3.3 Applications of Linear Functions
A function f is a linear function if
The graph of a linear function is a line with slope m and y-intercept b. The rate of change of a
linear function is the slope m.
Example 1: Graph
2
3
Solution: The slope of the line
Journal of Hospitality &
Tourism Research
http:/jht.sagepub.com/
Casino Loyalty: The Influence of Loyalty Program, Switching Costs, and
Trust
Seyhmus Baloglu, Yun Yin Zhong and Sarah Tanford
Journal of Hospitality & Tourism Research published online 24 Se
BEYOND HARDCORE GAMBLING:
UNDERSTANDING WHY MAINLAND
CHINESE VISIT CASINOS IN MACAU
IpKin Anthony Wong
Institute for Tourism Studies, Colina de Mong-Ha
Mark S. Rosenbaum
Northern Illinois University, DeKalb
Casinos are important travel attractions, but th
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Vacation Marketing
Relationship marketing in the casino industry
Catherine Prentice and Brian King
Journal of Vacation Marketing 2011 17: 51
DOI: 10.1177/1356766710391135
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LANDING
PAGELADDER
TEMPLATE
THE PERSUASION
BLUEPRINT
Llama a la Accin
La Escalera
de la Persuasin
Aumenta Su Deseo
Muestra tu Solucin
Prueba tu Solucin
Atiende las Objeciones
Logra la Venta!
Provee Razones
Emocionales y Lgicas
Aumenta su Inters
Confianza
Chapter 7 Homework Problems
1.
If a carefully made die is rolled once, it is reasonable to assign probability 1/6 to each of the six
faces.
A.
What is the probability of rolling a number less than 3.
B.
Use your TI-83 to simulate rolling a die 100 times,
affect the performance. Most respondents at 55% indicated that the workers
prefer both financial and non financial rewards.
From the study its indicated that 84% of the respondents agree that
promotions are used by the company to influence workers perform
by recognizing high education certification. The opinion on how recognition
on employee effort affects performance. 47% indicated that recognition had
high affect on their performance .this shows that recognition is valuable
factor in performance especial
company does not. Similarly majority 58% of the respondent indicated that
promotion influence workers performance. This showed that not only the
financial rewards that affect staff performance but other non financial factors
such promotion also plays impo
contract basis. This shows that the company may have high staff turnover
due to the nature of contract and casual terms of employment as indicated by
low experience levels of employees.
On the effect of rewards on workers performance in the company. Major
5.2 SUMMARY OF MAJOR FINDINGS
The objective of the study was to effect of non financial benefit on workers
performance in water provision Services Company in Embu County in
Kenya. The research was conducted on a sample of 48 respondents which
consisted of
8
0.13
CHAPTER 0. A SHORT MATHEMATICAL REVIEW
Complex numbers
view tutorial: Complex Numbers
view tutorial: Complex Exponential Function
We define the imaginary number to be one of the two numbers that
satisfies
the rule ()2 = 1, the other number being .
10
CHAPTER 0. A SHORT MATHEMATICAL REVIEW
Useful trigonometric relations can be derived using and properties of the
exponential function. The addition law can be derived from
(+) = .
We have
cos( + ) + sin( + ) = (cos + sin )(cos + sin )
= (cos cos sin si
12
CHAPTER 1. INTRODUCTION TO ODES
with the first constant of integration; and the second integration yields
1
= + 2 ,
2
with the second constant of integration. The two constants of integration
and can then be determined from the initial conditions. If
0.8. DEFINITE AND INDEFINITE INTEGRALS
5
to choose the same in both limits. With () = (), we have
() =
()
= lim
0
(
)
+ ( 1)
=1
(
)
( + ) + ( 1)
0
=1
= lim
= lim
0
(
)
( + ) + ( 1) .
=1
The last expression has an interesting structure. All the v
Chapter 2
First-order differential
equations
Reference: Boyce and DiPrima, Chapter 2
The general first-order differential equation for the function = () is written
as
= (, ),
(2.1)
where (, ) can be any function of the independent variable and the depende
16
CHAPTER 2. FIRST-ORDER ODES
Now () > 3, so that 3 > 0 and integration yields
1 ]
,
4
2 0
1
ln ( 3) = ,
2
1
3 = 2 ,
ln ( 3)
]
=
1
= 3 + 2 .
The solution curves for a range of initial conditions is presented in Fig. 2.1.
All solutions have a horizont
0.12. TAYLOR SERIES
7
Commonly, the above integral is done by writing
= ()
= ()
= ()
= ().
Then, the formula to be memorized is
= .
0.12
Taylor series
A Taylor series of a function () about a point = is a power series representation of () developed s
6
CHAPTER 0. A SHORT MATHEMATICAL REVIEW
Trigonometric functions can also be integrated:
cos = sin + ,
sin = cos + .
Easily proved identities are an addition rule:
(
)
() + () = () + ();
and multiplication by a constant:
() = ().
This permits integratio
18
CHAPTER 2. FIRST-ORDER ODES
The first-order linear differential equation (linear in and its derivative) can be
written in the form
+ () = (),
(2.8)
with the initial condition (0 ) = 0 . Linear first-order equations can be integrated using an integratin
Chapter 1
Introduction to odes
A differential equation is an equation for a function that relates the values of
the function to the values of its derivatives. An ordinary differential equation
(ode) is a differential equation for a function of a single va
14
2.2
CHAPTER 2. FIRST-ORDER ODES
Separable equations
view tutorial
A first-order ode is separable if it can be written in the form
()
= (),
(0 ) = 0 ,
(2.2)
where the function () is independent of and () is independent of . Integration from 0 to results
2.2. SEPARABLE EQUATIONS
15
dy/dx + y/2 = 3/2
6
5
y
4
3
2
1
0
0
1
2
3
4
5
6
7
x
Figure 2.1: Solution of the following ode:
+ 21 = 32 .
The integrals in (2.5) need to be done. Note that () < 3 for finite or the
integral on the left-side diverges. Therefore
2.3. LINEAR EQUATIONS
17
(3+2y) dy/dx = 2 cos 2x, y(0) = 1
0
0.2
0.4
y
0.6
0.8
1
1.2
1.4
1.6
0
0.5
1
1.5
x
Figure 2.2: Solution of the following ode: (3 + 2) = 2 cos 2, (0) = 1.
To solve sin 2 = 1/4 for in the interval /2 < < 3/4, one needs to
recall the