document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76625>Question 76625</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diameter of the Milky Way disc is approximately 9 x 10^20 meters.  How long does it take light, traveling at 10^16 m/year to travel across the diameter of the Milky Way?\r<BR>\n" );
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document.write( "900,000 years <BR>\n" );
document.write( "90,000 years<BR>\n" );
document.write( "9,000 years<BR>\n" );
document.write( "900 years </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54966 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=54966\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can use the standard equation for distance (D) when a rate (or speed) R is involved and<BR>\n" );
document.write( "so is the time (T) that the rate will be in effect.  The equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+R%2AT ALIGN=MIDDLE  ALT=\"D+=+R%2AT\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In this problem, the distance (D) and the rate (R) of travel are given, and you are asked<BR>\n" );
document.write( "to solve for the time involved.<BR>\n" );
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document.write( "To solve for T, divide both sides of the equation by R and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+D%2FR ALIGN=MIDDLE  ALT=\"T+=+D%2FR\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You are given that D, the distance, is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A10%5E20 ALIGN=MIDDLE  ALT=\"9%2A10%5E20\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the rate of light is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A10%5E16 ALIGN=MIDDLE  ALT=\"1%2A10%5E16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Note that I added the multiplier 1 to the exponential value of 10 for the rate that light <BR>\n" );
document.write( "is traveling. And always be sure to check that the units involved are compatible.  <BR>\n" );
document.write( "In this case the distance is in meters, the rate is in meters per year, and the answer is to<BR>\n" );
document.write( "be in years.  We have no inconsistencies in units so we don't have to do any conversions.<BR>\n" );
document.write( "All distances are in meters and all times are in years.<BR>\n" );
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document.write( "Take the equation for time and substitute the values of D and R and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+D%2FR+=+%289%2A10%5E20%29%2F%281%2A10%5E16%29 ALIGN=MIDDLE  ALT=\"T+=+D%2FR+=+%289%2A10%5E20%29%2F%281%2A10%5E16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We sort of split this into two problems .... divide the 9 by the 1 and also divide the<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E20 ALIGN=MIDDLE  ALT=\"10%5E20\"   DISABLED_style= \"max-width:90%; height:auto;\" > by the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E16 ALIGN=MIDDLE  ALT=\"10%5E16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Recall that when you divide a base with an exponent by<BR>\n" );
document.write( "the same base with an exponent, the answer is the same base with the difference between<BR>\n" );
document.write( "the exponents. Maybe the work will give you the idea:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+%289%2A10%5E20%29%2F%281%2A10%5E16%29+=+%289%2F1%29%2A%2810%5E20%2F10%5E16%29=+9%2A10%5E%2820-16%29+=+9%2A10%5E4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E4 ALIGN=MIDDLE  ALT=\"10%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > part of the answer tells you that it is 10,000.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E1+=+10 ALIGN=MIDDLE  ALT=\"10%5E1+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E2+=+100 ALIGN=MIDDLE  ALT=\"10%5E2+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E3+=+1000 ALIGN=MIDDLE  ALT=\"10%5E3+=+1000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E4+=+10000 ALIGN=MIDDLE  ALT=\"10%5E4+=+10000\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So we can say that the answer is 9 times 10,000<BR>\n" );
document.write( "which is 90,000 and the units is years. So the correct answer is the second one down in<BR>\n" );
document.write( "your list of answers ... 90,000 years.<BR>\n" );
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document.write( "Hope the problem has taught you a couple of things ... first the equation for distance when<BR>\n" );
document.write( "rate and time are involved. And second, how to divide numbers that are in the form of<BR>\n" );
document.write( "scientific notation ... an integer times ten raised to a power divided by an integer times<BR>\n" );
document.write( "ten raised to a power ... divide the integers and raise ten to the difference of the two <BR>\n" );
document.write( "exponents ... and the difference is found by subtracting the exponent in the denominator from<BR>\n" );
document.write( "the exponent in the numerator. </SPAN>\n" );
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