4 Let po, p₁, and p2 be the orthogonal polynomials described below, where the inner product on P is given by evaluation at −2, − 1, 0, 1, and 2. Find the orthogonal projection of t³ onto Span{p.P₁,P2}- Po(t) = 4 P1(t) = 3t P2(t)=2-2 The orthogonal projection of t³ onto Span{P0, P1, P2} is (Simplify your answer.)

Find the point of intersection of the pair of straight lines. y  =  −7x  −  10 −y  =  8x  +  2 (x, y) =

Maximize p = 7x + 6y + 3z subject to x + y + z ≤ 150 x + y + z ≥ 100 x ≥ 0, y ≥ 0, z ≥ 0. p= (x, y, z)=

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find the Laplace {e^(1−t)sin(1 − t)u(t − 1)}

If the Poisson's ratio of an elastic material is 0.4,  then find the ratio of modulus of rigidity to Young's modulus..If the Poisson's ratio of an elastic material is 0.4,  then find the ratio of modulus of rigidity to Young's Modulus If the Poisson's ratio of an elastic material is 0.4,  then find the ratio of modulus of rigidity to Young's modulus...?

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Using back-substitution, show that an ARMA(1, 1) model may be written as eitheran AR or an MA model.

Consider the problem of calculating the median m of the following numbers: 4,5,9. (a) Write down the linear program that you could solve, to find the median m. Then put this LP in the form: min c^T x s.t. Ax ≥ b, x ≥ 0, where x is your list of variables. (b) Now write down the dual of the problem above. Call the list of dual variables y. (Hint: there are 6 components of y.)

Consider the two-dimensional incompressible velocity potential Φ=xy-x²-y² Find the equation of the streamline that passes through (x,y)=(13,12) The equation of the streamline is ψ=______