Question

When a baseball is hit by a batter, the height of the ball, h(t), at time t, t=0, is determined by the equation h(t)=-16t^2+64t+4. If t is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?

Answer 1

For anyone who is lazy to read question above, it's D

Step-by-step explanation:

Edg2020

Answer 2

The time interval is
`1\leq t\leq 3` in which the height of the ball greater than or equal to 52 feet.

Step-by-step explanation:

We have given,When a baseball is hit by a batter, the height of the ball, h(t), at time t, t=0, is determined by the equation
`h(t)=-16t^2+64t+4` where t is time in seconds.

We have to find, If t is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?

Solution :

The equation represented as
`h(t)=-16t^2+64t+4`

Where, t is time in seconds and h is the height.

We can solve the equation by putting h(t)=52

`-16t^2+64t+4\geq 52`

`-16t^2+64t+4-52\geq 0`

`-16t^2+64t-48\geq 0`

`-t^2+4t-3\geq 0`

`-t^2+3t+t-3\geq 0`

`t(-t+3)-1(-t+3)\geq 0`

`(t-1)(-t+3)\geq 0`

`t=1,3`

Therefore, The time interval is
`1\leq t\leq 3` in which the height of the ball greater than or equal to 52 feet.

Now, We plot the graph of the given equation.

Refer the attached graph below.