document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=703591>Question 703591</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I really appreciate any help with this question:)<BR>\n" );
document.write( "A ball is thrown vertically upward with an initial speed of 35m/s.  Its height h metres, after t seconds is given by the formula h=-4.9t^2+3.5t.  <BR>\n" );
document.write( "a)What is the maximum height reached by the ball?<BR>\n" );
document.write( "b)How long is the ball in the air?<BR>\n" );
document.write( "c)How many seconds is the ball highter than 30m?<BR>\n" );
document.write( "I know<BR>\n" );
document.write( "a=-4.9<BR>\n" );
document.write( "b=35<BR>\n" );
document.write( "c+0  I also found the height (which I don't need) using t=-b/2a<BR>\n" );
document.write( "Really...really appreciate any help:)!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #433575 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=433575\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown vertically upward with an initial speed of 35m/s. Its height h metres, after t seconds is given by the formula h=-4.9t^2+35t.<BR>\n" );
document.write( "a)What is the maximum height reached by the ball?<BR>\n" );
document.write( "because the coefficient associated with the t^2 term is negative, we KNOW it is a parabola that opens downwards.  Thus, the VERTEX will be the MAX.<BR>\n" );
document.write( "Time t when it reaches max:<BR>\n" );
document.write( "t = -b/2a<BR>\n" );
document.write( "t = -35/(2*(-4.9))<BR>\n" );
document.write( "t = -35/(-9.8)<BR>\n" );
document.write( "t = -35/(-9.8)<BR>\n" );
document.write( "t = 3.57 seconds<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Max height, plug t above into equation to find h:<BR>\n" );
document.write( "h=-4.9t^2+35t<BR>\n" );
document.write( "h=-4.9(3.57)^2+35(3.57)<BR>\n" );
document.write( "h= 62.5 metres<BR>\n" );
document.write( ".<BR>\n" );
document.write( "b)How long is the ball in the air?<BR>\n" );
document.write( "set h to zero and find t:<BR>\n" );
document.write( "h=-4.9t^2+35t<BR>\n" );
document.write( "0=-4.9t^2+35t<BR>\n" );
document.write( "0=4.9t^2-35t<BR>\n" );
document.write( "0=t(4.9t-35)<BR>\n" );
document.write( "t = {0, 35/4.9)<BR>\n" );
document.write( "t = {0, 7.14)<BR>\n" );
document.write( "throw out the 0 (that's when it started) leaving:<BR>\n" );
document.write( "t = 7.14 seconds<BR>\n" );
document.write( ".<BR>\n" );
document.write( "c)How many seconds is the ball highter than 30m?<BR>\n" );
document.write( "set h to 30 and solve for t:<BR>\n" );
document.write( "h=-4.9t^2+35t<BR>\n" );
document.write( "30=-4.9t^2+35t<BR>\n" );
document.write( "0=-4.9t^2+35t-30<BR>\n" );
document.write( "0=4.9t^2-35t+30<BR>\n" );
document.write( "apply \"quadratic equation\" to get:<BR>\n" );
document.write( "x = {6.15, 1.0}<BR>\n" );
document.write( "time higher than 30m:<BR>\n" );
document.write( "6.15 - 1.0 = 5.15 seconds<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic follows:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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%2B-35x%2B30+=+0 ALIGN=MIDDLE  ALT=\"4.9x%5E2%2B-35x%2B30+=+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=%28-35%29%5E2-4%2A4.9%2A30=637 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-35%29%5E2-4%2A4.9%2A30=637\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=637 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--35%2B-sqrt%28+637+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--35%2B-sqrt%28+637+%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-%28-35%29%2Bsqrt%28+637+%29%29%2F2%5C4.9+=+6.14682233961713 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-35%29%2Bsqrt%28+637+%29%29%2F2%5C4.9+=+6.14682233961713\"   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-%28-35%29-sqrt%28+637+%29%29%2F2%5C4.9+=+0.996034803240008 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-35%29-sqrt%28+637+%29%29%2F2%5C4.9+=+0.996034803240008\"   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%2B-35x%2B30 ALIGN=MIDDLE  ALT=\"4.9x%5E2%2B-35x%2B30\"   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%2B-35x%2B30+=+4.9%28x-6.14682233961713%29%2A%28x-0.996034803240008%29 ALIGN=MIDDLE  ALT=\"4.9x%5E2%2B-35x%2B30+=+4.9%28x-6.14682233961713%29%2A%28x-0.996034803240008%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 6.14682233961713, 0.996034803240008.\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%2B-35%2Ax%2B30+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4.9%2Ax%5E2%2B-35%2Ax%2B30+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );