## Intermediate Algebra (6th Edition)

Published by Pearson

# Chapter 6 - Section 6.7 - Variation and Problem Solving - Exercise Set: 18

#### Answer

$k=4$, $y=\frac{4}{x}$

#### Work Step by Step

If y varies inversely as x, we know that the variables x and y can be related by the function $y=\frac{k}{x}$, where k is the constant of proportionality. If $y=\frac{1}{10}$ when $x=40$, then we know that $\frac{1}{10}=\frac{k}{40}$. Multiply both sides by 40. $k=\frac{40}{10}=4$ Therefore, the constant of variation is $k=4$ and the inverse variation equation is $y=\frac{4}{x}$.

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