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 - Page 488: 74



Work Step by Step

RECALL: When $y$ varies jointly as $x$ and $z$, the variation is represented by the equation $y=kxz$ where $k$ is the constant of variation. $y$ varies jointly as $x$ and $z$ so the equation of the variation is $y=kxz$ with $k$=constant of variation. To find the value of $k$, substitute the given values into $y=kxz$ to obtain: $$y=kxz \\\frac{3}{2}=k(2)(10) \\\frac{3}{2}=20k \\\dfrac{\frac{3}{2}}{20}=\frac{20k}{20} \\\frac{3}{2(20)}=k \\\frac{3}{40}=k$$ Thus, the equation of the variation is: $\color{blue}{y=\frac{3}{40}xz}$.
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