5. If r = (r, (x, y, z) and ro = (xo, Yo, 20), describe precisely the set of all points (r, y, z) such that %3D |r- rol = 1.

Q: Show that the subset of R2 given by {(x, y) E R² : xy 1, x > 0} is closed.

A:

Q: 2. If (x, y) → (x +3, y- 7)maps TUVWTO T'U'v'w', what is the algebraic description that will map…

A: Note: Multiple questions posted simultaneously, answer to the first question is given. If there is a…

Q: Suppose that l is a line. Let H be one of the two half-planes bounded by l. Give a proof that l U H…

A: Answer is mentioned below

Q: Let X=ℝ2 and define d,:ℝ2×ℝ2→ℝ d2((x1 ,y1),(x2,y)2)) = max{|x1 - x2|,|y1 - y2|}. Draw the…

A:

Q: If F(x, y, z) = (x²z, –2xz, yz), then curl F(6, –3, 1) equals %3D O (12, 39, –5) O (9,34, 2) O (13,…

A:

Q: Show that the subset of R2 given by {(x, y) E R² : xy = 1, x > 0} is closed.

A:

Q: B = { t,f,-3 is compact. IS %3D

A: See the attachment

Q: Let X and Y be two T, spaces, then X×Y. :is

A:

Q: Suppose that receiving stations​ X, Y, and Z are located on a coordinate plane at the points…

A: Given:X≡4,4Y≡-12,-4Z≡-6,9The epicenter of an earthquake is determined to be 5 units from X​, 13…

Q: O Let X,X. X3 beasamPle of size n=3From the Bernolli Pmf Assune Ti ヒ(X、メ,メ) X、+メz+Xg and こ I= X,X t…

A: Using the Neymann factorisation theorem we can find out the sufficient statistic.

Q: a. Let C = C, U C2 where C, is the line segment from (2,0,0) to (3,4,5) and C2 is the line segment…

A: c1: Line segment from (2,0,0) to (3,4,5)The equation is…

Q: - (19,8) (10,0) (19,8) ) Show that So fdx + gdy = Sao.0 24x?y dx + 24y2x*dy is independent of path:…

A: Let's find.

Q: 5. Evaluate f (x²zdx – yx²dy + 3dz) where C is the boundary of the triangle with vertices (0,0, 0),…

A:

Q: Suppose n is an integer and z-z3D =r is a contour traversed n dz %3D once in counter clockwise, then…

A:

Q: Consider the sets X = {(x, y) E R²: x² + y² ≤ 1) and Y = ((x, y) = R²: x ≥ 0]. Sketch on R²the sets…

A:

Q: Find fxTy and f,, and evaluate each at the given point. (x, y, z) = x2y3 + 2xyz- 4yz, (-2, 1, 2) %3D…

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Q: 10. Given: YX = ZX WX bisects ZYXZ Prove: AWYX AWZX

A:

Q: Let w = -4xy – 5yz – 4xz, x = st, y = et, z = t Compute (3,4) = as (3,4)%3D at

A:

Q: Let W = Lin and U= Lin 2 (a) Show that R' = W U. Explain.

A: Note:- As per our guidelines, we can answer the first part of this problem as all the parts are…

Q: Find the angle (in DMS) between the line L1 through the points P1(2, 1, 4) and P2(–1, 4, 1) and the…

A:

Q: (b)* Show that Y' is closed.

A: Actually we shall show, closure of the set = the set. Then this set will be closed.

Q: Let r, y EN such that y # 0, then y+r#0.

