\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 2019} \\
\end{center}
\vspace{0.3in}
\textbf{Name}\ \rule{4in}{0.4pt} \hfill
\vspace{0.4in}
$\bullet$ You have 20 minutes \hfill $\bullet$ No calculators \hfill $\bullet$ Show sufficient work
\vspace{0.3in}
\noindent
\begin{enumerate}
\item (3 points) Suppose that $p$ is a function of $w$ which satisfies the following two conditions.\\
\begin{itemize}
\item $\D{\frac{dp}{dw} = 0.5p}$
\vspace{0.1in}
\item $\D{p\left(ln(25)\right) = 20}$
\end{itemize}
\vspace{0.1in}
Evaluate $\D{p\left(ln(81)\right)}$ and simplify your answer.
\vfill
\newpage
\item (3 points) For $t \geq 0$, the position in meters of a particle is given by
$$s(t) = \frac{t^{3}}{3} - 2t^{2} + 10t + 17$$
where $t$ is measured in seconds.\\[0.2in]
What is the particle's acceleration at the moment when the particle's velocity is $15$ $m/s$ ? Use correct units in your final answer.
\vfill
\newpage
\item (4 points) A camera is positioned on the ground $4000$ feet from the base of a rocket launching pad. The angle of elevation of the camera has to change at the correct rate in order to keep the rocket in sight. Suppose the rocket rises vertically and its speed is $750$ feet per second when it has risen $3000$ feet. How quickly is the camera's angle of elevation increasing at that moment?
\vfill
\end{enumerate}
\end{document}