R.4. Prove that the set of real numbers in the interval (0, 1) which have a terminating decimal representation is a countable set.

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Q: f F = x 2 yz, G = xy-3z 2 , find (a) ∇[(∇F). (∇G)] (b) ∇- [(∇F)x(∇G)] , (c)∇x [(∇F)x(∇G)] .

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Q: Consider integers from 1,000 to 9,999. Then, answer the following questions. a) How many even…

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A: Solution

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Q: ý = -9y + 4t + 3

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Q: Find the inverse Laplace transform of H(s) +ed

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Q: SOLVE FOR THE LAPLACE TRANSFORM OF THE GIVEN EQUATION. 1.f(t) = te¯3t cos² 2t

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Q: Which of the following best describes the graph shown below? B 1. It is Eulerian. II. It is…

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Q: { (3i – 2)² = -n(6n² – 3n (b) Prove by induction that | i=1

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Q: 2. Let R be the relation on the set {1,2,3,4} containing the ordered pairs (1,2), (1,4), (2,1),…

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Q: dx dy + y = x , dt = 3y dt dx dy 1.

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Q: x?y" - xy' + y = In(x), y(1) = 0, y(2) = -5; n = 8 1.125 |- 372 1.250 -1.31 1.375 |-1.708 1.500…

A: Given,x2y"-xy'+y=ln(x) , y(1)=0 , y(2)=-5, n=8To find: Solution of given Boundary value problem

Q: 9. Find the general solution of (D² – 2D+ 1)y= 6e*. A) y= (c, +c,x)e* + 3e™* B) y= (c, +c,x+ 3x² )e*…

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Q: A= (a) Find the singular value decomposition (factorization) of A. That is, find orthogonal…

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Q: Given L1 hit time is 2 clock cycle. L1 hit rate is 75%. L2 hit time is 5 clock cycles. L2 hit rate…

A: The solution is given below

Q: (a) Let G be any group. Let H <G and K < G be subgroups with |H|= |K| = p, where %3D is prime. Show…

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Q: 2. (D2 – 4)y = 0 when y(0) = 0, y' = 3

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Q: Let X and Y be sets. Let us say that a subset S of the cartesian product X x Y is a rectangle if S =…

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Q: Let G be the group of symmetries of the graph Answer the following, giving a full justification for…

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Q: 5. An n x n matrix P is said to be orthogonal if P'P = I. (P'P is "the matrix product of P-transpose…

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Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 95 and the upper cone z2 = 4x2…

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Q: A tank initially contains 100 L of a well-mixed water-and-salt solution, with salt concentration of…

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Q: Let T: R3 → R3 be a linear transformation such that T(1, 1, 1) = (2, 0, –1), T(0, –1, 2) = (-2, 3,…

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Q: Find the volume of the solid bounded by the cylinder x2 + y2 =16 and the planes y=z, x=0, z=0 in the…

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Q: (a) Sketch the graph. Use correct line style. (b) Indicate the solution set region of the system of…

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Q: A business includes a monthly promotion funding of $154000. The commerce division calculates that if…

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Q: 10. What is the general solution of the nonhomogeneous differential equation (D² – D– 2)y = 6x +…

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Q: 2. Find the cerntroid of the area bounded by the curve y= 2x + 1 x+y =7 and x= 8

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Q: Evaluate the surface integral (x + y + z) dS where S is the part of a plane parametrized by S: r(u,…

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Q: 8. In the prism, assume all dimensions have different lengths. a. State 3 equal vectors to DC. b.…

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Q: 18. Evaluate L (s² + 1)²

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Q: What is the radiusoof convergence of the power series solutios for the differential equation: x²-16…

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Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: 1) = det(A) for any A E M2,2(R). Is ƒ a linear transformation? [b11 b12] [b21 b22 a12 A = a21 and B…

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Q: Let's assume that we have the following system of linear equations Ax = b where 3 2 A = 7 -2 -3 2 8.…

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Q: a. Find the area of the parallelogram formed by u and v. b. Find the volume of the tetrahedron whose…

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Q: 19. Solve y'(1) + y(t) = sin t; y(0) = 1 by Laplace transfrom. %3D

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Q: 8. The transition probability (branching fraction) from the 3P, F = 5/2 state to the 3S, F' = 7/2…

A: Solution :-