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- Solve the following linear programming problem using the simplex method: Maximize Z = 5x + 3y Subject to: 2x + 3y ≤ 10 4x + 2y ≤ 12 x, y≥0• Use the definition of Laplace transform to find L{f (t)} for the given f (t). a) f(t) = cos2(t – n) %D b) f(t) = 2 sin 3t cos 3t 2 c) f(t) = sinh t 3Verify the following definite integrals that were used when developing a Fourier series representation over the interval -LMultiply the Following Vectors using cross Product method. W = † x F F = ( 5i + 3j – 8 k) N f = (2i – 4j – 5k) mTranslate the given problem into a second - degree polynomial in x using Lagrange interpolating formula. X 5 6 9 12 y 13 14 Then find P'(x) and P'(x)Q 1: Find the first and second order partial derivatives of f(x,y, z) = x³ + Зx?у + ysinzRecommended textbooks for you