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: 8

Answer

When $x=40$, the value of $y$ is $12$.

Work Step by Step

$y$ varies directly so its equation is of the form $y=kx$. When $x=30$, $y=9$. Substitute these values into $y=kx$ to obtain: $y=kx \\9=k(30) \\\frac{9}{30}=\frac{k(30)}{30} \\\frac{3}{10}=k$ Thus, the direct variation is $y=\frac{3}{10}x$. To find the value of $y$ when $x=40$, substitute $40$ to $x$ in the equation above to obtain: $y=\frac{3}{10}x \\y=\frac{3}{10}(40) \\y=\frac{120}{10} \\y=12$
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