document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246029>Question 246029</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Differential calculus: Two automobiles start from point A at the same time.one travels west at 60mph and the other travels north at 35 mph. how fast is the distance between them changing 3 hours later. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179699 by </B><A HREF=/tutors/aboutme.mpl?userid=marcsam823><B>marcsam823(57)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=marcsam823><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=179699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine how far each car has travelled in 3 hours using <BR>\n" );
document.write( "Distance = rate x time <BR>\n" );
document.write( "Car A = 60mph x 3 hrs = 180 miles<BR>\n" );
document.write( "Car B = 35 mph x 3 hrs = 105 miles\r<BR>\n" );
document.write( "\n" );
document.write( "Draw a right triangle <BR>\n" );
document.write( "Label the horizontal leg \"x = 180\"<BR>\n" );
document.write( "Label the vertical leg \"y = 105\"<BR>\n" );
document.write( "Label the hypotenuse \"z\"\r<BR>\n" );
document.write( "\n" );
document.write( "Using the Pythagorean Theorem, solve for z:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+=+z%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+=+z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5E2+%2B+105%5E2+=+z%5E2 ALIGN=MIDDLE  ALT=\"180%5E2+%2B+105%5E2+=+z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32400+%2B+11025+=+z%5E2 ALIGN=MIDDLE  ALT=\"32400+%2B+11025+=+z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43425+=+z%5E2 ALIGN=MIDDLE  ALT=\"43425+=+z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+208.39 ALIGN=MIDDLE  ALT=\"z+=+208.39\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Before you proceed with the calculus identify your variables:<BR>\n" );
document.write( "Distances<BR>\n" );
document.write( "Let x = 180<BR>\n" );
document.write( "Let y = 105<BR>\n" );
document.write( "Let z = 208.39<BR>\n" );
document.write( "Rates of change<BR>\n" );
document.write( "Let dx/dt = 60 <BR>\n" );
document.write( "Let dy/dt = 35<BR>\n" );
document.write( "The variable you are solving for is dz/dt, the rate of change (i.e. how fast the two cars are moving apart after 3 hours)\r<BR>\n" );
document.write( "\n" );
document.write( "Differentiate the Pythagorean Theorem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+=+z%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+=+z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%28dx%2Fdt%29+%2B+%282y%29%28dy%2Fdt%29+=+%282z%29%28dz%2Fdt%29 ALIGN=MIDDLE  ALT=\"%282x%29%28dx%2Fdt%29+%2B+%282y%29%28dy%2Fdt%29+=+%282z%29%28dz%2Fdt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify the equation by dividing each term by 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%28dx%2Fdt%29+%2B+%28y%29%28dy%2Fdt%29+=+%28z%29%28dz%2Fdt%29 ALIGN=MIDDLE  ALT=\"%28x%29%28dx%2Fdt%29+%2B+%28y%29%28dy%2Fdt%29+=+%28z%29%28dz%2Fdt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Substitute the values from above<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28180%29%2860%29+%2B+%28105%29%2835%29+=+%28208.39%29%28dz%2Fdt%29 ALIGN=MIDDLE  ALT=\"%28180%29%2860%29+%2B+%28105%29%2835%29+=+%28208.39%29%28dz%2Fdt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for dz/dt:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10800+%2B+3675+=+208.39+%28dz%2Fdt%29 ALIGN=MIDDLE  ALT=\"10800+%2B+3675+=+208.39+%28dz%2Fdt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14475+=+208.39+%28dz%2Fdt%29 ALIGN=MIDDLE  ALT=\"14475+=+208.39+%28dz%2Fdt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing both sides by 208.39:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dz%2Fdt+=+69.46mph ALIGN=MIDDLE  ALT=\"dz%2Fdt+=+69.46mph\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is how fast the two cars are moving away from each other.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );