5) Consider the surface S shown in the graph, whose parametrization is given by by: r(u, v) = (v², 2uv, 4 – u), donde 0

Q: Find the coordinates of the centroid of the curve given belov x = cos t+tsin t, y =t cos t- sin t,…

A: Given data: The x-coordinate of the curve is x=cos t+tsin t. The y-coordinate of the curve is y=tcos…

Q: Show that the curve r= Vti + Vtj + (2t – 1)k is tangent to the surface x +y² – z = 1 when t=1

A: Given that r=ti+tj+2t-1k and f=x2+y2-z-1 Take the derivative for f, ∇f=ddx,ddy,ddzf=2x,2y,-1…

Q: 3.4.8 Evaluate the area of the surface z = 2-x² - y² lying above the (x, y) plane. (Hint: Use polar…

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Q: Find the line integral with respect to arc length (8x + 9y)ds, where C is the line segment in the…

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Q: This is a three part problem. Given: Find the line integral with respect to arc length (6x + 8y)ds,…

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Q: calc 3 13.7#1 make sure its right Evaluate the surface integral. ∫∫S yz dS S is the surface with…

A: Given a surface with parametric equations, x=u2, y=usin3w, z=ucos3w, 0≤u≤1, 0≤w≤π6. To evaluate the…

Q: 5.Consider the ellipsoid V(x,y,z)=rx2+σy2+σ(z−2r)2=c>0.Vx,y,z=rx2+σy2+σz−2r2=c>0.…

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Q: Fi for oec ind volume of the solid of revolution by rolahng about the -ais each regton boundad b the…

A: To calculate the volume of the given solid of revolution

Q: 7. Use Stokes's Theorem to write S.(2y² + 6x*)dx + (2x² + 7y³)dy+ (2z° – yz)dz as a surface integral…

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Q: 16 The area under the curve 4y? (x2 + 1)3 was rotated about a line located to the left 9 of y – axis…

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Q: Consider the surface S shown in the gure and whose parameterization is given by: r(u, v) = (sin v,…

A: Consider the surface S shown in the gure and whose parameterization isgiven by: r(u, v) = (sin v, u…

Q: (a) Given a surface function, z(x, y) == + xy with x cos0 and y= sin 0, 2 %3D az and əz (i) find ax…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 2. a. Calculate the surface integral of /(x.y,z) = obtained by parametric equation: over the full…

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Q: 14. (a) Give a parametrization for the intersection of y = x² and z = e". (b) Set up an integral…

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Q: (4) Use Stokes' Theorem to evaluate 11. Vx (yz, xz, xy) dS where S is the surface S that is the part…

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. x? from the origin to the (a) Find a vector parametric…

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: (6) Calculate the surface integral SSs F · ñdS where F = (ze", –3ze"V, xy) and S is the…

A: Given that,

Q: .... ........ 4.8. Find the area of the surface generated by revolving the curve x = cost, y =…

A: See the details solution in below

Q: 4. The surface described by the equation x2 + y + z² = 0 is a(an) (a) elliptic paraboloid symmetric…

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Q: 4. Consider the surface given by z = x x²esin y. (a) Find the equation of the tangent plane to z =…

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Q: Evaluate the unoriented line integral (2æ² + y² + z²) ds along the parametric curve a : [0, 1] → R³…

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Q: Find the line integral with respect to arc length / Q = (0,3). (2x + 7y)ds, where C is the line…

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Q: 5. On the surface z-3x^2+2y^2 (an elliptic paraboloid), (x,y) changes from (1,1) to (0.99,1.02). Use…

A: Since you have asked multiple questions, we will solve the first question (Question 5) for you. If…

Q: B. Compute the shared mass between the polar curves (r = 1+ cose) and (r = 1- cose), usę density…

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Q: Find the line integral with respect to arc length ∫C(6x+4y)ds, where C is the line segment in the…

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Q: Consider the spherical surface E of center at C= (0,0.2) and radius 3. There are two planes parallel…

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Q: Solve the problem. 15) Find the centroid of the solid with constant density a enclosed between the…

A: Given :- The centroid of the solid with constant density α enclosed between the sphere of radius 2…

Q: 1. Find the area of the surface generated by revolving the parametric curve x=r cos 0, y = r sin 0…

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Q: Suppose the divergence of the electric field in some spherical region is found to be V E = 5kr³.…

A: as given,   the divergence of electric field in some spherical region is ∇·E=5kr3 claim- to find the…

Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: Find the volume of the solid bounded by the plane z = 0 and the paraboloid z = 9 - x2 - y2. SOLUTION…

A: Solution

Q: 4. Obtain the equation of the tangent plane to the surface with parametric representation r(u, v) =…

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

Q: u' cos u?, r? EXAMPLE 6.6.3 For a surface of revolution defined by x u sin u?, x3 = f (u'), where f…

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Q: 6. Compute the flux of F = [0, 0, z²] through the spherical surface S given as the upper hemisphere…

A: To find- Compute the flux of F→ = 0, 0, z2 through the spherical surface S given as the upper…

Q: # 4. Use Green's Theorem to evaluate the line integral P (y*dx +2xy° dy), where C is the positively…

A: Given integral is, ∮Cy4dx+2xy3dy

Q: u' cos u?, x? EXAMPLE 6.6.3 For a surface of revolution defined by x u' sin u?, x³ = f (u'), where f…

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: 3. Find the surface area of the surface generated by revolving the graph of the "curve" given…

A: The given parametric curve is: x=t,     y=t2,         0, 2

Q: Let C be the intersection curve of the paraboloid z = x2 − y2/2 with the cylinder x2 + y2 = 1,…

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Q: S Find the voleime of the solid generated by revolving the region baunded by the given lines Cnd…

A: Hint: Try Disk Method to find the volume.

Q: (10) Sketch the solid bounded by z = x2 + y? and z 4- x2 - y². Use cylindrical coordinates to find…

A: Given ∫∫∫Dx2+y2dVand solid bounded by z=x2+y2 and z=4-x2-y2

Q: 1. Use the cylindrical coordinate to evaluate fll. x² + y²dV where G is the solid bounded by…

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Q: (9) Evaluate by converting to cylindrical polar coordinates 322dV where E is the solid bounded by y…

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Q: Let F = (x'e* +2.xy - 2y)i+(cos y+x² +3x)j and let C be the ellipse with equation (2x - 2y) +(x+ y)°…

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Q: A) dS = v36u4 + 16u² + 36v² dA B) dS = V16u4 + 36u² + 36v² dA C) dS = v6u? – 4u – 6v dA D) dS =…

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Q: 2)Use Stokes' Theorem to evaluate | F.dr where F =2xyi- yj+2xzk and S is the first octant surface of…

A: The given problem is to evaluate the line integral in the surface of first octant with upward…

Q: 3. Set up the formulation to find the surface generated when the curve y = x² is revolved about the…

A: 1st we need to convert the curve in x=f(y) form and corresponding limits for y , Then use given…

Q: Find the line integral with respect to arc length (2x + 6y)ds, where C is the line segment in the…

A: The solution of line integral is given as follows :