document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119281>Question 119281</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if y varies directly as the square of x, and y = 32, when x = 2, find y when x = 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87361 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=87361\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since y varies directly as the square of x we can write the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+k%2Ax%5E2 ALIGN=MIDDLE  ALT=\"y+=+k%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "where k is just a constant that makes the equation true. Notice in this equation that if x<BR>\n" );
document.write( "gets bigger, then y must also get bigger. This is what is meant by \"y varies directly as\"<BR>\n" );
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document.write( "We can find the value of k because we are told that when x = 2, then y = 32. Substitute these<BR>\n" );
document.write( "two values into the above equation and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32+=+k%2A%282%5E2%29 ALIGN=MIDDLE  ALT=\"32+=+k%2A%282%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Square the 2 on the right side and the equation is then:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32+=+k%2A4 ALIGN=MIDDLE  ALT=\"32+=+k%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for k by dividing both sides by 4 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+k ALIGN=MIDDLE  ALT=\"8+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we can return to the original equation and substitute 8 for k to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+8%2Ax%5E2 ALIGN=MIDDLE  ALT=\"y+=+8%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This the complete equation that relates x to y for this problem.<BR>\n" );
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document.write( "To find the value of y when x is 5 all we need to do is to substitute 5 for x in the equation<BR>\n" );
document.write( "to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+8%2A%285%5E2%29 ALIGN=MIDDLE  ALT=\"y+=+8%2A%285%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Squaring the 5 on the right side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+8%2A25+ ALIGN=MIDDLE  ALT=\"y+=+8%2A25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the right side multiplies out to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+200 ALIGN=MIDDLE  ALT=\"y+=+200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the answer to your problem is that when x = 5, y equals 200.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
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