# mathematics extension

1. ### How to find the shortest distance between two lines ?

The question basically is: Find the shortest distance between lines r = i+2j+3k + lambda (2i+j+4k) and r = 2i+4j+5k + mu (3i+4j+5k). I don't get these sort of questions and I really need help. Can someone give me a solution that doesn't involve the use of matrices please.
2. ### Can anyone please provide some feedback on my proof

The question was asking: Prove the following statement using either direct or contrapositive proof: If n is an integer then 4 does not divide n^2-3 Here is my working out: let n^2 - 3 = 4m By way of contradiction assume n^2 - 3 is rational, ie; n^2 - 3 = a/b (BTW in the funky looking...
3. ### Integration Question

I came across an integral that my teacher gave me to do. I have an answer but am unsure if my answer is correct. Other softwares (wolfram alpha and symbolab) are giving me different answers, but I suspect they are algebraically equivalent since they probably have different constants of...
4. ### The Cover Up Rule Proof

I am up to the last question in the exercise and I am a bit stuck on this question: Can anyone please help me out on this ?
5. ### Proof Question

I am really confused for the following proof question and am unsure where to start (I don't really get the hint) I would really appreciate it if anyone helped me out with this question
6. ### Proof Question

I am just wondering if anyone can have a look at my solution to the following proof question: Question: "Prove by contradiction that there exists no 'n' that is an element of the natural numbers, such that n^2 + 2 is divsible by 4" My Solution: By way of contradiction assume their exists...
7. ### Integration Question

I am pretty confused with my solution to this integration proof question. I feel like it isn't the right way to prove it. d/dx (uv) = u(dv/dx)+v(du/dx) take the integral with respect to x of both sides: uv = ∫ u(dv/dx ) dx + ∫ v(du/dx) dx therefore, ∫ u(dv/dx ) dx = uv - ∫ v(du/dx)...
8. ### Need help on a math exam question

I would be grateful for any ideas on this question :) , I know the use of the difference between cubes is used but how do you proceed from there?
9. ### HSC Maths Tutor - Adv, Ext 1 & 2 - HSC 3/4U Marker - Over 30 Years Teaching Experience

Hey all, Hope everyone has been well. I am advertising for my father who has availability for more students to tutor. A little about himself: - Numerous past/current students have been from a variety of selective schools such as James Ruse, North Sydney Boys and Girls, Baulkham Hills...etc. -...
10. ### Should I Drop It?

Hello members of BOS ! Currently doing Mathematics Extension 1, knowing that it will never make it into my 10 best units, should i drop it? Some factors i am considering right now: I wish to get into an engineering course when i graduate, and in most universities it is recommended that i do...