1. Find the perimeter of the quadrilateral with vertices at Pi (0,0), P2 (3, 4), P3...
Find the area of the quadrilateral with vertices (0,0),(3,1),(5,4), and (1,4). Use determinants. Find the area of the quadrilateral with vertices (0,0)3,154 and (1,4) Use determinants Round to the nearest tenth 0
vi) Consider the following polynomials in the vector space of polynomials of degree 3 or less, P3. Pi(x) 12 +3r2 +a3 P2(x) 132 Pa(r) 1242 P4(z) = 1-r + 3r2 + 2r3 Which of the following statements are true and which are false? Explain your answer. a) The set {Pi, P2,P3} is a basis for P3. b) The set {Pi,P2, p3,P4,P5} İs a linearly independent set in P3. vi) Consider the following polynomials in the vector space of polynomials of...
Answer Question #12. Question #11 is only for reference 11. Let po, pi, and p2 be the orthogonal polynomials described in Example 5, where the inner product on P4 is given by evaluation at -2, -1, 0, 1, and 2. Find the orthogonal projection of tonto Span {po, pi, p2). 12. Find a polynomial p3 such that {po, p1, p2.p3} (see Exercise 11) is an orthogonal basis for the subspace P3 of P4. Scale the polynomial p3 so that its...
4. Determine whether the polynomials Pi = 1 + x, P2 = 1 + x2, P3 = x + 2 are linearly independent or linearly dipendent in P3.
QUESTION 2 Find an equation for the hyperbola described. Vertices (1, -3) and (- , -3) and (- 2.-3); asymptotes y+3 = + (x+2) 4(x + 2)2 (v + 3)2 = 1 25 9 = 1 (x + 2)2 4(y + 3)2 9 25 4(x - 2)2 (y - 3)2 25 9 (v + 3)2 4(x + 2)2 9 (5532 = 1 = 1 25 QUESTION 4 Find the center, foci, and vertices of the ellipse. 25x2 + 49y2 =...
6. Consider the weighted voting system [23:8,9,15,8]. Find the Banzhaf power distribution of this weighted voting system. (P1P2,P3) (P1,P2,P4) P1,P3,P4) P2 P3P4) (P1,P2,P3,P4) P1.P2) P1P3) Player Times critical Power index P2.P3) (P2 P4) (P3,P4) P3 7. Cindy, Jamal, Monique, and Ryan are dividing a piece of land using the lone-divider method. The values of the four pieces of land in the eyes of the each player are: Piece 1 35% 20% 25% 15% Piece 2 15% 40% 25% 25% Piece...
T А 1 Price, Cost P4 a P3 P2 B Pi Quantity 0 Q1 Q2 If a positive externality exists then the socially optimal price is OP2 OP3 Op4 OP1
3. Consider the two planes, P and P2, where Pi is given by the general equation 2x y+2-5 and P2 passes through the points (0,0,-1), (3,2,4) and (2, 4,5). (a) Find L, the line of intersection of the two planes. (b) Suppose another line, L2, has vector equation (x, y, z) = (8,3,-2) + t2(-2, 1, 1). 6 marks] Find where Land L2 intersect 4 marks 3. Consider the two planes, P and P2, where Pi is given by the...
Let P3 be the vector space of all polynomials of degree 3 or less. Let S = {p1 (t), p2(t), p3 (t), p4(t)}, Q = span{pı(t), p2(t), P3 (t), p4(t)}, where pi(t) =1+3+ 2+2 – †, P2(t) = t +ť, P3(t) = t +ť? – ť, p4(t) = 3 + 8t+8+3. The basis B of Q chosen from the set S is given by: Select one alternative: O pi(t), p2(t), pä(t) Opı(t), p3(t), p4(t) O pi(t), p2(t), pä(t), p4(t) O...
You choose a random permutation (p1, p2, p3, p4, p5, p6, p7) of 1, 2, 3, 4, 5, 6, 7, with each of the 7! permutations equally likely. What is the probability that (1 + p1)(2 + p2)(3 + p3)(4 + p4)(5 + p5)(6 + p6)(7 + p7) is even? Give an exact answer as a simplified fraction and justify your answer.