Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.7 - Variation and Problem Solving - Exercise Set - Page 397: 10


$9.9 \text{ miles}$

Work Step by Step

The variation model described by the problem is $ d=k\sqrt{e} ,$ where $d$ is the distance to the horizon and $e$ is the elevation of the observer. Substituting the given values in the variation model above results to \begin{array}{l}\require{cancel} 7.4=k\sqrt{36} \\\\ 7.4=k(6) \\\\ \dfrac{7.4}{6}=k .\end{array} Therefore, the variation equation is $ d=\dfrac{7.4}{6}\sqrt{e} .$ Using the variation equation above, then \begin{array}{l}\require{cancel} d=\dfrac{7.4}{6}\sqrt{64} \\\\ d=\dfrac{7.4}{6}(8) \\\\ d=9.8666666666666666666666666666667 .\end{array} Rounded to the nearest tenth, the distance to the horizon is $ 9.9 \text{ miles} .$
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