2 Suppase G is an abeli Group of Order 6 Contauining an element' of order 3. Prove G is Cyclic. 2 Suppase G has only one element (Say a) of order 2. Show xa = ax 'for all % for all in G.

Q: f) justify your conclusion) Coordinates of any points of inflection (State all points that you…

A: Given function is f(x)=x4+x3-2x2+2x2+x-2 Domain is -2<x<1 Point of inflection: For a given…

Q: what would the sketch of the graph look like?

A: The graph of x versus y'(x) is as follows:

Q: Find the solution of dy dy +2 - 3y = 2e2", y (0) = 0, y' (0) = 0 dt2 dt

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 4. A = 3 -6 -12 -3 -6 -9 -3 Find an orthonormal basis of the kernel of A.

A: Note: We know that the kernel of a matrix A is the set of solutions of the corresponding homogeneous…

Q: Which of the following is an "even" function of t? O sin(t) / t O sin(2t) O 1-t^3 O cos(t) + t

A: Consider the function ft=sintt, gt=sin2t, ht=1-t3, kt=cost+t. Substitute -t for t in the functions…

Q: 5. A group of 60 music students were surveyed. 15 play the piano, 20 play the flute, and 30 play…

A: We will construct a Venn diagram according to the given informations.  Let P, F and G be the group…

Q: Exercises: Sketch the region of integration and write an equivalent double of integration reversed.…

A:

Q: Consider the function f(x) = 2/x + 5 on the interval [2, 5]. Find the average or mean slope of the…

A:

Q: 2. Find the roots of the give vectors) in the plane; find c real parts and the imagina to (iii) and…

A: # As per the guidelines we are entitled to solve one question at a time , please resubmit the other…

Q: Which of the following is an "even" function of t? sin(2t) O cos(t) + t O 1-t^3 O sin(t) /t

A:

Q: Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given…

A:

Q: QUESTION 5 a) What is the maximum possible order of an element in S,? Give an example of one of…

A: (a) any element in S7 is either a cycle or composition of disjoint cycles.     Now, maximum order of…

Q: Sketch the region R of integration and switch the order of integration. 10 *In(y) f(x, y) dx dy Jo

A: To find- Sketch the region R of integration and switch the order of integration. ∫110∫0lnyfx, y dx…

Q: Which of the following is not a properties of Convolution? O Modulation O Convolution Theorem O…

A: Solution

Q: Evaluate the solution of differential equation at zero initial condition. d?y + 4y = 2cos(2t) dt?

A: Given differential equation is d2ydt2 + 4y = 2cos(2t)

Q: Solve xb =9 mod11

A: Solution:        As 11 is a prime number, by fermat's theorem,        x11-1 = 1 (mod 11)      =>…

Q: Question 2 Hence evaluate the scalar surface integral. x do.

A: (2) The given surface is S: x+y+z=3 in the first quadrant. We have to find ∬Sx dσ

Q: Prove that 2^? +3^? is a multiple of 5 for all odd ?∈N.

A: We will solve this problem using principle of mathematical induction.

Q: Use the Laplace transform to solve for the given initial value problem. y' – 2y = 1 - t y(0) = 4 y"…

A: We will use the following Laplace formulas to solve IVPs

Q: Σ 00 2 4 A, x" + 2 6 A, x" n =0 n =0 Combine the two power series together into a single power…

A: ∑n=0∞4Anxn+∑n=0∞6Anxn

Q: 2. The inverse Laplace Transform of the function F(s) = 4s+2 / s²+2s+5 is : (a) e* cos 2t + 2e* sin…

A: Given function is Fs=4s+2s2+2s+5

Q: Suppose S and T are balls with the same center. Show that one of them must be a subset of the other.

A: It is given that S and T are balls with same center. Let the center of the balls be a. Assume that…

Q: – 2) dt. Then fC

A:

Q: Find the inverse Laplace transform of the function F(s)= (s- 4)e^-3s/(s^3 + 4s)

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Q: Max Z=3 x1+2 X2 s.to -X,+2x2 <4 3x1+2x2 S14 using Graphical Method X1-X2 S 3 X1 , X2 20

A:

Q: 3. Show that if x is an eigenvector of the matrix product AB and Bx # 0, then Bx is an eigenvector…

A: 3) Let , A and B two matrices. Let , x  be an eigenvector of the matrix product  AB , and Bx ≠ 0. We…

Q: Three hundred draws are going to be made at random with replacement from the box . 0,0,0,1  The…

A: Solution

Q: 4. a). Write the second-order-order Maclaurin series for the S(4) - fin (1 + x*r }t function

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: In(]æ| – 1) lim %3D (cos(x))=

A:

Q: 19U - 6)(1 - 15)2 What are the possible dimensions for eigenspaces of A? (dimension is denoted as D)…

A: Given : The characteristic polynomial of a matrix A, is given as C(λ) = λ4(λ-6)(λ-15)2 To find : We…

Q: Given the power series expression 00 2 3 A x" + 2 2A x" n = 1 n = 3 1. Force the first power series…

A:

Q: Verify that the points are the vertices of a parallelogram, and find its area A( 1, 1, 3), B(-5, 7,…

A: let the points be A1,1,3 , B-5,7,1 , C-3,10,-6 , D3,4,-4 verify that the points are the vertices of…

Q: iangle with an angles A

A:

Q: Scott and Shen want to find the mean time students in their class spent watching TV last week. So…

A: Note: We know that the mean (average) of a sample set is found by adding all numbers in the set and…

Q: An open map is a map f : X → Y such that for every open U C X, the set f(U) is open in Y. Prove that…

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Q: B. Jse Gauss-Jordan method to solve the following simultaneous equations: K+3X2=2X, K2-3X+X=8…

A: We have to solve the given system of linear equations using Gauss -Jordan method.

Q: a. Find a bijection between Zt and the set {1,1/2,1/4, 1/8, 1/16, 1/32, ...}. b. Show that if A is…

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Q: 3 d²y +3y[ dy + dy .3 2 dx = 5x dx dx

A: We have to identify the independent variable, dependent variable , order and degree of the given…

Q: Jack is driving his car from his home to a nearby city on a straight road. 1.5 hours after his…

A: Jack is driving his car from his home to a nearby city on a straight road. 1.5 hours after his…

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 - V1, Vị + V2,…

A:

Q: Let E be the region be the region between the spheres x^2 + y^2 + z^2 = 4 and x^2 + y^2 + z^2 = 9,…

A:

Q: What is the order of G? 5 8 18 9

A: Order of a graph is the number of vertices. Here the given adjacency matrix A has 5 rows and 5…

Q: The matrix 0 3 0 3 -6 A = -6 has two real eigenvalues, one of multiplicity 1 and one of multiplicity…

A: The solution is below.

Q: 7. If L' { f(p)} = F (t) then L' {f( p - a) }is : c) (1/a)F (t/a) d) t"F (t) a) eat F (t) b) (-1)"t…

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Q: A pizza parlor offers 12 toppings. a. How many 7-topping pizzas could they put on their menu? Assume…

A: (a) we can choose 7 toppings for the pizza from 12 toppings in 12C7 = 792 different ways.     Hence,…

Q: Find the orthogonal projection of V = onto the subspace W of R' spanned by U1 = , U2 Uz = VW ||

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Q: -2 Find eigenvalues and eigenvectors for the matrix 3 -1 The smaller eigenvalue has an eigenvector…

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Q: Is it true that there is a basis for R^4 that consists of five vectors?

A: False. First I recall you what is the definition of basis. set B of vectors in a vector space V is…

Q: Area. Suppose the area of a circle is decreasing at a rate of2m2/sec, the rate of change of the…

A: Introduction: We know that the area of the circle with radius r is given by, A=πr2

Q: nd the volume of the solid generated by revolving the area bounded by y = x2 a axis from [0, 2]…

A: