A Character Analysis of Old Man Warner in Shirley Jacksons The Lottery - Free Essay Example

Sample details Pages: 2 Words: 577 Downloads: 2 Date added: 2019/08/16 Category Literature Essay Level High school Tags: The Lottery Essay Did you like this example? The personality of Old Man Warner is constructed over the communitys unwillingness to abandon traditions at all costs. Shirley Jackson portrays Old Man Warner as an individual who has traditions instilled in him to a fault. Throughout the story, Old Man Warner is constantly at odds with the younger community members who start questioning the point of such a lottery. Jackson reveals through Old Man Warners personality that he is deeply traditional, resistant to change and is at times illogical and/or delusional. Jacksons description of the setting in The Lottery shows a town that relies heavily on the custom of having a yearly lottery. An example of reliance is how the black box now resting on the stool had been put into use even before Old Man Warner, the oldest man in town (Jackson 391). This shows that Old Man Warner has been raised into believing that the lottery has a significant role in society. The town still dons the same box it has and is reluctant to change the box in fear of upsetting anyone. A prime example of this is: Mr. Summers spoke frequently to the villagers about making a new box, but no one liked to upset even as much tradition as was represented by the black box (Jackson 391). This again shows how the past has affected the towns beliefs, consequently having a major impact on Old Man Warners personality. Don’t waste time! Our writers will create an original "A Character Analysis of Old Man Warner in Shirley Jacksons The Lottery" essay for you Create order Another personality trait of Old Man Warner is that he is illogical and/or delusional at times. Jackson shows this with Old Man Warners responses to the younger villagers wanting to abandon the lottery. A quote that demonstrates is when Mr. Adams said to Old Man Warner, who stood next to him, that over in the north village theyre talking of giving up the lottery (Jackson 393). An equally important quote is also, Old Man Warners response pack of crazy fools (Jackson 393). This shows his inability to function rationally and reveals how deeply rooted not only Old Man warner is but the entire community. Another piece of strong evidence suggests Old Man Warner was delusional is his full belief that the lottery had a direct effect on the villagers lives. Additionally, Jackson shows how in-depth Old Man Warners reliance on old deeply rooted traditions is to a fault. Jackson demonstrates this by displaying his fears of abandoning the lottery. Jackson shows extensively that Old Man Warner is afraid of change with his quotes. An excellent example of his fear of change is the quote: There has always been a lottery (Jackson 393). Another equally important example is his quote: The lottery in June, corn be heavy soon (Jackson 393). The author demonstrated by Old Man Warner that a community is so enthralled with traditions that they refuse to change regardless of outcomes. Jackson with the setting of the story was able to demonstrate not only how Old Man Warner was, but how the older community in the village was. The village had a common theme of fear of change and a community stuck in the past. The quotes from Old Man Warner indicate that he is stuck in an illogical past where he is resistant to change regardless of the outcomes. Jackson demonstrated the personality of Old Man Warner in an exceptional way. The Lottery is an exciting work of literature overall, with deep undertones. Work Cited Jackson, Shirley. The Lottery. The Art of the Short Story, by Dana Gioia and R. S. Gwynn, Pearson Longman, 2006, pp. 390 396.

Happiness Is Not Free State Of Mind - 814 Words

First, as I begin, I will briefly explain what happiness is. Happiness: For some, it is simply being able to live freely and do whatever they want, without having any restrictions that may prevent them from doing so, whether it be money or other restraints. For others, happiness is also merely an elusive, worry-free state of mind. On the other hand, for different individuals, the meaning of happiness varies. For instance, for an individual who has been starving for days, receiving a piece of food is happiness. By answering this â€Å"question at issue,† Nosich explains that one will be able to accurately â€Å"explore their thinking and also the thinking of others† (52). Therefore, although it is likely for individuals to define happiness differently, I am certain that materialistic possessions will definitely not lead one to their definition of happiness. Along the quest to obtaining material possessions, individuals can occasionally fail to understand that money cannot provide one with everlasting happiness since they may never obtain what they view as an acceptable amount of money. To validate my claim, I will be using various well-known individuals from different walks-of-life that have admitted that material possessions alone, such as money itself, cannot supply anybody with a consistent source of happiness. The hip-hop artist and three times Grammy winner from St. John s University, Jermaine Cole, convincingly claims that, â€Å"The things you place your importance on can neverShow MoreRelatedEssay on What is Happiness?751 Words   |  4 PagesWhat is happiness? People have agonized over this question for centuries. Let me start this essay by answering a somewhat easier question: what isn’t happiness? Happiness is NOT feeling good all the time. Happiness is a combination of human emotions and states of mind. 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Everybodys happy nowadays.† (Page 79) Ironically, Huxley was trying to convey the exact opposite messageRead MoreThe Emancipation On The Mind, Soul, And Spirit1380 Words   |  6 PagesShackles on the mind, soul, and spirit kept a race of people in slavery during a dark time in American history. Narrative of Sojourner Truth, a Northern Slave, Emancipated from Bodily Servitude by the State of New York, in 1828 follows her life as a slave, known as Isabell, growing up and experiencing many different masters. Sojourner Truth’s meaning of freedom was largely shaped by her religious and family beliefs as well as her experiences as a chattel. Freedom is not just a release from the bondageRead MoreBrave New World By Aldous Hux ley983 Words   |  4 Pagesis portrayed in Brave New World by Aldous Huxley. The focus of the World State is on society as a whole rather than on individuals. Some characters from the novel have a harder time accepting the conditioning. 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Localization Function in the Brain Essay Sample free essay sample

Localization of map refers to the belief that specific countries of the intellectual cerebral mantle are associated with specific physical or behavioural maps. Examples of instance surveies to turn out how specific locations of the encephalon can be affected and have an impact on behaviour are demonstrated by the HM and Phineas Gage incident. In 1848. when Phineas Gage was fiddling Fe to press explosives into a hole. an detonation sent a rod through his caput. His physician J. M Harlow recognized some important alterations in his personality and described him as holding small restraint. utilizing highly ill-mannered linguistic communication. and doing expansive programs for the hereafter that would be immediately replaced with others. Because the frontal lobe of the encephalon was damaged. Pot became disinhibited which meant he wanted to get down making things that might he might usually hold stopped himself from making. Although he wanted to go on working. We will write a custom essay sample on Localization Function in the Brain Essay Sample or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page his unprompted and ill-mannered behaviour was non conductive to working with other people hence could non go on. Sperry had a survey to assist neuroscientists understand the manner the encephalon maps and look to be non merely localized in specific parts. but besides lateralized ( left and right hemispheres seem to be more or less responsible for certain activities ) . The participants in Sperry’s work had all undergone an operation to cut down the badness of their epilepsy by break uping the principal callosum. The principal callosum is a portion of the encephalon that joins the two hemispheres and it appears to be responsible for the communicating between them. Without this communicating and under the right experimental conditions the two hemispheres could be studied individually and their sometimes-subtle differences identified. A similar incident happened with HM ( 1953 ) . where he had to undergo a surgery to take the median temporal lobes in order to cut down the frequence of his epileptic ictuss. The operation resulted in the remotion of more of his encephalon than was intended and had effects on his memory. When taken an MRI encephalon scan ( 1996 ) . there was a surprising extent of harm to the temporal lobes and other parts of the encephalon. and it is supposed that this was caused by a bad reaction to his epileptic medicine that HM was taking. HM was hence incapable to make long-run memories. He had anterograde amnesia where he had an inability to retrieve associating to the clip since of his operation. HM’s temper reported by Ogden ( 2005 ) was that he was unagitated and he may besides be truly content and good-natured. How we exercise the encephalon is wedged observations of theoretical accounts and how motivated we feel we should larn things. In the split-brain surveies. each hemisphere constitutes a separate head or domain of consciousness that may be why we have different witting watercourses and because we exercise one more hemisphere. it may be why we are better at some cognitive activities and cognize yourself more. The encephalon is organized in the signifier of faculties that work in parallel and frequently non-consciously. This may explicate why we act and react impetuously and have no control of actions. Two hemispheres differ in their processing manners which means people can believe and memorise information depending on the manner they think and memorize information. There may be a biological nexus on how we process information and execute our activates and associate to others. It may be possible to pull decisions about causes and effects in footings of the interactions between knowledge and physiology in the Phineas Gage and HM incident. The environment besides plays an of import portion in determining the construction of the encephalon. We need to account for single differences in encephalon construction and map and how that affects individual’s behaviour and societal interactions with others. An illustration of this can be how you learn can act upon the encephalon. If you develop a side more than the other you will get different accomplishments. You besides entree the universe and interact with others depending on how developed your cognitive side of the encephalon is and how accurate you perceive the universe. Social interactions are hence determined by the manner we process information. The manner we are raised. educated. civilization impacts on how stimulated the encephalon is. For illustration Japan or China emphasize on academic public presen tation that may be due to the left hemisphere being more developed. Mental unwellness can besides happen if the encephalon harm occurs or for inability to see a point of view.

Alternative Dispute Resolution by ACAS

Question: Describe the purpose of Alternative Dispute Resolution (ADR) with references to services provided by ACAS? Answer: An introduction to Alternative Dispute Resolution The process of Alternative Dispute Resolution can be considered as a collection of the processes which can be used for the resolution of various conflicts and other disputes in a more private or casual manner. The entire process of Alternative Dispute Resolution attempts to give a possible substitute for the traditional courts for resolution of disputes (Broadbent, 2009). The resolution of processes includes different complaints and grievances. However, it should also be noted that even though the process of Alternative Dispute Resolution is friendlier process of resolving disputes it cannot replace the traditional practices of the court. There are a number of reasons for using the Alternative Dispute Resolution method instead of the court processes traditionally practiced. The foremost reason is that this method is far less expensive and easy as compared to the traditional court practice. The number of challenges and the number of formalities involved in the process of Alternative Dispute Resolution is far less and it also promotes the creativeness of individuals and look for even better and viable solutions to the disputes (Hayford, 2000). The Alternative Dispute Resolution process tries to keep away from the volatility which is generally attached to the decisions that is given by a number of decisions of the court as these courts have been following traditional ways to solve disputes that has been followed for a number of years. Also it must be noted that the process of Alternative Dispute resolution usually results in giving these parties improved outcomes and connections with the parties to the disputes so that t he parties are able to maintain a better relationship and morale in the workplace (Atlas, Huber and Trachte-Huber, 2000). In general, there are two types of Alternative Dispute Resolution