document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062337>Question 1062337</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A parabolic bridge is built across the water. It is 50m long, and its highest point is 4.5m high. \r<BR>\n" );
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document.write( "a)What is the equation of the graph, where y= The height above the water, and x=the horizontal distance from the origin.\r<BR>\n" );
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document.write( "b)A floating platform 20m wide is towed under the bridge. What is the greatest height of the deck above water level if the platform is to be towed under the bridge with at least 30cm horizontal clearance on either side.\r<BR>\n" );
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document.write( "Any help would be appreciated :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677225 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=677225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The solutions, or roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+0+ ALIGN=MIDDLE  ALT=\"+x+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+50+ ALIGN=MIDDLE  ALT=\"+x+=+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and half-way between these points at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+25+ ALIGN=MIDDLE  ALT=\"+x+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "I have the point ( 25, 4.5 )<BR>\n" );
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document.write( "(a)<BR>\n" );
document.write( "The general equation would look like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-a%2Ax%5E2+%2B+b%2Ax+ ALIGN=MIDDLE  ALT=\"+y+=+-a%2Ax%5E2+%2B+b%2Ax+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( I need the squared term to be negative, since<BR>\n" );
document.write( "that gives me a peak and not a dip )<BR>\n" );
document.write( "The solutions are:<BR>\n" );
document.write( "( 0,0 )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-a%2A0%5E2+%2B+b%2A0+ ALIGN=MIDDLE  ALT=\"+0+=+-a%2A0%5E2+%2B+b%2A0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+0+ ALIGN=MIDDLE  ALT=\"+0+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "( 50,0 )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-a%2A50%5E2+%2B+b%2A50+ ALIGN=MIDDLE  ALT=\"+0+=+-a%2A50%5E2+%2B+b%2A50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2500a+=+50b+ ALIGN=MIDDLE  ALT=\"+2500a+=+50b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+50a+ ALIGN=MIDDLE  ALT=\"+b+=+50a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "The peak, or vertex, is at ( 25, 4.5 ), so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4.5+=+-a%2A25%5E2+%2B+b%2A25+ ALIGN=MIDDLE  ALT=\"+4.5+=+-a%2A25%5E2+%2B+b%2A25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+625a+=+25b+-+4.5+ ALIGN=MIDDLE  ALT=\"+625a+=+25b+-+4.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug (1) into (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+625a+=+25%2A50a+-+4.5+ ALIGN=MIDDLE  ALT=\"+625a+=+25%2A50a+-+4.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1250a+-+625a+=+4.5+ ALIGN=MIDDLE  ALT=\"+1250a+-+625a+=+4.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+625a+=+4.5+ ALIGN=MIDDLE  ALT=\"+625a+=+4.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+.0072+ ALIGN=MIDDLE  ALT=\"+a+=+.0072+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+50a+ ALIGN=MIDDLE  ALT=\"+b+=+50a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+50%2A.0072+ ALIGN=MIDDLE  ALT=\"+b+=+50%2A.0072+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+.36+ ALIGN=MIDDLE  ALT=\"+b+=+.36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So, the equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-.0072x%5E2+%2B+.36x+ ALIGN=MIDDLE  ALT=\"+y+=+-.0072x%5E2+%2B+.36x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( Note there is no constant term because the<BR>\n" );
document.write( "parabola goes through ( 0,0 ) )<BR>\n" );
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document.write( "(b)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+-+20+=+30+ ALIGN=MIDDLE  ALT=\"+50+-+20+=+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m<BR>\n" );
document.write( "There is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15+ ALIGN=MIDDLE  ALT=\"+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m clearance on both sides<BR>\n" );
document.write( "So, I have the points<BR>\n" );
document.write( "( 15, y[1] ) and<BR>\n" );
document.write( "( 35, y[2] ) as points on the bridge that are<BR>\n" );
document.write( "directly above the ends of the floating platform<BR>\n" );
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document.write( "( 15, y[1] )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B1%5D+=+-.0072%2A15%5E2+%2B+.36%2A15+ ALIGN=MIDDLE  ALT=\"+y%5B1%5D+=+-.0072%2A15%5E2+%2B+.36%2A15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B1%5D+=+-.0072%2A225+%2B+5.4+ ALIGN=MIDDLE  ALT=\"+y%5B1%5D+=+-.0072%2A225+%2B+5.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B1%5D+=+-1.62+%2B+5.4+ ALIGN=MIDDLE  ALT=\"+y%5B1%5D+=+-1.62+%2B+5.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B1%5D+=+3.78+ ALIGN=MIDDLE  ALT=\"+y%5B1%5D+=+3.78+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "( 35, y[2] )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B2%5D+=+-.0072%2A35%5E2+%2B+.36%2A35+ ALIGN=MIDDLE  ALT=\"+y%5B2%5D+=+-.0072%2A35%5E2+%2B+.36%2A35+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B2%5D+=+-.0072%2A1225+%2B+12.6+ ALIGN=MIDDLE  ALT=\"+y%5B2%5D+=+-.0072%2A1225+%2B+12.6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B2%5D+=+-8.82+%2B+12.6+ ALIGN=MIDDLE  ALT=\"+y%5B2%5D+=+-8.82+%2B+12.6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B2%5D+=+3.78+ ALIGN=MIDDLE  ALT=\"+y%5B2%5D+=+3.78+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m<BR>\n" );
document.write( "( this makes sense because the platform is<BR>\n" );
document.write( "exactly in the middle )<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "If you want <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20%2F100+=+.2+ ALIGN=MIDDLE  ALT=\"+20%2F100+=+.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m on each side,<BR>\n" );
document.write( "then what value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+ ALIGN=MIDDLE  ALT=\"+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > goes with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B1%5D+=+15+-+.2+ ALIGN=MIDDLE  ALT=\"+x%5B1%5D+=+15+-+.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B2%5D+=+35+%2B+.2+ ALIGN=MIDDLE  ALT=\"+x%5B2%5D+=+35+%2B+.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B3%5D+=+-.0072%2A14.8%5E2+%2B+.36%2A14.8+ ALIGN=MIDDLE  ALT=\"+y%5B3%5D+=+-.0072%2A14.8%5E2+%2B+.36%2A14.8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B3%5D+=+-.0072%2A219.04+%2B+5.328+ ALIGN=MIDDLE  ALT=\"+y%5B3%5D+=+-.0072%2A219.04+%2B+5.328+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B3%5D+=+-1.577+%2B+5.328+ ALIGN=MIDDLE  ALT=\"+y%5B3%5D+=+-1.577+%2B+5.328+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B3%5D+=+3.751+ ALIGN=MIDDLE  ALT=\"+y%5B3%5D+=+3.751+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m<BR>\n" );
document.write( "This is the height of the platform that gives me <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20+ ALIGN=MIDDLE  ALT=\"+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm<BR>\n" );
document.write( "clearance on the sides. <BR>\n" );
document.write( "The points on the platform are below the bridge, and they are at<BR>\n" );
document.write( "( 15, 3.751 ) and<BR>\n" );
document.write( "( 35, 3.751 )<BR>\n" );
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document.write( "I would definitely get a 2nd opinion<BR>\n" );
document.write( "I coiuld easily miscalculate<BR>\n" );
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document.write( "Here's a plot of my equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-6%2C+60%2C+-1%2C+6%2C+-.0072x%5E2+%2B+.36x+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-6%2C+60%2C+-1%2C+6%2C+-.0072x%5E2+%2B+.36x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );