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anonymous

  • 5 years ago

Why can't the mean proportional be negative?

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  1. dumbcow
    • 5 years ago
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    "mean proportional" ?? not sure what you mean

  2. dumbcow
    • 5 years ago
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    like average ratio

  3. anonymous
    • 5 years ago
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    when a/b = b/d, then b is the mean proportional.

  4. anonymous
    • 5 years ago
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    oops, i mean a/b=b/c. not that it makes a difference.

  5. dumbcow
    • 5 years ago
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    oh ok , and to answer your question, not sure it can't be negative but it doesn't make a difference really a/b = b/c --> b^2 = ac --> b = +-sqrt(ac) usually ratios deal with lengths which by definition are always positive

  6. dumbcow
    • 5 years ago
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    example: say b = -3, a = 1, c = 9 -1/3 = -3/9 , the negative cancels out so the proportion is equivalent to 1/3 = 3/9

  7. anonymous
    • 5 years ago
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    ah....i see. i understood that the negative cancels out (which is why i sort of asked the question, because my textbook says mean proportional can't be negative). and is it true, ratios are defined to be positive things?Thenn that would make sense.

  8. anonymous
    • 5 years ago
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    Thanks for answering, btw. :) And i find it amusing we both have the same name almost, dumb cow and dumb duck :D

  9. anonymous
    • 5 years ago
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    But the question is still unanswered :/

  10. dumbcow
    • 5 years ago
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    i agree, sorry I don't have a sophisticated mathematical reason for you I have never considered it before

  11. anonymous
    • 5 years ago
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    oh. thanks anyhow :]

  12. dumbcow
    • 5 years ago
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    http://regentsprep.org/Regents/math/geometry/GP12/LMeanP.htm look at definition. It is just positive by definition

  13. anonymous
    • 5 years ago
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    oh!. i didn't know that.

  14. anonymous
    • 5 years ago
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    am i allowed to ask now, why they defined it to be positive? :P

  15. dumbcow
    • 5 years ago
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    It comes from the definition of a function y = +-sqrt(x) is not a function because it does not pass the vertical line test y = sqrt(x) is however, so the mean proportional is always positive

  16. anonymous
    • 5 years ago
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    ah. how come it has to be a function?

  17. dumbcow
    • 5 years ago
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    http://en.wikipedia.org/wiki/Geometric_mean#cite_note-1 it applies only to positive numbers, and it wouldn't make sense if the mean of positive numbers were negative

  18. anonymous
    • 5 years ago
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    I didn't comprehend fully.....but ah, thanks anyway. I'll keep asking why forever lol.

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