document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=912916>Question 912916</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bridge design: A cable of a suspension bridge is suspended (in the shape of parabola) between two towers that are 120 meters apart and 20 meters above the roadway. The cable touches the roadway midway between the towers.<BR>\n" );
document.write( "a) Find an equation for the parabolic shape of the cable.<BR>\n" );
document.write( "b) Find the length of the parabolic cable. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #554323 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=554323\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A cable of a suspension bridge is suspended (in the shape of parabola) between two towers that are 120 meters apart and 20 meters above the roadway. The cable touches the roadway midway between the towers.<BR>\n" );
document.write( "a) Find an equation for the parabolic shape of the cable.<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "You have 3 points and want to find a parabola that passes thru them<BR>\n" );
document.write( "Make the points (-60,0), (0,-20) and (60,0)<BR>\n" );
document.write( "-60 and 60 are solutions of the equation of the parabola, and -20 is the vertex.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = k(x-60)*(x+60) = k*(x^2 - 3600)<BR>\n" );
document.write( "To make the vertex -20, k = 1/180<BR>\n" );
document.write( "--> y = (x^2 - 3600)/180<BR>\n" );
document.write( "That's \"an equation.\"  You can add 20 to make the road at y = 0<BR>\n" );
document.write( "==================================<BR>\n" );
document.write( "b) Find the length of the parabolic cable.<BR>\n" );
document.write( "It's symmetrical about the y-axis, so find 1/2 the length from x = 0 to x = 60.<BR>\n" );
document.write( "L/2 = INT<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%281+%2B+%28dy%2Fdx%29%5E2%29%29dx ALIGN=MIDDLE  ALT=\"%28sqrt%281+%2B+%28dy%2Fdx%29%5E2%29%29dx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "dy/dx = x/90<BR>\n" );
document.write( "L/2 = INT<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%281+%2B+x%5E2%2F8100%29%29dx ALIGN=MIDDLE  ALT=\"%28sqrt%281+%2B+x%5E2%2F8100%29%29dx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "L/2 = (1/90)*INT<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2890%5E2+%2B+x%5E2%29%29dx ALIGN=MIDDLE  ALT=\"%28sqrt%2890%5E2+%2B+x%5E2%29%29dx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "L/2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F90%29%2A%281%2F2%29%2A%28x%2Asqrt%28x%5E2+%2B+8100%29+%2B+8100%2Aln%28x+%2B+sqrt%28x%5E2+%2B+8100%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "@ x = 0 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F180%29%2A%288100%2Aln%2890%29%29+=+45%2Aln%2890%29 ALIGN=MIDDLE  ALT=\"%281%2F180%29%2A%288100%2Aln%2890%29%29+=+45%2Aln%2890%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "@ x = 60 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F180%29%2A%2860%2Asqrt%2811700%29+%2B+8100%2Aln%2860+%2B+sqrt%2811700%29%29%29 ALIGN=MIDDLE  ALT=\"%281%2F180%29%2A%2860%2Asqrt%2811700%29+%2B+8100%2Aln%2860+%2B+sqrt%2811700%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "@ x = 60 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2811700%29%2F3+%2B+45%2Aln%2860+%2B+sqrt%2811700%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2811700%29%2F3+%2B+45%2Aln%2860+%2B+sqrt%2811700%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=~ 266.6784<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "@ x = 0 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2Aln%2890%29 ALIGN=MIDDLE  ALT=\"45%2Aln%2890%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=~ 202.4914<BR>\n" );
document.write( "--> L/2 =~ 64.187<BR>\n" );
document.write( "L = 128.374<BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "A hanging cable is not a parabola.  It's not that simple. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );