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 91: 121

Answer

She can travel in the interval of $[0, 60]$ $0\leq v \leq 60$

Work Step by Step

We have to find range of speed where stopping distance is less than or equal to $240ft.$ It means, that we have to find : $d \leq 240$ $v+\frac{v^2}{20}\leq 240$ $v+\frac{v^2}{20}-240\leq 0$ We can write it as a quadratic equation and then solve it using interval notation: $v+\frac{v^2}{20}-240= 0$ $v^2+20v-4800=0$ $v_1=-80$ ; $v_2=60$ We have three possible interval: $(-\infty, -80]$ - Positive $[-80, 60]$ - Negative $[60, +\infty)$ - Positive Note, we're looking for interval where it is less than or equal to $0$, so the answer is second interval: $[-80, 60]$ But, we also have to note that we're looking for interval of range of speeds. and speed cannot be negative number. So the actual interval of speed will be: $[0, 60]$ $0\leq v \leq 60$
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