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Given the vector-valued function for curve C as r(t) = (3t², 8et, 2t), answer the following. (a) Provide an arc length reparametrization of the curve measured from the point (0,8,0) moving in the direction c increasing t. (b) Determine the curvature of the function r(t) at a general point (i.e. leave in terms of t). (c) Determine the curvature at the point (0,8, 0). d) Determine the normal vector at the point (0,8,0).

Given the vector-valued function for curve C as r(t) = (3t², 8et, 2t), answer the following. (a) Provide an arc length reparametrization of the curve measured from the point (0,8,0) moving in the direction c increasing t. (b) Determine the curvature of the function r(t) at a general point (i.e. leave in terms of t). (c) Determine the curvature at the point (0,8, 0). d) Determine the normal vector at the point (0,8,0).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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Can you help me how to do this problem can you please do it step by step And can you do the parts as well 

Given the vector-valued function for curve C as r(t) = (3t², 8et, 2t), answer the following. (a) Provide an arc length reparametrization of the curve measured from the point (0,8,0) moving in the direction of increasing t. (b) Determine the curvature of the function r(t) at a general point (i.e. leave in terms of t). (c) Determine the curvature at the point (0,8,0). d) Determine the normal vector at the point (0,8, 0).
Transcribed Image Text:Given the vector-valued function for curve C as r(t) = (3t², 8et, 2t), answer the following. (a) Provide an arc length reparametrization of the curve measured from the point (0,8,0) moving in the direction of increasing t. (b) Determine the curvature of the function r(t) at a general point (i.e. leave in terms of t). (c) Determine the curvature at the point (0,8,0). d) Determine the normal vector at the point (0,8, 0).
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