3.6 Determine the positive root of the polynomial x3 + 0.6x2 + 5 .6-4.8 .(a) Plot the polynomial and choose a point near the root for the first estimate of the solution. Using Newton's method, determine the approximate solution in the first four iterations.(b) From the plot in part (a), choose two points near the root to start the solution process with the secant method. Determine the approximate solution in the first four iterations. 15:47X3.11 Problems3.5the ecout theNumerical Method...3.4 The lateral surface area, S, of a cone is given by:S = πr√√r²+h²where r is the radius of the base and h is the height. Determine the radius of acone that has a surface area of 1800 m² and a height of 25 m. Solve by usingthe fixed-point iteration method with r = S/(√√√² + h²) as the iteration func-tion. Start with r = 17 m and calculate the first four iterations.CopiarSelecionar Tudoo3.6 Determine the positive root of the polynomial x³ +0.6x² + 5.6 — 4.8 .(a) Plot the polynomial and choose a point near the root for the first estimate of the solution. Using New-ton's method, determine the approximate solution in the first four iterations.(b) From the plot in part (a), choose two points near the root to start the solution process with the secantmethod. Determine the approximate solution in the first four iterations.3.7 The equation 1.2x³ + 2x²-20x-10 = 0 has a root between x = -4 and x = -5. Use these valuesfor the initial two points and calculate the next four estimates for the solution using the secant method.Destacar3.8 Find the root of the equation √x + x² = 7 using Newton's method. Start at x = 7 and carry out thefirst five iterations.3.9 The equation x³-x-e¹-2 = 0 has a root between x = 2 and x = 3.(a) Write four different iteration functions for solving the equation using the fixed-point iteration method.(b) Determine which g(x) from part (a) could be used according to the condition in Eq. (3.30).(c) Carry out the first five iterations using the g(x) determined in part (b), starting with x = 2.x =3.10 The equation f(x) = x²-5x¹/3 + 1 = 0 has a root between x = 2 and x = 2.5. To find the root byusing the fixed-point iteration method, the equation has to be written in the form x = g(x). Derive two pos-sible forms for g(x) - one by solving for x from the first term of the equation, and the next by solving forx from the second term of the equation.Solve the following system of nonlinear equations:(a) Determine which form should be used according to the condition in Eq. (3.30).(b) Carry out the first five iterations using both forms of g(x) to confirm your determination in part (a).3.11 The equation f(x) = 2x³-4x² - 4x-20 = 0 has a root between x = 3 and x = 4. Find the root byusing the fixed-point iteration method. Determine the appropriate form of g(x) according to Eq. (3.30).Start the iterations with x = 2.5 and carry out the first five iterations.3.12 Determine the positive root of the equation cosx-0.8x² = 0 by using the fixed-point iterationmethod. Carry out the first five iterations.Solve the following system of nonlinear equations:5-2x³ + 3y² +42 = 05x²+3y³-69 = 0Use Newton's method. Start at x = 1, y = 1, and carry out the first five iterations.Use the fixed-point iteration method. Use the iteration functions y =- (³y² + 42)¹/³.Start at x = 1, y = 1, and carry out the first five iterations.x²+2x+2y²-26 = 02x³y2 +4y-19 = 089Use Newton's method. Start at x =Use the fixed-point iteration method. Start at x = 1 y = 1Chapter 3 Solving Nonlinear Equations5x2+69)\1/33be freet Gue iterations.and carry out the first five iterationsand

(a).To determine the positive root of the polynomial x^3 + 0.6x^2 + 5.6x - 4.8, let's start by…

Answered: 3.6 Determine the positive root of the…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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3.6 Determine the positive root of the polynomial x3 + 0.6x2 + 5 .6-4.8 .
(a) Plot the polynomial and choose a point near the root for the first estimate of the solution. Using New
ton's method, determine the approximate solution in the first four iterations.
(b) From the plot in part (a), choose two points near the root to start the solution process with the secant method. Determine the approximate solution in the first four iterations.