PPT-Theory of Equations

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 . e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations 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 . using Elimination. Steps:. 1. Place both equations in Standard Form, A. x . + B. y . = C.. 2. Determine which variable to eliminate with Addition or Subtraction.. 3. Solve for the variable left.. Hands-On Algebra with Fractions and Mixed Numbers. Connecting to Algebra . When you hear the word “algebra”, what do you think of?. What are some things you know about algebra?. How might you use algebra in real-life?. I can identify the products and reactants in a chemical reaction.. I can state the law of conservation of matter.. I can determine the number of each atom in a compound based on subscripts and coefficients.. Re-Made Version. Coupled Motion. Coupled motion problems are problems in which the movement of one object directly impacts the motion of another object.. We have already briefly covered this topic when talking about pulleys.. By: Morgan Shade . Absolute Value. The number’s distance away from zero. Can’t be a negative number. Examples:. │3│= 3. │-10│= 10. │0│= 0. Absolute Value Equations. Isolate the Absolute Value. 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). 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 “ . Unit 3. What are . parametrics. ?. Normally we define functions in terms of . one . variable. – . for example, . y . as a function of x. . . Suppose in a graph, each (x, y) depended on a . third variable . Ch. 1.6. Absolute Value Equations and Inequalities . EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. . Bell Work. Solve the inequality. Graph the solution. . 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. Introduction. This chapter gives you several methods which can be used to solve complicated equations to given levels of accuracy. These are similar to methods which computers and calculators will use, and hence can be used in computer programming. Net ionic equations are useful in that they show only those chemical species directly . participating in . a chemical . reaction. The keys to being . able to . write net ionic equations are the ability to recognize monatomic and polyatomic ions, .