1. Let F(x, y, z) = (x + y², y + z²,z +x²). Let C be the triangle with vertices (1,0,0), (0,1,0), (0,0,1), traversed in that order. Calculate f, F • dr.

Q: 4. Consider the point M 2t,31 – 1,-t+ Determine t for that M belongs to the mediator plane of [AD].

A: Question: (4) Given points A-1,4,2,B1,1,0,C-3,5,-32 and D232,15,10 Objective is to find the value of…

Q: 2. An is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and two…

A: We know that, The sum of distances to any point on the ellipse x,y from the two foci c,0 and -c,0 is…

Q: Let g(x) = b,x² + bx + b,x + bg, x E R be a polynomium whose graph intersects the points (-2, 4),…

A:

Q: 4. For the linear canonical system x' = Jx, x € R², determine the nature of the origin as a fixed…

A: Given canonical system x'= Jx  Case-1:-  det >0 if both Eigen value positive:- The product of the…

Q: Let C be the line segment joining A(1,1,-2) to 0(0,0.0). A parameterization of C is given by* None…

A: NOTE : As per Bartleby guidelines only one question will be answered. Please upload other parts…

Q: 1. Let F(x, y,z) = (x + y², y + z²,z + x²). Let C be the triangle with vertices (1,0,0), (0,1,0),…

A: Consider the provided question,

Q: (G) G)- The projection of onto the line through zero 1 is and а. (;) () " () b. C. d.

A: Let u→=11, and the line l through zero v→=00, and w→=1-1. Need to find the projection of u→ onto the…

Q: (34) Compute SSp (6e3y + 1) dA where D is the solid triangle with vertices (0,0), (1,0), and (1,2).

A: Equation of the linejoining the points 0,0 and1,2  is  y-0x-0=2-01-0  Or,  yx=21=2  Or, y=2x…

Q: graph the points z = x + iy that satisfy the givenconditions.a. | z | = 2 b. | z | < 2 c. | z |…

A: a. We have given z=2 Then, put z=x+iy This implies that x+iy=2x2+y2=2x2+y2=4 Therefore, x2+y2=4…

Q: Let p(x) = kx* + kx + kx + k,x + kg, x E R be a polynomium without a first degree term whose graph…

A: The given polynomial is: p(x)=k4x4+k3x3+k2x2+k1x+k0

Q: 4. Evaluate . F.ds , where C is the triangle with vertices (1,0,0), (0,2,0), and (0,0,3) oriented by…

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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: Let A₁, A2, A3,..., A,, are n points in a plane whose co are (x₁, y₁), (x2, y2),..., (x, y),…

A:

Q: Let p(x) =-2x* + c,x' + c,x + c,x + c, x ER be a polynomium whose graph insersects the points (-2,…

A: Given. We are given a fourth degree polynomial and also four points on the curve of the polynomial…

Q: 2. Consider a natural cubic spline model with two knots at ci and c2 given by y = Bo + B1r+ B2(r -…

A: Given, spline model, y=β0+β1x+β2x-c13+β3x-c33+∈                         β2+β3=0  ,  β2c1+β3c2=0…

Q: Show that, in the triangular region with vertices (0,0), (1,0) and (1,1) the following double…

A: Double integral

Q: If (x, y) → (x + 3, y - 7)maps TUVWto T'U'V'W', what is the algebraic description that will map…

A: Given x,y→x+3,y-7 maps TUVW to T'U'V'W'. Let (x,y)→(a,b) where a=x+3, b=y-7 x=a-3,y=b+7 Therefore,…

Q: Show that if a two-parameter family of surfaces f(x, y, z, 1, µ) = 0 has an envelope, then the…

A:

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

A:

Q: If the plane F contains the points P(1, 0, 0), Q(3, 2, 0), R(0, 2, 1), L O 1 6 -6 O -2

A:

Q: 34) Show there is no plane perpendicular to n= î +î that passes through points P(1, 2, 3) and Q(2,3,…

A: Since you have submitted multiple question, we will solve the first question for you. To get the…

Q: 1)Prove that the curves o, = {|z|=2} y 0, = {|z- i|=4} are homotypic. 2)calculate O z*dz and o z*dz…

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Q: 11. Given the coordinates X(0,0), Y(6,3) 0/4 and Z(2,1), find the ratio where point Z partitions the…

A: Use Section formula to solve this question. According to section formula: let coordinates of X is…

Q: Let R = (c, 1,-1) where c denotes a real number. Let ä denote the plane x + y – z = 2. Find the…

A: Given Information -  The distance from the point R = (c,1,-1) to the plane x+y-z = 2 is 2. We have…

Q: (b) ſf f(x,y) dA if f(x, y) = y², where R is the triangular region with vertices (0, 1), (1, 2) and…

A:

Q: Let C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Green's…

A:

Q: Show there is no plane perpendicular to n=i+jn=i+j that passes through points P(1,2,3)P(1,2,3) and…

A: This is the rough image Point P(1,2,3) and Q(2,3,4) are the points on the plane…

Q: dA where R is the quadrilateral with the 5: Evaluate RI+y vertices (1,0), (4,0), (0,1), (0,4) using…

A: The solution are next step

Q: Let C denote the triangle with vertices at (0, 0), (0, 1) and (2, 1), oriented positively. Then f(x²…

A: We have to apply the green's theorem here.

Q: xy−5yz−7xz,x=st,y=e^(st),z=t^2 Compute ∂w/∂s(1,−2)=

A: The equation given as  w=-2xy-5yz-7xz , x=st , y=est ,z=t2. The partial derivative of the function…

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: Aa, Bb, and Cc are medians of triangle ABC with centroid at G , if aG = x, what is AG?  a. x b. 2x…

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Q: Let C, be the straight line path z = (1 + í)4, 0 sts 1; Ca the quarter circle z = 1 - cos t + i sin…

A: Only zdz for curves C2 and C3 are in question 7 the answer is i, in question 8 it must be z*dz for…

Q: 2. Show that the equations f(r, y,P. q) = 0 and g(r, Y.P. q) = 0 are compatible if %3D %3D a(f,g)…

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Q: 4 6 Let y = 7 2 40 Compute the distance d from y to the plane in IR spanned by ui and uz d =

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Q: Let f(z) = 5z + 14, and let C1 be the line segment from z = 0 to z = 2, let C2 be the line segment…

A: In this question, we calculate the complex integral along the given contour joining vertices of the…

Q: Find the maximum value of f(r, y) = 10ry(4 – 8z - 4y) over the triangle with vertices (0, 0), (,0)…

A:

Q: 4 Let y = U2 = -7 U1 = -4 4 -6 -2 -9 Compute the distance d from y to the plane in IR° spanned by u̟…

A:

Q: Let f: R → R be the function which satisfies for all (z. y, z) € R° that z cos(ry) and let C C R' be…

A: Here we have to find out line integral of function f(X,Y,Z).

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: Let f(x, y, z) = eª + zy² and let C be a straight line segment connecting the points (4,2,1) and…

A: Given: The function is fx,y,z=ex+zy2 and let C be a straight line that will connect the points 4,2,1…

Q: Let C be the rectangle in the xy-plane with vertices (0,0), (1,0), (0, 2) and (1, 2), and let F(r,…

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Q: I need help w/ following integration by pullback

A: Given that R be the parallelogram with the vertices at (1,0), (3,1), (4,4), (2,3). And…

Q: Use Green's Theorem to evaluate $. xydx + x²y³dy, where C is the triangle with vertices (0,0), (1,0)…

A: Consider the provided question, ∮cxydx+x2y3dy,     where c is the triangle with vertices 0,0, 1,0…

Q: c. Let P(x, y) = y² + sin¬1 x² and Q(x, y) = 2xy + 4x. Suppose that C is the parallelogram with…

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Q: Given Fxy 2) = (z², xy, yz) and C is a triangle in the plane x + y + z = 2 with vertices (1,1,0),…

A: We will use basic knowledge of vector calculus.

Q: 4. Show that the distance between the two points z1 and z2 in an Argand diagram is |z1 – z2). In…

A: (6) z-1=2 Given that:The points z=x+iy satisfies the condition z-1=2 The complex number z=x+iy…

Q: Let ƒ (x, y) = x² - y² . Find all all points (x, y) such that Vf(x,y) =±(1, 1).

A: