document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184247>Question 184247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 114. Surface area of a cube. The formula A =6V^2/3 gives<BR>\n" );
document.write( "the surface area of a cube in terms of its volume V. What is the volume of a cube with surface area 12 square feet? \r<BR>\n" );
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document.write( "94. Find all real or imaginary solutions to each equation.<BR>\n" );
document.write( "49x^2+9=42x \r<BR>\n" );
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document.write( "98. x-1/x+2= 2x-3/x+4 \r<BR>\n" );
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document.write( "110. Winston works faster. Winston can mow his dad’s lawn in 1 hour less than it takes his brother Willie. If they take 2 hours to mow it when working together, then how long would it take Winston working alone? \r<BR>\n" );
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document.write( "114. Maximizing profit. The total profit (in dollars) for sales of x rowing machines is given by P(x)=-0+2x^2+300x-200 . What is the profit if 500 are sold? For what value of x will the profit be at a maximum? \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 #138385 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=138385\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 114. Surface area of a cube. The formula A =6V^2/3 gives the surface area of<BR>\n" );
document.write( " a cube in terms of its volume V. <BR>\n" );
document.write( "What is the volume of a cube with surface area 12 square feet?<BR>\n" );
document.write( "write it:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6V%5E%282%2F3%29 ALIGN=MIDDLE  ALT=\"6V%5E%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 12<BR>\n" );
document.write( "divide both sides by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5E%282%2F3%29 ALIGN=MIDDLE  ALT=\"V%5E%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F6 ALIGN=MIDDLE  ALT=\"12%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5E%282%2F3%29 ALIGN=MIDDLE  ALT=\"V%5E%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
document.write( "Cube both sides and you have<BR>\n" );
document.write( "V^2 = 8<BR>\n" );
document.write( "V = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288%29 ALIGN=MIDDLE  ALT=\"sqrt%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "v = 2.828 cu/ft<BR>\n" );
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document.write( "94. Find all real or imaginary solutions to each equation.<BR>\n" );
document.write( "49x^2 + 9 = 42x<BR>\n" );
document.write( "49x^2 - 42x + 9 = 0<BR>\n" );
document.write( "(7x-3)(7x-3) = 0<BR>\n" );
document.write( "7x = 3<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F7 ALIGN=MIDDLE  ALT=\"3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "98. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-1%29%29%2F%28%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"%28%28x-1%29%29%2F%28%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x-3%29%29%2F%28%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"%28%282x-3%29%29%2F%28%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "(x-1)(x+4) = (x+2)(2x-3)<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "x^2 + 3x - 4 = 2x^2 + x - 6<BR>\n" );
document.write( "combine on the right<BR>\n" );
document.write( "0 = 2x^2 - x^2 + x - 3x - 6 + 4<BR>\n" );
document.write( " x^2 - 2x - 2 = 0<BR>\n" );
document.write( "Solve this using the quadratic formula: a=1; b=-2; c=-2<BR>\n" );
document.write( "You should get: x = 2.732 and x = -.732<BR>\n" );
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document.write( "110. Winston works faster. Winston can mow his dad’s lawn in 1 hour less<BR>\n" );
document.write( " than it takes his brother Willie. If they take 2 hours to mow it when<BR>\n" );
document.write( " working together, then how long would it take Winston working alone?<BR>\n" );
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document.write( "let x = W's mowing time working alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x+1) = brother's time working alone<BR>\n" );
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document.write( "Let the completed job = 1<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fx ALIGN=MIDDLE  ALT=\"2%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"2%2F%28%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply eq by x(x+1), results<BR>\n" );
document.write( "2(x+1) + 2x = x(x+1)<BR>\n" );
document.write( "2x + 2 + 2x = x^2 + x<BR>\n" );
document.write( "4x + 2 = x^2 + x<BR>\n" );
document.write( "0 = x^2 + x - 4x - 2<BR>\n" );
document.write( "x^2 - 3x - 2 = 0; a quadratic equation<BR>\n" );
document.write( "Use the quadratic formula to solve this a=1; b=-3; c=-2<BR>\n" );
document.write( "Positive solution: x=3.56 hrs W working alone<BR>\n" );
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document.write( "114. Maximizing profit. The total profit (in dollars) for sales of x rowing machines is given by P(x)=-0+2x^2+300x-200 . What is the profit if 500 are sold? <BR>\n" );
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document.write( "Assume you mean<BR>\n" );
document.write( " P(x)=-.2x^2+300x-200<BR>\n" );
document.write( "substitute 500 for x<BR>\n" );
document.write( " P(x)=-.2(500^2) + 300(500) - 200 <BR>\n" );
document.write( " P(x)=-.2(250000) + 150000 - 200<BR>\n" );
document.write( " P(x)=-50000 + 150000 - 200<BR>\n" );
document.write( " P(x)= $99,800 profit <BR>\n" );
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document.write( "For what value of x will the profit be at a maximum?<BR>\n" );
document.write( "Use the axis of symmetry formula: x = -b/(2a); in this eq: a=-.2; b=300<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-300%2F%282%2A-.2%29 ALIGN=MIDDLE  ALT=\"-300%2F%282%2A-.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-300%2F%28-.4%29 ALIGN=MIDDLE  ALT=\"-300%2F%28-.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 750 unit for max profit </SPAN>\n" );
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