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Unread 2 Jul 2003, 03:29   #1
Mirai
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Answer me this, MrL..

There is a rectangle with a semicircle on top of it.

This shape has a perimeter of 24.

Assume this shape is a window

What are the dimensions that yield the greatest amount of sunlight?
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Last edited by Mirai; 2 Jul 2003 at 06:01.
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Unread 2 Jul 2003, 03:34   #2
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he's not online :\
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Unread 2 Jul 2003, 03:47   #3
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This question is a bit below him.


so:
There's is no unique solution.
If the rectangle is x by y, x+xπ/2+2y=24.
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Unread 2 Jul 2003, 04:00   #4
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I'm so ****ing confused....
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Unread 2 Jul 2003, 04:03   #5
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15 + 18 = 31
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Unread 2 Jul 2003, 05:35   #6
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You need a little more information, don't you?

I got:

Assuming the length of the semicircle (ie. half the circumference, if it was a whole circle) is "z"
And the two sides of the rectangle (ie. those that are part of the 24) are "x"
And the remaining side is "y".

z = 0.5 x (2 x Pi x 0.5y)
:. z ~ 1.57y

z + y + 2x = 24
:. 1.57y + y + 2x = 24
:. 2.57y + 2x = 24

Not sure where to go after this
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Unread 2 Jul 2003, 05:59   #7
Mirai
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I know it's a little below him, but it took me an hour and a half to get the answer.

And no, you don't need any more information.

Edit: Added a line that makes the answer a little more clear
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Die You Bitch Minister of Insanity - "Timete Nostrum Piscem Furoris"

My fellow Americans, I'm pleased to tell you today that I've signed legislation that will outlaw Russia forever, we begin bombing in 5 minutes - President Ronald Reagan, in a radio check where he did not realize the microphone was on and the station broadcasting
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Unread 2 Jul 2003, 12:25   #8
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It's a better question with a square.

Differentiate the equation you get for the area when you sub in the one you have for the perim, and set to 0.

Ta ****ing da.
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Unread 2 Jul 2003, 18:28   #9
Mirai
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don't use calculus. More fun that way.

And, btw, a rectangle is still a square.

And it's all nice and good that you can explain the answer, but theory is different from proof.
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Mirai - An Astral Being From Outer Space

Die You Bitch Minister of Insanity - "Timete Nostrum Piscem Furoris"

My fellow Americans, I'm pleased to tell you today that I've signed legislation that will outlaw Russia forever, we begin bombing in 5 minutes - President Ronald Reagan, in a radio check where he did not realize the microphone was on and the station broadcasting
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Unread 2 Jul 2003, 18:33   #10
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Quote:
Originally posted by Mirai
And, btw, a rectangle is still a square.
Not necessarily.

Lets have a quadralateral with sides of length 2cm and 1cm, and right angles at the corners.

Does that look like a square to you?

(The opposite, square => rec, is true however)

ps

Calculate 5109241 * 1231231 by hand.

Sure you can do it, but there are much better ways and it's pretty damn trivial.
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Unread 2 Jul 2003, 20:28   #11
Mirai
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Quote:
Originally posted by MrL_JaKiri
Not necessarily.

Lets have a quadralateral with sides of length 2cm and 1cm, and right angles at the corners.

Does that look like a square to you?

(The opposite, square => rec, is true however)

ps

Calculate 5109241 * 1231231 by hand.

Sure you can do it, but there are much better ways and it's pretty damn trivial.
Fine, a square is a rectangle. Happy?

<-- this was inputted by a co worker

And I recognize the reason to use calculus, but I forgot what I was going to say, so..

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Mirai - An Astral Being From Outer Space

Die You Bitch Minister of Insanity - "Timete Nostrum Piscem Furoris"

My fellow Americans, I'm pleased to tell you today that I've signed legislation that will outlaw Russia forever, we begin bombing in 5 minutes - President Ronald Reagan, in a radio check where he did not realize the microphone was on and the station broadcasting
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