help-23

[rugged marsh]

can someone help me this is complicated math

2 people struggled helping me

[viscid garden]

Cuz they didnt know the definition of rays ☠️

[rugged marsh]

yea ik complicated math

this is very hard stuff

its alr though I ask some 1 else cuz u dont know

[viscid garden]

Bro if you're calling this hard, then you haven't seen actual math ☠️

[rugged marsh]

SOMEONE PLEASE HELP ME I WASTED SO MUCH TIME. SOmeone smart please help me

[rugged marsh]

don't talk bro

u couldent solve this

[viscid garden]

BTW, I can help you with other parts...

Like I dunno much about rays..

But I know else...

trust

[ionic venture]

A ray originates from a point and goes to infinity in one direction

[rugged marsh]

thank you bro

so is LA a ray

and LB

and DE?

@ionic venture

[rugged marsh]

cap

[rugged marsh]

cap

[viscid garden]

Can you tell me 3 collinear points?

[rugged marsh]

do u know what collnear is

[viscid garden]

Yeah

[rugged marsh]

its E, D, C

[viscid garden]

Yep

How about 3 coplanar points?

[rugged marsh]

thats ez

[ionic venture]

I was on a call

[rugged marsh]

vc

[viscid garden]

tell

[ionic venture]

What do you wanna ask?

I told you the definition so do you want a example?

[rugged marsh]

ok

[rugged marsh]

no

[ionic venture]

Check your ans?

[rugged marsh]

yes

is CE a ray

LA

GH

[ionic venture]

Yeah

[rugged marsh]

is LA a ray?

@ionic venture

[ionic venture]

Yeah

[rugged marsh]

is GH a RAY?

@ionic venture

is LB a ray?

and 3 coplaner points is E D C

?

[viscid garden]

But I was confused that doesn't LA have both end points infinite?

[ionic venture]

Yeah

[viscid garden]

yeah

[rugged marsh]

@ionic venture can u do super hard question

this is very hard

will ube able to solve and teach

[ionic venture]

It'd depend on how you denote

[viscid garden]

I mean, in geo we always would ahve cosidered it as a line...

[ionic venture]

If it's LA with a arrow on top then a ray

[viscid garden]

I dunno why it's a ray in this case...

[rugged marsh]

@ionic venture help

[ionic venture]

Bro stop spamming that

[rugged marsh]

ur the only smart 1 here

@viscid garden kinda stupid ngl

[viscid garden]

shut up! you're the only dumb one

[rugged marsh]

be quiet

[viscid garden]

my point is valid! We never would say LA is a ray if we do geometry

[rugged marsh]

we would

lol

[ionic venture]

TE and EK are equal so equate their lengths

[rugged marsh]

make them = to each other

?

[ionic venture]

You're probably talking in higher maths , no?

[ionic venture]

Yeah

[viscid garden]

Olympiad math

[rugged marsh]

bro u do pre-cal

u dont know shit

[ionic venture]

Yeah we won't do that I guess but the question here is about rays

[viscid garden]

Yeah you better help him... This guy is mad af

[rugged marsh]

@desert swallow is pulling up

[ionic venture]

He's right, and he's not dumb

[rugged marsh]

bro u wasted 40 min of lines telling me a ray i snot a ray

[ionic venture]

Equate them

[desert swallow]

It's pretty weird tbh. You could define a ray on a any line given a some point on it and a direction

[ionic venture]

Yeah

[rugged marsh]

-3x+29=7x+4

20=9x+4

16=9x

[desert swallow]

Idk any way of uniquely denoting a ray in this case

[viscid garden]

Wait so is DC a line segment then?

[ionic venture]

But it's not on the level where we concern ourselves about this

[rugged marsh]

yes

it is

likebro

[viscid garden]

CD is a ray and DC is a line segment... This is just directions...

[ionic venture]

IF I remember correctly, it'd be denoted with an arrow on top

[ionic venture]

Yeah and?

[rugged marsh]

x=16/9

now u do for y?

[desert swallow]

Oh okay, that's one way you distinguish them

[ionic venture]

Yeah

[rugged marsh]

4y square-4=-5y+2

[ionic venture]

I don't remember if I'm correct as we also use arrows for vectors

[desert swallow]

Yeah. I guess you would have to denote the ray from D passing through C another way

[desert swallow]

Yes, we do

[rugged marsh]

4y square+5y-6=0

[viscid garden]

Yeah... Its so confusing other wise...

[desert swallow]

I've never seen any standard notation for defining rays tbh

[rugged marsh]

@ionic venture do I factor?

?

[ionic venture]

I saw them in like 5 grade or something

[ionic venture]

Yeah

[desert swallow]

Maybe "standard" is the wrong word. I would interpret AB (arrow on top) as a vector unless specified otherwise. Maybe in an actual question, it would be stated as "ray AB->"

Much more clear

[ionic venture]

Well that's what I was taught so idk

You're right though

I'd assume it as a vector too

[safe radish]

@rugged marsh Has your question been resolved?

[safe radish]

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[uneven veldt]

The frontward implication is by definition of bounded but, for backward implication, I was thinking of taking a cauchy sequence in A and showing it will be convergent, I am facing an issue in that specifically, please also let me know if approach is incorrect

[uneven veldt]

<@&286206848099549185>

[junior smelt]

What’s the definition of bounded you have?

And by definition, Banach spaces are complete, aren’t they?

[uneven veldt]

yes

[obsidian oracle]

so... what is it?

[uneven veldt]

Definition of bounded: For a metric space (S,d) for all s,t belonging to S, there exist a r>0 belonging to real numbers such that d(s,t)<r

[obsidian oracle]

the "exists r > 0" should be before "forall s,t"

and what is d in a Banach space?

(or any normed vector space)

[uneven veldt]

|v| ig

[obsidian oracle]

?

a distance takes 2 elements as input

[uneven veldt]

d(x,y) = |x-y| for x,y in normed linear space

[obsidian oracle]

alright yes

so what implication seems the easiest for you?

[uneven veldt]

frontward

[junior smelt]

Which you said you did in the original post (I’m happy taking your word for that)

For the backward direction, you don’t really need the completeness to be fair: assume you have a K such that norm{x} <= K for all elements x of the set A, and assume that you’ve taken two x, y from A

[junior smelt]

You’ve said that this is the metric induced by the norm, can you find some constant that bounds this above from that?

[safe radish]

@uneven veldt Has your question been resolved?

[obsidian oracle]

(hint: some form of inequality with norm)

[safe radish]

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[nocturne cloak]

im not sure how to solve

[safe radish]

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[lean otter]

is this right

[fathom jewel]

It's rather f(-x) = -(1+x)/(1-x)

[lean otter]

im not following

[fathom jewel]

which is the same as (1+x)/(x-1) = (x+1)/(x-1) = 1/f(x)

If you factorize the minus

[lean otter]

do you mean this

[fathom jewel]

from here you get -(x+1)/(1-x)

[lean otter]

ok yea

i see it

so that is

so that's 1/f(x)

?

[fathom jewel]

ye

[lean otter]

alright

thanks

.close

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[coral rapids]

Hello, here is an integration by parts question where i dont know where i'm going wrong... Can someone please help?

[craggy sedge]

how did you x/x^2+1?

[coral rapids]

because I need the integral of v(du/dx)

[craggy sedge]

how is ln|1/2|=2ln|2|?

[coral rapids]

omg

i thought it was ln(1/4

thank youu

[craggy sedge]

np

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[signal kiln]

Hi, I need to solve this differential equation : x'(t) = 1 + x²(t), with x(0) = 0. I also need to make sure the solution is on the biggest interval possible.
I don't have much more information, and it's the first time i'm asked to solve a non linear differential equation

(also is there a LaTeX bot on this server maybe ?)

[junior smelt]

$x'(t) = 1 + x^2(t)$, yes

[flat frigate]

@junior smelt

[signal kiln]

nice, good to know

[junior smelt]

And do you know other types of differential equations?

[signal kiln]

No, i've only ever solved linear first order (similar to : y' + fy = g, where f and g are function), or second order linear with constant coefficients (like : ay'' + by' + c = f, where a b c are real numbers and f is a function)

[junior smelt]

Have you not done any that are of the form y' = f(x) * g(y) then (with f, g being functions)?

[signal kiln]

no, y and y' were never in functions in the problems i've encontered this far

maybe i'm supposed to learn how to solve this kind of equations next class, but the teacher doesn't give us the solution if someone doesn't go to the board to solve the problem, so I need to at least try it myself

[junior smelt]

That's fair enough, then a related question: do you know what differentiates to give you y' * g'(y), where as before, g is a (differentiable) function?

[signal kiln]

yes, that's the chain rule right ?

$(f \circ g)' = g' \times (f' \circ g)$

[flat frigate]

Grui

[signal kiln]

Do I need to make that form appear somehow ?

(Also sorry if my english is not too good, I'm french and I don't usually talk about math when I speak english haha)

[junior smelt]

Yep, chain rule backwards y' * g(y) can be gotten by differentiating g(y)

[signal kiln]

ooooh maybe i see where you're going with this

if I multiply by 2t on both sides, i can try to integrate that ?

wait no

2x

[frozen marlin]

tbh your english is pretty good

[signal kiln]

ok i'll stop trying to guess and let you explain XD

[junior smelt]

And, well, the idea is that for differential equations of this form, you can split them up (separable differential equations) so that you have the stuff that depends only on y with the y', and the stuff that depends on x only on the other side

Then, you can use the fact you know the chain rule backwards to get the antiderivative of the side you'd have rearranged for (so trying to find an antiderivative of y' * 1/g(y) of course), and the other side is just "normal integration", if any of that is clear?

[signal kiln]

I'll try that

So something like :

$y'(1-\frac{y^2}{y'}) = 1$

[flat frigate]

Grui

[signal kiln]

no that doesn't sound right since I still have y' in the factor

[junior smelt]

You basically want it to be something like y' * (something with only y's in) = (something with only x's in)

Of course, the "something"s can just be constants, those are fine too

[signal kiln]

the +1 is annoying me cause i cant just divide by y² because of that

[junior smelt]

It's annoying, but also, not annoying

You may not be able to divide only by y^2, but...

