Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.1 Four Ways to Represent a Function - 1.1 Exercises - Page 22: 60

Answer

$h = \frac{8}{3w}$

Work Step by Step

Since length is twice the width we can create a variable for length $l$ and set it to $2w$ where $w$ is the width. $l = 2w$ Knowing that the formula for the volume of a box is $V = lwh$, we can plug in the given $8ft^{3}$ for the volume and $2w$ for the length. This gives us $8ft^{3} = 3wh$ and since we want the height in terms of the width, we just have to isolate h on one side of the equation by dividing $3w$ over to the other side giving us $h = \frac{8}{3w}$ as our final equation.
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