uuid
stringlengths 36
36
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stringclasses 6
values | has_image
bool 2
classes | image
stringclasses 160
values | problem_statement
stringlengths 32
784
| golden_answer
stringlengths 7
1.13k
|
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15ae9179-a0f2-4848-9b6e-0a1f50f70491 | algebra | true | 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 | Use the graph in figure, which shows the profit, $y$, in thousands of dollars, of a company in a given year, $t$, where $t$ represents the number of years since $1980$:
Find the slope. | Slope: $30$ |
15c84a6a-1fd0-4fb0-977a-daae876ccb9b | sequences_series | false | null | Find the Fourier series of the function $u = \left| \sin\left( \frac{ x }{ 2 } \right) \right|$ in the interval $[-2 \cdot \pi,2 \cdot \pi]$. | The Fourier series is: $\frac{2}{\pi}+\frac{4}{\pi}\cdot\sum_{k=1}^\infty\left(\frac{1}{\left(1-4\cdot k^2\right)}\cdot\cos(k\cdot x)\right)$ |
15dd94cf-dae0-43c2-837b-d48e826a391b | sequences_series | false | null | Find the expansion in the series of the integral $\int_{0}^x{\frac{ \arctan\left(x^2\right) }{ 4 \cdot x } d x}$, using the expansion of the integrand in the series. Find the radius of convergence of the series. | 1. $\int_{0}^x{\frac{ \arctan\left(x^2\right) }{ 4 \cdot x } d x}$ = $\sum_{n=1}^\infty\left((-1)^{n+1}\cdot\frac{x^{2\cdot(2\cdot n-1)}}{4\cdot2\cdot(2\cdot n-1)^2}\right)$
2. $R$ = $1$ |
15ddf157-e25a-4c30-aa8b-dcc9d5b8abb5 | precalculus_review | false | null | Calculate $E = \frac{ \cos(70) \cdot \cos(10) + \cos(80) \cdot \cos(20) }{ \cos(68) \cdot \cos(8) + \cos(82) \cdot \cos(22) }$. | The final answer: $E=1$ |
15e0826d-2594-436a-a05c-e9872b5222e4 | integral_calc | false | null | Solve the integral:
$$
\int \frac{ -9 \cdot \sqrt[3]{x} }{ 9 \cdot \sqrt[3]{x^2} + 3 \cdot \sqrt{x} } \, dx
$$ | $\int \frac{ -9 \cdot \sqrt[3]{x} }{ 9 \cdot \sqrt[3]{x^2} + 3 \cdot \sqrt{x} } \, dx$ = $-\left(C+\frac{1}{3}\cdot\sqrt[6]{x}^2+\frac{2}{27}\cdot\ln\left(\frac{1}{3}\cdot\left|1+3\cdot\sqrt[6]{x}\right|\right)+\frac{3}{2}\cdot\sqrt[6]{x}^4-\frac{2}{3}\cdot\sqrt[6]{x}^3-\frac{2}{9}\cdot\sqrt[6]{x}\right)$ |
16393e13-072d-439a-b975-4363298c4da4 | algebra | false | null | Find all real solutions of the following equation:
$$
\frac{ 2 }{ x+7 }-\frac{ 3 }{ x-3 }=1
$$ | The real solution(s) to the given equation are: $x=-3$, $x=-2$ |
16c8afab-e3d5-432e-8e76-b8d3674e86cd | multivariable_calculus | false | null | Determine a definite integral that represents the region common to $r=2$ and $r=4 \cdot \cos\left(\theta\right)$. | The final answer: $4\cdot\int_0^{\frac{\pi}{3}}1d\theta+16\cdot\int_{\frac{\pi}{3}}^{\frac{\pi}{2}}\cos\left(\theta\right)^2d\theta$ |
16e404c3-c9da-465c-a97d-0b7a6e1e5ef9 | integral_calc | false | null | Compute the integral:
$$
\int \frac{ 6 }{ \sin(3 \cdot x)^6 } \, dx
$$ | $\int \frac{ 6 }{ \sin(3 \cdot x)^6 } \, dx$ = $-\frac{2\cdot\cos(3\cdot x)}{5\cdot\sin(3\cdot x)^5}+\frac{24}{5}\cdot\left(-\frac{\cos(3\cdot x)}{9\cdot\sin(3\cdot x)^3}-\frac{2}{9}\cdot\cot(3\cdot x)\right)+C$ |
171de471-6ade-4285-bf3c-033a5f936e58 | differential_calc | true | data:image/png;base64,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 | List all inflection points and intervals where the function $f$ is concave up and concave down: | Inflection points at: $x=0$, $x=1$
Intervals where function concaves up: $(-\infty,0)\cup(1,\infty)$
Intervals where function concaves down: $(0,1)$ |
177da421-b0f6-4ac2-9fe5-ca0ad9019fcc | integral_calc | true | 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 | Evaluate the integral of the functions graphed using the formulas for areas of triangles and circles, and subtracting the areas below the $x$-axis: | The final answer: $5\cdot\pi-4$ |
17da1e7d-97b0-4d23-b930-90c988aec14d | multivariable_calculus | false | null | Find the curvature for the vector function: $\vec{r}(t) = \left\langle 2 \cdot \sin(t), -4 \cdot t, 2 \cdot \cos(t) \right\rangle$. | The final answer: $\frac{1}{10}$ |
17e5455e-6eec-45ee-8ff2-6ed4855fe878 | algebra | false | null | Solve the inequality $|-6 x-6| \le 1$.
Express your answer using interval notation. | Solution using interval notation: $\left[-\frac{ 7 }{ 6 },\ -\frac{ 5 }{ 6 }\right]$
*Note: enter an interval or union of intervals. If there is no solution, leave empty or enter "none"* |
181d4ee1-d2bd-43d2-b77e-2d5c94992059 | sequences_series | false | null | Integrate the approximation $\sin(t) \approx t - \frac{ t^3 }{ 6 } + \frac{ t^5 }{ 120 } - \frac{ t^7 }{ 5040 } + \cdots$ evaluated at $\pi \cdot t$ to approximate $\int_{0}^1{\frac{ \sin(\pi \cdot t) }{ \pi \cdot t } d t}$ | $\int_{0}^1{\frac{ \sin(\pi \cdot t) }{ \pi \cdot t } d t}$ ≈ $0.58678687$ |
182fed94-4634-460f-a70e-7958a2033664 | sequences_series | false | null | Find the Fourier integral of the function $q(x) = \begin{cases} 0, & x < 0 \\ 2 \cdot \pi \cdot x, & 0 \le x \le 1 \\ 0, & x > 1 \end{cases}$ | $q(x) = $\int_0^\infty\left(\frac{2\cdot\left(\alpha\cdot\sin\left(\alpha\right)+\cos\left(\alpha\right)-1\right)\cdot\cos\left(\alpha\cdot x\right)+2\cdot\left(\sin\left(\alpha\right)-\alpha\cdot\cos\left(\alpha\right)\right)\cdot\sin\left(\alpha\cdot x\right)}{\alpha^2}\right)d\alpha$ |
18b1ee59-f5ad-4c3b-b9b7-fd2b634b16fd | differential_calc | false | null | Find the second derivative $\frac{d ^2y}{ d x^2}$ of the function $x = \left(2 \cdot \sin(3 \cdot t)\right)^2$, $y = \sin(2 \cdot t)$. | $\frac{d ^2y}{ d x^2}$ = $\frac{\left(288\cdot\left(\sin(3\cdot t)\right)^2-144\right)\cdot\cos(2\cdot t)-96\cdot\cos(3\cdot t)\cdot\sin(2\cdot t)\cdot\sin(3\cdot t)}{13824\cdot\left(\cos(3\cdot t)\right)^3\cdot\left(\sin(3\cdot t)\right)^3}$ |
18fc468f-42f0-4606-b4f3-92f1f552c344 | integral_calc | false | null | Calculate the integral:
$$
I = \int 4 \cdot \cos\left(3 \cdot \ln(2 \cdot x)\right) \, dx
$$ | The final answer: $\frac{1}{10}\cdot\left(C+4\cdot x\cdot\cos\left(3\cdot\ln(2\cdot x)\right)+12\cdot x\cdot\sin\left(3\cdot\ln(2\cdot x)\right)\right)$ |
1924526f-31e1-40a9-8f23-7a27b272596c | sequences_series | false | null | Find the sum of the series $\sum_{n=1}^\infty \frac{ 7 }{ 2 \cdot n \cdot 3^n }$. (Use the formula $\int_{3}^\infty \frac{ 7 }{ 2 \cdot x^{n+1} } \, dx = \frac{ 7 }{ 2 \cdot n \cdot 3^n }$) | The sum of the series is $-\frac{7\cdot\ln\left(\frac{2}{3}\right)}{2}$ |
193fcb07-99e8-4fd6-8954-283c505ec24e | precalculus_review | false | null | A vehicle with a 20-gallon tank gets 15 mpg. The number of miles $N$ that can be driven depends on the amount of gas $x$ in the tank.
1. Write a formula that models this situation.
2. Determine the number of miles the vehicle can travel on
* a full tank of gas and
* $\frac{ 3 }{ 4 }$ of a tank of gas.
3. Determine the
* domain and
* range of the function.
4. Determine how many times the driver had to stop for gas if she has driven a total of 578 mi. | 1. The formula for the function is $N(x)$ = $15\cdot x$
2. The number of miles the vehicle can travel on
* full tank of gas is $300$
* $\frac{ 3 }{ 4 }$ of a tank of gas is $225$
3. Domain and range (in interval notation)
* domain is $[0,20]$
* range is $[0,300]$
4. Number of times that the driver had to stop = $1$ |
19877db1-15f2-43a7-962d-f116bd6032a8 | differential_calc | true | 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 | Use the following graph and find: $\lim_{x \to 2^{+}}\left(f(x)\right)$ | $\lim_{x \to 2^{+}}\left(f(x)\right)$: $2$ |
19e6fecd-10a0-4497-b9dd-72c176820215 | sequences_series | false | null | Find the radius of convergence of the series:
$$
\sum_{n=1}^\infty \left( \frac{ \prod_{i=1}^n(2 \cdot n) }{ (2 \cdot n)! } \cdot x^n \right)
$$ | $R$ = $\infty$ |
1a9033ba-a210-4168-b474-3d3b70ee389d | multivariable_calculus | false | null | Consider points $A(1,1)$, $B(2,-7)$, and $C(6,3)$.
1. Determine vectors $\vec{BA}$ and $\vec{BC}$. Express the answer in component form.
2. Determine the measure of angle $B$ in triangle $ABC$. Express the answer in radians, rounded to two decimal places. | 1. $\vec{BA}$ = $\left\langle-1,8\right\rangle$ , $\vec{BC}$ = $\left\langle4,10\right\rangle$
2. $B$ = $0.50$ |
1af0e1dd-7848-4c91-a8bd-ef00777094a3 | algebra | false | null | An epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students, $P$, who contracted the flu $t$ days after it broke out is given by the model $P=-t^2+13 \cdot t+130$, where $1 \le t \le 6$. Find the day that $160$ students had the flu. Recall that the restriction on $t$ is at most $6$. | The final answer: $3$ |
1af5b10f-762e-4cf3-a07d-e97b59ef24ed | multivariable_calculus | false | null | Evaluate $\int\int\int_{E}{(2 \cdot x+5 \cdot y+7 \cdot z) d V}$, where $E$ is the region defined by:
$$
E = \left\{(x,y,z) | 0 \le x \le 1, 0 \le y \le -x+1, 1 \le z \le 2\right\}
$$ | $I$ = $\frac{77}{12}$ |
1b031f17-e90a-462e-aee1-ff2751ce3e06 | integral_calc | true | data:image/png;base64,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 | On a cylinder with a diameter of 6 cm, a channel is cut out along the surface, having an equilateral triangle with a side of 1 cm in cross section. Compute the volume of the cut out material. | $V$ = $\frac{6\cdot\sqrt{3}-1}{4}\cdot\pi$ |
1b15a0e5-a050-4df5-b065-654906cb02e0 | differential_calc | true | 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 | Given $f(t) = g(t) \cdot h(t)$, find $f'(1)$ using the table below: | $f'(1)$ = $-18$ |
1b5e0373-2602-49cd-8ef8-a49f3828292d | algebra | true | 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GGBgC9evUyXyAmJsZuH+ByuYw97O9nY3knRMzsacG7UKPRaNqFCGNLGXR///vfa2s/6tu3r1JPW7ZsW7Z8eXZOTlnpuujo6ECLzG903Lo8VBaPGUtvRML/iESbvGo0Gs23Eb843bNUCxFGL6qjmpoaAIaWGzHiNgZGjhy5Zs2a6dOnB4piXJ2IEDJqWCCEl9+BAweWLFkKgNkjhJqI9Da+7bbbfvSjH8FnY2o0Gg2CRVVccMEF3/nOd9rQVQSC22sMeHcOHTIEzHv2Vkjwlf36lZauc7kaY6IjDTkaG11EtsjIyOioKACNjY3mjlyuxrq6uluG32YYfebLNTY2lpSUwJjOJAkGACLbwYMHzzvvvNjYWOiJQI1GA8Bkq0kplcFERJdeeukVfS9rQ28RltdOp3P37t0jRoww9ihtFR0dTSCHwwHgwIGaYUOTAUkkANTU1AwcOPD7Nw0FYLfba2trm3UnUFVdDUE33PhfCKZnHY743bt3m1WbavHss8+uX7/+8ssv/973rmvDu9JoNN962mfwa3DkyJHY2KvHjx9vqD8GduzcCSD5xlQwp6bcCIg9u3cOG5qsRqkul+u97dtHjRql2o8aNertt992u1zR0dFKtr1790LSkNTkoJePiYlKDXYoMioKkNri02g0oWiH9QCL02B+/nxA5OfPVy83b948Iu2O8Rn3GnEgqkFZWZmU0uVyTZw40W6PO3z4iGp/+PBhu92enZ2tHKdLS0sBUVCwwOJteFpPxQczJwDYtbui5WYajUbTZqxRH8xcXFyclnaHoR+LiooCG9jtdnU0Ozv78OHD5qOHDx9WpdoA2O324uI1Zl3XShdtrf40Gs25hqSUoWxIDl1WPNS2eY/572lPsZCZNXFNyepduytCjZo1Go3mLBEWBWfeDnBItgZsGNts8v6Dv2dfYHJTtJ/Ttkaj0bQZrw8hBySeCjToWtgw67jArji0s7RGo9F0FsJsryFE/Y2WFZx5SBt0VNuaPRqNRtPBCIs6C2oAmsOBLVN45r60UtNoNF0Ib7rTlhsF1Y+nNfT0mFej0YQzpy+iFnRhF/56MOiJyq40j6m1eajRaMKH06s/CijSZpkoDFRqRnsVnWf2fWkXoTUajebsCan+zKoqcGEkVNIq8+qHuTFaLHep0Wg0HU9I9Rc0o7RZr/mvh/g1Q2i3Qa0BNRpNmNDS4Nftdt9xxx1EVFVVpfaocpdCCKMAptpYtmw5fKqwuvpATs5ktd9S6FLPAGo0mvChJfX39NMLN23aAggiG/vS8AGiqGiZJXR32rRHABDR4cOH09PTmVmlPFi2bNkiU6FLPQOo0WjCh5Dqr7x8Q2FhoUpewMzKYjty5EjL3a1YsQJAYWGhqhU3YsSImTNnzZ07t6pqv2UqUKPRaDoXv6A3A6fbNWfOnOzsCTcmpxp59xgqE7PsFRmpNnzNjQ1vocvo6EhjT3y8AyT3VOw7raNMULSpqNG0QIBvrd8eD6SER/10GQBLaEx41Z9lRSIvL4+IFi5caGl97NgxdRaZzjU2VKHL+Ph48ymJgwaBsa9ir7En6OqH4SFoQZuKGk0LECSzB4Z1QpIkAAlIZthYCNiYAAIBTN8G9WfxQjkbC8la6BLAmjVrV61cnZ+fHxMTYzmkrlRXezAj414iIrKNHHlnccnLABhoOHYMEBf26gWTOouOjrTb7Uahy6CrHxxQA8Q8S6iTPms0ofEmbSIGoYkhIAAWEnT8+NdgBqTPIpQUUNyiKxKYSqrNGtA691dff3ThwoXZ2dljx6bDUEDS+9BQ1p/b7X7ssceYWcqmQYmJE7KyzMu7RDZDnfnEkkYESNDVj0C/Qv8wu7a9NY3m2493YorVdgQBYDDJfXs/SbmvcNLsEkgSIEZTZ0p5jmnzGNH6NMjLyxNCLFq0yNyv0XtW1oMTsh40ty8sXNjQ0LBo0TPpY8YoLWnkTw2a9NQi7p49e4YMGWLe79WAZAPw+eeff/zxx5JJEHMrAlQ0mm4HSbAQLD3E4Ahhk+xBY+M3s4o2Ov/zf+v//mnj5OeefPROEkwsiCG7uDERdPjYu3fvi/rEtKE3P51SUlJSVlaWn/+UsXbRbKYppeQvBxETkJycfOjQoR07/9K/f38AJ0+6VQMlotvtrq39SC0Eh3ozQV6azEBf/V+NRmNFQjBOQdgk0JNkk4QQYvHKbR/+4ySoB0ke8cNBNhBYMEkpuvzcn/+w8mxdif2sv5qaGkCOGzdu3Lhxvqv1AHDd4MEE6XS5oqKiyss3pI8dLaCm6hiAIGLmmKjopMQEu31AbU2Nuc/9+w8CSE4OnrN+yJAhQbPtq2T3ffv2vfbaa/Xqh0bTAoZpwBJCYN6vNvzhk3/YCB72PH7Xf/9szA8BMHtANmJ/E6YLcto6GWeEn+PL4sWL2Q/P6tWrAXxYWSklR0VFFRQsGDdu3NatW83G2J7dex0Ox7BhwwCMGjVq+/btTqez+WhFBQjJqSmhJGghR1b7vlWN5tuIJN/ITAiU/Wbn81srmsCSMPZ6x7QpaQDAINgIXV73ob1dQZodXwKPMRNBEtnADAIz33ffz+x2+/PLX6iu2q9Oz83NKy1bl5ubp06ZMmUKIGfNeszlagRQXr5hxvTpBfkLBifFB/YfiFZ2Gk0IJJR3C3vUa1Y+fT53Fgb2VXw6++VNUthsLL53SfRTs8aBhWTA6+/S5Ue+7U5L6wlEBEjz2kVsbOy2bdsSEhIGD05Ug/DGRtemTZsyMx9Qp/Tv33/btm2AjImJIrLNmTOnuLj4iSceg3Zg1mjOCgEA7F0VBEAQgm1gASYAJ776eubyN09+w8LDUefblj/5i0sv+g4IRGBmpgAHaQ1wepeZlkegoY5a9rf8MhBd6FKjMcMAMUCSlfseQ83jSUCQBIu7s5b8qeEL4giSnldn/zztlngGg2zkPRkMSdp9wp+WPo5QLsowmXKhcp0GzXalw341mrahZu4kCBBK90lqYpKCIFnkPfXanxr+aZMRJPmxu36QdssgJuHVfb6wAWKt+6y0lO400BsZpkSnQc3GUGcZ57aP1BpNt0SAvBYcSQFBLJg9L7+2fc2O/TYpmiTGfc8+fXKaJA9BEiQkQxATjKlDjZnTpDsNTFVvvGwhfsPi52zWhqE0o0ajaQUSvrVekgLAnn31T69/T5I4xfL6vr3nzb6bSQrYADAEBDEz+RY9tPVh4fTJ7i2xdUFHteZTLIEiFnUZKku+RqM5PVIAaj1DQMgvTpx85Jl1zn+fIqJLzuv54tyf9el9IbEAAyyYIRmk/GKk+qXrxV8/WrL+ApVUy2or6Cyh+vTNRp/WfRpNG5A4BQGo6F0GQ0zKLfm48V9MEpDPTx1tH3ApwQaSTGCwIAgCQ3jzIBBaU9qsW3EOPw6fmhNmA1APezWatiHQA968BhKEvCfX/enIFwSbAC28d8RttyUSEZME+xXvJj3mDY1A62bigmboa00z+Gs9bfppNG1CAip+owksSl75Q8nOahsIJMdcN+CBX/y3+i0ThErtp2kNfg+KQCxqy38JmJVTtLl9YDNznivoRQ+Npk0wC0CCwIjY9bdPF6z/M8HG7Ln+kl4vLn6gWeMxmFkv8bYS6+C3ZXXmryiFkWrR0oMlt5W2/jSas4W8yu/48caHn3698VQT8amo83uULZ3KEAQCgyFB6ifm6WxxuwZ+6s/i4+J0OkeOHElE1dXV5mbFxWscjnil1yZNmlLljf/1Ul1dnZ2drY46HI7VxWuga7xpNGcHMQQYwIS8knr3v6VHsLD9+qn7L7rkAviS+BGEN/upLzBO0zLN6s+s+9TG008/vWXLFssJBfOfnjBhQkFBgap1KaVMT08/XH9UHa2vrx89egyR7cSJE8y8dOnSxYsX5/sKXWo0mrbBBIZ46NGX//zJFyw8JPiZe3449L+uZUhvOAdJbzorBmkHl9ZhrfVh6L7y8g2LFz87cWKOGuSqNlVV++fOmVNUVDRmTLpq9tJLLwJ44YUXVIMVK1YQ0aJFi1SdkLS0tJkzZz45d64qlK5XfjWatkFAydp336g6JEQES1v69VdNuP8WtZ8JUPOCACSDpHZwaSXBB78ulyp0mW2kKVVaq6KiAiRTUlJU/IzSZcOHD9/49m9Vs7feeuuWW24xF7qMi4vznghAz/1pNG1iT8WhWev+SIAkmfzdqBcLJ/j7MEsBIsmqCKM2MVqJX7pTQzfl5c0GsGjRM5JJxUyrA7W1tWAMGjTIHNzmiEv4qPbQX3fsqqw6WPdRnd0R7/v0JYCkxAQAe/f+rWU5LNmrlbo1aUptzGu6Bb4K2n43/FfHG8fnvwaAJMf0jHh9+WRvS5VtHfD+kIXX01abGK0kAgFrtcXFa1566aWysrLo6GhLTFtDQ4PdblfGneHJHBl5IQC32+12nwQQGRlpvkB0dLS50KUZ83UtGwFGojbmNd0CUtYGC5CR5ArjHlrh/uYbksw28esnf97n4l7E8JCwwQN0x1WO9gqcjbBkKKivr//Vr341ceJEc6FLRdCZO8PQM0p/BA2VC+Uf43S6a2trAw+53W7/rvR0hqb7IIxFDAA5uS9X/tMJgG0Ri+79YcoNA9QhGzWnPu1WBC7StpkISyaCWbMeY/YUFi5kU+nxoCEfwTWaEKrcJTMbx40ywWaULq2tPThkyBBAKGvfNKYmCPro0KGICO/Ci57O0HQHJMHGUnDPJpwiwb/ffmDDh4eICUR3Dex7Q+LFH1T9jT2CYGPvEkf3mhcySj+qDSmlEOLSSy+9ou9lbeitudIbEZWUvFxW9kZpaamqS6muAWNRGOjXr19p6Tqn0x0TE2VoQGWpRUVFRUdFsUeePOlWClWlkna73YcOHRo+fDisalsQITIyOjNzAlgwPF59yoLh+fOf/3zok4+++93vXn311ap993zQabobgmWTEMQeYnzw4dHFmw+AhSD531d+t7BgHImeLJsgCJJBPTw4Zet+g1/LpJmU8vzzz29bV5ZClwcAGIUuiYjZBlXokviEyznQbgew/8CBYcOG+HQi19XV2e32YcOGEGC322tMhS6VyzQzp6amwmTcEXnTdCckxBUXrwoUKytr4qFDdVGRkb1792aGXi7WdCckAye+/CbrV2+CBQTHRvZa9asJvXufT2Tz5qxnSPIIsOUn3K04+8GvX8qDxYsXK2dmhZRydXExgA+rPpBSRkVGpaamEtkqKvaxz/HF7Xa/++67o0aNUlKMGjXqve3vOl2NqkPJqNi3F8CNN96odpjEDVm83BIyTL5ctRpN90BIKcZNfcF9qolFU3SPni/MuueSi3qpyDbvD0flNOXuq/vQHl501pQHFtVjuUxS0qB58+bNmD59/fr1Svfl5eUJETFlysOqwZQpUwDk5eWpUr/r12+YMe2X+fn5gwcnBpU+8HKBIcOGnBpNt4Dx0Oziyi9OMHME2x4fe1Ny8tXEYBLKF4xUCJzP01nTZqxqxZqtAE0A2CPhSxw2Z87jxcUr5z4xRwgRExMjQNu2vhMb20+dEhsbu3XrVoLs3bs3Ec2d83hx8ao5cx5v5eVgmmeEXu7QfKtRRXvZ++CXPo8/FL349m/e/7RJCAAPDIvP/MWtqs6RL7DX2NY2wdkSMgotcFxt2RNY0yPoWW1DF7rUfLvx+vQBoCZwhFSLu4ytf6i8Z1E5SAqW/++qvr8pfoghyAg80LQrpyl1ZNmjNoLW9LC0saBDfTUaM80erRwBkgQCTtXVffFQ0QYbSxBdFR350qL7YZS31JwDWrKfQ+myoB5/lu1QqlOj0QDwztyxhwgqPf1XX34zJf+1E00ej2jq3bPHczPHXnxRFENA1+c9Z5zmk7WG4gZsK4JO4bU+G75G0w1hAMKmUrYQMLew/IMvviQ+RdQjL/3/DUkd6C1pSVLPgp8jTqP+DC1mDv84rWoLVdHNmC7USlDTzWEI+NY7CFj6wu9K/36IBUnqMSElMev+m725mwGwkKSzN58TTu83ZA6vMztbt7Do0cKo2dCAZyu4RtOlYQakIALztncPLPjtrgjiJu7xg9jez8zPUOaeAIGU00W3C+3oGFrrNhk0kYHlZSijL7CZngrUdHdIVaWkjw79I6doAwtmiBsvjlq9cAIYTJIA9iWz0iu/54jWFro05yALuriBEJldzKcYzdoiqUbTFWFVdkh6XVnZ43NqZZA8/uU3D8973X2qiSRHndejYNpPL764Fwik6ogB3ukp/Ys5NzTXIA+6ymFpqbbO1IILvIRG001ggo0l2JuClMgmiQFJIHDEE7/69b4vviLJLKjw/jtSUq7pZHG7GSJwwm7r1q3Z2dlCCCIisi1dutzXwOZ0upWJ5ztKRDYi29KlS40eKysrc3Jy1DGHI7645OX2Ss6l0XRBJFioKTwGIJnAzMQkl63YsuH9j20sWdAjtyanj05mbeZ1LNZaH2XlG9LS7gDZPB4PM2/atOnFF1/IGP9zQDJDCAGgqGiZSojAzMweZs+0adNUD4cPHxk7djyA48ePM/OyZcsWL148L38+9JhX0y0hCAjJTN5ylIIZRETr39yT/9afAcGC7rD3mzPzbsBbylLTYVhrfaxdu3ZEWtrKlSuUtkpLuz0nZ3Jp2bodO3YRob6+3jddaAkC8U4LrlixgpkXLlzYu3dvACNG3Jabm/vUU09VVlYHXluj6R4IIgYLrwkBqtj30ay1WwQDkN+75OJnn7qPvCHA2kToULzqz9Blt9926+i7f6peqJm6qMjeIHmwpk7CO3qNjIw0W3JmR5aNGzcOHz5cVbkEwMzx8fEE7N27F3ruT9MNYYA9yokFggn46kv340UbT/6flISo886bN/3HF190gTf8V4+QOhY/6w/A1KlTs7Ky4Eu0x8yffXYMQFxcHIGOHD0WtBciG4Cqqv11dXV2h8O0nxIHDWJmpf70t6vpdjBUNSIGGIKB6fPWffCF04NTDDxz/4hhNw5QGVyIATR1srTdDK/jS+ACCBExe9asWTv3qceWLHlu2E0pAJT7S01NTUZGhloAGTnyzpKSlwEw0HDsGICoqCjzBaKjI+12u8t1wtijbUBN94GFVOseAAhNBYs3bD54RNpOAZh663+NHT2kuSXQnVM3dwredKcWlVRVtZ+IhOiZlZWVP2/+9GkPCdjA+Pyzz4iosbHx8ccfZ2aPRyYmJmZlZSkNCCBohXkiS/ZmpWGlzxfKu9+74a0X580wqNF0CXxp+3w3MOCt3gV4f2XAhjf3PrelsglEHDHK3v/xvLuJJVio04h0SvNW0Y72U5A6v8xIShqkrrF58+bXXnv9nnt+9vTTT191Vf8HH7w/M/MBoyURCgsXHj16tLCwcHR6OquqHM1KTVqsS1WWyXdUQODI0WO/+907AT4xsqH+c/9OdKFLTVhDLEECkKTuVRYgoSr2MgDCnr11j63Z5BFsI/m9i/osKLg/AuydE4Q6Fzq447SYdUU7FLoM7IIIRnWhtLS0K6644rrrrouPd8yZM8fn8OyNAAYkM6WmppaWrtu1a9eVV14JSSdPnjT35nQ11tUdGj78h0aFOvPlPv+s4eGHcth4XrIhgw3Ahx9Uff3112DBzLp0vSacIUgPbEJKJsnCZgMxe4gFk5Qk/32Si36968tvmNDUK0JM+GniwQ8qDrJgeEAECAFieFg/40+HKu1maBIpJRHFxsYOuDa2Db1FmFQpjhw5+uabb8bHx48YcZtvJ8fGXg2IgwcPqj3r168fO3asocGM06MiIwcnDbLb7TW1B3znEhGqq6sBJCcnW3NHA8y4vO+Vzz2/Uu1R70Q9DTdu3Ljt91uuuz4pVWd71nQNpHpEe9dw/ccrD05e+eFX/44gD0Arf5kx4oeDwILBIA8QAWYiNodgaVomMN9K2/ox1/kFgF/+8pfjxo0z1B8R7d+/H0B8/CAABQUFc+fOjYyMTku7XZl+RNizZ4/DEX/TTUMBjBo1auPGjaoQsOpBrfmmpKQYQntNRwYB/ftdMXnSBJNRyUQ2Zn7/7/t0dTdNV4IFeesQqWe7YF+0bsHCNzd+9AkoQiLi8VGpI36YBIZvPSRCnaTGW6THvq2jlUnmT4ufsR0b2+/ZZ58tLS2dOXOW2lNVtf+5555zOBz33XcfM+677z673f78cyuqqvYrLZabm1daui43N1c5Pz/00EOAnD17tsvlIqLy8g0zpk+fN29eUtIgQ0qvrCQZHqP0JREBQuk+/QDUdD0IDKmqF4HAQjkxyzd+u3PpH/9mQw8iGvu92OmT7wSDvYpSkAQY7F340DFvZ0C7LIBYi+1Onz61rKzs6NGjKmh38ODE/v37l5eXx8b2I0JsbOy2bdsGJcYPHjxYiAi1Crx589YHH7xf6a/+/a/ctm0bM8fExBDRnDlzVq9ePXfuE0EvTWSzLmj4gkkC8i9oS1AT7qhSiN61DoBAe/Yembt6K0sJ4HuX9C7Iy/AIqepUsmxO5eK1AKA9ws6Adsmi0kLmUb912xBGWZAFWV9LafapPlODbsKE7OKSVbt3VaSmJjN7i/tpNOGNlCwEqUnApn989e87sosOO7+WNoqO6Ll56STHgO+ChUrzDO/kOEmwgDHxx9rDoSNpwc3SLx4uhP4K8lX5WoqAPWeAZDUkUKef6dkaTSfAEALGJGBEdt7qete/JEF4eGVuumPgZcrRBV4XGe+NLbxWo/qZ6Hu9Q9GPGo2mfSAGUxODGfKxOev+XP+5hyIEi8fvuunWHyapKT9WLn56lBse6CAbjaYdYFb12iJAsnjt9pd2VxLZSPLoG66dNuXHAMCSALBggl7iDRO09afRtANELIkBVFR8smjDnwk9WNquvzRqwcwxvhYCECBJzfM6mk5Gqz+Nph1gZgH66iv3Q4VvuP7tYZzq09P2wtxf9Lm4F6Ry8vcYGf2ENv7CAz341WjaAVWLMif3lU/d/2ZiRsSv591rd1wCFiwkfHGcADFJ0mZHeKC/Bo2mHfAQZj31+nv1Dcrrb+HPbkm90c4QTCD2BcMxfFXctB9rWKDVn0bTDqx95Y+rd+wnsnnAY7537cT7boHPEdpDUJXevKnsGfp3Fya0vs4vmuv8InDm9vRPM2bPmQim0YQl7L3/WYK9/qnYU3HomfV/hmBB/L1Leq8szGRqznJqgy+6Q73W835hg1+6U/V369at2dmTVBFLIUTRkueUG7JBScnLdnuciorLycmprKw0P82qqvbn5Ew2Cl2uWbPWV0fJpvM8a7o6TACzBEhIgiDC8a++nlJY5vzGA8kX9vxO2XOTpdfO04PccKc5tEOFppWXl48YMVK9ZD71zjubV770fEbGz8mXxnn+/KcnZGXNnz+fmZkZEGPGjKuvP6r6qa+vT09PZ2an08nMy5YVPbNw4YIFzxiV5DrrfWo07QKDiUiwB1BZmj3jH3nxsPtfjFNCiHVP3dunz4VCeQECepAb7rA/aWl3pKXdoUr4qr9Lnl0Owl937GLmDz+sAkTR0uVGeynZ7ojPzc1TL3NzcwcOdDidbl8VYC4ueRkQlZXVvvaSW8GDmRMA7Npd0ZrGGk2H4pHsu5Mn5Zb0vvXxPrfmfffWWS+t+T1LVpWvpWrEnk4VVHMarE+n2267bfTo0d6UVARmjoyOAnDgwAH2Ju+TycnNKUiJ8IMf/GDjxo3q5caNG2+55Zbo6EhjQO1wOABUVFT42msDUNOlkSy8P4/il/9Y/kFtBMiGHnddb5/4wM0AmIkhwESQgb8vTVjhl/CKmadNe8S/mgd99tlnAFS53traWgCDEuKaTwHi4+M/+qj2rzt2VVbtr/voY4ep0CWAxMRE+JKeajTfCiQD+/Z8Mqv0j8w2DzyJl124svABRgQAIiZW+Qx0fYZwJ8KczCrANJNr1rz65JOPLfnV8u/flMqMo0eP2u12o4q5IioqipkbGxsbGxvBHOkrdKl6i4mOtNsHuN1utZN1NlNNV0ayEISvjrvHF7wqJSJAUef1WF802ZvFj0AsmE6p9V499xfmBCl1BKCqqmrw4MFq6aogf+H0GVMAoQrxBZZZklI2vwyh2gwbU+s+TZdGWXQZD69s/M//EWweFuueuveii6MAeMM5CASbL7WBDvAIa/ysP4OkpCQ1Nbh169ZXXnktI+PnCxcujI3thwBF5ktRJizeM/4IXx0Pq+7bvXv30KFDLTuJSC2cff755x9//DFDMDzC+zjVaDoCVg97GQGSkB6PzabCOQhy4fJNf/uHk2GLAM3+aXKf3hGHDn2in+sdg0WNqGJvF110Ue/e0W3ozev3F/QYEd1+++2PPfZYWVnZq6++CqBfv351dXVOt8us4xpPngQQGRnZr18/wKMKXRoNnE53XV1dZGR00MpMQS/N1kz3OkRc09EwM7Hw2P7jIUCQYDA8guXbm6rePPB5BAlI+vkNV49MGwRqIv1s7iRUecg2n+5NeaB06uHDh9966624uLgRI0ao/UTUv39/Zj5w4AAAh8NBZKuuOvD9m4YaarimpsZutw8bNpQIDrujtqYGJkfC/QcOAEhJSTHam/V3ampqMGsRmVkT15Ss7tu37zXXXKMHzJqOR4XoNldZkMyC9lUcWvC7PQCd8vDNV1/6q0VZCKhpqelgzmY5wZrRfvqMR9e+8ppZIalCl4MGDQKQnJzMzPv27WPfKU5X43vvvfeTn/xEEMD84x//+L333nO5Go0+lctLamqqIaIxTIbPvlMD7aDyqWrqoY5qNOcIgiRA0ilW+aoEnfiqcdy815kJRPboC1Ytut/jLdOmdV9nYtYnZ0rzN8fMsbGxzz77bFlZWW5untpZVVX1/PPP2+32n//85wAGD07Mz8+fPm1aefkGAC6XKy8vj5kfemiykuOhhx5i5ry8vBMnTgAoKyubMWPGU/PmJSYmWCSGpeyvN84kpBJs29vTaNqKWsToASaQ/OK4e+zUF13fnAJkTI+I5bPHX3RRVAR7G2k6HrMJ1Xbrz7C/VBczpk8tfeP1z44ZhS4HX3ll3w0bytW6B4A5cx5fXVw8d84cIurduzdBbtu2LTY2Fj4FqgpdXnTRRUQ0d+7cVatWPekrdGlZGzF727AvKs6sAbXW03Qm7CGGJIIU8xa++eH/OkFNoB6Pjf1BSvLVBMmkLEMpdfbmDqddnElashs5RIlL9k9aYX15Jso4VOPMrIkvryneuWvPkNTkM+1To2kPVL1KCYiiF955+re7CLZT9O+Jw65b9NQ9TMaUn1Sjl86WtlvTZv3gN/i1HAvlC229DrM5s0ULcoS6RCD+84PaDNR0PIIASNry7ocFb+0gcaoJ/74l9oqF88Z7sxlAAE3K5atT5dS0XT80J7tvdRfWid7W1yc9I6vQdFYrT9Jo2oBkCG/AhvfGk0TEEBL4+KP/fajoTRvDA7JHXfjSwix/N2ZdK6Jro78/TbeGofIwS5/3Pnvzk7J0fvWvKfmvHf/mVARRzHfOWzr73osv/k4ni6tpV/SavaZbQzCyzwsAYOFhCUASzSks/+CL40TkgScv/QdDboxl/Xv5dqGtP023hySxYLCaZxEESH5u5eb17x9iQeSRU0ekTvzFzYAgbuU0j6ZroJ9mmm4NQ0pW3nsEZuXGt2V7df7GP0mCZLoz7qo5uXdJENhXq0jzbUFbf5pujapCqdY/CATImrovHnm2THhsED2vv+SCwvx7AQiQ1n3fPrT1p+nWqLRUTQKqDuGXXzVOf3Ldl6fAgqJ6cMG0n15y0QWAVPG/hKZOFlfTrmjrT9OtIQZIRACABMTcRb+t+PIrkJQsFmWOGJJs98UWAAAjQpuA3yas1h8DH1ZWZ+dMJqHC3ii/4Bmn2wUAkC6XSxXAJB9CCCIqWrYUPme9yspqU6FLR3HJKxw6Z0Fg7gPjpZH1T6NpF5rza3hj1VQCP6N6tZhfuKH074cINpuMePSHN95191BW+tHn1U86ti2cCJ1gtLU0lzlXf3fu3H39ddcBOHH8hJRy8+atr7/+Wk72ZNVYLfwvXbpUSqmqWKl6V9OnTgNARIcPHxkzZgwAX6HLZYWFhQUFC8w5os2XN6eBMb8UQjAz6dtN034059dgAQIENQHenwCwYUNF0bt/i6BTkr65w3Fl3qy7BZr04zdsCV2i4wxoTneqbo7nn1tmtw9YtGhRTEwMEY0YcVt2dnZZaenOnbsBHDlyBM2mmZ9uUi9XrFhBRAsXPh0VFQXg9ttvnznz0SeffLKyslI1s4YPmzSvSppv3q/RtBfe/H3EgPQ5r8gIBgMMWVFxaNYr77BHSkTccPEliwt+YYMER4CbzUNAe72EEe0Sa9hs/akeU1NTZ86cGRMd6TP45ZVXxoLkwQO13vaEyMhI5iDnAti4cePNN9+sVKfSknFxcQTs27fPcmEjxQt8mldZfEGbMXvO/q1qujsElZuPIQEJFiAJ5q++Ovn48jfd/3dKCMT0OO+ZaaMu6XM+IIgAamImZmLIFuZwNB3J2Y95DZqtP9XdtGnTMjMzjUMAXC4XCL169QLQ0NCgdhI1DyXgy1daXX2grq7GYY/3tSEAg5OSmNmo8xsqTY3Rm6XwJhFJMJFOJq45K0g9zgm+yA3BBAaIefqTr3/wjxOSpGTb05m3J6fYAfge/xEq5a4yHPVsTKfTLmNeA2Hp1KJTXa7GN99cn5Y2ctz40QCIGIyampqMjHuJSIiIkSPvLC4uVgsdSjlG+QpdqhsoMvJCu92u8j9bhA6cBwysYwLofJKa9oCFuiEJYK8mBEnxVOGbm+uOeGAj0XPGj24ce1eqb01EqCR+RGBmoTxfdGLnziao1muzJRgBf91n7t3lcuXlzd6yZctf/vIXtefYsWMAGhsbH3ts1htvvA5g5sxZEyZkE9kyMx+QymmeiNlj2GsqkXOod+JyuQ4ePGjRiUSk6gJ7jUGd8kVz9ng9V0CQQgg1p1e6cc/zf/w7SepJnruvu/bxmXcDgFoYaZ4iFEZOI19eGE2nEST96FkkA1V16f2WXxWH648+Nnv23/6295133rnpJm8tyqzMB7IyH4BJ3RYWLmxoaFhUWDh6zN3kK/sbSr5AQWtqagIKXaqntCCiQ4cO9exh80g1DaPRtB2GADV5ENFDNjEimPnjw/94bM17LInpVOJFUeN+Mujv73/A7CH0UAlgvDYgAGoCC29RBlNqS02no1TKZZdd1rfvZW043c/6M9i8Zdu0qVMHDBiwfv36wYMH+11PjRpM7ZOT/+uN0tJdO/dcccUVgO3rfzX6xtQCgNPVWFd36Oabb0HAyJeIIiMjMzMz/fPlSgDv/ekvHx+qu/TSS6+66irzIolG02aUBgQEsXQ5/z3z2c3uJoBkTM/vLM5Lv+bqS8ARJAn0HxY2PcsX5pgnAXv27Nm2TiICdd+WLdtGpqVlZGSsWLEiJibK0qC8fMO4senmnUQE5sjIyKSkQQMHXHPw4EFzb1VVVSBKTk4OFBpAQkJCcXFxoFiZWRM/PlTXq1ev3r17t+2NaTSBMIOAJsLUJ16sPO5mlgBWTEu/8fo4QDKBIBiqept+3HYNzqrUkWWxtb6+furUqePHj1e6D/5mV0FBwfhx47Zs2WY+a8+evQPt9u/fNJSAn/70p3/84x+dTrdxyr59+8CcmupVf20TVDscaNoDCZIgPF345