(1) Verify that y = 2 sin(4x) + 3 cos(4x) is a solution of the differential equation d²y dx² + 16y = 0.

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A: Given: Matraville Public School has installed an intercom system. There are 9 classrooms, a…

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A: We have to find the general solution to the differential equation y4-y''=0.

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Q: (III) Use the Cauchy criterion to show the convergence in R of (an)n, where -- an (2k-1)! (2k)!,…

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Q: Exercise 4.2.6 Let 2₁ = [1] and $22= [3 0 20 4 Verify that both are hermitian. Do they commute with…

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Q: Let E and F be events in a sample space S with probabilities p (E)= and p (F) = such that the…

A: You have asked multiple questions. So I have solved the first question for you. For the remaining…

Q: Transform the differential equation 2y2y + 5y = cos(at) y(0) = 1 y = 2 into an algebraic equation by…

A: Given that the differential equation is               2y''-2y'+5y=cos(at); y(0)=1, y'(0)=2.

Q: max z = 3x₁ +5x₂ s.t. x₁ ≤ 4 2x₂ ≤ 12 3x₁ + 2x₂ = 18 X1, X2 ≥0

A: Objective Function: Maximize: Z = 3X1 + 5X2 Subject to: 1X1 + 0X2 ≤ 4 0X1 + 2X2 ≤ 12 3X1 + 2X2 = 18…

Q: Evaluate fc z dz, where C is the line segment from i to 1 and z(1) = t + (1 − t)i for 0 ≤t≤ 1.

A: Given   zt = t + 1-t i ,   for  0 ≤ t ≤1                ⇒  dz = dt - dt i      Now   z…

Q: 2. is the circle with positive orientation: Evaluate the given integral, where C fo -2023z e 24 +22³…

A: In the given curve C is  C:|z+2-3i|=5. C is the circle with center at 2-3i and radius 5. Poles of…

Q: If A and B be 3×3 matrices where |A| = 2 and |B| = 3, then |AT BT| = .

A: 1) AT=A, where AT is the transpose of the matrix A2)AB=AB, where A and B are square matrices of…

Q: 4. value problem: Use the Laplace transform to solve the initial y" - y - 6y = f(t) 4, - - 6t, if 0…

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Q: IfT: R³ R³ is a linear transformation such that 0 4 (ED)-E (C)-E) (C)-8- T " 0 2 T -(1)- then T T

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Q: a. GRAPH one correct (and correctly labeled) cycle of the given b. State the Domain and Range of the…

A: A function y=tanπx3. To Find: a) Sketch the graph of the function. b) Domain and range.

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A: Applicant MonthlyGrossIncome MonthlyPITIExpense Other MonthlyFinancialObligations…

Q: 7. (D+1) [u]-(D + 1) [v] = e', (D-1) [u]+(2D+1) [v] = 5

A: According to the given data, find the general solution.

Q: Consider the power series Σ (x + 4)" Find the radius of convergence R and Vn7h 71==1 the interval of…

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Q: پاه به ۸۵ه نام

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Q: 6 Basics of 3-dimensional integration = x² + 4y² and z = 8 - x² - 4y². Compute the volume sandwiched…

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Q: d.) Jacobi Iteration Method- 4 iterations

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Q: Exercise 8.3. In the schematic figures below, f: U → V is a linear transfor- mation. a. Draw f(au)…

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Q: Consider the fourth order differential equation (E): y(s) + y² = 0 The general solution of (E) is:…

A: The given differential equation is, y4+y''=0, To Solve: This differential equation, and to choose:…

Q: The function f(x) = tan лx - 6 has a zero at (1/) arctan 6 ≈ 0.447431543 .Let Po = 0 and P₁ = 0.48…

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Q: Form an augmented matrix for the linear system of equations. 5x + 2 = 3 x-7y = 15 2 = 4 5 1 0:3 0 0…

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Q: Let f: R → R be defined by f(x) = 6 - 6x. Is f a linear transformation? a. f(x + y) = f(x) + f(y) +…

A: Given that f:ℝ→ℝ be defined by fx=6-6x. We to find whether fis a linear transformation or not.

Q: n n Let A = k², B=(k+1)², C = k₁ D = 1 and E=Ĺ5-k. Consider k=1 k=1 k=1 k=1 k=1 Σ(+48) (6-j)* j=1 a)…

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Q: Evaluate the integral ]][ Fn dA directly or, if possible, by the divergence theorem. S F = [3y, 3x,…

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Q: 3. (a) (z² + 1)-³(z − 1)-4 (c) (z + 1)-1 (e) (3z + 10z² + 3) 1 4. (a) z cot z (d) z-¹csc z (b) z¹(z²…

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Q: Initials (first, mid Solve the initial value problem for y(t) using the method of Laplace transform…

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Q: (3) Solve the Initial Value Problem, dy dx solution. = xy(2), y(0) = 4. Give the explicit

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Q: 2. (a) Reduce the following first order equation to canonical form, then find the general solution:…

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Q: Find an equation for the ellipse whose graph is shown. y 0 F(0,5) 5 X

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Q: 5-x 2x² + x - 1 Σx¹ [a(bn) - b(c)" X n=0

A: Consider  5-x2x2+x-1 = 5-x2x-1x+1                                                   =…

Q: Let M= Find formulas for the entries of M", where n is a positive integer (Your formulas should not…

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Q: In a vector space of dimension 5, every set of 6 vectors would span the vector space.

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Q: Verify that the differential equation x² dy = (xy - y²) dx is homogeneous of the same degree. Then…

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Q: Select all pairs of non-comparable elements in the poset (A,|) if A is the set of all positive…

A: Non-comparable elements are those where numbers does not divide. i.e., (a,b) are not comparable if a…

Q: : Iff [a, b] →→ R is integrable, then there exists a sequence Pn of partitions of [a, b] for which…

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