Aball is dropped from a height of 24 inches above the ground. each time the ball hits the ground, it rebounds upwards 3 4 of the distance just fallen. how far will the ball have traveled vertically when it comes to rest?

  168 inches

Step-by-step explanation:

From the drop point to the point at which the rebounding ball is highest again is 24 + (3/4)·24 = 42 inches. Each successive drop and bounce adds 3/4 of the total travel from the previous high point. Hence the total distance is the sum of an infinite geometric series with first term 42 inches and a common ratio of 3/4. That sum is given for first term a1 and ratio r as ...

  S = a1·1/(1-r)

For the values given here, that sum is ...

  S = (42 in)(1/(1 -3/4)) = (42 in)·(4) = 168 in

The ball will have traveled 168 inches.

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2