A metallurgist thas one alloy containing \( 32 \% \) aluminum and another containing \( 50 \% \) aluminum. How many pounds of each alloy must he use to make \( 55 \) pounds of a third alloy containing \( 42 \% \) aluminum? (Round to two decimal places if necessary.)
step \( 1 \) of \( 2 \) : Use the variables \( x \) and y to set up a system of equations to solve the given problem.
x+y=55
0.32x+0.5y=55*0.42
Determine the following limits. If infinite, specify \( \infty \) or \( - \infty \) . If an answer does not exist, explain why. (NO POINTS WILL BE GIVEN IF A TABLE OF VALUES IS USED) b. \( \lim _ { x \rightarrow 1 ^ { + } } [ \frac { x } { x - 1 } + \frac { 1 } { \ln ( x ) } ]\)
9. A board game company models the profit on its latest board game using the quadratic relation
\( P = - 2 x ^ { 2 } + 28 x - 90 , \) where \( x \) is the number of games it produces in hundred thousands and \( P \) is the profit in millions of dollars.
a) What are the break-even points for the company?
b) What is the maximum profit that the company can earn?
