## College Algebra (6th Edition)

Published by Pearson

# Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.7 - Page 432: 34

#### Answer

$72$ ergs

#### Work Step by Step

Solving Variation Problems (see p. 424) 1. $\ \$Write an equation that models the given English statement. 2. $\ \$Substitute the given pair of values into the equation in step 1 and find the value of k, the constant of variation. 3. $\ \$Substitute the value of k into the equation in step 1. 4. $\ \$Use the equation from step 3 to answer the problem's question. ----------- 1. Let $E_{k}$ be the kinetic energy (ergs), m the mass (grams) v the velocity (cm/s), $E_{k}$ varies jointly (directly) as $m$ and $v^{2},\ \qquad E_{k}=kmv^{2}$ 2. $36=k(8)(3^{2})$ $36=k(72)\qquad /\div 72$ $k=\displaystyle \frac{36}{72}=\frac{1}{2}=0.5$ 3. $E_{k}=\displaystyle \frac{1}{2}mv^{2}$ 4 $m=4, v=6, E_{k}=?$ $E_{k}=\displaystyle \frac{1}{2}(4)(6^{2})=72$ ergs

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