help-23

[fringe dock]

for b it’ll be x = 0, x = -3

but the new translation is a fraction

which has put me off

[fringe dock]

shall I times this by 2?

[radiant isle]

No, 1/2 is added to x so you subtract 1/2 from each of the zeroes

[fringe dock]

I see

I get that now

but how about if it was

(2x + 1)

or

(1/2x +1)

[radiant isle]

As in, y = g((1/2)x + 1)?

[fringe dock]

yea sir

[radiant isle]

You would shift the graph of g(x) 1 unit to the left and scale it vertically by a factor of 1/2

[fringe dock]

will the graph get wider or thinner?

[radiant isle]

Wider. Sorry it wasn't clear from what I initially said

[fringe dock]

ahh I see ty

[fringe dock]

quick question

if a question was like “factor x^2 + 5x -3”

am I allowed to do x(x+5) -3

[radiant isle]

Usually factoring means you factor the whole equation. This does not give you any information about the zeroes.

[fringe dock]

i’m very confused on how to work with this

[radiant isle]

You can start by factoring 3

[fringe dock]

i’m always use to (x+2)(x-2)(x+3) etc etc

[fringe dock]

okay

[radiant isle]

So $f(x) = 3(x^3 - 3x - 2)$

[fringe dock]

3(x^3-9x-2)

[fringe dock]

isn’t it x^3

[flat frigate]

rays

[radiant isle]

Right

[fringe dock]

idk what to do next im always use to x^2 has the highest degree

[radiant isle]

Does it ask you to factor it?

[fringe dock]

no but I thought it’ll help

[radiant isle]

You can get the factored form by looking at the graph.

[fringe dock]

so (x+2)^2(x-4)

[radiant isle]

Well the x-axis is scaled by 1/2, so $f(x) = 3(x + 1)^2(x-2)$. But yeah that's the right idea

[flat frigate]

rays

[radiant isle]

But really for the questions you don't need the factored form

[fringe dock]

ah

[fringe dock]

how do u know it’s scaled by 1/2

[radiant isle]

Expand your equation. You should get something like $x^3 - 12x - 16$, which isn't quite right.

[flat frigate]

rays

[fringe dock]

how shall I get it into the same form 3x^3 - 9x - 6

[radiant isle]

Just adjust the zeroes to be at -1 and 2

[fringe dock]

ah okay

[safe radish]

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[upbeat sparrow]

linear algebra question (change of basis), so I got this example but I have no idea how to correlates to eachother? How do they even have 300 and 2?

[frozen veldt]

In the S basis, if you take 300 of the first vector and 1 of the first vector, you get the point (300, 1)

In the B basis, if you take 2 of the first vector and 1 of the second vector you get (200+100, 0+1) which is again (300, 1)

[upbeat sparrow]

so you add the vectors from the basis?

[frozen veldt]

Yes, and you scale them according to the coordinates given by the coordinate vector

[upbeat sparrow]

What about the last example

-1

How did he get there

[frozen veldt]

Well if you take zero of (1, 0) and add 1 of (0, 1) then you get (0, 1)

If you add -1 of (100, 0) (which gives (-100, 0)) to 1 of (100, 1) then you get (0, 1)

Therefore you get the same point

[upbeat sparrow]

thanks

.close

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[frozen veldt]

np ^^

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[plucky elk]

Correct

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[alpine grove]

Hello friends, I'm having a very big issue with finding a general formulae.

[alpine grove]

I have this:

But no matter what I try, I can't find a good exact formulae.

Is there something wrong so far in my analysis?

[safe radish]

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[alpine grove]

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[quick crater]

$$x+y-z=2$$
$$x^2+y^2-z^2=2$$
$$xy=\frac{1}{2}z^2$$
if $z>0$ find $z$

[flat frigate]

Skill_Issue

[quick crater]

so subtituting third into second equation (x-y)^2=2

so x-y=±sqrt2

thats where im stuck

[plucky elk]

Square the first equation

[quick crater]

x^2+y^2+z^2+2xy-2xz-2yz

2+z^2+z^2+z^2-2z(x+y)-2=0

uhh

hear me out

x^2+y^2-2xy=2
x^2+y^2+2xy=2+2z^2
(x+y)^2=2+2z^2

ugh but this becomes ugly

oh im stupid

2+z^2+z^2+z^2-2z(2+z)-2=0
5z^2-4z=0
z(5z-4)=0

ugh but these are the ans choices

wait no

z^2-4z
z(z-4)=0

.close oh shit i have to go sorry ill open a new one later

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[plucky elk]

Where did this -2 come from

[safe radish]

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[forest bridge]

.close

[wary dagger]

determine the x-intercepts of the graph of the polynomial function x^4 - 29x^2 + 100

[forest bridge]

ok, so

[junior smelt]

Do you know how to factor the polynomial u^2 - 29u + 100? If so, from there, can you factor your original more?

[wary dagger]

no i do not

im not sure which method to use

im thinking product sum but i cant find the two numbers i need to add to get the 29 and multiply to 100

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@wary dagger Has your question been resolved?

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[wind abyss]

just want to make sure

[wind abyss]

this is positive?'

only because when we isolate

it will be

-dx = -6.14?

make it positive right?

