Converting from Polar to Rectangular

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The discussion focuses on converting the polar equation r=3/(4cosθ-sinθ) into rectangular form. The key equations used include r=√(x²+y²), x=rcosθ, and y=rsinθ. The solution process involves eliminating the denominator, leading to the equation 4x-y=3. Participants confirm that this transformation is correct. The conversion successfully translates the polar coordinates into rectangular coordinates.
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Homework Statement



Convert r=3/(4cos\theta-sin\theta) to rectangular form

Homework Equations



r=\sqrt{}x^2+y^2

The Attempt at a Solution



4x-y=3 ?
 
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Relevant equations: x=rcos0, y=rsin0

All you need to do is get rid of the denominator and you're home free.
 
tachu101 said:

Homework Statement



Convert r=3/(4cos\theta-sin\theta) to rectangular form

Homework Equations



r=\sqrt{}x^2+y^2

The Attempt at a Solution



4x-y=3 ?
Yes, that's correct.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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