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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The unique culinary art of dim sum means "dot-hearts"‚ small treats that touch the heart‚ and originated in China hundreds of years ago. It is said to have started along the Silk Road where farmers‚ laborers and travelers often stopped at roadside teahouses to have afternoon tea‚ regain sustenance and relax‚ an olden days version of the local neighborhood bar At first‚ it was considered inappropriate to combine tea with food‚ because people believed that this would lead to excessive weight gain.
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In Hong Kong‚ Dim Sum is a traditional food.There are many elderly go to Dim Sum restaurants regularly‚ not only in the morning‚ but also at lunch time. In addition to satisfy their appetite‚ it is already a part of life for some people who go to Dim Sum restaurant every day in Hong Kong. In my view‚ Dim Sum should be the best item to represent Hong Kong culture. It is because Dim Sum exemplify unique characteristic of Hong Kong culture. In the following‚ I will introduce some of the characteristics
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