ubaoyRJyJ5zfvrfP/pRkgovkhAMScq9S9NFaB+3Z8WsWbMAuXDhQqX7LHrnvvvutzscy5cvr6qqUmfl5uaWlpbOnDlTNZgyZQqA2bNnO51OAOXlG2ZMn56fn5+UlHQ2KkyPfDVnjSpdhOJX/7Ds9/tYELMn/Yarp025Q7DyrhI2ABCQrAu3dRP8FvJdLldpaWldXd1VV/VXviw2mze8Ny8vD0BsbL+tWzYlJiYMHjxY7T958uSmTf+j1kMAxMbG/v73W6Vs6tOnDxHNmTOnuLh4zpzHzT59Fs8+y4b5pdZ6mnaDBYDdez9ZuH4HEUspr7+0z/zZ6WrMywLEahMQ7NH3XfcgiJvxac8xF8AMdUprumphRTgza+KaktU7d+0ZOiSlVe9Dozkd//jq5E+yl37s/BexiOwV8c7i7Dj75WBIYuFzaGH2EJFOBBfmtJd51Oz2bHRnUYgtF8AMlKD1kpl1X9Chsbb+NO0FA9l5qz9x/Z+kJo+QL05Jdwy8TDn3CZB3uOstqap1X7ijhp5n3483btfoKzDu4kwvE8oYDDX3Z1GjepVDcy6Y9eSvd9R/6QET2Z64a+httyUQsVG6SHnmMwEsVHIETXfAWuY8lDXXAqHyFJgxq9GWO9QWn+bskEp/SZW/mQFGydrtxTurm8CCMeY6+/TJPwYAKdDswyygAjvI+1fTHWhWf0Fjfi3GYFBNF6jXWlBhLQx1NZqzhyEIEgzBNkhmkrv3fjr/N9ttsBHk9Zf2Kcgb4735hCQ9zu3eCIs+CgzMMLcO1Fzm9dxWrnVo3ac5dxAkICAAgkfQV//8+uHCX3/9b4+EiOl5XtnySRddfIEvoiNIgjVNt0KQf94q89+gA+FA/5VQayCBGNfSI1zNOYK9MeMSgAAmzXr5Y9f/eeBhnFo37/4+F13oTfXsDebV6q9b4+f2bFnSNdYrzJrOErVm0ZiqWQsPVa34NOcUYm9GPwZmPfnrd+uPRYAIPQp/dlvqjVcz1Lxek3emW+q7sVvT0tyHYaZZ1oItbRDCAAzq3qzRnFMYHrDHA1Hy8h+Ld1ZGUAQzp19/TeYvbkFz3aIIIm6CzqXW3bGu/IYiaFRGqEOB7tDa6NN0EGRjEn/b+/HC3/zJhh5N4O99t8/KxQ+ogQyDwYLZwxAROpFut8e68gugqqoqJyeHfBQUFLhcLvM5JSUl8fHx6mhOTk51dbX5aHV1dXZ2tiqA6XA4SkpKOuBtaDQKkjhx/OT4gldPnPqPB9z7vJ6vP58NlYdXMhExgWAj3/ygpjtjXfzasWPX4MHXA+KEy8nMmzZv/fWvf52dM9kXE4SCggVZWTn5+fnMrGqzjUnPOHz4CABA1tfXp6ePBdlUoculy5ctKvxVQcGCM5KJVX1f87NZD501/ijnPmZvrTa1S4JBGPvwSve//y08RMTrnvr5JX0iobI1C59Ln3fpQ3u9dHvYh6rYm5Fx78CBDqfTbexcUrQMEH/961+ZubKyGhBLip4z2jPzQHvczJkz1fajjz7qcMSfME5nXl28BhAfflhlvopxruXqBpmZEwDs3l0RtLFGw5IleySzh//D7JHMUjYxeyblvnzxDx+/6EeP9bl19uq177G+fzSh8Rv8MnNKyo15ebnR0ZHKeZ5AffteCciDNXUA9lRUADI5+b9gGizfcsstb731lnoAv/322zcPHx4dFentE0iIjwewd+9e9q9sadHCQScHTXOIepyisUIQBBB6gAWxh8i2+tU/lX1YK6mJJI/53rVZv/hvj/fW0vfPtwRuRYxZ6/Fb+iCiqVOnegtdessMwe12A0IVuqytrQUwOCmp+SzA4XDU1dXt3Lm7srL6o48+stvtZlWWkJBARBUVu80Ozxwk85Wx4TH8trh5/USPUzT+UPP/TGCIir2fznrt98JDLOj6S/u8uOh+QHgLbkl9/3xLaKXl1Eqaa31Y7TICgU443W/99jcj0tLGjxsD4OiRIw6HIzKyl7kLpRldLpfb7WZwVFQMe29OCYiYmKgBA65pbGyE1e1Zqgv6dJz3JF+JOL8a6hqNBWYPyEaAB002RBw/8c34eSVEHpK2mIie656bBCIJlclKshB6jVcTSHOlN7aE9wJul2vWrNmbNv3PX3fsAiSzEEIFyfl1EcLpz1sgVSk7NdL2j/cQAI4ePfb2795pPk2tzcFzpL7Bv7HUBqDGD7IRJFgI2ACMe6io8T8RAEdeELFuzv2X9L7Q69VHvihgff9oAohQ/3GAs1794SOzZ+f97f0PNm/eOmzYEPjqPQd2wczNpd2UJgULf51oyfjim44RDZ8dfejhHEgCqdLTpIbBBBszf/hB1cmTJwm2c/b2NV0YVY5Sslj3ZsXf/tkYIcE2um/ogK+/PvLH7Z8yIjxgGwQxM+nwtm8JRCSlFEIYf4koNjb22gGxbegtwugUpvwFW7dunTp1+rXXXvubDeWJSUnG0LRfv36lpetcrsbo6Eiji8bGrwFERkZGRcWA2e12k28kC8DlctXV1Q0fPtz8BgAojXlF337PP7dS7WdmQBLZALlx4+9+v23LddcnGTWSNBozzCCSDFGy9i+/rfunjSKabJ4JQwc/OfsekAQEJNib00Wbft82uBUJVlpDhOU1EW3Zsi0t7Y5x48e/tHKloebUpewOB4D9+/cPHZrq1ZhAbc0Bu33A928aCsA+0F5Xe5AMYxCoqj4ACKPQpYX+/a6YMnli4P7333/fm7hN0+1RtwExoMYfRMQggCH27P1k1rpNEdxD4j83x165cN54AF5lJ2C+DzXfJtorisx6Z9TXH1WFLpXus4x2U1NSALFnzx7j8k6n+09/+tOoUXepl6NGjdq+fbvL1WicWFFRASAlJUWvY2jaAoOh3OCVKxaTZA+BCV99efJn814VLFjwgKjI1QsfJNaaTnMG+NX6ADBr1kwifuaZZ5TdZ0nPl5iYkJ+fP2PGjLKy9QCcTuesWbOYWdW3BDBlyhRmzsvLc7vdAMrLy385Y8a8/PykpCSdzl7TBphU1V2v4x5BQLANOP6lO2PqSvc3p5g5+ryI5bN+3ufiXrpCpeaMMGodEDM7nc6ysrLa2tqrr44lIhW3q/6qSr5ENGfO48XFxXPnziWi3r17A9i2bVtsbD/Vjyp0CciYmBgimjt37qrVq+c88Zg6avZ81mhag7pX2EhGz4AUYMxd+Jv3//ElAElNs0YPT02+iiD1raU5I1oqdNnC/CL757hv/W3Xysaq0OWu3RVD9NJH94aZiVgtZXiEelzLZS9sLnhrByAhKDslaUHBPQQwJEkVCaLRtApr1If5mDmhqQUi8oVnhLTmgoan6Oez5oxonn4RsEEy+A9/qJq/cafypfp+v8ueLrgHkMwgFqx1n+ZMEEb8Wai5OQpWnYOZiWyh1tRCDXJb0KcaTVAkPEQ2qdKUsvjoo39OXPqWZAbJa3pduLZwgu8ZLJlAaOpseTVdCXHafM6h9oR2gT7N7J42ADWtR7BNxW0wxPHjX0+Zt7bxP/+J4KaYnj2fn53RO+Z8AATBUhAkBzhyaTQtYF35PUvTzDJ1aDmq7T5NaKQ3YZ9KwgZviV5W1ccBAuY8U1r5xQmW5CFReP+I5ORrWTR5qxUKCT3tpzlD/FZ+cTrTzJyp5bSOLBRQLEnbfZqQqOwE8ECCQATJBA+BvFlv5fLn3i6r/MQDtrF85Nbku0cPBSQ4AqzuK+3xpzljmq2/1kzMWWLjQik1oxMj34Ge9dOcFmaAbSCAJJiJYUMTQwLY9oeDT729m5lt6DEirv+TeaOBU2AiIu3rp2kz1memRbWpdPaBaosCihkpjMwu8FeC0DXONS1DEARSUR0QgA0kgQhiUVP3+eSl5SBJRIMvjS4quBeQhB7kzZZm3FE6p6nmzGge/KoNQ3kpVSVEcyFgy/ygeaeh01pwBrRYjhqNGYZk9nizFTCrRFUM+dWX/3r4yV87/9NkY09Mzx4Lpv6kT+8LvB4L5DfsVRViNJrW05xV1F+pISdnshARS5cuNZoSkcvlUnEgKhTEiAlZtmy50UN19YGcnMmmSm8vGz3oGUBNKAiCYAMEQRIxA8QgFtPzX33/+HFmJvR85v6RKcl233M0yIikMwTXdGGajTvDLnM63ZMnTzly5IjRAH4qUhQVLbOUj5k27RHVw+HDh9PT01X8HDMvW7ZsUWGhUelNzwBqWoEa/AKEec9u2HrwKCQzxJQfXZ+enkIA2APANG8jTRM1evyrOQP8tBsROZ3uSZMmOezxjzzyiNHIGMkePXq05e5WrFgBoLCwMDo6GsCIESNmzpw1d+7cqqr9lqlAjcafJhA8ABAB9hBk6Zs7n9/yfhOxYHFn3JVP5o5RkW2gHv4nen1XhYBe/9WcEda5v6NH62+99dZp0x9iAJAeEuajDAHIXpGR6qivk+ZH7saNG4cPH25Ohhof7wDJPRX7gjrKhHSaMf3VdA8iANhU6C5se/bVP75mGwCC7brL+vzqqZ95J5iZvC6BQdC679tPa7RH6/GL+QWQlJSUmflAqNYNDQ3qLPI717tRVbW/rq4uPj7efErioEFg7KvYa+wxLy4HWIIy9CHNtx4JCUAcP/7140vLGr/5BkDMeWLBI3d/t3cvFgwJUuUQ9K3RXTEm0NpFRTQvfVisM/Nfy7Xrag9mZNxLRES2kSPvLC55GQADDceOAeLCXr0M+QBER0fa7XaXy2XuPDDSzndIkF4g7rawgACxfHTOa+9/4ZYEQC544I7UlKsgwN7kzZK08uvetKMfsXdsa+7IrJssGurYsWMA3G73Y489xsxSNg1KTJyQlWVe3iWysanAGwBAkqnYm0/u5onqVoaRaL7VSCYwMG/x+rcP1dsYzPTE3d8fd3eKB2Bm4dN6TKEGv5pugaGazt76a67zazkQNKNfZuYDWf5D48LChQ0NDYsWPZM+ZozykVa1l4yzzH/93wAx4+DBmiVLlgRcUf7pT38B8PXXXx8/fhwQRMx6ZudbDUEy8/9sqVr2+w+JBIHSB8fel3HTP53OCJX0xSNInGJEMDzE3pqCmu6MYWadd955F5x/Xht68Nb5DVRS5ojdoFrW53BPycnJZaXrduz8S//+sQBOnnQbPQBwu921tR/d/IPbAnsggtvtXLOm2OSwqopySUAIIT7//POYmChAqJrWbXh7mq6ChO3LL44/9ettEWAPI+mi8+8d9b1PPzkKANTkIWGTAtTEEAQwSeiyHt0Sy+yZennZZZddcP5lbegtSKFL87jaV9e8Wf2Vl29IHztaQFmeDK9txjFR0UmJCXb7gNqaGvMF9u8/CCBUpbf4+EE7d+625Ikh4mefLVq/vmzgwIE33HBDG96VpsuhhrNjdh9bvbO6z3k9XirIGmC/COgBSILwVk6VAKkEMJL0aKDbc/arH0EKXZrj3tR41qCgYMGTc+duin5nxO0jjMvu2b3X4XAMGzYMwKhRozZu/J3T6YyJifEeragAITk1JeDSEkB0dOSQIYGHEBUVBT0J2J0g9oBsC+eNt6/905VXXDLA/l1SmawgmCQIBLAAQRBDVbHUdHPaZ+U3aKeCmJkj4DFf4xf3/cxutz+//IXqqv3q9NzcvNKydbm5earBlClTADlr1mMuVyOA8vINM6ZPL8hfMDgpPuA6ogVHLTb91XQLyAaAIDLvH377jxLJiEciFQ8n4P0LkPYI1bQPVgW0dOlSFcmblpYGYPr06WpyUVV6i42N3bZtW0JCwuDBiWp/Y6Nr06ZNhqtg//79t23bBsiYmCgi25w5c4qLi5944jFoU06j0YQZp3eva3mAHeqoZX/LLwPRld40Gs25pqX548BlX2MtuIUA3qCLxUEzAGo0Gk0nIlqw/gKVlOHMHCoqw3wosIHWehqNJnwQLaukQBVmXhcObBDUhTAwik7PA2o0mk4npPUXLKVzyFFt4CmBESOBroUajUbTiYhQw9iAGLXTpyEIlsLAm5W3BQWq0Wg0nYJfOr9g+Lk9n5Hm8jUWZgNQD3s1Gk2YYC1zHrDdkstLK3eatZ42/TQaTZhgLXOOFqu1mSFiIzupaad1PcSSmFBbfxqNJkxoqcx54LJGwLlBFo4Dc1tp60+j0YQhfrU+zJorJyeHiJYuXW5q4J0HLC5e43DEK702adKUKm/8r5fq6urs7Gx11OFwrC5egxBeMhqNRtOJ+NX5VWaay+XKzpl85OgxACyV2vIYJxTMf3rChAkFBQWq1qWUMj09/XC9twJcfX396NFjiGwnTpxg5qVLly5evDjfV+hSo9Fowgdh8VJ2NbqzcyY7HI6HH34YZHXTq6o8OHfOnKKiojFj0tXOl156EcALL7ygGqxYsYKIFi1apBJepaWlzZw588m5c6uqqqBXfjUaTTghLAruSH3DrbfeOn36VF8DMs/WVVRUgGRKSopKRqV02fDhwze+/VvV4K233rrlllvMhS7j4uK8J/q6O8fvSKPRaFqF1e9vcNKgrMwHSKk2BpPKcaCmCEVN7QEwBg0aZA5uc8QlfFR76K87dlVWHaz7qM7uiPcZeBJAUmICgL17/9ayHIZV6N1QDtLNx2WQczQajeYssGZ7NrAU/VAvjx07ZrfblXFneDJHRl4IwO12u90nAURGRpr7iY6ONhe6NGMpLWLeCDASdWZzjUbjpb0CZ0OqP3PulhayvBiGnlH6I1SemKD9O53u2trawENut9u/K6k1oEajgb+X3lkqwZasvxYuE7I2phCqPAgzG8ctBUN8/TMzamsPDhkyxFfdzaxnCYI+OnQoIsKbE1+vmGg0GmZW9dfUhpRSCHHppZde0fcsKr0FvYzx11CC/fv3Ly1d53S6Y2KiDA2oLLWoqKjoqCj2yJMn3Wr4qlJJu93uQ4cODR8+HFa1LYgQGRmdmTkBLNgoKsKC4fnzn/986JOPvvvd71599dVeMXShS41GEzBpJqU8//zz29ZVSPUXeD0istvtAPYfODBs2BCvIgPX1dXZ7fZhw4YQYLfba0yFLomourqamVNTU2Ey7nxO1CIhIa64eFXgFbOyJh46VBcVGdm7d29mXdJao9FYOfvB72km1Cy9p6SkENkqKvaxz/HF7Xa/++67o0aNUu1GjRr13vZ3na5G1V4yKvbtBXDjjTeqHaYOT5Nq0Ngmgl751Wg0Fs5+9eP06wlmFZuUNGjevHkzpk9fv3690n15eXlCREyZ8rBqMGXKFAB5eXlOpxPA+vUbZkz7ZX5+/uDBiUGlD8w0Exgy3Eo5NRqN5sxgE1LKoqKioM1yc3ONZsXFxWoUDCAnJ+fw4cPmTj799NPs7Gx11G63FxcX85nzYOYEALt2V7ThXI1Go2kNzWWJLPldTmtYckBNj1ae2Bp0oUuNRnOu8cv4YhA01ZVlI6h/cijdxzrUV6PRhBnWbM/KJjS3sIR/IJiO42BTeEE70Wg0mjAhSL6/FjM8B0/bF7hYESq5izYDNRpNmOC3otrKoetpVVsLRqI6VytBjUbT6TSnO0Vo0yxoHnxLYw6WvyCwn/ZaG9FoNJqzRFjUVqBSM7YtRwMXPVpj1mkNqNFowgRrraJWvgyq5lqeNwzVp0aj0XQKZxBN0fLgt239aDQaTWfRWvUXOGJtvYufxatGW38ajSYcaJX6M3SW0+kkf4QQRLR06VL41Fx1dXVOzmQimxARDoejuHiNeW5R6z6NRhMmtKT+DKvNpL9sgFiyZIkRNKfKXU6bNk01q6+vT08fS0ROp1PKpqVLlxYuXlygC11qNJrwo6V8f4GrtPX19QDY5y4TmAv6+eefB/DMM8+oeiBpaWnHPvvfCVlZP/3pTxITE7Xpp9FowofT5/vzm8sjAhAVFQX/QBGjze9+987w4cNjYqKMM+Lj40FUUbFPvdTrHhqNJkw4/dyf2WRraGgIelRpwKqqqtraWlXY12DQoEFg3rt3r/b402g0YcUZrPwCEMQA6moPjh9/j1r3uOOOH5cUv8IAER079jlI9oqMZm9yZgkgJjrSbh9gVG4zuUZLSGuiBADsrRcn4VfnV6PRaIB2HUG2qtYHfFZeQ0MDIN3uk48/Pru0dB2A3Ny8CRMzQTIz8wFDuEC1FbiKAggIHDl67He/eyfAKpQN9Z8b2746cDrhs0bT3THrirMfTZ5G/VkulpWVlZmZ6dsjAbF48aKGhiOFhYWjx9wtVaYDhkVVqTwyQSX+/LOGhx/KYaOMpe9/IhuADz+o+vrrr8GCmSG0LajRdHdUaTdV61JtE1FsbOyAa2Pb0NtpypwHKlc/8w0SEKmpQ0tLS3ft2tWvX38wTp48aW7vcjUeOnRo+PAfwLROQkQMMOPyvlc+9/xK1VK9EwECsHHjxm2/33Ld9UmpOtuzRqPxJzDJfNv6aanMedA9ZWXrx40bE9g+KioqMTHBbrfX1B4wqTlUVVczc3JyMvyqmDOBCOjf74rJkyb49quYEBszv//3fbq6m0ajCUorI9BOS8gJtcAEzgDy8/PHjx+7Zcs2Zjbm4/bs2WW3x900dBiYR426a/v27Y2NjfANYPfu3QtgyJAh1hT5JBkeo/QlEQFC6T69OqzRaFqmXRZAQqo/szef4eL3i1/8wm63L1++vLq6Wp07c+as0tLy3Nxc1UwVusydOcvlcjFzefmGGdN/+dS8ecF8noWKIfF/T9bcgs3LxBqNRuMjVOb5M6Il6y/QwoyNjd267Q+DBsUPHny9mhl0u92b3tmSmfWgOiU2tt+WrVsBxPSOsdlsc+bMWbV69dy5T7RWHN8FhVBzgEoLA6yXfTUajZWzHCm2PW/VOUUXutRoNOcabVVpNJpuilZ/Go2mm6LVn0aj6aZo9afRaLopWv1pNJpuilZ/Go2mm6LVn0aj6aacE/XHjMA4DWbPubiWRqPRGJyRI3P7q7/KyspJkyYT2YjI4XCsWbPWF+1rC08Xa41G8y3AnFXAQlXV/r/+dWfg/nZWf/X1R8eMGQPA6XQyc1FR0TMLFy5Y8EwLkmk0Gs3ZE0q9OJ3O9PT0FStWBJpf7az+XnjhBWZetOiZ6OhoKeXIkSNnzZo1Z86c6uoDqoE2ADUazbnGnDNl7dq1dXV1cXFx5qTLaqPd1J/qcePGjbfccmt0dDRU2gLA4XAAqKioUM20AajRaM4FZtNKJawqLl4jhJg+fTqAp556isi2efNWmLRQu6k/Iqqq2q+0rHl/YmIifFn/NBqN5hxhSYGlarFlZNwLAJDjxo3Jzs5OSEgwn9LaUketQZXBjIyMhClflrnSG4Ll0dJoNJqzx6jPYSiZBx+8n5nfeON1InrxxRdjYmIsp7Tn3J/30tLI3uwnmdGmHa+o0Wg0CkO3mJVMbW0tgBEjRgTqPrSj9ceAZGYmiMDFDeGr42HViQcP1i5ZssTSDwHvbd8O4FeLF1944flENg6/mr9ekViApPGXSYabnIquYnSHv5wMAALURDJCVaOGf2r0MKGryAkARPBIFiSImD0tF3VU0lsqUN5xxx3jxqYHbV9dXQlgUOLgoDqk3dQfAf2uvBJAY2OjuaKb0+muq6u7+eabLZWZjGTRa9as8f9Kmv2lf/Ob9WH6hQGm6sOWv+FLGH+YfoS1nGR65nm/7rD83ruKnAAgBFiSr94t2RA6RCLw3iCipMSEoI1dLtfmzZvhW4BFwPO1Pef+EhMTHA5HXW2tqXoR9h84ACAlJcW4sFmChIS4nTt3GiN2pUSklEVFRRs2bFj78qt2x4CwNQeYuWjJsvL1pa+sfc3uGKBqj3a2UFZULdShQ4cC2LVrd2eLE5KuIicDtQfr7n/gZ2PSx8345TTzTFNY0WXkZP6fdzYvmJ//xBNP3XlHmlFAreVTjLejbpsrrrgiaMvq/QfVRnx8PABzgWC1vz3VHxGNGjXqt7/9rcvlUr4v8Lm8pKammkfmhgSRkZFDhqTApBPVRklJFLPHETcwJeVGU1X1sEIA6BV5ARE74gaa6hGHo5xKKiWk76PWcrYNIYgAREX3UreuDy1n2xB/e/99QF566SX+Rb1Dydmq8kTMDKKDBw8aL5lh6D6jZTu7PU+aNImIZs6c6XK5AJSXb5gxY8ZT8+Yl+lunFlWIYNOWhgnpM6lEWP1TUgWz+DpfNv9/fphukU4XrKvKaakBG573ZxeS0/d7t7XudxS8Bq/FtrU4wbz22mvz5y+w6D6YL98uXHVV/23bthBRTEwMEc2dO3fVqlVP+iq9KWksRSxDFaxjJlXgLQwtdljE7gqF6MwzEuFMF5BTfd0sjPFXZwsUgq4ip1cLqR8UcLrYMN9Pr3kbQecEgfT09PHjxwNYtWrVsWPHzKcr2nPwq4iNjV25cuXKlSsRQiWbB7lGA//vRnr/kfRfWAg3pCrTzvAwe4hs4SonEPo5GW50ATlJEoHhITKWE8Pye+8ackrfOJfVj4jZQ0Sn9fUIvDXMI1+13Tsm6o033li4cCFDxMb2O4crv2YCjUyLWGjxIc9M6ksionM0SG8nBGA8Wm2+PWFK0LnXMKQLyMmCWclpfN1h+b13DTmNIa13/BswCm4VgSurxkb//v2DKEvftdufUKqtlbeyMekjpQxrHwgvwjKoD0+6gFUFoEvISc02VFh/6V1BTgaUTUokz0bGUIsHaiOUMXlOrL+zx263Z2ZmRkdH+x5fYUpXkTMzMzPwtghDuoSckZEXZmZmDhw4EGEsJLqOnJdffvmDmZl9L7/ckLHDnnzhb1tpNGFKqEmecKNLyNkpQobhXED4GuoWuoqc6Dqihr+clqxKCFfDqqvICZMHiHnarmMuHY7qzzzfF86/h64iJ8I8jMxE+Mvp51jrIwxl7ipy4iwWCc6ecFR/gQvE4UlXkROmkUVnC3IauoqcCOZmEZ6Ev5zGymHHi9c1bjXN2WCZVQnnn0GXkBMBVXXCVtSuImdnEdbqr6t8W11FTnQdUbuEnF1CSHQdOTueMBr8BiriLvGdhdO9JX1/A4ssB083Gz4PP2vEUsBH2vGiBs6atSikDNjuoOQCKpqXveLJgBtAmuSUlhMtGx0Mh/6IOkaksFB/wQJ+T//FdMwHdFqX5nCaqxK+v8G/1sBPtRMVd6Aqafm7DjqXf06xxGsGunb6CyIsOztKTq92Y6ipAwpIDRDyZujImWvLpxEoW9BUAKFOby/CQv0ZMz7M7HK5CgoKbDYbERHRggULnE5nqLM6RjYE/DiLli4nE0IItaHy3HQWhqaur6/PyLhXCKHqWpkDqysrq7Ozs9XH63A4SkpKOiVkRYm0efNmVX7Q5XKZp/yWLl1KZAv8hNWd0FEqW6rPpKTkZbvdTmQTgjIy7l2//jdGCyKUla3PyMhQQmZk3FteXk6kojbbGLzVNlxu14L5z6gPSoiInJzJlZWVxgd1zz33ENl8/7wf5r333tth4sH3rW3avDU7e5IhQ1HRMkuD4uLiuLgE9Xnm5ORUVe03H233u7Qz1Z/FNUn9ACZNmrJ7d8UHH1Qy86ef1h84UDNp0pSgp3SwnM3Wh2//iRMn2IeUkpmNLIedgrJQ9u8/OGnSFKfLxWD4O3ypIvRCiOPHjzPzsmXPFRb+asGCZ5Rd05GfLRGVla2fNm3GNdcMsDxgyBej6nQ62Z+YmJgOVNaCiHJyJmdNeHD+/KeZPcwcHR05duzY8vINqkV5+Ybx48cnJCQo8W699dZx4zLKytZ3rKEqnE5nxvh7d+3aVVmpfjWfutzuMWPG1NcfVQJIKcePH6/egnGvrlu3rgOFBICy8g13jLxTfdHMvHnz1pUrV6mMLIr585+eMHFCwfz5ktWAHunp6ca7OCezTBxOrF69GhCbNm1RL6XkHTt2AaK4eI36ztj35XUikvnR3DwE+312OpWV1XZ73DubthQtfR4Q7/g+SUVubp7dHmfW2sXFawBRWVndwXKuXl2SlnbH4cNHxo+/B/4PEmZ+9NGZRDbLTkVHfvubNm0hsi0pes63w3PixAmHIz47e5ISIy0tbfy4n5lPmTgxZ+TIOztYzqKiZcZ3ra77zqYtAFavLlF7HA5HRsa9nf274bSRd45I+7HxUkp+dslyAH/9605mrqysBrCkaJlklr43YrfH5ebmmU5p5/cQLtafYt++fXa7PS3tdniVPYYNG2K32/fu3Wu2DgJP7EjUA8jhcHSurReUgwcPbthQnpZ2u5RNqsCN+bN6a+PG4cOHm0teqSTgFRUVHfaRGl/iG2+8ERvbT21bnupCiAEDBhi2nvncczQICoFc8uzSu+/6sdoGRExMzDXXXLN9+3Yi2rGzYvOWzbfeeqv5hJSUlE2bNu3YsasjJ1V79er17JIlI9NuNz6fhEFxAOrq6uD7vURGRnb6+txtP/rR6NF3GS+JEBUVBaCmpoaZVVr4lORklZ5AvZHhw4dvfPtt1Z7PgfXXmeov8Fbevn37DTfcYD4K4IYbbti+fTuCpYbuLBqOHjXE7lxd7I8cOzY9KSkJ6kbxH1RWVu3/qK7O4V+EPiEhgYgqKio67CNV8mRmPhAdHQkgaAnAI0eOkP+wHZ3hZJ6WljZ12pTY2FgAxi/l448/vvbaaxk4cOAAgMuv6Gs+5fK+fSH4YE1NB4hnkJX14IzpU2H6QR1r+BxAr169ADidzrq6OpWVw0zH37dTpz6clfkAmiep8dlnDYBwxMWBqKamBkBS0iDzKXHx8XW1tTt27j4Xug/hsPRh/D5dLpf6niwN+vW7oq6uTq0qdLrpZ2b+/PnGJO7MmTPr6+s7XTa/x4O/F7HKdquK0BvExEQNHHit2+1EB/4eyD9YkIiktDpAEFFBwQJj3WPmzJlHjhzpGPF8yMCfXHHxmrq6utGjRwM4efIkgOjoaLObS79+/cDc2NjYsaL6QUSvvvoqgLvuGgXfzXD06NFJkyYbn2dRUVHH2xBExOzxbWDNmpefnDt3SVHRTTcNBdDQcMThiFf2IHx344UXXgjA5XKdI2k7Wf0FWnORUTG+Q/CtvgmjUGmnowR+//19dXV1l19+uZpB2Lx5a3X1gUmTpjhdnXnfq9l6Yxts8RfxZlG0nGM2qTpSAxrbgRd9//33a2tr+/a9TH2877yzWa3nuDr04xWWn1x5+YYJEyZkZ2c/+OADAJS+69XrAl/CR+VrouwvYpxV9rqzYf78p1e99FJx8ZqkpCQAR44cAYTb7R4+fLj6PFevLpkxY0ZO9kMd7J8IgMhWVVUlhBCCsrKy5uXnT5/2iC8Zn2BvfUtpePMQ2UAqofo5oTPz/Vmerupn0Oh2qpfqiPdTQHMUVKgBUcegLldTU0NExn0zYsRtANLSbl+7du30aY90pDwtI4RZ2flNBbLPNmQmw0Wjs2YVjFGb2qitPWgcYua0tNuJKC0t7eWXX5469eEOE9I81bhmzdqsrAezsyetXLkCxuo/i5Mn/+X/jPE+ztVd21FII+t4TvZDL616obh4zYMP3q+OJSYmqjVfQ8jMzAcaGxunT5/+07t+MmLEbR1sAyUlJXk8HiLavHnrK6++mpGRsXBhYWxsP78ntw/fMJnp2z33x8wxMTF2e5wa5JotgqNHjw4cODA6OjrQPOmYX0KgeeK7rjB0ytChqYDYU7GrA+RpAQk/UY1BJTP369cPwMmTbrVHfZhu98m6ujpjxNFhNN/WpoCEoN+m2jl0aCoR79ljLCl0hMFiyJOTM3nixKx58wqU7gMAZvWhNbqdZrE/++wzBMwwnHsEgCNHjmSM//lLq14oLS3PzHzA92MxzCi/CQdHXAJIHqyp60jTj32PDfXYTUu7ffbs2WVlZa+88gqAK65Qc1x+Bn5jowvAubs/w2Luz/g7fPjw99/fZ/pVCADvv//+8OE/NDfuSIKuNjqdzi1btvkklD5XNRkVGdPB4lkwzGTvC9PAdtCgBIfDUWOalSei6v37AdyY7K2v2sGDX//nWfOt6HQ6N2/ebLw0DFXTvHDH3bc5OZNXrVq5cuWqub6ChQCIKD4uDr4ZVfg+us8ajgGIj7N38C+rvr5+0qQpf/9g74cfVo0bN8YnpDKbZFXV/vr6ejVeMT9y1NpIx3D4SP3Spcu3bN2C5klpXHXVVcysqvHaHQ4QqqurYboP62prBw6M+/5NQ3Fufvvh5fiSnJxcV3doy5ZtxpEtW7bV1dUlJye3fOK5wzwuU8bU4cOH+/Tpox5Z8E337Ny5ExApKSktdNUBMMxLH36HBOHHP/nJe9u3G1E0zd4GKSlhsqQOoL7+aO/eF7322uvqS1af/M6duwGRnJzawYtLBQULXnrpxeLiNRMmZFoODRs2ZOTIkX/4wx/US/WD/sO729JGpKm5/I5kVt4Tn3xyqLx8w+DBieYnChGVl785eHDim79529gD4ODB/WCRkBDXcRqAxYwZU19Z+zq8n5UgQlVVFYCEhAQAqampIFI+WOQLANu+fftPR406l1J1NhZXxvHj70lLu0M54n74YVVa2h0ZGRmtObHDkFLm5+cDYt68ArVn06YtygP2uPNEp4hkCGZsLylaRkTvNDuQS2b+5NN6h8MxMXuSctguLy8HREHBgs5yiFXRCAhwIM/Pnw+I/Pz5qs2WLdvS0u7IyLj3xAmXcWIHiLd581YiUmIESs7MpaXlhpzMrO6K0tLyDpDNjAodKytbz82fjMfcYPy4nxHZSkvL1VHl667ciTvyR7Sk6DnzdSsrq8dn3OtwOD79tF41mDdvHpGtrKxMSul0OrOzJzkcjsOHj6ij50LUzld/geTnz1eqmcg2b968zhYnOKtXl4wcOdIoyFlUtIyZO9uvnjMyMuBdNTLSH4AIq0uKmT2S+dNPP52YPUkdGjjQG/PbwYQK4gZQWVkpJUupPt47jf1FRUUdL2dRUZHPXLKaSJWVlVI2MfPmzZszMrzBsxkZGZv8w2w6ACl5/PixQeOL7Xa7asA+FalMvxEjRhYXF3OHGxBSyrKy9erjUpI8mpunAvUMiovXqAhrANnZkz799FNmZvacI1HDyI0uAKNMX8jazNypyaYCr84dudzXEpba8JIhyPvX9194wAGr/+ZV1BCH1Gz9uR21GV9l6Hss+G3J3kjrDkLJ2YYfQof/doJ8XIG/l8BPjxlElvu53Qhn9afRaDTnkM5f+dVoNJpOQas/jUbTTfn/OFW/wqWui/cAAAAASUVORK5CYII= | Use the graph in the figure, which shows the profit, $y$, in thousands of dollars, of a company in a given year, $t$, where $t$ represents the number of years since 1980:
Find the $t$-intercept (also known as the $x$-intercept). | $t$-intercept: $P(10,0)$ |
1bd5a8d0-b561-403f-b059-e34ad635cec0 | integral_calc | true | 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 | The graph of $y=\int_{0}^x{f(t) d t}$, where $f$ is a piecewise constant function, is shown here:
1. Determine:
1. Over which intervals is $f$ positive?
2. Over which intervals is $f$ negative?
3. Over which intervals, if any, is $f$ equal to zero?
2. What are the maximum values of $f$?
3. What are the minimum values of $f$?
4. What is the average value of $f$? | 1. Intervals when function:
1. is positive: $(1,2)$, $(5,6)$
2. is negative: $(0,1)$, $(3,4)$
3. equal to zero: $(2,3)$, $(4,5)$
2. The maximum value of $f$: $2$
3. The minimum value of $f$: $-3$
4. The average value of $f$: $0$ |
1bfa31b8-3fee-48fc-94d6-22cb63f39329 | multivariable_calculus | false | null | Let $Q$ be the solid situated outside the sphere $x^2+y^2+z^2=z$ and inside the upper hemisphere $x^2+y^2+z^2=R^2$, where $R>1$. If the density of the solid is $\rho(x,y,z) = \frac{ 1 }{ \sqrt{x^2+y^2+z^2} }$, find $R$ such that the mass of the solid is $\frac{ 7 \cdot \pi }{ 2 }$. | $R$ = $\frac{\sqrt{138}}{6}$ |
1c5ea0f7-a6c7-4a84-a172-9fca7a4b4b37 | differential_calc | false | null | Find the minimum value of $y = \frac{ \left(\cos(x)\right)^2 - 4 \cdot \cos(x) + 5 }{ 3 - 2 \cdot \cos(x) }$. | The final answer: $\frac{1+\sqrt{5}}{2}$ |
1ccc052c-9604-4459-a752-98ebdf3e0764 | sequences_series | false | null | Compute the first 5 nonzero terms (not necessarily a quadratic polynomial) of the Maclaurin series of $f(x) = e^{\sin(x)}$. | $f(x)$ = $1+x+\frac{x^2}{2}-\frac{x^4}{8}-\frac{x^5}{15}+\cdots$ |
1ce0ac9d-1bd3-4e51-8bd1-90c41444fb8e | differential_calc | true | 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 | Use the following graph and find: $\lim_{x \to 2}\left(f(x)\right)$ | $\lim_{x \to 2}\left(f(x)\right)$: $1$ |
1d6724cb-e2de-4789-bf24-cab32e9438d1 | differential_calc | false | null | Compute the limits:
1. $\lim_{x \to \infty}\left(x \cdot \left(\sqrt{x^2+1}-x\right)\right)$
2. $\lim_{x \to -\infty}\left(x \cdot \left(\sqrt{x^2+1}-x\right)\right)$ | 1. $\frac{1}{2}$
2. $-\infty$ |
1db212f0-2fac-410d-969d-fe3b5b55d076 | integral_calc | false | null | Solve the integral:
$$
\int \frac{ 3 }{ \sin(2 \cdot x)^7 \cdot \cos(-2 \cdot x) } \, dx
$$ | $\int \frac{ 3 }{ \sin(2 \cdot x)^7 \cdot \cos(-2 \cdot x) } \, dx$ = $C+\frac{3}{2}\cdot\left(\ln\left(\left|\tan(2\cdot x)\right|\right)-\frac{3}{2\cdot\left(\tan(2\cdot x)\right)^2}-\frac{3}{4\cdot\left(\tan(2\cdot x)\right)^4}-\frac{1}{6\cdot\left(\tan(2\cdot x)\right)^6}\right)$ |
1db350b9-5d62-4e83-9751-fccda80f11cc | differential_calc | false | null | Find the extrema of a function $y = \frac{ 3 \cdot x^4 }{ 4 } - \frac{ 4 \cdot x^3 }{ 3 } - \frac{ 3 \cdot x^2 }{ 2 } + 2$. Then determine the largest and smallest value of the function when $-2 \le x \le 4$. | 1. Extrema points: $P\left(\frac{4-2\cdot\sqrt{13}}{6},1.8363\right)$, $P(0,2)$, $P\left(\frac{4+2\cdot\sqrt{13}}{6},-2.7931\right)$
2. The largest value: $\frac{254}{3}$
3. The smallest value: $-2.7931$ |
1e317fe8-3370-43d7-a9fe-efa7691e872b | sequences_series | false | null | Compute $\lim_{x \to 0}\left(\frac{ 2 \cdot \cos(x)+4 }{ 3 \cdot x^3 \cdot \sin(x) }-\frac{ 6 }{ 3 \cdot x^4 }\right)$. Use the expansion of the function in the Taylor series. | The final answer: $\frac{1}{90}$ |
1e67594e-d4d6-420e-8e63-caa6f3d285fa | algebra | false | null | Rewrite the quadratic expression $x^2 - 9 \cdot x - 22$ by completing the square. | $x^2 - 9 \cdot x - 22$ = $(x-4.5)^2-42.25$ |
1e6b9832-43f4-4214-bfa2-5884ac2d279f | precalculus_review | false | null | Find the degree, $y$-intercept, and zeros for the polynomial function $f(x) = x^3 + 2 \cdot x^2 - 2 \cdot x$.
1. Degree
2. $y$-intercept
3. Zeros | 1. Degree: $3$
2. $y$-intercept: $0$, $\sqrt{3}-1$, $-1-\sqrt{3}$
3. Zeros: $0$, $\sqrt{3}-1$, $-1-\sqrt{3}$ |
1e99cf2f-e67e-45fd-9560-c7d532daf02a | sequences_series | false | null | Find the Fourier series of the periodic function $f(x) = \frac{ x^2 }{ 3 }$ in the interval $-4 \cdot \pi \le x < 4 \cdot \pi$ if $f(x) = f(x + 8 \cdot \pi)$. | The Fourier series is: $\frac{16\cdot\pi^2}{9}+\sum_{n=1}^\infty\left(\frac{64\cdot(-1)^n}{3\cdot n^2}\cdot\cos\left(\frac{n\cdot x}{4}\right)\right)$ |
1ea61b4b-45e2-493c-8d9a-14357d27796d | algebra | false | null | Rewrite the quadratic function $h(x) = 2 \cdot x^2 + 12 \cdot x - 4$ in standard form and give the vertex.
### Forms of quadratic functions
A quadratic function is a polynomial function of degree two. The graph of a quadratic function is a parabola.
The general form of a quadratic function is $f(x) = a \cdot x^2 + b \cdot x + c$ where $a$, $b$, and $c$ are real numbers and $a \ne 0$.
The standard form of a quadratic function is $f(x) = a(x - h)^2 + k$ where $a \ne 0$.
The vertex $P(h, k)$ is located at
$k = f(h)$ and $h = -\frac{b}{2 \cdot a}$ | The final answer: The standard form of the quadratic function: $2\cdot(x+3)^2-22$ Vertex $(h,k)$ = $P(-3,-22)$ |
1ecd4b7b-49ad-4fad-848b-95a689622f1a | multivariable_calculus | false | null | Evaluate $L=\lim_{P(x,y) \to P(a,2 \cdot b)}\left(\frac{ a^2 \cdot x \cdot y-2 \cdot a \cdot b \cdot x^2+a \cdot b \cdot y^2-2 \cdot b^2 \cdot x \cdot y }{ a^2 \cdot x \cdot y-2 \cdot a \cdot b \cdot x^2-a \cdot b \cdot y^2+2 \cdot b^2 \cdot x \cdot y }\right)$ | The final answer: $L=\frac{a^2+2\cdot b^2}{a^2-2\cdot b^2}$ |
1f898401-6ced-46c3-963d-b2312f6050a7 | integral_calc | true | 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 | Find the surface area of the cylinder $x^2 + y^2 = x$, which is contained within the sphere $x^2 + y^2 + z^2 = 1$. | The final answer: $4$ |
1fb06482-1ecc-444f-b93d-73a9a2e17ebe | algebra | true | 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 | Using the given graphs of $f(x)$ and $g(x)$, find $g\left(f(3)\right)$. | The final answer:
$g\left(f(3)\right)$ = $0$ |
1fd375be-b4ea-4035-b84a-c91779dafe26 | integral_calc | false | null | Compute the integral:
$$
\int \frac{ x-\sqrt[3]{4 \cdot x^2}-\sqrt[6]{2 \cdot x} }{ x \cdot \left(4+\sqrt[3]{2 \cdot x}\right) } \, dx
$$ | $\int \frac{ x-\sqrt[3]{4 \cdot x^2}-\sqrt[6]{2 \cdot x} }{ x \cdot \left(4+\sqrt[3]{2 \cdot x}\right) } \, dx$ = $C+36\cdot\ln\left(\left|4+\sqrt[3]{2}\cdot\sqrt[3]{x}\right|\right)+\frac{\left(3\cdot2^{\frac{2}{3}}\right)}{4}\cdot x^{\frac{2}{3}}-3\cdot\arctan\left(\frac{1}{2^{\frac{5}{6}}}\cdot\sqrt[6]{x}\right)-9\cdot\sqrt[3]{2}\cdot\sqrt[3]{x}$ |
2086d032-660b-4d65-bdc3-fe27a82e8ee2 | multivariable_calculus | false | null | A person is standing 8 feet from the nearest wall in a whispering gallery. If that person is at one focus and the other focus is 80 feet away, what is the length and the height at the center of the gallery? | Length is $96$ feet and height is approximately $26.53$ feet. |
20e1df0a-f00d-4545-8ad0-f44adad1d83e | sequences_series | false | null | Find the radius of convergence $R$ and interval of convergence for the power series $\sum_{n=0}^\infty a_{n} \cdot x^n$:
$$
\sum_{n=1}^\infty (-1)^n \cdot \frac{ x^n }{ \sqrt{n} }
$$ | * $R$ = $1$
* $I$ = $(-1,1]$ |
21207f35-779e-4510-91cd-89f0afe29a82 | integral_calc | true | 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 | The graphs of $y=4-x^2$ and $y=3^x$ are shown in the figure above. Find the combined area of the shaded regions. | $8.013$ |
213c8058-a2a8-43e2-b8f6-91371fe234b2 | algebra | false | null | Using the scoring system in the game of Jeopardy (you earn points for correct responses and lose points for incorrect responses), what would be the final score after the following 5 responses:
1. Player 1 answers a 200-point question correct, a 50-point question wrong, a 250-point question correct, a 50-point question wrong, and a 150-point question correct.
2. Player 2 answers a 200-point question wrong, a 100-point question correct, a 100-point question wrong, a 100-point question wrong, and a 50-point question correct.
3. Player 3 answers a 150-point question correct, a 100-point question wrong, a 50-point question wrong, a 100-point question correct, and a 250-point question correct. | 1. The final score for Player 1 is $500$
2. The final score for Player 2 is $-250$
3. The final score for Player 3 is $350$ |
217dbc0c-03b5-4b38-b4df-60f8ce6951d3 | multivariable_calculus | false | null | Determine a definite integral that represents the region common to $r = 3 \cdot \cos\left(\theta\right)$ and $r = 3 \cdot \sin\left(\theta\right)$. | The final answer: $9\cdot\int_0^{\frac{\pi}{4}}\sin\left(\theta\right)^2d\theta$ |
21b8ca26-51d9-4663-b145-8e74540fe9c2 | differential_calc | true | 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pj4Rm33ZKW5EQ6A0Z8a5LVOh/eT6JAn8/HsqzxocViyWazZFrImBNCCDmdzkgkMj4+7vV60+n0+++/f+fOne9///ukO40xVlX1008/7e3tRQjF4/FkMvmv//qvAMBxXFtbW1VV1ZoSrQ5RLckMJCqK4nHYaFO3KwtNURzLAEIZWclmFYal9Zmg/ICiKIqiVFXN7eiqqsowjNGKGrz++uupVKq5udnr9UqS9P777//4xz/es2fPCy+8gHQ2b95cX18PAJOTk7/61a+eeeYZAKBpuri4+BFf2uoAT0VqRCBKCsbYwrEFU33lq24BgGNpq8Am05loPO332EgUqnzxdbTZbDabLZlMptNp8omqqtFo1G63C4IwbeP9+/crikIS3mKM7Xb7D37wg46OjgMHDpDJXoqiNm/eTDYeGRkRBIHodm2DjYp8PJyQFexzWQsmY3AeX4ZV4DwOWyYjJ8UMRiTGVx4oluB2u8vLy8fHx4eHh4lDxdjYWH9/f0VFhcvlUhQlkUhkMhmMcSaT6ezsHBoakmUZABBCiqIAAM/za7L3uzRIpJRIIiUr2O+2MYWi23xubxnGwnOyoopZRbNEYDLQzQM4jtu0adOFCxe++OILj8fD8/znn38eDodfeukln88XjUa/+OKLxsbGhoYGSZLeeecdAPja175WWlqazWbfe+89t9u9detWU7dzo60cQwDpTFZSFJaleI4pmBuWx7rlOcZuYdOiFE+J9waxzo+Hs2XLlo6OjuvXr4uiKAhCZ2fn5s2bt2/fbrVag8Hgp59+StN0TU0Nz/NVVVUff/zxO++8U1lZmclkLl269PLLL2/cuLFgen0PAWwsxw5OJmRZ9bmsBdPYQl7r1iqwHoclHBfjSUkPS58nkgUAgLKysldfffXUqVNjY2Oqqm7btm3Hjh319fUURVmt1o0bN5aUlNA0zXHcN77xDZfL1dPTk8lkKIp69tln9+3bZ0wgmcwFwoARxFKioqheZ+EYkyGvdcsytIVnx8LJdEYi7kD5MglEoGm6qampqKgoEomoqup0On0+H8dxAOD1el988UWbzUZmicrKyl588cXJyclsNkvTtNvt9vv9ZmM7L0gLeg4QT0mqqlp5rpBuWB7rVmAZu4VPi1IslYYcR9x8aXTJWoJAIBAIBKZ9xbLstPkbr9fr9XofYenyH31RQTCSlGTZ7bAUzGIgyGvdWgTW5RDSGSmR0qKfm3Yakxy00LyxREZWcMDjYPTVVAVA/nYdMMvQAs9mZFnMyDnxz01MCNpcfjyZUlTVZuEpytTtyoMEjnHYhLSYjSVFU7Qm9zKV6zwYjsuy4nVZzX7yqkDgObfNIkpKIi1N5RUHyJfxrcmjAEM8LSkKDrgLZ1EB5HN7ixka8RxDAU5lJDGT1cczpmhNgFilSHipaCItK6rdwhbM4lvIZ90ijMHCMw47n0xnogkRYTOko4kBNkJ8BiOJrKL6XTa6gCaC8vhKEEIWnnVaLdmsImZkmErYZ2ICZGUnACRFSVWwz20rpH5y/o5vMcbAcazNwqUzUjKdAbSyXhfG1LFRcSBVVeOpTDAcT2ayAscGXDaXMYtI4oTqOVRW77Bcz80+LfAeBlBkNZpIheIpnqEDHqeFZ/SJOLIPxiuZIVFzckwkRSkrCzwrcCzKv4Cfc5K/ukUIsJXnXHZLIi1Fk+LCezxMsBaefUqA0UT6UufAlTsjQ2PRhCgKHFvqc9ZXBJpriqpL3FaLAEYqbi1Wx2p7qzDoiWT1WkYrYSSevN0XvNM7PhyKBqNJgWVLfI62xopNTWV2C29Un5p0Vu6aEELBSFKWlYDHxtAUzqN4KAuRv7oFQMBzrNXCh2PJTFZe6ZdeEyBZlxQMpz46c+vQqWs9Q2GnVXDZ+UQ6c+JKt8tmaakt2dpSuaOttrLIw7P0Kg61qKfqmErhgtIZ6UbP6KmOngu3Bjp7xxGinDY+lZGTyfS6mpL9O9bt395c4nNSFNKXv67UAi1t3XxKlBUFO+0WmqLyyQl2IfJZt4B4lrYJ7Egwm0hlVjqCMsZa7iIUiibe++L6O0e+nIyltjRXbllf5Xdbo8l091Coc2Di9NWejq7hq3dH9z7esH1DlddlXekaZ07utfOhgdHwyY7uTy50Xro9xLFsc01pQ6W/xGePp6RbPaMXbw0MB8NDY/E/eWFLWbGbJkmhV+7KSKyfiXBckuWAx1FIxmTIc92CTWA9diGZzkQT6ZUtCSIBJRFEE+mjZzvf/uhCNCn9wZ7WA0+0NJT7WIbKqjiRzHQNTpy+2nP2Wv8n5zo7+8Z6Ryae29lSXeKhKGql651Z0Ybrsqxe7R45fOLGpxc7J6LJ5qqSXe112zdUVRS5BZ5RVDw0Hv34Que/Hb34648vWXj6u3+402XjievpipSbrCnAGAcj8ayMizw2likcZynIc91ijqOtAivJOJNVF978IRcGEIiZ7MVbA7/88OJkNPW1vW3/7qubK0s8AsuQF8lttwQ8toZyX3tjxScXbp+40v3WBxeHxmMv7924ob5M4FbXs9C88gESqcypjt7ff95x+mqfw8q/tLv12S3NTbUBj8PCMQyJBeOyW4p8djvH/N2/Hv/1J1dK/M7X9m1iuRWri7SRB0IZGSsqclotNL06a8ZlsrrelSWCrDzrtFkS6UwkntJHNCvwYIwx6nAw+q/HvuwcCO7dVP/avvbaMh9DkyZLC8Bt4ZmKYpfPbasqcVcWez46c/uD0zeD4cTXn27b2VbjtFkefeHngtijRifiR87e+v3nV+8MhNbXFB/YuX7PpvqygJvnyaQKMeJjlqFKvI6v72sfiSTfPHjuzYNnH2so31BfspJDdwwI4WA4kc1m/S6raZdaNWBsETiX05oUM7FkSl9xuQIFITFR4qnMiSs9xy/drSrxvPaVx+urAgxtmFSn7M2IomwWvrmmyOuyVpZ4fv9px9nr/cFIfDKW+uqO9V6XdQUuYDZkRb3dN3b4xM2Dp6/HEuJTmxtefmrjY43lbofFuC4wnPcxphD43PZvH9ja2Rc8cbnrZ++d/h9//qLdyq6QWLRcBaFwLKvIfq+DYQpqgJvPugXEMDTH0KqCpawsywpJvfFQwVrGTpybsRwwYIy7RyZ++1kHhdBXtq3bvqGa1Wb5c15bhAyTJsswxT7nM9saA27rvx67cvzS3X96/+xkNPnSno0VRW6tddaCeCAAFQBpIaJBWw6+UKcPg55/Bc1IpTklualwLroNCgMASorShRv9v//86heXuu027tVnNz3/xPp1lQELz+rHucdQTD6kEKop9fz7F7dd6xr44NTNAzs3fGV7I8qd4NJyRT+COGCIPKuUmFVUzPMspd3GAnG9yGPdYgQAyGHhPXZLPCVFEqLPbXvYDgxI7xneE1sDQSwhnrhy92rXcHtD2Uu7W+1WXvOQnb0wGABoinLaLNs21DgsgsdhOXzyxj9/cG4sknxl32NN1UUsw5Ck6FPnIfO9CAMYsRzmLqa2q15oQzyk4HqAAV0+SLudGADQ6GTikwu33/v86tW7I3Xlvm/se+zpLY2lfhd3j2ln5tkRRkAjakdrzVd3rv/lh5d+fujMk4/V2Kw8AqwVGGGtAnroaJPjY+G4lM2W+Z0sSxfO6Dafdav5GtksnMthTYlyMp31ux/BaUFranNbEYCxyfhHp29bBO6ZbQ2Nlf6Fqg9jahTxLLuhocxuE4q8jl8d/fL3n3UMjk6++GTrvq3r3HYBtOoBAQBGGLDuiDR/Fi9A2kRyjsiR5rOLtcQ5egdXuwAEAEhW1Zs9o++fuHb03O1QJLHrsdqvP922ZX2V12Gl6HtcwWa5MZhk08IOC//6ga2fXug+fa33REfP/u3r0NT59R0fsiVC62hgHEmIWUUt8tgYhi4k9/X81S2Q94BmaI5lMpKcykiP7rwYAULGcDolSl/eHrrdM9baUPbczhaGoWGhlCe5bzHHUHXl3m8+217ksf/mk45TV3v6x8J3BsZf2r2xodLPsghhRDw6MOlAL/TCY8CAVGx0C0jLjylyXoRUDICAmrIZI8CAJ8KJLy51HTp149z1fpuV+8a+9j/YvbGp2i/ofeP5rQd6b1wFRK+vLf3a3o0//vUX//j+md2bai08bzh0oqm67qF2iwADJNJiNqtwDMPQFMqr9FELkr+61d4kh4X3Oi3xVCYaTz+qfpDWWCDdK2ciHP/g5HWOoXe311eX+QEQvqcdm/sC9N4+TVEBj+OFXRvKA+7fft7x8fnOX3x48Vbv+L6t6/Zubij1uxhaG/Jqh4UFHZFIAzc1uMR69x7rhjTSJiGEY8nM1a6Rj8/f/uzLrpGJ+Ib6kpeebHnq8YaKgJuYYXVHx/n7EMbxMUfT3/zKpl8duXDmau/VrtFtLZWAKNAth48kiRNGGMbDyUxWKfG6OJbOl8DaiyR/dau9iQLH2ixcNJEWpeyjiAqnv+v6cBFnZbVrMHT+Rl9Nqf/Z7U3U9B7hIg6pjcWQ3cptb632e2wt1UXHznWeuNJ7u2/8dEfvlpbKx5srWmpLOIbWzNKavWmOA059q2J9PKn5hWhex0De7EgyfaVz6HRHz7lrfXcGJ+w24ZVn2g/sbG6pK3FYeVpr3jHWu8GwwGIBXdpIrS/zvbBr4z8dOvfm+2e2b6jCAIBVQJTen374dimkJsWsqqgeh0BrkaUKZ4Sbz7pFGGHgOcYqcEPBaDyZJgbYR6FcbZAJCFAkKX725d1MVt20rryhwqe1baThmbNjhrWBMpEF0v33MbAM1VgZKPU6WuvLPrnY9en5zg9O3Th3o6+xsqipOlBb7i8LOEp8TruFm+syg+MRlbH1DIckGY+MhTBQWBMsBUjV7VE4LcmDY9GuoeCtnvGugXGWpna21e3bsm7HxuqKIhdNI4QRJjZt0K3aJNbtXFelVScqIAoDpmn4d1/Z9KuPLx49d6dnOFxb5gWkmbXxI5mvw4AmI4msnPV5rAxFF4hedfJZt4AAgd3KeZzWRCobTWYegWiN6VikdwrDseTH524F3PZnt6/jOQYwCeW8wEwNcdUgv2nZHvWGkUbIabds3VBVU+bZ1lJ1o3vk9LW+G93DZ671+Nx2v0vwuOwCyyJQ8WyzGqIoSr72//EPH2UVmIzEMCajY0BI0w1ghEDNZOVgOJlIi36PY8+mxp1t1VtaqurK/Bae0brjus8RGD8R8Tie77K0rTFSETTXFe/cUHP0/J3DJ2/+36/sNKbB0CPyj0HBSDKTVYq8To6hH0nn/NHxUHR7P1mSl7gvZhmKZxlVVWVlydX4MsupDxIRhnRGunSrf2A0vGNj7ePrK5E2s6K9vfOMbafe3dz/tC8BAaIRKvY6izzOHa3VT7bX9gyHOgcme4eC8XS2fzioqDDXiygrWZV337w7wjC03+cSOAYBBqwSu7S+dhCzLN2+rqK6xFNb4W+s8FeVei056dhzC3NvsfUp2Nz7QW5jzow2KRvDsd96pu3YuTtvH734p3+wjecZfB/CXerDQgAJMZNVVTvPT09MulymT4OvXDbwh6Jb0hda/CXJsvzjH//4+eefr6urM/Zd6AiaX4FV4F0OIZJIhaJJwNoU54Jn/OEPf/j88883NDQssoQ5IN28AoAgkhQ/uXDXahV2tde57IJuctV7owAIoK+v79q1a7W1tS0tLfceaKEzIYQQ2K38400Vm5oqwwlxPBRNZZRgKKpimGuJXDgc/v7/8+7/+4P/i6Yol9PGMjRgFRAQVxHSgccANE27bILPabVbl5bXb9rGJ0+ejEQie/bscTjs+pB/6vHt2txQEXDe6Ru/1Dm4o7Vmapnx0t92ct6PPvpIluUXXnhh/o3J2UcnYpKk+D02hqXvWRu9OJLJ5GeffeZ0Onfv3p2bSdw4hfHz0av3Qeo2V2lLuhJVVd9///1NmzaRzMuLOwJxJ8I2gXc7rMmMHEtJZLfFnPG9995rb29fhm41SzJCgLEKeHwycfJqj99tf2ZLoxbgYUpNmnrHx8fPnz/PMMw03S4BRCEAr8PidZDUuOUYA8zhczQyMsIkhg7s2qAVYuqhYKx7SpM1hw/kXbtx48bQ0NCWLVscDsfUzQFtxtbrcu7f2fzm+2cPn7q5fUONZmhfYAwxHxcvXpQkaUHdkpnkaCItZ5WAV1sMtNRTiqJ4/vz54uLi3bt3z7xbiUTi1KlTly9fbmxsbGlpqa6uZlmW5Bx/BDJ+YLrFOsvYlySAxRiTX0CvxhY8J7GE0AgojMWMlExnrAK3+AIbp1sSWJ9ISWWyVzoHQ9Fke31pfZlXxarm3YRRzobIuDPLO920kwOAPrEDeDZHAnKW3HPl3Ey97ABoeY9qZoHuvbqZx3zxyQ3/dPD0kdOdf/3H+6w8q2IVEL1s3S7+TmKAaFLMKqpdYCjAWMW5LmSLQVXVeU6XTCZPnz79k5/8pLS0tLKysra2tr6+nmi4tLQUIUTT9MPT8APTrSRJw8PDyWRykdvnpPMBWZYTiURvb6/H45l1g9kgC14pAIiFQw4LMzQyevHyVZ9z4SU1CKFkMtnX1+fz+RZZ2nt2Jy4MGIcT2WNnb/AMVWzH3XfvYgoT93qMEUIUxip5O7u7u4PBYH9//40bN5Zxutxi4yk/Yt3WO4NgMJjNStq5yJyUFmAGa9PKaD63p6UyMjISDAY7OzsnJiZmlBYDAJvNuCxc3+jE0ZOXmoqdKqUAppAxxb1EgsGgJEmLvJO9g0FJhlR88s6dTpqmqCXqNhKJBINBjHHu6YzrmpycHBkZGRsbGxsbu3z5siAIxcXFRMN1dXUtLS0bN26sr693OBwPQ7oPTLfRaPTjjz/u7e1dzMbTRrCKooyOjh47duz27duQ07Wbf4irj5NwTxhRWO3s6v633/a6hIXvEUJodHT0448/7uzsXOTVzUBVVAjG4ewQT2M5PHjjnV91YcAIU1MujKD5Jw8PD3d1dYXD4f7+/uWdDOnuttrcJ7l7oM7aT47HE8lk6p13fqWZqlXjVmOtrrvHKHS/oWQuXboUj8d/97vf2Ww2o6jTnm+pRb6Rov+/d45uKZJkGlN4Ya+Ruejo6JBlmSTynh8V4/4BVcXs6VMnui+TSS2YraKbk1Qqde3aNZvNNld7e/36dUPGmUxmYGBgeHj48uXLJKt4NBoVBKGxsfFhLHd5MEfEGFut1tbW1vLy8qXuiBDKZrMfffRRa2tra2srLCTXqX21uRjs6o/difVaWLyuqbqhwrPgjgBw8OBB43RLBgMgNSXKR873xMWJrU0Vrx1oxIoEQOZIdZdg/eXs7OyUJKm5uXnz5s3LOV2ObsEwhADSvS+mMzk5+fbbb+/atQtABTBe1amlQQAYgMrR7n1NysTj8VAotG3bNi0fL2nZ73Ghxo2PM9//6RfXBxP//sBOu1VA93HKoaGhbDa7a9euhbccj/A9d1wAWzZtqPZZEKIwKEtaDxSLxcbHx91u96yni0Qio6OjAMAwDMuyLMs6nc6Ghobm5uaGhoba2tqKigqfz7eq+8kIIbvdvmPHjuXtLknSj370o507d+7atWvR14kNbfiu95+8k5AVddPWHU+21y1m5//1v/7X9u3b9+zZs9Si6nNAOBRJfnLnQ5s18fS29c99Ze9UW0gMvfoyPATg9/vD4fDWrVv379//QJ4imR+eq8UaGRmxWCwHDjx3z2DYKDxMjbtzdlp+qQYHB4eGhvbt21dUXGx4MN9rDIN4MvOjd6+OhGLFdW17NtXf4365RC5duiRJ0oEDBxbc8mrXyD+fCrKCvHfP7ubqgLb+ciknDYVCN2/eLC4uPnDgwMw5jmAw2N3d/dlnn1VVVbW0tDQ0NFRXV1dWVpaXl5eUlNjt9mVc3eJZMb+LaTfCYrGQcfyiD0CceDAC4FlG4LlgJJHOSIusyQXB8H1bGsQ/AmOIJcWzN/rcdsuutlp9eRpoP9E987cURXEct8Srm870+QYEcjabSqVEUQQAnuftdntOf2x2j0/D1q//tUzH0Nxnx7Isx3Ga+cUo3b1X6rDwezbV/8tHF49/efepTXX4PvwuOI5bjEENY5zOZBUVOyw8S1PanPgSz4UQ4jiOpA43jOTGt1arde/evSUlJYZW3W738l6qZbBius0VLUVRu3fvzrUSLaarrI9VkMMmeF3W7qFgOL5AdDjjsHv27PH7/csoNmlVs7Jyq298dCK6dX1Nc23xvS/h9GJ7vd6WlpaSkpJlnG5asY1ZRFVVr1+//sknn/T09ABATU3NM88809bWtsQk9MusR3Jf4pqaGrfbLQjCnNuCCoC+sn39Lz64cPJKV1Z5hr2Pl7u5uTmbzcJCbwhCMB6OZyS5oczPscYk0NKul+O4lpYWp9M58yuMscVi2bx585YtW3ieX+JFPABWuL0lv9M0/Y1vfKOoqAhyXs2F9iedZAoB2ATOaeNTmWxKlObvCRmVxauvvkpOt1TIEdKifOJKN0tTbQ2lDis/v2mnpKTEZrNZrcsPQGMYP4zyT0xM/M//+T+TySSZEz5x4sTFixf/7u/+bnkXtWwwxm1tbdlsdp6rI89zU1OZw8Z3D0/2j4bry/3LHuFu3759ca4OKJoQs7LidVnJ5C1aunuTxWJ54oknaJqeuSN5ReeurR46K9/ekp+1tbXTPof5b7QRsgmQwNN2C5dMSfGkuOBjMVqJBY4/BxhjAJwQM2evD9os/LbWqpy1cbNjsVgslvsK+DbNoQVjfPTo0c8///x//+//vWPHDoTQmTNn/tN/+k9Hjhx544037udEyyiVx+OZ/x4SO7bXwT++vvL0le4Tl3vry/zLNmEHAoFFbhmKJqWs7LELRlqgpT5rmqZz68EV9GqcycqE25nWehifTGOBF0Lfw2bhnDYhlZHi6cwivQlmDlcWCUJIVfFwMHp3cMLrsLSvq4Dlue0t8aTGdZE7dujQoYqKigMHDlRUVJSVlR04cKCqqurQoUMPtRgGuS3eIu4hAgQURT39eL0sy59dvKPiZQ9vZynGXISiCSmr+Dx2PXIyns0rZFFnmf9E6XR6bGwsGAym02kAUBQlEokMDw9HIhFFUZZxxsWwMu3tTHfI3Mdv/L5QDae1uTTNCDyLANJiNiPJAs8uqQxLBEtZtaNrWMpmm6qLir0OvByTxxJPOcOB9MKFC08//TTHceQTnuc3btz48ccfP9Ri5BZmcT7kZAdNt0+01VEUc7VrKJZMux3LHDUs0pcWA8QSoiwrTrtAM8Q5eZlGuNyu36zX29/ff/DgwWw2u2/fvs2bNw8MDBw7dmxoaOjJJ5/csWMHmdZ+4Kz8Oj5FUeLxeDabRQg5HI7cUf48b4Y2iQlkoIvtFs5lFeIJMZZIz6/bdDqdSqVUVbVarRaLZYmGHABAmax8/uaAhWceb6qktdgv86GqqiRJxKq8xHPpp7z3PmCMQ6GQMTdIWgO/3x8KhZZ3/KUWJrdIsixns1me5+e+k8QZGtWU+qpKvOPh2I2e0SfaFjVdd89RMBZFMZ1Oq6oqCILVap3n2SGAYCSZycqlfifPMkYArWWcNJPJJJNJjDHLsjabbdZ5gdu3b3/22WeSJDmdzsOHD//ud79raGh49tlnH16A0RXWrSiKt2/fvnr1qiiKiqKsW7euvb19mrfjrDvqzgSahd9u4Z12SzKTTYjSXJYZRVFGRkauXbs2OjoqSVJpaWlzc3N1dfWS5IQxTorSlc4Bu8Btaq7QpivntkuJojg4ONjb21taWrphw4bFn2geZtpIyC9Lr4PutxjRaPTOnTvj4+O7d+92OBxzbAdEugLHbF1f+bvj185d732irdb4bjFIkjQ6Onr79u2hoSFFUQKBwPr16ysrK+eyDEmyEk9LAMhtt+gBcZfcOVdVdXx8/MaNG319faqqWiyW1tbWxsbGadaKioqKzZs3f/DBB8eOHYtEImfPnnW73V//+tc3btz48EzND163Sxq+X7hw4ac//SnHcV6vd3Jy8siRI1/72tdef/31Rc6DGaexWXiHnY+nMvFUZq6NBwYG3nrrrTt37hBTyokTJ0pKSr773e82NDQsftpNUdX+sfDweKypumh9balukpr9euPxeEdHx9GjR0+fPv3CCy/cj25zbynxTiONgPFhMpkkHksPaL3AwgwPD585c+bgwYN3795tamqaS7eG+ZCmqO2tNb/+5PLFm4OqqlIUpbmoLGKFXX9//69//etbt245HA6GYSYnJysrK7/1rW+1trbO+rKFoklJyrrtvGaUwkt29cAYx2Kx3/72t6dOnfJ4PCzLjo2NnTx58jvf+c6WLVtyt7TZbE888cSOHTuOHTvW3d1dVVX1zW9+86mnnpqzInsQPGDdLtZFUd/s/fff7+/v/y//5b8EAoFIJPKjH/3oH/7hH1588UWv17vYMwIGAJuFc1j5ZFqKp+aM6njx4sXTp0/v2LHjySef5Hn+7Nmzv/jFL9atW1deXm54tyxY/qysXLjehzFuqS9x2QWYd+B09+7dgwcPDg0N9fb29vX1LfKKZmWajX3jxo03b96UZZl4BWQymRs3brS0tDxKm+dHH310/fr18fHxS5cupVKpuTYj4T8AMEVBe1M5z9K3B4LhuOh12bRQWTMKPO0qVFW9devWuXPnmpubn3nmGUEQPv/8848++qiioqKhoWFWWz3Rrddl5VjG8ImZp8mddnuJLWp8fPzo0aPl5eWvvPIKRVGXLl365S9/WVRUNE23GGOn01laWppMJkVRfOmll/bu3TvrrO8D5IH5Jy/JQmvcI6/X+53vfOfAgQMMw2QymevXr//t3/7txMSE1+td5CtIthB41mrhx0OxVHrO9pbjuKeffvqFF15oamqiabqqquqtt966ffu2KIqGbhc8YzarnOro4Thmc1Nlzlsw+16qqpaWljY2Ng4ODi54IfMzbR7ohRde+MEPfnDlypWmpiYA6OjouHXr1l//9V8/yokKSZJ27tzpdDrPnz8/z2bEvwwDpihU7netqyrqGQlf7xnd3V5vBNibpqdp43kyP7xnz569e/e2tbXRNM3z/IkTJ7q7u1Op1Ky6nYymxKzitltZmtIb8/m6IdPmHYlnCwBs3br12Wef3bZtm6qqXq/3yJEj169f165L3zgSiRw/fryjo8Pv90uSlEqlJOmhhwR+YP7JS9recK545ZVXPB6PoijJZDIUCsXj8bKyMjJoWay5EhDG2GkVPA5r98B4PDV74nmM8bZt29rb2wOBAOkVx+NxiqJ8Pl+u8WCBFUgYEmnp2t0Rq8BtaipH8w1sAQDq6uoCgcDQ0NCDmqA37ttXv/rVX/3qV//8z/+8detWADhz5sz69eufe+65R9ZJBoD9+/f7fL5QKDT/KENbhoMAAxJ4ZktL1e2+4IUb/XuIJznKvedT+s19CjRNt7W1NTU1eb1emqZVVRVFkaZp0mee9aSTsaSUlYt9Tp5jyDoPhOYNjDXjpBRFlZaWvv7660VFRaQhHRkZoWm6tLTU2BhjnEgkjh8//vbbbyuK8uqrr165cuX8+fNnzpyprKx8qH5UD8suNT4+nsnM3vTxPO/3+8ll19fXY4w7Ojo6Ojq6u7svXLjw8ssvG5PdC4kWk3hq6XQ6GplQpFQiLQ2PTQwMDORu5PV6rVYrQqioqMg44NDQ0G9+85uioqJt27ZZrdZpVv651KtiPDgWmYgmq4ocjJoeGBgAPfSLsY0gCIZvgNvtdrvdo6OjC84BLhKjeDU1Nf/xP/7HU6dOkbbOZrP95//8n2tqah5le0tcZRY8I8YYgbb0labRpnXl//T+2S9vDyqKqkWH0Dec6wgMwxCnVIyxqqpDQ0PHjx/nef7xxx+fa5YlmhAlWfE4rQzJQUZG0Yu7OUbl6HA4HA5HIpH44osvhoaGvvzyS57nv/rVrxrbJJPJkydPvvXWW6FQ6LXXXjtw4MDbb7/9k5/85OOPP966dSvpCj0kHpZuZy6kNvD5fF6vlzwz8sng4OD58+dHR0dJ95WM2RYDqcojkUhPV2d0MphIZTq7ei5akrkvwaZNm6qrq0F/wxRF6e7uPnTo0I0bN772ta+1tbWxLDutkz/XA1YU5fKdIYzBLai3rl8j6baMgpBtiouLc316HkYDiBCiafq5555rbm4OBoMAEAgEiHXtUba3i4WsjMIqRhRNUS21JQxLdfUHJ6KpYq/DCJyzGA+qbDbb19f3wQcf3Llz55lnntmyZctc7W0wnBAzssdhYRlas4Es1NzOVXeLonjt2rW7d++OjIyUl5eTGoR8FY/Hu7q6KIp68cUXv/71r1dXV+/evbuzsxMh9LDn5B6Wbu12uyzLc32Ve2sQQi0tLTabLRQKnTt37t133927dy/xQ5wXPfQDxizLlhT5i/zBzI1wVgG7w0nTU8rLneYRRfHmzZu//e1vR0ZG9u3bd+DAgZluevN0lbOycvZ6L8cwW1uq3W6XviLOmGbQri53l8U4CSwJ46bZ7fZlrh9+tOhuKRSpGkt8zpoybzCUvNkzWux16A7/GIy8JznkPotkMnnr1q2PPvqou7v7iSeeeO655+Zxxo7EUtms7HfbOIbSExfNd/+nGWhyz2uz2fbt29fe3t7Z2XnhwoVjx45t3LiRDKodDseePXs2bdpUXl5eWVlJUdSWLVt8Pp8kSYt4ge+Lh6XbhoaGuZy8aJomM42JROLOnTu1Oslk0uVy/eM//uOlS5cWcdkIAJNxi9vt3ti64dJARjgzaHW61zWvd9oFpMdRMuwWiqJcuXLl3XffnZiY2L9//549e4yx7j3HnS6wqVWrCVHquDNoEbgDe7a01haRKnxa8oCZLQCR2UKXs1imvViryml2DogytfZO4JktTRXvfnb9Sufg3s0NyNggd2OdXNPU1atXDx06FIlE9u7d++yzzxYVFVHUzBTy2p/heCojK363nWO14LJIr2VnZWZLqyjK8PBwLBYjAQ8URamuru7u7v7888+//e1vV1ZWAoDdbm9ra8s9jtfrXfxUyP3wENvbBbdJJpM//OEPn3vuuVdeeYVhGEEQXC4XiTW1uJNoj5VlWYZhAh6nw8ZJKqJYwe1y6X3XqQfV29v7u9/9LplMvvzyy0888YTT6VzsG6/HcBgci46E4jUlgbamKoeVX/x04APvvj7wZvwBMrMqISZjYgpgGGpzc9W/Hr1ytWtED+KBEQm8Mzd9fX2HDh0KhUJ/8Ad/sHXrVq/XO8+FK6oajqelrOp32ziW0YuwkLv7vbc0m81euXLlyJEjf/EXf9HS0kLTtNPppGk6nU7P1ZF8lKykv5TD4RgbG/v5z3/ucDj8fn88Hj969GhlZeX69euXcTSbwNstXDyZjqdEADcATNPVsWPHjh49un379kQicfr0aaMMmzZtmnsZGjbyYSmKeqN7RFWhpb40R7RzTt7G43HiS9TZ2RkMBnt6ej788EMScGip0XxWIcPDw52dnWTsl8lkTpw4MTQ05HK5Hn/88Rn+ZwhpoScRRsDQdHNNKUVB58BELCm6bJYcq/zsuspkMmfOnDly5MiGDRsSicS5c+cAACHk8/kaGxtz4uNoyo8l0qmMZLewdgtHU6QhXYK3FKl3KIrief7ixYtvvvnmiy++yDBMV1fX9evXW1pacv35VoqV1K3NZnvjjTcOHTp0+PBhj8cTiUQSicQf/dEfNTc3L/VQCCGbVXDaLPFUJpHrMpXzuKLRqNfrTaVSJ0+eNL6vqKhoamqaRbeaJWPKVqGoyvmb/RzDPN5UBjnR32adzccYx+PxS5cuXb16NZlMBgIBhNCHH35IjNv5rluM8fDw8PHjx8Ph8MTERGtr6+XLl2/fvl1dXd3a2srz/GwLVjVhURRV6neWBdyheLJrYGJzU4WuuTnFRdySXS6XJEknTpwwPm9ubi4qKnK73fdE3MEwGUtlpGyxx8azDJCF+xjN7dU2HVJyEu/6q1/9amdn53vvvccwzMTEREVFxR/+4R8+VEeoRbLC6+ZJjoLbt29LklRWVkYCWC4lNo8x+MR2K+e0CbGUmExLYEQmy3lUTz31FJl2QjnL4jwejyAIs4wS9U6T8ZWiqhdvDTA03dZQmjvROGuxEEI2m239+vUul8v4hPgnFhcXL/rqVikIoUAgsHXrViPsLrk6r9ebG9UlZwfQ06ABANgszIb60i8u3bl2d3Rzc4VmUZ77dBzHbdu2jbji5H5eXFzscEy9KloqBoRC0aSYkV12K0s6yQgtI6IVRVHFxcXf/va3b968OTQ0hDFev359U1MT6TMv/jgPiZXRrSEet9u9bdu2devWSZKEEHK5XEtZYp7zFBGyW3mnjR8KRojrhfHqGA3jY489NtNDmKIoQRDmGvkgQIBUEng4GE32D4eLfc51VcWgv4r6sWe5QLvdvmnTpo0bN+baPBBCy14VtKooKyvz+/2qquZeHelb5q7OhRwDuLYnBo6hH2soPXb21rW7I6At6CJHmG6SIAiC0NzcbNS5xuc0TXMcC9ohyH4IAQTDybQkF3ud+spbRHKbzS/bmXU3wzA1NTUlJSWxWAxjzHGcw+FY/CTlQ2Ul19+SnzRNzxp/fEmWUgRgt7AOGxdPZeKpnOhwensMMEtUkXlOoZlSQIsnijG+emdYktX6Cp/bYdHm8TUj5SyHIFOs9xnmYjVDIo/Os8H0mZWcbjDLMG2NZVJWvdM/npYUgWW0TWbsS0AI8Tw/l/sRvudfhIH0kxWvy8axtOa/rr8D8xR4WkVjVDdGuJJVZbpfmXgXC7K0e4QBMNitvMsmJJJiIiXmhLfGCOO5TJULnEJ7fggQKCq+eGOAYai2hlKGokCv4iEng8CCV7TYyykI7rm3eqwO8j+GpqtLvE4bPzYZHZ2I6T3YKYvBUuVhTMSRQ0zGkhkpG3DbeZYBRMxhcwSbNgqY83TQHA62q0e0sGp1u7h7pI1sMcKAsM3C221COiMlUhlVy8+MgXS+ln7HtT4X1oyhKsZf3hqkGWpTY5kRSFwrac4f931Fs4NzUr/lfpI3GOZiRGazwW7l11UF4knpdu/Y/V+J3qKSp40nY6lMVva6rDzLgH6j0LypCmZY0VaRRGdllep20SBDkyxNO20WnmdjyUxKzGrfa490We8GmhJHIi3d7huzcExLfYnWLuTkTX/YD9loAQy5rv4XazamysyzTGtDWVqSb3SPGcONZd1InPOUNHNDKJISM9mAx85zzNTny0xItErJZ93q0/a6nRI7bYLTbokk0rGkSBSLp7ZaFoj44OG7AxPRpFTmc5QE3MaxiJDu6/ik3HM0nkYzu9RlkqsfjmNa68vSUvZ694g+0rinG7NoNNVjbbQEsqJEEqmsrPg9No6lc9YBLSmn12onf3WLc4ZNmqOyy8a77UI4kY4mRN2PHCEMsMxeJdIcGTFcvj0AFNpQV8ozjPZ+GU3fffdacxtSg9wGdqYH9f2cbjXAMfS6ygBgtXdkMpYUQVPX0qZqdJBxgzBAJJZOiVmrhbcLHE0BMiqCgmpu81i3ZCwDoLeqGMBpszjtlmQqk0pnMMaI/IcWsEnMCybt3ZW7ozSF2tdVTNPSfTaDGGNZlicnJ4PBoLHs0Th+7gyKodVVZdVcNjRFFXlspT5nNCX2j4Q0i9Wy6tccezJGANF4KpOVfS6boHWSyTwTzLpuIX9Z+XiO9wUiUzXaH3Yr77QKE+FELJlGOb5My3vNjdErxuql2wMUBZtItORc6WLNp2p5xe/u7j5z5kx3d7csy6Wlpbt3725sbDQmeA3pnjx58tatW7n5NUpKSojz3fLOuxqwCmxTTcnlO4M3e8c21peBMQW7RHJaVIwQTESSaVEq9tgFjgWsr2cgmr6vhKGrizx+8Lpb65RF12EVHFbh7mAonpLw9FynS3tiZEEomb0dnYj2jUy4HdaGKj2l0FTHbPmiHRsb++1vf3v+/HkSl/DYsWN37tz5y7/8y4aGBrjXXeHw4cOffvqpsXwMAERRzPfeMs8xG+vLTl/tvtEzpk8NLMPwPzUPR/adiKbTklxV5CGRLvT3gwygC0W1+azbnM6v7lxht/J2Kx+OpaOJtBGNfHnPCmlLNhEAdHQNSzKuKfE7bDw5GbpXV8sblp09e/bkyZOPPfbYyy+/bLVaP/vss3feeeeLL74gWRhzZxHHxsYA4IUXXjBW5Nvt9tXgbXc/CBy7sb40LSmd/UFAmkPp8g6VK8ixcDwlSh6nlSPuHDmONw+m3KuD/NUtmvpH/89p4512PpZMxVMZ3Sd2zvU6C0IWAmFAHXdGKIQeW1dOoam5inscepZ+cFmWv/zyS1mW9+zZ09raSlGU0+k8dOjQuXPnnn76abvdnuu1o6pqXV3dpk2bjJXiFEVNi5acd+NehmUqSzw8wwyHosFIMuCyouXIK8fDBiOEcCiaEjNywGMTOBam/JLREnPfrnbyV7czQQLHumwWmqbiybQoSoLAafFP7sMshRC+2j1CUdTjTeXzvFRLlU0kEhkYGPD5fJWVlWSYWlRUVFFR0dfXF41GIcfihTGenJwsKSm5fPmyKIqqqjY3N7e2ti54xtwNVqGqKYScdqE84EokM3f6xwNtNQDL7CtrZjuEAGAymhAlOeB1CDwLuqdqYfWRAQpLt4AQctstDqsQTWTiaUkQOIQQsUiQ75d2NAAAlJGy17qHKQSPN1fMf2rQ5ZFKpeaKrcUwjMvlstls8Xg8kUgUFRUZkc0oivJ4PDdu3Ein07kyQwiNjo4ODw+T/BqxWOzQoUMvv/zySy+9ZNilVFX95JNPSKypSCSSTCbffvttjDHxjN+2bdtqEy0AIMACxzRUer+8MdTVH9zZVquZE5aIMYjFABjQZDSVkbJ+j4PnGH36/Z4tC4OC0i0AuOyCi0zhJsWAx4b16L1LfyEwYIQRDIzHxkLxUr+rqtizwA662CYnJ3OX+OZitVrb2tpqa2tVVSUx+6etp5nV2rRv375wOLxlyxYSXPs3v/nN//k//6e+vp4sNiKnnpiYIFGa4/G4oijkd5ZltWXlqxAMFp5trS09cbmna2hi+arCWipkQBBLirGUxLGM2y6wRvrMghKsRuHp1uK0WyIJUV/NB8vtIWodr0u3hhRFXVdTxDDz2YFyh6MWi2WulfEkIRUAMAxD07Qsy4qiGNrLZrOCIDAMM821/Tvf+Y6iKCUlJRzHYYyLiopeeeWVkydPbtiwgVinKIrauXMniXUUDAZ/9rOfvfDCC+RzYwHwqgMhK8+1r6sQM9m7gxParMCSn5YR3QsjgHA0lcpIPpfNKrDaHB7pIt/HdODqpNB067QLLpsQjidjCRFgGXlhDIghA1+82U8haK0rhXnfqlwHDLKoeK7NSOfW4/H4fL6JiYloNFpZWUlEOzY25vF4SM85V7p1dXWZTEYQBNIgP/744yRqmeECiRCqqKggf5I1oo2NjUYbPn/JVxCWpStKPHabZTQUC07G/J5FR/yaQo+jgTDGEAzHU2LGY+dJpAstkuOqvPb7JH/9pWbHbRdcdiGaEOOpzNRsznLQHnVH1yCiqM3NVQDqPI8/t39LEmEIMyCLSEkL6XA4GhoaJiYmuru7SZN78+bNrq6uxsZGEshzaGgoHo+rqhqPx//+7//+ww8/FEUtFcPVq1cVRamvryeKJaemaZphGBIij9QO5JOZaxJWDwiwTeBqy73xlNjZNzFtFe5i0C9Kq75CsVRKzAY8DgvPGhauqae26m7A8im09tZlE1w2IRxNx5LiPT5wSxQvqcVFWb49EAREbW6uAFDnqeamWW5nruHM7UiT7Xft2nXixIl33nknlUrZbLZDhw6xLPvEE0+43e6xsbGf/vSne/bsefLJJymKunLlyu9///u+vr6WlpZUKvXWW281NjaSr3JPPe1cuQVbjW0OBkBY4NnGCv+nY+E7Q6Fdm+qWbDtECLAKABhRADAeTqbErNdj5zk2pxZAmsfUarsD90HB6dZuddotkWSatLcAy3xnyeCocyAYTYr1pb4ij22R2p8mmGmf5364YcOG119//dChQwcPHiTZkP/4j/948+bNHMfJshyJRIhh2Wq1fuc733nrrbc+//zzy5cvE6vyf/tv/626unrxl7UaX1kEZOquoaLo4Kmb3YMTyzD7Y6NPhQEAT0aSYkYq8jgsAqsfamqpUSFRaLrlOcZlFxgahWOppChZefZ+Xtkvb/ZjFT3eRPJTP+Axhc1m279/f11dXV9fn6IoFRUV69atI2akoqKi73znO8XFxTzPI4R27Njh8/m6urrS6TTDMNXV1Rs2bFglgY7uBwxgFdgNdSViWuoeGidrr5b2vIx4cxgQgolwPC1mAy6rwBk3B834pRAoNN0CaXKtQjSZTqYyNoFd9rwdxnDhRj8FamtD+UMaG9nt9scee6ytrQ1jbMwJAYDNZmtvbzfeYJqmm5qa1q1bR/40/CvzHQTAMHSZ3+m2C6OT8bFQvMS3tBCnCAFgFZAWPmEilkhJUrHXYeEL8MXOpdDsUgDgsfMuGz8+GZ+Mp4yu8nIOhNCFW4OA1Q11JQ9v0StCiKIo0k+GnA6tlqsu15sSIeLeWBiiBQCiO6vA1VUEoknpatfIkg9AloNhhDBE4mI8lbUIrNdl4/J5pdRiKEDduhwWp90SS4jJVAYAMKBlOazjcDw9NB6jEGqtL8YkLdUDYp46YFooqdzANAUkVwCYWshuEZi6cn88lb7dPz59EdeCx9BMxhgjPBlNpjKS322z8Hk/gliQAtStz2X3OGyTsVQsmSYL39Fyerm4qz8oZZWaioDfbQOgHuD4yOgPzxTwtFZ3dc7fPBiQFvJJ4Lh1FYGUKPYMhZYepUb3RwUYnYgkkumAy24VTN3mIW4777TyE5FUJCnqbjLL8bu4dncUA97VXkfSYz9Y9SxmWnXWIDUFgxYBCMBmYZtrA9ksHhiLZLLZhfabDlkmDQChmJgSs0Ueu5VnC2qudjYKUrdWp02IxFOxZAZjTKYvl34YdPFmH6jqluYKpMeZerDlzG1aZ3aMAe6ZE4aHN8JeIYyLZxm61O/yOG3heHI0FF3iYbARN2o8nEiIUqnfbVtKqsQ8pfB0ix02wWkXxIwUjiRFSTZWeM2xuR7b6J7IYVhR1XPXewBQa10pCV/1EJQ7xVyzvrkfFlrDi