There are 120 subsets of size 3 from {1,2,...,10}. Using the pigeonhole principle, prove that if we choose 23 such subsets, there must be two of them whose elements have the same sum

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Q: how that the set S={(1,2,1),(3,1,5),(3,-4,7)}  is linearly dependent where, S⊆V\index{3}(R).

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Q: QUESTION 1 The solution of 2²u Əxəy (Use separation of variables constant ->) O u(x,y) = Ae u(x,y) =…

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Q: Q-1 Solve the pair of equations using the placement method. x 5.y=-4 6 x 5.y=1 - - Example of…

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Q: Find the general solution of the given system. dx dt dy dt (x(t), y(t)) = = 3x + 4y = 8x + 7y

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Q: Suppose that f is twice differentiable at a. (a) Prove that there exist a 0ħ € (0, 1) such that f(x…

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Q: ) Solve for the general solution of the equation: 2x’’+ 200x = 0 B) Solve for the particular…

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Q: Integrate g(x,y,z) = 3x + 4y +z over the portion of the plane 4x + 8y + z = 16 that lies in the…

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Q: 3. Verify the divergence theorem calculating in two different ways the flux of vector field: F = (x,…

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Q: What is the polar moment of inertia of the half-disk R defined by x² + y² ≤ 1 and y ≥ 0, assuming…

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Q: A diet is being prepared for the University of Arizona dorms. The objective is to feed the students…

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Q: The critical speeds of oscillation, λ, of a loaded beam are given by the equation:  λ3 − 3.250λ2 + λ…

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Q: Find the Laplace transform, F(s) of the function f(t) = cos(2t), t > 0 F(s) = ,s> 0

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Q: Select the classification for the system given by: 1.92 s² +11s +4 H(s): = O Over Damped O Undamped…

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Q: 1. (a) Calculate the the gradient (Vo) and Laplacian (Ap) of the following scalar field: $₁ = ln r…

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Q: 8 Σ n=1 κ 4 n!

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Q: 2. Find an LU decomposition of: [1 2 8 0 3 Lo -1] 6

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

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Q: 5. a) Prove that T is one to one but not onto. b) Attempt to define T-¹: P4 → P3 as in for- mula (1)…

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Q: Write formulas for the indicated partial derivatives for the multivariable function. k(a, b) = 2ab3…

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Q: Problem 3. Let A € M3x3(R) be the matrix 1 0 2 2 5 4 -2 -1 (i) Determine all the eigenvalues of A.…

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Q: If I let f(x,y) be continously differentiable, how do I prove gradf = (fx, fy)?

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