The Proof is Trivial!

Original post by Lord of the Flies

So how many kids do you have? :tongue:

One kid. Lots of other deformed monsters though. :tongue:

Reply 1521

Original post by Lord of the Flies

So how many kids do you have? :tongue:

Original post by ukdragon37

One kid. Lots of other deformed monsters though. :tongue:

Ermm... WTF?

Reply 1522

Lord of the Flies

Original post by bananarama2

Ermm... WTF?

Spoiler

Reply 1523

Original post by bananarama2

Ermm... WTF?

In-joke

Reply 1524

Original post by Mladenov

I do not understand this. From

f(x)(f(-x)-x)=0

it does not follow that

f(-x)=x

for all

x

f(x)=0

for all

x

. Can I not take

f

to be zero over the rationals and

-x

over the irrationals?

Oops there was a few typos! Especially in having f(x)=0 in the last paragraph but not at the end! Is it fine now?

Reply 1525

We should allow ciphers on this thread :colone:

Reply 1526

Original post by ukdragon37

I've decided to give you a taste of what I do :tongue:

Spoiler

Haha, no idea what's going on I'm afraid! :lol:

Those diagrams look cool though! Your child look awesome! :lol:

Problem 224*

'Bananarama 2' is at the top of the Eiffel Tower with twelve coins. All coins are of equal size and appearance though one of them is of a different weight (as it is a counterfeit coin). We do not know whether it is heavier or lighter. He has two bags of equal size and weight labelled A and B and the french government have told him that, if he is going to drop coins off the Eiffel tower, he is obviously going to have to do so using these bags otherwise he would be violating the health and safety regulations. He may place however many coins in bag A and however many coins in bag B and drop them from the tower. 'LOTF' is at the bottom of the tower and, every time the coins are dropped from the tower, he notes which bag hits the ground first or whether they both hit the ground at the same time. Unfortunately, the joke is getting old and so, whilst 'Bananarama 2' would happily drop coins from the Eiffel Tower all day, 'LOTF' had only agreed to stick around for 20 minutes from the time the first pair of bags are dropped. The lift in the Eiffel tower takes 6 minutes to queue for each time 'LOTF' brings the bags and coins back up. We cannot predict exactly how long the lift will take but the time taken to go from the bottom to the top, measured in minutes, can be modelled as having a continuous uniform distribution on the interval

[\frac{1}{2} , 2]

.

Are they going to be able to find the counterfeit coin? Give reasons for your answer.

(edited 10 years ago)

Reply 1527

Original post by Jkn

Problem 224*

...

I'm going to guess no because Galileo says so :colonhash:

Reply 1528

Original post by ukdragon37

I'm going to guess no because Galileo says so :colonhash:

**** Galileo! :colonhash:

We may assume that 'LOTF' is incredibly good at seeing which (if either) bag hits the ground first.

Spoiler

Problem 225*

Let

\rho_0

be a density such that, if the density of the universe were greater than

\rho_0

, the gravitational forces would be strong enough to halt the expansion of the universe (i.e. the universe would be closed).

Assuming that the universe is both isotropic and homogenous, prove that

\displaystyle \rho_0 \approx \frac{3H^2_0}{8 \pi G}

, where

H_0

is Hubble's constant and

G

is the universal gravitational constant.

(edited 10 years ago)

Reply 1529

Original post by Jkn

**** Galileo! :colonhash:

We may assume that 'LOTF' is incredibly good at seeing which (if either) bag hits the ground first.

Spoiler

Yes I recognise the problem but the way you framed it makes the solution impossible. The latter outcome of one hitting the ground before the other is not going to happen, as famously shown by Galileo. You can put one coin in one bag and 100 in the other and they are still going to land at the same time.

(edited 10 years ago)

Reply 1530

Lord of the Flies

Solution 224

The queue to the lift of the Eiffel tower does not take 6 minutes, it takes 2 hours. Thus LotF never gets to the top, people get injured from the falling coins, banarama gets arrested, and LotF goes to a nearby café to enjoy a glass of 1981 Petrus.

Reply 1531

Original post by Lord of the Flies

Cheers for that! :rolleyes:

You're just going to roll up at Cambridge and fill your room with vintage wine aren't you?

Reply 1532

und

Original post by ukdragon37

I'm guessing the fact that there is air resistance means that the bag that weighs more will indeed hit the ground first.

Reply 1533

Original post by und

I'm guessing the fact that there is air resistance means that the bag that weighs more will indeed hit the ground first.

But as Jkn so strongly protested yesterday, that's such an important unstated assumption like assuming I am Obama for "How likely I am to go into the White House?". :laugh:

Reply 1534

Original post by ukdragon37

................... are they? :colone:

Spoiler

Original post by Lord of the Flies

The queue to the lift of the Eiffel tower does not take 6 minutes, it takes 2 hours. Thus LotF never gets to the top, people get injured from the falling coins, banarama gets arrested, and LotF goes to a nearby café to enjoy a glass of 1981 Petrus.

Hahahahahaha PRSOM :lol:

Is that the French equivalent of going to the Winchester, pouring a nice cool pint and waiting for everything to blow over? :lol:

What makes you think LOTF needs to go up in the lift with the coins? :colone:

If he did, we would not have enough information as to how long it would take him to get down :colone:

We may assume that they're going to let him chuck the bag of coins in every time the elevator is about to go up and that this time is, in fact, such that he has to wait 6 minutes each time! :tongue:

Reply 1535

Original post by und

I'm guessing the fact that there is air resistance means that the bag that weighs more will indeed hit the ground first.

Given the size, the quadratic drag law would be best to describe the motion and mass cancels out. The shape has an impact and volume but not mass.

Reply 1536