1. ## Re: Science Trivia

Originally Posted by vlach
Im not sure if this is the optimal strategy or if it counts as a solution but it will certainly ensure 0.75 success rate in that the guy who sees hats of the same colour guesses the opposite of what he sees and the others shut up since 2 "same" 1 "different" combinations are more likely.
Yes, that's it. I'm pretty sure that's the best possible strategy. My proof is as follows: you have zero information about your own hat, so if you guess, you will always be wrong exactly 50% of the time. If everyone guesses the opposite color when the other two hats are the same, and say nothing if they're different, then out of 24 guessing opportunities in eight scenarios, twelve guesses are made: in two scenarios everyone guesses wrong (when all hats are the same color), and in six scenarios one person guesses right (otherwise). As required, six of the twelve guesses are wrong. If you could get seven of the eight scenarios right, you'd have to have seven wrong guesses somewhere, but there are at most three possible guesses in the last scenario.

(I guess this assumes that everyone's following a deterministic strategy. Not sure if the logic works for probabilistic strategies.)
Originally Posted by vlach
As for the two man problem if a predetermined strategy is allowed then one of them should answer the opposite of what he sees whilst the other should copy what he sees ensuring 100% success. is this game theory type bollocks?
That'll work if you can listen to the other guy's guess before making your own. But it's not specified in the problem.

2. ## Re: Science Trivia

well they could agree beforehand but that makes for a pretty constant vote

3. ## Re: Science Trivia

I have a Math challenge for anyone out here.
The diameter of the top base of a frustum of right circular cone equal to its slant height. The height of the frustum is 4 ft. The perimeter of the vertical section of the frustum is 26 ft.
Find:
1. diameter of top base
2. diameter of lower base
3. lateral area of the frustum
4. volume of the cone

You can use any method as long as it is equal to the correct answer.

4. ## Re: Science Trivia

Alright, did it all by hand, assuming the given slant height is for the frustrum and not the whole cone ...

1.) Dtop = (16π˛+169)/(26π) ~ 4.0023 ft

2.) Dbot = (26 - 4π)/(π) ~ 4.2761 ft

3.) Lateral Area = (16π˛ - 104π + 845)/(13π) ~ 16.5567 ft˛

4.) Cone volume = ~27.2847 ftł

5. ## Re: Science Trivia

Just imagine the frustum and its vertical perimeter.

X
= Slant height and Diameter of top circle
A = Triangle formed by subtracting Y by X, and dividing it by 2
Y = Diameter of lower circle

Perimeter of vertical section=26
26=3X+Y

A = (Y-X)/2
How? Because if we subtract X from Y, the result would be 2A.

Now that we have A, we need to find X using the Pythagorean Theorem.

X = [A^2 + 4^2]^1/2, or X is equal to the square root of A to the power of 2 plus 4 to the power of 2

Wait. A = (Y-X)/2, what do we need to do to the equation? We need to remove Y. Y = 26-3X.
So:
A = [(26-3X-X)/2]
= [(26-4x)/2]

We can now solve for X:

x = [A^2 + 4^2]^1/2
= {[(26-4X)/2]^2 + 16}^1/2
= {[(676-208X+16X^2)/4] + 16}^1/2
X^2 = {(676-208X+16X^2)/4} +16
4X^2 = 676-208X+16X^2 + 16(4)
4X^2 = 676-208X+16X^2 + 64
= 16X^2 - 4X^2 - 208X + 676 + 64
= 12X^2 - 208X +740
We now calculate X using the quadratic. After using the quadratic formula, we are given two answers: 12.3333 & 5. If we select 12.3333, the perimeter would be higher than 26, since:

26 = 3(12.3333) + Y
26 = 37 +Y
That is wrong, because both side aren't equal. We need a smaller number that would fit in 26, that is 5.

