A boat is travelling due west at a speed of 47miles per hour. If the boat started off 170miles directly north of the city of Smithville, how fast is the distance between the boat and Smithville changing when the boat has travelled 78miles? (Do not include units in your answer, and round to the nearest hundredth.)

Question
Asked Oct 12, 2019
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A boat is travelling due west at a speed of
47
miles per hour. If the boat started off
170
miles directly north of the city of Smithville, how fast is the distance between the boat and Smithville changing when the boat has travelled
78
miles? (Do not include units in your answer, and round to the nearest hundredth.)

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Expert Answer

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The boat is travelling due west at a speed of 47 miles per hour. ,miles =47 dt dc That is, the rate of change of speed hour From the given information, the curent situation can be representing as follows N x = 78 mi Вoat, y170mi W E Smithville N

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Use the Pythagorean Theorem, the value of z2 = 2 2(78)+(170) z 608428900 z2 34984 z =34984 Differentiate the z2 =x2 +28900 with respect to t d -(x2 +28900) dt dt dz dx 2x dt 2z 0 dt dz dx = x Z dt dt dz х dх dt z dt

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