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[thorny python]

https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_13

[thorny python]

45 is open

if u need

why does bijection mean

[ashen axle]

Also, AOPS 😍

[thorny python]

48 is not an answer

[thorny python]

yes

[ashen axle]

bijection means injective and surjective function

[thorny python]

why would that like exclude 48 though

like from what im seeing the other solutions exclude because n choose 2 is n! / (n-2)! * 2!

which simplifies to n(n-1) / 2 but i dont see why you can see it immediately excludes 48 from being in the answer

[ashen axle]

So

its actually very simple

[ashen axle]

bijection here is a bit more formal

intuitively

since each player played against a pair at most once

and exactly once

for n players

there is N choose 2 games

48 is not an n choose 2

so D is elimated

[thorny python]

wait how do u know its not

[ashen axle]

Bijection is stated as this formally that the two must be equal

[thorny python]

do u have to factorize 48

[ashen axle]

do math

[ashen axle]

that can work

look at 10 C 2 and 11 C 2

in a very informal fashion, it just isn't

i suck at aops and competitive math so i can help pretty much up to here, i hope this answers the question?

[thorny python]

alr i think i see why

thanks

[ashen axle]

bijection in this context just means the two numbers must be equal

[thorny python]

👍

[ashen axle]

now close so i can open 😈

[thorny python]

.close

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[ashen axle]

gl with AMC? though

or aime

ig

[thorny python]

thnkx

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[gilded veldt]

Hello, I'm confused about how i would describe the end behaviour of a rational function using limitnotation

[gilded veldt]

Sorry for the rough sketch but how would i describe the end behaviour of this using limit notation

I'm just confused about where to put my U and how to properly write it down

[trim swan]

End behavior is the limit at infinity or negative infinity

If the horizontal asymptote is y=1, you can say

$\li{x}{\infty} f(x) = 1$

[flat frigate]

tatpoj

[trim swan]

and likewise for negative infinity

[trim swan]

I'm not sure what you mean about the U.. do you mean the domain maybe?

[gilded veldt]

I mispoke on that I'm sorry

[trim swan]

all good

[gilded veldt]

I forgot limit notation and domain are different

Could I write down what I think the limit notation could be for this and see if I'm understanding it?

[trim swan]

to describe the end behavior?

[gilded veldt]

yes

[trim swan]

Sure, but I kind of already gave you the answer for that one lol

[gilded veldt]

I'm just confused because there's 3 different parabolas and I'm not sure how to describe them all

[trim swan]

oh, end behavior just means at the extreme left and right ends of the graph

[gilded veldt]

so if either of parabolas go infinitely to the right or left then it would be infinite on both end?

[trim swan]

The vertical asymptotes are not end behavior

Wait, just to be clear, can you show exactly what the question is asking?

[gilded veldt]

Ye no problem I second

Well it's asking to analyze and my teacher says that means describing the end behaviour and the domains

It's not specifically asking for anything

[trim swan]

Okay, so the end behavior just means what does the graph do as you go all the way to the left, and all the way to the right

[gilded veldt]

ok I think i understand that

[trim swan]

In other words, as x approaches -infinity and +infinity

[gilded veldt]

so it's just related to the x axis not the y axis

[trim swan]

Right yeah

[gilded veldt]

Ok I think I understand now

[trim swan]

So like, for your function, as x goes farther and farther to the right (toward infinity), the y is going closer and closer to 1

[trim swan]

which is what this means

as x goes to infinity, the function goes to 1

on the left, you would say $\li{x}{-\infty} f(x) = 1$

[flat frigate]

tatpoj

[trim swan]

as x goes toward -infinity, the function also approaches 1

[gilded veldt]

so I also put down what it approaches?

[trim swan]

that's all you're putting down, that's the whole thing

is that the function is approaching 1 on both sides

on the +infinity side and the -infinity side

[gilded veldt]

ok and what about if it's a slant Asymptote

and x - 5 is the slant

and as it goes to the left it's also approaching the slant

How would i describe that?

[trim swan]

That means as x goes left, y is going up, correct?

[gilded veldt]

yes

[trim swan]

It's not approaching any particular value like 1, it's just going up, toward infinity

So we could say $\li{x}{-\infty} f(x) = \infty$

[flat frigate]

tatpoj

[trim swan]

as x goes toward -infinity, the function goes toward infinity

[gilded veldt]

And this would only apply to slants right? because they do not have a constant value?

[trim swan]

well not just a slant asymptote, but also something like just f(x) = x^2

It doesn't have a slant asymptote, but it does also approach infinity at both ends

[gilded veldt]

Just just to recap

When describing the end behaviour in limit notation

I should describe which infinity it's approaching

and the horizontal asymptote that it's approaching

[trim swan]

Yes, but just to clarify, the infinity under the lim just describes whether you're talking about the left or right end

You should describe both

[gilded veldt]

yes

[trim swan]

Yeah, you got it

[gilded veldt]

and for slant it's just infinity because x increases or decreases with y

[trim swan]

it could also be -infinity if it's going downward

but yes

[gilded veldt]

ok I understand now

thank you

[trim swan]

np 👍

[gilded veldt]

.close

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[weak charm]

Can anyone help me with this? I figured out that the amplitude or A equals 4, but i'm not certain how to find b c or d

[delicate sphinx]

The amplitude isn't 4 btw

[weak charm]

Oh...
do you know how to find it properly then?

