then x0 = 5 -2y for every y‚ which is not possible. 8. Determine whether the following argument is valid: pr qr (p q) ________ r Ans: Not valid: p false‚ q false‚ r true 9. Prove that the following is true for all positive integers n: n is even if and only if 3n2 8 is even. Ans: If n is even‚ then n 2k. Therefore 3n2 8 3(2k)2 8 12k2 8 2(6k2 4)‚ which is even. If n is odd‚ then n 2k 1. Therefore 3n2 8 3(2k 1)2 8 12k2 12k
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CLASS VII CBSE-i Introduction to Rational Numbers nt’s Section Stude Shiksha Kendra‚ 2‚ Community Centre‚ Preet Vihar‚Delhi-110 092 India UNIT-3 CLASS VII UNIT-3 CBSE-i Mathematics Introduction to Rational Numbers Shiksha Kendra‚ 2‚ Community Centre‚ Preet Vihar‚Delhi-110 092 India The CBSE-International is grateful for permission to reproduce and/or translate copyright material used in this publication. The acknowledgements have been included
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Quadratic Equation For the equation ax2 + bx + c = 0‚ –b ± √ b2 – 4ac x = –––––––––––––– . 2a Binomial Theorem (a + b)n = an + (n) a 1 n – 1b + (n) a 2 n – 2 b2 +…+ ( nr ) a n – r br + … + b n‚ where n is a positive integer and –––––––– ( nr ) = (n –n! r! . r)! 2. TRIGONOMETRY Identities sin2 A + cos2 A = 1. sec2 A = 1 + tan2 A. cosec2 A = 1 + cot2 A. Formulae for ∆ ABC c b a –––– = –––– = –––– . sin A sin B sin C a2 = b 2 + c2 – 2bc cos A. 1 ∆ = – bc sin A
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Let’s Discuss (p. 1.30) The solution obtained by using the factor method is the exact value of the root. However‚ the solution obtained by using the graphical method is an approximation only. Classwork Classwork (p. 1.8) (a) Integer (b) Natural number (c) Negative integer (d) Terminating decimal (e) Recurring decimal (f) Fraction (g) Irrational number Classwork (p. 1.11) 1. (a) When x = 3‚ L.H.S. == 0 R.H.S. = 0 Since L.H.S. = R.H.S.‚ 3 is a root of the equation. (b) When x = 6
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OLYMPIC TIN HỌC HUFLIT 2014 BÀI 11 (NC) UNION-FIND DISJOINT SETS THEORY In computing‚ a disjoint-set data structure‚ also called a union–find data structure or merge–find set‚ is a data structure that keeps track of a set of elements partitioned into a number of disjoint (nonoverlapping) subsets. It supports two useful operations: o Find: Determine which subset a particular element is in. Find typically returns an item from this set that serves as its "representative"; by comparing the
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September 25‚ 2010 Revised June 1‚ 2011 A number of graph coloring problems have their roots in a communication problem known as the channel assignment problem. The channel assignment problem is the problem of assigning channels (non-negative integers) to the stations in an optimal way such that interference is avoided‚ see Hale [4]. The radio coloring of a graph is a special type of channel assignment problem. Here we develop a technique to find an upper bound for radio number of an arbitrary
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INTERNATIONAL PUBLIC SCHOOL‚ BHOPAL HOLIDAY – HOMEWORK (2013-2014) CLASS-X ENGLISH Section- A: BBC: Reading Comprehension: Ex.1‚ 2 & 3. Section- B: BBC: Writing Skills: E-mail 1 & 2; Letter writing 1 & 2; Speech 1 & 2; Article 1& 2. Section- C: BBC: Grammar: Preposition‚ Voice‚ Speech‚ Tenses. Section- D: 1. Value based: Which poem do you appreciate the most – ‘The frog and the nightingale’ or ‘Mirror’? Why? Write the literary devices used in that poem. Write about the poet. (150 words) 2. Extrapolatory:
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SPOOLER 5. (TCO 2) A variable name should always have _____. (Points : 5) double quotes spaces only lowercase letters a descriptive identifier 6. (TCO 2) If a variable holds the value "Ferrari‚" what is its data type? (Points : 5) Numeric Integer Floating point String 7. (TCO 2) What is the multiplication operator? (Points : 5) = ^ * % 8. (TCO 2) What is the best choice for a variable name representing a bank balance? (Points : 5) bankBalance balance bb b 9. (TCO 2) What
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Introduction to Prepare For Math Symbol Definitions: Symbol is denoted the unspoken words in math. Symbol can be explained as the operation which helpful to make the expression. The symbol in the expression has to make definitions for the expression. In this article‚ we see about the math symbols and its definitions and how to use the math symbols in expression. Prepare for Math Symbol Definitions: Prepare Basic Math Symbol: Basic Math Symbol Spell - math Symbol Math Symbol in expression Definitions
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Overtime hours (a float: OverTimeHours) Item Net pay (a float: NetPay) Output: Gross pay (real: GrossPay) Design Main Module Declare EmployeeID as String Declare HourlyRate as real Declare RegHours as integer Declare GrossPay as integer Declare Tax as real Declare Parking Declare OverTimeHours Delcare NetPay Write “hourly rate” Write “This program computes the total hours” Call Input Data Module Call Perform Calculations Module Call Output
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