Application Problems with formulas such as w=Cr^-2

[Gr8fu13]

Here is my problem:
Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on Earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation: , where C is a constant, and r is the distance that the object is from the center of Earth.

Solve the equation w=Cr^-2 for r.
There is no value given for R in this equation so I am not sure where to begin.

Suppose that an object is 100 pounds 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.)
This problem I would think would just be w=C*3,963^-2. I started by making the exponent a positive (1/3963^2). This would equal (15,705,396). If I divide that by the 100 pounds it would be 157053.69. I am totally lost from here. I feel as though I am totally off track!

I cannot answer the proceeding questions unless I solve the first 2
Use the value of C you found in the previous question to determine how much the object would weigh in

Death Valley (282 feet below sea level).

The top of Mount McKinley (20,320 feet above sea level).

 

[Deleted member 4993]

Here is my problem:
Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on Earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation: , where C is a constant, and r is the distance that the object is from the center of Earth.

Solve the equation w=Cr^-2 for r.
There is no value given for R in this equation so I am not sure where to begin.

It is asking you to write 'r' as a function of 'w' - like you did while you worked with "inverse of a function"

I'll do a similar but different problem

Given V = k * r[sup:2o2ws7lr]3[/sup:2o2ws7lr]

Solve the equation for 'r'

k * r[sup:2o2ws7lr]3[/sup:2o2ws7lr] = V

r[sup:2o2ws7lr]3[/sup:2o2ws7lr] = V/k

r = [V/k][sup:2o2ws7lr]1/3[/sup:2o2ws7lr]

That's it....
Suppose that an object is 100 pounds 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.)
This problem I would think would just be w=C*3,963^-2. I started by making the exponent a positive (1/3963^2). This would equal (15,705,396). If I divide that by the 100 pounds it would be 157053.69. I am totally lost from here. I feel as though I am totally off track!

I cannot answer the proceeding questions unless I solve the first 2
Use the value of C you found in the previous question to determine how much the object would weigh in

Death Valley (282 feet below sea level).

The top of Mount McKinley (20,320 feet above sea level).

 

[Gr8fu13]

Okay, so I have r = (C/w)^1/2 for the first problem now. Thanks for the example So if I used this for the second problem it would be:
3,963 = (C/100)^1/2
3,936= C^1/2 / 100^1/2
3936=Square root of C / square root of 100
3963= square root of C * 10 /Square root of 100 * 10
3963= C^2 / 100
3963= c * c/ 100
3963*100= c*c
396300 = c*c
396300= 629.524 * 629.524
C= 629.524
Does this look correct?

 

[Deleted member 4993]

Okay, so I have r = (C/w)^1/2 for the first problem now. Thanks for the example So if I used this for the second problem it would be:
3,963 = (C/100)^1/2
3,936= C^1/2 / 100^1/2
3936=Square root of C / square root of 100
3963= square root of C * 10 /Square root of 100 * 10 <<< What are you doing here?
3963= C^2 / 100 <<< How did you get this?
3963= c * c/ 1003963*100= c*c
396300 = c*c
396300= 629.524 * 629.524
C= 629.524
Does this look correct? <<< No - try again

 

[Gr8fu13]

Let me try again:

100= c/3963^2
100 * 3963^2 = c
c = 1,570,536,900
Is this correct? I think I was mixing several methods before

 

[Denis]

Let me try again:
100= c/3963^2
100 * 3963^2 = c
c = 1,570,536,900
Is this correct? I think I was mixing several methods before

Answer correct!

Also as per ypou 1st attempt: 3,963 = (C/100)^1/2
3963 = sqrt(C / 100)
3963 = sqrt(C) / 10
sqrt(C) = 39630
C = 39630^2
C = 1570536900
Got that?