document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=382728>Question 382728</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this: A bridge is to be built in the shape of a parabolic arch and is to have a span of 100 feet. The height of the arch at a distance of 40 ft from the center is to be 10 ft. Find the height of the arch at its center. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #271377 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=271377\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A bridge is to be built in the shape of a parabolic arch and is to have a span of 100 feet.<BR>\n" );
document.write( " The height of the arch at a distance of 40 ft from the center is to be 10 ft.<BR>\n" );
document.write( " Find the height of the arch at its center.<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Find the equation using the form ax^2 + bx = y<BR>\n" );
document.write( ":<BR>\n" );
document.write( "From the information given, we can find two x,y coordinates<BR>\n" );
document.write( "x = the width of the bridge, y = height of the bridge at x<BR>\n" );
document.write( "x=100, y=0<BR>\n" );
document.write( "and it says,\"height of the arch at a distance of 40 ft from the center is to be 10 ft\"<BR>\n" );
document.write( "The center of the bridge = 50 ft, 40 ft to left of center: x=10<BR>\n" );
document.write( "x=10, y = 10<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x=100, y=0<BR>\n" );
document.write( "100^2a + 100b = 0<BR>\n" );
document.write( "10000a + 100b = 0<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x=10, y=10<BR>\n" );
document.write( "10^2a + 10b = 10<BR>\n" );
document.write( "100a + 10b = 10<BR>\n" );
document.write( "Multiply the above equation by 10 subtract from the 1st equation<BR>\n" );
document.write( "10000a + 100b = 0<BR>\n" );
document.write( "1000a + 100b = 100<BR>\n" );
document.write( "-----------------------subtraction eliminates b, find a<BR>\n" );
document.write( "9000a = -100<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-100%29%2F9000 ALIGN=MIDDLE  ALT=\"%28-100%29%2F9000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = -.011<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find b using 100a + 10b = 10<BR>\n" );
document.write( "100(-.011) + 10b = 10<BR>\n" );
document.write( "-1.11 + 10b = 10<BR>\n" );
document.write( "10b = 10 + 1.11<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11.11%2F10 ALIGN=MIDDLE  ALT=\"11.11%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = 1.111<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The equation: y =  -.011x^2 + 1.11x, graph would look like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-20%2C+130%2C+-10%2C+35%2C+-.011x%5E2%2B1.11x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-20%2C+130%2C+-10%2C+35%2C+-.011x%5E2%2B1.11x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can see that 40' either side of the center (50') the arch is 10' high<BR>\n" );
document.write( ":<BR>\n" );
document.write( "What is the height at the center? Substitute 50' for x in the equation, find y<BR>\n" );
document.write( "y =  -.011(50^2) + 1.11(50)<BR>\n" );
document.write( "y = -27.5 + 55.5<BR>\n" );
document.write( "y = 28 ft, which is about right on the graph \r<BR>\n" );
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document.write( " </SPAN>\n" );
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