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\begin{center}
{\Large TEST 1

Math 1090 - 2}
\end{center}
\vspace{.1in}
You have 1 hour to complete the test.
Make sure you show \emph{all} your work, or else you will not get the credit.
Make your work legible, if I can't read it, I can't grade it.  
Each problem is worth 10 points.
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Name \rule{5in}{.2pt}

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\begin{enumerate}

\item  
\begin{enumerate}
\item  Find a decimal approximation of the following (using your calculator):
\[
-\left(-1.8 \right)^{\frac{4}{5}}
\]

\item  Simplify the expression using no negative exponents
\[
\left(
\frac{2^{-4} x^4 y^{-3}}{6^{-3} x^{-2} y^2}
\right)^{-2}
\]
\end{enumerate}

\item  Suppose you buy and sell used books.  
In order to keep the business alive, you need 28\% of the selling price of a book to be your mark-up.
If you buy a used book for \$18, what do you need to sell it for?

\item  For the function $f(x)=-x-3x^2$, find and simplify the following:
\[
\frac{f(x+h)-f(x-h)}{2h}
\]

\item  Suppose a mining company will supply 100,000 tons of ore per month if the price is \$30 per ton.
The mining company will supply 80,000 tons per month if the price is \$25 per ton.
Assuming the supply function if linear, write its equation.
Use $p$ for price and $q$ for quantity.

\item  Suppose you are in the T-shirt business.
You sell shirts for \$13 each and they cost \$7 each to produce.
You also rent some office space, have a phone line and some other fixed costs that total \$2000 per month.
\begin{enumerate}
\item  What is the cost function?
\item  What is the revenue function?
\item  What is the profit function?
\item  What is the break even point?
\end{enumerate}

\item  Use the matrices to perform the operations.
If any operation is not possible, explain why.
\[
A = 
\left[
\begin{array}{rr}
-1 & 0 \\
5 & 2 \\
3 & -4 
\end{array}
\right]
\quad
B = 
\left[
\begin{array}{rr}
2 & 6 \\
0 & -1
\end{array}
\right]
\quad
C = 
\left[
\begin{array}{rr}
0 & -2 \\
1 & -3
\end{array}
\right]
\quad
D = 
\left[
\begin{array}{rrr}
1 & 1 & 0 \\
0 & 0 & -2 \\
0 & 1 & 1 
\end{array}
\right]
\]

\begin{enumerate}
\item  $AB$
\item  $BA$
\item  $4C-B$
\item  Is the matrix $E$ below equal to $D^{-1}$?
Why or why not?
\[
E = 
\left[
\begin{array}{rrr}
1 & -3/2 & -1 \\
0 & 3/2 & 1 \\
0 & -1/2 & 0 
\end{array}
\right]
\]
\end{enumerate}

\item  Using Gauss-Jordan elimination, solve the system of equations:
\begin{eqnarray*}
2x-y-13z & = & 17 \\
x+y-z & = & 0 \\
x+2y+3z & = & -5
\end{eqnarray*}

\item  The temperature of 1 gram of water as it changes from ice at 
$-10^\circ C$ to steam at $110^\circ C$ is given by
\[
T(x) = \left\{
\begin{array}{ll}
x-10 & \mbox{ if } 0 \leq x < 10 \\
0 & \mbox{ if } 10 \leq x < 100 \\
x-100 & \mbox{ if } 100 \leq x < 200 \\
100 & \mbox{ if } 200 \leq x < 700 \\
x-600 & \mbox{ if } 700 \leq x \leq 710
\end{array}
\right.
\]
where $x$ represents calories of heat.
\begin{enumerate}
\item  If the number of calories is 5, then what is the temperature of the water?
\item  If the number of calories is 709, then what is the temperature of the water?
\end{enumerate}

\item  Suppose that a certain product has the following supply and demand functions.
\begin{eqnarray*}
\mbox{Demand: } & p = -4q+220 \\
\mbox{Supply: } & p = 15q+30
\end{eqnarray*}
Find the market equilibrium point.

\end{enumerate}

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