Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.10 - Modeling with Functions - Exercise Set - Page 294: 33

Answer

The volume of the package in terms of the length of a side of its square front $x$ is $V=300{{x}^{2}}-4{{x}^{3}}\text{ cubic inches}$.

Work Step by Step

Consider the length plus girth of the provided package: $\text{300 inches}$ Now, the measurement of the length plus girth is the sum of the distance around that package and the longest side of girth $4x+y=300$ Or $y=300-4x$ The volume of provided package, $V=l\cdot w\cdot h$ Substitute $y$ for $l$ , and $x$ for $w$ and $h$ in the above equation $\begin{align} & V=y\cdot x\cdot x \\ & =y\cdot {{x}^{2}} \end{align}$ Substitute $300-4x$ for $y$ in the above equation $V=\left( 300-4x \right)\cdot {{x}^{2}}$ Or $V=300{{x}^{2}}-4{{x}^{3}}$ The required volume of the package in terms of the length of a side of its square front $x$ is, $V=300{{x}^{2}}-4{{x}^{3}}\text{ cubic inches}$.
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