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Best CAPTCHA ever [Jul. 19th, 2007|10:52 am]
 [ Tags | funny, tech ]

A CAPTCHA gives you a little test to see if you're human, not a computer auto-generating accounts.

You know, this sort of crap:

But these guys have a way better one:

 From: 2007-07-19 05:58 pm (UTC) (Link)
42cos(x) - 28sin(7x + pi/2)

-28?
 From: 2007-07-19 05:59 pm (UTC) (Link)
70
 From: 2007-07-19 06:00 pm (UTC) (Link)
D'oh. No, 42 - 28 ... uhhh. *gets out calculator* 14?
 From: 2007-07-19 09:24 pm (UTC) (Link)
 From: 2007-07-19 06:00 pm (UTC) (Link)
Guess I'm not human.
 From: 2007-07-19 06:00 pm (UTC) (Link)
I got a real easy one...

p(x) = x^2 + 2x + 1
find the real roots of the polynomial

hillarious though!
From:
2007-07-19 06:08 pm (UTC)

### 14

I got -3 * (-4) - (-2) = ?

See, I didn't need to take Calculus after all!
 From: 2007-07-19 06:11 pm (UTC) (Link)
that should be the test to prove you're Asian.
 From: 2007-07-19 06:26 pm (UTC) (Link)
That's better than a password ;)
 From: 2007-07-19 06:46 pm (UTC) (Link)
7*6*cos(12pi) - 4*7*sin(14pi + pi/2) = 42-28 = 14
 From: 2007-07-19 06:50 pm (UTC) (Link)

Quick! Write an OCR system that can grok mathematical notation!

 From: 2007-07-19 07:08 pm (UTC) (Link)
The answer is 7 you guys. I just did it in my head.
From:
2007-07-19 07:20 pm (UTC)

### possibly embarrassing myself here

I forget calculus syntax. Is that asking you to just evaluate at x=2pi?
In that case, the sin is +1 and the cos is -1 at that point, so it's just 7 - 4 = 3.
From:
2007-07-19 07:54 pm (UTC)

### Re: possibly embarrassing myself here

You mean I was only off by 4?! Not bad!
From:
2007-07-19 08:22 pm (UTC)

### Re: possibly embarrassing myself here

You have to take the derivative first, then evaluate it at the point x=2pi. Anyway, sin(N*2pi)=0, cos(N*2pi+pi/2)=0.
From:
2007-07-19 09:22 pm (UTC)

### Re: possibly embarrassing myself here

I meant "evaluate the derivative", and "the sin is +1" I meant "the derivative at that point is +1". Nikolas did it more thoroughly below.
From:
2007-07-19 09:45 pm (UTC)

### Re: possibly embarrassing myself here

He messed up too. :) Must be a lot of programmers hanging around here, and not enough engineers.
From:
2007-07-19 10:18 pm (UTC)

### Re: possibly embarrassing myself here

I think you both forgot to apply the chain rule. The derivative of 7Sin[6x] is 42 Cos[6x], etc.
(Deleted comment)
From:
2007-07-19 09:23 pm (UTC)

### Re: Spelling it out ...

Alternatively, what I did was visualize what the derivatives at those well-known points are: the sin is maximally sloping upwards (+1) and the cos maximally downwards (-1), which got me to your second-to-last step without computing any derivatives directly. :)
From:
2007-07-19 09:44 pm (UTC)

### Re: Spelling it out ...

You missed a factor on the derivative. D[ sin(ax) ] = a*cos(ax) . Remember D[ sin(u) ] = cos(u)du . See my solution above.
From:
2007-07-19 10:15 pm (UTC)

### you forgot the chain rule

has the correct answer above, 14.
From:
2007-07-19 10:23 pm (UTC)

### Re: Spelling it out ...

Haha, we suck. Chain rule?
From:
2007-07-19 07:40 pm (UTC)

### LOL!

There was a time when I could actually do the math. Now it's like a bad dream. uffff.
From:
2007-07-19 11:12 pm (UTC)

### Re: LOL!

I took 2 years of AP Calc in high school, and now, I hardly remember a lick of it!
From:
2007-07-20 01:21 pm (UTC)

### Re: LOL!

Cincinnati State Tech. a looong time ago :)
 From: 2007-07-19 08:35 pm (UTC) (Link)
Yeah, yeah, it's funny and all, but wouldn't this be pretty simple for a computer, and pretty damn hard for most humans.
 From: 2007-07-19 09:23 pm (UTC) (Link)
I think it may have been intentionally constructed to be easy. See my comments above.
 From: 2007-07-19 10:17 pm (UTC) (Link)
Except for the fact that you have to OCR and parse a math equation correctly.
 From: 2007-07-19 08:38 pm (UTC) (Link)
so if you know the answer does that mean you're a computer or human? i think humans would get the wrong answer. i know i would.
 From: 2007-07-19 08:41 pm (UTC) (Link)
Either I'm not a human or I'm totally blonde... -_-"
 From: 2007-07-19 09:56 pm (UTC) (Link)
i always knew i wasnt a real person...
 From: 2007-07-19 10:42 pm (UTC) (Link)
cause computers are terrible at math
 From: 2007-07-19 11:17 pm (UTC) (Link)
very cool )
 From: 2007-07-20 03:14 am (UTC) (Link)
So, if you get the correct answer, you must be automated.
From:
2007-07-20 09:17 am (UTC)

I got the question

-6+7-1=?

so I am human