Chapter 4, Problem 9PS

a.

To determine

To graph: The blood vessels of patient is modeled by $p=100-20\cos \left(\frac{8\pi }{3}t\right)$ .

Explanation of Solution

Given information:

Consider the statement blood vessels of patient is modeled by $p=100-20\cos \left(\frac{8\pi }{3}t\right)$ .

Graph:

The graph of the statement is mentioned below

  

The graph above mentioned is on real number line on the x axis and y axis.

The graph mentioned above is of $p=100-20\cos \left(\frac{8\pi }{3}t\right)$ .

b.

To determine

To explain: The period of the statement $p=100-20\cos \left(\frac{8\pi }{3}t\right)$ .

Answer to Problem 9PS

The mentioned statement $p=100-20\cos \left(\frac{8\pi }{3}t\right)$ is periodic and period is $\frac{3}{4}$ .

Explanation of Solution

Given information:

Mentioned statement in the problem is $p=100-20\cos \left(\frac{8\pi }{3}t\right)$ .

Formula: period of $\cos x=2\pi$ and $\cos ax=\frac{2\pi }{a}$ .

Consider the statement $p=100-20\cos \left(\frac{8\pi }{3}t\right)$ as mentioned in the problem.

Since the periodic function of $\cos x=2\pi$ .

Therefore $p=100-20\cos \left(\frac{8\pi }{3}t\right)$ is periodic because from the above mentioned graph the curve is equal interval on every cycle.

Recall that period of $\cos x=2\pi$ and $\cos ax=\frac{2\pi }{a}$ .

Therefore period of $p=100-20\cos \left(\frac{8\pi }{3}t\right)$ is $\frac{2\pi *3}{8\pi }=\frac{3}{4}$ .