Practice Math

1. The nth term of an arithmetic sequence is given by un = 5 + 2n. (a) Write down the common difference. (1) (b) (i) (ii) Given that the nth term of this sequence is 115, find the value of n. For this value of n, find the sum of the sequence. (5) (Total 6 marks) 2. A sum of $ 5000 is invested at a compound interest rate of 6. 3 % per annum. (a) Write down an expression for the value of the investment after n full years. (1) (b) What will be the value of the investment at the end of five years? (1) (c) The value of the investment will exceed $ 10 000 after n full years. i) (ii) Write down an inequality to represent this information. Calculate the minimum value of n. (4) (Total 6 marks) 3. (a) Consider the geometric sequence ? 3, 6, ? 12, 24, †¦. (i) (ii) Write down the common ratio. Find the 15th term. (3) Consider the sequence x ? 3, x +1, 2x + 8, †¦. IB Questionbank Maths SL 1 (b) When x = 5, the sequence is geometric. (i) (ii) Write down the first three terms. Find the co mmon ratio. (2) (c) Find the other value of x for which the sequence is geometric. (4) (d) For this value of x, find (i) (ii) the common ratio; the sum of the infinite sequence. (3) (Total 12 marks) . Clara organizes cans in triangular piles, where each row has one less can than the row below. For example, the pile of 15 cans shown has 5 cans in the bottom row and 4 cans in the row above it. (a) A pile has 20 cans in the bottom row. Show that the pile contains 210 cans. (4) (b) There are 3240 cans in a pile. How many cans are in the bottom row? (4) IB Questionbank Maths SL 2 (c) (i) There are S cans and they are organized in a triangular pile with n cans in the bottom row. Show that n2 + n ? 2S = 0. Clara has 2100 cans. Explain why she cannot organize them in a triangular pile. 6) (Total 14 marks) (ii) 5. Ashley and Billie are swimmers training for a competition. (a) Ashley trains for 12 hours in the first week. She decides to increase the amount of time she spends training by 2 hou rs each week. Find the total number of hours she spends training during the first 15 weeks. (3) (b) Billie also trains for 12 hours in the first week. She decides to train for 10% longer each week than the previous week. (i) (ii) Show that in the third week she trains for 14. 52 hours. Find the total number of hours she spends training during the first 15 weeks. (4) (c)In which week will the time Billie spends training first exceed 50 hours? (4) (Total 11 marks) IB Questionbank Maths SL 3 6. The diagram shows a square ABCD of side 4 cm. The midpoints P, Q, R, S of the sides are joined to form a second square. A Q B P R D (a) (i) (ii) Show that PQ = 2 2 cm. Find the area of PQRS. S C (3) The midpoints W, X, Y, Z of the sides of PQRS are now joined to form a third square as shown. A W Q X B P Y S R Z D C (b) (i) (ii) Write down the area of the third square, WXYZ. Show that the areas of ABCD, PQRS, and WXYZ form a geometric sequence. Find the common ratio of this sequence. 3) IB Questi onbank Maths SL 4 The process of forming smaller and smaller squares (by joining the midpoints) is continued indefinitely. (c) (i) (ii) Find the area of the 11th square. Calculate the sum of the areas of all the squares. (4) (Total 10 marks) 7. Let f(x) = log3 (a) x + log3 16 – log3 4, for x > 0. 2 Show that f(x) = log3 2x. (2) (b) Find the value of f(0. 5) and of f(4. 5). (3) The function f can also be written in the form f(x) = (c) (i) Write down the value of a and of b. ln ax . ln b (ii) Hence on graph paper, sketch the graph of f, for –5 ? x ? 5, –5 ? y ? , using a scale of 1 cm to 1 unit on each axis. (iii) Write down the equation of the asymptote. (6) (d) Write down the value of f–1(0). (1) IB Questionbank Maths SL 5 The point A lies on the graph of f. At A, x = 4. 5. (e) On your diagram, sketch the graph of f–1, noting clearly the image of point A. (4) (Total 16 marks) 8. Let f(x) = Aekx + 3. Part of the graph of f is shown below. The y-inte rcept is at (0, 13). (a) Show that A =10. (2) (b) Given that f(15) = 3. 49 (correct to 3 significant figures), find the value of k. (3) (c) (i) (ii) (iii) Using your value of k, find f? (x).Hence, explain why f is a decreasing function. Write down the equation of the horizontal asymptote of the graph f. (5) IB Questionbank Maths SL 6 Let g(x) = –x2 + 12x – 24. (d) Find the area enclosed by the graphs of f and g. (6) (Total 16 marks) 9. Consider the function f(x) = px3 + qx2 + rx. Part of the graph of f is shown below. The graph passes through the origin O and the points A(–2, –8), B(1, –2) and C(2, 0). (a) Find three linear equations in p, q and r. (4) (b) Hence find the value of p, of q and of r. (3) (Total 7 marks) IB Questionbank Maths SL 7 10. Let f (x) = 4 tan2 x – 4 sin x, ? a) ? ? ? x? . 3 3 On the grid below, sketch the graph of y = f (x). (3) (b) Solve the equation f (x) = 1. (3) (Total 6 marks) IB Questionbank Maths SL 8 11. A city is concerned about pollution, and decides to look at the number of people using taxis. At the end of the year 2000, there were 280 taxis in the city. After n years the number of taxis, T, in the city is given by T = 280 ? 