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" );
document.write( "\n" );
document.write( "94. Find all real or imaginary solutions to each equation.<BR>\n" );
document.write( "49x^2+9=42x \r<BR>\n" );
document.write( "\n" );
document.write( "98. x-1/x+2= 2x-3/x+4 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138369 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=138369\">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<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? <BR>\n" );
document.write( "I'll take your word for the formula.<BR>\n" );
document.write( "A =6V^2/3<BR>\n" );
document.write( "A^3 = 216V^2<BR>\n" );
document.write( "V^2 = A^3/216<BR>\n" );
document.write( "V^2 = 1728/216 = 8<BR>\n" );
document.write( "V = sqrt(8) = 2sqrt(2) cubic feet<BR>\n" );
document.write( "---------------------------------<BR>\n" );
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( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49x%5E2%2B-42x%2B9+=+0 ALIGN=MIDDLE  ALT=\"49x%5E2%2B-42x%2B9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-42%29%5E2-4%2A49%2A9=0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-42%29%5E2-4%2A49%2A9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=0 is zero! That means that there is only one solution: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-42%29%29%2F2%5C49 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-42%29%29%2F2%5C49\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "      Expression can be factored: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49x%5E2%2B-42x%2B9+=+%28x-0.428571428571429%29%2A%28x-0.428571428571429%29 ALIGN=MIDDLE  ALT=\"49x%5E2%2B-42x%2B9+=+%28x-0.428571428571429%29%2A%28x-0.428571428571429%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "    Again, the answer is: 0.428571428571429, 0.428571428571429.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+49%2Ax%5E2%2B-42%2Ax%2B9+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+49%2Ax%5E2%2B-42%2Ax%2B9+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "x = 3/7<BR>\n" );
document.write( "--------------\r<BR>\n" );
document.write( "\n" );
document.write( "98. x-1/x+2= 2x-3/x+4 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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? <BR>\n" );
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? <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );