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Question 1 Let Si be the part of the paraboloid z = x2 + y that is inside the cylinder x + y? = 9, S2 the part of the cylinder x2 + y? = 9 between the planes z = 0 and z = 9 and S3 the part of the plane z = 0 that is inside the cylinder x2 + y? = 9. Let R be the region that is enclosed by S1, S2 and S3. %3D !! %3D a) Assume that units of x, y, z are metres. Calculate the surface area of S1. b) Using polar coordinates, calculate the volume of R. Consider the vector field v(x) = (2x + 2y)i + (2y – 5z)j + (4x – z)k. c) >>

Question 1 Let Si be the part of the paraboloid z = x2 + y that is inside the cylinder x + y? = 9, S2 the part of the cylinder x2 + y? = 9 between the planes z = 0 and z = 9 and S3 the part of the plane z = 0 that is inside the cylinder x2 + y? = 9. Let R be the region that is enclosed by S1, S2 and S3. %3D !! %3D a) Assume that units of x, y, z are metres. Calculate the surface area of S1. b) Using polar coordinates, calculate the volume of R. Consider the vector field v(x) = (2x + 2y)i + (2y – 5z)j + (4x – z)k. c) >>

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter7: Locus And Concurrence
Section7.2: Concurrence Of Lines
Problem 20E
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Question 1 Let Si be the part of the paraboloid z = x2 + y that is inside the cylinder x + y? = 9, S2 the part of the cylinder x2 + y? = 9 between the planes z = 0 and z = 9 and S3 the part of the plane z = 0 that is inside the cylinder x2 + y? = 9. Let R be the region that is enclosed by S1, S2 and S3. %3D %3D %3D a) Assume that units of x, y, z are metres. Calculate the surface area of S1. b) Using polar coordinates, calculate the volume of R. Consider the vector field v(x) = (2x + 2y)i + (2y – 5z)j+ (4x – z)k. c) <<
Transcribed Image Text:Question 1 Let Si be the part of the paraboloid z = x2 + y that is inside the cylinder x + y? = 9, S2 the part of the cylinder x2 + y? = 9 between the planes z = 0 and z = 9 and S3 the part of the plane z = 0 that is inside the cylinder x2 + y? = 9. Let R be the region that is enclosed by S1, S2 and S3. %3D %3D %3D a) Assume that units of x, y, z are metres. Calculate the surface area of S1. b) Using polar coordinates, calculate the volume of R. Consider the vector field v(x) = (2x + 2y)i + (2y – 5z)j+ (4x – z)k. c) <<
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