document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011305>Question 1011305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> y is directly proportional to x^2. When y = 5, x = 10.\r<BR>\n" );
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document.write( "Write down the equation of proportionality with full working </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #626924 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=626924\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the direct proportion formula is y = kx.\r<BR>\n" );
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document.write( "when x = x^2, the formula becomes y = kx^2.\r<BR>\n" );
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document.write( "when y = 5, x = 10 is the statement.\r<BR>\n" );
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document.write( "you can use this to solve for k.\r<BR>\n" );
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document.write( "you get y = kx^2 becomes:<BR>\n" );
document.write( "5 = k*10^2 which becomes:<BR>\n" );
document.write( "5 = k*100\r<BR>\n" );
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document.write( "solve for k to get k = 5/100 = 1/20 = .05\r<BR>\n" );
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document.write( "now that you know the value of k, you can use that value to solve all other problems involving this proportion.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "when y = 50, what is the value of x^2?\r<BR>\n" );
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document.write( "you know the value of k is equal to .05.\r<BR>\n" );
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document.write( "the formula of y = kx^2 becomes y = .05*x^2\r<BR>\n" );
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document.write( "y = 50 so the formula becomes 50 = .05*x^2\r<BR>\n" );
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document.write( "divide both sides of this equation by .05 to get 50/.05 = x^2\r<BR>\n" );
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document.write( "simplify to get 1000 = x^2\r<BR>\n" );
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document.write( "solve for x to get x = sqrt(1000)\r<BR>\n" );
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document.write( "the equation becomes 50 = .05 * (sqrt(1000))^2 which becomes 50 = .05 * 1000 which becomes 50 = 50 which is true.\r<BR>\n" );
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document.write( "here'e another example:\r<BR>\n" );
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document.write( "what's the value of y when x = 25?\r<BR>\n" );
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document.write( "the formula is y = kx^2.\r<BR>\n" );
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document.write( "k is equal to .05.\r<BR>\n" );
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document.write( "when x = 25, the formula becomes y = .05 * 25^2.\r<BR>\n" );
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document.write( "simplify to get y = .05 * 625\r<BR>\n" );
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document.write( "simplify further to get y = 31.25\r<BR>\n" );
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document.write( "the equation becomes 31.25 = .05 * 25^2 which becomes 31.25 = .05*625 which becomes 31.25 = 31.25 which is true.\r<BR>\n" );
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document.write( "since these are direct proportions, a/b^2 should be equal to c/d^2 which should be equal to e/f^2\r<BR>\n" );
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document.write( "a = 5<BR>\n" );
document.write( "b^2 = 100\r<BR>\n" );
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document.write( "c = 50<BR>\n" );
document.write( "d^2 = 1000\r<BR>\n" );
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document.write( "e = 31.25<BR>\n" );
document.write( "f^2 = 625\r<BR>\n" );
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document.write( "a/b^2 should be equal to c/d^2<BR>\n" );
document.write( "replace a/b^2 and c/d^2 with their respective values and you get 5/100 should be equal to 50/1000<BR>\n" );
document.write( "cross multiply to get 5*1000 = 100*50<BR>\n" );
document.write( "simplify to get 5000 = 5000<BR>\n" );
document.write( "this is true.\r<BR>\n" );
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document.write( "c/d^2 should be equal to e/f^2<BR>\n" );
document.write( "replace c/d^2 and e/f^2 with their respective values andyou get 50/1000 should be equal to 31.25/625<BR>\n" );
document.write( "cross multiply to get 50*625 = 1000*31.25<BR>\n" );
document.write( "simplify to get 31250 = 31250<BR>\n" );
document.write( "this is true.\r<BR>\n" );
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document.write( "based on the law of equations that states if x = y and y = z, then x = z, you also get a/b^2 = e/f^2, which will also be true.\r<BR>\n" );
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document.write( "that's how the value of k is used to solve direct proportion type problems.\r<BR>\n" );
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document.write( "y = kx.\r<BR>\n" );
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document.write( "when x = x^2, the formula becomes y = kx^2.\r<BR>\n" );
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document.write( "when you know the value of y and and x, you can solve for the value of x^2 and then solve for the value of k.\r<BR>\n" );
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document.write( "once you know the value of k, you can solve other problems using the same formula of y = kx^2.\r<BR>\n" );
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document.write( "if you know the value of y and k, you can solve for the value of x^2 and then solve for the value of x.\r<BR>\n" );
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document.write( "if you know the value of of x and k, you can solve for the value of x^2 and then solve for the value of y\r<BR>\n" );
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document.write( " </SPAN>\n" );
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