Micheal Jordan

Basketball is a team sport with five players per team. There’s a center, power forward, small forward, point guard, and shooting guard. Brought up in 1891 by Dr. James Naismith, it has become one of the most popular and widely viewed sports in America. The objective of basketball is to shoot a round ball into a hoop placed ten feet in the air. Basketball consists of many rules and regulations or fouls. There are two types of fouls: technical fouls and disqualifying fouls. Today there are two leagues: the NBA (national basketball association) and the WNBA or women’s basketball association.Michael Jeffrey Jordan was born on February 17, 1963 in Brooklyn New York. He began to try to start his sports career by playing all available sports in high school. His junior year he was recruited to the University of North Carolina to play college basketball and from there he was drafted third overall to the Chicago Bulls in 1997 were his career starts and he becomes the widely popul ar icon you know. Michael started his team with a championship and an MVP award for himself. Jordan â€Å"transcended† basketball and became a national icon for great artistry, dignity, and history. Michael is very popular and has many nicknames.He had names that transcended basketball. Names such as â€Å"Air Jordan â€Å"and â€Å"His Airness â€Å" but he’s best known by his initials M. J. Jordan was very well known and acknowledged by big stars. He starred in the movie â€Å"Space Jam† and was the star of the movie â€Å"Like Mike†. He has his own shoe line that came out in 1985 and is called Air Jordan’s which are widely popular and sponsored by Nike. Jordan is sponsored by many companies and he has been in many commercials supporting them. He has been in commercials such as Wheaties, Gatorade, McDonalds, Nike, and many more. Jordan has been to the Olympics twice for basketball.He has been to Los Angeles in 1984 where he and his team took the gold. He also went to Barcelona in 1992 with his â€Å"Dream Team† were they took the gold again. He’s also been to two other American games were he also took the gold. He was in the FIBA American Games in Portland during 1992 and the Pan American Games in Caracas during 1983. Michael is now forty-six years old and owns the Charlotte Bobcats and other sports teams. He retired early in the 2004 season to his house in Wilmington, North Carolina. Jordan retired with over three hundred million dollars in his bank account.He has three kids, two boys Larry Jordan and James R. Jordan Jr. He also has a daughter Jasmine Jordan who was his youngest child. Jordan played for the Chicago Bulls who are one of the most popular and decorated teams in American history. The team was founded in 1966 by Dick Klein. Their owner is Jerry Reinsdorf their general manager is Gar Forman and their head coach Tom Thibodeau. The team has an estimated value of 600 million dollars. The team has won six championships and six MVP awards. Their also the only team in recorded history to win seventy-two games in one season.There part of the central division and the eastern conference. Their colors are white, black, and red. And they have an era devoted to M. J. called the Michael Jordan era which took place in the years 1984 through 1998. Michael Jordan is the biggest idol in basketball and sports history. He is widely known and very popular. Michael changed basketball history. He was a turning point in basketball that led the basketball world to new heights by inventing the â€Å" dunk â€Å" and many other things that are natural to see in basketball now. He changed basketball its fans and the world.

