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Part 4 of 8 Since we want the portion of the sphere which is above this circle, we return to the parametric representation z = V 100 - u? - v2 and limit z to be at least 50. We, therefore, have V 100-u? -v2 = z 2 V50,

Part 4 of 8 Since we want the portion of the sphere which is above this circle, we return to the parametric representation z = V 100 - u? - v2 and limit z to be at least 50. We, therefore, have V 100-u? -v2 = z 2 V50,

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 36E
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Part 4 of 8 Since we want the portion of the sphere which is above this circle, we return to the parametric representation z = V 100 – u? – v² and limit z to be at least 50. We, therefore, have V 100-u? -v² = z 2 50, which means u? + v2 < 50. Part 5 of 8 An alternative approach involves using spherical coordinates (p, 0, 4). In spherical coordinates, the sphere has the equation p = 10 10 Part 6 of 8 Therefore, we can use 0 and p as parameters and use the equations that allow us to convert from spherical to rectangular coordinates. We would then have x = 10 sin o cos 0 y = 10 sin (0)sin () 10 sin () sin (0) z = 10 cos () 10 cos (o) Part 7 of 8 The cone z = Vx2 + y? makes an angle of 45° with the z-axis. Therefore, to restrict to the portion of the sphere above the cone, we must require that Part 8 of 8 We must also specify that 0 sos TT. Submit Skip (you cannot come back)
Transcribed Image Text:Part 4 of 8 Since we want the portion of the sphere which is above this circle, we return to the parametric representation z = V 100 – u? – v² and limit z to be at least 50. We, therefore, have V 100-u? -v² = z 2 50, which means u? + v2 < 50. Part 5 of 8 An alternative approach involves using spherical coordinates (p, 0, 4). In spherical coordinates, the sphere has the equation p = 10 10 Part 6 of 8 Therefore, we can use 0 and p as parameters and use the equations that allow us to convert from spherical to rectangular coordinates. We would then have x = 10 sin o cos 0 y = 10 sin (0)sin () 10 sin () sin (0) z = 10 cos () 10 cos (o) Part 7 of 8 The cone z = Vx2 + y? makes an angle of 45° with the z-axis. Therefore, to restrict to the portion of the sphere above the cone, we must require that Part 8 of 8 We must also specify that 0 sos TT. Submit Skip (you cannot come back)
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