[delicate sphinx]

This might be helpful

[weak charm]

Wait isn't the amplitude half of the height covered by the graph
And the graph ranges from 5 to -3 which is 8 units?

[rich elm]

its going from 5 to -1?

[weak charm]

OH
i counted wrong 😭

so the amp is 3?

[rich elm]

yes

[weak charm]

Can you help me find the phase shift because i don't really know how to do that

[twilit moat]

do you know what sin(0) is?

[rich elm]

u might find it helpful to find the centre of motion first

once u find the centre of motion, try to shift your graph such that it starts at the centre of motion when x=0

[twilit moat]

^

[rich elm]

im saying centre of motion because im assuming this is simple harmonic question but it doesnt rly matter what u call it

[safe radish]

@weak charm Has your question been resolved?

[weak charm]

0?

[weak charm]

i'm not really sure how to find that though

[twilit moat]

yep

so usually at 0 sin(0) should equal 0

[rich elm]

centre of motion is max + min divided by 2

or the midpoint between the maximum and minimum

[twilit moat]

what you can do to find the shift is through interpreting where the sine graph does hit 0

giving you how much the graph is shifted to the left or the right

[weak charm]

So wouldn't it be (5+1)/2=3

[rich elm]

no

5-1

/2

it should be centred around y=2

[weak charm]

The sine graph hits 0 at 2 pi and -2pi?

[weak charm]

wait im confused how does y=2 help though

[twilit moat]

and 0

0+-2pi

[rich elm]

once u find the centre of motion u should realise that is where your phase shift should shift towards

u have to find a phase shift such that at x=0, y=2

[weak charm]

is the phase shift just pi???

.close

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[woven jewel]

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[woven jewel]

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[river oriole]

uhhhh

[finite igloo]

u have to prove

continuity first

[woven jewel]

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[finite igloo]

does the left and right limit approach the same value there for the function f(x)

and is f(x) = f(a) at point of interest a

[woven jewel]

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[finite igloo]

since the function is not continuous there

it fails to meet the criteria for differentiability

[woven jewel]

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[median vigil]

f(1) = 2

[shadow epoch]

f(1) is 2

jinx @median vigil

[river oriole]

its the x^2+x one

[woven jewel]

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[river oriole]

the second eq is not inclusive of x=1

so we use the first equation

[woven jewel]

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[river oriole]

thats just the formula mate

[woven jewel]

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[river oriole]

no-

[median vigil]

,, f'(x) = \lim_{h\to 0}\frac{f(x+h)-f(x)}{h}

[flat frigate]

cloud

[river oriole]

the h-->0^+ is different

[woven jewel]

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[woven jewel]

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[median vigil]

f(0) does not depend on the sidedness of the limit

[woven jewel]

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[median vigil]

that just means you change [ \lim_{h \to 0} ] to [ \lim_{h \to 0^+} ] the function you are taking the limit of does not change

[flat frigate]

cloud

[woven jewel]

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[river oriole]

? were choosing the limit approaching from the right

[woven jewel]

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[river oriole]

the x^2+x is inclusive of 1

the other eq doesnt

it doesnt have a point at 1

[woven jewel]

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[median vigil]

you are suggesting that the ``left hand derivative'' should mean [ \lim_{h \to 0^+} \frac{f(x+h) - \lim_{x \to 0^+} f(x)}{h} ] but that's not how the derivative is defined, it's based on the value of $f(x)$ not its limit

[flat frigate]

cloud

[woven jewel]

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[median vigil]

because 1 is included in x <= 1 and 1 + h is included in x > 1 (when taking the right limit because the right limit has h > 0)

[woven jewel]

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[median vigil]

the part where we are using the right limit

if we were considering the left limit we would use h < 0

[woven jewel]

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[median vigil]

the right hand limit as h approaches 0 means h > 0, which means 1 + h > 1

[woven jewel]

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[median vigil]

yes

[safe radish]

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[desert pasture]

True, by defn

[hardy lion]

wdym by defn

[leaden pulsar]

almost by definition

there's like a trivial step

[desert pasture]

A set of vectors is said to be orthogonal if the dot product all possible double pairs of the elements of the set is 0

[leaden pulsar]

yes but that information wasn't given as true

only xi . yj = 0 was given

[hardy lion]

the statement also says the sets are orthogonal

i would suggest noting how all 5C2 are accounted for

[desert pasture]

For all i,j

[leaden pulsar]

yes

but be careful

look at what i and j are

[leaden pulsar]

this suggestion also works

you'll probably think it's obvious once you see it

xi . yj, for all i and j

does this cover all possibilities?

[desert pasture]

yes?

[leaden pulsar]

what about x1 . x2

[desert pasture]

No. But that's already given to be orthogonal

[leaden pulsar]

right

so the proof should combine those

so the entire proof isn't a single application of a single definition, ig

[desert pasture]

Got it.

Thanks!

