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Mathematics...and therefore, it is important to realize as what is it that is integrated or summed up. It is essentially the product of the dependent variable (y) and infinitesimally small increment in the independent variable or ?x which is continuously summed up. If we know from which point to which point this summation is to be done, then we get a definite answer and this integral is known as definite integral. **Mathematically** it is expressed by indicating the limits or boundaries of integration as shown below. This is a definite integral with integration being carried out between ‘a’ and ‘b’ (a < b) for y, which is a function of x. This definite integral gives many useful parameters like area under curve, area of a curved surface,...

10 Pages(2500 words)Essay

The Pythagorean Theorem...THE PYTHAGOREAN **THEOREM** [Source: http www.arcytech.org/java/**pythagoras**/preface.html] April 30, 2008 The Pythagorean **Theorem** In **mathematics**, the Pythagorean **Theorem** is a relation in Euclidean geometry among the three sides of a right triangle. The **theorem** is named after the Greek mathematician **Pythagoras** who lived in the 6th century B.C.
The **theorem** is as follows:
"In any right angle triangle, the area of the square of the side opposite the right angle i.e. whose side is the hypotenuse is equal to the sum of the areas of the squares of the two sides that meet at a right angle i.e. whose sides are the two legs"
In other words
The square on the hypotenuse is equal to the sum of the squares on the other two sides
Geometric... ...

14 Pages(3500 words)Essay

Mathematics...Instructions: Independent study. Choose a topic within algebra for independent study. Your topic should be **mathematics** that you have not studied before or that goes beyond what you have studied. For example, you may use this topic on"Nuclear salvation or nuclear folly" by R.E Lapp.
Do not think about developing a lesson plan, or to teach your topic to children. A little story of **mathematics** is welcome, but that should not be the main theme of your paper. The objective is to describe some **mathematics** that you have learned. Include a summary of why you selected your topic, and what you learned about it from each resource that you used. Also include some questions provoked by what you...

4 Pages(1000 words)Article

Mathematics...Waring’s Problem and Goldbach’s Conjecture 20-2008 Waring’s Problem Lagrange’s 4 square **theorem** s that every number can be written as the sumof four integer squares. Waring proposed a generalisation of this **theorem** in 1770, stating that every natural number is the sum of a fixed number g(k) of kth power integers, where k is any given positive integer and g(k) depends only on k. In this paper, we will investigate what is currently known about this problem.
Warings Problem was proven for all k by Hilbert in 1909 (Ellison 1971), with the Hilbert-Waring **Theorem**. Prior to that, the problem was solved in the affirmative for specific ks, especially for small k.
If we let "s" stand for the...

6 Pages(1500 words)Essay

Mathematics...1. An instance in my daily life where I rely on the skills of rounding and estimating is when I do the grocery shopping. In order to get a fair estimate of what my bill is up to, I roughly calculate the value of each shopping item by rounding to the closest whole number. An occupation such as a shop teller would need to have sound multiplication and division skills because their job requires them to give and receive the right amount of change.
2. The concept of negative numbers is harder to grasp because there cannot be anything less than nothing, which is what zero is. An example of where it is important to understand integers in the financial world is with banking (Glydon). If someone spends more than they have available... An instance in...

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Pythagorean Theorem...Pythagorean **Theorem** (Add (Add (Add
Pythagorean **Theorem**
Introduction
Evidences show that Pythagorean **Theorem** was popular even among ancient civilizations. This famous **theorem** was developed by the Greek mathematician and philosopher **Pythagoras**. Historical writings argue that though Babylonian mathematicians had knowledge in the **theorem**, they could not develop it into a **mathematical** framework. Unlike any other **mathematical**...

3 Pages(750 words)Essay

Coase Theorem...Coase **Theorem** Coase **Theorem** Coase **theorem** targets economic efficiency that is attributed to economic allocation and outcome when externalities are present. The theory stipulates that if trade is possible in the presence of an externality when transaction costs are significantly low, the end result will be an efficient outcome when initial allocation of property is not considered. The major obstacles to Coasian bargaining emerge when property rights have been defined poorly (Buchanan, 2005). This paper will discuss Coase **theorem** as an alternative to government regulation in terms of facilitating for the provision of goods and services.
Ronald Coase stipulated that...

2 Pages(500 words)Essay

Mathematics...**Mathematics**: Open/Closing Credit The credit card will largely depend on the credit card holder purchasing behavior. Your current card charges 16.5% annually. Therefore, interest charges on a balance of $5,000 will be given by:
This is the interest charged on your current card, regardless of the duration. On the other hand Visa Student Card charges a lower annual percentage of 10.8% after a 6 month 0% interest period. On a balance of $5,000, the interest will be;
Obviously, the student card charges a lower interest compared to your current card and even offers a grace period of 6 months interest free which makes it an attractive option. However, since you usually have a large outstanding balance, chances of defaulting or exceeding...

1 Pages(250 words)Speech or Presentation

Bayes' Theorem...Bayesian **Theorem** Introduction Reverend Thomas Bayes developed Bayes’ **theorem** of probability. The **theorem** provides understanding about the how the probability of a **theorem** is affected by a new set of evidence. It is applied to in a variety of context to explore a relationship between theory and evidence. Contemporary, the **theorem’s** application is broad, ranging from **mathematics** to the field of science. It explains the relations between two theories and evidences. It allows the researcher to determine the relation between current beliefs with respect to previous beliefs and evidences.
Simon Jackman (2009) defines Bayes’...

15 Pages(3750 words)Essay

The Pythagorean Theorem...The Pythagorean **Theorem** The Pythagorean **Theorem** The Pythagorean **Theorem** is used to determine the areal distance of a right angled road trip. Through determining the length of each road and applying the Pythagorean formula [c= √(a2+b2)], the areal distance is determined (Kramer, 2011). Pythagorean **Theorem** is highly effective and easy to use as compared to the other **mathematical** tools. For measuring the length of each road, the odometer tool of car or other motor are used. For determining the distance, no other geometrical tool is required. Moreover, for resolving such kind of issues Global Positioning System (GPS) navigation is used in the modern day. This...

1 Pages(250 words)Coursework