document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=268286>Question 268286</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with this problem, this is what I have so far:\r<BR>\n" );
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document.write( "Problem: Height of a projected ball, <BR>\n" );
document.write( "An astronaut on the moon throws a baseball upward. The astronaut is 6ft., 6in. tall, and the initial velocity of the ball is 30 ft. per sec. The height S of the ball in feet is given by the equation<BR>\n" );
document.write( "S= -2.7t^2 + 30t + 6.5<BR>\n" );
document.write( "where t is the number of seconds after the ball was thrown.\r<BR>\n" );
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document.write( "A.) After how many seconds is the ball 12ft above the moon's surface? Round to the nearest hundreth.\r<BR>\n" );
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document.write( "I know I have to look for the seconds, which is t so then I have to solve for S, the height. This is have I've got so far:<BR>\n" );
document.write( " 12 = 2.7t^2 + 30t + 6.5<BR>\n" );
document.write( "-12                 -12<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "  0 = 2.7t^2 + 30t - 5.5<BR>\n" );
document.write( " <BR>\n" );
document.write( "B.)How many seconds will it take fore the ball to return to the surface? Round to the nearest hundredth.\r<BR>\n" );
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document.write( "So on the second part of the equation I have to look for the time, so that means that I have to solve for the height...<BR>\n" );
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document.write( "Thanks for your help in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #196652 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=196652\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An astronaut on the moon throws a baseball upward. The astronaut is 6ft., 6in. tall, and the initial velocity of the ball is 30 ft. per sec. The height S of the ball in feet is given by the equation<BR>\n" );
document.write( "S= -2.7t^2 + 30t + 6.5<BR>\n" );
document.write( "where t is the number of seconds after the ball was thrown. <BR>\n" );
document.write( "A.) After how many seconds is the ball 12ft above the moon's surface? Round to the nearest hundreth. <BR>\n" );
document.write( "I know I have to look for the seconds, which is t so then I have to solve for S, the height. This is have I've got so far:<BR>\n" );
document.write( "12 = 2.7t^2 + 30t + 6.5 *** It's -2.7<BR>\n" );
document.write( "-12 -12<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "0 = -2.7t^2 + 30t - 5.5<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.7x%5E2%2B30x%2B-5.5+=+0 ALIGN=MIDDLE  ALT=\"-2.7x%5E2%2B30x%2B-5.5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2830%29%5E2-4%2A-2.7%2A-5.5=840.6 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2830%29%5E2-4%2A-2.7%2A-5.5=840.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=840.6 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-30%2B-sqrt%28+840.6+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-30%2B-sqrt%28+840.6+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%2830%29%2Bsqrt%28+840.6+%29%29%2F2%5C-2.7+=+0.18646247628908 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2830%29%2Bsqrt%28+840.6+%29%29%2F2%5C-2.7+=+0.18646247628908\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%2830%29-sqrt%28+840.6+%29%29%2F2%5C-2.7+=+10.924648634822 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2830%29-sqrt%28+840.6+%29%29%2F2%5C-2.7+=+10.924648634822\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.7x%5E2%2B30x%2B-5.5 ALIGN=MIDDLE  ALT=\"-2.7x%5E2%2B30x%2B-5.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.7x%5E2%2B30x%2B-5.5+=+%28x-0.18646247628908%29%2A%28x-10.924648634822%29 ALIGN=MIDDLE  ALT=\"-2.7x%5E2%2B30x%2B-5.5+=+%28x-0.18646247628908%29%2A%28x-10.924648634822%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.18646247628908, 10.924648634822.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2.7%2Ax%5E2%2B30%2Ax%2B-5.5+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2.7%2Ax%5E2%2B30%2Ax%2B-5.5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "---------------<BR>\n" );
document.write( "Notice there are 2 numbers, the smallest is going up, the other coming back down.<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "B.)How many seconds will it take for the ball to return to the surface? Round to the nearest hundredth.<BR>\n" );
document.write( "It's at the surface when h = 0<BR>\n" );
document.write( "-2.7t^2 + 30t + 6.5 = 0<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.7x%5E2%2B30x%2B6.5+=+0 ALIGN=MIDDLE  ALT=\"-2.7x%5E2%2B30x%2B6.5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2830%29%5E2-4%2A-2.7%2A6.5=970.2 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2830%29%5E2-4%2A-2.7%2A6.5=970.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=970.2 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-30%2B-sqrt%28+970.2+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-30%2B-sqrt%28+970.2+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%2830%29%2Bsqrt%28+970.2+%29%29%2F2%5C-2.7+=+-0.212598823296627 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2830%29%2Bsqrt%28+970.2+%29%29%2F2%5C-2.7+=+-0.212598823296627\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%2830%29-sqrt%28+970.2+%29%29%2F2%5C-2.7+=+11.3237099344077 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2830%29-sqrt%28+970.2+%29%29%2F2%5C-2.7+=+11.3237099344077\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.7x%5E2%2B30x%2B6.5 ALIGN=MIDDLE  ALT=\"-2.7x%5E2%2B30x%2B6.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.7x%5E2%2B30x%2B6.5+=+%28x--0.212598823296627%29%2A%28x-11.3237099344077%29 ALIGN=MIDDLE  ALT=\"-2.7x%5E2%2B30x%2B6.5+=+%28x--0.212598823296627%29%2A%28x-11.3237099344077%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.212598823296627, 11.3237099344077.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2.7%2Ax%5E2%2B30%2Ax%2B6.5+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2.7%2Ax%5E2%2B30%2Ax%2B6.5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "------------<BR>\n" );
document.write( "Ignore the negative number.<BR>\n" );
document.write( "t = 11.32 seconds\r<BR>\n" );
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document.write( "So on the second part of the equation I have to look for the time, so that means that I have to solve for the height... </SPAN>\n" );
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