1. Find the general solution of the linear differential equation using undetermined coefficients, variation of parameters and reduction of order. y" – y = cos x – 5 sin(2.x) = COS 5 sin(2x)

Q: The Fourier transform of f(t) = -1<t<1 is otherwise O 2sin(w + 2) w +2 O 2sin(w – 2) w - 2 2…

A: Fourier transform of the function

Q: Proposition and Connectives. 1. Let p be "It is cold" and let q be "It is raining". Give a simple…

A: The answers are below.Hope it is useful

Q: 3. Consider the quadric surface S2 : - + (y + 1)² – (z – 3)2 = 1 3 (a) Find an equation for the…

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Q: Let V be a vector space of dimension 4, and let W be a vector space of dimension 2. Let L : V → W be…

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Q: Compute the left regular representation of the group G = {e, a, b} given by the group table below by…

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Q: 6. "Find the mserse Laplaie fnanform 10 11 25+3 12

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Q: (1 2 3 4 5 O = \3 1 4 5 6 2 3 4 5 6 6 5). 2 4 1 3 6 (1 2 3 4 5 6' 5 2 4 3 1 6- Compute o-27 1. 2.…

A: Note: (1) The order of a cyclic subgroup generated by an element is equal to the order of the…

Q: 3. The square is dilated under the dilation (x, y) → (0.25x, 0.25y). 4 2 -2 2 -2 a. Graph the image.…

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Q: „Let F be a subfi eld of the complex numbers, let f be a polynomial over F, and let f be the…

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Q: that 10348+4303 is divisible by 47. the remainder of 123 is divided

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Q: 7くt<12 t.

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Q: Find the absolute value of z: b. z= (2+ 3)/(3- 4)

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Q: . Let a be any non – zero vector in V and let p. be the T – annihilator of a. (i) The degree of pa…

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Q: (a) Find r()of the vector- valued function (b) Evaluate the integral of the following vector- valued…

A: This is a problem of Vector Calculus.

Q: Cardinality: Let A and B be sets. We write A B (and say A has the same cardinality as B) if there is…

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Q: Let R be a ring such that for each a e R there exists XE R such that ax = a. Prove the following :…

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Q: yi = 2y1 – 4y2, y2 = y1 – 3y2, yi(0) = 3, %3D - | Vo(0) = 0

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Q: Đuse the imProved method Solve the:

A: To solve the given differential equation using improved Euler's Method we will use the following…

Q: Answer the following using Jacobi Method. Show complete solutions. The iteration should have atleast…

A: The Given equations are: 9x1 - 13x2 + 4x3 = 111 4x1 + 22x2 -13x3 = -128 8x1 + 8x2 + 17x3 = 10   To…

Q: Section 3.2 In Exercises 1-3, (a) compute the eigenvalues and the associated eigenvectors; (b) for…

A: Note: according to our guidelines we can answer only first question because there are multiple…

Q: [A] A bakery bakes two brands of birthday cakes: cake city and chocolate cake and sells them at a…

A: We have to formulate the given problem as a linear programming problem and solve it by graphical…

Q: 4) Consider the function g defined by gx, y) = car (7x Jj ) + logg(x-y) does 9 have the maximum (c)…

A: Given the function gx,y=cosπxy+1log3x-y To find in which direction, the function has the maximum…

Q: 1.37] Consider the following problem: Мaximize subject to 3x1 -X1 -2x1 + 6x2 + 2x2 < 2 + X1 X1, 2x2…

A: 1st we will draw graphs for constraints and then use corner points method to find optimal solution…

Q: 4 a Evaluate In 3. b On the axes below, sketch the graph of y = Inx -3 2 3 -2 -3 The graph y = In x…

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Q: iii) a) Prove that Pa(-x) (-1)".Pn(x) u (2n)! 22 (n!) b) Prove that P2n(0) = (-1)".- %3D

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Q: 3. Find the inverse Laplace transform of the ff. а. (s+1)(s+2)2 10 b. s(s+2)(s+3)2

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Q: Let S be the set of all 2 x 2 matrices A = (a;) such that a1 = an. Determine whether or not S is a…

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Q: Consider the series E 1+ n=1 (a) Find the series' radius and interval of convergence. (b) For what…

A: We have given a series ,  ∑n=1∞ 1 + 1nn x7n (a) We need to find interval of convergence and radius…

Q: SUseThe improved Methods SoNe the: dy x(i+メy)yc0)=3 h2o.て dx

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Q: Let R be a non-zero row - reduced echelon matrix. Then the non-zero row vectors of R from a basis…

A: It is a Vector Space problem and let us solve it in the next steps.

Q: 2000+6000t The number of individuals of a species after t>0 days is given by N(t) 5+t Q(t) R(t)' b)…

A: Given,No. of individuals of a species is given by-N(t)=2000+6000t5+tTo: a) Write N(t) in the form…

Q: 1-24. A electrie ninen a a ueinntt on the end ska 3m si pele Daier mine seae you S.5

A: Consider the diagram in the problem and sketch the diagram of triangle as shown below, The cosine…

Q: (a) Evaluate the integral using integration by parts rule if x' cos' 2x dx (b) Express the…

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Q: 2)2

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Q: Question 2 ( ). a) Test the series 2 W6-1)" for convergence n =1 or divergence (show all your works)…

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Q: Suppose the symmetric equations of lines l1 and l2 are = 2 - y = z and r = -1, 3 respectively. (a)…

A: If two lines are neither intersecting nor parallel then they are know as skew lines  If vector form…

Q: Determine the Laplace transforms of * 3, 0 12

A: We use the definition of Laplace transforms to answer this question. All that is required is to…

Q: 5 3. Use partial fraction decomposition, linearity and s-shifting theorem to find the inverse…

A: To find the inverse laplace transform of given function H(s) first we will take the partial fraction…

Q: (a) Evaluate the integral (cosx-cos x )dx b) Find the total area between the region and x-axis f(x)…

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

Q: Use Gauss-Jordan Elimination to find the inverse of -1 4 2 2 4 2 0 2

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Q: x(t)= -1 x(t)=2 0 2

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Q: 3:) Consider the function g defined by g(x ,y) = cos( mxVy) + log3 (x-y) (b) calculate the…

A: Given,g(x, y)=cosπxy+1log3(x-y)To find: Instantaneous rate of change of g(x, y) at point (4,1,2) in…

Q: ation (1+xcos 2y)dr-x'sin 2 ydy = 0. %3D

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Q: Raul has a wall 4 units long and 2 units wide in the Cartesian plane centered on the origin. On this…

A: Given equations: f(x)=(x+12)(x+1)(x-1)(2x)g(x)=(2x+2)(2x-2)(x)(-x-12) on simplifying we get,…

Q: d'y + 6 + 7y = 0. dt2 dy Consider the following second-order equation: (a) Convert the equation to a…

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Q: Logical Equivalence 1. Show that p J (q V r) and (p l q) V (p l r) are logically equivalent using a…

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Q: . Consider the initial-value problem y'= 0.1!y+0.4x², y(2) =4. Use Euler's method to obtain the…

A: Given Initial value problem: y'=0.1y+0.4x2 , y(2) = 4   To Find: Use Euler's method to obtain an…

Q: x2 – 2x – 8 lim - 21. = 6

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Q: What is the equation of the radical axis of the curves x^2 + y^2 – 1 = 0 and x^2 + y^2 – 6x + 6y +…

A: Let us consider the curve C1 and C2 To determine the Radical axis between the curve solve  C1-C2=0…

Q: 2s – 10 -5s

A: We have to solve given problems: