The height of a ball t seconds after it is thrown upward from a height of 5 feet and with an initial velocity of 64 feet per second is f (t) = -16t2 + 64t + 5. (a) Verify that f(1) = f(3). f (1) = ft f (3) = ft (b) According to Rolle's Theorem, what must be the velocity at some time in the interval (1, 3)? ft/sec Find that time. t = s

(a) f(1) = ft(3) = 53 ft

(b) t = 2.156 s

Step-by-step explanation:

The function for the height of the ball is:

(a) For t = 1s

For t = 3s

Therefore, f(1) = f(3)

(b) According to Rolle's Theorem, if the function yields the same height in two distinct points, there must be a stationary point between them, that is, a point where the velocity is zero.

The velocity function is found by differentiating the height function:

When the velocity is zero:

the highest percentage for deaths in construction from highest to lowest is as follows: falls, struck by objects, electrocution, and caught-in/between. these four are collectively known as fatal four.

in the case of falls, the type that is responsible for the overall highest death in the category is falls from roofs.

step-by-step explanation: