Question 136225
a.  Solve {{{w=Cr^(-2)}}} for {{{r}}}.  Remember {{{x^(-n)=1/x^n}}}, so {{{w=Cr^(-2)=C/r^2}}}.   Multiply both sides by {{{r^2}}}, divide both sides by {{{w}}}, then take the positive square root of both sides.


b. You first need to solve for C.  Use what we discovered in part a.  {{{w=C/r^2}}}.  Multiply both sides by C.  Substitute 100 for w and 3963 for r and do the arithmetic.  The result will be the value for C.


c.i.  The radius of the earth is given in miles, and you calculated C on that basis, so you need to convert the difference between Death Valley's elevation and sea level, 282 feet into miles, {{{282/5280}}}, and then <i>subtract</i> this value from 3963.  This is your new value for r.  Using the value for C from part b and this new value for r, use the original formula {{{w=C/r^2}}} to calculate the weight in Death Valley.


c.ii.  Same process, except that you need to calculate {{{20430/5280}}} and <i>add</i> that result to 3963 to get your radius.