document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=314082>Question 314082</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the radius if: <BR>\n" );
document.write( "degree of measurement of arc=30 <BR>\n" );
document.write( "length=1/3xy(pi) <BR>\n" );
document.write( "My answer was 8xy.\r<BR>\n" );
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document.write( "degree of measurement of arc=40<BR>\n" );
document.write( "length=8/9(t)(pi)<BR>\n" );
document.write( "My answer was 9t.\r<BR>\n" );
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document.write( "degree of measurement of arc=18<BR>\n" );
document.write( "length=6(y)pi<BR>\n" );
document.write( "My answer was 45y.\r<BR>\n" );
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document.write( "These are the questions I missed, along with my answers. I would be grateful if someone could explain what I did wrong and work out the problem, so that I may understand why I missed these questions. Cheers!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #224530 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=224530\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The circumference of a circle is equal to 2*pi*r\r<BR>\n" );
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document.write( "The measurement of the arc of a circle is equal to the degree of the arc divided by 360 times the circumference of the circle.\r<BR>\n" );
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document.write( "Since the circumference of the circle is equal to 2 * pi * r, this means that the measurement of the are of the circle is equal to the degree of the arc divided by 360 times 2 * pi * r.\r<BR>\n" );
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document.write( "If you let L = the length of the arc and D equal the degree of the arc, then the equations you should be working with are:\r<BR>\n" );
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document.write( "L = D/360 * C which is equivalent to L = D/360 * 2 * pi * r\r<BR>\n" );
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document.write( "Then all you have to do is solve for r.\r<BR>\n" );
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document.write( "In your first problem, you are given:\r<BR>\n" );
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document.write( "What is the radius if: <BR>\n" );
document.write( "degree of measurement of arc=30 <BR>\n" );
document.write( "length=1/3xy(pi) \r<BR>\n" );
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document.write( "The equation you have to work with is L = D/360 * 2 * pi * r\r<BR>\n" );
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document.write( "Substituting in this equation, you get:\r<BR>\n" );
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document.write( "1/3 * x * y * pi = 30/360 * 2 * pi * r\r<BR>\n" );
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document.write( "Simplify this equation to get:\r<BR>\n" );
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document.write( "1/3 * x * y * pi = 1/6 * pi * r\r<BR>\n" );
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document.write( "Divide both sides of this equation by pi to get:\r<BR>\n" );
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document.write( "1/3 * x * y = 1/6 * r\r<BR>\n" );
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document.write( "Multiply both sides of this equation by 6 to get:\r<BR>\n" );
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document.write( "2 * x * y = r\r<BR>\n" );
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document.write( "That's your answer.\r<BR>\n" );
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document.write( "To confirm, substitute for r in the equation for the circumference of the circle to get:\r<BR>\n" );
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document.write( "C = 2 * pi * r = 2 * pi * 2 * x * y = 4 * pi * x * y\r<BR>\n" );
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document.write( "Since L = D/360 * C, then substitute for C to get:\r<BR>\n" );
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document.write( "L = D/360 * 4 * pi * x * y\r<BR>\n" );
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document.write( "Substitute for D to get:\r<BR>\n" );
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document.write( "L = 30/360 * 4 * pi * x * y\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "L = 4/12 * pi * x * y which simplifies further to L = 1/3 * pi * x * y\r<BR>\n" );
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document.write( "Since this is the length of the arc you started with, then you are good.\r<BR>\n" );
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document.write( "In your second problem, you are given:\r<BR>\n" );
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document.write( "degree of measurement of arc=40<BR>\n" );
document.write( "length=8/9(t)(pi)\r<BR>\n" );
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document.write( "The equations you need to work with are L = D/360 * C and L = D/360 * 2 * pi * r.\r<BR>\n" );
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document.write( "To find the radius, use L = D/360 * 2 * pi * r\r<BR>\n" );
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document.write( "Substitute for L to get:\r<BR>\n" );
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document.write( "8/9 * t * pi = 40/360 * 2 * pi * r\r<BR>\n" );
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document.write( "Simplify to getr:\r<BR>\n" );
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document.write( "8/9 * t * pi = 2/9 * pi * r\r<BR>\n" );
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document.write( "Divide both sides of this equation by pi to get:\r<BR>\n" );
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document.write( "8/9 * t = 2/9 * r\r<BR>\n" );
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document.write( "Multiply both sides of this equation by 9/2 to get:\r<BR>\n" );
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document.write( "4*t = r\r<BR>\n" );
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document.write( "That should be your answer.\r<BR>\n" );
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document.write( "If r = 4*t then C = 2 * pi * r = 2 * pi * 4 * t = 8 * pi * t\r<BR>\n" );
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document.write( "Since L = D/360 * C, substitute 40 for D and 8 * pi * t for C to get:\r<BR>\n" );
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document.write( "L = 40/360 * 8 * t * pi which simplifies to 8/9 * t * pi.\r<BR>\n" );
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document.write( "Since this is the length of the arc you started with, then you are good.\r<BR>\n" );
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document.write( "In your third problem, you are given:\r<BR>\n" );
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document.write( "degree of measurement of arc=18<BR>\n" );
document.write( "length=6(y)pi\r<BR>\n" );
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document.write( "Use the formula L = D/360 * 2 * pi * r to get:\r<BR>\n" );
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document.write( "6 * y * pi = 18/360 * 2 * pi * r\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "6 * y * pi = 1/20 * 2 * pi * r which simplifies further to get:\r<BR>\n" );
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document.write( "6 * y * pi = 1/10 * pi * r\r<BR>\n" );
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document.write( "Divide both sides of this equation by pi to get:\r<BR>\n" );
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document.write( "6 * y = 1/10 * r\r<BR>\n" );
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document.write( "Multiply both sides of this equation by 10 to get:\r<BR>\n" );
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document.write( "60 * y = r\r<BR>\n" );
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document.write( "That's your answer.\r<BR>\n" );
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document.write( "Since C = 2 * pi * r, then you get:\r<BR>\n" );
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document.write( "C = 2 * pi * 60 * y which simplfies to C = 120 * pi * y\r<BR>\n" );
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document.write( "Since L = D/360 * C, then you get:\r<BR>\n" );
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document.write( "L = 18/360 * 120 * pi * y which simplifies to L = 120/20 * pi * y which simplifies further to:\r<BR>\n" );
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document.write( "L = 6 * pi * y.\r<BR>\n" );
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document.write( "Since this is the length of the arc you started with, they you are good.\r<BR>\n" );
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document.write( "The key to solving this problem is to use the equations:\r<BR>\n" );
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document.write( "C = 2 * pi * r\r<BR>\n" );
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document.write( "L = D/360 * C\r<BR>\n" );
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document.write( "C is equal to the circumference of the circle.<BR>\n" );
document.write( "L is equal to the length of the arc<BR>\n" );
document.write( "r is equal to the radius of the circle.<BR>\n" );
document.write( "D is equal to the degree of the arc.\r<BR>\n" );
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