document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=52878>Question 52878</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321279085/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 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 then folding up the flaps. Let x denote the length of each side of the square to be cut out. Find the function V that represents the volume of the box in terms of x. Graph this function and show the graph over the valid range of the variable x. Using the graph, what is the value of x that will produce the maximum volume?\r<BR>\n" );
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document.write( "I need help with this ASAP! Thank you so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #35349 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=35349\">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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