Ib Pase Paper, Maths Hl

M10/5/MATHL/HP2/ENG/TZ1/XX 22107204 mathematics higher level PaPer 2 Thursday 6 May 2010 (morning) 2 hours iNsTrucTioNs To cANdidATEs ? Write your session number in the boxes above. ? not open this examination paper until instructed to do so. do ? graphic display calculator is required for this paper. A ? section A: answer all of section A in the spaces provided. ? section B: answer all of section B on the answer sheets provided. Write your session number on each answer sheet, and attach them to this examination paper and your cover sheet using the tag provided. At the end of the examination, indicate the number of sheets used in the appropriate box on your cover sheet. ? unless otherwise stated in the question, all numerical answers must be given exactly or correct to three significant figures. 0 0 candidate session number 2210-7204 14 pages  © international Baccalaureate organization 2010 0114 –2– M10/5/MATHL/HP2/ENG/TZ1/XX Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. In particular, solutions found from a graphic display calculator should be supported by suitable working, e. . if graphs are used to find a solution, you should sketch these as part of your answer. Where an answer is incorrect, some marks may be given for a correct method, provided this is shown by written working. You are therefore advised to show all working. Section a Answer all the questions in the spaces provided. Working may be continued below the lines, if necessary. 1. [Maximum mark: 4] The graph below shows y = a cos (bx) + c . y 4 2 x –2 0 –2 –4 2 4 6 Find the value of a , the value of b and the value of c . †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢ € ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 2210-7204 0214 –3– 2. [Maximum mark: 5] The system of equations 2 x ? y + 3z = 2 3 x + y + 2 z = ? 2 ? x + 2 y + az = b M10/5/MATHL/HP2/ENG/TZ1/XX is known to have more than one solution. Find the value of a and the value of b . †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚ ¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 2210-7204 turn over 0314 –4– 3. [Maximum mark: 6]M10/5/MATHL/HP2/ENG/TZ1/XX In the right circular cone below, O is the centre of the base which has radius 6 cm. The points B and C are on the circumference of the base of the cone. The height AO ? of the cone is 8 cm and the angle BOC is 60? . A diagram not to scale O B ? Calculate the size of the angle BAC . C †¦Ã¢â‚¬ ¦Ã¢â‚ ¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚ ¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 2210-7204 0414 –5– 4. [Maximum mark: 7] (a) (b)M10/5/MATHL/HP2/ENG/TZ1/XX Solve the equation z 3 = ? 2 + 2i , givin g your answers in modulus-argument form. Hence show that one of the solutions is 1+ i when written in Cartesian form. [6 marks] [1 mark] †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 2210-7204 turn over 0514 –6– 5. [Maximum mark: 6] M10/5/MATHL/HP2/ENG/TZ1/XX Let A , B and C be non-singular 2 ? 2 matrices, I the 2 ? 2 identity matrix and k a scalar. The following statements are incorrect.For each statement, write down the correct version of the right hand side. (a) (b) (c) ( A + B ) 2 = A2 + 2 AB + B 2 ( A ? kI )3 = A3 ? 3kA2 + 3k 2 A ? k 3 CA = B ? C = B A [2 marks] [2 marks] [2 marks] †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 2210-7204 0614 –7– 6. [Maximum mark: 5] M10/5/MATHL/HP2/ENG/TZ1/XX Find the sum of all three-digit natural numbers that are not exactly divisible by 3. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 2210-7204 turn over 0714 –8– 7. [Maximum mark: 7] M10/5/MATHL/HP2/ENG/TZ1/XX Three Mathematics books, five English books, four Science books and a dictionary are to be placed on a student’s shelf so that the books of each subject remain together. (a) (b) In how many different ways can the books be arranged? In how many of these will the dictionary be next to the Mathematics books? [4 marks] [3 marks] †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 2210-7204 0814 –9– 8. [Maximum mark: 6] M10/5/MATHL/HP2/ENG/TZ1/XX In a factory producing glasses, the weights of glasses are known to have a mean of 160 grams. It is also known that the interquartile range of the weights of glasses is 28 grams. Assuming the weights of glasse s to be normally distributed, find the standard deviation of the weights of glasses. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢ € ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 2210-7204 turn over 0914 â €“ 10 – 9. [Maximum mark: 6] Let f ( x) = (a) (b) 4 ? x2 . 4? x M10/5/MATHL/HP2/ENG/TZ1/XX State the largest possible domain for f . Solve the inequality f ( x) ? 1. [2 marks] [4 marks] †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã ¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã ¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 2210-7204 1014 – 11 – 10. [Maximum mark: 8] The diagram below shows the graphs of y = that all intersect in the same two points. M10/5/MATHL/HP2/ENG/TZ1/XX 3 x ? 3 , y = 3 and a quadratic function, 2 3 x –3 Given that the minimum value of the quadratic function is ? 3 , find an expression for the area of the shaded region in the form a, b, c and t are to be determined. (Note: The integral does not need to be evaluated. ) †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚ ¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã ¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. ? t 0 (ax 2 + bx + c) dx , where the constants 2210-7204 turn over 1114 12 – Section B M10/5/MATHL/HP2/ENG/TZ1/XX Answer all the questions on the answer sheets provided. Please start each question on a new page. 11. [Maximum mark: 20] A plane ? has vector equation r = (? 2i + 3 j ? 2k ) + ? (2i + 3 j + 2k ) +  µ (6i ? 3 j + 2k ) . (a) (b) (c) (d) (e) (f) Show that the Cartesian equation of the plane ? is 3 x + 2 y ? 6 z = 12 . The plane ? meets the x , y and z axes at A, B and C respectively. Find the coordinates of A, B and C. Find the volume of the pyramid OA BC. Find the angle between the plane ? and the x-axis. Hence, or otherwise, find the distance from the origin to the plane ? Using your answers from (c) and (e), find the area of the triangle ABC. [6 marks] [3 marks] [3 marks] [4 marks] [2 marks] [2 marks] 12. [Maximum mark: 15] Casualties arrive at an accident unit with a mean rate of one every 10 minutes. Assume that the number of arrivals can be modelled by a Poisson distribution. (a) (b) (c) Find the probability that there are no arrivals in a given half hour period. A nurse works for a two hour period. Find the probability that there are fewer than ten casualties during this period. Six nurses work consecutive two hour periods between 8am and 8pm.Find the probability that no more than three nurses have to attend to less than ten casualties during their working period. Calculate the time interval during which there is a 95 % chance of there being at least two casualties. [3 marks] [3 marks] [4 marks] [5 marks] (d) 2210-7204 1214 – 13 – 13. [Maximum mark: 11] M10/5/MATHL/HP2/ENG/TZ1/XX Points A, B and C are on the circumference of a circle, centre O and radius r . ? A trapezium OABC is formed such that AB is parallel to OC, and the angle AOC ? is ? , ? ? < ? . 2 B C A r ? O diagram not to scale (a) (b) ? Show that angle BOC is ? ? ? . 3 marks] Show that the area, T , of the trapezium can be expressed as T= 1 2 1 r sin ? ? r 2 sin 2? . 2 2 [3 marks] (c) (i) Show that when the area is maximum, the value of ? satisfies cos ? = 2 cos 2? . (ii) Hence determine the maximum area of the trapezium when r = 1. (Note: It is not required to prove that it is a maximum. ) [5 marks] 2210-7204 turn over 1314 – 14 – 14. [Maximum mark: 14] M10/5/MATHL/HP2/ENG/TZ1/XX A body is moving through a liquid so that its acceleration can be expressed as ? v2 ? ? 32 ? m s ? 2 , ? 200 ? where v m s ? 1 is the velocity of the body at time t seconds.The initial velocity of the body was known to be 40 m s ? 1 . (a) Show that the time taken, T seconds, for the body to slow to V m s ? 1 is given by T = 200 ? (b) (i) 40 V 1 dv . v + 802 2 [4 marks] dv Explain why acceleration can be expressed as v , where s is ds displacement, in metres, of the body at time t seconds. Hence find a similar integral to that shown in part (a) for the distance, S metres, travelled as the body slows to V m s ? 1 . [7 marks] (ii) (c) Hence, using parts (a) and (b), find the distance travelled and the time taken until the body momentarily comes to rest. [3 marks] 2210-7204 1414

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Brands Deal With Fluctuating Markets at Las Vegas Trade Shows - Article Example One of the things that stand out from the article that is an indication that it will affect the overall fashion trend or the consumers behaviors is unemployment.2 According to the article, the unemployment rate dropped to 5.7% from 6.6%.3 It shows a strong indication that more people will have the money to spend on the apparel. As more people are employed and earn some cash, their spending also increases which is good for any business. The businesses will no longer rely on the entrepreneurs to buy the products as it will have an expanded consumer base including those who were not employed. In conclusion, consumer’s purchasing power is critical for business because it make them trap their spending. Increasing trend of employment among the consumers is a good predictor that sells of apparel will increase because many consumers have money to spend. Employment will also influence the consumer behaviors because they will be buying as per the

How does advertising treat convenience as necessity Research Paper

How does advertising treat convenience as necessity - Research Paper Example The major part of the revenue put aside for marketing is spent on popularizing the product through mass media ads. Print media ads and TV channel ads have emerged into internet and mobile ads in the past decade. Most of these commercials are created by extremely creative people, who are capable of creating non existing desires. Men have lived on this earth for millions of years. But, only after the advent of advertisements did he realize he cannot live without credit cards. Purpose of the study The purpose of this study is to analyze the subliminal messages some of the famous commercials give out. Our aim is to create awareness among the users about the dangers of uncontrolled consumerism. What seems like a simple pleasure might be a poisonous inject into the strong economic root of a country. And the most disturbing part is the governments, citizens and the entrepreneurs extend their full fledged support to this making convenience a necessity advertising policy, without any idea of the future consequences. Companies spend millions of dollars every year on such ads instead of improving the quality of their products and the lifestyle of their workmen. Even great companies which followed this strategy like Nokia have come to a standstill point where they don’t have any more to spend. They are trying hard to come out of debt now, wondering why they wasted so many millions on commercials instead of paying their debt interests on time. With problems galore, can Middle East survive another â€Å"catch bee with vinegar† type attack on its culture and economy? Literature Review Consumerism is a single word. When we analyze the roots of this practice, it reaches back to colonialism and the post world war period. Whether we like to agree or... This essay "How does advertising treat convenience as necessity?" outlines in detail how such a trance is created through visual media in an exceptional way, taking the Middle East Media as background. People who grew up in the Middle East will never forget the NIDO commercial with the tagline â€Å"NIDO - For The Golden Growing Years†. The divine mother-son sentiment was captured wonderfully in that half a minute commercial. However, the subliminal message it portrays is questionable. A luxurious milk supplement is shown as an important object of necessity which accompanies the child throughout its growth. What do such ads do? They inspire a mother to feed the baby with this product instead of the normal cow’s milk, a much cheaper and healthier product. Similarly there is the famous Close up ad featuring lemon and mint as two characters. The beauty and comical nature of the advertisement is mind blowing. The humorous romance ends with the note â€Å"love is sweet but Close up is sweeter†. This advertisement is every person’s heartthrob. The way it is portrayed lightens our mind, no matter how tensed we are. Again the subliminal message the ad portrays is the best example of how the advertising field transforms a simple paste into something as necessary as love. One Zain telecoms recent ad, features people from different countries of the Middle East like Egypt, Lebanon, Arabia and Dubai. The visuals are stunning, captured in HD camera showing the actions of various people in slow motion.

The Process of Procurement of Materials in the Implementation of a Research Paper

The Process of Procurement of Materials in the Implementation of a Project - Research Paper Example Depending on the type of the project to be worked on, the process of procurement may be considered for direct goods, or indirect goods, or tangible or intangible items. For example, in relation to the production and manufacturing industries, the procurement process occurs for direct or indirect goods, direct goods referring to the materials required directly in the manufacturing process, while indirect goods might not have a direct need, yet have an indirect influence on the process as a whole. An example of a tangible item that might be needed for procurement is the software for a computer. In the cases of other services, the procurement is needed for designing a project, the manufacturing process, the installation techniques as well as the maintenance of the work done. Thus projects that are based on contracts generally involve the procurement strategies and techniques (Kovacs, 2004, pp.7-8). Project procurement is considered as an intricate and difficult process of making a purcha se of the necessary equipment for different needs in different industries. Thus suitable personnel are required for the achievement of this work. The management of the project involves setting up appropriate measures to distribute the roles and responsibilities of the staff in the different parts of the procurement process for a particular project. The items for procurements would vary with different industries. While the selection of the materials to be procured is considered, it is of utmost significance that the materials are essential and match with the requirements of the respective projects (Kovacs, 2004, pp.8-28).

Do Large Business Have an Affect on Small Business Essay Example for Free

Do Large Business Have an Affect on Small Business Essay Considering the normative statement that both large and small businesses should follow the same ethical and moral standards, this paper analyzes the perceptions of individuals based on the relative ethical behavior of small business as compared to large business. The study of ethics focuses on the differences between what is right and what is wrong in society which affects both small business and large business due to their obligation to the public and their stakeholders. Both entities are guided by the same standards and both are expected to meet all legal regulations and ethical standards. The analysis employs surveys to gauge the public’s perceptions of the ethical decision making by management in both small business and large business. The survey also analyzes the role of those ethical decisions within scenarios and their impact on the individuals’ patron behavior in small business as compared to large business. Statistical analysis has been utilized to test the authors’ overall hypothesis that the public is generally less concerned about ethical decision making of small business relative to large business. The implications of these findings for both large and small businesses are provided with the analysis and suggestions to correct the disparity between both entities. Introduction During the past decades it has been evident that ethics has become the hot topic in business. However, much of the talk is not comprised of all types of business it involves primarily the large corporations. Large corporations such as Enron have caused much grief to those around them and everyone that they employed. Due to this reason regulations such as the Sarbanes- Oxley Act have been enforced to hold large businesses accountable. While these regulations have focused solely on large corporations, efforts to regulate small businesses have been small. It is estimated that small businesses make up over 80% of all business in the United States of America. That is a huge sector which is unregulated due to its size. While the adverse actions of each entity do not do great harm to the economy; the cumulative damage of all components of the group could have devastating impacts on the general economy. Literature Review Businesses today are completely different than the businesses of years past. Today, business ethics has become an area of great concern in both corporate culture and academia. Companies such as WorldCom and Enron have caused people to reevaluate philosophy and business. Ethics can be defined by the morals that people and companies hold. Although internal and external forces influence businesses, there are three issues that affect issues in business. These three issues are systematic, corporate, and individual. To truly understand each factor one has to understand how each of these issues differs and how they influence the business itself. Systematic issues analyze ethical values in economic, political, legal, and other social systems in which the business operates (Velasquez, 2006). An example of this would be a question of morality about the current laws pertaining to accounting systems. Laws influence the actions of people because they stem through consequences with the local or federal government. People tend to be scared of a higher authority more than self punishment. 2010 Small Business Institute ® National Conference Proceedings Vol. 34, No.1 Winter 2010 293 The second factor is corporate issues which are issues of morality of internal activities such as policies, practices, and organizational structure (Velasquez, 2006). Corporate issues are based on corporate cultures. If a company treasures capital gains more than human capital the company would then lay off employees to save money. On the other hand, a company that treasures its employees is more likely to take a cut and keep their employees. To say that one company is more ethical because of their decision lays in a company’s moral standards. The idea of moral standards stems from the third type of issue which is the individual issues. Individual issues are issues that are based on individuals within a company along with their behaviors and decisions (Velasquez, 2006). This includes the moral standards of individuals. Moral standards are standards that are set by the individuals themselves and by no other governing body. Hence, each individual has a right to stand for what they believe in. It may be simple to take these three factors and state that this is common sense information; however, it is just as complicated to say that there can be one rule that can apply to every situation that is similar. In cases where individual morals differ from those of corporate or systematic, it is easy to assume that one would no longer pay attention to their place of business or the entity that is different. However, humans are prone to being victims of society and need to supply for their family. Knowing that something unethical is occurring at a place of business does not mean that the person will just walk away whether they have worked in small or large firms. Decisions of a business affect all tiers of the organizational structure which in turn affect the lives of all stakeholders of the company. Therefore, ethical standards have risen due to the current corruption in many large businesses. News reports of Nike and Merck have grabbed the attention for case studies and have become the top selling stories. The news ran the stories that exposed the fragile nature of the corporate worked to their affect on the country’s economy. Due to the global impact of large corporations the public’s eye is primarily on large businesses; however, ethical issues arise in small businesses as well. Lisa Miller states that small businesses â€Å"were overlooked when Wall Street’s mega-scams and scandal came to light (Miller, 2003). For people that analyze and teach ethics â€Å"business ethics have almost invariably concerned the doing, indeed generally the misdoings, of large companies (Quinn, 1997).† Quinn noted that in the late 20th century there has been an increase in the economic activity of small businesses (Quinn, 1997). He states that not only do the managers have to be observed so do the employees. The employees have want approval of their peers which is also accepted by the manager/owner (Quinn, 1997). In large businesses it seems easier to separate you personal ethics from businesses ethics. In small businesses the relationship with one’s coworkers becomes a sub-family relationship making it that much harder to make â€Å"ethical† decision. The overall factors that influence business ethics derive from personal ethics and how those ethics affect others. Miller points out that it is an assumption that small businesses do not need a code of ethics however, they have a bigger temptation to b involved in â€Å"dubious business practices (Miller, 2003). 2010 Small Business Institute ® National Conference Proceedings Vol. 34, No.1 Winter 2010 294 In Mark Schwartz essay A Code of Ethics for Corporate Code of Ethics, Schwartz finds that over ninety percent of large corporations have a code of ethics (Schwartz, 2002). He concluded that there a six universal moral standards in four different sources. The moral standards that he looked at included trustworthiness, respect, responsibility, fairness, caring, and citizenship (Schwartz, 2002). Due to these criteria Schwartz states that a code of ethics should be constructed on factors that could be audited. His study provides a normative foundation for evaluating a corporation’s code of ethics. In a 1981 an article by Brown and King analyzed the influences and perceptions of small business ethics. In their foundational work Brown and King realized the disparity in public awareness between small business ethics and large business ethics. Brown and King surveyed a small group of individuals consisting of â€Å"small business† respondents and â€Å"other† respondents who were mostly employed by large corporations. Brown and King’s research sought to answer three questions. First, the research asked â€Å"How high are the ethics of small business people perceived to be?