Find a mapping G that maps the disk u² + v² < 1 onto the interior of the ellipse ()² + (² ≤1. Identify the correct mapping. G(u, v) = (bu, av) G(u, v) = (au, bu) G(u, v) = (alu, blu) G(u, v) = (ula, vlb) Then use the Change of Variables Formula to find the area A of the ellipse. (Express numbers in exact form. Use symbolic notation and fractions where needed.) A =

Q: Find the equation of the tangent plane to the surface z =9-(r² +y2) at the point (1,1,7). Write the…

A: Given surface is z=9-x2+y2⇒x2+y2 +z=9⇒x2+y2 +z-9=0 Take  fx, y, z= x2+y2 +z-9 And, Point say P is 1,…

Q: 2. (§1.1) Sketch the following set of points in the x-y plane. {(x, y) = R²: (y - x²) (y + x²) < 0}.

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Q: Find a scalar equation of the plane that contains the points (−1, −3, 1), (1, 0, 3), and (2, 7, 0).

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Q: Let 5x + 3y + 10% = 0 be the equation of the 3 plane in R³ spanned by (1, a, 0) and (1,0, b). Find…

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Q: Determine the Cartesian equation of a plane that has x-, y-, and z- intercepts 1/3, 1, and -1/2,…

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Q: Find an equation for the plane containing the three points (0, 1, -1), (1,0,1), and (2, 1, 0). Where…

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Q: Find an equation of the plane through the points P(0, 1, 1), Q(1, 1,1), and R(1,1,0). Write the…

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Q: classify and sketch the surface given by x2+2y2+z2-4x+4y-2z+3=0 (indicate the vertex coordinate)

A: Here we have given a surface equation as below:  x2+2y2+z2-4x+4y-2z+3=0 The surface given by the…

Q: Let the solid form in the orthogonal coordinate system xyz be surrounded by points A, B, C, D and F,…

A: The given co-ordinates of vertices are A = (-4, 1, 3), B = (6, 1, 1), C = ( 9, 5, 0), D = (4, 5, 1),…

Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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Q: Q3: Find the distance between the origin and the plane containing the points A(1,1,0), B(-1,0,1) and…

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Q: Find a parametric representation for the surface. the plane that passes through the point (0, -1, 5)…

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Q: Surface Plane Point z = V 98 - x? x = 9 (9, 1, 4) 100 100 50 of -50 -100 50 10 10 -50 -100 -10 -10…

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Q: Consider the three following points of R'. A = (0, 2, 2) B = (1, 1, 1) C = (-1, 1,2) (a) Find the…

A: The scalar equation of a plane is of the form: ax+by+cz+d=0, where a, b, c ,d are constants. The…

Q: t G(u, v) = (6u + v, 32u + 9v) be a map from the uv-plane to the xy-plane. Find the image of the…

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Q: Find a mapping G that maps the disk u? + u < 1 onto the interior of the ellipse () + G) : <I.…

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Q: Find a parametrization for the line SEGMENT between (- 5, 7, 6) and (2, – 6, – 9). |

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Q: - 3 - 2 Let y = u2 = Find the distance from y to the plane in R' spanned by u, and u2. - 6 u = - 5 1…

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Q: Find a parametric form for the line through the point (0, –7, -9) and parallel to the vector 6i – 7j…

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Q: Find a parametric representation for the surface. the plane that passes through the point (0, -1, 2)…

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Q: Find the distance from Po = (3, 9, 6) to the plane 3x + 4y – 5 = 0.

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Q: the scalar equation of the plane containing both the line of intersection of the planes defined by…

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