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January 25th, 2009, 07:15 PM   #1
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Determine value of X and Y

Dear all,

Would appreciate some guidance for this question:

If q = ax + by and r = bx - ay, determine the value of:
[attachment=0:2v3b4rrt]equation.JPG[/attachment:2v3b4rrt]

Thank you.
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January 29th, 2009, 06:43 AM   #2
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Re: Determine value of X and Y

I think you should clarify your expression, what do your symbols mean?
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January 29th, 2009, 03:36 PM   #3
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Re: Determine value of X and Y

the question wants me to differentiate dq/dx with y treated as a constant and dx/dq with r treated as a constant.
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January 31st, 2009, 09:30 AM   #4
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If a, b and y are constant, differentiating the first equation gives dq/dx = a.

If a, b and r are constant, dr/dx = 0, so differentiation the second equation gives 0 = b - a dy/dx, and so dy/dx = b/a. Also, differentiating the first equation gives dq/dx = a + b dy/dx, so dq/dx = a + (b^2)/a, and so dx/dq = a/(a^2 + b^2). This assumes that a and b are not both zero, which would mean that q was zero and dx/dq undefined.
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