processes. The first method includes the resolving of the disputes outside the formal judicial process. The second method for alternative dispute resolution is the attachment to the official judicial mechanisms. Some of the other methods available for dispute resolution include programs on mediation or the offices on ombudsman in the organizations. Irrespective of whether the methods are pending, the methods are more or less same having skill sets or sub-sets for negotiations (Briefing: Most GPs are also employers. The Advisory, Conciliation, and Arbitration ..., 1997). Alternative Dispute Resolutions also includes tribunals, processes of mediation, some formal tribunals and formal processes of mediation. The typical form of tribunals in ADR is arbitration where the decision can be either binding or advisory or may also be non-binding (Pareek, 2014). Another typical form is the presence of private judges who either sit alone or in panels or at jury trials. The typical form for mediation is the appointment of mediator or a mediation panel by the court. The Advisory, Conciliation and Arbitration Service The ACAS or the Advisory, Conciliation and Arbitration Service provide service for the alternative dispute resolutions for the people in the United Kingdom. This is a non departmental body that is under the powers of the Crown in United Kingdom. The main objective of this Alternative Dispute Resolution body is to make improvements in the organization and also the work culture. The service further aims to promote and facilitate stronger and more supportive performances in the field of industrial relations (Clark, 2001). The service of Advisory, Conciliation and Arbitration can be done with a number of different mediums and these include the processes of arbitration or mediation or conciliation. It must be noted that the service is most known for the dispute resolving process of conciliation. This process of conciliation includes the resolution of disputes for various groups of workers and employees with the employers. These employees are mostly represented by the trade unions. The ACAS is an independent organization that is also fair and usually it avoids taking any sides for any party and assists them to come to a probable solution for the resolution of dispute. Services of the ACAS The service commenced in 1896 when the government of United Kingdom decided to start a voluntary service for arbitration and conciliation. The duties of the service include the giving of free direction for the employers, unions having industrial and personal disputes. Previously, this service was named as Industrial Relations Services in 1960. Later in the year 1972 the name was modified to Conciliation and Advisory Service. Further, in the year 1976, the Advisory, Conciliation and Arbitration Service was transformed into a statutory body in accordance to the Employment Protection Act 1975. The main services of the ACAS are the promotion of the settlement of claims and the issuance of the employment tribunals. As mentioned earlier this service is more involved in the rendering of conciliation services to the parties. The services here are notified of the claims which are applied according to the services that are provided by the ACAS (Stuart and Martinez Lucio, 2008). The service also reports the various proposals that are to be settled, gives advice to the parties on such matters that is related to the procedures of the tribunals and gives encouragements on the different ways for solving the problems and also listening to the views of others. This process of resolving dispute through conciliation is generally more successful and it focuses on the mind of the parties and their pros and cons of the class. It is further helpful for the people who are not interested to be represented in the traditional court of law. It must also be noted that the discussions that has been conducted during this service is usually kept private and is also not referred for any hearing of the tribunals until the person for whom the communication is made has consented for the referral. After through the process of conciliation any argument is reached the terms and conditions of the settlement should be made formal by making a legal and binding agreement which involves all the records with regard to the terms for the settlement. The claims before and after are dealt with the appropriate services of ACAS. Advantages of ADR and ACAS The advantages of Alternative Dispute Resolution or ACAS are many. The increase in this form of dispute resolution is gradually on the increase and in the international level it has been integrated formally into the legal system. Some of the advantages of alternative dispute resolution have been listed below (Freeman, 1995). Firstly, ADR is more suitable for cases where there is more number of parties. Secondly, the process of ADR is more flexible as it is decided by the parties themselves. Thirdly, the cost is comparatively lower and less complex procedures are to be followed. Fourthly, parties can choose the third parties for negotiations. Fifthly, the solutions offered are generally based on the needs and requirements of the parties (Bevan, 1992). Further, the entire process is confidential and the agreements are durable. And finally, the process assists in preserving the disputes even after the resolution of disputes. Conclusion The Alternative Dispute Resolution permits the solving of disputes through a number of ways and primarily through conciliation, mediation and arbitration. All of these methods are preferred by the United Kingdom government and also the well known business organizations when compared with the traditional court processes. The ACAS provides such service that shows that this method of alternative dispute resolution is gradually becoming more and more popular and a huge number of people prefer this mode of dispute resolution (BLANCERO, DelCAMPO and MARRON, 2010). Nonetheless, it also needs to be noted that even though the methods of alternative dispute resolution is preferable, when disputes are not solved in this manner they have to be resolved in the traditional court of law. ii) The precedence of European Union Laws over Domestic UK laws Introduction The dominance of the European Union laws in the United Kingdom is based on the principle that the laws which are prepared by all the member states together in the European Union would be given preference when any such law conflict with the domestic laws of the country. Therefore, courts in United Kingdom should take into consideration the European Union laws instead of the national laws on the same subject. This principle had arisen from the European Court of Justice and this principle can be observed in a number of decisions of the court (Hartley, 2005). Legal decisions