Question 3We consider a thin plate having the shape of the surface S parametrized byŘ(u, v) = v cos(u)i + v sin(u)j + uvkwith 0sus 4n and 0s v s 3 (indicated below). The thin plate is made of a material of varying density, which isproportional to the square of the distance from the central axis, i.e. the z axis.20-10 2010For the next two questions, you must give an exact answer and then a decimal approximation. You must show all themajor steps of your approach, but you can use software for algebraic calculations and evaluation of integrals.a) Calculate the mass of the plate.b) What height above the z = 0 plane is the center of mass of the plate located?

The equation of the thin plate is as given below. Ru,v=vcosui+vsinuj+uvk and 0≤u≤4π 0≤v≤3

We consider a thin plate having the shape of the surface S parametrized by Ř(u, v) = v cos(u)i + v sin(u)j + uvk with 0sus 4n and 0s v s 3 (indicated below). The thin plate is made of a material of varying density, which is proportional to the square of the distance from the central axis, i.e. the z axis.

We consider a thin plate having the shape of the surface S parametrized by Ř(u, v) = v cos(u)i + v sin(u)j + uvk with 0sus 4n and 0s v s 3 (indicated below). The thin plate is made of a material of varying density, which is proportional to the square of the distance from the central axis, i.e. the z axis.

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 31E

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