Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 7 - Functions and Graphs - 7.5 Formulas, Applications, and Variation - 7.5 Exercise Set: 50

Answer

variation constant $=k=320$ equation of variation: $y=\frac{320}{x}$

Work Step by Step

$y$ varies inversely as $x$ so the variation is inverse. The equation of an inverse variation is of the form $y=\frac{k}{x}$ where $k$ is the constant of variation. To find the value of $k$ substitute the given values of $x$ and $y$ into $y=\frac{k}{x}$ to obtain: $$y=\frac{k}{x} \\40=\frac{k}{8} \\8(40) = k \\320=k$$ Thus, the equation of the variation is $y=\frac{320}{x}$.
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