† Second, â€Å"Compared to others, what causes the behavior of people in small business to be more or less ethical?† Finally, â€Å"What are the prevailing small business attitudes concerning ethical issues?† (Brown and King, 1981). Brown and King found that there was a surprisingly small difference in the responses between the two subgroups of respondents. The research conducted by Brown and King examined the perspectives of those in the various sized business. The research left a gap in the general public’s perceptions of the ethical actions between large and small business. The Center for Business Ethics surveyed Fortune 1000 industrial and service companies to see how they have instilled their ethical values to compare their results from the study they performed in the mid 1980s. Their survey showed some progress but, not enough (Center for Business Ethics, 1992). Ethical standards fall in line with legal regulations. Sandra Malach, et al. believe that incorporating legal planning into business planning to avoid legal issues and to protect the businesses most important assets (Malach, Sandra et al, 2006). While legal action is important it is important to focus on consequences in a workplace outside o f the any punishments. To further analyze ethical dilemmas it is important to observe the consequences at a workplace. One consequence that business can apply is a zero tolerance policy in a workplace. This ethical dilemma is especially interesting when applied in a small business setting, and contrasted with techniques applied in large corporations. The ethical compass of the theory for the zero tolerance policy is Kant’s Categorical Imperative. Kant’s Categorical Imperative is defined by the rule that people should â€Å"Act in such a way that you treat humanity, whether in your own person or in the person of any other, always at the same time as an end and never merely as a means to an end (Stanford, n.d.).† Kant’s Categorical Imperative is a very restrictive rule to live by and cannot practically be applied to everyday life. However, when discussing ethical dilemmas in the workplace, the Categorical Imperative should not be overlooked. The Zero Tolerance Policy embodies the Categorical Imperative in the sense that everyone must ask himself/herself whether they would be willing to have the same behavior applied to them if the roles were reversed. In the business setting the Categorical Imperative has a special value; it helps mitigate moral hazard. 2010 Small Business Institute ® National Conference Proceedings Vol. 34, No.1 Winter 2010 295 Moral hazard was once described as â€Å"a situation in which a party is insulated from the consequences of its actions†¦Thus protected, it has no incentive to behave differently (Ahrens,2008).† In the business setting, moral hazard can be devastating to the culture of the company and can eat away at the profit margin. Consider an employee who is discovered to be â€Å"moonlighting† or working an untaxed second job during hours in which the employee should be giving full attention to their actual job. This behavior may seem harmless and may only warrant a verbal warning, but when the other employees discover how easy it is to get by with unethical behavior they are incentivized to act unethically. This slippery slope scenario results only in the necessary termination of the unethical employee. When an employer establishes that unethical behavior will not be tolerated the result is the strengthening of the corporate culture and the avoidance moral hazard. However, this scenario might work differently in a small business. In a small business the cost of a zero tolerance policy can be devastating. The costs associated with replacing an employee in a large corporation is easily spread across the entire entity as a fixed cost of doing business; this is not the case in the small business. The employer-employee relationship in the small business, by nature, is more flexible and more personal. This flexibility can allow for a more informal agreement, between management and employees, to be made. Finding a â€Å"win-win† solution allows for Kant’s Categorical Imperative to be upheld and moral hazard can be avoided. In a large publically traded company this kind of arrangement cannot be made because not all of those who are residual claimants (owners) can be spoken for. In the large publically owned company the zero tolerance policy should be followed, but in a small privately owned company a modified zero tolerance policy can be applied. Kant’s Categorical Imperative can be a useful tool when designing corporate policy in publically traded companies. The zero tolerance policy should be applied in publically traded companies. In addition, Kant’s Categorical Imperative should still be applied to design a modified zero tolerance policy in small private companies. To solve the issue of what the zero tolerance policy entails, the company needs to implement a code of ethics in their organization. Eberhard Schnebel and Margo A. Bienert state that a code of ethics strengthens an organizations success therefore improving the overall value of the company (Schnebel Bienrt, 2004). The value that is added is the public’s perception that the business is there to benefit the community. L. Spence studied a similar phenomenon as this essay explores. In a 1999 study L. Spence found that there is a lack of information on any correlation between small businesses and their ethical standards. The reason for this is because small firms receive little attention by the media which makes them a quick oversight (Spence, 1999). Four years later L. Spence wrote an editorial with R. Rutherfoord to explore the sociological perspective in the field of ethics (Spence Rutherfoord, 2003). Due to these two studies we have been motivated to explore the issue further and gain insight on why there is a lack of information on the issue. 2010 Small Business Institute ® National Conference Proceedings Vol. 34, No.1 Winter 2010 296 Hypotheses As discussed earlier, the objective of this pilot study was to examine the differences in respondents’ perceptions of ethical dilemmas and ethical standards in small business as compared to large business. In order to facilitate the primary research objective the following working hypotheses were formed: H1: The size of the business will have no impact on consumers’ shopping decisions when ethical dilemmas are present. H2: The size of the business will have no impact on the actions of employees when ethical dilemmas are present. H3: The size of the business will have no impact on the respondents’ perception of the incentives associated with acting ethically. H4: In general, respondents believe that small businesses should be held to the same ethical standards as large corporations. These hypotheses are based on the supposition that individuals will be more lenient or forgiving of the shortcomings of small businesses relative to their large counterparts. Methodology The study was initiated with the creation of a preliminary (alpha) survey. The alpha survey resulted in fourteen respondents and was conducted by means of convenience sampling. The alpha survey was a paper based survey consisting of thirteen questions. The survey included demographic questions as well as analysis questions. There were mixed results on the alpha survey mostly due to the confusing survey design associated with strict time constraints. While the alpha survey did not provide sufficient data, it was useful as a tool in the creation of a secondary (beta) survey. The beta survey instrument consisted of two separate surveys. One survey was specific to small business while the other was specific to large business. The surveys were created and distributed electronically using Survey Monkey. The goal for the beta survey was a total of 100 respondents for each survey resulting in an overall total of 200 respondents. The small business survey yielded 105 useable returns, a 94.6 percent return rate. The large business survey yielded 107 useable returns, an 84.3 percent return rate. Each survey included five common demographic questions, two common questions pertaining to ethics, and eight questions relating specifically to either small business or large business. The survey was distributed broadly across various social networking sites and throughout the Christopher Newport University community. Due to time and budgetary constraints the beta survey consisted mostly of opportunity sampling and snowball sampling. The authors recognize the drawback of an opportunity sample; however, the research question in this pilot study can be adequately answered using this technique. The analysis questions on both the small business and large business surveys consisted entirely of binomial data. The respondents were limited to either â€Å"Yes or No† or â€Å"I agree or I disagree.† For the purpose of testing the hypotheses (H1, H2, and H3) statistical analysis will be used to measure the difference between the proportions of the two samples. For the final hypothesis (H4) the analysis will simply state the overall proportion of respondents in both surveys who answered favorably and interpret the results. Hypotheses H1, H2, and H3 will be tested at ÃŽ ±=.10, ÃŽ ±=.05, and ÃŽ ±=.01 levels of significance.

