document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=210894>Question 210894</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1592009425/algebrahomeworkh>COLLEGE ALGEBRA</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Pls. Help can't figure it out<BR>\n" );
document.write( "The law   of divine proportion, according to early Egyptians and Greek, states, “the most beautiful division of a line segment into two parts is such that the ratio of the longer part to the total length is equal to the ratio of the length of the shorter part to that of the longer part”<BR>\n" );
document.write( "a.)	If we consider the length of the line to be one unit and call t the length of the longer of the two parts, Find t.<BR>\n" );
document.write( "b.)	What is the proportionality constant for this ratio?\r<BR>\n" );
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document.write( "thank you very much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159349 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=159349\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The law of divine proportion, according to early Egyptians and Greek, states, “the most beautiful division of a line segment into two parts is such that the ratio of the longer part to the total length is equal to the ratio of the length of the shorter part to that of the longer part”<BR>\n" );
document.write( "a.) If we consider the length of the line to be one unit and call t the length of the longer of the two parts, Find t.<BR>\n" );
document.write( "Draw a line segment and mark a point that is not in the middle.<BR>\n" );
document.write( "Label the larger part as \"a\" and the smaller as \"1-a\"<BR>\n" );
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document.write( "Write the proportion as described above.<BR>\n" );
document.write( "a/1 = (1-a)/a<BR>\n" );
document.write( "Cross-multiply and solve for \"a\":<BR>\n" );
document.write( "a^2 = 1-a<BR>\n" );
document.write( "a^2+a-a = 0<BR>\n" );
document.write( "a = [-1+-sqrt(1-4*-1)]/2<BR>\n" );
document.write( "Positive solution:<BR>\n" );
document.write( "a = [-1+sqrt(5)]/2 = 0.618<BR>\n" );
document.write( "Then b = 1-0.618 = 0.3817<BR>\n" );
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document.write( "b.) What is the proportionality constant for this ratio?<BR>\n" );
document.write( " a/b = 1.618 which is called the Golden Proportion.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );