The rate of change in the distance between two ships can be calculated by using the Pythagorean theorem and basic physics. The equation for this is as follows: d = √(x^2+y^2) where x is the horizontal distance between them, y is the vertical distance, and d is the total distance. In this scenario we have a ship A that is 20 km west of another ship B. If A sails at 10km/hr while B sails north at 30km/hr then we can calculate the rate of change in their distance after half an hour.

First, let us calculate how far each ship will have moved in 30 minutes. Ship A will have gone 300 km (10km/hr * 30min), and Ship B will have gone 450 km (30km/hr * 15min). This means that after half an hour, Ship A has moved 300 km west from its original position and Ship B has moved 450 km north from its original position.

Using these values we can now calculate the new distances between them using our equation above. The new horizontal distance between them would be 300 – 20 = 280, and vertical distance would be 450 – 0 = 450 (since it was already 0 to begin with). Plugging these numbers into our calculation gives us a total displacement of d = √(280^2+450^2) = 514 kilometers.

We also know that time elapsed for displacement was 0.5 hours so in order to find rate of change simply divide total displacement by time taken i .e., Rate of Change=514/0.5=1028 Km/hrs or 28 Km./min.

In conclusion , calculating rate of change between two objects requires not just knowledge related mathematical equations but also understanding physical principles which govern motion involved throughout entire process . Such information becomes invaluable when attempting make sense large amounts data available today thus helping visualize trends present within system being studied here

.References:

Gathen Jörg von & Gerhard Johannes 2003 “Modern Computer Algebra” Accessed April 23 2021 https://booksgooglecom / books?id=jU6lSXo7dQkC&pg=PA314&dq=Pythagorean+theorem+rate +of +change&hl=en&sa=X&ved=0ahUKEwjfz-Ls9LTnAhWbVH0KHQryBJcQ6AEIRjAA#v-onepage&q- Pythagorean%20theorem%20rate %20of %20change < ; br > ;

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