Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 3 - 3.1 - Quadratic Functions and Models - 3.1 Exercises - Page 249: 66


$x=21$ $y=7$ $P=147$

Work Step by Step

Quadratic function in standard form: $y=a(x-h)^2+k$, in which $(h,k)$ is the vertex. And, the maximum (or the minimum) occurs at the vertex. Two positive real numbers: $x$ and $y$ $x+3y=42$ $x=42-3y$ Product: $P=xy$ $P=(42-3y)y=42y-3y^2$ $P=-3(y^2-14y)$ $P=-3[(y^2-2(7)y+7^2)-7^2]$ $P=-3(y-7)^2+147~~$ (Notice that: $a=-3$. Parabola opens downward.) So the vertex $(7,147)$ is the maximum. $x=42-3(7)=21$
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