document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155433>Question 1155433</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a bridge is built in the shape of a parabolic arch. the bridge has a span of 184 ft. and a maximum height of 40 ft. find the height of the arch at 15 ft. from 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 #778025 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=778025\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let the center of the arch at ground level be the origin of a coordinate system.  Then the parabola passes through the points (-92,0), (0,40), and (92,0).<br><BR>\n" );
document.write( "With the y-intercept at (0,40), the equation is of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-ax%5E2%2B40 ALIGN=MIDDLE  ALT=\"y+=+-ax%5E2%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Use the point (92,0) to determine the value of a to complete the equation.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-a%2892%5E2%29%2B40 ALIGN=MIDDLE  ALT=\"0+=+-a%2892%5E2%29%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2892%5E2%29+=+40 ALIGN=MIDDLE  ALT=\"a%2892%5E2%29+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+40%2F%2892%5E2%29 ALIGN=MIDDLE  ALT=\"a+=+40%2F%2892%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<br><BR>\n" );
document.write( "The equation of the parabola is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%2840%2F92%5E2%29x%5E2%2B40 ALIGN=MIDDLE  ALT=\"y+=+-%2840%2F92%5E2%29x%5E2%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-100%2C100%2C-10%2C50%2C-%2840%2F92%5E2%29x%5E2%2B40%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-100%2C100%2C-10%2C50%2C-%2840%2F92%5E2%29x%5E2%2B40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Evaluate y when x=15 to find the answer to the problem.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2840%2F92%5E2%29%2815%5E2%29%2B40 ALIGN=MIDDLE  ALT=\"-%2840%2F92%5E2%29%2815%5E2%29%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 38.936673 to several decimal places.<br><BR>\n" );
document.write( "Here is a way to find this value without finding the equation of the parabola.<br><BR>\n" );
document.write( "The basic form of the equation of a parabola is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2 ALIGN=MIDDLE  ALT=\"y+=+ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "This equation tells us directly that the vertical displacement is proportional to the square of the horizontal displacement.<br><BR>\n" );
document.write( "We know, from the points (0,40) and (92,0) on the parabola, that the vertical displacement is -40 for a horizontal displacement of 92.<br><BR>\n" );
document.write( "The question asks for the height of the bridge 15 feet from the center; we can find that height by determining the vertical displacement from the vertex at (0,40) for a horizontal displacement of 15 from the vertex.<br><BR>\n" );
document.write( "The ratio of horizontal displacements for the two points is 15/92; the ratio of the vertical displacements will be the square of that.  So the vertical displacement 15 feet from the center of the arch is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2F92%29%5E2%28-40%29+=+-1.063327 ALIGN=MIDDLE  ALT=\"%2815%2F92%29%5E2%28-40%29+=+-1.063327\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "and so the height of the arch 15 feet from its center is 40-1.063327 = 38.936673 feet.<br><BR>\n" );
document.write( " </SPAN>\n" );
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