that support the laws of European Union Regarding the principle that the laws of the European Union should precede there has been court decisions that have supported this view. This principle has been very apparent since the case of Van Gend en Loos (Van Gend en Loos v Nederlandse Administratie der Belastingen, [1963]) in the year 1963. In this case the European Court of Justice had stated that the European Union is such a community that constitutes a fresh legal order in the international law. It is for the broader benefit of the entire European community that the countries have decided to restrict their sovereignty. Hence this legal order would protect the benefits of the European community. The doctrine of Supremacy does not have a fundamental base in the treaty of European Community and the European Court of Justice formed this legal order. The primary focus of the decision of this case relies on the terms of the direct application and effect. The European Court of Justice mentioned about the legal order since this Union was not any ordinary international organization. This community was considered to be more independent and was supposed to impact profu sely on the legal systems of the member states. The case of R v Secretary of State for Transport(R v Secretary of State for Transport, Ex p Factortame, [2001]) is an example in this regard. The House of Lords decided in the case that when the conditions are such that any act of the Parliament contradicts the European Union laws, it is the duty of the United Kingdom Judicial system to apply the European Union laws instead of the laws of United Kingdom. Lord Bridge had further clarified that this sort of a restriction on the sovereignty had been decided upon and accepted by the Parliament of the country. This restriction even though not inherited from the Treaty of Rome, in the European Communities Act 1972, it was established by the Parliamentary jurisprudence. In another case of Costa v Enel (Costa v Enel, [1964]), the European Court of Justice stated that when the laws of the member states conflicts with the laws of the European Union, the latter would prevail and any other consequent act that is unilateral will not prevail when it is contrary to the conceptual laws of the society. In this regard the treaty of Maastricht may also be mentioned. In accordance to this treaty, no European Union laws can prevent the creation of laws on different subjects that includes work conditions, the socio-political issues or environment. The only thing that needs to be kept in mind is that the laws made need to be well matched with the Treaty of Rome and be in the proper jurisdiction for consideration of the treaty (Konstadinidis, 1998). Another significant case may be mentioned in this regard. The case of Italian Minister of Finance v Simmenthal (Italian Minister of Finance v Simmenthal, [1978]), is a significant case where the European Court of Justice focused on the predominance of the European Union laws which tend to affect the past as well as the future enactments. In the given case the facts stated that a fee had been charged for health inspections when Simmenthal imported beef from the country of France to his own country Italy. This was according to a law in Italy. This law was however inconsistent with the laws given in the Treaty of European Community and other regulations passed in 1968. During the trial two vital points were raised. The primary point was that the law of Italy should prevail since it was passed after the community regulations have been passed. The second contention was that even though the law conflicted with the treaty obligations, it is not applicable as the law was applied by courts in Italy when it was considered unconstitutional by the Constitutional court in the country. Finally the courts in Italy had to comply with the community provisions and were restricted from applying the provisions which conflicted with the national laws. The controversies regarding the issue of European Union laws taking over the domestic laws of the member countries have come under scrutiny a number of times. It must be mentioned that United Kingdom is a member of the European Union and hence it is a requirement for the country to abide by the regulations of the European Union. Supremacy of the EU Laws Primarily these restrictions with regard to the domestic laws first came up with the implementation of the European Communities Act 1972 (Pearson of Rannoch, 2013) and the restriction was voluntarily accepted by all the member states of the European Union (Wiesbrock, 2010). This 1972 Act had mentioned the conditions that the court of United Kingdom has a certain duty while delivering judgment and that is to give more importance to the European Union laws and not the domestic laws of the country. The laws of the European Union consist of treaties, regulations and also directives. With regard to the regulations, these treaties and directives have dominance over the laws of the country that stands contradicting them. Further the laws also include that the member state will be not permitted to make any more domestic laws in that area for implementing the treaties or directives. Directives can be defined as that kind of goals which are which can be achieved in a particular span of time. In order to reach that goal the member states can make laws accordingly. The British government is allowed to enter into international treaties binding the country in accordance with the Royal Prerogative. Further, the country also has the doctrine of parliamentary sovereignty. According to this doctrine, no modification exists with regard to the rights of the British citizens or any individuals and such a thing cannot be carried out without the parliamentary consent. In order to change any such act the legislation of the Parliament may be required. Therefore, for the protection of the country from the breach of international rules or regulations it is a must that United Kingdom includes the international treaties and obligations win the national laws of the country. Conclusion The United Kingdom needs to override any such law that is contradicting to the European Union laws. The Parliament in Britain presently upholds that the laws of the European Union are ultimate (Wall, 1973). The rule of Dicey may be mentioned in this regard. Accordingly, the European Communities Act 1972 may be repealed at any time. For the theories the laws of the European Union is the one that is ultimate, but logically the internal laws of the country is the one that is ultimate. References Atlas, N., Huber, S. and Trachte-Huber, E. (2000).Alternative dispute resolution. Chicago, Ill.: Section of Litigation, ABA. Bevan, A. (1992).Alternative dispute resolution. London: Sweet Maxwell. BLANCERO, D., DelCAMPO, R. and