[signal kiln]

oooh

i can just divide by 1+y² dirrectly and call it a day XD

[junior smelt]

Yep, there you go

[signal kiln]

ok so now I have :
$y' \times (\frac {1}{1+y^2}) = 1$

(damn that ² again XD)

[shadow briar]

I sent the question you initially sent to a math AI. I'll say ahead of time, I don't personally know how to read the equation and cannot fact check. However, the math AI does explain everything, in this case, a six step process. I am not a helper here, but would it be okay if I sent what the AI sent over and TeXit could fact check?

[flat frigate]

Grui

[junior smelt]

!nogpt

[safe radish]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[shadow briar]

Er, Sorry, chartbit could fact check

[junior smelt]

Happens

[signal kiln]

and that 1/1+x² is a pretty easy integral hihi

[shadow briar]

Understood. I'm just reading some questions on here and sending them to AI to learn stuff. But jeez, everyone's questions are way more complex than any quest I'd have.

Anyway, good luck fellas!

[signal kiln]

WHICH I SOMEHOW FORGOT

give me a sec to find it again XD

isn't it tan ?

[junior smelt]

Almost, not tan itself, arctan

[signal kiln]

oh right

sooooo g is arctan

and now our problem becomes :
arctan(y) = x

or, y = tan(y)

+c, right

which i can solve for y(0) = 0 in my problem

[junior smelt]

Yep, say arctan(y) = x + c, then you can rearrange that, y = tan(x + c)

[signal kiln]

(i cant believe you have a +1 emoji here XD)

[junior smelt]

Hehe there are a nice selection of emotes in some of the servers I have

[signal kiln]

I have this other problem that I think i can try to solve on my own now that I know this new technique, and if not, i'll open a new channel (if I understand how this discord works)

thank you very very much for your help

[junior smelt]

Awww, best of luck I’m sure this one you’ll be fine with

[signal kiln]

.close

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[unkempt pawn]

hi i have a question about entropy. to my understanding, conditional entropy makes the outcome less uncertain because you have more information. but why in this case does the uncertainty get larger? doesn't that violate the principle? can someone explain please

[unkempt pawn]

helppp

please

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@unkempt pawn Has your question been resolved?

[unkempt pawn]

.close

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[vapid inlet]

Bro, this website wont accept my answer 😭

[vapid inlet]

been staring at it for like 15mins, and nothings popping up

and modifying it

heres a refresher

is it a website problem?

[cedar void]

I think you have to sub the value of tan(2pi)

[vapid inlet]

this is referring to the answer inside the blue box right?

the one above the box got accepted

[cedar void]

yeah, I think you have to sub the value of tan(2pi) without converting it to sine or cosine

[vapid inlet]

I tried it earlier, but let me try it again

and might as well rewrite it using the keys on the right side instead of typing it by keyboard

[vapid inlet]

wait, you mean to just make it 0?

[cedar void]

yeah ig that's what they want

[vapid inlet]

oop, already tried that earlier too 😭

[cedar void]

can you share the exact form?

[vapid inlet]

alr wait

oh wait, lemme try not ultiplying it with tanx

IT WORKED

Yessir!

thank youu

[cedar void]

nice

[vapid inlet]

.close

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[clear lark]

how to do this

[clear lark]

<@&286206848099549185>

like

i understand what tis saying

when you do f(x)-L the equation is factortable

im pretty sure its true

i just dont understand how to prove it

[light shoal]

do they mean factorable into linear factors or what?

if not, seems like you could choose a polynomial with a linear factor times something unfactorable like x^2+1 ?

[safe radish]

@clear lark Has your question been resolved?

[clear lark]

no but that is factorable if u think about it

bc if u have something like

as the limit as x approaches 1 of x^2+1

its x^2+1=2

which just becomes x^2-1

which is very easily factorable

[light shoal]

ok, let's say L = 1 and p(x) - 1 is something like x(x^2+1)

that's not fully factorable

[safe radish]

@clear lark Has your question been resolved?

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[tranquil ore]

hi

is there a shortcut to this?

i dont want to split it up into five cases

<@&286206848099549185>

[viscid garden]

whats the question?

[tranquil ore]

is there some trick i can do to turn it all into multiplication

instead of splitting into five cases and summing

like with the choose function or something

[viscid garden]

Please share the full question

[tranquil ore]

im just asking for the probability of getting exactly 1 gold ball

[viscid garden]

Oh right!

[viscid garden]

You are solving for part a?

[tranquil ore]

yes

[viscid garden]

I am not sure what a PMF is...

Please tell me what probability are you trying to find?

[lean otter]

Probability mass function

[tranquil ore]

this is all im asking

[viscid garden]

Right!

What are the total number of ways?

To take out 5 balls?

@tranquil ore

[tranquil ore]

25c5

oh i think i got it from there

15c4 / 25c5?

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[devout glacier]

Hi.

it's more general help question.

I take PDE in class and i understand theory very well but when it comes to practice i have a blank mind, it may be related to calculus because we went through it fast so i dont really remember it well.
Should i do some practice problems of calculus or that's unnecessary and i should just continue with PDEs

[lean otter]

if you're taking a class in PDEs, you should already be very comfortable with calculus

not to mention the other analysis prerequisites

[safe radish]

@devout glacier Has your question been resolved?

[devout glacier]

I had 2 year gap so i forgot lots of it

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[random charm]

How do i find x?

[soft prism]

Do you know vertically opposite angles?

And interior alternate angles?

[random charm]

No

[lean sparrow]

u need to know corresponding angles alt int angles etc before proceeding

[fathom jewel]

If you use properties of angles you can deduce that 3x + (x+36°) = 180°

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[wind plover]

what does it mean by ,t

[cedar void]

, is just used to separate the given equation from the inequality

[wind plover]

so it basically giving a equation then giving info that t>=0 meaning it can have between 1 and 2 roots

right?

[lean sparrow]

its asking u to ignore any negative root

[cedar void]

your first assertion is correct, but not sure what you mean by your 2nd assertion

[wind plover]

oh wait i mixed it up with finding the discriminant LOL

mb

[wind plover]

AH ok thanks

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[vapid crescent]

I need to find all value of a for which the proposition is true.
x and a are real numbers

[vapid crescent]

for b) is it fine to say that because x=2 results in 9 = 0 then there is no a for which this holds?

[stoic dune]

That only proves that a = 0 doesn't work

[vapid crescent]

what do you mean?

[stoic dune]

Oh mb, the a cancels out, doesn't it

[stoic dune]

Then yes, this is a valid thing to say

[vapid crescent]

what about for c? Can I just say that because the x^2-2ax+4a +5 concaves up for all a then there is always a value x for which it is positive?

[hard crest]

easier to just find a value right?

then again yeah that's fine

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[mellow iron]

If you have a vector space with an infinite dimension, does it have a base or not

[mellow iron]

Also forgive my english for it is lacking, i know the words in french

thanks

[plucky elk]

yes

https://www.math.ucla.edu/~tsmits/Teaching/115A/Handouts/zorn.pdf

[mellow iron]

it can have a base?

amazing

@plucky elk

sorry to tag you like this but i have one more question

[plucky elk]

?

[mellow iron]

Uhhh do the bases of that vector space have the same cardinal

like do they have the same amount of elements

like it is the case in the finite version

[flat phoenix]

an infinite-dimensional vector space does have a basis, but the basis itself will also be infinite.

[mellow iron]

amazing

thank you so much

[mellow iron]

https://tenor.com/view/happy-happy-dog-dog-happiest-dog-super-happy-gif-17885812

[flat phoenix]

https://tenor.com/view/goodnight-gif-5295116536817772197

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@mellow iron Has your question been resolved?

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[tardy cosmos]

Hi everyone! can someone help me how can I solve this? I saw the comments and it says the answer is 1/2

[tardy cosmos]

tried everything and maybe I'm dumb or stupid

[safe radish]

@tardy cosmos Has your question been resolved?

[brave wolf]

I solved it by many conjugates

Wait

actually

there is a simpler answer

$\frac{\sqrt{x}+\sqrt{x-2}-\sqrt{2}}{\sqrt{x-2}\sqrt{x+2}}=\frac{\frac{\sqrt{x}-\sqrt{2}}{\sqrt{x-2}}+\frac{\sqrt{x-2}}{\sqrt{x-2}}}{\sqrt{x+2}}$

[flat frigate]

MæthIsAlwaysRight

[brave wolf]

and because there is a limit

sqrt(x+2) will just approach 2

and sqrt(x-2)/sqrt(x-2) will be 1

$\frac{\frac{\sqrt{x}-\sqrt{2}}{\sqrt{x-2}}+1}{2}$

so you get this

and after this, it should be a simple conjugating

[flat frigate]

MæthIsAlwaysRight

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[tardy cosmos]

Thanks appreciate it

[tardy cosmos]

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[hot urchin]

1. This appears to be implying that by isolating a singular X and solving for it the entire equation is solved.

2. I am confused how they can simply take the sqrt of each of them without breaking equality since they need to make sure the answer results in zero. I thought it was likely thatd just result in a mess where everything equates to different answers. They also added one earlier to construct a perfect square polynomial.

[hot urchin]

https://cdn.discordapp.com/attachments/972908483877945354/1283885094049677503/R.png?ex=66e49eab&is=66e34d2b&hm=f37d8012620d7b149daba2d9770fc352ad5bc632c9cb36a02d73e6d7af20114b&https://www.mathlearnit.com/static/images/square-root-rules.png

https://www.mathlearnit.com/static/images/square-root-rules.png

[hot urchin]

TLDR: When taking the sqrt of the entire polynomial to remove a power does that break equality when trying to get a root and if not why. Yes I know they scaled it down to remove and solve for a singular X which can be applied to the whole problem (i think)```

[fathom adder]

1. Thats the purpose of equation
2. Why would taking the sqrt leads to break equality (?!)

[hot urchin]

well it was just a bit confusing to me to work out mentally because i was thinking

and

it looked like if you took sqrt of the answer it wouldnt be equal anymore

because of how

well if 5 + 10 = 15

the power is 25 + 100 = 125

[fathom adder]

??

[hot urchin]

and 15^2 is not 125

[fathom adder]

Bro

(a+b)^2 rq ?

[hot urchin]

wdym

oh

[fathom adder]

What is (a+b)^2

Its not a^2 + b^2

[hot urchin]

o h

[fathom adder]

So no taking the sqrt or putting a square or anything you want, don't disturb the equality sign

[hot urchin]

225 ermmmm

(5+10)^2 then....

[fathom adder]

Which is 15^2

[hot urchin]

calculating...

[fathom adder]

25 + 100 + 2*50 = 225

[hot urchin]

yes

thank you

its solved now

https://media.discordapp.net/attachments/1015759484708208792/1045835008012714017/a_3a6633f55a6525e045c618e50b97782a12.gif

i was just having a really hard time formatting it because i forgot the () again

[fathom adder]

Don't in the future now

[hot urchin]

alr

[fathom adder]

Perfect

[hot urchin]

https://media.discordapp.net/attachments/1015759484708208792/1045835008012714017/a_3a6633f55a6525e045c618e50b97782a12.gif

.close

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[cloud gust]

I have this question but I'm just confused on what the a, b, c are representing? I'd assume not the lines because it's not like line a-c, c-b, c-a

[sleek plank]

they are coordinate distances on each of the axes

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[celest coral]

Part C im trying to understand after the practice questions basically guided me

[celest coral]

I understand subtracting the 14.5 to help isolate the t but that leaves you with -1.3 to divide how does it become positive

[viscid garden]

They divide by -1.3

And then multiply the whole expression by -1/-1

To just get the denominator positive...

It's usually better to have the denominator positive...

[celest coral]

Ohhhhh okay thats why what would be -14.15 becomes positive then it subtracts the positive V

thank you

[viscid garden]

YEP

[viscid garden]

No problem

[celest coral]

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[lean otter]

I have no idea how to solve this, though I'm sure the answer's 6

[tired harbor]

the cotangent is one over the tangent

[lean otter]

Ik that

[tired harbor]

so tan 10x = 1/tan(5x)

[lean otter]

Then? I did come this far, then?

[tired harbor]

tan10x * tan5x = 1

[lean otter]

Ok?

This is where im stuck

U cant do anything after this

[tired harbor]

ooh i am also stuck here

[torn star]

use double angle identity for tan

[lean otter]

What?

[tired harbor]

ah there it is

[torn star]

tan(2x)=2tanx/(1-tan^2x)

iirc

simplify and youll get a quadratic where you sub u=tan5x

[lean otter]

I... Never even learnt this

[torn star]

theres really no other way to do it other than guessing probably

but yeah you should know your double angle identities at least for trig stuff

[lean otter]

Whoa

[torn star]

cos(2x)=cos^2x-sin^2x as well iirc

[lean otter]

Do u think this works?

[torn star]

i dont think so

where did you get 10x+5x=90

[lean otter]

Click on the image

[torn star]

90-10x=5x ahh i guess that works as well

[lean otter]

Mmm

[lean otter]

Wait, im trying with this

[torn star]

dont if you didn't learn it

its much more difficult compared to how you figured it out

[lean otter]

Ah..ok

Stilp

Still*

Imma give it a try

[exotic bolt]

Pretty sure you have to use double angle

Identity

[lean otter]

@exotic bolt

[exotic bolt]

No

[lean otter]

Why not?

[exotic bolt]

There should be infinite anwers

First of all

[lean otter]

Actually, therez only 4 answers with the double angle identity thing

[exotic bolt]

No

…

There’s infinitely many

If you think about it

Or even just plug into demos

You’ll see

Because they are sinusodial

If you don’t know double angles

And even if you do

This problem is difficult

[lean otter]

Nah mate, look

Even with double angle, itz 4 answers

Tho my calculator says the only answer should be 6

[exotic bolt]

Oh wtf you’re using degrees

What the hell

[lean otter]

I have to put the value of x in the first equation and see if all of them fits ig

[exotic bolt]

Who the hell uses degrees

For these types of problems

[lean otter]

Me

[exotic bolt]

But there is infinitely many answers

[lean otter]

We will see

[exotic bolt]

Your calc isn’t ever going to tell you that

Bro😭😭😭😭

[lean otter]

Bro, why would my friend's teacher would set this thing in their exams and they are in grade 10, if it is unsolvable?

[lean otter]

Eh?

[exotic bolt]

Does this look like 4 intersections

[lean otter]

It looks ah. .

[exotic bolt]

No you have to include a variable either n or k

And said “k is contained as an integer”

Because your teacher never set a domain restriction

If you have never learned that

I wouldn’t bother putting it but

6 is a correct answers btw

[lean otter]

So is 30, 42 and 66

So.. It has infinite amount of answers?

[exotic bolt]

Yes

Do you understand

Why tho

It’s not just every single x value is an answer

But instead ever equal distance from 6 degrees is an answer

And you have to find that distance

[lean otter]

I see

I wonder what his teacher actually wanted

[exotic bolt]

Idk I liked how you did it

Easier but

Doesn’t really give you the easiest answers

[lean otter]

Anyways, Ig we will leave this here and close the channel?

[exotic bolt]

Do you want to see the complete answer

Or do you want to figure it out

[lean otter]

Yes

Ah..

[exotic bolt]

One sec let it write it out

[lean otter]

What about both?

I think, my friend forgot to tell me something, usually in this type of questions we have a range like, 0<5x<90 or something

[exotic bolt]

oh

Well

[lean otter]

Ah.. I see..

[lean otter]

So.. Those circled two are the answers?

[exotic bolt]

Ye both work

[lean otter]

Im sure this is what happened tbh

[exotic bolt]

Well

[lean otter]

So..

