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 Expansion Plan NAME Kaplan University April 22‚ 2014 AB 140 Professor NAME Question 1: How would creating a new coordinating position between the CEO and location managers help the business to grow? Answer 1: Creating a new coordinating position would help The Sandwich Blitz organization would allow the owners to focus on the business aspect of opening more locations instead of having to deal with the day to day duties of trying to manage the stores. They could now delegate
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During the Second World War‚ the United States and the Soviet Union fought as allies against the Axis powers. The relationship between the two nations was strained. Americans were wary of Soviet communism and worried about Russian leader Joseph Stalin’s totalitarian rule the country. At the same time‚ the Soviets disliked the Americans’ drawn out refusal to treat Russia as an acknowledged force of the international community. They were also upset at the United States’ delayed entry into World War
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Riley Mangieri 12-19-15 Mr. Rauschenbach Grade 8 Progressives in the late 1800’s-1900’s Our nation lost its way during the Gilded Age (1870s-1920s). The Gilded Age was a term made up by Mark Twain due to him having a book called the Gilded Age‚ which satirized American society in the late 1800s. It was a time of government corruption‚ poverty‚ and awful labor conditions but it being covered up by big businesses‚ or “gilded”. Progressives were people
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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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The westward expansion‚ which started in the 1820s‚ was one of the biggest steps forward our country has ever taken. It nearly tripled the size of our country and increased the population by monstrous amounts. It also improved the economy greatly though agricultural means‚ prompted political leaders to sent people to explore (Lewis and Clark)‚ started a civil war‚ motivated huge amounts of people to move west‚ and almost destroyed our country. The expansion was magnified greatly by the
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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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our time of day. Even when slavery was abolished in 1865‚ it has unfortunately not been concluded to an end. The relevance of slavery in the modern United States is still sincere and yet hasn’t vanished. Many people will think about slavery in the 1800’s when one perceives the phrase “Slavery in the United States”. This is the problem of our society‚ no one has cognitioned the thought of modern slavery and at the end of the day‚ it’s not helping anyone. Under slavery‚ victims go through a rough time
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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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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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