Find the area of the plane xtay-zt 10=0 that lies above the disk xy-plare

Q: Find the centroid of the solid hemisphere of radius a that is enclosed between the ry-plane and z =…

A: Given solid hemisphere of radius a enclosed by xy-plane and z=a2-x2-y2 The centroid is given by the…

Q: Evaluate the surface integral. || x²yz ds, S is the part of the plane z = 1 + 2x + 3y that lies…

A: Given: ∫∫sx2yzdS where S is the part of the plane z=1+2x+3y that lies above the rectangle…

Q: Evaluate the surface integral LL 6xzdS where S is the part of the plane 2x + 2y + z = 4 that lies in…

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Q: Evaluate the surface integral. x dS, S is the part of the plane 16x + 8y + z = 16 that lies in the…

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Q: Evaluate the surface integral. xz ds, S is the part of the plane 2x + 2y + z = 4 that lies in the…

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Q: Evaluate the surface integral. ) ر م(ل 2) ds S is the part of the cylinder x² + y2 = 16 that lies…

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Q: The area of the plane z = 2x + 1 above the disk of radius 1 centered at the origin is (а) 4л. (b)…

A: As we know, z=fx,y defines a surface in xyz-space.  Formula for the surface area of the surface…

Q: Find the area of the part of the plane  z = ax + by + c  that projects onto a region in the…

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

A: Find your answer below below

Q: Find the surface area of that portion of the surface z = V4 -x that lies above the rectangle R in…

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Q: Evaluate fR z = Jx2 + y2 x2 + y2 + z2dxdydz, where r is the region bounded by the plane z = 3 and…

A: We will convert integral into spherical co ordinate system . 1st relation between cartesian and…

Q: Evaluate the surface integral. || x²yz ds, s is the part of the plane z = 1 + 2x + 3y that lies…

A: To find ∬Sx2yz dS Here 0≤x≤5  and 0≤y≤2 S→=xi→+ yj→+…

Q: Consider the area of the part of the plane z=ax+by+c that projects onto some region D in the…

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Q: Find the surface area of the part of the plane z = 5 + 4x + 3y that lies inside the cylinder a² + y?…

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Q: Find the value of the integral fs (V x A). da if the vector A = yi + zj + xk and Sis the surface…

A: Given the vector A=yi+zj+xk and S is the surface defined by the paraboloid z=1-x2-y2

Q: Evaluate the surface integral. /| x*yz ds, s is the part of the plane z=1+ 2x + 3y that lies above…

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Q: Miscellaneous volumes Use a triple integral to compute thevolume of the following regions.

A: The given equation of cone is and plane is, z=1-x2+y2 x+y+z=1

Q: Evaluate the surface integral  ffR(x+y)dS where σ is the portion of the plane z = 6 − 2x − 3y in the…

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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: Find the area of the surface defined by x + y + z = 1, x2 + 8y2 s 1.

A: Given,            x+y+z=1,     x2+8y2≤1

Q: Evaluate the surface integral. /| xz ds, S is the part of the plane 2x + 2y + z= 4 that lies in the…

A: We need to find surface integral.

Q: Evaluate the surface integral. J[x²³x² x²yz ds, S is the part of the plane z = 1 + 2x + 3y that lies…

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Q: Evaluate the surface integral: x dS,  S is the part of the plane  12x + 6y + z = 12  that lies in…

A: From the given statement, the plane is 12x + 6y + z = 12 and it is lies in the first octant.

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: * Find the surface area of the part of the plane 2x + 5y + z = 2 that lies inside the cylinder x? +…

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Q: Evaluate the surface integral. || x²yz dS, S is the part of the plane z = 1 + 2x + 3y that lies…

A: Given: The surface integral, ∫∫Sx2yz dS, S is the part of the plane z=1+2x+3y that lies above the…

Q: Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2…

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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: Find the surface area of that part of the plane 6x + 8y + z = 7 that lies inside the elliptic…

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Q: Find all points where the surface z = xy e-* + 2y-) has a horizontal tangent plane. %3D O A. O B.…

A: Given the surface

Q: Determine the element of surface area dS in the special case of the paraboloid of revolution z = x2…

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Q: Find the volume of the Intersection curve C C Projection of C on ay-plane

A: Given: Given paraboloids are z=x2+y2 and z=8-x2-y2 We want to find the volume bounded by the…

Q: Find the average height of the hemispherical surface z = √(a2 - x2 - y2) above the disk x2 + y2 ≤ a2…

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Q: Use Stoke's Theorem to evaluate the line integral / 7ydx + 3zdy + dz where C is the intersection of…

A: Use Stoke's Theorem to evaluate the line integral ∫C7y dx+3z dy+ dz, where C is the intersection of…

Q: The region cut from the solid elliptical cylinder x2 + 4y2≤ 4 by the xy-plane and the plane z = x +…

A: Given that, z=x+2 , x2+y2≤4

Q: Find the area of the part of the plane z=3x+5 y+3 that lies above the region R=(x,y) 2≤x≤3; 1sys5.

A: The given plane is z=3x+5y+3. Differentiate partially with respect to x, y respectively to obtain…

Q: Find the surface area of the paraboloid z = x² + y², 0 < z < 1. .

A: The surface is same as revolving the curve x2=z or x=z1/2, y=0 about z- axis. So surface area is:…

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

A: Average distance is given as

Q: Find the area of the surface obtained by rotating thecircle x2 + y2 = r about the line y =r.

A: We have to find the area of the surface obtained by rotating the circle x2 + y2 = r about the line y…

Q: need ASAP B. Find the area of the portion of the cylindrical surface y = 4 − x2 in the first…

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Q: Find the surface area of the portion of the semi cone z = x2 + y? that lies between the planes z = 6…

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Q: ~F = z(x2+ y2) ~k through the disk of radius 4 in the plane z = 2, centered on the z-axis, oriented…

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Q: Find a parametrization of the curve x^(2/3)+y^(2/3)=8^(2/3) and use it to compute the area of the…

A: Finding the parameters:

Q: Find the surface area of part of the paraboloid z = f(x, y) = x^2 + y^2 that lies under the plane z…

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Q: Find the surface area of z =1-(x^2)-(y^2) that is above the xy plane

A: Given equation of plane is  z=f(x,y)=1-x2-y2 we have to find the surface area above xy plane.

Q: Use Stokes' Theorem to calculate fe F-dĩ, where F = zyi+3=j+5zk, and C is the closed path around a…

A: Here given that F→=xy i^+3z j^+5x k^ and curve C in xz-plane. To find: ∫C F→·dr→ by Stokes' theorem.

Q: Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant. (Use…

A: Part of the plane equation   5x+4y+z=20⇒z=20-5x-4yPlane lies in the first octant , so x≥0 ,…

Q: Evaluate the surface integral. || x2yz ds, s is the part of the plane z = 1+ 2x + 3y that lies above…

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