Question

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by

V=1.72sin(pit/5). t is the time. Find the number of cycles per minute

Answer 1

Using the period of the sine function in the given velocity equation, we determine that the respiratory cycle is at a rate of 6 cycles per minute.

Step-by-step explanation:

To find the number of respiratory cycles per minute from the given velocity equation V=1.72sin(πt/5), we need to understand the properties of the sine function.

The sine function has a period of 2π, which means that it completes one full cycle when its argument changes by an amount of 2π.

In the given function, the argument of the sine function is πt/5, which means that the period T (the time for one complete cycle) is when πt/5 changes by 2π.

Therefore, we can set up the equation:

πT/5 = 2π → T = 10 seconds per cycle

To convert this to cycles per minute, we divide 60 seconds by the time per cycle:

60 seconds/minute / 10 seconds/cycle = 6 cycles/minute

So, the person's respiratory cycle is at a rate of 6 cycles per minute.