Consider the following long division problem. 5x-3)25x3 +7x2 + 10x -5 Begin the division process by...
a, b, c & d . please this is one full problem. Consider the division of two polynomials: f(x)+(x-c). The result of the synthetic division process is shown here. Write the polynomials representing the (a) Dividend, (b) Divisor, (c) Quotient, and (d) Remainder. 5 -13 17 -19 46 10 -15 10 -45 2 -3 2 -9 2 1 Part 1 of 4 (a) The dividend is Part 2 of 4 (b) The divisor is Part 3 of 4 (c) The...
d) Given the primal problem Max z= 8x/+3x2+xz Subject to: x;+6x,+8x3<118 X, + 5x+10x<240 X1, X2,X3, 20 Write down its problem (5 marks) dual Question Nine R=622 R4 2 02. V-24V R = 422. R5=2.522. (a) What are the voltage across and the current in each of the resistors Ri through Rs in figure above? (6 Marks) (b) How much power is dissipated in R.? (4 marks)
(1 point) Consider the following maximization problem. Maximize P = 9x1 + 7x2 + x3 subject to the constraints 13x1 x1 - x2 + 6x2 + - 10x3 12x3 = = 20 56 xi 20 x2 > 0 X3 > 0 Introduce slack variables and set up the initial tableau below. Keep the constraints in the same order as above, and do not rescale them. P X X2 X3 S1 RHS
3. Consider the following linear programming problem: Maximize 10X + 12Y Subject to: 8X + 4Y ≤ 840 2X + 4Y ≤ 240 X, Y ≥ 0 Graph the constraints and shade the area that represents the feasible region. Find the solution to the problem using either the corner point method or the isoprofit method. What is the maximum feasible value of the objective function?
When long division is used to divide 16x3 - 3x + 5 by 4x + 3, there are four terms in the result. Which of the following terms appear in the correct answer? There may be more than one correct answer. Select all correct answers. 2(4x+3) O 04x2 0-3x O-X 3x
4) Consider the following constrained optimization problem: S.1 2x, + 5x, + x, =3 a) (10pts) Determine a null space matrix Z for A (given the constraint set A b b) (25pts) Perform two iterations of the reduced Newton method starting from the point r0
Problem 6: (a) Consider the following problem: max y = 5x + 4.02 + x112-ri-23 + 10 subject to x + 12 = 5. Solve the problem using the method of Lagrange multipliers. (b) Sketch by hand the level curves of the objective function as well as the constraint in part (a) using the same set of axes. On the sketch, label the solution from part (a).
Consider the following 2nd order nonhomogeneous linear equation x 00 + 4x 0 + 5x = cos 2t 1. Solve for the fundamental solutions of its associated homogeneous equation. 2. Find a particular solution of the nonhomogeneous equation. 3. Based on your answer to the previous two questions, write down the general solution of the nonhomogeneous equation. Problem II (15 points) Consider the following 2nd order nonhomogeneous linear equation x" + 40' + 5x = cos 2t 1. (6 points)...
Consider the following two fun9ctions: y1= (x2+3x-1)/(x+4) ; y2= x-1+(3/x+4) Perform long division on Y1 to verify it equals Y2
321pts Consider the following sets of polynomials. > {-1,,3P+1, , *), B = {5x +3*, 2, 2+2, 3, 2-1), C = {3r", 22-1, 7+2, 2+1, 5 Which set is a basis for P.? Justify your answer.