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Fanduekisses

  • one year ago

What am I doing wrong?? pls help!

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  1. Fanduekisses
    • one year ago
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  2. Fanduekisses
    • one year ago
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    I came up with this...?\[\sum_{n=0}^{4}27(\frac{ 1 }{ 9 })^{n}\]

  3. Fanduekisses
    • one year ago
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    so I'll have to find the sum then square that???

  4. Fanduekisses
    • one year ago
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    idk I thought I got it but then I checked the answer key and It wasn't :(

  5. jim_thompson5910
    • one year ago
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    You square first, then sum \[\Large (A+B)^2 \ne A^2 + B^2\]

  6. Koikkara
    • one year ago
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    hmm, i don't remember how to do it that way... I tried this way, The area of the 1st square = \(27^2 \) After \(÷ 9 \) the area of the center square would be \((27^2)/9\) If repeat once, the area would be\( ((27^2)/9) /9 \) Then if repeat three times, the area would be \((27^2)/(9^4)\)...\(right~~ ?\)

  7. jim_thompson5910
    • one year ago
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    and also, 27^2 is not included because the whole 27x27 square isn't shaded

  8. Fanduekisses
    • one year ago
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    wait, still something weird...

  9. Fanduekisses
    • one year ago
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    the answer should be 273.88

  10. Koikkara
    • one year ago
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    @Fanduekisses i tried this way, In the first step it is applied to an area of 27². and for The 2nd Box, (1/9) of the area to which it is applied. now looking at the second step to the remaining area: 27²-(1/9)27² = (8/9)27². Let us consider, previous unshaded area as A, then an area (1/9)A is added to the shaded area and A-(1/9)A=(8/9)A is left still unshaded. So the shaded areas are: (1/9)27² + (1/9)(8/9)27² + (1/9)(8/9)²27² + (1/9)(8/9)³27² = ? Alternatively, the shaded areas form a Geometric Sequence with a common ratio of (8/9). So the shaded area after 4 steps is just: 27² - (8/9)⁴27² = ? i think so...

  11. Fanduekisses
    • one year ago
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    I thought I had to us sum of finite geometric series or so, that's what the chapter is about.

  12. Fanduekisses
    • one year ago
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    So the common ratio is actually 8/9? not 1/9?

  13. Fanduekisses
    • one year ago
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    :(

  14. jim_thompson5910
    • one year ago
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    hmm well I thought it was 8/9, but I keep getting this S = a*(1-r^n)/(1-r) S = 81*(1-(8/9)^6)/(1-8/9) S = 369.406035665294 but it's not the answer your book is saying

  15. Fanduekisses
    • one year ago
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    :( so confusing. The chapter was on geometric sequences and series.

  16. Fanduekisses
    • one year ago
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    I thought the common ratio was 1/9.

  17. Fanduekisses
    • one year ago
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    if 273.88 is the area of the shaded region, then the sum would have to be around 16?

  18. jim_thompson5910
    • one year ago
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    each smaller square is 1/9 of the area of the previous bigger square but there are 8 smaller squares added each time, so that's why we get 8*(1/9) = 8/9

  19. Fanduekisses
    • one year ago
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    How is it related to the topic, geometric series and sequences then? how would I use the summation stuff?

  20. jim_thompson5910
    • one year ago
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    you started off with the first term of 81. The largest square area in the center then you add on 8 squares each 3*3 = 9 square units there are 8 of these smaller squares, so 8*9 = 72 square units is added on first term = 81 second term = 72 common ratio = 72/81 = 8/9

  21. jim_thompson5910
    • one year ago
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    this pattern repeats where the next term (the sum of the smallest squares in figure 3) is 64 64/72 = 8/9 and so on

  22. Fanduekisses
    • one year ago
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    ohhhh my God, I was focusing more on the side than on the area!

  23. Fanduekisses
    • one year ago
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    So using the sum of finite geometric series: \[\frac{ 27(1-(\frac{8 }{ 9 })^4 )}{ 1-\frac{ 8 }{ 9 } }= 273.88\]

  24. Fanduekisses
    • one year ago
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    :D

  25. jim_thompson5910
    • one year ago
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    first term isn't 27

  26. Fanduekisses
    • one year ago
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    haha yeah I meant 81

  27. jim_thompson5910
    • one year ago
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    and you're going to have n = 6 because the problem is showing 3 cases (n=1, n=2, n=3) already and they say repeat the pattern 3 more times

  28. Fanduekisses
    • one year ago
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    ohh ok thanks so much!

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