SOLUTION: A typical car's stopping distance on dry pavement "d" in feet can be approximated by the function d= 0.034s2(squared) + 0.56s - 17.11. Where "s" is the sp

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: A typical car's stopping distance on dry pavement "d" in feet can be approximated by the function d= 0.034s2(squared) + 0.56s - 17.11. Where "s" is the sp      Log On


   

Question 303155: A typical car's stopping distance on dry pavement "d" in feet can be approximated by the function

d= 0.034s2(squared) + 0.56s - 17.11. Where "s" is the speed in miles per hour, of the car before braking.


A. How fast is the car going if it requires 100 feet for the car to stop after the brakes are applied?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
A typical car's stopping distance on dry pavement "d" in feet can be approximated by the function
d= 0.034s2(squared) + 0.56s - 17.11. Where "s" is the speed in miles per hour, of the car before braking.

A. How fast is the car going if it requires 100 feet for the car to stop after the brakes are applied?
.
Replace d with 100 and solve for s:
d= 0.034s^2 + 0.56s - 17.11
100= 0.034s^2 + 0.56s - 17.11
0= 0.034s^2 + 0.56s - 117.11
Solve using the quadratic formula. Doing so yields:
s = {51.0, -67.5}
Toss out the negative solution -- doesn't make sense.
so, the car was moving at 51 mph.
.
Details of quadratic formula:
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 0.034x%5E2%2B0.56x%2B-117.11+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280.56%29%5E2-4%2A0.034%2A-117.11=16.24056.

Discriminant d=16.24056 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0.56%2B-sqrt%28+16.24056+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280.56%29%2Bsqrt%28+16.24056+%29%29%2F2%5C0.034+=+51.0287914140646
x%5B2%5D+=+%28-%280.56%29-sqrt%28+16.24056+%29%29%2F2%5C0.034+=+-67.4993796493587

Quadratic expression 0.034x%5E2%2B0.56x%2B-117.11 can be factored:
0.034x%5E2%2B0.56x%2B-117.11+=+0.034%28x-51.0287914140646%29%2A%28x--67.4993796493587%29
Again, the answer is: 51.0287914140646, -67.4993796493587. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.034%2Ax%5E2%2B0.56%2Ax%2B-117.11+%29