PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Question
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Chapter 5.3, Problem 104E

a.

To determine

To graph: A scatter plot of the given data.

a.

Expert Solution
Check Mark

Explanation of Solution

Given information:

The following table with Temperature T (in degree Fahrenheit) for month t with t=1 corresponding to January:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.3, Problem 104E , additional homework tip 1

Graph:

Plot the points in the above table on a graph using a graphing utility. t represents values on the x-axis while T represents values on the y-axis. The scatter plot will be as follows:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.3, Problem 104E , additional homework tip 2

Interpretation:

The graph is in the form of a half wave.

b.

To determine

To find: A sine model for the temperature.

b.

Expert Solution
Check Mark

Answer to Problem 104E

A sine model for the temperature is as follows:

  84.3713+4.4503sin(0.5193x−2.4928)

with x corresponding to month.

Explanation of Solution

Given information:

The following table with Temperature T (in degree Fahrenheit) for month t with t=1 corresponding to January:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.3, Problem 104E , additional homework tip 3

Calculation:

To find a sine model for the temperature, 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:

  84.3713+4.4503sin(0.5193x−2.4928)

c.

To determine

To graph: The scatter plot and the sine model in the same widow

c.

Expert Solution
Check Mark

Explanation of Solution

Given information:

The following table with Temperature T (in degree Fahrenheit) for month t with t=1 corresponding to January:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.3, Problem 104E , additional homework tip 4

Graph:

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

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.3, Problem 104E , additional homework tip 5

Interpretation:

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

d.

To determine

To find: The average temperature using the term in part (b).

d.

Expert Solution
Check Mark

Answer to Problem 104E

The average temperature using the term in part (b) is as follows:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.3, Problem 104E , additional homework tip 6

Explanation of Solution

Given information:

The following table with Temperature T (in degree Fahrenheit) for month t with t=1 corresponding to January:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.3, Problem 104E , additional homework tip 7

The model obtained in part(b) is as follows:

  t=84.3713+4.4503sin(0.5193x−2.4928)

Where t corresponds to average daily temperature and x corresponds to the number of month.

The average daily temperature using this model is obtained by creating a table of values using this model. Create a table that shows the values of t for different values of x . The table is obtained as follows:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.3, Problem 104E , additional homework tip 8

Here f(x) corresponds to t .

e.

To determine

To describe: The months in which the daily high temperature is above 86°F .

e.

Expert Solution
Check Mark

Answer to Problem 104E

The months in which the daily high temperature is above 86°F are:

June, July, August, September and October.

Explanation of Solution

Given information:

The following table with Temperature T (in degree Fahrenheit) for month t with t=1 corresponding to January:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.3, Problem 104E , additional homework tip 9

As obtained in part(c), the graph of the daily high temperatures is as follows:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.3, Problem 104E , additional homework tip 10

As observed from the graph, the daily high temperature is above 86°F for months 6,7,8,9 and 10 .

These months correspond to June, July, August, September and October.

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Chapter 5.3, Problem 103E
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Chapter 5.3, Problem 105E

Chapter 5 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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