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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 A - Spring 2008 \hfil \pp
\hfil Mid-Term Exam Number One\hfil  \pp
\hfil April 24, 2008 \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}
{\large
\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 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,
or read a numerical solution from a graph on your calculator
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 Show all work for full credit.  
\item You have 50 minutes to complete the exam. 
\end{itemize}
\vfil
.

\newp

\begin{enumerate}


\item You are sailing your boat near a radar antenna.
The radar will detect anything within 10 km in any direction.
You start sailing from a point 12 km East and 8 km North of the
radar.  You will sail directly to a point 8 km West and 14 km South
of the radar.

You sail at a constant speed of 6 km per hour.  For what length of 
time will your sailboat be detectable by the radar?


\newp

\item You decide to take a walk.  You start walking due North at 5 feet per second.
After walking 200 feet, you turn and walk due West at 4 feet per second for 30 seconds.
You then turn and walk due South at 3 feet per second for 100 seconds.

Express the (straight-line) distance from your starting point as a multipart function of $t$, the
number of seconds since you started walking.

\newp

\item You will use 100 feet of fencing to make two enclosures.
One will be a square, and one will be a rectangle that is twice as long as it is wide.

What is the \textit{minimum} possible combined area of the two enclosures?



\newp

\item Let
$f(x) = 2x-|x+2|$ and $g(x)=1-x$.

\begin{enumerate}

\item Write the multipart rule for the function $f(g(x))$.
\vfil
\item Find all solutions to the equation
\[
f(g(x))=-\frac{1}{2}x
\]


\end{enumerate}

\end{enumerate}


\end{document}


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