BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.7, Problem 117E
To determine

The range of speed for which the vehicle has stopping distance that do not exceed 240ft.

Expert Solution

Answer to Problem 117E

The range of speed is between 0 mi/h and 60 mi/h_.

Explanation of Solution

The formula for distance to stop the car is d=v+v220 with the stopping distance 240ft or less, where d is the distance measured in feet (ft) and v is the speed of the car measured in mi/h.

Substitute the value of 240ft for d in d=v+v220 and calculate the value of v as follows.

Since the stopping distance is 240ft or less, the formula d=v+v220 will become 240v+v220. That is,

240v+v220v+v2202400v2+20v48000

On further simplification,

v2+20v48000v2+(8060)v48000v2+80v60v48000

Further solve the equation as follows.

v(v+80)60(v+80)0(v+80)(v60)0

Thus, v80 and v60.

Since the speed cannot be negative, 0v60.

Therefore, the range of speed is between 0 mi/h and 60 mi/h_.

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