help-19

[unreal pasture]

ok so i would like have to seperate them right

[short terrace]

In this case it's much easier

You have 1 = -A

So what's A

[unreal pasture]

-1

[short terrace]

Good

And now A + B = 4

So what's B

[unreal pasture]

4

[short terrace]

No

A is -1

[unreal pasture]

so b is 1?

ohh

5

[short terrace]

Yes

Now try doing another problem this way

Collect the terms

And then solve for A and B

[unreal pasture]

ok i have another problem so ill send it then ill try it

[short terrace]

Sure sure

[unreal pasture]

this one is a bitt different

[short terrace]

Oh god this one's a lot different

[unreal pasture]

yeaaa

[short terrace]

So when you have a power in the denominator

[unreal pasture]

so ik the denmon would be x-2 x-2 ^2 then x-2^3

[short terrace]

You want to split it and still have all powers in the partial fractions

[short terrace]

Ah good

I don't have to explain this phew

[unreal pasture]

after that idk what to do though haha

[short terrace]

Well set up the partial fractions

[unreal pasture]

x ^ 2 = a / x-2 + B / x-2^2 + c / x-2^3

[short terrace]

Always the first step

Okay firstly

Use parentheses

Secondly, missing a /

[unreal pasture]

i did on the page just not on the text sorry

[short terrace]

Just makes it easier for me to know if you made a mistake

[sturdy cape]

-# as in a / ((x-2)^2)

-# or a / (x-2)^2, since it's clear enough from context yet still legible

[short terrace]

I love that the inline code blocks aren't transparent

[unreal pasture]

ok got it

but what do i do from there

[short terrace]

Well we get rid of the denominator from both sides

[unreal pasture]

so A(x-2)^2 + B (x-2) + C

[short terrace]

And this is equal to...?

[unreal pasture]

x^2

[short terrace]

Yes

Now time to expand

Distribute

Whatever, same thing

[unreal pasture]

x^2 = Ax^2 - 4 + Bx - 2 + C

[short terrace]

...no

[unreal pasture]

...

[short terrace]

(x-2)² isn't x² - 4

Also you haven't properly distributed

(or haven't used parentheses again)

[unreal pasture]

sorry 😓

so what did i do wrong

[short terrace]

Well firstly

Are you familiar with (a+b)²

[unreal pasture]

i think i just forgot it

[short terrace]

Well time to derive it

What's (a+b)(a+b)

[unreal pasture]

a^2 + ab + ab + b^2

[short terrace]

Good

Now do the same for (x+2)²

[unreal pasture]

should i do it for x-2 instead or do you weant me to do it that way firsr

[short terrace]

Oh right x-2

I'm dumb sorry

[unreal pasture]

lmaoo if ur dumb im a brick

[short terrace]

Let's build a house together

Either way

(x-2)²

[unreal pasture]

x^2 - 2x - 2x + 4

[short terrace]

Good

And you can add to get..

[unreal pasture]

x^2 - 4x + 4

[short terrace]

Good

[short terrace]

Now let's return to this

Write (x-2)² as what you just calculated

And then distribute

[unreal pasture]

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

[short terrace]

Yes

[unreal pasture]

ok let me add the rest

[short terrace]

Brb filling water

[unreal pasture]

alr 🙏

for the B would it be Bx - 2B

[short terrace]

Yes

[unreal pasture]

ok so it would be x^2 = A( x^2 - 4X +4) + Bx - 2B + C

sorry if i forgot parentheses

[odd edge]

@unreal pasture Has your question been resolved?

[unreal pasture]

its still active ✌️

[short terrace]

Yes

Now distribute

Sorry I dozed off

[unreal pasture]

ok im back

letr me do that

so x^ =A 4x^2 + A4x + A4

[short terrace]

Needs more terms

Also Lemme ask someone else to take over cuz I'm too sleepy and keep dozing off

[unreal pasture]

its fine ill just finsih tomorrow since im going to head to bed

[short terrace]

Ah fair enough

Hopefully I'm less sleepy next time you come around

Feel free to tag me

[odd edge]

@unreal pasture Has your question been resolved?

[unreal pasture]

ok thank you a lot

[odd edge]

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[hollow geode]

Hello, wanted to do this question graphically and wanna double check that its indeed B as x=3 and x=9 show to be cusps and x=6 doesnt appear to be either

[warped glacier]

you're missing the exponent of 4/5

or I think you typed it but it got cut off

[hollow geode]

Ah yeah the latter

[warped glacier]

that's correct, so it's B indeed

[hollow geode]

Alr thank you

.close

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[placid python]

Could someone walk me through this?

-# If you see this in time, please ping whenever replying!

[woeful briar]

Replace the numbers with nonzero x,y,z

[wooden python]

you need to show at least one of xy, yz, xz is >=0

if you can luck into an idea to prove that a particular one of these 3 is nonegative then go ahead and do that

[placid python]

I’m not sure how I would even do this

[woeful briar]

Look at the possible signs of x,y,z

Given the signs of x,y,z how would you know the sign of xy?

[placid python]

Well if I write out each case, eventually one of them will be negative and one will be positive meaning one is negative

[wooden python]

"one of the products is negative" is somewhat tangential to your goal

tbh i do think this problem is a real thinker even for me

i have one idea in mind but i would need to seriously write it out and give it a good amount of thought

[placid python]

Well:
negative*positive = negative,
positive*positive = positive,
negative*negative = positive

not sure if thats relavant here

[woeful briar]

Very relevent

[placid python]

ok thats good 😂

i just dont get how i could assume the signs of the variables since every case doesnt equal a positive

[mortal trench]

If you can show that x is +; then they all must be +

Likewise for y and z

[placid python]

why?

