Differential Equations with Boundary-Value Problems (MindTap Course List)
9th Edition
ISBN: 9781305965799
Author: Dennis G. Zill
Publisher: Cengage Learning
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Textbook Question
Chapter 8.1, Problem 7E
In Problems 7–10 write the given linear system without the use of matrices.
7.
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Scenario
Sales of products by color follow a peculiar, but predictable, pattern that determines how many units will sell in
any given year. This pattern is shown below
Product Color
1995
1996
1997
Red
28
42
21
1998
23
1999
29
2000
2001
2002
Unit Sales
2003 2004
15
8
4
2
1
2005 2006
discontinued
Green
26
39
20
22
28
14
7
4
2
White
43
65
33
36
45
23
12
Brown
58
87
44
48
60
Yellow
37
56
28
31
Black
28
42
21
Orange
19
29
Purple
Total
28
42
21
49
68
78
95
123
176
181
164
127
24
179
Questions
A) Which color will sell the most units in 2007?
B) Which color will sell the most units combined in the 2007 to 2009 period?
Please show all your analysis, leave formulas in cells, and specify any assumptions you make.
5. (20%) The linear transformation L: P3 → P2 defined by L(f(x)) = f'(x)+
f(0).
(a) Find the representing matrix A of L with respect to the ordered basis
{x2, x, 1} for P3, and the ordered basis {2,1 - x} for P2.
(b) Find the coordinates of the f(x) = 2x² +2 in P3 with respect to the
ordered basis {x2,-x, 1}, and find the coordinates of L(f(x)) with respect
to the ordered basis {2,1-x}
One hundred students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey.
Preference
Male
Female
TOTAL
Prefers dogs
\[36\]
\[20\]
\[56\]
Prefers cats
\[10\]
\[26\]
\[36\]
No preference
\[2\]
\[6\]
\[8\]
TOTAL
\[48\]
\[52\]
\[100\]
problem 1
Find the probability that a randomly selected student prefers dogs.Enter your answer as a fraction or decimal.
\[P\left(\text{prefers dogs}\right)=\]
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Preference
Male
Female
TOTAL
Prefers dogs
\[\blueD{36}\]
\[\blueD{20}\]
\[\blueE{56}\]
Prefers cats
\[10\]
\[26\]
\[36\]
No preference
\[2\]
\[6\]
\[8\]
TOTAL
\[48\]
\[52\]
\[100\]
There were \[\blueE{56}\] students in the sample who preferred dogs out of \[100\] total students.
Chapter 8 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - Prob. 2ECh. 8.1 - Prob. 3ECh. 8.1 - Prob. 4ECh. 8.1 - Prob. 5ECh. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - In Problems 710 write the given linear system...Ch. 8.1 - Prob. 8ECh. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - Prob. 10E
Ch. 8.1 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - Prob. 23ECh. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - Prob. 3ECh. 8.2 - Prob. 4ECh. 8.2 - Prob. 5ECh. 8.2 - Prob. 6ECh. 8.2 - Prob. 7ECh. 8.2 - Prob. 8ECh. 8.2 - Prob. 9ECh. 8.2 - Distinct Real Eigenvalues In Problems 112 find the...Ch. 8.2 - Prob. 11ECh. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - In Problem 27 of Exercises 4.9 you were asked to...Ch. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - Prob. 21ECh. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - Prob. 27ECh. 8.2 - Prob. 28ECh. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - Prob. 34ECh. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Prob. 40ECh. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - Prob. 46ECh. 8.2 - In Problems 47 and 48 solve the given...Ch. 8.2 - Prob. 48ECh. 8.2 - The system of mixing tanks shown in Figure 8.2.7...Ch. 8.2 - Prob. 50ECh. 8.2 - Prob. 51ECh. 8.2 - Prob. 53ECh. 8.2 - Show that the 5 5 matrix...Ch. 8.2 - Prob. 55ECh. 8.2 - Prob. 56ECh. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.3 - Prob. 4ECh. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - Prob. 6ECh. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - Prob. 9ECh. 8.3 - Prob. 10ECh. 8.3 - Consider the large mixing tanks shown in Figure...Ch. 8.3 - Prob. 12ECh. 8.3 - Prob. 13ECh. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - Prob. 17ECh. 8.3 - Prob. 18ECh. 8.3 - Prob. 19ECh. 8.3 - Prob. 20ECh. 8.3 - Prob. 21ECh. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - Prob. 24ECh. 8.3 - Prob. 25ECh. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - Prob. 28ECh. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.3 - Prob. 31ECh. 8.3 - Prob. 32ECh. 8.3 - Prob. 33ECh. 8.3 - Prob. 34ECh. 8.3 - The system of differential equations for the...Ch. 8.3 - Prob. 36ECh. 8.4 - Prob. 1ECh. 8.4 - Prob. 2ECh. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - In problem 58 use (1) use to find the general...Ch. 8.4 - In problem 58 use (1) use to find the general...Ch. 8.4 - Prob. 7ECh. 8.4 - Prob. 8ECh. 8.4 - Prob. 9ECh. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Prob. 15ECh. 8.4 - Prob. 16ECh. 8.4 - In problem 1518 use the method of Example 2 to...Ch. 8.4 - Prob. 18ECh. 8.4 - Prob. 19ECh. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 25ECh. 8.4 - Prob. 26ECh. 8 - fill in the blanks. 1. The vector X=k(45) is a...Ch. 8 - fill in the blanks. The vector...Ch. 8 - Consider the linear system X=(466132143)X. Without...Ch. 8 - Consider the linear system X = AX of two...Ch. 8 - In Problems 514 solve the given linear system. 5....Ch. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RE
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