document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=232437>Question 232437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> big bertha a canon used in could fire shots incredibley long distances. The path of a shell could be modeled by y=-0.0196x(squared) plus 1.137x where x was the horizontal distance traveled(in miles) and why was the height(in miles).How far could Big Bertha fire a shell? what was the shells maximum height?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171775 by </B><A HREF=/tutors/aboutme.mpl?userid=Stitch><B>Stitch(470)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Stitch><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=171775\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+%28-.00196%2AX%5E2+%2B+1.137%2AX%29 ALIGN=MIDDLE  ALT=\"Y+=+%28-.00196%2AX%5E2+%2B+1.137%2AX%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Y is the height in miles.  When Y = 0, the shell is on the ground.<BR>\n" );
document.write( "Solve for Y = 0 and that will give you the distance of the shot.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+%28-.00196%2AX%5E2+%2B+1.137%2AX%29 ALIGN=MIDDLE  ALT=\"+0+=+%28-.00196%2AX%5E2+%2B+1.137%2AX%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract .00196*X^2 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.00196%2AX%5E2+=+1.137%2AX ALIGN=MIDDLE  ALT=\"+.00196%2AX%5E2+=+1.137%2AX\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by X<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.00196%2AX+=+1.137 ALIGN=MIDDLE  ALT=\"+.00196%2AX+=+1.137\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by .00196<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+580+miles ALIGN=MIDDLE  ALT=\"X+=+580+miles\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the shell traveled 580 miles\r<BR>\n" );
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document.write( "To find the max height of the shell, you need to see where the slope of the line equals 0.<BR>\n" );
document.write( "The derivative of the lines equation will give you the slope of the line.\r<BR>\n" );
document.write( "\n" );
document.write( "The equation for the line:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+%28-.00196%2AX%5E2+%2B+1.137%2AX%29 ALIGN=MIDDLE  ALT=\"Y+=+%28-.00196%2AX%5E2+%2B+1.137%2AX%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now take the derivative<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y%5E1+=+%282%2A-.00196%2AX+%2B+1.137%29 ALIGN=MIDDLE  ALT=\"Y%5E1+=+%282%2A-.00196%2AX+%2B+1.137%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Set the equation equal to 0 to find the max height.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%28-.00392%2AX+%2B+1.137%29 ALIGN=MIDDLE  ALT=\"0+=+%28-.00392%2AX+%2B+1.137%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract -.00392 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.00392%2AX+=+1.137%29 ALIGN=MIDDLE  ALT=\".00392%2AX+=+1.137%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by .00392<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+290+miles ALIGN=MIDDLE  ALT=\"X+=+290+miles\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we know that the maximum height occurs when X = 290 miles.<BR>\n" );
document.write( "Plug X 290 into the original equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+-.00196%2AX%5E2+%2B+1.137%2AX ALIGN=MIDDLE  ALT=\"Y+=+-.00196%2AX%5E2+%2B+1.137%2AX\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+-.00196%2A290%5E2+%2B+1.137%2A290 ALIGN=MIDDLE  ALT=\"Y+=+-.00196%2A290%5E2+%2B+1.137%2A290\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+-164.826+%2B+329.73 ALIGN=MIDDLE  ALT=\"Y+=+-164.826+%2B+329.73\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+164.90+miles ALIGN=MIDDLE  ALT=\"Y+=+164.90+miles\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );