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Consider the curve with parametrization given by: r(t) = (-4 cost, 4 sint, 8t) • Now re-parametrize the same curve by arc length. • If start at the point (-4, 0, 0) and follow this curve for 11 units of length, where will you be? Find the curvature of this curve. .

Consider the curve with parametrization given by: r(t) = (-4 cost, 4 sint, 8t) • Now re-parametrize the same curve by arc length. • If start at the point (-4, 0, 0) and follow this curve for 11 units of length, where will you be? Find the curvature of this curve. .

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the curve with parametrization given by: r(t) = (-4 cost, 4 sint, 8t) • Now re-parametrize the same curve by arc length. • If start at the point (-4, 0, 0) and follow this curve for 11 units of length, where will you be? Find the curvature of this curve. .
Transcribed Image Text:Consider the curve with parametrization given by: r(t) = (-4 cost, 4 sint, 8t) • Now re-parametrize the same curve by arc length. • If start at the point (-4, 0, 0) and follow this curve for 11 units of length, where will you be? Find the curvature of this curve. .
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Consider the curve from the previous probelm. 

Consider the curve you encountered in problem #1. Suppose that you are at the point (0, 0, 0) and subjected to a force given by: That force is given by: (mint (x²+y². +2³² +2²) = ² ( 2²³² +2²³ +2²) { ¹ (2²+z²+2²) = How much work will you do traveling along the curve from (-4, 0, 0) to (-4, 0, 16 π) ? Make sure to provide a clear, complete, and detailed solution. If you use any theorems, state which ones you are using clearly and also show why those theorems are appropriate to this problem. F(x, y, z) = (It's very similar, but not identical, to gravity)
Transcribed Image Text:Consider the curve you encountered in problem #1. Suppose that you are at the point (0, 0, 0) and subjected to a force given by: That force is given by: (mint (x²+y². +2³² +2²) = ² ( 2²³² +2²³ +2²) { ¹ (2²+z²+2²) = How much work will you do traveling along the curve from (-4, 0, 0) to (-4, 0, 16 π) ? Make sure to provide a clear, complete, and detailed solution. If you use any theorems, state which ones you are using clearly and also show why those theorems are appropriate to this problem. F(x, y, z) = (It's very similar, but not identical, to gravity)
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