Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Question
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Chapter 5.3, Problem 119E

a.

To determine

To find: A sine model using sine regression feature of a graphing utility to fit each set of data.

a.

Expert Solution
Check Mark

Answer to Problem 119E

A sine model for the temperature P is as follows:

  86.8653+20.2276sin(0.5313x2.1862)

with x corresponding to month.

A sine model for the temperature Y is as follows:

  37.3893+14.383sin(0.5778x2.4656) with x corresponding to month.

Explanation of Solution

Given information:

The following table with Temperature P for Phoenix and Y for Yakima(in degree Fahrenheit) for each month t with t=1 corresponding to January:

  Precalculus with Limits: A Graphing Approach, Chapter 5.3, Problem 119E , additional homework tip  1

Calculation:

To find a sine model for the temperature P , plot all the points on the graph Then, make a list of all the points using the LIST feature in the graphing utility. The list will be created as:

  l1={A, B, C, D, E, F, G, H, I, J, K, L}

Then use the sine regression feature of the graphing utility. To find a sine model, enter the following equation:

  f(x)=fitsin(l1)

Press Enter.

The following equation will be obtained:

  86.8653+20.2276sin(0.5313x2.1862)

Follow the same procedure to find the sine model for temperature Y .

The sine model for temperature Y will be obtained as:

  37.3893+14.383sin(0.5778x2.4656)

b.

To determine

To graph: Each model from part(a) with original data.

b.

Expert Solution
Check Mark

Explanation of Solution

Given information:

The following table with Temperature P for Phoenix and Y for Yakima(in degree Fahrenheit) for each month t with t=1 corresponding to January:

  Precalculus with Limits: A Graphing Approach, Chapter 5.3, Problem 119E , additional homework tip  2

Graph:

On plotting the data and on finding the sine model using the Fitsin() command(explained in subpart a), the graph for temperature P is obtained as follows:

  Precalculus with Limits: A Graphing Approach, Chapter 5.3, Problem 119E , additional homework tip  3

On plotting the data and on finding the sine model using the Fitsin() command(explained in subpart a), the graph for temperature Y is obtained as follows:

Interpretation:

The graph of the sine model is a best fit line for the scatter plot of the temperature.

c.

To determine

To find: The month(s) in which the given high temperature is most likely reported in each city.

c.

Expert Solution
Check Mark

Answer to Problem 119E

Yakima may report a daily high temperature of 50°C in June, July and August.

Explanation of Solution

Given information:

The following table with Temperature P for Phoenix and Y for Yakima(in degree Fahrenheit) for each month t with t=1 corresponding to January:

  Precalculus with Limits: A Graphing Approach, Chapter 5.3, Problem 119E , additional homework tip  4

Normal daily high temperature reported = 50°C

Phoenix has high temperatures above 50°C . So, Phoenix will not report a daily high temperature of 50°C in any month. On the other hand, Yakima reports a temperature of 48.3°C , 53.3°C and 51.8°C in June, July and August respectively. These values are very close to 50°C . So Yakima may report a daily high temperature of 50°C in June, July and August

d.

To determine

To find: The month(s) in which the given high temperature is most likely reported in each city.

d.

Expert Solution
Check Mark

Answer to Problem 119E

A daily high temperature of 60°C is not reported in any month in both the cities.

Explanation of Solution

Given information:

The following table with Temperature P for Phoenix and Y for Yakima(in degree Fahrenheit) for each month t with t=1 corresponding to January:

  Precalculus with Limits: A Graphing Approach, Chapter 5.3, Problem 119E , additional homework tip  5

Normal daily high temperature reported = 60°C

Phoenix has high temperatures above 60°C . So, Phoenix will not report a daily high temperature of 60°C in any month. On the other hand, Yakima has high temperatures below 60°C . So Yakima, will also not report a daily high temperature of 60°C in any month.

e.

To determine

To find: The month(s) in which the given high temperature is most likely reported in each city.

e.

Expert Solution
Check Mark

Answer to Problem 119E

Phoenix may report a daily high temperature of 76°C in March and November.