:D

.close

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[leaden pulsar]

😄

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[pale quartz]

Let T be a set of 5 distinct positive integers with a maximum of at most 9. Prove that the sum of the elements in all the nonempty subsets of T cannot all be different.
so obviously this problem is asking for pigeonhole principle, and theres 31 non empty subsets of T, and the maximum possible sum is 35
but the # of actual achievable sums is less than 31, which I need to have to use pigeonhole principle
but im confused on how I can show that the real # of achievable sums is less than 31 without brute forcing each possible combination

[hardy lion]

you only need to worry about subsets of size two, something will go wrong

[safe radish]

@pale quartz Has your question been resolved?

[pale quartz]

What do you mean by something will go wrong?

[safe radish]

Channel closed

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[pale quartz]

.reopen

[safe radish]

✅

@pale quartz Has your question been resolved?

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[naive stump]

hrlp

[naive stump]

hey

would this be correct?

erm I saw u buddy 😭 :

[burnt notch]

Yeah don't worry

[hasty marsh]

f(x) is greater than 0

so you're trying to find y values that are greater than 0

[naive stump]

mhm?

[hasty marsh]

so you're answer is not correct

[burnt notch]

If the interval you wrote is correct, it means that if I pick like x = 0 the function gives a non negative value, right?

[naive stump]

it could be -8 all the way to 6, so it really depends

[burnt notch]

??

[naive stump]

oh yeah mb

[naive stump]

mhm?

im just asking to see if what I wrote was correct

[burnt notch]

I mean, can you explain with your own words why you answered that interval?

[naive stump]

so would I just do everything greater than 0

[burnt notch]

@naive stump

[burnt notch]

What do you mean?

[naive stump]

greater er equal to

[hasty marsh]

the red line is what ur answer is rn

[naive stump]

oh wait but thats not how u do it

[naive stump]

yeah, I know that

[hasty marsh]

so can u find any point on the red line where y > 0

[naive stump]

no??

[hasty marsh]

exactly

[naive stump]

im confused

so how would I do that in an answer

[hasty marsh]

ok, so the question is asking you to find all the points where y is greater than 0

[naive stump]

yeah there are none

or wait

bruuh

😭

[hasty marsh]

do you see the blue lines

[naive stump]

yeahh

I get it

idk why I thought it was the other way around

😭

so dis?

[hasty marsh]

nope

[naive stump]

aww

how come

[hasty marsh]

what u did there was just saying netagive infinity is smaller than -8 and infinity is bigger thn 6

[naive stump]

fuck

😭

[hasty marsh]

the question is asking you to find all points of f(x) where the y value is bigger than 0

[naive stump]

leme run it back

[hasty marsh]

so look at the curve and find where the y values are greater than 0

[naive stump]

yeah im doing that rn

[hasty marsh]

hint: the blue lines

[naive stump]

yeah

ik

[hasty marsh]

u don't need the +-infinity

[naive stump]

ok

[hasty marsh]

so just replace them with x

[naive stump]

just this?

[hasty marsh]

yes

[naive stump]

k

[hasty marsh]

and x<=8

[naive stump]

erm so this?

[hasty marsh]

yes

[naive stump]

ok so this is correct?

[hasty marsh]

yes

[naive stump]

okay, okay just making sure

what about for this one?

[vagrant ice]

yes, that's correct

[naive stump]

ok

[naive stump]

for the previous one I put "," instead of or and it fucked me up a point

why does it matter

[vagrant ice]

that's just what the software wants
it's not really your fault

[naive stump]

then this?

[vagrant ice]

careful

it's $x \le -7$

[flat frigate]

higher's secret twin brother

[vagrant ice]

the other part is correct though

[naive stump]

mk

its because its left to right?

[vagrant ice]

yes

[naive stump]

but doesnt it still make sense?

[vagrant ice]

the arrow to the left just indicates that the function continues like that
you always read functions from left to right

[vagrant ice]

no

[naive stump]

ok

.

[vagrant ice]

say when x = -9, f(-9) >= 0

so when x is less or equal to -7

[naive stump]

alright

thanks

how do I close

since I dont want to leave this open

.close

[safe radish]

Channel closed

Closed by @naive stump

Use .reopen if this was a mistake.

[naive stump]

alr

ty

[vagrant ice]

np

[safe radish]

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[trail otter]

k=2n+3 how to find all n for which k is prime?

[trail otter]

n is from natural numbers

[long bay]

Isn't it theoretically infinite

2n+3 covers all odd numbers and hence all primes except for 2

[severe pond]

not 3

or 1 for that matter

unless you say 0 is a natural number

[long bay]

yeah not 3 either

but it covers all other primes

[trail otter]

Yes it definitely is but is there some notation for n that would produce only primes k

[long bay]

doubt there is

considering prime patterns are really hard to detect

[main mural]

$n \in {\all a : 2a+3 \text{ is prime}}$

[flat frigate]

artemetra
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[main mural]

[trail otter]

Xdd nice

.close()

[hasty wagon]

it's .close 🙂

[trail otter]

.close

[safe radish]

Channel closed

Closed by @trail otter

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[safe radish]

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[fast mulch]

@versed bronze

<@&286206848099549185>

[safe radish]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[mystic matrix]

show working

[fast mulch]

i dont know how to start

[mystic matrix]

I would be setting up a system of three equations to create a function to sub in 5 into.

it is given that the leading coefficients is 3 so you don't need the fourth equation. I imagine there's a better way to go about it though

[real turtle]

I think I have seen a similar q

But I don't see how it wld apply here :(

[peak fable]

nop

[real turtle]

I believe u can do it like this

And then using the leading coefficient fact u can trivially finish off the problem

I believe

Then plug in 5

Bob's ur uncle

[hearty niche]

Hello, I think the result is 122

If you want to know the reason, I can explain about it.

