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# I'm bored. Give me a challenging maths problem to work on. watch

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1. (Original post by SGHD26716)
Try searching Hilbert's paradox of the Grand Hotel
Already know it, but thanks anyway.
2. (Original post by JPencil)
For AQA board? Surely you're mistaken
Not AQA. Pretty sure this was Edexcel proof by induction
3. (Original post by Student403)
Not AQA. Pretty sure this was Edexcel proof by induction
Phew
4. What's 1+1? JK, just revise them.
5. (Original post by User23)
I'm in year 11 however in Sixth Form I wish to study Biology, Chemistry, Maths and Further Maths. And I'm sorry I shall contribute by giving you this question:

Oh and if you get an answer please be an angel and explain it to me.
The question is poorly phrased as it fails to explain the significance of the barn's length. A diagram would help. I would argue that the goat's maximum distance from the barn is its radius. That means the goat can occupy an area of pi*r^2 / 2 (ie half a circle as the barn bisects the circle. Therefore the value is 8pi*a^2 exactly.
6. (Original post by User23)
r u crazy?!?!?!
This is C1-3 knowledge, and would take quite a while to complete.
(Original post by JPencil)
Phew
Yeah it's Edexcel. Proof by induction is rather simple once you know the method.
7. (Original post by multiratiunculae)
The question is poorly phrased as it fails to explain the significance of the barn's length. A diagram would help. I would argue that the goat's maximum distance from the barn is its radius. That means the goat can occupy an area of pi*r^2 / 2 (ie half a circle as the barn bisects the circle. Therefore the value is 8pi*a^2 exactly.
Oh damn you and your brains.
8. (Original post by User23)
Oh damn you and your brains.
It's really not beyond you. You have a too pessimistic attitude! All I require is a diagram for clarification.
I'm under the impression the goat can enter the barn; why else would they give you the barn's length?
9. (Original post by multiratiunculae)
It's really not beyond you. You have a too pessimistic attitude! All I require is a diagram for clarification.
Yeah I am quite a pessimist. It doesn't come with a diagram unfortunately. This question is from 16+ past paper because I'm going to be sitting exams for Sixth form I've applied to.
10. (Original post by multiratiunculae)
It's really not beyond you. You have a too pessimistic attitude! All I require is a diagram for clarification.
I'm under the impression the goat can enter the barn; why else would they give you the barn's length?
Because that would mean at the minimum (or maximum) positioning of the pivot of the rope, the goat can fully stretch along two sides of the barn. (2a on one side + 2a on the adjacent side = 4a, the length of the rope)

I doubt it can enter the barn
11. (Original post by Student403)
Because that would mean at the minimum (or maximum) positioning of the pivot of the rope, the goat can fully stretch along two sides of the barn. (2a on one side + 2a on the adjacent side = 4a, the length of the rope)

I doubt it can enter the barn
Pivot of the rope? The goat is tethered; I do not care what to and what its dimensions are. The only thing of value here is knowing the radius (ie the goat's rope's length), which is 4a. It forms a semi-circle. So 8pi*a^2 is the answer. The question is poorly phrased. QED.
12. Re-arrange the Schrodinger equation

Divide it by 2.

Multiply it by 2.

Minus you age.

Minus 10.

You have arrived at the number of shiny sh*ts I and society give about you and your boredom.
14. (Original post by multiratiunculae)
Pivot of the rope? The goat is tethered; I do not care what to and what its dimensions are. The only thing of value here is knowing the radius (ie the goat's rope's length), which is 4a. It forms a semi-circle. So 8pi*a^2 is the answer. The question is poorly phrased. QED.
It's not poorly phrased. You just misunderstand.

The fact that you are meant to prove an inequality and show a minimum means that there is a variable. In this case, it is the position of the tether along a given wall of the barn. Notice how the length of the tether is greater than the length of a barn wall. This means that (because the tether can be bent), there is a range of areas around the barn which the goat can graze.
15. (Original post by multiratiunculae)
A-levelish.
Evaluate

16. (Original post by JPencil)
Was that on an FP2 paper somewhere? I'm sure I have done this before!
Can be done by induction so probably FP1.
17. (Original post by multiratiunculae)
I am disgusted that a male would say that of a mathematics thread. Please leave.
Please find a hobby that doesn't involve maths questions. I am disgusted that a male cannot partake in the playing or watching of sport (whether team or by yourself), discuss politics, news and current affairs, or even use the internet to admire the female figure.

Now I'm leaving.
18. (Original post by i<3milkshake)
Please find a hobby that doesn't involve maths questions. I am disgusted that a male cannot partake in the playing or watching of sport (whether team or by yourself), discuss politics, news and current affairs, or even use the internet to admire the female figure.

Now I'm leaving.
The entire morning was spent watching MOTD, watching the news followed by a decent masturbation session. I am well-rounded; what's wrong with mathematics. Are you intellectually intimidated? I hope not, mathematics is interesting and if you disagree you can feck off.
19. 8a + 5x = ?

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