Step by step solution is provided in the pic attached here.
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20. Let u = (2).= (1) and w = (1) . If ou+yv=w, (x, y € R), then x + y = (A) 1/5 (B) 2/5 (C) 1 (D) 4/5 (E) 3/5
*Note: Please answer all parts, and explain all workings. Thank
you!
3. Consider the follo 2 lu The boundary conditions are: u(0,y, t) - u(x, 0,t) - 0, ou (a, y, t) = (x, b, t) = 0 ay The initial conditions are: at t-0,11-4 (x,y)--Yo(x,y) . ot a) Assume u(x,y,t) - X(x)Y(y)T(t), derive the eigenvalue problems: a) Apply the boundary conditions and derive all the possible eigenvalues for λι, λ2 and corresponding eigen-functions, Xm,Yn b) for any combination of...
5. Given the initial-boundary value problem as below: ди ди at +u=k 0<x<1, 1>0, Ox?? Ou -(0,1) Ox Ou (1,t)=0, @x t>0, u(x,0) = x(1 - x) 0<x<1. where k is a non-zero positive constant. (i) By separation of variables, let the solution be in the form u(x,t) = X(x)T(t), show that one can obtain two differential equations for X(x) and T(t) as below: X"-cX = 0 and I' + (1 - ck)T = 0) where c is a constant....
Suppose U(x, y) = 4x2+ 3y2 1. Calculate ∂U/∂x, ∂U/∂y 2. Evaluate these partial derivatives at x= 1, y= 2 3. Calculate dy/dx for dU= 0, that is, what is the implied trade-off between x and y holding U constant? 4. Show U= 16 when x= 1, y= 2. 5. In what ratio must x and y change to hold U constant at 16 for movements away from x= 1, y= 2?
Given two utility functions U(x, y) = x2/3 y4/5 and U(x, y) = x2 + y, with Px = 2, Py = 1, budget is 10 unit, show the consumer choice respectively.
)Given a 4-node element in x-y plane as shown here: Node X 3 3 1 8 a) Using the shape functions in u-v plane, determine an expression for mapped points from u-v to x-y, i.e. x- x(u, v) and y -y(u, v), for points within the 4-node element in u-v plane. Then, determine value of x and y for a point with (u, v)-(0.3,0.3). (10 points) b) Determine the value of Jacobian matrix, [J], and its determinant for such mapping...
U 1 3 x 3 y 4 = Suppose the price of x is given by px and the price of y is given by Py and the budget income of the consumer is given by 1. Price of x, Price of y and Income are always strictly positive. Assume interior solution. a) Write the statement of the problem (1 point) b) Compute the parametric expressions of the equilibrium quantity of x & y purchased and the maximized utility. You...
Solve heat equation in a rectangle du = k ( ou + dou), 0<x<t, 0<y< 1, t> 0 u(x, 0, 1) = 0, uy(x,1,1) = 0, with boundary conditions u(O, y,t) = 0, u(r, y, t) = 0, and initial condition u(x, y,0) = (y – į v?) sin(2x).
tion? (2) Calculate E(X), E(X2), and Var(X). (3) Calculate F(a) P(X s a) for a (0, 1]. (4) Let Y =-log X. Calculate F(y)-P(Y v) for u 20. Calculate the density of Y.
tion? (2) Calculate E(X), E(X2), and Var(X). (3) Calculate F(a) P(X s a) for a (0, 1]. (4) Let Y =-log X. Calculate F(y)-P(Y v) for u 20. Calculate the density of Y.
3. If the utility is given by U(X,Y)= X +4Y and px = 1, the indirect utility is given by PY I (a) 4py I (b) py 41 (c) рү 21 (d) py