Precalculus (MindTap Course List)
10th Edition
ISBN: 9781337271073
Author: Ron Larson
Publisher: Cengage Learning
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Question
Chapter 1.CR, Problem 95CR
To determine
a)
To graph:
The
To determine
b)
To find:
The equation of the least squares regression line that fits the data of the amount of beef produced on private farms for the years from 2007 through 2014 and to graph the model and the scatter plot in the same graph and to interpret how closely the model represents the data.
Solution:
The least squares regression equation is
The model represents a very close relationship with the data.
Explanation:
Definition:
Regression is a statistical method used to model the relationship between two sets of variables. The least squares equation is defined as,
Here, X is the independent variable, Y is the dependent variable, a is the y-intercept and b is the slope of the line.
Calculation:
Consider the provided information of the amount B (in millions of pounds) of beef produced on private farms for years from 2007 through 2017.
Assume that t represents the year with
Excel can be used to determine the least squares regression equation. The steps followed to construct the scatter plot are:
Step 1: Open Excel worksheet. Enter the provided data of years and amount of beef.
Step 2: In the menu bar, select Data➔Data Analysis.
Step 3: In the dialog that appears, select Regression. Click ‘Ok’.
Step 4: In the window that appears, select the Input Y-Range and Input X-Range and click Ok.
The least squares regression equation is obtained as,
Now, graph the model with the scatter plot in the same graph. The steps followed in Excel are:
Step 1: Open the obtained scatter plot in part (a).
Step 2: Right click on the graph and select Add Trendline from the dropdown list.
Step 3: Again Right click on the trend line added and select Format Trendline.
Step 4: In the window that appears select “Display Equation on Chart”. Click Ok.
The graph is obtained as:
The obtained graph shows the scatter plot and the regression model on the same graph. The graph shows that the data points are very close to the regression line. This indicates that there is a close relationship between the data and the model.
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Chapter 1 Solutions
Precalculus (MindTap Course List)
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The ______ of a...Ch. 1.5 - Vocabulary: Fill in the blanks. A function f is...Ch. 1.5 - Vocabulary: Fill in the blanks. A function value...Ch. 1.5 - Vocabulary: Fill in the blanks. The _______...Ch. 1.5 - Vocabulary: Fill in the blanks. 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In Exercises 71 76,...Ch. 1.5 - Even, Odd, or Neither? In Exercises 71 76,...Ch. 1.5 - Even, Odd, or Neither? In Exercises 77 82, sketch...Ch. 1.5 - Even, Odd, or Neither? In Exercises 77 82, sketch...Ch. 1.5 - Even, Odd, or Neither? In Exercises 77 82, sketch...Ch. 1.5 - Even, Odd, or Neither? In Exercises 77 82, sketch...Ch. 1.5 - Even, Odd, or Neither? In Exercises 77 82, sketch...Ch. 1.5 - Even, Odd, or Neither? In Exercises 77 82, sketch...Ch. 1.5 - Height of a Rectangle In Exercises 83 and 84,...Ch. 1.5 - Height of a Rectangle In Exercises 83 and 84,...Ch. 1.5 - Length of a Rectangle In Exercises 85 and 86,...Ch. 1.5 - Length of a Rectangle In Exercises 85 and 86,...Ch. 1.5 - Error Analysis Describe the error. The function...Ch. 1.5 - Geometry Corners of equal size are cut from a...Ch. 1.5 - Coordinate Axis Scale Each function described...Ch. 1.5 - Temperature The table shows the temperatures y in...Ch. 1.5 - True or False? In Exercises 91-93, determine...Ch. 1.5 - True or False? In Exercises 91-93, determine...Ch. 1.5 - True or False? In Exercises 91-93, determine...Ch. 1.5 - HOW DO YOU SEE IT? Use the graph of the function...Ch. 1.5 - Think About It In Exercises 95 and 96, find the...Ch. 1.5 - Think About It In Exercises 95 and 96, find the...Ch. 1.5 - Writing Use a graphing utility to graph each...Ch. 1.5 - Graphical Reasoning Graph each of the functions...Ch. 1.5 - Even, Odd, or Neither? Determine whether g is...Ch. 1.6 - Write the linear function f for which...Ch. 1.6 - Evaluate the function f(x)=x+2 when x=32,1,and52.Ch. 1.6 - Sketch the graph of f(x)={12x6,x4x+5,x>4Ch. 1.6 - Vocabulary In Exercises 1-9, write the specific...Ch. 1.6 - Vocabulary In Exercises 1-9, write the specific...Ch. 1.6 - Vocabulary In Exercises 1-9, write the specific...Ch. 1.6 - Prob. 4ECh. 1.6 - Prob. 5ECh. 1.6 - Prob. 6ECh. 1.6 - Prob. 7ECh. 1.6 - Prob. 8ECh. 1.6 - Prob. 9ECh. 1.6 - Prob. 10ECh. 1.6 - Prob. 11ECh. 1.6 - Prob. 12ECh. 1.6 - Writing a Linear Function In Exercises 11-14, a...Ch. 1.6 - Prob. 14ECh. 1.6 - Prob. 15ECh. 1.6 - Prob. 16ECh. 1.6 - Prob. 17ECh. 1.6 - Prob. 18ECh. 1.6 - Prob. 19ECh. 1.6 - Prob. 20ECh. 1.6 - Prob. 21ECh. 1.6 - Prob. 22ECh. 1.6 - Prob. 23ECh. 1.6 - Graphing a Function In Exercises 15-26, use a...Ch. 1.6 - Prob. 25ECh. 1.6 - Prob. 26ECh. 1.6 - Evaluating a Step Function In Exercises 27-30,...Ch. 1.6 - Prob. 27.2ECh. 1.6 - Prob. 27.3ECh. 1.6 - Prob. 27.4ECh. 1.6 - Prob. 28.1ECh. 1.6 - Prob. 28.2ECh. 1.6 - Prob. 28.3ECh. 1.6 - Prob. 28.4ECh. 1.6 - Evaluating a Step Function In Exercises 27-30,...Ch. 1.6 - Prob. 29.2ECh. 1.6 - Prob. 29.3ECh. 1.6 - Prob. 29.4ECh. 1.6 - Prob. 30.1ECh. 1.6 - Prob. 30.2ECh. 1.6 - Prob. 30.3ECh. 1.6 - Prob. 30.4ECh. 1.6 - Prob. 31ECh. 1.6 - Prob. 32ECh. 1.6 - Prob. 33ECh. 1.6 - Prob. 34ECh. 1.6 - Graphing a Piecewise-Defined Function In Exercises...Ch. 1.6 - Graphing a Piecewise-Defined Function In Exercises...Ch. 1.6 - Graphing a Piecewise-Defined Function In Exercises...Ch. 1.6 - Graphing a Piecewise-Defined Function In Exercises...Ch. 1.6 - Graphing a Piecewise-Defined Function In Exercises...Ch. 1.6 - Prob. 40ECh. 1.6 - Prob. 41ECh. 1.6 - Prob. 42ECh. 1.6 - Wages A mechanics pay is 14 per hour for regular...Ch. 1.6 - Wages A mechanics pay is 14 per hour for regular...Ch. 1.6 - Wages A mechanics pay is 14 per hour for regular...Ch. 1.6 - Prob. 44ECh. 1.6 - Prob. 45ECh. 1.6 - Prob. 46ECh. 1.6 - Prob. 47ECh. 1.6 - HOW DO YOU SEE IT? For each graph of f shown...Ch. 1.6 - Prob. 49ECh. 1.6 - Prob. 50ECh. 1.7 - Checkpoint Use the graph of f(x)=x3 to sketch the...Ch. 1.7 - Prob. 2CPCh. 1.7 - Prob. 3CPCh. 1.7 - Checkpoint Compare the graph of each function with...Ch. 1.7 - Prob. 5CPCh. 1.7 - Prob. 1ECh. 1.7 - Prob. 2ECh. 1.7 - Prob. 3ECh. 1.7 - Prob. 4ECh. 1.7 - Shifting the Graph of a Function For each...Ch. 1.7 - Prob. 6ECh. 1.7 - Prob. 7ECh. 1.7 - Prob. 8ECh. 1.7 - Sketching Transformations In Exercises 9 and 10,...Ch. 1.7 - Sketching Transformations In Exercises 9 and 10,...Ch. 1.7 - Writing Equations from Graphs Use the graph of...Ch. 1.7 - Writing Equations from Graphs Use the graph of...Ch. 1.7 - Prob. 13ECh. 1.7 - Prob. 14ECh. 1.7 - Prob. 15ECh. 1.7 - Prob. 16ECh. 1.7 - Prob. 17ECh. 1.7 - Prob. 18ECh. 1.7 - Prob. 19ECh. 1.7 - Prob. 20ECh. 1.7 - Describing Transformations In Exercises 21 38, g...Ch. 1.7 - Describing Transformations In Exercises 21 38, g...Ch. 1.7 - Describing Transformations In Exercises 21 38, g...Ch. 1.7 - Prob. 24ECh. 1.7 - Prob. 25ECh. 1.7 - Prob. 26ECh. 1.7 - Prob. 27ECh. 1.7 - Prob. 28ECh. 1.7 - Prob. 29ECh. 1.7 - Prob. 30ECh. 1.7 - Prob. 31ECh. 1.7 - Prob. 32ECh. 1.7 - Prob. 33ECh. 1.7 - Prob. 34ECh. 1.7 - Describing Transformations In Exercises 21 38, g...Ch. 1.7 - Describing Transformations In Exercises 21 38, g...Ch. 1.7 - Prob. 37ECh. 1.7 - Prob. 38ECh. 1.7 - Prob. 39ECh. 1.7 - Prob. 40ECh. 1.7 - Prob. 41ECh. 1.7 - Writing an Equation from a Description In...Ch. 1.7 - Prob. 43ECh. 1.7 - Prob. 44ECh. 1.7 - Prob. 45ECh. 1.7 - Prob. 46ECh. 1.7 - Prob. 47ECh. 1.7 - Prob. 48ECh. 1.7 - Writing Equations from Graphs Use the graph of...Ch. 1.7 - Writing Equations from Graphs Use the graph of...Ch. 1.7 - Prob. 51ECh. 1.7 - Prob. 52ECh. 1.7 - Prob. 53ECh. 1.7 - Prob. 54ECh. 1.7 - Prob. 55ECh. 1.7 - Prob. 56ECh. 1.7 - Prob. 57ECh. 1.7 - Prob. 58ECh. 1.7 - Prob. 59ECh. 1.7 - Prob. 60ECh. 1.7 - Prob. 61ECh. 1.7 - Prob. 62ECh. 1.7 - Prob. 63ECh. 1.7 - Prob. 64ECh. 1.7 - Prob. 65ECh. 1.7 - Prob. 66ECh. 1.7 - Prob. 67ECh. 1.7 - Prob. 68ECh. 1.7 - Prob. 69ECh. 1.7 - Prob. 70ECh. 1.7 - Prob. 71ECh. 1.7 - Prob. 72ECh. 1.8 - Given