The monkey saddle z = x³ - 3xy² can be intersected with the cylinder x² + y² = 1 to produce the curve shown in blue. The next few questions pertain to this curve. -10 Which vector function parametrizes this curve? (It may be helpful to use the identity cos 30 cos³ - cos 0 sin²0.) Or(t) =< cost, sint, cos 3t>, t = [0, 2π] Or(t) =< cost, sin 3t, cost >, t€ [0, 2π] Or(t) =< cos 3t, sin 3t, cos 3t >, t€ [0, 2n/3] r(t): =< cos 3t, sint, cost >, t€ [0, 2n] 16) What are the maximum and minimum distances of points on this curve from the origin? 1c) If a solenoidal force field F=<-y, x, 0> moves a particle once around this curve, counterclockwise as viewed from above the xy-plane, how much work does it do?

The monkey saddle z = x³ - 3xy² can be intersected with the cylinder x² + y² = 1 to produce the curve shown in blue. The next few questions pertain to this curve. -10 Which vector function parametrizes this curve? (It may be helpful to use the identity cos 30 cos³ - cos 0 sin²0.) Or(t) =< cost, sint, cos 3t>, t = [0, 2π] Or(t) =< cost, sin 3t, cost >, t€ [0, 2π] Or(t) =< cos 3t, sin 3t, cos 3t >, t€ [0, 2n/3] r(t): =< cos 3t, sint, cost >, t€ [0, 2n] 16) What are the maximum and minimum distances of points on this curve from the origin? 1c) If a solenoidal force field F=<-y, x, 0> moves a particle once around this curve, counterclockwise as viewed from above the xy-plane, how much work does it do?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.5: Polar Coordinates

Problem 98E

See similar textbooks