Free Essays - All Quiet on the Western Front :: All Quiet on the Western Front Essays

  All Quiet on the Western Front   The setting of this novel takes place in Germany during World War I. the war is being fought at the fronts- which is almost every side of Germany where other countries lie. For the most part, Paul Baumer stays on the western front, (north west of Belgium), during the three years when the novel takes place. The setting is very important because it shows the darkest part of the war, when most of Germanys fighting takes place.   Paul Baumer, a young soldier who enjoys writing poems and plays, becomes a man during his three years of service. He wants the war to be over so he can go back home to his family and read and write again with out being disrupted by his thoughts of the front. By the end of the novel, he does not achieve this because he was killed on the western front. When they found his body, it had an appearance of calm gladness because the war was finally over for him. In this novel, Paul faced drastic changes. He went from a child who knew nothing about death, despair or fear to a grown man who only knew those three things. At the end of the novel Paul had nothing, for every thing he had loved or cared about was taken from him by the war. I liked this character because he was well written. He was head strong about life or what he knew of it.   Stanislaus Katczinsky also know, as Kat is a forty-year-old veteran of war who teaches Paul and others about life on the battlefield. He is head strong and very smart and is depended on by Paul and others for food, and helping them cope with war. I believe Kat wants what every soldier wants, for the war to be over. I liked this character he was fun to read and a great teacher to me about the war.   The minor character that was most interesting to me was Corporal Himmelstoss because he was unfair to other soldiers, in a mean bullying manner. However, when it finally came down for the Corporal to fight, he became a coward. In the end, he gained the respect of Paul and others for rescuing Haie.   I believe the most important conflict in the story was when Paul volunteered to be part of a patrol to spy on the allied position.

Hindi as a Language

The constitution of India (Article 343) recognises Hindi as the official language of India. Hindi is also the main language in many states of India such as Haryana, Rajasthan, Uttar Pradesh, Uttaranchal/ Uttarakhand, Bihar, Madhya Pradesh, Chhatisgarh and Himachal Pradesh. It is spoken by more than 437 million people in the world. The other dialects of Hindi are Brajbhasha, Bundeli, Awadhi, Marwari, Maithili, Bhojpuri, to name only a few. Hindi can be traced back to as early as the seventh or eighth century.The dialect that has been chosen as the official language is Khariboli in the Devnagari script. Other dialects of Hindi are Brajbhasa, Bundeli, Awadhi, Marwari, Maithili and Bhojpuri. It was in the 10th century that authentic Hindi poetry took its form and since then it has been constantly modified. History of Hindi literature as a whole can be divided into four stages: Adikal (the Early Period), Bhaktikal (the Devotional Period), Ritikal (the Scholastic Period) and Adhunikkal (th e Modern Period). Adikal-Adikal starts from the middle of the 10th century to the beginning of the 14th century. The poetry of this period has been divided into three categories Apabhramsha Poetry, Heroic Poetry and Miscellaneous Poetry. Apabhramsha Poetry includes the Siddha literature (750-1200), the Nath literature and the Jain literature. Siddha literature was written in the popular language and this echoed devotional themes combined with a strong erotic feeling. Between the 7th and the 14th century, the poet Gorakhnath and his followers mainly composed the Nath literature.They avoided eroticism, scorned racial discrimination and put stress on moral values, using the Doha (couplet) and the Chaupai (quartet) styles in their poems. These compositions had a great influence on the Sant (devotional literature made popular by Rahim and Kabir et al) literature. During this period Jain poets like Swayambhu, Som Datt Suri, Sharang Dhar and Nalla Singh composed the Charit Kavyas, which pr opagate moral tenets and portrayals of Nature. Heroic Poetry was composed wholly in the native speech. Bhakti Kal or the Devotional Period :The bhakti kal stretched between the 14th and the 17th century. During this age Islamic customs were heaped upon the common people and the Hindus were quite dejected by this. The poets of this period felt that it was their moral duty to arouse a sense of devotion through religious poetry. These poets have been divided into two groups: Nirguna and Saguna poets, depending upon the devotional attitude towards the Lord. Nirgunas have been further divided into two groups on the basis of different sadhanas (disciplines) followed