Chapter 4.4, Problem 123E

a.

To determine

To find: the normal daily high temperature for January month.

Answer to Problem 123E

  $T=60.4\text{degree Fahrenheit}$ .

Explanation of Solution

Given information: The normal daily high temperature T (in degree Fahrenheit) in S G

can be approximated by $T=76.4+16\cos (\frac{\pi t}{6}-\frac{7\pi }{6})$ .where t is the time (in months), with t =1 corresponding to January.

Formula used:

Monthly sales S over two-year period to be The normal daily high temperature T can be approximated by $T=76.4+16\cos (\frac{\pi t}{6}-\frac{7\pi }{6})$ .

Calculation:

To find the normal daily high temperature for January month substitute t =1 in the normal daily high temperature equation.

  $\begin{array}{l}T=76.4+16\cos (\frac{\pi t}{6}-\frac{7\pi }{6})\\ \text{Substitute}t=1.\\ T=76.4+16\cos (\frac{\pi \times 1}{6}-\frac{7\pi }{6})\\ T=76.4+16\cos (-\pi ).\\ T=60.4\text{degree Fahrenheit}.\end{array}$

b.

To determine

To find: the normal daily high temperature for July month.

Answer to Problem 123E

  $T=92.4\text{degree Fahrenheit}$ .

Explanation of Solution

Given information: The normal daily high temperature T (in degree Fahrenheit) in S G

can be approximated by $T=76.4+16\cos (\frac{\pi t}{6}-\frac{7\pi }{6})$ .where t is the time (in months), with t =1 corresponding to January.

Formula used:

Monthly sales S over two-year period to be the normal daily high temperature T can be approximated by $T=76.4+16\cos (\frac{\pi t}{6}-\frac{7\pi }{6})$ .

Calculation:

To find the normal daily high temperature for July month substitute t =7 , in the normal daily high temperature equation.

  $\begin{array}{l}T=76.4+16\cos (\frac{\pi t}{6}-\frac{7\pi }{6})\\ \text{Substitute}t=1.\\ T=76.4+16\cos (\frac{\pi \times 7}{6}-\frac{7\pi }{6})\\ T=76.4+16\cos (0).\\ T=92.4\text{degree Fahrenheit}.\end{array}$

c.

To determine

To find: the normal daily high temperature for October month.

Answer to Problem 123E

  $T=76.4\text{degree Fahrenheit}$ .

Explanation of Solution

Given information: The normal daily high temperature T (in degree Fahrenheit) in S G

can be approximated by $T=76.4+16\cos (\frac{\pi t}{6}-\frac{7\pi }{6})$ .where t is the time (in months), with t =1 corresponding to January.

Formula used:

Monthly sales S over two-year period to be The normal daily high temperature T can be approximated by $T=76.4+16\cos (\frac{\pi t}{6}-\frac{7\pi }{6})$ .

Calculation:

To find the normal daily high temperature for October month substitute t =10 in the normal daily high temperature equation.

  $\begin{array}{l}T=76.4+16\cos (\frac{\pi t}{6}-\frac{7\pi }{6})\\ \text{Substitute}t=10.\\ T=76.4+16\cos (\frac{\pi \times 10}{6}-\frac{7\pi }{6})\\ T=76.4+16\cos (\frac{\pi }{2}).\\ T=76.4\text{degree Fahrenheit}.\end{array}$