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Let o be the surface 3r+ 10y+9z = 4 in the first octant, oriented upwards. Let C be the oriented boundary of a. Compute the work done in moving a unit mass particle around the boundary of o through the vector field (5z - 8y) i + (8y – 102) j + (10z – 5z) k using line integrals, and using Stoke's Theorem. Assume mass is measured in kg, length in meters, and force in Newtons (1 nt = 1kg-m). LINE INTEGRALS Parameterize the boundary of a positively using the standard form, tv-P with 0

Let o be the surface 3r+ 10y+9z = 4 in the first octant, oriented upwards. Let C be the oriented boundary of a. Compute the work done in moving a unit mass particle around the boundary of o through the vector field (5z - 8y) i + (8y – 102) j + (10z – 5z) k using line integrals, and using Stoke's Theorem. Assume mass is measured in kg, length in meters, and force in Newtons (1 nt = 1kg-m). LINE INTEGRALS Parameterize the boundary of a positively using the standard form, tv-P with 0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Let o be the surface 3r + 10y + 9z = 4 in the first octant, oriented upwards. Let C be the oriented boundary of a. Compute the work done in moving a unit mass particle around the boundary of o through the vector field (5r - 8y) i+ (8y – 10z) j + (10z – 5x) k using line integrals, and using Stoke's Theorem. Assume mass is measured in kg, length in meters, and force in Newtons (1 nt = 1kg-m). LINE INTEGRALS Parameterize the boundary of o positively using the standard form, tv-P with 0 <t< 1, starting with the segment in the xy plane. C1 the edge in the xy plane) is parameterized by C2 (the edge following C1) is parameterized by C3 (the last edge) is parameterized by F. dr= F dr= F dr- C3 F dr = STOKE'S THEOREM a may be parameterized by r(r, y) = (r,y, f(r,y)) = curl F.
Transcribed Image Text:Let o be the surface 3r + 10y + 9z = 4 in the first octant, oriented upwards. Let C be the oriented boundary of a. Compute the work done in moving a unit mass particle around the boundary of o through the vector field (5r - 8y) i+ (8y – 10z) j + (10z – 5x) k using line integrals, and using Stoke's Theorem. Assume mass is measured in kg, length in meters, and force in Newtons (1 nt = 1kg-m). LINE INTEGRALS Parameterize the boundary of o positively using the standard form, tv-P with 0 <t< 1, starting with the segment in the xy plane. C1 the edge in the xy plane) is parameterized by C2 (the edge following C1) is parameterized by C3 (the last edge) is parameterized by F. dr= F dr= F dr- C3 F dr = STOKE'S THEOREM a may be parameterized by r(r, y) = (r,y, f(r,y)) = curl F.
C1 (the edge in the xy plane) is parameterized by C2 (the edge following C1) is parameterized by C3 (the last edge) is parameterized by F dr= F dr = %3D F dr = F dr= %3D STOKE'S THEOREM o may be parameterized by r(r, y) = (r, y, f(r,y)) = curlF= (curl F) - nds = dy dr
Transcribed Image Text:C1 (the edge in the xy plane) is parameterized by C2 (the edge following C1) is parameterized by C3 (the last edge) is parameterized by F dr= F dr = %3D F dr = F dr= %3D STOKE'S THEOREM o may be parameterized by r(r, y) = (r, y, f(r,y)) = curlF= (curl F) - nds = dy dr
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