Explanation Given Info: Given r ( t ) = 〈 R cos ( 2 π N t h ) , R sin ( 2 π N t h ) , t 〉 and 0 ≤ t ≤ h Formula Used: General parametric equation for helix is given by, r ( t ) = 〈 a cos t , a sin t , b t 〉 with radius a Calculation: Compared to the general parametric equation for helix, the given parametric equation represents a helix. For the given parametric equation, radius of the circle in the X-Y plane is given by, x 2 + y 2 = [ R cos ( 2 π N To determine b) To guess which of the two springs in the given figure uses more wire. To determine c) To compute and compare the lengths of two springs.

ACHIEVE FOR CALCULUS 4 TERM >CSI CUSTOM<

21st Edition

ISBN: 9781319438333

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 13.3, Problem 23E

To determine

a)

To show that $r (t)$ parametrizes a helix of radius $R$ and height $h$ making $N$ complete turns.

To determine

b)

To guess which of the two springs in the given figure uses more wire.

To determine

c)

To compute and compare the lengths of two springs.

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Chapter 13.3, Problem 22E

Chapter 13.3, Problem 24E

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