by them.Those that put emphasis on the importance of knowledge for the realization of God were called the Saint poets. Kabir Das, Guru Nanak, Dharma Das, Maluk Das, Dadudayal, Sunder Das belong to this genre. In their Sakhis (couplets) and Padas (songs) they condemned rituals and laid emphasis on the theory of Monotheism (the belief that there is one God). Poets who believed love was the path of realizing God were called Sufi Poets. Jayasi, Manjhan, Kutuban and Usman were the pioneers of this school. Poets of the Saguna style are also divided into two groups: the followers of Rama and those of Krishna.Tulsi Das is the leading poet of the former group along with Agra Das, Nabha Das and Pran Chand Chauhan. Tulsi Das depicts Rama as the Ideal Man in his classical works Ramacharitamanasa, Gitavali, Kavitavali and Vinay Patrika. The devotees of Krishna have, however, portrayed him according to his popular image, that of the playful Krishna. These poets like Surdas, Nand Das, Parmananda Das and Meera have written about love and beauty. The devotional period created immortal literature and is distinguished as the golden age of Hindi Poetry. Ritikal or the Scholastic period:The poets of Ritikal can be classified into two groups on the basis of their subject: Ritibaddha (those wedded to rhetorics) and Ritimukta ( free from rhetorical conventions). The former poets composed on definitional and (Lakshana) and illustrative (Lakshya) themes. The essential nature of Rasa, Alankara, Nayikabheda were illustrated by them through Saviyas and Kavithas. Poets like Chintamani, Keshav, Mati Ram, Deva, Kulpati Misra and Bhikari Das were leaders of this style. The second group consists of free-minded poets like Alam, Ghananand, Bodha and Thakur. They wrote in a spontaneous manner ith feelings of love, quite quite dissilimar to rhetorical poetry. This age saw two more poetic trends. Didactic poetry in stray verses composed by Vrinda, Vaital and Giridhar and Heroic Poetry by Bhushan, Sudan, Lal and various others. Adhunikkal or Modern Period: Modern Hindi literature has been divided into four phases; the age of Bharatendu or the Renaissance (1868-1893), Dwivedi Yug (1893-1918), Chhayavada Yug (1918-1937) and the Contemporary Period (1937 onwards). Bharatendu Harishchandra (1849-1882) brought in a modern outl ook in Hindi literature and is thus called the ‘Father of Modern Hindi Literature'.Mahavir Prasad Dwivedi later took up this vision. Dwivedi was a reformist by nature and he brought in a refined style of writing in Hindi poetry, which later acquired a deeper moral tone. This was the age of revival when the glory and grandeur of ancient Indian culture was fully adopted to enrich modern life. Social, political and economic problems were portrayed in poetry while songs were of social awakening. This trend helped in the emergence of National Cultural Poetry whose leading poets were Makhanlal Chaturvedi, Balkrishna Shama ‘Navin', Siyaram Gupta and ‘Dinkar'.These poets put more stress on moral aspect of life rather than on love or beauty, which later evolved in the Chhayavada style of poetry. Kamayani is the zenith of this school and Chhayavada was best represented by Prasad, Nirala, Pant and Mahadevi Verma. After the decline of this movement in came the leftist ideology which found voice in two opposite styles of Hindi poetry. One was Progressivism and Prayogavada or later called Nai Kavita. The former was an effort of translating Marx's philosophy of Social realism into art. The most notable figure of this movement was Sumitranandan Pant.The latter safeguarded artistic freedom and brought in new poetic content and talent to reflect modern insight. The pioneers of this trend were Aggeya, Girija Kumar, Mathur and Dharamvir Bharati. A third style called Personal Lyrics also appeared, aiming at free and spontaneous human expressions with Harivansh Rai Bachchan as the leader of this trend. The history of Hindi poetry, thus, extends over a period of almost one thousand years. The proper development of Hindi prose followed the rise and growth of Khari Boli (colloquial dialect).Pre-Bharatendu writers like Ram Prasad Niranjani, Sadasukh Lal, Insha Allah Khan and Sadal Misra composed proses mainly based on mythological stories. Insha Allah Khan used the ty pical Khari Boli while others were more influenced by Sanskrit and Braj Bhasha. The development of Hindi prose has been classified into three periods: The first phase (1868-1918), the period of growth (1918-1937) and the present age of excellence (1938 onwards). The First Phase: Prose literature of Bharatendu and Dwivedi era covers the first phase.The writers of this age developed drama, novel, short story, essay and literary criticism. Popular dramatic compositions were done mainly by Bharatendu Harishchandra, Bal Krishna Bhatt and Radha Krishna Das. They inclined more towards satires on