5. For each element below and specified UFD, find a factorization of the element as a...
7,8,11,12,19,21,24 Find the average rate of change of each function on the interval specified. 5. ༼(x) = ན on [,5] 6. q(x)=r on [4, 2] 7, g(x)= 3r -1 on [3,3] 8 h(x) =5-2r on [2. 4] 10. p0=! - +| on[3] 9. f(0) = 6 +m 1:1.3] Find the average rate of change of each function on the interval specified. Your answers will be expressions involving a parameter (b or h). IL ༼(x) =4x -༡ on [1, bj 12....
Find the area under the standard normal curve over the interval specified below. To the left of z = 1 Select one: a. 0.159 b. 0.999 c. 0.841 d. 0.001 e. 0.023
Only B Problem 5. Show that an element ū is a unit in R/PR, and find its inverse. (a) (15 pts) R=F3 [C], p= x4 + 2x +1, u = x2 +1. (b) (15 pts) R=Z[i], p= 8+ 7i, u = 1 – 2i.
Which of the following statements are true? The element (1,2,3,4,5) € Shas order 5. The element (1, 2, 3)(4,5) € S has order 6. The element (1,2,3) (4,5,6) E S6 has order 6. The element (1, 2, 3)(4,5)(6, 7, 8, 9, 10) E S5 has order 30. Which of the following statements are true? The elements (1,2,3)(4,5) and (1, 2)(3, 4)5,6) are conjugate in Se. The element (1, 2, 3, 4, 5, 6, 7)(8,9,10)(11, 12) is an even permutation. The...
5. (a) Show that Q(V2) C Q V2). (b) Find [Q( 12): Q(V2)]. (c) Show that r - V2 is irreducible in Q(V2)[].
(2) The matrix A-[-5 12 12 5 represents a reflection combined with a scaling by a factor of 13. (a) Find vectors ui and v2 such that A is reflection over the line L = span(n) and such that v2 is orthogonal to vi (b) Find the eigenvectors of A with their associated eigenvalues. (c) Find an eigenbasis B for A (a basis of R2 consisting of eigenvectors of A). (d) what is the matrix of the linear transformation T(z)...
11·The current through each element and voltage drop across each element are given for the circuit shown below. 7.273 mA -7273 mA a10V7.273 う-" . | c | |-5455 n1A d - 2.727 V 1.818 mA a. Use passive sign convention to determine the power for each circuit element. b. Which circuit elements are absorbing energy from the circuit? c. Which circuit elements are supplying (delivering) energy to the circuit? d. Is this circuit balanced? In other words, is the...
2. Find the inverse DTFT of each trasform specified below, for-π < Ω < p -i, ipi < 0.2π 0, Otherwise (a) 5 points: X(Ω) (b) 5 points: X(Q)=
-3 12. Find the area under the standard normal curve over the interval specified below. To the right of: a. 0.841 b. 0.977 c. 0.001 d. 0.159 c. 0.999
Problem 4. Consider f(x) = x5+ x4 + 2x3 + 3x2 + 4x + 5 ∈ Q[x] and our goal is to determine if f is irreducible over Q. We compute f(1), f(−1), f(5), f(−5) directly and see that none of them is zero. By the Rational Roots Theorem, f has no root in Q. So if f is reducible over Q, it cannot be factored into the product of a linear polynomial and a quartic polynomial (i.e. polynomial of...