Class: X REAL 1. 2. 3. Subject : Mathematics Assignment No. 1 4. 5. 6. 7. 8. 9. 10. 11. 12. NUMBERS Show that square of any odd integer is of the form of 4p+1 for some integer p. Show that (12)n‚ where n is a natural number cannot end with the digit 0 or 5. Prove that each of the following are irrational : 1 a] 7 − 3 2 b] c) 3 + 5 5 +2 Use Euclid’s division algorithm‚ to find the HCF of a] 455 & 42 b] 392 & 267540 Express each of the following as a non-terminating recurring decimal a] 1/7 b] 13/44
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What is the closed-form expression for the below sum of Geometric Progression (GP) sequence‚ S n ? S n a aR aR 2 ... aR n (1) where R is called the common ratio (between consecutive terms) of the GP sequence. The reason why we want to derive a closed-form expression for S n is for the sake of calculating the summation‚ or otherwise we need to add all terms one-by-one together‚ which does not make a sense if the number of terms is huge‚ say a million terms! Most importantly
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INFORMATION TECHNOLOGY ASSIGNMENT ON ALGORITHM Done by Densil Hamilton INTRODUCTION This Assignment was done to show the methods of algorithm. It outlines the meaning of algorithm and steps to be carried out to complete a give problem. Examples were also shown for the methods of representing algorithm. What is an Algorithm? An algorithm consists of a set of explicit and unambiguous finite steps which‚ when carried out for a given set of initial conditions‚ produce the corresponding
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The RSA Algorithm Evgeny Milanov 3 June 2009 In 1978‚ Ron Rivest‚ Adi Shamir‚ and Leonard Adleman introduced a cryptographic algorithm‚ which was essentially to replace the less secure National Bureau of Standards (NBS) algorithm. Most importantly‚ RSA implements a public-key cryptosystem‚ as well as digital signatures. RSA is motivated by the published works of Diffie and Hellman from several years before‚ who described the idea of such an algorithm‚ but never truly developed it. Introduced at the
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TIME VALUE OF MONEY SUMS 1. A finance company advertises that it will pay a lumpsum of Rs 8000 at the end of 6 yrs to investors who deposit annually Rs 1000 for 6 yrs. What is the rate implicit in this offer? 2. You want to take a trip to the moon which costs Rs 10‚00‚000-the cost is expected to remain unchanged in nominal terms. You can save annually Rs 50000 to fulfil this desire. How long will you have to wait if your savings earn an interest of 12 percent p.a.? 3. Suppose a firm borrows
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Addition and Subtraction of Integers Addition of Positive Integers Consider the addition of 2 + 3. The plus sign‚ +‚ tells us to face the positive direction. So‚ to evaluate 2 + 3‚ start at 2‚ face the positive direction and move 3 units forwards. This suggests that: Positive integers can be added like natural numbers. Addition of Negative Integers Consider the addition of (–2) + (–3). The plus sign‚ +‚ tells us to face the positive direction. So‚ to evaluate
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This file contains the exercises‚ hints‚ and solutions for Chapter 5 of the book ”Introduction to the Design and Analysis of Algorithms‚” 2nd edition‚ by A. Levitin. The problems that might be challenging for at least some students are marked by ◃; those that might be difficult for a majority of students are marked by . Exercises 5.1 1. Ferrying soldiers A detachment of n soldiers must cross a wide and deep river with no bridge in sight. They notice two 12-year-old boys playing in a rowboat by the
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ANACOR The ANACOR algorithm consists of three major parts: 1. 2. 3. A singular value decomposition (SVD) Centering and rescaling of the data and various rescalings of the results Variance estimation by the delta method. Other names for SVD are “Eckart-Young decomposition” after Eckart and Young (1936)‚ who introduced the technique in psychometrics‚ and “basic structure” (Horst‚ 1963). The rescalings and centering‚ including their rationale‚ are well explained in Benzécri (1969)‚ Nishisato (1980)
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PageRank Algorithm December 9‚ 2012 Abstract This paper dicsusses the PageRank algorithm. We carefully go through each step of the algorithm and explain each procedure. We also explain the mathematical setup of the algorithm‚ including all computations that are used in the PageRank algorithm. Some of the topics that we touch on include the following‚ but not limited to‚ are: linear algebra‚ node analysis‚ matrix theory‚ and numerical methods. But primarily this paper concerns itself with
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to please some guy I also need feminism because when my little cries‚ gets upset‚ or happy or expresses any emotion he’s told by family members (also guys) to stop acting like a girl. As if being a means keeping things bottled up and being tough all the time or that being a girl or even a little feminine is bad Girls and boys are expected to act a certain way always to please someone else or to be someone else. To act like anything but them. And that is why I need gender equality. And why boys
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