Chapter 4.5, Problem 82E

(a)

To determine

To use the graphic utility to graph v.

Explanation of Solution

Given information: $v=0.85\sin \frac{\pi t}{3}$

Calculations:

  

(b)

To determine

To find time for one full respiratory cycle.

Answer to Problem 82E

6 seconds.

Explanation of Solution

Given information: $v=0.85\sin \frac{\pi t}{3}$

  $v=0.85\sin \frac{\pi t}{3}$

One full respiratory system is one period.

  $\frac{2\pi }{\frac{\pi }{3}}=6$ seconds.

(c)

To determine

To find number of cycles per minute.

Answer to Problem 82E

10 cycles

Explanation of Solution

Given information: $v=0.85\sin \frac{\pi t}{3}$

One cycle takes 6 seconds, there are 60seconds in a minute.

60/6 = 10 cycles.

(d)

To determine

To determine the model change for a person.

Answer to Problem 82E

A person exercising usually breathes faster and harder, so the period will shrink and the amplitude will increase. The graph will be compressed horizontally and stretched vertically.

Explanation of Solution

Given information: $v=0.85\sin \frac{\pi t}{3}$

A person exercising usually breathes faster and harder, so the period will shrink and the amplitude will increase. The graph will be compressed horizontally and stretched vertically.