Two cars start moving from the same from the same point. One...

Two cars start moving from the same from the same point. One travels south at $ 60 mi/h $ and the other travels west at $ 25 mi/h. $ At what rate is the distance between the cars increasing two hours later?

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Key Concepts

Pythagorean Theorem

The Pythagorean theorem is used to relate the sides of a right triangle, which in problems like this is applied to find the distance between two points moving perpendicularly. It states that the square of the hypotenuse (the distance between the two moving objects) is equal to the sum of the squares of the other two sides (the distances traveled in the perpendicular directions).

Related Rates

Related rates problems involve finding the rate at which one quantity changes by relating it to other quantities whose rates of change are known. In this context, the distances traveled by the cars are functions of time, and their relationship through the Pythagorean theorem helps determine the rate of change of the distance between them.

Implicit Differentiation

Implicit differentiation is a technique used when variables are related by an equation that is not solved for one variable in terms of the other. By differentiating both sides of an equation with respect to time, one can find the relationship between the rates of change of the variables involved, which is essential for solving the rate at which the distance between the cars increases.

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