24. the function f(t) = -16t^2 +20t +4 gives the height of a ball, in feet, t seconds after it is tossed.
what is the average rate of change, in feet per second, over the interval [0.75, 1.25]

-16feet/second

Step-by-step explanation:

If the height or the ball is modelled nu the equation f(t) = -16t^2 +20t +4

The average rate of change is the velocity of the ball.

Velocity = {d(f(t)}/dt = -32t+20

The velocity of the ball over the interval [0.75, 1.25] can be gotten by taken the difference of the velocity at t = 0.75 from when t = 1.25

f'(t) = -32t+20

f'(0.75) = -32(0.75)+20

f'(0.75) = -24+20

f'(0.75) = -4ft/s

At t = 1.25s

f'(1.25) = -32(1.25)+20

f'(1.25) = -40+20

f'(1.25) = -20ft/s

Rate of change = f'(1.25) - f'(0.75)

Rate of change in height = -20-(-4)

Rate of change in height = -16ft/s

40 minutes

step-by-step explanation:

add the time and multiply by 2

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8