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------------------------------------------------ Assuming that the Earth is a sphere with a radius of 4000 miles, what is the difference in latitude (in degrees) between two cities, one of which is 500 miles due north of the other?

To determine the difference in latitude between two cities where one is 500 miles due north of the other, we calculate the distance per degree of latitude using the Earth's circumference and divide 500 by this distance, resulting in approximately 7.16 degrees.

Explanation:

To calculate the difference in latitude between two cities with one being 500 miles due north of the other, we'll use the average length of a degree of latitude and the given radius of the Earth.

Assuming the Earth is a perfect sphere with a radius of 4000 miles, the formula for the circumference of the Earth along the equator (which is also the longest circumference due to the equatorial bulge) is C = 2πr, where r is the radius of the Earth.

With a radius of 4000 miles, the equatorial circumference is thus 2π(4000) ≈ 25133 miles.

Since there are 360 degrees in a circle, dividing the total equatorial circumference by 360 gives us the approximate distance per degree of latitude, which is approximately 25133/360 ≈ 69.8 miles.

Having this value, we can then find the difference in latitude for 500 miles by dividing the distance traveled (500 miles) by the distance per degree of latitude (approximately 69.8 miles).

≈ 500 mi / 69.8 mi/degree

≈ 7.16 degrees

Therefore, the difference in latitude between the two cities is approximately 7.16 degrees.