Could you please check my work on these word problems? My solutions just don't seem right, could you please let me know where I may have messed up.

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: w=Cr^-2 , where C is a constant, and r is the distance that the object is from the center of Earth.
Hint: Pay attention to the units of measure. You may have to convert from feet to miles several times in this assignment. You can use 1 mile = 5,280 feet for your conversions."

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

b. 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.)

c. 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) 282ft=0.053409mi??

My solutions:

a. r=sqrt(C/w)

b. w=Cr^-2 or w=C*1/(r^2) ??
100=C(1/3,963^2)
100=C(1/15,705,369)
100*15,705,369=C(1/15,705,369)*15,705,369
C=1,570,536,900 ??

c. w=1,570,536,900(1/0.053409^2)
w=1,570,536,900(1/0.002853)
w=1,570,536,900(350.508237)
???? w=550,486,119,962.4453??

If you could let me know if and where I may have made any mistakes I'm sure I could complete the rest of the assignment.

Thank you!

a is wrong. r=sqrt(W/C)

b. You need units on C.

c. nope, r would be below sea level,
r=3963-.053209
now find that r, and rework.

How did you come up with your answer to a? Everytime I try to rework it I get r=sqrt(C/w)

asd, I get the same answer as you do to a.

W = Cr^-2 = C(1/r^2)

Multiply both sides by r^2 and divide both sides by W.

r^2 = C/W

r = √(C/W)

Let's go through each part of your solution and check for any mistakes.

a. To solve the equation w=Cr^-2 for r, you need to isolate r. You did this correctly. The correct solution is r = sqrt(C/w).

b. You correctly set up the equation as w = C(1/r^2). However, there is a mistake in your calculations. It seems like you misunderstood the meaning of "sea level" in this context. Sea level refers to the distance from the center of the Earth, not the elevation above the surface.

To find the value of C, you should use the given information that the object weighs 100 pounds at sea level, which is 3,963 miles from the center of the Earth. The correct calculation is:

100 = C / (3963^2)

Solving for C:

C = 100 * (3963^2)

c. You correctly converted the elevation in Death Valley from feet to miles. However, there is a mistake in your calculation of weight. You multiplied the value of C (1,570,536,900) by 350.508237, but the correct calculation should be dividing (1/0.053409^2):

w = 1,570,536,900 / (0.053409^2)

Calculating:

w ≈ 1,570,536,900 / 0.002853

w ≈ 550,577,767,439.789

So, the correct weight of the object in Death Valley would be approximately 550,577,767.44 pounds (rounded to two decimal places).

To summarize:

a. The correct solution for r is r = sqrt(C/w).
b. The correct value of C is C = 100 * (3963^2).
c. The correct weight in Death Valley is w ≈ 550,577,767.44 pounds.

Please double-check these calculations and let me know if you have any further questions or need assistance with any other part of the assignment.