While the ultimate goal is the same‚ to determine the value(s) that hold true for the equation‚ solving quadratic equations requires much more than simply isolating the variable‚ as is required in solving linear equations. This piece will outline the different types of quadratic equations‚ strategies for solving each type‚ as well as other methods of solutions such as Completing the Square and using the Quadratic Formula. Knowledge of factoring perfect square trinomials and simplifying radical expression
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Colleen Cooper Solving Quadratic Equations MAT 126 Survey of Mathematical Methods Instructor: Kussiy Alyass October 1‚‚ 2012 Solving Quadratic Equations Using correct methods to solve quadratic equations can make math an interesting task. In the paper below I will square the coefficient of the x term‚ yield composite numbers‚ move a constant term and see if prime numbers occur. I will use the text and the correct formulas to create the proper solutions of the two projects that are
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------------------------------------------------- Equations and Problem-Solving * An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance travelled before take-off. ------------------------------------------------- Solutions Given: a = +3.2 m/s2 | t = 32.8 s | vi = 0 m/s | | Find:d = ?? | d = VI*t + 0.5*a*t2 d = (0 m/s)*(32.8 s) + 0.5*(3.20 m/s2)*(32.8 s)2 d = 1720 m ------------------------------------------------- Equations and Problem-Solving * A
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Solving systems of linear equations 7.1 Introduction Let a system of linear equations of the following form: a11 x1 a21 x1 a12 x2 a22 x2 ai1x1 ai 2 x2 am1 x1 am2 x2 a1n xn a2 n x n ain xn amn xn b1 b2 bi bm (7.1) be considered‚ where x1 ‚ x2 ‚ ... ‚ xn are the unknowns‚ elements aik (i = 1‚ 2‚ ...‚ m; k = 1‚ 2‚ ...‚ n) are the coefficients‚ bi (i = 1‚ 2‚ ...‚ m) are the free terms
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Solving Exponential and Logarithmic Equations Exponential Equations (variable in exponent position) 1. Isolate the exponential portion ( base exp onent ): Move all non-exponential factors or terms to the other side of the equation. 2. Take ln or log of each side of the equation. • Make sure to use ln if the base is “e”. Then remember that ln e = 1 . • Make sure to use log if the base is 10. • If the base is neither “e” nor “10”‚ use either ln or log‚ your choice.. 3. Bring the power (exponent)
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To solve a system of equations by addition or subtraction (or elimination)‚ you must eliminate one of the variables so that you could solve for one of the variables. First‚ in this equation‚ you must look for a way to eliminate a variable (line the equations up vertically and look to see if there are any numbers that are equal to each other). If there is lets say a –2y on the top equation and a –2y on the bottom equation you could subtract them and they would eliminate themselves by equaling zero
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Applications: Graphing Simultaneous Equations − − − − Relating linear graphs and simultaneous equations Analysing graphs Practical applications of linear graphs Writing algebraic equations Jane Stratton Objectives: • Use linear graphs to solve simultaneous equations • Use graphs of linear equations to solve a range of problems • Translate worded problems into graphical and algebraic form Finding the Solution to an Equation from a graph • Finding solutions to an equation when we have a graph is easy‚ we
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QUADRATIC EQUATIONS Quadratic equations Any equation of the form ax2 + bx + c=0‚ where a‚b‚c are real numbers‚ a 0 is a quadratic equation. For example‚ 2x2 -3x+1=0 is quadratic equation in variable x. SOLVING A QUADRATIC EQUATION 1.Factorisation A real number a is said to be a root of the quadratic equation ax2 + bx + c=0‚ if aa2+ba+c=0. If we can factorise ax2 + bx + c=0‚ a 0‚ into a product of linear factors‚ then the roots of the quadratic equation ax2 + bx + c=0 can be found
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Balancing Equations Balancing equations is a fundamental skill in Chemistry. Solving a system of linear equations is a fundamental skill in Algebra. Remarkably‚ these two field specialties are intrinsically and inherently linked. 2 + O2 ----> H2OA. This is not a difficult task and can easily be accomplished using some basic problem solving skills. In fact‚ what follows is a chemistry text’s explanation of the situation: Taken from: Chemistry Wilberham‚ Staley‚ Simpson‚ Matta Addison Wesley
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imaginary axis of the earth‚ with one revolution representing one day. However‚ this axis that goes through the earth from the North Pole to the South Pole is not just up and down‚ but is on a tilt of 23.5°. This tilted axis is the primary cause of the four seasons of the year - spring‚ summer‚
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