Chapter 6.8, Problem 39E

To determine

Tofind:The moths in which the average temperature is 54.5 degrees.

Answer to Problem 39E

The moths in which the average temperature is 54.5 degrees is April and October.

Explanation of Solution

Given information:The equation is $y=54.5+23.5\sin \left(\frac{\pi }{6}t-\frac{2\pi }{3}\right)$ .

Calculation:

Consider the equation.

  $y=54.5+23.5\sin \left(\frac{\pi }{6}t-\frac{2\pi }{3}\right)$

Substitute $y=54.5$ in above equation.

  $\begin{array}{l}54.5=54.5+23.5\sin \left(\frac{\pi }{6}t-\frac{2\pi }{3}\right)\\ 0=23.5\sin \left(\frac{\pi }{6}t-\frac{2\pi }{3}\right)\\ \sin \left(\frac{\pi }{6}t-\frac{2\pi }{3}\right)=0\\ \frac{\pi }{6}t-\frac{2\pi }{3}=0,\pi \\ t=4,10\end{array}$

Thus, the moths in which the average temperature is 54.5 degrees is April and October.