Ztlo6T8gooCKWwRJoAThCNOojkFpF/Uayik8g5Xr+7ffuOkBBoggTfIwguPB9aT2LPUjz92Pj2rffMZvUll1//0efrQwGCADkpr6AqqA5h44NzEqCaJskR8rYnR5y+ZxyaEGiCBN8nEJG2cCSAIJNt5uDRP4zdt23risrsL64d88ni9dYr8LMmDG3a87QNtrCAvMI+xq3f3/qhTdfPmPhAEyTY8bAEIQgkhDDGSKUCYFMWZ196y+LlK0sKUn/8w297dirhrCYLrSBlFIbKg+IB/ihniXia872KxDddkkoINEGCHQ4iI4SwICJScAD4IQlPbAhw4WXjP1u0rLDAffyhu/ZpU+gYpBUkbN3yoCRZrl+r9h3FZvg+EWhuCG/zvg7mLK11GIbRTETE06M3WmsAxhhjTPSRf6K1jn/kKbx8nmKMISKewnNGi40QBDVjB54nQYIE/yMIsEIYWAFSeZpLucIFylw8+ocb9+nYdnM2OPdn13y2KhAKhiAgQSbwM/kKeCGgARtVs69BFF/6PkH6vg9ASskUls1mATiO47qu1pqItNZCCCGEtZaIhBBBEDiOM3r06EGDBn366afZbNZxHGvtwoULjzvuuHQ6nU6njzvuuIULFzJLOo6TzWZHjhy5xx57CCH69u37+uuvSymttUopALx8Y4zNw/M8IQQAInIcJzFFEyTYEbDIpxsRZBQUEgRPoMTDIw/ccsC+Hb/9duMFF18574tyKxAYQCgvlQJRTkJvNcgiXjqP8k09v3+QqVQqMvestQUFBQCMMWEYSikBOI7DTGqMkVKGYeh53pQpU8aMGfOvf/1r/fr16XQ6m81u2rSpf//+a9asee6555577rk1a9b0799/06ZNbG8OGzbsjTfeuPvuu999990OHTocf/zxb7/9tpSSWRIAU7OUMqLyiLsRM5ATJEjwX0MAEkaALBwLaVifxLeggUfYLYVH7rnxoAP2k1CX/+qWuYuqjEImRDYwUA4sTBhAClgdNZEHR+d56d/DoDTzFA+is9ksEyXlkclkiCgMQ4ohm8326tVrwIABAKZOncqW6dixY5s1a7ZhwwYewm/YsKFZs2Zjx44lorfeesvzvMmTJ0dLGDx48KBBg3jV1lrf940x/J5H90zfvF6emCBBgv8ZhihLFGiikMgnCon47tKBISJNtDmkr6vomJE3dhp0bp/jfzpz8cYMkU+UCTVR6GcreAlkQ/6lzb++n5DZbFYpxUZoKpWKiJVpK51OExEbochbgqNHj3Yc59Zbb3Uchz0AxpjJkyf37NmzrKxMKaWUKisr69mz5+TJk33fnzNnThAE/fv354VorYcPHz5jxoxMJqOUEkJ4niel5OF8EARCCB628192syZIkGAHgBRIIV/pMz8M19KVYRgitCUKexTi6YfHddmnfXll9pIrrpn12bdZIJRKw3FTaT8bxOWhoiatM5fZ+b2CTKfTWmvP87TWbAnyyF1KGQ3tjTHMlVLKDz/88L777vvjH/9YXV0NoKCggF2ZkydPHjp0KGKRpaFDh06ePDmVSr399tt9+/b1PI+J2HGcQw89NAiC2bNns8fTGMPrYjLllRIRT3EcJ+HQBAl2AEjCOrBSASrGngQCrJRSKQlCUFVdnMJDf7ilS+c2m6r8q64f99nSSpKoDClryEsXhNpASCDn/awdpv9+QTI5hmHoOI7neWwGArDWskFKRDwxlUqFYfizn/3sqquu6tOnD3/LBmwYhlEgiC1QYwxPCcPQWltYWMgWL6+rsLDQcZyqqip2eiqlXNdFPuCezWa11qlUisNKAJjTEyRI8L+Cs4gMFFmFEAgNYCFMGCqpSFsAXkGhAnYvwKMPjG7fsdPaiuDCy3/58bJy5QqpXAupXKfOUr+XEXgAcJibhg8fHgRBYWFhEARMc1LKbDbrum737t1///vfczDn1ltv/eabb0aPHs2hHjYnich1XebHiH+VUtEUtl45fO95nuu6VVVVWuvCwkKmSGZP3/cXLly4YcOGTCbTvHlz3/enT5/OnoQWLVr06tXruztKCRLsKhDxap5WAhYKkI4rYUm4EvlRuQPd3HUe+9PNF1x228KFX1xy2dWPP3h3lzbNrKG0cuJ6z9pV9GwuHL/lwnqIAk3xsiQ7Lxxmxvfee6/OF9ZaKWVkSBpjVq5c+fvf//7555+XUrKpyOqlSPHO80ccSkTFxcVSyurq6nQ6DcDzPCZEHqeXlJRE7ElEqVTqwQcfXLhw4caNG0tLS6WUo0ePZo7u2bPnPffc02gHJUGCXRPxzh1Cchq7BHJ/cjWWIAUIkHAE0FzhkXuvO/9nYxctWXnOxVc/dv+dPTqUGkNKwRgIBUuQAmSNwz5VsaWETopNEeAqorV70O+02EaAKR6O11qPGzcOABMuq50YRx55pLV22LBhHFjnGLq19vDDDz/qqKOI6MYbbxRCsDifl3bNNdcA4I9BEPBPeI38JpvNsvKUtyG+JQkSJGgcWCKfqJJoqU/HXDR2nyFn9z7uginzlmeJAiJNVOUHmkhbw3PrrE/WkDWx2LwhMkQh2fyLDC9ZE+mdP3y/Ld8iW5oc4VFK/d///d/06dOnTJkyefLk1157jU3CBx544M477ySiH/7wh9OmTVu1ahWHfZYtW/bhhx8ygZ566qlE9Pbbb7O31Bjz3HPPHX/88WzAOo7DP6moqJBSspM0lUoRUaQSTZAgwXcFE2JvDxPuvalL5w6Z0LnixjtnL64KAWNN2iVpfQWbrawIdShTHoSEkBC50k35kndOfnpU/i73xc5+h2813zwMQ9d1+S8Adl8ymRYUFGitp06deswxx/zjH/8YMGBAKpXasGHDvvvu27Fjx+uvv15KOW7cuHXr1s2dO7e0tFQIcfTRR0+bNu1Pf/pTmzZt7rvvvhdffHHBggVdu3aNzEymUcpnOrGwKYrR8zYkSJCgMRENtBVpQ86qCpx32c1fr6ts3iz18p9va+4ghRDQsA6EIOEYIGoOWt/rKWpVINlFsNU9cV03CAJmrri2KRq877777oMGDWrevHkqlfJ9v6ys7J133mnTps3JJ5988sknt2vXbvLkyWVlZZxu9Oyzz55yyikXX3zxUUcd9fnnn0+dOnW//fbj1HgpJcegkI/Ce57H5nH0bZKJlCBB40MQlIWyRNoqidbN8LdHx+69x25r1m06+7JbVpUHBAGyILJhaEmLmp52OUT1mC0ia1TG5trp7+utWqAcRIq/rz8FABFxcifyViqHlSJzEvnqIY5TV/rAiOJOHC+K/J577LHHN998w0H8+KoTJEjQSCDAGBgD1wOQ9UkWiIVrcdq5P6nIVPbt1eXeW67arcjxHGWNEcrVBEfkGszZ/AIYPFSvqX2HfGRJ1K1JsnNhqwTK9JfNZlOpVOSL1Fpz7lA0QzS9Pj/WmYFLhFhrWbfPflW2T9lRwEwa/YopOB7WT5AgQePCwhgIAetAwhJIodpgyeqqMy64ojqT7XFA54d+P6alBxc21MZ1XBGVFsn9PgeqxaG7DoFuddOFEL7vp9NppjMebjN7xivRIV8wiZOFohJ2LFfi91y9iV2oUko2V1m0zyzJjgIOMSGfg4SYcZoM4RMk+G7ASicBsrnSyo7V+7cpevpPD5SVNFvw5arzLx/7bQZZSOW4VgP5/kgCWkAraAmL2pRKOzNj1kHTLVqcFFROkKAJwILyfYxz/62F1MCcLzdf+stbNlSUDx1wyN1jLk0THA0ljFQEq6EUyMIaKJcACxd5OzRfg5npdhe1QBMkSJCAOOMo14YzBwlAo1eXZvfdMb7Qcz/45/ybb/9zlkAuhKMgpNYaZBH6kAKwZIzMj+ZrenzmVE07NwXt3FufIEGCBgWndRoBLcBxcwtpAceBJBzcpeium3/lb658970ZN93+ZAbwAYJ0UoU6COGmANhMtVRCbCE9aVcgn11hHxIkSNAgiJWqs7AWsHnGkOCGSjiyf+c7x9zgV5S/PXnKLXdOyBB8goF0UsVcrlmm01wFfxeQzddHQqAJEiTYOgggcCzIQBpAslqeSAp4KSiDHwzY/47RVwmBV9569/nX/xUK+IAGNCmyBEjIGiGN2LVIZ1falwQJEjQIBKSqxRWWrAZABkoi7eK44X0u/8n5rpJ33nv/317/SAMhIBxHOKl8EyaJeCUTALA5nf3OjIRAEyRIsE0QYKUg6cG60BbaAFI4IEgJCASAAUaNOPyEYUeE2t75+4denfRxAGRCECSUZ/xw+2vZOdF0pUKJjClBgu8e+R6eEIDQABkIsEFqCdbCUQGgAQUEwI23PfnGO+/pwH/hrxM6t3bSgDDaVRIx+ed/2UeemqIPNbFAEyRIsHWI2AsSUDInqAeEgFIAXCAFOEABcPu1Z5905HBHFYy68LLPlm2qJFjlhBBVQTWgYbUgkLFEGpC5jqC1uirVetX6oknmzicEmiBBgu0hZ/pxDWYpooki91/lXzLEdb/4cdu9WpDRV1978+fLN2YAA5HyigUgBLJV5UJaAH7gR0v6D9DEBqUJgSZIkGCHQXhIuXjuiTu6tGm5dPGa626659tKhIA10KGxFKSLPeNnhZBeKhXWHpVvr6uSbILS0Sa3QQkSJNh5QYAhNEvjT3/4zWGH9P36q2+v/MXtG7OwCo6bstaCtEq5YZi1wH9TML2JuUETAk2QIMGOglUIU8IKoKgAV/zknGZF3udffn3xz+7MEkLAUYXGJ0vG8dzaEiZb7xVDLT9s00JCoAkSJNgxELDChgqhsaQEDuq22x/vvW235qULFy399Z3PhIAlqVLNpPQCa7BLsM8usAsJEiRoKlBSCQBSaMABunUquPFXFzki++Kr7978m78GAhrwjePItLFZQAMWopa9KSKZPexW4/JNBgmBJkiQYEdBwsIaAFCACUkAQw9re/0vL5VSvvbW5Kdf/GcgYAAAjvRqtTveObEtAuUmw/yeNe381/d9fsNFlOOIN/yMLyf+kYvSR0uLLz9BggQ7MyRESsqUCziA5woFpIBTjj346ssvUJ4af+8f//bGApNrRS+VcIgEUdSjE8jXYo/bod/d7mwfWyXQMAyVUq7r+r4PQAhhjOH27lGTD6WUMYZ3mDmR04eithxaayKKuoCEYai15t7FyLeYj5BwaIIEOz0EICAICjavD7Ue8H8/OrT/od28ooLxd9y9ZGV1RgMEoyWRiILxQaC5+9lO1M98W105+U20M0TEzTkAWGuDIOCJUsqoqwc37ZBS8vuoURLbqq7rOo6TzWajBUakGfVZaoidTJAgQeMgNqiUClYCLLwvELhzzE+GD+lrhT37kp8uWZ3xAyhASFRlwyAkAlzPE9JBrF1QEw6/57AdH6gxhjvBZbNZ7muEfJdjbj7MPYvYtFRKRQ3g+L3Wmnsrsa1aXV0NIJ1Ob3Fd3MtzR+5cggQJvlNEdZQFfAe45spzu+/XoTIbnnfpFZU+SKKiyhakXeWKbJib0xjaifpIbpVAuY8bM5q1lg1SHs5H4EE9gFQqFRmbcbuSJ/JfpVRhYWF8hqj78Y7frQQJEnwXEPF/VoIkt1Fy4Hqglq79492j9+nYaXNlePWNd3y9Eekiydp715UGCEOjlBJiCwTaNO3QbfEXW5o8SEesRyaDHZ05j2++EXGdJbBvlO3WaE4e4NdfVN0tS7g1QYKdDnzLivh7SwA3PQb0hoxZuUGcf/FVa9euHTbwsN//9mpPgDRcFwIwFp6EtVbWMu2arlhoWyTFDt0ohu44zuLFixctWpROp5kNXdctLCw86KCD2KiUUs6ZM+f1118HcNxxx/Xu3ZuXwG3flyxZ8s4773z11Vc9e/Y86aSTwjB0HCeycOuP3xMCTZBg50OeNOtNl6E2rqO0gXEwf3H5qCuuC4Lgx8f0v+aK8zyFis3Z5s3SAGxoXFfVCr7HU+CbmhVKWwHzJhMlf7TWDhw4MBqPAxBCDBkyJJPJ8DxnnnmmUqp79+7du3dXSp155pnR0h599FEAbdu2HTZsGICePXtWVlYGQcDfWmujFcVVUFvbtgQJEjRRWCJLRIbIWDKWDJHhiTowZCgMKNRURfTYu/PbDT6zyxGnPPnytPU+ZYhCouqAaSe+REOxhTQ1gIiy2SzFuJKIjDGsQNJaR0zq+/6gQYMGDRrEX8UFTNbaqVOnApgwYQJPfOqppwBMnTo1DMPKysqysrKIT+fOnduiRYubbropvh38K/7LxBonUF5jggQJdl4YY7RmxrCaqFzTsxNndRl8YYcjzn/67XnlRFkiTaRD0iGRIWtznGkpJApzHNrEII0xqVTK933WeDItSimVUhUVFXFPped5QoguXboIIbLZbCTXYpnnXXfddcghh5xxxhk88fTTTz/44IPvuOMOx3EeffTRjRs3/uEPf2BO7Nmz52mnnXb//fdznIpVTUQU6Uxd1w2CIPKcBkGwE0XlEiRIUB+UC6VYAFJCWNtM4eiBfX7wgx+Qcm+/8575n32dtTCAVFD1fJ4E/Ae16xsRUimVzWZTqRTy2iP2WhJRSUkJAI4jRUr4Vq1aCSFYisTGKYu2Zs+e3bVrV8dxmIUdx+nevfv8+fONMTNmzNhnn33KysqQF4T2799/06ZNS5cu1VrzopiyrbWO4xCR53msM7XWMpMmSJBg50UU7WAy4VFm2sP1vxxx5MBe2YqKm2749YrlmdCiygdJQEIIK8AvB3Cabi58pJmPwFOstWEYcoSHp7///vuzZs069NBDOeZz0UUXZTIZ/mrlypVt27YFwBQMoG3btsuXL1dKffPNN+3atctmsxw4CsOwdevWRMTfAqiqqqJYbihbpgBYt8/j94Y/FAkSJGgosJnF1hiAdDothCCLFHDb6Iu77tdlzdffjhn7Wz+ASiG0BPiADxguIiIol9TZ1IjAAUBE48aNC4Ig0hgJIThErpTaa6+9zjrrLM/zfN9Pp9MzZsy46aabbr/99pUrV1566aUfffTRjBkzAKRSqSiyRHnHKEecmDfT6XSUj+S6LhG5rsvUXFRUxMIm13WjoH8qlfI8L57OlCBBgp0UfFMrpYiInYQAlKQUhCU8dN+tZ5511ZIly37y01ueeHSMFAKwgAFJkIpG7k2NPQE4vu+nUqkBAwbwLnEKfDqdrqqqUkpVV1e3bduW2TOVSlVVVUXPECFE+/bthwwZ8sILL4waNcr3fbYc2bfqOA5nIvEgneNUSil2brIgn4j4I//VWv/iF7+YP3++tVYpxTErtlh79uzJLtQECRLsjGDbiOMlXKLIdV2yRimRVsotwK1jb7jm2hsgwlVfb2zbqpkj2A+a94Y2Pe8nw0mlUsaYwYMHa63Z/4i8zSjzYtaqqqqioiIAHORxHIcrKg0aNAjA2rVrgyDo3LnzokWL2MHBduWKFSt69OjhOM7ee+/97rvvAmDnJoBVq1YJIbp168Yf2SB1HGfkyJEbN24sKiqqqqqaNGnSbbfdxjy+++67f0fHJ0GCBDsGHChWSkVRDVc5BAS+TaVkr+67jR1zRc+eB6ZdCAJB1UpqAgArgKYmqneYEDmTHflgGe8hV04iIh5iV1VVzZ49u0OHDm3atGF6XbJkCZuZnucdfvjhkydPjtcEeffdd4888khjzLBhw5555pkVK1a0b9+ej+CkSZM6dOhQWlrKG0H5iiQHHXQQr5eXf+ihh/Lyk1F8ggQ7NdhCQn6MK6Xk+1oQCjypCUqg/8H7V4dZhTS7OyUBoqaoXUyI05Q4dBsSp0jpydiwYUOzZs1OPPHEjRs3svR95MiRSqklS5YQ0XvvvQfgscceI6IwDO+66y7Xdd955x0iWr9+fWlp6VlnncVfzZw5E8CYMWM41s8rYtdnHNvetgQJEuz0sGQty+ZDomqiSqJqS6Qpp/wMiXROBxoQBWRDorpE8d1iqyQVZzdrLRPck08+6ThOYWHhsGHDOnbsCODhhx/mb33fP/fccx3H6dWrV8+ePR3Hufbaa6Pl/PGPf3Qcp3379oMGDSooKDjiiCO4KnOUxRStq2bLEgJNkGBXB6vliQKiCqJyokqeGBL5RD5RGBGobYoEutV8c46U5WaKJaovXrz4nXfeWblyZWlp6WmnndauXbuoMkgYhp988snLL79MRCeeeGKfPn0oViXkyy+/fPPNN1evXt23b98RI0ZwmTvWn0ZKKcoXLkGSC58gwfcA+dojGjCABTmAS4I/gPvGK1gFCwKshGxacvptkRQXAUG+DhN/ZE6MIk7xxCGegUf9EaU6jhMEARNlnE9Z0sTRdv62jq8zIdAECXZ5ECy4bCjli4YICQEDUL6giAIU8h+aWFW7rbpj48Ygg8mR8ziZ6bLZLFMqF12OdKDxn7C2lBVOrGrir+LVlxETzydIkOB7AwsYwAAO4EBI5NRLkLAKlqkzPyZtWtTJ2M4QHnnDMF7Bk99TPiWL5e78Lb+JXJmu60Z2ZXykz7H1SEgPILJDa7YssUATJNjFYQFDEAJOjUpeINZLTgKyVo3RJobtkBRnJXF6ErtEwzBMpVJMi9GYPfKW8hu2Rnl6/C9iboEIQRBEbebi3yYEmiDB9wAWAEHGR6A5jychLqQnActj+aaEbSmqWAcasSeHkiL2NMYw2UVWpJSS80GjhC3mTS7dBCAIgijLPhrLc6c5bIlbEyRIsIuDahoab6FcSD0LqqmZVE3Xykss0AQJvj+I3+oC9ZhS5OZpauP4JMMnQYIE3z3q9UT7N+ZpAmhKSVEJEiRIsFMhIdAECRIk+C+REGiCBAkS/JdICDRBggQJ/kskBJogQYIE/yUSAk2QIEGC/xJNkUDryz+TTPkECRI0QTRFHShnhRYVFYVhyImkdcqaJEiQIEFTQFMkUKbL/fbbL8nsTJAgQVPG/wOvU05rBMCRwQAAAABJRU5ErkJggg==
A projectile is shot in the air from ground level with an initial velocity of $500$ m/sec at an angle of $60$ deg with the horizontal. At what time is the maximum range of the projectile attained? The graph is shown here:
$t$ = $88.37$
c487e6c3-04f0-44a1-9e8f-4512dccbeacf
differential_calc
true
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
The graph below is the derivative of a function, $f$, whose domain is the set of all real numbers and is continuous everywhere. Determine the x values for the relative extrema for $f$.
There is a local maximum at x-value(s): $x=-3$, $x=4$ There is a local minimum at x-value(s): $x=-1$
c57070ee-de68-4104-beda-984585448856
differential_calc
false
null
For the function $y = (3 - x)^3 \cdot (x + 2)^2$ specify the points where local maxima and minima of $y$ occur. 1. The point(s) where local maxima occur 2. The point(s) where local minima occur
1. The point(s) where local maxima occur: $P(0,108)$ 2. The point(s) where local minima occur: $P(-2,0)$
c57bcca2-8fe0-433f-98b9-bd31a9a66e49
integral_calc
false
null
Solve the integral: $$ \int \frac{ 4 }{ \cos(-3 \cdot x)^3 \cdot \sin(-3 \cdot x)^2 } \, dx $$
$\int \frac{ 4 }{ \cos(-3 \cdot x)^3 \cdot \sin(-3 \cdot x)^2 } \, dx$ = $C+\frac{4}{3}\cdot\left(\frac{3}{4}\cdot\ln\left(\left|1+\sin(3\cdot x)\right|\right)-\frac{1}{2\cdot\left(\left(\sin(3\cdot x)\right)^2-1\right)}\cdot\sin(3\cdot x)-\frac{3}{4}\cdot\ln\left(\left|\sin(3\cdot x)-1\right|\right)-\frac{1}{\sin(3\cdot x)}\right)$
c600dd96-8ec6-4564-8cfc-0dcecb9d1084
integral_calc
false
null
Solve the integral: $$ 2 \cdot \int \sin(-2 \cdot x)^5 \cdot \cos(2 \cdot x)^2 \, dx $$
$2 \cdot \int \sin(-2 \cdot x)^5 \cdot \cos(2 \cdot x)^2 \, dx$ = $C+\frac{1}{3}\cdot\left(\cos(2\cdot x)\right)^3+\frac{1}{7}\cdot\left(\cos(2\cdot x)\right)^7-\frac{2}{5}\cdot\left(\cos(2\cdot x)\right)^5$
c6544023-d8e0-45df-9798-832448bac8aa
sequences_series
false
null
Find the Fourier expansion of this function: $$ f(x) = \begin{cases} -\frac{ \pi }{ 4 }, & -\pi \le x < 0 \\ \frac{ \pi }{ 4 }, & 0 \le x \le \pi \end{cases} $$ at $(-\pi, \pi)$.
The Fourier series is: $\sum_{n=1}^\infty\left(\frac{\sin\left((2\cdot n-1)\cdot x\right)}{2\cdot n-1}\right)$
c65eeba7-8616-499c-97b1-31abc7253b2d
sequences_series
false
null
Find the Taylor series of $f'(x)$ about $a=0$ if $f(x) = \frac{ \sin(x) - x }{ x^2 }$. Use sigma notation in the final answer.
The final answer: $\sum_{k=1}^\infty\left((-1)^k\cdot\frac{(2\cdot k-1)\cdot x^{2\cdot k-2}}{(2\cdot k+1)!}\right)$
c6e74489-488e-4d9a-8ad5-45abc3c647e9
sequences_series
false
null
Given that $\frac{ 1 }{ 1-x } = \sum_{n=0}^\infty \left(x^n\right)$ with convergence in $(-1,1)$, find the power series for the function with the given center $a$, and identify its interval of convergence: 1. $f(x) = \frac{ x^2 }{ 5-4 \cdot x+x^2 }$; $a=2$.
1. $f(x)$ = $\sum_{n=0}^\infty\left(x^2\cdot\left(-(x-2)^2\right)^n\right)$ 2. $I$ = $(1,3)$
c724aa02-d543-4850-97d9-517c1f1eeb74
differential_calc
false
null
A rocket shot into the air that then returns to Earth. The height of the rocket in meters is given by $h(t) = 600 + 78.4 \cdot t - 4.9 \cdot t^2$, where $t$ is measured in seconds. Compute the average velocity of the rocket over the given time intervals. Round your answer to eight significant digits. 1. $[9,9.01]$ 2. $[8.99,9]$ 3. $[9,9.001]$ 4. $[8.999,9]$
1. $-9.8490000$ m/sec. 2. $-9.7510000$ m/sec. 3. $-9.8049000$ m/sec. 4. $-9.7951000$ m/sec.
c7fcefca-8951-42f5-99b4-83026cbb571f
algebra
false
null
Perform the indicated operation and express the result as a simplified complex number: $i^{15}$
The final answer: $-i$
c80d8185-edc4-4a44-9e58-dcab9d666178
differential_calc
false
null
Find any local extrema for $s = \left| \arctan\left(4 \cdot x^2 - 12 \cdot x + 8\right) \right|$. Submit as your final answer: 1. The point(s), where the function has local maximum(s); 2. The point(s), where the function has local minimum(s).
1. Local Maximum(s) $P\left(\frac{3}{2},\frac{\pi}{4}\right)$; 2. Local Minimum(s) $P(1,0)$, $P(2,0)$.
c890e92c-0ebd-42a5-a3d3-fce40464ed16
precalculus_review
false
null
Calculate the derivative $\frac{ d }{d x}\left(\log_{x}(a)\right)$ for $x > 0$, $a > 0$, $x \ne 1$, $a \ne 1$.
$\frac{ d }{d x}\left(\log_{x}(a)\right)$ = $\frac{-\ln(a)}{x\cdot\left(\ln(x)\right)^2}$
c89d463c-5220-451b-80db-0200a72cbdcb
sequences_series
false
null
Consider the power series $\sum_{k=0}^\infty \frac{ (1-3 \cdot x)^k }{ 4^k \cdot \sqrt{k+1} }$. 1. Find the center of convergence of the series. 2. Find the radius of convergence of the series.
1. The center of convergence is $\frac{1}{3}$. 2. The radius of convergence is $\frac{4}{3}$.
c89f34ab-0533-4173-aba0-76f2b2800224
algebra
false
null
Solve the following inequality: $-5 x^2 + 10 x + 15 \le 0$. Express your answer in the interval form.
Solution in the interval form: $\left(-\infty,\ -1\right] \cup \left[3,\ \infty\right)$ *Note: enter an interval or union of intervals. If there is no solution, leave empty or enter "none".*
c8c08145-397a-4331-8934-956d0e39af2d
sequences_series
false
null
Determine the Taylor series for $f(x) = \frac{ 2 \cdot x - 1 }{ x^2 - 3 \cdot x + 2 }$, centered at $x_{0} = 0$. Write out the sum of the first four non-zero terms, followed by dots.
The final answer: $\left(1-\frac{3}{2}\right)+\left(1-\frac{3}{2}\cdot\frac{1}{2}\right)\cdot x+\left(1-\frac{3}{2}\cdot\frac{1}{2^2}\right)\cdot x^2+\left(1-\frac{3}{2}\cdot\frac{1}{2^3}\right)\cdot x^3+\cdots$
c8dc16e5-519c-4ebe-9432-d1f13b782008
algebra
false
null
To convert from $x$ degrees Fahrenheit to $y$ degrees Celsius, we use the formula $f(x) = \frac{ 5 }{ 9 } \cdot (x-32)$. Find the inverse function, if it exists. If it doesn't exist, write $\text{None}$.
Inverse function: $g(x)=\frac{9}{5}\cdot y+32$
c9256ca7-b498-433f-975c-11aa311ca307
precalculus_review
false
null
Use the Rational Zero Theorem to find all real zeros of the following polynomial: $p(x) = 9 \cdot x^3 + 6 \cdot x^2 - 29 \cdot x - 10$
The real zeros are $-2$, $-\frac{1}{3}$, $\frac{5}{3}$
c92615c8-ce81-46c3-8693-7b13461c9371
multivariable_calculus
true
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
Find the surface area bounded by the curves $q = a \cdot \cos(\varphi)$, $p = b \cdot \cos(\varphi)$, $b > a > 0$.
$S$ = $\frac{\pi}{4}\cdot\left(b^2-a^2\right)$
c9286655-d7f7-45da-a36c-6736332eca0d
integral_calc
false
null
Compute the integral: $$ 3 \cdot \int \frac{ \cos(3 \cdot x)^4 }{ \sin(3 \cdot x)^3 } \, dx $$
$3 \cdot \int \frac{ \cos(3 \cdot x)^4 }{ \sin(3 \cdot x)^3 } \, dx$ = $C+\frac{3}{4}\cdot\ln\left(\frac{1+\cos(3\cdot x)}{1-\cos(3\cdot x)}\right)-\frac{\left(\cos(3\cdot x)\right)^3}{2-2\cdot\left(\cos(3\cdot x)\right)^2}-\frac{3}{2}\cdot\cos(3\cdot x)$
c93e2665-a4ed-40fb-85e2-4c28ad0dced4
sequences_series
false
null
Evaluate $\sum_{n=2}^\infty\frac{ n \cdot (n-1) }{ 2^n }$ as $f''\left(\frac{ 1 }{ 2 }\right)$ where $f(x) = \sum_{n=0}^\infty x^n$.
$\sum_{n=2}^\infty\frac{ n \cdot (n-1) }{ 2^n }$ = $4$
c9dd4213-29b4-46b3-86dd-b34b06ed004a
precalculus_review
false
null
Find the zeros of $f(x) = (2 - x)^4 + (2 \cdot x - 1)^4 - (x + 1)^4$.
The final answer: $x_1=2 \land x_2=\frac{1}{2}$
c9e88bba-f8b2-49e6-8c20-2bb176663e89
sequences_series
false
null
Using the Taylor formula, decompose the function $f(x) = \ln\left(1+\frac{ x }{ 5 }\right)$ in powers of the variable $x$ on the segment $[0,1]$. Use the first nine terms. Then estimate the accuracy obtained by dropping an additional term after the first nine terms.
1. $\ln\left(1+\frac{ x }{ 5 }\right)$ = $\frac{x}{5}-\frac{x^2}{5^2\cdot2}+\frac{x^3}{5^3\cdot3}-\frac{x^4}{5^4\cdot4}+\frac{x^5}{5^5\cdot5}-\frac{x^6}{5^6\cdot6}+\frac{x^7}{5^7\cdot7}-\frac{x^8}{5^8\cdot8}+\frac{x^9}{5^9\cdot9}$ 2. Accuracy is not more than $\frac{1}{10\cdot5^{10}}$
c9fab8b1-59aa-4e6f-9428-ef2aa6679b28
algebra
false
null
A local band sells out for their concert. They sell all 1175 tickets for a total purse of $28,112.5. The tickets were priced at $20 for student tickets, $22.5 for children, and $29 for adult tickets. If the band sold twice as many adult as children tickets, how many of each type was sold?
Student tickets: $500$ Children tickets: $225$ Adult tickets: $450$
ca5a60b8-627d-46bb-af40-542e361e629d
differential_calc
true
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
Use the following figure to find the indicated derivatives, if they exist (enter 'undefined' if the derivative doesn't exist): Let $h(x) = f(x) + g(x)$. Find: 1. $h'(1)$ 2. $h'(3)$ 3. $h'(4)$
1. $h'(1)$ = $0$ 2. $h'(3)$ = None 3. $h'(4)$ = $1$
ca5b0525-4e4c-4698-8367-146ba9ca18e3
algebra
false
null
Luna is going bowling. Shoe rental costs $3 and the lane costs $2 per game. If Luna paid a total of $17, how many games did she bowl?
Luna bowled $7$ games.
ca5ffe7c-f495-43dc-a653-de477cabc185
sequences_series
false
null
Find the radius of convergence of the series: $$ \sum_{n=1}^\infty \left(\frac{ \left((2 \cdot n)!\right) \cdot x^n }{ n^{2 \cdot n} }\right) $$
$R$ = $\frac{e^2}{4}$
ca6b1413-d76d-4992-89ed-aaad88dc94ef
multivariable_calculus
false
null
Evaluate $L=\lim_{P(x,y) \to P(m+n,m-n)}\left(\frac{ x^2-m \cdot x-x \cdot y+m \cdot y-2 \cdot n \cdot x+2 \cdot m \cdot n }{ x \cdot y-n \cdot x-y^2-n \cdot y+2 \cdot n^2 }\right)$, given $m-2 \cdot n=7 \cdot n$
The final answer: $L=\frac{1}{7}$
cac53af9-3149-4ea9-b0c9-13b6a9d9a18f
algebra
false
null
Use the Rational Zero Theorem to find the real solution(s) for the equation: $8 \cdot x^4 + 26 \cdot x^3 + 39 \cdot x^2 + 26 \cdot x + 6 = 0$
By the Rational Zero Theorem, possible solutions occur at values $-\frac{1}{2}$, $-\frac{3}{4}$, $1$, $-1$, $2$, $-2$, $3$, $-3$, $\frac{ 1 }{ 2 }$, $\frac{ 3 }{ 2 }$, $-\frac{ 3 }{ 2 }$, $\frac{ 1 }{ 4 }$, $-\frac{ 1 }{ 4 }$, $\frac{ 3 }{ 4 }$, $\frac{ 1 }{ 8 }$, $-\frac{ 1 }{ 8 }$, $\frac{ 3 }{ 8 }$, $-\frac{ 3 }{ 8 }$, $6$, $-6$. (Be sure to submit each possibility only once; hint: there are 20 unique possibilities by RZT). $x$ = $-\frac{1}{2}$, $-\frac{3}{4}$, $1$, $-1$, $2$, $-2$, $3$, $-3$, $\frac{ 1 }{ 2 }$, $\frac{ 3 }{ 2 }$, $-\frac{ 3 }{ 2 }$, $\frac{ 1 }{ 4 }$, $-\frac{ 1 }{ 4 }$, $\frac{ 3 }{ 4 }$, $\frac{ 1 }{ 8 }$, $-\frac{ 1 }{ 8 }$, $\frac{ 3 }{ 8 }$, $-\frac{ 3 }{ 8 }$, $6$, $-6$
cb4f082e-28c9-4e3d-bc92-12d111f5c953
sequences_series
false
null
Compute $\int_{0}^{\frac{ 1 }{ 5 }} e^{-2 \cdot x^2} \, dx$ with accuracy $0.00001$.
The final answer: $0.1948$
cb72c058-1dd3-47a6-bf34-25ab75f7a436
integral_calc
false
null
Find the integral: $$ \int \frac{ 4 \cdot x^2+25 \cdot x+7 }{ \sqrt{x^2+8 \cdot x} } \, dx $$
$\int \frac{ 4 \cdot x^2+25 \cdot x+7 }{ \sqrt{x^2+8 \cdot x} } \, dx$ = $(2\cdot x+1)\cdot\sqrt{x^2+8\cdot x}+3\cdot\ln\left(\left|x+4+\sqrt{x^2+8\cdot x}\right|\right)+C$
cbb4b10b-ecb3-497b-8a66-81c54a1d265a
precalculus_review
false
null
Evaluate the definite integral. Express answer in exact form whenever possible: $$ \int_{\frac{ -\pi }{ 3 }}^{\frac{ \pi }{ 3 }} \sqrt{\left(\sec(x)\right)^2-1} \, dx $$
$\int_{\frac{ -\pi }{ 3 }}^{\frac{ \pi }{ 3 }} \sqrt{\left(\sec(x)\right)^2-1} \, dx$ = $0$
cc16099c-195d-4735-9d83-0b18f8f27a27
sequences_series
false
null
Find a “reasonable” upper-bound on the error in approximating $f(x) = x^7$ by its 3rd order Taylor polynomial $P_{3}(x)$ about $a = -1$ valid for all values of $x$ such that $|x + 1| \leq 0.1$.
The final answer: $840\cdot(1.1)^3\cdot\frac{(0.1)^4}{4!}$
cc733108-05a4-4478-9f32-0eea85157535
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 $x^{\frac{ 1 }{ 2 }}+y^{\frac{ 1 }{ 2 }}=5^{\frac{ 1 }{ 2 }}$.
Volume = $\pi\cdot\frac{25}{3}$
cc73f597-71ca-49bd-8bc4-62c5b0c48753
differential_calc
false
null
Make full curve sketching of $y = \arcsin\left(\frac{ 1-3 \cdot x^2 }{ 1+3 \cdot x^2 }\right)$. 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) $(-1\cdot\infty,\infty)$ 2. Vertical asymptotes None 3. Horizontal asymptotes $y=-\frac{\pi}{2}$ 4. Slant asymptotes None 5. Intervals where the function is increasing $(-\infty,0)$, $(0,\infty)$ 6. Intervals where the function is decreasing $(-\infty,0)$, $(0,\infty)$ 7. Intervals where the function is concave up $(-\infty,0)$ 8. Intervals where the function is concave down None 9. Points of inflection None
cc752972-ff6b-4b03-8a40-722afdd8bb50
multivariable_calculus
false
null
Determine the coordinates, if any, for which $f(x,y) = x^3 - 3 \cdot x \cdot y^2 + 6 \cdot y^2 - 8$ has 1. a Relative Minimum(s) 2. a Relative Maximum(s) 3. a Saddle Point(s) If a Relative Minimum or Maximum, find the Minimum or Maximum value. If none, enter None.
1. The function $f(x,y)$ has Relative Minimum(s) at None with the value(s) None 2. The function $f(x,y)$ has Relative Maximum(s) at None with the value(s) None 3. The function $f(x,y)$ has a Saddle Point(s) at $P(2,-2)$, $P(2,2)$
ccfa5962-71e5-4955-bc2d-c91098f2cd13
integral_calc
false
null
Solve the integral: $$ \int \frac{ 20 \cdot \cos(-10 \cdot x)^3 }{ 21 \cdot \sin(-10 \cdot x)^7 } \, dx $$
$\int \frac{ 20 \cdot \cos(-10 \cdot x)^3 }{ 21 \cdot \sin(-10 \cdot x)^7 } \, dx$ = $C+\frac{1}{21}\cdot\left(\frac{1}{2}\cdot\left(\cot(10\cdot x)\right)^4+\frac{1}{3}\cdot\left(\cot(10\cdot x)\right)^6\right)$
cd1538cc-ca04-4235-819e-b0d2b3542eb2
algebra
false
null
The unit price of an item affects its supply and demand. That is, if the unit price goes up, the demand for the item will usually decrease. For example, a local newspaper currently has $84\ 000$ subscribers at a quarterly charge of $\$30$. Market research has suggested that if the owners raise the price to $\$32$, they would lose $5000$ subscribers. Assuming that subscriptions are linearly related to the price, what price should the newspaper charge for a quarterly subscription to maximize their revenue?
The final answer: $31.8$
cdfb4e3a-81b3-4b5e-84f0-0e48d5898fe4
sequences_series
false
null
Find the Taylor polynomial $P_{5}$ for the function $f(x) = x \cdot \cos\left(x^2\right)$.
