Question

A batter strikes a baseball. the equation y = -0.005^2 +0.7x + 3.5 models its path, where x is the horizontal distance, in feet, the ball travels and y is the height, in feet, of the ball. how far from the batter will the ball land? Round to the nearest tenth of afoot.

a. -4.8 feet

b. 4.8 feet

c. 145.9

d. 144.8

Answer 1

(D)144.8 feet

Explanation:

Given the equation which models the path of the baseball

`y = -0.005x^2 +0.7x + 3.5`

where x is the horizontal distance, in feet, the ball travels and y is the height, in feet, of the ball.

To determine how far from the batter the ball will land, we determine the distance x at which the height, y=0.

`y = -0.005x^2 +0.7x + 3.5=0`

`-0.005x^2 +0.7x + 3.5=0`

We use the quadratic formula to solve.

In the quadratic equation above, a=-0.005, b=0.7, c=3.5

`x=(-b\pm√(b^2-4ac) )/(2a) \\=(-0.7\pm√(0.7^2-4(-0.005*3.5)) )/(2*-0.005) \\=(-0.7\pm√(0.49+0.07) )/(-0.01)\\=(-0.7\pm√(0.56) )/(-0.01)\\x=(-0.7+√(0.56) )/(-0.01) \: or\: x=(-0.7-√(0.56) )/(-0.01)\\x=-4.83 \: or\: x=144.83`

Since x cannot be negative, x=144.8 feet to the nearest tenth of a foot.

The correct option is D.