If f: G→ G be a homomor phism of groups and e,e be the identities in Gand's respectivel Then (c) f(e) = e'. (ii) f(a-¹) = [f(a)]-¹ where a € G. y-

Q: c) y" - 4y + 3y = e³t

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Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x+2y-z = 3. 0=0

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Q: Evaluate the following double integral over the region R. 2 ſſ⁹(x³ – y5) ²dA; R = {(x,y): 0≤x≤ 1, −…

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Q: a. Calculate the Laplacian of the graph. b. Calculate the eigenvalues of the graph. c. Use…

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Q: Divergence theorem Consider the vector field F(x, y, z) = y¹zi+xz³j+x²zk and the surface S that is…

A: Calculation:

Q: Evaluate the line integral in Stokes' Theorem to evaluate the surface integral SS(VXF). VXF)•n dS. S…

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Q: Compute the indicated product. -1 5 24 01 212 423

A: In the given question we need to compute the following product

Q: Compute the indicated product. -1 2 6 [48][9] 40 3

A: Let,    and Since A is a 2 by 2 Matrix and B is a 2 by 1 Matrix, then the product of AB is possible.

Q: Write the 3x - 7y = 8 7x - 5y = 2 X 8 D-A y 2

A: We note that

Q: 9. Find the value(s) of x such that the angle between the vectors (2, 1,-1) and (1, x, 0) is π/4.

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Q: Let P3 → M22 be the linear transformation L(at³ +bt² + ct+d) = 1. The polinomial 2t³ + 4t² + 2t − 4…

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Q: II. Verify if the given function is a solution of the indicated differential equation. 1. xy³2= cxy;…

A: A function is a solution of the differential equation if it satisfy the differential equation.As per…

Q: For each of the following parametrized family of differential equations plot phase lines for λ =…

A: The objective is to find the bifurcation values

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A: The given equation  is  Let    be  a  power series  solution of (1).Now,   and  Putting  this…

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Q: Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t…

A: Consider the following vector equation:The objective is to sketch the curve with provided vector…

Q: Compute the indicated product. 46 -1 4 51 i][i] 51

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Q: [B] = -5 -11 18 -10 0 -14 14 -12 13 5 -16 -8 17 9 12 -17 If matrix [B] has element brc = −10, what…

A: The given matrix is .The element .We have to find the values of  and .

Q: F and H are sets of real numbers defined as follows. F={w|w<3} H={w | w≤9} Write FU H and FN H using…

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Q: 3. Let i = -B (a) Calculate projcol Au for the following matrices A: A= 2 (b) A 11 2 1 0

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Q: If fiz)= 2³+e², and Cis the contour е z = 8e¹t 04+≤2π ost≤2 Find [ f(z)dz = ? (z+iR)³

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Q: Let I be the linear operator on R2 defined by L i). Find the matrix A representing I with respect to…

A: Calculation:

Q: Let I be the linear operator on IR³ defined by L(2₁])= i). Find the matrix A representing L with…

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Q: A trough is 8 meters long, 1.5 meters wide, and 5 meters deep. The vertical cross-section of the…

A: We write the data's

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Q: Fast pls solve this question correctly in 5 min pls I will give u like for sure Sini y=(-1/2)x^2 + c…

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Q: Let 0<0<T and n E R. Evaluate the following integral. tan-¹ (¹) x2+2x cos 0+1 To dx

A: To evaluate the integral∫[0,∞] (arctan(x^n))/(x^2 + 2x*cos(theta) + 1) dxWe can start by making a…

Q: 3) C2 -4 C=C₁UC₂ 3 C₁: line from -4 to (-4+21) C₂: line from (-4+2i) to (3+2) (Cxtiy) dz= ?

A: (.) Given ,          where    line from  to    line from  to we know that   , differentiating both…

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A: A plastic sheet of area 286 is joined to make the tube of volume 134 and the sheet is longer than…

Q: Select all that apply: The set 1(-j,j) as a subset of X = R is open in - the indiscrete topology on…

A: In the given question we have to tell about the set s s.t why the set  is open in Discrete topology…

Q: By experimenting with the fourth-order Runge-Kutta subroutine, find the maximum value over the…

A: The given initial value problem is  with .We need to experiment with fourth order Runge-Kutta method…

Q: Which Riemann sum represents the illustration shown? 1.75 1.5 1.25- 1 0.75 0.5- 0.25 3 1.Σ.2x; i=0…

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Q: Determine the equation of the line that passes through the point A(1,0,2) and intersects the line r:…

A: Given that a line L(say) is passing through the point A(1,0,2) and it intersect the line   at right…

Q: By implicit differentiation, find the equation of the tangent line to the curve x² + 4xy²-y = 38 at…

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Q: K Evaluate both integrals of the Divergence Theorem for the following vector field and region. Check…

A: Gauss Divergence Theorem:

Q: How many distinct 5-letter words can be formed using the letters from the word "MATHS" if repetition…

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Q: 4. Let f and g be functions defined on an open interval I containing the point z = a. Suppose that…

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Q: Compute the first-order partial derivatives of the given function. eV+z P = ev (Use symbolic…

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Q: Find the equation y = Bo + B₁x of the least-squares line that best fits the given data points.…

A: The given data points are (0, 4), (1, 4), (2, 5), and (3, 5).Our aim is to find the straight-line…

Q: A particle is moving in a straight line in such a way that its position at time t (in seconds) is…

A: To find the velocity of the object at a specific time, we need to differentiate the position…

Q: 2 2. Find the eigenvalues and eigenvectors of the matrix A= -3 3 3 -4 -3 3 3 2 If A is…

A: The given matrix is The objective is to diagonalized the given matrix.First find the eigenvalues and…

Q: Use Fourier transforms to solve the infinite string problem with initial position f(x) and zero…

A: we assume that the solution can be written as a product of two functions:one depending on time (t)…

Q: Compute Uxxx for u(x, t) = 9 sech² (2x - 1). (Use symbolic notation and fractions where needed.)

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Q: Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105…

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Q: Let f(x) be a quadratic function such that f(0) = −2 and √ x²(x + 5/6 dx is a rational function.…

A: We are given that f(x) is a quadratic function that satisfies the condition f(0) = -2.Also, is a…

Q: The amount of money invested in a certain account increases according to the following function,…

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Q: What is the equation of the tangent plane to the surface defined by the function f(x, y, z) = xy +…

A: The surface We have to find tangent plane to the given surface.

Q: 8) Find the volume of the solid whose base is the region in the xy - plane that is bounded by the…

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Q: f E is a ring of even integers, then show  that an ideal (4), generated by 4 is a   maximal ideal of…

A: If E is a ring of even integers, then our claim that an ideal (4), generated by 4 is a  maximal…

Q: Let Are the vectors 1, 2 and 3 linearly independent? linearly dependent If the vectors are…

A: The given vectors are .We have to check whether the vectors are linearly independent or not and find…