A stone is thrown straight down from a tall building. The relation h = 150 - 5t - 5t^2 approximates its path, with h in metres and t in seconds.
a) How tall is the building?
b) Factor the right side of the equation fully.
c) When does the stone hit the ground?

a) The building is 150 m tall

b) h(t)=-5(t+6)(t-5)

c) The stone hits the ground at 5 seconds.

Step-by-step explanation:

Function Models

The path of a stone thrown down from a tall building is modeled by the function:

Where h is the height in meters and t is the time in seconds after the stone is thrown.

a) To find the height of the building, we set t=0 because it's the moment when the stone is thrown and has the same height as the building:

The building is 150 m tall

b) The function is

Factoring out -5:

Rearranging:

To factor the polynomial in parentheses, we must find two numbers whose product is -30 and sum is 1. We can also use the quadratic formula to find the roots and factor later.

These numbers are 6 and -5, thus the function is:

c) The stone hits the ground when h=0:

The equation has two solutions:

t = -6

t = 5

The only feasible solution is t = 5, thus the stone hits the ground at 5 seconds.

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

step-by-step explanation: