document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=914105>Question 914105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> calculus-rate of change\r<BR>\n" );
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document.write( "A pulley system on a pier is used to pull boats towards the pier for docking. Suppose that a boat is being docked and has a rope attaching the boat's bow on one end and feeding through the pier's pulley system on the other end. The pulley system is 1 meter higher than the height of the boat's bow. The rope is being pulled in at a rate of 1 m/s. When the boat is 6 meters from the pier, how fast is the boat approaching the pier? (Give your answer correct to five decimal places.)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #554868 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=554868\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A pulley system on a pier is used to pull boats towards the pier for docking. Suppose that a boat is being docked and has a rope attaching the boat's bow on one end and feeding through the pier's pulley system on the other end. The pulley system is 1 meter higher than the height of the boat's bow. The rope is being pulled in at a rate of 1 m/s. When the boat is 6 meters from the pier, how fast is the boat approaching the pier? (Give your answer correct to five decimal places.)<BR>\n" );
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document.write( "x = boat's distance<BR>\n" );
document.write( "r = rope length<BR>\n" );
document.write( "Get the distance as a function of the rope length.<BR>\n" );
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document.write( "Differentiate wrt time.<BR>\n" );
document.write( "dx/dt = (1/2)*2r*(r^2 + 1)^(-1/2)*(dr/dt)<BR>\n" );
document.write( "@ r = sqrt(37):<BR>\n" );
document.write( "dx/dt = sqrt(37)/sqrt(38)<BR>\n" );
document.write( "=~ 0.98675 m/sec </SPAN>\n" );
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