1-) Let M = {(x,y)| (x-3)² + (y + 2)² = 4 and x,y ER}. Define an atlas for M.

Q: Consider the simple linear model Y; = Bo + B1Xi + €¿, where e~N(0,0²); i = 1,2, .. 1. Show that a)…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts(a, b-i,…

Q: The plane z = Ax+By+C is to be "fitted" to the following points (XkYkZk): (1,-1,0), (-1,-1,1),…

A: Let Put the given points in f we have Now, we have minimize this function.

Q: Let R denote the rectangle with corners (−1, −2), (4, −2), (4,1), and (-1,1), and let P denote the…

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Q: If a line L is parallel to the y-axis and pass through the point (1, 0, 1), which of the following…

A: Given query is to find the point which are on line L.

Q: What are the coordinates of the point on the directed line segment from (-1, –6) to (8, –3) that…

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Q: Compute the value of ( G. dL for G = 2ya, with A(1, -1, 2) and a) straight-line segments A(1,-1, 2)…

A: Given the line integral ∫APG·dL for G=2y,0,0 with the initial point A1,-1,2 and P2,1,2 using the…

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: if u = <1,-3,1> and v = <2,2,2> then find the projection of u onto v

A: The objective of this question is to find the projection of vector u onto vector v. The projection…

Q: Find the area of JEN if the coodrinates of the vertices are J(0,3) E(6,0), and N(8,3)

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Q: Q1 find acubie palonemiat ofk given-points for27,3},(2,12)e

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Q: Give an example of (v1, v2, v3) and (w1,w2, w3) independent se- quences in the Rº such that…

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Q: Consider, 21u = 2x – 3y and 21v = -–x+y Find the value of the Jacobian a (x, y) a (u, v)

A: 21 u = 2x - 3y, 21 v = -x + y

Q: 3. Let Path A denote the straight line segment from (0,0,0) to (1,1, 1). Let Path B denote the…

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Q: Find the stundand matices * and a for ToT,OT and て:→ド,1)- (-3y, fn + 3) T:→ド, 1.(4)): (J,)

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Q: (d) Let (Fn) be a sequence of closed subsets of M, and S, (j = 1,...,5) be subsets of M such that.…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 4) Verify that Green's theorem is true for f,xy?dx – x²ydy ,where C consists of y = x² from (-1,1)…

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Q: What are the coordinates of the point on the directed line segment from (3, 3) to (10,-4) that…

A: General formula

Q: FIS Paralebgram WXZ with vertices WH 2). X-2 6), LCE, 7) and Z4 3). 6c 1) → 6x - 3. y- Rectange ABCD…

A: The solution is given below in the next step:

Q: The plane z = Ax+By+C is to be "fitted" to the following points (XkYk Zk): (1,0,0). (1,0, -1),…

A: Let  S = ∑k=14 Axk+Byk+C-zk2  For minimizing S , we have  ∂S∂A = 0 ,  ∂S∂B = 0  and  ∂S∂C = 0…

Q: 4.)It is known that the plane α passes through the point (2, 1, 3) and contains the line g with the…

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