OC userin Mathematics·30 Dec 2017The demand equation for a product is given by p= " +6 (in dollars), and the supply equation is q=4(p-1) (in dollars), with the equilibrium point (90; P.)=(8,9). Calculate consumers' surplus (CS) and producers' surplus (PS) under market equilibrium. Round your answer to two decimals.
OC userin Mathematics·31 Dec 20171. Consider a linear system of equations whose augmented matrix is 1 1 3 2 1 1 2 43 11 3 alb (a) Reduce the augmented matrix to echelon form. [4 marks) (b) For what values of a and b will the system have infinitely many solutions? [2 marks] (c) For what values of a and b will the system have a unique solution? (2 marks] (c) For what values of a and b will the system have no solution? [2 marks]
OC userin Mathematics·29 Dec 2017p/2 cost 2 p#/2 cos Suppose that - dx = k. Find the value dx and express your answer JR/4 sinºr JR/4 sin' in terms of k. Simplify your final answer as much as possible.
OC userin Mathematics·29 Dec 20177. A student pays rent of $1,300 a month due at the beginning of each month. Interest is 2.4% APR compounding monthly. What would be the total amount payable (rounded up to the nearest dollar) at the beginning of September, 2014 if the student wanted to pay nine months of rent in advance? (A) $12, 884 (B) $11,818 (C) $11, 608) (D) $11,597 (E) none of (A) - (D)
OC userin Mathematics·30 Dec 2017F. Each letter in a short message has been assigned a number according to its order in the alphabet: n op T V W X Y Z Blank 14 15 19 20 21 22 23 24 25 26 27 The numbers have been placed in an appropriate-sized message matrix "M", arranged left to right, top to bottom, and encoded with the matrix: A51 211 You and I have agreed to code messages by multiplying the message matrix on the LEFT, by the matrix A. In other words, if "M" is the message matrix, and "C" is the coded message matrix, then "C"= A "M" F2) Find the inverse of the matrix A Show your work.
OC userin Mathematics·28 Dec 201711. The area of the region enclosed by y=4x-x and the x-axis, is C) 0 D Ž E) none of these
OC userin Mathematics·26 Dec 20171 23. Find det -1 1 3 2 0 1 2 1 -3 2 1 0 -2] 6 0 4 mark A: 0 B:4 C: 12 D:2 E: 6 Use the following information for questions 24, 25 and 26. [a b c] det de f = 3 | g h i
OC userin Mathematics·27 Dec 2017(b) Show that this equation has only 1 solution. Justify your answer. (Hint: Explain why there can't be a second solution.)
OC userin Mathematics·26 Dec 2017(t) in °C of the pot of soup at time t (in The initial temperature of a pot of soup is 80°C. The temperature minutes) satisfies the differential equation dT di T-20 10 (a) Solve the differential equation, and find an explicit expression for the function ().
OC userin Mathematics·26 Dec 20178. Which function is an injection? Circle the correct answer f: RR f(x) = r2 g: QQ g(x) = 22 h: Z+Z h(x) = r p: NN p() = 22
OC userin Mathematics·27 Dec 2017(9) Consider the power series - - 1)". Find its interval of convergence. kso (A) (, 3) (C) [1,1] (D) (2, 1) (E) None of the above.
OC userin Mathematics·26 Dec 2017PROBLEM 23: A traveler must pack his carry on luggage for an international flight. He only has room to pack one pair of pants, two shirts, and two pairs of socks. If there are four pairs of pants to choose from, five shirts to choose from, and three pairs of socks to choose from, how many different ways can he pack his carry on luggage? A) 480 B) 4 C) 60 D) 120 E) none of the above