document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=372144>Question 372144</A>: <I><SPAN STYLE=\"word-break: break-all;\"> American astronauts working on the space station toss a ball into the air. the height of the ball is represented by the quadratic y=-2.7x^2+13.5x+14, where x represents the number of seconds since the ball was thrown and y represents the height of the ball in feet.\r<BR>\n" );
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document.write( "a) to the nearest hundredth of a second, after how much time does the ball hit the ground?\r<BR>\n" );
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document.write( "b) to the nearest tenth of a foot, what is the greatest height the ball achieves?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #265101 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=265101\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "To answer the questions precisely as you posed them would require knowing the distance from the surface of the earth to the space station plus a bunch of data and physics about the orbital decay of a ball left in earth orbit.  This is in view of the fact that \"the ground\" is back on earth.\r<BR>\n" );
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document.write( "On the other hand, if what you really meant to ask is:\r<BR>\n" );
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document.write( "a) to the nearest hundredth of a second, after how much time does the ball hit the <i><b>deck of the space station above which the ball was thrown</b></i>?\r<BR>\n" );
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document.write( "b) to the nearest tenth of a foot, what is the greatest height <i><b>above the deck of the space station</b></i> the ball achieves?\r<BR>\n" );
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document.write( "Then for part a:  Set the quadratic equal to zero and solve for the positive root.  And for part b:  Evaluate the function at the x-coordinate of the vertex of the parabola.  The x-coordinate of the vertex of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p(x)\ =\ ax^2\ +\ bx +\ c\"> is found by calculating <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{-b}{2a}\">.  Evaluating the function at that point means calculating <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\left(\frac{-b}{2a}\right)\ =\ a\left(\frac{-b}{2a}\right)^2\ +\ b\left(\frac{-b}{2a}\right) +\ c\"> and then rounding appropriately, of course.  \r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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