[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
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[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
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[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 236: fputs() expects parameter 1 to be resource, bool given
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[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 236: fputs() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 237: fclose() expects parameter 1 to be resource, bool given
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[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 236: fputs() expects parameter 1 to be resource, bool given
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[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 236: fputs() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 237: fclose() expects parameter 1 to be resource, bool given
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forum.virtualchallengemeets.com • View topic - optimize this

optimize this

What could be so hard. It's a multiple-choice test for Pete's sake.

optimize this

Postby bradp » Sat Oct 27, 2007 8:29 pm

Find the maximum area of a rectangle bounded by [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula].
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Postby collegebookworm » Sat Oct 27, 2007 9:48 pm

We're searching in the range [unparseable or potentially dangerous latex formula], because those are the x-value endpoints of the closed area between [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula]. I'll define a new function, [unparseable or potentially dangerous latex formula] to make this optimization easier.

The area of a rectangle enclosed in the region is [unparseable or potentially dangerous latex formula]. To optimize the problem, one should look at the area of rectangles when x and y are at their endpoints and at their critical points.

The critical points of function A are where the derivative equals zero, so we have: [unparseable or potentially dangerous latex formula]. When the derivative is zero, [unparseable or potentially dangerous latex formula].

The value of A at the the endpoints and critical points are:

[unparseable or potentially dangerous latex formula]

Notice how the area for the endpoints is zero, which we would expect since the y-values at those x-values are zero. Notice too how the area for the [unparseable or potentially dangerous latex formula] x-value is exactly the negative of the area for the [unparseable or potentially dangerous latex formula] x-value, because [unparseable or potentially dangerous latex formula] is even. Thus, we can calculate the area at all more points on the curve, but we can safely say that the largest area is about [unparseable or potentially dangerous latex formula]
(NS/CA/MA/CS/SC) "**" indicates TMSCA State
08 HI(LO): 142?-**(88-D2)/224-D2(17x-**)/320-D2(202-**)/248?-D2(206-**)/210-D2(17x-NovA+?)
08 D2: 88/224/320/210/248

Next meet: Texas Tech (Region, 4/11-12)
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Postby bradp » Sat Oct 27, 2007 10:20 pm

13.01 is adding the y axis as another bound, so the max rectangle area without the y axis as a bound would have twice the x coordinate, making the area 26.02

i think?

thanks, just needed to check my take home test :D
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Postby collegebookworm » Sat Oct 27, 2007 10:27 pm

oops, I'll be more careful next time :)
(NS/CA/MA/CS/SC) "**" indicates TMSCA State
08 HI(LO): 142?-**(88-D2)/224-D2(17x-**)/320-D2(202-**)/248?-D2(206-**)/210-D2(17x-NovA+?)
08 D2: 88/224/320/210/248

Next meet: Texas Tech (Region, 4/11-12)
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Postby AuSmith » Sun Oct 28, 2007 2:36 pm

You could have shown that the maximum area rectangle has to have horizontal and vertical sides... sure, it's mostly intuitive since [unparseable or potentially dangerous latex formula] is so steep. But hey, no one ever asked you to prove anything on a math test - don't be silly.

Admittedly, I frown a little on this problem because if [unparseable or potentially dangerous latex formula] weren't so steep, it wouldn't be obvious that the maximum area rectangle was upright.
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Postby bradp » Sun Oct 28, 2007 6:43 pm

any even function should have its max rectangle as upright

don't get creative!
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Postby AuSmith » Sun Oct 28, 2007 6:54 pm

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Postby bradp » Sun Oct 28, 2007 7:02 pm

I knew you would catch me.
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Postby AuSmith » Sun Oct 28, 2007 7:23 pm

Then, once [unparseable or potentially dangerous latex formula] increases past [unparseable or potentially dangerous latex formula], I think the rectangle has to tilt because if it keeps its diagonals perpendicular, it's a rhombus. A rectangular rhombus is a square. And, if it's an untilted square, it can't touch all four corners to the boundary. All maximal area rectangles should touch every corner to the boundary, else you might push some of the other corners off, then stretch it some more.
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