Find the area of the surface. The portion of the paraboloid  z = 49 − x2 − y2 in the first octant

Q: z-1 Sc dz, E C ez -3z

A: ez=1+z+z22!+z33!+---+znn! Cauchy integral test ∫Cfzdz=2πilimz→z0fz0 if zeros lies in C. ∫Cfzdz=0 if…

Q: Use x = au, y = bv to show that the area of the ellipse x2 y? = 1 is rab. 62 a2

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Q: Suppose z = e23"/4 and w = 2e"/4, find 2 and express your answer in rectangular form. %3D

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Q: 33. Find the directrix. (y- 9)2 - 8 O y = -9 O y = -7 O x = -7 | x = -9

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Q: Evaluate .(x+y² +=?) dS, where S is the portion of the paraboloid x=5+y² + z? contained within the…

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Q: Q.1 Determine the centroid - 240 mm- r= 90 mm 120 mm

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Q: COWS is an isosceles trapezoid with legs CO and WS. The diagonals intersect at A. WA = 2x, CA =…

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Q: 3. Find the dimension of the largest rectangle (in terms of area) that can be inscribed in a circle…

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Q: A satellite dish is the shape of a paraboloid. The dish is 30 inches wide, and 10 inches deep. How…

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

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Q: Sketch the surface (−x2/16 + y2/16) = z.  Choose the correct graph of the equation.

A: We need to sketch the surface (−x^2/16 + y^2/16) = z.

Q: 2√ab y y² = 4ax b X

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Q: Determine the graph of the cylinder z=6y2−1.  Choose the correct graph of the equation.

A: Answer:-Option (C) The equation z= 6y2-1 will have a 2D plot in z-y plane. Now its 3-D graph will be…

Q: nd the area of th surra 2 The portion of the cone z = 6√√√x² + v² inside the cylinder x² + 2

A: In this question, we will find the area of the surface.

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.