THEOREM OBJECTIVES Recognize patterns in binomial expansions. Evaluate a binomial coefficient. Expand a binomial raised to a power. Find a particular term in a binomial expansion Understand the principle of mathematical induction. Prove statements using mathematical induction. Definition: BINOMIAL THEOREM Patterns in Binomial Expansions A number of patterns‚ as follows‚ begin to appear when we write the binomial expansion of a b n‚ where n is a positive integer. a
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the earth‚ are the chosen people of god." These claims helped fuel the manifest destiny. Manifest Destiny was a movement started by journalist John O’Sullivan to state his opinion that expansion was a part of the "the great experiment of liberty." This promoted the great Westward expansion. The Westward Expansion highlights 3 of the largest characteristics of the American spirit‚ the desire for freedom‚ the need of wealth‚ and the willing to sacrifice for others. With new land ownership available
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increased from 2‚500 in 1826 to 35‚000 in 1850. The Lowell Machine Shop became a center for innovation not only in textile machinery but waterpower technology as well. It also trained a generation of industrial engineers that spread throughout the economy. Lowell attracted further international attention because of its labor system that employed young women housed in corporate boarding houses with an extensive corporate welfare and cultural program. The expansion of textile manufacturing was not only
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Confederation: A false sense of unity? Marc Estrada Dr. Robert L. Fraser JWH100Y1 Section L5101 March 5‚ 2013 Confederation geographically united the colonies of a fledgling Canada. The union defined borders‚ created governments and brought the various peoples of Canada together under a single dominion. However‚ the imposition of geographic union on the people did not immediately bring union amongst the people themselves. Political‚ cultural‚ economic‚ and
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Purpose: In this lab‚ we will heat up a metal rod and measure how much it expands. We will calculate its Coefficient of Linear Expansion‚ α‚ and prove the formula for thermal expansion‚ ΔL = αLiΔT. Also‚ we heat up a known volume of methyl alcohol and calculate its Coefficient of Volume Expansion‚ β‚ and prove the formula for volume expansion of a liquid ΔV = βViΔT. Equipment: Hollow Metal Rods of different metals‚ Steam Generator‚ Stand‚ Burner‚ Flexible Hoses‚ Motion Amplifier‚ Micrometer
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1. How did the introduction of factories in the 1800s change the lives of people in Britain? The introduction of factories in Britain had some positives and negatives changes‚ it made the production of cotton‚ cigarettes and all the other things easier and cheaper‚ but it begun the child labour and people had terrible conditions. It was an evolution of the technologies‚ but also destroyed the life of many people. 2. What were the key differences between working in the domestic system and working
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then exercised today. As time progressed‚ the role and influence of the federal government became more prominent. Examples of expansion in federal authority are evident in events surrounding the Civil War‚ Reconstruction‚ the Progressive Era‚ the Great Depression‚ and the Civil Rights Era. Identify and describe four (4) examples of U.S. federal government expansion of authority between the beginning of the U.S. Civil War and the end of the Civil Right Era. These examples must be placed
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Thermal Expansion happens a lot in everyday life. When something is heated and expands this is Thermal Expansion. The way Thermal Expansion works‚ is when it is heated the atoms expand‚ and then when it is cooled it shrinks. Several examples of Thermal Expansi Thermal Expansion happens a lot in everyday life. When something is heated and expands this is Thermal Expansion. The way Thermal Expansion works‚ is when it is heated the atoms expand‚ and then when it is cooled it shrinks. Several
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Assess to what extent differing national cultures are relevant to an understanding of the reasons for accounting differences‚ and therefore to the process of classification of countries. 12/11/2008 ABSTRACT Culture was broadly ignored and was flooded in the concept of environmental factors influencing the accounting changes. However‚ research has shown that culture had a huge role in accounting development and changes. In this essay‚ we are going to develop Gray’s theory about the relationship
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How the Refugee Crisis Will Impact Our National Security The Unite States is required by law to protect the refugees from all over the world. Many of them come from war zone. Among them‚ are Children‚ men and women who are subject to crimes and violence. In the recent day‚ and due to the security reason‚ our Lawmakers decided to stop refugees from specific countries from entering in our country. The real reason behind that is the screening process which takes approximately six months before the
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