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: 24

Answer

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.
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