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Consider the following system of ODES: X' = 10x - 6y – xy2 V = 8x...
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?
Consider the system of coupled ODES: x' = x - y, y = x + xy - 6y (+) (a) Find the critical points (C+, Y*) € R2 of this system. [3 marks] Hint: One critical point is (0,0) and there are two more critical points. (b) For each critical point, find the approximate linear ODE system that is valid in a small neighbourhood of it. [6 marks] (c) Find the eigenvalues of each of the linear systems found in...
Consider the following. x = 8x + y y' - 2x + 6y. X(O) = (-1,2) (a) Find the general solution (x(t), y(t) = Determine whether there are periodic solutions. (If there are periodic solutions, enter the period. If not, enter NONE.) NONE (b) Find the solution satisfying the given initial condition (x(6), y(t)) - (c) With the aid of a calculator or a CAS graph the solution in part (b) and indicate the direction in which the curve is...
(1 point) Consider the function f(x, y) = e-8x=x2-4y—y2 Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank. fx = fxx = fxy =
Consider the following.
x'
=
6x − 10y
y'
=
10x − 6y, X(0) = (6, 10)
(a) Find the general solution.
(x(t), y(t)) =
Determine whether there are periodic solutions. (If there are
periodic solutions, enter the period. If not, enter NONE.)
(b) Find the solution satisfying the given initial condition.
(x(t), y(t)) =
(c) With the aid of a calculator or a CAS graph the solution in
part (b) and indicate the direction in which the curve is...
Consider the spring model
x″−8x+2x3=0, x ″ − 8 x + 2 x 3 = 0 , we looked at in the previous
problem. Linearize the first-order system that you obtained there
at the third of the critical points you found. [x′y′]=A[xy] [ x ′ y
′ ] = A [ x y ] , where
Consider the spring model x"-8x2x30, we looked at in the previous problem. Linearize the first-order system that you obtained there at the third of...
Problem #10: Consider the following function. 8(x,y) = 8x? - 7y2 + 16V7x (a) Find the critical point of g. If the critical point is (a, b) then enter a b (without the quotes) into the answer box. (b) Using your critical point in (a), find the value of D(a,b) from the Second Partials test that is used to classify the critical point. (c) Use the Second Partials test to classify the critical point from (a). Problem #10(a): Enter your...
Consider the following elementary step X + 2Y → XY2 If the initial rate of formation of XY2 is 0.0026 M/s and the initial concentrations of X and Y are 0.66 Mand 0.76 M, what is the rate constant for the reaction? Answer will be in M^-2s^-1 Thank you
(1 point) Use the Laplace transform to solve the following initial value problem x, = 10x + 4y, y=-6x + e4, x(0) = 0, y(0) = 0 Let x(s) L {x(t)) , and Y(s) = L {y(t)) Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s): S)E Y(s) = Find the partial fraction decomposition of X(s) and Y(s) and their inverse Laplace transforms to find the solution of the...
Consider the function G(x,y) = 2x4 + 4xy + 3y2 + 8x Find an expression for D(x,y), the function that is used to determine if a critical point is an extremum or a saddle point. You do NOT have to find any critical points, only the function D.