1. 12n. (a) (i) (ii) Find the number of taxis in the city at the end of 2005. Find the year in which the number of taxis is double the number of taxis there were at the end of 2000. (6) (b)At the end of 2000 there were 25 600 people in the city who used taxis. After n years the number of people, P, in the city who used taxis is given by P= (i) (ii) 2 560000 . 10 ? 90e – 0. 1n Find the value of P at the end of 2005, giving your answer to the nearest whole number. After seven complete years, will the value of P be double its value at the end of 2000? Justify your answer. (6) (c) Let R be the ratio of the number of people using taxis in the city to the number of taxis. The city will reduce the number of taxis if R ? 70. (i) (ii) Find the value of R at the end of 2000.After how many complete years will the city first reduce the number of taxis? (5) (Total 17 marks) IB Questionbank Maths SL 9 12. The function f is defined by f(x) = 3 9 ? x2 , for –3 < x < 3. (a) On the grid below, sketch the graph of f. (2) (b) Write down the equation of each vertical asymptote. (2) (c) Write down the range of the function f. (2) (Total 6 marks) IB Questionbank Maths SL 10 13. Let f (x) = p ? 3x , where p, q? x ? q2 2 + . Part of the graph of f, including the asymptotes, is shown below. (a) The equations of the asymptotes are x =1, x = ? , y = 2. Write down the value of (i) (ii) p; q. (2) (b) Let R be the region bounded by the graph of f, the x-axis, and the y-axis. (i) (ii) Find the negative x-intercept of f. Hence find the volume obtained when R is revolved through 360? about the x-axis. (7) (c) (i) Show that f ? (x) = 3 x 2 ? 1 ?x ? 2 ?1 ? 2 ?. (8) (ii) Hence, show that there are no maximum or minimum points on the graph of f. IB Questionbank Mat hs SL 11 (d) Let g (x) = f ? (x). Let A be the area of the region enclosed by the graph of g and the x-axis, between x = 0 and x = a, where a ? . Given that A = 2, find the value of a. (7) (Total 24 marks) 14. Two weeks after its birth, an animal weighed 13 kg. At 10 weeks this animal weighed 53 kg. The increase in weight each week is constant. (a) Show that the relation between y, the weight in kg, and x, the time in weeks, can be written as y = 5x + 3 (2) (b) (c) (d) Write down the weight of the animal at birth. (1) Write down the weekly increase in weight of the animal. (1) Calculate how many weeks it will take for the animal to reach 98 kg. (2) (Total 6 marks) IB Questionbank Maths SL 12

Frito-Lay It Strategy Essays

Frito-Lay It Strategy Essays Frito-Lay It Strategy Paper Frito-Lay It Strategy Paper Frito-Lay in the mid to late 1980’s was looking to change its way of doing business. As with many large companies, decisions were made on a corporate level, with field operations carrying out the business plan. This model, though efficient in terms of use of resources on the corporate level, did not allow for the kind of flexibility that the snack foods market demanded. The outgoing CEO, Willard Korn, had set forward a micromarketing strategy where each field office would be responsible for identifying demand, conducting promotions and other marketing activities and ordering replenishment. The problem with this approach was that Frito-Lay lacked the technological framework to make it happen in an efficient manner. (Frito-Lay, 1992) Overlap Between IT and Corporate Strategy Frito-Lay’s corporate strategy, set forward by the new CEO, Michael Jordan, was to initiate the micromarketing strategy begun by his predecessor, but do so in a way that will allow the company to retain overall control while allowing regional decision making to adapt to market changes. Essentially, Mr. Jordan was implementing the same strategy, but his approach was to garner much more success. The key to success would be to use technology to improve the flow of information to and from production, sales, marketing and the corporate level. The IT strategy would center on understanding the information needs of the business and designing and executing a technology solution that will help achieve corporate goals. Overlap Between IT and Functional Area Strategy The central problem Frito-Lay was experiencing was that information gathering and decision making was most efficient when closest to the consumer process, or â€Å"where the rubber meets the road†. : Given variations from region to region, different marketing efforts needed to be developed and no corporate marketing plan would allow for the most efficient use of resources across the entire company. To achieve this, IT strategy would center on developing an efficient and usable system to allow the free flow of information from consumer purchases up to regional sales offices. The primary tool that would be used in this effort would be the handheld computer (HHC). This tool would allow field representatives to gather restocking information, sell-through and other sales data when visiting each store that sells the product. This information could then be sent, in real-time, to the regional office for ordering replenishment and marketing analysis. (Frito-Lay, 1992) The functional area strategy is the plan for Frito-Lay to implement the new IT and corporate plans on the operational level. Obviously, any well-laid out corporate and IT strategy is useless if it isn’t implemented properly in the operation of the business. Strategic Plan Items Needing Review Obviously such a large change in operating procedure would require review of the plan by management of both the IT process and business processes. If a review is not conducted, then money and resources may be spent on projects that end up not working as intended, thereby wasting those resources. (Turban, 2010) The first thing that should be reviewed is the overall business strategy and whether the plan will achieve the objectives of moving operational and marketing decision making downstream, closer to the consumer. This includes the following items: 1)Will the sales force be able to use the information quickly? 2)Will replenishment be more efficient than under the current model? )How will marketing decisions be made and what influence will the corporate strategy have on them? Secondly, the IT strategy must be analyzed to determine if the technology solutions will meet the business need: 1)Can the HHCs be used by the current workforce without a significant investment in training? 2)Will the regional sales offices be able to make accurate and timely decisions based upon the information gathered? 3)Can the corporate offices aggre gate the information into usable analytics? 4)Is there any potential for cost or time overruns? What is the critical path? Justification of Key Components 1)Will the sales force be able to use the information quickly? – A central goal of the business strategy is to allow decentralized, micromarketing to be done in each of the 32 regions. Since the gathering of data is done in each vendor store, the lead time will be dependent upon operations. For example, if a given region has several large stores and dozens of smaller ones, is the replenishment done on a regular basis in all of them? If the larger stores order new inventory less often, it may result in a delay in pertinent sales data. )Will replenishment be more efficient than under the current model? – Obviously gathering restocking information â€Å"at the store shelf† is very efficient, but can that be translated into just-in-time inventory? Can the information be used to accurately forecast demand in the future? On a smaller, regional scale, activities by the consumer can affect demand. A good example of this may be a parade in a given town. If more people have taken to the streets to celebrate, they may purchase more snack food? How will this scenario affect stock and sales? 3)How will marketing decisions be made and what influence will the corporate strategy have on them? – Armed with more timely information about regional sales, the micromarketing strategy will allow regional managers to decide the best marketing mix to use in order to meet goals. What portion of the decision should be theirs? How will the local efforts align with national advertising campaigns? 4)Can the HHCs be used by the current workforce without a significant investment in training? Aside from the regional sales force, the biggest change in job functions under the new strategy will be the field representatives. Where before they used essentially pen and paper to order new inventory, now they will be confronted with an automated computer system in an age when computers were generally a luxury item for most people. What kind of training must be done? Will the new system have a negative effect on efficiency in the short run? What will the cost of that be? 5)Will regional sales offices be able to make accurate and timely decisions based upon the information gathered? On the back-end of the HHCs will be a new decisions support system, which will assist management in making decisions that are aligned with the corporate goals. Can the staff be trained in its use? Will managers previously accustomed to independent decision making will now be confronted with a computer telling them the best course of action, which will not always seem most evident. This can lead to implementation problems much like the HHC and the field staff. 6)Can the corporate offices aggregate the information into usable analytics? On a national level, the data gathered regionally will be used to decide the best impact for advertising dollars. How will the data differ from the old method, which had a much longer lead time? Can this improvement in timeliness be leveraged at the corporate level? A good example would be a news story about tainted corn supplies. Obviously this may lead to a drop in sales of corn-based products across the country. How will the company respond? Can they measure the drop effectively and decide the response in time? )Is there any potential for time or cost overruns? What is the critical path? – Lastly, Frito-Lay needs to look at the overall schedule and ensure the implementation is done in a way that will put all relevant departments on schedule. A clear understanding of the schedule of the project and its critical activities will ensure that the company gives