[hearty niche]

No. the Expression is follow.

[real turtle]

William this problem has been solved...

It's 122 from MY method

[hearty niche]

P(x)=3x^4+ax ^3+bx ^2 +cx+d

[sterile lantern]

Didnt get ans i tried

[pine horizon]

!occupied

[safe radish]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[pine horizon]

how did u get that expression?

[real turtle]

William I believe this method requires more than 3 lines considering u need SO many eqs

[real turtle]

Well well well a star I have seen a similar problem before

It just has to be A polynomial that works right and has leading coefficient four

See the motivation

[pine horizon]

yes you deduced it, but how do you know it will work for x=5 too

[pine horizon]

this is an occupied help channel, get your own #❓how-to-get-help

[real turtle]

Astar777

It is quite a trivial solution

[hearty niche]

@sterile lantern Hello, If you want my help, let's meet friend's room

[real turtle]

We notice that the first three terms are double the square numbers

So we create a 4th power polynomial with roots that will give you zero and add 2x^2 to get our desired pattern

Enjoyable creative solution, the beauty of mathematics never fails to stun me

True elegance

[pine horizon]

thats what im saying, how do you know the pattern will hold for x=5 too

[sterile lantern]

William Robert where is it

[real turtle]

Bro

It's not that hard I swear

[pine horizon]

i didnt say it is, im just asking how do you know the pattern holds for x=5 too

[real turtle]

Pretty much

[hearty niche]

The expression given by me and another expression in the problem, you can get the coefficients.

[quick ibex]

To be honest, the owner of this channel has sent their question in a bunch of already occupied channels

[real turtle]

The solution

Is

We have to work out the polynomial

[sterile lantern]

I want help

[real turtle]

Right

So we can work out P(5)

We can work out the polynomial

Using the data

[pine horizon]

doesnt mean you or someone else should do the same

[real turtle]

In the q

As so

[hearty niche]

that is 4-variable linear equations

[quick ibex]

I literally never said that, but the fact is they've sent it in, what, about 5 other channels, and they're still doing it? They're more of a concern

[pine horizon]

yes, which is done by what william said

what you did was just deduce a polynomial based on the pattern

but how do you know the pattern holds for x=5 too

[sterile lantern]

@hearty niche indeed help pls

Bruh auto correct

[hearty niche]

If you want to know about that, contact with me anytime.

[real turtle]

Yes but u can do it quicker w my method

[hearty niche]

HOW?

[sterile lantern]

Dued

[hearty niche]

@real turtle

[sterile lantern]

I am contacting with you @hearty niche

[real turtle]

Bro read my method

p(x) holds for 1,2,3,4

Therefore

It's the correct polymomial

[hearty niche]

I'm sorry. Just my mother have come back. After 10 minutes, Let's contact. I'm really sorry.

[safe radish]

@fast mulch Has your question been resolved?

[peak fable]

brh, you have a giant chalkboard in your house

and yes is correct the polymomial

[safe radish]

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[safe radish]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[split fulcrum]

I have a question, if $h(x) =f\left(g\left(x\right)\right)$ where f is odd and g is even, why is h even? and what happens if f is even and g is odd

[flat frigate]

water beam

[peak estuary]

h(-x)=f(g(-x)) and now use that f is odd and g is even. you want to get back to h(x)

[honest kraken]

+1

[obsidian oracle]

g(-x) = g(x), so the input f receives if you send -x is already g(x)

so in total h is even

if f is even and g odd, then f receives -g(x)

so it's the same as f(g(x))

and once again h is even

[obsidian oracle]

to come back to your example specifically, no matter what type of function f is (can be neither odd nor even)

if g is even

then f composed with g is even

[split fulcrum]

ohhhhh okay

[rich elm]

u can try this with random functions that are simple just to convince yourself

[obsidian oracle]

like e^(cos(x))

that function is even

[split fulcrum]

wait so say f is odd so f(-x) = -f(x), g is even g(-x)=g(x)

h(-x) = f(g(-x))
h(-x) = f(g(x)) so what do i do then?

[rich elm]

f(g(x)) = h(x)

therefore h(-x) = h(x)

[split fulcrum]

o okay

i see

[obsidian oracle]

see that we never had to use the fact that f was odd

so f can be any function at all

wouldn't have changed that "f(g(x))" is even

[split fulcrum]

gotcha

[rich elm]

i did my hsc math adv last year ahead of time and if u ever come across questions like this in the exam, if its not multi choice ,they generally accept diagrams to supplement your answer as well

i bought my paper back and they accept diagram solutions

[solar hazel]

water beam

[split fulcrum]

and if both f and g were odd does that mean h is even or odd ?

[split fulcrum]

o shit u did hsc last year?

are u accelerated or something

[rich elm]

just only math advanced

yeah

[split fulcrum]

damn nice

[split fulcrum]

layla

[obsidian oracle]

yes if both are odd then h is odd

[split fulcrum]

[obsidian oracle]

f(g(-x)) = f(-g(x)) = -f(g(x))

[split fulcrum]

what do u think is the hardest 2u paper?

i might give it a crack tmrw

[rich elm]

james ruse trial paper and north sydney boys

the actual HSC papers are slightly easier than those 2

[split fulcrum]

i heard 2020 hsc was pretty hard

[rich elm]

HSC 2u is becoming a bit more conceptual i think, what i mean by that is i think they favour thinking over just mechanical work

so just be sure u cover all ur bases

[split fulcrum]

people think this years 2u paper is gonna be harder than last years since last years was easy

[split fulcrum]

i rlly suck at finance and stats

[rich elm]

yeah last year was quite easy

[rich elm]

stats and probability should definitely be ur focus

[split fulcrum]

are finance questions all the same format?

they llook pretty similar

like across the years

[rich elm]

finance questions tend to be just sequences and series which are generally kinda the same but just practise reading the wording

[rich elm]

if they are different, it would just be more layers

[split fulcrum]

i see

[rich elm]

like

maybe they change it into 1st 10 yrs the interest rate is XXX, but after 10yrs their account savings inncreased to a higher rate etc.

finance questions are more or less the same once u get sufficient practise

[split fulcrum]

right

okay

[rich elm]

also i would recommend having some understanding of integral inequality or inequalities derived from calculus results although they are very rare to appear in 2U

[split fulcrum]

integral and diff calc is my strong point so im hoping for this years paper to be a lot of calc 🤣

[rich elm]

im aware u are time poor(as i am too T=T) so just do whatever is most time efficient

[split fulcrum]

yeah

sequences and series is fun too except with finance included

[rich elm]

again tho, just be prepared to see less 'mechanical work' and more conceptual questions

at least the shift is pretty clear for 4U

[split fulcrum]

yep

i wonder what this years optimisation question will be

i bet nesa is cooking something gnarly up

[split fulcrum]

ya only 3 kids in my year does 4u and it looks super hard

[rich elm]

depends on teacher and how much time u are willing to dedicate it really

[split fulcrum]

their 4u teacher is pretty good and passionate so im sure theyre fine

[rich elm]

i have a good teacher so i find this subject pretty chill

[split fulcrum]

hes been teaching 4u for many years

calc in 4u looks fun tho

love integrals

the only 4u knowledge i have is integral related otherwise i know nothing lol

[rich elm]

like these kind of questions are kinda more favoured by math advanced now

they aren't hard but just not something ppl would be used to

[split fulcrum]

ive never seen any wuestion similar to that 😭

[rich elm]

give it a crack, u might find it easier than u imagined it to be

tbh a lot of hsc for math at least, is a resilience exercise

[split fulcrum]

hm yeah

i always suck at multiple choice idk why

[rich elm]

if u dont crumble to pressure of being unable to solve a question u will generally do well in math for hsc

[split fulcrum]

ya i think a lot of it is time stress but 3hrs should be enough granted u dont spend too long on one q

[rich elm]

im sure u will be fine

at the end of the day its just one exam and u are done with it

u dont need perfect marks for good contribution for math advanced

[split fulcrum]

yeah true

even more so for 4u right the scaling is crazy

[rich elm]

yep

realistically im spending too much time on 4u but im trying for a state rank (probably not going to get it lol)

[split fulcrum]

dammnnnn nice

sr is crazy

[rich elm]

do u have any teachers in ur school that marks HSC?

[split fulcrum]

is ur cohort really good?

[rich elm]

i would say the top end of my current cohort is quite good

[split fulcrum]

i know one of my teachers is doing legal studies this year but thats about it

[rich elm]

3 of them besides me are contending for state rank as well

[rich elm]

ah ok, my math advanced teacher for accelerated class was a hsc marker so he kinda showed us the marking guidelines for 2023 hsc

u would be surprised how little u could write to get parital marks

so if u cant solve a queston

at least write something

usually even the smallest progression in the question might result u being able to get a mark

[split fulcrum]

yeah thats what my math teacher always tells me

they do mistake carry forward marks too right

[rich elm]

yes

[split fulcrum]

cool cool

[rich elm]

as long as the mistakes aren't egregious

[split fulcrum]

yep

[rich elm]

the general rule of thumb is that if ur mistake doesnt simplify the question completely, then the carry on is accepted

but that pretty much never happens

[split fulcrum]

gotcha

[rich elm]

hmm anyhow, stay on top of probability and stats, ive heard a lot of 2u students find those topics harder than the rest

[split fulcrum]

yep

hope thats not the focus for this years paper

🤣

[rich elm]

im sure u probably know thsc website as well so theres always that

[split fulcrum]

ye

what other subjects do u do btw?

[rich elm]

english advanced, 3u and 4u math, modern history, chemistry (math 2u in 2023 but it doesn't count towards my hsc anymore)

[split fulcrum]

ah i see

nice nice

i dropped chem in y11

[rich elm]

i will be honest, chem has become some brain dead now

[split fulcrum]

lol how do u mean

[rich elm]

more often than not, the question assesses your wording rather than your knowledge

nesa verbs T=T

anyhow, close the channel if u dont have more questions, feel free to add me on disc if u have other questions about 2u math

dont want to hog the channels for too long since theres only 3 other free ones rn

[split fulcrum]

yep

haha

u prepped for eng?

