SOLUTION MANUAL
Finite Mathematics & Its Applications
13th Edition by Larry J. Goldstein,
all Chapters 1-12, Complete
, Contents
Chapter 1: Linear Equations and Straight Lines
e e e e e 1–1
Chapter 2: Matrices
e 2–1
Chapter 3: Linear Programming, A Geometric Approach
e e e e e 3–1
Chapter 4: The Simplex Method
e e e 4–1
Chapter 5: Sets and Counting
e e e 5–1
Chapter 6: Probability
e 6–1
Chapter 7: Probability and Statistics
e e e 7–1
Chapter 8: Markov Processes
e e 8–1
Chapter 9: The Theory of Games
e e e e 9–1
Chapter 10: The Mathematics of Finance
e e e e 10–1
Chapter 11: Logic
e 11–1
Chapter 12: Difference Equations and Mathematical Models
e e e e e 12–1
, Chapter 1 e
Exercisese1.1 5
6.e Lefte1,edowne
2
1. Righte2,eupe3 y
y
(2,e3)
x
x
( )
–1,e – e52e
7.e Lefte20,eupe40
2. Lefte1,eupe4 y
y
(–20,e40)
(–1,e4)
x
x
8.e Righte25,eupe30
3.e Downe2 y
y
(25,e30)
x
x
(0,e–2)
9. PointeQeise2eunitsetoetheelefteande2eunitseupeor
4. Righte2
y (—2, e2).
10. PointePeise3eunitsetoetheerighteande2eunitsedowneor
(3,—2).
x
(2,e0) 1e
11. —2(1) e+e (3) e=e— 2e+1e=e—1soe yese thee pointe is
3
onetheeline.
5. Lefte2,eupe1 1e
y 12. —2(2) e+e (6) e=e— 1eise false, e soe noe thee pointe ise not
3
onetheeline
(–2,e1)
x
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, Chaptere1:eLineareEquationseandeStraighteLines ISM:eFiniteeMath
1e 24.e 0e=e5
13 — 2xe+e ye=e— 1e Substitute e thee xe ande y noesolution
3
. x-
coordinateseofetheepointeintoetheeequation:
f 1e hı e f h intercept:enonee
' ,e3 →e—2 ' 1 ı +e1e(3)=e e—1e→e—1+1e=e—1e is Whenexe=e0,eye=e5e
y' ı 'e ı
y-intercept:e(0,e5)
2eee J ye2J 3
aefalseestatement.eSoenoetheepointeisenoteonet 25.eWheneye=e0,exe=e7ex
heeline. -
f 1h f1h intercept:e(7,e0)e0e
14 —2 ' ı + ' ı (—1)e=e—1e isetrueesoeyesetheepointeis =e7
.
noesolution
'y 3ıJeee'y 3ıJ y-intercept:enone
onetheeline. 26.e 0e=e–8x
15.e me=e5,ebe=e8 xe=e0
x-intercept:e(0,e0)
16.e me=e–2eandebe=e–6 ye=e–8(0)
ye=e0
17.e ye=e0xe+e3;eme=e0,ebe=e3 y-intercept:e(0,e0)
2e 2e 1e
ye=e xe+e0;e me=e ,ebe=e0 27 0e=e xe –e1
18 3
3 3 .
. xe=e3
19.e 14xe+e7eye=e21 x-intercept:e(3,e0)
1e
7eye=e—14xe+e21 ye =e (0) e–e1
3
ye =e—2xe+e3
ye=e–1
y-intercept:e(0,e–1)
20 xe— eye =e3 y
. —ye=e—x e+e3
ye=ex e—e3
(3,e0)
21.eee 3xe=e5 x
5 (0,e–1)
xe=e
3
1 2
28. Whenexe=e0,eye=e0.
22 – xe+ ye =e10
. 2 3 Whenexe=e1,eye=e2.
2e 1e y
ye =e xe+10
3 2
3e
ye =e xe+15 (1,e2)
4 x
(0,e0)
23. 0e=e—4x e+e8
4xe =e8
xe=e2
x-intercept:e(2,e0)
ye=e–4(0)e+e8
ye=e8
y-intercept:e(0,e8)
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