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chaotic_butterflies

  • one year ago

Geometric Series problem - Drake received 80 points on a project for school. He can make changes and receive one-tenth of the missing points back. He can do this 10 times. Create the formula for the sum of this geometric series, and explain your steps in solving for the maximum grade Drake can receive.

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  1. chaotic_butterflies
    • one year ago
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    @amistre64 if you're not busy could you possibly help me?

  2. amistre64
    • one year ago
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    show me your idea ... and lets see if we can correct it

  3. amistre64
    • one year ago
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    we may need to clarify this part: "He can make changes and receive one-tenth of the missing points back." what does it mean to you?

  4. chaotic_butterflies
    • one year ago
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    Does it mean that he can receive 1/10th of the 20 questions that he missed?

  5. chaotic_butterflies
    • one year ago
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    Pardon my slow reply, my laptop keeps freezing >~<

  6. amistre64
    • one year ago
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    it may mean, the 1/10 of the remaining points, after a submission.

  7. chaotic_butterflies
    • one year ago
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    So wait, you mean like he'll be tested on the 20 that he missed and if he got them all right, then he would only receive a potion of that score to be added to his original score? If that makes sense...

  8. amistre64
    • one year ago
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    sounds like that to me. but its pretty vague still say he gets all of them correct in the submission, he gets an extra credit of 20(.1) = 2 but then what about any subsequent submission seeing how he got them all correct on the second try?

  9. amistre64
    • one year ago
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    the grading scheme is rather senseless to me. he can obtain more extra credit by getting things wrong and resubmitting? it doesnt seem to be a well thought out question to me.

  10. amistre64
    • one year ago
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    Drake received 80 points on a project for school. He can make changes and receive one-tenth of the missing points back. make changes? say 1+1 = 3 and receive 1/10 of the missing points back? How is this grading?

  11. chaotic_butterflies
    • one year ago
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    That's the thing about virtual school, they focus so much on silly scenarios for their questions, and not enough time explaining the content in the lessons! I've tried to get help from the sources that have been offered to me, but it just doesn't seem to connect

  12. chaotic_butterflies
    • one year ago
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    Oh hold on a minute I might have an idea

  13. amistre64
    • one year ago
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    I have an idea too, but the question still makes no real sense we can determine the number of points remaining after each submission, if .10 is used, we have .90 remaining submission 0: 20 submission 1: 20 (.90) submission 2: (20 (.90))(.90) submission 3: (20 (.90)(.90))(.90) ... right?

  14. chaotic_butterflies
    • one year ago
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    I don't know if this has to do with anything but virtual school allows its students to retake tests if they need to, and they can reset it however many times until they have reached a certain amount of retakes. Each retake isn't influenced by the other... so if Drake is trying to get extra credit and he isn't satisfied with what he has, then he could reset and test himself on only the portion he got wrong - basically what all that rambling meant is that each retake probably doesn't influence another, I don't know if that's helpful or not it sounded better in my head

  15. chaotic_butterflies
    • one year ago
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    What you said sounds more logical than what I just spewed out.

  16. amistre64
    • one year ago
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    the thing is, it says he can make changes and receive .10 of the missing points back. it does not say: "up to" .10 it does not say: "correct changes" it does not say: anything at all to me

  17. amistre64
    • one year ago
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    the remaining points after 10 submissions looks to be 20(.90)^(10)

  18. amistre64
    • one year ago
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    but that isnt a series, its not a summation process that is being asked for.

  19. chaotic_butterflies
    • one year ago
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    And this is why it's so important to have a physical math teacher for high school math, I used to actually know what on earth I was doing...

  20. amistre64
    • one year ago
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    score0 = 80 score1 = 80 + 20(.10) score2 = 80 + 20(.10) + 20(.90)(.10) score3 = 80 + 20(.10) + 20(.90)(.10) + 20(.90)(.90)(.10) this is what its looking at in my head ...

  21. amistre64
    • one year ago
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    adding on 10% of the 90% thats left over from the previous submission

  22. amistre64
    • one year ago
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    it actually gets us to the same amount as the sequence setup

  23. chaotic_butterflies
    • one year ago
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    So should I go with that and assume the he gets the highest score on all of the tries to see what his maximun should be? I mean I guess I could do that but technically it's not creating a overall function

  24. chaotic_butterflies
    • one year ago
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    Sequence setup?

  25. amistre64
    • one year ago
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    its creating it, you just have to see it for what it is. we an form a function from it

  26. amistre64
    • one year ago
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    sequence is a list series is a summation of the terms in a list.

  27. chaotic_butterflies
    • one year ago
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    I understand that much, but I don't know what you're meaning

  28. amistre64
    • one year ago
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    20(.90)^n gives us a list of values depending on n 20(.90)^10 = 6.97 which is the remaining points that cannot be claimed since its been submitted 10 times.

  29. amistre64
    • one year ago
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    100 - 6.97 is the maximum score they can obtain.

  30. amistre64
    • one year ago
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    the actual score process: score1 = 80 + 20(.10)(.90)^0 score1 = 80 + 20(.10)(.90)^0 + 20(.10)(.90)^1 score2 = 80 + 20(.10)(.90)^0 + 20(.10)(.90)^1+ 20(.10)(.90)^2 each score is a term, but part of it is also the summation of a geometric series. score n = 80 + 20(.10)(.90)^0 + 20(.10)(.90)^1+...+ 20(.10)(.90)^(n-1) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ this is a geometric series

  31. amistre64
    • one year ago
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    do you know the formula for a geometric series?

  32. chaotic_butterflies
    • one year ago
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    No Sir (or M'am)

  33. amistre64
    • one year ago
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    then all this harder processing has been rather in vain dont you think ..

  34. amistre64
    • one year ago
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    find the formula for the sum of a geometric series for me ..

  35. chaotic_butterflies
    • one year ago
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    If you're asking me if I don't understand anything that you've shared with me, I've gotten the basic gist of it. I'll go look for that formula.

  36. amistre64
    • one year ago
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    our initial score is 80, which means there is 20 points missing we submit it and our score goes from 80, to 80 + 20(.10), and there is 20(.90) points left to plunder thru we submit it again and our score goes from 80 + 20(.10), to 80 + 20(.10) + 20(.90)(.10) and there is 20(.90)(.90) points left to plunder thru we submit it again and our score goes from 80 + 20(.10) + 20(.90)(.10) to 80 + 20(.10) + 20(.90)(.10) + 20(.90)(.90)(.10) and there is 20(.90)(.90)(.90) points left to plunder thru etc etc etc

  37. chaotic_butterflies
    • one year ago
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    I found yhe formula I think and it's terrifying

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  38. amistre64
    • one year ago
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    lol, that A formula, but thats the summation of an arithmetic series we want:\[S=g_1\frac{1-r^n}{1-r}\]

  39. chaotic_butterflies
    • one year ago
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    That's a little less scary but what do the letters stand for ?

  40. amistre64
    • one year ago
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    g1 is a constant term, its a common factor among the setup forget the 80, what is the common factor of the rest of it?

  41. chaotic_butterflies
    • one year ago
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    1/10...?

  42. amistre64
    • one year ago
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    80 + 20(.10)(.90)^0 + 20(.10)(.90)^1+...+ 20(.10)(.90)^(n-1) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ each term in the underlined part has 20(.10) in common, we can factor them out 80 + 20(.10) [(.90)^0 + (.90)^1+...+ (.90)^(n-1)] ^^^^^^^^^^^^^^^^^^^^^^^^^^ this is our series in terms of its ratio g1 = 20(.10) what is r?

  43. chaotic_butterflies
    • one year ago
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    I've gotten to the point where I have to say the dreaded "I have no idea.."

  44. amistre64
    • one year ago
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    hint: ratio starts with an 'r' the setup in terms of our common ratio is: (.90)^0 + (.90)^1+...+ (.90)^(n-1) what is now common among this?

  45. chaotic_butterflies
    • one year ago
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    (.90)

  46. amistre64
    • one year ago
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    correct :) so, g1 = 20(.10) r = .90 what is n?

  47. amistre64
    • one year ago
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    n = 1-, the number of submission we are allowed to make ... \[score_{n}=80+g_1~\frac{1-r^n}{1-r}\] \[score_{10}=80+20(.10)\frac{1-.90^{10}}{1-.90}\] which is the same value as the more simpler route: \[score_{10}=100-20(.90)^{10}\]

  48. amistre64
    • one year ago
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    n=10

  49. amistre64
    • one year ago
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    im going to run an errand now, so good luck, ask about what it is you are still concerned with.

  50. chaotic_butterflies
    • one year ago
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    Alright, thank you very much!

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