document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189231>Question 1189231</A>: <I><SPAN STYLE=\"word-break: break-all;\"> t<BR>\n" );
document.write( "he center of a suspension bridge forms a parabolic arc. The cable is suspended from the top of the support <BR>\n" );
document.write( "towers, which are 800 ft apart. The top of the towers 170 ft above the road and the lowest point on the cable is <BR>\n" );
document.write( "midway between the towers and 10 ft above the road. Find the height of the cable above the road at a distance of <BR>\n" );
document.write( "100 ft from the towers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820536 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=820536\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the center of a suspension bridge forms a parabolic arc. The cable is suspended from the top of the support towers, which are 800 ft apart. <BR>\n" );
document.write( "The top of the towers 170 ft above the road and the lowest point on the cable is <BR>\n" );
document.write( "midway between the towers and 10 ft above the road. <BR>\n" );
document.write( "Find the height of the cable above the road at a distance of 100 ft from the towers<BR>\n" );
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document.write( "A parabola has the form y = ax^2 + bx + c<BR>\n" );
document.write( "Find the parabola with its vertex at (0,0) and the towers at (-400,0) and (400,0).<BR>\n" );
document.write( "Add the 10 feet later.<BR>\n" );
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document.write( "0 = 0*a + 0*b + c ---> c = 0<BR>\n" );
document.write( "160 = a*(-400)^2 + b*(-400)<BR>\n" );
document.write( "160 = a*(400)^2 + b*(400)<BR>\n" );
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document.write( "160 = 160000a - 400b<BR>\n" );
document.write( "160 = 160000a + 400b<BR>\n" );
document.write( "--------------------------------- Subtract<BR>\n" );
document.write( "0 = -800b ---> b = 0<BR>\n" );
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document.write( "160 = 160000a<BR>\n" );
document.write( "a = 1/1000<BR>\n" );
document.write( "======================<BR>\n" );
document.write( "y = x^2/1000 + 10 is the equation of the cable<BR>\n" );
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document.write( "For 100 feet from the towers and between the towers:<BR>\n" );
document.write( "At x = 300:<BR>\n" );
document.write( "y = 90000/1000 + 10 = 100 feet\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );