document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105369>Question 1105369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A machine has two wheels tangent to each other.  The distance between centers is 9 in.  The sum of the areas is 198 sq. in.  Find radius of each wheel, to the nearest hundredth of an inch.\r<BR>\n" );
document.write( "\n" );
document.write( "Area of circle; pi * r^2.\r<BR>\n" );
document.write( "\n" );
document.write( "radius; d/2.\r<BR>\n" );
document.write( "\n" );
document.write( "Let wheels = x and y.\r<BR>\n" );
document.write( "\n" );
document.write( "Not sure how to solve.  Non-homework. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #720187 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=720187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A machine has two wheels tangent to each other.  The distance between centers is 9 in.  The sum of the areas is 198 sq. in.  Find radius of each wheel, to the nearest hundredth of an inch.<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "x + y = 9<BR>\n" );
document.write( "pi*(x^2 + y^2) = 198<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "x^2 + y^2 = 198/pi<BR>\n" );
document.write( "y = 9-x<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x^2 + 81-18x+x^2 = 198/pi<BR>\n" );
document.write( "2x^2 - 18x + 81-198/pi = 0<BR>\n" );
document.write( "2x^2 - 18x + 17.9746 = 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=2x%5E2%2B-18x%2B17.9746425356094+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-18x%2B17.9746425356094+=+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=%28-18%29%5E2-4%2A2%2A17.9746425356094=180.202859715125 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-18%29%5E2-4%2A2%2A17.9746425356094=180.202859715125\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=180.202859715125 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--18%2B-sqrt%28+180.202859715125+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--18%2B-sqrt%28+180.202859715125+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-18%29%2Bsqrt%28+180.202859715125+%29%29%2F2%5C2+=+7.85599146783708 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-18%29%2Bsqrt%28+180.202859715125+%29%29%2F2%5C2+=+7.85599146783708\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-18%29-sqrt%28+180.202859715125+%29%29%2F2%5C2+=+1.14400853216292 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-18%29-sqrt%28+180.202859715125+%29%29%2F2%5C2+=+1.14400853216292\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B-18x%2B17.9746425356094 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-18x%2B17.9746425356094\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B-18x%2B17.9746425356094+=+%28x-7.85599146783708%29%2A%28x-1.14400853216292%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-18x%2B17.9746425356094+=+%28x-7.85599146783708%29%2A%28x-1.14400853216292%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 7.85599146783708, 1.14400853216292.\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+2%2Ax%5E2%2B-18%2Ax%2B17.9746425356094+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-18%2Ax%2B17.9746425356094+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "------------<BR>\n" );
document.write( "x & y are the 2 solutions, they're interchangeable.<BR>\n" );
document.write( "The sum of the 2 is 9.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );