Obtain the solution of the following initial value problem using Laplace transform! y"+y=t, y(0) = 0, y'(0) = 1.

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A: A particle moves along line segments from the origin to the points (2, 0, 0), (2, 4, 1), (0, 4, 1),…

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A: Solution :- ∑n=0∞ -3n3n2+6nThe series has positive and negative elements, check for…

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Q: Use the simplex method to solve the problem:  Maximize: P = 3x1 + 2x2  subject to: 5x1 + 2x2 ≤ 20…

A: We Use the simplex method to solve the problem:  Maximize: P = 3x1 + 2x2  subject to: 5x1 + 2x2 ≤ 20…

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A: The given problem is to find the flux of vector field F over the given surface S is the triangular…

Q: Solve the following problems by the Branch and Bound Method. max z = 8x₁ + 5x₂ I s.t. ₁+₂ ≤6 9x1 +…

A: The given linear programing problem is: Max z=8x1+5x2 Subject to: x1+x2≤69x1+5x2≤45x≥0 Where…

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Q: 5. Draw the complete shear and bending moment diagrams. Set P = 800 lb, a = 5 ft, and L = 12 ft P P

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Q: Find an invertible matrix P and a diagonal matrix D such that P-¹AP=D. -1 0 0 0 92-18 0 0 0 -1 0 000…

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Q: (Q) solve the following system of a equation using Gauss-Jordon 80 X₁ - 20X₂-20X3 = 20 -20X₁₂+ Y0X₂…

A: We will apply elementary row operations on the augmented matrix to reduce it into reduced row…

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Q: 5) U₂ = 5 Uxx t U(0,€) = 2 U(3,4)=-1 U(x,0) = -x

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Q: Given that: dy lim da Ax÷0 Ax(√x√√x+^x) (√x+√x+^x) - dy dx Determine 1 r=1 - Ax A (To one decimal…

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Q: 79-85. Limits of sums Use the definition of the definite integral to evaluate the following definite…

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Q: Answer the question 3 1 2] Let A = -3 -1 -4 Find the cofactor C23 3 0 -9 -18 9 10 6 5

A: Please check the answer in the next step, note that cofactor is signed minors, where minor of an…

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Q: Use Gauss's law to find the charge contained in the solid hemisphere x² + y² + z² s a², z ≥ 0, if…

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Q: 4. Suppose that the square matrix A has a negative eigenvalue. Show that the linear system x = Ax…

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Q: a. २२१६ -4-3-2- ✓✓✓17 2 C. -4-3-2- ✓✓✓t! 2 1 Describe the vector fields below. -2 =11131 2- 1-2-3 ↑…

A: Given : Four vector fields.   To describe : The given vectors field.

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Q: Consider a point at x = 5 on the curve Ax³y + Bx²+ Cy+D=0, where A = 3, B = 4, C = 5, and D = 1. If…

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Q: 14. Area functions The graph of f is shown in the figure. Let A(x) = f f(t) dt and F(x) = √₂ f(t) dt…

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Q: Evaluate the following integrals using contour integration ( 1 -dx 13+5sinx

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Q: Find the parametric vector solution to the homogeneous system. A= 2 -6 0 4 2 1 -3-4-2 61 1-3 4 60 2…

A: We have  A=2-60421-3-4-261-34602-6-13-1 To solve Ax=0 Let's first find its row reduced echelon form…

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Q: Suppose f : A →R is a function, c is a limit point of A, and limx→c f(x) = L. Prove limx→c kf(x) =…

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Q: What can we say about 5"-2" for any natural number n? Justify your response. which 15 divisible by 3

A: For n = 1,       5n - 2n = 51 - 21                   = 5 - 2 = 3 = 3.1 For n = 2,      5n - 2n = 52…

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Q: Solve the IVP y" + 2y + y = 8(t-2), y(0)=0, y'(0) = 1

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Q: Define T by T: Pn → R by T(p) = =S² p(x) dx, where P is the set of all polynomials whose degree less…

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Q: Consider the curve with parametrization given by: r(t) = (-4 cost, 4 sint, 8t) Now re-parametrize…

A: Given Data: Let us consider the given curve with parametrization given by, rt =-4 cost ,4 sint , 8t…

Q: The sequence {a} begins with 2, 1,-1, -2, -1, 1, 2, ... n From the list below select a recurrence…

A: Option (B) is wrong as the initial conditions a0 = 3 and a1 = -1 are not true.    Option (C) is…