cory drops a bouncing ball form a height of 50 ft and it rebounds to 90% of its previous height.find the total distance the ball will have travelled when it hits the ground for the fifth time

50 + .9 * 2 * 50 + .9^2*2*50 +.9^3*2*50 +.9^4 *2 * 50

= -50 +100 + 100 (.9^1 +.9^2 + .9^3 + .9^4)

-50 + geometric series g=100 n = 5, r = .9 in

Sum5 = 100(1-.9^4)/(1-.9)
= 100 (.3439)/.1 = 344
-50 + 344 = 294

An apple farmer went to town to sell a truck full of apples. At his first stop, he sold 1/3 of his apples. On the way to the next stop, he wrecked his truck and lost 1/3 of the remaining apples. Of those left, the farmer gave away 1/2 to some children. He then has 80 apples left. How many apples did the farmer have when he started his trip?

To find the total distance the ball will have traveled when it hits the ground for the fifth time, we need to calculate the distance traveled during each bounce and add them up.

Let's break down the problem step by step:

1. First, we should calculate the distance traveled during each bounce. The ball is dropped from a height of 50 ft and rebounds to 90% of its previous height. So, the distance traveled during each bounce is the sum of the height it falls from and the height it rebounds to.

First bounce: Distance = 50 ft (falling from 50 ft and rebounding to 45 ft)
Second bounce: Distance = 45 ft (falling from 45 ft and rebounding to 40.5 ft)
Third bounce: Distance = 40.5 ft (falling from 40.5 ft and rebounding to 36.45 ft)
Fourth bounce: Distance = 36.45 ft (falling from 36.45 ft and rebounding to 32.805 ft)
Fifth bounce: Distance = 32.805 ft (falling from 32.805 ft and rebounding to 29.5245 ft)

2. Next, we need to add up the distances traveled during each bounce to find the total distance. Calculate the sum of the distances of all five bounces.

Total distance = Distance (first bounce) + Distance (second bounce) + Distance (third bounce) + Distance (fourth bounce) + Distance (fifth bounce)

Total distance = 50 ft + 45 ft + 40.5 ft + 36.45 ft + 32.805 ft

Total distance = 204.755 ft

Therefore, when the ball hits the ground for the fifth time, it would have traveled a total distance of approximately 204.755 feet.