SOLUTION: Solve for the r in the equation w=Cr^-2. To is the negative power the equation is raised to. then if an object is 100 pnds at sea level. find the value of C that makes the equation

Algebra ->  Radicals -> SOLUTION: Solve for the r in the equation w=Cr^-2. To is the negative power the equation is raised to. then if an object is 100 pnds at sea level. find the value of C that makes the equation      Log On


   

Question 324447: Solve for the r in the equation w=Cr^-2. To is the negative power the equation is raised to. then if an object is 100 pnds 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. Use the value of C to answer a place at 282 feet below sea level. and one at 20,320 above sea level. Please show me how to find these answers.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Part a: "Solve for (something)" means to do whatever is legal to get that something all by itself on one side of the equal sign (typically the left because we read left to right) and everything else on the other side.

w+=+Cr%5E%28-2%29


Remember that a%5E%28-2%29=1%2Fa%5E2, so the equation becomes:

w=C%2Fr%5E2

Multiply both sides by r%5E2




wr%5E2=C

And divide both sides by w

r%5E2=Cw

And finally take the square root of both sides. We only need the positive square root because we are interested in a radius which is a distance.

r=sqrt%28Cw%29

And that's all there is to that.

Part b: Here you need to solve the equation for C and then plug in the values of 100 for weight and 3963 for r at sea level. We could start over from the original equation, but let's take the easy way and go back to an intermediate result that we obtained doing part a: wr%5E2=C, which can be written:

C=wr%5E2

C=100%283963%29%5E2

C=100%2815705369%29=1570536900

Part c:
Here's where you need to be careful with your units. Death Valley is 282 FEET below sea level, but the earth's radius is given in miles. Now we could either convert 282 feet to miles, or 3963 miles to feet. The first way, the numbers are going to be a horror, but the second way, they will be sublimely ridiculous, so let's go with the lesser of two evils.

282%2F5280=.053 (approximately, and plenty close enough)

That means that the radius in Death Valley has to be 3963+-+.053=3962.947

So, using the original formula:

w=C%2Fr%5E2
w=1570536900%2F%283962.947%29%5E2
w=100.003

So if something weighs 100 lbs at sea level, it will gain three thousanths of a pound if you take it to Death Valley.

The Mt. McKinley part is done the same way, just different numbers:

20430%2F5280=3.87 (close enough)

So the radius becomes 3966.87 and

w=C%2Fr%5E2
w=1570536900%2F%283966.87%29%5E2

I'll let you do the calculator work from here.

John