6 Systems Represented by Differential and Difference Equations Recommended Problems P6.1 Suppose that y 1(t) and y 2(t) both satisfy the homogeneous linear constant-coeffi cient differential equation (LCCDE) dy(t) + ay(t) = 0 dt Show that y 3 (t) = ayi(t) + 3y2 (t)‚ where a and # are any two constants‚ is also a solution to the homogeneous LCCDE. P6.2 In this problem‚ we consider the homogeneous LCCDE d 2yt + 3 dy(t) + 2y(t) = 0 dt 2 dt (P6.2-1) (a) Assume that a solution to
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requires just 1 gallon per acre. What is the maximum profit he can make? SOLUTION TO PROBLEM NUMBER 1 let x = the number of acres of wheat let y = the number of acres of barley. since the farmer earns $5‚000 for each acre of wheat and $3‚000 for each acre of barley‚ then the total profit the farmer can earn is 5000*x + 3000*y. let p = total profit that can be earned. your equation for profit becomes: p = 5000x + 3000y that’s your objective function. it’s what you want to maximize the constraints
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because they knew what was coming. There really weren’t any issues that were brought up with in both of the interviews
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number of different persuasive techniques in order to try and persuade the viewer to believe that this is the case. He uses certain visuals‚ music‚ sequences the scenes in a specific order and uses facts and opinions to achieve this. The first scene that shows persuasive techniques is "The Wonderful World" sequence. In this sequence‚ it shows horrible images of dead people‚ with various facts and figures shown at the bottom of the screen. In the background‚ the song "What a Wonderful World" by Louis
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LINEAR ALGEBRA Paul Dawkins Linear Algebra Table of Contents Preface............................................................................................................................................. ii Outline............................................................................................................................................ iii Systems of Equations and Matrices.............................................................................................
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Duality in Linear Programming 4 In the preceding chapter on sensitivity analysis‚ we saw that the shadow-price interpretation of the optimal simplex multipliers is a very useful concept. First‚ these shadow prices give us directly the marginal worth of an additional unit of any of the resources. Second‚ when an activity is ‘‘priced out’’ using these shadow prices‚ the opportunity cost of allocating resources to that activity relative to other activities is determined. Duality in linear programming
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Symbolic processing is the most powerful feature of matlab. We can solve even most complex equations very easily in matlab that are very difficult to solve by hand. Matlab performs symbolic processing to obtain answers in the form of expressions. Symbolic processing is the term used to describe how a computer performs operations on mathematical expressions. To improve engineering designs by modeling it with mathematical expressions that do not have specific parameter values are very difficult to
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DIFFERENTIAL EQUATIONS 2.1 Separable Variables 2.2 Exact Equations 2.2.1 Equations Reducible to Exact Form. 2.3 Linear Equations 4. Solutions by Substitutions 2.4.1 Homogenous Equations 2.4.2 Bernoulli’s Equation 2.5 Exercises In this chapter we describe procedures for solving 4 types of differential equations of first order‚ namely‚ the class of differential equations of first order where variables x and y can be separated‚ the class of exact equations (equation
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Linearity: A linear correlation coefficient factor was obtained between the peak area used and the absorbance Verses concentrations of lamivudine‚ zidovudine and nevirapine. The calibration curves were linear for concentrations between 15-150 µg/ml. The linearity of the calibration curves was validated by the values of the correlation coefficients (r2). The correlation coefficients were 0.999 for lamivudine‚ 0.999 zidovudine and 0.999 for nevirapine. The results of the linearity experiment are listed
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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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