priority to those that will result in delays. A delay on this scale could significantly hurt profits, since executive management needs to know completion in order to have an accurate business plan. Turban, 2010) Effective Communication Strategies Communicating an IT strategy to executives is a challenge because of the different background they often come from and the different way of looking at the business. While any business perso n can understand cost savings and extended costs over time, the unique nature of technology requires that each detail be explained in the context of the overall initiative, in this case, the transition from central decision making to regional offices supported by a strong information systems infrastructure. The best method for communicating the overall IT concept to executives is an in-person presentation with supporting analysis in the form of a chart or graph. This allows the executive team to look at the big picture in a format that will allow questions and feedback. It also summarizes the scenario without providing so much detail that the presentation will be mired in questions and discussion. A second approach is a cost analysis report with full detail. While not as personal or interactive as a presentation, the full report will give every detail of the project with upporting data. (Turban, 2010) Communication of a new initiative to senior management may take on a similar approach as executive communication, but with additional detail on implementation plans and less â€Å"big picture† numbers such as extended costs, IT hardware investment, etc. Senior management will want to know the schedule of the rollout and any required modifications to workflows from other departments in order to plan effectively for resources and budgets in their own areas. When one looks at the team level of communication, a different approach is needed. Since this level isn’t making large scale decisions, but instead carrying out an objective set forward by management, documentation is more effective. While all teams could be placed into a large meeting to go over the proposed changes, the best way of conveying the changes are in written form, either via email, internal memo or even posted to a company intranet. This allows each team member to read about the changes independently and understand what needs to be done. These team members can then work together to achieve the objectives. Evaluation of Effective Communication Strategies In the context of the Frito-Lay case study, communicating IT strategies becomes much more important. In the mid-1980’s, the average level of technological understanding was lower among everyone, including executives. Technology was just starting to be leveraged to realize internal cost savings through improved efficiency in the 1980’s. Because of this, it was far more unproven than it is today. The most effective approach would probably be to do both of the aforementioned methods in order to communicate the plan to management. A detailed report with complete numbers should be provided to the executive team days to weeks in advance of the presentation. This allows them time to review and formulate questions and concerns to bring up in the discussion following the presentation. Senior management would need a slightly altered presentation compared to executive management. This is because senior management will be concerned with budgeting, resource allocation and project planning for the new initiative instead of information required to make a decision. This also means that any reports presented before or after the in-person presentation should focus on smaller operational level numbers instead of larger market data. Team-level communication, in the form of a meeting followed by emails/memos is effective for this group because of the need for detailed information about the processes that will be changing, new workflows, changes in organization, new equipment, etc. This can then be followed up with additional training as required for each functional area. For example, only the team level would need to learn how to use the handheld computers, so only they would really need the documentation for the HHCs. Differences in Communication Needs Between IT Staff and Executive Staff As mentioned before, the executive team is unlikely to understand the details of the technology being deployed. A person with a traditional business background looks primarily at a small number of factors in making a decision. Questions they will ask include: What is the up-front investment cost? What are the extended costs over time? What is the payback period? These are all business indicators that involve the profitability of the company and the costs versus benefit. IT staff is much more likely to look at the scalability and utility of the technology as opposed to the business bottom line. While cost is still a concern, the IT professional is likely to have a longer view of the costs, in the scope of years as opposed to quarterly budgets. Further, the communication may take the form of a more detailed analysis of the standards of the hardware being purchased and whether those standards are expected to change in the future with contingency planning for a migration. For this purpose, a full report may be more useful than a presentation. (Turban, 2010) Strategic Framework that Aligns IT Strategy with Business Strategy The best approach Frito-Lay could use to align its IT and Business strategies would be Business Service Management. Under this methodology, each component of the project will have a key performance indicator (KPI) to determine its impact on the business as a whole. In addition to IT having a KPI, the business side of the company will also have a complimentary KPI. This approach is useful because in a project of this size, a constant measure of the impact and progress must be done to ensure the company is meeting its goals. By setting forward the plan ahead of time and determining what areas must achieve goals and to what extent, the project can be kept on track with an eye to the bottom line. In this case its even more important because of the large investment required of Frito-Lay. A poorly executed initiative could badly damage the profitability of the company. IT Assistance to Business Unit Strategy Development IT can help develop strategy in a number of ways: )A robust and widespread data mining and analytics system will allow business managers to understand where the maximum impact for their investment is being made, thereby allowing them to maximize those dollars. Moreover, the ability to trend out sales data in real time based upon real figures allows each business unit the ability to understand where they are going based upon where the y have been. 2)A well designed decision support system will allow different managers in different business units to make decisions that are complimentary to one another and align with the company goal. While the facts available to one area of the business may signal a given course of action, the decision should be made with an eye to the overall objective as well as what other business units are doing. The further use of an automated decision support system (ADS) will further assist management in ensuring that the BU strategy aligns with the overall company direction. 3)A final area where IT may help business strategy is in understanding the trends in the technology itself. This can include internal infrastructure and technology trends in general. For example, Frito-Lay may have looked to invest in a company network to link each regional office. This would have required a big investment. As of the late 1990’s, the internet as we know it wasn’t yet around for the general public. A few years later, it was established, and that investment would not be needed. ? References: Frito-Lay, (1992) Frito-Lay Inc, A Strategic Transition (Abridged) Turban, Efriam. (2010). Information technology for management: improving performance in the digital economy, 7th edition . Manoa, HI: Wiley.

Growth of the Internet Essay

Growth of the Internet Essay Growth of the Internet Essay This is a free sample essay on Growth of the Internet: The Internet opens up new worlds accessible to anyone with a computer and an Internet server. The Internet can provide the user with a new means of communication, entertainment, shopping and possibly even the answers to the most rhetorical questions on the planet. For instance, Delaware is a small state that relatively few people know much about. Currently there is a Internet site insisting that Delaware is not really a state. The creators of the site say Delaware may not actually be a state at all, but a huge spaceship that crashed eons ago. Maybe, it also is an alien breeding ground or a government test site for intergalactic engines. Whatever the question, whether informative or senseless, the Internet has an answer. Search engines such as Yahoo and Excite are todays card catalogs. Search engines perform millions of queries each day. Whatever the theme, search engines can usually locate up hundreds, if not thousands of topics, all in matter of minutes. Not so long ago, this required many hours of research at the local library. The Internet contains thousands of images on file. Unlimited information and services are easily accessible. The diversity of materials available on the net goes far beyond the scope of the traditional library. Buying a house is a less complicated task with the help of a computer. Companies such as ERA, Prudential, and Patterson-Schwartz have Web sites. Real estate Web sites show properties in desired price ranges and locations. Properties are viewed from the convenience of one’s home. Mortgage companies also have Web sites. To compare interest rates is simple. Computing mortgages based on salary, insurance rates, and taxes require just a few keystrokes. Online banking services are a relatively new service. Banking customers can save an extraordinary amount of time performing such tasks as updating balances and making transfers between accounts. Bills are paid without writing checks or licking stamps. Scheduled monthly payments such as loan payments and utility bills can automatically be