document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1049462>Question 1049462</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the acute angle between the lines:<BR>\n" );
document.write( "4x+3y-1=0 and 2x-5y-11=0 (1dp)\r<BR>\n" );
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document.write( "after finding the angle of inclination of each line, then what do i do? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #665003 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=665003\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x+%2B+3y+-+1+=+0+ ALIGN=MIDDLE  ALT=\"+4x+%2B+3y+-+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+-+5y+-+11+=+0+ ALIGN=MIDDLE  ALT=\"+2x+-+5y+-+11+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+=+-4x+%2B+1+ ALIGN=MIDDLE  ALT=\"+3y+=+-4x+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-%284%2F3%29%2Ax+%2B+1%2F3+ ALIGN=MIDDLE  ALT=\"+y+=+-%284%2F3%29%2Ax+%2B+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5y+=+2x+-+11+ ALIGN=MIDDLE  ALT=\"+5y+=+2x+-+11+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%282%2F5%29%2Ax+-+11%2F5+ ALIGN=MIDDLE  ALT=\"+y+=+%282%2F5%29%2Ax+-+11%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "For (2), think of a unit vector in the 1st<BR>\n" );
document.write( "quadrant with an angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > that has<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan%28a%29+=+2%2F5+ ALIGN=MIDDLE  ALT=\"+tan%28a%29+=+2%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+arctan%28+.4+%29+ ALIGN=MIDDLE  ALT=\"+a+=+arctan%28+.4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+21.8014+ ALIGN=MIDDLE  ALT=\"+a+=+21.8014+\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "Think of (1) as a unit vector in the 4th quadrant<BR>\n" );
document.write( "with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan%28b%29+=+-4%2F3+%29+ ALIGN=MIDDLE  ALT=\"+tan%28b%29+=+-4%2F3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+arctan%28+-4%2F3%29+ ALIGN=MIDDLE  ALT=\"+b+=+arctan%28+-4%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-53.1301+ ALIGN=MIDDLE  ALT=\"+b+=+-53.1301+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "The angle between the lines is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+-+b+=+21.8014+%2B+53.1301+ ALIGN=MIDDLE  ALT=\"+a+-+b+=+21.8014+%2B+53.1301+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+-+b+=+74.9315+ ALIGN=MIDDLE  ALT=\"+a+-+b+=+74.9315+\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees is<BR>\n" );
document.write( "the acute angle between the lines<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "Here's the plot of lines:<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+-10%2C+10%2C+-%284%2F3%29%2Ax+%2B+1%2F3%2C+%282%2F5%29%2Ax+%2B+11%2F5+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "My answer looks possible\r<BR>\n" );
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document.write( " </SPAN>\n" );
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