Answer:
The ball is higher than 10 feet off the ground when the time is between 2 to 5 seconds
Explanation:
In the above question, we are given the equation:
h(t) =-t²+7t.
We are asked to find the time (t) when the ball will be higher than 10 feet.
h(t) = height = 10 feet.
So we have:
10 = -t² + 7t
t² - 7t + 10 = 0
We have a quadratic equation hence we factorise.
t² - 5t - 2t + 10 = 0
(t² - 5t) +(2t - 10)= 0
t(t - 5) + 2 (t - 5) = 0
(t - 2) (t - 5) = 0
t - 2 = 0, t = 2
t - 5 = 0, t = 5
t = 5 and t = 2
Therefore, the ball is higher than 10 feet off the ground when the time is between 2 to 5 seconds.