Let the surface S be part of the cone z2 = x2 + y2 which is inside the cylinder x2 + y2 = 2y, outside cylinder x2 + y2 = 1 and above the xy plane.

Q: Find the equation of the tangent line to the trace y-3 of the quardic surface defined by 9x² + 2y²…

A: We have to find the equation of the tangent line to the trace y=3 of the quardic surface defined by…

Q: A surface is defined by coordinate or parametric functions of more than two variables. Select one:…

A: A surface is defined by coordinate or parametric functions of more than two variables.

Q: III. Find a set of parametric equations for the curve of intersection of the cylinder (x-1)² + ² x²…

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Q: Sketch the graph of the parametric surface. x= sinh u, y=v, z=2cosh u.

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Q: Determine the surface area of the solid obtained by rotating the following parametric curve about…

A: Given: x=9+t2, y=2t, 0≤t≤2

Q: The parametric equations I= 11 + (I2- 1)t, y=y+ (y2- y1)t where 0<t< 1 describe the line segment…

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Q: Find the lines curvatures, the first and second fundamental forms of the surface: the surface

A: As per the question we are given a surface. And we have to find its first and second fundamental…

Q: Find an equation of the tangent plane to the parametric surface

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Q: Determine an equation for the plane that's tangent to the surface z = 6x2 + 7y2 at point (-3, -2,…

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Q: Which of the following is the coordinates of all points on the surface with equation z = x³-5xy¹…

A: To find the coordinates of all points on the surface where the surface has a horizontal plane, we…

Q: Determine the parametric equations of the curve of intersection of the paraboloid x? – y? + z² = 0…

A: Detailed explanation mentioned below

Q: Find polar coordinates (r, 0) of the point (1, -V3), where r <0 and 0 s0 < 2m

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Q: Folve differential equation by variation of parameters. y" – 4y' + 4y = 2e2

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Q: Let u (41, U2, Uz). Explain why u•u > 0. When is u•u 0?

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Q: 1) let L be the line of intersection of the planes x+y+z=6 and x-y + 2z = 0. Find parametric…

A: To find the parametric equation for the line through the point that is perpendicular to the line of…

Q: Find an equation for the surface obtained by rotating the line z = 7y about the z-axis.

A: On solving this we will get

Q: Use polar coordinates to integrate under z=xy above the first quadrant of the unit circle on the xy…

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Q: 1) Let S be the surface of the cylinder r+y = 4 with y >0 and -15z<1. Find a parametric equation…

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Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y z 1…

A: Given:

Q: Find the distance on the xy plane between the two points, given below as polar coordinates (7,…

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Q: y2 f(x, y)dx dy Let f(x, y) = e-x2-y² and

A: answer is in next step