contemporary conditions, social and patriotic plays. Eminent prosateurs of this age included Devaki Nandan Khatri (novelist), Chandradhar Sharma (short-story writer), Mahavir Prasad Dwivedi (essayist) and Padma Singh Sharma (critic). The period of growth This is represented by Jayshankar Prasad, Rai Krishna Das and Mahadevi Varma.Drama acquired a distinct place for itself in this period but the the atre did not respond to it. Again, fiction attained new proportions with Premchand as its most outstanding representative. The period of excellence This period came more whole-heartedly after the Independence of India in 1947. Hindi drama of this period laid emphasis on realistic expressions and two new forms evolved like poetic Drama and radio play. Now the theatre also became interested in enacting these plays. ‘Ashka' Jagdish Chandra Mathur, Mohan Rakesh and Lakshminarayan Lal have acquired distinction amongst modern playwrights.Fiction made a wonderful progress during this period. Realism, psycho-analytical techniques and prose-style was the main ingredient of the plot structure. Modern Hindi fiction found its mentors in Yash Pal, Agyeya and Renu. Essay and literary criticism also developed during this period. Essayists like Hazari Prasad Dwivedi, Mahadevi Varma and Siyaram Sharan Gupta found new ways of expressing themselves through reminiscences, reportage and sketch. Th e history of Hindi prose is not expansive, as it had started out quite late. However, it has progressed at a rapid pace.

A Critical Appraisal of Beowulf and Gilgamesh Essay examples

A Critical Appraisal of: Beowulf and Gilgamesh There are many differences and critical comparisons that can be drawn between the epics of Beowulf and Gilgamesh. Both are historical poems which shape their respected culture and both have major social, cultural, and political impacts on the development of western civilization literature and writing. Before any analysis is made, it is vital that some kind of a foundation be established so that a further, in-depth exploration of the complex nature of both narratives can be accomplished. The epic of Gilgamesh is an important Middle Eastern literary work, written in cuneiform on 12 clay tablets about 2000 BC. This heroic poem is named for its hero, Gilgamesh, a tyrannical†¦show more content†¦Much like Beowulf, there is, however, no historical evidence for the exploits narrated in poems and the epic. The Ninevite version of the epic begins with a prologue in praise of Gilgamesh, part divine and part human, the great builder and warrior, knower of all things on land and sea. In order to curb Gilgameshs seemingly harsh rule, the god Anu caused the creation of a Enkidu, a wild man who at first lived among animals. Soon, however, Enkidu was initiated into the ways of city life and traveled to Uruk, where Gilgamesh awaited him. Tablet II describes a trial of strength between the two men in which Gilgamesh was the victor; thereafter, Enkidu was the friend and companion (in Sumerian texts, the servant) of Gilgamesh. In Tablets III-V the two men set out together against Huwawa (Humbaba), the divinely appointed guardian of a remote cedar forest, but the rest of the engagement is not recorded in the surviving fragments. In Tablet VI Gilgamesh, who had returned to Uruk, rejected the marriage proposal of Ishtar, the goddess of love, and then, with Enkidus aid, killed the divine bull that she had sent to destroy him. Tablet VII begins with Enkidus account of a dream in which the gods Anu, Ea, and Shamash decided that he must die for slaying the bull. Enkidu then fell ill and dreamed of the house of dust that awaited him. Gilgameshs lament for his friend and the state funeral of

Why should my conscience bother me - 1224 Words

Fin 330 Hand in Problem â€Å"Wy Should My Conscience Bother Me?† Howard Hehrer 12/3/2013 1. Identify some of the moral issues that are present in this case. a. There are many moral issues, but the story seems to revolve around several cases of ‘passing the buck’, or rationalizing how small of a part each respective individual plays in the conspiracy. In most of these cases, like Gretzinger’s scuffle with Line, the individual is charged with risking his job for potentially little or no change. Each instance seems to have stemmed from the inability of anyone to challenge the hot-headed Warren and his faulty design. As the conspiracy developed further, to speak out about the conspiracy would mean a less believable narrative. This†¦show more content†¦b. Using Utilitarianism argue why the decision was bad. i. The results show that more harm was done than good. LTV was worse off, and the Air Force was worse off. The plant may have been okay in the end, but clearly redesigning the wheel at the expense of the anger of one hot-headed engineer (Warren) and possibly the job of himself (Lawson) would have caused less harm than the results of the resulting conspiracy. c. Using Kant’s Categorical Imperative argue why the decision was bad. i. If all engineers decided to ‘go along with the plan’, instead of employing their technical skills and standing up against fraud or conspiracy to commit fraud, many people would die from faulty inventions. Nobody would be able to trust what an engineer built. Further, if all people decided to ‘go along with the plan’ or if all people decided to lie, everybody would be worse off. Nobody could trust anyone, and nothing would get done as a society. Therefore, nobody should lie or go along with a lie, according to the Categorical Imperative. 