After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by $\pi$ $v = 1.75 \sin \left( \frac { \pi t } { 3 } \right)$ ,

Where t is the time (in seconds) .
(Inhalation occurs when v > 0 and exhalation occurs when v < 0.)

Find the number of cycles per minute.

Question

After exercising for a few minutes, a person has a respiratory cycle for which the velocity of airflow is approximated by $\pi$ $v = 1.75 \sin \left( \frac { \pi t } { 3 } \right)$ ,
 
Where t is the time (in seconds).
(Inhalation occurs when v > 0 and exhalation occurs when v < 0.)
 
Find the number of cycles per minute.
 
A)12 cycles/min
B)10 cycles/min
C)15 cycles/min
D)13 cycles/min
E)11 cycles/min

Quizplus · Accepted Answer

The period of the function $v = 1.75 \sin \left( \frac{\pi t}{3} \right)$ is 6 seconds. Therefore, the number of cycles per minute is $ \frac{60}{6} = 10 $ cycles/min.

After Exercising for a Few Minutes, a Person Has a Respiratory