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.

1. 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.

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

i. Death Valley (282 feet below sea level).

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

a. To solve the equation w = Cr^-2 for r, we can rearrange the equation as follows:

w = C / r^2
r^2 = C / w
r = sqrt(C / w)

b. Based on the information given, we know that when the object is at sea level, w = 100 pounds and r = 3,963 miles. We can use these values to find the constant C:

100 = C / (3,963)^2
100 = C / 15,702,369

Multiplying both sides by 15,702,369:
C = 100 * 15,702,369

c. i. To find the weight of the object in Death Valley, which is 282 feet below sea level, we need to find the corresponding value of r and substitute it into the equation:

r = 3,963 - (282 / 5280) miles

Now we can calculate the weight:

w = C / r^2

ii. To find the weight of the object at the top of Mount McKinley, which is 20,320 feet above sea level, we need to find the corresponding value of r and substitute it into the equation:

r = 3,963 + (20,320 / 5280) miles

Now we can calculate the weight:

w = C / r^2

To solve this problem, we need to use the given equation w = Cr^(-2), where w represents the weight of an object, C is a constant, and r is the distance of the object from the center of the Earth.

a. To solve the equation w = Cr^(-2) for r, we need to isolate r. Start by taking the reciprocal of both sides:

1/w = (1/C)r^2

Next, multiply both sides by C:

C/w = r^2

Finally, take the square root of both sides to solve for r:

r = √(C/w)

b. In this question, we're given that an object weighs 100 pounds at sea level, which is 3,963 miles from the center of the Earth. We need to find the value of C that makes the equation true.

Using the given values, we have w = 100 pounds and r = 3,963 miles. Substituting these values into the equation and solving for C:

100 = C/(3,963)^2
100 = C/15,688,769
C = 100 * 15,688,769

Therefore, the value of C is 1,568,876,900.

c. Now that we have the value of C, we can use it to determine the weight of the object in different locations.

i. Death Valley, which is 282 feet below sea level. First, we need to convert 282 feet to miles. Using the conversion factor 1 mile = 5,280 feet:

282 feet * (1 mile / 5280 feet) = 0.0534 miles

Now, we substitute this value of r into the equation:

w = C/r^2
w = 1,568,876,900 / (0.0534)^2

Calculating this expression will give you the weight of the object in Death Valley.

ii. The top of Mount McKinley, which is 20,320 feet above sea level. Similar to part i, we need to convert 20,320 feet to miles:

20,320 feet * (1 mile / 5280 feet) = 3.85 miles

Now, substituting this value of r into the equation:

w = C/r^2
w = 1,568,876,900 / (3.85)^2

Calculating this expression will give you the weight of the object at the top of Mount McKinley.