Explanation Formula used: Quadratic formula: The solution of a quadratic equation of the form a x 2 + b x + c = 0 is given by the formula x = − b ± b 2 − 4 a c 2 a . Calculation: The given equation is x 2 + 2 x y + y 2 − 3 x + 8 y = 0 . Use quadratic formula to simplify the equation y 2 + ( 2 x + 8 ) y + ( x 2 − 3 x ) = 0 . y = − ( 2 x + 8 ) ± ( 2 x + 8 ) 2 − 4 ( 1 ) ( x 2 − 3 x ) 2 ( 1 )

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Chapter 21, Problem 64RE

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To display: The curve of the given equation x2+2xy+y2−3x+8y=0 on a calculator.

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Chapter 21, Problem 63RE

Chapter 21, Problem 65RE

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2. Consider the ODE u' = ƒ (u) = u² + r where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r: (a) Sketch ƒ(u) = u² + r and determine the equilibrium points. (b) Draw the phase line. (d) Determine the stability of the equilibrium points. (d) Plot the direction field and some sample solutions,i.e., u(t) (e) Describe how location of the equilibrium points and their stability change as you increase the parameter r. (f) Using the matlab program phaseline.m generate a solution for each value of r and the initial condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption. (g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to turn in a plot for (g), just describe what happens.

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4. Solve the system of equations and express your solution using vectors. 2x1 +5x2+x3 + 3x4 = 9 -x2+x3 + x4 = 1 -x1-6x2+3x3 + 2x4 = -1

Chapter 21 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 21.1 - Find the distance between (−2, 6) and (5, −3). Ch. 21.1 - Prob. 2PE Ch. 21.1 - Prob. 1E Ch. 21.1 - Prob. 2E Ch. 21.1 - Prob. 5E Ch. 21.1 - In Exercises 5–14, find the distance between the...Ch. 21.1 - Prob. 7E Ch. 21.1 - Prob. 8E Ch. 21.1 - Prob. 9E Ch. 21.1 - Prob. 10E

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To display: The curve of the given equation x 2 + 2 x y + y 2 − 3 x + 8 y = 0 on a calculator.

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To display: The curve of the given equation x2+2xy+y2−3x+8y=0 on a calculator.

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Chapter 21 Solutions