f(x)=x2andg(x)=1x,find(f+g)(x). Then...Ch. 1.8 - Prob. 2CPCh. 1.8 - Prob. 3CPCh. 1.8 - Find (f/g)(x)and(g/f)(x) for the functions...Ch. 1.8 - Prob. 5CPCh. 1.8 - Prob. 6CPCh. 1.8 - Prob. 7CPCh. 1.8 - Prob. 8CPCh. 1.8 - Prob. 1ECh. 1.8 - Prob. 2ECh. 1.8 - Graphing the Sum of Two Functions In Exercises 3...Ch. 1.8 - Graphing the Sum of Two Functions In Exercises 3...Ch. 1.8 - Skills and Applications Finding Arithmetic...Ch. 1.8 - Prob. 6ECh. 1.8 - Prob. 7ECh. 1.8 - Prob. 8ECh. 1.8 - Finding Arithmetic Combinations of Functions In...Ch. 1.8 - Finding Arithmetic Combinations of Functions In...Ch. 1.8 - Prob. 11ECh. 1.8 - Prob. 12ECh. 1.8 - Prob. 13ECh. 1.8 - Prob. 14ECh. 1.8 - Prob. 15ECh. 1.8 - Prob. 16ECh. 1.8 - Prob. 17ECh. 1.8 - Prob. 18ECh. 1.8 - Prob. 19ECh. 1.8 - Prob. 20ECh. 1.8 - Prob. 21ECh. 1.8 - Prob. 22ECh. 1.8 - Prob. 23ECh. 1.8 - Prob. 24ECh. 1.8 - Prob. 25ECh. 1.8 - Prob. 26ECh. 1.8 - Prob. 27ECh. 1.8 - Prob. 28ECh. 1.8 - Prob. 29ECh. 1.8 - Prob. 30ECh. 1.8 - Prob. 31ECh. 1.8 - Finding Compositions of Functions In Exercises...Ch. 1.8 - Finding Compositions of Functions In Exercises...Ch. 1.8 - Prob. 34ECh. 1.8 - Prob. 35ECh. 1.8 - Prob. 36ECh. 1.8 - Prob. 37ECh. 1.8 - Prob. 38ECh. 1.8 - Prob. 39ECh. 1.8 - Prob. 40ECh. 1.8 - Finding Domains of Functions and Composite...Ch. 1.8 - Prob. 42ECh. 1.8 - Prob. 43ECh. 1.8 - Prob. 44ECh. 1.8 - Prob. 45ECh. 1.8 - Prob. 46ECh. 1.8 - Evaluating Combinations of Functions In Exercises...Ch. 1.8 - Prob. 48ECh. 1.8 - Prob. 49ECh. 1.8 - Prob. 50ECh. 1.8 - Prob. 51ECh. 1.8 - Prob. 52ECh. 1.8 - Prob. 53ECh. 1.8 - Prob. 54ECh. 1.8 - Prob. 55ECh. 1.8 - Prob. 56ECh. 1.8 - Prob. 57ECh. 1.8 - Prob. 58ECh. 1.8 - Prob. 59ECh. 1.8 - Pets Let d(t) be the number of dogs in the United...Ch. 1.8 - Prob. 61ECh. 1.8 - Prob. 62ECh. 1.8 - Prob. 63ECh. 1.8 - Consumer Awareness The suggested retail price of a...Ch. 1.8 - Prob. 65ECh. 1.8 - Prob. 66ECh. 1.8 - Siblings In Exercises 67 and 68, three siblings...Ch. 1.8 - Prob. 68ECh. 1.8 - Prob. 69ECh. 1.8 - Prob. 70ECh. 1.8 - Prob. 71ECh. 1.8 - Prob. 72ECh. 1.8 - Proof a Given a function f, prove that g is even...Ch. 1.9 - Find the inverse function of f(x)=15x. Then verify...Ch. 1.9 - Prob. 2CPCh. 1.9 - Prob. 3CPCh. 1.9 - Prob. 4CPCh. 1.9 - Prob. 5CPCh. 1.9 - Prob. 6CPCh. 1.9 - Prob. 7CPCh. 1.9 - Fill in the blanks. If f(g(x)) and g(f(x)) both...Ch. 1.9 - Prob. 2ECh. 1.9 - Prob. 3ECh. 1.9 - Prob. 4ECh. 1.9 - Prob. 5ECh. 1.9 - Prob. 6ECh. 1.9 - Prob. 7ECh. 1.9 - Prob. 8ECh. 1.9 - Prob. 9ECh. 1.9 - Finding an Inverse Function Informally In Exercise...Ch. 1.9 - Prob. 11ECh. 1.9 - Prob. 12ECh. 1.9 - Finding an Inverse Function Informally In Exercise...Ch. 1.9 - Prob. 14ECh. 1.9 - Prob. 15ECh. 1.9 - Prob. 16ECh. 1.9 - Prob. 17ECh. 1.9 - Prob. 18ECh. 1.9 - Sketching the Graph