Question

Under certain conditions, the number of feet a car will skid after the brakes are fully applied is given by the function d(x)=0.05x2+x, where x is the speed of the car in miles per hour. For what values of x will the car skid at most 120ft ?

Answer 1

x ≤ 40 . . . miles per hour

Explanation:

You want to know the values of x for which d(x) = 0.05x² +x is at most 120.

Solution

d(x) ≤ 120 . . . . . . . . the required limit

0.05x² +x ≤ 120 . . . . . substitute the expression for d(x)

x² +20x -2400 ≤ 0 . . . . . multiply by 20, subtract 2400

(x -40)(x +60) ≤ 0 . . . . . . . . factor. Factors are zero for x=40, x=-60.

The product will be negative for x-values between the zeros:

-60 ≤ x ≤ 40

We only care about positive values of x:

0 ≤ x ≤ 40 . . . . . miles per hour