w=Cr^-2 solve for r
w = Cr^-2
w = C/r^2
wr^2 = C
r^2 = C/w
r = +/- sqrt (C/w)
Check mu work.
i came up with r=sqrt of C/w
what is the +/- for ? could it be either positive or negative?
ANYTIME you take the square root of something, you get a + or -. Let me show you why.
Take the square root of 4. That is 2. Now if we multiply +2 x +2 we get +4. BUT if we multiply -2 x -2 we also get +4. So the square root of 4 is +/- 2. Same with anything else because a minus number x a minus number = a + number.
To solve the equation w = Cr^(-2) for r, you can follow these steps:
Step 1: Start by isolating the variable r on one side of the equation. Since r is in the exponent, we need to apply exponent rules to eliminate it.
Divide both sides of the equation by C:
w/C = r^(-2)
Step 2: Inverse both sides of the equation by taking the reciprocal of each side:
1 / (w/C) = 1 / (r^(-2))
Simplifying further, we get:
C/w = r^2
Step 3: Take the square root of both sides of the equation to remove the exponent:
√(C/w) = √(r^2)
Step 4: Simplify the expression on the right side of the equation:
√(C/w) = |r|
Note: The absolute value signs are added because we take the square root of both sides, and the square root of a positive number has two possible solutions, positive and negative.
Step 5: Finally, to get the value of r, we can consider two cases:
Case 1: If you are looking for a positive value of r, you can drop the absolute value signs:
r = √(C/w)
Case 2: If you are looking for a negative value of r, you can include the negative sign:
r = -√(C/w)
Therefore, the solutions for r in the equation w = Cr^(-2) are r = √(C/w) and r = -√(C/w).