document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005396>Question 1005396</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a parkway 80 ft. wide is spanned by a parabolic arc 100 ft. long along the horizontal, if the parkway is in the center, how high must the vertex of the arch be in order to give a minimum clearance of 20 over the parkway? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #621699 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=621699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The parabola needed, drawn over a conveniently placed set of axes, with all measures in feet, looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-70%2C70%2C-20%2C80%2C%0D%0Arectangle%28-40%2C0%2C40%2C20%29%2C%0D%0Alocate%2818%2C20%2C40%29%2Clocate%28-22%2C20%2C40%29%2C%0D%0Alocate%2834%2C12%2C20%29%2C%0D%0Agraph%28400%2C400%2C-70%2C70%2C-20%2C80%2C20%2C-x%5E2%2F45%2B500%2F9%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The equation will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=f%28x%29=ax%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=f%28x%29=ax%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28f%2840%29=20%2Cf%2850%29=0%29 ALIGN=MIDDLE  ALT=\"system%28f%2840%29=20%2Cf%2850%29=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=f%28x%29=ax%5E2%2Bk%2Cf%2840%29=20%2Cf%2850%29=0%29 ALIGN=MIDDLE  ALT=\"system%28y=f%28x%29=ax%5E2%2Bk%2Cf%2840%29=20%2Cf%2850%29=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=f%28x%29=ax%5E2%2Bk%2Ca40%5E2%2Bk=20%2Ca50%5E2%2Bk=20%29 ALIGN=MIDDLE  ALT=\"system%28y=f%28x%29=ax%5E2%2Bk%2Ca40%5E2%2Bk=20%2Ca50%5E2%2Bk=20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=f%28x%29=ax%5E2%2Bk%2C1600a%2Bk=20%2C2500a%2Bk=0%29 ALIGN=MIDDLE  ALT=\"system%28y=f%28x%29=ax%5E2%2Bk%2C1600a%2Bk=20%2C2500a%2Bk=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=f%28x%29=-x%5E2%2F45%2B500%2F9%2Ca=-1%2F45%2Ck=500%2F9%29 ALIGN=MIDDLE  ALT=\"system%28y=f%28x%29=-x%5E2%2F45%2B500%2F9%2Ca=-1%2F45%2Ck=500%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The height at the vertex (in feet) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=highlight%28500%2F9=%2255.55+%28+rounded+%29%22%29 ALIGN=MIDDLE  ALT=\"f%280%29=highlight%28500%2F9=%2255.55+%28+rounded+%29%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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