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# Mega A Level Maths Thread MK II Watch

1. (Original post by tigerz)
Wopps I need to quote in >.< thank you
haha, no problem at all
(Original post by justinawe)
You should use it on \lim (for limits).

You can use it fractions (\frac), but you achieve the same thing by typing in "\dfrac" instead, which is a lot easier to do.
ah right, thank you, I'll try to remember that. May need to create a latex factsheet
2. (Original post by mynameisntbobk)
couldn't work that bit
I'll give an example.
[\dfrac{ln(keron)}{kinara}] yields
and \left[\dfrac{ln(keron)}{kinara}\right] yields
3. (Original post by reubenkinara)
I'll give an example.
[\dfrac{ln(keron)}{kinara}] yields
and \left[\dfrac{ln(keron)}{kinara}\right] yields
oh alright, I'll try that now thanks
4. (Original post by DJMayes)
Here's a problem I posted a while back that hasn't yet been solved.
Is this okay, or am I somewhere along the right lines:

Spoiler:
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Assume true for

For

Therefore when it is true for n=k, it is true for n=k+1

As it is true for n=1, it is true for all natural numbers n
5. (Original post by DJMayes)
Here's a problem I posted a while back that hasn't yet been solved.
I just want to ask whether something I'm about to type is possible to model/solve using A level knowledge. I try not to post questions I can't do, so if you tell me "yes, it's in M4" for example, I can put it away to solve then.
Spoiler:
Show
We've all heard the problem about a fox crossing a room, each step moves them 1/2 of the distance between them and the rooms edge, so 1st 1/2, 2nd 1/4 and so on.
My question, suppose me and a mouse were having a race to reach the end of the room.
The room is 50m in length. The mouse sets off 10s before me from the centre of the room and has a starting speed of and moves at constant acceleration of . The problem: assuming that I, like the fox am limited to moving a fraction of the original distance each time, find the lowest fraction that I have to advance by each time to pass the mouse.
6. (Original post by brittanna)
Is this okay, or am I somewhere along the right lines:

Spoiler:
Show

Assume true for

For

Therefore when it is true for n=k, it is true for n=k+1

As it is true for n=1, it is true for all natural numbers n
Looks good to me. The only thing I would suggest is a change of the base step, as this is a result for all values of x that can be written as the sum of two squares, not simply 5. Your logic is fine though for the general induction.
7. Hi, I'm retaking M2 (MEI) and need to get at least a C in it but i am really struggling. If anyone thinks they would be able to explain moments, impulses, frameworks or work/power then please let me know. I need to get a B overall in Further Maths to get into my firm choice uni and its this module that is gonna drag me down x
8. (Original post by reubenkinara)
I just want to ask whether something I'm about to type is possible to model/solve using A level knowledge. I try not to post questions I can't do, so if you tell me "yes, it's in M4" for example, I can put it away to solve then.
Spoiler:
Show
We've all heard the problem about a fox crossing a room, each step moves them 1/2 of the distance between them and the rooms edge, so 1st 1/2, 2nd 1/4 and so on.
My question, suppose me and a mouse were having a race to reach the end of the room.
The room is 50m in length. The mouse sets off 10s before me from the centre of the room and has a starting speed of and moves at constant acceleration of . The problem: assuming that I, like the fox am limited to moving a fraction of the original distance each time, find the lowest fraction that I have to advance by each time to pass the mouse.
Your question isn't clear what your movement is - do you mean constant speed, distances in successive seconds form a geometric series, or something else? The answer is yes to both but if you're going to post a question it needs to be clear what you're asking.
9. (Original post by DJMayes)
Looks good to me. The only thing I would suggest is a change of the base step, as this is a result for all values of x that can be written as the sum of two squares, not simply 5. Your logic is fine though for the general induction.
Spoiler:
Show
So would I just replace the 5 with the and show it the same way I did towards the end of the question?
10. (Original post by DJMayes)
Your question isn't clear what your movement is - do you mean constant speed, distances in successive seconds form a geometric series, or something else? The answer is yes to both but if you're going to post a question it needs to be clear what you're asking.
I wasn't too sure about that but I suppose the movement could be in successive seconds.
As said though, I wasn't really looking at a solution at least I know that only Alevel knowledge is required. Sorry, about the lack of specifics.
11. (Original post by brittanna)
Spoiler:
Show
So would I just replace the 5 with the and show it the same way I did towards the end of the question?
Spoiler:
Show

Yes - Explicitly take and use this to derive the result you did. The nice thing about this question is that the base step and the inductive step are essentially identical.

12. (Original post by DJMayes)
Looks good to me. The only thing I would suggest is a change of the base step, as this is a result for all values of x that can be written as the sum of two squares, not simply 5. Your logic is fine though for the general induction.
It still won't let me rep you, and I still owe you some rep from the other question you helped me with! I will get it all done eventually though .
13. (Original post by DJMayes)
There don't seem to be many questions being thrown about tonight. Here's one for you all:

Spoiler:
Show

Let be an integer which can be written as the sum of two square numbers. Prove that can be written as the sum of two square numbers for all natural numbers n.

I'm stuck
Spoiler:
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an integer which can be written as the sum of two square numbers where a and b are two square numbers

also..
14. (Original post by tigerz)
I'm stuck
Spoiler:
Show
an integer which can be written as the sum of two square numbers where a and b are two square numbers

also..
I'd help you out here, but I'm not sure how to prove this without induction, if that's at all possible.

Have you done FP1?
15. (Original post by justinawe)
I'd help you out here, but I'm not sure how to prove this without induction, if that's at all possible.

Have you done FP1?
Nope >.< I've only done c1, c2 and s1 :P
So its not provable without further knowledge?

If it was specific i'd sub in random numbers, but this is for all natural numbers

Edit: Can I just sub in n=1 then 2 etc ?
16. (Original post by tigerz)
Nope >.< I've only done c1, c2 and s1 :P
So its not provable without further knowledge?

If it was specific i'd sub in random numbers, but this is for all natural numbers

Edit: Can I just sub in n=1 then 2 etc ?
You can't sub in n=1, then 2 etc... because how are you going to sub in every single natural number? That's just not possible. Which is where induction comes in.

I don't know if there's another way of proving it. There probably is, but I can't think of any other proof.
17. (Original post by justinawe)
You can't sub in n=1, then 2 etc... because how are you going to sub in every single natural number? That's just not possible. Which is where induction comes in.

I don't know if there's another way of proving it. There probably is, but I can't think of any other proof.
Isn't it possible, if she spent an infinite time pluggin in numbers?
18. (Original post by justinawe)
You can't sub in n=1, then 2 etc... because how are you going to sub in every single natural number? That's just not possible. Which is where induction comes in.

I don't know if there's another way of proving it. There probably is, but I can't think of any other proof.
True :P can we just say that 2n=evens and 2n+1=odds and sub in both, and if it works YAY lmao
Ahh well its cools
19. (Original post by echelonprincess)
Hi, I'm retaking M2 (MEI) and need to get at least a C in it but i am really struggling. If anyone thinks they would be able to explain moments, impulses, frameworks or work/power then please let me know. I need to get a B overall in Further Maths to get into my firm choice uni and its this module that is gonna drag me down x
I can explain them, but I'm too tired for now so remind me in the morrow
20. (Original post by reubenkinara)
Isn't it possible, if she spent an infinite time pluggin in numbers?
LOOL, knowing me i'd cheat and say 'right 1-10 works so every number does' >.<

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