To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Step 1: Determine the distance each car has traveled after 4 hours.

The car traveling south at 48 mi/h will have traveled 48 mi/h * 4 h = 192 miles.

The car traveling west at 20 mi/h will have traveled 20 mi/h * 4 h = 80 miles.

Step 2: Use the Pythagorean theorem to find the distance between the cars.

The distance between the cars is the hypotenuse of a right triangle with sides of 192 miles and 80 miles.

So, the distance is sqrt((192 miles)^2 + (80 miles)^2) = 208 miles.

Step 3: Find the rate at which the distance is increasing.

The rate at which the distance is increasing is the derivative of the distance with respect to time.

The derivative of sqrt((48t)^2 + (20t)^2) with respect to t (where t is time in hours) is (48^2*t)/(sqrt((48t)^2 + (20t)^2)) + (20^2*t)/(sqrt((48t)^2 + (20t)^2)) = 52 mi/h.

So, four hours later, the distance between the cars is increasing at a rate of 52 mi/h.

Question

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Step 1: Determine the distance each car has traveled after 4 hours.

The car traveling south at 48 mi/h will have traveled 48 mi/h * 4 h = 192 miles.

The car traveling west at 20 mi/h will have traveled 20 mi/h * 4 h = 80 miles.

Step 2: Use the Pythagorean theorem to find the distance between the cars.

The distance between the cars is the hypotenuse of a right triangle with sides of 192 miles and 80 miles.

So, the distance is sqrt((192 miles)^2 + (80 miles)^2) = 208 miles.

Step 3: Find the rate at which the distance is increasing.

The rate at which the distance is increasing is the derivative of the distance with respect to time.

The derivative of sqrt((48t)^2 + (20t)^2) with respect to t (where t is time in hours) is (48^2*t)/(sqrt((48t)^2 + (20t)^2)) + (20^2*t)/(sqrt((48t)^2 + (20t)^2)) = 52 mi/h.

So, four hours later, the distance between the cars is increasing at a rate of 52 mi/h.

Knowee AI · Accepted Answer

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Step 1: Determine the distance each car has traveled after 4 hours.

The car traveling south at 48 mi/h will have traveled 48 mi/h * 4 h = 192 miles.

The car traveling west at 20 mi/h will have traveled 20 mi/h * 4 h = 80 miles.

Step 2: Use the Pythagorean theorem to find the distance between the cars.

The distance between the cars is the hypotenuse of a right triangle with sides of 192 miles and 80 miles.

So, the distance is sqrt((192 miles)^2 + (80 miles)^2) = 208 miles.

Step 3: Find the rate at which the distance is increasing.

The rate at which the distance is increasing is the derivative of the distance with respect to time.

The derivative of sqrt((48t)^2 + (20t)^2) with respect to t (where t is time in hours) is (48^2*t)/(sqrt((48t)^2 + (20t)^2)) + (20^2*t)/(sqrt((48t)^2 + (20t)^2)) = 52 mi/h.

So, four hours later, the distance between the cars is increasing at a rate of 52 mi/h.

Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west at 20 mi/h. At what rate is the distance between the cars increasing four hours later?

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