[wooden python]

how so

[mortal trench]

Or wait nvm

[placid python]

it comforts me knowing im not the only one confused here 😂

[woeful briar]

Can you try understanding this?

I am looking for something a bit more precise

[placid python]

Well I had my written out multiplication rules, but I dont understand how I can just assume the signs

because one positive and one negative will be negative

[wooden python]

wait hold on

[woeful briar]

If x>0 and y < 0 what does it say about yz and xz

[wooden python]

the realization JUST hit me

but no spoilers

[placid python]

i still cant answer that tho right? because we dont know if z is positive or negative

[placid python]

good, its really fun when im actually walked through it like this 😂

[wooden python]

think about both cases

[placid python]

if z is positive:
yz = negative
xz = positive

if z is negative:
yz = positive
xz = negative

[woeful briar]

Yeah, so one of them must be positive

[wooden python]

rather prefer to say ">0" and "<0" instead of "=positive" or "=negative" resp

[placid python]

ah wait and the proof is just asking for 2 of the products to be >0

not all of them to be positive

right?

[woeful briar]

Its asking for one of xy,zx,yz to be >=0

[placid python]

ahhh

ok so backtracking here just so i understand

even if we flipped them and made x<0 and y>0, the signs would just flip, and if we made them both >0, xy would now be >=0, and if we made them negative, two negatives make a positive

am i able to use that in a proof or is that just because i knew the answer already 😂

[woeful briar]

Sure

Just there is a more efficient way to phrase this

[placid python]

i was gonna say im not sure if thats how you were thinking about it

whats the more efficient way?

[woeful briar]

Do you know of the pigeonhole principle?

[placid python]

the what

no 😂

[woeful briar]

Do you want a short explanation or forget it

[placid python]

uh since i cant use it on the assignment im guessing, ill just skip it for now

[woeful briar]

Sure

Maybe give it a read later

It will be insightful

[placid python]

yeah ill look into it

i searched it so its saved in my history haha

for the proof, can i assign those variables their signs like we did at the start? do i need to assume anything before it?

[woeful briar]

Not reallt

Every real number is either negative, 0 or positive

[placid python]

thats true

ok sweet thanks you and everyone else for the help tonight

[woeful briar]

Tonight

[placid python]

its 10pm for me 😂

im sure youre probably on the other side of the world

[woeful briar]

Its morning here

[placid python]

yep not surprised haha

alright ill probably be back next week with more questions so goodbye for now

.close

[odd edge]

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[mystic saffron]

Lowest positive rational number a and b for which lcm of e^(a pi i) and e^(b pi i) is defined. (not taking 0 as a positive solution)

[woeful briar]

How do you define lcm in this context?

[mystic saffron]

Just how it normally, is, yk the deal for integers, for irrationals and stuff, yk, if its in same family its defined

Not too sure of complex numbers tho

[woeful briar]

Lcm is usually talked about in the context of UFD's

Which the complex numbers are not

[mystic saffron]

Hm, so e^( a/b pi i) reduces to (-1)^a/b, so this eqn mustn't be complex? Then we can care to find the answers

And btw that "/" i mean a or b, not a divided by b

[woeful briar]

I think every non-zero number can be considered a lcm

For these two numbers

[mystic saffron]

So the (-1)^a must be real, if imaginary then LCM isnt defined, so a also cant be something like... A fraction

[short terrace]

Tbf they are UFDs, it's just that everything that isn't zero is a unit

[mystic saffron]

Since if, lets say a=1/2 then (-1)^1/2 is i, thus it cant be a solution

[mystic saffron]

Hm

[woeful briar]

I guess

[woeful briar]

Well if its real it must be +-1

But anyway lcm is not uniquely defined

[mystic saffron]

The question says "positive rational", so i guess 1 is the solution?

[short terrace]

The way LCM is defined only really makes sense in naturals. Even in integers, you cease to have a unique LCM

[short terrace]

!original please

[odd edge]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[woeful briar]

Lcm is usually a principal ideal in these contexts

[mystic saffron]

Lowest positive rational number a and b for which lcm of e^(a pi i) and e^(b pi i) is defined.

[short terrace]

True true but this guy has pre-uni maths as a flair

[short terrace]

Do you have a screenshot or an image of the question

[mystic saffron]

Ahh no

Js saw somewhere

[mystic saffron]

learning can never go wrong

[short terrace]

it can take a lot of time

[mystic saffron]

Yep, but thats fine

[short terrace]

Well if you saw it somewhere there must be some more context attached

[mystic saffron]

I am sure, no

[odd edge]

@mystic saffron Has your question been resolved?

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[lucid gorge]

Help

[narrow crypt]

i need somebody help

[lucid gorge]

Ok thank u

I can't solve this problem

can you take a look at it

Heyy

HELP

[wicked olive]

Send the problem

[lucid gorge]

waitt

[silk valley]

Where is the problem?

@lucid gorge

[lucid gorge]

here

help

it's difficult

[mint narwhal]

I think you are just counting

[silk valley]

Bro effortless

[mint narwhal]

are you a not a native speaker? if you speak Chinese, I can help

[silk valley]

In order
At the top
9, 10, 11, 12, 13, 14
Start at 15, 16, 17… 22
Then once again 38

Biggest waste of my time

Is this actually the problems you guys recieve

[lucid gorge]

i can speak chinese

[silk valley]

This is like 1st grade level probably

[lucid gorge]

Ohh thank..

