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:

50 min

step-by-step explanation:

they will be decreasing both their times in half

60 / 2 = 30

40/2 = 20

30 + 20 = 50

y=mx+b

step-by-step explanation:

m is slope, b is y-intercept