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\textbf{Math 220 \hfill Quiz 7 (take-home) \hfill Fall 2011} \\
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\textbf{Name}\ \rule{3.5in}{.4pt}
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\begin{itemize}
\item You may work with other students in this class. However each student should write up solutions separately and independently -- nobody should copy someone else's work.
\item You may use your notes or the textbook.
\item Computers are not allowed on any problem. You may use a calculator only for basic arithmetic.
\item You must show sufficient work to justify each answer.
\item The quiz should be turned in to your TA at the beginning of your discussion section meeting on Tuesday, October 11th.
\item Be sure that the pages are nicely stapled -- do not just fold the corners.
\item \textbf{Note to TAs and Tutors -- you should not help students with these specific problems or go over solutions until after 4pm Tuesday.}
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\item (3 points) Suppose $y_1$ is a function of $x$ for which $\D{\frac{dy_1}{dx} = 3y_1}$. Suppose $y_2$ is a function of $x$ for which $\D{\frac{dy_2}{dx} = 8x + 5}$. If the graphs of $y_1$ and $y_2$ have the same $y$-intercept and they intersect at $x=2$, then determine the value of the $y$-intercept.
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\item (4 points) A bullet is fired upwards from the ground at an initial velocity of $1200$ feet per second. The height $s$ (in feet) of the bullet above the ground after $t$ seconds is $s = 1200t - 6t^2$ on Mars and $s = 1200t - 16t^2$ on Earth. How much higher will the bullet travel on Mars than on Earth?
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\item (3 points) An observer stands $200$ meters from the launch site of a hot-air balloon. The balloon rises vertically at a constant rate of $4$ meters per second. How fast is the angle of elevation of the balloon increasing $30$ seconds after the launch?
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