5. (a) (4) Find the area of the surface S, which is the part of x² + y² + ² = 4 that lies inside the cylinder x² + y² = 3. Find the mass of the surface S where S is given by rly 1).

Q: 2. Let r > 0, and let R be the semicircular region bounded below by the x axis and above by the…

A: Consider the provided question, Let r > 0, and let R be the semicircular region bounded below by…

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Q: 1. What is the differential for the total surface area of a frustum of a cone with l as the slant…

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Q: Find the volume of the solid lying above the cone z = /x² + y² and below the sphere x2 + y² + z² = 2…

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Q: Let S be the solid with base given by the triangle in the ry-plane with vertices (0,0), (1,0), (0,3)…

A: The complete solutions are given below

Q: A fluid has density 900 kg/m³ and flows with velocity v = zi+yj + zk, where x, y, and z are measured…

A: Given: Density ρx,y,z=900 kg/m3  , v→=xi^+yj^+zk^. To find: The rate of flow outward through the…

Q: (27) Find the surface area of the part of the sphere x² + y² + above the xy-plane and it is…

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Q: 6. Find the area of the part of the surface z = x² - y², which lies in the first octant that is…

A: The given problem is to find the area of part of the surface, which lies in the first octant that is…

Q: 2. A solid is in the first octant lies inside the hemisphere z = 4 - x² - y², outside the cone z =…

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Q: usuƏp seu pin 100 kg/m and flowS With Ve Zk, whei y, and z are measurec in meters, and the…

A: Density of fluid=1100kg/m3 Flow with velocity v=xi^+yj^+kz^ To find the rate of flow outward through…

Q: 4 The area of the surface S = {(x, Y, z) E R³ : z = 5 – x² – y², z > 3} equals (A) 4ñ 9. (B) 5* 13…

A: 4 Given S=x,y,z∈R3:z=5−x2−y2,z≥3.. We have to find the surface area of S At z=3 ⇒3=5−x2−y2⇒x2+y2=2…

Q: A fluid has density 600 kg/m³ and flows with velocity xi+yj + zk, where x, y, and z are measured in…

A: From the given information we get:

Q: The semicircle above the x-axis centered at origin with a radius=1 is rotated about x-axis to create…

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Q: VI? + y? and (3) Find the centre of mass (, ỹ, 2) of the solid enclosed by the cone z = the sphere…

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Q: (a) y² + ² = 4 that lies inside the cylinder x² + y² = 3. Find the area of the surface S, which is…

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Q: 2. Find the exact location of the center of mass (x,y), given the region bounded by the parabola y =…

A: As per Bartleby guidelines we are supposed to answer only one question per post.  This post contains…

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Q: Find the volume of the solid bound by the surface z=(2x-y)^2+(x-y-1)^2 and the plane z=4. Question:…

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Q: 12. Determine the volume of the solid above the surface z = √x² + y² and inside the sphere x² + y² +…

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Q: - Cone o Find the volume of the solid region above the cone (zv3)" (z 2 0) and below the sphere x² +…

A: Using spherical coordinates,