–––– Run ∆y y 2 - y1 ––– = ––––––– ∆x x 2 - x1 1- Solve for y to put the equation in slope intercept form. 2- Plot the y-intercept. 3- Using the slope as a fraction‚ rise y and run x to get second point. 4- Graph the line. Ex: 2x+3y=12 -2x -2x ––––––––– 3y=-2x+12 –– –––– 3 3 y= -2/3x+4 m= -2/3 b= 4 Horizontal and Vertical Lines: - A Horizontal Line has the form y=#. (In an equation of a horizontal line‚ there is no x) - The slope of a horizontal line is 0. Picture:
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mass-spring-damper system. The governing differential equation of a mass-spring-damper system is given by m x + c x + kx = F . Taking the Laplace transforms of the above equation (assuming zero initial conditions)‚ we have ms 2 X ( s ) + csX ( s ) + kX ( s ) = F ( s )‚ X ( s) 1 ⇒ = . 2 F ( s ) ms + cs + k Equation (1) represents the transfer function of the mass-spring-damper system. Example 2 Consider the system given by the differential equation y + 4 y + 3 y = 2r (t )‚ where r(t) is the input to
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Differential Equations 1 2 NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS Introduction Differential equations can describe nearly all systems undergoing change. They are ubiquitous is science and engineering as well as economics‚ social science‚ biology‚ business‚ health care‚ etc. Many mathematicians have studied the nature of these equations for hundreds of years and there are many well-developed solution techniques. Often‚ systems described by differential equations are so complex
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Straight Lines‚ Pair of Lines & Circles A straight line through the point A 3‚ 4 is such that its intercept between the axes is bisected at A . It’s equation is 1. (a) 4 x 3 y 24 Ans: a (b) 3x 4 y 25 (c) x y 7 (d) 3x 4 y 7 0 Sol: By formula required equation is given by x y 2 4 x 3 y 24 3 4 2. The equation of the line which is the perpendicular bisector of the line joining the points 3‚ 5 and 9‚3 is (a) 4 x 3 y 14 0 Ans: d Sol: A 3‚
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Point-Slope Form of the Equation of a Line 9 Section 2.3 Linear Functions and Slopes Write the point-slope form of the equation of the line with slope of 3 that passes through (-1‚2). Substitute into the point-slope form; y-y1 m( x x1 ) y 2 3( x 1) y 2 3( x 1) 10 Section 2.3 Linear Functions and Slopes Solving in Both Forms A. Write the equation in point slope form of the line with slope 4 that passes through the point (4‚-3). B. Then solve the equation for y. x1 y1 y-y1 = m(x-x1)
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and the rate of deceleration (dec). D=W/g dec (5) With the total amount of drag forces on the aircraft at various angles of attack‚ the coefficient of drag (C_D) can be calculated. This calculation process follows similar equation to the coefficient of lift (C_L) in equation 4; however‚ it includes the force of drag (D) instead of the force of lift (L). The information needed for this calculation was collected from the flight
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Design of a Polystyrene Plant for Differing Single-Pass Conversions November 25‚ 2013 Introduction Polystyrene is one of the most widely used plastics‚ with applications ranging from food packaging to appliances to manufacturing (Maier). On an industrial scale‚ polystyrene is derived from its monomer‚ styrene. This is achieved by free-radical polymerization of a solution of monomer‚ polymer‚ and initiator. This reaction is a multistep radical reaction that
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one-dimensional‚ one-phase flow equations As an introduction to reservoir simulation‚ we will review the simplest one-dimensional flow equations for horizontal flow of one fluid‚ and look at analytical and numerical solutions of pressure as function of position and time. These equations are derived using the continuity equation‚ Darcy’s equation‚ and compressibility definitions for rock and fluid‚ assuming constant permeability and viscosity. They are the simplest equations we can have‚ which involve
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17. In a sample of solid Al(NO3)3‚ the ratio of aluminum ions to nitrate ions is (1) 1:1 (2) 1:2 (3) 1:3 (4) 1:6 19. What is the total number of atoms in (NH4)2SO4? (1) 10 (2) 11 (3) 14 (4) 15 22. Write the correct formula for the following binary ionic compounds. (a) Lithium fluoride LiF (b) Calcium oxide CaO (c) Aluminum nitride AlN (d) Beryllium chloride BeCl2 (e) Potassium iodide KI (f) Aluminum oxide Al2O3 23. Write the correct formula for the following binary molecular
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Investigation 7: How Can The Waste Be Made Useful? February 20‚ 2014 Mian Yang Tuesday 8:30am Group #6 Steven Hengen‚ Joe Wahl‚ Colleen Strom‚ Nicole D Introduction: Chemical interactions can often lead to the production of environmentally unsafe byproducts. If the byproducts have no use‚ they are disposed as waste. Waste disposal companies make profit by collecting and disposing large amounts of these unused byproducts. These companies often concentrate the byproduct solutions so that they
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