Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.8 - Inequalities - 1.8 Exercises - Page 90: 119

Answer

The interval is $[0, 3]$ $0\leq t \leq 3$

Work Step by Step

To find the interval, we can simply calculate when the ball will be at $h=32$ and all the values greater than the point will be $32ft$ or more above the ground. $h<128+16t-16t^2$ $-16t^2+16t+128=32$ $-16t^2+16t+96=0$ $-t^2+t+6=0$ $t^2-t-6=0$ $t_1=-2$ ; $t_2=3$ (time cannot be negative) $t=3$ So, the interval during which the ball will be at least $32ft$ above the ground is $[0, 3]$ $0\leq t \leq 3$
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