of an Inverse Function In...Ch. 1.9 - Prob. 20ECh. 1.9 - Prob. 21ECh. 1.9 - Prob. 22ECh. 1.9 - Prob. 23ECh. 1.9 - Prob. 24ECh. 1.9 - Prob. 25ECh. 1.9 - Prob. 26ECh. 1.9 - Prob. 27ECh. 1.9 - Verifying Inverse Functions In Exercises 2132,...Ch. 1.9 - Prob. 29ECh. 1.9 - Prob. 30ECh. 1.9 - Prob. 31ECh. 1.9 - Verifying Inverse Functions In Exercises 2132,...Ch. 1.9 - Prob. 33ECh. 1.9 - Prob. 34ECh. 1.9 - Prob. 35ECh. 1.9 - Prob. 36ECh. 1.9 - Prob. 37ECh. 1.9 - Applying the Horizontal Line Test In Exercises...Ch. 1.9 - Prob. 39ECh. 1.9 - Prob. 40ECh. 1.9 - Prob. 41ECh. 1.9 - Prob. 42ECh. 1.9 - Prob. 43ECh. 1.9 - Prob. 44ECh. 1.9 - Prob. 45ECh. 1.9 - Finding and Analyzing Inverse Function In...Ch. 1.9 - Finding and Analyzing Inverse Function In...Ch. 1.9 - Finding and Analyzing Inverse Function In...Ch. 1.9 - Prob. 49ECh. 1.9 - Prob. 50ECh. 1.9 - Prob. 51ECh. 1.9 - Prob. 52ECh. 1.9 - Prob. 53ECh. 1.9 - Prob. 54ECh. 1.9 - Prob. 55ECh. 1.9 - Prob. 56ECh. 1.9 - Prob. 57ECh. 1.9 - Prob. 58ECh. 1.9 - Prob. 59ECh. 1.9 - Prob. 60ECh. 1.9 - Prob. 61ECh. 1.9 - Prob. 62ECh. 1.9 - Prob. 63ECh. 1.9 - Finding an Inverse Function In Exercises 5570,...Ch. 1.9 - Prob. 65ECh. 1.9 - Prob. 66ECh. 1.9 - Prob. 67ECh. 1.9 - Prob. 68ECh. 1.9 - Prob. 69ECh. 1.9 - Prob. 70ECh. 1.9 - Prob. 71ECh. 1.9 - Prob. 72ECh. 1.9 - Prob. 73ECh. 1.9 - Restricting the Domain In Exercises 7178, restrict...Ch. 1.9 - Prob. 75ECh. 1.9 - Prob. 76ECh. 1.9 - Prob. 77ECh. 1.9 - Prob. 78ECh. 1.9 - Prob. 79ECh. 1.9 - Prob. 80ECh. 1.9 - Prob. 81ECh. 1.9 - Prob. 82ECh. 1.9 - Prob. 83ECh. 1.9 - Prob. 84ECh. 1.9 - Prob. 85ECh. 1.9 - Prob. 86ECh. 1.9 - Prob. 87ECh. 1.9 - Prob. 88ECh. 1.9 - Prob. 89ECh. 1.9 - Prob. 90ECh. 1.9 - Prob. 91ECh. 1.9 - Prob. 92ECh. 1.9 - Prob. 93ECh. 1.9 - Prob. 94ECh. 1.9 - Prob. 95ECh. 1.9 - Prob. 96ECh. 1.9 - Prob. 97ECh. 1.9 - Prob. 98ECh. 1.9 - Prob. 99ECh. 1.9 - Prob. 100ECh. 1.9 - The number of miles n a marathon runner has...Ch. 1.9 - Prob. 102ECh. 1.10 - The ordered pairs below give the median sales...Ch. 1.10 - Prob. 2CPCh. 1.10 - The simple interest on an investment is directly...Ch. 1.10 - Prob. 4CPCh. 1.10 - Prob. 5CPCh. 1.10 - Prob. 6CPCh. 1.10 - Prob. 7CPCh. 1.10 - Prob. 1ECh. 1.10 - Prob. 2ECh. 1.10 - Prob. 3ECh. 1.10 - Prob. 4ECh. 1.10 - Prob. 5ECh. 1.10 - Prob. 6ECh. 1.10 - Prob. 7ECh. 1.10 - The joint variation model z=kxy can be described...Ch. 1.10 - Mathematical Models In Exercises 9 and 10, a plot...Ch. 1.10 - Prob. 10ECh. 1.10 - Prob. 11ECh. 1.10 - Prob. 12ECh. 1.10 - Sketching a Line In Exercises 11-16, sketch the...Ch. 1.10 - Prob. 14ECh. 1.10 - Prob. 15ECh. 1.10 - Prob. 16ECh. 1.10 - Sports The ordered pairs below give the winning...Ch. 1.10 - Broadway The ordered pairs below give the starting...Ch. 1.10 - Prob. 19ECh. 1.10 - Prob. 