Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Review - Modeling with Functions - Problems - Page 241: 14

Answer

$P(x)=60x-x^2$

Work Step by Step

Suppose that the positive numbers are represented by $x$ and $y$, so $x+y=60$. We want to find $P=x\cdot y$ but only in terms of $x$, so we solve the first equation for $y$: $x+y-x=60-x$ $y=60-x$ Now, we replace that $y$ in $P=x\cdot y$: $P=x(60-x)$ $P=60x-x^2$ And that's our answer.
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