document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011968>Question 1011968</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A stone is thrown straight up from the ground. The height above the ground, h(t) metres is a function of time, t seconds (t >0) according to the rule h(t) = 20t - 5t^2. Find:\r<BR>\n" );
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document.write( "a. the domain of h\r<BR>\n" );
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document.write( "I do not understand how to acquire the domain of the function. Can you please explain how to get to the answer of 0 < t < 4\r<BR>\n" );
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document.write( "b. the greatest height achieved<BR>\n" );
document.write( "I solved this part: \r<BR>\n" );
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document.write( "-5t^2 + 20t + 0<BR>\n" );
document.write( "-5(t^2 - 4t) + 0<BR>\n" );
document.write( "-5(t^2 - 4t + 4) + 20<BR>\n" );
document.write( "-5( t - 2)^2 +20\r<BR>\n" );
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document.write( "So the maximum distance is 20 <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 #627819 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=627819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The domain (possible t values) must be greater than zero<BR>\n" );
document.write( "because t is time of the stone in air and in this case<BR>\n" );
document.write( "negative time has no meaning.<BR>\n" );
document.write( "The stone will be thrown and will hit the ground again, <BR>\n" );
document.write( "and time in air will again be meaningless. The stone will <BR>\n" );
document.write( "hit the ground when the height (h(t)) is zero again so:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29=20t-5t%5E2 ALIGN=MIDDLE  ALT=\"h%28t%29=20t-5t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ". <BR>\n" );
document.write( "When h(t)=0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=20t-5t%5E2 ALIGN=MIDDLE  ALT=\"0=20t-5t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28t%29%2820-5t%29 ALIGN=MIDDLE  ALT=\"0=%28t%29%2820-5t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0 ALIGN=MIDDLE  ALT=\"t=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OR ALIGN=MIDDLE  ALT=\"OR\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20-5t=0 ALIGN=MIDDLE  ALT=\"20-5t=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0 ALIGN=MIDDLE  ALT=\"t=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OR ALIGN=MIDDLE  ALT=\"OR\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20=5t ALIGN=MIDDLE  ALT=\"20=5t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0 ALIGN=MIDDLE  ALT=\"t=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=OR ALIGN=MIDDLE  ALT=\"OR\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=t ALIGN=MIDDLE  ALT=\"4=t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "So the only valid times when the rock is in the air are between<BR>\n" );
document.write( "t=0 (when the stone is thrown) and t=4 (when the stone lands).<BR>\n" );
document.write( "Any other values give a negative height.   <BR>\n" );
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