Solve the initial-value problem using Laplace Transforms. x'' + x = e^-t sin2t;   x(0) = 2, x'(0) = 1

Q: T: R2 R2 is defined by х + 7х, [3x, – 4x2] X1 %3D and B = {u,,u,} and B' = {v,v,}, where %3D -- --…

A: Given transformation T:R2→R2, defined by Tx1x2=x1+7x23x1-4x2 and B=u1, u2 and B'=v1,v2 Here u1=22,…

Q: Consider the following difference equation y (n) + 5y (n- 1)+ 6y (n – 2) = 6 (n) at the initial…

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Q: what is the maximum size of matching? And give examples

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Q: Is the point (13, -6) on the circle defined by (x– 13)²+ (v-+ 6)² =9? O Yes O No

A: Solution

Q: 6. Find the general solution of the system: sint -2 cost

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Q: Consider the polar curves C2 :r = 4 cos 0 and C3 : r = 4 sin 0. (a) Determine the slope of the…

A: here we can use simple calculation and formula to solve this question.

Q: Prove that both polar curves are symmetric with respect to the polar axis. Find the polar…

A: For symmetry with respect to the polar axis ( x-axis). We replace (r,Ѳ) by (r,-Ѳ) to determine…

Q: Question 4 If + 3x + 6a2 + 12x°+... %3D then C equals 11 8. 19 8 -2 19 11 215 2/5

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Q: Given the definite integral | f(x)dx a you can split this into two integrals 9. S. | f(x)dx + /…

A: Here in this question we have to says that the given definite integral ∫abf(x)dx can split into two…

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Q: ACBinf fCx) şinf R Cx). X6 A XE13

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Q: (a) Consider the real linear map T: R' - R', expressed as follows: X1 + 2x2 - x3 4x1 + 9x2 - x3 X1 1…

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Q: Let f : R2 -→ R and suppose that lim f (x, y) = -10. (х, у)-(3,0)° What can you say about the value…

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Q: :Q3 Classify PDEs below и ди y2 и + и = ue 5x — - ду

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Q: 1) Prove that for any space, X, with any topology, T, that: (i) CI(X) = X and (ii) Int(X) = X.

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Q: Find an open cover of the interval (−∞, 3]. Justify why that open cover has no finite subcover.

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Q: Let ? and ? be permutations on the set {1,2,3,4,5,6,78,9}, defined as follows

A: Introduction: A permutation is a bijective mapping from a set to itself. The general way to…

Q: Question 8 of 25 An equation of an ellipse is given. (a) Identify the center of the ellipse. (b)…

A: Introduction: The standard form of the vertical ellipse is given by, (x-h)2a2+(y-k)2b2=1 Where (h,k)…

Q: Question 3. Prove using the short north-east diagonals or any other mathematical method of your…

A: Given that A is an enumerable set The fact that the Cartesian product of ℕ and any finite set is…

Q: Mike has 5 sweaters and 7 hoodies in one of his dresser drawers. He reaches in the drawer without…

A: Answer: 2.5

Q: R.3. Let X = {1,2,3, 4}, and suppose f:X→X is a one-to-one function. Prove or disprove: f maps X…

A: Since f in one-to-one function so for x1, x2 belongs to X with x1≠x2 we have f(x1)≠f(x2).

Q: Factor -21 + 27i into Gaussian Primes.

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Q: If the determinant of a 5 x 5 matrix A is det(A) = 8, and the matrix D is obtained from A by adding…

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Q: For the following differential equations (i) show that the singularity points are regular and then…

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

Q: ts) Find the general solution of the system of linear differential equations

A: Solution of the system of differential equations, using eigen values and eigen vectors

Q: What is the next number in this 63 72 76 code sequence? 112 ?

A: We have to find the next term of given code sequence.

Q: :01 Solve the second order differential equation Y" – 5Y' + 9Y = 0 %3D

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Q: Find the directional derivative of the function f(x,v) at point p in the direction of vector a. 1)…

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Q: Find the amount accumulated FV in the given annuity account. (Assume end-of-period deposits and…

A: Use the following formula to calculate the accumulated FV.

Q: ду 8- x2 + xy + y² = 0 find ax az .2

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Use Laplace transform to solve the initial value problem x" - 9x = e;x(0) = 1, x'(0) = –1

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Q: Example 3.32. Solve, by Relaxation method, the equations = 50; x + 5y-3z = 18 ; - 2x + 2y + 7z = 19.…

A: The system of equations given is as follows: 9x-2y+z=50x+5y-3z=18-2x+2y+7z=19 The residual from the…

Q: Does the senes below Converge or erge? Give eason for your answer. (wie checking youl answer,…

A: To determine the series converges or diverges.

Q: { (1, 2, 1), (2, 1, 5) , (1, –4, 7) } (i) Prove that is linear dependent subset of R³. (ii)…

A: A set is linearly dependent if and only if one vector is linear combination of other vectors.

Q: Two student measure the density of an unknown metal three times each Below the data Student1…

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Q: Let f(x,y) = x° + y?. Find the slope of the line tangent to this surface at the point (-1, – 1) and…

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Q: an = 2an-1 + 8a,-2 + 81n for n > 2 with initial conditions ao = :-23, aj = -59. An =

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Q: L3x3 + M (subspace sum). sym 3×3 !! L3x3 O M (direct sum). sym 3×3 !! express A E M3x3 as A = L+U…

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Q: Let Si be the hemisphere with Cartesian equation z = 6 – V36 – x² – y² and S2 be the upper nappe of…

A: "Since you have asked a question with multiple sub-parts, according to our guidelines we will solve…

Q: Give a recursive definition of the following sequences {a,},n = 1,2, 3, ..... Put the appropriate…

A: 1)   an=6n an=6n .............(1) To find value at n=1 a1=61=6 to find n+1 term put n+1 an+1=6(n+1)…

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Q: a bc If det de f ghi -- a b c then det 8d 8e 8f g hi

A: We want to find determinant of given matrix.

Q: cos y dy – x sinx dx = 0

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Q: If 1 d] 1 d] a a det b 1 -5, and det b 2 5, e [c 1 f 3 f then a 3 d] det |b 3 and 3 f] d] det b -3 a…

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Q: Give a recursive definition of the following sequences {a,}, n = 1,2, 3, ..... Put the appropriate…

A: We have to match the given recurring relation.

Q: y - 2)2 + (x-2)2 . Find the direction of heat flow in the plate at the point (2, 1). Heat flows in…

A: Introduction: The gradient of the temperature function at the point is the direction of the greatest…

Q: Find a pair of integers x and y such that 66x + 48y = gcd(66, 48)

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Q: List the ordered pairs in the relations on {1,2,3} corresponding to the matrix, [1 0 = 10 1 1 11 1.

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Q: e expected value of this random variable is 7.9, mplete the table. Show your work. P(x) 10 0.5

A: In this question, the expected value is given. Unknown entries are to be determined.