Solve the equation w=Cr^-2 for r.
This is what I got so far....
w/C=r^-2
Then I think it's...
ok so I don't really know. I want to put w/C=1/r^2 but the r is still not alone and I'm not sure where I'd take it from there. Please help.
W = Cr^-2
W = C * 1/r^2
Multiply both sides by r^2
r^2 W = C
r^2 = C/W
I think your right. I got the same thing but for some reason I thought that the r is still not alone. Are you sure i don't go one step further and say that
r=sqrt(c/w)
what do you think?
Sorry, I forgot the last step.
r = +- (sqrt(C/W))
Thanks. one more question. Why did you do the +- thing?
To solve the equation w=Cr^(-2) for r, you can follow these steps:
1. Start with the equation w=Cr^(-2).
2. Divide both sides of the equation by C to isolate the term involving r: w/C = r^(-2).
3. Now, to eliminate the negative exponent, you can take the reciprocal of both sides of the equation (which means flipping the fraction): (w/C)^(-1) = r^(-2)^(-1).
4. Simplify the right side of the equation: (w/C)^(-1) = r^(2).
5. The left side of the equation is a negative exponent raised to the power of -1. Applying the exponent rule, this becomes: (w/C)^(-1) = 1/(w/C).
6. Simplify the left side of the equation: 1/(w/C) = r^(2).
7. To remove the fraction on the left side, you can multiply both sides of the equation by C/w: (C/w) * 1/(w/C) = (C/w) * r^(2).
8. Simplify the left side of the equation: (C/w) * 1/(w/C) = C * (w/C) = w/w = 1.
9. Now the equation becomes 1 = (C/w) * r^(2).
10. Divide both sides of the equation by (C/w) to isolate r^2: (C/w) * r^(2)/(C/w) = 1/(C/w).
11. Simplify the left side of the equation: r^2 = 1/(C/w).
12. Finally, take the square root of both sides of the equation to solve for r: sqrt(r^2) = sqrt(1/(C/w)).
13. The square root of r^2 simplifies to |r| (absolute value of r): |r| = sqrt(1/(C/w)).
Therefore, the solution for r (in terms of w and C) is r = sqrt(1/(C/w)). Note that |r| represents both positive and negative values of r.