Help with solving negative exponenets

[Sissy Devane]

The weight of an object follows this equation, W=Cr^(-2) where C is a constant and r is the distance that the object is from the center of the earth.
Solve the equation for W = Cr^(-2 )for r, then apply the following
The object is 100 pounds at sea level, find the value of C that makes the equation true ( sea level is 3,963 miles from the center of the earth).
Here is what I did to solve for r
1/r^2 = cw
1/?3963?^2 =(c) 100
I am not sure that this is correct, now I am totally lost about this problem.

 

[galactus]

\(\displaystyle W=\frac{C}{r^{2}}\)

\(\displaystyle r^{2}=\frac{C}{W}\)

\(\displaystyle r=\sqrt{\frac{C}{W}}\)

 

[galactus]

Since we want C and not r, the best thing to do is solve for C and plug in the knowns, r and W.

\(\displaystyle W=\frac{C}{r^{2}}\)

\(\displaystyle C=W\cdot r^{2}\)

Now, you are given W and r. Just plug them in.

 

[Sissy Devane]

what happens with the -2 exponenet...we just get rid of it?

 

[galactus]

\(\displaystyle Cr^{-2}\) is the same thing as \(\displaystyle \frac{C}{r^{2}}\)

 

[pka]

what happens with the -2 exponenet...we just get rid of it?

As a matter of definition \(\displaystyle x^{-1}=\frac{1}{x}\text{ if }x\not=0\).

So \(\displaystyle x^{-n}=\frac{1}{x^n}\) or \(\displaystyle x^{-2}=\frac{1}{x^2}\)

 

[Sissy Devane]

okay so this is what I have
W = c/r^2
c = w • r^2
c = 100 • (3,963)^2
c = 100 • 15,705,369
c = 1,570,536,900
Is this correct, if it is thank you very much for the help.

 

[Deleted member 4993]

okay so this is what I have
W = c/r^2
c = w • r^2
c = 100 • (3,963)^2
c = 100 • 15,705,369
c = 1,570,536,900 <<< Correct
Is this correct, if it is thank you very much for the help.