\documentclass[12 pt]{article}
\pagestyle{empty}
\addtolength{\topmargin}{-0.9in}
\addtolength{\textheight}{1.9in}
\addtolength{\oddsidemargin}{-0.7in}
\addtolength{\textwidth}{1.4in}
\newcommand{\D}{\displaystyle}
\begin{document}
\begin{center}
\textbf{Math 220 (section AD?) \hfill Quiz 6 \hfill Fall 2012} \\
\end{center}
\vspace{0.3in}
\textbf{Name}\ \rule{4in}{0.4pt} \hfill
\vspace{0.4in}
$\bullet$ You have 15 minutes \hfill $\bullet$ No calculators \hfill $\bullet$ Show sufficient work
\vspace{0.3in}
\noindent
\begin{enumerate}
\item (3 points) A ladder $12$ feet long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of $0.5$ feet per second, how quickly in radians per second is the angle between the ladder and the wall increasing when the bottom of the ladder is $5$ feet from the wall?
\vfill
\newpage
\item (4 points) A rock is thrown vertically upward from the surface of a planet. The rock's height above the planet's surface is given by the equation $s=t(24-1.2t)$, where $t$ is measured in seconds and $s$ is measured in meters.
\begin{enumerate}
\item Find a formula for the rock's velocity at time $t$.
\vspace{1in}
\item What is the maximum height reached by the rock?
\end{enumerate}
\vfill
\item (3 points) Determine a formula for $P$ as a function of $t$ given that $\D{8P' + 2P = 0}$ and $P(0) = 5$. Hint: You may recognize the solution more quickly if you first solve the given equation for $\D{P'}$.
\vfill
\end{enumerate}
\end{document}