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

answer: he is 272195

step-by-step explanation: all you have to do is multiple 3535 and 77 and it equals 272195

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4