Answer:
The number of times the fan blade revolves each minute is 1,000 times
Step-by-step 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.