Explanation of Solution

Given information:

The following table with Temperature P for Phoenix and Y for Yakima(in degree Fahrenheit) for each month t with t=1 corresponding to January:

  Precalculus with Limits: A Graphing Approach, Chapter 5.3, Problem 119E , additional homework tip  6

Normal daily high temperature reported = 76°C

Phoenix has a high temperature of 76.9°C and 75.5°C in March and November. Since these temperatures are very close to 76°C , Phoenix may report a daily high temperature of 76°C in March and November. On the other hand, Yakima has high temperatures below 76°C . So Yakima, will not report a daily high temperature of 76°C in any month.

e.

To determine

To find: The month(s) in which the given high temperature is most likely reported in each city.

e.

Expert Solution
Check Mark

Answer to Problem 119E

Phoenix may report a daily high temperature of 103°C in June and August.

Explanation of Solution

Given information:

The following table with Temperature P for Phoenix and Y for Yakima(in degree Fahrenheit) for each month t with t=1 corresponding to January:

  Precalculus with Limits: A Graphing Approach, Chapter 5.3, Problem 119E , additional homework tip  7

Normal daily high temperature reported = 103°C

Phoenix has a high temperature of 103.9°C and 104.4°C in June and August. Since these temperatures are very close to 103°C , Phoenix may report a daily high temperature of 103°C in June and August. On the other hand, Yakima has high temperatures below 103°C . So Yakima, will not report a daily high temperature of 103°C in any month.

