After keying in the combination, rotate the handle clockwise by pi/2 then counterclockwise by pi.
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Math Club Fun - June 15, 2010Rating: 4.1/5 (66 votes cast)
After keying in the combination, rotate the handle clockwise by pi/2 then counterclockwise by pi.
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4 - by substitution
5 - by calculation (any faster way ?)
3 - evidently as only the cube will remain
1 - thanks to wikipedia
Nice to do some simple mathematics once in a while :D
And to learn about yet another of Euler's achievements
Oh! I read it as x^(3/2) and was a little confused as to how the third derivative was in {1,2,3,4,5}.
Me too, then I remembered "Please Excuse My Dear Aunt Sally"... Exponent before Division.
I think the notation is ambiguous: the question isn't which operation to do first, but whether it is the x^3 is divided by 2, or just the 3. Still, might as well go with the only one that makes sense.
The first one can also be factored
x³ - 4x² + 6x - 24 =
x²(x-4) + 6(x-4) =
(x²+6)(x-4)
The only real root is 4
how can you substitute the first one?
@brainyac you forgot to turn the know a quarter turn clockwise and half a turn anticlockwise after entering the combination
A (slightly) faster way for digit 2:
This matrix is obviously singular (since the second row is twice the first one), so it has one eigenvalue 0. The other eigenvalue therefore is equal to the trace, which is 5.
Nice to point this out... I hadn't observed this and had done for direct computation! Thanks
This is definitely the approach I would take! I work with matrices wayyy too much so eigenvalues are second nature.
We could also hope they have publicly available WiFi and use Wolfram|Alpha :-)
This isn't actually correct since the derivative of a function is a function again, not a number (the function may be constant, but it is not a constant).
Actually, it's an expression, not a function (there is no equals sign or other mapping to an output). Coincidentally, the label next to the third button on the door is also an expression that happens to be constant.
yeah, but there's nothing wrong with canonically identifying the constants with their imbedding in the ring of functions.
You never met Mr H. B. Curry, did you? ;)
So what about digit five?
Judging by this discussion, the Math clubbers are still arguing about it.
There is no fifth digit in the combination. The numbers on the door are buttons.
Isn't the third derivative of the given function = 6? Since (x^3)' = 3x^2, (3x^2)' = 6x, and (6x)' = 6? So you can't actually get in...
it's x^3/2 ... so (x^3/2)' = 3x^2/2 and (3x^2/2)' = 3x ans (3x)' = 3.
So what happens when an Eng Phys students enters the door and says that Heaviside was one of the greatest mathematicians because he made Laplace Transforms easy to deal with in the engineering world?
I'm just poking fun
He gets hit with a fast Fouier transform.
I prefer to think of it as a rotation by -pi/2 followed by one of pi.
why do I feel the button 2 is too neglected?? :P