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: , where C is a constant, and r is the distance that the object is from the center of Earth.

a. Solve the equation 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).

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What formula do I need to use to solve for r

convert 1.88x10^-6 g to each of the following units mg

a. Solve the equation \(W = \frac{{C}}{{r^2}}\) for \(r\).

To solve for \(r\), we need to isolate it on one side of the equation.

First, multiply both sides of the equation by \(r^2\):

\(Wr^2 = C\)

Next, divide both sides of the equation by \(W\):

\(r^2 = \frac{{C}}{{W}}\)

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

\(r = \sqrt{\frac{{C}}{{W}}}\)

b. To find the value of \(C\) that makes the equation true when the object weighs 100 pounds at sea level (3,963 miles from the center of the Earth), we can substitute the given values into the equation:

\(100 = \frac{{C}}{{(3963)^2}}\)

To solve for \(C\), multiply both sides of the equation by \((3963)^2\):

\(C = 100 \times (3963)^2\)

Using a calculator, compute the value on the right-hand side to find the value of \(C\).

c. We will use the value of \(C\) obtained in the previous question to determine the weight of the object in Death Valley (-282 feet below sea level) and at the top of Mount McKinley (20,320 feet above sea level).

To calculate the weight in Death Valley, we need to find the distance from the center of the Earth in miles. Since Death Valley is 282 feet below sea level, we subtract 282 from the distance at sea level (3,963 miles):

Distance in Death Valley = 3,963 - (282 / 5280)

Next, substitute the distance and the value of \(C\) into the equation:

Weight in Death Valley = \(\frac{{C}}{{(Distance \, in \, Death \, Valley)^2}}\)

To calculate the weight at the top of Mount McKinley, we add 20,320 feet to the distance at sea level (3,963 miles):

Distance at the top of Mount McKinley = 3,963 + (20,320 / 5280)

Finally, substitute the distance and the value of \(C\) into the equation to find the weight at the top of Mount McKinley:

Weight at the top of Mount McKinley = \(\frac{{C}}{{(Distance \, at \, the \, top \, of \, Mount \, McKinley)^2}}\)