let f(xyz)=xy Sis surface of cylneder x+y²=4 14741 Ⓒ parametrize s S M(u, v) = ? @ N find Ň SS fds=? S
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- Find the surface area for the portion of the hemisphere z =sqrt(4 − x^2 − y^2) that sits above the annular region in the firstquadrant of the xy-plane between the circles x^2 + y^2 = 1 and x^2 + y^2 = 4.Consider the surface x^2 +y^2 −2xy−x+ 3y−z = −4 at the point P0(2, −3, 18).Find the center and radius of sphere x^2+y^2+z^2-20z =0.
- et △ABC be a triangle in S^2 (the two-dimensional sphere). Let the dual point C'∈S^2 of C be defined by the following three conditions:(i) d(C' , A)=π/2(ii) d(C' , B)=π/2(iii) d(C' , C)≤π/2A' and B' are defined analogously. Thus we get a dual triangle △A' B' C'. More precisely, △ABC is a non-degenerate triangle, andit follows (you may assume) that △A' B' C' is too.(question) Are there triangles △ABC in S^2 identical to their own dual △A'B'C'? I would be very thankful if you could provide some explanation with the steps, thank you in advance.Sketch the surfaces 1. 9x2 + y2 + z2 = 9 2. 4x2 + 9y2 + 4z2 = 36What is the total length of the curve of intersection of the surfaces x2 + y2 + z2 = 4 and y2 + 2z2 = 4?