MARRON, G. (2010). Just Tell Me! Making Alternative Dispute Resolution Systems Fair.Industrial Relations: A Journal of Economy and Society, 49(4), pp.524-543. Briefing: Most GPs are also employers. The Advisory, Conciliation, and Arbitration ... (1997).BMJ, 314(7086), pp.3a-3a. Broadbent, N. (2009). Alternative Dispute Resolution.Legal Information Management, 9(03), p.195. Clark, J. (2001). Employment Relations in Britain: 25 Years of the Advisory, Conciliation and Arbitration Service.Industrial Law Journal, 30(2), pp.252-253. Costa v Enel[1964]ECR p.585. Freeman, M. (1995).Alternative dispute resolution. New York: New York University Press. Hartley, T. (2005).The European Union and the Systematic Dismantling of the Common Law of Conflict of Laws.International Comparative Law Quarterly, 54(04). Hayford, S. (2000). Alternative dispute resolution.Business Horizons, 43(1), pp.2-4. Italian Minister of Finance v Simmenthal[1978]Case 106/77. Konstadinidis, S. (1998). Nationality Laws in the European Union. Edited by Bruno Nascimbene [London: Butterworths. 1996. xv + 771 pp. ISBN 88-14-06139-4. 80].International Comparative Law Quarterly, 47(01). Pareek, N. (2014). Enforceability of alternative dispute resolution clauses: position in UK, USA and India.International Journal of Private Law, 7(2), p.175. Pearson of Rannoch, M. (2013).A bill to repeal the European Communities Act 1972, and to make provision for the Secretary of State to repeal any enactment that has been a consequence of the European Communities Act 1972. London: Stationery Office. R v Secretary of State for Transport, Ex p Factortame[2001] NO. 7. Stuart, M. and Martinez Lucio, M. (2008). The New Benchmarking and Advisory State: The Role of the British Advisory, Conciliation and Arbitration Service in Facilitating Labour--Management Consultation in Public Sector Transformation.Journal of Industrial Relations, 50(5), pp.736-751. Van Gend en Loos v Nederlandse Administratie der Belastingen[1963]Case 26/62. Wall, E. (1973).European Communities act 1972. London: Butterworths. Ware, S. (2001).Alternative dispute resolution. St. Paul, Minn.: West Group. Wiesbrock, A. (2010).Legal migration to the European Union. Leiden: MartinusNijhoff Publishers.

Pythagoras was a Greek mathematician and philosopher Essay Example

Pythagoras was a Greek mathematician and philosopher Essay He lived in 400 BC and was one of the first great mathematical thinkers. He spent most of his life in Sicily and southern Italy. He had a group of follows who went around and thought other people what he had taught them who were called the Pythagoreans.Pythagoras himself is best known for proving that the Pythagorean Theorem was true. The Sumerians, two thousand years earlier, already knew that it was generally true, and they used it in their measurements, but Pythagoras proved that it would always be true. The Pythagorean Theorem says that in a right triangle, the sum of the squares of the two right-angle sides will always be the same as the square of the hypotenuse (the long side). A2 + B2 = C2Pythagoras theorem can also help in real life. Here is an example:Say you were walking though a park and wanted to take a short cut. With Pythagorass theorem you could work out exactly how long you would have to walk though the grass, rather then talking the long route by walking on the paths .PLANI am going to investigate the three triangles I have been given. They are all right-angled triangles, with 3 sides, all different lengths.The three triangles satisfy the Pythagoras theorem. The theorem states that the hypotenuse side (longest side) must equal the 2 shorter sides squared.Here is the Pythagoras theorem:PYTHAGORAS = a2 + b2 = c2Here are the three triangles I have been given:a) b) c)I am now going to test if three triangles I have been given:Triangle A = 32 + 42 = C29 + 16 = C225 = C25 = CTriangle A is a Pythagorean triplet because when I put in the shortest and middle side into the formula, it gave me the answer that the hypotenuse was 5. Checking this against what I have been given, I can verify that it was correct. I will now test the other two triangle I have been given.Triangle B = 52 + 122 = C225 + 144 = C2169 = C213 = CThis is also correct and matches with that I have been given.Triangle C = 72 + 242 = C249 + 276 = C2625 = C225 = CAll these triangles are Pyt hagorean triplets.ACTIONI am going to put all the numbers I have been given into a table. I want to investigate how I cold work out what the next numbers in the next triangle would be. I am putting it into a table because it is easier to see if there is any pattern.TrianglesABCPerimeterArea1345126251213303037242556844940419018051160611323306128485182548nth term2n + 12n2 + 2n2n2 + 2n + 1Everything that I add to my table after this point will be in blue.I will now work out what the next three triangles in the family will be.Sequence for shortest side3 5 7 9 11 13 / / / / /2 2 2 2 2Every time 2 is being added to the previous number. I can work out that the next numbers will be 9, 11, and then 13.Sequence for middle side4 12 24 40 60 84 / / / / /8 12 16 20 24 / / / /4 4 4 4Here there is a continuous second difference of 4. I can tell that the number after 24 will be 40. I worked this out by finding the difference between 12 and 24 (12), adding 4 to it (16) then adding it on to 24.Sequen ce for hypotenuse side5 13 25 41 61 85 / / / / /8 12 16 20 24 / / / /4 4 4 4On this sequence the second difference is 4, and by adding 4 every time to the first non continuous difference I can tell that the next numbers will be 41, 61 then 85.Test that triangles are PythagorasI will now test to see if the three new triangles I have got numbers for do comply with Pythagoras theorem. I will to this by adding side a2 and side b2 and see if I get the answer I get matches what I got for side C in my table.Triangle 4A2 + B2 = C292 + 402 = C281 + 1,600 = C21681 = C2V1681 = C241 = Side CThis answer matches with what I predicted with my table. Therefore it is defiantly a Pythagoras triangle.Triangle 5A2 + B2 = C2112 + 602 = C2121 + 3600 = C23721 = C2V3721 = C261 = Side CAgain this is a Pythagoras triangle.Triangle 6A2 + B2 = C2132 + 842 = C2169 + 7056 = C27225 = C2V3721 = C285 = Side CI now can be sure that all the new triangles are Pythagoras.Perimeter and AreaI am going to work out the per imeter and area of each triangle.PerimeterI will work out the perimeter by adding all the sides of the triangles and see what they total.Triangle 1: 3 + 4 + 5 = 12Triangle 2: 5 + 12 + 13 = 30Triangle 3: 7 + 24 + 25 = 56Triangle 4: 9 + 40 + 41 = 90Triangle 5: 11 + 60 + 61 = 132Triangle 6: 13 + 84 + 85 = 182nth term for perimeter12 30 56 90 132 182 / / / / /18 26 34 42 50 / / / /8 8 8 8Now to work out the nth term I will use the formula explained on page 10.Tn = a + ( n 1 ) d + 1/2 ( n 1 ) ( n 2 ) c12 + ( n 1 ) 18 + 1/2 ( n 1 ) ( n 2 ) 812 + 18n 18 + 4 [n2 3n + 2]12 + 18n 18 + 8n2 12n + 84n2 + 6n + 2AreaTo work out the area of the six triangles I will be using the formula:Base x Height2Triangle 1: 4 x 3 = 62Triangle 2: 12 x 5 = 302Triangle 3: 24 x 7 = 842Triangle 4: 40 x 9 = 1802Triangle 5: 60 x 11 = 3302Triangle 6: 84 x 13 = 5462nth termNext, I am going to find out the nth term for the shortest side, the middle side and the hypotenuse side. I will do this because it makes i t much easier to find out the length of a side for triangle n.To work out the nth term I will use the formula: Tn = d n + ( a d )Where: a = the first termd = common differencen = termTn = nth termnth term for shortest side3 5 7 9 11 13 15 / / / / / /2 2 2 2 2 2Tn = d n + ( a d )= 2 n + ( 3 2 )= 2 n + 1I will now test this nth term to see if it is correct. I will do this by finding out the 7th term using the nth term then checking it against my sequence.So when: n = 72 x 7 + ( 3 2)14 + 1 = 15This proves that the nth term is correct because it matches with what I worked out what would be the 7th term in my sequence.nth term for middle side4 12 24 40 60 84 112 / / / / / /8 12 16 20 24 28 / / / / /4 4 4 4 4Because this has a second difference I will use a second formula to work out the nth term.Forumla: Tn = a + ( n 1 ) d + 1/2 ( n 1 ) ( n 2 ) cWhere: Tn = nth termA = the first termD = the first number in the changing sequenceC = the second, continuous differenceN = termI will no w substitute the numbers from the sequence into the formula.Tn = a + ( n 1 ) d + 1/2 ( n 1 ) ( n 2 ) c4 + ( n 1 ) 8 + 1/2 ( n 1 ) ( n 2 ) 44 + 8n 8 + 2 [n2 3n + 2]4 + 8n 8 + 2n2 6n + 42n2 + 2n + 0I will now test this nth term again like last time to see if it is correct. I will find out the 7th term by using the nth term I have just worked out then check it against what I have in my sequence.So when n = 72 x 72 + 2 x 7 + 02 x 49 + 1498 + 14 = 112In my sequence under the 7th term I have 112. This proves that my nth term is correct.nth term for hypotenuse sideI will find out this nth term using the same formula I used finding out the middle side, as it has a second difference.5 13 25 41 61 85 113 / / / / / /8 12 16 20 24 28 / / / / /4 4 4 4 4Tn = a + ( n 1 ) d + 1/2 ( n 1 ) ( n 2 ) c5 + ( n 1 ) 8 + 1/2 ( n 1 ) ( n 2 ) 45 + 8n 8 + 2 [n2 3n + 2]5 + 8n 8 + 2n2 6n + 42n2 + 2n + 1I will now again test this nth term using the same method as above.So when n = 72 x 72 + 2 x 7 + 12 x 49 + 14 + 198 + 14 + 1 = 113Both say the 7th term is 113, so it must be correct.Testing the nth termsI am now going test all the nth terms. I will do this by seeing if they comply with Pythagoras theorem.nth term for shortest side2 + nth term for middle side2 = nth term for hypotenuse side2So: ( 2n + 1)2 + ( 2n2 + 2n )2 = (2n2 + 2n + 1)2I will now expand the brackets for each nth term.( 2n + 1 )2 expanded:( 2n + 1) ( 2n + 1)= 4n2 + 4n + 1( 2n2 + 2n )2 expanded:( 2n2 + 2n ) ( 2n2 + 2n )= 4n4 + 4n3 + 4n3 + 4n2= 4n4 + 8n3 + 4n2(2n2 + 2n + 1)2 expanded:(2n2 + 2n + 1) (2n2 + 2n + 1)= 4n4 + 4n3 + 2n2 + 4n3 + 4n2 + 2n +2n2 + 2n + 1= 4n4 + 8n3 + 8n2 + 4n + 1So: 4n2 + 4n + 1 + 4n4 + 8n3 + 4n2 = 4n4 + 8n3 + 8n2 + 4n + 18n2 + 4n + 1 + 8n3 + 4n4 = 4n4 + 8n3 + 8n2 + 4n + 14n4 + 8n3 + 8n2 + 4n + 1 = 4n4 + 8n3 + 8n2 + 4n + 1This proves that the nth terms are all right and work with Pythagoras theorem.CONCLUSIONI have now generalized the problem given to me at the beginning. I do not thi nk I can go any further with it. I have proved and tested all my formulas.However, I do think I could extent this though by looking at a different family of Pythagorean triplets. In this family there was a difference of 1 between the values of the middle side and longest side. I will now look at a family that has a difference of 2. I want to see if there if the nth terms will be linked or have something in common.I can now produce any triplet in this family with my nth terms easily.EXTENSIONIn this extension I will do the same with what I did with the first family but with the new family and sides.To work out the new family I will double all the values from the last Pythagorean triplets.So Triangle 1 will be:3, 4, 5 doubled to 6, 8, 10Triangle 25, 12, 13 doubled to 10, 24, 26Triangle 37, 24, 25 doubled to 14, 48, 50Here is the new family:I will now check to see if these triangles are Pythagorean triplets by putting the shortest side and middle find into the formula and see if it giv es me the answer for the hypotenuse.Triangle 1A2 + B2 = C262 + 82 = C236 + 64 = C2100 = C2C = 10This triangle is a member of a Pythagorean triplet.Triangle 2A2 + B2 = C2102 + 242 = C2100 + 576 = C2676 = C2C = 26Again, this triangle is a member of a Pythagorean triplet.Triangle 3A2 + B2 = C2142 + 482 = C2196 + 2304 = C22500 = C2C = 50All these triangles are Pythagorean triplets.Like last time I will now put these triangle into a table for the same reasons.TrianglesABC16810210242631448504188082522120122626168170Nth term4 n + 24n2 + 4n + 04n2 + 4n + 2Everything that I add to my table after this point will be in blue.I will now work out what the next three triangles in the family will be.Sequence for shortest side6 10 14 18 22 26 / / / / /4 4 4 4 4Every time 4 is being added to the previous number. I can work out that the next numbers will be 18, 22, and then 26.Sequence for middle side8 24 48 80 120 168 / / / / /16 24 32 40 48 / / / /8 8 8 8Here there is a continuous second difference of 8. I can tell that the number after 48 will be 80. I worked this out by finding the difference between 24 and 48 (24), adding 8 to it (32) then adding it on to 48.Sequence for hypotenuse side10 26 50 82 122 170 / / / / /16 24 32 40 48 / / / /8 8 8 8On this sequence the second difference is 8, and by adding 8 every time to the first non continuous difference I can tell that the next numbers will be 82, 122 then 170.Test that the three new triangles are in the Pythagorean familyI will again, like I did with the last family, test to see if the three new triangles I have got numbers for do comply with Pythagoras theorem. I will to this by adding side a2 and side b2 and see if I get the answer I get matches what I got for side C in my table.Triangle 4A2 + B2 = C2182 + 802 = C2324 + 6400 = C23360 = C2V6724 = C282 = Side CThis answer matches with what I predicted with my table. Therefore it is defiantly a Pythagoras triangle.Triangle 5A2 + B2 = C2222 + 1202 = C2484 + 14400 = C214884 = C 2V14884 = C2122 = Side CAgain this is a Pythagoras triangle.Triangle 6A2 + B2 = C2262 + 1682 = C2676 + 28224 = C228900 = C2V28900 = C2170 = Side CI now can be sure that all the new triangles are Pythagoras.nth term of new familyNext, like last time, I am going to find out the nth term for the shortest side, the middle side and the hypotenuse side. I will do this because it makes it much easier to find out