College Algebra 7th Edition

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

Chapter 1, Equations and Graphs - Chapter 1 Review - Exercises: 94

Answer

Interval: $[\sqrt[3]{\frac{6}{\pi}}, \sqrt[3]{\frac{9}{\pi}}]$

Work Step by Step

We know that the volume $V$ is restricted to fall between $8$ and $12$: $8 \leq\frac{4}{3}\pi r^{3}\leq 12$ We solve this inequality for $r$: $8*\frac{3}{4\pi} \leq r^{3}\leq 12*\frac{3}{4\pi}$ $\frac{6}{\pi}\leq r^{3}\leq\frac{9}{\pi}$ $\sqrt[3]{\frac{6}{\pi}}\leq r\leq\sqrt[3]{\frac{9}{\pi}}$ Interval: $[\sqrt[3]{\frac{6}{\pi}}, \sqrt[3]{\frac{9}{\pi}}]$
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