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: 17

Answer

$R = k \cdot \dfrac{P^2t^2}{b^3}$ where k = constant of proportionality

Work Step by Step

RECALL: (i) If the quantities (or variables) $x$ and $y$ are related by the equation $y=kx$, then $y$ is directly proportional to $x$, where $k$ is the constant of proportionality. (ii) If the quantities (or variables) $x$ and $y$ are related by the equation $y=\dfrac{k}{x}$, then $y$ is inversely proportional to $x$, where $k$ is the constant of proportionality. $R$ is given to be directly proportional to the product of $P^2$ and $t^2$ and inversely proportional to $b^3$ therefore the equation that expresses the given statement is: $R = k \cdot \dfrac{P^2t^2}{b^3}$ where k = constant of proportionality
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