Problem 52. Use Stoke's theorem to evaluate fy°dx – x³dy + z³dz where C is the trace of the cylinder x² + y? =1 in the plane r + y + z = 1 oriented counterclockwise.

Q: 7. Identify the surface for each of the following equations. (a) z = r² (b) r² + z² = rl (c) p = 4…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Problem 3. Calculate the first fundamental forms of the following surfaces: (a) x(u, v) = (u - v, u…

A: According to guidelines we should have been able to solve only first question at a time #3

Q: 42. Whatever the value of p > 0 in the equation y = x²/(4p), the y-coordinate of the centroid of the…

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Q: 2 7 Find the projection of v = -1 onto the line tlof R'Igiven by the parametric equation e = tul…

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Q: Question 13 Solve the problem. Find parametric equations for the normal line to the surface x² +…

A: Find parametric equations for the normal line to the surface x2 + 2xyz + y2 = 4z2 at the point (1,…

Q: Problem 4 B Find, by using polar coordinates in R?, the volume of the region bounded above by the…

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Q: Problem #8: Use Stokes' Theorem to evaluate F. dr where F = (x + 9:)i + (7x + y) j + (6y – =) k and…

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Q: Problem 1. Parametrize the following surfaces: (a) 2x + 3y + z = 6. (b) z = 9 – Vx² + y?. - (c) x² +…

A: As per Bartleby's answering policy, we can answer only one question with a maximum of three…

Q: Problem 2. Find the value of a > 0 such that the cone 22 = x² + y?, z > 0 is orthogonal to the…

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Q: Question 11 Calculate the surface area of the given surface. The parabolic cylinder with equation z…

A: Given: The parabolic cylinder lies over the triangle in the xy-plane with vertices (0,0),(0,4) and…

Q: 3.4.6 Use Green's theorem in a plane to evaluate the line integral 110²-35²) x + ( [(e¹-3y²) dx +…

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Q: Problem 2. (6 Points) Calculate the first fundamental forms of the following surfaces: (a) x(u, e)…

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Q: Chapter 13, Section 13.7, Question 017 (a) Find all points of intersection of the line x = -1+t, y…

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Q: Problem 2. Consider the space curve 7(t) = (et, e2at, e3at) for a postitive constant a > 0. (a) Find…

A: Given the space curve r→t=eαt,e2αt,e3αt, α>0. The equation of the plane obtained in problem 1 is…

Q: Problem 3. Calculate the first fundamental forms of the following surfaces: (a) x(u, v) = (u – v, u…

A: Hi! You have posted multiple questions. As per the norm, we will be answering only the first one. If…

Q: Work Problem1 a) Find the exact length of the curve 1 ,1< < 2. y = 4 3x b) Find the exact area of…

A: Given  curve  y=x34+13x    , 1≤x≤2

Q: Question 8. Consider the surface defined by x² – - = 1. Draw the traces of this surface…

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Q: Problem 3. Calculate the surface area, Area (S) = || ds z+ z3 +1 dA, of the part of the paraboloid z…

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Q: Problem 1. Find Fn dS if S is the sphere (x-1)´+y+z=1 , S and F(x, y,z)= (x³, x²y , zy°) . 2

A: n = 820 , x=22 Po=xn=22820=0.0268 npo(1-Po)=820(0.0268)(1-0.0268)     = 22(0.9732)           = 21.41…

Q: Problem 5 Let D be the region in the ay-plane where * + y < 2r, * + y* < 1 y 20 and and For any…

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Q: Problem 3: Evaluate ff,F· dA using Gauss, where F = half of the sphere x2 + y? + z²2 = 9. (2²x, y³ +…

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Q: Problem 1: Use spherical coordinates to evaluate the integral of Vr2+ y? + z2 over the ball of…

A: Since you have posted multiple question we are supposed to be answer only first one... kindly repost…

