document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165726>Question 1165726</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the towers of a parabolic suspension bridges 200 meter long are 40 meter high. If the lowest point of the cable is 10 meter above the roadway.find the:<BR>\n" );
document.write( "a) standard equation of the parabola<BR>\n" );
document.write( "b) vertical distance from the roadway to the cable at 50 meter from the center. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790270 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=790270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  the towers of a parabolic suspension bridges 200 meter long are 40 meter high. If the lowest point of the cable is 10 meter above the roadway.<BR>\n" );
document.write( "find the:<BR>\n" );
document.write( "a) standard equation of the parabola<BR>\n" );
document.write( "let the center of the bridge be at the origin 0,0 then when x=0 and y=10<BR>\n" );
document.write( "using the form ax^2 + bx + c = y, we know c=10<BR>\n" );
document.write( "x=-100, y=200<BR>\n" );
document.write( "10000a - 100b + 10 = 200<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x=100, y=200<BR>\n" );
document.write( "10000a, + 100b + 10 = 200<BR>\n" );
document.write( "use elimination with these two equations<BR>\n" );
document.write( "10000a - 100b + 10 = 200<BR>\n" );
document.write( "10000a + 100b + 10 = 200<BR>\n" );
document.write( "----------------------------Addition eliminates b, find a<BR>\n" );
document.write( "20000a + 20 = 400<BR>\n" );
document.write( "20000a = 400 - 20<BR>\n" );
document.write( "20000a = 380<BR>\n" );
document.write( "a = 380/20000<BR>\n" );
document.write( "a = .019<BR>\n" );
document.write( "therefore our equation is simple (b=0)<BR>\n" );
document.write( "y = .019x^2 + 10 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-150%2C+150%2C+-50%2C+250%2C+.019x%5E2%2B10%2C+200%2C+57.5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-150%2C+150%2C+-50%2C+250%2C+.019x%5E2%2B10%2C+200%2C+57.5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "green line is 200 meters<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b) vertical distance from the roadway to the cable at 50 meter from the center.<BR>\n" );
document.write( "x = 50<BR>\n" );
document.write( " y = .019(50)^2 + 10<BR>\n" );
document.write( " y = 57.5 vertical dist at 50 meters (blue line) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );