Minimize Q= 6x² + 3y?, where x+y=9. х y= (Simplify your answer. Type an exact answer, using rac the expression.)
Minimize f(x,y) = x² +ysubject to - 6x +8y= 200. X=
where does the line y=x+30 intersect the parabola y=6x^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
(2) Let Y be a linear function of X, i.e. Y- bo biX where bo and bi are fixed real numbers. We want to minimize the discrepancy of Y from Y, i.e. minimizing the quantity we=E[rMb, that minimize«Q (a) Find the values of bo and bi that minimizes Q (b) Use (a) to show that the minimal value of Q is σ-ar 2 Cov2(x,Y) m Hint: You may use the fact that Q(bo,Y-YVar (Y -Y)+E (Y -Y)where Y.-bg + bİX...
5- Let F(x, y, z)= (-6x,0,-6z). Evaluate F.dS where S is the cylinder x2z2 = 2, 0 < y < 2 oriented by the unit normal pointing out of the cylinder.
5- Let F(x, y, z)= (-6x,0,-6z). Evaluate F.dS where S is the cylinder x2z2 = 2, 0
PROBLEMS 7.3 1. Minimize Z= 6x + 14y subject to 14x + 7y > 43 3x + 7y > 21 --x+y> -5 x,y > 0 2. Maximize Z= 2x + 2y subject to 2x - y > -4 x - 2y < 4 x+y = 6 Xy0
Let Y be a linear function of X, i.e. Y = bo + bịX where bo and bl are fixed real numbers. We want to minimize the discrepancy of Y from Y, i.e. minimizing the quantity (a) Find the values of bo and bi that minimizes Q (b) Use(a) to show that the minimal value of Q is Co - Hint: You may use the fact that Q(bg, b) [(Y-Y*)2] = Var (Y-Y*) +E(Y-Y*)]2 where Y*-bg + bİX and bi,...
=> (x² - 6x) y - y = 0 Find the singular point and ordinary point of this equation.
Q. 3 (14 marks) Consider the following data set where y is the response variable and x is a predictor. 7 14 5 -1 2 -2 a) (1 mark) Write down a linear model for y, and with i = 1,2,3. b) (2 marks) Write out the coefficient matrix X c) (4 marks) Find the hat matrix H = X(X"X)-'XT. d) (4 marks) Find the LSEs of the coefficients. e) (3 marks) Find the residuals by using the hat matrix