• Find the area of the surface generated by revolving about the x-axis the upper half of the ellipse 4x2 + 16y² = 64. • Answer: 8t (47 + 3V3) 3/3 sq. units

Q: Find the surface area of the object obtained by rotating y = 1 +. 8x2 , 2<x 3 about the x-axis. 4

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Q: Find the surface area of the portion of the sphere generated by revolving the curve y = 1- x², 0sis…

A: y=1-x2,  0≤x≤12 Differentiating with respect to x, we get dydx=121-x2·0-2x=-x1-x2

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V8 - x, 25…

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Q: 7. The ellipse with the equation y2 = 1 is rotated about the x axis to form a solid shape. A…

A: Given:  An ellipse:x252+y242=1  , rotated around x-axis. A cylinderical hole of radius 2cm along…

Q: 4. By revolving the semicircle x = cost, y = sint (0 <t< ) about the x-axis, show that the surface…

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Q: A rectangle of maximum perimeter is to be inscribed in the ellipse x^2/22^2 + y^2/10^2 = 1. The…

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Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

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A: Area of the ellipse = πab.

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Q: the solid cut from the first octant by the surface z = 81-x2-y

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A: Topic:- cutting of surface

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Q: Find the points on the ellipse 3x2 + y2 = 3 that are farthest away from the point (1, 0). What I…

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Q: Classify the quadric surface. 4x2-y?- z2 = 1 O hyperboloid of one sheet O hyperbolic paraboloid O…

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Q: If tangent lines to the hyperbola 9x2 − y2 = 36 intersect the y-axis at the point (0, 6), find the…

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Q: Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that…

A: Given equation 2x2+72y2=72which can be writtenx236+y21=1

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Q: A space probe in the shape of the ellipsoid 4x + y +4z = 16 enters the earth's atmosphere and its…

A: To determine the hottest and coldest points on the probe's surface.

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Q: A rectangle of maximum perimeter is to be inscribed in the ellipse x^2/20^2 +y^2/11^2=1. The…

A: Explained below

Q: A Find the area of the surface generated by revolving the curve y = /2x-x² , 0.75sxs 1.75, about the…

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Q: x, y From a variable point of an ellipse - + 2 = Inormal is drawn to the ellipse. %3D a' b? Find the…

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Q: Find the volume of the solid formed if we rotate the ellipse+ = 1 about the line 4x + 3y = 20.

A: Calculation of Volume.

Q: Find the exact area of the surface obtained by rotating the curve about the y-axis: y = 3 + 5x2 ; 3…

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Q: Find the area of the surface generated by revolving the curve y = /2x-x, 0.75sxs1.25, about the…

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Q: You are given a y=sqrt(36-x^2), -3≤x≤3, curve that rotates about the x-axis. What is the area of the…

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Q: 4. Find the area of ​​the surface of the revolution formed by rotating the part of the 4x^2 + y^2= 4…

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Q: The area of the surface obtained by rotating the curve y = 36-x2, -6<xS6 about the x-axis is

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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: Sana wants to recycle some elliptic cardboard into rectangular name plates. The minor and major axes…

A: Given problem is : Sana wants to recycle some elliptic cardboard into rectangular name plates. The…

Q: Find the area enclosed by the ellipse x2  / a 2    +   y2   /b 2    =1

A: Given ellipse is The ellipse meet x-axis at points (-a,0) and (a,0) and y-axis at points (0,-b) and…

Q: Find the dimensions of the rectangie of largest area that can be inscribed in the ellipse x + 256y =…

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