Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 9 - Mid-Chapter Check Point - Page 1000: 31


No, see explanations.

Work Step by Step

Step 1. Based on the given conditions, assume the center of the road is the origin. We can write the equation of the ellipse as $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with $a=\frac{30}{2}=15, b=10$ Step 2. The truck has a width of 10 feet; its upper right corner will have coordinates of $(5, 9.5)$ Step 3. At $x=5$, we have $\frac{5^2}{15^2}+\frac{y^2}{10^2}=1$, which gives $y^2=\frac{800}{9}$. Thus $y\approx9.4\ ft$ which means that the truck with a height of $9.5\ ft$ will not be clear to pass.
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