0n+FjIbxNWVeeOpzO2+iXu2WPiOk94UBkDjk/FkSvK5cyeBCpbC0y2iaMrntjttlslYOp4SF3jb73WOMN6ToWB0JJSwCGxdhZ8ELrqvdbwmM8kZv1gFrq48EEtm7gyM52gVLarZ1Poi6kQ0kRKzAY/dYo5v8w7ScPqdVrfdEowkYmSIO3fNrS0UId7noLnEYUA3ukcUjOvKvXYLhxBafgwVkznInVW38kxDpS+ZzvQOTy5tNKB1plBGksMJUcWqn6QpKHQKTbcIAAHyOi1OuzAZS8VSGWx8PMf2WuTyqRC8gDC+0T2KMWxrqQKsankJCmp0uRrQnwxgq8Ctqy7KyvJQMJrOyGAM6ae2nOPu6w9tIpxKpqWAx+6yWWiq0N7qmRTkFWKf2+Z2WscnE9F4Wg+oPafsdMFijFVM1oMBvn53RMH4ibb6qSX3eDHDLZPFYlSECIBlmRKv0+e0TUbTIxNRbQ1AjoVu7g4ziXKBxsPxRFIs8TptltnT9hUYBalb5HFanDZhIprUE47AnA9+ylKLECIvDMrIytWuEQqhjY0VgCjQutCLG26ZLJbcxVJgt3D15f5YItXZN6Znb1nM7dYq1WA0kRIzRR671VII6YUXpCB1i30um8dhjcbTsWRGXXhBCEKIrLKmyDLrnsHQWDjpd1lLvA5dsbBcb0mTudC6NmSIarfwTTXF0ZTYNTihRU4lLqpwj6F/NjAGPBaKx5Jikc9hFfjFGaLzm4LULditgtdlURVlMpoSs/J8XVx9ihRAJf8iBJfvDCmq0lxTzLNaqlttCPxICr92QIY7CwabhW+sCiTSmd6RSVXFhjWR3PN57zxCgEYn49GUWOSx26ZW8BUyBalbRFGU321z2IWJSCKeEAHQnI6vWl4anKvga92jiqo+vr5Cj5dBZFtYmaFWBSQlFwIEFoGtLvGqqjo4Ho3GRe1bLYL1vHceI0VRxyfjaVEu8TntFragEu/NQeHpVquk/S6by24ZmYhG4kndE242ND9IpDenWFVxR9eQouLHmyoMkxQCIOEdTR4spEeMAWga+d32Ep97MpYcHI/qfV2MEdLzRswFTqQy4ViaoSm/28Zz7Fp4SoWnWwL2u+wuhyUYScZS0vyrTMgULsaIGKciiXTPUIhn6I11pQD6jK42EjMb3AdHziQPsfw5bXxTdVE8KXYPh0Af4C4kQgwIxiOJWEr0u+0um7CMIFX5SOHpVrP6lvidPpdtPJKIJsX5NtenCcl0EQa43TeeSGWqSj1+t10PDooQQlBgmSpWHq1CNDy0nTa+qSoQjoud/eMwtc5n4Zs+HIxG4qlir91mKXzPZELh6ZbIDwU8do/DOhaKhmOp+Tzykb7WR3ebutw5JMtqe1MFhXSbCELaRNGjuYI1wowVizYLX1/hS6TFuwNBSVa0zRZoOxEABMOJeCpT6nXYrZzhzFHYFKBuSQZNh413OwQxkw3HklMvweyQ2R/SW1O/vDmYVdTNTRW5ibP0ur/wO2ArApmIEzi2LOC2cOxoKDEWioPeEVpw7/FwPJ7MVBZ7XHYLLrBlU3NQeLolYcKAY+gij8NmEUZC8Xtisk5HtyQjhAGnM/L1u6MA8FhjBaIQYH31nOks9RDRbixFIa/LWl3qDSfEu4NBmKop57vzqopHJ2KxZLrE77Rb+OUu28wzClC3AEDUWOJzeByWwfFI2Ag0Ne9uCKHekXAolvS6LNWlXgohYvbIcb0o/A7YyuKyCY1VRZF4qnuALOhbuLpMidJENIWA8rvtFp4pwIA+s1F4ugXAiKyYLfE63Q7LyEQsmpjbNIX11UIYANCVruGsrGyoL7NZOH34tXj7yKOjsDqDUzfWbbesry6KJtLdQyFFVWHhwQkeCyfCsXTA4/A6rTRdiO/zbBTidWoaQ6V+p9dlH56IRRLpeTeeGkd13BnKysrW9dWrcE2JoigjIyOjo6OqOj3jyYLBbvIFu1VoqApQgAbHI7Fk2pjAm+caRidikXiqxGd32AQt9k1eXfLyWHVv5wMBAUYYBzw2r9MyEU4GwwlZUefa2IicncnK1+6OZBV1c1MZTa+i1hUAksnkhQsX3n777YMHD2Yymdyv5s/HkF+dRoamiryOsoBrPJzsGZ7McXWcS4poPJyIpcQSn9NpIyuB1sTyj8LULcFuFQJuG8bqaCiWTEtzbWY85KHxaP9YxGHh1lUVUaupvU0mk0ePHj18+PDvfve7Dz/8UJK0aynEwHHYbRMaKv0T0eTtvnGj6zTPKr6hYHQylq4odrvtFi1HNTLb2/wDaxGjEGIYuqLI43ZYR0OJWGpe7wvAgNGVO8OJlLi+ptjlsK4qKYRCoYsXL/r9foqigsGgqmp9h0KM0oo8TmtzdXEomrwzEFRUw2989gciZeXBscl4Ml3qczpsgu62CgVv/C883ZLaVgsXVlHs9rpsA2PhSHzuIS7ZCcH5m/2SJG/bUM3Om6L60UNR1K5du1588cWioqJZ04URCkPDDqvQUOVXVLV3JBRNpOe/pMlYKhhJ8BwT8NgEjgEwBLuqKt4HTyFG4kFT3oslPofHLnQPT4Siybl3wACQlrIdXcPZrLp9Q9Vq063f79+zZ4/FYiG5cw1yIzDHYrFsNosQCofDqqqGQiEAQAhxHGe321em3MuCZZnSgLPE5xybSPQOT3qcVv2JziLF4GQikhDL/G6/24YoZMwLPPJSP2oKT7f3TNuU+Zw+t/Vy19BEJKUoao61KffRYoxhaDwyNB5xWvl11cWPbHB79+7dkZGRae0kkaLNZmtqaiK55wVBmOcgCCFVVc+ePTs+Pg4A0WhUFMUPPvgAAFiWramp2b59+8O8iAcMQuB32Zuqim73jt/uDz7eXKF/c690MQDCQ8HIZCRVU+rzue2Gw+SjLvFKUHi6JQ422qoQr8ta5ndhFYbGIwlRctm4mZUxMcd+eXMwkRIfW1fmdlge2aMPhUI9PT2zfuXxeGpra4luDXLDo+dmx0YIpVKpWCyGEEokEiRLPQCwLJtOzz9AWHUgwD6Xtamm+OSVns6+cSmrcFp8RoSnolIhMhzqHwuPT8Z3ttV6nbk3avbGuZAoPN2CEScQI2AZpqrE47LzvcMTkXjKZeNBm/jRH60e9+1UR09ayu56rI5jGS2r6sOnrq7O5/PN+hXHcVarddqHM8OjGyHRt27dKooixjgYDP7whz/8yle+QvL32e321Zhsfj6Q08o3VgYQgp7hifFwoqLIPdPxBQPKSNLgWCSezpQFnC4b6ZKQB7vo6FR5S+HpFpF1BaA7qtZX+AIe+92h0GQ0VV3sNWYDkZ7yGANOJLM3ekZVDFvWV3Es/cgqbL/f7/f759lgLsnN/Ly8vJz8YrPZGIZpaGiYZ/dVDsfSVSWumjLv4HjszsBERZFb/+aeeZ6JcHJ0IsazTLHXIfAsxgi0PLiFP4VbcPZkfUkekKeHobbMF3A7uocng+Gkio2ltmB4MiOAa3dHJiZj5QFnTZmXpqnVsM42d242FouNj4+Pj4+LopjNZoPB4Pj4eCKRmN+AnLu09dGU+YFAMtqW+pytdWUjodjNntGZpSd+NQNj4bHJeLnfVeS20SQrMNbisq5AuR8thdfeAtzbXBZ5nMU+56mrvQNjk2Ima7XoGeg1IyUCDF9cuRtLiS9ubnXaLDmrCB5mCedtCQ1DMdnm888/v379uizL3d3diUTi5z//ucVi2bVr11NPPZW72TTmzzm0aiEjV5/Ltr626N0vOm73jUfiKY+DDBkQNipmhHtHwsOheFt9aZFXM5ijNdBDJhScbvW2UnuACFl4trbMaxO42/3ByXjaamFIi2tEr0hlsl/e6k9nlN3tDQJH63s/3Gc/v5amJfKSZVmSpGw2u2fPHlmWASCTySiKYmycp03rHGAAsAhcXYW/yG3vHgzd6Rvf1lqdM8TFACiTVXpHwsFwor7CX+x15uyLCt8qVYC6JUwZJ4CiUGOlP+C2Xrs7EgwnKoocWkAp0MyTd4eCvcOTfpdtQ10py1K60XKFH31uK/rkk0+2t7cbblIEj8dD5qvydBA7F8QkSFNQXeJpayw/d72/4+7IttYa42tACABPRJIDY2GGQtWlHqfdouu18Ee2hALV7b3J81pqS4p9jiudQyMT0baGEpqmiAmDNLknLnVPxlJ72usCHjtCNAKAVRBJKleKgUAgEAgsZssCEDCJvIowKvE52pvKP75w53rP2GQ85XVYtC0wBgT9Y5ND49HKIk+Z38VQCGMj3ibWtV3IFJxdajbKi9x1FX4pq9zuD8aSGdASrwJgiCXEE5e7JTn79JZ1Nouef7HQn/pqRgtwgcBu4Zurikp9js6+8Rs9Y7pHjVal3h0M9Y9NNlYFyotc+seal9xaeHprQrccQ7c1lPs99vM3+sYmE7rtAwPgC7cGO/uDpX5Xe1MFzzD6E59z0Z/JwwZhbaROUai23Le5qaJncOLCjb6MlDWyF6TEbM9gKJoQm2sCpX5nzszAWtAswBrRLQA8vq6i1O/suDPUPxaWFZUMolIZ+eCJa2PRxJ72+hKfA1EUnop9YbJiYG0eFhX7HJtbqgDBhRt9XQMT+rPB3UOh2/1Br8vaUBmwW/l7o2KsiSHuWtFtTal3Q21JOpM9e61vMpIkfaqLNwfOXuux89wz25rsVl6bsseA0Vq5LasQrKUOxwDYwnNtDWUbG8o67ox8cfmulJURgKwolzuHbvSMrq8taagIUIjSXeQKX64Ga+UFtfD0rsfqinyOj07f6uwPyoo6Hkn85tNLQ8HIvs2NrfWlHEvpE/ZmjuoVBCPt/wCAKYC6Mu+Tj9WLknLsXOeVziEANByMn78xEI6lNtaVVpZ4MAlMoztur4lojgVrT54BRmjz+srW2rKjZ2+/+8U1h50/caXn+MUut8P6B0+1+lw2MCZt9Rkik5WALAgxXMfBaRN2t9edu9l39lrf20cuYYCbPWPnrvdVl3geayzXeknG2j0MuBBs6guzVnSLAJV4HQd2Nt/sGf3wzM1IPHn97lhakv/4+a3tTRUcSwMmaQl0/1aTlUO//QgDRhRaVxX4xr7HhsdjR87dHp2MhuPpiUj8j/ZvbmssoxDSM0lgLWbunP5jBcVa0S1goCi0e1Pd2GT80Ilr52702QX+W/sf/+ZXHve5bPp0L9b9mtdCV2vVYshWeypWgXuyrTaVlt49fr2zf5xCaP/29S/t3kDcG3O3ztmpwFkzukUAgHxu+zf2tTdU+HtHwy67sHNjTZnfRVMzF9OvgSefRyDwuWzPP9FSV+6/1TfGIOqxdeXrqgI5D27NUXiBxWbHWG6rYlBUjFWMENA0RRVcj2pkZGTHjh19fX0rXZAHDMagYFVRVASIpimKQveu61pbrJX21uhNUQAUhUCL07Qm6qwCAQEDFMNQmukKY1gbXeJZWSvzQHq3ApPc8+RPU7V5hDG5TmZ6MEJr2T9m7bS3ORMMU2vfVrRMJotGz8pHchFr0z56ELG1+BTXTHsLRLUYsAp6ouq1MbQvBDS/ZKwiEgdPi0a0JlwaZ2WttLekb4z0Felr0DMu38mZ4NEmatewWWrN6DYn+ozx02xt8w40z19rirXST56NNfzYTfKctaxbE5N8xdStiUn+YerWxCT/MHVrYpJ/mLo1Mck/1so80Kolk8nEYjFFUdxu91z5MsPhcDKZzF0BwvN8IBAo/GWmJnNg6vbBs8iF2xjjeDx+69atTz75JJVKfetb32ppaZl1y0OHDp09e9bIW40xrq6u/tM//VOWZadtmavtNbF+fK1i9pMfPHNl0Jv2iSiKp0+ffvfddw8ePHj48OGRkZG5DvjFF18cO3YMY2zV4Xl+5sFz08/PVQyTwsBsbx8wC2bZMojH4z09PX6/v7Gx8c6dO/McU5bl2trab3/728XFxeQTlmUZZurZ5eYTmnkis+EtPEzdPmAWma4WAFiW3bFjh9/vz2Qyc2WdJ0iSVFZWxrKsJEkAYLfb3W73gq26cVJTtIWHqdsHDMZYUZRMJgP6asHcbymKMppKp9PZ1tZGURRJzzUPY2NjXq/32LFj2WxWkqTy8vI9e/ZUVlYaO2KMx8bGMpkMxnh8fFyW5d7eXnI6q9U6f2psk3zE1O2DJx6Pd3Z2wmy65Xm+oqKCCIkYmWAR7aHFYgmFQr29vU6nMx6Pnzt37u7du3/1V3/l8/nIKTDGp0+fHh0dxRhHo1FRFA8fPgwADMM0Njbu3bvXbHILDFO3DxiEUDqdHhwchJxeq5Gc1mq1ejyeaQ3ggiG+Xn311VgstmHDhkAgIIriu++++8tf/nLHjh379+9HCBHpWq1Wh8NBWnuKopxOJ8aYYRiLxWKKtvAwdfvgcTgcra2tMJtuWZZ1u91LPeCLL76oqqrL5aJpGmPscrl++MMfXr58+dlnnyVdZYqitm/fTlJaj42N/e3f/u2BAwfI+Haa5dmkMDB1++BxOBxNTU3L3h1jrKqqKIosy7IsK8vy4OAgz/MOh4OmaYQQx3EAQFpaYy+jOshmsxRF+Xy++7sIk1WNqdsVIxwOT0xMyLI8NjaWSqX6+/tv3rzpcDgCgUA6nT579mxdXV1NTY0oir/61a9omn7++edLS0uz2ezhw4cdDsemTZvMDvCaxdTtinH37t1Tp07F4/H+/n6E0Pnz54eHh1taWp566ql4PH706NF9+/aVl5dzHOdwOMiW1dXVmUzmzJkzzz///KZNmxY0RJsUKqZuVwyapnmez2az7e3tGzZssFgsDMNwHEcGpbW1tV6vl2zz2muvOZ3Ovr6+iYkJANi+ffv+/fvNnvBaZq3kK1iFxGKxSCRCjEkGdrvd4/FgjIPBoMPhsNvtpFENBoPj4+OZTIZhGJ/PV1paOldjW6j5CkxyMdvbFcPpdDqdzrm+LS8vz/0zEAgEAgHjT7O2XeOYA6TVyzziNC1SaxxTt6sXU5wmc2Hq1sQk/zB1a2KSf5i6NTHJP0zdmpjkH6ZuTUzyD1O3Jib5h6lbE5P8w9StiUn+YerWxCT/MHVrYpJ/mLo1Mck/TN2amOQfpm5NTPIPU7cmJvmHqVsTk/zD1K2JSf5h6nZ1YcS4MCPRmMyDqVsTk/zD1O3qwohNM2sa21l/N1mDmLpdvcyazJZghp5a45hxWFcXufo0soEBwMjIyNWrVycmJliWbWhoaGtry803b7LWMJ/96sLQau4vFy5c+Jd/+ZeBgQGbzZbNZjOZzDe/+c2XX37ZlO6axewnr0ZyRStJ0o9//OPjx48/8cQTr7/++muvvZZKpf7mb/4mGAyudDFNVgyzwl6lGE1uJpMpLS3dsmXL66+/TvIbpFKp733ve729vcXFxWZqr7WJqdsVYJqRaf4NeJ7/y7/8S4vFYrPZAEBVVUVRSL6v3INgjMlImPxUVZV8Pi1NrklhYOp2BTCEJMuyoijTviWiRQixLEuyVJNcQSSf9eDg4Hvvvbdz587a2lrjOBjjgYEBURQBYHx8PJvNdnV1YYwpinI6ncXFxbCIysIkjzB1u5J8+eWXt2/fnvUrj8eza9cuj8dD/sQYK4rS3d395ptvRiKR73//+7k5wTDGn3322eDgIMY4Ho+n0+lf//rXAMCybGtr6/PPPw/m1FFhYep2xcAY0zTNsuys39I0jRAyGklJkjo6On7xi18MDw//xV/8xd69e2mazt2+vLyc53mMcTgcZhimvr4eABiG8fv9j+BaTB4xZv7blYeIc1o/ljwX8rksy0eOHDl48GA6nX7jjTeeeuqpudQOAMPDwzt37uzr65v1sCaFgWmNXHlmVRcZ4hL1Xrp06Sc/+YnFYvmzP/uzXbt2AUA2mzUsTwaG1CFnNGuKtiAx+8krz6xNomGdSiaTP//5z3t7e1955RWKoq5du0Y2KC0tLS8vz1XpTEdIs7EtVEzdrjyzSsv4MBQK3bx502q1Hj9+/OzZs8a3+/fvLysrm79RndbxNjVcMJi6Xe1Yrdbvfve78Xh8mvBKSkqWdBxTtIWEqdvVjt/vf/3118FsME1yMO1Sq5Rpdn7DOGza/03A1O3qxFCp8Ykxjp32ucnaxNTtamSueVdTsSYEU7erlHmMzGaTa2LqNv8wDVQmpm7zD1O0JqZuTUzyD1O3Jib5h6lbE5P8w9StiUn+YerWxCT/MHVrYpJ/mLotNOx2+1/91V+tdClMHi6m542JSf5htrcmJvmHqVsTk/zD1K2JSf5h6tbEJP8wdWtikn+YujUxyT/+fye1Ws882m9TAAAAAElFTkSuQmCC | Determine where the local and absolute maxima and minima occur on the graph given. Assume domains are closed intervals unless otherwise specified. | Absolute minimum at: $-2$, $2$
Absolute maximum at: $-2.5$, $2.5$
Local minimum at: $0$
Local maximum at: $-1$, $1$ |
2210a30a-0583-4c62-8efb-026cf9df28be | algebra | false | null | Solve the following equations:
1. $4 a - 15 = -23$
2. $44 = 5 x - 6$
3. $-3.7 x + 5.6 = -5.87$
4. $\frac{ x }{ 5 } + 3.5 = 4.16$
5. $-\frac{ x }{ 4 } + (-9.8) = -5.6$
6. $3.7 x - 2.2 = 16.3$
7. $\frac{ x }{ 6 } - 3.7 = 11$ | The solutions to the given equations are:
1. $a=-2$
2. $x=10$
3. $x=\frac{ 31 }{ 10 }$
4. $x=\frac{ 33 }{ 10 }$
5. $x=-\frac{ 84 }{ 5 }$
6. $x=5$
7. $x=\frac{ 441 }{ 5 }$ |
221b4d54-e3dd-4490-b838-5b045216ed65 | differential_calc | true | 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| The graph of $f'(x)$, the derivative of $f$, is shown. For what values of $x$ on the closed interval $[-3,3]$ does $f(x)$ have a horizontal tangent line? | The function $f$ has horizontal tangent lines at $x$ = $-3$, $-1$, $2$ |
222eb5cb-a7b1-4579-9f0a-2955d79998d4 | multivariable_calculus | true | 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 | Find the coordinates of point $P$ and determine its distance to the origin. | $P$ : $P(2,3,1)$
$d$ = $\sqrt{14}$ |
22637bf3-6a19-4afe-bf21-7635c9389518 | differential_calc | false | null | Evaluate $\lim_{x \to \frac{ \pi }{ 2 }}\left(\frac{ \tan(3 \cdot x) }{ \tan(5 \cdot x) }\right)$ using L'Hopital's Rule. | $\lim_{x \to \frac{ \pi }{ 2 }}\left(\frac{ \tan(3 \cdot x) }{ \tan(5 \cdot x) }\right)$ = $\frac{5}{3}$ |
2282fbd1-3761-499d-91d7-97a38c7d2371 | sequences_series | false | null | Let $f(x) = \ln\left(x^2+1\right)$.
1. Find the 4th order Taylor polynomial $P_{4}(x)$ of $f(x)$ about $a=0$.
2. Compute $\left|f(1)-P_{4}(1)\right|$.
3. Compute $\left|f(0.1)-P_{4}(0.1)\right|$. | 1. $x^2-\frac{x^4}{2}$
2. $0.1931$
3. $0.0003\cdot10^{-3}$ |
22af6a45-4daa-492f-af67-2ddea807e859 | differential_calc | false | null | Differentiate $y = b \cdot \tan\left(\sqrt{1-x}\right)$. | The final answer: $\frac{dy}{dx}=\frac{b\left(\sec\left(\sqrt{1-x}\right)\right)^2}{2\cdot\sqrt{1-x}}$ |
22cc1731-e35c-4492-b6dc-7cbe9bc1a9a7 | integral_calc | true | 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 | Let $g$ and $h$ be the functions given by $g(x) = \frac{ 1 }{ 5 } + \sin(\pi \cdot x)$ and $h(x) = 5^{-x}$. Let $T$ be the shaded region in the first quadrant bounded by the $y$-axis and the graphs of $g$ and $h$, and let $M$ be the shaded region in the first quadrant enclosed by the graphs of $g$ and $h$, as shown in the figure above. What is the total area covered by the shaded regions? | The total area is $0.481$ units². |
23010800-a63a-4bf5-85f6-314fa321b6f8 | precalculus_review | false | null | Use the double-angle formulas to evaluate the integral:
$$
\int \sin(x)^2 \cdot \cos(x)^2 \, dx
$$ | $\int \sin(x)^2 \cdot \cos(x)^2 \, dx$ = $\frac{1}{8}\cdot x-\frac{1}{32}\cdot\sin(4\cdot x)+C$ |
23883ab4-3177-4e59-9298-2e6f1717d1fb | differential_calc | false | null | Compute the derivative of the implicit function $e^{\frac{ y }{ 2 }} = x^{\frac{ x }{ 3 } - \frac{ y }{ 4 }}$. | $y'$: $y'=\frac{4\cdot x\cdot\left(\ln(x)+1\right)-3\cdot y}{3\cdot x\cdot\left(\ln(x)+2\right)}$ |
23ae23ae-f790-409a-bbdd-48cfeb156dc4 | differential_calc | true | 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| Complete the following table for the function $f(x)=rac{ x^2-1 }{ |x-1| }$. Round your solutions to four decimal places.
The table is given. | 1. $-1.9000$
2. $-1.9900$
3. $-1.9990$
4. $-1.9999$
5. $2.1000$
6. $2.0100$
7. $2.0010$
8. $2.0001$ |
23f5fc3d-68f0-42c8-82a4-e91a293a9ecc | sequences_series | false | null | Solve the following series via differentiation of the geometric series:
1. $\sum_{n=1}^\infty\left(\frac{ n }{ 6^{n-1} }\right)$
2. $\sum_{n=2}^\infty\left(\frac{ n }{ 3^{n-1} }\right)$
3. $\sum_{n=3}^\infty\left(\frac{ n }{ 2^{n+1} }\right)$
4. $\sum_{n=2}^\infty\left(\frac{ n+1 }{ 5^n }\right)$
5. $\sum_{n=2}^\infty\left(\frac{ n \cdot (n-1) }{ 4^n }\right)$
6. $\sum_{n=2}^\infty\left(\frac{ n^2 }{ 4^n }\right)$ | 1. $\frac{36}{25}$
2. $\frac{5}{4}$
3. $\frac{1}{2}$
4. $\frac{13}{80}$
5. $\frac{8}{27}$
6. $\frac{53}{108}$ |
2416152a-a967-4e43-9ad3-c412f0ee1d0a | multivariable_calculus | false | null | Determine the polar equation form of the orbit given the length of the major axis and eccentricity for the orbit of the comet or planet. Distance is given in astronomical units (AU):
1. Halley’s Comet: length of major axis = $35.88$, eccentricity = $0.967$. | 1. $r$ = $\frac{1.16450334}{1+0.967\cdot\cos(t)}$ |
24830b9a-f570-4094-9ca3-77216d3081a1 | precalculus_review | false | null | Find the zeros of the function $f(x) = x^3 - (3 + \sqrt{3}) \cdot x + 3$. | The final answer: $x_1=\sqrt{3}$, $x_2=\frac{-\sqrt{3}-\sqrt{3+4\cdot\sqrt{3}}}{2}$, $x_3=\frac{-\sqrt{3}+\sqrt{3+4\cdot\sqrt{3}}}{2}$ |
24ca0d32-0edc-4da0-8284-8a9ff5367ce8 | multivariable_calculus | false | null | Evaluate the triple integral $\int_{0}^2 \int_{4}^6 \int_{3 \cdot z}^{3 \cdot z+2} (5-4 \cdot y) \, dx \, dz \, dy$ by using the transformation $u=x-3 \cdot z$, $v=4 \cdot y$, and $w=z$. | $I$ = $8$ |
24f973aa-2278-4395-a6d8-04f362b5b698 | precalculus_review | false | null | Solve the trigonometric equation $6 \cdot \cos(x)^2 - 3 = 0$ on the interval $[-2 \cdot \pi, 2 \cdot \pi]$ exactly. | $x$ = $\frac{\pi}{4}$, $-\frac{\pi}{4}$, $\frac{3}{4}\cdot\pi$, $-\frac{3}{4}\cdot\pi$, $\frac{5}{4}\cdot\pi$, $-\frac{5}{4}\cdot\pi$, $\frac{7}{4}\cdot\pi$, $-\frac{7}{4}\cdot\pi$ |
2516247b-6387-402e-ac1c-88774804cefc | differential_calc | true | 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 | Given $s(t) = \left(h(t)\right)^2$, find $s'(0)$ using the table below: | $s'(0)$ = $18$ |
2522fa02-210e-4fa6-a658-73f26d3df1a2 | integral_calc | true | 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 | Let $R$ be the region in the first quadrant bounded by the graph of $y = 3 \cdot \arctan(x)$ and the lines $x = \pi$ and $y = 1$, as shown in the figure above.
Find the volume of the solid generated when $R$ is revolved about the line $x = \pi$. | The volume of the solid is $36.736$ units³. |
2590af47-b424-44fb-9ea3-cd88319511c1 | integral_calc | false | null | Calculate $I=\int_{\pi}^{\frac{ 5 }{ 4 } \cdot \pi}{\frac{ \sin(2 \cdot x) }{ \left(\cos(x)\right)^4+\left(\sin(x)\right)^4 } \, dx}$ | The final answer: $I=\frac{\pi}{4}$ |
268ca3a8-6509-4de9-8ad8-2c035609fae6 | algebra | true | 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 | Find a formula for $q(x)$, the quadratic polynomial whose graph is shown below: | The final answer: $q(x)=\frac{1}{2}\cdot(x-6)\cdot(x-10)$ |
2690fe65-791c-427f-909a-f4de8a01874c | multivariable_calculus | false | null | The period $T$ of a simple pendulum with small oscillations is calculated from the formula $T = 2 \cdot \pi \cdot \sqrt{\frac{ L }{ g }}$, where $L$ is the length of the pendulum and $g$ is the acceleration resulting from gravity. Suppose that $L$ and $g$ have errors of, at most, $0.5\%$ and $0.1\%$ respectively. Use differentials to approximate the maximum percentage error in the calculated value of $T$. | The maximum percentage error is: $0.003$ |
26f9dc9c-b9b4-4a40-9d75-4433f718752a | algebra | false | null | Solve the quadratic equation by completing the square. Show each step. (Give your answer either exactly or rounded to two decimal places).
$2 \cdot x^2 - 8 \cdot x - 5 = 0$ | $x$ = $\sqrt{\frac{13}{2}}+2$, $-\sqrt{\frac{13}{2}}+2$ |
272ed29b-1de2-48d4-a63d-c8c7173b76ef | differential_calc | false | null | Compute the derivative of the function $f(x) = \sqrt[x]{3} + \frac{ 1 }{ 6^{5 \cdot x} } + 4^{\sqrt{x}}$ at $x = 1$. | $f'(1)$ = $-0.5244$ |
273e613f-b3e1-4221-8dfb-a1364757f4ae | differential_calc | false | null | For the curve $x = a \cdot \left(t - \sin(t)\right)$, $y = a \cdot \left(1 - \cos(t)\right)$, determine the curvature. Use $a = 4$. | The curvature is: $\frac{1}{16\cdot\left|\sin\left(\frac{t}{2}\right)\right|}$ |
2745c073-ef92-4748-9387-783f4937bf15 | sequences_series | false | null | Determine the Taylor series for $y = \left(\cos(2 \cdot x)\right)^2$, centered at $x_{0} = 0$. Write out the sum of the first three non-zero terms, followed by dots. | The final answer: $1-\frac{2^3}{2!}\cdot x^2+\frac{2^7}{4!}\cdot x^4+\cdots$ |
2756b56e-7460-417d-8887-1069f48cab9e | differential_calc | true | 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 | Use the following graph and find: $\lim_{x \to -2^{+}}\left(f(x)\right)$ | $\lim_{x \to -2^{+}}\left(f(x)\right)$: $2$ |
275f7ceb-f331-4a3f-96ec-346e6d81b32a | integral_calc | false | null | Solve the integral:
$$
\int \frac{ 1 }{ \sin(8 \cdot x)^5 } \, dx
$$ | The final answer: $C+\frac{1}{128}\cdot\left(2\cdot\left(\tan(4\cdot x)\right)^2+6\cdot\ln\left(\left|\tan(4\cdot x)\right|\right)+\frac{1}{4}\cdot\left(\tan(4\cdot x)\right)^4-\frac{2}{\left(\tan(4\cdot x)\right)^2}-\frac{1}{4\cdot\left(\tan(4\cdot x)\right)^4}\right)$ |
27bf3a57-31a0-4228-99e0-097019b8eb40 | precalculus_review | false | null | Find the domain of the function $g(x) = \ln(2 \cdot x - 3) + \sqrt{1 - x}$. Give your answer using interval notation. | The final answer: $\varnothing$ |
28349b87-6fef-4032-a4fa-3293f8f8f962 | algebra | false | null | Rewrite the quadratic expression $2 \cdot x^2 - 10 \cdot x - 15$ by completing the square. | $2 \cdot x^2 - 10 \cdot x - 15$ = $2\cdot(x-2.5)^2-27.5$ |
28aee58e-6261-4432-b15d-ef0d23395d05 | integral_calc | false | null | Leaves of deciduous trees fall in an exponential rate during autumn. A large maple has 10,000 leaves and the wind starts blowing. If there are 8,000 leaves left after 3 hours, how many will be left after 4 hours? | There will be $7426$ leaves after 4 hours. |
29315747-d98d-4c5c-8399-22390eec8c48 | algebra | false | null | The fox population in a certain region has an annual growth rate of 9 percent. In the year 2012, there were 23 900 fox counted in the area. Create a function representing the population.
What is the fox population to be in the year 2020? Round your answer to the nearest whole number. | The final answer: $47622$ |
296b39cb-0c02-4c19-80e9-77e35ea51b02 | precalculus_review | false | null | Evaluate the definite integral. Express answer in exact form whenever possible:
$$
\int_{0}^\pi \left(\sin(3 \cdot x) \cdot \sin(5 \cdot x)\right) \, dx
$$ | $\int_{0}^\pi \left(\sin(3 \cdot x) \cdot \sin(5 \cdot x)\right) \, dx$ = $0$ |
29933b1c-f96c-4df4-9f53-d9b8900e1597 | sequences_series | false | null | The $k$ th term of the given series has a factor $x^k$. Find the range of $x$ for which the ratio test implies that the series converges:
$$\sum_{k=1}^\infty \left(\frac{ x^k }{ k^2 }\right)$$ | $|x|$ < $1$ |
2a797d22-d902-4bf9-afea-9ff2d5690b7c | differential_calc | false | null | Make full curve sketching of $f(x) = \frac{ 3 \cdot x^3 }{ 3 \cdot x^2 - 4 }$.
Submit as your final answer:
1. The domain (in interval notation)
2. Vertical asymptote(s)
3. Horizontal asymptote(s)
4. Slant asymptote(s)
5. Interval(s) where the function is increasing
6. Interval(s) where the function is decreasing
7. Interval(s) where the function is concave up
8. Interval(s) where the function is concave down
9. Point(s) of inflection | 1. The domain (in interval notation) $\left(-1\cdot\infty,-2\cdot3^{-1\cdot2^{-1}}\right)\cup\left(-2\cdot3^{-1\cdot2^{-1}},2\cdot3^{-1\cdot2^{-1}}\right)\cup\left(2\cdot3^{-1\cdot2^{-1}},\infty\right)$
2. Vertical asymptote(s) $x=\frac{2}{\sqrt{3}}$, $x=-\frac{2}{\sqrt{3}}$
3. Horizontal asymptote(s) None
4. Slant asymptote(s) $y=x$
5. Interval(s) where the function is increasing $(-\infty,-2)$, $(2,\infty)$
6. Interval(s) where the function is decreasing $\left(-2,-\frac{2}{\sqrt{3}}\right)$, $\left(-\frac{2}{\sqrt{3}},0\right)$, $\left(0,\frac{2}{\sqrt{3}}\right)$, $\left(\frac{2}{\sqrt{3}},2\right)$
7. Interval(s) where the function is concave up $\left(-\frac{2}{\sqrt{3}},0\right)$, $\left(\frac{2}{\sqrt{3}},\infty\right)$
8. Interval(s) where the function is concave down $\left(-\infty,-\frac{2}{\sqrt{3}}\right)$, $\left(0,\frac{2}{\sqrt{3}}\right)$
9. Point(s) of inflection $P(0,0)$ |
2aafde85-809f-4cc5-a0e7-ef098bfc2e4c | algebra | false | null | Find the degree and leading coefficient for the given polynomial $f(x) = x^3 \cdot (4 \cdot x - 3)^2$. | The degree of the polynomial: $5$
The leading coefficient of the polynomial: $16$ |
2ac1f00d-e481-43d0-8af8-3a40003255ab | differential_calc | false | null | Compute the limit using L'Hopital's Rule:
$$
\lim_{x \to 0} \left( \frac{ 1 }{ x^2 } - \cot(x)^2 \right)
$$ | The final answer: $\frac{2}{3}$ |
2ac945ef-fd61-419c-8564-32e46fef157c | differential_calc | false | null | Evaluate $\lim_{x \to 0}\left(\left(\frac{ \sin(2 \cdot x) }{ 2 \cdot x }\right)^{\frac{ 1 }{ 4 \cdot x^2 }}\right)$. | $\lim_{x \to 0}\left(\left(\frac{ \sin(2 \cdot x) }{ 2 \cdot x }\right)^{\frac{ 1 }{ 4 \cdot x^2 }}\right)$ = $e^{-\frac{1}{6}}$ |
2aed35f2-99fd-4a0a-ba04-4f6f9c2b3096 | sequences_series | false | null | Using the fact that:
$$
e^x = \sum_{n=0}^\infty \left(\frac{ x^n }{ n! }\right)
$$
Evaluate:
$$
\sum_{n=0}^\infty \left(\frac{ 3 \cdot n }{ n! } \cdot 7^{1-3 \cdot n}\right)
$$ | The final answer: $\frac{3}{49}\cdot e^{\frac{1}{343}}$ |
2aee6b67-afa7-427f-90a3-daffc1044c8f | integral_calc | false | null | Compute the integral:
$$
\int \sin(2 \cdot x)^6 \cdot \cos(2 \cdot x)^2 \, dx
$$ | Answer is: $\frac{1}{32}\cdot x-\frac{1}{32}\cdot\frac{1}{8}\cdot\sin(8\cdot x)-\frac{1}{8}\cdot\frac{1}{4}\cdot\frac{1}{3}\cdot\sin(4\cdot x)^3+\frac{1}{128}\cdot x-\frac{1}{128}\cdot\frac{1}{16}\cdot\sin(16\cdot x)+C$ |
2b05093d-b9a0-447b-87af-c2ffe13e010a | precalculus_review | false | null | Simplify the following expression:
$$
E = 2 \cdot \left( \left( \sin(x) \right)^6 + \left( \cos(x) \right)^6 \right) - 3 \cdot \left( \left( \sin(x) \right)^4 + \left( \cos(x) \right)^4 \right)
$$ | The final answer: $E=-1$ |
2b0b5339-ba8d-460a-991d-c0a4b8452626 | algebra | true | 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 | Using the graph of $f(x)$ given below, find $f^{-1}(3)$. | $f^{-1}(3)$ = $0$ |
2b575acf-e40a-4b0a-9ad7-099c38d6206c | precalculus_review | false | null | For both $y=a^x$ and $y=\log_{a}(x)$ where $a>0$ and $a \ne 1$, find the $P(x,y)$ coordinate where the slope of the functions are $1$. Write your answers only in terms of natural logarithms. | Coordinates of $a^x$: $x$ = $-\frac{\ln\left(\ln(a)\right)}{\ln(a)}$ , $y$ = $y=\frac{1}{\ln(a)}$
Coordinates of $\log_{a}(x)$: $x$ = $x=\frac{1}{\ln(a)}$ , $y$ = $-\frac{\ln\left(\ln(a)\right)}{\ln(a)}$ |
2b811576-774b-43ed-bed4-15f5b2cd794b | differential_calc | true | 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 | Use the following graph and find: $\lim_{x \to 1^{-}}\left(f(x)\right)$ | $\lim_{x \to 1^{-}}\left(f(x)\right)$: $1$ |
2b8e2958-1ef8-4d3f-adfb-a05baa324f8a | differential_calc | false | null | Find the first derivative of the function: $y = (x + 11)^5 \cdot (3 \cdot x - 7)^4 \cdot (x - 12) \cdot (x + 4)$. | $y'$ = $\left(\frac{5}{x+11}+\frac{12}{3\cdot x-7}+\frac{1}{x-12}+\frac{1}{x+4}\right)\cdot(x+11)^5\cdot(3\cdot x-7)^4\cdot(x-12)\cdot(x+4)$ |
2c34f270-20d2-4a0f-ba88-2883a71b7e30 | differential_calc | true | 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 | Given $h(x) = f(x) \cdot g(x)$, find $h'(2)$ using the table below: | $h'(2)$ = $-29$ |
2ce8f8fe-faae-4c62-9c73-692fbc4aeeb9 | differential_calc | true | 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 | Let $f$ be a differentiable function defined onthe closed interval $-2 \le x \le 3$ with $f(2) = -4$.
The graph of $f'(x)$, the derivative of $f$, is shown.
Write an equation for the line tangentto the graph of $f$ at $x=2$. | The equation of the tangent line is: $y+4=-(x-2)$ |
2cec29f7-4a99-4553-9211-8f39de5520b5 | multivariable_calculus | false | null | Find the directional derivative of $f(x,y,z) = x^2 + y \cdot z$ at $P(1,-3,2)$ in the direction of increasing $t$ along the path
$\vec{r}(t) = t^2 \cdot \vec{i} + 3 \cdot t \cdot \vec{j} + \left(1-t^3\right) \cdot \vec{k}$. | $f_{u}(P)$ = $\frac{11}{\sqrt{22}}$ |
2d167fb0-1096-474b-96fe-75a2a95ddc78 | algebra | false | null | Find the solution to the following inequality and express it in interval notation:
$$-4 (x-5) (x+4) (x-1) \le 0$$ | The solution set to the inequality is: $\left[-4,\ 1\right]\cup\left[5,\ \infty\right)$ |
2d16ea33-5993-4872-a76a-a21c70e522b5 | integral_calc | false | null | Compute the integral:
$$
\int \cos\left(\frac{ x }{ 2 }\right)^4 \, dx
$$ | $\int \cos\left(\frac{ x }{ 2 }\right)^4 \, dx$ = $\frac{\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)^3}{2}+\frac{3}{4}\cdot\left(\sin\left(\frac{x}{2}\right)\cdot\cos\left(\frac{x}{2}\right)+\frac{x}{2}\right)+C$ |
2d1a9f91-c6a7-458f-b4b7-f764d6826606 | differential_calc | true | data:image/png;base64,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 | Use the following graph and find: $\lim_{x \to -2^{-}}\left(f(x)\right)$ | $\lim_{x \to -2^{-}}\left(f(x)\right)$: $0$ |
2d2c80a0-257a-411f-ade4-12e1906ab93b | algebra | false | null | Find the inverse function of $f(x) = \frac{ 2 \cdot x + 3 }{ 5 \cdot x + 4 }$. | $f^{-1}(x)$ = $\frac{3-4\cdot x}{5\cdot x-2}$ |
2d3c3b27-060d-45bc-8f0f-3ff0be69b15b | precalculus_review | false | null | Find zeros of $f(x) = \sqrt{(x+3)^2} + \sqrt{(x-2)^2} + \sqrt{(2 \cdot x-8)^2} - 9$ | The final answer: $x\in[2,4]$ |