5. [5 marks] (a) A= = (4) B = (23) Calculate AB and BA (b) Evaluate...
5. This is a bonus question. You will get extra marks for doing it. Four probabilists are playing a game of cards. Each of them has been dealt a hand of 13 cards from a standard wel shuffled pack of 52 cards. Note that there are 12 pictures cards namely the Jack, Queen and King of each of the four suits (Clubs, Diamonds, Hearts and Spades). Suppose that one of the probabilists is picked uniformly at random. (a) What is...
-4 2 5 5 -5 Find (if possible) a. AB and b. BA, if A = 2 - 5 B = 4 4 - 2 0 3 a. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. AB = (Simplify your answers.) OB. This matrix operation is not possible. b. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. BA=...
Question 4 6-69) Consider the following three points: a-0 b-3and c-1 a) Find the parametric vector equation of the plane which passes through these three [3 marks] b) Find the vector cartesian equation of the plane passing through the three points listed [2 marks] c) Hence, or otherwise, find the non-vector cartesian equation of the plane passing through 3 marks] points above. the points above. Question 4 6-69) Consider the following three points: a-0 b-3and c-1 a) Find the parametric...
6.a) Let -2 5 -6 10 ), 2) an Evaluate the matrix 8 marks) b) Find the area enclosed between the following curves and sketch the region. 5x2-2. f(x)--3x2 + 30 and g(x) marks) c) Evaluate the following integrals. Give your answers to 2 decimal places. dac i) 2 (3+2 dx. (8 marks) [25 marks] 6.a) Let -2 5 -6 10 ), 2) an Evaluate the matrix 8 marks) b) Find the area enclosed between the following curves and sketch...
2. Evaluate the following integrals. (a) [5 marks] | el cos 4xdx -1 x (b) [5 marks] / cosdx -x³+3x²-x- dr. 1dx (c) [10 marks] (п -3)(12+2) 4 (d) [5 marks]/ dx V4-5x-2x2 dx cosh x-sinh x (e) [5 marks]] (Give the final answer in terms of e.)
5. Rewrite the following in radical (root) form, then evaluate. [4 marks) a) 643 b) 817 6. Solve the following exponential equations. Make sure to show your work! Leave your answers as fractions if necessary. [2, 3, 4 marks) a) 2x-3 = 32 c) 16*+1 = 83x-2 b) 3x+3 = 1
plz show steps thx 5. a) Evaluate st -2x + 7x? dx. b) Evaluate: [** sin(x* +1]dx. c) Evaluate: [(3x? –5x+4-4e”)dx
1. Find the matrices of x and yif.... (23 marks) 2x - y = and x+2y=[] { 5,). 2. Find matrix C if: G 1-6. 9 (18 marks) 3. Given that: b = -32+4- k c = -91 + 12 - 3k Q =(5,4,0) and P = (-1,4,-3) Find a. The unit vector along the direction of a vector has Q as initial point and P as a terminal point Prove that vector b is parallel to vector ĉ using...
If A is the event of rolling a prime number (2,3, &5) with a die. B is the event of rolling a perfect square (1&4) with a die. C is the event of rolling an even number (2, 4, & 6) with a die. 2 is stated carcable 36. If A is the event of rolling a prime number (2,3,& 5) with a die. B is the event of rolling a perfect square (1 & 4) with a die. C...
Question 5 (20 marks) a) [10 marks] Evaluate: 1 el-X Vx+y(y – 2x)2 dydx. 0 Jo (Hint: consider a change of variable.) b) [10 marks) Find the volume of the solid bounded by the sphere x2 + y2 + z2 = aand the cylinder x2 + y2 = ax, a > 0.