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

T over x is your starting debut
add 40 from your original answer and divide by two
triplemente the second number and switch your trinomial by three

Answer 2

Answer:

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.