Math Hl Type 1 Shadows - 3091 Words

Higher Level Mathematics Internal Assessment Type I Shadow Functions Contents Introduction: Functions/Polynomials 3 Part A: Quadratic Polynomials 4 Part B: Cubic Polynomials 12 Introduction: In mathematics, function is defined as a relationship, or more of a correspondence between the set of input values and the set of output values. Also, a rule is involved, or as it may be referred to, a ‘set of ordered pairs’ that assigns a unique output for each of the input. The output correspondence is usually defined as f and the output is x. The correspondence is denoted as f(x). All functions are mainly defined by two factors, as was mentioned before, set of inputs - which are called arguments; and outputs - which†¦show more content†¦So it can be said that: -(x+2)2-9+18 = -Y1+2Ym = Y2 At this point, the real and imaginary components of the complex zeros of Y1 can be found using the values for zeros of Y2. As it is known, Y1 has complex zeros of a form of a ±ib and Y2 has zeros of a ±b. With this information available, I will show you how to obtain value for complex zeros of Y1. Consider a function Y1, with a general statement of: Y1 = (x-a)2+b2 As it has been found earlier, this function has zeros of a ±ib. It also has a shadow function Y2: Y2 = -(x-a)2+b2 With zeros of a ±b. If we say that a = 2 and b = -3, then this function has zeros of 2 ±(-3). In this form of zeros, we can say that 2 is the x value of the vertex coordinates, lying on the axis of symmetry of Y2 on the x-axis, and  ±3 are just the distances between the mid point 2 to the points where Y2 intersects x-axis. It is clearly shown on the graph below. As we know the zeros of Y2, it will be very easy to determine the complex zeros of Y1. 2 will equal to the real part of the complex zeros of Y1, and subsequently,  ±3 will equal to the imaginary part of the complex roots. Although, as we know that y-axis is the imaginary axis, the imaginary parts of the complex roots obtained, of the Y1, will be plot according to the y-axis. As you may have observed, in order to get the complex zeros ofShow MoreRelatedProject Managment Case Studies214937 Words   |  860 Pagesmanagement : case studies I Harold Kerzner. -- 2nd ed. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-471-75167-0 (pbk.) ISBN-10: 0-471-75167-7 (pbk.) 1. Project management-Case studies. I. Title. Printed in the United States of America Contents Preface xi 1 PROJECT MANAGEMENT METHODOLOGIES 1 Lakes Automotive 3 Fems Healthcare, Inc. Clark Faucet Company 2 5 7 11 IMPLEMENTATION OF PROJECT MANAGEMENT Kombs Engineering 13 Williams Machine Tool CompanyRead MoreOne Significant Change That Has Occurred in the World Between 1900 and 2005. Explain the Impact This Change Has Made on Our Lives and Why It Is an Important Change.163893 Words   |  656 Pagestwentieth century history / edited by Michael Peter Adas for the American Historical Association. p. cm.—(Critical perspectives on the past) Includes bibliographical references. ISBN 978-1-4399-0269-1 (cloth : alk. paper)—ISBN 978-1-4399-0270-7 (paper : alk. paper)—ISBN 978-1-4399-0271-4 (electronic) 1. History, Modern—20th century. 2. Twentieth century. 3. Social history—20th century. 4. World politics—20th century. I. Adas, Michael, 1943– II. American Historical Association. D421.E77 2010

