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anonymous

  • one year ago

Christina bought a yoyo from a company that claims that, with each retraction, the string rolls up by 70% of the original length. She sets up a tape measure and throws the yoyo 3 times. Her data are charted below. Throw Length of string (feet) 1 3 2 2.1 3 1.47 Christina 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. tkhunny
    • one year ago
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    1) Does70% prove to be correct? 2) Break out your best Geometric Series sum formula.

  2. anonymous
    • one year ago
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    idk??

  3. tkhunny
    • one year ago
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    Well, why not? What's 70% of 3?

  4. anonymous
    • one year ago
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    2.1

  5. anonymous
    • one year ago
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    ahhh 0.121060821

  6. tkhunny
    • one year ago
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    Okay, you now have 10 throws to throw. 3 + 3*.7 + 3*.7^2 +...+ 3*.7^9 Is that 10 throws? You have to believe.

  7. anonymous
    • one year ago
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    I believe ...!! praise the LAWD

  8. anonymous
    • one year ago
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    OMG THE SUM

  9. tkhunny
    • one year ago
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    Add them up: \(\dfrac{3 - 3*0.7^{10}}{1-0.7}\) This should be looking somewhat familiar.

  10. anonymous
    • one year ago
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    YES, IT DOES

  11. ckaranja
    • 29 days ago
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    This is a geometric series that follows a decreasing order. He simply should use \[ar^{n-1}\] In this case a=3, r=\[\frac{ 2.1 }{ 3 }\] and n=10 So, \[(3*\frac{ 2.1 }{ 3})^{9}\]

  12. tkhunny
    • 29 days ago
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    @ckaranja Except that you probably should reread the problem statement.

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