document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155921>Question 1155921</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 19. The product of two consecutive positive integers is 42. Write and solve a quadratic equation to find the solutions.  Then show how you use those solutions to find the two consecutive positive integers.<BR>\n" );
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document.write( "20. A cannon ball is shot from a cannon on top of a hill that is 73.5 meters above sea level. The cannon ball leaves the cannon with a velocity of 9.8 m/s. Write and solve a quadratic equation to determine when the cannon ball will reach sea level </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #778603 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=778603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "19.\r<BR>\n" );
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document.write( "Let first integer be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let second integer be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if their product  is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42 ALIGN=MIDDLE  ALT=\"42\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B1%29=42 ALIGN=MIDDLE  ALT=\"x%28x%2B1%29=42\"   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=x%5E2%2Bx=42 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx=42\"   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=x%5E2%2Bx-42=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx-42=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >..factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B7x-6x-42=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B7x-6x-42=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=%28x%5E2%2B7x%29-%286x%2B42%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B7x%29-%286x%2B42%29=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=x%28x%2B7%29-6%28x%2B7%29=0 ALIGN=MIDDLE  ALT=\"x%28x%2B7%29-6%28x%2B7%29=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=%28x+-+6%29+%28x+%2B+7%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+6%29+%28x+%2B+7%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> solutions:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+6%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+6%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+7%29+=+0 ALIGN=MIDDLE  ALT=\"+%28x+%2B+7%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> disregard negative solution\r<BR>\n" );
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document.write( "so,  the two consecutive positive integers are\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=7 ALIGN=MIDDLE  ALT=\"x%2B1=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "20.\r<BR>\n" );
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document.write( "the projectile height is modeled by the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-16t%5E2%2Bvt%2Bs ALIGN=MIDDLE  ALT=\"h=-16t%5E2%2Bvt%2Bs\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and can be written using metric units as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-4.9t%5E2%2Bvt%2Bs ALIGN=MIDDLE  ALT=\"h=-4.9t%5E2%2Bvt%2Bs\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the units are converted from feet to meters\r<BR>\n" );
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document.write( "so, using<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-4.9t%5E2%2Bvt%2Bs+ ALIGN=MIDDLE  ALT=\"h=-4.9t%5E2%2Bvt%2Bs+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...plug in given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=9.8+m%2Fs ALIGN=MIDDLE  ALT=\"v=9.8+m%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=73.5m ALIGN=MIDDLE  ALT=\"s=73.5m\"   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=h=-4.9t%5E2%2B9.8t%2B73.5+ ALIGN=MIDDLE  ALT=\"h=-4.9t%5E2%2B9.8t%2B73.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when the cannon ball reach sea level,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h=0 ALIGN=MIDDLE  ALT=\"+h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-4.9t%5E2+%2B+9.8t+%2B+73.5 ALIGN=MIDDLE  ALT=\"0+=+-4.9t%5E2+%2B+9.8t+%2B+73.5\"   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=0+=+-4.9%28t%5E2+-+2t+-+15%29 ALIGN=MIDDLE  ALT=\"0+=+-4.9%28t%5E2+-+2t+-+15%29\"   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=0+=+-4.9%28t+-+5%29%28t+%2B+3%29 ALIGN=MIDDLE  ALT=\"0+=+-4.9%28t+-+5%29%28t+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+-+5+=+0 ALIGN=MIDDLE  ALT=\"t+-+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5 ALIGN=MIDDLE  ALT=\"t=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+%2B+3+=+0 ALIGN=MIDDLE  ALT=\"t+%2B+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-3 ALIGN=MIDDLE  ALT=\"t=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "your solution will be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+5+ ALIGN=MIDDLE  ALT=\"t+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >since<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+-3 ALIGN=MIDDLE  ALT=\"+t+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not acceptable <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=negative ALIGN=MIDDLE  ALT=\"negative\"   DISABLED_style= \"max-width:90%; height:auto;\" > value \r<BR>\n" );
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document.write( "Hence, the cannon ball will reach sea level at<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+ ALIGN=MIDDLE  ALT=\"+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );