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\begin{center}
{\Large TEST 2

Math 1090 - 2}
\end{center}
\vspace{.1in}
You have 50 minutes to complete the test.
Show all relevant work (or else no credit).  
Make your work legible, if I can't read it, I can't grade it.  
Each problem is worth 10 points.
Use the back of the pages if necessary.
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Name \rule{5in}{.2pt}

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\begin{enumerate}

\item  Given the two functions: find the composition: (don't simplify it)
\[
f(x)=3x^2-5x
\]
\[
g(x)=\sqrt{x-5}
\]
Find the composition $g \circ f(x)$ (don't simplify it)

\item  Write the function as a composition.
(Find $f$ and $g$ so that $R(x)=f(g(x))$)
\[
R(x)=\sqrt[3]{-2x^3-\sqrt{x}}
\]

\item  Solve the system of equations: (use any method you wish)
\[
\begin{array}{ccccccc}
x & + & 3y & - & 8z & = & 20 \\
 &  & y & - & 3z & = & 11 \\
 &  & 2y & + & 7z & = & -4 \\
\end{array}
\]

\item  Suppose that you are selling veggie burritos at the upcoming Phish
concert.
You can sell a burrito for \$5.  
You have fixed costs of \$50 (cooler, gas, ticket, parking), and 
each burrito costs you \$2 to produce.
How many burritos must be sold in order to break even?

\item  Find, if possible.  If not possible state why not.
\[
A=\left[ \begin{array}{rrr}
3 & 0 & 1 \\
-2 & 1 & 0
\end{array} \right]\hspace{.5in}
B= \left[ \begin{array}{rr}
2 & -1\\
3 & -2 \\
-5 & 7 \\
\end{array} \right]
\]
\begin{enumerate}
\item $2A-3B$
\item  $AB$
\item  $BA$
\end{enumerate}

\item  Consider the following system of equations.
\[
\begin{array}{ccccccc}
x & - & 3y & + & 3z & = & 7 \\
3x & + & 2y & + & 4z & = & 5 \\
x & + & 2y &- & z & = & -2 \\
\end{array}
\]
\begin{enumerate}
\item  Write the augmented matrix for the system of equations.
\item  Using the ``legal operations'' on the matrix, 
how would you make the $(2,1)$ position a 0?
\item  Make the $(2,1)$ position a 0 as described above.
\item  If you were working with the equations, what would you have just done?
(Explain what making the $(2,1)$ position means in terms of $x,y,z$.)
\end{enumerate}

\end{enumerate}


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