document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=196582>Question 196582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi!\r<BR>\n" );
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document.write( "I'm having some difficulty with the following problem:\r<BR>\n" );
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document.write( "If F is the focal length of a convex lens and an object is placed at a distance x from the lens, then its image will be at a distance y from the lens, where F, x, and y are related by the lens equation below. Suppose that a lens has a focal length of 2.1 cm, and that the image of an object is 4 cm closer to the lens than the object itself. How far from the lens is the object?\r<BR>\n" );
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document.write( "1/F = 1/x + 1/y \r<BR>\n" );
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document.write( "thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147333 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=147333\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If F is the focal length of a convex lens and an object is placed at a distance x from the lens, then its image will be at a distance y from the lens, where F, x, and y are related by the lens equation below. Suppose that a lens has a focal length of 2.1 cm, and that the image of an object is 4 cm closer to the lens than the object itself. How far from the lens is the object? <BR>\n" );
document.write( "1/F = 1/x + 1/y<BR>\n" );
document.write( "y-4  = distance the image is from the lens<BR>\n" );
document.write( "y = distance the object is from the lens <BR>\n" );
document.write( "----<BR>\n" );
document.write( "1/2.1 = 1/(y-4) + 1/y<BR>\n" );
document.write( "Multiply thru by 2.1y(y-4) to get:<BR>\n" );
document.write( "y(y-4) = 2.1y + 2.1(y-4)<BR>\n" );
document.write( "y^2-4y = 2.1y + 2.1y - 8.4<BR>\n" );
document.write( "y^2 - 8.2y + 8.4 = 0<BR>\n" );
document.write( "10y^2 - 82y + 84 = 0<BR>\n" );
document.write( "(10y-12)(y+7) = 0<BR>\n" );
document.write( "y = 1.2 cm (distance the object is from the lens)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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