document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186180>Question 1186180</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.) Write each fraction in terms of the LCM of the denominators.<BR>\n" );
document.write( "15/16a3b3, 17/30a5b ??..\r<BR>\n" );
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document.write( "2.) The Water Cube was built in Beijing, China, to house the National Swimming Center for the 2008 Olympics. Although not actually a cube (its height is not equal to its length and width), the Water Cube is designed to look like a \"cube\" of water molecules. The volume of the 31-meter-high Water Cube is <BR>\n" );
document.write( "971,199 m3.<BR>\n" );
document.write( " Find the length of a side of its square base. Recall that <BR>\n" );
document.write( "V = LWH. ??...\r<BR>\n" );
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document.write( "3.) A square piece of cardboard is formed into a box by cutting 10-centimeter squares from each of the four corners and then folding up the sides, as shown in the figure below. If the volume V of the box is to be 81,000 cm3, what size square piece of cardboard is needed? Recall that V = LWH. Length ??.. cm, Width ??.. cm. ??..\r<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 #817117 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=817117\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write each fraction in terms of the LCM of the denominators.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F%28%2816a%5E3b%5E3%29%29 ALIGN=MIDDLE  ALT=\"15%2F%28%2816a%5E3b%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2F%28%2830a%5E5b%29%29 ALIGN=MIDDLE  ALT=\"17%2F%28%2830a%5E5b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "LCM: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240a%5E5b%5E3 ALIGN=MIDDLE  ALT=\"240a%5E5b%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > so we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2815a%5E2%2815%29%29%29%2F%28%28240a%5E5b%5E3%29%29 ALIGN=MIDDLE  ALT=\"%28%2815a%5E2%2815%29%29%29%2F%28%28240a%5E5b%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28225a%5E2%29%29%2F%28%28240a%5E5b%5E3%29%29 ALIGN=MIDDLE  ALT=\"%28%28225a%5E2%29%29%2F%28%28240a%5E5b%5E3%29%29\"   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=%28%288ab%5E2%2817%29%29%29%2F%28%28240a%5E5b%5E3%29%29 ALIGN=MIDDLE  ALT=\"%28%288ab%5E2%2817%29%29%29%2F%28%28240a%5E5b%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28136b%5E2%29%29%2F%28%28240a%5E5b%5E3%29%29 ALIGN=MIDDLE  ALT=\"%28%28136b%5E2%29%29%2F%28%28240a%5E5b%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2.) The Water Cube was built in Beijing, China, to house the National Swimming Center for the 2008 Olympics.<BR>\n" );
document.write( " Although not actually a cube (its height is not equal to its length and width), the Water Cube is designed to look like a \"cube\" of water molecules.<BR>\n" );
document.write( "The volume of the 31-meter-high Water Cube is 971,199 m3.<BR>\n" );
document.write( "Find the length of a side of its square base.<BR>\n" );
document.write( "Base is square and height 31,<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "31b^2 = 971199<BR>\n" );
document.write( "b^2 = 971199/31<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2831329%29 ALIGN=MIDDLE  ALT=\"sqrt%2831329%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = 177 meters<BR>\n" );
document.write( "the dimensions: 177 by 177 by 31<BR>\n" );
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document.write( "3.) A square piece of cardboard is formed into a box by cutting 10-centimeter squares from each of the four corners and then folding up the sides, as shown in the figure below.<BR>\n" );
document.write( " If the volume V of the box is to be 81,000 cm3, what size square piece of cardboard is needed?<BR>\n" );
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document.write( "let s = length and width of the cardboard, <BR>\n" );
document.write( "Removing the 10 cm squares reduces the cardboard dimension by 20<BR>\n" );
document.write( "The height is give as 10<BR>\n" );
document.write( "(s-20)^2 * 10 = 81000<BR>\n" );
document.write( "simplify, divide by 10, then square the sides<BR>\n" );
document.write( "s^2 - 40s + 400 = 8100<BR>\n" );
document.write( "s^2 - 40 + 400 - 8100 = 0<BR>\n" );
document.write( "s^2 - 40s - 7700 = 0<BR>\n" );
document.write( "Use the quadratic formula a=1, b=-40,c=-7700, but this will factor<BR>\n" );
document.write( "(s-110)(s+70) = 0<BR>\n" );
document.write( "positive solution<BR>\n" );
document.write( "s = 110 cm the length of the square base<BR>\n" );
document.write( "Dimensions of piece of cardboard; 110 by 110<BR>\n" );
document.write( "Box dimensions: 90 by 90 by 10<BR>\n" );
document.write( " Check<BR>\n" );
document.write( "(110 - 20)^2 * 10 = 81000 cu/cm  </SPAN>\n" );
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