The rate at which the distance between the two cars is increasing 2 hours after they have left the intersection is 0 mph.
To find the rate at which the distance between the two cars is increasing, we can use the Pythagorean theorem, as the distance between them forms a right triangle. Let's label the distance between the cars as 'd' and the time after they left the intersection as 't'.
According to the problem, the car traveling north has a constant speed of 80 mph and the car traveling east has a constant speed of 60 mph. Since both cars have been traveling for 2 hours, the distance the northbound car has traveled is 80 * 2 = 160 miles, and the distance traveled by the eastbound car is 60 * 2 = 120 miles.
Using the Pythagorean theorem, we can write the equation as:
d^2 = (160)^2 + (120)^2
Simplifying this equation, we get:
d^2 = 25600 + 14400 d^2 = 40000 Taking the square root, we find:
d = 200 miles
Now, to find the rate at which the distance between the cars is increasing, we need to take the derivative of the equation with respect to time. Taking the derivative on both sides, we get:
2d * dd/dt = 0b
Simplifying this equation, we find:
dd/dt = 0 / (2d)
dd/dt = 0
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