document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169281>Question 169281</A>: <I><SPAN STYLE=\"word-break: break-all;\"> center oA suspension bridge has twin towers that are 1300 feet apart. Each tower extends 180 feet above the road surface. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cable at a point 200 feet from the f the bridge. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124852 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=124852\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A suspension bridge has twin towers that are 1300 feet apart. Each tower extends<BR>\n" );
document.write( " 180 feet above the road surface. The cables are parabolic in shape and are<BR>\n" );
document.write( " suspended from the tops of the towers. The cables touch the road surface at<BR>\n" );
document.write( " the center of the bridge. Find the height of the cable at a point 200 feet<BR>\n" );
document.write( " from the from the center of the bridge.<BR>\n" );
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document.write( "Find the equation for this:<BR>\n" );
document.write( "Three coordinates:<BR>\n" );
document.write( "0, 180; the vertical suspension point on the left<BR>\n" );
document.write( "650, 0; the center point that touches the road<BR>\n" );
document.write( "1300, 180; vertical suspension point on the right<BR>\n" );
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document.write( "Using: ax^2 + bx + c = y<BR>\n" );
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document.write( "0,180, we know c = 180<BR>\n" );
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document.write( "write equation from coordinates;<BR>\n" );
document.write( "(650^2)a + 650b + 180 = 0<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(1300^2)a + 1300b + 180 = 180<BR>\n" );
document.write( ":<BR>\n" );
document.write( " 422500a +  650b + 180 = 0<BR>\n" );
document.write( "1690000a + 1300b + 180 = 180<BR>\n" );
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document.write( "Multiply the 1st equation by 2, subtract from the 2nd equation<BR>\n" );
document.write( "1690000a + 1300b + 180 = 180<BR>\n" );
document.write( " 845000a + 1300b + 360 = 0<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "845000a - 180 = 180<BR>\n" );
document.write( "845000a = 180 + 180<BR>\n" );
document.write( "845000a = 360<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F845000 ALIGN=MIDDLE  ALT=\"360%2F845000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = .000426\r<BR>\n" );
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document.write( "find b:<BR>\n" );
document.write( ".000426(650^2) + 650b + 180 = 0 <BR>\n" );
document.write( "180 + 650b = -180<BR>\n" );
document.write( "650b = -180 - 180<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-360%29%2F650 ALIGN=MIDDLE  ALT=\"%28-360%29%2F650\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = -.5538<BR>\n" );
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document.write( "The equation; y = .000426x^2 - .5538x + 180<BR>\n" );
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document.write( "Looks something like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-500%2C+1500%2C+-100%2C+500%2C+.000426x%5E2-.5538x%2B180%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-500%2C+1500%2C+-100%2C+500%2C+.000426x%5E2-.5538x%2B180%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"Find the height of the cable at a point 200 feet<BR>\n" );
document.write( " from the from the center of the bridge.\"<BR>\n" );
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document.write( "200' before the midpoint of 650': x = 450<BR>\n" );
document.write( "and<BR>\n" );
document.write( "200' after the midpoint of 650': x = 850<BR>\n" );
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document.write( "Substitute these values for x and find y:<BR>\n" );
document.write( "y = .000426(450)^2 - .5538(450) + 180<BR>\n" );
document.write( "y = 86.265 - 249.21 + 180<BR>\n" );
document.write( "y = 17.055 ft<BR>\n" );
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document.write( "You can do the same for x = 850; it is 17.055 ft as you would expect.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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