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New Year

The JVI mathematician (MJVI) finds a friend with whom he had not talked for a long time. The friend was intensely seeking the Being of Time and thought he had found its essence. He did not know that his friend was engaged in the Individual's Game of Life and thought he had discovered the nature of Time. MJVI. Dear friend, how much time has passed.
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Trigonometric Integrals

Integration of Sine and Cosine Powers In the reduction formulas section, we obtain the formulas: In the case where n = 2, these formulas are: Alternative forms for these integration formulas can be obtained using trigonometric identities. that come from the double-angle formulas These identities give rise to the integration of sine and cosine products. If m and n are positive integers, then the integral can be calculated in a number of ways, depending on whether m and n are odd or even.
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Product of same base powers

Consider the product. Note that: Thus: Based on the example above, we can conclude that: To multiply powers of the same base, we must conserve the base and add the exponents. Generically: Next: Division of powers of the same base
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Decimal fractions

Note the fractions: The denominators are powers of 10. Thus: Decimal fractions are all fractions that have powers of 10 in the denominator. The French Viète (1540 - 1603) developed a method for writing decimal fractions. Instead of fractions, Viète would write comma numbers.
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The natural family

0 It was a chubby boy His nickname was little ball But he was very cute And was looking for a sweetheart. One day strolling Down the street found 1 A cute girl Who unlike him was skinny 0 Fell in love with 1 And 1 fell in love with 0 Love as 1, 0 had found no 1 knew that his love for 0 was right.
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