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Find the altitude of a parallelepiped determined by vectors A, B, and C if the base is taken to be the parallelogram determined by A and B and
A=i+j+k
B=2i+4j-k
C=i+j+3k.
Based on the parallelogram law, show that the norms ||.||_1 (1-norm) and ||.||_infinity ( infinity or maximum norm) in R^2 are not induced by any inner product.
Solve the system of equations by the substitution method. State whether equation is independent, dependent, or inconsistent.
Problem solving on linear programming
A toy making company has at least 300 squares of felt, 700 oz of stuffing, and 230 ft of trim to make dogs and dinosaurs. A dog uses 1 square of felt, 4 oz of stuffing, and 1 ft of trim. A dinosaur uses 2 squares of felt, 3 oz of stuffing, and 1 f..
Calculate the real part and the imaginary part of the complex polynomial p(z)= z^3-3z. Do the same for q(z)=(|z|^2)z + zbar. (here, z= x +iy, x,y belgon to R)
Determining if null hypothesis will be rejected for given test statistics, State whether the standardized test statistic χ2 allows you to reject the null hypothesis for a two-tailed test with χ2 = 8.907
Consider 4 couples (4 husbands and their wives) stand in random order in a line. What is the probability that no husband is lined up directly
Find the derivative of the function by using quotient rule.
Fitting of simple linear regression
Solve without graphing. Find the slope and the y-intercept for the graph of each equation in the given system. Use this information (and not the equations graph) to determine if the system has no solution or an infinite number of solutions.
A pulley is suspended 13.5 m above a small bucket of cement on the ground. A rope is put over the pulley. One end of the rope is tied to the bucket and the other end dangles loosely to the ground.
Formulate a mathematical program that can be used to determine where the "hub" should be located in the plane. Clearly define your decision variables, objective and constraints
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