Intermediate Algebra (8th Edition)
8th Edition
ISBN: 9780134178967
Author: John Tobey Jr., Jeffrey Slater, Jamie Blair, Jenny Crawford
Publisher: PEARSON
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Chapter 3, Problem 9RP
A line has a slope of
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You are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by twovectors, w1 and w2. Your task is to project the plane Π onto the subspace W.First, answer the question of what the projection matrix is that projects onto the subspace W and how toapply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidtmethod to find an orthonormal basis for subspace W, before then using the resulting basis vectors for theprojection. Last, compare the results obtained from both methods
Plane II is spanned by the vectors:
- (2) · P² - (4)
P1=2
P21
3
Subspace W is spanned by the vectors:
2
W1
- (9) ·
1
W2
1
= (³)
Chapter 3 Solutions
Intermediate Algebra (8th Edition)
Ch. 3.1 - Verbal and Writing Skills, Exercises 1-4
1. Graphs...Ch. 3.1 - Verbal and Writing Skills, Exercises 1-4
2. The...Ch. 3.1 - Verbal and Writing Skills, Exercises 1-4 Explain...Ch. 3.1 - Verbal and Writing Skills, Exercises 1-4 (5, 1) is...Ch. 3.1 - Find the missing coordinate. ( − 2 , _ _ _ _ ) is...Ch. 3.1 - Find the missing coordinate. ( − 5 , _ _ _ _ ) is...Ch. 3.1 - Find the missing coordinate.
7. is a solution of...Ch. 3.1 - Find the missing coordinate. ( _ _ _ _ _ , 2 3 )...Ch. 3.1 - Graph each equation. y = 2 x − 3Ch. 3.1 - Graph each equation.
10.
Ch. 3.1 - Graph each equation. y = 1 − 3 xCh. 3.1 - Graph each equation.
12.
Ch. 3.1 - Graph each equation.
12.
Ch. 3.1 - Graph each equation. y = 5 2 x + 1Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify each equation if possible. Then graph the...Ch. 3.1 - Simplify each equation if possible. Then graph the...Ch. 3.1 - Simplify each equation if possible. Then graph the...Ch. 3.1 - Simplify each equation if possible. Then graph the...Ch. 3.1 - Simplify each equation if possible. Then graph the...Ch. 3.1 - Graph each equation. Use appropriate scales on...Ch. 3.1 - Graph each equation. Use appropriate scales on...Ch. 3.1 - Income of Men Versus Women The following graph...Ch. 3.1 - Income of Men Versus Women The following graph...Ch. 3.1 - Income of Men Versus Women The following graph...Ch. 3.1 - Income of Men Versus Women The following graph...Ch. 3.1 - Income of Men Versus Women The following graph...Ch. 3.1 - Prob. 42ECh. 3.1 - 43. Baseball If a baseball is thrown vertically...Ch. 3.1 - 44. Gasoline Storage Tank A full storage tank on...Ch. 3.1 - [1.3.3] Evaluate 36 ÷ ( 8 − 6 ) 2 + 3 ( − 4 )Ch. 3.1 - Prob. 46ECh. 3.1 - 47. [2.4.1.] Balloon Giveaway A novelty company is...Ch. 3.1 - Prob. 48ECh. 3.1 - Prob. 1QQCh. 3.1 - Prob. 2QQCh. 3.1 - Prob. 3QQCh. 3.1 - Prob. 4QQCh. 3.2 - Verbal and Writing Skills, Exercises 1-6 Slope...Ch. 3.2 - Verbal and Writing Skills, Exercises 1-6 A...Ch. 3.2 - Verbal and Writing Skills, Exercises 1-6 The slope...Ch. 3.2 - Verbal and Writing Skills, Exercises 1-6
4. Two...Ch. 3.2 - Verbal and Writing Skills, Exercises 1-6
5. Does...Ch. 3.2 - Prob. 6ECh. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - 19. Snowboarding Find the slope (grade) of a...Ch. 3.2 - 20. Grade of a Road Find the grade of a mountain...Ch. 3.2 - Rock Formation Find the slope (pitch) of a...Ch. 3.2 - Pitch of a Roof Find the slope (pitch) of a roof...Ch. 3.2 - 23. Slope of Street Baldwin Street in Dunedin, New...Ch. 3.2 - 24. Slope of a Roller Coaster Goliath at Six Flags...Ch. 3.2 - Find the slope of a line parallel to the line that...Ch. 3.2 - Find the slope of a line parallel to the line that...Ch. 3.2 - Find the slope of a line parallel to the line that...Ch. 3.2 - Find the slope of a line parallel to the line that...Ch. 3.2 - Prob. 29ECh. 3.2 - Find the slope of a line parallel to the line that...Ch. 3.2 - Find the slope of a line perpendicular to the line...Ch. 3.2 - Find the slope of a line perpendicular to the line...Ch. 3.2 - Find the slope of a line perpendicular to the line...Ch. 3.2 - Find the slope of a line perpendicular to the line...Ch. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - A line k passes through the points ( − 3 , − 9 )...Ch. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - 40. Do the points , and C(8,1) lie on a straight...Ch. 3.2 - 41. Architect Most new buildings are required to...Ch. 3.2 - Rate of Climb of Aircraft A small Cessna plane...Ch. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 1QQCh. 3.2 - Prob. 2QQCh. 3.2 - Prob. 3QQCh. 3.2 - Prob. 4QQCh. 3.3 - Verbal and Writing Skills, Exercises 1 and 2 You...Ch. 3.3 - Verbal and Writing Skills, Exercises 1 and 2
2....Ch. 3.3 - Write an equation of the line with the given slope...Ch. 3.3 - Write an equation of the line with the given slope...Ch. 3.3 - Write an equation of the line with the given slope...Ch. 3.3 - Write an equation of the line with the given slope...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Write each equation in slope-intercept form. Then...Ch. 3.3 - Prob. 17ECh. 3.3 - Write each equation in slope-intercept form. Then...Ch. 3.3 - Write each equation in slope-intercept form. Then...Ch. 3.3 - Write each equation in slope-intercept form. Then...Ch. 3.3 - Write each equation in slope-intercept form. Then...Ch. 3.3 - For each equation find the slope and the...Ch. 3.3 - Prob. 23ECh. 3.3 - For each equation find the slope and the...Ch. 3.3 - For each equation find the slope and the...Ch. 3.3 - Prob. 26ECh. 3.3 - Find an equation of the line that passes through...Ch. 3.3 - Find an equation of the line that passes through...Ch. 3.3 - Find an equation of the line that passes through...Ch. 3.3 - Find an equation of the line that passes through...Ch. 3.3 - Find an equation of the line that passes through...Ch. 3.3 - Find an equation of the line passing through the...Ch. 3.3 - Find an equation of the line passing through the...Ch. 3.3 - Find an equation of the line passing through the...Ch. 3.3 - Find an equation of the line passing through the...Ch. 3.3 - Find an equation of the line passing through the...Ch. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Find an equation of the line satisfying the...Ch. 3.3 - Find an equation of the line satisfying the...Ch. 3.3 - Find an equation of the line satisfying the...Ch. 3.3 - Find an equation of the line satisfying the...Ch. 3.3 - Prob. 44ECh. 3.3 - Find an equation of the line satisfying the...Ch. 3.3 - Prob. 46ECh. 3.3 - Without graphing, determine whether the following...Ch. 3.3 - Prob. 48ECh. 3.3 - Without graphing, determine whether the following...Ch. 3.3 - Prob. 50ECh. 3.3 - Without graphing, determine whether the following...Ch. 3.3 - Prob. 52ECh. 3.3 - Prob. 53ECh. 3.3 - Prob. 54ECh. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - Cost of Homes The median sale price of...Ch. 3.3 - Prob. 58ECh. 3.3 - Prob. 59ECh. 3.3 - Prob. 60ECh. 3.3 - Prob. 61ECh. 3.3 - Prob. 1QQCh. 3.3 - Prob. 2QQCh. 3.3 - Prob. 3QQCh. 3.3 - Prob. 4QQCh. 3.4 - Verbal and Writing Skills, Exercises 1-6 Explain...Ch. 3.4 - Prob. 2ECh. 3.4 - Verbal and Writing Skills, Exercises 1-6 When...Ch. 3.4 - Prob. 4ECh. 3.4 - Verbal and Writing Skills, Exercises 1-6
5. When...Ch. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Graph each region.
9.
