document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328491>Question 328491</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5.	An airplane flies over an observer with a velocity of 400 mph and at an altitude of 2640 ft. If the plane flies horizontally in a straight line, find the rate at which the distance x from the observer to the plane is changing 0.6 min after the plane passes over the observer. RE sketch below.\r<BR>\n" );
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document.write( "                                               400        mph                           P\r<BR>\n" );
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document.write( "                     2640 ft                             X\r<BR>\n" );
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document.write( "                                        O<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 #235292 by </B><A HREF=/tutors/aboutme.mpl?userid=galactus><B>galactus(183)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=galactus><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=galactus><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=235292\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There a different ways to go about it, but I am going to convert everything to miles.\r<BR>\n" );
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document.write( "Since the plane is traveling 400 mph, in .6 minutes it travels x=4 miles.\r<BR>\n" );
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document.write( "We can build a right triangle. Let y=1/2 miles (2640 feet). This remains constant because the plane is not going higher or lower. Thus, dy/dt=0\r<BR>\n" );
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document.write( "dx/dt=400 mph\r<BR>\n" );
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document.write( "By Pythagoras, the distance from the observer to the plane is the hypoteneuse of the triangle: D=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281%2F2%29%5E2%2B4%5E2%29=sqrt%2865%29%2F2=4.031 ALIGN=MIDDLE  ALT=\"sqrt%28%281%2F2%29%5E2%2B4%5E2%29=sqrt%2865%29%2F2=4.031\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles.\r<BR>\n" );
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document.write( "So, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=x%5E2%2By%5E2 ALIGN=MIDDLE  ALT=\"D%5E2=x%5E2%2By%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Differentiate implicitly w.r.t time(t).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%2A%28dD%2Fdt%29=x%2A%28dx%2Fdt%29%2By%28dy%2Fdt%29 ALIGN=MIDDLE  ALT=\"D%2A%28dD%2Fdt%29=x%2A%28dx%2Fdt%29%2By%28dy%2Fdt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Enter in the knowns and solve for dD/dt, the rate of change of the distance between the observer and the plane.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2865%29%2F2%2A%28dD%2Fdt%29=4%2A%28400%29%2B%281%2F2%29%280%29 ALIGN=MIDDLE  ALT=\"sqrt%2865%29%2F2%2A%28dD%2Fdt%29=4%2A%28400%29%2B%281%2F2%29%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1600%2F%28sqrt%2865%29%2F2%29=640%2Asqrt%2865%29%2F13=396.91 ALIGN=MIDDLE  ALT=\"1600%2F%28sqrt%2865%29%2F2%29=640%2Asqrt%2865%29%2F13=396.91\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph </SPAN>\n" );
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