document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167553>Question 1167553</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Beginning at the origin, a spiral is constructed from 3 semi circles with centres at (1,0),(0,0),(2,0). The area of the shaded region, in u^2 is:\r<BR>\n" );
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document.write( "A) 7 π-2 √3/6<BR>\n" );
document.write( "B) 8 π-√3/3<BR>\n" );
document.write( "C)8 π-6 √3/3<BR>\n" );
document.write( "D) 3 π -2 √3<BR>\n" );
document.write( "E) 11 π -6√3/3\r<BR>\n" );
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document.write( "https://imageshack.com/i/pmBbsOMDj </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792184 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=792184\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Call the origin O.  Let A(2,0) be the center of the third semicircle, and let B(0,b) be the y-intercept of that third semicircle.<br><BR>\n" );
document.write( "Triangle AOB is a 30-60-90 right triangle, because OA=2 and AB=4.  That makes OB <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "The shaded region is (a) one-half the area of the second semicircle with radius 2, plus (b) one-third the area of the third semicircle (because angle BAO is 60 degrees), minus (c) the area of triangle AOB.<br><BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28pi%282%5E2%29%2F2%29+=+pi ALIGN=MIDDLE  ALT=\"%281%2F2%29%28pi%282%5E2%29%2F2%29+=+pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%28pi%284%5E2%29%2F2%29+=+%288%2F3%29pi ALIGN=MIDDLE  ALT=\"%281%2F3%29%28pi%284%5E2%29%2F2%29+=+%288%2F3%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%282sqrt%283%29%29%282%29+=+2sqrt%283%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%282sqrt%283%29%29%282%29+=+2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2B%288%2F3%29pi-2sqrt%283%29+=+%2811%2F3%29pi-2sqrt%283%29 ALIGN=MIDDLE  ALT=\"pi%2B%288%2F3%29pi-2sqrt%283%29+=+%2811%2F3%29pi-2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Note answer choices A, B, C, and E are all shown incorrectly, because required parentheses are missing.<br><BR>\n" );
document.write( "Answer choice E is supposed to be the right answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811pi-6sqrt%283%29%29%2F3 ALIGN=MIDDLE  ALT=\"%2811pi-6sqrt%283%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "But answer choice E as shown, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11pi-6sqrt%283%29%2F3 ALIGN=MIDDLE  ALT=\"11pi-6sqrt%283%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is incorrect.<br><BR>\n" );
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