Chapter 5 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Prob. 60ECh. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - 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Prob. 99ECh. 5.5 - Prob. 100ECh. 5.5 - Prob. 101ECh. 5.5 - Prob. 102ECh. 5.5 - Prob. 103ECh. 5.5 - Prob. 104ECh. 5.5 - Prob. 105ECh. 5.5 - Prob. 106ECh. 5.5 - Prob. 107ECh. 5.5 - Prob. 108ECh. 5.5 - Prob. 109ECh. 5.5 - Prob. 110ECh. 5.5 - Prob. 111ECh. 5.5 - Prob. 112ECh. 5.5 - Prob. 113ECh. 5.5 - Prob. 114ECh. 5.5 - Prob. 115ECh. 5.5 - Prob. 116ECh. 5.5 - Prob. 117ECh. 5.5 - Prob. 118ECh. 5.5 - Prob. 119ECh. 5.5 - Prob. 120ECh. 5.5 - Prob. 121ECh. 5.5 - Prob. 122ECh. 5.5 - Prob. 123ECh. 5.5 - Prob. 124ECh. 5.5 - Prob. 125ECh. 5.5 - Prob. 126ECh. 5.5 - Prob. 127ECh. 5.5 - Prob. 128ECh. 5.5 - Prob. 129ECh. 5.5 - Prob. 130ECh. 5.5 - Prob. 131ECh. 5.5 - Prob. 132ECh. 5.5 - Prob. 133ECh. 5.5 - Prob. 134ECh. 5.5 - Prob. 135ECh. 5.5 - Prob. 136ECh. 5.5 - Prob. 137ECh. 5.5 - Prob. 138ECh. 5.5 - Prob. 139ECh. 5.5 - Prob. 140ECh. 5 - Prob. 1RECh. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - Prob. 4RECh. 5 - Prob. 5RECh. 5 - Prob. 6RECh. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Prob. 9RECh. 5 - Prob. 10RECh. 5 - Prob. 11RECh. 5 - Prob. 12RECh. 5 - Prob. 13RECh. 5 - Prob. 14RECh. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - Prob. 17RECh. 5 - Prob. 18RECh. 5 - Prob. 19RECh. 5 - Prob. 20RECh. 5 - Prob. 21RECh. 5 - Prob. 22RECh. 5 - Prob. 23RECh. 5 - Prob. 24RECh. 5 - Prob. 25RECh. 5 - Prob. 26RECh. 5 - Prob. 27RECh. 5 - Prob. 28RECh. 5 - Prob. 29RECh. 5 - Prob. 30RECh. 5 - Prob. 31RECh. 5 - Prob. 32RECh. 5 - Prob. 33RECh. 5 - Prob. 34RECh. 5 - Prob. 35RECh. 5 - Prob. 36RECh. 5 - Prob. 37RECh. 5 - Prob. 38RECh. 5 - Prob. 39RECh. 5 - Prob. 40RECh. 5 - Prob. 41RECh. 5 - Prob. 42RECh. 5 - Prob. 43RECh. 5 - Prob. 44RECh. 5 - Prob. 45RECh. 5 - Prob. 46RECh. 5 - Prob. 47RECh. 5 - Prob. 48RECh. 5 - Prob. 49RECh. 5 - Prob. 50RECh. 5 - Prob. 51RECh. 5 - Prob. 52RECh. 5 - Prob. 53RECh. 5 - Prob. 54RECh. 5 - Prob. 55RECh. 5 - Prob. 56RECh. 5 - Prob. 57RECh. 5 - Prob. 58RECh. 5 - Prob. 59RECh. 5 - Prob. 60RECh. 5 - Prob. 61RECh. 5 - Prob. 62RECh. 5 - Prob. 63RECh. 5 - Prob. 64RECh. 5 - Prob. 65RECh. 5 - Prob. 66RECh. 5 - Prob. 67RECh. 5 - Prob. 68RECh. 5 - Prob. 69RECh. 5 - Prob. 70RECh. 5 - Prob. 71RECh. 5 - Prob. 72RECh. 5 - Prob. 73RECh. 5 - Prob. 74RECh. 5 - Prob. 75RECh. 5 - Prob. 76RECh. 5 - Prob. 77RECh. 5 - Prob. 78RECh. 5 - Prob. 79RECh. 5 - Prob. 80RECh. 5 - Prob. 81RECh. 5 - Prob. 82RECh. 5 - Prob. 83RECh. 5 - Prob. 84RECh. 5 - Prob. 85RECh. 5 - Prob. 86RECh. 5 - Prob. 87RECh. 5 - Prob. 88RECh. 5 - Prob. 89RECh. 5 - Prob. 90RECh. 5 - Prob. 91RECh. 5 - Prob. 92RECh. 5 - Prob. 93RECh. 5 - Prob. 94RECh. 5 - Prob. 95RECh. 5 - Prob. 96RECh. 5 - Prob. 97RECh. 5 - Prob. 98RECh. 5 - Prob. 99RECh. 5 - Prob. 100RECh. 5 - Prob. 101RECh. 5 - Prob. 102RECh. 5 - Prob. 103RECh. 5 - Prob. 104RECh. 5 - Prob. 105RECh. 5 - Prob. 106RECh. 5 - Prob. 107RECh. 5 - Prob. 108RECh. 5 - Prob. 109RECh. 5 - Prob. 110RECh. 5 - Prob. 111RECh. 5 - Prob. 112RECh. 5 - Prob. 113RECh. 5 - Prob. 114RECh. 5 - Prob. 115RECh. 5 - Prob. 116RECh. 5 - Prob. 117RECh. 5 - Prob. 118RECh. 5 - Prob. 119RECh. 5 - Prob. 120RECh. 5 - Prob. 121RECh. 5 - Prob. 122RECh. 5 - Prob. 123RECh. 5 - Prob. 124RECh. 5 - Prob. 125RECh. 5 - Prob. 126RECh. 5 - Prob. 127RECh. 5 - Prob. 128RECh. 5 - Prob. 129RECh. 5 - Prob. 130RECh. 5 - Prob. 131RECh. 5 - Prob. 132RECh. 5 - Prob. 133RECh. 5 - Prob. 134RECh. 5 - Prob. 135RECh. 5 - Prob. 136RECh. 5 - Prob. 137RECh. 5 - Prob. 138RECh. 5 - Prob. 139RECh. 5 - Prob. 140RECh. 5 - Prob. 1CTCh. 5 - Prob. 2CTCh. 5 - Prob. 3CTCh. 5 - Prob. 4CTCh. 5 - Prob. 5CTCh. 5 - Prob. 6CTCh. 5 - Prob. 7CTCh. 5 - Prob. 8CTCh. 5 - Prob. 9CTCh. 5 - Prob. 10CTCh. 5 - Prob. 11CTCh. 5 - Prob. 12CTCh. 5 - Prob. 13CTCh. 5 - Prob. 14CTCh. 5 - Prob. 15CTCh. 5 - Prob. 16CTCh. 5 - Prob. 17CTCh. 5 - Prob. 18CTCh. 5 - Prob. 19CTCh. 5 - Prob. 20CTCh. 5 - Prob. 21CTCh. 5 - Prob. 22CTCh. 5 - Prob. 23CTCh. 5 - Prob. 24CT
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