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Math Help - variation help

  1. #1
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    variation help

    h is inversely proportional to the third power of t and h=3/16 when t=4.

    Do you divide the #'s? Multipy? I am completely confused.
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  2. #2
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    h is inversely proportional to the third power of t and h=3/16 when t=4.

    Do you divide the #'s? Multipy? I am completely confused.
    I assume the aim of this exercise is to find h in terms of t then?

    So you know that h is inversely proportional to the third power of t.

    What does that mean? Let's turn it from maths-speak into real words.

    Well, it means that 1/h (the "inversely" bit) equals some number (call it k) times (the "proportional" bit) t^3 (the "third power of t" bit).

    (By the way, if a is PROPORTIONAL to b, then a = some number times b.)

    Now let's turn the real words back into maths again ;-)

    In maths,

    1/h = k * t^3

    Fantastic. Oh wait. We still need to know what k is. But we know that when t is 4, h is 3/16.

    So

    16/3 = k * (4)^3

    You can use that to find k.

    Then voila, you've got a relationship between h and t.

    I hope this helps.
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  3. #3
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    ok maybe this will help you explain it the way they are wanting it. I have been given the answer to the question now.
    so again the question states
    h is inversely proportional to the third power of t and h = 3/16 when t= 4.

    the answer I have here in the key is.....
    h= 12/t^3

    I am guessing that 12 would be the k that you were referring to earlier.

    I do have a question about the equations you set up. When you plugged in the h value of 3/16 I noticed that you flipped it when you put it in the equation. you put it as 16/3. Why is that?

    thanks for the help so far!
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  4. #4
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    I see. I did guess what the question was properly.

    We got as far as this earlier:

    1/h = k * t^3


    And we know that when t = 4, h = 3/16

    So let's substitute them

    I flipped h because we need 1/h in that equation, not h.

    1/ (3/16) = k * (4)^3

    So

    16/3 = k * 64

    16 = 3*64*k
    Work that out and you'll get k = 1/12

    So we've got our k. Putting it all together gives:

    1/h = 1/12 * t^3

    Now, they wrote the answer as h =, not 1/h =

    So we'll just rearrange it a little. There's nothing clever here - it's just rearranging it.

    h = 12 / (t^3)

    Sorted?
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  5. #5
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    ok let me try the next probelm and see how I do. thanks!
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  6. #6
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    You're welcome.

    Good luck.
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  7. #7
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    i got the next problem right. thanks so much! hopefully i can do the rest with no help!
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