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Expert: - 5/28/2011


Question
I am not sure how to set  up this problem at all, it is as follows:

Solve the equation w= Cr^(-2) for r.

What I got was r= √(2&c/w).

Then question number two is I I set this up right how would I solve for the following problem:
Suppose that that an object is 100 ounds when it is 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. To solve I am suppose to use the equation found in my first question.
I am very confused by this problem and if you can help it is greatly appreciated!

Answer
To solve for r, take w = Cr^(-2) and get r by itself.
First, divide both sides byC, giving w/C = r^(-2).
Since r^(-2) = 1/r^2, invert both sides, giving C/w = r^2.
Lastly, take the squareroot of both sides, giving r = √(C/w).
I'm not sure what the '2&' is doing in the answer.

Since w = 100 and r = 3,963, put them in the equation.
This gives 3963 = √(C/100).  This is the same as 3963 = √C / 10 since √100 = 10.
Multiplying both sides by 10 gives 39,630 = √C.
Squaring both sides gives C = 1,579,537,000.

In physice, this would probably be written as C = 1.58E6
since they usually narrow down answers to three digits
in scientific notation.

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