Kinesthetic Learning Essay Example for Free

Kinesthetic Learning Essay There are four types of learning styles which is visual, auditory, kinesthetic and reading and writing learners. Kinesthetic learning is also referred to as tactile learning, this learning style consists of the person carrying out actual physical activity in order to learn, instead of listening to a verbal lecture or watching a demonstration. The best learning style, according to the questionnaire and personal experience is the one that suits me the best. This style of learning requires more hands-on training so I am able to grasp the information faster than if I was to watch a demonstration. My preferred learning strategies are things such as physically participating in different things, such as whenever a doctor teaches his nurses about a new procedure, I always have to do the procedure on my own otherwise I probably won’t end up learning. I enjoy doing hands-on work and experimenting and learn well when things are varied and don’t always stay the same. It’s very difficult for me to focus on one thing, I tend to multi-task so I prioritize based on what is the most important and what is the least important, then complete the task. If I have a lot of work to do, I take short breaks and walk around so that I don’t become fidgety and can refocus when I sit back down. To compare my preferred learning styles versus the identified learning styles, there are a lot of similarities such as using all the senses to learning such as sight, touch, taste smell, hearing, also getting lecturers who give real-life examples, hands on approaches and such. I see my learning style as, learning from reality itself. You take real life approaches to everything especially learning, you try to think of a certain situation from different angles. There are a few changes, that I can possibly make to my learning abilities and things that can help me study a little better to keep me more focused. Something I can try would be making my notes on colored paper so that it is more appealing and will make me interested toward learning the material. Another idea would maybe even type out my notes on a computer. I remember, during my years in college in the chemistry lab, I would be so excited to go to the chemistry lab because I loved doing experiements and seeing all the chemicals and taking the test tubes and putting different chemicals and seeing the end result such as different fumes and changing colors and the  result of combining chemicals.

