Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.12 - Modeling Variation - 1.12 Exercises - Page 127: 4

Answer

$z=0.5xy$

Work Step by Step

$z$ is directly proportional to the product of $x$ and $y$. This means that the variables are related by the equation $z=kxy$ where $k$ is the constant of proportionality. When x=4 and y=5, z=10. Substitute these values into the equation above to have: $z=kxy \\10=k(4)(5) \\10=20k \\\frac{10}{20}=k \\0.5=k$ The constant of proportionality is $0.5$ Therefore, the three variables are related by the equation $z=0.5xy$
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