number of dots. Finally‚ we can generate a simplified formula or general statement for to find the number of dots in each stage. Triangular numbers are sequence of number that has certain pattern and if we plot it into a diagram it will create a geometrical triangular shape. Each triangular number has its own number of dots and formula. Now‚ we will start with triangular number first. Aim: In this task I will consider geometric shapes which lead to special numbers. The simplest example of these
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square numbers‚ 1‚ 4‚ 9‚ 16‚ which can be represented by squares of side 1‚ 2‚ 3 and 4. The following diagrams show a triangular pattern of evenly spaced dots. The numbers of dots in each diagram are examples of triangular numbers (1‚3‚6‚)…. 1 3 6 10 15 Complete the triangular numbers sequence with three more terms. Find a general statement that represents the nth triangular number in terms of n. Consider stellar (star) shapes with p vertices‚ leading to p-stellar numbers. The first four representations
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MGT 409 Case 1: Arbitrage in the Government Market 1. In 1991‚ major discrepancies in the prices of multiple long maturity US Treasury bonds seemed to appear in the market. An employee of the firm Mercer and Associates‚ Samantha Thompson‚ thought of a way to exploit this opportunity in order to take advantage of a positive pricing difference by substituting superior bonds for existing holdings. Thompson created two synthetic bonds that imitated the cash flows of the 8¼ May 00-05 bond; one for
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Arbitrage in LIQUIFIED Natural Gas December 2012 Take a look at the long-term charts of crude oil and natural gas. The historical oil-to-gas price ratios have ranged from 6:1 to 10:1 before the economic crisis. Since one barrel of oil contains the energy equivalent of the 5.825 million BTU of natural gas‚ an implied BTU arbitrage kept this relationship in check. Spot natural gas traded as low 1.905 earlier in the week implying an energy equivalent price of a barrel
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it involves geometric shapes which form special number patterns. The simplest of these is that of the square numbers (1‚ 4‚ 9‚ 16‚ 25 etc…) The diagram below shows the stellar triangular numbers until the 6th triangle. The next three numbers after T5 would be: 21‚ 28‚ and 36. A general statement for nth triangular numbers in terms of n is: The 6-stellar star‚ where there are 6 vertices‚ has its first four shapes shown below: The number of dots until stage S6: 1‚ 13‚ 37‚ 73‚ 121‚ 181
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The slave trade began with the Portuguese and the Spanish taking African slaves to their American colonies. By the 18th century around 6 million Africans were taken to the Americas as slaves. The slave trade went through a process called the ‘triangular slave trade’. This meant that: • Slaves were taken from Africa to the Americas. This was called the ‘Middle Passage’. • Americans then paid for the slaves to the Europeans by giving them rum and sugar. • Finally‚ the Europeans gave the Africans
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special patterns evolve‚ such as the square numbers‚ triangular numbers‚ and much more. The Stellar Numbers are mostly used in astronomy and astrology. Stellar Numbers are figurate numbers based on the number of dots that can fit into a midpoint to form a star shape. The points of the star determine the number of points plotted around the midpoint. Triangular numbers is a figurate number system that can be represented in the form of a triangular grid of points where the first row contains a single
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MATLAB BEGINNER’S GUIDE 0 About MATLAB MATLAB is an interactive software which has been used recently in various areas of engineering and scientific applications. It is not a computer language in the normal sense but it does most of the work of a computer language. Writing a computer code is not a straightforward job‚ typically boring and time consuming for beginners. One attractive aspect of MATLAB is that it is relatively easy to learn. It is written on an intuitive basis and it does not
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VOCABULARY 1. Triangular Trade – it connected Europe‚ Africa‚ and Asia‚ and the American continents. Europe sent goods to Africa‚ Africa sent slaves to America‚ and America sent stuff to Europe. 2. Middle Passage - the journey of slaves from Africa to the Americas. 3. Depopulation - the condition of having reduced numbers of inhabitants (or no inhabitants at all). 4. Corruption –fraudulent conduct by those in power‚ typically involving bribery. 5. Lament – a depressed‚ sad‚ feeling
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• • • • • • • • • • • • • • • • Solitary Neglect Navigation Act Trade Stamp/tea/impressment Act/Sugar/Currency Quakers/Puritans/Pilgrams Native Americans moved off Virginia House of Burgesses Cotton/Rice/Indigo/Tobacco Triangular Trade Route Mercantilism First Continental Congress/Stamp Act Congress/Albany Plan John Rolfe and Pocahontas “Join or Die” Proclamation of 1763 Sons of Liberty George Washington‚ John and Sam Adams‚ Ben Franklin‚ Thomas Paine‚ Patrick Henry
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