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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 - Spring 2011 \hfil \pp
\hfil Final Exam\hfil  \pp
\hfil June 4, 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
 5 & 10 &       \\ \hline
 6 & 10 &      \\ \hline
7 &  10 &    \\ \hline
Total & 70 & \\ \hline 
\end{tabular}
}
\end{center}
\vfil
\begin{itemize}
\item Complete all questions. 
\item Show all work for full credit. 
\item You may use a scientific calculator during this
examination.  Graphing calculators are not allowed.
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. 
\item You have 170 minutes to complete the exam. 
\end{itemize}
\vfil
.

\newp

\begin{enumerate}

\item Toshiro is walking near the Circular Forest, which has the
shape of a perfect circle, and radius of 8 km.
He begins from a point 10 km WEST and 3 km SOUTH of the center of 
the forest.  He heads directly toward a point 20 km EAST and 4 km NORTH 
of the center of the forest.  However, when he reaches a point due
EAST of the center of the forest, he turns and walks due SOUTH until
he leaves the forest.

Toshiro walks at a constant 5 km per hour.  How much time did he spend
in the forest?

\newp

\item Arnoldo and Hamda are running around a circular track.
Arnoldo starts from the northernmost point of track and runs clockwise.
Arnoldo takes 23 second to run each lap of the track.
Hamda runs counterclockwise, and takes 27 seconds to run each lap of the track.
Arnoldo and Hamda start running at the same time, 
and pass each other for the first time after 8 seconds.

\begin{enumerate}

\item How long have Arnoldo and Hamda been running (i.e., time since they started running)
when they pass each other for the second time?

\vfil

\item Let $R$ be the radius of the track.   With the origin at the center of
the track, express Hamda's $x$- and $y$-coordinates
as functions of the time, $t$, since Hamda started running (your answers will involve $R$).

\end{enumerate}

\newp


\item The volume of a certain weather balloon is a sinusoidal 
function of time.  At 1 AM today, the volume was at a minimum, 2 m$^3$.
The volume then increased, reaching a maximum of 22 m$^3$ at 5 AM today.

\begin{enumerate}

\item Express the volume of the balloon as a sinusoidal function of time, $t$, where
$t$ is hours after midnight today.

\vfil

\item In the first 14 hours after midnight, for how much time was the
balloon's volume less than 6 m$^3$?

\end{enumerate}

\vfil


\newp

\item You wish to cut a piece of steel shaped as shown in the figure below.
All dimensions are in centimeters.

A vertical cut will be made $x$ centimeters from the left-most edge.

Express the area to the left of the cut as a multipart function of $x$.

 \epsfig{file=multipart01.eps, 
 width=6cm,
 angle=0 }

\newp

\item A tree is growing.  Its height is a linear-to-linear rational function of time.
Today, the tree is 5 feet tall.  Twenty years from today it will be 40 feet tall, and
21 years from today it will be 41 feet tall.

\begin{enumerate}
\item Express the tree's height as a linear-to-linear function of $t$, where $t$
is years from today.

\vfil \vfil

\item When (in years from today) will the tree be 50 feet tall?

\end{enumerate}

\newp

\item The population of city A increase by $2.38\%$ per year.  City B doubles in the
length of time it takes city A to increase from a population of 4,000 to a population of 9,500.
In the year 2000, city B had a population of 11,000.  

When will city B's population reach 30,000?  Express your answer in years after the
year 2000.

\newp

\item Let $f(x)=x+3|x+1|$, and $g(x)=2x+4$.

\begin{enumerate}
\item Express $f(g(x))$ as a multipart function.

\vfil

\item Find all solutions to the equation $f(g(x))=12x$.


\end{enumerate}

\newp  
  
\end{enumerate}

\end{document}


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