(3)Method. Print the code and the answer for an error tolerance &₁ = 0.01%.Problem 5.14: Hint: you can reuse code from above. Print the Matlab code,and clearly indicate your answer. 5.14 Use bisection to determine the drag coefficient needed so thatan 82-kg parachutist has a velocity of 36 m/s after 4 s of free fall.Note: The acceleration of gravity is 9.81 m/s². Start with initialguesses of x = 3 and x₁ = 5 and iterate until the approximaterelative error falls below 2%. Also perform an error check by sub-stituting your final answer into the original equation.

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Answered: (3) Method. Print the code and the…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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3. 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) = 0
3. 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) = 0
We have designed a divide-and-conquer algorithm that runs on an input of size n. This algorithm works by spending O(1) time splitting the problem in half, then does a recursive call on each half, then spends O(n2 ) time combining the solutions to the recursive calls. On small inputs, the algorithm takes a constant amount of time. We want to see how long this algorithm takes, in terms of n to perform the task. (a) First, write a recurrence relation that corresponds to the time-complexity of the above divide and conquer algorithm. (b) Then, solve the relation to come with the worst-case time taken for the algorithm. Please show all work in depth.
15. You are part of a team working in a machine parts mechanic's shop. An important customer has asked your company to provide springs with a very precise force constant k. To measure the spring constant, you fasten two of the springs between the ends of two very long wires of length L, separated by the unstretched length l of the springs as shown in Figure P29.15. The specific attachment method that you use insulates the springs from the wires so that no current passes through the springs. You lay the apparatus flat on a table and then pass a current of magnitude I through the wires, in opposite directions. As a result the springs stretch by a distance d and come to equilibrium. You determine an expression for the spring constant in terms of L, I, l, and d. Figure P29.15
Only part d. please show all work.
f(x)=-0.9x? +1.7x+2.5 Calculate the root of the function given below: a) by Newton-Raphson method b) by simple fixed-point iteration method. (f(x)=0) Use x, = 5 as the starting value for both methods. Use the approximate relative error criterion of 0.1% to stop iterations.
How do you code this fixed point iteration in MATLAB? Just assume values for r, R. c is the speed of light.
QUESTION 1 Solve the following differential equation in Matlab using ode45.m. Use time interval of 0.1 second. (Don't use options in ode45 to change teh tolerance.) d²x (1) +x(t) dx(1) dt +x(t)=0 dx x(0) = 0, =1. dt =0 What is x(t=0.8)? 0.653 ○ 0.726 ○ 0.498 0.547 ○ 0.651 ○ 0.895
Given the data below: Xo = 1 X1= 2 x2 = 4 Axo) = 2 Ax1) = 3 Ax2 : = 8 (i) Calculate the second-order interpolating polynomial using the method of the Newton's interpolating polynomial. (ii) Use the interpolating polynomial in (i) to calculate the approximated/interpolated functional value at x = 3, i.e., (3). (iii)Calculate the percentage relative error if the true value of f(3) is 4.8.
For 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) Ea
33.2 solve using MATLAB. do not use syms.
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