document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203363>Question 1203363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A truck with 48-in.-diameter wheels is traveling at 50 mi/h.\r<BR>\n" );
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document.write( "a.) Find the angular speed of the wheels in rad/min, *hint convert miles to inches & hours to minutes:         \r<BR>\n" );
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document.write( "b.) How many revolutions per minute do the wheels make? <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 #838859 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "1 hour = 60 min<BR>\n" );
document.write( "5280 feet = 1 mile<BR>\n" );
document.write( "12 inches = 1 ft<BR>\n" );
document.write( "1 revolution = 48pi  inches<BR>\n" );
document.write( "2pi radians = 1 revolution\r<BR>\n" );
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document.write( "The 48pi refers to the circumference of the circle of diameter 48 inches.<BR>\n" );
document.write( "C = pi*diameter\r<BR>\n" );
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document.write( "Each of those equivalences then form a fraction as shown in this long conversion string<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28matrix%281%2C2%2C50%2C%22mi%22%29%2Fmatrix%281%2C2%2C1%2C%22hr%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22hr%22%29%2Fmatrix%281%2C2%2C60%2C%22min%22%29%29%0D%0A%28matrix%281%2C2%2C5280%2C%22ft%22%29%2Fmatrix%281%2C2%2C1%2C%22mi%22%29%29%0D%0A%28matrix%281%2C2%2C12%2C%22in%22%29%2Fmatrix%281%2C2%2C1%2C%22ft%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22rev%22%29%2Fmatrix%281%2C2%2C48pi%2C%22in%22%29%29%0D%0A%28matrix%281%2C2%2C2pi%2C%22rad%22%29%2Fmatrix%281%2C2%2C1%2C%22rev%22%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The placement of each item is to form the next set of cancellations as I'll describe below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28matrix%281%2C2%2C50%2Ccross%28%22mi%22%29%29%2Fmatrix%281%2C2%2C1%2C%22hr%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22hr%22%29%2Fmatrix%281%2C2%2C60%2C%22min%22%29%29%0D%0A%28matrix%281%2C2%2C5280%2C%22ft%22%29%2Fmatrix%281%2C2%2C1%2Ccross%28%22mi%22%29%29%29%0D%0A%28matrix%281%2C2%2C12%2C%22in%22%29%2Fmatrix%281%2C2%2C1%2C%22ft%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22rev%22%29%2Fmatrix%281%2C2%2C48pi%2C%22in%22%29%29%0D%0A%28matrix%281%2C2%2C2pi%2C%22rad%22%29%2Fmatrix%281%2C2%2C1%2C%22rev%22%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \"miles\" units cancel\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28matrix%281%2C2%2C50%2C%22%22%29%2Fmatrix%281%2C2%2C1%2Ccross%28%22hr%22%29%29%29%0D%0A%28matrix%281%2C2%2C1%2Ccross%28%22hr%22%29%29%2Fmatrix%281%2C2%2C60%2C%22min%22%29%29%0D%0A%28matrix%281%2C2%2C5280%2C%22ft%22%29%2Fmatrix%281%2C2%2C1%2C%22%22%29%29%0D%0A%28matrix%281%2C2%2C12%2C%22in%22%29%2Fmatrix%281%2C2%2C1%2C%22ft%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22rev%22%29%2Fmatrix%281%2C2%2C48pi%2C%22in%22%29%29%0D%0A%28matrix%281%2C2%2C2pi%2C%22rad%22%29%2Fmatrix%281%2C2%2C1%2C%22rev%22%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \"hours\" units cancel\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28matrix%281%2C2%2C50%2C%22%22%29%2Fmatrix%281%2C2%2C1%2C%22%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22%22%29%2Fmatrix%281%2C2%2C60%2C%22min%22%29%29%0D%0A%28matrix%281%2C2%2C5280%2Ccross%28%22ft%22%29%29%2Fmatrix%281%2C2%2C1%2C%22%22%29%29%0D%0A%28matrix%281%2C2%2C12%2C%22in%22%29%2Fmatrix%281%2C2%2C1%2Ccross%28%22ft%22%29%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22rev%22%29%2Fmatrix%281%2C2%2C48pi%2C%22in%22%29%29%0D%0A%28matrix%281%2C2%2C2pi%2C%22rad%22%29%2Fmatrix%281%2C2%2C1%2C%22rev%22%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \"feet\" units