SOLUTION: In A = xy - (1 - z/4)r^2, solve for r in terms of the other variables, r a positive number.

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Question 252222: In A = xy - (1 - z/4)r^2, solve for r in terms of the other variables, r a positive number.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
A+=+xy+-+%281+-+z%2F4%29r%5E2 Start with the given equation.


A+-+xy+=+-+%281+-+z%2F4%29r%5E2 Subtract xy from both sides.


%28A+-+xy%29%2F%28-%281+-+z%2F4%29%29+=+r%5E2 Divide both sides by -+%281+-+z%2F4%29.


-%28A+-+xy%29%2F%281+-+z%2F4%29+=+r%5E2 Reduce.


sqrt%28-%28A+-+xy%29%2F%281+-+z%2F4%29%29+=+r Take the square root of both sides. Note: Since 'r' is positive, we don't have to worry about the negative square root.


So the answer is r=sqrt%28-%28A+-+xy%29%2F%281+-+z%2F4%29%29


Note: if the original problem was A+=+xy+-+%28%281+-+z%29%2F4%29r%5E2, then the answer is r=sqrt%28-%28A+-+xy%29%2F%28%281+-+z%29%2F4%29%29 which simplifies to r=sqrt%28-%284%28A+-+xy%29%29%2F%281+-+z%29%29