Prove: Let G be a group and let a be a non-identity element of G. Then |a| = 2 if and only if a = a-1.

Q: Find the steady state temperature of the quarter circle shown u = f(O) u = 0 u= 0 with r= 1 & f(0) =…

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Q: Let T : R" -→ R" be a linear transformation. Which of the following statements is false? OT can be…

A: The linear transformation T:ℝm→ℝn can be represented by n×m matrix. Therefore option (1) is wrong.…

Q: Which pairs of polynomials f, g e C[X] do have exactly one common root? O f = (X8 – 1)³, 9 = (X + X?…

A: Use the following formulae, to obtain the solution. a2-b2=a-ba+ba3-b3=a-ba2+ab+b2a3+b3=a+ba2-ab+b2

Q: 1 2 Consider the matrix A %3D Find the entry in row 1, column 2 of the matrix A16 • Previous

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Q: How many units has the quotient ring Z/I, where IC Z is the ideal generated by the integers 36 and…

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Q: Determine the following function is differentiable F (z) = e¯²

A: Cauchy-Riemann Equations: The function fz=ux, y+i vx, y satisfies the Cauchy-Riemann equations if…

Q: log (a cos 6+6° sin 8) do=T log a+b a>0, b>0.

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Q: It takes 8 vertices to represent the letter N and hence, D is a 2 × 8 matrix. In addition to D, it…

A: To construct: The coordinate matrix D for the capital letter L in a 6 unit × 8 unit cell of line…

Q: Prove the following limit. ) f(x)=x²+2x+6 where lim, 3 f (x)= 21 >) lim x – x+1=-5 =) lim x³ = 8

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Q: Find L-1: 2+6s+8 g4+882+16

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 10 cos(t)i+11…

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Q: A cylindrical water tank 6 meters high with a radius of 2 meters is buried so that the top of the…

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Q: **Use the following five trigonometric equations to answer questions 2 and 3 below.*** Equation 1:…

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Q: 2200x A firm has the marginal-demand function D'(x) = where D(x) is the number of units sold at x…

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Q: The eigenvalues of A will be complex conjugates. Analyze the stability of equilibrium (0,0). Is it a…

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Q: For which na listed below does there exist a field extension F Z/2 of degree n such that the…

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Q: If -18(x + 1) – 12(x + 1)² + 6(x + 1)³ if – 1< x < 0 а + bx + сx? + dx3 S(x) = if 0 < x < 1. is a…

A: Let the cubic spline interpolation be Sjx on the interval xj,xj+1, where j=0,1,2,⋯,n-1. Use the…

Q: A deli sells 640 sandwiches per day at a price of $8 each.       Question content area bottom Part 1…

A: here in given question we need to find the total revenue in both case one is when deli charge $8 and…

Q: Prove by contradiction that if 3x? 2 is irrational then r is irrational.

A: We have to show that x is irrational if 3x2-25 is irrational. We have to prove the statement by…

Q: 1: Evaluate F dS whereF = (r',, ) and S is the solid bounded by the ry plane and the elliptic…

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Q: - Solve the following partial differential equations X) = 30,T(t,0) = 50, T(t,1)

A: The partial differential equation given is as follows: ∂T∂t=α∂2T∂x2 with α=0.5. The PDE will be as…

Q: Let H = {β ∈ S5 : β(4) = 4}. Prove that H is a subgroup of S5. (Reminder: The group operation of S5…

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Q: (a) Graph G, Graph G2 (b) Graph H1 Graph H2 Figure 7-58 Graphs for Exercise 1. 2. Explain why graphs…

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Q: Given, (4x-6) -e"- =e" -4y () Determine the integrating factor of the given equation. (ii) Solve the…

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Q: Suppose A is a 4 x 3 matrix, B is a 3 x 5 matrix, and C is a 4 x 5 matrix. Which of the following…

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Q: A cannonball is shot into the air. Its height can be described by the equation h = -4(t - 2)(t - 10)…

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Q: = 1 is revolve generated by th

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Q: Consider the set S of all 5-tuples of positive real numbers, with usual addition and scalar…

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Q: Determine the parametric equations of the path of a particle that travels the circle:

A: Given,        (x-4)2+(y-3)2=49 Time interval is 0≤t≤2π

Q: The eigenvalues of A will be complex conjugates. Analyze the stability of equilibrium (0,0). Is it a…

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Q: PLEASE answer number 7 only, be clear and show all steps, thanks

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Q: If Se)=S-18(x + 1) – 12(x + 1)² + 6(x + 1)³ if – 1< x < 0 if 0 < x < 1. а + bx + сx? + dx3 is a…

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Q: a) Show that if u, v, and w are differentiable vector functions of t, then d du V X w +u - dt dv X w…

A: According to our guidelines we are supposed to answer only one asked question.kindly repost other…

Q: Let a, b and m be integers. Prove that if 2a + 3b ≥ 12m + 1, then a ≥ 3m + 1 or b ≥ 3m + 1.

A: Here I have corrected the statement of the Question and provide a detailed solution of the problem.

Q: Problem 6. Let -oo and oo denote two distimct objects, neither of which is in R. Define an addition…

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Q: Solve the following initial value problems using Laplace transform: 1. y" – 4y' + 3y = 0, y(0) = 3,…

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Q: Scheinerman, Exercise 38.3(d) Solve the following system of equa- tions. 3x = 8 mod 10 and 2x + 4 =…

A: This is a problem of number theory, discrete math.

Q: Use the method of undetermined coefficients to solve the differential equations

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: If u = ln( °+y³ x+y ). then find the value of ди ?

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Q: The set S = {v1, V2, V3} where vị = (-1,1,1), v2 (1,-1,1), v3 = (1,1,-1) is a The vector v whose…

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Q: Show that for any integer n , n2 – 2 is not divisible by 3.

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Q: Determine the greatest common divisor of the polynomials X4 + X? + 1 and X + X³ + x² +1 in F[X],…

A: We want to find gcd of given polynomials

Q: Let function f: N →N be defined on the non-negative integers by if n = 0 f(n) = {f(n – 1)+ 5 (…

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Q: for fa(a, y), let flg(2)) = (2² + y*)! %3D fa (2)%3D (2r)D %3D 2V + y2 3z (0) (i) (ii) 33z+y for…

A: We have to calculate the partial derivatives.

Q: 1. Solve the initial-boundary value problem ди 2 02u 0 0 3 dx2 u(0, t) = u (4, t) = 0 t20 3Tx u(x,…

A: As per guideline solving only 1 question

Q: 6. If c is a positive integer and a and b are integers with a = b(mod c), show that a2 = b²(mod c).…

A: Let c is positive integers and  a and b are integers with a ≡ b ( mod c)

Q: 3. Find a basis among the vectors [1, 2, 3], [2, 6, 10], [0, –3, –6],[-1,-3,-5] (which are surely…

A: Q3 asked and answered.

Q: 0 2 1 f). y" + 4y = g(x) ;y(0) = 3 and y'(0) = 0 where g(x) {-1

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Q: Suppose that you are told the matrix a C - 26 A = 36 с 2b — а -а — 2b + 2с b a+2b nas an eigenvalue…

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Q: 5. 24)2.16

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