[mint narwhal]

好的，你是哪不懂？

[silk valley]

How is your role pre university math? This is like underage to be on discord math

[lucid gorge]

Hey can I tell you something?

[silk valley]

?

[lucid gorge]

@mint narwhal and @silk valley where are you from?

[silk valley]

USA

[lucid gorge]

Woww

[mint narwhal]

I'm Chinese, but am in New Zealand

[lucid gorge]

my dream is to grow up and study abroad in china

Nice

Can you teach me a few words?

@mint narwhal

[silk valley]

Hello is Nihao

All I know

[mint narwhal]

sure, though maybe not in this group

[lucid gorge]

yep

@mint narwhal how old are you?

And.. @silk valley how old are you?

[silk valley]

13

[mint narwhal]

14

[lucid gorge]

you are 2 years older than me @mint narwhal

...

[mint narwhal]

cool

[lucid gorge]

I am so young

😭

[silk valley]

Reported

You are underage

[mint narwhal]

do you still need help with the question? if you want help with chinese, maybe not in this group

[mint narwhal]

tbf, you were probs 12 when you first joined too

[lucid gorge]

then can you and I be private friends

[mint narwhal]

okay

[lucid gorge]

okay

you send invitation

[silk valley]

YAY YOU HAVE FRIENDS

[lucid gorge]

Do you want them? @silk valley

[silk valley]

Want what?

[mint narwhal]

I don't think this convo should carry on....

[silk valley]

.close

[lucid gorge]

yeah..okay

[silk valley]

I don’t have mod powers :(((

[mint narwhal]

it's fine, though maybe we should aim to be kinder...

[silk valley]

I just can’t help it after seeing him request help on elementary level work

I just got so confused

[mint narwhal]

yeah, i understand

[mint narwhal]

tbf, i was as well

[silk valley]

Was that his like method to making friends, he goes off topic and looks for a topic both him and the other person like?
If so, I saw it in action

[mint narwhal]

maybe

@lucid gorge , can you close the thing so other's can get help if needed?

[silk valley]

.close

<@&268886789983436800> If I had to guess you could probably close it

[mint narwhal]

well, good night/day

[proud cradle]

.close

[odd edge]

Channel closed

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[silk valley]

It’s 3AM my place

[mint narwhal]

then have a good day

[odd edge]

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[sick pier]

is this correct?

[woeful briar]

Are you trying to find the negation?

not (P --> Q) is not equivalent to (P --> not Q)

[short terrace]

!original please, especially the question heading

[odd edge]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[sand horizon]

Not(P => Q) = P and not(Q)

[sick pier]

yes negate and simplify

[odd edge]

@sick pier Has your question been resolved?

[woeful briar]

.

[keen scroll]

is this

soem sort of weird rage bait

[sick pier]

this should be correct then

[keen scroll]

oop is occupied sorry

[sick pier]

why is this wrong

[sick pier]

<@&286206848099549185>

[sturdy hazel]

not one number to be seen

[sick pier]

wdym not one nnumber to be seen

this is the answer

[pulsar current]

I'm pretty sure the outer quantifiers should remain unchanged

[sick pier]

but why

[pulsar current]

Think about it in words

If there just exists some x or y, it isnt sufficient to act as a contraposition for the original statement which involves ALL x and y

However if the quantifier was part of P or Q

That would have been a different story

[sick pier]

hmm

[sick pier]

and is this correct?

[sick pier]

but here it changes hmmm

[sick pier]

<@&286206848099549185>

[pulsar current]

They're asking for the negation here

Not contrapositive

[solemn gale]

What's the matter?

[odd edge]

@sick pier Has your question been resolved?

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[shell gulch]

I need help understanding Hydrostatic. I know it's Physics but if I can't understand the concept itself, I won't understand the calculation either. Can someone help me?

[austere jolt]

hi, welcome to the server! while the question itself is not an issue, since you are asking for help with a physics concept and not calculations, you may find better help in the Physics discord server!
(link to the server is discord.gg/physics)

[odd edge]

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[leaden karma]

How can I do part (iii)?

[odd edge]

@leaden karma Has your question been resolved?

[vernal pilot]

let $\beta$ be a root of $P'$ not a root of $P$. then you have $$0 = \sum_{i=1}^{k}\frac{1}{\beta - \alpha_i}\implies 0 = \sum_{i=1}^{k}\frac{\bar{\beta} - \bar{\alpha_i}}{|\beta - \alpha_i|^2}$$ this gives us $$0 = \bar{\beta}\left(\sum_{i=1}^{k}\frac{1}{|\beta - \alpha_i|}\right) - \sum_{i=1}^{k}\frac{\alpha_i}{|\beta - \alpha_i|^2}$$
$$\implies |\bar{\beta}| = \frac{|\sum\frac{\alpha_i}{|\beta - \alpha_i|^2}|}{|\sum \frac{1}{|\beta - \alpha_i|^2}|}$$
Now use the triangle inequality on the numerator + the fact that $|\alpha_i| < R$

[clever fjord]

Asteroid

[vernal pilot]

and also that if x is a positive real then |x| = x and |\bar z| = |z|

there is som nice cancellation where you have R(that thing)/(that thing) = R

[odd edge]

