PPT-Theory of Equations

Chapter 4 In the 17th century the belief in the algebraic solvability in radicals of all polynomial equations seems to have been in little dispute The question of solvability was not an issue . 4 Di64256erence Equations At this point almost all of our sequences have had explicit formulas for their terms That is we have looked mainly at sequences for which we could write the th term as for some known function For example if 1 3 then i orgpublicinformationatefaqsgammaandexposurehtml It is a very good white paper by George Chabot CHP PHD that takes you from electric charge produced in the air by the photons to a usable equation and also explains where the simplified rule of thumb Rh Lesson Objective:. An equation is like a set of scales.. To keep it balanced, whatever you. do to one side you must do to the other.. Use this idea to solve equations like:. 3x + 1 = x + 7 . 2 (3x + 1) = 3 (x – 2). Formulation and Solution Strategies. Review of Basic Field Equations. Compatibility . Relations. Strain-Displacement Relations. Equilibrium . Equations. Hooke’s . L aw. 15 Equations for 15 Unknowns . I.3 Variables, expressions, and equations. Objective. Essential Question. Key Vocab. To translate words into algebraic expressions and equations. In what order are the terms written in the expression “less than?” (i.e. 5 less than 4). Chapter . 6. Algebraic . Unsolvability. . of the . Quintic. :. limiting . the class of solvable equations. . In spite of the efforts of RUFFINI and GAUSS, the search for algebraic solution . formulae for . Parts of a chemical equation:. Reactants. : a substance present at the beginning of a chemical reaction. (Left side). Products. : a substance that is produced during a chemical reaction (Right Side). Substitution and Elimination. Elimination. Arrange the equations in STANDARD FORM. . . Your goal is to find a way to eliminate one of the variables so you can solve a one-variable equation.. . If you read from left to right . 10 . “is greater than “ . 5. . X. If you read from right to left . 5. . “is less than “ . 10. . X. If you read from left to right . 5. . “is less than “ . Problem 1. There are 25 toys in a playground. . The toys are either bicycles (2 wheels) or tricycles (3 wheels). . In total in the playground there are 61 wheels. . How many bicycles are in the playground?. By graphing. Definition. A system of linear equations, aka linear system, consists of two or more linear equations with the same variables.. x + 2y = 7. 3x – 2y = 5. The solution. The solution of a system of linear equations is the ordered pair that satisfies each equation in the system. . Standards 8-10. Graphs of Quadratic Functions . U- Shaped Graph . Vertical y=x. 2. or Horizontal x=y. 2. Positive Negative . Summary: The of a Quadratic Function is U shaped. . Positve. If you read from left to right . 10 . “is greater than “ . 5. . X. If you read from right to left . 5. . “is less than “ . 10. . X. If you read from left to right . 5. . “is less than “ . Examples:. . 1). . . x 3 = 15. . 2) p – 5 = 20. 3) 2d = 16. 4). . = 24.  . Multi-Step Equations. Examples—. 5). 2p 15 = 29. 6). 14 – 3n = -10. 7). 27 = -9(y 5). 8). 7a – 3a 2a – a = 16.