paid. Computer processed loans have cut processing time from weeks to hours. Computers have cut down on one of banking’s costliest mistakes, that of human error. Banking online is accurate, convenient, and accessible. No longer must customers wait in long lines. Every day financial institutions add new services for online customers. The Internet will be the banking of the future. Retail companies now use the Internet to reach consumers. Every day millions of computer users are inundated with computer generated ads. Millions of potential customers are reached when computers are turned on. Companies such as Lands End electronically mails customers every week with their latest sale items. Egghead Software Company sells computers and computer software by Internet, and has closed all of its traditional retail stores. Products from Egghead are now only available from its online store. Internet stores provide twenty-four hours a day access. Consumers are no longer bound by traditional retail hours. Retail companies have expanded the customer base. Potential profits are enormous, all being accomplished with a few keystrokes. The computer has revolutionized communication. The use of Local Area Networks, Wide Area networks, satellite links, and the Internet, the user can now send electronic mail or data across an ocean. This takes less time than it takes to address an envelope. Internet telephone service allows subscribers to talk long distance without incurring charges associated with conventional long distance service. Today it is possible not only to hear a person over long distance lines, but to see them as well. Computer technology has created a world at our fingertips. The Internet is opening new doorways for any user with access to an Internet server. The number of Web sites increases daily, with the services provided growing larger each day. Companies now must be accessible to the Internet to be competitive. Computers are like the televisions of the 1940s when few people had them. Today, televisions are a part of everyone’s lives. Five years from now, it will be unheard of not to have a computer with access to the Internet. ______________ is a professional essay writing service which can provide high school, college and university students with 100% original custom written essays, research papers, term papers, dissertations, courseworks, homeworks, book reviews, book reports, lab reports, projects, presentations and other assignments of top quality. More than 700 professional Ph.D. and Master’s academic writers. Feel free to order a custom written essay on Internet from our professional essay writing service.

Harald Bluetooth, Former King of Denmark and Norway

Harald Bluetooth, Former King of Denmark and Norway Harald Bluetooth (c. 910–c. 987), otherwise known as King Harald I of Denmark, was best known for three major achievements. First, he completed the work of unifying Denmark under a single ruler. Second, he conquered Norway- an event which had major historical consequences. Finally, he converted the Danes and Norwegians to Christianity. The dynasty he founded went on to rule over an increasingly large kingdom that, at its height, included much of the British Isles and parts of Sweden. Fast Facts: Harald Bluetooth Known For: King of Denmark and NorwayAlso Known As:  Haraldr Gormsson, Harald Blà ¥tand Gormsen, Harald IBorn: c. 910 in Jelling, DenmarkParents: King  Gorm the Old  and Thyra  DannebodDied: c. 987, probably in Jormsborg in the northern part of modern PolandSpouse(s): Gunhild, Thora  (Tova) the daughter of  Mistivir, Gyrid OlafsdottirChildren: Thyra Haraldsdatter, Sweyn Forkbeard, Haakon, Gunhilde Early Life Harald Bluetooth, or Harold Bluetooth, was born around 910, the son of the first king in a new line of Danish royalty, Gorm the Old. His mother was Thyra, whose father was a nobleman of Sunderjylland (Schleswig). Gorm had established his power base in Jelling, in northern Jutland, and had begun to unify Denmark before his reign was over. Thyra was inclined toward Christianity, so it is possible that young Harald had a favorable view toward the new religion when he was a child, even though his father was an enthusiastic follower of the Norse gods. So fierce a follower of Wotan was Gorm that when he invaded Friesland in 934, he demolished Christian churches in the process. This was not a wise move; shortly after that he came up against the German king, Henry I (Henry the Fowler); and when Henry defeated Gorm, he forced the Danish king not only to restore those churches but to grant toleration to his Christian subjects. Gorm did what was required of him but died a year later, leaving his kingdom to Harald. Haralds Reign Harald set out to continue his fathers work of unifying Denmark under one rule, and he succeeded very well. To defend his kingdom, he strengthened existing fortifications and built new ones. The Trelleborg ring forts, which are considered among the most important remains of the Viking age, date to his reign. Harald also supported the new policy of toleration for Christians, allowing Bishop Unni of Bremen and Benedictine monks from the Abbey of Corvey to preach the gospel in Jutland. Harald and the bishop developed a cordial working relationship, and although he did not agree to get baptized himself, Harald appears to have supported the spread of Christianity among the Danes. Once he had established internal peace, Harald was in a position to take an interest in external matters, especially those concerning his blood relatives. His sister, Gunnhild, fled to Harald with her five sons when her husband, King Erik Bloodaxe of Norway, was killed in battle in Northumberland in 954. Harald helped his nephews reclaim territories in Norway from King Hakon. He was met with serious resistance at first and Hakon even succeeded at invading Jutland, but Harald was ultimately victorious when Hakon was killed on the island of Stord. Haralds Christian nephews took possession of their lands and, led by Harald Greycloak (the eldest nephew), they embarked on a campaign to unify Norway under one rule. Unfortunately, Greycloak and his brothers were somewhat heavy-handed in spreading their faith, breaking up pagan sacrifices and despoiling pagan places of worship. The unrest that resulted made unification an unlikely prospect and Greycloak began to forge alliances with former enemies. This did not sit well with Harald Bluetooth, to whom his nephews owed much for his aid in obtaining their lands, and his concerns were borne out when Greycloak was assassinated, ostensibly by his new allies. Bluetooth took the opportunity to assert his rights over Greycloaks lands and was able to take control of Norway not long after. In the meantime, Christianity had been making some notable headway in Denmark. The Holy Roman Emperor Otto the Great, who professed a deep devotion to the religion, saw to it that several bishoprics were founded in Jutland under papal authority. Due to conflicting and unsubstantiated sources, it is not clear exactly why this led to war with Harald; it may have something to do with the fact that these actions made the dioceses exempt from taxation by the Danish king, or perhaps it was because it made the territory appear to be under Ottos suzerainty. In any case, war ensued, and the exact outcome is also unclear. Norse sources maintain that Harald and his allies held their ground; German sources relate that Otto broke through the Danevirke and imposed strictures on Harald, including making him accept baptism and evangelize Norway. Whatever burdens Harald had to deal with as a result of this war, he showed himself to retain considerable clout in the following decade. When Ottos successor and son Otto II was busy fighting in Italy, Harald took advantage of the distraction by sending his son, Svein Forkbeard, against Ottos fortress in Slesvig. Svein captured the fortress and pushed the emperors forces southward. At the same time, Haralds father-in-law, the king of Wendland, invaded Brandenburg and Holstein and sacked Hamburg. The forces of the emperor were unable to counter these attacks, and so Harald reclaimed control of all of Denmark. Death In less than two years, Harald had lost all the gains he had made in Denmark and was seeking refuge in Wendland from his son. Sources are silent as to how this turn of events came to be, but it may have had something to do with Haralds insistence on converting his people to Christianity when there was still a considerable number of pagans among the nobility. Harald was killed in battle against Svein in or around 987; his body was brought back to Denmark and laid to rest in the church at Roskilde. Legacy Harald was by no means the most Christian of medieval kings, but he did receive baptism, and he did do what he could to promote the religion in both Denmark and Norway. He had his fathers pagan tomb converted to a Christian place of worship. Although the conversion of the populace to Christianity was not completed in his lifetime, he did allow a fairly robust evangelization to take place. In addition to constructing the Trelleborg ring forts, Harald extended the Danevirk and left a remarkable runestone in memory of his mother and father in Jelling. The modern Bluetooth technology used to connect electronic devices was named for the ancient Viking king. According to Jim Kardach, one of the founders of Bluetooth SIG: â€Å"Harald had united Denmark and Christianized the Danes! It occurred to me that this would make a good codename for the program. At this time I also created a PowerPoint foil with a version of the Runic stone where Harald held a cellphone in one hand and a notebook in the other and with a translation of the runes: Harald united Denmark and Norway and Harald thinks that mobile PC’s and cellular phones should seamlessly communicate. Sources The Editors of Encyclopaedia Britannica. â€Å"Harald I.†Ã‚  Encyclopà ¦dia Britannica. 4 Apr. 2018.â€Å"The Jelling Stone.†Ã‚  National Museum of Denmark.â€Å"Legendary Harald Bluetooth King Of Denmark - Who Made The Danes Christian.  Ancient Pages, 16 May 2017.â€Å"Bluetooth: Why Modern Tech Is Named After Powerful King of Denmark and Norway.†Ã‚  Ancient Origins, Ancient Origins, 20 Jan. 2017.

