A: First split into partial fractions [pic] Write out the first three terms and last two or three terms. Last term will be the one where you substitute in r=n. [pic] See what cancels [pic] • Properties of the roots of polynomial equations If [pic] and [pic] are the roots of quadratic equation [pic]‚ then [pic] [pic] If [pic]‚ [pic] and [pic] are the roots of cubic equation [pic]‚ then [pic] [pic] [pic] If [pic]‚ [pic]‚ [pic] and [pic] are
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COMPUTER-AIDED INSTRUCTION ON SELECTED TOPICS ON MATHEMATICS IN HIGH SCHOOL A Thesis Presented To the Faculty of the College Of Science Bulacan State University In Partial Fulfillment of the Requirements for the Degree Bachelor of Science in Mathematics Major in Computer Science By: Jad Maverick A. Vicente Jeffrey D. Madlang-Awa Patrick Y. Cabazal March 2014 APPROVAL SHEET The thesis entitled “COMPUTER-AIDED INSTRUCTION ON SELECTED TOPICS
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A Brief History of Computing - Mechanical Computing Devices © Copyright 1996-2005‚ Credit to: Stephen White Source: http://trillian.randomstuff.org.uk/~stephen//history/timeline-MECH.html#17 For reading purposes only by: Lornilo S. Alimpuangon Pictures: credit to Google Hardware History Overview • • • • • Modern computing can probably be traced back to the ’Harvard Mk I’ and Colossus (both of 1943). Colossus was an electronic computer built in Britain at the end 1943 and
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Aron Persaud Absolute Value -How far a number is from zero. Example "-6" is 6 away from zero‚ but "-6" is also 6 away from zero. So‚ the absolute value of 6 is 6‚ and the absolute value of -6 is also 6. The symbol "|" is placed either side to mean "Absolute Value"‚ so we can write: |-6| = 6 Associative property- mathematical expression means that the order of the operations can be changed or regrouped so long as the operands (numbers or terms) are not changed. Example addition: (6 + 3) + 4
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The Complete Set of Lyrics Susan E. Cantey scantey@cinci.rr.com © 2010 Happy Snappy Algebra by Susan Cantey On the road I often think “How long until I sleep?” Then I see how many miles are left‚ And divide by my vehicle’s speed‚ But when I’m driving in the car‚ And junior says “Are we there yet?” If daddy answers “About an hour‚” He’s not doing algebra. Happy snappy algebra‚ Do it all the time‚ Happy snappy algebra‚ It’s so fine. Once I needed some cement‚ So I
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Dq 2 week 1 I would explain that when multiplying polynomial is when all the variables have integer exponents that are positive. This works with addition‚ subtraction and multiplication. It has to be possible to write the equation without division for it to be a polynomial. This is an example of what a polynomial looks like: 4xy2+3X-5. To multiply two polynomials‚ you must multiply each term in one polynomial by each term in the other polynomial‚ and then add the two answers together. After
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understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients). a. Explain how long division of a polynomial expression by a binomial expression of the form x − a‚ a∈ I ‚ is related to synthetic division. b. Divide a polynomial expression by a binomial expression of the form x − a‚ a∈ I ‚ using long division or synthetic division. c. Explain the relationship between the linear factors of a polynomial expression and the zeros
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correct answer is B. Q2) Use the following information to answer the next question. The given figure shows the graph of polynomial‚ p(x) = x2 + kx − 15 What is the value of k? A. 3 B. 2 C. −2 D. −3 Answer In the given figure‚ the graph intersects x-axis at two points‚ (−3‚ 0) and (5‚ 0). Therefore‚ x = −3 and x = 5 are the zeroes of the polynomial p(x). Substituting x = 5 in p(x)‚ we obtain p(5) = (5)2 + k(5) − 15 = 0 ⇒ 25 + 5k − 15 = 0 ⇒ 5k = −10 ⇒ k = −2 Thus‚ the value
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Reaction Paper Ric Michael P. De Vera IV- Rizal Mr. Norie Sabayan I. A and B Arabic mathematics: forgotten brilliance? Indian mathematics reached Baghdād‚ a major early center of Islam‚ about ad 800. Supported by the ruling caliphs and wealthy individuals‚ translators in Baghdād produced Arabic versions of Greek and Indian mathematical works. The need for translations was stimulated by
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we cannot prove it yet. We can find the limit at of any polynomial or rational function‚ as long as that rational function is defined at (so we are not dividing by zero). That is‚ must be in the domain of the function. Limits of Polynomials and Rational functions If is a polynomial or rational function that is defined at then We already learned this for trigonometric functions‚ so we see that it is easy to find limits of polynomial‚ rational or trigonometric functions wherever they are defined
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