Describe the surfaces obtained by setting one of the coordinates equal to a constant in cylindrical coordinates (a-c) and spherical coordinates (d-f). That is, describe (separately) the meaning of:

Q: 8. Set up and evaluate a spherical coordinates integral for the volume of the solid bounded below by…

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Q: :f (x, y, 2) = x + y; E = {(x, y, z) |1 0, y > 0}

A: In this question given that a function and it is in the cartetion coordinate. We can convert in…

Q: Determine the direction angles for the line with parametric equations x = 5 + 2t, y = 12 - 8t, and z…

A: Direction angle

Q: Evaluate I/| V x2 + y² dV, where E is the region that lies inside the cylinder x2 + y? = 16 and…

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Q: 5. Find the volume of the region bounded by the paraboloids z = 12 – x² - y² and z = 2x² + 2y². 2

A: To find volume using triple integral in cylindrical co ordinate system We will use relation between…

Q: Given the equaition 4x-12y=20 a.) Write a set of paametic cqyatan to olescnbe a paint miving aling…

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Q: Evaluate II| 6x(x2 + y2) dv, where E is the solid in the first octant that lies beneath the…

A: Since the integral lies in first octant so 0≤θ≤π/2 and z≥0.  Converting into cylindrical coordinates…

Q: convert the sphere function to spherical coordinates.

A: The given sphere equation is                                     x2 + y2 + z-232 = 1 ---------(1)…

Q: 4. Find the volume of the region bounded below by the cone z = 2√x² + y² and above by the sphere x²…

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Q: Evaluate z dv, where E is enclosed by the paraboloid z = x² + y2 and the plane z = 16.

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