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- Newton Method - solve by hand Solve by hand function bellow using Newton method. Repeat 5 times. (5 iterations) f(x) = x°-7.x+43: The function f(x)= max x, searches for the maximum value between a number. Prove formally that the function f(x) is convex.Write a program that does the following: 1- Ask the user to enter the number of variables on a Linear- System 2- Ask the user to enter matrix elements 3- Ask the user enter vector elements 4- Ask the user to enter initial approximation for the solution 5- Solve the linear-system using Jacobi iteration and show the results and number of iterations needed 6- Solve the linear-system using Gauss-Seidel iteration and show the results and number of iterations needed 7- Show which of the two methods is better
- 3. Given that x is an integer, what does if(x % 2 == 0) check for?Equation does have x in it. Other.The spring in the figure below is stretched from its equilibrium position at x = 0 to a positive coordinate xo. ko HINT x = 0 x = xo PE sn PE 50 The force on the spring is F and it stores elastic potential energy PESO. If the spring displacement is tripled to 3x, determine the ratio of the new force to the original force, and the ratio of the new to the original elastic potential energy, Fo Fo PESO (a) the ratio of the new force to the original force, PE ST PE SO (b) the ratio of the new to the original elastic potential energy,
- please write your answers legibly2. Find the value of square root of 5 using a maximum of 4 iterations of Newton Raphson method. (hint: x=5(1/2) = x2-5=0 ).Q10: Using (ode45, ode23, or ode15s), solve the below dynamic electrical system differential equation. 1. The charge Q(t) on the capacitor in the electrical circuit shown satisfies the differential equation where d²Q dQ 1 +R- + √ √e dt2 dt L = 0.5 R = 6.0 C= 0.02 and V(t) is the applied voltage. V(t) = V(t), henrys is the coil's inductance ohms is the resistor's resistance farads is the capacitor's capacitance ellee (i) Is the circuit oscillatory? (ii) If V(t) = 24 sin(10r) volts and Q(0) = 0 = Q'(0), find Q(t). (iii) Sketch the transient solution, the steady state solution, and the full solution Q(t).
- For f(1) = r³ – 4, perform 3 iterations of Newton's method with starting point ro = 2. (By hand, but use a calculator.) Calculate the solution (r* = 4/3) on a calculator and find the errors and percentage errors of ro, 11, T, and 13. Use enough digits so that you do not falsely conclude the error is zero. Put the results in a table.What is the value of x after the 5th iteration of performing fixed-point iteration on the equation f(x) = x3 –x – 2? (Use the equation where the root converges and use an initial guess of 1) Group of answer choices 1.2599 1.5206 1.5158 1.5213-A laboratory test was performed to obtain the change of concentration with time. Test results are shown on the table. The student noticed that one datum at t=20s is missing. Concentration Time (s) (mg/L) 194 - Use interp1() function to predict the missing value using different methods: 10 246 15 369 >linear 25 384 > cubic > spline • Plot the results on the same figure. 30 271 40 24