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A ventilation fan is installed in a vertical position. As the fan rotates, the distance, in inches, between the tip of a fan blade and the ceiling is modeled by y = 6 cos(2,000 pi x) + 11, where x is time in minutes. How many times does the fan rotate each minute?

User Ignorant
by
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2 Answers

0 votes

Answer:

A

Explanation:

RPM is 1000
got it right on edge

User EverydayXpert
by
8.3k points
6 votes

Answer:

The number of times the fan blade revolves each minute is 1,000 times

Explanation:

The given function, y, that gives the distance between the tip of (one of the fan) blade(s) and the ceiling is given as follows;

y = 6·cos(2,000·pi·x) + 11

Where;

x = The time, in minutes, at which the distance is measured

The general form of the cosine function is y = a·cos(b·x - c) + d

Therefore, by comparing with the given function, we have;

b = 2,000·pi

a = 6

c/b = The horizontal shift or phase shift

The period, p, (which is the time to complete one revolution of the fan blade) of the function is given as follows;

p = 2·pi/b

Therefore;

p = 2·pi/(2,000·pi) = 1/1,000 = 0.001 minutes/revolution

The number of revolution the fan completes per minute, which is the rpm is given as follows;

rpm = 1/p = 1/(0.001) ×1/minutes/revolution) = 1,000 revolutions/minute

Therefore;

The fan blade revolves 1,000 times each minute.

User Eselskas
by
9.1k points
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