Ch. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Graph each region. 6 y − x ≤ 12Ch. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Graph each region.
17.
Ch. 3.4 - Graph each region. x − 3 y ≥ 0Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Prob. 22ECh. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Prob. 27ECh. 3.4 - Prob. 28ECh. 3.4 - Prob. 29ECh. 3.4 - Prob. 1QQCh. 3.4 - Prob. 2QQCh. 3.4 - Prob. 3QQCh. 3.4 - Prob. 4QQCh. 3.5 - Verbal and Writing Skills, Exercises 1-4 Explain...Ch. 3.5 - Prob. 2ECh. 3.5 - Verbal and Writing Skills, Exercises 1-4 What are...Ch. 3.5 - Prob. 4ECh. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - Prob. 10ECh. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - Prob. 12ECh. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - Prob. 14ECh. 3.5 - Prob. 15ECh. 3.5 - Prob. 16ECh. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a...Ch. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a...Ch. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a...Ch. 3.5 - Prob. 26ECh. 3.5 - Given the function defined by , find the...Ch. 3.5 - Prob. 28ECh. 3.5 - Given the function defined by , find the...Ch. 3.5 - Prob. 30ECh. 3.5 - Given the function defined by h ( x ) = 3 4 x + 1...Ch. 3.5 - Prob. 32ECh. 3.5 - Prob. 33ECh. 3.5 - Prob. 34ECh. 3.5 - Given the function defined by r ( x ) = 2 x 2 − 4...Ch. 3.5 - Prob. 36ECh. 3.5 - Given the function defined by , find the...Ch. 3.5 - Prob. 38ECh. 3.5 - Given the function defined by t ( x ) = x 3 − 3 x...Ch. 3.5 - Given the function defined by t ( x ) = x 3 − 3 x...Ch. 3.5 - Given the function defined by t ( x ) = x 3 − 3 x...Ch. 3.5 - 42. If , find
Ch. 3.5 - 43. If , find
Ch. 3.5 - Prob. 44ECh. 3.5 - 45. If , find g (2).
Ch. 3.5 - Prob. 46ECh. 3.5 - Find the range of the function for the given...Ch. 3.5 - Prob. 48ECh. 3.5 - Find the domain of the function for the given...Ch. 3.5 - Prob. 50ECh. 3.5 - Prob. 51ECh. 3.5 - Prob. 52ECh. 3.5 - Prob. 1QQCh. 3.5 - Prob. 2QQCh. 3.5 - Prob. 3QQCh. 3.5 - Prob. 4QQCh. 3.6 - Graph each function. f ( x ) = 3 4 x + 2Ch. 3.6 - Prob. 2ECh. 3.6 - Graph each function.
3.
Ch. 3.6 - Prob. 4ECh. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Wildlife Biologist Ning is a wildlife biologist...Ch. 3.6 - Insulation in a House The R value of insulation in...Ch. 3.6 - Graph each function.
9.
Ch. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Graph each function.
13.
Ch. 3.6 - Prob. 14ECh. 3.6 - Prob. 15ECh. 3.6 - Prob. 16ECh. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Graph each function.
19.
Ch. 3.6 - Prob. 20ECh. 3.6 - Graph each function.
21.
Ch. 3.6 - Prob. 22ECh. 3.6 - Prob. 23ECh. 3.6 - Prob. 24ECh. 3.6 - Prob. 25ECh. 3.6 - Prob. 26ECh. 3.6 - In each of the following problems, a table of...Ch. 3.6 - Prob. 28ECh. 3.6 - Prob. 29ECh. 3.6 - Prob. 30ECh. 3.6 - In each of the following problems, a table of...Ch. 3.6 - Prob. 32ECh. 3.6 - Computer Manufacturing The following table shows...Ch. 3.6 - Prob. 34ECh. 3.6 - Prob. 35ECh. 3.6 - Prob. 36ECh. 3.6 - Prob. 37ECh. 3.6 - Prob. 38ECh. 3.6 - Prob. 1QQCh. 3.6 - Prob. 2QQCh. 3.6 - Prob. 3QQCh. 3.6 - Concept Check Explain how you would find f ( 1 4 )...Ch. 3 - Graph the straight line determined by each of the...Ch. 3 - Graph the straight line determined by each of the...Ch. 3 - Prob. 3RPCh. 3 - Prob. 4RPCh. 3 - Prob. 5RPCh. 3 - Prob. 6RPCh. 3 - Prob. 7RPCh. 3 - 8. Find the slope of a line perpendicular to the...Ch. 3 - 9. A line has a slope of and a y-intercept of (0,...Ch. 3 - Find the standard form of the equation of the line...Ch. 3 - 11. Find the standard form of the equation of the...Ch. 3 - 12. Computer Company Profit A computer company's...Ch. 3 - In exercises 13 - 16, find an equation of the line...Ch. 3 - In exercises 13 - 16, find an equation of the line...Ch. 3 - Prob. 15RPCh. 3 - In exercises 13 - 16, find an equation of the line...Ch. 3 - In exercises 17 - 18, find the slope and...Ch. 3 - In exercises 17 -18, find the slope and...Ch. 3 - Prob. 19RPCh. 3 - Graph the region described by the inequality.
