The video tutorial explains how to calculate the rate at which the distance between two ships is changing. Ship A is initially 30 nautical miles west of Ship B and sails west at 16 knots, while Ship B sails north at 15 knots. Using the Pythagorean theorem, the tutorial sets up an equation to relate the distances and differentiates it to find the rate of change of the distance between the ships at 4:00 p.m. The final calculation shows that the distance is changing at approximately 2.56 knots.

What is the initial distance between Ship A and Ship B?

• 30 nautical miles

• 50 nautical miles

• 20 nautical miles

• 40 nautical miles

At what speed is Ship A moving west?

• 10 knots

• 12 knots

• 16 knots

• 18 knots

What is the rate of change of Y, the distance Ship B travels north?

• 18 knots

• 15 knots

• 10 knots

• 12 knots

Which theorem is used to relate the distances X, Y, and S?

• Fundamental theorem of calculus

• Binomial theorem

• Pythagorean theorem

• Mean value theorem

What is the value of X at 4:00 PM?

• 94 miles

• 80 miles

• 70 miles

• 60 miles

What is the value of Y at 4:00 PM?

• 60 miles

• 70 miles

• 80 miles

• 50 miles

What is the approximate value of S, the distance between the ships, at 4:00 PM?

• 100 miles

• 110 miles

• 120 miles

• 115.2 miles

What is the formula for the derivative of S^2 with respect to time?

• 2S * dS/dt = 2X * dX/dt + 2Y * dY/dt

• dS/dt = X * dX/dt + Y * dY/dt

• S = X + Y

• S^2 = X^2 + Y^2

What is the final calculated rate of change of the distance between the ships at 4:00 PM?

• 4.56 knots

• 1.56 knots

• 2.56 knots

• 3.56 knots

What mathematical operation is performed to find the rate of change of the distance between the ships?

• Differentiation

• Integration

• Addition

• Multiplication