document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123366>Question 1123366</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. What is the velocity of the top of the ladder when the base is given below?<BR>\n" );
document.write( "a.) 20 feet away from the wall </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #739661 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=739661\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the ladder be y feet above the ground and x feet from the wall<BR>\n" );
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document.write( "use Pythagorean theorem <BR>\n" );
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document.write( "x^2 + y^2 = 25^2<BR>\n" );
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document.write( "take first derivative of each vaiable with respect to time<BR>\n" );
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document.write( "1)  2x * dx/dt + 2y * dy/dt = 0<BR>\n" );
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document.write( "we are given dx/dt = 2 feet per second<BR>\n" );
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document.write( "we want to find dy/dt when the ladder is 20 feet from the wall(x=20)<BR>\n" );
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document.write( "when x=20<BR>\n" );
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document.write( "20^2 + y^2 = 25^2<BR>\n" );
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document.write( "400 + y^2 = 625<BR>\n" );
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document.write( "y^2 = 225<BR>\n" );
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document.write( "y = 15 feet (we ignore the negative root, -15)<BR>\n" );
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document.write( "now use equation 1<BR>\n" );
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document.write( "(2 * 20 * 2) + (2 * 15 * dy/dt) = 0<BR>\n" );
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document.write( "80 + (30 * dy/dt) = 0<BR>\n" );
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document.write( "dy/dt = -80/30 is approximately -2.67<BR>\n" );
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document.write( "the velocity of the top of the ladder is -2.67 feet per second<BR>\n" );
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document.write( "the velocity is negative because the top of the ladder is sliding down the wall<BR>\n" );
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document.write( " </SPAN>\n" );
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