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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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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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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When I started to plan my presentation‚ I had a hard time deciding what‚ exactly‚ I was going to say. I had started with the idea that I would just basically go over the main points in my paper in the order I wrote them in. I had a hard time getting anywhere with that idea. Then I did the Exhibition Fair. I realized that one of my more common talks that I did during the fair would be a good order for me to cover things in my presentation. So away went my old order and in came my new idea that
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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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Summarize the motives‚ expectations‚ problems‚ and rewards associated with the age of European expansion. Describe the impact of Europeans on Native American (Indian) cultures and the impact of native cultures on Europeans. Then explain why it was or was not a good thing that European culture prevailed. Which one of the following do you think made the most important contribution to European expansion: Renaissance thought‚ the search for new trade routes‚ or new developments in technology? Explain
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enact criminal matters that arise under its constitutional powers‚ such as importing/exporting drugs and other prohibited items (under its customs power) Structure of the Unit Offences Defences Punishmen t PART 1: OFFENCES Refer to group presentation power points Textbook pages will cover most major offences Refer to Queensland Criminal Code (1899)for more detail Part 2: Defences • Chapter 5 of the QLD Criminal Code (1899) is entitled Criminal Responsibility • If the accused can prove
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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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partnerships that have experience in local markets will help to make international expansion possible. Identify a foreign market that you feel this company should enter next‚ and explain why it should enter that market and which of the strategies should be used. Explain the challenges from competition in the local market‚ and how the company might respond strategically to the competition. International Expansion The strategic partnerships which do not only have the knowledge to succeed in
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