\documentclass[12pt]{report} 

\usepackage{palatino}
\usepackage{epsfig}
\usepackage[margin=0.8in]{geometry}

\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{math}

%\markboth{Dr. Matthew M. Conroy - University of Washington}{Dr. Matthew M. Conroy - University of Washington}


\pagestyle{empty} %%% this results in no pagenumbers (footer is empty}

\setlength{\parindent}{0in}
\setlength{\parskip}{0.05in}

\baselineskip=20pt

\newcommand{\dsps}{\displaystyle}
\newcommand{\pp}{\par \noindent}
\newcommand{\newp}{\vfil \eject}



\newcommand{\bikeChain}[6]{
	%%% written by Matthew Conroy (conroy "at" math.washington.edu)
	%%% April 2015
	%%%
	%%% format is \bikeChain{x1}{y1}{r1}{x2}{y2}{r2}
	%%% where one circle is centered at (x1,y1) with radius r1,
	%%% and the other is centered at (x2,y2) with radius r2
	%%%
	%%% known bug: fails if x1=x2
	%%%


	\draw (#1,#2) circle (#3 cm);
	\draw (#4,#5) circle (#6 cm);
	\def\xa{#1}
	\def\ya{#2}
	\def\xb{#4}
	\def\yb{#5}
	\def\ra{#3}
	\def\rb{#6}
	

	\tikzmath{
		if ((\xa==\xb) && (\yb<\ya)) then {\betty=-90;} 
		else {
				if ((\xa==\xb) && (\yb>\ya)) then {\betty=90;}
				else {
					if ((\xa!=\xb)) then {\betty=atan((\yb-\ya)/(\xb-\xa));};
				};
		};
	}		
		
	
	%% distance between circle centers
	\pgfmathsetmacro{\alpha}{ sqrt((\xa-\xb)*(\xa-\xb)+(\ya-\yb)*(\ya-\yb))} 
	%% length of free chain segment
	\pgfmathsetmacro{\gamma}{ sqrt((\alpha)*(\alpha)-(\ra-\rb)*(\ra-\rb)) }  
	%% angle between radii and line through centers
	\pgfmathsetmacro{\theta}{(90-atan(abs(\ra-\rb)/\gamma))}; 
	%% if rb>ra, we have theta plays a different role
	\pgfmathsetmacro\theta{ifthenelse(\rb>\ra,180-\theta,\theta)}\pgfmathresult; 
	%% another geometry flip
	\pgfmathsetmacro\theta{ifthenelse(\xb<\xa,180-\theta,\theta)}\pgfmathresult; 
	%% angle the line through centers makes with horizontal
	%\pgfmathsetmacro\beta{betafun(\xa,\ya,\xb,\yb)}\pgfmathresult; 
	\pgfmathsetmacro\beta{\betty}\pgfmathresult;
	
	%\draw (\xa,-4) node {$\beta$};
	
	%% calculate points of contact with chain
	\pgfmathsetmacro{\xxa}{\xa+\ra*cos(\theta+\beta*1)};
	\pgfmathsetmacro{\yya}{\ya+\ra*sin(\theta+\beta*1)};
	\pgfmathsetmacro{\xxb}{\xb+\rb*cos(\theta+\beta*1)};
	\pgfmathsetmacro{\yyb}{\yb+\rb*sin(\theta+\beta*1)};
	%% draw first part of chain
	\draw (\xxa,\yya) -- (\xxb,\yyb);
	%% calculate the symmetrically located contact points
	\pgfmathsetmacro{\xxa}{\xa+\ra*cos(-\theta+\beta*1)};
	\pgfmathsetmacro{\yya}{\ya+\ra*sin(-\theta+\beta*1)};
	\pgfmathsetmacro{\xxb}{\xb+\rb*cos(-\theta+\beta*1)};
	\pgfmathsetmacro{\yyb}{\yb+\rb*sin(-\theta+\beta*1)};
	%% draw second part of chain
	\draw (\xxa,\yya) -- (\xxb,\yyb);
}	


\usetikzlibrary{arrows,decorations.markings}



\begin{document}
\noindent
\vfil \noindent

{\LARGE{
\hfil Math 120 A Spring 2017 \hfil \pp
\hfil Final Exam\hfil  \pp
\hfil June 3, 2017 \hfil \pp
\hfil Answers \hfil \pp
}}

\normalsize

\begin{enumerate}
\item (a) $r(t) = 12.5+9.5 \sin \left( \frac{2\pi}{6} (t-7) \right)$
(b) $13.8015$ hours after midnight

\item (a) $150.663706$ seconds
(b) $260.5559$ meters north

\item $260.255469$ feet 

\item $50$ feet by $\frac{250}{13}$ feet

\item $\frac{82}{13}$ seconds

\item (a) $g(f(g(x))) = \begin{cases}
\frac{1}{4}x -2 & \text{if } x \ge -4 \\
-\frac{1}{4}x - 4 & \text{if } x < -4
\end{cases}$
(b) $h^{-1}(x) = \frac{5x-34}{2x-17}$

\item $(10,-16.46424\dots)$

\end{enumerate}

\end{document}


% \epsfig{file=pizza01.eps, 
% width=11cm,
% angle=0 }