of “Complex and Imaginary Numbers” and its applications. I chose the topic “Complex and Imaginary Numbers” because I am interested in mathematics that is hard to be pictured in your mind‚ unlike geometry or equations. An imaginary number is the square root of a negative number. That is why they are called imaginary‚ what René Descartes called them‚ because he thought such a number could not exist. In this paper‚ I will discuss how complex numbers and imaginary numbers were discovered‚ the interesting
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Section 4.1 Divisibility and Modular Arithmetic 87 CHAPTER 4 Number Theory and Cryptography SECTION 4.1 Divisibility and Modular Arithmetic 2. a) 1 | a since a = 1 · a. b) a | 0 since 0 = a · 0. 4. Suppose a | b ‚ so that b = at for some t ‚ and b | c‚ so that c = bs for some s. Then substituting the first equation into the second‚ we obtain c = (at)s = a(ts). This means that a | c‚ as desired. 6. Under the hypotheses‚ we have c = as and d = bt for some s and t . Multiplying
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OCR supplied materials: None Other materials required: • Scientific or graphical calculator • Geometrical instruments • Tracing paper (optional) * A 5 0 1 0 1 * INSTRUCTIONS TO CANDIDATES • • • • • • • Write your name‚ centre number and candidate number in the boxes above. Please write clearly and in capital letters. Use black ink. HB pencil may be used for graphs and diagrams only. Answer all the questions. Read each question carefully. Make sure you know what you have to do before starting
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THE REAL NUMBER SYSTEM The real number system evolved over time by expanding the notion of what we mean by the word “number.” At first‚ “number” meant something you could count‚ like how many sheep a farmer owns. These are called the natural numbers‚ or sometimes the counting numbers. Natural Numbers or “Counting Numbers” 1‚ 2‚ 3‚ 4‚ 5‚ . . . * The use of three dots at the end of the list is a common mathematical notation to indicate that the list keeps going forever. At some point‚ the
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universal precautions. Suppose the spread of a direct contact disease in a stadium is modeled by the exponential equation P(t) = 10‚000/(1 + e3-t) where P(t) is the total number of people infected after t hours. (Use the estimate for e (2.718) or the graphing calculator for e in your calculations.) 1. Estimate the initial number of people infected with the disease. Show how you found your answer. Answer: A total of 474 people would be initially infected. Equation: p(0)=10‚000/(1+3^3) ~ 474
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8 l SUFFIXES l l l The Suffixes are letters added to the end of words to make new words. (The suffixes change the word class of the words they attached to) - Common Noun Suffixes: 1. –er / -or: these suffixes are added to Verbs to derive nouns of a person who does the a action. Verbs + –er ــــــــــــــــــــــــ> noun of a person
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his study about the human voice he opened a workshop. He also did important work in communication for the deaf. Throughout his life he held more than 18 patents. Bell was one of the primary inventors of the telephone. Through many years of experimentation with sound waves he created the telephone. Bell got the idea from the phonautograph version that he created. The phonautograph worked by drawing sound waves so this made him think that it was possible to create electrical currents that correlated
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2. Category of Number of the Noun. Regular – one. Plural – more than one. Regular Plurals: 1. Nouns ending in vowels & voiced consonants - -s(bee-bees‚ dog-dogs‚ [z]) 2. Voiceless consonants - -s(book-books‚ [s]) 3. –s‚-sh‚-ss‚-ch‚-x‚-z - -es (actress-actresses‚ [iz]) 4. –o: -es-hero-heroes. But: -os: after a vowel – bamboos‚ embryos‚ folios‚ kangaroos‚ radios‚ studios‚ zoos. In proper names – Romeos‚ Eskimos‚ Filipinos. In abbreviations - kilos‚ photos‚ pros(professional). Also: pianos
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Assignment answers 1. The educator as researcher‚ scholar and lifelong learner. (EDRHODG) 1) c 2) E 3) E 4) C 5) E 6) E 7) D 8) A 9) A 10) E 11) E 12) A 13) B 14) D 15) E 16) D 17) D 18) B 19) E 20) D 21) C 22) D 23) E 24) C 25) A 26) E 27) E 28) E 29) E 30) D 31) A 32) E 33) A 34) D 35) C 2. The educator in a pastoral Role (EDPHOD8) 1) 4 2)
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Introduction The 19th century developments of firstly the telegraph‚ and later the telephone‚ opened a gateway to a new‚ closer‚ more interdependent world. For a country as large as the United States‚ with a population now scattered from east to west‚ the implications were tremendous. The infamous tyranny of time and distance had been conquered. Widespread acceptance and appreciation‚ however‚ were not immediate. Both inventions met with initial scepticism‚ ridicule‚ and even elements of fear.
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