(a) Let a and b be two elements of Sn with the same cycle structure. Explain how to produce an element g of Sn which conjugates a to b. (b) Show that even if a and b belong to An, we cannot always take g € An.

Q: A software organisation employs 80,000 staff members. 16,000 employees are in the sales team, 24,000…

A: A software organization employs 80,000 staff members. 16,000 employees are in the sales team, 24,000…

Q: Give an example of TEL(C5) with dim E(2, T) = 2, dim E(4, T) = 1, and dim E(X. T) = 0 for all other…

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Q: Solve the given differential equation. All solutions should be found. 2xy + y² +3 x² + 2xy dy d.x…

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Q: 1. In answering the following questions you will show that K3,3 is not planar. Suppose that K3,3 is…

A: In the question first, we have to show whether K3, 3 is a planar graph or not. Also, it is asked it…

Q: Let A= [−2,2] ×[−2,2] and B= [−1,1] ×[−1,1]. Graph A, B, A∪B, A∩B, and A∆B. (ATTN: All the sets…

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Q: Problem 2. Do the following for the function f: R²R given by f(x, y) = 1² + y (a) For A = {(-1,0),…

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Q: Let P be the vector space of all polynomials of degree at most 3 with real coefficients, and let H =…

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Q: A smooth curve is normal to a surface ƒ(x, y, z) = c at a point of intersection if the curve’s…

A: The given curve is rt=ti+tj-14t+3k. We have to show that this curve is normal to the surface…

Q: x²y" − 4y" + 4y' − 4 = x² + 4x - y'(0) = 0

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Q: Determine the truth value of the following statements if A, B, and C are true and X, Y, and Z are…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Step 4: Provide an intuitive explanation why f(x) a(x + 2)² − a² + a² will behave exactly like the…

A: The given function is f(x)=ax+b2a2-ab24a2+aca. To Prove: f(x)  will behave like the function ax2…

Q: Prove that ala for all natural numbers a.

A: Details attached as step 2.

Q: Problem 8 let f(x) = x ₁ extensions of Period 4. Csine survey: Sme series 0 nzl (-1) vel n Us (2n-1)…

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Q: Consider the following linear time-invariant ordinary differential equations: • x(t) – 2x(t) = 0,…

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Q: 3. Use the secant method to solve f(r)=rln2−1 with zo = 2 and 2₁ = 1. Iterate until the absolute…

A: we use formula of secant method: xn+1 = x(n-1).f(xn) - xn.f(xn-1)/ f(xn) - f(xn-1)

Q: Solve the following for x 1. ii. 1 16 23x-1 = 4*2*12 = 0

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Q: The example T(x) = x² is not invertible because x² = b has two solutions for positive b a ution for…

A: As per our guidelines only first three subquestions are solved. To solution of remaining…

Q: Exercise 3.2.13. Let H(R) a - {(1; i)=ancex} = a, b, 0 0 1 (1) Show H(R) is a group under matrix…

A: The main objective is to prove H(R) is group.

Q: Question 1-1 Denasia and Kenya are training to run a half marathon. In the first week of training,…

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Q: 1.) an initial investment amount P, an annual interest rater, and a time t are given. Find the…

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Q: Derive a finite difference approximation formula for the second derivative ƒ"(x;) using three -…

A: Here  Using three points xi-1, xi, xi+1  and xi-xi-1=2h, xi+1-xi=h

Q: Consider ∂/∂t f(tx, ty). Prove that if f is homogenous of degree n, then the attatched equation is…

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Q: Solve the initial value problem with y(0) = 1 and y'(0) = 3. Use undetermined coefficients method to…

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Q: I can use a given slope field to sketch a solution to a first-order ODE. Sketch the soution to the…

A: Given IVP dydt = t-2y, y(-3) = 0 We are asked to sketch the solution of given IVP in the slope…

Q: Prove that if B is a basis for a topology on, then the topology spanned by is X, then the topology…