We now need to find Y:
Y = 26 - 3X
Y = 11

Now that we have X and Y, we can now calculate if 26=3X+Y
26 = 3(5) + 11
26 = 26

1. Dtop = 5 ft
2. Dbot = 11 ft
3. Just calculate
4. Just calculate

6. ## Re: Science Trivia

And now for round 4 of Name that Beurnolli

- Was a part of the whole Newton-Leibniz kerfuffle
- Was invited by Peter the Great to be a prof. at the new St. Petersburg Academy
- Upon his death , the immortal Euler took over his professorship position.

Which Bernoulli was it?

7. ## Re: Science Trivia

^ Haha, I should use that line in my exams:
Generic question:
"Name the 2nd law of Thermodynamics "
Professor:

As for your question: I'd say Nicolaus II Bernoulli

Correct.

9. ## Re: Science Trivia

Alright, Since this is the first time I pose a question, ill choose an easy one:
He was educated by a monk at an early age on math and philosophy
His work involved fluid speed when exiting a pipe or a hollow object, and a Barometer.
And he has a horn/trumpet named after him.

EDIT: is this question too hard??

10. ## Re: Science Trivia

Its Evangelista Torricelli, his "trumpet" is what is also known as Gabriel's horn (the 2pi rotation of the graph of y =1/x (for x>1) about the x-axis)

It has the property of having a finite volume but an infinite surface area.

11. ## Re: Science Trivia

Yes that is correct. Evangelista Torricelli, is the correct answer,

12. ## Re: Science Trivia

This is going to get sad if it is just you and me ... that requires another martini ....

Alright, I'm back.

I think something more esoteric is required to broaden the participation.

If σx = 1 and σy = 2 what is the maximum possible value of of τxy assuming equilibrium.

13. ## Re: Science Trivia

Not exactly trivia but:

14. ## Re: Science Trivia

The triangles are not actually proportional (2:5 vs 3:8 = 0.4 vs 0.375 ) but they are close enough to fool your eye. If you think about the white area above the red and blue triangles

At first you have

Above red = 1/2 (8)*(5+2) = 28

Above blue = 1/2 (2) * (5) = 5

Total = 33

At the end you have

Above red = 1/2 (3)*(8) = 12

Above blue = 1/2 (5)*(3+5) = 20

Total = 32

Therefore you need that extra open square in order to have the same white area at the beginning and at the end.

15. ## Re: Science Trivia

Originally Posted by Sphere
This is going to get sad if it is just you and me ... that requires another martini ....

Alright, I'm back.

I think something more esoteric is required to broaden the participation.

If σx = 1 and σy = 2 what is the maximum possible value of of τxy assuming equilibrium.
I assume TXY has a max value of root of 5
I must be honest, what do the sigma and tau values actually represent? I just worked with vectors, but is there some deeper meaning?

16. ## Re: Science Trivia

I assume TXY has a max value of root of 5
I must be honest, what do the sigma and tau values actually represent? I just worked with vectors, but is there some deeper meaning?
Find a man named Mohr, he will show you the way.

17. ## Re: Science Trivia

I'd go for some cognac, really.
Originally Posted by Ritterbruder44
I assume TXY has a max value of root of 5
I must be honest, what do the sigma and tau values actually represent? I just worked with vectors, but is there some deeper meaning?
The sigma represents normal stress, and tau represents shear stress.

For now, On quick and simplified math (and mostly likely wrong), I'd say τxy is 0.5 or 0.968

18. ## Re: Science Trivia

.5 is correct.

19. ## Re: Science Trivia

Sweet, my turn then, I suppose.

I'll look for something interesting.

EDIT: This one should be easy.

20. ## Re: Science Trivia

Originally Posted by Sphere

Originally Posted by Sarry
EDIT: This one should be easy.
Radioactivity are particles emitted as a result of nuclear instability, radiation describes how waves and radioactive particles travel through space.
Radioactivity can be divided into neutron, x-ray, alpha, beta and gamma radiation. Other types of radiation are ultra violet light, microwaves, radio waves, heat (thermal radiation), errr, I'm pretty sure I've forgotten some. Ow, and visible light of course.