Explanation Formula used: 1. d ( cos − 1 u ) d x = − 1 1 − u 2 d u d x Calculation: The angle between the beam and the perpendicular to the wall is increasing at the rate of 1.5 deg s . That is, the value of d θ d t = 1.5 deg s . From the given figure, the value of the adjacentside is 225 and the hypotenuse is x . By the basic property of trigonometry, the value of cos θ = Adjacent side Hypotenuse . cos θ = 225 x θ = cos − 1 ( 225 x ) Differentiate θ = cos − 1 ( 225 x ) with respect to t . d θ d t = d d t ( cos − 1 ( 225 x ) ) = − 1 1 − ( 225 x ) 2 ⋅ d d t ( 225 x ) = − 1 1 − 225 2 x 2 ⋅ − 225 x 2 ⋅ d x d t = 225 x 2 1 − 225 2 x 2 ⋅ d x d t On further simplification, d θ d t = 225 x 2 1 − 225 2 x 2 ⋅ d x d t 1

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 27.4, Problem 27E

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The speed that the length of the beam is increasing if the length of the beam is 315 ft long.

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Chapter 27.4, Problem 26E

Chapter 27.4, Problem 28E

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Chapter 27 Solutions

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