document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160797>Question 1160797</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The cable of a suspension bridge hangs in the form of a parabola when the load is uniformly distributed horizontally. The distance<BR>\n" );
document.write( "between the two towers is 1500 ft, the points of support of the cable on the towers are 220 ft above the roadway, and the lowest<BR>\n" );
document.write( "point on the cable is 70 ft above the roadway. Find the vertical distance of the cable from a point in the roadway 150 ft from the<BR>\n" );
document.write( "foot of a tower. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784236 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=784236\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The cable of a suspension bridge hangs in the form of a parabola when the load is uniformly distributed horizontally.<BR>\n" );
document.write( " The distance between the two towers is 1500 ft, the points of support of the cable on the towers are 220 ft above the roadway, and the lowest point on the cable is 70 ft above the roadway.<BR>\n" );
document.write( " Find the vertical distance of the cable from a point in the roadway 150 ft from the foot of a tower.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let the first support be at x=0, y=220<BR>\n" );
document.write( "let the 2nd support be at x=1500, y=220<BR>\n" );
document.write( "the lowest point: x=750, y=70 (half way across the bridge)<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Using the form ax^2 + bx + c = y, <BR>\n" );
document.write( "x=0, y=220, we know c = 220<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x= 750, y= 70<BR>\n" );
document.write( "750^2a + 750b + 220 = 170<BR>\n" );
document.write( "5625000a + 750b = 70 - 220<BR>\n" );
document.write( "5625000a + 750b = -150<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x=1500, y=220<BR>\n" );
document.write( "1500^2a + 1500b + 220 = 220<BR>\n" );
document.write( "2250000a + 1500b = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "multiply the 1st equation by 2, subtract from above equation<BR>\n" );
document.write( "2250000a + 1500b = 0<BR>\n" );
document.write( "1125000a + 1500b = -300<BR>\n" );
document.write( "--------------------------subtraction eliminates b, find a<BR>\n" );
document.write( "1125000a = 300<BR>\n" );
document.write( "a = 300/1125000<BR>\n" );
document.write( "a = .0002667<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find b<BR>\n" );
document.write( "2250000(.0002667) + 1500b = 0<BR>\n" );
document.write( "600 + 1500b = 0<BR>\n" );
document.write( "1500b = -600<BR>\n" );
document.write( "b = -600/1500<BR>\n" );
document.write( "b = -.4<BR>\n" );
document.write( "The equation: y = .0002667x^2 - .4x + 220<BR>\n" );
document.write( "looks like this, green is 70 ft<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-500%2C+1700%2C+-50%2C+250%2C+.0002667x%5E2-.4x%2B220%2C+70%2C+166%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"Find the vertical distance of the cable from a point in the roadway 150 ft from the foot of a tower.\"<BR>\n" );
document.write( "x = 150<BR>\n" );
document.write( "y = .0002667(150^2) - .4(150) + 220<BR>\n" );
document.write( "y = 6 - 60 + 220<BR>\n" );
document.write( "y = 166 ft height at 150 ft from the tower (blue line)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );