Pre-Calculus—Prerequisite Knowledge &Skills III. Polynomials A. Exponents The expression bn is called a power or an exponential expression. This is read “b to the nth power” The b is the base‚ and the small raised symbol n is called the exponent. The exponent indicates the number of times the base occurs as a factor. Examples—Express each of the following using exponents. a. 5 x 5 x 5 x 5 x 5 x 5 x 5 = b. 8 x 8 x 8 x 8 x 8 x 8 x 8
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any input from the user after executed. Also‚ include your variable names and definitions. Be sure to describe any necessary formulas and sample calculations. The variables in this program will be declared are num_1‚ num_2 and will be used as integers. The formula that will be used in this program is num_1 * num_2 adding 1 each repetition using num_2 = num_2 +1 One of the overlooked features of this program is the “Write” statement that makes the proceeding count occur on the next line not
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ANSWERS/HINTS 345 APPENDIX 1 ANSWERS/ HINTS EXERCISE 1.1 1. (i) 45 3. 8 columns 4. An integer can be of the form 3q‚ 3q + 1 or 3q + 2. Square all of these integers. 5. An integer can be of the form 9q‚ 9q + 1‚ 9q + 2‚ 9q + 3‚ . . .‚ or 9q + 8. (ii) 196 (iii) 51 2. An integer can be of the form 6q‚ 6q + 1‚ 6q + 2‚ 6q + 3‚ 6q + 4 or 6q + 5. EXERCISE 1.2 1. 2. 3. (i) 2 × 5 × 7 (iv) 5 × 7 × 11 × 13 (i) LCM = 182; HCF = 13 (i) LCM = 420; HCF = 3 2 (ii) 22 × 3 × 13 (v) 17 × 19 × 23 (ii) LCM = 23460;
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in the above equations -12+13=23 02+13=13 S = {2/3‚ 1/3‚ 5/3‚ 17/3‚ 50/3} 22+13=53 42+13=173 72+13=503 “Q8: Construct a proof that a) If m is odd‚ then m^2 is odd b) for all integers m and n‚ if m is even and n is odd‚ the m+n is odd” a) If m is odd‚ then m=2k + 1 We have to prove that m^2
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will be placed in the sections where the circles overlap. The universal set is often the "type" of values that are solutions to the problem. For example‚ the universal set could be the set of all integers from -10 to +10‚ set A the set of positive integers in that universe‚ set B the set of integers divisible by 5 in that universe‚ and set C the set of elements -1‚ - 5‚ and 6. The Venn diagram at the left shows two sets A and B that overlap. The universal set is U. Values that belong
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programming. (Hint: The square root to be used for testing should be rounded up‚ i.e.‚ take the ceiling function) Draw (by hand or using Computer CAD tools‚ such as Visio) a flowchart for the testing algorithm. In this lab‚ we assume that the test integer is smaller than 100‚000‚ (if it is greater than 100‚000‚ your code simply returns to indicate that it is a non-prime number). Include a snapshot of your hand-drawn flowchart or computer generated one and all other prelab requirements in your lab
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Introduction to Modern Algebra David Joyce Clark University Version 0.0.6‚ 3 Oct 2008 1 Copyright (C) 2008. 1 ii I dedicate this book to my friend and colleague Arthur Chou. Arthur encouraged me to write this book. I’m sorry that he did not live to see it finished. Contents 1 Introduction 1.1 Structures in Modern Algebra . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Operations on sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Fields . . . . .
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Home Maintenance Team C PRG/211 March 18‚ 2011 Home Maintenance Living in the bay area makes your home one of‚ if not the most‚ expensive investment you will ever make. With housing prices sky-rotting above half a million‚ it behooves you to maintain your house. When you maintain it on a regular basis‚ you avoid the much larger expenses of structural issues that come from putting things off. For example‚ a crack in the shower or bath tub in the second floor of your two story home will
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values shown. Sandra throws one die‚ and her score is the square of the value shown. What is the probability that Sandra’s score will be strictly higher than Eric’s score? a. b. c. d. 137/216 17/36 173/216 5/6 9. What is the largest integer that divides all three numbers 23400‚272304‚205248 without
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PS Solution from Forums 2 1. Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30‚ what is the remainder that n leaves after division by 30? (A) 3 (B) 12 (C) 18 (D) 22 (E) 28 How to approach this Problem? Positive integer n leaves a remainder of 4 after division by 6 --> --> 4‚ 10‚ 16‚ 22‚ 28‚ ... Positive integer n leaves a remainder of 3 after division by 5 --> --> 3‚ 8‚ 13‚ 18‚ 23‚ 28‚ ... - we
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