document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181925>Question 181925</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a ball is thrown into the air with an initial velicity of 52 m/s from a height of 6 m above the ground, its height after t seconds is given by the equation s(t)= -4.9t^2 +52t +6\r<BR>\n" );
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document.write( "a) what is the time it takes to het to maximum height?<BR>\n" );
document.write( "b) what is the maximum height?<BR>\n" );
document.write( "c) how long does it take the ball to get to ground level? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136547 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=136547\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a ball is thrown into the air with an initial velicity of 52 m/s from a height of 6 m above the ground, its height after t seconds is given by the equation s(t)= -4.9t^2 +52t +6<BR>\n" );
document.write( "a) what is the time it takes to het to maximum height?<BR>\n" );
document.write( "that would be the \"axis of symmetry\" found at<BR>\n" );
document.write( "t = -b/2a<BR>\n" );
document.write( "t = -52/2(-4.9)<BR>\n" );
document.write( "t = -52/(-9.8)<BR>\n" );
document.write( "t = 5.306 seconds<BR>\n" );
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document.write( "b) what is the maximum height?<BR>\n" );
document.write( "Plug the answer above into:<BR>\n" );
document.write( "s(t)= -4.9t^2 +52t +6<BR>\n" );
document.write( "s(5.306)= -4.9(5.306)^2 +52(5.306) +6<BR>\n" );
document.write( "s(5.306)= -4.9(28.153636) + (275.912) +6<BR>\n" );
document.write( "s(5.306)= -137.9528164 + 281.912<BR>\n" );
document.write( "s(5.306)= 143.959 feet<BR>\n" );
document.write( ".<BR>\n" );
document.write( "c) how long does it take the ball to get to ground level?<BR>\n" );
document.write( "set s(t) to zero and solve:<BR>\n" );
document.write( "s(t)= -4.9t^2 +52t +6<BR>\n" );
document.write( "0= -4.9t^2 +52t +6<BR>\n" );
document.write( "Applying the quadratic equation yields:<BR>\n" );
document.write( "t = {-0.114, 10.726}<BR>\n" );
document.write( "Toss out the negative solution.<BR>\n" );
document.write( "t = 10.726 seconds<BR>\n" );
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document.write( "Below is the details of the quadratic solution:<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=quadratic.solver>SOLVE quadratic equation with variable</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%2B52x%2B6+=+0 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B52x%2B6+=+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=%2852%29%5E2-4%2A-4.9%2A6=2821.6 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2852%29%5E2-4%2A-4.9%2A6=2821.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=2821.6 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+=+%28-52%2B-sqrt%28+2821.6+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-52%2B-sqrt%28+2821.6+%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-%2852%29%2Bsqrt%28+2821.6+%29%29%2F2%5C-4.9+=+-0.114156624968866 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2852%29%2Bsqrt%28+2821.6+%29%29%2F2%5C-4.9+=+-0.114156624968866\"   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-%2852%29-sqrt%28+2821.6+%29%29%2F2%5C-4.9+=+10.726401522928 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2852%29-sqrt%28+2821.6+%29%29%2F2%5C-4.9+=+10.726401522928\"   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=-4.9x%5E2%2B52x%2B6 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B52x%2B6\"   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%2B52x%2B6+=+-4.9%28x--0.114156624968866%29%2A%28x-10.726401522928%29 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B52x%2B6+=+-4.9%28x--0.114156624968866%29%2A%28x-10.726401522928%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.114156624968866, 10.726401522928.\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%2B52%2Ax%2B6+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B52%2Ax%2B6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );