Braking distance The braking distance y in feetthat it takes for a car to stop on wet ,level pavement can be estimated by y = 1/9 x^2, where the x is the speed of the car in miles per hour Find the speed associated with with each braking distance.
(a.) 25 feet (b.) 361 (c.) 784
Y = (1/9)(X^2) = X^2/9.
a. Y = X^2/9 = 25 ft.
X^2/9 = 25,
Multiply both sides by 9:
X^2 = 225,
X = 15 Miles/hr.
post it.
To find the speed associated with each braking distance, you need to solve the equation y = 1/9 x^2 for x (speed of the car). Let's substitute the given braking distances into the equation and solve for x.
(a.) For a braking distance of 25 feet:
25 = 1/9 x^2
Multiplying both sides of the equation by 9, we have:
225 = x^2
Taking the square root of both sides, we get:
x = ±√225
x = ±15
So, for a braking distance of 25 feet, the speed associated with it can be either 15 miles per hour or -15 miles per hour. Since speed cannot be negative in this context, the answer is 15 miles per hour.
(b.) For a braking distance of 361 feet:
361 = 1/9 x^2
Multiplying both sides of the equation by 9, we have:
3249 = x^2
Taking the square root of both sides, we get:
x = ±√3249
x = ±57
So, for a braking distance of 361 feet, the speed associated with it can be either 57 miles per hour or -57 miles per hour. Since speed cannot be negative in this context, the answer is 57 miles per hour.
(c.) For a braking distance of 784 feet:
784 = 1/9 x^2
Multiplying both sides of the equation by 9, we have:
7056 = x^2
Taking the square root of both sides, we get:
x = ±√7056
x = ±84
So, for a braking distance of 784 feet, the speed associated with it can be either 84 miles per hour or -84 miles per hour. Since speed cannot be negative in this context, the answer is 84 miles per hour.