Exercise 4.1 2. Establish each of the following for all n ≥ 1 by the Principle of Mathematical Induction. Solution a) S(n): ==‚ S(1): = = =1‚ So S(1) is true. Assume S(k): = Consider S(k+1) = = +=-1+= -1. Hence‚ it follows that S(k)⇒S(k + 1) is true for all n ∈ Z+ by the Principle of Mathematical Induction. b) S( n) for n=1‚ = 2 = 2+(1-1). So S(1) is true. Inductive Step: assume S(k)is true‚ for some (particular) k ∈ Z+—that is‚ assume that =2+(k-1). For n=k+1‚ = + (k+1)
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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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OprahphicationNation “It is said that the United States has become the most influential country in the history of the world because of this nation’s ability to communicate our popular culture. “ (Winfrey‚ O.‚ & Lowe‚ J.‚1998‚ pg.1) After over 20 years of hosting her own talk show‚ Oprah Winfrey has become one of the most influential people in the world. Whether it bd her entertaining spirit or uplifting words of advice‚ America has become addicted to Opraphacation‚ in other words "public confession
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1. Software refers to: Programs 2. Logical errors are mistakes that cause the program to produce erroneous results. (True/False) True 3. Another term for programs is: Software 4. Java source files end with the .class extension. (True/False) False 5. The major components of a typical computer system consist of: -Secondary storage devices -The CPU -Input/Output devices -Main memory 6. The contents of a variable cannot be changed while the program is running. (True/False) False 7. The two
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w w ap eP m e tr .X w UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS for the guidance of teachers 0420 COMPUTER STUDIES 0420/11 Paper 11‚ maximum raw mark 100 This mark scheme is published as an aid to teachers and candidates‚ to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began‚ which
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"Canada-United States Border Drug Threat Assessment." Public Safety Canada. Oct. 2004. 15 Feb. 2008 <http://www.publicsafety.gc.ca/prg/le/bs/uscabdta-en.asp>. Canada and the United States are firmly committed to the fight against illicit drugs and their two-way movement across our shared border. The strong relationship between our two governments‚ and in particular‚ our respective law enforcement agencies on this issue is a model of international cooperation. Traffickers of each of the illicit
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Submittal Date: __________________________ Proposal Approval Sign-off: ____________________ _______________________ ____________ ECET493L Professor Signature Date ____________________ _______________________ ____________ Senior Project Advisor Signature Date Executive Summary Hospitals have always had certain needs which must be met in order to properly treat their patients. Patient medical information needs to be maintained in a way that is secure yet
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UML. 4 marks. j) Q2 Answer ALL parts. Total marks awarded for this question: 30. a) b) What are the characteristics of good software? 5 marks. Describe the unique features of the Object-Oriented paradigm‚ and illustrate polymorphism with pseudocode or coding fragments. 5 marks. Distinguish multiple classification from generalisation‚ and illustrate with a diagram. 5 marks. How are contracts supported in software engineering‚ and illustrate with a diagram. You should briefly discuss support
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with the lowest cost per inch b. Identify the processing needed to convert the inputs to the outputs. A: Area of each pizza in square inches = pi * (diameter / 2)^2 Cost per square inch = cost / area c. Design an algorithm in pseudocode to solve this problem. Make sure to include steps to get each input and generate each output. 1. Get diameter of first size pizza and cost of first person 2. Find area of first pizza 3. Find cost per square inch of first pizza 4. Get diameter
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outputs‚ and any additional requirements. • To satisfy the needs of the customer. 2. Plan the logic • Plans the logical steps to the program and decides what steps to include and how to order them. • There are two common design tools: flowchart and pseudocode. • The programmer breaks a large programming problem into reasonable units. • These reasonable units are typically called as modules‚ subroutines‚ procedures‚ functions or methods. • The process of breaking down a large program into modules is called
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