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Transcript
EGR 1101 Unit 2 Quadratic Equations in Engineering (Chapter 2 of Rattan/Klingbeil text) Mathematical Review In linear equations, which we studied last time, the two variables (x and y) are both raised to the first power: y 5 x 10 In a quadratic equation, the dependent variable is raised to the first power and the independent variable is raised to the second power. For example: y 2 x 3x 10 2 Graphical Interpretation The graph of a quadratic equation is a parabola. In MATLAB: > fplot('2*x^2 + 3*x + 10', [-10, 10]) Two Common Questions Involving Quadratic Equations 1. 2. Given a quadratic equation, find the value of y for a particular value of x. (Easy!) Given a quadratic equation, find the value of x for a particular value of y. (Harder!) Three Methods 1. 2. 3. We’ll study three ways to answer the second type of question: Factoring Quadratic formula Completing the square Today’s Examples 1. 2. 3. Height of a projectile Power and current in a circuit Resistors in parallel Some Symbols Used in Electrical Drawings Resistor: Voltage Source: Lamp (light bulb): Circuit containing these three components: Three Basic Electrical Laws Kirchhoff’s Voltage Law (KVL): Around any closed loop in a circuit, the sum of the voltage rises is equal to the sum of the voltage drops. • Ohm’s Law: For a resistor, voltage equals current times resistance: V = IR • Power Law: For any component, power equals current times voltage: P = IV Resistors in Series or Parallel If two resistors are connected in series (end-to-end), total resistance is the sum of the two resistances: If two resistors are connected in parallel (connected at both ends), total resistance is given by the product-over-sum rule: