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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

At noon, ship A is 100 km west of ship B. Ship A is sailing south at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 pm?

To determine

To find:

The rate at which the distance between ships is changing.

Explanation

1. Concept:

We can plot the figure from the given situation, and then we can apply the Pythagorean Theorem to write the equation. Then apply the differentiation on this equation to find the required rate.

The figure is as shown below.

Let x = distance traveled by ship A

y = distance traveled by ship B and

z = distance between two ships.

2. Formula:

i. Pythagorean Theorem:

Hypoteneous2=Sum of squares of perpendicular sides

ii. Power rule of differentiation:

ddxxn=n*xn-1

 iii. Chain rule of differentiation:

ddtfx=ddxfx*dxdt

3. Given:

Speed of ship A  =35 km/h Speed of ship B  =25 km/h

4

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