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Find necessary and sufficient conditions (with proofs) such that the points z1, z2, z3, and z4 in the complex plane are the vertices of a parallelogram.
Is there a line in the x-y plane such that both coordinates of every point on the line are rational? Prove your answer is correct.
What are the objective function and the constraints?What are the values of the variables at optimality
If a > e prove that the equation a*z^n=e^z has n solutions (counting multiplicities) inside of the circle |z|=1.
Show that if b < a the conformal transformation ? = z + b2zmaps a circle of radius 'a' in the z plane into an ellipse in the ? plane.
Linear Programming : Objective Function and Optimal Solution.Pet Supplies Company produces 16-ounce cans of dog food by combining meat by-products
How is the assignment linear program different from the transportation model?
If you wanted to build a circuit that would oscillate forever without any input voltage (V(t) ? 0) what could you do?
Subject to these restraints, the client's goal is to maximize projected return on investments.
Obtain the Taylor series.Provide complete and step by step solution for the question and show calculations and use formulas.
Suppose f: X --> omega is continuous and X is compact; then f is uniformly continuous.
A certain fluid is flowing with a constant speed V in a direction making an angle ß with the positive x-axis. Find the complex potential for the fluid.
The Friendly family;LPP and sensitivity analysisOn their farm, the Friendly family grows apples that they harvest each fall and make into three products-apple
For each weighted voting system , find all dictators (d), veto power players( vp), and dummies (d) ( 7: 7,3,2,1)
The Mill Mountain Coffee Shop blends coffee on the premises for its customers.Formulate a Linear programming model for this problem.
What choice should be made by the optimistic decision maker? What choice should be made by the conservative decision maker?
Let V be a circle lying in S. Then there is a unique plane P in R^3 such that p / S = V ( / = intersection).
What is the difference between natural and clamped Cubic Splines?Solve the following problems with a clear explanation.
Prove that if p is a polynomial with real coefficients, and if z ? [z1 ,z2,...] is a (complex) solution of P(E)z = 0, then the conjugate of z, the real part.
Systems of Inequalities from Word Problems and Maximizing Profit.A furniture company displays bedroom sets which require 21 square meters of space
Linear programming problem:Graphical solution.Your company makes two sizes of globes, large and small.
Show that a Mobius transformation T satisfies T(0) = infinity and T ( infinity) = 0 if and only if Tz = az^-1 for some a in C ( C is complex plane).
The Warner Corporation has three branch plants with excess production capacity.Formulate a linear programming model for this problem.
Develop a table giving each of the CPF solutions and the corresponding defining equations, BF solution, and nonbasic variables.
Let f = u + iv be an analytic function on an open connected set G in C ( C = complex plane) where u and v are its real and imaginary parts.