A:

Q: 5. If (x, y) → (x+3,y-7)maps TUVWto TU'v'W', what is the algebraic description that will map…

A: As per rules we will solve only first question: 5. Given that (x,y)→(x+3,y-7) maps TUVW to T'U'V'W'…

Q: Which of the following points are collinear to (1,0) and (3,6)? Show graphically and analytically.…

A:

Q: Let r = ⟨x, y, z⟩ and r0 = ⟨1, 1, 1⟩. Describe the set of all points (x, y, z) such that r − r0 =…

A: Given: r=x,y,z and r0=1,1,1 To describe the set of all points x,y,z such that r-r0=2 Solution:…

Q: and for the following situation Determine forulas for w=(z,y, ) 2=z (t), y=y(w, v, p), z==(v,p),…

A:

Q: 28. Bounded by the planes z = x, y = x, x + y = 2, and z

A: Solution:-

Q: Let f(x, y, z) = x³ – yz?. Find af af of and ax' dy az

A: Given : fx,y,z = x3-yz2

Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

Q: if T(x,y) = (x,0) then Null(T) = span{(0,1)} Select one: True False

A:

Q: Prove that y, + y, +2y, 56 is a valid Gomory cut for the following feasible region. X-{yeZ: 4y, +5y,…

A: We have, y2+y3+2y4≤6 X=y∈Z+4 ;X=4y1+5y2+9y3+12y4≤34X=y∈Z+4 ;X=5y2+9y3+12y4+5y2≤34X=y∈Z+4 ;…

Q: Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find ∂z/∂t.

A: Solution:- The given question is  Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find…

Q: Show that the linear map (x, y)H (x+ y, x- y) from (R?, || - |1,) to (R?, I| - ||is an isometry.

A:

Q: 3. Suppose that f(1) = 2, f(4) 7, f'(1) 5, f'(4) = 3, and f" is continu- %3D | af" (x) da. ous. Find…

A: The given data is: f1=2f4=7f'1=5f'4=3  f'' is continuous  To find the value of ∫14xf''xdx.

Q: Let P = {(z, y, 2) E R° | az + by + cz = 0} where (a, b, c) # (0,0,0). (a) Prove that (a, b, c) ¢ P.…

A: Given that P=x,y,z∈ℝ3 : ax+by+cz=0 where a,b,c≠0,0,0 (a) The objective is to prove that a,b,c∉P Let,…

Q: Let a and b be nonzero and f(x, y) = (ax + by)e-x Show that if a ± b, then there are five critical…

A:

Q: 3. Show that X = (x|Ax=b, x ≥ 0} is convex. following ure which no

A: As per our guidelines we are supposed to answer only one question.

Q: (3) In R² with the standard topology: {(x, y) | x² + y² {(x, y) | x² + y? > 1}. = 1}, {(x, y) | x² +…

A: In a topological space R2with standard topology. A  subset O is open if at each point x in O there…

Q: 2 Given u -1 and U , for which w is the set {u, v, w} linearly independent?

A:

Q: 32. Let y = (1, 2, 6) and u = (1, 1, 1). Compute the distance from y to the line through u and the…

A: line through u(1, 1, 1) and v(0, 0,…

Q: If w = f(u, v), u = x + y, and v = x - y, show that w,wy = w - w?. %3D %3D

A:

Q: graph the points z = x + iy that satisfy the givenconditions. | z |> 2

A: Complex numbers

Q: Compute ∮c (ydx+zdy+xdz) where C is the triangle with vertices (3,0,0), (0,0,2), and (0,6,0)…

A: The given points can be plotted as A(3,0,0) B(0,0,2) C(0,6,0)

Q: Evaluate F dr where F(x, y, z)= (x', y’, xyz) and C is the line segment from х, у, со (1, 4, 3).

A: Use parametric to solve

Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by fX,Y (x, y) = x + y/21…

A: Solution

Q: Let u = (1, 1), v = (3, -2), w = (4, 3), and y = ( map from R² -3, 4). Let L be a linear | to R?…

A: We know Let  Given

Q: Let F(x, y, z) = (z, x, y), ar (0,0,0), (0, 1, 1), vertices are ar

A: Introduction: Stroke's theorem is simply a higher-dimensional version of Green's theorem. The line…

Q: Consider a S = {x|x"=1} is S, equals to S?

A:

Q: Show that a triangle with vertices (x,Y;), (x2,y2), and (x;,y;) has area + x,y3 + X3Y, – X,Y3 – X,Y,…

A: