document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187268>Question 1187268</A>: <I><SPAN STYLE=\"word-break: break-all;\"> NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)= −4.9t2 squared + 325t + 353.\r<BR>\n" );
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document.write( "Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? For intermediate work, keep at least five decimal places. For the final answer, round to the nearest hundredth.\r<BR>\n" );
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document.write( "The rocket splashes down after             seconds.\r<BR>\n" );
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document.write( "How high above sea-level does the rocket get at its peak?\r<BR>\n" );
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document.write( "The rocket peaks at                      meters above sea-level.<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 #818214 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=818214\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)= −4.9t2 squared + 325t + 353.<BR>\n" );
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document.write( "Rockets launched by NASA have thrust.<BR>\n" );
document.write( "That's a projectile.\r<BR>\n" );
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document.write( "Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?<BR>\n" );
document.write( "It's when h(t) = 0<BR>\n" );
document.write( "h(t)= −4.9t^2 + 325t + 353 = 0<BR>\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=-4.9x%5E2%2B325x%2B353+=+0 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B325x%2B353+=+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" );
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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" );
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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=%28325%29%5E2-4%2A-4.9%2A353=112543.8 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28325%29%5E2-4%2A-4.9%2A353=112543.8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  Discriminant d=112543.8 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+=+%28-325%2B-sqrt%28+112543.8+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-325%2B-sqrt%28+112543.8+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28325%29%2Bsqrt%28+112543.8+%29%29%2F2%5C-4.9+=+-1.06892688325969 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28325%29%2Bsqrt%28+112543.8+%29%29%2F2%5C-4.9+=+-1.06892688325969\"   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-%28325%29-sqrt%28+112543.8+%29%29%2F2%5C-4.9+=+67.3954574955046 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28325%29-sqrt%28+112543.8+%29%29%2F2%5C-4.9+=+67.3954574955046\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.9x%5E2%2B325x%2B353 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B325x%2B353\"   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=-4.9x%5E2%2B325x%2B353+=+%28x--1.06892688325969%29%2A%28x-67.3954574955046%29 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B325x%2B353+=+%28x--1.06892688325969%29%2A%28x-67.3954574955046%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -1.06892688325969, 67.3954574955046.\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+-4.9%2Ax%5E2%2B325%2Ax%2B353+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B325%2Ax%2B353+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " t = 67.395 seconds<BR>\n" );
document.write( "++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++<BR>\n" );
document.write( "Do NOT include this<BR>\n" );
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document.write( "The rocket splashes down after seconds.\r<BR>\n" );
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document.write( "How high above sea-level does the rocket get at its peak?\r<BR>\n" );
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document.write( "The rocket peaks at meters above sea-level. </SPAN>\n" );
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