A Super Happy Fun Ball is dropped from a height of 11 feet and rebounds 6/7 of the distance from which it fell. How many times will it bounce before its rebound is less than 1 foot?
It will bounce ___?_____ times before its rebound is less than 1 foot.
How far will the ball travel before it comes to rest on the ground?
It will travel ___?_____feet before it comes to rest on the ground.
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Answer:
16. 143.
Step-by-step explanation:
when dropped from 11ft it will bounce up to 11*(6/7)ft
after 2nd drop it will bounce up to 11*(6/7)²ft..
so after n drops it will bounce up to 11*(6/7)^n ft
for n=16, the height is less than 1ft.
the second part is a geometric progression infinite summation... with starting term 11, the common ratio 6/7
and taking the sum twice from the second term..
that is 11 + 11*(6/7) + 11*(6/7) + 11*(6/7)² + 11*(6/7)² + 11*(6/7)³ + 11*(6/7)³+ 11*(6/7)⁴ + 11*(6/7)⁴+ ...
= 2*{11/(1-6/7)}-11
=2*77 - 11
=154-11
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