document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33660>Question 33660</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321279085/algebrahomeworkh>College Alegbra</A><BR>\n" );
document.write( ": <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" );
document.write( "Answer	\r<BR>\n" );
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document.write( "b)Graph this function.<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	\r<BR>\n" );
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document.write( "2)The volume of a cylinder (think about the volume of a can) is given by V = pr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters.<BR>\n" );
document.write( "a)Write h as a function of r.<BR>\n" );
document.write( "Answer	\r<BR>\n" );
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document.write( "b)What is the measurement of the height if the radius of the cylinder is 2 centimeters?<BR>\n" );
document.write( "Answer	\r<BR>\n" );
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document.write( "Show work in this space	\r<BR>\n" );
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document.write( "c)Graph this function.<BR>\n" );
document.write( "Show graph here </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #20084 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=20084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> WHEN WE CUT X LONG PIECES ON ALL 4 SIDES THE CARD 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 =  8-2X AND WIDTH = 6-2X..AND HEIGHT =X ...SO VOLUME V IS GIVEN BY LEMGTH*WIDTH*HEIGHT						<BR>\n" );
document.write( "V=(8-2X)(6-2X)X...DOMAIN OF V IS GIVEN BY THE FACT THAT LENGTH OR WIDTH CAN NOT BE NEGATIVE...CRITICAL VALUE BEING WIDTH WE GET ....						<BR>\n" );
document.write( " 8-2X>0...AND 6-2X>0...SO X <3						<BR>\n" );
document.write( "RANGE.....MAXIMUM VALUE........						<BR>\n" );
document.write( "V=X(8-2X)(6-2X)=X{48-16X-12X+4X^2)=4X^3-28X^2+48X...IF 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 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+-2%2C+3%2C+-2%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+-2%2C+3%2C+-2%2C+200%2C+4%2A%28x%5E3%29-28%2A%28x%5E2%29%2B48%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The volume of a cylinder (think about the volume of a can) is given by V = pr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters.<BR>\n" );
document.write( "a)Write h as a function of r.<BR>\n" );
document.write( "Answer<BR>\n" );
document.write( "100=PI*R^2*H<BR>\n" );
document.write( "H=100/(PI*R^2)<BR>\n" );
document.write( "b)What is the measurement of the height if the radius of the cylinder is 2 centimeters?<BR>\n" );
document.write( "Answer<BR>\n" );
document.write( "H=100/(PI*2^2)=25/PI=7.96 CM.\r<BR>\n" );
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document.write( "Show work in this space\r<BR>\n" );
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document.write( "c)Graph this function.<BR>\n" );
document.write( "Show graph here<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-2%2C+10%2C+-2%2C+10%2C+100%2F%283.14%2A%28x%5E2%29%29%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-2%2C+10%2C+-2%2C+10%2C+100%2F%283.14%2A%28x%5E2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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