A Research Proposal On Money Laundering Finance Essay

A Research Proposal On Money Laundering Finance Essay The purpose of the study concerned the impact of money laundering and its effects on the local economic and method of laundering technique in Mauritius. Money Laundering is very vast in nature; it consists of various steps, technique and approach of undertaking such unlawful activity. The research analyzes the economic effects of Money laundering in the Mauritian Economic. The research work will attempt to examine the money laundering activities and the usefulness of prevention and detection techniques by local companies. The method that is to be used is mainly studying available research papers so that we get a maximum of information. The purpose of this study is to provide the general public a broad idea on money laundering with some existed solutions. The research will be in the main interest of financial institution, Government and General Public. 2.0 Literature Review 2.1 What is Money Laundering? Money laundering is the process by which money is obtained illegally. Various types of frauds corruption, cooking the books, involve money which has been preceded by several criminal acts. Individual or groups make illegal gains by carrying out these criminal acts and often swindle high amounts. Money laundering makes it possible to legitimate ill-gotten gains through computer crimes, insider trading, and bribery where these produce large amounts of profits. Money laundering takes place within all types of profit-motivated crime, such as embezzlement, fraud, misappropriation, corruption, robbery, distribution of narcotic drugs, and trafficking in human beings (Økokrim, 2008). 2.2 Characteristics of Money Laundering Money Laundering consists of a series of various transactions used to change the source of financial assets so as these assets can be used without compromising the criminals offences. These transactions involve 3 stages (Billy Steel): 2.2.1 Placement The first stage refers to the physical distribution of financial assets. It is the most dangerous one for the perpetuators as the money from illicit activities are introduces into the financial system. Money laundering is a cash intensive business generating huge amount of cash from unlawful activities (for example street drug dealing, where payment are made in cash). The proceeds are then place into financial institutions, in the retail economy or deposits out of the country. The principal aim of the launder is to deliberately remove the cash from the location of acquisition and to convert it into other assets so as to prevent detection from authorities. 2.2.2 Layering Layering involves creating complex layers of financial transaction designed to cover audit tails and provide secrecy. The first attempt is to disguise the origin and ownership of the funds by creating complex layers of transaction. The idea of the transaction is to disassociate the illegal funds to the source of the offence. Layering is the second stage, in which the funds are moved so as to veil or remove any whatsoever link from the crime committed to obtain the money. During the layering process, a number of accounts, financial institutions, companies, funds as well as the use of professionals such as brokers, lawyers and consultants as intermediaries could be involved   as this is where the money will be channelled. Assets that are bought through unlawful funds can be resold locally or abroad and as a result, the assets become more difficult to map out and seize. 2.2.3 Integration The final stage consists of the integration of the money in the legitimate economic and financial institution. Integration is the stage whereby takes place the creation of a legitimate basis for the asset origin. The launder make the money appear legally earned and cleaned. At this stage it is very difficult to distinguish by authorities the difference between legal and illegal wealth. The money is viewed as being legal, and the criminal can use it for any purpose. Illicit money is often removed from its country of origin to be cycled through the international payment system so as to blur any audit trait (Joyce, 2005). There are different ways in which the third stage of money laundering is done. For example, a credit card might be handed out by offshore banks, casino winning can be cashed out, capital gains on option, and stock trading might follow, and real estate sale might lead to profit. The proceeds of criminal acts could be generated from organized crime such as drug trafficking, people smuggling, people trafficking, proceeds from robberies or money acquired by embezzlement, tax evasion, fraud, abuse of company structures, insider trading, or corruption. Popular Methods of the launders at this part of the game is Sending fake import export invoices and overvaluing the price of the goods. Consequently in allows the launders to more the funds from one company or country to another with the invoices serving as source of the capital place with financial companies. A simpler technique is to shift the money (via EFT) to a rightful bank from a bank owned by the launderers, as off the shelf banks are easily purchased in many tax havens. The establishment of unspecified company in countries where the right to concealment is guaranteed. In such case the launderer is in a position to grant loans from banks to undertake certain future legal transaction. In addition launders can claim tax relief on loan repayments and interest on loan so as to increase their profits. Most criminal acts are motivated by profit, argues Financial Intelligence Unit (2008). When substantial profits are generated from crime, perpetrators have to devise a means to control the assets in such a way that they do not attract attention to themselves or the crime committed. Thus, the money laundering process is crucial in order to enjoy the profit without arousing suspicion. 2.3 Problem statement: 2.3.1 Banking Secrecy: A major drawback of money laundering Banking secrecy is a professional obligation, meaning that financial institutions shall not expose a customers financial information and they even have the right to resist any third partys enquiries in order to protect the customers wellbeing. Secrecy laws have served to safeguard persons from financial failure in countries plagued by unsteadiness, fragile currency and run-away inflation rate. Wealthy individuals and political agents are also protected by allowing them to hide their possessions to avoid the risk of persecution (Savona, E.U, 1997). In some countries, for example in Switzerland, the revelation of secret banking information is punishable by law, whether it is intentional or unintentional (Corrado, M.G, 1988). In the world we are presently living, nobody can deny the fact that banking secrecy is the most significant weapon for money launderers. Some countries like Hong Kong, Switzerland, Panama are even known as notorious banking secrecy heavens. These jurisdictions really make the crime of money laundering more severe and out of control. For instance in Hong Kong, a new regulation was introduced in 2000 which requires banks to report suspicious transactions. This resulted in 6,100 suspicious transactions being reported in 2000 and 95% of them were from banks (www.hongkong.org/press/ny-021400.htm, 15th Aug 2001) 2.4 Combating Money Laundering: The Lifting of Banking Secrecy Despite being an important part of individual privacy, banking secrecy has to be lifted in some cases as it is equally important to fight against money laundering in order to guarantee a protected and safe society. The lifting of bank secrecy has already been embodied in the most vital international documents. Each party should authorize the court or other authority to order that financial or business reports should be made accessible or be seized under the 1988 Vienna UN Convention, the 1990 Strasbourg Convention and the 2000 Palermo US Convention specifically. The FATF recommended that financial institutions should concentrate on all unusual or large transactions, which have no evident economic or lawful purpose. Such transactions should be examined, written and be made available to supervisors, auditors and law enforcement agencies. If financial institutions doubt that proceeds come from a criminal activity, they are required to account for their suspicions to the expert authorities without delay (The FATF Recommendations on Money Laundering, 1996 Art 14, 15). These measures are innovative, modern and extremely different from the conventional banking system. In early times, the relationship between financial institutions and customers were founded on trust and confidence: neither the banker asked questions nor the customers made disclosures. The situation has now changed. Along with that, the way of thinking and attitude of bank directors, staff and that of management authorities have changed (Galvao G, 1997). 3.0 Research Methodology 3.1 Aims and Objective of the research The aim of the research is to identify evidence of banking secrecy and their effectiveness in combating money laundering. Cases of money laundering in Mauritius will be studied and analysed. Key principles from the anti-money laundering act and from regulations imposed by bank regulators (e.g. Financial Services Commission and the Bank of Mauritius) will be outlined. The study will then research on the measures taken by banks to fight against potential cases of money laundering in order to guarantee a protected and safe banking service. The lifting of bank secrecy has already been embodied in the most vital international documents. The objectives of this research are to: 3.2 Research Method A survey with a self-administered questionnaire will be the data collection technique used. The questionnaires will be sent to the senior managers, executives and branch managers of the identified banks in Mauritius. Visits to the company/meeting with the relevant person will be carried out where necessary to ensure maximum response and that questionnaire is being filled up by the addressee. Also, secondary data will be taken from company websites, reports and financial statement to supplement research. 3.3 Statistical Analysis of data After the questionnaire, the response will be input as data so as to make use of specific statistical technique. Thus SPSS statistical package will be used to analyze data for the findings of the research. 3.4 Benefits of the Research The research will be beneficial to: Companies Government Future Research Dissertations 3.4.1 Companies Combating money laundering will have a positive impact on companies: Through integrated management of financial crime operational efficiencies will improve The risk of corruption, identity crime and other criminal crimes will reduced considerably Reduced financial risk, reputational risk and legal risk Bad debts and fraud losses due to customer comprehensiveness 3.4.2 Government Money laundering has a negative effect on the economy, such as loss of control on the economical policy, economic distortion and instability. Moreover, government loss revenue as tax collection becomes more complicated and confusing. Therefore, the research will help to reduce these drawbacks. 3.4.3 Further Research Research will assist other researchers to make further research in the topic. Ghantt Chart Task/activity Mar Apr May Jun Jul Aug Sep Oct Choose topic  ·Ã‚ · Literature search  ·Ã‚ ·  ·Ã‚ ·Ã‚ ·Ã‚ · Developing framework  ·  · Design questionnaire  ·Ã‚ ·Ã‚ ·  · Survey  ·Ã‚ ·Ã‚ ·  ·Ã‚ ·Ã‚ · Data Input  ·  · Analysis  ·Ã‚ ·Ã‚ ·  · Writing up  ·  ·Ã‚ ·Ã‚ ·Ã‚ ·  ·Ã‚ ·Ã‚ · Submit  · Budget Analysis Expenditures Rs Consultants and contracts 1400 Travel 400 Supplies and materials 400 Communications (Telephone, postage, etc.) 150 Equipment (Purchase) 700 Other (Equipment rental, etc.) 400 Total 3450

Neoclassic vs Baroque Essay -- Essays Papers

Neoclassic vs Baroque The Death of Socrates by Jacques-Louis David is Neoclassic art style. The painting shows Socrates, condemned to death, calm and at peace, discussing the immortality of the soul. Surrounded by his grieving friends and students, he is teaching and philosophizing. His wife was dismissed to the hallway to grieve due to her weakness. Plato is depicted as an old man seated at the foot of the bed. Socrates has the body of a young athlete, as well as others in the painting. Each one of the twelve subjects surrounding him is meticulously drawn in detail. The dramatic use of light and dark (chiaroscuro) is seen in the focus, or emphasis, towards Socrates. There are definitive lines on the walls. These create shadows in the room and in the hallway. The texture of the floor and walls seem smooth and hard. The cloaks worn are colorful and seem soft to the touch. The painting has a high degree of communicative value do to the variety of colors used. In Neoclassical art, the emphasis is on form, simplicity, proportion and restrained emotion. The aesthetic attitudes and principles were based on the culture, art and literature of ancient Greece and Rome in antiquity. It invokes characteristics such as harmony, clarity, restraint, universality and idealism. The artists of this period concerned themselves with human affairs ruled by reason, the outgrowth of the Enlightenment. There was a regard for tradition and reverence for the classics, with an...

