Find the area of the surface. The part of the plane 3x + 5y + z = 15 that lies in the first octant

Q: Find the area of the paraboloid x? + y +z² = 2 by the plane y = 0.

A: We need to calculate the area of the paraboloid x2+y+z2=2 that is cut by the plane y=0. The equation…

Q: Find the area of the surface. The portion of the paraboloid  z = 49 − x2 − y2 in the first octant

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Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 4z that lies inside the…

A: Given sphere is x2+y2+z2=4z that lies inside the paraboloid  z=x2+y2. We have to find the area f the…

Q: Find the surface area of the part of the plane 4+ 2x + 3y that lies inside the cylinder x² + y? 9.

A: The area is given by using double integral

Q: Find the surface area of the tetrahedron bounded by the coordinate planes and the plane 8x + 12y +…

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Q: Find the area of the surface S where S is the cap cut from the paraboloid z = 2– x – y by the cone z…

A: Given that : z=2-x2-y2z=x2+y2 Now, to find the point of intersection , 2-x2-y2=x2+y2Put…

Q: Find the area of the surface. The part of the plane z = 9 + 2x + 5y that lies above the rectangle…

A: Given: The part of the plane z=9+2x+5y that lies above the rectangle0, 9×1, 6. To Find: Area of…

Q: Find the area of the surface. The part of the plane 2x + 4y + z = 8 that lies inside the cylinder x?…

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Q: Find the area of the surface. The part of the paraboloid z = 1 − x2 − y2 that lies above the plane…

A: Given that the part of the parabola z=1-x2 -y2 that lies above the plane z= -6 . Here we have to…

Q: Evaluate the surface integral. ∫∫sxdS, S is the part of the plane 6x+3y+z=6 that lies in the first…

A: The plane has intercepts at (1,0,0), (0,2,0), (0,0,6). The parameterize the surface S by. where

Q: 1. Find the area of the surface the part of the plane 3x + 2y + z = 6 that lies on the first octant

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Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: Solution:-

Q: Find the area of the surface. The surface cut from the bottom of the paraboloid z = x2 + y2 by the…

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Q: Find the surface area of that part of the plane 9x + 6y + z = 4 that lies inside the elliptic…

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Q: The volume of the tetrahedron enclosed by the coordinate planes and the plane 9x +y +Z = 18 is ?

A: We want to find the volume of the tetrahedron enclosed by the co-ordinate planes, i.e. x=0, y=0, z=0…

Q: 1. Find the area of the part of the surface z = a? + 2y that lies above the triangle with vertices…

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Q: Find the surface area of the plane ( 15x- ? 5z+20y=D35) if it is in the first octant

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Q: Find the area of the surface. The portion of the plane z = 6 - 3x – 2y in the first octant

A: We need to find the area of the portion of the plane z=6-3x-2y in the first octant. Let f(x, y) =…

Q: The area of the surface p = 2, 0sz<5,0<¢< T is 201 Select one: O True O False

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Q: Find the area of the surface. The part of the paraboloid z = 1 – x² – y2 that lies above the plane z…

A: Givenz=1-x2-y2z=-2Suppose the surface is defined byz=f(x,y) for x∈R, then the area of the surface is…

Q: Find the area of the surface of the part of the plane 3x + 2y + z = 6 that lies in the first octant.

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Q: Find the surface area of the portion of the part of the paraboloid z = 3 – x² – y² that lies above…

A: Given z = 3-x2-y2 , above the plane z=-1

Q: Find the surface area of the portion of the surface z = xy which is inside the cylinder p2 +3? = 9.

A: It is given that the portion of the surface is z=xy=fx,y. The surface area of the surface is…

Q: Find the area of the part of the sphere x2 + y? + z² = 4z that lies inside the paraboloid z = x2 +…

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Q: Find the area of the part of the plane 3x + 3y + z = 9 that lies inside the cylinder x2 + y2 = 25.

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Q: Find the surface area for the portion of the hemisphere z =sqrt(4 − x^2 − y^2) that sits above the…

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Q: Use polar coordinates to find the volume of the solid below the paraboloid z = 48 – 3x2 – 3y and…

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Q: Find the surface area of the part of the plane 3x + 2y + 4z = 24 that lies in the first octant…

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Q: SSx x dA; R is the portion of the disk x +y s 16 in the second quadrart

A: According to the given information, it is required to find the value of the given integral.

Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 49 that lies above the plane z =…

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Q: Find the area of the part of the sphere r? + y + z² = 4 that lies within the first octant and inside…

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Q: Find the area of the surface. The part of the paraboloid x = y² + z² that lies inside the cylinder…

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Q: 3) Find the surface area of the portion of the paraboloid z = x2 + y2 below the plane z = 1. %3D

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Q: Find c > 0 such that the area of the region enclosed by the parabolas y = a? – c² and y = c – a? is…

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Q: Find the area of the surface. The part of the plane  z = 4 + 3x + 2y  that lies above the rectangle…

A: Consider the part of the plane that lies above the rectangle .

Q: Find the surface area of the part of the plane z = 2 + 6x + 3y that lies inside the cylinder a? + y?…

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Q: Evaluate ffp(4xy + 1) dA, where R is the region in the upper half-plane bounded by the circles a? +…

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Q: )الكــره the Sphere OThe Portion of planes z=l x +y+Z² = \6 between the %3D and z=2.

A: Volume of the sphere x2+y2+z2=16 or x2+y2=16-z2 is: V=∫z=12∬x2+y2≤16-z2dxdydz   =∫z=12π16-z2dz…

Q: Find the surface area of the part of the sphere x2+y2+z2=9 that lies above the cone z=√x2+y2

A: answer is below

Q: Find the surface area of that part of the plane 3x + 10y + z = 9 that lies y? inside the elliptic…

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Q: Find the area of the surface. The part of the plane 3x + 2y + z = 6 that lies inside the cylinder…

A: Find the area of the surface. The part of the plane 3x + 2y + z = 6 that lies inside the cylinder…

Q: Find the area of the surface z = x² + y? that lies below the plane z = 2.

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Q: Find the area of the finite part of the paraboloid  y = x2 + z2 cut off by the plane y = 4.

A: To find the area of the finite paraboloid y=x2+z2 cutt off by the plane

Q: Find the area of the part of the plane x + 4, y + z = 4 that lies in the first octant. 1. A = 12 2.…

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Q: Find the area of the surface. The part of the paraboloid z = 1 - x² – y2 that lies above the plane z…

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Q: Find the area of the finite part of the paraboloid y = x² + z? cut off by the plane y = 16. [Hint:…

A: Surface area in xy-plane

Q: Find the area of the surface. The part of the plane 2x + 4y + z = 8  that lies inside the cylinder…

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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: Find the area of the part of the plane  5x + 3y + z = 15  that lies in the first octant.

A: From the given statement, the plane is 5x + 3y + z = 15 and it is lies in the first octant.