Question

The police department uses a formula to determine the

speed at which a car was going when the driver applied the
brakes, by measuring the distance of the skid marks. The
equation d = 0.0015r^2 + r models the distance, d, in feet
traveled after applying the brakes in a car moving
r miles per hour (r is the speed of the car).
If the distance the car traveled after applying the brakes
equals 88 feet, what, what was the speed of the car? *
*Round your answer to the nearest hundredth miles per hour.
Answer:
mph

Answer 1

9514 1404 393

Answer:

78.71 mph

Explanation:

You're looking for the solution to ...

d = 88

0.0015r^2 +r = 88

0.0015r^2 +r -88 = 0

Using the quadratic formula*, we find ...

r = (-1 +√(1² -4(0.0015)(-88)))/(2×0.0015)

r = (-1 +√1.528)/0.003 = 0.236123/0.003 = 78.7077

The speed of the car was about 78.71 mph.

_____

* The quadratic formula will also give a negative answer of about -745 mph, which is not relevant to the situation.