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

Answer:

25 feet

Step-by-step explanation:

Answer 2

Answer:

solving the quadratic equation it is found that the ball travels 26.4 feet horizontally before it hits the ground.

Step-by-step explanation:

the height of the ball,  after an horizontal distance of x feet, is given by

y (x)=  -1/4x2 + 33/4x

converting the fractions to decimel

y ($x$)= -0.25$x2$ + 6.6$x$

it hits the ground when

y($x$)= 0

then

$-0.25x2 + 6.6x = 0\\0.25x2 - 6.6x = 0\\x ( 0.25x - 6.6 )= 0\\x= 0,\\0.25x - 6.6 = 0\\0.25x = 6.6\\x = 6.6/0.25\\x = 26.4$

the ball travels 26.4 feet horizontally before it hits the ground.