document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=52991>Question 52991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) 	An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.<BR>\n" );
document.write( "a) 	Find the function V that represents the volume of the box in terms of x.<BR>\n" );
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document.write( "b) 	Graph this function and show the graph over the valid range of the variable x..<BR>\n" );
document.write( "Show Graph here\r<BR>\n" );
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document.write( "c) 	Using the graph, what is the value of x that will produce the maximum volume?<BR>\n" );
document.write( "Answer </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #35346 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=35346\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An open-top box is to be constructed from a 6 by 8<BR>\n" );
document.write( "foot rectangular cardboard by cutting out equal<BR>\n" );
document.write( "squares at each corner and the folding up the flaps.<BR>\n" );
document.write( "Let x denote the length of each side of the square to<BR>\n" );
document.write( "be cut out.<BR>\n" );
document.write( "a)Find the function V that represents the volume of<BR>\n" );
document.write( "the box in terms of x.<BR>\n" );
document.write( "b)Graph this function.<BR>\n" );
document.write( "c)Using the graph, what is the value of x that will<BR>\n" );
document.write( "produce the maximum volume?<BR>\n" );
document.write( "Thank you for your help. !!!!! ;')<BR>\n" );
document.write( "1 solutions<BR>\n" );
document.write( "Answer 19558 by venugopalramana(1619) About Me on<BR>\n" );
document.write( "2006-04-10 12:13:41 (Show Source):<BR>\n" );
document.write( "I AM ABLE TO FIND ONE SUCH QUESTION I ANSWERED<BR>\n" );
document.write( "EARLIER.SEE THAT AND BY THE SIDE CORRESPONDING ANSWER<BR>\n" );
document.write( "TO YOUR QUESTION<BR>\n" );
document.write( "Volume/30504: an open box is to be constructed from a<BR>\n" );
document.write( "piece of cardboard 15 inches by 25 inches by cutting<BR>\n" );
document.write( "squares of length x from each corner and folding up<BR>\n" );
document.write( "the sides. Express the volume of the box as a function<BR>\n" );
document.write( "of x. what is the domain v?<BR>\n" );
document.write( "1 solutions .........IN YOUR CASE THE DIMENSIONS ARE<BR>\n" );
document.write( "6' AND 8'\r<BR>\n" );
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document.write( "Answer 17192 by venugopalramana(1167) About Me on<BR>\n" );
document.write( "2006-03-17 06:08:55 (Show Source):<BR>\n" );
document.write( "an open box is to be constructed from a piece of<BR>\n" );
document.write( "cardboard 15 inches by 25 inches by cutting squares of<BR>\n" );
document.write( "length x from each corner and folding up the sides.<BR>\n" );
document.write( "Express the volume of the box as a function of x. what<BR>\n" );
document.write( "is the domain v?<BR>\n" );
document.write( "WHEN WE CUT X LONG PIECES ON ALL 4 SIDES THE CARD<BR>\n" );
document.write( "BOARD WILL GET REDUCED BY<BR>\n" );
document.write( "X+X=2X...ALONG LENGTH AND...X+X=2X.....ALONG WIDTH<BR>\n" );
document.write( "SO OPEN BOX LENGTH = 25-2X ..(IN YOUR CASE 8-2X) AND<BR>\n" );
document.write( "WIDTH = 15-2X..(IN YOUR CASE 6-2X)..AND HEIGHT =X<BR>\n" );
document.write( "...SO VOLUME V IS GIVEN BY LEMGTH*WIDTH*HEIGHT<BR>\n" );
document.write( "V=(25-2X)(15-2X)X...(IN YOUR CASE<BR>\n" );
document.write( "(8-2X)(6-2X)X...DOMAIN OF V IS GIVEN BY THE FACT THAT<BR>\n" );
document.write( "LENGTH OR WIDTH CAN NOT BE NEGATIVE...CRITICAL VALUE<BR>\n" );
document.write( "BEING WIDTH WE GET ....<BR>\n" );
document.write( "15-2X>0...OR....15>2X...OR....7.5>X....OR X<7.5...(IN<BR>\n" );
document.write( "YOUR CASE 8-2X>0...AND 6-2X>0...SO X <3)<BR>\n" );
document.write( "RANGE.....MAXIMUM VALUE....IN YOUR CASE....<BR>\n" );
document.write( "V=X(8-2X)(6-2X)=X{48-16X-12X+4X^2)=4X^3-28X^2+48X...IF<BR>\n" );
document.write( "YOU KNOW CALCULUS<BR>\n" );
document.write( "DV/DX=12X^2-56X+48=0..OR...3X^2-14X+12=0....<BR>\n" );
document.write( "X=(14+SQRT.(52))/6...OR......(7+SQRT.(13))/3...OR....(7-SQRT.13)/3<BR>\n" );
document.write( "X=3.54..OR...1.13.<BR>\n" );
document.write( "D2V/DX2=6X-14=- VE AT X=1.13...SO MAXIMUM VOLUME IS<BR>\n" );
document.write( "OBTAINED AT X=1.13'<BR>\n" );
document.write( "YOU CAN SEE IT BY PLOTTING THE GRAPH.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+0%2C+3%2C+0%2C+200%2C+4%2A%28x%5E3%29-28%2A%28x%5E2%29%2B48%2Ax%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+0%2C+3%2C+0%2C+200%2C+4%2A%28x%5E3%29-28%2A%28x%5E2%29%2B48%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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