Question 1 R* At 1 :-0--0--0--4 1 1 -> -> And set {91,92,93,94 } want to...
Problem 1 An inverted pendulum driven by a d-c motor is governed by the following differential and algcbraic equa tions: (a) Determine the transfer function of the process. (b) It is proposed to control the process using "proportional control": where yr is a constant reference value. Determine the value Kmir for which the gain K must exceed in order that the closed-loop system be stable. (c) Determine the value of K for which the magnitude of the error is less...
QUESTION 6 (20 Marks) CO CO6 Marks20 Use five decimals points throughout your calculations when solving this question. Evaluate the performance of fourth order Runge-Kutta (RK-4) by using different values of h using the given function. The analytical value of y-r+21+1-0.5e Rungo-Kutta 4 Oder Equation Page 12/21 Firal Esam, SKKK 2133 1617-1 You are given an option to select h癰 0.5. a 45, 0.4, 0.35, 0.3 and h 0.25), to solve the (a) given function. Which h can give the...
Question 1: Let R be the set of real numbers and let 2R be the set of all subsets of the real numbers. Prove that 2 cannot be in one-to-one correspondence with R. Proof: Suppose 2 is in one-to-one correspondence with R. Then by definition of one- to-one correspondence there is a 1-to-1 and onto function B:R 2. Therefore, for each x in R, ?(x) is a function from R to {0, 1]. Moreover, since ? is onto, for every...
Question 1 (4 Marks) A weird vector space. Consider the set R+ = {2 ER: I >0} = V. We define addition by zey=ry, the product of x and y. We use the field F=R, and define multiplication by cor = xº. Prove that (V, e, Ro) is a vector space. ONLY HAND IN : i) The zero vector ii) what is 6-7 iii) proof of e) of the axioms.
the two photos above are information need so solve the question below Practice 08: Reactions With Multiple Pathways Key In the presence of O ferrous ion, Fe is oxidized to ferrie lon, Fet. The rate law for this reaction depends on the pH, following one rate law when the pH is greater than 3.6 and a different rate law when the pH IN below 3.5. Part 1: pH > 3.5 The following initial rates (defined is greater than 3.5. ***/dt)...
Problem 5 [10 points] Set up integrals for both orders of integration. Use the more convenient order to evaluate the integral over the plane region R: A R region bounded by y 0, y x, x 4 R 1+x2 a) [2 points] First order b) [2 points] Second order c) [6 points] Evaluate the integral using the more convenient order Problem 5 [10 points] Set up integrals for both orders of integration. Use the more convenient order to evaluate the...
L-8 29 -15 22] 111 4 3 2 1 10. The differential equations of high order: 2 And boundary conditions fo)-0, f' (0)-0, f'(5)-1, g(o)-1.5, g(5)-1 Can be solved using The Shooting-Newton-Raphson and multivariable Runge-Kutta for a value of (y-1.7), re write the system of equations in the canonical form (i.e. as a set of ODES of first order and its boundary conditions). It is not required to solve the equations, just list the system of first order differential equations...
I do not need the two metrics to be proved (that they are a metric). Problem 2. Let C[0, 1] be the set of all continuous functions from [0, 1] to R. For any f, g є Cl0, 11 define - max f(x) - g(z) and di(f,g)-If(x) - g(x)d. a) Prove that for any n 2 1, one can find n points in C[O, 1 such that, in daup metric, the distance between any two points is equai to 1....
I want the solution for this. Stat 352 Homework Set 2 Fall 2019: Conditional Probability and Independence Deadline: Monday November 11, 2019 (1) In throwing two dice with the sample space Define the following events on : = {(x,y):x, y = 1,2,3,4,5,6). A = {sum less than 4) = {(x, y): x + y < 4, x, y = 1,2,3,4,5,6) B = {first number is 1) = {(x,y): x = 1, y = 1,2,3,4,5,6) C = {sum of number is...
Question 8 (Chapters 6-7) 12+2+2+3+2+4+4-19 marks] Let 0メS C Rn and fix E S. For a E R consider the following optimization problem: (Pa) min a r, and define the set K(S,x*) := {a E Rn : x. is a solution of (PJ) (a) Prove that K(S,'). Hint: Check 0 (b) Prove that K(S, r*) is a cone. (c) Prove that K(S,) is convex d) Let S C S2 and fix eS. Prove that K(S2, ) cK(S, (e) Ifx. E...