document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042719>Question 1042719</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The towers supporting the cable of suspension bridge are 1200m apart and 170m above the bridge it supports.Suppose the cable hangs,following the shape of parabola,with its lowest point 20m above the bridge.How high is the cable 120m away from a tower? Sketch the graph. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #657758 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=657758\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The towers supporting the cable of suspension bridge are 1200m apart and 170m above the bridge it supports.<BR>\n" );
document.write( "Suppose the cable hangs,following the shape of parabola,with its lowest point 20m above the bridge.<BR>\n" );
document.write( "How high is the cable 120m away from a tower? Sketch the graph.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "lets have the bridged centered at the origin<BR>\n" );
document.write( "Three points are needed on the parabola<BR>\n" );
document.write( "x = 0, y = 20<BR>\n" );
document.write( "x = -600, y = 170<BR>\n" );
document.write( "x = +600, y = 170<BR>\n" );
document.write( "using the form ax^2 + bx + c = y, we know that c=20<BR>\n" );
document.write( "x=-600, y = 170 and x =+600, y = 170; write two equations<BR>\n" );
document.write( "-600^2a - 600b + 20 = 170<BR>\n" );
document.write( "+600^2a + 600 + 20 = 170<BR>\n" );
document.write( "use elimination<BR>\n" );
document.write( "360000a - 600b + 20 = 170<BR>\n" );
document.write( "360000a + 600b + 20 = 170<BR>\n" );
document.write( "------------------------------addition eliminates b<BR>\n" );
document.write( "720000a + 40 = 340<BR>\n" );
document.write( "720000a = 300<BR>\n" );
document.write( "a = 300/720000<BR>\n" );
document.write( "a = .0004167<BR>\n" );
document.write( "Now we can write the equation<BR>\n" );
document.write( "y = .0004167x^2 + 20<BR>\n" );
document.write( "Graphically<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-700%2C+700%2C+-100%2C+200%2C+.0004167x%5E2%2B20%2C+170%2C+116%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-700%2C+700%2C+-100%2C+200%2C+.0004167x%5E2%2B20%2C+170%2C+116%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"How high is the cable 120m away from a tower? \"<BR>\n" );
document.write( "600 - 120 = 480<BR>\n" );
document.write( "Solve for x=480<BR>\n" );
document.write( "y = .0004167(480^2) + 20<BR>\n" );
document.write( "y = 96 + 20<BR>\n" );
document.write( "y = 116 m high (blue line) </SPAN>\n" );
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