Solve the initial value problem. Sketch the graph of the solution. d²x (a) = 4- dt2 dx dt x(0) = 3, dx dt It=0 = 4

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A: Since there are multipart, hence find the solution of first three parts.

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A: Explanation of the answer is as follows

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Q: 5. (a) Find the LU decomposition of the matrix [2 1 1] A = 4 0 2 635 (b) Find the LDU decomposition…

A: (.)  LU  and LDU  decomposition of the matrix ,                A= 211402635 In  LU decomposition ,…

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Q: T(n) = 2T(n − 1) + 1, T(0) = 1. Use the iteration method to find a ☺() evaluation for T(n).

A: T(n) =2n+2n-1+2n-2+2n-3+...+22+21+1

Q: 4. Now consider the undamped version of (0.1), with forcing term F(t): = cos ßt, mu" = -ku + cos Bt.…

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Q: A B D E (i), (iv) (i), (iii) (ii), (iii) (i), (v) (ii), (iv) Find U10 and U12: (i): U10 = {1,3,7,9}…

A: Please find attachment

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A: Given,         f(x)=2x2+4,     g(x)=x-12 and  h(x)=1. To find                  projvf=?.

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Q: t²-t-20 t-1 1²-5t-6 t+2

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Q: Consider the following points: A(1, 1, −2), B(−1, 2, 1) and C(1, 0, 1). Determine the parametric…

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Q: Let F(w) be the Fourier transform of f(x) and G(w) be the Fourier transform of f(x + a). show that…

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Q: [4 5 01 10. If A 67 1 2 [1 0 3 and B 0 1 3] Lo 0 [1 5 41 го 5 A) 6 8 3 B) 6 7 3 L3 2 11 L3 2 1 0 1₁…

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Q: (b) Which critical value makes sense in this model? Recall that P(t) = 30t + 6t²-3 is only defined…

A: b Given that Pt=30t+6t2−t3 is only defined for 0≤t≤8. Differentiate Pt=30t+6t2−t3 with respect to t,…

Q: Problem 21. For the system given below, find the echelon form U, the free variables, and the special…

A: Given : A=01030206  ,  b=b1b2 To Find : echelon Form U and free variable

Q: Here is the optimal tableau for a Max LP z x1 X3 81 82 83 rhs 1 0 0 0 10 10 280 0 0 0 1 5/2 -8 24 0…

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Q: Solve the system by any method. 50. y = 2 y = 4 2x + 3y = 9 3x - 2y = 6 x - x +

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Q: = { [" -d] | a,bER} a X = Prove that and X* are isomorphic

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Q: (9) Show that the set E of indefinite sequences from {0 1 33 0,13 13. countable Hint: Lot fiNg E.…

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Q: Let S be the surface obtained by revolving the plane curve 2x=sqrt(9−y2) about the y-axis.Obtain a…

A: Given- Let S be the surface obtained by revolving the plane curve 2x = 9 - y2 about the y-axis. To…

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Q: The graph of y = x³ − 7x² + 14x − 8 is given in Figure 1. = √₁² (²2² -=[₁²² (3) Use the solutions to…

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Q: If you generalize the solution of Exercise 1.7.2, you get the answer in the form Check that this…

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Q: c) Solve 38² 168 - 13 = 8² +5. e) Solve 3x + 11 = 2x + 11 + 12 2+1 d) Solve t²-3t+28-23 = 28 +5. f)…

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Q: Function f is given by 2y + 1 √²+² he X f(x, y) = consider h as a continuous function of 1 variable,…

A: Use taylor approximation and leibnitz rule

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A: If set is orthonormal then norm of vector is 1 and scalar product of vectors is 0

Q: Why do we need to know how many triangles exist in Side-Side-Angle triangles?

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Q: A) .3 Find the determinant of -21 B) 63 1 2 4 -1 -1 '1 -1] 1 -1 3 -2 3 1 3 -2 -11 C) 21 d) -42

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Q: Matrix [x 8 226 A and its invers 8 y -10 -4

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Q: 5. Given : Matrix A and its inverse matrix B,Find the value of x 1 31 8 y 0-1 2 and B 8 -10 -4 4 L4…

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Q: Suppose that p(x) is a quadratic polynomial with rational coefficientsand is irreducible over Q.…

A: It is given that,  p(x) is a quadratic polynomial with rational coefficients and is irreducible over…

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Q: 2x₁ - 7x₂ + 4x₂ = 9 X₁ +9x₂ −6x3 = 1 − 3x₁ +8x₂ +5×3 = 6

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Q: Consider the map T: M₂(F) → P4(F) such that T([₁])=a²²+ dr. You are given that T is linear. Т a.…

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Q: Section: Name: 1. Write the following statement as an English sentence: "Em EZ, VnE Z, m = n +5" 2.…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Problem 17. Which of the following are subspaces of R? (a) All sequences (x₁,x2,...) with xj = 0…

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Q: Problem 1. Informal statement: Suppose two 8.5 x 11 inch pieces of paper are each divided into 374…

A: Let us solve the given problem in the next step.

Q: Provide Solution for this. find the Attachment.

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Q: Use the Laplace transform to solve each of the following equations: (a) f'(t) + f(t) = 3 where f(0)…

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Q: A=P+en+c r

A: The given relation is A=P+ert+rCr .........(A) with A(240)=0.  We have to find P.

Q: 2. Multiply by the conjugate and simplify this radical expression 2 3√5t-4' >0

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Q: Solve for the values of x₁, x₂ and x3using: 0.30x₁ +0.52x₂ +1.50x3 = -0.01 0.50x₁ + 1.25x₂ +0.25x3 =…

A: Gaussian Elimination: The augmented matrix of the given system is changed to reduced echelon form…

Q: Define the set {(x1 , x2 ); x1 x2 = 4} the smallest distance from the origin and the points where…

A: To solve this problem, first we have to solve the given set definition and form the set and then use…