document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137661>Question 1137661</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Maxine and Ramon are in a hot air balloon. They drop a sand bag from the balloon. The height of the sandbag can be modelled by the function h(t)=-5t^2+80 where h(t) is the height of the sand bag above the ground, in metres, at time t seconds after it is dropped.<BR>\n" );
document.write( "a) Determine the domain and range of the function.<BR>\n" );
document.write( "b) Graph the function with any restrictions.<BR>\n" );
document.write( "c) Graph h^-1 for the same domain and range.<BR>\n" );
document.write( "d) Determine the equation for h^-1(t)<BR>\n" );
document.write( "e) Is the graph of the inverse a function? Explain your answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755527 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=755527\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <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;\" > is when bag is dropped<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%280%29+=+-5%2A0%5E2+%2B+80+ ALIGN=MIDDLE  ALT=\"+h%280%29+=+-5%2A0%5E2+%2B+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%280%29+=+80+ ALIGN=MIDDLE  ALT=\"+h%280%29+=+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+0+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is height when bag hits ground<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-5t%5E2+%2B+80+ ALIGN=MIDDLE  ALT=\"+0+=+-5t%5E2+%2B+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5t%5E2+=+80+ ALIGN=MIDDLE  ALT=\"+5t%5E2+=+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5E2+=+16+ ALIGN=MIDDLE  ALT=\"+t%5E2+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+4+ ALIGN=MIDDLE  ALT=\"+t+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > s<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "The domain is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+ ALIGN=MIDDLE  ALT=\"+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+ ALIGN=MIDDLE  ALT=\"+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec<BR>\n" );
document.write( "The range is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+ ALIGN=MIDDLE  ALT=\"+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+80+ ALIGN=MIDDLE  ALT=\"+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-1%2C+5%2C+-10%2C+100%2C+-5x%5E2+%2B+80+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-1%2C+5%2C+-10%2C+100%2C+-5x%5E2+%2B+80+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( with above restrictions )<BR>\n" );
document.write( "c<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+-5%2At%5E2+%2B+80+ ALIGN=MIDDLE  ALT=\"+h+=+-5%2At%5E2+%2B+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5t%5E2+=+-h+%2B+80+ ALIGN=MIDDLE  ALT=\"+5t%5E2+=+-h+%2B+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5E2+=+%28+80+-+h+%29%2F5+ ALIGN=MIDDLE  ALT=\"+t%5E2+=+%28+80+-+h+%29%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%28h%29+=+sqrt%28+%28+80+-+h+%29%2F5+%29+ ALIGN=MIDDLE  ALT=\"+t%28h%29+=+sqrt%28+%28+80+-+h+%29%2F5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-2%2C+100%2C+-5%2C+5%2C+%2Bsqrt%28+%28+80+-+x+%29%2F5+%29%2C+-sqrt%28+%28+80+-+x+%29%2F5+%29+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(d)<BR>\n" );
document.write( "The inverse is not a function, since there are<BR>\n" );
document.write( "2 values for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%28h%29+ ALIGN=MIDDLE  ALT=\"+t%28h%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > for every <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+ ALIGN=MIDDLE  ALT=\"+h+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );