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anonymous

  • one year ago

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?

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  1. anonymous
    • one year ago
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    13.39 feet 15.00 feet <--my answer 4.46 feet 0.40 feet

  2. mathmate
    • one year ago
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    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.

  3. anonymous
    • one year ago
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    So, wasn't I right then? :)

  4. zepdrix
    • one year ago
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    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.

  5. zepdrix
    • one year ago
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    blah typos... bust out your calculator*

  6. anonymous
    • one year ago
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    2.092 is what I got :)

  7. anonymous
    • one year ago
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    @zepdrix

  8. zepdrix
    • one year ago
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    Hmm you shouldn't get less than 3 -_-

  9. zepdrix
    • one year ago
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    \[\large\rm S_{10}=3*((1-.8\wedge(10))\div(1-.8))\]

  10. anonymous
    • one year ago
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    ok :) Hold on.

  11. anonymous
    • one year ago
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    That's so weird! Now I got 2.077?? My calculator must be broken..

  12. anonymous
    • one year ago
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    Ok, so for the first part I got 3.32212255

  13. anonymous
    • one year ago
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    Then 1.25 for the second part

  14. zepdrix
    • one year ago
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    uhhhhh 0_o

  15. zepdrix
    • one year ago
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    (1-.8^(10))/(1-.8) = 4.463129... And then multiply by 3. I dunno what you're doing there :d weird

  16. anonymous
    • one year ago
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    13.389 :)

  17. anonymous
    • one year ago
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    Thanks<3!!!

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