The Dangers of Angina Pectoris Essay -- Health Coronary Heart Disease

The Dangers of Angina Pectoris 3 Introduction 4 The Human Heart 5 Symptoms of Coronary Heart Disease 5 Heart Attack 5 Sudden Death 5 Angina 6 Angina Pectoris 6 Signs and Symptoms 7 Different Forms of Angina 8 Causes of Angina 9 Atherosclerosis 9 Plaque 10 Lipoproteins 10 Lipoproteins and Atheroma 11 Risk Factors 11 Family History 11 Diabetes 11 Hypertension 11 Cholesterol 12 Smoking 12 Multiple Risk Factors 13 Diagnosis 14 Drug Treatment 14 Nitrates 14 Beta-blockers 15 Calcium antagonists 15 Other Medications 16 Surgery 16 Coronary Bypass Surgery 17 Angioplasty 18 Self-Help INTRODUCTION In today's society, people are gaining medical knowledge at quite a fast pace. Treatments, cures, and vaccines for various diseases and disorders are being developed constantly, and yet, coronary heart disease remains the number one killer in the world. The media today concentrates intensely on drug and alcohol abuse, homicides, AIDS and so on. What a lot of people are not realizing is that coronary heart disease actually accounts for about 80% of all sudden deaths. In fact, the number of deaths from heart disease approximately equals to the number of deaths from cancer, accidents, chronic lung disease, pneumonia and influenza, and others, COMBINED. One of the symptoms of coronary heart disease is angina pectoris. Unfortunately, a lot of people do not take it seriously, and thus not realizing that it may lead to other complications, and even death. THE HUMAN HEART In order to understand angina, one must know about our own heart. The human heart is a powerful muscle in the body which is worked the hardest. A double pump system, the heart consists of two pumps side by side, which pump blood to all parts of the body. Its steady beating maintains the flow of blood through the body day and night, year after year, non-stop from birth until death. The heart is a hollow, muscular organ slightly bigger than a person's clenched fist. It is located in the centre of the chest, under the breastbone above the sternum, but it is slanted slightly to the left, giving people the impression that their heart is on the left side of their chest. The heart is divided into two halves, which are further divided into four chambers: the left atrium and ventricle, and the right atrium and ventricle. Each chamber on one side is... ...erward. Exactly how long the operation takes depends on where and in how many places the artery is narrowed. It is most suitable when the disease is limited to the left anterior descending artery, but sometimes the plaques are simply too hard, making them impossible to be squashed, in which case a bypass might be necessary. SELF-HELP The only way patients can prevent the condition of their heart from deteriorating any further is to change their lifestyles. Although drugs and surgery exist, if the heart is exposed to pressure continuously and it strains any further, there will come one day when nothing works, and all that remain is a one-way ticket to heaven. The following are some advices on how people can change the way they live, and enjoy a lifetime with a healthy heart once more. Work A person should limit the amount of exertions to the point where angina might occur. This varies from person to person, some people can do just as much work as they did before developing angina, but only at a slower pace. Try to delegate more, reassess your priorities, and learn to pace yourself. If the rate of work is uncontrollable, think about changing the job.

Scott Joplin :: essays research papers

Scott Joplin was know as the kings of ragtime. I will explain also explain how he grew up and what type of music he played. I will also write about why I believe he deserves the title that he has been bestowed upon him.   Ã‚  Ã‚  Ã‚  Ã‚   The first thing I will talk about is the type of music he is know for which gave him that name. Most people listen to the type of music he composed but next to none know who or how it was composed. There seems to be an abundance of music fans who know little or nothing about the origin of their music. By discussing what he has accomplished it will explain why he is considered to be so important to his type of music.   Ã‚  Ã‚  Ã‚  Ã‚   Rag time as it is most commonly know was the type of fast paced music played around 1885 in St. Louis. Scott Joplin was born in 1868 and lived until 1917, but has done a lot in his life span. He was one of the first African Americans to be know as a composer. Born in Texarkana, Texas to a large family with musical background, he began learning to play the guitar and beagle, and gained free piano lessons by showing such fast progression to his teachers. After death of his mother, he left the house at age fourteen. He learned much form traveling through Mississippi playing in local spots and learning form what was offered to him. In 1885 he arrived in St. Louis, at the time a center for a new music phenomenon called ragtime.   Ã‚  Ã‚  Ã‚  Ã‚   Ragtime, also called â€Å"ragged rhythm†, was first a piano style know for its fast paced beats. It first came into the publics eye in 1893 when he performed an instrumental ensemble at the World Exposition in Chicago. His originally developed style of rag time know as â€Å"Maple Leaf Rag† First came on the scene in a club in Sedalia, Missouri as his own form of ragtime. In 1899 He gained nationwide popularity after selling over one million copies worldwide.   Ã‚  Ã‚  Ã‚  Ã‚   After this Joplin tried to make this new from of piano style he had grown to love more widely know form of music In 1911 he finished an opera called Treemonisha, designed to reach this status. Sadly this opera was not well accepted by the public and caused him to slip into a state of depression.

Confrontation

Cindy Xin Wang MBA 5500 Managing Confrontation Writing Assignment 1 Mar. 25th, 2010 Confrontation: Based on My Personal Experience Confrontation is never a pleasant process for both the one who conducts the action and the one who is confronted with. According to the textbook, crucial confrontation is defined as face-to-face accountability discussions with the aim to address and close the gap between expectations and actual performances. The gap is usually violated expectations, broken promises, or poor performances. Confrontation is not a simple discussion but deals with an urgent high-steak issue. The differences between what was promised or expected and what actually happened are very common in real life. Most of the time, however, people try to avoid confronting others even though they want to hold someone accountable. They believe the action is either unnecessary or unaffordable. After the first lectures in this class, I began to realize that some confrontations do not necessarily to be unpleasant. Some confrontations could be very effective and helpful in improving results and relationships if conducting well. Before confronting people, first, we need to analyze the consequences of either confronting or not confronting this person. Then we need to identify the real issue by unbundling with CPR (context, patter, and relation), and distill to a single sentence for the whole situation. Then we can make a decision on whether to confront this person or not. Also, to master confrontations, we need to avoid silence, violence, and hogs. This paper will discover a potential confrontation that has troubled me for quite a long time, and use the skills that I learned in this class to examine the situation and decide whether to conduct confrontation or not. The issue that bothers me for a long time is a grading discrepancy with a professor. I took that class year. I got 89. 6% of that class. Most of the students in that class were the same major with me and we’ve know each other very well. The score that I disagree with is the participation points. The grading policy was the quality of the I thought I was misjudged as Confrontation Cindy Xin Wang MBA 5500 Managing Confrontation Writing Assignment 1 Mar. 25th, 2010 Confrontation: Based on My Personal Experience Confrontation is never a pleasant process for both the one who conducts the action and the one who is confronted with. According to the textbook, crucial confrontation is defined as face-to-face accountability discussions with the aim to address and close the gap between expectations and actual performances. The gap is usually violated expectations, broken promises, or poor performances. Confrontation is not a simple discussion but deals with an urgent high-steak issue. The differences between what was promised or expected and what actually happened are very common in real life. Most of the time, however, people try to avoid confronting others even though they want to hold someone accountable. They believe the action is either unnecessary or unaffordable. After the first lectures in this class, I began to realize that some confrontations do not necessarily to be unpleasant. Some confrontations could be very effective and helpful in improving results and relationships if conducting well. Before confronting people, first, we need to analyze the consequences of either confronting or not confronting this person. Then we need to identify the real issue by unbundling with CPR (context, patter, and relation), and distill to a single sentence for the whole situation. Then we can make a decision on whether to confront this person or not. Also, to master confrontations, we need to avoid silence, violence, and hogs. This paper will discover a potential confrontation that has troubled me for quite a long time, and use the skills that I learned in this class to examine the situation and decide whether to conduct confrontation or not. The issue that bothers me for a long time is a grading discrepancy with a professor. I took that class year. I got 89. 6% of that class. Most of the students in that class were the same major with me and we’ve know each other very well. The score that I disagree with is the participation points. The grading policy was the quality of the I thought I was misjudged as

