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: 24

Answer

$S=9pq$

Work Step by Step

$S$ is directly proportional to the product of $p$ and $q$ so the equation that relates the variables is: $A=k(pq)$ where k = constant of proportionality. If p = 4 and q = 5, then S = 180. Substitute these values into the equation above to have: $S=k(pq) \\180 = k(4)(5) \\180=20k \\\frac{180}{20}=k \\9=k$ The constant of proportionality is $9$. Thus, the equation that relates S, p, and q is: $S=9pq$
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