6. There are several points in this narrative where there were opportunities to fix the problem. Pick out at least two examples of points at which moral imagination and or moral courage by the various participants could have headed off the catastrophe. Indicate the person and what they could have done to fix the problem. a. Lawson i. Lawson displayed courage by approaching Sink and laterShow MoreRelatedCriminal Law Case Study1596 Words   |  7 Pagesagree with my partner and say that the suspect resisted arrest. I’d tell the Internal Affairs (IA) investigators that my partner did disregard regulations and rode with the suspect in the backseat but, the suspect seemed depressed and we didn’t want him to hurt himself. When asked how the suspect received his injuries, I’d say I wasn’t paying attention to what was happening in the backseat but his injuries came from resisting arrest. I wouldn’t be confirming or denying what happened. My partnerRead MoreWho Is An Antisocial Personality Disorder?1459 Words   |  6 Pagessuperficially charming; They are masters of influence and deception. They have no guilt or remorse about exploiting or manipulating other people; winning is the most important thing. It is chiefly characterized by something wrong with the person s conscience. Sociopaths only care about fulfilling their own needs and desires. Everything and everybody else is mentally twisted around in their minds. They often believe they are doing something good for society, or at least nothing that bad (dsm-iv-definition-ofRead MoreMaking Excuses For My Own Mind1669 Words   |  7 Pageshours the time I ruined when we should be having fun together left no window for issues to be cooperatively resolved. He avoided everything in life that was uncomfortable to him, even brushing his teeth. The pain of cavities or a broken tooth was somehow not significant until it happened. When it did it was news to everyone and an excuse for even greater irritability.Without foresight, fear or any appreciation for the consequences of his own actions I made excuses in my own mind. I came up with rationalizationsRead MoreAnalysis Of The Story The Mansion 1426 Words   |  6 Pagesmansion there heart fills with admiration. But even at my young age of 13 I know the truth behind the rich man’s intentions. He is a man who does not bring money to the town for others but instead for his own greed. This is a man who lives a flamboyant life, his money paying for all his expenses and getting him all that he desires. For four years I’ve watched this man through my bedroom window. The bedroom that I share with my two brothers and my widowed mother. In the one story, one bedroom, andRead MoreThe Merchant of Venice Is a Tragicomedy....I Got 32/35 so Its a Good Essay1558 Words   |  7 Pagesend of the play. In the beginning of the play he is displayed as a rich man, who has no reason to be unhappy. 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Atticus Finch stands out as an exceptional father compared to Bob Ewell and Walter Cunningham Sr. as he possesses the qualities of racial acceptance, compassion, and forgiveness reminding the reader that a fair conscience and good parenting is not race specificRead MoreThe Myers Briggs Type Indicator : Extraverted, Feeling With Sensing And Judging1502 Words   |  7 Pagesended with my tears, and thus, compromising and accommodating became the easy route out. When I took this class, I was aware of my idealist beliefs. I pride myself on my well-defined values and morals. The other schools of negotiation ethics may consider me naà ¯ve, but that does not bother me. I would rather live by a free conscience, and a satisfaction that I did my best to please someone else. Social ties are something that I cherish above all else; sometimes even at the cost of my own profitabilityRead MoreDoubt in Macbeth1395 Words   |  6 Pagesplague th’inventor. This even-handed justice †¨ Commends th’ingredience of our poisoned chalice †¨ To our own lips. He’s here in double trust: First, as I am his kinsman and his subject, Strong both against the deed; then, as his host, †¨ Who should against his murderer shut the door, †¨ Not bear the knife myself. Besides, this Duncan †¨ Hath borne his faculties so meek, hath been †¨ So clear in his great office, that his virtues †¨ Will plead like angels, trumpet-tongued against †¨ The deepRead MoreWhy I Don t Do Not Take One More Step !1718 Words   |  7 Pages â€Å"Do not take one more step!† my mother’s voice is pounding in my ears. If leaving was this easy I would have done it ages ago, in each hand I hold bags bulging with a collection of clothes, shoes and miscellaneous objects. â€Å"I dare you!† As if everything is in slow motion, I lift my leg and step out of the house. â€Å"Charlotte, you just made the biggest mistake of your life.† I don’t care anymore. I don’t want to care anymore. I slam the door on my mother, finally free. I shiver, the feeling of beingRead MoreEssay about Divorce in American Society1338 Words   |  6 Pagesmost couples get into a marriage wanting the best out of it. Unfortunately, people are getting married without thinking of the responsibilities that come with marriage. What is happening to the meaning of a family? Where are we taking it and why arent we doing much about it? A family is suppose to be the love and support of both a mother and father for their children. There is not much time spent at home building new bonds and expressing the love. Instead, Americans have become more

Piaget Essay - 1672 Words

Piagets Theory of Cognitive Development During the 1920s, a biologist named Jean Piaget proposed a theory of cognitive development of children. He caused a new revolution in thinking about how thinking develops. In 1984, Piaget observed that children understand concepts and reason differently at different stages. Piaget stated childrens cognitive strategies which are used to solve problems, reflect an interaction BETWEEN THE CHILDS CURRENT DEVELOPMENTAL STAGE AND experience in the world. Research on cognitive development has provided science educators with constructive information regarding student capacities for meeting science curricular goals. Students which demonstrate concrete operational thinking on Piagetian tasks seem to†¦show more content†¦Piagets states many secondary level science courses taught in the past at the have been too abstract for most students since they are taught in lecture or reception learning format. Thus, students who only have concrete operational structures available for their reasoning will not be successful with these types of curricula. Programs using concrete and self-pacing instruction are better suited to the majority of students and the only stumbling block may be teachers who cannot understand the programs or regard them as too simplistic. Since the teacher is a very important variable regarding the outcome of the science, the concern level of the teacher will determine to what extent science instruction is translated i n a cognitively relevant manner in the classroom. Educators who prefer to have children learn to make a scientific interpretation rather than a mythological interpretation of natural phenomena, and one way to introduce scientific interpretations is to analyze any change as evidence of interaction. One way in which this teaching device can function is if there is an instructional period of several class sessions in which the students are engaged in quot;playquot; with new of familiar materials; followed by is a suggestion of a way to think about observations; lastly there is a further extermination inShow MoreRelatedPiaget2552 Words   |  11 PagesJean Piaget Intelligence Piaget was opposed to defining intelligence in terms of the number of items answered correctly on a so- called intelligence test. (Olson amp; Hergenhahn, 20090 To him intelligence is what allows an organism to deal effectively with its environment. Intelligence changes constantly because both the environment and the organism change constantly. Intelligence is a dynamic trait because what is available as an intelligent act will change as the organism matures biologicallyRead More Piaget Essay1409 Words   |  6 Pages Piaget’s Theory of Cognitive Development nbsp;nbsp;nbsp;nbsp;nbsp;Jean Piaget was born on August9, 1896, in the French speaking part of Switzerland. At an early age he developed an interest in biology, and by the time he had graduated from high school he had already published a number of papers. After marrying in 1923, he had three children, whom he studied from infancy. Piaget is best known for organizing cognitive development into a series of stages- the levels of development correspondingRead MoreJean Piaget775 Words   |  4 PagesJean Piaget was a theorist who studied child development; one of the many aspects of early childhood Piaget studied was preoperational thinking. Preoperational thinking usually occurs from ages 2 through 7 according to Piaget. It’s when a child is not able to think logically and perform activities that require logic. In other words, a child is not yet ready at this stage, to reason many situations. Piaget created many experiments that could help educators observe and detect the stages and levelsRead Morejean piaget1284 Words   |  6 Pagesï » ¿Jean Piaget Jean Piaget (1896 - 1980) was employed at the Binet Institute in the 1920s, where his job was to develop French versions of questions on English intelligence tests. He became intrigued with the reasons children gave for their wrong answers on the questions that required logical thinking. He believed that these incorrect answers revealed important differences between the thinking of adults and children. 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The ‘Stage-based theory of cognitive development’ from Jean Piaget explores the sequential development of thinking process through a series of stages include sensorimotor stage for births to ageRead MoreKindergarten and Piaget1761 Words   |  8 Pages Kindergarten and Piaget Child Development Instructor: Jaclyn Scott December 17, 2013 As a preschool teacher, I am responsible for ensuring that I provide my students with engaging experiences through discovery learning as well as making sure that I am supporting the interests of the children in the classroom. Using Piaget s Stage theories, children cannot do certain tasks until they are psychologically mature enough to do so and was believed thatRead MorePiaget Observation1518 Words   |  7 PagesCognitive Development: Transition between Preoperational Concrete Stages Piaget believed that human development involves a series of stages and during each stage new abilities are gained which prepare the individual for the succeeding stages. The purpose of this study is to evaluate the differences between two stages in Piagets Cognitive Development TheoryÂâ€"the preoperational stage and concrete operational stage. Cognitive development refers to how a person constructs thought processes to gainRead MorePiaget Of Piaget s Sensorimotor Stage Essay1789 Words   |  8 PagesVignette I This behavior can be explained by Piaget’s sensorimotor stage. Piaget discovered that from the time they are born until they reach about the age of two, children experience the world through their senses (Myers, 2010, p. 181). Infants, up until about 8 months, also are also extremely focused on the present and have not yet developed a sense of object permanence, which can lead to the â€Å"out of sight, out of mind† mindset (Myers, 2010, p. 181). This is evident in the situation at hand, inRead MoreJean Piagets Theory1170 Words   |  5 Pagesthat of Jean Piaget and his theories on the cognitive development stages. Jean Piaget was born in Neuchatel, Switzerland, where he studied at the university and received a doctorate in biology at the age of 22. Following college he became very interested in psychology and began to research and studies of the subject. With his research Piaget created a broad theoretical system for the development of cognitive abilities. His work, in this way, was much like that of Sigmund Freud, but Piaget emphasized

Investigating Ratios of Areas and Volumes Free Essays

Investigating Ratios of Areas and Volumes In this portfolio, I will be investigating the ratios of the areas and volumes formed from a curve in the form y = xn between two arbitrary parameters x = a and x = b, such that a b. This will be done by using integration to find the area under the curve or volume of revolution about an axis. The two areas that will be compared will be labeled ‘A’ and ‘B’ (see figure A). We will write a custom essay sample on Investigating Ratios of Areas and Volumes or any similar topic only for you Order Now In order to prove or disprove my conjectures, several different values for n will be used, including irrational, real numbers (? , v2). In addition, the values for a and b will be altered to different values to prove or disprove my conjectures. In order to aid in the calculation, a TI-84 Plus calculator will be used, and Microsoft Excel and WolframAlpha (http://www. wolframalpha. com/) will be used to create and display graphs. Figure A 1. In the first problem, region B is the area under the curve y = x2 and is bounded by x = 0, x = 1, and the x-axis. Region A is the region bounded by the curve, y = 0, y = 1, and the y-axis. In order to find the ratio of the two areas, I first had to calculate the areas of both regions, which is seen below. For region A, I integrated in relation to y, while for region B, I integrated in relation to x. Therefore, the two formulas that I used were y = x2 and x = vy, or x = y1/2. The ratio of region A to region B was 2:1. Next, I calculated the ratio for other functions of the type y = xn where n ? ?