cancel\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28matrix%281%2C2%2C50%2C%22%22%29%2Fmatrix%281%2C2%2C1%2C%22%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22%22%29%2Fmatrix%281%2C2%2C60%2C%22min%22%29%29%0D%0A%28matrix%281%2C2%2C5280%2C%22%22%29%2Fmatrix%281%2C2%2C1%2C%22%22%29%29%0D%0A%28matrix%281%2C2%2C12%2Ccross%28%22in%22%29%29%2Fmatrix%281%2C2%2C1%2C%22%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22rev%22%29%2Fmatrix%281%2C2%2C48pi%2Ccross%28%22in%22%29%29%29%0D%0A%28matrix%281%2C2%2C2pi%2C%22rad%22%29%2Fmatrix%281%2C2%2C1%2C%22rev%22%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \"inches\" units cancel\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28matrix%281%2C2%2C50%2C%22%22%29%2Fmatrix%281%2C2%2C1%2C%22%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22%22%29%2Fmatrix%281%2C2%2C60%2C%22min%22%29%29%0D%0A%28matrix%281%2C2%2C5280%2C%22%22%29%2Fmatrix%281%2C2%2C1%2C%22%22%29%29%0D%0A%28matrix%281%2C2%2C12%2C%22%22%29%2Fmatrix%281%2C2%2C1%2C%22%22%29%29%0D%0A%28matrix%281%2C2%2C1%2Ccross%28%22rev%22%29%29%2Fmatrix%281%2C2%2C48pi%2C%22%22%29%29%0D%0A%28matrix%281%2C2%2C2pi%2C%22rad%22%29%2Fmatrix%281%2C2%2C1%2Ccross%28%22rev%22%29%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \"revolution\" units cancel\r<BR>\n" );
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document.write( "There's a lot of cancellations going on. <BR>\n" );
document.write( "After the dust settles, we have \"radians\" up top and \"minutes\" in the bottom.<BR>\n" );
document.write( "Those are the only two units left.\r<BR>\n" );
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document.write( "Multiply the values along the top: 50*1*5280*12*2pi = 6,336,000pi\r<BR>\n" );
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document.write( "Multiply the values along the bottom: 1*60*1*1*48pi*1 = 2880pi\r<BR>\n" );
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document.write( "We end up with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286336000pi%29%2F%282880pi%29+=+2200 ALIGN=MIDDLE  ALT=\"%286336000pi%29%2F%282880pi%29+=+2200\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer to part (a) is <font color=red>2200 radians per minute</font>\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "We'll have this conversion string<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28matrix%281%2C2%2C50%2C%22mi%22%29%2Fmatrix%281%2C2%2C1%2C%22hr%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22hr%22%29%2Fmatrix%281%2C2%2C60%2C%22min%22%29%29%0D%0A%28matrix%281%2C2%2C5280%2C%22ft%22%29%2Fmatrix%281%2C2%2C1%2C%22mi%22%29%29%0D%0A%28matrix%281%2C2%2C12%2C%22in%22%29%2Fmatrix%281%2C2%2C1%2C%22ft%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22rev%22%29%2Fmatrix%281%2C2%2C48pi%2C%22in%22%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The key difference is we don't involve \"2pi radians = 1 rev\" at the very end. \r<BR>\n" );
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document.write( "So we haven't multiplied by 2pi. We can divide the previous result 2200 rad/min by 2pi to get the rpm (revolutions per min)\r<BR>\n" );
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document.write( "rpm = (rads per min)/(2pi)<BR>\n" );
document.write( "rpm = (2200)/(2pi)<BR>\n" );
document.write( "<font color=red>rpm = 350.14087480217 approximately</font>\r<BR>\n" );
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document.write( "I used the calculator's stored version of pi to get the most accuracy possible.<BR>\n" );
document.write( "If your teacher instructs you to use something like pi = 3.14, then be sure to do so. Round the final answer however your teacher instructs.<BR>\n" );
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