SOLUTION: A pile driver drives a post 9 feet into the ground on its first hit. Each additional hit drives the post 2/3 the distance of the prior hit.
a) find the total distance the post ha
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Question 447635: A pile driver drives a post 9 feet into the ground on its first hit. Each additional hit drives the post 2/3 the distance of the prior hit.
a) find the total distance the post has been driven after 4 hits.
b) what is the greatest distance the pole could be driven into the ground?
If you could help me with this problem, I would really appreciate it. Thanks.
Found 2 solutions by solver91311, edjones:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
First hit: 
.
Second hit: \ =\ 6)
Third hit: (9)\ =\ \frac{2}{3}(6)\ =\ 4)
Fourth hit: \left(\frac{2}{3}\right)(9)\ =\ \frac{2}{3}\left(\frac{2}{3}\right)(6)\ =\ \frac{2}{3}(4)\ =\ \frac{8}{3})
In general: 
-th hit: ^{n\,-\,1}(9))
John
My calculator said it, I believe it, that settles it
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
a)
9+6+4+ 8/3 = 65'/3 Easier than using the formula S[n}=a[1]((1-r^n)/(1-r)) where r=2/3, n=4, a[1]=9
.
b)
S=a[1]/(1-r)=9/(1-(2/3))
=9/(1/3)
=27'
.
Ed
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