Question

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 = Equals 6 cosine (2,000 pi x) + 11, where x is time in minutes.

How many times does the fan rotate each minute?

A 1,000
B 2,000
C 4,000
D 6,000

Answer 1

The number of times that the fan rotate each minute is: 1,000 times.

Number of times that the fan rotate

Given:

y = Equals 6 cosine (2,000 pi x) + 11

Where x is time in minutes.

Hence:

Using cosine function:

y = a·cos(b·x - c) + d

Where:

b = 2,000·pi

a = 6

c/b =horizontal shift

While,  period (p)

p = 2·pi/b

Hence:

p = 2·pi/(2,000·pi)

p = 1/1,000

p = 0.001 minutes per revolution

rpm = 1/p

rpm= 1/(0.001) ×1/minutes)

rpm= 1,000 times per minutes

Therefore the correct option is A.

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