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watching The Crow now

i did solutions to 2024 ext 1 and 2 cssa https://4unitmaths.com/cssa-2024-e1-sol-tywebb.pdf https://4unitmaths.com/cssa-2024-e2-sol-tywebb.pdf many of my methods differ from cssa solution methods often leading to more efficient soutions

That's two hundred and fifty two quadrillion one hundred and ninety six trillion eight hundred and fifty seven billion six hundred and thirty eight million four hundred and twenty nine thousand seven hundred and thirty three over two hundred and ninety eight quadrillion twenty three trillion two...

Actually the exact value for alternative methods 1 and 2 are both

12e - did you use continuity correction? If so you get approximation 0.8461 The actual answer using binomial sum is 0.8462 - very close to 0.8461 Binomial sum is very cumbersome - but there is another way which very few students (or teachers) know about - which gives same answer much more...

with my fingers and keyboard and latex dude

Here's subtle question. \text{In scalar triple product why can I write it like }\bold a\cdot\bold b\times\bold c\text{ and not have to write }\bold a\cdot(\bold b\times\bold c)\text{?}

here is another way: and i added it to https://4unitmaths.com/cssa-2024-e2-sol-tywebb.pdf So they did it in 1½ pages and I can do it in 1 line! .......... haha :lol:

Some copyrighted papers are legally available to download, as the copyright holder allows them to be downlaoded like the western maths: http://www.westmaths.com.au/home/ or next education: https://www.nexteducation.com.au/resources but most commercial trials don't have this somewhat better attitude

although the security period is over one refrains from putting paper up here

also you know it is going to be much easier if the i is in the cosh than if it isn’t think about it what is going to happen if the i is in the cosh? imaginary parts cancel and it simplifies what is going to happen if the i isn’t in the cosh? nothing! so nothing cancels.

makes it quicker cosh(ix)=cos(x)

They took 8 pages to get up to 12b. I did all that in 1 page. Here are the rest of my solutions, many of which are quite different to the official ones https://4unitmaths.com/cssa-2024-e2-sol-tywebb.pdf Haven't checked for typos though. I'll do that tomorrow.

Here is another shorter way, but less algebraic, more of a combinatorial approach. if you have m girls and n boys, you can line them up in m!n! ways such that all girls come before all boys, and in (m+n)! ways without that restriction. Hence m!n!<(m+n)!

Hey how about 16a. The official solutions are very long. You can do it in 1 line like this:

Well I thought they could have found a better way to find the minimum distance between skew lines. Here is my alternative solution to 15ciii which is much more efficient than the method in the paper, and also doesn't rely on any previous parts either.

yes indeed they did. the new one is version 31.00 as of a few days ago: https://www.fortnite.com/news/fortnite-returns-to-ios-in-the-european-union

yeah but sideloading the new fortnite which is supposed to only be available in the eu as of a few days ago? That’s kind of new.

Well I think it was a mistake. I think it should have been version 17.6.2. Not many people are going to get this update if they have to plug into computer to get it Had they made it version 17.6.2 instead many more people would have installed it. Someone figured out a way to put fortnite on...

Well officially it says “This update includes important bug fixes and addresses an issue that prevents enabling or disabling Advanced Data Protection.” but when you do the update it also says “This update fixes an issue that may prevent access to Apple Fitness+” There is also a conspiracy...