Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.1 Review of Functions - 1.1 Exercises - Page 10: 24


Domain: $[0, \sqrt[3] \frac{3}{4\pi}]$ Independent Variable: $r$ (the radius of the balloon) Dependent Variable: $V$ (the volume of the balloon)

Work Step by Step

The volume of a balloon is given by $f(r) = \frac{4}{3}\pi r^3$. The maximum volume is $1$ $m^3$. The value of $r$ that yields us $1$ $m^3$ is $\sqrt[3] \frac{3}{4\pi}$, meaning that the radius can range from $0$ through $\sqrt[3] \frac{3}{4\pi}$. An independent variable is a variable we can change. Thus $r$, the radius of the balloon, is the independent variable. A dependent variable is a variable that changes when the independent variable variable changes. Thus, $V$, the volume of the balloon, is the dependent variable.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.