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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?
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.013.39 feet 15.00 feet <my answer 4.46 feet 0.40 feet

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0With initial length of \(a_1\)=3 feet, and common ratio r= 0.8, the total length of n throws is given by the sum: \(S(n)=a_1(1r^n)/(1r)\) For example, after 1 throw, n=1, S(1)=3(10.8)/(10.8)=3 feet After 2 throws, \(S(2)=3(10.8^2)/(10.8)=5.4 feet.\) You can then calculate S(10) but putting n=10.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So, wasn't I right then? :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1The example mathmate gave,\[\large\rm S_2=3\cdot\frac{1(0.8)^2}{10}\]As was mentioned though, we want the sum of the first 10,\[\large\rm S_{10}=3\cdot\frac{1(0.8)^{10}}{10.8}\]So ummmm, yes maybe you are right :o But our your calculator.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1blah typos... bust out your calculator*

anonymous
 one year ago
Best ResponseYou've already chosen the best response.02.092 is what I got :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Hmm you shouldn't get less than 3 _

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm S_{10}=3*((1.8\wedge(10))\div(1.8))\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's so weird! Now I got 2.077?? My calculator must be broken..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, so for the first part I got 3.32212255

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Then 1.25 for the second part

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1(1.8^(10))/(1.8) = 4.463129... And then multiply by 3. I dunno what you're doing there :d weird
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