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

Answer:

(D)144.8 feet

Step-by-step 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

$x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a} \\=\dfrac{-0.7\pm\sqrt{0.7^2-4(-0.005*3.5)} }{2*-0.005} \\=\dfrac{-0.7\pm\sqrt{0.49+0.07} }{-0.01}\\=\dfrac{-0.7\pm\sqrt{0.56} }{-0.01}\\x=\dfrac{-0.7+\sqrt{0.56} }{-0.01} \: or\: x=\dfrac{-0.7-\sqrt{0.56} }{-0.01}\\x=-4.83 \: or\: x=144.83$

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

The correct option is D.