Suppose the system
2x + 4y = f
cx + dy = g
is consistent for all possible values of f and g. What can you say about c and d? Justify your answer.
Suppose that a, b, c, d are constants such that a is not zero and the system is consistent for all possible values of f and g. What can you say about the numbers a, b, c and d? Explain your answer. ax1 + bx2 = f cx1 + dx2 = g
2. Find the value(s) of h which make each system consistent. 5 (b) (a)22y h 1 (d)-2r3y 5 2rthy9 3. Suppose the system below is consistent for all possible values of f and . What can you say about the coefficients e and d Justify your answer
Consider the system of two coupled differential equations: y-cx + dy, x-ax + by, with the equilibrium solution (xe,ye) = (0,0) (a) Rewrite the coupled system as a matrix differential equation and identify the matrix A. Obtain a general solution to the matrix differential equation in terms of eigenvectors and eigenvalues of A. Justify your answer (b) Classify possible types and stability of the equilibrium with dependence on the eigenvalues of A. (Note: You are not asked to compute the...
76. Let F(x) = 2x' + bx' + ... + cx +1.(4 pts) A) How many real zeros could there be? a) 7 6 6 c5 d4 e 3 f 2 g) 1 no 6A B what are the possible rational zeras? a) = 6) + 2 c) = 1 + 2) = 2 e) = 1 f) *2 g) + 7 26 B
2. Consider the systems: dz =2x(1-5)-yr dt dy dt a) Which system corresponds to a predator-prey one? Which is the predator and which the prey? Briefly justify your answer. b) Find the equilibrium solutions only for the predator-prey one. c) Sketch its phase plane showing the equilibrium solutions and the behavior on the r- and y-axis (only for the predator-prey one) d) Describe briefly what kind of situation could the other system represent. 2. Consider the systems: dz =2x(1-5)-yr dt...
f. g(f(x)) 5) Solve the system of equations (4.1) (5x + 4y = 7 (2x + 7y=-8 6) Graph the inequality 3x + 5y > 30. (5.1) 7) Graph the system of linear inequalities (5.2) 3x + 2y = 22 (5x + 7y = 55 8) Find the value of an investment in an account (2.5, 3.1, 3.2) a. Bearing 4% simple interest after 5 years.
write c++ to solve this linear system. Given 2x+4y-z 2 -2x -3y +7z 10 Write a program to solve the linear system above using Gauss- Elimination. Question2 Let f(x) = x3-6x2 + 11x-6, Write a program to i) Check whether the root exist in the interval: a) .5, 5.0] b) 2.5, 4.0] ii Based on interval found in 4(i), find the root using Bisection method. Do your calculation in 4 decimal points and 0.0001. Programming language: C or C++ Given...
some help please o D. go Given y=f(u) and u = g(x), find dy/dx = f(g(x))g'(x). y = sin u, u = 2x + 12 Select one: A. 2 cos (2x + 12) B. cos (2x + 12) C. - 2 cos (2x + 12) D. - cos (2x + 12)
(1 point) Set up a double integral for calculating the flux of F -4xi + yj + zk through the part of the surface z =-2x-4y + 4 above the triangle in the xy-plane with vertices (0,0), (0,4), and (2,0), oriented upward. Instructions: Please enter the integrand in the first answer box. Depending on the order of integration you choose, enter dx and dy in either order into the second and third answer boxes with only one dx or dy...
Solve the system by any method. x + 4y = 18 2x + 5y = 21 3x + y = 24 4x + 7y = 27 Select the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. The solution to the system is (Type an ordered pair.) ( y), where y is any real number OB. This system has infinitely many solutions of the form (Type an expression using y as the...
> Thank you
Aolt Thu, Dec 16, 2021 7:54 PM