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Finding a formula of a math problem

  1. Oct 15, 2005 #1
    i dont know what to do for this question, what does it mean by A = 1 when x = 1 and y = 0 ??? do i just sub it in or what? is this some sort of equation in an equation thingy?


    The quantity A is proportional to X^2 and inversely proportional to (y-a)^3
    Find a formula for A given that A = 1 when x = 1 and y = 0
     
  2. jcsd
  3. Oct 15, 2005 #2

    Gokul43201

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    Please post such questions in the Coursework Forum, not here !

    First write A as a function of (x,y) using arbitrary constants. For instance if told that V is proportional to I, you can write the equation V=kI, where k is some constant.

    Next you are told that when you substitute the given values of x and y, you get a certain value of A. This helps determine the value of such a constant. In my example, if told that V = 5 when I = 2, I have 5 = 2k, which tells me that k=2.5. So my Original equation can be becomes V = 2.5I
     
    Last edited: Oct 15, 2005
  4. Oct 17, 2005 #3
    okay after following ur example, i have A=x^2, it's the inversely proportional part that i can't understand...
     
    Last edited: Oct 17, 2005
  5. Oct 20, 2005 #4

    Gokul43201

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    If you are told that A is inversely proportional to some z, then that is the same as saying that A is proportional to 1/z. Or A = k/z, where k is some constant.
     
  6. Oct 20, 2005 #5

    HallsofIvy

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    "The quantity A is proportional to X^2 and inversely proportional to (y-a)^3"

    A is "proportional" to B means A is just a constant times B: A= kB.

    A is "inversely proportional" to B means A is a constant time 1/B or is a constant divided by B: A= k/B.

    A is proportional to x2 and inversely proportional to (y-a)3 gives both: A= kx2/(y-a)3.

    " given that A = 1 when x = 1 and y = 0" means that if you replace A in the formula with 1, x with 1, and y with 0, it is still true. That is:
    1= k(12)/(0-a)3= -k/a3. You can use that to find k: k= -a3 (a was part of the original information but we are not given a specific value for a so all we can do is leave it in there.)
    Putting that value for k back into the original formula,
    A= -a3x2/(y-a)3.
     
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