help-26

[thorny flame]

Sleepy

[ancient cloud]

how do i continue

@flint stump

[flint stump]

Honestly, I'm lost on this path

[ancient cloud]

💀

[flint stump]

dont 💀 its not like you dont have a solution. You just dont have a solution that you prefer

[ancient cloud]

both path are hard

[flint stump]

your path looks like it needs some clever term added and subtracted to make the things equal, and Im too tired to think what would lead to the solution

[ancient cloud]

both path need some addition or subtraction

<@&286206848099549185>

my question is proof that $\frac{cos2 \alpha + cos2 \beta}{1 + cos2 (\alpha + \beta)} = \frac{cos(\alpha - \beta)}{cos(\alpha + \beta)}$

[thorny flame]

Sleepy

[ancient cloud]

so yall dont need to scroll up

and im stuck at L.H.S=$\frac{cos^2 \alpha - sin^2 \alpha + cos^2\beta - sin^2\beta}{1 + cos^2 (\alpha + \beta) - sin^2(\alpha + \beta)}$

[thorny flame]

Sleepy

[ancient cloud]

@merry hill can i get some help from you?

[merry hill]

i wish i could

but i absolutely suck at trigonometry

[ancient cloud]

aw man

[merry hill]

gonna try tho

okay so we have $\frac{\cos(2\alpha) + \cos(2\beta)}{1 + \cos(2(\alpha + \beta))}$

[thorny flame]

Astar777

[ancient cloud]

correct

[merry hill]

then use this

[ancient cloud]

the thing is i havent learn that yet

and my teacher wont let me use that

[merry hill]

oh damn

[ancient cloud]

wait

are u talking about using the image or the cos2a= 2cos^2a-1

[merry hill]

both

[ancient cloud]

ive learn the cos2a= 2cos^2a-1 but not the image

now i got denominator = 2cos^2(alpha+beta)

and do i turn it into 2(cosacosb-sinasinb)^2?

[merry hill]

idk

[ancient cloud]

nvm i figured it out

.close

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[ivory sorrel]

Prove that sin(x)/x tends to 0 at infty

[ivory sorrel]

so to start the den

defn

so $sin(x)/x<\varepsilon$

[thorny flame]

Veni, vidi, perii

[vestal totem]

you have to use epsilon delta?

[ivory sorrel]

I want to

yes

so another way I was thinking is

[storm hearth]

Oh so you know the squeeze theorem method?

[vestal totem]

Oh I'm not sure I can help with that

[ivory sorrel]

yea

bound between 1/|x|

[vestal totem]

Squeeeze theorem isn't quite epsilon delta though lmao

[ivory sorrel]

so say x>N

so 1/N>1/x

now I also know that $sin(x)<x$

[thorny flame]

Veni, vidi, perii

[ivory sorrel]

ooh

nvm

oh

$1/Nx<1/sin(N)sin(x)$

[thorny flame]

Veni, vidi, perii

[ivory sorrel]

so sin(x)/x<N/sin(N)

So here's the proof

$sin(x)<x$

[thorny flame]

Veni, vidi, perii

[ivory sorrel]

and $N<x$

[thorny flame]

Veni, vidi, perii

[ivory sorrel]

$\frac{1}{x}<\frac{1}{sin(x)}$

[thorny flame]

Veni, vidi, perii

[ivory sorrel]

and $\frac{1}{N}<\frac{1}{sin(N)}$

[thorny flame]

Veni, vidi, perii

[ivory sorrel]

combining them we get

$\frac{1}{xN}<\frac{1}{sin(x)sin(N)}$

[thorny flame]

Veni, vidi, perii

[ivory sorrel]

so $sinc(x)< \frac{N}{sin(N)}$

[thorny flame]

Veni, vidi, perii

[ivory sorrel]

so $\varepsilon. = \frac{N}{sin(N)}$

[thorny flame]

Veni, vidi, perii

[ivory sorrel]

is that it?

[thorny remnant]

what is sinc(x)?

[ivory sorrel]

sin(x)/x

also, hi, convergence

Hello water beam

[thorny remnant]

hello

[opal vault]

you're not trying to find the epsilon here

for every fixed value of epsilon, there exists N such that

[ivory sorrel]

so what I did doesn't help at all?

[ivory sorrel]

right

[opal vault]

also bounding |sin(x)/x| by 1/|x| is not a bad idea

if you want an easy value of N

[ivory sorrel]

can I do that though, did consider that not sure if it's allowed

seems too hand wavey

[opal vault]

?

you want something that looks like A <= C

there is no shame in going through A <= B

and then showing B <= C

this is just transitivity

[ivory sorrel]

$|sin(x)/x|<1/|x|$

[opal vault]

with absolute values tho

and there is no strict inequality

[thorny flame]

Veni, vidi, perii

[ivory sorrel]

Ok so how woul I structure this proof?

[opal vault]

"Let epsilon > 0. set N = (something in terms of epsilon)
Then for x > N, |sin(x)/x|<= 1/|x| < epsilon.
Thus lim(sin(x)/x) = 0"

[ivory sorrel]

got it

thanks

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[balmy pine]

Prove that at 0 =< a, b, c =< 1 the inequality is fulfilled

(1 - a)(1 + ab)(1 + ac)(1 - abc) =< (1 + a)(1 - ab)(1 - ac) (1 + abc).

[hearty turret]

ok i know this is a bit of a lame solution

but you can take (1 + a)(1 - ab)(1 - ac) (1 + abc) - (1 - a)(1 + ab)(1 + ac)(1 - abc)

then you can find the minima of that ^ with partial derivatives

[balmy pine]

I don’t how find min with partial derivatives

[hearty turret]

ah right

[fresh lynx]

Multiple it out for gits an shigs?

[golden blade]

actually cool approach but seems like a ton of work too

[hearty turret]

oh wait yeah i've got it

(a non-dumb solution that is)

multiply out and cancel

then rearrange and ur done

[fresh lynx]

Kapiche ‼️

Only 4 brackets so shldnt be too bad

[hearty turret]

doing that will result with

||a^3bc(1-b)(1-c) + a(1-b)(1-c) >= 0||

[topaz sinew]

@balmy pine Has your question been resolved?

[hearty turret]

did u manage to get this @balmy pine

[balmy pine]

I think that’s not true

I got: 2bc - c - b + a^2b^2c^2 + 1 - bc(c+b) >= 0

@hearty turret

[hearty turret]

unfortunately the intended solution to some inequality questions is literally just to multiply everything out and simplify

ngl i don't really wanna look through what u've done to find out where u've lost the + or smth

[balmy pine]

Ok I will try

[hearty turret]

but it is good practice to occasionally check through ur expanding brackets cus it'll be helpful in competitions

[balmy pine]

Thanks

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[pseudo karma]

After that?

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[golden blade]

That's a good question

[strong sable]

yes

[golden blade]

I think it's too difficult for me

[strong sable]

You always have a bias towards my questions

[golden blade]

No

I read it

I thought

I concluded

[strong sable]

for a min

[golden blade]

I think

Multiply both sides by [ \frac{\partial x \partial y}{\partial z} ]

[thorny flame]

bacc

[golden blade]

Then integrate

I think it's a family of ellipses

[strong sable]

wait

it worked?

[golden blade]

Yea

I think at least for me

I mean you wanted a hint?

[strong sable]

[ y\partial y +(2x+1) \partial x=0]

[thorny flame]

Aya

[golden blade]

yea

Now integrate both sides

it's lowkey like a differential equation

no

[strong sable]

wait wait

[thorny flame]

bacc

[golden blade]

Then I simply did

[thorny flame]

bacc

[strong sable]

wait how can I integrate stuff with partial things, can we rewrite it to smth else

[golden blade]

It just means you end up with a constant C(x) and K(y)

You can integrate a function partially as you differntiate it partially

[strong sable]

no I mean, can we rewrite like this :

$$
y \frac{dy}{dx} + (2x + 1) = 0.
$$

[thorny flame]

Aya

[strong sable]

I have trouble integrating this thing ig

[golden blade]

I just integrated as usually LOL

Maybe was too steps ahead and it's wrong

[strong sable]

can you show it maybe? not usually to me i think

[golden blade]

I will restart

So basically we have
[ y \frac{\partial z}{\partial x} + (2x+1) \frac{\partial z}{\partial y } = 0 ]
I think my first approach was just not really legitimate in terms of math, but I think I know another one.
[ \Rightarrow \frac{\partial z}{\partial x} = - \frac{2x+1}{y} \frac{\partial z}{\partial y } ]

[thorny flame]

bacc

[golden blade]

Now we can integrate both sides wrt x

[ \Rightarrow \int \frac{\partial z}{\partial x} : \dd x = \int - \frac{2x+1}{y} \frac{\partial z}{\partial y } : \dd x ]

[thorny flame]

bacc

[golden blade]

hmm i am a bit unsure actually

[strong sable]

I'm confused, how can we integrate things with \partial xyz, i can only integrate things with dx dy etc

[golden blade]

but this just worked out so well 😭

[strong sable]

I don't understand, why ? why can you integrate partials, did I miss some knowledges?

[golden blade]

The thing is x and y are independent variables actually

[golden blade]

So here y is a actually a constant

But the question is how do you integrate that

integration by parts won't work

[golden blade]

I actually think that's the way to do it

[strong sable]

I spent time searching the answer, the answer is hyperbola

[golden blade]

yeah I noticed I was off by a minus

no actually

[golden blade]

how

[strong sable]

idk...I dont have the soln, I only find the answer

[golden blade]

Can you send?

[strong sable]

It's just a word: hyperbola

[golden blade]

bruh

[strong sable]

if i have the soln i wont ask here

[golden blade]

what

[strong sable]

does this have name or something

[golden blade]

,w plot y^2/2+x^2+x +1/4 = 1/4

[thorny flame]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by adoniszgks

[golden blade]

no

[strong sable]

then i doubt it

[golden blade]

https://math.stackexchange.com/questions/754742/integrating-a-partial-derivative

[golden blade]

No there is truth to it when you integrate a partial derivative normally with dx

The difference is you end up with constant function

[golden blade]

If you differentiate this partially you end up with the same

as f_x

[strong sable]

then what's wrong with this soln, why is it unmatched with the answer

I'm cooked can we ping aslan maybe

[strong sable]

it looks reasonable tho, what on earth wrong

[golden blade]

Either the task is designed that way to when you take the easy route you get an ellipse, but if you take the correct mathematical whatever that route is you get a hypoerbola

see my bias towards my problem is not hate

i have my reasons

I never fucking get nowhere

everything is just new

and each idea that comes up invokes ten new questions

i dont know whats going on

[golden blade]

I mean look at this 😭

It's like wearing socks instead of gloves for your hands but it both works 😭

both keep you warm 😭

@shadow salmon can you help

my friend in need

I am cold I have neither socks nor gloves

[strong sable]

@shadow salmon Are you even online

[golden blade]

I think he is solving the Riemann hypothesis

[limber prairie]

I thought that was Asian 😭

[strong sable]

LMAO

[golden blade]

I thought you can read 😭

[limber prairie]

Thought it was a role

[strong sable]

any smart asian plz just come to help

I'm really cooked

[limber prairie]

I thought so too 😭

we have so much in common

Well Imma read the problem

[golden blade]

and then disappear

like your pookie friend

[limber prairie]

Bro what you talking about

[thorny flame]

bacc

[strong sable]

@neon iron I'm not sure if you can help but maybe take a look

[golden blade]

Miles Morales?

[leaden swallow]

whats going on here? 👀

[strong sable]

none of your bussiness

[golden blade]

☠️

Maybe he was our last hope

[strong sable]

I mean he's pre uni

[golden blade]

Nah don't judge

There are alot Preunis that cook here on the server more than undergraduates or even postgraduates

[strong sable]

ooh I dont know that

[golden blade]

And he had IN

probably indian

[strong sable]

I only know bluemoon is like that

bluemoon disappeared tho

I knew that

[limber prairie]

I was reading bruh

[shadow salmon]

Lmao

Well one way would be to just check what they’re saying

You have three cases

[golden blade]

said that

[shadow salmon]

Let z be such that its level curves are ellipses or hyperbolas and then check if it satisfies the equation

I.e make a so called Ansatz

[strong sable]

but like how can we do in general

and what's wrong with bacc's method?

[shadow salmon]

Uh not really a PDE expert, but in general these are not gonna be nice to solve so there’s a reason you were given the fact that they could of been either; it let’s you make a good assumption about z to check the equation (in separate cases)

With nice enough equations you can transform it using a substitution and ideally you want something left where the partials only depend on one variable, that way you can treat it as a familiar ODE

[strong sable]

@shadow salmon Is this legal

[golden blade]

everything i did is legal

because math itself is irrational

[shadow salmon]

Usually for PDE’s you can do some stuff similar to this when derivatives are viewed as linear operators. But i dunno about that specifically, I don’t even know if you deal with differentials for PDE’s so maybe someone else can answer that.
In any case as far as you’re concerned the ideal approach is to use the information which was given and not solve it in general when it’s not needed

[strong sable]

ok maybe just adopt aslan advice for now

[golden blade]

How would we conclude it's ellipse/hyperbola without solving

[golden blade]

YEAH

dont ask me for help in general haha

[shadow salmon]

Well by assuming z is off either form and seeing if it satisfies the equation as a described above

So for example if I’m not mistaken if z gives a family of ellipses, it’s safe to assume z is of the form (x/a)^2 + (y/b)^2 and then a minus instead when we check the case when we suppose it gives hyperbolas

[shadow salmon]

:(

[golden blade]

I feel dumb

[strong sable]

YOU'RE NOT

[shadow salmon]

I think youre really smart

[strong sable]

YOU'RE SMARTER THAN ME

[golden blade]

It was so obv

[strong sable]

I need your help

[limber prairie]

me too

[strong sable]

Thank you all, really cooked by this q

[shadow salmon]

Feeling dumb in math is a shared experience, if you’re not you’re probably not learning

[neon iron]

[strong sable]

you're late

[neon iron]

Yeah, class

[limber prairie]

Bro sounds smart in every line he speaks😭

[strong sable]

true

whatever I will solve it tmr feel so cooked now

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[elder river]

i managed to show that roots being α, 1/α, β imply that a^2 - d^2 = ac - bd
but idk how to show that a^2 - d^2 = ac - bd imply that the roots are α, 1/α, β

[topaz sinew]

@elder river Has your question been resolved?

[topaz sinew]

@elder river Has your question been resolved?

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@elder river Has your question been resolved?

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[cosmic plaza]

am I allowed to use lhopitals rule to calculate limits of coordinate sequences?

[hearty turret]

you can as in it will give you the right answer

but have u proved l'hopital's rule in lectures yet?

if not, most courses often advise against using l'hopital's rule

cus then you're just using a theorem which u don't know why it's true

[cosmic plaza]

yes we did it but in calc 1

rn its calc 3

i was jus wondering maybe its different for such sequences

[hearty turret]

in which case it's fine

[cosmic plaza]

thanks

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[hard vigil]

hey hwo do i do this? I'm not so sure how to approach it at first, ty!

[neon iron]

what is the question ?

[hard vigil]

Here is an image

[neon iron]

i mean i didnt understand the question

[hard vigil]

me too :/ its complicatioed

i think its like when you expand one of the brackets it gives 89,700x

but i dont understand the rest sorry

[neon iron]

it is 89 700 *x ?

[hard vigil]

no clue

[odd forge]

yes

its 89700*x

[hard vigil]

So what am i supposed to do?

[neon iron]

ah ok

[hard vigil]

Is there actually an answer?

im not that great at maths sry im only 14 lol

[neon iron]

there is k((k+1)*x+(k+2))

idk how to write it in latex

[hard vigil]

,, k((k+1)*x+(k+2))

[thorny flame]

wdg :)

[hard vigil]

like that?

[neon iron]

yes

[hard vigil]

how did u get that?

[neon iron]

it is thz formula to get a bracket

look for example if u replace k by 2

u have

[hard vigil]

ohkok wait so

[neon iron]

,,2(3x+4)

[thorny flame]

skiou_hhd

[hard vigil]

but what am i supposed to substitute

like what number?

[neon iron]

i think the question is that knowing ,,k*(k+1), u must find the constant

[hard vigil]

,,k*(k+1)

[thorny flame]

wdg :)

[neon iron]

yes

[hard vigil]

The constant is which bit again, sorry?

[neon iron]

what ?

[hard vigil]

What bit is the constant?

liek whhat is it

like*

wait never mind i think i got your point, let me write this down sec

[cunning kayak]

what is swagistan (off topic)

[neon iron]

with every bracker u get smthg lik ax+b

,,ax+b

[thorny flame]

skiou_hhd

[hard vigil]

a guild

[hard vigil]

right

[neon iron]

country of swag 😎

[cunning kayak]

okay

how do u get that badge

[neon iron]

so u see what i mean wgd ?

[hard vigil]

yes i do

[hard vigil]

click the icon and then press requeest to join or sm

just google discord guilds and ull understand

[cunning kayak]

oh okay

[hard vigil]

im doing it rn @neon iron ty, one sec

[cunning kayak]

thanks, peace out

[neon iron]

k

[hard vigil]

first i expand @neon iron ?

[neon iron]

precise what u mean

[hard vigil]

I just expand the brackets first right ?

Both of the terms, that they're talking about in the question?

[neon iron]

wait maybe i misunderstood the question

ill try smthg 2 sec

[hard vigil]

k

[neon iron]

ok good

[hard vigil]

i think i did it, i might be wrong, i got some help though i think it could be wrong though

[neon iron]

so u know the constant made by the product of the coefficient before the brackets and the term before the x

[hard vigil]

yea

[neon iron]

i dindnt rly understand what u did

[hard vigil]

lme ask ai wait lol

Does that make sensee?

[neon iron]

is the coefficient before the bracket given in your solution ?

[neon iron]

bof bof

[hard vigil]

im confuding myself tbh lol

im sorry for wasting ur time

im gonna head off to bed ill take a look at it tmrw

😭

[neon iron]

wait im checking

and i have lotta time to waste

the good one is

,,299(300x+301)

[thorny flame]

skiou_hhd

[neon iron]

because

,,299*300=89 700

[thorny flame]

skiou_hhd

[neon iron]

and

,,299*301= 89 999

[thorny flame]

skiou_hhd

[neon iron]

@hard vigil

[topaz sinew]

@hard vigil Has your question been resolved?

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[green orchid]

I don't understand why the interval is only pi/2 to 3pi/2

cuz isnt it also defined from 3pi/2 to 5pi/2 for instance

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@green orchid Has your question been resolved?

[green orchid]

.close

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[vernal lagoon]

Can someone explain where I went wrong?

I checked the constants with the bot here and I think they're right

and this application does take unsimplified answers

for example:

[topaz sinew]

@vernal lagoon Has your question been resolved?

[vernal lagoon]

<@&286206848099549185>

[vestal sigil]

the denominator of the integrand is x(x+8)^3

you did x(x+3)^3

[vernal lagoon]

💀

[vestal sigil]

lol

[vernal lagoon]

how did I not see that

[vernal lagoon]

Thanks for seeing that LOL...I am to slow to see that

.close

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[neon iron]

can someone pls help no clue how to ans this one

[fair thorn]

you found out the x-intercept correctly

for the y intercept simply set x = 0

because at x = 0 you arrive at the y-axis

[neon iron]

but y^2 here

[fair thorn]

yeah

you get y^2 = 16

[neon iron]

how do i find the smaller y and larger y values

from the graph

when i set x = 0 i get y^2=16

[fair thorn]

yes...

so what's the

problem

you don't know how to solve for y?

find 'y' such that y times y = 16

that is, the square of y is 16

[cursive patrol]

?

[fair thorn]

??

OH SHOOT

AHAHAHAH

tysfm mqnic

[fair thorn]

yeah mqnic's right you didn't find the x-intercept correctly either

set y = 0 and solve for x

[hollow drum]

You don't even need to do that

It says graphically estimate the intercepts

So she would just use the graph

[fair thorn]

"verify your results algebraically"

[hollow drum]

You verify by plugging the result back into the equation

[topaz sinew]

@neon iron Has your question been resolved?

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[woven hatch]

Hi

[woven hatch]

I’m prepping for the British maths Olympiad and was doing some simple questions

1234x5678 is divided by 5 what is the remainder?

I’ve put it in a calculator and it’s remained 4 but the mark scheme says it’s 2

[thorny remnant]

it is 2

[restive inlet]

what calc are you using?

[woven hatch]

Casio fx cg 50

[restive inlet]

what exactly are you putting into the calc

and what outputs are you getting

[woven hatch]

1234x5678

ANS/5

[restive inlet]

that doesn't give the remainder if that's all you're doing

[woven hatch]

It gives 1401330.4

[restive inlet]

the stuff after the dp isn't the remaidner

[woven hatch]

What is it?

[icy sky]

its the remainder/5

[woven hatch]

Oh I see thanks

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[unkempt eagle]

I know that one rule of absolute value is that it can't be equal to a negative number. But, is it possible to solve this expression? I'm not sure. Please, help me.

[spiral oak]

Need help determining some values… just want to double check answers

[restive inlet]

what do you think the answer should be?

[hearty turret]

!occupied

[topaz sinew]

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).

[spiral oak]

Super easy, but I haven’t done this math in like 2 years, so it’s all foggy

[hearty turret]

you can post in here

[spiral oak]

Okay

[hearty turret]

but yeah there are no solutions to this equation

you said in another channel that ur teacher said that there are solutions to this

in which case can u ask them what they're smoking?

[unkempt eagle]

The problem is that she we'll give me a bad score anyway

[hearty turret]

that's unfortunate and idk what to do about that

[hearty turret]

but yeah the answer is there is just no way for that to have a solution

[unkempt eagle]

I send her a message but never get answer

Thank u

[hearty turret]

even if u go "well actually || here just refers to any metric" a defining property of a metric is that it's always non-negative so there is just no way to rectify it

[unkempt eagle]

Idk what to do with those kind of teachers

[hearty turret]

when u get to university you'll get lecturers who actually know maths

it's kinda unfortunate in school but i just kinda learnt to just deal with it until i get to uni

[unkempt eagle]

Yeah. Thank you so much

[hearty turret]

like there was a question in one of my tests that was like "what's the range of this function"

i gave it like {x | x >= 5} or smth like that

but my teacher marked it wrong and said ranges are always y

[unkempt eagle]

Oh

[hearty turret]

but like {y in R | y >= 5} and {x in R | x >= 5} are the same set

anyway hf!

[hearty turret]

if you do find out what sort of nonsensical answer she thinks there is can u let me know cus i'm curious

[unkempt eagle]

I'll tell u

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[brittle breach]

What is the final answer for these 2

[sudden temple]

!noans

[topaz sinew]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[terse abyss]

!status

[topaz sinew]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[brittle breach]

7

!status

[topaz sinew]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[brittle breach]

!noans

[topaz sinew]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[brittle breach]

.close

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[barren sigil]

How do i solve sin 2x + sin 3x = 0

[carmine marten]

You incorrectly factored out the sin x

It should be $\sin x\left(2\cos x+3\cos^2x-\sin^2x)=0$, not a cube on the sine

[thorny flame]

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

[barren sigil]

Thank you

How do i close

[carmine marten]

.close

[topaz sinew]

Channel closed

Closed by @carmine marten

Use .reopen if this was a mistake.

[carmine marten]

wtf

I was not aware I can close for others

[loud oasis]

it is a power granted to helpfuls, to be used with discretion

[barren sigil]

Wait

I got another question

[carmine marten]

.reopen

[topaz sinew]

✅

[carmine marten]

ig that answers my follow up question of whether I also have reopening ability

[barren sigil]

Whats wrong with last answer

?

[carmine marten]

why do you think there's something wrong

[barren sigil]

According to my book

The only answer is 22,5 + 180 n

The last one is wrong matbe

Maybe

[carmine marten]

no -67.5 + 180n degrees also works

[barren sigil]

Is my book wrong then?

[carmine marten]

probably, by which I mean yes unless there's something extremely strange going on

[barren sigil]

Cuz they saying only 22,5 is riggt answer

Okay

Last quiestion

Whats wrong?

The answers are wrong

The book says

[wispy pier]

What question?

[barren sigil]

Sin 2x

• sin 3x

=

0

[wispy pier]

sin2x + sin3x = 0

Okk let's check with Wolfram

[barren sigil]

Ok

[wispy pier]

,w solve sin2x + sin3x = 0

[thorny flame]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by xor_11

[wispy pier]

If you're calculating principal values just put n = 1

[barren sigil]

Huh?

I didnt understand

[wispy pier]

What?

[barren sigil]

This

But what have i done wrong

[wispy pier]

Wait let me check

[barren sigil]

Okay

[wispy pier]

sin3x = 3sinx - 4sin³x , there's a formula , you could have used

[barren sigil]

Well

We havent learnt that formula

And they want us to do it by sin 3x = sin 2x+x

[wispy pier]

Okk

[barren sigil]

This

[wispy pier]

Ok

[barren sigil]

Yes

[wispy pier]

sinx = 0 , this gives x = n*pi

[barren sigil]

Lets solve in degrees

Yes it gives 180 n

[wispy pier]

Why only 180 ?

[wispy pier]

0 ?

[barren sigil]

Well it gives x= 360n

And

180 + 360n

But its same as 180 n

Its taken

Go to a room thats not taken

[lethal hornet]

okay thx

[barren sigil]

Np

[wispy pier]

4t²+2t -1 = 0
or (2t +1/2)² = 1+1/4 = 5/4
or 2t + 1/2 = ±√5/2

[barren sigil]

Huh

[barren sigil]

What do u mean

[wispy pier]

Yours is correct , I don't have copy so just doing rough work

[barren sigil]

Ok

Did u find what i did wrongv

?

Hello?

<@&286206848099549185>

[topaz sinew]

@barren sigil Has your question been resolved?

[blissful lynx]

What’s your question @barren sigil

Can you put in the chat box again

[topaz sinew]

@barren sigil Has your question been resolved?

[tropic osprey]

derivative of ln(2y+1)^5?

isnt the formula g’(x) / g(x)

so 5(2y+1)^4 • 2 = 10(2y+1)^4 = g’(x)

over (2y+1)^5 but its wrong?

[topaz sinew]

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[silk jetty]

0.37 for 3 ounces

[silk jetty]

How do I calculate for 1 ounce

Is it just the 3 ounces divided by .37

$.37 cents for 3 ounces

[loud oasis]

so we have an equation
$0.37 = 3 ounces
we can multiply or divide both sides by any number to change the quantities involved

[silk jetty]

I'm trying to figure this out

Which one is cheaper? I think I just multiply each ounce by the $ amount

[onyx cloak]

you could try simplifying fruit b to

15/4

[loud oasis]

we are trying to find $/ounce

[silk jetty]

fruit b is 3.75 ounces

I think I simply have to find how much each costs

[loud oasis]

when we want to know how cheap something is, we want to know its price per ounce. mathematically that means ($/ounce), (price in $)/(weight in ounces)

[silk jetty]

Hm, ok

Ok, think I got it thanks.

.close

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[graceful leaf]

so like if a word problem

It would be negative right?

g = -9.8

[loud oasis]

well you have to pick which direction is positive. is up positive, or is down positive?

[graceful leaf]

up

[loud oasis]

so then acceleration due to gravity is negative because it's always down

[graceful leaf]

ok thnx

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@graceful leaf Has your question been resolved?

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[velvet atlas]

Im struggling currently with figuring out to get the domain ive watched multiple youtube videos but i can't seem to understand like for the first problem the division one (f/g) (x) ive set up the fraction but dont know what to do afterwards 😦 can someone pls explain

[snow basalt]

finding f/g is not the hard part, there's not really anything you need to do after just writing out the fraction unless your teacher expects you to rationalise the denominator, in which case you should do that

after that, you should think about what needs to happen for the square root to be defined (whats under the root > 0)

and what needs to happen for the fraction to be defined (denominator nonzero)

find the x for which both of those things are fulfilledf

[velvet atlas]

Okay but when you say what needs to happen for the square root to be defined what do you mean? Is there any way you could give an example?

[snow basalt]

suppose f(x)=sqrt(x+3). Then, the domain of f is all the x for which sqrt(x+3) is defined. You can't take the square root of a negative number, so you need x+3 >= 0 which is just x >=-3, and the implied domain for f would be [-3, inf)

[velvet atlas]

Ohhhhh okay that makes a lot more sense thank you

[snow basalt]

no worries

[topaz sinew]

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[hushed nova]

How can i do parts b and c? i already did part a

[hushed nova]

(grade 12 advanced functions)

[topaz sinew]

@hushed nova Has your question been resolved?

[frank jay]

Let $v = \frac{\Delta x}{\Delta t}$.

1. The average over a given interval is the sum of the velocities for each part divided by the number of parts.

2. For the graph of $v(t)$ vs. $t$, you should find the constant positive value of $v$ for the interval between levels 5 and 6. The speed should drop to a lower constant positive value for the interval between levels 6 and 7. At level 7, the graph should drop to 0 for 2 hrs. Find the constant positive value of $v$ for the interval between levels 7 and 8, and 8 and 9. Then, for the interval between levels 9 and 10, $v$ is some positive constant most of the way, before increasing at some rate.

[thorny flame]

S'Mor

[frank jay]

@hushed nova

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[snow valve]

hey can someone help me with this problem

[snow valve]

i don't know what part b is asking me to do

[fickle needle]

what's a derivative

[snow valve]

the tangent of the slope i think

[fickle needle]

essentially the slope of the tangent line at a point of a curve

so we gotta find what this specific tangent line might be written as an equation

[snow valve]

do we just plug in a?

[fickle needle]

into what

[snow valve]

f(x)

to find the slope

[verbal crater]

not f(x)

[snow valve]

f'(x)?

[fickle needle]

yes

remember definition of derivative f'(x)

[snow valve]

ah alright

[fickle needle]

so what'll u get?

[snow valve]

x=-1?

m=-1

[fickle needle]

yeah!

ok cool

so we have the slope at that point

[snow valve]

is that it?

[fickle needle]

what other information might be important to finding this equation?

[snow valve]

y?

as in finding y?

[fickle needle]

the original function, yes

what might this output?

[snow valve]

-3

[fickle needle]

coolio

now there's one last bit of information

what might that be

[snow valve]

y int?

[fickle needle]

not necessarily

we're trying to find the tangent line to the curve at a given point

we know where to place it on the y-axis, y=-3

and we have the slope, -1

isn't there another axis we have to consider?

[snow valve]

x axis?

[fickle needle]

yes

so we need to find the x value for which the line will be at

[snow valve]

how do we find that?

[fickle needle]

what value were you plugging into f(x) and f'(x) to get -3 and -1 respectively?

[snow valve]

0

[fickle needle]

so that must mean..

[snow valve]

a=x?

[fickle needle]

yes

[snow valve]

ahh alright

[fickle needle]

more specifcally x = 0

[snow valve]

what do i do with the x though?

[fickle needle]

great! now you've got everything you need
now you just have to put it all into a certain form

[snow valve]

usually the x isn't useful in slope intercept

[fickle needle]

i'd suggest working with point slope form

since we have our slope, y-coord and x-coord already

then you'll just have to convert it to slope intercept form through algebra

[snow valve]

y-1=-3(x-0)?

[fickle needle]

careful with the y coordinate

[snow valve]

y+1?

[fickle needle]

yeah since y-coord = -1

so putting it all into slope intercept form, what do you get as your equation?

[snow valve]

y=3x-1

[fickle needle]

good job!

wait

you forgot the negative on the slope

[snow valve]

oh yes

y=-3x-1

[fickle needle]

ding ding ding

[snow valve]

it didn't work

oh i think i got hte slope wrong

[fickle needle]

oh we mixed up f(x) with f'(x)

[snow valve]

yeah

[fickle needle]

just switch those 2

[snow valve]

y+3=-1(x-0)

y=-1x-3

[fickle needle]

see if it's right

[snow valve]

yippie 🥹

[fickle needle]

awesome sauce

hope i was a good help

[snow valve]

you were thank you

[fickle needle]

np bro

[snow valve]

quick questino though, it would still apply to this right? just plug in the values?

[fickle needle]

pretty much the same thing

[snow valve]

alright

[fickle needle]

u got this

[snow valve]

thank you

f' = m and f =y right? or am i mixing it up

correct setup?

[topaz sinew]

@snow valve Has your question been resolved?

[fickle needle]

yeah

[topaz sinew]

@snow valve Has your question been resolved?

Channel closed

Closed by @snow valve

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• Show your work, and if possible, explain where you are stuck.
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[orchid charm]

Need help with part 2

[orchid charm]

I got t = 2.667 sec, Vi in the y = 13.07m/s

And the velocity when it hits the other wall is 14.4m/s

Tried to use inverse cos to find the angle using my Vi in the x and the velocity when it hits the other end

If you can help me would appreciate a ping

[ornate osprey]

Tan inverse of (Vy/Vx)

[orchid charm]

Tried that too

[ornate osprey]

What value did u use for the Vx ?

[orchid charm]

Isn't it constant?

[ornate osprey]

Yes 6

[orchid charm]

6m/s?

[merry hill]

yes

[ornate osprey]

Yup

And Vy ?

[orchid charm]

Yeah I used it

13.07m/s

For vy

[ornate osprey]

Okay

[orchid charm]

Got 65.3deg

This site accepts between 1% of the answer

And tells me if I am close

But it hasn't like told me I'm close so idk what's going on

[ornate osprey]

What if the unit is not degree but rad

[orchid charm]

Nah I'm using desmos

[ornate osprey]

Okay

[orchid charm]

It's in deg form

[merry hill]

u have to input answer in degrees or radians

[orchid charm]

Yeah I know

I have already used the same calculator and gotten deg questions right

Like a few min ago no changes made

Not a deg/rad problem

[merry hill]

are u sure the y value is correct

[orchid charm]

Yes because the system already says it's right

Wait

I actually don't know

My initial velocity in the y was 13.07m/s

But I don't know how to solve for my final Y velocity

[merry hill]

it would be the same

at same height

magnitude would be same

[orchid charm]

Oh yeah

But then I'm still getting the wrong answer

[merry hill]

idk

maybe issue in the system's answer

i dont see any problem

[orchid charm]

Yeah maybe

I genuinely hate this site

And I still gotta use it for a year

Idk guess I'll close channel

.close

[topaz sinew]

Channel closed

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• Show your work, and if possible, explain where you are stuck.
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[thorny trout]

plz help me

[sudden temple]

.pin

not implemented

[sudden temple]

have you tried anything?