[rich elm]

aight, enjoy rest of ur evening studying

[rich elm]

LOL

i just finishd memrising

english trials was traumatising for me

[split fulcrum]

i think 1 or 2 of our students from our cohort is gunning for SR

or at least has a good chance

[rich elm]

im not cooking for english

[split fulcrum]

😭

[rich elm]

is it a private school>

or selective

[split fulcrum]

public

[rich elm]

ah ok

[split fulcrum]

but our school came in top 10th in the state

[rich elm]

ive generally heard private girl schools especialyl are really good at english

[split fulcrum]

for eng adv last year

[rich elm]

some of the north shore ones have 70% band 6 rate for english advanced

[split fulcrum]

haha yeah

u think nsb is gonna beat ruse again this year?

[rich elm]

from the ruse kids ik, they arne't too sure either

school ranking is baesd on % of students with % of band 6 rates

from what ive heard, ruse has really strong top end

but the bottom end isn't doing too great

[split fulcrum]

ruse is strong all round but they got dethroned because their english game was weak

[rich elm]

its not based on average atar which is a bit silly but thats not really important

how do u feel about hsc tho

are u comfortably hitting ur atar goal (if ur school gives a predicted)

[split fulcrum]

i really want a 90 or above

[rich elm]

nice nice thats a good goal

[split fulcrum]

and its gonna be scraping really close because legal is dead weight like ive actually gotten cooked in that subject so i need to b6 english and b6 physics if i want a chance of getting 90

if i dont b6 both of those it actually might be joever

[rich elm]

what u planning to study in uni (or other things)

[split fulcrum]

get physics degree so i can study astronomy

[rich elm]

also dont feel awkward if u want to discontinue the conversation and go back to ur studies

[rich elm]

🫡 high achiever

[split fulcrum]

haha its allg

[split fulcrum]

wbu?

[rich elm]

im doing math and comp sci

[split fulcrum]

ah yeah nice

[rich elm]

or just only math if i enroll into oxford but i dont think im going to do that well in the entrance test so probably not getting in

[split fulcrum]

comp sci is very popular nowadays

[rich elm]

professionally homeless

[split fulcrum]

wowie oxford

ivy leagues huh

GL

[rich elm]

wrong country but same thing

[split fulcrum]

that sounds tough

[rich elm]

(im not making it)

[split fulcrum]

math dux for last year is now at oxford i think

[rich elm]

nah realistically im not making oxford, my math isn't good enough

[rich elm]

damn thats quite impressive

[split fulcrum]

ya angie wang

[rich elm]

oh what

plc?

[split fulcrum]

yep

i dont go there LOL

sorry

that made it sound like

shes from my school

[rich elm]

nah shes crazy good at math from what ive heard

been told she got perfect score

[split fulcrum]

well yeah sr1 for 4u maths will do that for u ig

and she was like sr2 for 3u or someting

[rich elm]

i tried last years paper and wasn't close to perfect

[split fulcrum]

i believe in u and in the scaling 🫡

[rich elm]

im not stressing too much for hsc

its kinda like whatever at this point

i felt so burnt out after trials

[split fulcrum]

lmao

[rich elm]

been brain dead and autopilot for past month

[split fulcrum]

u can feel burnt out after the hsc now its time to kick the gears up again

🔥

[rich elm]

real

anyhow, im gonna og back to doing english advanced

its the only subject im procrastinating on

[split fulcrum]

haha goodluck

[rich elm]

(anchoring my atar)

[split fulcrum]

are u hoping to b6 eng?

[rich elm]

hopefully but i htink my school gave me predicted to be tail end of b6

like right on the edge between b5 and b6

i got dumpstered in paper 2

for trials

[split fulcrum]

ahh i see

is ur rank good atleast?

[rich elm]

50 💀

[split fulcrum]

out of

[rich elm]

i think 200 some ppl

[split fulcrum]

damn thats a lot of people

[rich elm]

my grade has 380 ppl i think

pretty big school

[split fulcrum]

jeez

i think paper 1 is scarier than paper 2

imo

[rich elm]

opposite for me

[split fulcrum]

i was a lot less well paced in paper 1

[rich elm]

i damaged my hand nerves when i was younger and + i have a bad writing position and habit so longer exams are bad for me

[split fulcrum]

oof

[rich elm]

my hand gets sore really quickly

[split fulcrum]

u can get special provisions no?

[rich elm]

nah

its not severe enough

[split fulcrum]

damn really?