+ between x = 0 and x = 1. The first value of n that I tested was 3. Because the formula is y = x3, the inverse of that is x = y1/3. In this case, the value for n was 3, and the ratio was 3:1 or 3. I then used 4 for the value of n. In this case, the formula was y = x4 and its inverse was x = y1/4. For the value n = 4, the ratio was 4:1, or 4. After I analyzed these 3 values of n and their corresponding ratios of areas, I came up with my first conjecture: Conjecture 1: For all positive integers n, in the form y = xn, where the graph is between x = 0 and x = 1, the ratio of region A to region B is equal to n. In order to test this conjecture further, I used other numbers that were not necessarily integers as n and placed them in the function y = xn. In this case, I used n = ?. The two equations were y = x1/2 and x = y2. For n = ? , the ratio was 1:2, or ?. I also used ? as a value of n. In this case, the two functions were y = x? and x = y1/?. Again, the value of n was ? , and the ratio was ? :1, or ?. As a result, I concluded that Conjecture 1 was true for all positive real numbers n, in the form y = xn, between x = 0 and x = 1. 2. After proving that Conjecture 1 was true, I used other parameters to check if my conjecture was only true for x = 0 to x = 1, or if it could be applied to all possible parameters. First, I tested the formula y = xn for all positive real numbers n from x = 0 to x = 2. My first value for n was 2. The two formulas used were y = x2 and x = y1/2. In this case, the parameters were from x = 0 to x = 2, but the y parameters were from y = 0 to y = 4, because 02 = 0 and 22 = 4. In this case, n was 2, and the ratio was 2:1, or 2. I also tested a different value for n, 3, with the same x-parameters. The two formulas were y = x3 and x = y1/3. The y-parameters were y = 0 to y = 8. Again, the n value, 3, was the same as the ratio, 3:1. In order to test the conjecture further, I decided to use different values for the x-parameters, from x = 1 to x = 2. Using the general formula y = xn, I used 2 for the n value. Again, the ratio was equal to the n value. After testing the conjecture multiple times with different parameters, I decided to update my conjecture to reflect my findings. The n value did not necessarily have to be an integer; using fractions such as ? and irrational numbers such as ? did not affect the outcome. Regardless of the value for n, as long as it was positive, the ratio was always equal to n. In addition, the parameters did not have an effect on the ratio; it remained equal to the value used for n. Conjecture 2: For all positive real numbers n, in the form y = xn, where the graph is between x = a and x = b and a b, the ratio of region A to region B is equal to n. . In order to prove my second conjecture true, I used values from the general case in order to prove than any values a and b will work. So, instead of specific values, I made the x-parameters from x = a to x = b. By doing this, region A will be the region bounded by y = xn, y = an, y = bn, and the y-axis. Region B is the region enclosed by y = xn, x = a, x = b, and the x-axis. The formulas used were y = xn and x = y1/n. The ratio of region A to region B is n:1, or n. This proves my conjecture correct, because the value for n was equivalent to the ratio of the two regions. . The next part of the portfolio was to determine the ratio of the volumes of revolution of regions A and B when rotated around the x-axis and the y-axis. First, I determined the ratio of the volumes of revolutions when the function is rotated about the x-axis. For the first example, I will integrate from x = 0 to x = 1 with the formula y = x2. In this case, n = 2. When region B is rotated about the x-axis, it can be easily solved with the volume of rotation formula. When region A is rotated about the x-axis, the resulting volume will be bounded by y = 4 and y = x2. The value for n is 2, while the ratio is 4:1. In this case, I was able to figure out the volume of A by subtracting the volume of B from the cylinder formed when the entire section (A and B) is rotated about the x-axis. For the next example, I integrated the function y = x2 from x = 1 to x = 2. In this case, I would have to calculate region A using a different method. By finding the volume of A rotated around the x-axis, I would also find the volume of the portion shown in figure B labeled Q. This is because region A is bounded by y = 4, y = x2, and y = 1. Therefore, I would have to then subtract the volume of region Q rotated around the x-axis in order to get the volume of only region A. In this case, the value for n was 2, and the ratio was 4:1. After this, I decided to try one more example, this time with y = x3 but using the same parameters as the previous problem. So, the value for n is 3 and the parameters are from x = 1 to x = 2. In this case, n was equal to 3, and the ratio was 6:1. In the next example that I did, I chose a non-integer number for n, to determine whether the current pattern of the ratio being two times the value of n was valid. For this one, I chose n = ? with the parameters being from x = 0 to x = 1. In this case, n = ? and the ratio