document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=982924>Question 982924</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i have a 20.5\" cylinder (core) and I need to put 1800' of material on the outside of it.  the material is .022 thick.  what would the diameter be of the material after it has all of the material on it?\r<BR>\n" );
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document.write( "better yet, how can I do this calculation with different size cylinders, different gauges and different lengths?\r<BR>\n" );
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document.write( "thank you in advance for your efforts.\r<BR>\n" );
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document.write( "-michael </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #603746 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=603746\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i have a 20.5\" cylinder (core) and I need to put 1800' of material on the outside of it.  the material is .022 thick.  what would the diameter be of the material after it has all of the material on it?<BR>\n" );
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document.write( "If the 20.5\" is the diameter:<BR>\n" );
document.write( "The 1st turn adds 0.044 to the diameter.<BR>\n" );
document.write( "The length of the 1st turn = pi*d = 20.5*pi =~ 64.4 inches<BR>\n" );
document.write( "Each turn adds 0.044 to the ID --> adds 0.13823 to the circumference.<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "For n turns,<BR>\n" );
document.write( "Length = 20.5*pi + pi*(20.5 + n*0.044)*n<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "1800' = 21600 inches<BR>\n" );
document.write( "21600 = 20.5pi + 20.5*n*pi + 0.044n^2<BR>\n" );
document.write( "0.044n^2 + 20.5*pi*n + (20.5pi - 21600) = 0<BR>\n" );
document.write( "------<BR>\n" );
document.write( "--> 0.044n^2 + 64.4n - 21535.6 = 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=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=0.044x%5E2%2B64.4x%2B-21535.6+=+0 ALIGN=MIDDLE  ALT=\"0.044x%5E2%2B64.4x%2B-21535.6+=+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=%2864.4%29%5E2-4%2A0.044%2A-21535.6=7937.6256 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2864.4%29%5E2-4%2A0.044%2A-21535.6=7937.6256\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=7937.6256 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+=+%28-64.4%2B-sqrt%28+7937.6256+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-64.4%2B-sqrt%28+7937.6256+%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-%2864.4%29%2Bsqrt%28+7937.6256+%29%29%2F2%5C0.044+=+280.606287357235 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2864.4%29%2Bsqrt%28+7937.6256+%29%29%2F2%5C0.044+=+280.606287357235\"   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-%2864.4%29-sqrt%28+7937.6256+%29%29%2F2%5C0.044+=+-1744.2426509936 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2864.4%29-sqrt%28+7937.6256+%29%29%2F2%5C0.044+=+-1744.2426509936\"   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=0.044x%5E2%2B64.4x%2B-21535.6 ALIGN=MIDDLE  ALT=\"0.044x%5E2%2B64.4x%2B-21535.6\"   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=0.044x%5E2%2B64.4x%2B-21535.6+=+%28x-280.606287357235%29%2A%28x--1744.2426509936%29 ALIGN=MIDDLE  ALT=\"0.044x%5E2%2B64.4x%2B-21535.6+=+%28x-280.606287357235%29%2A%28x--1744.2426509936%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 280.606287357235, -1744.2426509936.\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+0.044%2Ax%5E2%2B64.4%2Ax%2B-21535.6+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.044%2Ax%5E2%2B64.4%2Ax%2B-21535.6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Ignore the negative solution<BR>\n" );
document.write( "n =~ 281 turns<BR>\n" );
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document.write( "dia with 281 turns = 20.5 + 281*0.044<BR>\n" );
document.write( "dia = 32.82 inches<BR>\n" );
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document.write( "I'll do the general case later.\r<BR>\n" );
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