the length of a side for triangle n. I will use the same formula I describe when investigating the last family.nth term for shortest side6 10 14 18 22 26 30 / / / / / /4 4 4 4 4 4Tn = d n + ( a d )= 4 n + ( 6 4 )= 4 n + 2I will now test this nth term to see if it is correct. I will do this by finding out the 7th term using the nth term then checking it against my sequence.So when: n = 74 x 7 + ( 6 4)28 + 2 = 30This proves that the nth term is correct.nth term for middle side8 24 48 80 120 168 224 / / / / / /16 24 32 40 48 56 / / / / /8 8 8 8 8Because this has a second difference I will use a second formula to work out the nth term that I have noted above when working out the nth term for the middle side on the first family.Tn = a + ( n 1 ) d + 1/2 ( n 1 ) ( n 2 ) c8 + ( n 1 ) 16 + 1/2 ( n 1 ) ( n 2 ) 88 + 16n 16 + 4 [n2 3n + 2]8 + 16n 16 + 4n2 12n + 84n2 + 4n + 0I will now test this nth term again like last time to see if it is correct. I will find out the 7th term by using the nth term I have just worked out then check it against what I have in my sequence.So when n = 74 x 72 + 4 x 7 + 04 x 49 + 28196 + 28 = 224In my sequence under the 7th term I have 224. This proves that my nth term is correct.nth term for hypotenuse sideI will find out this nth term using the same formula I used finding out the middle side, as it has a second difference.10 26 50 82 122 170 226 / / / / / /16 24 32 40 48 56 / / / / /8 8 8 8 8Tn = a + ( n 1 ) d + 1/2 ( n 1 ) ( n 2 ) c10 + ( n 1 ) 16 + 1/2 ( n 1 ) ( n 2 ) 810 + 16n 16 + 4 [n2 3n + 2]10 + 16n 16 + 4n2 12 n + 84n2 + 4n + 2I will now again test this nth term using the same method as above.So when n = 74 x 72 + 4 x 7 + 24 x 49 + 28 + 2196 + 28 + 1 = 226Both say the 7th term is 226, so it must be correct.Testing the nth terms of new familyI am now going test all the nth terms. I will do this by seeing if they comply with Pythagoras theorem.nth term for shortest side2 + nth term for middle side2 = nth term for hypotenuse side2So: ( 4n + 2)2 + ( 4n2 + 4n )2 = (4n2 + 4n + 2)2I will now expand the brackets for each nth term.( 4n + 2 )2 expanded:( 4n + 2) ( 4n + 2)= 16n2 + 16n + 4( 4n2 + 4n )2 expanded:( 4n2 + 4n ) ( 4n2 + 4n )= 16n4 + 16n3 + 16n3 + 16n2= 16n4 + 32n3 + 16n2(4n2 + 4n + 2)2 expanded:(4n2 + 4n + 2) (4n2 + 4n + 2)= 16n4 + 16n3 + 8n2 + 16n3 + 16n2 + 8n +8n2 + 8n + 4= 16n4 + 32n3 + 32n2 + 16n + 4So:16n2 + 16n + 4 + 16n4 + 32n3 + 16n2 = 16n4 + 32n3 + 32n2 + 16n + 432n2 + 16n + 4 + 32n3 + 16n4 = 16n4 + 32n3 + 32n2 + 16n + 416n4 + 32n3 + 32n2 + 16n + 4 = 16n4 + 32n3 + 32n2 + 16n + 4T his proves that the nth terms are all right and work with Pythagoras theorem.Extension conclusion for Difference of 2Comparing the 2 nth terms I can conclude that when there is a different of 2 between the middle side and the hypotenuse side the nth term is doubled from when there was a difference of 1. I predict that when there is a difference of 3 between the middle side and the hypotenuse side and nth term will be tripled.Difference of 3I will now look at a family with a difference of 3 to see if my prediction will be correct.TrianglesABC19121521536393217275427120123533180183639252255Nth term6 n + 36n2 + 6n + 06n2 + 6n + 3To get these triangle sides I have just trebled the numbers from the first family. To make sure that these are correct I will pick a triangle and check whether it is a Pythagorean triplet.Triangle 4 = A2 + B2 = C2272 + 1202 = C2726 + 14,400 = C215,126 = C2123 = CThis proves that this triangle and all of the new ones are Pythagorean triplets of a new family.nth t erm of the new familyI am now going to find out the new nth terns for all the sides using the same techniques as I have used before and for the same reasons I have stated above.nth term for shortest side9 15 21 27 33 39 45 / / / / / /6 6 6 6 6 6Tn = d n + ( a d )= 6 n + ( 9 6 )= 6 n + 3I will now like last time test to see if this nth term is correct by finding out the 7th term using the nth tern then checking it against my sequence.So when: n = 76 x 7 + ( 9 6 )42 + 3 = 45This proves that the nth term is correct.nth term for middle side12 36 72 120 180 252 336 / / / / / /24 36 48 60 72 84 / / / / /12 12 12 12 12Because this has a second difference I will use a second formula to work out the nth term that I have noted above when working out the nth term for the middle side on the first family.Tn = a + ( n 1 ) d + 1/2 ( n 1 ) ( n 2 ) c12 + ( n 1 ) 24 + 1/2 ( n 1 ) ( n 2 ) 1212 + 24n 24+ 6 [n2 3n + 2]12 + 24n 24 + 6n2 18n + 126n2 + 6n + 0I will now test this nth term again like last time to see if it is correct. I will find out the 7th term by using the nth term I have just worked out then check it against what I have in my sequence.So when n = 76 x 72 + 6 x 7 06 x 49 + 42294 + 42 = 336In my sequence under the 7th term I have 336. This proves that my nth term is correct.nth term for hypotenuse side15 39 75 123 183 255 339 / / / / / /24 36 48 60 72 84 / / / / /12 12 12 12 12I will find out this nth term using the same formula I used finding out the middle side, as it has a second difference.Tn = a + ( n 1 ) d + 1/2 ( n 1 ) ( n 2 ) c15 + ( n 1 ) 24 + 1/2 ( n 1 ) ( n 2 ) 1215 + 24n 24+ 6 [n2 3n + 2]15 + 24n 24 + 6n2 18n + 126n2 + 6n + 3I will now again test this nth term using the same method as above.So when n = 76 x 72 + 6 x 7 + 36 x 49 + 45294 + 45 = 339In my sequence under the 7th term I have 336. This proves that my nth term is correct.Both say the 7th term is 336, so it must be correct.Testing the nth terms of difference of 3I am now go ing test all the nth terms. I will do this by seeing if they comply with Pythagoras theorem.nth term for shortest side2 + nth term for middle side2 = nth term for hypotenuse side2So: ( 6n + 3)2 + ( 6n2 + 6n )2 = (6n2 + 6n + 3)2I will now expand the brackets for each nth term.( 6n + 3 )2 expanded:( 6n + 3) ( 6n + 3)= 36n2 + 36n + 9( 6n2 +6 )2 expanded:( 6n2 + 6n ) ( 6n2 + 6n )= 36n4 + 36n3 + 36n3 + 36n2= 36n4 + 72n3 + 36n2(6n2 + 6n + 3)2 expanded:(6n2 + 6n + 3) (6n2 + 6n + 3)= 36n4 + 36n3 + 18n2 + 36n3 + 36n2 + 18n +18n2 + 18n + 9= 36n4 + 72n3 + 72n2 + 36n + 9So:36n2 + 36n + 9 + 36n4 + 72n3 + 36n2 = 36n4 + 72n3 + 72n2 + 36n + 972n2 + 36n + 9 + 72n3 + 36n4 = 36n4 + 72n3 + 72n2 + 36n + 936n4 + 72n3 + 72n2 + 36n + 9 = 36n4 + 72n3 + 72n2 + 36n + 9This proves that the nth terms are all right and work with Pythagoras theorem.Extension conclusion for Difference of 3 and final conclusionComparing the 3 nth terms I can conclude that when there is a different of 2 between the middle side and t he hypotenuse side the nth term is doubled from when there was a difference of 1. When there is a different of 3 between the middle side and the hypotenuse side the nth term is tripled. I predict that when there is a difference of 4 between the middle side and the hypotenuse side and nth term will be quadrupled and so on.

Graduate School Essay Sample For Clinical Counseling - Questions To Consider

Graduate School Essay Sample For Clinical Counseling - Questions To ConsiderA graduate school essay sample for clinical counseling must have the ability to engage a reader and retain their attention. It should also be able to address the main ideas in the essay and be well written.Clinical counselors are an important part of a college or university's counseling program. They are also responsible for helping students understand, process, and accept what they have learned about their particular field of study. Because the student's interests and abilities will change as they grow older, it is crucial that a counselor is able to remain current on the most up-to-date knowledge in their field. One way to do this is to read a variety of academic journals and attend seminars on the most recent trends in counseling.These are all topics that are typically studied in graduate school, but even if you don't need to learn about them at a professional level, it will benefit you to hone your writin g skills. One of the first steps in this direction is the preparation of a graduate school essay sample for clinical counseling.This writing sample can be used to demonstrate that you are capable of crafting a respectable academic paper. However, it should also be something that other students can be encouraged to read, so that their opinions of you will be improved. Here are some guidelines that you should follow to prepare your essay for clinical training.Clinical training does not necessarily mean completing an entire Master's degree. Some students may already be in the position where they need to earn more than a Bachelor's degree, and it is important that they choose to move ahead without putting the same amount of effort into their work as they would into their Master's program. This is why a Graduate School essay sample for clinical counseling is so important.Clinical training can vary widely from student to student. In addition to the standards of an accredited institution, each individual has a different set of skills that are necessary to take care of a patient. Because of this, a typical student will write their own curriculum vitae in order to express their personality, interests, and goals.Unfortunately, this type of writing cannot stand alone; it must stand next to other forms of academic writing to demonstrate that they are a strong candidate for a promotion or a job in the education field. This is why a graduate school essay sample for clinical counseling is so important. It shows the admissions committee that you are serious about your career by demonstrating that you understand the impact that you will have on the admissions office.The most important thing to remember about your Graduate School essay sample for clinical counseling is that you must answer every question with specificity. For example, it is very important that you use the exact nouns and verbs that you will be using throughout the document. This makes it easy for the student to write this type of document and feels more relaxed when they are completing the task.

How to Write a Perfect Thesis

How to Write a Perfect Thesis How to Write a Perfect Thesis What is a thesis statement Key features of thesis statement Considerations before writing a thesis How to write a strong thesis statement Tips on how to write a proper thesis Revising thesis statement: Tips on thesis revision Thesis sample (Crime and Punishment Essay Thesis) Example of a good thesis statement What is a thesis statement Essays or research papers always have the main idea, central message or main point. All the discussions, arguments and elaborations center on the main idea which captures the position of a writer. Therefore, a thesis statement is a view of an essay writer that captures the theme of the whole essay or research as well as the central message on the discussion. In most cases, thesis statements have one to two sentences that present the topic of the paper as well as comment on the position of the student about the subject of discussion. Therefore, it gives the reader a snapshot of what the paper is about besides giving guidance to the author to remain focused on the topic. Key features of a thesis statement The thesis statement is argumentative: when students write a thesis statement, they should bring out the contentious aspect of the central message hence should not have a factual statement that is irrefutable. The thesis statement is specific: the central message of an essay or a research paper is usually specified what the essay is about for the students to elaborate and prove the argument adequately. The thesis statement is engaging: students ensure that the central message of the essay usually attracts interest. Thus, the thesis statement is provocative and pulls the audience into the whole essay. Thesis statement alludes as well as support the stand of a writer: writers indicate thesis statements that support or alludes to support their points of argument. Thus, the statements appear to have some positive aspect besides giving a clear position of the writer. Considerations before writing a thesis Before writing a thesis statement, students should consider various aspects that entail thesis. For example, students should be aware of the arguable claims that they are about to put across. Besides, students should consider the content of the paper that the thesis statement will control. Separately, authors should think of the best structure of the paper before developing a thesis statement. Elsewhere, writers delve in the best way of summarizing the entire paper before developing a thesis statement since the statement gives a summary of the whole paper. On another note, writers ensure that thesis statements appear in the middle or the end of the first paragraph. Besides, they provide that it is precise and clear, gives the purpose of the paper and gives guidance to the journal. How to write a strong thesis statement Strong thesis statements have three parts that include the argument, the reason for discussion and the opposing views. Consequently, it gives a research paper a clear direction and scope that the writer will cover. Also, it informs a reader on the items that the author will cover within the paper. Therefore, students ensure that a strong thesis statement is narrow, summarize the entire paper, and develops a claim. Besides, it provides the position of the writer, the reason for the position and the opposite view. Also, writers ensure that the statement is complete, guides the writer on the essay and peculiar to the length of the paper and should be debatable. Tips on how to write a proper thesis Students who write research works are aware of the different tips when making strong thesis statements. Therefore, students should: Break the topic into three portions namely the position of the writer, the reason for the stance and the opposing view. Students should ensure that the statement forms a complete sentence and summarizes the authors view. Ensure that the thesis statement captures the purpose of the essay and mentions the most important points that the author will discuss. Students should elaborate thesis statement in a way that guides the paper. Ensure that the thesis statement answers the question in the entire paper. Revising thesis statement: Tips on thesis revision When reviewing a thesis statement, writers should note that the statement is a complete sentence that is simple and meets the requirement of the assignment. Besides, it should answer the research question in either explanatory or argumentative point of view and has a defined idea. Separately, students should ensure that the thesis statement challenges the reader to think and hold the attention of the reader. Also, they should make sure that the report gives new information regarding the topic and avoids mere announcement of the subject as well as stating an obvious idea. Thesis sample (Crime and Punishment Essay Thesis) ‘At least 25 percent of the first-degree murder crimes committed in America pass death penalties’. Example of a good thesis statement ‘American government should spend more than 30 percent of its budget on control of pollution, research on best alternative sources of energy gives a reason for the stance, is engaging and reforestation’. The thesis statement is narrow and debatable, summarizes the paper, gives the position of the student, provides a claim on the solution and highlights the scope of the paper. Example of a bad thesis ‘Crime is detrimental to the society. The thesis stamen is broad and vague. The reader cannot tell what is entailing n the category of offense. Also, the user is unable to understand how crime is detrimental. Besides, the author does not give clarity on the scope of the paper and the area whether it is in USA or Canada, the statement is general and lacks engagement to the reader besides not argumentative.