was 2? :1, or 2?. After this, I decided to make a conjecture based on the 4 examples that I had completed. Because I had used multiple variations for the parameters, I have established that they do not play a role in the ratio; only the value for n seems to have an effect. Conjecture 3: For all positive real numbers n, in the form y = xn, where the function is limited from x = a to x = b and a b, the ratio of region A to region B is equal to two times the value of n. In order to prove this conjecture, I used values from the general case in order to prove than any values a and b will work. So, instead of specific values, I made the x-parameters from x = a to x = b. By doing this, region A will be the region bounded by y = xn, y = an, y = bn, and the y-axis. Region B is the region enclosed by y = xn, x = a, x = b, and the x-axis. In this example, n = n and the ratio was equal to 2n:1. This proves my conjecture that the ratio is two times the value for n. When the two regions are rotated about the x-axis, the ratio is two times the value for n. However, this does not apply to when they are rotated about the y-axis. In order to test that, I did 3 examples, one being the general equation. The first one I did was for y = x2 from x = 1 to x =2. When finding the volume of revolution in terms of the y-axis, it is important to note that the function must be changed into terms of x. Therefore, the function that I will use is x = y1/2. In addition, the y-parameters are from y = 1 to y = 4, because the x values are from 1 to 2. In this example, n = 2 and the ratio was 1:1. The next example that I did was a simpler one, but the value for n was not an integer. Instead, I chose ? , and the x-parameters were from x = 0 to x = 1. The formula used was x = y1/?. In this example, the ratio was ? :2, or ? /2. After doing this example, and using prior knowledge of the regions revolved around the x-axis, I was able to come up with a conjecture for the ratio of regions A and B revolving around the y-axis. Conjecture 4: For all positive real numbers n, in the form y = xn, where the function is limited from x = a to x = b and a b, the ratio of region A to region B is equal to one half the value of n. In order to prove this conjecture, I used values from the general case in order to prove than any values a and b will work. This is similar to what I did to prove Conjecture 3. So, instead of specific values, I made the x-parameters from x = a to x = b. By doing this, region A will be the region bounded by y = xn, y = an, y = bn, and the y-axis. Region B is the region enclosed by y = xn, x = a, x = b, and the x-axis. The ratio that I got at the end was n:2, which is n/2. Because the value of n is n, this proves that my conjecture is correct. In conclusion, the ratio of the areas formed by region A and region B is equal to the value of n. n can be any positive real number, when it is in the form y = xn. The parameters for this function are x = a and x = b, where a b. In terms of volumes of revolution, when both regions are revolved around the x-axis, the ratio is two times the value of n, or 2n. However, when both regions A and B are revolved around the y-axis, the ratio is one half the value of n, or n/2. In both situations, n includes the set of all positive real numbers. How to cite Investigating Ratios of Areas and Volumes, Papers

Harriet tubman Essay Example For Students

Harriet tubman Essay Harriet tubman Essay was born in 1820 on a large plantation in Dorchester County, Maryland. She was the sixth of eleven children. She was born in a very small on-room log hut, that was located behind her families owners house. The huthad a dirt floor, no windows, and no furniture. Her fater, Benjamin Ross, and mother, Harriet Green, were both slaves. They were from the Ashanti ribe of West Africa. Edward Brodas, Harriets owner, hired her out The buying and selling of humans was a big deal in America between the late 1600s and the 1800s. By 1835 there were over two million black men, women, and children who were slaves. These people were bought and sold. No one cared if husbands and wives got weparated or if children were separated from their parents. Slaves were not treated like people. Hard work toughened her, and before she was 19 she was as strong as the men she worked with were. In Philadelphia, Pa, and later in Cape May, NJ, Harriet Tubman worked as a maid in hotels and clubs. By December 1850 she had saved up enough money to make the first of her nineteen daring journeys back into the south. She went back the lead other slaves out of bondage. In 1851 she returned for her husband to find that he had remarried. Bibliography Harriet Tubman: Comptons Encyclopedia (http://comptonsv3. web.aol.com) (2000) Harriet Tubman: Hutchinson Encyclopedia (http://ukab.web.aol.com) (2000) Harriet Tubman: Encarta Online Concise (http://www. encarta.msn.com) (2000) .