[exotic bolt]

Then you just add

K values till you reach a max of pi/2

[lean otter]

Thatz possible?

[exotic bolt]

Like for k=0

pi/6

k=1

Pi/6 plus pi/5

K=2

[lean otter]

And it goes on?

[exotic bolt]

Pi/6 + 2pi:5

Till you max at pi/2 or right under it

[lean otter]

I wonder when do we max?

Oh tan 90= Undefined

[exotic bolt]

Just when it’s within your domain

Like if you sub in 100 for k

It will be way above the pi/2 domain restriction you said your friend has

[exotic bolt]

Nothing to do with that

[lean otter]

Btw..

[lean otter]

What is a domain? 🗿 Why didnt our teachers ever tell us these?

[exotic bolt]

Like the x values the answers must be between

Like if they said

Find the x values on the domain of (0,90)

[lean otter]

oh

[exotic bolt]

That means find all values between 0 degrees and 90 degrees

That satisfy the equation

Do not worry about the whole k stuff

I don’t think you learned it

The way you did it works

[lean otter]

And if it is an infinite domain, there will be infinite answers?

[exotic bolt]

I overcomplicyed the problem

[exotic bolt]

Yes because both functions are sinusodial

[lean otter]

Doesnt matter tbh, i learnt something new, that matters

[lean otter]

So, i think i have my answer

I will just.. close this channel ig?

[exotic bolt]

Periodic is a better word

Over sinusodial oops

[exotic bolt]

Ye u can if you understand

[lean otter]

The funny thing is i sometimes have troubles with mathematical terms in English, we learn mathematics in Bengali, you see

Welp

.close

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[wild helm]

I have a precalc exam on these things

The ticks are things I’m 100% confident with, the black squiggly line is mostly confident and the xs are things I need to relearn

It’s on Saturday at 10 and I got all day tmr to study, yall think I can grind it out in like 2-3 hours? Only things I need to fully learn is exact trig values but do I need to know them if I have a calc

[plucky elk]

,tex .unit circle

[flat frigate]

[wild helm]

Y’all think I could get it done, like revise all of the crosses and skim over the checks in 2-3 hours

[plucky elk]

Sir this is a Wendy's

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@wild helm Has your question been resolved?

[dense wadi]

einstein can and so can you

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[wild helm]

No

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[wild helm]

My question hasn’t been resolved

[wild helm]

<@&286206848099549185>

[plucky elk]

You don't have a math question

Ask about something specific, not for studying tips or motivation

That belongs in #discussion

[wild helm]

I’m simply asking is it realistic for me to be able to revise all and learn all of that content in 2-3 hours

[plucky elk]

.

[mossy lotus]

whether you have the capability to understand the concepts you havent managed to understand till today,, within 2-3 hours is something only you can tell after spending that time. We cant tell you if you can or cannot

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[void slate]

hi!! how do I solve this?? i've never worked with e before

[molten hawk]

well

have you tried plugging in x

[smoky nacelle]

you don't need to worry about it being an e

just treat it like any constant

and yes plug in x

[void slate]

okayokay

is this right??

[smoky nacelle]

uh

slight issue

-4-4 is not 0

rest is fine

[void slate]

i hate math

[smoky nacelle]

take the negative common if it feels weird

$-4-4 = -(4+4)$

[flat frigate]

Percy

[void slate]

did i do something else wrong? cause when I fix that I get e^8 but my teacher's answer key also says 1

[smoky nacelle]

let's just

,wolf lim x approaches -2 e^(2x-x^2)

[flat frigate]

Results provided by WolframAlpha

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

Requested by percykel

[smoky nacelle]

yep

you're right

you need a new instructor /lh

[smoky nacelle]

e^(-8) though

[void slate]

whoops

thank you!!

wait photomath is also saying 1 though

oh wait

i figured it out

the limit is 2 not -2

my bad!!

.close

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[jaunty trench]

What's the possibility of two people having the same birthday?

[buoyant shadow]

1/365

[jaunty trench]

Why?

[pine horizon]

because there are 365 possible birth dates

[buoyant shadow]

well not really

[pine horizon]

(not accounting for leap year)

[jaunty trench]

was leap year in 2008?

[buoyant shadow]

it's something else because many people avoid being born on any of the 365

[simple gazelle]

yes

[pine horizon]

yes

[simple gazelle]

because it is divisible by 4

[jaunty trench]

1/365 is how many %?

[simple gazelle]

multiply it by 100

[jaunty trench]

0,27%

wow...

two my classmates have on 20th nov

[pine horizon]

thats theoretical tho

[buoyant shadow]

yeah the real answer depends on when it's asked

[pine horizon]

check the birthday paradox

[jaunty trench]

do all birthdays have the same chance of possiblity?

[buoyant shadow]

that's a different thing

[simple gazelle]

accounting for human reproduction

[jaunty trench]

?

[simple gazelle]

no

some are rarer than others

[jaunty trench]

THATS what the question meant

[buoyant shadow]

it's 1/365 if you decide on which two people first

[jaunty trench]

wym?

[buoyant shadow]

otherwise it's 100%, somewhere, two people definitely have the same birthday

[jaunty trench]

so whats the chance of two people having the same birthday?

[buoyant shadow]

100% or 1/365,

[jaunty trench]

how is that possible

100%

[buoyant shadow]

depends on what you;re asking

"two people have the same birthday" is true

[simple gazelle]

if you get 2 people randomly off the street and compare their birthdays, the chance of them sharing it is 1/365

if you ask what is the probability that 2 people share a birthday in this world, it's 100%

it depends on context

[jaunty trench]

how much chances did my class mates have of having the same birthdayÞ?

[simple gazelle]

theoretically

if your class has 23 people, then the chance is 23/365

there's the birthday paradox but

[buoyant shadow]

with no information, it's 50%

at least i'm used to think that way

if we know how many people in the class, we can give a better guess

probability is about using information to make a guess

[jaunty trench]

ok

.close

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[primal gazelle]

how do i solve this from the start?

[obsidian oracle]

You have to compute (f o g)(x) for example

So f(g(x))

If you have the expression of both f and g, you know how to compute their composition right?

[primal gazelle]

then?

[obsidian oracle]

Well if you end up with x, you win

As the question statement suggested

[primal gazelle]

am i not right its same right the f times g and g times x

why they’re mentioning it

[obsidian oracle]

No

[primal gazelle]

is it like im gonna choose?

[obsidian oracle]

f(g(x))

Means that f takes the INPUT g(x)

It is not f(x) * g(x)

[primal gazelle]

oh

[obsidian oracle]

If f(x) = 3x-2 for example

Then f(input) = 3*input - 2

So f(g(x)) = ...

[burnt notch]

Have you done/seen this notation in class? I hope so, otherwise how can you do these exercises?

[primal gazelle]

3(1/3(x+2))-2

am i right?

<@&286206848099549185>

so it will be

3(1/3x+2/3)-2

x+2-2

x

please help

badly need this rn

[leaden vortex]

its coming like
1/3(3x-2+2)

[primal gazelle]

how

what did u use?

@leaden vortex

its not f(g(x))

@obsidian oracle hey please help

[leaden vortex]

its the only way imo

[safe radish]

@primal gazelle Has your question been resolved?

[safe radish]

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[safe radish]

@left fulcrum Has your question been resolved?

[pine horizon]

assume 4 terms in ap are

a-3d, a-d, a+d, a+3d

then proceed from there

like sum of these four terms is 24 and product is ...

then solve

[untold scaffold]

shouldnt it be a+2d

[pine horizon]

no

for even number of terms the cd is 2d

and for odd its d

[untold scaffold]

its consecutive terms in the ques

not even terms

[pine horizon]

doesnt matter

its just how u assume the terms

[untold scaffold]

a+3d will give the 2nd term from a+d so its not consecutive

[pine horizon]

wait

[untold scaffold]

yee

[pine horizon]

but then how will you assume the terms if not like that

945 = 3^3.5.7

so 3,5,7,9 are the four integers

[pine horizon]

but u get the same answer with this too

[safe radish]

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[lucid raven]

I need to prove that OD/OA + OE/OB = 1

[digital vine]

what does the title say

i read it as "6ambar no 2"

[lucid raven]

its a word for picture no2

in my language

[digital vine]

is there any other information about the question?

[lucid raven]

Nope

[digital vine]

did you get anywhere with it?

[lucid raven]

what?

[pine horizon]

what have you tried

[digital vine]

yeah like can we see your working out so far?

[lucid raven]

oh

AD/AO = OE/OB

so AD = OA - OD and OA-OD/OA = OE/OB
?

this implies 1 = OE/OB + OD/OA

[smoky nacelle]

infinite chocolate problem. /j

[digital vine]

what theorem did you refer to in order to make this statement?

[lucid raven]

i think i make a mistake

on the point

i name it wrong

i should make point F

to complete DOEF

so AD/AO = AF/AB = DF/OE

[digital vine]

then 1 = 1 = 1 ?

since DF = OE -> DF/OE = 1

[lucid raven]

i guess?

[digital vine]

do you see why that doesn't make sense?

[lucid raven]

if OD/OA = 1 then OE/OB = 0

[digital vine]

yeah

but also OD and OA would be the same length

when OD should be a fraction of OA

[lucid raven]

ok but how do we get OE/OB

[safe radish]

@lucid raven Has your question been resolved?

[untold scaffold]

this makes the calculation simpler

but the common difference in this different from the original series

[digital vine]

we're on a different question now mate

[safe radish]

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[raven phoenix]

can you factorize x3 + y3 + z3?

[digital vine]

yes?

[raven phoenix]

How to do that?

Is it just 3(x+y+z)?

[digital vine]

yes

[raven phoenix]

Oh would 3xyz work or not?

i dont think it would

[digital vine]

no that's a different number

[raven phoenix]

Oh ok thanks

[raven phoenix]

Someone said it would and i was confused

[arctic raven]

do you mean 3x+3y+3z, or x^3 + y^3 + z^3?

[raven phoenix]

the first one but what would the second one look like?

[digital vine]

you can check if 3xyz = 3(x+y+z) by choosing your own numbers for x,y & z

[arctic raven]

a mess

[digital vine]

lol

[raven phoenix]

oop

Lol

[raven phoenix]

so i can choose 1 2 3 for x y z

ok so

3(123)

[arctic raven]

that's incidentally a bad choice

[raven phoenix]

why?

[raven phoenix]

Im solving the first one

[arctic raven]

because 1×2×3=1+2+3=6

[raven phoenix]

not the second one

Oh

ok ill choose 2 3 and 5

[arctic raven]

try 2,3,5

ayy

[raven phoenix]

LOL

ok soooo

[arctic raven]

the primes

[raven phoenix]

3(2 x 3 x 5)

[raven phoenix]

Yep

60

and then

3(2+3+5)

Ohhh now i see the difference

So that means that

3(x+y+z) is not equal to 3xyz

[digital vine]

correct

[raven phoenix]

Btw

Why do you need to find a common factor when factorizing

[pine horizon]

u need factors for factorizing

[raven phoenix]

Ye i realized because if you have
3x + 3 3 and 1 are common factors

so you can do

[pine horizon]

yes

[raven phoenix]

3(x+1)

and

1(3x+1) which is essentially our first equation but people dont use it since it gives the same thing

[pine horizon]

yes

[raven phoenix]

Ty

[safe radish]

@raven phoenix Has your question been resolved?

[safe radish]

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[prisma swift]

how did we get to 1/2

[cedar void]

you did a mistake in second line

[junior smelt]

Second numerator term should not be squared

[prisma swift]

isnt it a difference between two squares

a²-b²

[pine horizon]

yes

[prisma swift]

oh

[pine horizon]

but

[prisma swift]

the sqrt

[pine horizon]

that second term is sqrt

yeah

[prisma swift]

mb

ill try again

oh i just got half

foolish mistake on my part

tysm everyone

[safe radish]

@prisma swift Has your question been resolved?

[safe radish]

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[flat igloo]

Q3

First I converted it in form of half angle

Took sin alpha common

We get
2 sin alpha( 2 sin alpha+ i cos alpha)

[vagrant ice]

the modulus is just $\sqrt{(1 - \cos 2 \alpha)^2 + (\sin 2 \alpha)^2}$

[flat frigate]

south

[vagrant ice]

for the argument you have to be careful cause there's a domain given

but it should definitely be like $2 \pi + \arctan \frac{\sin 2 \alpha}{1 - \cos 2 \alpha}$

[flat frigate]

south

[flat igloo]

Btw angle lies in 4th quadrant

[vagrant ice]

and $\frac{\sin 2 \alpha}{1 - \cos 2 \alpha} = \cot \alpha$

[flat igloo]

Shouldn’t the sign of sin change to negative

To -sin alpha

[vagrant ice]

no, sin(2 alpha) is already the y-coordinate

if the y-coordinate is negative it doesn't matter

[flat frigate]

south

[vagrant ice]

oh it definitely depends on which quadrant 2 alpha lies

[flat igloo]

Here’s the solution

[vagrant ice]

oh that's clever

[flat igloo]

I don’t understand the 4th step

Why did everything get negative

Even the cos?

[vagrant ice]

so that's just $xy = (-x)(-y)$

[flat frigate]

south

[vagrant ice]

I don't get why they did that either

[flat igloo]

Oh and not because of sign transformation?

[vagrant ice]

wdym by sign transformation

[flat igloo]

In 4th quadrant sin in negative

I really have a lot of confusions with this concept

[vagrant ice]

I guess that's why they made both brackets negative, cause of the 4th quadrant

ah I see, so you want |z| to be positive by definition

but sin alpha is negative in the 4th quadrant

[flat igloo]

Yes

[vagrant ice]

so you want -sin alpha or similar to make it positive

[flat igloo]

I get it somewhat

[vagrant ice]

that's very very clever, yeah the issue is just the domain of alpha

and then you can rewrite -sin alpha - i cos alpha in the form cos x + i sin x

so that you know the argument as well, put it in modulus-argument form

then you can just read it off once you've finished transforming z

[flat igloo]

What do they mean when they say alpha is between 3pi/2 and 2pi? They are measuring alpha from positive x axis?

[vagrant ice]

yes

[flat igloo]

What is the convention of measuring an angle?

It’s always from positive x?

[vagrant ice]

yep

[flat igloo]

I mean like first going from 1st Quadrant then 2nd quadrant then 3rd and 4th anti-clockwise

Or sometimes if angle is in 3rd or 4th quadrant they just measure the angle from positive x in clockwise direction

[vagrant ice]

yeah so that's why say -80 degrees is the same as 360 - 80 = 280 degrees

[flat igloo]

But what is the convention?

Measure from anti-clockwise or both

[vagrant ice]

the convention is that you always measure from the positive x-axis

and go anticlockwise

so positive is anticlockwise and negative is clockwise

[flat igloo]

So 280 degree is the conventionally correct

So in the original question when they said Alpha is greater than 3pi/2 and smaller than 2pi they were talking about the greater angle measured anti clockwise right?

[safe radish]

@flat igloo Has your question been resolved?

[safe radish]

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[wild bobcat]

Can this expression be simplified any further?

[icy lance]

good lord

[fickle monolith]

lcm ?

[wild bobcat]

I expanded myself into a mess yeah

I'm pretty sure it's still as simplified as it can be but if there's an identity I'm forgetting let me know

[grim kraken]

I think so

May you give me 5 minutes to make it on word ?

[wild bobcat]

yeah definitely. Thanks

This is the original expression

[grim kraken]

And you are suppose to get something nice out of that... thing ?