a) The parameterization of the curve on the surface of the sphere with 0 (t) of the spherical radius R is given by the angles & = (t) and 0 = coordinate system, when t = [a, b]. Prove that an expression can be obtained for the arc length of the curve ·b [{"* |r′(1)\ dt = f*°* √\x²′(1)² + y'′(1)² + z'(t)}² dt = R 2 √ (1)² + sin² (1) · 0¹ (1) ² dt. b) According to the latest research by a docent on duty at the equator, the equator has bulged due to thermal expansion due to climate change Calculate its approximate length in case R = 1. ㅠ +0,1 cos(10t), 0=t, 0≤ t ≤ 2π. 2
a) The parameterization of the curve on the surface of the sphere with 0 (t) of the spherical radius R is given by the angles & = (t) and 0 = coordinate system, when t = [a, b]. Prove that an expression can be obtained for the arc length of the curve ·b [{"* |r′(1)\ dt = f*°* √\x²′(1)² + y'′(1)² + z'(t)}² dt = R 2 √ (1)² + sin² (1) · 0¹ (1) ² dt. b) According to the latest research by a docent on duty at the equator, the equator has bulged due to thermal expansion due to climate change Calculate its approximate length in case R = 1. ㅠ +0,1 cos(10t), 0=t, 0≤ t ≤ 2π. 2
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
Section10.6: The Three-dimensional Coordinate System
Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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