Question

Nate tosses a ball up a hill for his dog to chase. The path of the ball is modeled by the function y= -1/4x^2 + 33/5x where x is the ball's horizontal distance from Nate in feet and y is the ball's height in feet. The hill is modeled by the line y= 1/5x. How far does the ball travel horizontally before it hits the ground? Round your answer to one decimal place.

Answer 1

The ball travels horizontally for 165/4 feet before it hits the ground.

Step-by-step explanation:

To find how far the ball travels horizontally before it hits the ground, we need to find the x-coordinate at the point where the ball hits the ground. When the ball hits the ground, its height is 0. So, we set the function y = -1/4x^2 + 33/5x equal to 0 and solve for x:

0 = -1/4x^2 + 33/5x

0 = -1/4x(x-165/4)

x(x-165/4) = 0

x = 0 or x = 165/4

The ball travels horizontally for a distance of 165/4 feet before it hits the ground.