document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1014571>Question 1014571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A child has a toy chest with wheels. When the wheels of the toy chest turn through an angle of 2 radians, the toy chest moves forward by 3.75 inches.\r<BR>\n" );
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document.write( "What is the length, in inches, of the radius of each wheel? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #631020 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=631020\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the length of an arc is equal to (the central angle of the arc divided by the central angle of the whole circle * the circumference of the circle.\r<BR>\n" );
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document.write( "if you let l = the length of the arc and a = the central angle of the arc and w = the central angle of the whole circle and c = the circumference of the circle, then the formula becomes:\r<BR>\n" );
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document.write( "l = (a/w) * c\r<BR>\n" );
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document.write( "since the circumference of a circle is equal to 2 * pi * r, this formula becomes:\r<BR>\n" );
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document.write( "l = (a/w) * 2 * pi * r\r<BR>\n" );
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document.write( "r is the radius of the circle.\r<BR>\n" );
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document.write( "since the central angle of the whole circle is equal to 2 * pi radians, this formula becomes:\r<BR>\n" );
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document.write( "l = (a / (2 * pi)) * (2 * pi * r)\r<BR>\n" );
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document.write( "since a = 2 radians and l = 3.75 inches, this formula becomes:\r<BR>\n" );
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document.write( "3.75 = (2 / (2 * pi)) * (2 * pi * r)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "3.75 = (1/pi) * (2 * pi * r)\r<BR>\n" );
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document.write( "this formula can also be written as:\r<BR>\n" );
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document.write( "3.75 = (1 * 2 * pi * r) / pi\r<BR>\n" );
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document.write( "the pi in the numerator and denominator cancel out and you are left with:\r<BR>\n" );
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document.write( "3.75 = (1 * 2 * r) which becomes 3.75 = 2 * r\r<BR>\n" );
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document.write( "solve for r to get r = 3.75 / 2 = 1.875 inches.\r<BR>\n" );
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document.write( "the radius of the wheels of the toy chest are 1.875 inches in length.\r<BR>\n" );
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document.write( "with a radius of 1.875 inches, the wheels, turning through an angle of 2 radians, will move 3.75 inches on the ground.\r<BR>\n" );
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document.write( "the formula for the length of the arc is, once again, ...\r<BR>\n" );
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document.write( "l = (a/w) * (2 * pi * r)\r<BR>\n" );
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document.write( "r is the radius which is equal to 1.875 inches.<BR>\n" );
document.write( "w is central angle of the whole circle which is equal to 2 * pi radians.<BR>\n" );
document.write( "a is equal to the central angle of the arc which is equal to 2 radians.\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "l = (2 / (2 * pi)) * (2 * pi * 1.875) \r<BR>\n" );
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document.write( "this can also be written as:\r<BR>\n" );
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document.write( "l = (2 * 2 * pi * 1.875) / (2 * pi)\r<BR>\n" );
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document.write( "the (2 * pi) in the numerator and denominator cancel out and you are left with:\r<BR>\n" );
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document.write( "l = 2 * 1.875) which results in l = 3.75 inches.\r<BR>\n" );
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document.write( "your solution, as far as i can tell, is:\r<BR>\n" );
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document.write( "the radius of the wheels is 1.875 inches in length.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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