Find the area of the ellipse cut from the plane z = 6x by the cylinder x + y = 9. .... Surface area = (Type an exact answer in terms of T.)

Q: Find the surface area of the portion of the paraboloid given by the equation z = 1– x2 – y² that is…

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Q: Consider the unit sphere x² + y² + z² = 1. Find the average distance from its north pole to a point…

A: Given: x2+y2+z2=1 It is equation of sphere of radius r=1 unit. We have to find the average distance…

Q: Find the area of the surface generated by revolving the curve about the (a) x-axis and (b) y-axis.…

A: Explanation and solution is given below....

Q: Find the surface area of the cone frustum generated by revolving the line segment y = (x/2) + (1/2),…

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Q: 3. Find the surface area of the surface created when the cylinder y + 2- intersects the cylinder 1²…

A: surface area of the surface given by equation z=f(x,y) A=∫∫Dfx2+fy2+1dA D is the region on xy plane

Q: (b) Find the surface area of the portion of the paraboloid given by the equation z = 1- x? – y? that…

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Q: 5a. Consider the right square pyramid with a horizontal plane intersecting the pyramid halfway up…

A: The horizontal plane will be parallel to the base of the pyramid.

Q: Find the area of the surface generated by revolving the curve y = Vx + 3, 4 < y <7 around the…

A: We have to find area of the surface . Given y=x3+3                                 4≤y≤7

Q: Find the area of the surface generated by revolving the curve 1 V1 + eb", 5x 0 < x < 2 around 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 area of the surface obtained by rotating the curve y = 4x + 4, 0 < x< 8, about %3D the…

A: To find- Find the area of the surface obtained by rotating the curve y2 = 4x + 4, 0 ≤ x ≤ 8, about…

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: 2-By revolving the semicircle: X= r cos t, Y=r sin t, (0<t<n) About the x-axis, Show that the…

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Q: 2. Find the area of surface that is generated by revolving the portion of the curve x = V16 – y , 0…

A: Given, x= √(16-y) Therefore, f(y)= √(16-y) Differentiating the above equation with respect to y we…

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. The part of the plane  x + 2y + 3z = 1  that lies inside the cylinder…

A: Compute the partial derivative as follows.

Q: 3. Find the area of the surface generated by revolving the curve = 2/1- y (-1 < y < 0) X about the…

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Q: Find the surface area of the portion of the surface x2- 2 In a+ V15 y - z = 0 above the rectangle 1…

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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: 2 Find the surface area of the portion of the cone x² + y² = 2² above the region inside the…

A: we have to find the surface area of the portion of the cone x2+y2=z2 above the region inside the…

Q: Solve for the surface area of a plane curve rotated about y-axis. y = ((x^6)/12)+(1/(8x^4)), 1 ≤ x…

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Q: III Find the area of the portion of the cylindrical surface y = 4- a2 in the first octant that is…

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Q: (1) Find the area of the surface of the portion of the cone 2 +y² between the cylinder y? = x and…

A: To find the surface area of cone between given cylinder and plane, use the surface area formula as…

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

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Q: Find the area of the surface. The portion of the plane y + z = 4 that lies above the region cut from…

A: Given:

Q: Find the area of the surface generated by revolving the curve y=−x^3/18​, −2√2≤x≤0​, about the​…

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Q: Find the area of the ellipse cut from the plane z= 8x by the cylinder x +y = 4. Surface area = (Type…

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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: 4. Find the area of the surface generated by revolving the curve y = v9 – x², - 2 < x < 2, about the…

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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 the surface area of the portion of the cone 22 = 4x² + 4y? nat is above the region in the first…

A: Given: The portion of the cone is Z2=4x2+4y2 which is bounded by the line y=x and the parabola y=x2

Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y² + z? = = 24 and the…

A: We have to write the intersection curve

Q: 6. Find the exact area of the surface obtained by rotating the curve, y = x³, 0 < x < 2, about the…

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Q: The area of the surface obtained by rotating the curve y = V4-x², -2 s xs 2 about the x-axis is

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Q: Calculate the surface area of the paraboloid with top radius R> 0 defined by 2 a² + y? 0< x² + y? <…

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Q: Compute the surface area of the surface generated by revolving one arch of the cycloid…

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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: Show that the volume of the segment cut from the paraboloid x2 /a2 + y2/ b2 = z/ c by the plane z =…

A: Show that the volume of the segment cut from the paraboloidX^2 /a^2 + y^2/ b^2 = z/ cby the plane z…

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 that is generated by revolving the portion of y=x2 between x=1 and x=2…

A: To the area of the surface that is generated by revolving the portion of y=x2 between x=1 and x=2…

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: (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

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

Q: • Find the area of the surface generated by revolving about the x-axis the upper half of the ellipse…

A: IN THIS QUESTION WE HAVE TO FIND AREA FROM REVOLUTION OF A ELLIPSE.

Q: Find the area of the surface obtained by rotating the curve y2 = 4x + 4 0<x<8 about the x-axis? %3D

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Q: Find the area of the surface generated by revolving the curve 1 V1+e*, 5x 0 < x < 2 around the…

A: We can find the area of the the surface as follows

Q: ii) Find the exact area of the surface obtained by rotating the curve 1 12x 3 y = x³ + 9 1 ≤ x ≤ 2,

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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: 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: The exact area of the surface obtained by rotating the following curve 6x = y + 12, 2 < x < 3 about…

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Q: 4. Find the centroid of a thin flat plate covering the region enclosed by the parabolas y = 2r and y…

A: The given problem is to find the centroid of the thin flat plate covering the region enclosed by…