Question

PLEASEEEE HELPPPPP A flying disk is thrown into the air from a height of 25 feet at time t=0. The function that models this situation is h(t) = -16t2 + 75t + 25, where t is measured in seconds and h is the height in feet. Which values best describe the domain of the function in the context of the problem?

A. 0 ≤ t ≤ 5
B. 0 ≤ t ≤ 25
C. All real numbers
D. All positive integers

Answer 1

A)

Explanation:

Given function:

`h(t)=-16t^2+75t+25`

The domain (input values) will be the x-intercepts, so the values of t when h(t) = 0.

The quickest way to find these is to use the quadratic formula.

Quadratic Formula

`x=(-b \pm √(b^2-4ac) )/(2a)\quad\textsf{when}\:ax^2+bx+c=0`

`\implies t=(-75 \pm √(75^2-4(-16)(25)) )/(2(-16))`

`\implies t=(-75 \pm √(7225))/(-32)`

`\implies t=(75 \pm 85)/(32)`

`\implies t=5, t=-(5)/(16)`

Time cannot be negative.

When h(t) = 0, the disk will hit the floor.

Therefore, the domain is restricted to 0 ≤ t ≤ 5