Algebra Archit Pal Singh Sachdeva 1. Consider the sequence of polynomials defined by P1 (x) = x2 − 2 and Pj (x) = P1 (Pj−1 (x)) for j = 2‚ 3‚ . . .. Show that for any positive integer n the roots of equation Pn (x) = x are all real and distinct. 2. Prove that every polynomial over integers has a nonzero polynomial multiple whose exponents are all divisible by 2012. 3. Let fn (x) denote the Fibonacci polynomial‚ which is defined by f1 = 1‚ f2 = x‚ fn = xfn−1 + fn−2 . Prove that the inequality 2 fn
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Difference and inequality City Road is a good place to investigate inequality and differences as it plays host to a variety of different people‚ businesses and cultures. Inequalities and differences can be observed just by walking along City Road in the changes that have taken place‚ in the people that we meet and in the shops that we see‚ and can be measured in in many different ways. Inequality is prevalent all over the world and can be for various reasons. To discover where inequality and difference
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In your own words‚ define difference and inequality‚ and provide an example of each on City Road. This essay serves to define difference and inequality and provide an example of each within City Road‚ situated in Cardiff. It is clear that within city road‚ many differences are apparent‚ between the people that live and work there. From some of these differences‚ inequality can become apparent (The Open University‚ 2014). Difference and inequality although
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1. Which of the following could be a value of x‚ in the diagram above? A. 10 B. 20 C. 40 D. 50 E. any of the above 2. Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes per hour‚ or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required? A. 10 B. 15 C. 20 D. 25 E. 30 3. Jo’s collection contains US‚ Indian and British stamps. If the ratio of US to Indian stamps is
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Graded Assignment Unit Test‚ Part 2: Polynomials and Power Functions Answer the questions and show your work. When you are finished‚ submit this assignment to your teacher through the appropriate dropbox basket. (3 pts) 1.) Factor 100x^2 – 49 to factor‚ use the difference of squares formula‚ because both the terms are perfect squares the difference of squares formula is a^2 – b^2 = (a-b)(a+b) therefore 100x^2 – 49 = (10x)^2 – 7^2 = (10x – 7)(10x +7) (5 pts) 2.) Solve x^2 –
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things being “natural” to him. Despite this the use of “quite” doesn’t fully convince the reader that he accepts his outsider status. It could be said that Larkin has not so much an aspiration‚ but a fascination for the norm. Similarly there is a feeling of distance in Here as Larkin describes the “Frinton folk” who “Put him up” for the summer. The use of fricative is showing an immediate lack of intimacy as the literary device uses harsh‚ sharp words. The vague description of “Folk” further confirms
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Documentary *enriches our background knowledge Drama *predisposes us to confront such similar dolorous situations steadily Horror *makes poltroon and coward people face their fears Action *Incarnates our negative hidden power and thus easing us Comedy *makes us feel free *perfect cure for psychological problems Fantasy *it’s a comfortable way for human to escape from this stressing life. Biography *extols unsurpassed
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predicting organizational performance was the ratio of positive statements to negative statements. In the predictive studies of successful marriages by Gottman‚ the best predictor of the sustainability and quality of a marital relationship was the ratio of positive communication to negative communication. Another study by Fredrickson and Losada found that people who experience more positive emotions than negative emotions tend to flourish in mental health and individual performance. Conversationally
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Imagine being chosen for the most important job‚ feeling alone and apart‚ feeling pain and misery‚ and being different from everyone else. Jonas becoming the Receiver of Memory is a punishment. Jonas feels like is is separate from everyone else. He is different. Everyone in the community is the same‚ except him. Some of the rules that Jonas has to follow for being the Receiver of Memory doesn’t let him do some activities that he is familiar with. Those rules allow him do things that he doesn’t want
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intoxicated and when he abused her. The father violently asked her whether she loved him or not. Her younger sister was home‚ but she could not help because she feared his strength and demeanor. Although‚ the three family members were at home‚ a feeling of loneliness struck them all. Peacock tries to convey this frightening scenario to acknowledge that children and women are vulnerable to a man’s strength. Also‚ she reveals how the people who are being abused may feel in this type of situation. Her
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