Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 3 - Polynomial and Rational Functions - 3.6 Variation - 3.6 Exercises - Page 387: 11



Work Step by Step

$y$ varies inversely as $x$ therefore $y=\frac{k}{x}$ $y=10$ when $x=3$. Substitute these values into $y=\frac{k}{x}$ to obtain: $y=\frac{k}{x} \\10=\frac{k}{3} \\10(3)=\frac{k}{3}(3) \\30=k$ Thus, the equation for $y$ is $y=\frac{30}{x}$. To find the value of $y$ when $x=20$, substitute 20 to x in the equation above to obtain: $\require{cancel} \\y=\frac{30}{x} \\y=\frac{30}{20} \\y=\frac{3}{2}$
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