document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172385>Question 172385</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780321331793/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> In each of the following, determine the number of sides of a regular polygon with the stated property.  If such a regular polygon does not exist, explain why.\r<BR>\n" );
document.write( "\n" );
document.write( "b.  Each exterior angle measure 25 degrees\r<BR>\n" );
document.write( "\n" );
document.write( "d.  The total number of diagonals is 4860 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127338 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=127338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> b)since the sum of the exterior angles must equal 360...we have 360/25=14.4....therefore there is no such polygon since this is not a positive integer<BR>\n" );
document.write( ":<BR>\n" );
document.write( "d)the formula for diagonals is as follows:d= n/2 (n-3)<BR>\n" );
document.write( "where d is the number of diagonals and n is the number of sides in the polygon<BR>\n" );
document.write( ": the answer needs to be a positive integer<BR>\n" );
document.write( "4860=n/2(n-3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4860=%28n%5E2-3n%29%2F2 ALIGN=MIDDLE  ALT=\"4860=%28n%5E2-3n%29%2F2\"   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=9720=n%5E2-3n ALIGN=MIDDLE  ALT=\"9720=n%5E2-3n\"   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=n%5E2-3n-9720=0 ALIGN=MIDDLE  ALT=\"n%5E2-3n-9720=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this does not produce a positive integer solution therefore this polygon does not exist<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=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=an%5E2%2Bbn%2Bc=0 ALIGN=MIDDLE  ALT=\"an%5E2%2Bbn%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1n%5E2%2B-3n%2B-9720+=+0 ALIGN=MIDDLE  ALT=\"1n%5E2%2B-3n%2B-9720+=+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=n%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"n%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=%28-3%29%5E2-4%2A1%2A-9720=38889 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-3%29%5E2-4%2A1%2A-9720=38889\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=38889 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--3%2B-sqrt%28+38889+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--3%2B-sqrt%28+38889+%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=n%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+38889+%29%29%2F2%5C1+=+100.101470577269 ALIGN=MIDDLE  ALT=\"n%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+38889+%29%29%2F2%5C1+=+100.101470577269\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B2%5D+=+%28-%28-3%29-sqrt%28+38889+%29%29%2F2%5C1+=+-97.1014705772688 ALIGN=MIDDLE  ALT=\"n%5B2%5D+=+%28-%28-3%29-sqrt%28+38889+%29%29%2F2%5C1+=+-97.1014705772688\"   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=1n%5E2%2B-3n%2B-9720 ALIGN=MIDDLE  ALT=\"1n%5E2%2B-3n%2B-9720\"   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=1n%5E2%2B-3n%2B-9720+=+1%28n-100.101470577269%29%2A%28n--97.1014705772688%29 ALIGN=MIDDLE  ALT=\"1n%5E2%2B-3n%2B-9720+=+1%28n-100.101470577269%29%2A%28n--97.1014705772688%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 100.101470577269, -97.1014705772688.\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+1%2Ax%5E2%2B-3%2Ax%2B-9720+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B-9720+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );