EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Chapter 5.3, Problem 93E

(a)

To determine

To Find: The graphing utility to create the scatter plot of the data.

(a)

Expert Solution
Check Mark

Answer to Problem 93E

The required plot is shown in Figure 1

Explanation of Solution

Given:

The given table is shown in Table 1

Table 1

    Month
      t    		Chicago, C
    131.0
    235.3
    346.6
    459.0
    570.0
    679.7
    784.1
    881.9
    974.8
    1062.3
    1148.2
    1234.8

Calculation:

From the given table the model for the scatter plot is shown in Figure 1

  EBK PRECALCULUS W/LIMITS, Chapter 5.3, Problem 93E , additional homework tip 1

Figure 1

(b)

To determine

To Find: The cosine model for the temperature.

(b)

Expert Solution
Check Mark

Answer to Problem 93E

The required model is c=26.55cos(πt6−7π6)+57.55 .

Explanation of Solution

The general form for the cosine model is of the form,

  c=acos(bt−c)+d

Then, the amplitude of the model is,

  a=12(84.1−31.0)=26.55

The cosine function complete one half of the cycle between the times at which the temperature occur then, the period is,

  p=2|1−7|=12

Then, the value of b c and d is obtained as,

  b=2πpc=7π6

The value of d is obtained as,

  d=12(84.1+31.0)=57.55

Thus, the required equation for the model is,

  c=26.55cos(πt6−7π6)+57.55

(c)

To determine

To Find: The graph for the model and the scatter plot in the same viewing window and determine how well the model does fit the data.

(c)

Expert Solution
Check Mark

Answer to Problem 93E

The graph is shown in Figure 2 and the model fits the graph very well.

Explanation of Solution

From the given table the model for the scatter plot is shown in Figure 2

  EBK PRECALCULUS W/LIMITS, Chapter 5.3, Problem 93E , additional homework tip 2

Figure 2

The model c=26.55cos(πt6−7π6)+57.55 fits the graph very well.

(d)

To determine

To Find: The overall normal daily high temperature.

(d)

Expert Solution
Check Mark

Answer to Problem 93E

The overall daily high temperature is the average given by d=57.55° .

Explanation of Solution

The overall daily high temperature is the average given by d=57.55° .

(e)

To determine

To Find: The months during which the normal high temperature is above 72°F and below of 72°F .

(e)

Expert Solution
Check Mark

Answer to Problem 93E

The temperature above 72°F is June to September and below 72°F is between Octobers to May.

Explanation of Solution

The overall daily high temperature is the average given by d=57.55° .

Consider the graph shown in Figure 3

  EBK PRECALCULUS W/LIMITS, Chapter 5.3, Problem 93E , additional homework tip 3

Figure 3

The month in which the temperature is above 72°F is June to September.

The month in which the temperature is below 72°F is between Octobers to May.

Previous
Chapter 5.3, Problem 92E
Next
Chapter 5.3, Problem 94E

Chapter 5 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
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