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29. A closed surface is defined in spherical coordinates by 3

29. A closed surface is defined in spherical coordinates by 3

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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can you answer number 29, then graph the given coordinates

VCTOR ANALYS 25 25 Using the coordinate system named, give the vector at point AQ,-1.-3) that extends to B1,34 (a) cartesian; (b) cylindrical (e) spherical 26. An electric field intensity is given as E- (100 cos mr + (50 sin r. At the point whose spherical coordinates are r-2,0- 60, 20, find: (a) E; (b) a unit vector (in cartesian coordinates) in the direction of E. 27. (a) Find , in spherical components at PO,-4,5). (b) Find , in cartesian componenta at P. 28. Given the points M(r 5,0-20, -120) and N( -2,0- 80,= 30 (a) find the distance from M to N; (b) give a unit vector in cartesian coordinates at M that is directed toward N: (e) give a unit vector in spherical coordinates at M that is directed toward N. 29. A closed surface is defined in spherical coordinates by 3<r< 5, 0.1n <0<03%, 1.2x << 1.6n. (a) Find the volume enclosed. (b) Find the distance from Pr-3,0-0.1n. = 1.2x) to P,(r- 5,0 - 0.3n, - 1.6n). (e) Find the total surface area. 34. (a) Give the vector in cartesian coordinates that extends from P(r- 4,0- 20°, - 10) to Qir- 7,0 - 120", - 75). (b) Give the vector in spherical coordinates at M(x - 5, y= 1,- 2) that extends to N(2,4,6). (c) How far is it from A(r= 110,0-30,- 60) to Bir = 30,0 - 75", - 125"? 31. Points A(r- 100,0- 90", - 0") and Br- 100,0 -90,- 5") are located on the surface of a 100-m-radius sphere. (a) What is their separation, using a path on the spherical surface? (h) What is their separation, using a straight-line path? 32 (a) Express a, in spherical components and variables. (b) Express a, in cylindrical com- ponents and variables.
Transcribed Image Text:VCTOR ANALYS 25 25 Using the coordinate system named, give the vector at point AQ,-1.-3) that extends to B1,34 (a) cartesian; (b) cylindrical (e) spherical 26. An electric field intensity is given as E- (100 cos mr + (50 sin r. At the point whose spherical coordinates are r-2,0- 60, 20, find: (a) E; (b) a unit vector (in cartesian coordinates) in the direction of E. 27. (a) Find , in spherical components at PO,-4,5). (b) Find , in cartesian componenta at P. 28. Given the points M(r 5,0-20, -120) and N( -2,0- 80,= 30 (a) find the distance from M to N; (b) give a unit vector in cartesian coordinates at M that is directed toward N: (e) give a unit vector in spherical coordinates at M that is directed toward N. 29. A closed surface is defined in spherical coordinates by 3<r< 5, 0.1n <0<03%, 1.2x << 1.6n. (a) Find the volume enclosed. (b) Find the distance from Pr-3,0-0.1n. = 1.2x) to P,(r- 5,0 - 0.3n, - 1.6n). (e) Find the total surface area. 34. (a) Give the vector in cartesian coordinates that extends from P(r- 4,0- 20°, - 10) to Qir- 7,0 - 120", - 75). (b) Give the vector in spherical coordinates at M(x - 5, y= 1,- 2) that extends to N(2,4,6). (c) How far is it from A(r= 110,0-30,- 60) to Bir = 30,0 - 75", - 125"? 31. Points A(r- 100,0- 90", - 0") and Br- 100,0 -90,- 5") are located on the surface of a 100-m-radius sphere. (a) What is their separation, using a path on the spherical surface? (h) What is their separation, using a straight-line path? 32 (a) Express a, in spherical components and variables. (b) Express a, in cylindrical com- ponents and variables.
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