document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119148>Question 119148</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solving a science application. Suppose that a ball is thrown upward with an initial velocity of 80 ft/s. (the initial velocity is the speed with which the ball leaves the throwers hand. The spped will then decrease as the ball rises.) If the ball is  released at a height of 77ft, the height equation may be written as follows:  h= -16t^2+80t+5, round to the nearest hundredth of a second\r<BR>\n" );
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document.write( "77= -16t^2+80t+5\r<BR>\n" );
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document.write( "this is all i got, now I am lost, can someone please help me, thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87253 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=87253\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Do you want to solve for t?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=77=-16t%5E2%2B80t%2B5 ALIGN=MIDDLE  ALT=\"77=-16t%5E2%2B80t%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-16t%5E2%2B80t%2B5-77 ALIGN=MIDDLE  ALT=\"0=-16t%5E2%2B80t%2B5-77\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract 77 from both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-16t%5E2%2B80t-72 ALIGN=MIDDLE  ALT=\"0=-16t%5E2%2B80t-72\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for t:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=at%5E2%2Bbt%2Bc=0 ALIGN=MIDDLE  ALT=\"at%5E2%2Bbt%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16%2At%5E2%2B80%2At-72=0 ALIGN=MIDDLE  ALT=\"-16%2At%5E2%2B80%2At-72=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=80 ALIGN=MIDDLE  ALT=\"b=80\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-72 ALIGN=MIDDLE  ALT=\"c=-72\"   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=t+=+%28-80+%2B-+sqrt%28+%2880%29%5E2-4%2A-16%2A-72+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-80+%2B-+sqrt%28+%2880%29%5E2-4%2A-16%2A-72+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-16, b=80, and c=-72\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-80+%2B-+sqrt%28+6400-4%2A-16%2A-72+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-80+%2B-+sqrt%28+6400-4%2A-16%2A-72+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 80 to get 6400  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-80+%2B-+sqrt%28+6400%2B-4608+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-80+%2B-+sqrt%28+6400%2B-4608+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-72%2A-16 ALIGN=MIDDLE  ALT=\"-4%2A-72%2A-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4608 ALIGN=MIDDLE  ALT=\"-4608\"   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=t+=+%28-80+%2B-+sqrt%28+1792+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-80+%2B-+sqrt%28+1792+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-80+%2B-+16%2Asqrt%287%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-80+%2B-+16%2Asqrt%287%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-80+%2B-+16%2Asqrt%287%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-80+%2B-+16%2Asqrt%287%29%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -16 to get -32\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-80+%2B+16%2Asqrt%287%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-80+%2B+16%2Asqrt%287%29%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-80+-+16%2Asqrt%287%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-80+-+16%2Asqrt%287%29%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-80%2F-32%2B16%2Asqrt%287%29%2F-32 ALIGN=MIDDLE  ALT=\"t=-80%2F-32%2B16%2Asqrt%287%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-80%2F-32-16%2Asqrt%287%29%2F-32 ALIGN=MIDDLE  ALT=\"t=-80%2F-32-16%2Asqrt%287%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5+%2F+2-sqrt%287%29%2F2 ALIGN=MIDDLE  ALT=\"t=5+%2F+2-sqrt%287%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5+%2F+2%2Bsqrt%287%29%2F2 ALIGN=MIDDLE  ALT=\"t=5+%2F+2%2Bsqrt%287%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So these expressions approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1.1771243444677 ALIGN=MIDDLE  ALT=\"t=1.1771243444677\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3.8228756555323 ALIGN=MIDDLE  ALT=\"t=3.8228756555323\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our solutions are:\r<BR>\n" );
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document.write( "So when the time is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1.1771243444677 ALIGN=MIDDLE  ALT=\"t=1.1771243444677\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3.8228756555323 ALIGN=MIDDLE  ALT=\"t=3.8228756555323\"   DISABLED_style= \"max-width:90%; height:auto;\" > the ball is  at a height of 77 ft.\r<BR>\n" );
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