Question

A periodic function goes through 5 complete cycles in 4 min . What is the period of the function?

Answer 1

The period of the given periodic function is 48 sec.

What is periodic function?

A periodic function is a function which returns same values at regular intervals. Let f be a periodic function then  

f( x +P ) = f(x) , for every x in the domain of f and P is some non zero constant

P is the regular interval or period after which a periodic function returns same values.

P=$\frac{1}{f}$

where $f$ is the frequency of the periodic function

or $f$ = no of cycles per unit time

Given that a periodic function goes through 5 cycles in 4 min

therefore frequency for this periodic function , f  is given by

$f=\frac{5}{4}$ cycles per min

or

$f=\frac{5}{4*60} \\f=\frac{5}{240}$

$f=\frac{1}{48}$   cycles per sec

Thus,

Period of the given periodic function , P =$\frac{1}{f}=1/\frac{1}{48}=48$ sec

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Answer 2

The period of the function is 48 minutes if the periodic function goes through 5 complete cycles in 4 min.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

A periodic function goes through 5 complete cycles in 4 min

From the question:

f = 5/4 cycles per minutes

f = 5/240 cycles per seconds  [1 minutes = 60 seconds]

f = 1/48

Period = 1/f

Period = 48 minutes

Thus, the period of the function is 48 minutes if the periodic function goes through 5 complete cycles in 4 min.

Learn more about the function here:

brainly.com/question/5245372

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