document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93421>Question 93421</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0201346249/algebrahomeworkh>addison-wesley</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> hello, <BR>\n" );
document.write( "I would be extremely grateful for any help or advice for this problem. It has been extremely difficult for me as there is no fore-explanation on how to solve this type of problem.<BR>\n" );
document.write( "it is in the section of Maximum and Minimum problems, I was not sure where to put it, I hope I got the right topic.\r<BR>\n" );
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document.write( "QUESTION:<BR>\n" );
document.write( "A straight section of railroad track crosses two highways at points that are 400m and 600m, respectively, from an intersection. <BR>\n" );
document.write( "Determine the Dimensions of the largest rectangular lot that can be laid out in the triangle formed by the railroad and highways.\r<BR>\n" );
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document.write( "now, I worked a few hours on this problem, coming to absolutely nothing.<BR>\n" );
document.write( "I found the remaining side of the right triangle, at 721.1, <BR>\n" );
document.write( "I tried any number of equations using variables, in the end coming up with 4(x-1/4L)²-1/2 meaning zilch without knowing L.<BR>\n" );
document.write( "I tried graphing it and solving from there, coming up with a rough esimate of the answer.<BR>\n" );
document.write( "I Know how to deal with turning into standard form and all that, but I just cannot seem to grasp which numbers I can use to come up with the (x²+1x+1)format, ... as you can see, I am very confused, any help that you can give will a lifesaver\r<BR>\n" );
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document.write( "yours truly,<BR>\n" );
document.write( "         Michael Demski <BR>\n" );
document.write( "ps The answer from the book is 200m by 300m, I just don't know how to get there\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68025 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=68025\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Put the intersection on the origin of an xy coordinate system.<BR>\n" );
document.write( "Mark the point (600,0) on the x axis.<BR>\n" );
document.write( "Mark the point (0,400) on the y axis.<BR>\n" );
document.write( "Draw a line thru those two points. <BR>\n" );
document.write( "That line is the railroad track.<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Find the equation of that line using the two points.<BR>\n" );
document.write( "You get slope = -400/600 = -2/3<BR>\n" );
document.write( "You have the y-intercept at 400<BR>\n" );
document.write( "The equation is y = (-2/3)x+400<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Sketch a rectangle inside the figure touching the railroad line at (x,y),<BR>\n" );
document.write( "with other vertices, (0,0), (0,y), (x,0)<BR>\n" );
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document.write( "The area of that rectangle is x*y<BR>\n" );
document.write( "A = xy<BR>\n" );
document.write( "But y = (-2/3)x+400, so you get<BR>\n" );
document.write( "A = x[(-2/3)x+400]<BR>\n" );
document.write( "A = (-2/3)x^2 + 400x<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "The maximum value for A occurs when x = -b/2a<BR>\n" );
document.write( "x = -(400/[2(-2/3)]<BR>\n" );
document.write( "x = 200/(2/3)<BR>\n" );
document.write( "x = 300<BR>\n" );
document.write( "Substitute that into y = (-2/3)x + 400 to get:<BR>\n" );
document.write( "y = (-2/3)*300 + 400<BR>\n" );
document.write( "y = -200 + 400<BR>\n" );
document.write( "y = 200<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "The dimensions of the rectangle with maximum area are 300 by 200<BR>\n" );
document.write( "===================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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