Find the average squared distance between the origin and the points on the paraboloid z = 4 – x² – y², for z z 0.

Q: Compute the surface area of the cone generated by revolving c(t) = (8t + 5, 7t) about the x-axis for…

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Q: Find the area and centroid bounded by the curve 5y? = 16x and the curve y2 = 8x – 24.

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

Q: Evaluate ∭E sqrt(x2+y2) dV where E is the region that lies inside the cylinder x2+y2=4 and between…

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Q: Find the area of the portion of the cylindrical surface Y = 4 – x² in the first octant that is…

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Q: The area bounded by the curve z 4y+7, the y-ax y =0 and y 2 is dy3D O 18 22 11 O 15

A: Area bounded by the curve can be calculated as

Q: Evaluate (x + 2y) dA, where R is the region bounded by the parabolas y = 2x² and y = 1 + r?.

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Q: Show that at any point (x,y) on the curve y=bex/a ,the length of the subtangent is constant and the…

A: The given curve is y=bexa.

Q: Find the average height of the paraboloid z = x+y over the square 0sxs1, 0 sys1. The average height…

A: Here in this problem we are given                                      z=x2+y2  ,0≤x≤1 and 0≤y≤1We…

Q: The volume of the solid generated by the curve y = e, between z = 2 and z = 6 about the z- azis is

A: Given: The curve is y=e-x   To determine: The volume of the solid generated by the curve y=e-x…

Q: Find the surface area of the part of the plane 2x+2y +z=4 that lies inside the cylinder x²+y² = 2.…

A: Given that, the equation of the plane is 2x+2y+z=4 and the equation of the cylinder x2+y2=2. Note…

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse…

A: Lagrange's multiplier method uses the system of the equations obtained from the partial derivatives.…

Q: Evaluate the triple integral (x + 2y) dV where E is bounded by the parabolic cylinder y = 7x² and…

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Q: Q3. A- Use Greens theorem to evaluate the cireulation or flus for the velocity fiekd : S(x, y)=- *+y…

A: Given velocity field is  f(x,y)=1x+yi-1x+yj we have to find the flux for the boundary of square…

Q: Consider the region enclosed by the curves y = a2 +1 and y = 2r + 1:

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Q: Evaluate the line integral xyld x + (x²+y)dy] +. where c is the saruare farmed by the lines

A: Let us consider a line integral ∫CP dx+Qdy then it can be written as  ∫D∫∂Q∂x-∂P∂y dA  Where, P and…

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse…

A: Using Lagrange Multipliers with Two Constraints

Q: Use the method of Lagrange multipliers to find the absolute extrema of the f(x, y, z) = y + xz² x² +…

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Q: Evaluate the following. dV where R is the portion of the ball of radius 1 in 4-dimensions with all…

A: We need to evaluate the value of integral in 4 dimensions.

Q: 2. Fnd the area of the sur face in the first octant cut from the cone z2 = x2 y2 by the plane x +y =…

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Q: a) Find the points at which the twisted cubic F(t) = ti + t} +tk intersects the plane 4.x +2y+z = 24…

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Q: Find ||/ y dV, where E is the solid bounded by the parabolic cylinder z = x and the planes y = 0 and…

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Q: Find the plane tangent to the given surfaces at the specific point f(x, y) = x2 ln(2x+y) in (-1, 3)

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Q: Evaluate fff (3x + 2y)dV, where S is the solid bounded above by the plane z=4, below by plane z=0…

A: ∫∫∫(3x + 2y) dV=∫∫∫(3x + 2y) dxdydz = ∫z = 04∫y = -13∫x =-11(3x + 2y) dxdydz = ∫z = 04∫y = -134y…

Q: (a) 'Find the orthogonal trajectories on the surface of the sphere x' + y? + z = 0 with the…

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Q: Find the point on the surface f(x,y)=x2+y²+xy+21x+7y at which the tangent plane is horizontal.

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Q: Evaluate z² dv. where E is the region above the zy-plane below the cone z = 2+2 and inside the…

A: The given problem is to evaluate the given triple integral over the given region E bounded above by…

Q: Find the value(s) of c such that the area of the region bounded by the parabolae y=x^2 - c^2 and…

A: Given: The given parabolas are y=x2-c2 and y=c2-x2. Determine the points of intersection.…

Q: (8) Find the point(s) where the line r(t) = ti+(1+t)j+5k intersects the paraboloid z = x² + y?.

A: A detailed solution is given below.

Q: 3. Find the volume under the paraboloid 3z = 2.12 + 2y2, above the triangle enclosed by the lines y…

A: First we have to draw graph and find limit according to which we have taken strip along y . Find…

Q: Evaluate the line integral ∫Cx2ds, where C is a the curve given by the equation y=f(x)=lnx, 1≤x≤e.

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Q: Evaluate the triple integral (* + 1y) dV where E is bounded by the parabolic cylinder y = 32² and…

A: We have to find the triple integral  ∫∫∫E(x+y)dVwhere E is bounded by the parabolic cylinder y=3x2…

Q: Find c > 0 such that the area of the region enclosed by the parabolas y = x 450. c and y = c – x² is…

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Q: Find the area of the band cut from the paraboloid x² + y² – z = 0 by the planes z = 2 and z = 6.…

A: Given equation is, x2+y2 = z Band cut from the given paraboloid by the planes z = 2; z = 6 Area of…

Q: Given the area bounded by the parabola x² – 4x + 12y- 20 = 0, the x- axis and the lines x = 1 and x…

A: Sol

Q: Find the centroid of the third quadrant area bounded by the following curves y2+ 2y + 8x = −1 and y…

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Q: Find the points on the surface xy + yz + zx - x- z =0 where the ant pla

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Q: Evaluate the line integral |(2? + y) dx – x dy where C is the line segment from (2,5) to (5,9) in…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 8x + 16y + 24z on the elipse…

A: To determine the maxima and minima of the function f(x, y, z) with respect to the function is…

Q: Evaluate (x + 5y) dV where E is bounded by the parabolic cylinder y = x² and the planes z = 3x, y =…

A: given is  a partial differential equation in dX , dY, dZ we can partially integrate the given…

Q: Use Cartesian coordinates to evaluate y²2 dV D where D is the tetrahedron in the first octant…

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Q: Compute ,F · dS for F = (xy, 5y,0), S being the cone z² = x + y²,x² + y? 0, with the normal %3D…

A: The vector field is F=⟨xy, 5y, 0⟩ and the parametric equation of the cone is  Rr, θ=rcosθ, rsinθ, r…

Q: Find the equetion of the targent pane to tre grven Surfface at the Specified point Z=XSin(x+y) at…

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Q: Find the average height of the (single) 34. Average height of a cone cone z = Vx² + y² above the…

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Q: ind the average height of the (single) cone z = sqrrt(x2 + y2) above the disk x2 + y2<= a2 in the…

A: Given equation of cone is, Bounded by the disk,

Q: Find the average distance from a point P(x, y) in the disk x2 + y2<=a2 to the origin.

A: Average distance is given as

Q: Find f[fp Vx2 + y2 + z² dV, where D is the sphere of radius a centered at the origin.

A: We need to find the integral:∫∫∫Dx2+y2+z2dVwhere D is the sphere of radius a centered at the…

Q: f(x) = V4x +1, = V4x + 1, with 1< x < 5

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Q: Compute the surface area of the cone generated by revolving c(t) = (2t + 2, 6t) about the x-axis for…

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Q: Calculate fSp(3x + 2y) dA where D is the region in the first quadrant that is inside the circle x2 +…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…