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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

13-16

(a) What quantities are given in the problem?

(b) What is the unknown?

(c) Draw a picture of the situation for any time t.

(d) Write an equation that relates the quantities.

(e) Finish solving the problem.

At noon, ship A is 150 km west of ship B. Ship A is sailing east 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 parts a to e

Explanation

a. At noon, ship A is 150 km west of ship B. If x = distance travelled by ship A and y is the distance travelled by ship B and t is the time in hours, then dxdt=35 km/h and dydt=25 km/h

b. If h is the distance between ships, then we need to find dhdt at t=4 hrs.

c. The picture of the situation looks like this

d. By applying Pythagorean theorem,h2=150-x2+y2

Differentiate with respect to t on both sides

2h*dhdt=2150-x-dxdt+2ydydt

e

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