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[split summit]

i got x = ln(3+4k) - ln(2) for the min and x = ln(1 + 4k) - ln(2) for the max

[split summit]

im confused because they say "find the coordinates" like its one point

but there's clearly infinite points

so thats the main thing i just want to ask

[peak anchor]

it says stationary 'points', meaning multiple points

[split summit]

yeah but by "multiple" there is infinite

multiple still implies that there's a finite amount to me

idk why

[peak anchor]

I don't see anything in the question that implies a finite number of stationary points. it just says find the points, doesn't say anything about how many, except possibly more than one

[split summit]

ok

fair enough

.solved

[odd edge]

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[void prairie]

Hey I was tryn to learn about complex numbers like learning from scratch can you all suggest me course or video but I haven't learned differentiation yet so no using differentiation for explaining

[woeful briar]

You don't need any calculus to learn what are complex numbers

Maybr 3b1b has something

[fair forum]

(or OChem Tutor)

[void prairie]

I did check out that but he is not explain the thaught process behind it and logic

Do they explain thaught behind it like how mathematicians thaught of it

[fair forum]

wdym?

[errant gust]

the basic idea was to fix the problem with the fundamental theorem of algebra

nth degree polynomial should have n roots

so complex numbers were introduced to allow these roots to exist

[woeful briar]

Was it?

In terms of history

[errant gust]

it was to solve polynomials was it not

[void prairie]

Ummmm like what lead us to imaginary number why i lies perpendicular to number line

[errant gust]

the first usage of complex mumbers

[woeful briar]

Yeah but I would imagine it was specifically for simple polynomials like x^2+1

[woeful briar]

Well we like to represent the complex numbers as such because they form a 2d vector space over R, which means they can be thought of as a plane

[void prairie]

Yeah so I need video or course that explain all these stuff

[odd edge]

@void prairie Has your question been resolved?

[odd edge]

@void prairie Has your question been resolved?

[odd edge]

@void prairie Has your question been resolved?

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[lunar marten]

I don’t get why the 2x turns into just an x and the 2^4^x^4 just becomes 2^4^x^2 + 1

[lunar marten]

On 7

[wooden python]

well 2x is 2*x

the x is left alone while the 2 is folded into the 2^(other shit) factor you've got going therte

namely 2^(other shit) * 2 = 2^(other shit + 1)

[lunar marten]

Alright that makes sense

How would I go about starting to solve 13

[odd edge]

@lunar marten Has your question been resolved?

[lunar marten]

?

[ember oak]

If $y=f^{-1}(x)$, what do you suppose $x$ is in terms of $y$?

[clever fjord]

SWR

[lunar marten]

What

[ember oak]

Basically, x=f(y)

[lunar marten]

Well yeah but like how do I start this problem to get what f(x) = 2

Like would it be f(6) = 2 then what do I do from there

[ember oak]

Solve $2=\sqrt{x-2}$

[clever fjord]

SWR

[ember oak]

Find f'(x)

Admittedly, the way they wrote the problem is confusing, so i don't blame you for being lost

[lunar marten]

Did I do anything wrong

?

I need this like soon

Like

Really soon

[ember oak]

How did you calculate f'(x)?

[lunar marten]

Chain rule

Oh wait

I forgot to put the -1/2

And it’s the reciprocal cause it’s inverse right?

Then that’s the answer right

[ember oak]

f'(x) is still wrong

But f'(6) is right

[lunar marten]

I’m running out of time besides f’(x) being wrong those are the right steps correct?

[ember oak]

Yes, you've calculated f'(6) correctly

[lunar marten]

Tysm

[ember oak]

But you're not done

Remember what the problem is asking you to do

[odd edge]

@lunar marten Has your question been resolved?

[odd edge]

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[odd edge]

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[wise forge]

@dusky marsh

[dusky marsh]

Hi

[wise forge]

okay so i need helo with verifying limits

[dusky marsh]

Ok

[wise forge]

cuz i follow the formula

but then i get lost

[woeful briar]

go to another channel

[wise forge]

cuz there are some logarithms and exponential things that i kinda kinda forgot

[woeful briar]

this one will close

[wise forge]

fhis is mine

[wise forge]

why

[woeful briar]

.

[wise forge]

where do i go then

[woeful briar]

read

[woeful briar]

for future reference don't delete the first message

[odd edge]

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[thorny hawk]

Can anyone show me where I went wrong here? I got points docked for calculating the gradient incorrectly, but after double checking I found that the values were correct.

[native moss]

Your gradient (4, 12, 36) is correct but I think the plane equation went off ,you used (x - 5) instead of (x - 3), and the constant +12 doesn’t fit (3, 2, 1) should be +2

[modern sundial]

I'm not familiar with that equation for the tangent plane but it doesn't look like the right answer to me at a glance. Does your answer key give your final solution as the final answer?