Q: Question 3 Find the tangent plane to the equation z 3r - 5y + 5y at the point (- 5, 2, 65). Submit…

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Q: Use Problem 6 to show that the area inside the ellipse x = a cos θ, y = b sin θ,0 ≤ θ ≤ 2π, is A =…

A: To show that the area inside the ellipse x=acosθ,y=bsinθ,0≤θ≤2π is A=πab. We know that…

Q: Problem II. Find the nonvanishing connection coefficients for the 2-dim space- time metric below ds?…

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Q: Chapter 13, Section 13.7, Question 031 Find parametric equations for the tangent line to the curve…

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Q: Chapter 5, Reserve Problem 5/054 Determine the coordinates of the centroid of the shaded area. 1.5"…

A: To determine the coordinates of the centroid of the given shaded region.

Q: The classification of az дх2 дхду ду dz, dz O A. Elliptic B. None of these О С. Нурerbolic D.…

A: Answer and explanation is given below

Q: Problem 2 (a) # fc [37 – + ] dz (z+3i)* Evaluate -- - z+3i where C is the circle Z + 3i| = 7+ 7, 0 <…

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Q: Question 18 Find the surface area of that portion of the surface 2 = V4 -x that lies above the…

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Q: Question 1 Consider the solid under the plane Z = x and above the rectangle 0 < x < 1 by 0 < y < 2

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Problem #4: Evaluate the following integral, xyz dS, where S is the surface with parametric…

A: We will find out the required value.

Q: Problem 4. Find fe F- di where C is a circle of radius 2 in the plane z + y+ z = 9, centered at (4,…

A: By stoke's theorem, ∫cF.dr =∫∫ScurlF. Nds We know that curl F=∇×F…

Q: Ex.9. An ellipsoid y2, z2 = 1 is surrounded by a luminous a? b2 ring x = 0, y2 + z² = a². Show that…

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Q: b) a dr+(x+yz) dy+(ry- VE) dz, C is the boundary of the part of the plane 3r+2y+z in the first…

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Q: Problem 4: Find the vector function that represents the curve of intersection for the following…

A: Given surface 1 is, x2+z2=9 Given surface 2 is, x2+y2+4z2=25........(1)

Q: Is it true or false that by using a suitable translation x = x' + xo, Y = y' + Yo, it is possible to…

A: Transforming the conic equation

Q: Problem 0.4. Give an orientation and orientation preserving parametrization to the following curve C…

A: Given that -

Q: Problem 6 / (3y – xª + 2) dx + (5x + sin y*) dy, where C is the counterclockwise- Use Green's…

A: Given ∫C3y-x4+2dx+(5x+siny3)dy Where C is the counterclockwise oriented boundary of the triangle…

Q: Problem 5 Find the volume of the wedge cut from the first octant by the cylinder z = 12-3y? and the…

A: To Determine: find the volume of the wedge cut from the first octant by the cylinder z=12-3y2 and…

Q: Ex.5 Given the Jordan curve y that is the counterclockwise oriented boundary of the set T= {z=x+iy :…

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Q: Question 8. [. t = 1. 'Let r(t) = 5i+ t²j-²k. Compute the curvature k(t) at the point where (1,0,0)…

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Q: Practic Problem # 2.5 RS that Find the parametric equa tious of the liue in through the poiuts.…

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Q: Problem II We consider a parametrization of a regular surface S, given by X (u, v) = (u+2v, 2uv, 2u…

A: Here the equation of the tangent plane to the surface will be Xu×Xv.x-6,y-8,z-2=0 where X=Xu,v is…

Q: If I have a pair of parametric equations  x=20cos(t) and y=10sin(t)  How can I increase the speed…

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Q: 9.45.) (a) Use the figure to show that x =r cos ø, y = r sin ø and x' = r cos( ø – 0),y' = r sin (4…

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Q: Problem 2. Find the value of a > 0 such that the cone 22 = x² + y², z > 0 is orthogonal to the…

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