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\textbf{Math 220 (section AD?) \hfill Quiz 6 \hfill Spring 2019} \\
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\textbf{Name}\ \rule{4in}{0.4pt} \hfill
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$\bullet$ You have 20 minutes \hfill $\bullet$ No calculators \hfill $\bullet$ Show sufficient work
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\item (4 points) There is a launch site for a hot-air balloon on the ground $20$ meters away from an observer. The balloon rises vertically at a constant rate of $2$ meters per second. How quickly is the angle of elevation of the balloon increasing $5$ seconds after its launch?
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\item (3 points) At each point on the curve $y = f(x)$, the slope of the curve is equal to its $y$-coordinate multiplied by $1/4$. If its graph goes through the point $\left(\ln{(81)}, 36\right)$, then find a formula for $f(x)$. Simplify your answer.
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\item (3 points) A bullet is shot upward from the surface of a planet so that its height in meters until coming to rest is given by the equation $s(t) = 195t - 6.5t^{2}$ where $t$ is measured in seconds. At what time does the bullet reach its maximum height?
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