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Unformatted text preview: 100 2 + b 2 ( t ) = c 2 ( t ) , (1) so diﬀerentiating this equation with respect to t , 2 b ( t ) b ( t ) = 2 c ( t ) c ( t ) . Solving for b ( t ), we have b ( t ) = c ( t ) c ( t ) b ( t ) , so at the time t ? of interest it follows that b ( t ? ) = c ( t ? ) c ( t ? ) b ( t ? ) = 300 · 600 b ( t ? ) . In order to determine the missing value b ( t ? ) we note that equation (1) holds for all time, and so in particular it holds for t = t ? . That is, 100 2 + b 2 ( t ? ) = c 2 ( t ? ) = 300 2 , so b ( t ? ) = √ 300 2100 2 = √ 80000 . It follows that b ( t ? ) = 300 · 600 √ 80000 = 180000 200 √ 2 = 450 √ 2 ft/hr . 2...
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This note was uploaded on 04/02/2012 for the course MTH 132 taught by Professor Kihyunhyun during the Fall '10 term at Michigan State University.
 Fall '10
 KIHYUNHYUN
 Calculus

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