[thorny hawk]

I wrote x -3 if you look closer

[native moss]

that's a 3? ok

[thorny hawk]

Yeah my handwriting lowkey just sucks

[tidal matrix]

graphically, this seems to intersect the surface at the point. i think they might have issue with the way you wrote it, i.e. $$F_x = y^2z^3 ;\bf{=}; (2^2)(1^3)$$
which seems to imply that this is the derivative for all $(x,y,z).$ Best practice would be to either:
\begin{itemize}
\item Calculate $F_x,$ then in a separate line you can write $$\implies F_x(3,2,1) = (2^2)(1^3)$$
\item Write $F_x \big|{(3,2,1)} = y^2 z^3 ; \big|{(3,2,1)} = (2^2)(1^3)$, to indicate your substitution
\end{itemize}

[clever fjord]

ηασιβ ♥

[tidal matrix]

there we go lol

they may also have issue with it being outside the border of the page? but since you can see it in the scan, i doubt it

[thorny hawk]

It was graded as if it was calculated completely incorrectly, not just a simple notation error. But I’ll definitely take that into consideration next time

5/10 points off

I’m probably gonna dispute this

They might have misinterpreted my handwriting

[tidal matrix]

possibly, although i could see it was a 3 pretty easily. believe you me, there are students with MUCH worse handwriting

[thorny hawk]

Thank you for your help, I appreciate it

[tidal matrix]

ofc, best of luck

[odd edge]

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[stone egret]

I tried separating cases of when f has a real eigenvalue, if so then the result is true... if not, meaning if the characteristic polynomial of f is a product of second degree polynomials with negative delta... then there must be a stable plane under f, I know it's a constructive problem(I need to construct the plane but I have no clue on what would that plane be)

[stone egret]

<@&286206848099549185>

[sand horizon]

You can try to extend the scalars to C

f will extend to a complex linear endomorphism after considering E<C> := E tensor_R C

There might be a not C way tho

[odd edge]

@stone egret Has your question been resolved?

[stone egret]

Sorry but I think we didn't cover tensor products in our course... so there must be a way of solving this without extending E to be a C-vector space. I think my approach was correct I just can't figure out how to find that always existing plane...

[sick epoch]

Hint, the complex roots of a real polynomial come in conjugate pairs

[stone egret]

Oh, so if I pick a a complex root ꟛ of the characteristic polynomial then the conjugate of ꟛ will also be a root, so ꟛ and its conjugate are two distinct eigenvalues... so any two vectors associated with ꟛ and its conjugate would form a plane... that's helpful thankss!

[sick epoch]

🙂

[stone egret]

Oh but that plane isn't necessarily stable.

[odd edge]

@stone egret Has your question been resolved?

[odd edge]

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[open pike]

Hello I don't understand what this is asking me to do and how they got the following answer. I know how to find the area but I'm confused on how and why the answer is what it is. Please help explain, thank you!!

Was I supposed to find the z-score? If so, what would the x even be? I mean, idk what i'm supposed to be doing 😭

[quasi falcon]

Yes, you had to find the z-scores

Which, btw, if you think about it, finding the z-scores just means looking at how many SD away youre from the mean

From the natural idea of it, the distance between -5 and -3 is 2 to the right, given that the SD is = 4, that means that the left bound is 0.5 SD from the mean.

Same idea for -5 to 1, thats a difference of 6 to the right, which is 1.5 SD from the mean

[open pike]

OHHH

ohhhh

wait so then

what was the x then?

[quasi falcon]

If you wanna go to the equation:

$\frac{x-\mu}{\sigma} = \frac{-3 - (-5)}{4} = \frac{2}{4}$

[clever fjord]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[open pike]

oh hum

[quasi falcon]

the x is basically a value in your distribution

the mean is x = -5

x = -3 and x = 1 are other values, which can be associated to z's on the standard normal dist

[open pike]

ohhh okay

so Im supposed to plug in both -3 AND 1?

when im doing it?

sorry im slow

[quasi falcon]

one at a time

You will find one z for -3

[open pike]

yeah

[quasi falcon]

and one for 1

which, tbh

[open pike]

ohhh

yeah that makes sense

[quasi falcon]

Have you ever seen the formula for the normal dist?

[open pike]

thank you so much

[open pike]

um

maybe?

i dont have my notes out right now

ill go check

[quasi falcon]

No need to understand how it works

Just so you know its a function of x

[open pike]

oh yeah i dont recognize that

[quasi falcon]

well, when you are looking for the probability between two values

You are just integrating the area between those x's

[open pike]

integrating?

[quasi falcon]

yep, as in $\int_a^b f(x) dx$

[clever fjord]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[quasi falcon]

The area under the normal distribution is the probability to land between the limits of integration

[open pike]

hmm okay

thank you for helping me

i think I get it now

.close

[odd edge]

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[verbal owl]

is this correct for drawing standard position for 195 degrees

[vernal yacht]

Not really

[sacred horizon]

other way

[verbal owl]

whys that so tho?

I thought positive 195 degrees is drawn anti clockwise

[sacred horizon]

you start from positive real axis and in math anticlockwise is positive

[vernal yacht]

From positive x-axis, rotate anti-clockwisely

[wooden python]

ccw starting from positive x-axis (you always start from the positive x-axis)

your starting pt is wrong

[verbal owl]

like this?

[amber schooner]

doesn’t look like 15 past 180 to me

[unkempt lichen]

minor nitpick though: like knief said, this looks a bit too big

[amber schooner]

you’re about 30 degrees too far

[wooden python]

ish. it's a bit too big

[verbal owl]

oh ya ok noted

then how we draw positive 405 degrees

cus this is larger than 360 degrees

[wooden python]

it's a full turn plus something

[amber schooner]

going 360 around puts you back where you started

[verbal owl]

like this?

[amber schooner]

how did you end up down there

[wooden python]

you went clockwise 💔

[amber schooner]

😭

[wooden python]

you yourself said positive 405

positive means ccw

not cw

[verbal owl]

oh ya

this should be it

[amber schooner]

wut

what’s 405 - 360?