Contracting and Procurement in Project Management- Phase 2 DB Essay

Contracting and Procurement in Project Management- Phase 2 DB - Essay Example ACME Development Corporation (ADC) wants to buy the scheduling tool from any software company. The first step in creating a contract is to make sure that both companies are talking regarding the identical deal, in this way when they would consequently have the same opinion to enter into the contract they would mutually agree to the similar thing. When the ACME Development Corporation (ADC) and software development company had a "meeting of the minds" as to the contract, they have to trade something of value in order to turn out a contract. Frequently Software Developer Company offers its services in exchange for the cash of the ACME Development Corporation. But forethought can take a lot of other forms, as long as every company is giving up something of worth to it to convince the other company to go into the agreement. Once both ACME Development Corporation and Software Developer Company understand the deal and recognize what kind of deliberation will be substituted by each company, then they would be ready to prepare a contract. Typically the companies disclose that negotiations are ended and a contract would be attained when the companies sign the contract. In this section I will try to incorporate contracting and procurement activities into an overall project cost and schedule. The Project Management Body of Knowledge (PMBOK) established six procedures/states for the Project Procurement Management and contracting between our company and Software Developer Company will discuss in the proceeding section in relation to our buying scheduling software and other above stated equipment. This is the first process in which we will determine the software development organization’s services and purchasing process plan. We also select the type of contract through which we will deal with other company. In the next phase we will place our contract details for purchasing the equipment and services and

Drugstore Cowboy Film Analysis Essay Example | Topics and Well Written Essays - 1250 words

Drugstore Cowboy Film Analysis - Essay Example In â€Å"Drugstore Cowboy† the weakness of the hero is drugs. The film as the title indicates is on drug abuse, but is not a â€Å"say no to drug† sort of a slogan mongering publicity campaign film. The film tells us about the generation of the early seventies who took to drugs. But the film produced in late eighties tells the story of the life of that generation of the seventies when America was almost obsessed with anti drug sentiment bordering on the verge of hysteria. The late eighties were the times of the winners. Only they counted. But this film is telling us about the losers belonging to the generation just earlier, who got lost in drugs and unreal hallucinatory lives. The film tries to understand that generation, while showing how comically meaningless and desperate the life of the addicts were. The border between medicine and drug is wafer thin. The change of meaning is only in how the human beings relate to it. Like drug abuse there is abuse of medicines; thi s is an issue raised by the traditional medical practitioners like the Ayurvedic doctors against Allopathic practices. To quote Angus Bancroft: A drug is a substance used in a drug-like way, a medicine is the substance applied to cure, and a poison the substance used to kill. The end point is that any object or relationship to an object is only formed by the way humans relate to it. Psychoactive substances become ‘drug’ only when they take on socially active characteristics, which incorporate human agency. (Drug Intoxication & Society, PP.176) PERSONEL BUT IMPASSIONATE: The film is based on the unpublished novel by James Fogle. This writer is one who had served imprisonment for drug abuse crimes. Thus the account of the life of the drug addict depicted here is very intimate and personal. It is something like an insider story. But the positive feature of the film’s handling of the issue is that it is not romanticizing drug addiction, in spite of it being an insider narrative. At the same

Timeline of Historical Events, Movements or Individuals (History of Research Paper

Timeline of Historical Events, Movements or Individuals (History of the USA to 1865) - Research Paper Example it was initiated by the Virginia Company. Thomas Jefferson is included among the list of Presidents of United States of America who played a vital role towards the constitution formation and obtaining the declaration of independence of United States of America. He was born in 1743 and he was an integral part of the American Revolution and overall process. Also he due to his innumerable achievements and contributions is listed among the few who are called the founding fathers of United States of America. He also remained the Secretary of State and further, remained the United States Minister to France. His other contributions in the professional capacity include his standing and duty performance as the Governor of Virginia. He remained the Vice President as well. A decade long war that started in 1753 and lasted till 1764. It is important in the history of American nation on number of accounts. Firstly, it served as the foundation step towards the internal resentment against the English, secondly it was fought in the form of a proxy war between the English and the French who had their influence and presence in the region. Third was the fact that it set the grounds for the later on Seven Years War which was to be fought directly between the Great Britain and France. The warring territories engaged in this battle were Nova Scotia and parts of Virginia in the modern day United States. The final outcome came about in the form of victory towards the English. The first Continental Congress proceedings lasted between September and October of 1774. It was important on number of grounds. The first was the fact that nearly all the states sent over their representatives for the grand gathering with the mere exception of Georgia. The event was held in Philadelphia. It was significant on the account of fact that a platform was made where it was established that this platform would make efforts to overcome the obstacles