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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 A Spring 2011 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil April 21, 2011 \hfil \pp
\normalsize
\vfil
\medskip
\hfil Name: \hrulefill \hrulefill \hspace{0.5in} Student ID no. : \hrulefill

\vfil

\hfil Signature: \hrulefill \hrulefill \hrulefill \hspace{0.5in} Section: \hrulefill 
 
\vfil
\begin{center}
{\Huge
\begin{tabular}{||c|c|r||} \hline 
 1 & 10 &\hspace{10mm} \hfil\\ \hline 
 2 & 10 &       \\ \hline
 3 & 10 &      \\ \hline
4 &  10 &    \\ \hline
Total & 40 & \\ \hline 
\end{tabular}
}
\end{center}
\vfil
\begin{itemize}
\item Complete all four questions. 
\item Show all work for full credit. 
\item You may use a scientific calculator during this
examination.  Graphic calculators are not allowed.
Also, other electronic devices are not allowed, and should be
turned off and put away for the duration of the exam.
\item If you use a trial-and-error or guess-and-check method
when an algebraic method is available, you will not receive full credit.
\item You may use one hand-written 8.5 by 11 inch page of notes.  Write
your name on your notesheet and turn it in with your exam.
\item You have 50 minutes to complete the exam. 
\end{itemize}
\vfil
.

\newp

\begin{enumerate}

\item Vera is running. 
She starts from a point which is 120 feet due north of a broken water main. 
She runs directly toward a point 600 feet east of the broken water main and will reach it after 60 seconds.  

\begin{enumerate}

\item Impose a coordinate system with the origin at the broken water main.
Express Vera's $x$ and $y$ coordinates as functions of $t$, the length of time she has been running.

\vfil

\item The water main started leaking at the moment that Vera started running.  The puddle created by
the water main is circular, centered on the water main, and has a radius which grows at 12 feet per second.  
Determine when Vera's feet get wet.

\end{enumerate}

\newp

\item Helga has a job. Her regular pay rate is 10 dollars per hour.
However, for the time she works between 8 hours and 12 hours in a day, she will be paid 15 dollars per hour.  
For time she works over 12 hours in a day, she will be paid 20 dollars per hour.

\begin{enumerate}

\item Express the amount of money Helga earns in a work day as a multipart function $M(x)$ of the number
of hours $x$ she works that day.

\vfil

\item Steve has a different job.  His job pays 11.50 dollars per hour regardless of how many
hours in a day he works.  One day, Steve and Helga work for the same amount of time and
make the same amount of money.  How many hours did Helga work on that day?

\end{enumerate}

\newp

\item The town of Baarn is located 30 km WEST and 20 km NORTH of the town of Cuijk.  The town of Delft
is located 50 km EAST and 10 km SOUTH of Cuijk.  

A train track follows a straight line from Baarn to Delft.  How close does the track come to Cuijk?

\newp

\item You are creating a window with the shape of a rectangle with a quarter circle on top.
An example is shown in the figure below.

 \epsfig{file=quadOpt2.eps, 
 width=4cm,
 angle=0 }

The perimeter will be 100 cm.  What is the maximum possible area for the window?


\end{enumerate}

\end{document}


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