[rich elm]

its not that big of a problem

it just affects my handwriting towards the end of the exam which can be annoying

[split fulcrum]

oph yeah hand writing is a big thing

[rich elm]

realest comment ive gotten from my english teacher was that it looks like a dog's breakfast towards the end of my paper

[split fulcrum]

LMAO

[rich elm]

my conclusio nwas probably 30% legible

[split fulcrum]

my old ancient history teacher was a hsc marker for 10+ years

and he always comes back to handwriting

[rich elm]

hand writing not doing me too hot

i get marker comments on my handwriting after every task pretty much lol

[split fulcrum]

and always urges you to not piss off the marker because the marker will be reading the script on a small screen at 9pm when they just wnna get off work and drink wine

anyways im probably gonna head to sleep early so i can get an early start tomorrow morning

[rich elm]

good night to you then

[split fulcrum]

yep gn to u whenever u sleep

[rich elm]

goodl uck for english advanced if i dont see u around in here

[split fulcrum]

gl with english

[rich elm]

ty, and im gonna need the luck very much so

[split fulcrum]

ill prob shoot a dm for a math question one day as well haha

[rich elm]

please do not give me the most diabolical mod c stimulus

🙏 nesa

[split fulcrum]

mod C stimulus' are always emotion related so keep that in mind

[rich elm]

i will head to sleep after doing a chem paper, anyhow, good night

[split fulcrum]

haha alright

gn

.close

[safe radish]

Channel closed

Closed by @split fulcrum

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• Show your work, and if possible, explain where you are stuck.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[raven sundial]

im trying to get the annualized returns out of this absolute returns but I dont know the second year absolute returns

[raven sundial]

what formula do I do to get the second years absolute return?

    1. Find the Total Return: If you don't have the total return for all three years, calculate it from the absolute return of the first and third years using:

(1+Rtotal)=(1+R1st year)×(1+R3rd year)
(1+Rtotal​)=(1+R1st year​)×(1+R3rd year​)

   2. Solve for the 2nd Year: Once you have the overall return for the three years, you can rearrange the formula to solve for R2nd yearR2nd year​:

1+R2nd year=(1+Rtotal)(1+R1st year)×(1+R3rd year)
1+R2nd year​=(1+R1st year​)×(1+R3rd year​)(1+Rtotal​)​

    Calculate R2nd yearR2nd year​: Subtract 1 from both sides to find the absolute return of the second year.

would these be correct? in solving my problem

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[raven sundial]

nvm haha that was stupid of me

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[fringe pivot]

How does the red one turn into the green one

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[safe radish]

Show your work, and if possible, explain where you are stuck.

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[cobalt sun]

Proof check / advice on multivariate, vector-valued, mean value inequality

[cobalt sun]

some existing questions that i am unsure of are the meaning of nabla_x in the proof statement? i assume it means that we are fixing time and considering the gradient along the spatial coordaintes. furthermore, the main step i am unsure of is the bound from the integral to the supremum. is uniformy boundedness in time enough?

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<@&286206848099549185>

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[steel remnant]

How do I use latex

[steel remnant]

I wanna turn this to a imagd

\Psi(x) = \sum_{n=1}^{\infty} \frac{1}{n^x}

[vagrant ice]

$\Psi(x) = \sum_{n=1}^{\infty} \frac{1}{n^x}$

[flat frigate]

south's secret twin brother

[steel remnant]

Ok thanks

[vagrant ice]

also isn't the standard notation for this $\zeta(x)$

[flat frigate]

south's secret twin brother

[steel remnant]

Yes

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[hearty niche]

Hello

[stiff cape]

Hello

What's your problem

[fair kite]

hello

nvm

[stiff cape]

what do you mean?

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Whats your question

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@random hazel hello

what question?

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hello

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you have occupied a help channel

so you must have a question?

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I have occupied a help channel?

@random hazel ?

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oh you're new here?

There are help channels in this server

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yeah.

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when someone messages

the bot

assigns the channel to that person

they can then ask for help with their question

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so when you said this

this channel got assigned to you

[hearty niche]

oh.. i see.

[random hazel]

to close this

you can do .close

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[hearty niche]

what does it mean?

[random hazel]

you can say hello there

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[lone dove]

If A ∩ B ≠ 0 then is it mutually exclusive or independent

[tight meteor]

Neither

[lone dove]

Then? What is it

How do I know if something is mutually exclusive or not and what about if something is independent

[tight meteor]

Mutually exclusive means that "A ∩ B = 0"
Independent means that P(A∩B) = P(A) * P(B)

[lone dove]

Ohh

I thought if there were elements within A intersect B then they are mutually exclusive

Cuz mutually exclusive means that A and B effect each other right

[tight meteor]

dependent mean that they effect eachother
Mutually exclusive means that they can't happen at the same time

[lone dove]

Ohh ok ok I see thanks

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[frozen pivot]

Ok it's just a general question but I wanted to ask if anyone knows bus stop method of division except the bigger number is outside and the smaller number is inside ?
My teacher did talk about it today but I couldn't take note because of his pacing
It was also kinda confusing in the way he did it
Any help helps

[dusty fable]

Could you give an example problem?

[frozen pivot]

Okk brb

Something like this but you would switch the number placements

And then like get 0s to carry on ??? I got really lost

[dusty fable]

Yeah theres 4 ways of divsion off the top of my head

Firstly are you familar with quotient, remainder, and divsior?

[frozen pivot]

I know remainder and divisor but quotient no

[dusty fable]

Quotient is what you get after dividing. Usually whole number

And you are familar that fractions are just division?

[frozen pivot]

Ohhh

Yes

Defense familiar

Definitely

Keyboard...

[dusty fable]

You dont need to recall the terms but its useful to know, the numerator is the top number and denominator the bottom number

[frozen pivot]

Yeah fractions

[dusty fable]

Ok to make your long divsion easier