\documentclass[12pt]{article}
%\pagestyle{empty}
\textwidth 6.5in
\textheight 9.5in
\topmargin -1in
\oddsidemargin -.1in
\parskip 1ex
\parindent 0em
\usepackage{epsfig}
\usepackage{subfigure}
\begin{document}
\sf
{
Math 120 (Pezzoli)\hfill Name \rule{10pc}{1mm}
\\
Winter  2014\hfill \\
Midterm \#1 \hfill TA:\rule{10pc}{1mm}\\
\\
.\hfill Section:\rule{10pc}{1mm}\\
}
\vskip .1in

\rule{40pc}{2mm}

Instructions: 

\begin{itemize}

\item Your exam contains 3  problems. 
\item Your exam should contain 4 pages; please make sure you
have a complete exam.

\item Box in your final answer when appropriate. 



\item  Unless stated
otherwise, you {\bf MUST} show
work for credit. No credit for answers only. 
If in doubt, ask for clarification. 

\item Your work needs to be neat and legible.

\item You are allowed one
$8.5\times 11$ sheet of  notes (both sides). Graphing calculators
are NOT allowed; scientific 
calculators are allowed. 
\item Round off your answers to 2 decimal places, unless you are asked for exact answers.
\end{itemize}

\rule{40pc}{2mm}
\vskip .25in


Problem \#1 (25 pts) \rule{5pc}{1mm}\hskip 2in
\vskip .2in
Problem \#2 (15 pts) \rule{5pc}{1mm}\hskip 2in
\vskip .2in
Problem \#3 (20 pts) \rule{5pc}{1mm}\hskip 2in
\vskip .2in

\vskip .5in

TOTAL (60 pts) \rule{8pc}{1mm}

\vfill\eject

\begin{enumerate}


\item At time $t=0$ Tom leaves his house and starts driving North on a straight road at a constant speed of 30 mph. At the same time Bob leaves from a location situated 20 mi East and 40 mi North of Tom's house and starts driving on a straight road directly towards a location situated 10 mi West of Tom's house; Bob drives at a constant speed of 50 mph.
Set up a coordinate system with the origin O corresponding to Tom's house, the $x$ axis in the West East direction, the $y$ axis in the South North direction.
 
\begin{enumerate}
\item Give Tom's coordinates at time $t$ ($t \geq 0$).
\vskip 1in
\item Give Bob's coordinates at time $t$  ($t \geq 0$).
\vskip 3in
\item When are Tom and Bob closest ?
%\item How close do Tom and Bob get ?
\end{enumerate}

\newpage

\item Given the function
$$\displaystyle f(x)=\cases{3x+2 ,&if $ x \leq 1 $ \cr
	5-\sqrt{1-(x-2)^2},&if $1 < x  \leq 3$ \cr
          6 &if $x >3    $\cr}
$$	



\begin{enumerate}
\item[(a)]Draw the graph of $y=f(x)$. Make sure to mark all relevant points on the axes.


\vskip 4in	

%\item[(b)] Draw the graph of $y=f(x+2)-7$. Make sure to mark all relevant points on the axes.



\item [(b)] Find all solutions of the equation $f(x)=4.5$
\end{enumerate}

\newpage

\item Allyson and Adryan have decided to connect their ankles with a bungee cord; one end is tied to each person ankle. The cord is 30 feet long, but it can stretch up to 90 feet . They both start at the same location. Allyson moves 10 ft/sec and Adrian moves 5 feet/sec in the directions indicated. Next to their starting location there is a lake that has the shape of a circle of radius 10 feet. 

\begin{figure}[ht]
\centering
\includegraphics[scale=0.3]{120mid1.eps}
\label{fig:subfig1}

\end{figure}

\begin{enumerate}
\item[(a)] Determine when the bungee cord first becomes tight (i.e. 30 feet long).

\vfill

\item[(b)] At time $t=6$ sec, how much of the bungee cord is over the water ?

 


\vfill


\end{enumerate}



\end{enumerate}
\end{document}
