document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202658>Question 202658</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073533490/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Decreasing Cube. Each of the three dimensions of a cube with sides of length S centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeter is given my \r<BR>\n" );
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document.write( "V(s) = S^3-13s^2+54s-72\r<BR>\n" );
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document.write( "a) Find V(10)<BR>\n" );
document.write( "b) If the new width is S-6 centimeters, then what are the new length and height<BR>\n" );
document.write( "c) Find the volume when S=10 by multiplying the length, width, and height.\r<BR>\n" );
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document.write( "I am not very good at word problems and don't know how to write them out in ever detail like my instructor wants.\r<BR>\n" );
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document.write( "I am greatful for any help thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152836 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=152836\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28s%29=s%5E3-13s%5E2%2B54s-72 ALIGN=MIDDLE  ALT=\"V%28s%29=s%5E3-13s%5E2%2B54s-72\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%2810%29=%2810%29%5E3-13%2810%29%5E2%2B54%2810%29-72 ALIGN=MIDDLE  ALT=\"V%2810%29=%2810%29%5E3-13%2810%29%5E2%2B54%2810%29-72\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=10 ALIGN=MIDDLE  ALT=\"s=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie replace each \"s\" with 10).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%2810%29=1000-13%2810%29%5E2%2B54%2810%29-72 ALIGN=MIDDLE  ALT=\"V%2810%29=1000-13%2810%29%5E2%2B54%2810%29-72\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cube <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000 ALIGN=MIDDLE  ALT=\"1000\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%2810%29=1000-13%28100%29%2B54%2810%29-72 ALIGN=MIDDLE  ALT=\"V%2810%29=1000-13%28100%29%2B54%2810%29-72\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%2810%29=1000-1300%2B54%2810%29-72 ALIGN=MIDDLE  ALT=\"V%2810%29=1000-1300%2B54%2810%29-72\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-13 ALIGN=MIDDLE  ALT=\"-13\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1300 ALIGN=MIDDLE  ALT=\"-1300\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%2810%29=1000-1300%2B540-72 ALIGN=MIDDLE  ALT=\"V%2810%29=1000-1300%2B540-72\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54 ALIGN=MIDDLE  ALT=\"54\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=540 ALIGN=MIDDLE  ALT=\"540\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%2810%29=168 ALIGN=MIDDLE  ALT=\"V%2810%29=168\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=LWH ALIGN=MIDDLE  ALT=\"V=LWH\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the volume equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E3-13s%5E2%2B54s-72=L%28s-6%29H ALIGN=MIDDLE  ALT=\"s%5E3-13s%5E2%2B54s-72=L%28s-6%29H\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the given expressions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28s%5E3-13s%5E2%2B54s-72%29%2F%28s-6%29=LH ALIGN=MIDDLE  ALT=\"%28s%5E3-13s%5E2%2B54s-72%29%2F%28s-6%29=LH\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s-6 ALIGN=MIDDLE  ALT=\"s-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28s-6%29%28s%5E2-7s%2B12%29%29%2F%28s-6%29=LH ALIGN=MIDDLE  ALT=\"%28%28s-6%29%28s%5E2-7s%2B12%29%29%2F%28s-6%29=LH\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28%28s-6%29%29%28s%5E2-7s%2B12%29%29%2Fcross%28%28s-6%29%29=LH ALIGN=MIDDLE  ALT=\"%28cross%28%28s-6%29%29%28s%5E2-7s%2B12%29%29%2Fcross%28%28s-6%29%29=LH\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2-7s%2B12=LH ALIGN=MIDDLE  ALT=\"s%5E2-7s%2B12=LH\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LH=s%5E2-7s%2B12 ALIGN=MIDDLE  ALT=\"LH=s%5E2-7s%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LH=%28s-3%29%28s-4%29 ALIGN=MIDDLE  ALT=\"LH=%28s-3%29%28s-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor\r<BR>\n" );
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document.write( "So the new length and height are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s-3 ALIGN=MIDDLE  ALT=\"s-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s-4 ALIGN=MIDDLE  ALT=\"s-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c)\r<BR>\n" );
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document.write( "I'll let you attempt this one on your own. Repost if you still need help.\r<BR>\n" );
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document.write( "Note: the answer is going to be the same as the answer in part a) (so you'll have something to check) </SPAN>\n" );
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