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June 18th, 2011, 10:46 PM   #1
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Variation Please Help!

Hello Everyone, I hope this is the right forum for this question. I had an instructor present a problem (well watched a video of it anyway), and I am not quite sure why she presented the problem the way she did, hopefully someone in here can help me understand. The problem is:

Find an equation of variation in which y varies jointly as x and z and inversely as the square of w, and y=105 when x=3, z=20, and w=2.

The problem was presented this way, and I am not sure why:

y=k * xz/w (y equals k times xz divided by w squared)

I realize that the formula states that:
y varies jointly as x and z if there is some positive constant k such that y=kxz
y varies inversely as the nth power of x if there is some positive constant k such that y=k/x^n (y equals k divided by x to the nth power)

I am wondering why she put the problem as she did, meaning why did she put xz over w? That is the only thing I am confused about, how did she know to put xz over w, and how would I know in a future problem like this? Is there a type of hierarchy in the different types of variation (direct, joint, inverse), and a specific formula to go by in this type of situation?
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June 22nd, 2011, 08:33 PM   #2
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How else could the equation y = k * xz/w have been described in words?
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