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\title{\vspace*{-1.5in}\textbf{Math 2300-007: Quiz 13/14}}
\date{}
\author{}


\begin{document}
\maketitle
%\underline{Math 1300-400: Quiz 1}
\lhead{Math 2300-007: Calculus II}
\rhead{April 27, 2018}
\chead{Quiz 13/14}
\vspace{-.5in}
\noindent
{Name: \underline{\phantom{Aalsdkjflaskdjflaskjflksdjflkdsjf}}} \hfill{Score: \underline{\phantom{lksdjflkdsjf}}}\\
\noindent
\begin{enumerate}
\item A ray (a half-line) is parameterized by $\begin{cases}x = 2+ 3t^2\\y = -1 +4t^2,\end{cases}$ where $-\infty < t < \infty.$
\begin{enumerate}[(a)]
%\item Does $(5,4)$ lie on the ray?\vfill
\item(2 points) Does $(2,1)$ lie on the ray? Explain.\vfill
%\item Does $(-1,-6)$ lie on the ray?\vfill
%\item When does the line hit the $y$-axis?\vfill
\item(2 points) What is the speed of motion along the line as a function of $t$?\vfill
\item(2 points) What is the slope of the line?\vfill
\item(1 point) On the axes provided, draw the graph of the ray.
\begin{center}
\begin{tikzpicture}
\begin{axis}[axis lines = center, xmin=-3, xmax=3, xtick ={-3,-2,-1,0,1,2,3}, ytick ={-3,-2,-1,0,1,2,3}, ymin=-3, ymax=3,x=1cm, y=1cm, grid = both]
\addplot[color=white]{x};
\end{axis}
\end{tikzpicture}
\end{center}
\end{enumerate}\newpage
\item(3 points) Eliminate the parameter to find a cartesian equation of the curve described by the parametric equations \[\begin{cases}x = 3\sin(t)\\y = \cos(t) - 1,\end{cases}\quad \text{where $0 \leq t < 2\pi$}.\] You do not need to solve for $x$ or $y$ in your answer. \vfill\vfill\vfill\vfill
\item(\textbf{Quiz 14}: 10 points) This weekend, something fun I'm doing is....\vfill
\end{enumerate}

\end{document}
