Double Integration and Ellipsoid Volume

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By EvaluativeSardonyx

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5 Questions

What is the volume of the ellipsoid described by $y^2 + rac{z^2}{4} = 1$ in the first octant?

What is the area of the circle $r = a(1+4 ext{cos} heta)$?

Find the angle between the surfaces $y^2 - z - 3 = 0$ and $y^2 + 9z = 0$ at the point $(2, -rac{1}{2})$.

What is the area between the curves $y = 0$, $y = 3x-6$, and $x^2 + y^2 = 36$?

Find the area enclosed by the curve $r = a(1+4 ext{cos} heta)$.

Description

This quiz involves solving double integration problems to find the area between given curves and the volume of an ellipsoid in the first quadrant. The solutions provided require understanding of triple integrals and bounds in the first octant.

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