20....Ch. 3 - Graph the region described by the inequality. 3 x...Ch. 3 - Graph the region described by the inequality. x ≤...Ch. 3 - Prob. 23RPCh. 3 - Prob. 24RPCh. 3 - What is the domain and range of each relation? Is...Ch. 3 - What is the domain and range of each relation? Is...Ch. 3 - Determine whether the graph represents a function.Ch. 3 - Determine whether the graph represents a function.Ch. 3 - If f ( x ) = − 2 x + 10 , find f ( − 1 ) and f ( −...Ch. 3 - If h ( x ) = x 3 + 2 x 2 − 5 x + 8 , find h ( − 1...Ch. 3 - Graph each function. f ( x ) = 2 | x − 1 |Ch. 3 - Prob. 32RPCh. 3 - Prob. 33RPCh. 3 - Prob. 34RPCh. 3 - Prob. 35RPCh. 3 - Prob. 36RPCh. 3 - Complete the table of values for each...Ch. 3 - 38. Find the slope and y-intercept of .
Ch. 3 - A line n is perpendicular to the line passing...Ch. 3 - A line p is parallel to the line passing through...Ch. 3 - Find the standard form of the equation of the line...Ch. 3 - 42. Find an equation of the line parallel to and...Ch. 3 - Find the slope-intercept form of the equation of...Ch. 3 - Prob. 44RPCh. 3 - Prob. 45RPCh. 3 - Prob. 46RPCh. 3 - Prob. 47RPCh. 3 - Prob. 48RPCh. 3 - Prob. 1TCh. 3 - Prob. 2TCh. 3 - Prob. 3TCh. 3 - Prob. 4TCh. 3 - Find the slope of the line passing through ( 2 , −...Ch. 3 - Prob. 6TCh. 3 - Prob. 7TCh. 3 - Prob. 8TCh. 3 - Prob. 9TCh. 3 - Write an equation of the horizontal line passing...Ch. 3 - Prob. 11TCh. 3 - Prob. 12TCh. 3 - Prob. 13TCh. 3 - Prob. 14TCh. 3 - 15. If , find f .
Ch. 3 - Prob. 16TCh. 3 - Prob. 17TCh. 3 - Prob. 18TCh. 3 - Prob. 19TCh. 3 - Prob. 20TCh. 3 - Prob. 21TCh. 3 - Prob. 1CTCh. 3 - Evaluate the expression. 3 ( 4 − 6 ) 2 + 16 + 12 ÷...Ch. 3 - Prob. 3CTCh. 3 - Prob. 4CTCh. 3 - Prob. 5CTCh. 3 - Prob. 6CTCh. 3 - Prob. 7CTCh. 3 - Prob. 8CTCh. 3 - Prob. 9CTCh. 3 - Prob. 10CTCh. 3 - Prob. 11CTCh. 3 - Prob. 12CTCh. 3 - Prob. 13CTCh. 3 - Prob. 14CTCh. 3 - Prob. 15CTCh. 3 - Prob. 16CTCh. 3 - Prob. 17CTCh. 3 - Prob. 18CTCh. 3 - Prob. 19CTCh. 3 - Prob. 20CTCh. 3 - Prob. 21CTCh. 3 - Prob. 22CTCh. 3 - Prob. 23CTCh. 3 - Prob. 24CTCh. 3 - Prob. 25CT
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