document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=44480>Question 44480</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The surface area A of a right circular cylinder is A=2Pi times the radius square + 2Pi times the radius times the height and \"h\" is the height. Find the radius of a right circular cylinder whose surface area is 96.3Pi square inches and whose height is 11.7 inches. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #29362 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=29362\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The surface area A of a right circular cylinder is A=2Pi times the radius square + 2Pi times the radius times the height and \"h\" is the height. Find the radius of a right circular cylinder whose surface area is 96.3Pi square inches and whose height is 11.7 inches.\r<BR>\n" );
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document.write( "A=2pir^2+2pirh\r<BR>\n" );
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document.write( "96.3pi=2pi(r^2+11.7r)<BR>\n" );
document.write( "48.15=r^2+11.7r<BR>\n" );
document.write( "100r^2+1170r-4815=0<BR>\n" );
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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=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ar%5E2%2Bbr%2Bc=0 ALIGN=MIDDLE  ALT=\"ar%5E2%2Bbr%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100r%5E2%2B1170r%2B-4815+=+0 ALIGN=MIDDLE  ALT=\"100r%5E2%2B1170r%2B-4815+=+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=r%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"r%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=%281170%29%5E2-4%2A100%2A-4815=3294900 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%281170%29%5E2-4%2A100%2A-4815=3294900\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3294900 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+=+%28-1170%2B-sqrt%28+3294900+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-1170%2B-sqrt%28+3294900+%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=r%5B1%5D+=+%28-%281170%29%2Bsqrt%28+3294900+%29%29%2F2%5C100+=+3.22592970444351 ALIGN=MIDDLE  ALT=\"r%5B1%5D+=+%28-%281170%29%2Bsqrt%28+3294900+%29%29%2F2%5C100+=+3.22592970444351\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D+=+%28-%281170%29-sqrt%28+3294900+%29%29%2F2%5C100+=+-14.9259297044435 ALIGN=MIDDLE  ALT=\"r%5B2%5D+=+%28-%281170%29-sqrt%28+3294900+%29%29%2F2%5C100+=+-14.9259297044435\"   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=100r%5E2%2B1170r%2B-4815 ALIGN=MIDDLE  ALT=\"100r%5E2%2B1170r%2B-4815\"   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=100r%5E2%2B1170r%2B-4815+=+100%28r-3.22592970444351%29%2A%28r--14.9259297044435%29 ALIGN=MIDDLE  ALT=\"100r%5E2%2B1170r%2B-4815+=+100%28r-3.22592970444351%29%2A%28r--14.9259297044435%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3.22592970444351, -14.9259297044435.\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+100%2Ax%5E2%2B1170%2Ax%2B-4815+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+100%2Ax%5E2%2B1170%2Ax%2B-4815+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Hope this helps<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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