anonymous
  • anonymous
Finn bought a yoyo from a company that claims that, with each retraction, the string rolls up by 80% of the original length. He sets up a tape measure and throws the yoyo 3 times. His data are charted below. Throw Length of string (feet) 1 3 2 2.4 3 1.92 Finn wants to find the sum of the length of string after 10 throws. What is the sum of the lengths, rounded to the nearest hundredth?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
13.39 feet 15.00 feet <--my answer 4.46 feet 0.40 feet
mathmate
  • mathmate
With initial length of \(a_1\)=3 feet, and common ratio r= 0.8, the total length of n throws is given by the sum: \(S(n)=a_1(1-r^n)/(1-r)\) For example, after 1 throw, n=1, S(1)=3(1-0.8)/(1-0.8)=3 feet After 2 throws, \(S(2)=3(1-0.8^2)/(1-0.8)=5.4 feet.\) You can then calculate S(10) but putting n=10.
anonymous
  • anonymous
So, wasn't I right then? :)

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zepdrix
  • zepdrix
The example mathmate gave,\[\large\rm S_2=3\cdot\frac{1-(0.8)^2}{1-0}\]As was mentioned though, we want the sum of the first 10,\[\large\rm S_{10}=3\cdot\frac{1-(0.8)^{10}}{1-0.8}\]So ummmm, yes maybe you are right :o But our your calculator.
zepdrix
  • zepdrix
blah typos... bust out your calculator*
anonymous
  • anonymous
2.092 is what I got :)
anonymous
  • anonymous
@zepdrix
zepdrix
  • zepdrix
Hmm you shouldn't get less than 3 -_-
zepdrix
  • zepdrix
\[\large\rm S_{10}=3*((1-.8\wedge(10))\div(1-.8))\]
anonymous
  • anonymous
ok :) Hold on.
anonymous
  • anonymous
That's so weird! Now I got 2.077?? My calculator must be broken..
anonymous
  • anonymous
Ok, so for the first part I got 3.32212255
anonymous
  • anonymous
Then 1.25 for the second part
zepdrix
  • zepdrix
uhhhhh 0_o
zepdrix
  • zepdrix
(1-.8^(10))/(1-.8) = 4.463129... And then multiply by 3. I dunno what you're doing there :d weird
anonymous
  • anonymous
13.389 :)
anonymous
  • anonymous
Thanks<3!!!

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