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Hi I am doing ACTL1101 at UNSW this semester, so I'd like to ask a few first year probability questions here: \\\text{Suppose that P(X=0)=1 - P(X=1). If E(X) = 3Var(X), find P(X=0).}

Thanks, figured out the ODE bit, couldn't find how to do the max. value... Got another question as well: \\\text{Solve } \frac{\mathrm{d} y}{\mathrm{d} x} =(y-x)^2\text{ using the substitution }u=y-x I found a VERY simple solution, I don't think it's right, and it certainly doesn't match with...

Thanks for the solution and the Wikipedia link! Any thoughts on the other question (ii)?

\\\text{(ii) Use the same substitution as (i) to solve }\frac{\mathrm{d} y}{\mathrm{d} t} =5y-ty^2\text{ given }y=1\text{ when }t=0.\\\text{Find the maximum value of }y\text{ for }t\geq 0

Onto ODE's now: \\\text{(i) Solve } \frac{\mathrm{d} x}{\mathrm{d} t} =y-2y^2\text{ by making the substitution }z=\frac{1}{y}\text{ to obtain a separable differential equation in }z\\\text{and }t

Yeah both methods work out very nicely. With the first one, you end up with \int \frac{1}{16}cot(t)cosec(t)dt which gives \frac{1}{16}cosec(t) +C while with the other approach you end up with \int \frac{1}{16}cosech^2(t)dt which gives \frac{-1}{16}coth(t) +C Then you sub. back in the x and voila!

Yeah thanks, figured it out.

That thread is for ALL 1231/1241 and 1251 subs. This one's exclusively for 1251 haha :p However, seriously, if you want to post your questions here you're more than welcome. I prefer one thread per subject because there are various topics that are different between MATH1231/41/51. Also, I know...

Wow thanks! The BoS link that you provided also has lots of other cool mathematical statements. I'll check those out too :)

Thanks, yeah I was applying the same approach with repeated IBP but trying to reduce (1-x) to the power of 0

Yeah, figured the second part of the question is pretty obvious. If z or w lie on the unit circle then |z| or |w|=1 and RHS of the equation derived =0 and so the statement is true. Got another one, though: \\\text{Show that }\int_{0}^{1}x^m(1-x)^ndx=\frac{m!n!}{(m+n+1)!}\text{ for all integers...

Thanks so much!

Hey everyone First of all I'd like to thank everyone, especially IG for helping me with MATH1151 last sem. I am doing MATH1251 this semester, and I have an inaugural question lol: :jump: \\\text{Use }z \overline{z}=|z|^2\text{ to show...

Great Guy! Without InteGrand I wouldn't have been able to get a HD in Maths at uni. Thanks so much for your continued help and support! :D

Well I guess if crystalline oxalic acid (just (COOH)2 without the hydrates) was used, adding it to water to get those extra dihydrates shouldn't impact the experimental results, so I think he shouldn't include it in his calculations. Because, according to me, adding the oxalic acid to the water...

Yeah, for some reason or another that I personally fail to understand, there is always this consensus that the only way to do really well in the HSC is by choosing extremely hard subjects (like extensions), so you can rely on their scaling to get you over the line. I for one know this isn't...

I didn't get that one

Wait so you're expecting 60/80?

What was your pre exam mark?

Yeah it seemed like it for sure. With The information they provided it read just impossible to figure out an answer