Is this answer correct?

A basketball is dropped from an original height of 9 feet and on each bounce, bounces up 2/3 the distance it fell. How far will it have traveled by the time it hits the ground the 4th time?

The total distance it will have traveled by the fourth time is 34.33 feet.

Question

Is this answer correct? 

A basketball is dropped from an original height of 9 feet and on each bounce, bounces up 2/3 the distance it fell. How far will it have traveled by the time it hits the ground the 4th time? 



	The total distance it will have traveled by the fourth time is 34.33 feet.

anonymous · Answer

(2/3) of 9=6
(2/3) of 6=4
(2/3) 0f 4=2.66
9+6+4+2.66= 21.66'
I am pretty sure that this is the answer, but a second opinion wouldn't be a bad idea.

anonymous · Answer

Distance traveled = 9 + 2[9(2/3) + 9(2/3)^2 + 9(2/3)^3 ] = 34.33

By the way, if you need to find the distance traveled by the time it stops, here's the answer:

Distance traveled = 9 + lim(n→α)⁡ 2[9(2/3) + 9(2/3)^2 + 9(2/3)^3+⋯+〖9(2/3)〗

^r+⋯9(2/3)^n ]

= 9 + 18[lim(n→α)⁡ ((1-(2⁄3)^n)/(1-2⁄3)) ]

= 9 + 18[1/(1⁄3)] = 9 + 18 * 3 = 63

anonymous · Answer

You're welcome!! Xo!

anonymous · Answer

@britneyspears could you help me with another problem?

anonymous · Answer

Yeah sure. Just message me the question.

anonymous · Answer

Sent it to you!