document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388858>Question 388858</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me with this problem. I do not understand it I am lost.\r<BR>\n" );
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document.write( "Solving a word problem using a quadratic equation with irrational roots<BR>\n" );
document.write( "When a ball is thrown, its height in feet h after t seconds is given by the equation <BR>\n" );
document.write( "h=vt-16t^2<BR>\n" );
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document.write( "where  is the initial upwards velocity in feet per second. If v = 36 feet per second, find all values of t for which h = 19 feet. Do not round any intermediate steps. Round your answer to  decimal places. <BR>\n" );
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document.write( "Thank you very much.<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 #275275 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=275275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, try to picture the situation. It<BR>\n" );
document.write( "will really help, since you can apply it<BR>\n" );
document.write( "to the same type of problem later.<BR>\n" );
document.write( "A parabola is the curve that an object <BR>\n" );
document.write( "follows when you throw it in the air and<BR>\n" );
document.write( "it comes back to the ground.<BR>\n" );
document.write( "If the object goes higher than 19 ft, then<BR>\n" );
document.write( "it's going to be 19 ft again when it's<BR>\n" );
document.write( "on it's way back down.<BR>\n" );
document.write( "Look at the equation.<BR>\n" );
document.write( "It is a general rule that when the squared term<BR>\n" );
document.write( "(that's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2 ALIGN=MIDDLE  ALT=\"-16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is negative, then the<BR>\n" );
document.write( "parabola has it's peak at the top, and not a dip at<BR>\n" );
document.write( "the bottom.<BR>\n" );
document.write( "Now I can just apply algebra<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+vt+-+16t%5E2 ALIGN=MIDDLE  ALT=\"h+=+vt+-+16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Observe that if you have height on the left side, the <BR>\n" );
document.write( "right side must also be height, since you can't have<BR>\n" );
document.write( "height = speed or height = time, etc.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vt ALIGN=MIDDLE  ALT=\"vt\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the contribution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > that is due <BR>\n" );
document.write( "to the push of sending the object up.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2 ALIGN=MIDDLE  ALT=\"-16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a negative contributiuon to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "due to gravity wanting to pull the object back down.<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+36t+-+16t%5E2 ALIGN=MIDDLE  ALT=\"h+=+36t+-+16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19+=+36t+-+16t%5E2 ALIGN=MIDDLE  ALT=\"19+=+36t+-+16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2+%2B+36t+-+19+=+0 ALIGN=MIDDLE  ALT=\"-16t%5E2+%2B+36t+-+19+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-16 ALIGN=MIDDLE  ALT=\"a+=+-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+36 ALIGN=MIDDLE  ALT=\"b+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+-19 ALIGN=MIDDLE  ALT=\"c+=+-19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-36+%2B-+sqrt%28+36%5E2-4%2A%28-16%29%2A%28-19%29+%29%29%2F%282%2A%28-16%29%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-36+%2B-+sqrt%28+36%5E2-4%2A%28-16%29%2A%28-19%29+%29%29%2F%282%2A%28-16%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-36+%2B-+sqrt%28+1296+-+1216+%29%29%2F%28-32%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-36+%2B-+sqrt%28+1296+-+1216+%29%29%2F%28-32%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-36+%2B-+sqrt%28+80+%29%29%2F%28-32%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-36+%2B-+sqrt%28+80+%29%29%2F%28-32%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2880%29+=+sqrt%2816%2A5%29 ALIGN=MIDDLE  ALT=\"sqrt%2880%29+=+sqrt%2816%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2880%29+=+4%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%2880%29+=+4%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-36+%2B-+4%2Asqrt%285%29%29%2F%28-32%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-36+%2B-+4%2Asqrt%285%29%29%2F%28-32%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The answers are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+9%2F8+%2B+sqrt%285%29%2F8 ALIGN=MIDDLE  ALT=\"t+=+9%2F8+%2B+sqrt%285%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+9%2F8+-+sqrt%285%29%2F8 ALIGN=MIDDLE  ALT=\"t+=+9%2F8+-+sqrt%285%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29+=+2.236 ALIGN=MIDDLE  ALT=\"sqrt%285%29+=+2.236\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1.125+%2B+2.236%2F8 ALIGN=MIDDLE  ALT=\"t+=+1.125+%2B+2.236%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1.125+%2B+.2795 ALIGN=MIDDLE  ALT=\"t+=+1.125+%2B+.2795\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1.4045 ALIGN=MIDDLE  ALT=\"t+=+1.4045\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1.125+-+sqrt%285%29%2F8 ALIGN=MIDDLE  ALT=\"t+=+1.125+-+sqrt%285%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1.125+-+2.236%2F8 ALIGN=MIDDLE  ALT=\"t+=+1.125+-+2.236%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1.125+-+.2795 ALIGN=MIDDLE  ALT=\"t+=+1.125+-+.2795\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+.8455 ALIGN=MIDDLE  ALT=\"t+=+.8455\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "On the way up, object is at height 19 ft in .8455 sec<BR>\n" );
document.write( "On the way down, object is at height 19 ft in 1.4045 sec<BR>\n" );
document.write( "You can check these<BR>\n" );
document.write( "I'll check one answer:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19+=+36t+-+16t%5E2 ALIGN=MIDDLE  ALT=\"19+=+36t+-+16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19+=+36%2A1.4045+-+16%2A1.4045%5E2 ALIGN=MIDDLE  ALT=\"19+=+36%2A1.4045+-+16%2A1.4045%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19+=+50.562+-+31.5619+ ALIGN=MIDDLE  ALT=\"19+=+50.562+-+31.5619+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19+=+19.0001 ALIGN=MIDDLE  ALT=\"19+=+19.0001\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Close enough\r<BR>\n" );
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