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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desire to expand from the Atlantic to the Pacific Coast. This migration west benefited America in many ways. Through unity and technological advancements‚ westward expansion led to America’s success‚ thereby justifying that enterprise. A countless amount of people were brought together as one during and after the westward expansion of North America. Those who were involved in this treated it as a community project in which the U.S unites itself to work as a whole. For example‚ families and
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COLONIAL EXPANSIONS AND RIVALRIES What is it? Colonialism expansion is where countries (such as Britain‚ France‚ Germany and Russia) settle on new land. They do this to expand their territories‚ and to use their resources for to benefit their empire. Rivalries between the empires are consequential. This is because many empires are involved in conflicts when attempting to regain new land. How did it contribute to the start of World War I? Imperialism was one of the causes of World War I.
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Tonecia Lee AP US History 5th Period Unit 2 Essay Exam October 10‚ 2012 The status of women‚ African Americans‚ and Native Americans did not change after winning the American Revolution. Although after the American Revolution winning the status of women didn’t change‚ because of what they had stood up for. The status of women did not change‚ because of what each Americans group had done to make it not change after the winning of the American Revolution. The African American women had been
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American experienced a strong and rapid change from 1770s to 1830s which led to the creation of a new regime‚ dominated in form of party and democratic culture. The regime lasted unchanged for a century‚ before the civil war which brought about changes; great transformations of American society and culture‚ increase in world’s industrial economy. American’s public life from 1830s to the 1930s was the consistent in the form and content‚ of its party politics‚ its government and legal system. The democrats
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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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The period from 1450 to 1650 is often referred to as the “Age of Discovery‚” an era of advances in geographical knowledge and technology. It was also a time of European migration to other parts of the world. This Age of Expansion and European exploration from 1450 to 1525‚ greatly promoted by economical‚ technological‚ political‚ and religious factors‚ launched a major turning point in world history. The economy of late fifteenth century played an important role in European conquest. The Ottoman
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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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"Lincoln hoped to slowly end slavery without tearing the nation apart‚ Blight says. "He was a gradualist‚" Blight says. "He was trying to prevent a bloody revolution over it. He couldn’t." He couldn’t because of the pressure exerted by the abolitionists and the slaves themselves‚ other historians say. Blacks did not wait for white people to free them‚ they say. At least 180‚000 blacks fought in the Civil War. And Douglass was one of Lincoln’s harshest critics. He constantly pushed Lincoln to
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