document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=470860>Question 470860</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A curve has the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28ax%2B3%29ln%28x%29 ALIGN=MIDDLE  ALT=\"y+=+%28ax%2B3%29ln%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where x is greater than zero and a is a constant. The normal to the curve at the point where the curve crosses the x-axis is parallel to the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+%2B+x+=+2 ALIGN=MIDDLE  ALT=\"5y+%2B+x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Find the value of a.\r<BR>\n" );
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document.write( "*Please answer as soon as possible bro : =) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #322958 by </B><A HREF=/tutors/aboutme.mpl?userid=Tatiana_Stebko><B>Tatiana_Stebko(1539)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Tatiana_Stebko><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=Tatiana_Stebko><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=322958\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the equation of the curve is y = f(x) then the slope of the normal line is m=-1/(f'(x0))<BR>\n" );
document.write( "f'(x)=((ax+3)lnx)'=(ax+3)'lnx+(ax+3)(lnx)'=a*lnx+(ax+3)/x<BR>\n" );
document.write( " the point where the curve crosses the x-axis is (x0,0)<BR>\n" );
document.write( "find xo<BR>\n" );
document.write( "Put into the curve equation y=0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ax%2B3%29lnx=0 ALIGN=MIDDLE  ALT=\"%28ax%2B3%29lnx=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then m=f'(x0)=f'(1)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Aln1%2B%28a%2B3%29%2F1=a%2B3 ALIGN=MIDDLE  ALT=\"a%2Aln1%2B%28a%2B3%29%2F1=a%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the slope of the normal line to the curve at the point where the curve crosses the x-axis is -1/(f'(1))=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F%28a%2B3%29 ALIGN=MIDDLE  ALT=\"-1%2F%28a%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If normal is parallel to the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+%2B+x+=+2 ALIGN=MIDDLE  ALT=\"5y+%2B+x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then their slopes are equal<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+%2B+x+=+2 ALIGN=MIDDLE  ALT=\"5y+%2B+x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y=-x%2B2 ALIGN=MIDDLE  ALT=\"5y=-x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F5%29x%2B2%2F5 ALIGN=MIDDLE  ALT=\"y=%28-1%2F5%29x%2B2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> the slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F5 ALIGN=MIDDLE  ALT=\"m=-1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F%28a%2B3%29=-1%2F5 ALIGN=MIDDLE  ALT=\"-1%2F%28a%2B3%29=-1%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%2B3=5 ALIGN=MIDDLE  ALT=\"a%2B3=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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