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: 63


$x=55$ $y=55$ $P=3025$

Work Step by Step

Quadric 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 $y$ $x+y=110$ $y=110-x$ Product: $P=xy$ $P=x(110-x)=110x-x^2=-x^2+110x$ $P=-(x^2-110x)$ $P=-[(x^2+2(55)x+55^2)-55^2]$ $P=-(x-55)^2+3025~~$ (Notice that: $a=-1$, so the parabola opens downward) So the vertex $(55,3025)$ is the maximum. $y=110-55=55$
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