Answer:
The time interval is [tex]1\leq t\leq 3[/tex] 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 [tex]h(t)=-16t^2+64t+4[/tex] 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 [tex]h(t)=-16t^2+64t+4[/tex]
Where, t is time in seconds and h is the height.
We can solve the equation by putting h(t)=52
[tex]-16t^2+64t+4\geq 52[/tex]
[tex]-16t^2+64t+4-52\geq 0[/tex]
[tex]-16t^2+64t-48\geq 0[/tex]
[tex]-t^2+4t-3\geq 0[/tex]
[tex]-t^2+3t+t-3\geq 0[/tex]
[tex]t(-t+3)-1(-t+3)\geq 0[/tex]
[tex](t-1)(-t+3)\geq 0[/tex]
[tex]t=1,3[/tex]
Therefore, The time interval is [tex]1\leq t\leq 3[/tex] 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.
Answer:
For anyone who is lazy to read question above, it's D
Explanation:
Edg2020
