College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Focus on Modeling - Modeling with Functions - Problems: 3

Answer

$V(w)= \frac{1}{2}w^{3}, w\gt 0$

Work Step by Step

We are told that the box has a height half the width ($h=0.5w$). We also know that the base is square ($l=w$). Thus the volume is: Volume=$l*w*h=w*w*0.5w=0.5w^3=\frac{1}{2}w^3$ We restrict $w>0$ to avoid negative sides.
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