Rebecca's little sister lies for her to push her in the swing at the park in her neighborhood. The other day Rebeca pulled theswing back and let it go. She would have kept pushing,but she suddenly saw a friend at the other end of the park. THe wing traveled a total didtance of 10 feet before heading back the other way. Each swing afterwards was only 80% as long as the previous one. Find the total distance the swing traveled before it stopped.
2006-12-17 07:16:53 · 5 answers · asked by Leah 1 in Science & Mathematics ➔ Mathematics
How do i answer it using the formula A(sub)n =A(sub)1*r to the power of 1-n?
2006-12-17 07:39:36 · update #1
First she travelled 10 feet, then 8 feet, then 6.4 feet, etc.
The distance she travelled is a geometric series, where 0.8 is the ratio (r) and 10 is the first term (a).
The formula for the sum of an infinite geometric series is:
a/(1-r)
So the answer would be:
10/(1-0.8) = 10/0.2 = 50 feet.
2006-12-17 07:21:51 · answer #1 · answered by Jim Burnell 6 · 1⤊ 1⤋
The formula for this is:
(first term) / (1- ratio)
Substitute (fill in the terms) to get:
10 / (1-0.8) = 10 / 0.2
= 50 feet
To make sure that it works, you can break it down step by step:
She starts out going 10 feet.
Add 80% of 10 feet (+8 feet).
Then add 80 % of 8 feet (+6.4 feet).
Then add 80% of 6.4 feet (+5.12 feet).
80% of 5.12 = 4.096
80% of 4.096 = 3.2768
80% of 3.2768 = 2.62144
...etc. If you continued to do this until you got to 0, it would equal 50 feet. I hope this helps you out!
2006-12-17 15:31:18 · answer #2 · answered by Happy 3 · 0⤊ 0⤋
This is a Geometric Progression problem. Here's the key to how I solved it.
a= initial number.
r= ratio
What you have to find is the sum of n terms. Since there is no final value, this is a sum to infinity problem.
The sum to infinity is found using S(inf)= a/(1-r)
Here a=10; r= 0.80
Therefore---------------- S(inf) = 10/(1 - 0.80)
----------------------------- = S(inf) = 10/0.20
----------------------------- = S(inf) = 50
The total distance travelled by the swing after the girl left it is 50 feet.
2006-12-17 16:14:11 · answer #3 · answered by grizzlybear :P 2 · 0⤊ 0⤋
The swing swings 10 times before it stops.
1st-10
2nd-8
3rd-6.4
4th-5.12
5th-4.096
6th-3.2768
7th-2.62144
8th-2.097152
9th-1.6777216
10th-1.34217728
add it all together equals= 44.63129088
Or you can do it one more time to get a more exact amount.
multiply the 10th time by .80
Its really simple!
2006-12-17 15:28:56 · answer #4 · answered by Dominique-Duh! 3 · 0⤊ 0⤋
igmore the whole story thats wat makes it look so hard just focus on the numbers:)
2006-12-17 15:19:21 · answer #5 · answered by JaQ™ 2 · 0⤊ 3⤋