document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=762491>Question 762491</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am really having troubles with these word problems.\r<BR>\n" );
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document.write( "the equation -16t^2 - 32t + 400 gives the height of a ball, thrown downward from the top of a 400 ft building with an initial velocity of 32 ft/s. find the time it takes for the ball to reach a height of 96 ft </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464000 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=464000\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+-16t%5E2+-+32t+%2B+400+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+-16t%5E2+-+32t+%2B+400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First of all, I'll show you the plot of this equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-2%2C+6%2C+-50%2C+450%2C+-16x%5E2+-+32x+%2B+400+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-2%2C+6%2C+-50%2C+450%2C+-16x%5E2+-+32x+%2B+400+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can see the height of the building at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+0+ ALIGN=MIDDLE  ALT=\"+t+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%280%29+=+-16%280%29%5E2+-+32%2A0+%2B+400+ ALIGN=MIDDLE  ALT=\"+h%280%29+=+-16%280%29%5E2+-+32%2A0+%2B+400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%280%29+=+400+ ALIGN=MIDDLE  ALT=\"+h%280%29+=+400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the height of the ball is the same as the height of the building<BR>\n" );
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document.write( "The problem doesn't ask you for it, but you can also see that<BR>\n" );
document.write( "the ball hits the ground at about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+4.1+ ALIGN=MIDDLE  ALT=\"+t+=+4.1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec or so.<BR>\n" );
document.write( "The height is zero, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+0+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+-16t%5E2+-+32t+%2B+400+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+-16t%5E2+-+32t+%2B+400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-16t%5E2+-+32t+%2B+400+ ALIGN=MIDDLE  ALT=\"+0+=+-16t%5E2+-+32t+%2B+400+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-t%5E2+-+2t+%2B+25+=+0+ ALIGN=MIDDLE  ALT=\"+-t%5E2+-+2t+%2B+25+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using 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+=+-1+ ALIGN=MIDDLE  ALT=\"+a+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-2+ ALIGN=MIDDLE  ALT=\"+b+=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+25+ ALIGN=MIDDLE  ALT=\"+c+=+25+\"   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-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2+-+4%2A%28-1%29%2A25+%29%29+%2F+%282%2A%28-1%29%29+ ALIGN=MIDDLE   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+2+%2B-+sqrt%28+4+%2B+100+%29%29+%2F+%28-2%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+2+%2B-+sqrt%28+4+%2B+100+%29%29+%2F+%28-2%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+2+-+sqrt%28+104+%29+%29+%2F+%28+-2%29+ ALIGN=MIDDLE  ALT=\"+t=+%28+2+-+sqrt%28+104+%29+%29+%2F+%28+-2%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+2+-+10.198+%29+%2F+%28+-2%29+ ALIGN=MIDDLE  ALT=\"+t=+%28+2+-+10.198+%29+%2F+%28+-2%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+-8.198+%29+%2F+%28-2%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-8.198+%29+%2F+%28-2%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+=+4.099+ ALIGN=MIDDLE  ALT=\"+t+=+4.099+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "My guess was pretty good<BR>\n" );
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document.write( "They are asking you for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+96+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+96+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+-16t%5E2+-+32t+%2B+400+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+-16t%5E2+-+32t+%2B+400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+96+=+-16t%5E2+-+32t+%2B+400+ ALIGN=MIDDLE  ALT=\"+96+=+-16t%5E2+-+32t+%2B+400+\"   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+-+32t+%2B+304+=+0+ ALIGN=MIDDLE  ALT=\"+-16t%5E2+-+32t+%2B+304+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4t%5E2+-+8t+%2B+76+=+0+ ALIGN=MIDDLE  ALT=\"+-4t%5E2+-+8t+%2B+76+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-t%5E2+-+2t+%2B+19+=+0+ ALIGN=MIDDLE  ALT=\"+-t%5E2+-+2t+%2B+19+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use 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+=+-1+ ALIGN=MIDDLE  ALT=\"+a+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-2+ ALIGN=MIDDLE  ALT=\"+b+=+-2+\"   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-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2+-+4%2A%28-1%29%2A19+%29%29+%2F+%282%2A%28-1%29%29+ ALIGN=MIDDLE   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+2+%2B-+sqrt%28+4+%2B+76+%29%29+%2F+%28-2%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+2+%2B-+sqrt%28+4+%2B+76+%29%29+%2F+%28-2%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+2+%2B-+sqrt%28+80+%29%29+%2F+%28-2%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+2+%2B-+sqrt%28+80+%29%29+%2F+%28-2%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+2+%2B-+sqrt%28+16%2A5+%29%29+%2F+%28-2%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+2+%2B-+sqrt%28+16%2A5+%29%29+%2F+%28-2%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+2+-+4%2Asqrt%28+5+%29+%29+%2F+%28-2%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+2+-+4%2Asqrt%28+5+%29+%29+%2F+%28-2%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+=+2%2Asqrt%285%29+-+1+ ALIGN=MIDDLE  ALT=\"+t+=+2%2Asqrt%285%29+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+3.472+ ALIGN=MIDDLE  ALT=\"+t+=+3.472+\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec<BR>\n" );
document.write( "This seems to agree with the plot<BR>\n" );
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document.write( "Just for explanation, suppose the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-32t+ ALIGN=MIDDLE  ALT=\"+-32t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > had been +<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+-16t%5E2+%2B+32t+%2B+400+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+-16t%5E2+%2B+32t+%2B+400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-2%2C+7%2C+-50%2C+500%2C+-16x%5E2+%2B+32x+%2B+400+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-2%2C+7%2C+-50%2C+500%2C+-16x%5E2+%2B+32x+%2B+400+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the case where the ball is thrown upward instead of down.<BR>\n" );
document.write( "Hope all this helps\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );