document.write( "Question 1193573: A ladder 10 meters long is leaning against a wall. If the bottom of the ladder is being pushed
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Algebra.Com's Answer #825627 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A ladder 10 meters long is leaning against a wall. If the bottom of the ladder is being pushed
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document.write( "Let x be horizontal distance from the wall and y be vertical coordinate.\r\n" );
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document.write( "Then from Pythagoras\r\n" );
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document.write( "    x^2 + y^2 = 10^2.    (1)\r\n" );
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document.write( "Here x = x(t) and y = y(t) are functions of time, t.\r\n" );
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document.write( "Differentiate equation  (1)  over t.  You will get\r\n" );
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document.write( "    2x*x'(t) + 2y*y'(t) = 0,\r\n" );
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document.write( "hence\r\n" );
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document.write( "    y't = - (x*x'(t))/y.\r\n" );
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document.write( "Evaluate it at the given values  x = -6 m,  x'(t) = 2 m/s,  y =  =  =  = 8.\r\n" );
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document.write( "You will get  y'(t) = -  =  =  m/s = 1 m/s = 1.5 m/s.    ANSWER\r\n" );
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