Precalculus (6th Edition) Blitzer

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

Chapter 9 - Section 9.1 - The Ellipse - Exercise Set - Page 967: 69


Yes, see explanations.

Work Step by Step

Step 1. Using the figure given in the exercise, we have $a=\frac{30}{2}=15\ ft, b=10\ ft$ and the equation can be written as $\frac{x^2}{225}+\frac{y^2}{100}=1, y\geq0$ Step 2. The best position for the truck to pass is to drive in the middle; we have the upper right corner point as $(\frac{8}{2},7)$ or $(4,7)$ Step 3. For $x=4\ ft$, the equation in step-1 becomes $\frac{4^2}{225}+\frac{y^2}{100}=1$, which gives $y\approx9.64\ ft$ Step 4. As $9.64 \gt 7$, we conclude that the truck can pass through under the bridge.
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