document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=949305>Question 949305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> y=x-4000x^2/35739\r<BR>\n" );
document.write( "\n" );
document.write( "Using this formula how far downrange does the cannonball travel?\r<BR>\n" );
document.write( "\n" );
document.write( "What is the maximum height of the cannonball and how far downrange does that height occur? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #579597 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=579597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Apparently <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-4000x%5E2%2F35739 ALIGN=MIDDLE  ALT=\"y=x-4000x%5E2%2F35739\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the height of a cannonball that has traveled a downrange distance of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > , with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > measured in some unit of length.<BR>\n" );
document.write( "The cannonball will travel downrange until it its the ground when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That happens when<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x-4000x%5E2%2F35739 ALIGN=MIDDLE  ALT=\"0=x-4000x%5E2%2F35739\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%281-4000x%2F35739%29 ALIGN=MIDDLE  ALT=\"0=x%281-4000x%2F35739%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=0%2C%22or%22%2C1-4000x%2F35739=0%29 ALIGN=MIDDLE  ALT=\"system%28x=0%2C%22or%22%2C1-4000x%2F35739=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=0%2C%22or%22%2Cx=35739%2F4000%29 ALIGN=MIDDLE  ALT=\"system%28x=0%2C%22or%22%2Cx=35739%2F4000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=0%2C%22or%22%2Cx=8.93475%29 ALIGN=MIDDLE  ALT=\"system%28x=0%2C%22or%22%2Cx=8.93475%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That means that the cannonball exits the cannon at ground level, and hits the ground at a distance of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=8.93475%29 ALIGN=MIDDLE  ALT=\"highlight%28x=8.93475%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > downrange (in whatever units <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is measured).<BR>\n" );
document.write( "Halfway to that point (parabolas are symmetrical) the cannonball reaches its maximum height.<BR>\n" );
document.write( "Naturally, that happens when<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2F2%29%2A%2835739%2F4000%29 ALIGN=MIDDLE  ALT=\"x=%281%2F2%29%2A%2835739%2F4000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-4000x%2F35739=1-%284000%2F35739%29%281%2F2%29%2A%2835739%2F4000%29=1-1%2F2=1%2F2 ALIGN=MIDDLE  ALT=\"1-4000x%2F35739=1-%284000%2F35739%29%281%2F2%29%2A%2835739%2F4000%29=1-1%2F2=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-4000x%5E2%2F35739=x%2A%281-4000x%2F35739%29=x%2A%281%2F2%29=%281%2F2%29%2A%2835739%2F4000%29%2A%281%2F2%29=35739%2F16000=highlight%282.2336875%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Of course, those numbers are exact mathematical calculation results with way to many decimal places. Rounding would be a good idea.<BR>\n" );
document.write( "I might say that the cannonball travels downrange a distance of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.9 ALIGN=MIDDLE  ALT=\"8.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > units,<BR>\n" );
document.write( "and reaches a maximu height of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.2 ALIGN=MIDDLE  ALT=\"2.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > units.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );