College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 3 - Section 3.6 - Variation - 3.6 Exercises: 4

Answer

$d=\frac{1}{4\pi nr^2}$, means that $d$ varies inversely with $n$ and also with the square of $r$, and the constant of this variation is $\frac{1}{4\pi}$

Work Step by Step

The general equation for inverse variation is $y=\frac{k}{x}$, where k is the constant of this variation. Here, $d=\frac{1}{4\pi nr^2}=\frac{1/4\pi}{nr^2}$, means that $d$ varies inversely with $n$ and also with the square of $r$. As both $n$ and $r^2$ are in the denominator there will be an inverse variation between $d$ and $n$; $d$ and $r^2$. In the numerator $\frac{1}{4\pi}$ is a constant, this will be the constant of the variation. Therefore, we can say that the distance traveled by a gas atom varies inversely with the square of its radius and with the number of atoms per unit volume.
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