Test the consistency of the following equations and solve them if they are  consistent  2? − ? + ? = 9, 3? − ? + ? = 6, 4? − ? + 2? = 7, −? + ? − ? = 4

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Q: If lim (a.) 2 (b.) 4 L(C.) 16 (d.) 64 1+ cx 4, then lim (1+2cx 1-2cx, IS

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A: Hint: We need to find the Fourier transformation of f(t)=A rect(tτ)

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Q: The differential equation Exact Bernoulli 2 √(x² + y² ]y² = xy is Separable Homogeneous

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Q: 10. Logical. Given a set in 0-1 variables n X = {x = Bajxj ≤ b } j=1 with aj 20 for j = 1,..., n,…

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Q: 2. For n ≥ 2, define the n-dimensional hypercube Qn to have vertex set V(Qn) = {(1, .,.£n) = R¹" :…

A: Definition of Hamiltonian cycle :  A Hamiltonian cycle is  a closed loop on a graph where every node…

Q: Pivot the matrix about the circled element. 4 -1 1(2) 6 1023 The result of pivoting is (Type an…

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Q: 5. Prove that for any integer n, at least one of the integers n, n+2, n +4 is divisible by 3.

A: According to guidelines we can solved only ist question thank you   we have to Prove that for any…

Q: (e) If o andare harmonic functions, show that OVVO is solenoidal. (Hint: replace solenoidal by…

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Q: 3. Form the partial differential equation by eliminating the arbitrary constants a and b from z =…

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Q: (a) Integrate g(x,y,z) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

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Q: 4) (a) Consider F(x, y, z) = e ²¹ yi - y³/²zx²j+ln(2z)k and calculate the divergence of F. (b)…

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Q: Prove that three dimentional volume element "dx d ment is invariant under Lorentz transformations.

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Q: 1. For the following proposition, describe (i) a model on which it is true, and (ii) a modelon which…

A: To find- For the following proposition, describe A model on which it is true A model on which it is…

Q: Find div (e" grad u x 7) u=x-y ex at (2,1,0) where and =(x²+1)i + sec¯¹(x² −y)j + 3y²zk

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Q: Queston} $²3 20c x²-4 Composite Trapezoidal rule with n=4 dx. 3.1.1. use the to approximate…

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Q: C) Let (X. r) be a topological space and A c X. If S is a sub-basis for the topology T, then S,=…

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Q: -x+y<y. 2 If x < y, prove that x <

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Q: Consider the function: f(x, y) = 4x² + 8y². (a) Find the minimum value of the function subject to x…

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Q: Consider p(x, y, z) = 2xyz - x²y³ v(x, y, z) = xy² + y sin(z) F(x, y, z)= F₂(x, y, z)i + F₂(x, y,…

A: Let F→=f1, f2, f3. The gradient of the scalar field: g is defined as: ∇g=∂g∂x i^+∂g∂yj^+∂g∂zk^. The…

Q: sider (x, y, z) = 2xyz - 2²y³ v(x, y, z) = xy² + y sin(z) F(x, y, z) = F₂(x, y, z)i + F(x, y, z)i +…

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Q: The number of hours spent studying for the exam and the grade on the exam would most likely show a…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1.1 Consider the quadratic sequence: 8; 18; 30; 44;... 1.1.1 Write down the next two terms of the…

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Q: Convert 294,0 to binary зако

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Q: Find the general solution of the system whose augmented matrix is given below. 1-4 0-1 0-6 0 10 0-9…

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Q: How do I find it using a graphing calculator?

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Q: Given a > 0 real, evaluate the following limit: lim x→a √2a³x-x4-ava²x a-vax³

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Q: Find F.T the: f(x) = 1+ (05 (6πt + I) let: and 1—2T8 (W) Coswo кро TT/S (W_W₁) + S(w+Wo) ]

A: To find: The Fourier Transform of ft=1+cos6πt+π8.

Q: A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded…

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Q: A. Transform each equation to center-radius form and determine its center and radius. 1. x² + y²…

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Q: 3. Form the partial differential equation by eliminating the arbitrary constants a and b from z = ď²…

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Q: Find g(5) given that f(5) -8, f'(5)= 9, and g(x) = 9 (5) 6 x 3x + 7 f(x) (Round your answer to four…

A: Given information  f5 =-8,  f'5 =9     and   gx =3x+7fx

Q: 2. S (cos 5x -sin 5x) dx cos²5x

A: ∫(cos5x-sin5x)cos25xdx…