In this chapter one of the first things we learned was that you can make complex equations look simpler by making substitutions. Take the equation: 2tan2-3tan-2=0
To make this look simpler you can substitute u for tan to get: 2u2-3u-2=0
From there you can us the quadratic formula to get:
u= -0.5, 2
With this you can now say tan=2 and tan=-0.5 which makes solving for much easier. In this case substitutions made solving much easier and less chaotic looking.

The next thing we learned was to rewrite equations in a way that suits your purpose. One key skill for rewriting equations is to get rid of negative exponents. The equation (x-1+y-2 )/(x+y) can be simplified to get rid of the negative exponents. X-1 =1/x therefore: (x-1+y-2 )/(x+y)=(1/x)+(1/y2/(x+y)

From there you can simplify it further by multiplying the top and bottom by a common factor, in this case it is: x+y2 So to finish simplifying the equation you take:
(1/x)+(1/y2/(x+y)
And multiply it by (x+y2)/(x+y2) to get:
(Y2+x)/(x2y2)/(xy3)

Other common rewrite is to rationalize the denominator or numerator. This is very helpful for solving equations with a square root on the bottom. Example: (3)+2/(3)+1
To rationalize this you multiply the numerator or denominator (which ever one you want to rationalize) by its difference of squares. For this:
To rationalize the denominator you multiply it by ((3)-1)/ ((3)-1) Giving you: 1+3/2.

Another thing we learned was how to tell when a graph is concave up or down and decreasing or increasing. A graph is concave up when the x values are above the x axis and concave down when they are below. A graph is Increasing when you increase the y value and the x value increases and its decreasing when the x value decrease.

...accounting concepts are rules and guidelines which the accountant follows and uses when deciding between differing options to make. They help to ensure the accounting information is presented accurately and consistently. All formal accounting statements should be created, preserved and presented according to the concepts and conventions’. The following will look at each of the concepts and conventions and relate them to the profit and loss account...

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Laura Balmer
“Politics is a many sided concept only to be understood if viewed from various angles”. Discuss.
Every day we will experience the activities and ideas of politics around us, despite not knowing its definition. When the majority consider politics they instantly think of government, laws, debates and scandal. However, the real question of what politics is has been pondered for thousands of years by many profound names, one of the many...

...desire to belong as portrayed by the individual, and it is thus that my personal views on belonging have been altered.
\An individual can forge relationships and a sense of belonging or not belonging through interests. Emily Dickinson explored this concept through her love and passion for writing, especially in her poems ‘A word dropped careless on a page…’ and ‘This is my letter to the world…’. In ‘A word dropped careless…’ she describes a sense of belonging through her...

...Concept of Learning
The concept of learning is having an understanding of how humans think. Having an understanding of how individuals think and learn, one will have a better understanding of the mental processes of the brain. This paper will review the concept of learning and distinguish between learning and performance. This paper will also compare and contrast the conceptual approaches to the study of learning.
Defining the Concept...

...The Concept of Power
Existence – Does it Exist?
1) Many people at different times have felt the need to attach the label “Power” to something. So it must exist. So it should be studied.
2) But it has different meanings in different cultures, so it must be many “Things”.
Study – To Study or Not?
1) Due to this complexity, students think that its study will lead to no conclusion.
2) This is a paradox. So there is not enough evidence that a systematic study will give a...

...Prejudice can be defined in one of several ways. There is an intellectual as well as a behavioral aspect to the concept of prejudice. Prejudice encompasses negative thoughts and feelings that a person has toward another person. Thoughts and feelings linked to prejudice are generally not based upon the experience the individual, but rather the prevailing thoughts and attitudes of the society within which the individual has been socialized. These thoughts and feelings may also...

...The concept of “we learn something new every day” is not just a saying but is a saying, which holds truth. We learn something new in school, our careers, our daily lives, and in the world. Some of our learning may change our behavior or our way of thinking. To fully understand the concept of learning, let us look at an in-depth knowledge, which will be addressed in the following: describe the concept of learning, distinguish between learning and...

...The Concept of the Self in the Social World
University Of Phoenix
Understanding What Self Concept is
Self Concept is the gathering of information about self, including ones personality, character, capabilities, and values. Self concept begins as an early as infancy, during this time the individual begins to formulate information about themselves. This process allows them to prepare and began to understand how they are related...