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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Self-Confidence December 31‚ 02:50 Definition • Self-confidence is characterized by: assertiveness‚ optimism‚ eagerness‚ affection‚ pride‚ independence‚ trust‚ the ability to handle criticism‚ emotional maturity‚ and the ability to accurately assess our capabilities. • What is Self-Confidence? – Self-confidence primarily refers to us having a positive and realistic perception of ourselves and our abilities. – A lack of self-confidence‚ on the other hand‚ is characterized by: self- doubt‚ passivity
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One of the first online virtual communities was: Select one: a. AOL. b. Myspace. c. Salon.com. d. The Well. Which of the following is a community of members who self-identify with a demographic or geographic category? Select one: a. affinity community b. sponsored community c. interest-based social network d. practice network A Web site designed to give parents of home-schooled children a common discussion area would be classified as a(n): Select one: a. practice network. b. sponsored
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Vincent Rafael P. Violago 1BSBA2 ACADEMIC READINGS The Triune Brain The first of our three brains to evolve is what scientists call the reptilian cortex. This brain sustains the elementary activities of animal survival such as respiration‚ adequate rest and a beating heart. We are not required to consciously “think” about these activities. The reptilian cortex also houses the “startle centre”‚ a mechanism that facilitates swift reactions to unexpected occurrences in our surroundings. That panicked
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1 Class X: Maths Chapter 2: Polynomials Top Concepts: 1. The graph of a polynomial p(x) of degree n can intersects or touch the x axis at atmost n points. 2. 3. 4. A polynomial of degree n has at most n distinct real zeroes. The zero of the polynomial p(x) satisfies the equation p(x) = 0. For any linear polynomial ax + b‚ zero of the polynomial will be given by the expression (-b/a). 5. The number of real zeros of the polynomial is the number of times its graph touches or intersects x axis. 6. 7
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If one has not heard the title “Woodstein”‚ then I sincerely doubt that they have read a newspaper in their life. This team consist of two journalist-one named Bob Woodward‚ and the other Carl Bernstein-at the peak of their career at the Washington Post. These two young journalist were paired together to cover an attempted break in at Democratic headquarters stationed at the Watergate Hotel in 1972. This usual routine story escalated into one of the most influential stories in America’s History‚
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Graphical Techniques to describe a set of Interval data ( cross-sectional data ) A. Histogram ~ A histogram is created by drawing rectangles whose bases are the class intervals (classes) and and whose heights are the frequencies. Determining number of class intervals No. of Observations No. of Classes 50‚000 17 - 20 ~ Alternatively using Sturges’s formula No. of class intervals = 1 + 3.3 log(n) where n = No. of observations ~ Determining class interval widths Class width = (Largest Observation
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Annotated Bibliography of System Theories BSHS 312 15 Oct 2010 Annotated Bibliography of Systems Theory Team C searched the internet and professional journals of counseling‚ social work‚ employee assistance‚ and other human services fields for two or three articles on systems theory and its application to human services workers. Then Team C had meetings‚ presented and discussed the articles that were found. During our meetings‚ we were able discuss the importance of each article that was
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Unit 2 Paper: A Modern Day Sir Thomas More After reading Utopia‚ I realized problems in today’s society itself. Hythloday compared and contrasted concepts of government between Utopia and European countries all throughout the book. The perfect Utopian society included all‚ but not limited to: rational thought‚ communal property‚ no love of gold‚ no class distinction‚ little to no crime‚ no poverty‚ religious tolerance‚ and little inclination to war. Many of these concepts are completely
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Q2 b) Consider the velocity field V = Ax/(x²+y²)i + Ay/(x²+y²)j in the xy plane‚ where A = 10 m²/s‚ and x and y are measured in meters. i) Show this is an incompressible flow field. ii) Derive an expression for the fluid acceleration. iii) Evaluate the acceleration along the x axis‚ the y axis‚ and along a line defined by y = x. (14 marks) Question 1 ( 15 markah ) a) Define and explain briefly the following : i) velocity potential‚ f (x‚y) ( 4 markah ) ii) stream function
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