RAMANUJAN He was born on 22na of December 1887 in a small village of Tanjore district‚ Madras. He failed in English in Intermediate‚ so his formal studies were stopped but his self-study of mathematics continued. He sent a set of 120 theorems to Professor Hardy of Cambridge. As a result he invited Ramanujan to England. Ramanujan showed that any big number can be written as sum of not more than four prime numbers. He showed that how to divide the number into two or more squares or cubes. when
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an algebraic expression in brackets eg. z1 z2 = (a + bi)(x + yi) = ax + ayi + bxi + byi2 = ax - by + (ay + bx)i (as i2 = -1) Division by a complex number is a very similar process to ‘rationalising’ surds – we call it ‘realising’ [pic] Argand Diagrams We can represent complex numbers on an Argand diagram. This similar to a normal set of x and y axes except that the x axis represents the real part of the number and the y axis represents the
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-2<2x<4 -1<x<2 Method 2 If ∣a+b∣ ≥x∣a+b∣ >x= a+b≥x ORa+b≤-x a+b>x OR a+b<x e.g. ∣2x-1∣≥3= 2x-1≥3 OR 2x-1≤-3 2x≥3+1 2x≤-3+1 2x≥4 2x≤-2 x≥2 x≤-1 Rationalizing Any fraction involving surds needs to have the denominator rationalised. Rationalise 23 23 = 23 ×1 =23 ×33 note that33 =1 =233×3 =233 The denominator is rationalised now Beta Trigonometry Basic rules Hypotenuse Adjacent Sin = Opposite/hypotenuse
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|TOK Essay Title : “That which can be asserted without evidence can be dismissed without evidence” Do you agree ? | |Word Count: 1240 Words | Evidence is a thing or things that help in attaining knowledge. The statement “that which can be asserted without evidence can be dismissed without evidence” means that it is possible
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0. Introduction The question of the relation between the individual and society is one of the most central questions in the literature of American Transcendentalism. Most of Ralph W. Emerson ’s Essays deal with it as well as the work of Henry D. Thoreau. Margaret Fullers ’feminist Transcendentalism ’ propagated emancipation of women from social norms‚ and George Ripley tried to develop an alternative to society in ’Brook Farm ’‚ a social experiment that aimed at giving the individual more freedom
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safe to hold the leads of the resistors. However‚ given a large enough resistance to be measured and enough current a human body can be harmed. We can now use the formula for Rt to calculate the resistance of a parallel circuit between ones body‚ infinite resistance‚ and R1. (Rt) B. Voltage: The main goal of exercise B is to teach students to safely and accurately take voltage measurements. Using the same circuit that was built to determine Rtot‚ we can take measurements of the voltage on multiple
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MANIPAL INSTITUTE OF TECHNOLOGY A constituent institute of Manipal Academy of Higher Education (MAHE) - Deemed University MANIPAL – 576 104‚ KARNATAKA‚ INDIA. Subject Code: ECE – 101/201 BASIC ELECTRONICS COURSE MATERIAL For 1ST & 2ND Semester B.E. (Revised Credit System) DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING CONTENTS Module 1. – SEMI CONDUCTOR THEORY Mr. Hemanth Kumar A.R.‚ Lecturer‚ Pg. 27 – 49 Pg. 1 – 26 Module 2. – PN JUNCTION DIODE AND ITS APPLICATIONS
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amount after (4 marks) 6. (a) (b) Expand ( x + 5)( x − 3) . Solve the inequality ( x + 5)( x − 3) ≤ x 2 − 2 x + 5 and represent the solution graphically. (6 marks) 7. Rationalize 6 3+ 2 and express the answers with the simplest surd form. (5 marks) 8. 9. Solve 27 2 x −1 = 9 x . In a class‚ there are 20 boys and n girls. are 71‚ 62 and 67 respectively. (a) (b) Find the value of n. After mark adjustment‚ each of the mark of x students is increased by 1. If the new mean
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http://countrystudies.us/india/34.htm. Last accessed 8th Feb 2014. 10. Kuhn‚ Thomas‚ S.‚ "The Structure of Scientific Revolutions"‚ Second Edition‚ Enlarged‚ The University of Chicago Press‚ Chicago‚ 1970(1962). 11. K. A. Tsokos (2010). Physics for the IB Diploma. 5th ed. Latimer Trend‚ UK: Cambridge University Press. p514-16. 12. Levy‚ A. (2006). Science is Cumulative. Available: http://abstractnonsense.wordpress.com/2006/10/23/science-is-cumulative/. Last accessed 8th Feb 2014. 13. Shuttleworth‚ M
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E FFECTIVENESS OF INDUSTRIALISED BUILDING SYSTEM (IBS) IMPLEMENTATION FOR MALAYSIAN CONSTRUCTION INDUSTRY MARDHIAH BINTI ZAWAWI A project report submitted in partial fulfillment of the requirements for the award of the degree of Master of Science (Construction Management) Faculty of Civil Engineering Universiti Teknologi Malaysia NOVEMBER 2009 A BSTRACT Generally‚ the used of Industrialised Building System (IBS) in construction industry throughout the world has positive perceptions
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