document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113067>Question 1113067</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The coin is in shape of a circle of radius 3cm with a square of sides x cm removed from its centre. The area of each face of the coin in 7&#960;cm^2.<BR>\n" );
document.write( "i) form an equation in x and show that it reduces to 2&#960;-x^2=0.<BR>\n" );
document.write( "ii) solve the equation  2&#960;-x^2=0.<BR>\n" );
document.write( "iii) find the perimeter of the square. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728125 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=728125\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this was hard to visualize, but i finally got it right, i think.\r<BR>\n" );
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document.write( "algebraically is's not that difficult.\r<BR>\n" );
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document.write( "what you have is a circle with a radius of 3 centimeters.\r<BR>\n" );
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document.write( "since the area of a circle is equal to pi * r^2, then the area of this circle is 9 * pi.\r<BR>\n" );
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document.write( "you are told that the area of the circle minus the area of the square is equal to 7 * pi.\r<BR>\n" );
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document.write( "you are told that the length of a side of the square is x.\r<BR>\n" );
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document.write( "that means the area of the square is x^2.\r<BR>\n" );
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document.write( "therefore, the area of the circle minus the area of the square must be equal to 9 * pi - x^2.\r<BR>\n" );
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document.write( "if the net area is 7 * pi, then you get:\r<BR>\n" );
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document.write( "9 * pi - x^2 = 7 * pi\r<BR>\n" );
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document.write( "subtract 7 * pi from both sides of this equation and you get:\r<BR>\n" );
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document.write( "9 * pi - 7 * pi - x^2 = 0\r<BR>\n" );
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document.write( "this reduces to 2 * pi - x^2 = 0\r<BR>\n" );
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document.write( "this is the formula you are looking for.\r<BR>\n" );
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document.write( "if you solve this formula for x^2, you will x^2 = 2 * pi.\r<BR>\n" );
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document.write( "the area of the square inside the circle is 2 * pi.\r<BR>\n" );
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document.write( "that makes each side of the square equal to sqrt(2 * pi).\r<BR>\n" );
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document.write( "the perimeter of the square is 4 * the length of each side of the square.\r<BR>\n" );
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document.write( "that makes the perimeter of the square equal to 4 * sqrt(2 * pi).\r<BR>\n" );
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document.write( "you can play games with this answer, but it will be the same.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "4 = sqrt(16), therefore the answer becomes sqrt(16) * sqrt(2 * pi) which then becomes sqrt(16 * 2 * pi) which becomes sqrt(32 * pi).\r<BR>\n" );
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document.write( "if i did this right, 4 * sqrt(2 *pi) should be equal to sqrt(32 * pi).\r<BR>\n" );
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document.write( "i used my calculator to confirm that they are, indeed, equal to each other.\r<BR>\n" );
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document.write( "so, your answer can be that the perimeter of the square is either:\r<BR>\n" );
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document.write( "4 * sqrt(2 * pi) or:<BR>\n" );
document.write( "sqrt(32 * pi) or, if you need a decimal answer:<BR>\n" );
document.write( "10.0265131 centimeters.\r<BR>\n" );
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document.write( "my problem was in visualizing the answer.<BR>\n" );
document.write( "i finally got that right.<BR>\n" );
document.write( "a graphical display of the circular coin and the square in the center of the coin would look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/032401.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "you can see from the graph, that the length of each side of the square is 2 * 1.25331413732 = 2.506628275.\r<BR>\n" );
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document.write( "square this to get 2.506628275^2 = 6.283185307.\r<BR>\n" );
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document.write( "multiply this by pi / pi and it becomes 6.283185307 * (pi / pi) which is the same as (6.283185307 / pi) * pi which can be reduced to 2 * pi.\r<BR>\n" );
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document.write( "in other words, 6.283185307 is equivalent to 2 * pi, which is the area of the square that we had calculated to be earlier.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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