Rotate the quadratic function 5x^2 + 3y^2 + 2z^2 + 4xz = 14 to its principal axis. ( express as a symmetric matrix).

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A: By Greens theorem ∫C[Pdx+Qdy]=∫∫R[∂Q∂x-∂P∂y]dxdy, where R is the region bounded a simple closed…

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Q: 7. Fill in the table and sketch the graph: Equation of function f(x)= 2x-5 x+4 Vertical Horizontal…

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Q: Evaluate the iterated triple integral using cylindrical coordinates 4-r²-y² √3 √4-1² 4-x²-y² fer: dz…

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Q: 36. Suppose a 5 x 6 matrix A has four pivot columns. Wha nullity A? Is Col A = R4? Why or why not?

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Q: Use the Limit Comparison Test to determine if the following series converges or diverges. 8 Hint:…

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Q: 8. Evaluate the following integrals geometrically by calculating the bounded area. (a) 1² (2-121) dx…

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Q: 1.1 Calculate the upper and lower sums for the region bounded by the graph of f(x) = between x = 0…

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Q: (b) By Parseval's formula ΣΙΑ*(v)||2 = ΣΣΚΑ*(vi), v;}/2 = ΣΣΚυ;, A(v;)}2 = ΣΙΑ(v;)||2 < 0. ji…

A: To Explain: The mentioned part of the proof:

Q: Consider the regression equation In Y = 4.37 +0.2X₁ +0.3X2 a. Predict the value of Y when X₁ = 8.5…

A: Given Data: Let us consider the given regression equation: Yi^=4.37+0.2X1i+0.3X2i

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Q: Are the polynomials x³+2x +2 and x4 + 3x -2 equal to mod(x² + 2x + 2) in Q[x]?

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Q: 24. Calculate the average rate of change for the function f(x) = -x + 4x + 3 over the interval…

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Q: Problem II Consider a linear operator L : R4 → Rª defined by the formula below, where V₁ = (1, 1, 1,…

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Q: 3. Prove that: 7: (not (for all x)(p(x, f(a))) if and only if ((for some x) not p(x, f(a))) is a…

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Q: Find the general solution for: y" - 7y' +12y = x²

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Q: 2. If A is an n x n matrix, show that det A = 0 if and only if some column of A is a linear…

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Q: 8 and 9

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Q: Polynomial function f(x) = 2x³ +5x²=x+4 Degree Odd or even Name of polynomial Sign of leading…

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Q: Suppose that f(x, y) = -2z4+3 zy2 + 3y2, z=rcos (t) and y=rsin (t). Find af af and (write your…

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Q: d)

A: Maclaurin Series: The formula to find the Maclaurin series is given by:…