10. Let A = {2 - 10.x | x € Z} and B = {5y - 8 ye Z}. Show that A CB.
For random variables X, Y, and Z, Var(X) = 4, Var(Y) = 9, Var(Z) = 16, E[XY] = 6, E[XZ] = −8, E[Y Z] = 10, E[X] = 1, E[Y ] = 2 and E[Z] = 3. Calculate the followings: (b) Cov(−3Y , −4Z ). (d) Var(Y − 3Z). (e) Var(10X + 5Y − 5Z).
Let F(x,y,z) = <7x, 5y, 2z> be a vector field. Find the flux of F through surface S. Surface S is that portion of 3x + 5y + 7z = 8 in the first octant. Answer:
Let F(x,y,z) = <7x, 5y, 2z > be a vector field. Find the flux of F through surface S. Surface S is that portion of 3x + 5y + 72 = 9 in the first octant. Answer: Finish attempt
Doreen has a utility function U(x, y) = 10x + 5y. The price of good x is $1, and the price of good y is $2. If Doreen's income is $100, how many units of good x would she consume if she chose the bundle that maximizes her utility subject to her budget constraint?
Let Ě =< 5x + 2, 2y +z, 10x + 10y> be a vector field in R3. Evaluate the following surface integral directly: Si F.25 = [] #(x 7)AA S D Where S is the part of the plane 5x + 2y+z= 10 in the first octant (with upward orientation). SHOW ALL OF YOUR WORK!
Doreen has a utility function U(x, y) = 10x + 5y. The price of good x is $1, and the price of good y is $2. If Doreen's income is $100, how many units of good y would she consume if she chose the bundle that maximizes her utility subject to her budget constraint?
2. Let Q(x,y) be the statement "x - 2 = 5y" and let the domain for x and y be all integers. Determine the truth value of each of the following statements. Justify your answers shortly. (i) Q(-3,-1) (ii) Vx3yQ(x,y) (iii) 3xVy-Q(x,y)
1(a) Given that f(x,y) = 6x²y3 – cosx + 5y - siny + 10x, establish the fact that, the order in which the mixed partials derivatives are taken is immaterial. AN [2] = (b) (i)Find the continuous function whose Laplace Transform is 3 F(p) AP [7] P(p2+4) (ii) Determine [-*[0-3]2+26] AP [2] (P-3)2 +16 (c) Find the solution of the IVP; 2y" - y' – 3y = 4x+ex y(0)=-1. y'(0) = -2 AN [9]
(4, -1,2) 2x + 3y - z = 3 x + y - z = 5 10x – 2y = 3 SHOP Supa lo color (4, 1) ) boda e 3x - 5y = 7 2x + 2y = 10