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Assuming Earth to be a sphere with a radius of 4000 miles, how many miles north of the equator is City A if it is [tex]34^\circ[/tex] north from the equator?

Answer :

Final answer:

We can determine how many miles north 'City A' is from the equator using the given latitude of 34 degrees and assuming Earth's radius to be 4000 miles. By calculating Earth's circumference (8000π miles) and dividing by total degrees (360), one degree equals approximately 70 miles. Therefore, 'City A' is approximately 2380 miles north of the equator.

Explanation:

The subject of this question is Mathematics, specifically applying the concepts of geometry and trigonometry. The problem here is related to finding 'how many miles north 'City A' is from the equa tor given that it is located 34 degrees north of the equator.

In this content loaded assuming earth example, we are assuming earth to be a perfect sphere with a radius of 4000 miles. Since there are 360 degrees in a complete circle (sphere), each degree on the earth represents a distance equivalent to the earth’s circumference divided by 360. The earth’s circumference can be calculated using the formula 2πr, where r is the radius of the sphere. So for our case the earth's circumference is 2π*4000=8000π.

The distance represented by one degree north or south of the equator, therefore, is (8000π)/360≈ 70 miles. So 34 degrees north would be 34*70≈2380 miles north of the equator.

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