[thorny trout]

nope

[sudden temple]

,w is 2011 prime?

[thorny flame]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by seventysevensquare

[sudden temple]

okay

[thorny trout]

okay , thanks

[sudden temple]

noice

[thorny trout]

.close

[topaz sinew]

Channel closed

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[sudden temple]

you got the idea?

[topaz sinew]

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[charred wyvern]

please help in proving them congruent

i am not able to

here angle BAD and angle ABE are equal

ap = bp since p is midpoint

now what do i need for the third point

i dont get it

<@&286206848099549185>

<@&268886789983436800>

[vestal totem]

holy

[magic raft]

Do not ping moderators for homework help

[vestal totem]

do not ping helpers immediately either

[magic raft]

And you should be waiting

Yeah

[charred wyvern]

sorry

im sorry

im new to this server

i wont do it again

[charred wyvern]

please help

[charred wyvern]

hello

please help

i seriously dont get it

[nimble garnet]

bruh

[vestal totem]

well !status

[charred wyvern]

what?

can anyone please help??

#help-26

.close

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[topaz sinew]

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[night imp]

<@&268886789983436800> ^^

[empty spoke]

muted for spamming links

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[worldly lake]

Can someone explain why this true only for primes?

[worldly lake]

This is a theorem on page 51 of the book Modern Olympiad Number Theory, and I can't seem to find where the proof uses the fact that p is prime.

[hearty turret]

it's only true for primes cus a has an inverse mod p

imagine if p=4 and a=2

and see what happens then

[worldly lake]

I thought it's assumed that a and p are coprime

[hearty turret]

oh right yeah they do specify a and p are coprime

[hearty turret]

then this is less of a case that it's only true for primes and more that they're only proving it for primes

[worldly lake]

that's also what I thought initially

but then I saw this page

Note that the only fact we used in the proof was that a and any element in S is coprime to p

[hearty turret]

yeah so i think they've stated the theorem as they have because that's how they stated it for p prime

[frail reef]

yeah i think all you need is that a is coprime to n

[hearty turret]

notice that S here does not contain 0

[frail reef]

to ensure that it has an inverse mod(n)

[worldly lake]

Ok so to confirm, this is true for all a and p, as long as gcd(a, p)=1

[frail reef]

i believe so, yes

[worldly lake]

Ok thanks guys

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[hearty turret]

i don't think this is relevant

(any element of S is coprime to p)

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[gleaming panther]

hi

[gleaming panther]

is the answer to this 8.4x 10^9?

[left tiger]

yes

[gleaming panther]

ok

then if its divide is ti same thing?

like for example

(4.2 x 10^6) divided by (2 x 10^2)

Would that be 2.1 x10^3?

[torpid sparrow]

No

10^4

Not 3

[trim ermine]

If we multiply, the powers add on
If we divide, the powers subtract

[gleaming panther]

Aur yes

Okay thankss

.close

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[trim tapir]

.help

[topaz sinew]

Commands:

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Type .help <command name> for more info on a command.

[trim tapir]

.1+1

[topaz sinew]

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[orchid agate]

Does anyone have advice on how to properly type this?

[fair thorn]

ln 1 = 0

[thorny flame]

ren

[orchid agate]

OH right, 10^0 = 1, yeah?

[fair thorn]

i mean -k

[sudden temple]

11^2 = 121

[merry hill]

it said only to expand tho

[sudden temple]

probably that too

[orchid agate]

it did say to expand as much as possible, not to solve it

[fair thorn]

still

you should absolutely change that to -2k ln 11

[orchid agate]

like .. that?

ah.

I see, I'm sorry for the trouble

11^2 = 121.. that makes sense 11 * 11

[fair thorn]

nw

[orchid agate]

I'm surprised I didn't see that

Alright, this makes sense to me

Thank you all for the help

[wary imp]

I can’t send a pic to this room

?

[orchid agate]

.close

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[fair thorn]

??

if you need help

#❓how-to-get-help

move to #help-3

[wary imp]

Okie

Guys How do I find the values of x in the problem f(x)= Under the root X square minus two X plus ten

[fair thorn]

move to #help-21｜아리스킨충1

please

[wary imp]

Ok sorry

[topaz sinew]

Available help channel!

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Remember:
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[calm trellis]

can sum1 help me

[calm trellis]

hello

[woeful drift]

!da2a

[topaz sinew]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[calm trellis]

can someone explain me why does -3x + 2x result to -x

[dusky sentinel]

ok

so

-3x+2x

the -3x has a higher value then 2x

meaning it subtracts more then the 2x and goes into the negatives

but since in math it is not necessary to put the -1 it should be

-x also represents the same

so it would just be -x