[verbal owl]

sorry wrong photo

[amber schooner]

right

[verbal owl]

45

[amber schooner]

this is like the same thing dawg

that you just sent

💀

[verbal owl]

the other dont look half of 90

[amber schooner]

so if you effectively rotate 45 degrees ccw how did you end up all the way over there?

[verbal owl]

aint it a round + 45 degrees?

[amber schooner]

nah bro that’s 135 degrees

[wooden python]

how did 45 degrees stretch over an entire quadrant and more

you just zoomed right past the 360+90 point

[verbal owl]

this

this is the one

[wooden python]

better

[amber schooner]

indeed

[wooden python]

tho a wee bit under target now

[amber schooner]

looks like 30 degrees but i’ll take it

[verbal owl]

alright thanks guys

[odd edge]

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[ruby marsh]

can someone give subtle hints without giving the answer, i tried combining the denominators to n!, but i dont think this is the way to rly progress

[odd edge]

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[wanton bison]

You need to open a new channel, also maybe try induction

[upper rock]

.close

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[paper bear]

excuse me can i ask for help..?

[solemn gale]

yea

[vernal yacht]

just post

[paper bear]

im from indo but it translate to

The remainder of 2025o + 20251 + 20252 + ... + 202520 when divided by 2029 is...(xy = x! / (y!(x−y)!), with n! = 1×2×3×...×n)(A) 761(B) 946(C) 1024(D) 1395

[thorny spindle]

do u know the formula of sum of combinations?

[paper bear]

em.. no..

[thorny spindle]

its 2^n

we will use the 6th property

do u want to try yourself first

[paper bear]

i did but i cant

[thorny spindle]

well what was ur approach

[paper bear]

em 2^2025/2029?

[thorny spindle]

have u guys studied fermats little theorem?

[summer wave]

this is not the whole sum though

[thorny spindle]

i didnt realize that

[paper bear]

no im still in middle school n got picked for a competition and this is one of the question they gave few years ago

[thorny spindle]

this problem is solved by modulo

but u haven't studied that yet :(

[paper bear]

aww alrr 😓

thankyouu tho

.close

[odd edge]

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[deft flicker]

can someone explaibn how they got the vector for the 25 N * m

i gathered that they are taking the magnitude of the vector and multiplying it by the unit vector

but im not sure how they got the unit vector

the -isin 40 - j cos 40 cos45 - k cos40sin45 is confusing me

[modest nacelle]

Hey, fellow Haskell lovers. Can I look at the original question?

[odd edge]

@deft flicker Has your question been resolved?

[late flint]

I would say to use direction cosine matrices but I've been cooking my brain trying to find an order that works

you can try a positive rotation about x of 45 degrees to line up with the horizontal component of the 500N?

[deft flicker]

what u mean

[late flint]

so you see the y axis right

you can make a new coordinate system that has y rotated 45 degrees counterclockwise about x

this lines you up with the horizontal component of the 500N

the direction of 500N also happens to be the axis about which the moment 25 Nm is acting on the metal thing

[deft flicker]

what do u mean make a new coordinate syste,

[late flint]

I mean exactly what I show in this image

[deft flicker]

what does this mean mathematically

[late flint]

It's done so that it becomes easier to express certain forces and moments in terms of the original coordinate system of x,y,z

[late flint]

were you taught of euler angles or direction cosine matrices

[deft flicker]

no

[late flint]

if this is an actual class then what's the most recent topic you have covered?

[deft flicker]

equivalent couple moment system]

[late flint]

I suggest looking at some literature or videos explaining euler angles and rotation matrices, because the fact that the unit vector shows products of sine and cosine with different angles is something I've absolutely seen before in my statics class

[deft flicker]

the textbook doesnt even use these for the solution

so why would i need to learn this

[late flint]

what does it use then

[deft flicker]

textbook solution is the first image i posted

[late flint]

that is not a solution, it is one single step that shows you the moment vector in terms of i j k

[deft flicker]

moment vector in terms of i j k

yes this is what im trying to find

[late flint]

if it doesn't show you what steps it takes then it doesn't really help you; I'm just speaking from experience based on the classes that I've taken that the unit vector looks reeeally similar to something that comes out of a rotation matrix problem

which is why I'm suggesting to look into them

[odd edge]

@deft flicker Has your question been resolved?

[odd edge]

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[void sphinx]

umh

[odd edge]

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/

[void sphinx]

this

idk what is this

[whole gyro]

anything specific you dont understand

[void sphinx]

like

what does mean x=gin (x+2)?

[modest nacelle]

gin?

[void sphinx]

i mean sin

[whole gyro]

its sin x = sin ( x+ 2pi )

basically

notice how the graph repeats in certain intervals

[void sphinx]

ye

[whole gyro]

that interval, if you notice carefully, is 2pi

which represents a complete angle

so basically this equation encodes the "periodicity"

[void sphinx]

OHHHHH

ok

thanks

[odd edge]

@void sphinx Has your question been resolved?

[void sphinx]

yes

[odd edge]

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[frank grotto]

Hi

how do you solve inverse functions

[quasi sparrow]

set y = f(x) = 11x - 8
swap x and y
x = 11y - 8
solve for y
x + 8 = 11y. (x+8)/11 = y
that new function is the inverse function

$f^\inv(x) = \frac{x+8}{11}$

[clever fjord]

riemann

[frank grotto]

wait

mb i was reading another question

is this a standard?

