= Solving a 3x3 syster Solve the system. -x +y +2z=-3 3x-y+z =-2
Find the partial derivative. f(x,y)= x3 + 6x²y + 3xy. Find fy(x,y). A. 6x² + 3xy? OB. x2 + 12xy +9xy? OC. 6x²y +9y? OD. 6x2 + 9xy
7–26. Lagrange multipliers Each function f has an absolute maximum value and absolute minimum value subject to the given constraint. Use Lagrange multipliers to find these values. 12. f(x, y) = x - y subject to x² + y2 – 3xy 20
14. The profit function for one acre of soybeans is: P(x, y) =.01(-x² + 3xy +160x - 5y2 + 200 y + 2600) where x is the unit cost of fertilizer and y is the unit cost of hybrid soybean seed. Hint: Use partial derivatives to set-up a system of equations to solve to find maximum values. a) Find x and y values that maximize profit. b) Find the value of maximum profit.
1) Classify the following quadratic forms. (a) 9(x, y) = 2x2 + 3xy + 3y2 (b) q(x, y, z) = x2 + 3xy – xz + 3y2 – 2yz
The covariance of X and Y is 1. E(X) =3, E(Y) = 2. What is E(3XY)? 21 Not enough information 18 7
Find the G.S. of the DE: (3xy - y2)dx + x(x - y)dy = 0
Trady 14. The profit function for one acre of soybeans is: P(x,y) = .01(-x + 3xy +160x - 5y +200 y +2600) where x is the unit cost of fertilizer and y is the unit cost of hybrid soybean seed. Hint: Use partial derivatives to set-up a system of equations to solve to find maximum values a) Find x and y values that maximize profit. b) Find the value of maximum profit. 15. Evaluate the following double integral. STE
complex anaylsis f(z) = f(x+iy) = (x + 3xy - by ²x) + (y3 + 3x²y+y) Find all points Zec at which differentiable. Then, find all the points at which ZEC t is analytic.
The electrostatic potential in a particular xy coordinate system is given by V(x,y)- 3xy 5y 2. Find the expression for the electric field. In a different system, the electric field is given by E(x.y) - 2xy3 î+ find an expression for the electrostatic potential.