Overview of formulas Formulas are equations that perform calculations on values in your worksheet. A formula starts with an equal sign (=). For example‚ the following formula multiplies 2 by 3 and then adds 5 to the result. =5+2*3 A formula can also contain any or all of the following: functions‚ references‚ operators‚ and constants. Parts of a formula Functions: The PI() function returns the value of pi: 3.142... References: A2 returns the value in cell A2. Constants: Numbers or text
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PROVING IDENTITIES Proving Identities Proving an identity is simply verifying that one member of the equation is identically equal to the other member. It is important to know that there is no general rule in proving an identity. The proper choice of the fundamental identities and algebraic operations will certainly make the verification process easier. Mathematical competence and familiarity with the fundamental identities are the basic tools that will greatly facilitate the transformations
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1 10/10/01 Fermat’s Little Theorem From the Multinomial Theorem Thomas J. Osler (osler@rowan.edu) Rowan University‚ Glassboro‚ NJ 08028 Fermat’s Little Theorem [1] states that n p −1 − 1 is divisible by p whenever p is prime and n is an integer not divisible by p. This theorem is used in many of the simpler tests for primality. The so-called multinomial theorem (described in [2]) gives the expansion of a multinomial to an integer power p > 0‚ (a1 + a2 + ⋅⋅⋅ + an ) p = p k1 k2 kn a1 a2
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Arithmetic is the ABC of math. Addition‚ subtraction‚ multiplication‚ and division are the basics of math and every math operation known to humankind. In one way or another‚ every equation‚ graph‚ and an enormous amount of other things can be broken down into the ABC’s of math‚ the four basic operations. As people say‚ math is a language‚ and addition subtraction‚ multiplication‚ and division are its alphabet‚ along with the number line as well. The properties are basically‚ proven ways to apply
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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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Name/Student Number: Jaqueline Albuerne JM0508824 Score: ______ / ______ Directions: Answer the questions below. Make sure to show your work when applicable. 1. Solve the absolute value equation. Check your solutions. | 5x + 13| = –7 5x + 13 = -7 5x = -20 X = -4 2. Simplify the expression below. 6n2 - 5n2 + 7n2 6 – 5 + 7 = 8 =8n2 3. The total cost for 8 bracelets‚ including shipping was $54. The shipping charge was $6. Write an equation that models the cost of
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POLYNOMIALS IN DAILY LIFE Polynomials are a combination of several terms that can be added‚ subtracted or multiplied but not divided. While polynomials are in sophisticated applications‚ they also have many uses in everyday life. Although many of us don’t realize it‚ people in all sorts of professions use polynomials every day. The most obvious of these are mathematicians‚ but they can also be used in fields ranging from construction to meteorology. Polynomials in Construction and Material
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Yvanna Escalera PT 1420 Unit 5 Assignment 1 Homework Short answer 1. Conditionally executed means it is performed only when a certain condition is true. 2. You would use a dual alternative decision structure. 3. You would use a nested decision structure. 4. The AND operator connects two Boolean expressions into one compound expression. Both must be true for the compound expression to be true. 5. The OR operator connects two Boolean expressions into one compound expression. One or both
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2.2.1 Reed-Solomon Codes Irving Reed and Gus Solomon [37] on January 21‚ 1959‚ submitted a paper which was published in June 1960 in the Journal of the society for Industrial and Applied mathematics with the title “Polynomial codes over certain finite fields”. This paper introduced a new class of error correcting codes that are now called Reed-Solomon codes. Reed-Solomon codes[38][39] are constructed and decoded by using finite field arithmetic. Finite fields were the discovery of French mathematician
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Higher Arithmetic Higher arithmetic‚ also known as the theory of numbers‚ is known for its basics of the natural numbers‚ simple numbers. The numbers‚ 1‚ 2‚ and 3 are numbers that are known as natural numbers. H. Davenport of Cambridge University once said “…in all the records of ancient civilizations there is evidence of some preoccupation with arithmetic over and above the needs of everyday life” (Introduction). The theory of numbers being a science‚ is simply just a creation invented for the
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