Evaluate fory³ dx-4x dy, where C is the portion of the circle centered at the origin of radius 1 in the first quadrant with clockwise rotation.

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A: Solution:Given that, find the mass of the lamina and center of mass:

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Q: 30. Suppose that A and B are orthogonal (n xn) matri- ces. Show that AB is an orthogonal matrix.

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Q: K Let f(L) be the area (in square inches) of a rectangle with width 5 inches and length L (in…

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Q: (Section 17.6, 17.8) Consider F = xî - 2yĵ + ½ 2²k. Let S be the surface of the solid bounded by S₁:…

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Q: sider the following lines. r(t) = (3t+1,3t+2, 2t+1), for oo<t<∞⁰0 R(s) = (s+ 4, 4s+5, -5s+3), for…

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Q: 5.1. THE LINEAR CONJUGATE GRADIENT METHOD 10 set of nonzero vectors {Po, P1, ..., Pi} is said to be…

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A: Since you have posted a multi subparts question according to guidelines I will solve first three…

Q: 2. Use Gauss' Lemma, to compute (²)=(-1)", μ= |a²°N, (31)

A: We recall Gauss's Lemma and using Gauss Lemma we solve the problem.

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Q: Consider the following function. f(x) = ²², a = 1, n = 2, 0.7 ≤x≤ 1.3 (a) Approximate f by a Taylor…

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Q: 1. The periodic function f(x) has period 27. It is defined in the interval 0≤x≤ by f(x) = 2x² (a)…

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Q: Find the polynomial of the lowest degree with real coefficients and zeros of -5/6 (multiplicity 2)…

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Q: Pls help on all the questions pls pls I highly request. They are True or False

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Q: f(x)=sin(x), n=4,05x (a) Approximate f by a Taylor polynomial with degree in at the number a. (b)…

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Q: Using n=4 equal-width subintervals, approximate the area of the region bounded by the graph of, ƒ(x)…

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Q: In Exercises 27-30, calculate ||x||. 1+i 2 27. x = 28. x = 3+i 2-i

A: Norm:

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Q: (Section 17.6, 17.8) Consider F = xî – 2yĵ + ½ 2²k. Let S be the surface of the solid bounded by S₁:…

A: Consider the function .Let  be the surface of the solid bounded by .(a)We need to use divergence…

Q: Find the condition of c such that x² + 2y² + 3z² + c(xy + yz) > 0 for all x, y, z ER with x² + y² +…

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Q: Factor f(x)=x^4+4x^3-x^2-20x-20, given that -2 is a zero and solve x^4+4x^3-x^2-20x-20=0

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Q: Air is being pumped into a spherical balloon at the rate of R(t)=t+cos(t-1) cm³/min, but there is a…

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Q: Consider a connected graph G and let e = wv € E(G) such that G' = G-e is disconnected. Let G₁ and G₂…

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Q: Let Q(x) = 15x² − 2x² – 2x² + 12x1x2 + 12x1x3 – 8x2x3. Find a unit vector x in R³ whose first entry…

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Q: Compute the value of f f(xy + y2) dA where R is the region in the ry-plane enclosed by y = x and…

A: Here we use limit in the order dydx, hence

Q: The discrete system is specified by the following difference equation 2y (k+2) = 7y (k+ 1) + 3y (k)…

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Q: A calculator may not be used for the following questions. For problems 3 and 4, region Q is bounded…

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Q: You deposit $2000 into a savings account with an APR of 5.5%. (a) Compute the amount of interest you…

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Q: 4. For an odd prime p, suppose that (=) = 1 and consider the congruence x² = a mod p. (i) For p = 3…

A: We shall be using basic results from quadratic reciprocity for solving this problem.

Q: Suppose 7 = (5, -5,2). Then (-10, 10,-4) is ✓ (2,-1,-1) is (7.5, -7.5, 3) is parallel perpendicular…

A: If the dot product u•v=0 , then u is perpendicular to v.If the cross product u×v =0 , then u is…

Q: (0,。) - V (10)

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Q: 4. For an odd prime p, suppose that (=) = 1 and consider the congruence x² = a mod p. (i) For p = 3…

A: We shall be using basic results from quadratic reciprocity for solving this problem. And

Q: Evaluate the line integral Jox² xz+yz ds where C is represented by r(t) = (t - 1,1-t, 1-t) with 0 ≤…

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Q: 1. Evaluate the following Legendre symbols: 2. Use Gauss' Lemma, (i) to compute (ii) (iii) In (ii) p…

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Q: Find and describe the region inscribed by the lines (x-axis), (y = -x+2) and (x = 2y-4) under the…

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