Solve the equation w=Cr^-2 for r.
Is this right?
w/C=r^-2
r=sqrt(C/w)
And if so, I still seem to be having troubles answering the next part.
2. 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.)
I got that C=1570536900
If all this is correct then how do i do the next part.
3. 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). (hint: 1 mile=5280 feet)
Lost completely... please help...
To solve the equation w = Cr^-2 for r, you correctly rearranged it as r = sqrt(C/w). Well done on that!
Now, let's move on to the next part of the problem.
To find the value of C that makes the equation true when an object weighs 100 pounds at sea level, we can substitute the given values into the equation.
Given:
w (weight) = 100 pounds
r (distance from the center of the Earth) = 3,963 miles
Using the equation r = sqrt(C/w), substitute the values:
100 = C / (3963^2)
To solve for C, we can multiply both sides of the equation by (3963^2):
100 * (3963^2) = C
Calculating that gives:
C = 100 * (3963^2)
C = 157,053,690,000 (rounded to the nearest whole number)
So, you correctly found that C = 157,053,690,000.
Now, for the third part of the problem, we need to determine how much the object would weigh in Death Valley (282 feet below sea level).
Given:
r (distance from the center of the Earth at Death Valley) = 3,963 - (282/5280) miles
Using the equation w = Cr^-2, we can substitute the values:
w = C / (3,963 - (282/5280))^2
To calculate the weight, substitute the value of C you found earlier:
w = 157,053,690,000 / (3,963 - (282/5280))^2
Calculating that will give you the weight of the object in Death Valley.
I hope this explanation helps you understand how to approach and solve the problem. If you have any more questions, feel free to ask!