each time a ball bounces it returns to a height 2/3 the hight of the previous bounce. after the third bounce, the ball returns to a hight of 4ft. from what height was it dropped
Please identify the School Subject carefully, not your grade, so the right teachers read and answer your post.
Sra
anyone with any thoughts
9 feet
9 X 2/3 = 6 feet
6 X 2/3 = 4 feet
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To determine the original height from which the ball was dropped, we can use the given information about the ball's bouncing behavior.
Let's break down the problem:
- After the first bounce, the ball reaches a height of (2/3) * h, where h represents the height from which it was dropped.
- After the second bounce, the ball reaches a height of (2/3) * [(2/3) * h].
- After the third bounce, the ball reaches a height of (2/3) * [(2/3) * [(2/3) * h]] = 4 ft.
To find the original height, we need to solve the equation:
(2/3) * [(2/3) * [(2/3) * h]] = 4
To simplify the equation, let's solve it step by step:
1. Distribute the (2/3) term:
(2/3) * (2/3) * (2/3) * h = 4
2. Simplify the left-hand side:
(4/9) * (4/9) * h = 4
3. Combine the fractions:
(16/81) * h = 4
4. Multiply both sides by the reciprocal of (16/81), which is (81/16):
h = 4 * (81/16)
5. Calculate the right-hand side:
h = 20.25 ft
Therefore, the ball was dropped from a height of 20.25 ft.