! Consider a solid hemispherical piece, of radius 1, whose pointdensity p (x, y, z) is equal to the distance between the point (x, y, z)and the origin of coordinates.Calculate the mass of the piece. For the resolution of the exercise,investigate thespherical coordinates and apply them in the calculation of thecorresponding integral.2t + 3r(t), In(t² + 2)t2 + 1for t> 0. Supposedescribes the position of a particle in the plantime is measured in seconds and distance in meters.a) Determine a unitary tangent vector to the displacement of theparticle at time t= 2.b) Determine the speed with which the particle is moving at theinstant t = 2.c) What is the acceleration of the particle at the same instant?

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Consider a solid hemispherical piece, of radius 1, whose point density p (x, y, z) is equal to the distance between the point (x, y, z) and the origin of coordinates. Calculate the mass of the piece. For the resolution of the exercise,

Consider a solid hemispherical piece, of radius 1, whose point density p (x, y, z) is equal to the distance between the point (x, y, z) and the origin of coordinates. Calculate the mass of the piece. For the resolution of the exercise,

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.1: The Rectangular Coordinate System

Problem 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...

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Question

Consider a solid hemispherical piece, of radius 1, whose point
density p (x, y, z) is equal to the distance between the point (x, y, z)
and the origin of coordinates.
Calculate the mass of the piece. For the resolution of the exercise,
investigate the
spherical coordinates and apply them in the calculation of the
corresponding integral.
2t + 3
r(t)
, In(t² + 2)
t2 + 1
for t> 0. Suppose
describes the position of a particle in the plan
time is measured in seconds and distance in meters.
a) Determine a unitary tangent vector to the displacement of the
particle at time t= 2.
b) Determine the speed with which the particle is moving at the
instant t = 2.
c) What is the acceleration of the particle at the same instant?

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