[quasi sparrow]

standard is subjective to your textbook/teacher

[frank grotto]

wait so

how do you solve the

3rd one

[quasi sparrow]

same procedure here, just more algebra

try it yourself and see

[frank grotto]

ok let me try

so

do i switch the 2 with the 6

sorry if i may be a little bit slow

[quasi sparrow]

nope

[frank grotto]

im learning this newly

[quasi sparrow]

no numbers were swapped here, just x and y

[frank grotto]

hm

wait

so it just becomes

2y 6y

instead of 2x 6x

right?

but then what

[quasi sparrow]

you should have a full equation after swapping x with y

x = ....

[frank grotto]

wait

do you mean

(6y + 1) = (2y + 14)

wait can we then like

switch the place of the y

and the 1

so its like

4y = 13

y = 13/4

is that how it works?

[quasi sparrow]

you're missing an x

[frank grotto]

what

didnt we switch x with y

[quasi sparrow]

x = (2y + 14) / (...)

[frank grotto]

Oh right

dude im stupid

so its x = 2y + 14 over 6y + 1

can we then do this

equal thing

[quasi sparrow]

yea nothing's stopping you

[frank grotto]

yea but where does the x go

do we put it in multiplication

x(6y + 1) = (2y + 14)

like this?

[quasi sparrow]

yes that's a good first step

[frank grotto]

ok then

hm

6xy + x = 2y + 14

i got here

now im stuck

[mystic saffron]

so

[quasi sparrow]

!nosols

[odd edge]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[mystic saffron]

sorry didn't know i put spoilers as linear hints

thanks!

[mystic saffron]

try factorizing

[frank grotto]

hm

[mystic saffron]

you switched them ig right?

[frank grotto]

yea

but i have no idea what to do now

WAIT

what if

we take out the y

[mystic saffron]

write it out and see if you got it

!

[frank grotto]

wait

does the answer have to be a solid number

[mystic saffron]

no!

inverse function

is also a function

[frank grotto]

ok then

it should be

14-x over 6x -2

[mystic saffron]

Yes!

congrats

it's right

do you understand the concept now?

[frank grotto]

eh its a bit scuffy

i dont know

wait

gimme 10 mins

ill watch a video

[mystic saffron]

alrr i can explain it to you if you want

[frank grotto]

yes please

from the begining

id really love it

because im confused as hell

[odd edge]

@frank grotto Has your question been resolved?

[mystic saffron]

are you online

[frank grotto]

yes

but after watching

i figured it out

its easy its just im a bit

thick skulled

[mystic saffron]

congrats ig you can close the channel

[odd edge]

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[fossil horizon]

whys the way i did it wrong

[fossil horizon]

heres the answer

[odd edge]

@fossil horizon Has your question been resolved?

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[fossil horizon]

nvm

[odd edge]

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[harsh chasm]

Represent sqrt2 on the real line

[harsh chasm]

What does that mean

[tepid pelican]

they probably want u to use some geometric construction to draw the point sqrt2 on the real line

[harsh chasm]

What even does the real line mean

[tepid pelican]

its just a line with all the real numbers on it

[harsh chasm]

Just nunber line of real numbers?

[tepid pelican]

yes

[harsh chasm]

Do I just put sqrt2 between the integers its closest to

[tepid pelican]

i think u should do it geometrically

[harsh chasm]

How so

[tepid pelican]

a pretty stupid example, but u could e.g. geometrically mark 1.5 by bisecting the segment defined by points 1, 2

for sqrt2, u'll have to construct some line segment of length sqrt(2)

how could u do that?

[harsh chasm]

Oh so a trianfle of height 1 and width 1?

And the hypotenuse is sqrt2?

[tepid pelican]

exactly

[harsh chasm]

Ahaaaa

[tepid pelican]

a good way to draw it would be sth like this

it's nice and compact

[harsh chasm]

Whars the point of the arc

[tepid pelican]

D?

that's the sqrt2

you have to represent it on the actual number line

the reason for using compass is to maintain the distance

(the radius in the compass stays the same)

so the distance between 0 and D is sqrt2, which makes D sqrt2

[harsh chasm]

Wasnt really taught how ro use a compass

[tepid pelican]

you cant draw circles with compass?

[harsh chasm]

Idk never used one

[tepid pelican]

do u have a compass?

[harsh chasm]

I think so

I got the kit thingie

[tepid pelican]

alright, its pretty simple

[tepid pelican]

here that arc is centered at 0 and "starts" at C

so you put the sharp needle on 0, the pencil thing on C and then twist it carefuly (so that the compass doesnt expand or contract) until the pencil gets on the number line (so that you have D on ur number line)

[harsh chasm]

Ahaa

[tepid pelican]

https://www.youtube.com/watch?v=efUlPZuezBU

this vid explains it and it includes the compass construction

[harsh chasm]

Can it look somrthing like this

[tepid pelican]

yep, that looks like it

[harsh chasm]

Alr ty

[tepid pelican]

maybe u could put at least -1, 0, 1, 2 on the number line

to make it look more like a number line

[harsh chasm]

Random question but why does the arc interest the x axis at sqrt 2

[harsh chasm]

Ah alr

[tepid pelican]

circles have the same radius, so the radius on the x-axis will be same as the diagonal, which is sqrt2

thats the whole point of using a compass

[harsh chasm]

Oh its a radius

Sorry took me a second to realize lol

Akr ty!

