Aaron throws a ball off the top of a building. The path of the ball can be modeled by the equation where y is the height of the ball and x is the time in seconds since the throw. a. How long will it take for the ball to hit the ground? Show all work to receive credit b. How tall is the building?

Complete question is;

Aaron throws a ball off the top of a building. The path of the ball can be modeled by the equation y = -3x² + 8x + 42 where y is the height of the ball and x is the time in seconds since the throw.

A. How long will it take for the ball to hit the ground? Show all work to receive credit.

B. How tall is the building?

A) 5.305 seconds

B) 42

Step-by-step explanation:

y = -3x² + 8x + 42

A) when the ball hits the ground, the height will be zero.

Thus;

-3x² + 8x + 42 = 0

Using quadratic formula, we have;

x = [-8 ± √(8² - 4(-3 × 42))]/2(-3)

x = (-8 - √568)/-6 or (-8 + √568)/-6

x = 5.305 or -2.369

We will pick the positive one.

Thus;

Time it will take to hit the ground ia;

x = 5.305 seconds

B) To find out how tall the building is, we will input a time of x = 0. This is because before throwing the ball from the top, the time of motion is zero.

Thus;

y = -3(0)² + 8(0) + 42

y = 42

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.