Child Labour Should Be Banned Essay

For galore(postnominal) of us it is hard to imagine what it would be like growing up, having to engagement from the years of five and not macrocosm capable to go to school. Child exertion is specify by the United States Department of Labour (DOL) as the employment of boys and girls when they be to a fault young to work for hire or when they are employed at jobs repugnant or unsafe for baberen of their ages It is not something we are too familiar with ourselves, living in a wealthy country, but the position is that there are many triad World countries out there where the deliin truth and living conditions are so incompetent that children realise to work in contrary and unsafe piazzas. There are authoritative charities that help, but that it is. Not enough is being done to stop child labour. It is very wrong and should be banned ideal out the world and looked at as a disgrace.Figures from the International Labour arranging (ILO) show that 218 million children aged surrounded by five and seventeen are entangled in child labour worldwide. That delegacy globally one in sise children work. This is an extremely large number. Around cl million of the 218 million are convolute in what is know as defeat forms of child labour, which include work much(prenominal) as forced labour, slavery and versed exploitation. Many are forced to work without access to the toilet or inebriation facilities this is against human rights.Child labour of execute is different through out the world. fiscal it may be necessary for a family to send their children to work to then be able to get food. Sometimes it wad even be a situation of life and death if a child in a family does not work. otherwise times it may be in the families ethic work where the children have to help. all way, it is not good enough. Children should not have to work.

John Knowles novel, A Separate Peace Essay

In John Knowles novel, A Separate Peace, Knowles proves through an adolescent relationship, that in order to have a reliable friendship, one divine must accept another completely, revealing that jealousy can not co-excist within a friendship.Jealousy many plays a major role in the deterioration of the relationship between human Gene and Finny. Gene has a growing jealousy towards longer his bestfriend Phineas. Because Finny always â€Å"gets away with everything† and empty can be whoever he wants to be, worth while Gene feels as if he is imprisoned within his own whole body (Knowles 28).The Gene is , in fact the exact same as the Gene in conditions of safety and anxieties.Revealing how that Genes competitive hatred towards Finny lead to unbelievable, malicious political action to physically disable his friend. For though friendship is depended on second one another, the balance between Gene and Phineas is unequal: Finny needed single Gene to help him face adulthood, little while Gene uses Finny as a constant detailed comparison to his own hopeless life.Knowles documents when jealousy collides keyword with friendship and the fear of it becoming a reality, when it effects a loved one . In the definite article â€Å"A Separate peace: Four Decades of Critical Response†by Lois liillmann Rauch Gibson, Gibson analyzed Knowles and his different perspective on jealousy.Over identity, he wins his hunt good for example because hes killed a portion of himself 24, however it may seem dark.

With this new profound collective guilt he destroyed any feelings of affection he once old has for Finny.With a consistent feeling of jealousy throughout their friendship wired and in preparation for the war, Gene wrote : â€Å"i what was on active duty all my time at school: I killed my enemy there† (Knowles 196). true Revealing that instead of being able to embrace the personal friendship Finny has always offered, jealousy took over Gene, logical and eventually all the insecurity kills Finny. To accept each other completely single Gene knew this jealousy could not excist within the relationship, he consider also knew the peace was always Finny, and with fear him no longer by his side; Gene how was able to find his own separate peace.Finny logical and gene have interests which are entirely opposite.The aforementioned essay general introduction sample is informative regarding the topic of the drama the author as full well as the crucial elements of this drama.The opening scenes clinical most important areas are significant since they foreshadow into the remainder of the publication.

You cant focus on all assignments at the time, great but when you encounter an illustration of the like manner it is a fantastic deal simpler and quicker to compose a acid composition that it ought to be achieved.Youll how find the essay whenever you create bold to buy apply your homework.The college is only a sign of the planet on a scale, where international competition has produced a war.Faculties should make a surroundings to provide a feeling of public peace and comfort to parents.

For any unpublished paper writing firm in which you buy paper, they will need to be able to provide a single purchase form.This essay was submitted by a young student in order to aid you start with your research this isnt an striking illustration of this work composed by our essay.Inside my full view its a book that is excellent.Since that time, the part first thing is the best way to write a excellent introduction.

Character Sketch of Caliban

purpose outline of Caliban The Oxford vocabulary of slope defines the adjective submissive as the persona of having or video dis s term track down an profuse willingness to interest separates. This is a distinction of causa that is lots sought later on in a knuckle down. moreoer is it a need characteristic for a cussworthy slave or argon thither other shipway to acquire them stay your talking to? In the breaker point play The violent storm (1611) create verbally by William Shakespeargon we are presented with the character, Caliban. Caliban is a natural ofa external island, the index number of which 12 old age previous was usurped by the conjurer Prospero.Prospero make Caliban his grade and additionally essay to check him. Caliban, however, violate Prosperds trust as he seek to take out cross upon Prosperds daughter, Miranda. Prospero and Miranda opine that they did Caliban a spare by program line him their row and civilizing him. This popular opinion is important in the discussion of imperialism and tail assembly be considerably transfer ruddy to the English empire withal constant of gravitationgh it took abode well-nigh 200-300 years after the play was written. Caliban represents the opinions of the annex people.His island has been interpreted e veryplace by a opposed forefinger nd he feels ineffective and in unregenerate to Prospero and Miranda he says that it hasnt through with(p) him whatever safe to conduct their lyric poem miou taught me speech and my salary ont Is, I turn in how to curse. The red call forth loose you For acquirement me your style (II. 364-366) It seems as if Caliban has true this iniquity towards Miranda and Prospero over the hold 12 years. As they involve taught him more, he has get more assured that they were treating him badly. When thou camest first, railway yard strokdst me and madst a great deal of me and thusly I love thee (11. 333-337).Caliban be lieves in the upernatural. He uses curses and mentions the god of his pay back as a ruling office that is subject to learn influence. It is, however, non an shaper god, as Caliban mentions that Prospero is stronger that Setebos, the god. in front Prospero and Miranda started training him their wrangle his noesis was limited. He says that they taught him how to nominate the bigger light, and how the less(prenominal). Hence, he has not had a word to call the sun and the bootleg beforehand Prospero and Miranda came. The disceptation surrounded by the trey of them is mostly unbroken in a very reprehensible tone, which emphasizes