[tepid pelican]

np

[harsh chasm]

Can i keep this open since ill prolly have more questions

Or do i close and open another kne later

[tepid pelican]

prolly close this and open another one later

[harsh chasm]

Ight

How do i close

[tepid pelican]

.close

[harsh chasm]

.close

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[dim thorn]

find the value of " K " so that the function " f " is continuous at the indicated point, i got stucked where we put f(pie/2) = 3, im getting 0/0 form what to do after it

[dim thorn]

how do i do it then

any one?

<@&286206848099549185>

[quasi sparrow]

maybe use a subsitution to find the limit as x goes to pi/2

try t = pi - 2x and use a trig identity

[dim thorn]

or maybe just L hospital rule

becz of the 0/0 form

yea got it

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[static locust]

how do i find the solutions for (8)/(2x-5) + 21 = 23

[wild spindle]

How do you start?

[static locust]

(2x-5) multiply?

[wild spindle]

You can but can't you do something before to get an easier expression

[static locust]

nmnot sure

[wild spindle]

If you multiply by 2x-5 directly, youll get a 8 + 21 * (2x-5) = 23 * (2x - 5)

[static locust]

no i meant

8/2x-5 + 42x -105/2x-5 = 23

do i also multiply the 23?

[wild spindle]

Dont develop ur expression

Will make it harder for you to understand what u are dealing with

Cant u substract the 21 beforehand?

[static locust]

oh yeah

[wild spindle]

So that makes it easier

[static locust]

dude how did i not catch that

im not locked in

now (2x-5) both sides

[wild spindle]

Happens, always try to simplify it as much as possible

Yes exactly

And hten you can developp, substract and all of that

[static locust]

alright thanks dude

il ldo that rn

[wild spindle]

np, gl

[static locust]

4,5 = x?

is that the only solution

[wild spindle]

8 = 2*(2x-5)

So 4 = 2x - 5

yes indeed

[static locust]

oh yeah

wait no

i got 8 = 4x - 10

[runic night]

Yh divide through by 2

[static locust]

divide what

i do 8 = 4x - 10

+10 both sides

18 = 4x

18/4

x = 4,5

[runic night]

Yh I’m tryna say u get the same result whichever way u do it

[static locust]

ah alright

but is that the only solution?

[runic night]

Yes

[wild spindle]

You got a polynomial equation of degree 1

It has at most 1 solution

, so if you found one it is the only

[static locust]

alright thanks guys

[wild spindle]

if you have osmething like ax + b, it will always have at most one solution

[static locust]

but if its ax^2 + b

then its 2 right

[wild spindle]

Then it CAN have two

does not mean it HAS two

But yes there can be more

[static locust]

oh alright

[wild spindle]

Also more like ax^2 + bx + c but yes

[static locust]

i see

[wild spindle]

And ax^3 + bx^2 + cx + d has at most 3

[static locust]

well again, thanks

.close

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[zealous garden]

unfortunately im back.. ive literally spent all day on this assignment. im not sure how to round this number or what i did wrong.

[zealous garden]

i also tried 1.7 and it was wrong

RAAH IM SO TIRED OF THIS

im abt to just fail

[quasi sparrow]

0.16657 does not round to 1.7%

[zealous garden]

idk thats just what someone said

ive been working on this for 4 hours. i have 2 questions done

[quasi sparrow]

you have to multiply by 100 to get a percentage.

[zealous garden]

16 and 17 are both wrong

im so tired of this i just wanna submit it and get an f ive missed out on so much stuff today because ive just been doing this

[quasi sparrow]

16 is not rounded to one decimal place

[zealous garden]

16.657

[quasi sparrow]

uhhhhh

[zealous garden]

16.66?

16.7…? 16.6….?

[zealous garden]

so 16.7?

thats wrong

[quasi sparrow]

and

[zealous garden]

idk what to do

ive tried like. everything i feel really stupid right now

[quasi sparrow]

well the more you guess without finding your error, the worse you'll feel

i don't suggest spamming numbers

[zealous garden]

well ive checked my answers on the other questions and everything is wrong i feel really unmotivated and this assignment is due tonight

[quasi sparrow]

¯_(ツ)_/¯

can't help someone who doesn't want to learn

[zealous garden]

.close

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[arctic cape]

Write the first four terms of the power series expansion of f(x) in the img.

My math is a bit rusty but I don’t think I could find the first four derivatives of this.

You can rewrite it as e^(xln(1+x))
I find the expansion of xln(1+x) in the second img and in the third that of e^y thinking I could substitute y= xln(1+x)
But then each y is an infinite power series so am I even doing the right thing?

[stark heart]

Hmm so you are going to expand e^y which is gonna be an infinite series expansion each with an infinite expansion exponent

[arctic cape]

is what Im doing correct or just absurd

[rough birch]

that looks good

[wicked kestrel]

you get a bunch of series but you only need to consider terms up to x^3

[arctic cape]

why

[wicked kestrel]

because you're only concerned with the first four terms

[odd edge]

@arctic cape Has your question been resolved?

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[shrewd trellis]

I dont understand this

[stark heart]

It would be clearer if you imagined the angle in a unit circle

If you add 360⁰ to the angle it should it will be the same angle as the original

[shrewd trellis]

yes I agree

Yeah I know that

also my second question is

since this graph has a period of pi instead of 2 pi, this tells us that the graph is zoomed in right?