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Q: Find the centroid of the region enclosed by the graphs of the equations y=3-x²₁ y=x- Round limits of…

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Q: One of the members of staff from the software organisation travels to Birmingham on a business trip.…

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Q: Verly that each of Umn (x14₁3) = e satisfies Laplace's equation Uxx+lay +lzz = 0 and the boundary…

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Q: Find the solution of the given initial value problem. (7) = 5, t > 0 Y || ty' + 2y = sint, y

A: Let us consider the initial value problem of the form dydt+P(x)y=Q(x), y(x0)=y0 To solve the…

Q: Problem 2. For the function defined by if -22x20 0<x<2 52 - 2 f(x) = 2x+2 sketch the 4- Period…

A: As per the question we are given a piecewise defined function f(x)  with period 4 and we have to…

Q: Solve: y"-qy = 8(+) +,S(+-3), y(o)=y'(0)=0. ~Delta

A: Given,        y''-9y=δ(t)+δ(t-3), y(0)=y'(0)=0.

Q: 2. Solve the initial value problem dy dt (mana ty + y cost. with y(0) = 3, using the method of…

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Q: Consider the function 1-х їв окны 1 if 12x22 f(x) = a) Plot the function 6). Plot its odd- Periodic…

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Q: Determine the truth-value of the following statements if A and B are known to be true, and X and Y…

A: TRUTH TABLE: P Q P·Q P∨Q T T T T T F F T F T F T F F F F

Q: ions 14-15; Convert the following LP primal problem into dual problem. Max P =-3x1…

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Q: Prove that if X ∩ Y = X ∩ Z and X ∪ Y = X ∪ Z, then Y = Z for all sets X, Y , and Z.

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Q: A closed rectangular box with a volume of 686ft³ is made from two kinds of materials. The top and…

A: Let l be the length w be the width and h be the height  Min Z=242lw+122lh+2hw…

Q: Determine the truth-value of the following statements if A, B, and C are true; and X, Y, Z false.…

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Q: answer true if the statementis always true and false otherwise. In the case ofa true statement,…

A: We know that ℝn is the vector space of n-tuples i.e., a vector x in the vector space ℝn has the…

Q: Determine the truth-value of the following statements if A and B are known to be true, and X and Y…

A: we solve these problems by truth table.

Q: an Suppose {an} and {bn} are sequences such that a+b→0. Prove that 0 and bn →0. Does this conclusion…

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Q: 1. Let S = {10, 11, 12, 13} and R = {(10, 11), (11, 11), (12, 13), (12, 10), (12, 12), (13, 10)}…

A: a. Composition relation of  R :   Let P and Q be two relations of R ;  P= {(12, 13)},  Q={(13, 10)}…

Q: how that each of the following graphs are planar by providing a planar representation of the graph.…

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Q: How do you rewrite the expression 4 logx — 3 log(x^2 + 1) + 2 log(x—1) as a single logarithm log A?

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Q: Match each of the following integers with its equivalent representation in a different base. (123) g…

A: Number system are of the type  Binary decimal with two bits 0 or 1. The decimal number is from 0 to…

Q: Solation:- we know that condition for equilateral & is | 21-22| = |22-231 = |23-211 | 21-22|=|22-231…

A: The required answer is in below step.

Q: 2 For any integer n, n² + 2n + 3 is even if and only if 4|(n² – 2n — 7).

A: What should be done in que 2 should be written clearly. This Que if to be proved seems not true, we…

Q: Find a unit vector with the same direction as the vector u = (7, 4, −3)

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Q: What value is a discontinuity of O x=-1 Ox= -4 Ox= -3 Ox=-2 x² + 8x +4 x²-x-6 ? (5 points)

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Q: Find the standard matrices A and A' for T = T₂° T₁ and T' = T₁° T₂- T₁: R² R², T₁(x, y) = (x - 3y,…

A: It is known that: T1∘T2 can be written that: T1T2(x, y) and T2∘T1 can be written that: T2T1(x, y).