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

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 plane z = 24 - 3x - 2y in the first octant

A: ⇒Given:-  Equation of plane                      z=24-3x-2y  in 1stoctant In intercept form,…

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: 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 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 portion of the plane 2x + 3y + 4z = 28 lyingabove the rectangle 1 ≤ x ≤ 3, 2 ≤…

A: GIVEN  2x + 3y + 4z = 28  We need to find the area of the plane  lyingabove the rectangle 1 ≤ x ≤ 3,…

Q: Find the area of the surface cut from the paraboloid x² + y² -z = 0 by the plane z = 6. The surface…

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

A: Given that, Area of plane is x+2y-z+10=0 It lies above the disk {(x,y)/x2+y2≤4} in x,y plane. The…

Q: ? Find the surface area of the plane ( 15x-5z+20y%3D35) if it is in the first octant

A: Here we have to find the surface area of the plane 15x-5z+20y=35 ................... (1) for the…

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: 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: Find the area of the part of the paraboloid z=x +y² that lies under the plane 2=9.

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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: 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: Integrate G(x, y, z) = xyz over the surface of the rectangular solid cut from the first octant by…

A: Given: G(x,y,z)=xyz We have to integrate G(x,y,z) over the surface of the rectangular solidcut from…

Q: Find the area of the part of the paraboloid z=x² + y² that lies under the plane z=9.

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Q: Find the surface area of the paraboloid z =1-x² - y? that is above the xy-plane.

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Q: 3. Use polar coordinates to find the surface area of the paraboloid z = x² +y² – 5 that lies below…

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Q: Find the surface area of the part of the plane 7+ 2x + 5y that lies above the rectangle [1, 4] x [0,…

A: Given that  Z=7+2x+5y To find the area of the surface of the plane that lies above the rectangle

Q: Find the region in the xy-plane in which the following equation is hyperbolic: ((x- y)? - 1]u + 2u,…

A: Given partial differential equation x−y2−1uxx+2uxy+x−y2−1uyy=0 We have to find the region in the…

Q: Find the area of the part of the plane 4x + 3y + z = 12 that lies in the first octant.

A: to find:- surface area, A.

Q: Q4(a) Find the surface area of the part of the paraboloid z=10-x -y' that lies above the plane :=1.

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Q: Find the area of the surface. The part of the plane z = 7 + 5x + 2y that lies above the rectangle…

A: The given equation is, z=7+5x+2y The partial derivatives are, fx=5fy=2

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: 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: Find the area of the ellipse cut from the plane z = 6x by the cylinder x + y = 9. .... Surface area…

A: Substitute the equation of plane in the cylinder equation

Q: Find the area of the part of the plane defined by 3z + 2y + z 12 that lies in the first octant.

A: Given equation of plane :  3x+2y+z= 12

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

A: Given plane,  3x+5y+z=15Intercepts of the plane axis are  x=5, y=3, z=15

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

A: Solution

Q: The surface area of the part of the paraboloid z=x+y that lies under the plane z=2 is: Z=,

A: Surface area is given as A=∬D1+δzδx2+δzδy2dA

Q: Find, by using polar coordinates in R2, the volume of the region bounded by the paraboloid z = 20 –…

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Q: 3. Find the area of the surface cut from the paraboloid x? + y +z = 2 by the plane y = 0.

A: Here we have to find the area of the surface cut from the paraboloid x2+y+z2=2 by the plane y=0.

Q: Find the area of the surface. The part of the plane z = 8 + 5x + 2y that lies above the rectangle…

A: Area of the surface z=f(x,y) A(s)=∬1+fx2+fy2f(x,y)=8+5x+2yfx=5fy=2

Q: Find the surface area of the part of the plane z = 7+ 5x + 3y that lies inside the cylinder 2+ y² =…

A: Surface area: -The definite double integrals determine the surface area of any surface enclosed by a…

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: yz ds where o is the part of the plane x + y+ z = 1 that lies in the first octant.

A: Given The given integral ∫∫σyzds over the region x+y+z=1 that lies in the first octant can evaluated…

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

A: If z=fx, y then surface area is, AS=∫∫D1+zx2+zy2dA

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.