Given
Use a root location technique to determine the maximum of this function. Perform iterations until the approximate relative error falls below 5%. If you use a bracketing method, initial guesses of
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- Find the three unknown on this problems using Elimination Method and Cramer's Rule. Attach your solutions and indicate your final answer. Problem 1. 7z 5y 3z 16 %3D 3z 5y + 2z -8 %3D 5z + 3y 7z = 0 Problem 2. 4x-2y+3z 1 *+3y-4z -7 3x+ y+2z 5arrow_forwardFor the DE: dy/dx=2x-y y(0)=2 with h=0.2, solve for y using each method below in the range of 0 <= x <= 3: Q1) Using Matlab to employ the Euler Method (Sect 2.4) Q2) Using Matlab to employ the Improved Euler Method (Sect 2.5 close all clear all % Let's program exact soln for i=1:5 x_exact(i)=0.5*i-0.5; y_exact(i)=-x_exact(i)-1+exp(x_exact(i)); end plot(x_exact,y_exact,'b') % now for Euler's h=0.5 x_EM(1)=0; y_EM(1)=0; for i=2:5 x_EM(i)=x_EM(i-1)+h; y_EM(i)=y_EM(i-1)+(h*(x_EM(i-1)+y_EM(i-1))); end hold on plot (x_EM,y_EM,'r') % Improved Euler's Method h=0.5 x_IE(1)=0; y_IE(1)=0; for i=2:1:5 kA=x_IE(i-1)+y_IE(i-1); u=y_IE(i-1)+h*kA; x_IE(i)=x_IE(i-1)+h; kB=x_IE(i)+u; k=(kA+kB)/2; y_IE(i)=y_IE(i-1)+h*k; end hold on plot(x_IE,y_IE,'k')arrow_forwardDISCUSSION Before posting to the discussion board, complete the following: The concept of a weak solution of a boundary value problem plays an important role in some numerical solutions including the finite element method. The idea of a "weak solution" can be a rather weak notion. The following problem was presented in lecture 3 of week 8. It is generally not solvable in closed form. 00 on 0arrow_forward2. Answer the question completely and write down the given, required and formula that had been used. Provide graph and accurate/comple solution. The value are: V- 1 X- 5 W- 7 Y- 6 Z- 8arrow_forwardT(1)=199.583 T(2)=198.67 T(3)=195.7569 Solve Using Finite Elemental method only need step wise step and correct ansarrow_forwardFor the equation: a. Secant Method. Use Secant Method to determine the root of the given function up to three iterations use x_1= 0 and xo = 2. Complete the table using the HAND Calculation. Maintain 6 decimal places XH ex = 3 f(x+1) X₁ f(x₁) Eaarrow_forwardA manufacturing company produces two types of products called X and Y. Each product uses four different machines like lathe, drilling, grinding & milling operations. The profit per unit of selling X and Y are 7 RO and 3 RO respectively. Formulate a linear programming model with the given constraints to determine the production volume of each product in order to maximize the total profit (in OR). Solve the following linear programming model by using Graphical method. Subject to, 6X + 4Y < 24 X + 2Y < 6 -X + Y< 1 Y< 2 and X,Y 2 0arrow_forward3. Using the trial function u¹(x) = a sin(x) and weighting function w¹(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx -2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx-2 = 0 u(0) = 1 u(1) = 0arrow_forward8. Use the Lagrange multiplier method to find the point on the line 3x + 8y = 146 that is closest to the origin.arrow_forward3. Using the trial function uh(x) = a sin(x) and weighting function wh(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx - 2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx - 2 = 0 u(0) = 1 u(1) = 0arrow_forward2-the pivot value is the point of the intersection of the row of the leaving variable and the column of the solution. * true falsearrow_forwardQ1 / Reduce the block diagram to the simple form R(s) S 13 S 0. S 1 S C(s)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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