Chapter MPS, Problem 13.5MPS

a.

To determine

To make a table showing the height of seaweed at $4,6.5,9,11.5,14$ and $16.5$ seconds.

Explanation of Solution

Given:

At time $t=4$ seconds, the highest point was $16$ feet. The wheel’s diameter is $18$ feet and it completes its revolution every $10$ second.

Calculation:

The following is the equation that represents the situation-

  $\begin{array}{l}y=a\sin b(t-h)+k\\ \\ a=16.5-\frac{16.5+4}{2}=16.5-6.25=10.25\\ 10=\frac{2\pi }{\left|b\right|}\\ b=\pm \frac{\pi }{5}\\ y=a\sin b(t-h)+k\\ y=10.25\sin \frac{\pi }{5}(t-0)+6.25\\ y=10.25\sin \frac{\pi }{5}t+6.25\end{array}$

The following is the table-

Time (in Seconds)	Height (in feet)
$4$	30.3
$6.5$	45.4
$9$	60.4
$11.5$	75.5
$14$	90.5
$16.5$	105.6

b.

To determine

To make the graph of the function.

Explanation of Solution

Given:

There graph of the normal distribution is given below-

Calculation:

The graph of the equation $y=10.25\sin \frac{\pi }{5}t+6.25$ is given below-