document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=194503>Question 194503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> an open- top box is to be made from an 8 in by 12 in rectangular piece of copper by cutting equal squares (x in by x in) from each corner and folding up the sides. write volume of the box V as a function of x. use a graphing calculator to find the maximum possible volume to the nearest hundredth of a cubic inch. what are the final dimensions of this box?<BR>\n" );
document.write( "I am having hard time for this problem. please help me please...... it is urgent for my midterm exam please.....   <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 #145944 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=145944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> an open- top box is to be made from an 8 in by 12 in rectangular piece of copper by cutting equal squares (x in by x in) from each corner and folding up the sides. write volume of the box V as a function of x. use a graphing calculator to find the maximum possible volume to the nearest hundredth of a cubic inch. what are the final dimensions of this box?<BR>\n" );
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document.write( "Draw this out and you will see the dimensions of the box will be:<BR>\n" );
document.write( "(8-2x) by (12-2x) by x<BR>\n" );
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document.write( "FOIL the length and width<BR>\n" );
document.write( "96 - 16x - 24x + 4x^2<BR>\n" );
document.write( "Write this<BR>\n" );
document.write( "4x^2 - 40x + 96<BR>\n" );
document.write( "Multiply this by the height (x) and you have the volume function<BR>\n" );
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document.write( "V(x) = 4x^3 - 40x^2 + 96x<BR>\n" );
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document.write( "Find the maximum volume on a graphing calc: enter: y = 4x^3 - 40x^2 + 96x<BR>\n" );
document.write( "Scale x:-4,+8; y:-50, +150<BR>\n" );
document.write( "Should look like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+8%2C+-50%2C+150%2C+4x%5E3-40x%5E2%2B96x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+8%2C+-50%2C+150%2C+4x%5E3-40x%5E2%2B96x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can see the max that we want is about x=1.6<BR>\n" );
document.write( "Use the max feature on the calc to find the exact value of x and y(volume)<BR>\n" );
document.write( "I got x = 1.57 in; y = 67.6 cu/in as the max volume<BR>\n" );
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document.write( "Sorry about that. If have any questions, email me.  Carl<BR>\n" );
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