document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1069403>Question 1069403</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function Q (t) = 0.003t^2 – 0.625t + 25 represents the amount of energy in a battery after t minutes of use.\r<BR>\n" );
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document.write( "(a) State the amount of energy held by the battery immediately before it was used.\r<BR>\n" );
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document.write( "(c) Given that Q (10) = 19.05, find the average amount of energy produced per minute for the interval 10  &#8804; t &#8804; 20.\r<BR>\n" );
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document.write( "(d) Calculate the number of minutes it takes for the energy to reach zero.<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 #684637 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=684637\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a)<BR>\n" );
document.write( "At <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Q%28t%29+=+.003t%5E2+-+.625t+%2B+25+ ALIGN=MIDDLE  ALT=\"+Q%28t%29+=+.003t%5E2+-+.625t+%2B+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Q%28t%29+=+.003%2A0%5E2+-+.625%2A0+%2B+25+ ALIGN=MIDDLE  ALT=\"+Q%28t%29+=+.003%2A0%5E2+-+.625%2A0+%2B+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Q%280%29+=+25+ ALIGN=MIDDLE  ALT=\"+Q%280%29+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Q%2810%29+=+19.05+ ALIGN=MIDDLE  ALT=\"+Q%2810%29+=+19.05+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Q%2820%29+=+.003%2A20%5E2+-+.625%2A20+%2B+25+ ALIGN=MIDDLE  ALT=\"+Q%2820%29+=+.003%2A20%5E2+-+.625%2A20+%2B+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Q%2820%29+=+.003%2A400+-+12.5+%2B+25+ ALIGN=MIDDLE  ALT=\"+Q%2820%29+=+.003%2A400+-+12.5+%2B+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Q%2820%29+=+1.2+-+12.5+%2B+25+ ALIGN=MIDDLE  ALT=\"+Q%2820%29+=+1.2+-+12.5+%2B+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Q%2820%29+=+13.7+ ALIGN=MIDDLE  ALT=\"+Q%2820%29+=+13.7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+13.7+-+19.05+=+-5.35+ ALIGN=MIDDLE  ALT=\"+13.7+-+19.05+=+-5.35+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "units of energy used in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20+-+10+=+10+ ALIGN=MIDDLE  ALT=\"+20+-+10+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" > min<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5.35%2F10+=+.535+ ALIGN=MIDDLE  ALT=\"+5.35%2F10+=+.535+\"   DISABLED_style= \"max-width:90%; height:auto;\" > average energy/min<BR>\n" );
document.write( "produced for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10+%3C=+t+%3C=+20+ ALIGN=MIDDLE  ALT=\"+10+%3C=+t+%3C=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "(c)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Q%28t%29+=+.003t%5E2+-+.625t+%2B+25+ ALIGN=MIDDLE  ALT=\"+Q%28t%29+=+.003t%5E2+-+.625t+%2B+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Q%28t%29+=+0+ ALIGN=MIDDLE  ALT=\"+Q%28t%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+.003t%5E2+-+.625t+%2B+25+ ALIGN=MIDDLE  ALT=\"+0+=+.003t%5E2+-+.625t+%2B+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+.003+ ALIGN=MIDDLE  ALT=\"+a+=+.003+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-.625+ ALIGN=MIDDLE  ALT=\"+b+=+-.625+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+25+ ALIGN=MIDDLE  ALT=\"+c+=+25+\"   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=+t+=+%28+-%28-.625%29+%2B-+sqrt%28+%28-.625%29%5E2+-+4%2A.003%2A25+%29%29%2F%282%2A.003%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-%28-.625%29+%2B-+sqrt%28+%28-.625%29%5E2+-+4%2A.003%2A25+%29%29%2F%282%2A.003%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+=+%28+.625+%2B-+sqrt%28+.3906+-+.3+%29%29%2F.006+ ALIGN=MIDDLE  ALT=\"+t+=+%28+.625+%2B-+sqrt%28+.3906+-+.3+%29%29%2F.006+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+.625+%2B-+sqrt%28+.0906+%29%29%2F.006+ ALIGN=MIDDLE  ALT=\"+t+=+%28+.625+%2B-+sqrt%28+.0906+%29%29%2F.006+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+.625+%2B+.301+%29+%2F+.006+ ALIGN=MIDDLE  ALT=\"+t+=+%28+.625+%2B+.301+%29+%2F+.006+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+.926%2F.006+ ALIGN=MIDDLE  ALT=\"+t+=+.926%2F.006+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+154.33+ ALIGN=MIDDLE  ALT=\"+t+=+154.33+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+.625+-+.301+%29+%2F+.006+ ALIGN=MIDDLE  ALT=\"+t+=+%28+.625+-+.301+%29+%2F+.006+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+.324%2F.006+ ALIGN=MIDDLE  ALT=\"+t+=+.324%2F.006+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+54+ ALIGN=MIDDLE  ALT=\"+t+=+54+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-5%2C+70%2C+-5%2C+50%2C+.003x%5E2+-+.625x+%2B+25+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-5%2C+70%2C+-5%2C+50%2C+.003x%5E2+-+.625x+%2B+25+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This tells me that at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+54+ ALIGN=MIDDLE  ALT=\"+t+=+54+\"   DISABLED_style= \"max-width:90%; height:auto;\" > min the energy is zero<BR>\n" );
document.write( "I can ignore the root <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+154.33+ ALIGN=MIDDLE  ALT=\"+t+=+154.33+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );