document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184546>Question 1184546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A radio telescope has a parabolic dish with a diameter of 110 meters. The<BR>\n" );
document.write( "collected radio signals are reflected to one connection point, called the focal point, being the focus of the parabola. If the focal length is 50 meters, find the depth of the dish, rounded to two decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #815193 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=815193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "A radio telescope has a parabolic dish with a diameter of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=110 ALIGN=MIDDLE  ALT=\"110\"   DISABLED_style= \"max-width:90%; height:auto;\" >  meters. The collected radio signals are reflected to one collection point, called the focal point, being the focus of the parabola. <BR>\n" );
document.write( "If the focal length is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters, find the depth of the dish, rounded to one decimal place.\r<BR>\n" );
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document.write( "To simplify my computations, I'll put the vertex of my parabola (that is, the base of the dish) at the origin, so (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >). \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4py+=+x%5E2 ALIGN=MIDDLE  ALT=\"4py+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the focal length is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+50 ALIGN=MIDDLE  ALT=\"p+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2850%29y+=+x%5E2 ALIGN=MIDDLE  ALT=\"4%2850%29y+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200y+=+x%5E2 ALIGN=MIDDLE  ALT=\"200y+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2%2F200 ALIGN=MIDDLE  ALT=\"y+=+x%5E2%2F200\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This parabola extends forever in either direction, but I only care about the part of the curve that models the dish. Since the dish has a diameter of a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=110 ALIGN=MIDDLE  ALT=\"110\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters, then I only care about the part of the curve from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-55+ ALIGN=MIDDLE  ALT=\"x+=+-55+\"   DISABLED_style= \"max-width:90%; height:auto;\" >to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2B55 ALIGN=MIDDLE  ALT=\"x+=+%2B55\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The height of the edge of the dish (and thus the depth of the dish) will be the y-value of the equation at the \"ends\" of the modelling curve. The height of the parabola will be the same at either x-value, since they're each the same distance from the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertex ALIGN=MIDDLE  ALT=\"vertex\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so it doesn't matter which value I use. I prefer positive values, so I'll plug <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+55+ ALIGN=MIDDLE  ALT=\"x+=+55+\"   DISABLED_style= \"max-width:90%; height:auto;\" >into my modelling equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%2855%29%5E2%2F200 ALIGN=MIDDLE  ALT=\"y+=+%2855%29%5E2%2F200\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3025%2F200+ ALIGN=MIDDLE  ALT=\"+y+=+3025%2F200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=121%2F8 ALIGN=MIDDLE  ALT=\"y=121%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.13 ALIGN=MIDDLE  ALT=\"15.13\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters \r<BR>\n" );
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