20ECh. 1.10 - Prob. 21ECh. 1.10 - Prob. 22ECh. 1.10 - Prob. 23ECh. 1.10 - Prob. 24ECh. 1.10 - Prob. 25ECh. 1.10 - Prob. 26ECh. 1.10 - Prob. 27ECh. 1.10 - Prob. 28ECh. 1.10 - Prob. 29ECh. 1.10 - Prob. 30ECh. 1.10 - Prob. 31ECh. 1.10 - Prob. 32ECh. 1.10 - Prob. 33ECh. 1.10 - Prob. 34ECh. 1.10 - Prob. 35ECh. 1.10 - Prob. 36ECh. 1.10 - Determining Variation In Exercises 35-38,...Ch. 1.10 - Prob. 38ECh. 1.10 - Prob. 39ECh. 1.10 - Prob. 40ECh. 1.10 - Prob. 41ECh. 1.10 - Finding a Mathematical Model In Exercises 39-48,...Ch. 1.10 - Prob. 43ECh. 1.10 - Prob. 44ECh. 1.10 - Finding a Mathematical Model In Exercises 39-48,...Ch. 1.10 - Prob. 46ECh. 1.10 - Finding a Mathematical Model In Exercises 39-48,...Ch. 1.10 - Prob. 48ECh. 1.10 - Prob. 49ECh. 1.10 - Prob. 50ECh. 1.10 - Prob. 51ECh. 1.10 - Prob. 52ECh. 1.10 - Prob. 53ECh. 1.10 - Prob. 54ECh. 1.10 - Prob. 55ECh. 1.10 - Prob. 56ECh. 1.10 - Prob. 57ECh. 1.10 - Finding a Mathematical Model In Exercises 53-60,...Ch. 1.10 - Prob. 59ECh. 1.10 - Prob. 60ECh. 1.10 - Simple Interest The simple interest on an...Ch. 1.10 - Prob. 62ECh. 1.10 - Prob. 63ECh. 1.10 - Measurement Use the fact that 14 gallons is...Ch. 1.10 - Prob. 65ECh. 1.10 - Prob. 66ECh. 1.10 - Prob. 67ECh. 1.10 - Prob. 68ECh. 1.10 - Ecology The diameter of the largest particle that...Ch. 1.10 - Work The work W required to lift an object varies...Ch. 1.10 - Ocean Temperatures The ordered pairs below give...Ch. 1.10 - Light IntensityThe ordered pairs below give the...Ch. 1.10 - MusicThe fundamental frequency in hertz of a piano...Ch. 1.10 - Prob. 74ECh. 1.10 - Prob. 75ECh. 1.10 - True or False?In Exercises 75 and 76, decide...Ch. 1.10 - Prob. 77ECh. 1.10 - Prob. 78ECh. 1.10 - Prob. 79ECh. 1.CR - Prob. 1CRCh. 1.CR - Plotting Points in the Cartesian Plane. In...Ch. 1.CR - Prob. 3CRCh. 1.CR - Prob. 4CRCh. 1.CR - Prob. 5CRCh. 1.CR - Prob. 6CRCh. 1.CR - Prob. 7CRCh. 1.CR - Prob. 8CRCh. 1.CR - Prob. 9CRCh. 1.CR - Prob. 10CRCh. 1.CR - Prob. 11CRCh. 1.CR - Prob. 12CRCh. 1.CR - Prob. 13CRCh. 1.CR - Prob. 14CRCh. 1.CR - Prob. 15CRCh. 1.CR - Prob. 16CRCh. 1.CR - Prob. 17CRCh. 1.CR - Prob. 18CRCh. 1.CR - Prob. 19CRCh. 1.CR - Prob. 20CRCh. 1.CR - Prob. 21CRCh. 1.CR - Prob. 22CRCh. 1.CR - Prob. 23CRCh. 1.CR - Prob. 24CRCh. 1.CR - Prob. 25CRCh. 1.CR - Prob. 26CRCh. 1.CR - Prob. 27CRCh. 1.CR - Prob. 28CRCh. 1.CR - Prob. 29CRCh. 1.CR - Prob. 30CRCh. 1.CR - Prob. 31CRCh. 1.CR - Prob. 32CRCh. 1.CR - Prob. 33CRCh. 1.CR - Prob. 34CRCh. 1.CR - Prob. 35CRCh. 1.CR - Prob. 36CRCh. 1.CR - Prob. 37CRCh. 1.CR - Prob. 38CRCh. 1.CR - Prob. 39CRCh. 1.CR - Prob. 40CRCh. 1.CR - Prob. 41CRCh. 1.CR - Prob. 42CRCh. 1.CR - Prob. 43CRCh. 1.CR - Prob. 44CRCh. 1.CR - Prob. 45CRCh. 1.CR - Prob. 46CRCh. 1.CR - Prob. 47.1CRCh. 1.CR - Prob. 47.2CRCh. 1.CR - Prob. 47.3CRCh. 1.CR - Prob. 47.4CRCh. 1.CR - Prob. 48.1CRCh. 1.CR - Prob. 48.2CRCh. 1.CR - Prob. 48.3CRCh. 1.CR - Prob. 48.4CRCh. 1.CR - Prob. 49CRCh. 1.CR - Prob. 50CRCh. 1.CR - Prob. 51CRCh. 1.CR - Prob. 52CRCh. 1.CR - Prob. 53CRCh. 1.CR - Prob. 54CRCh. 1.CR - Prob. 55CRCh. 1.CR - Prob. 56CRCh. 1.CR - Prob. 57CRCh. 1.CR - Prob. 58CRCh. 1.CR - Prob. 59CRCh. 1.CR - Prob. 60CRCh. 1.CR - Prob. 61CRCh. 1.CR - Prob. 62CRCh. 1.CR - Prob. 63CRCh. 1.CR - Prob. 64CRCh. 1.CR - Prob. 65CRCh. 1.CR - Prob. 66CRCh. 1.CR - Prob. 67CRCh. 1.CR - Prob. 68CRCh. 1.CR - Prob. 69CRCh. 1.CR - Prob. 70CRCh. 1.CR - Prob. 71CRCh. 1.CR - Prob. 72CRCh. 1.CR - Prob. 73CRCh. 1.CR - Prob. 74CRCh. 1.CR - Prob. 75CRCh. 1.CR - Prob. 76CRCh. 1.CR - Prob. 77CRCh. 1.CR - Prob. 78CRCh. 1.CR - Prob. 79CRCh. 1.CR - Prob. 80CRCh. 1.CR - Prob. 81CRCh. 1.CR - Prob. 82CRCh. 1.CR - Prob. 83CRCh. 1.CR - Prob. 84CRCh. 1.CR - Prob. 85CRCh. 1.CR - Prob. 86CRCh. 1.CR - Prob. 87CRCh. 1.CR - Prob. 88CRCh. 1.CR - Prob. 89CRCh. 1.CR - Prob. 90CRCh. 1.CR - Prob. 91.1CRCh. 1.CR - Prob. 91.2CRCh. 1.CR - Prob. 91.3CRCh. 1.CR - Prob. 91.4CRCh. 1.CR - Prob. 92.1CRCh. 1.CR - Prob. 92.2CRCh. 1.CR - Prob. 92.3CRCh. 1.CR - Prob. 92.4CRCh. 1.CR - Prob. 93CRCh. 1.CR - Prob. 94CRCh. 1.CR - Prob. 95CRCh. 1.CR - Prob. 96CRCh. 1.CR - Prob. 97CRCh. 1.CR - Prob. 98CRCh. 1.CR - Prob. 99CRCh. 1.CT - Prob. 1CTCh. 1.CT - Prob. 2CTCh. 1.CT - In Exercises 3-5, find any intercepts and test for...Ch. 1.CT - Prob. 4CTCh. 1.CT - Prob. 5CTCh. 1.CT - Prob. 6CTCh. 1.CT - Prob. 7CTCh. 1.CT - Prob. 8CTCh. 1.CT - Prob. 9CTCh. 1.CT - Prob. 10CTCh. 1.CT - Prob. 11CTCh. 1.CT - Prob. 12CTCh. 1.CT - Prob. 13CTCh. 1.CT - Prob. 14CTCh. 1.CT - Prob. 15CTCh. 1.CT - In Exercises 16-18, a identify the parent function...Ch. 1.CT - Prob. 17CTCh. 1.CT - In Exercises 16-18, a identify the parent function...Ch. 1.CT - Prob. 19CTCh. 1.CT - Prob. 20CTCh. 1.CT - Prob. 21CTCh. 1.CT - Prob. 22CTCh. 1.CT - Prob. 23CTCh. 1.CT - Prob. 24CTCh. 1.CT - Prob. 25CTCh. 1.CT - Prob. 26CTCh. 1.PS - Prob. 1PSCh. 1.PS - Prob. 2PSCh. 1.PS - Prob. 3PSCh. 1.PS - Prob. 4PSCh. 1.PS - Prob. 5PSCh. 1.PS - Prob. 6PSCh. 1.PS - Prob. 7PSCh. 1.PS - Prob. 8PSCh. 1.PS - Prob. 9PSCh. 1.PS - Prob. 10PSCh. 1.PS - Prob. 11.1PSCh. 1.PS - Prob. 11.2PSCh. 1.PS - Prob. 11.3PSCh. 1.PS - Prob. 11.4PSCh. 1.PS - Prob. 11.5PSCh. 1.PS - Prob. 11.6PSCh. 1.PS - Prob. 12.1PSCh. 1.PS - Prob. 12.2PSCh. 1.PS - Prob. 12.3PSCh. 1.PS - Prob. 13PSCh. 1.PS - Prob. 14.1PSCh. 1.PS - Prob. 14.2PSCh. 1.PS - Prob. 14.3PSCh. 1.PS - Prob. 14.4PSCh. 1.PS - Prob. 14.5PSCh. 1.PS - Prob. 14.6PSCh. 1.PS - Prob. 14.7PSCh. 1.PS - Prob. 15.1PSCh. 1.PS - Prob. 15.2PSCh. 1.PS - Prob. 15.3PSCh. 1.PS - Prob. 15.4PS
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- (2) (22 points) Let F(x, y, z) = (x sin y, cos y, ―xy). (a) (2 points) Calculate V. F. (b) (6 points) Given a vector field is everywhere defined with V G₁(x, y, z) = * G2(x, y, z) = − G3(x, y, z) = 0. 0 0 F(x, y, z) = (F₁(x, y, z), F₂(x, y, z), F(x, y, z)) that F = 0, let G = (G1, G2, G3) where F₂(x, y, y, t) dt - √ F³(x, t, 0) dt, * F1(x, y, t) dt, t) dt - √ F Calculate G for the vector field F(x, y, z) = (x sin y, cos y, -xy).arrow_forwardEvaluate the following integral over the Region R. (Answer accurate to 2 decimal places). √ √(x + y) A R R = {(x, y) | 25 < x² + y² ≤ 36, x < 0} Hint: The integral and Region is defined in rectangular coordinates.arrow_forwardFind the volume of the solid that lies under the paraboloid z = 81 - x² - y² and within the cylinder (x − 1)² + y² = 1. A plot of an example of a similar solid is shown below. (Answer accurate to 2 decimal places). Volume using Double Integral Paraboloid & Cylinder -3 Hint: The integral and region is defined in polar coordinates.arrow_forward
- Evaluate the following integral over the Region R. (Answer accurate to 2 decimal places). √4(1–2² 4(1 - x² - y²) dA R 3 R = {(r,0) | 0 ≤ r≤ 2,0π ≤0≤¼˜}. Hint: The integral is defined in rectangular coordinates. The Region is defined in polar coordinates.arrow_forwardEvaluate the following integral over the Region R. (Answer accurate to 2 decimal places). R - 1 · {(r,0) | 1 ≤ r≤ 5,½π≤ 0<1π}. Hint: Be sure to convert to Polar coordinates. Use the correct differential for Polar Coordinates.arrow_forwardEvaluate the following integral over the Region R. (Answer accurate to 2 decimal places). √ √2(x+y) dA R R = {(x, y) | 4 < x² + y² < 25,0 < x} Hint: The integral and Region is defined in rectangular coordinates.arrow_forward
- HW: The frame shown in the figure is pinned at A and C. Use moment distribution method, with and without modifications, to draw NFD, SFD, and BMD. B I I 40 kN/m A 3 m 4 marrow_forwardLet the region R be the area enclosed by the function f(x)= = 3x² and g(x) = 4x. If the region R is the base of a solid such that each cross section perpendicular to the x-axis is an isosceles right triangle with a leg in the region R, find the volume of the solid. You may use a calculator and round to the nearest thousandth. y 11 10 9 00 8 7 9 5 4 3 2 1 -1 -1 x 1 2arrow_forwardLet the region R be the area enclosed by the function f(x) = ex — 1, the horizontal line y = -4 and the vertical lines x = 0 and x = 3. Find the volume of the solid generated when the region R is revolved about the line y = -4. You may use a calculator and round to the nearest thousandth. 20 15 10 5 y I I I | I + -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 -5 I -10 -15 I + I I T I I + -20 I + -25 I I I -30 I 3.5 4 xarrow_forward
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