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Proportional Variation

  1. Nov 2, 2005 #1

    dx

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    Consider the following situation :

    There are three variables A, B and C. (and i,j,k are constants )
    Keeping C constant, and varying the other two, you find that

    A = kB ------(1)

    Now, Keeping B constant, and varying the other two, you find that

    A = iC ------(2)

    I know that it follows from these two observations that

    A = jBC

    But I am not sure how we can algebraically deduce this from the equations (1) and (2).

    We get [tex] A^2 = ikBC [/tex]

    Presumably, [tex] ik = \sqrt{j}BC [/tex]
    But how do we deduce this?
     
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  3. Nov 2, 2005 #2

    Tide

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    You have

    [tex]A = k(C) \times B = i(B) \times C[/tex]

    where k and i are functions of C and B, respectively. If B and C are independent variables then the only way k(C)B and i(B)C can be equal is if k is proportional to C and i is proportional to B. Therefore, A = jBC.
     
  4. Nov 3, 2005 #3

    dx

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    Thanks for the help.
     
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