$P_{5}$ = $x-\frac{1}{2}\cdot x^5$
ce47631d-a24b-4d1b-8f75-aeaf64f9da34
integral_calc
false
null
Solve the integral: $$ -\int \frac{ 1 }{ \cos(x)^3 \cdot \sin(x)^2 } \, dx $$
$-\int \frac{ 1 }{ \cos(x)^3 \cdot \sin(x)^2 } \, dx$ = $C+\frac{\sin(x)}{2\cdot\left(\left(\sin(x)\right)^2-1\right)}+\frac{3}{4}\cdot\ln\left(\left|\sin(x)-1\right|\right)+\frac{1}{\sin(x)}-\frac{3}{4}\cdot\ln\left(\left|1+\sin(x)\right|\right)$
ce5fb045-4688-4338-8225-f0a5c9b38ee2
sequences_series
false
null
Find the Fourier series of the function $\psi(x) = e^{-2 \cdot x}$ in the interval $(-2 \cdot \pi, 2 \cdot \pi)$.
The Fourier series is: $e^{-2\cdot x}=\frac{\left(e^{4\cdot\pi}-e^{-4\cdot\pi}\right)}{\pi}\cdot\left(\frac{1}{8}+\sum_{n=1}^\infty\frac{(-1)^n\cdot\left(4\cdot\cos(n\cdot x)+n\cdot\sin(n\cdot x)\right)}{16+n^2}\right)$
ce91d092-7d61-4244-85a6-f8d040bb6264
precalculus_review
false
null
Find zeros of $f(x) = \sqrt{2 \cdot x - 1} - \sqrt{x - 1} - 5$
The final answer: $x=145$
ce97eb96-8d97-4889-97b8-deb2bb3023a4
algebra
false
null
Write an expression for a rational function with the given characteristics: 1. vertical asymptotes $x=-6$ and $x=6$, 2. x-intercepts at $P(1,0)$ and $P(-1,0)$, 3. y-intercept at $P(0,2)$.
The rational function satisfying the given conditions is $f(x)=\frac{72\cdot(x-1)\cdot(x+1)}{(x+6)\cdot(x-6)}$
ceae34e5-3a64-44a0-95c9-a2e5f16fe8ae
integral_calc
false
null
Find the area of the figure enclosed between the curves $y = 4 \cdot x^2$, $y = \frac{ x^2 }{ 3 }$, and $y = 2$.
Area: $\frac{\left(8\cdot\sqrt{3}-4\right)\cdot\sqrt{2}}{3}$
cf789d84-24bd-45fa-89da-772ce496d1d0
multivariable_calculus
false
null
Find the measure of the angle $\theta$ between the three-dimensional vectors $\vec{a}$ and $\vec{b}$, expressed in radians rounded to two decimal places, if it is not possible to express it exactly. Given: $\vec{a} = 3 \cdot \vec{i} - \vec{j} - 2 \cdot \vec{k}$ $\vec{b} = \vec{v} - \vec{w}$, where $\vec{v} = 2 \cdot \vec{i} + \vec{j} + 4 \cdot \vec{k}$ and $\vec{w} = 6 \cdot \vec{i} + \vec{j} + 2 \cdot \vec{k}$
$\theta$ = $2.84$
cfeeda2e-b0df-47fc-89b0-3f8cb8938309
integral_calc
false
null
Evaluate the integral: $$ I = \int 3 \cdot x \cdot \ln\left(4 + \frac{ 1 }{ x } \right) \, dx $$
The final answer: $\left(\frac{3}{2}\cdot x^2\cdot\ln(4\cdot x+1)-\frac{3\cdot x^2}{4}+\frac{3\cdot x}{8}-\frac{3}{32}\cdot\ln\left(x+\frac{1}{4}\right)\right)-\left(\frac{3}{2}\cdot x^2\cdot\ln(x)-\left(C+\frac{3}{4}\cdot x^2\right)\right)$
cfef8ba8-ebc2-4ce0-a35f-c900e2bf8c99
sequences_series
false
null
A general telescoping series is one in which all but the first few terms cancel out after summing a given number of successive terms. Let $a_{n} = f(n) - 2 \cdot f(n+1) + f(n+2)$, in which $f(n)$ -> 0 as $n$ -> $\infty$. Find $\sum_{n=1}^\infty\left(a_{n}\right)$.
$\sum_{n=1}^\infty\left(a_{n}\right)$ = $f(1)-f(2)$
d0331d53-4efd-46ce-a9d3-d10570408bd7
precalculus_review
false
null
Solve $z^2 - (2 \cdot i + 1) \cdot z - (3 - i) = 0$.
The final answer: $z_1=2+i \lor z_1=-1+i$
d0e2146e-63e1-4b1d-8f2c-6c0c62ab256f
multivariable_calculus
false
null
Calculate the double integral: $$ \int\int_{R}{\left(x \cdot y \cdot \sqrt{x^2+y^2}\right) d A} $$ where $R=\left\{(x,y)|0 \le x \le 1,0 \le y \le 2\right\}$.
The final answer: $\frac{25\cdot\sqrt{5}-33}{15}$
d1263456-584b-4e04-be1c-20da3101099e
sequences_series
false
null
Find the Fourier series of the function $\psi(x) = e^{-x}$ in the interval $(-\pi,\pi)$.
The Fourier series is: $e^{-x}=\frac{e^\pi-e^{-\pi}}{2\cdot\pi}\cdot\left(\frac{1}{2}+\sum_{n=1}^\infty\left(\frac{(-1)^n}{1+n^2}\cdot\left(\cos(n\cdot x)+n\cdot\sin(n\cdot x)\right)\right)\right)$