# HSC 2016 Maths Marathon (archive) (1 Viewer)

Status
Not open for further replies.

#### leehuan

##### Well-Known Member
Re: HSC 2016 2U Marathon

Not sure if this is correct but if its the whole alphabet then (x-x)=0 and since its a factor the whole expression = 0?
Correct lol

#### Nailgun

##### Cole World
Re: HSC 2016 2U Marathon

Simplify (x-a)(x-b)...(x-z)
Do we need the polynomial sub and product of roots stuff for this?

I've found so many patterns trying to expand this without actually expanding this lele

I have no idea how this is meant to end up simpler lol

#### Nailgun

##### Cole World
Re: HSC 2016 2U Marathon

Not sure if this is correct but if its the whole alphabet then (x-x)=0 and since its a factor the whole expression = 0?
Correct lol

#### Nailgun

##### Cole World
Re: HSC 2016 2U Marathon

I did like 4 pages of working trying to figure out how to expand polynomials to the nth degree

#### Nailgun

##### Cole World
Re: HSC 2016 2U Marathon

why would you do this

#### Nailgun

##### Cole World
Re: HSC 2016 2U Marathon

#### Green Yoda

##### Hi Φ
Re: HSC 2016 2U Marathon

I did like 4 pages of working trying to figure out how to expand polynomials to the nth degree
lmao rekt
that was my first thought then I thought nah there must be a trick

##### -insert title here-
Re: HSC 2016 2U Marathon

why would you do this
you're the one who forgot x is a letter in the alphabet.

##### -insert title here-
Re: HSC 2016 2U Marathon

#### ThreeSciences

##### Member
Re: HSC 2016 2U Marathon

Isn't that just y = -x (for x => 0)

##### -insert title here-
Re: HSC 2016 2U Marathon

Isn't that just y = -x (for x => 0)
emptiness and width are abstract quantities, so they aren't commensurable.

However, I dare say that they are positive.

#### Nailgun

##### Cole World
Re: HSC 2016 2U Marathon

$\bg_white \noindent Let any ordered set of 3 consecutive terms in the sequence be a,b,c$

$\bg_white b-a=c-b\\ b=\frac { a+c }{ 2 } \\ \\ \frac { b }{ a } =\frac { c }{ b } \\ \\ { b }^{ 2 }=ac\\ \\ \\ \therefore \frac { { (a+c) }^{ 2 } }{ 4 } =ac\\ \\ { (a-c) }^{ 2 }=0\\ a=c\\ \\ b=\frac { c+c }{ 2 } =c\\ \\ \therefore a=b=c\\ \\ Therefore, it is a constant sequence$
good lord

an almost identical question was in my trial, except there was minor difference in the wording (the sequence was in a different order as a GP and a different order as an AP), but I didn't read it properly and ended up doing basically this working out to get a=b=c

#### InteGrand

##### Well-Known Member
Re: HSC 2016 2U Marathon

good lord

an almost identical question was in my trial, except there was minor difference in the wording (the sequence was in a different order as a GP and a different order as an AP), but I didn't read it properly and ended up doing basically this working out to get a=b=c
What was the Q. asking to prove/do?

#### Nailgun

##### Cole World
Re: HSC 2016 2U Marathon

What was the Q. asking to prove/do?
a, b, c form an AP with a sum of 9

and then in a different order they form a GP (I *think* it was b, c, a)

I didn't read that bit, and just thought that a,b,c was an AP and a GP and solved it like above and proved it was 3,3,3
but it wasn't

oh well, it was out of 3, and I'll probably still get at least 1 mark for it

I can live with 98%

#### InteGrand

##### Well-Known Member
Re: HSC 2016 2U Marathon

a, b, c form an AP with a sum of 9

and then in a different order they form a GP (I *think* it was b, c, a)

I didn't read that bit, and just thought that a,b,c was an AP and a GP and solved it like above and proved it was 3,3,3
but it wasn't

oh well, it was out of 3, and I'll probably still get at least 1 mark for it

I can live with 98%
If that's all it said, then 3,3,3 satisfies those conditions (AP with common difference 0 and GP with common ratio 1).

Were there some other conditions on the GP or anything?

#### Nailgun

##### Cole World
Re: HSC 2016 2U Marathon

If that's all it said, then 3,3,3 satisfies those conditions (AP with common difference 0 and GP with common ratio 1).

Were there some other conditions on the GP or anything?
jk you are right

there probably was lel, i've kind of zoned out of the memory now
i will update when we get it back lel

#### InteGrand

##### Well-Known Member
Re: HSC 2016 2U Marathon

NEW QUESTION

$\bg_white \noindent Let n be a positive integer. Find the n^{\text{th}} derivative of x^n.$

#### jathu123

##### Active Member
Re: HSC 2016 2U Marathon

NEW QUESTION

$\bg_white \noindent Let n be a positive integer. Find the n^{\text{th}} derivative of x^n.$
f'(x)=nx^(n-1)
f''(x)=n(n-1)x^(n-2)
f^n(x)=n!•x^(n-n)
=n!

#### pikachu975

Re: HSC 2016 2U Marathon

f'(x)=nx^(n-1)
f''(x)=n(n-1)x^(n-2)
f^n(x)=n!•x^(n-n)
=n!
Does 2 unit even use factorials?

#### LC14199

##### Member
Re: HSC 2016 2U Marathon

Does 2 unit even use factorials?
To my knowledge, no. It's taught half way through MX1. (Depending on teacher).

Status
Not open for further replies.