English- Short Story Analysis Free Essays

Valenzuela Instructor English 101 17 September 2012 Discovering an Identity Self-deliberation arises quicker during the stresses of life. Breaking forth through these stresses comes from the realization that freedom is obtained through the willingness to welcome a new world, leaving behind the past. Mrs. We will write a custom essay sample on English- Short Story Analysis or any similar topic only for you Order Now Mallard comes in contact with the experience itself, as she receives news of her husband’s death, Brently Mallard, in an accident. Grieving this pain she encloses herself within the room of her home, knowing no one will follow behind her. Left alone, she embarks on a reflection of her past, realizing the breakage that lies behind her and willingly steps forth to accept the future that lies ahead, foreshadowing the brightness of the identity she longs to discover. In the short story, The Story of An Hour by Kate Chopin, the symbolism of the window’s images support the idea that personal freedom constructs ultimate peace with an identity. Through the use of symbolism, the window was seen to be an image of the possibilities beyond the life she had as a sense of freedom conveyed the very willpower that allowed for her to find an identity. Alone the window has a significance of presenting possibilities to the speaker. â€Å"There stood, facing the window, a comfortable, roomy armchair† (299). Noticing the emphasis of the window being in front of the chair shows a possible escape from the truth the speaker just witnessed. Being invited by a comfortable chair to look through the window only emphasizes more to the point that this sort of reflection is needed, and that through this escape she will feel the freedom at once when she feels alone with herself to wonder. Beyond the window reveals a preview of the life that would complete the image of the life that Mrs. Mallard seeks to obtain. â€Å"She could see in the open square before her house the tops of the trees that were aquiver with the new spring life. The delicious breath of rain was in the air† (299). As Mrs. Mallard spies through the window- â€Å"the open square†- she witnesses the liveliness of spring. Analyzing the context of spring, the idea of rebirth drives through the mind of the speaker, however the connotation of â€Å"spring† can be analyzed much further. Spring can be seen as the liveliness of youth such as the possibilities of exploring sexual freedom as she experiences the rebirth after the loss of her husband. Rain also holds connotations that point towards the ideas of rebirth; through this, Mrs. Mallard smelling the scents of rain reveals a sort of spiritual cleansing, as she reacts towards the death of her husband and reflecting upon it. Because the window presents these images of, symbolically, reliving life, Mrs. Mallard experiences and sees the possibilities that face her ahead of time. This experience for the speaker then suddenly becomes more than just a reflection of the recent news, but a presentation- done by the window- for her to view the life beyond the closed door and suspend herself within the world she never had beyond the married life of her husband. With the presentation of her possibilities for a future, she senses the freedom that lives within her. There was something coming to her and she was waiting for it, fearfully†¦ she felt it, creeping out of the sky, reaching toward her through the sounds, the scents, the color that filled the air† (300). Feeling the window open up into her world, she senses that something beyond the clouds beseeches her to welcome them into her life. This sort of â€Å"monstrous joy† –as described later in the text- demands a welcome from Mrs. Mallard as an initiation towards the revival of her new world. Though she fears the unknown object that she describes, â€Å"†¦she was striving to beat it back with her will- as powerless as her two white slender hands† (300), realizing her weakness while fighting back the possession of the unknown entity, she shows a lack of true interest to fight back knowing that she must submit to the future that lies ahead of her. Through the experience of coming forth and welcoming the fear of moving on, she seeks the freedom presented by the window. Ultimately, a sign of an identity in the end shows her happiness through the imagination of the days that lie ahead of her. Spring days, summer days, and all sorts of days that would be her own. She breathed a quick prayer that life might be long. It was only yesterday she thought with a shudder that life might be long† (300). Discovering her days are meant to be lived without the intrusion from her husband, she senses that although her life was once the depression of her day, now became the essence of her identity. Living through this ideology, she feels that she can move on through whatever her life brings forth to her, because she would feel as though all was meant to be given to her. She brought this thinking forward even in the end when the surprise of finding her husband unharmed from the accident, which in the end killed her. â€Å"When the doctors came they said she had died of heart disease- of joy that kills† (301). The heart disease that had her worried for her life in the beginning of the short story then became the relief that she felt when she left the world to pursue the joy without her husband intruding on her sudden realization of an identity. Heart disease, in the context, reveals itself as the â€Å"joy that kills† emphasizing the discovery of her freedom through the disease that she feared would kill her. Noticing that the identity for herself lied within the freedom that she obtained from her husband, she died to achieve this ultimate peace with the identity she found. Through the use of the symbolism that the images of the window present to Mrs. Mallard, a sense of personal freedom constructs the idealness of obtaining an identity. And in this short story, The Story of An Hour, The breakthrough represents itself through the most peculiar ways. Mrs. Mallard through the story discovered her life was to be relived through the images of the window as they revealed the possibilities that brought forth her true identity. Henceforth, discovering in the end that her husband never allowed her freedom within the marriage by being alive brought forth her breakthrough; Revealing itself through the joys of being set free in death, she is brought to the haven she so desperately desired, growing to be the individual that lives or, in this case, dies without the handcuffed life she lived through with her marriage to Brently Mallard. How to cite English- Short Story Analysis, Essay examples

Explain the Role of Computer Systems in Different Environments free essay sample

Department of Business Computing Programme Title |BTEC HND/HNC in Computing Systems Development | |Unit Title |Computer Systems |Unit Number |2 / PART 1 | |Candidate’s Name: | | |Assessor’s Name: |Esam Harb |Verifier’s Name: |Mr R Jamei | |Date of IV of Brief: | |Signature of IV: | | |Issue Date: |28. 12. 2012 |Due Date: |27. 03. 2013 | |Plagiarism: | |Where there is evidence of plagiarism the assignment will be rejected and the candidate will not have an opportunity to re-submit the work. This will, | |inevitably, jeopardise your chances of completing the unit. | |Deadlines: | |Work that is not handed in on time will be subject to College policy on late submission of work and may not be graded or marked. This could result in you| |failing the course unless there are exceptional circumstances which must be explained to your tutor and agreed by the Curriculum Manager. | |Referral of Assignments: | |Questions marked â€Å"Pxx† need to be completed successfully to achieve a Pass grade. We will write a custom essay sample on Explain the Role of Computer Systems in Different Environments or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Only then can you achieve a Merit grade by completing the question(s) | |marked â€Å"Mxx†, and a Distinction by completing the question(s) marked â€Å"Dxx† in addition to the Merit questions(s). Where this identification of possible | |higher grades does not exist the general higher grades descriptors, which follow, will apply. |Work not meeting the minimum requirement for pass grade will be referred back to the learner who will have TWO weeks to rectify any shortcoming. | |All decisions or grades are subject to internal and/ or external verification and may be modified. If you feel that an assessment decision is | |unjustified, you are entitled to appeal. | |For further details on any of the above please refer to your Course Handbook