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: 70


Yes, see explanations.

Work Step by Step

Step 1. Using the figure given in the exercise, we have $a=25, b=20$ and the equation of the archway can be written as $\frac{x^2}{625}+\frac{y^2}{400}=1, y\geq0$ Step 2. The best position for the truck is to drive with one side on the middle line and the upper right corner will be $(10,14)$ Step 3. For $x=10$, the equation in step-1 becomes $\frac{10^2}{625}+\frac{y^2}{400}=1$, which gives $y\approx18.33\ ft$ Step 4. As $18.33 \gt 17$, we conclude that the truck can pass under the archway without going into the other lane.
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