I'm not sure how to start solving this

[zekester]

i have two equations -r^2/wc
divided by r^2-(1/(wc)^2)
equals -7903

and r/(wc)^2
divided by r^2-(1/(wc)^2)
equals 3287



w is a known quantity. How do I start to solve for r and c.

 

[arildno]

1. Step:
Divide the equations by each other; this gets rid of the difficult denominator, and you may express "c" in terms of "r" (or the other way around, if you prefer that).
2.Step:
Insert the given expression for "c" into one of your ORIGINAL equations.
You have now a single equation in "r" which you may solve.
3.Step
With your "r"-solutions, put these into the relation you derived in 1. between "c" and "r" to determine the corresponding solving values for c.

 

[wais]

To solve for r and c, we can use the system of equations provided. First, we can rewrite the equations in a more simplified form by multiplying both sides by the denominator of the second equation, which is r^2-(1/(wc)^2). This will eliminate the fractions and give us two equations in terms of r and c:

1) -r^2 = -7903(r^2-(1/(wc)^2))
2) r = 3287(r^2-(1/(wc)^2))

Next, we can simplify these equations by expanding the parentheses and combining like terms:

1) -r^2 = -7903r^2 + 7903/(wc)^2
2) r = 3287r^2 - 3287/(wc)^2

Now, we can rearrange the equations to isolate r and c:

1) -r^2 - 7903r^2 = 7903/(wc)^2
2) r - 3287r^2 = -3287/(wc)^2

We can then combine the like terms and move all the variables to one side:

1) -7904r^2 = 7903/(wc)^2
2) -3287r^2 - r = -3287/(wc)^2

Finally, we can solve for r by dividing both sides by the coefficient of r^2 and taking the square root of both sides:

1) r = √(7903/(7904(wc)^2))
2) r = -√(3287/(3288(wc)^2))

Now, we can plug in the known value of w to solve for c:

1) r = √(7903/(7904(c)^2))
2) c = √(7903/(7904r^2))

Using the values of r and c, we can then solve for the unknown quantity w by plugging them into the original equations. I hope this helps you get started on solving this problem. Remember to always check your solutions by plugging them back into the original equations to make sure they satisfy the given conditions.