CHAPTER 7 ARITHMETIC AND GEOMETRIC PROGRESSIONS 7.1 Arithmetic Progression (A.P) 7.1.1 Definition The nth term of an arithmetic progression is given by ‚ where a is the first term and d the common difference. The nth term is also known as the general term‚ as it is a function of n. 7.1.2 The General Term (common difference) Example 7-1 In the following arithmetic progressions a. 2‚ 5‚ 8‚ 11‚ ... b. 10‚ 8‚ 6‚ 4‚ ... Write (i) the first term‚ (ii) the common difference‚
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Math SL Investigation Type 2 Stellar Numbers This is an investigation about stellar numbers‚ it involves geometric shapes which form special number patterns. The simplest of these is that of the square numbers (1‚ 4‚ 9‚ 16‚ 25 etc…) The diagram below shows the stellar triangular numbers until the 6th triangle. The next three numbers after T5 would be: 21‚ 28‚ and 36. A general statement for nth triangular numbers in terms of n is: The 6-stellar star‚ where there are 6 vertices‚ has
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Complex Numbers and Applications ME50 ADVANCED ENGINEERING MATHEMATICS 1 Complex Numbers √ A complex number is an ordered pair (x‚ y) of real numbers x and y. For example‚ (−2.1‚ 3.5)‚ (π‚ 2)‚ (0‚ 0) are complex numbers. Let z = (x‚ y) be a complex number. The real part of z‚ denoted by Re z‚ is the real number x. The imaginary part of z‚ denoted by Im z‚ is the real number y. Re z = x Im z = y Two complex numbers z1 = (a1‚ b1) and z2 = (a2‚ b2) are equal‚ written z1 = z2 or (a1‚ b1) = (a2‚ b2)
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Soul music is the sound of an unforgettable era. There are a number of memorable hits that continue to get serious radio play even 30 to 40 years after their release. Here are some of the greatest soul album ever made. Number Ten: Rick James- Street Songs‚ 1981 This songwriter‚ singer‚ guitarist‚ and producer all rolled into one became known for something called "punk-funk." Quite an innovative concept! Number Nine: Jr. Walker and the Allstars- Shotgun‚ 1965 Walker started out as a solo saxophone
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Estimated Number of Animal and Plant Species on Earth Believe it or not‚ there are about 950‚000 species of insects No one knows for sure how many species of animals exist on Earth. In fact‚ some 10‚000 species of animals are discovered each year‚ with over one and a half million species already described. Projections for the total number of species on Earth range from 2 million to 50 million. Animal group Number of species Vertebrates Amphibians 6‚199 Birds 9‚956 Fish 30‚000 Mammals
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be wrong. Here are some of the most common misconceptions out there about bisexuality. Number Seven: ’It’s Only a Phase’ A lot of people assume that bisexual experimentation is just something you try once in college. This is a stereotype that may be true for some‚ but is usually completely untrue. Studies show that very few women who identified as bisexual changed their orientation later on in life. Number Six: Bisexuals are More Likely to Have STDs For some reason‚ this is a prejudice that persists
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2x+1* 2x+1 b) (2x+1)(2x+1)(2x+1)= (2x+1)(2x+1) 8x^3+8x^2+2x+4x^2+4x+1 Combine like terms 8x^3+12x^2+6x+1 5.5 46. (a) (x4y2)2 (-2 x2y-2)3 94. Distance to the Moon The moon is about 240‚000 miles from Earth. (a) Write this number in scientific notation. (b) If a rocket traveled at 4 * 10^4 miles per hour‚ how long would it take for it to reach the moon? 2.4 X 10^5 miles b. v = x/t Formula for velocity vt = x
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either from errors in DNA or from the harming impacts of mutagens‚ for example‚ chemicals and radiation‚ which respond with DNA and change the structures of individual nucleotides. All cells possess DNA-repair enzymes that attempt to minimize the number of mutations that occur. These enzymes work in two ways. Some are pre-replicative and look the DNA for nucleotides with irregular structures‚ these being replaced before replication happens; others are post-replicative and check recently synthesized
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Companionship Can Change a Life Louis Lowry skillfully captures a time where food shortages were a given‚ fear was ever present‚ riots were synonymous with regular life‚ and death eminent in her historical drama Number the Stars‚ which emphasizes how a devoted friend can change the life of another.Lowry elaborates on the lengths friends go to protect one another by engaging the reader with Annemarie’s thoughts‚pathos expressed through the character emotions‚ symbolism of Ellen’s necklace and growing
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DETERMINATION OF SAPONIFICATION AND IODINE NUMBERS OF SOME LIPIDS A.L. ASCANO1 C.V. OPONDA1 1INSTITUTE OF BIOLOGY UNIVERSITY OF THE PHILIPPINES‚ DILIMAN‚ QUEZON CITY‚ PHILIPPINES DATE PERFORMED: FEBRUARY 19‚ 2013 INSTRUCTOR’S NAME: FRANCESCA N. BELTRAN _____________________________________________________________________________________ ABSTRACT _____________________________________________________________________________________ INTRODUCTION Lipids are long aliphatic hydrocarbon chains
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