help-33

[lyric kelp]

so far i got to replacing <--> with a xor

[humble nebula]

what do you mean by “remove”? Just replace it with AND and OR and XOR?

[lyric kelp]

hi sorry for not mentioning this earlier i cannot do that in this one lmao i need to use xor

wait no

what i meant is that

okay forget what i said

i need to simplify this to a point where theres no negation sign anymore

.close

[marsh citrus]

Channel closed

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[marsh citrus]

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[shy mica]

why this solution is giving number of subjects...i don't get it

[short star]

His average score is sum of all scores divided by number of subjects

This average is increased by 5 due to the increases in certain individual subjects

So this increase is = the sum of additional scores in those subjects, divided by the total number of subjects

That's what the solution is explaining

[shy mica]

ok

.close

[marsh citrus]

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[marsh citrus]

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[buoyant jetty]

this implicit function theorem I dont get it

[elfin cairn]

It means if you have some equation of multiple variables. Under certain conditions, there is a continouous/differntiable/C1 function that satisfies the equation in some open set.

[buoyant jetty]

can you give an down to earth simple example

[elfin cairn]

x^2+y^2=1

there are two ways to consider y as a function of x

That give the upper and lower halfs the the circle

[buoyant jetty]

F(x,y,z) = 1

where F(x,y,z) = x^2 + y^2

ahh im so fucked dude

exam is this friday I am already cooked

im so fucked

[buoyant jetty]

what are the conditions we need to verify

I need to verify if all the derivatives are continous

like I need to verify if the partial derivative with respect to x is continous

i need to verify if the partial derivative with respect to y is continous for F

[elfin cairn]

You need your function to be continoualy differentiable at the point where you apply the function. And that the derivative w.r.t. z is not zero

[buoyant jetty]

so a C1 function

[elfin cairn]

You should trust your notes more then me on this

[elfin cairn]

Yeah

[buoyant jetty]

?

arent you from israeli?

[elfin cairn]

And?

[elfin cairn]

And this is equivalent to the partial derivarives existing and being continuous

[buoyant jetty]

there is this guy from technion very famous

on youtube

talking about C1 class of functions

[buoyant jetty]

yeah if a function is C1 on an interval of the domain then the function is differentiable at a point in the interval of the domain and the derivative at that or those points is continous

there is nothing much more to say about it, just C1 class functions

[elfin cairn]

Zensor!

[elfin cairn]

don't know how you spell his name in english

[buoyant jetty]

Aviv Censor

he is the goat, helped me a ton for basic linear algebra

[elfin cairn]

He is amazing

[buoyant jetty]

dunno if he has content about implicit function theorem but

[elfin cairn]

He should have

[buoyant jetty]

what where the conditions for in order for we to be able to apply the theorem

https://www.youtube.com/watch?v=bk9IKHS5KbY

[elfin cairn]

Nice

[buoyant jetty]

how is that this circle equation is not a function

[elfin cairn]

For every x there is are multiple y values

The point of theorem is that we can choose our "branches" and that they are nice enough

[buoyant jetty]

what is the definition of a function

one input cannot have 2 different outputs, vertical line test

[elfin cairn]

Yes

[buoyant jetty]

how is that not the case here?

[elfin cairn]

We don't say its a function. Its a curve defined by the equation

[buoyant jetty]

ahh, for example see x = 0

when x = 0 , y = 1 and y = -1

[buoyant jetty]

yeah my bad

where did he got this equation from?

he solved for y?

[elfin cairn]

Yep

But its rarely possible using elementary functions

Thats why the theorem exists, to tell you its possible

[buoyant jetty]

the issue is what are the conditions such that the implicit function theorem applies

[elfin cairn]

C1 function and invertibale Jacobian

[buoyant jetty]

the fuck does that invertible jacobian stablishes

[elfin cairn]

Its the most general version of the theorem

[buoyant jetty]

you know what the jacobian is? is like the rows are made out of the gradients of every component function

[buoyant jetty]

YES

this PHI thing is driving me insane

can we agree to that?

[elfin cairn]

Agree with what?

[buoyant jetty]

that the varphi thingy is confusing

[elfin cairn]

To me its not

[buoyant jetty]

can you explain

like I have an exercise we can work through if thats okay with you

about implicit theorem

[elfin cairn]

Ok.

[buoyant jetty]

Sea $F(x,y,z) = y^2x - e^{yz^2} - 2xz$ \ a) Probar que $F(x,y,z) = 1 \iff z = \varphi(x,y)$ cerca de $(1,0,-1)$ \ b) $h(s,t) = \varphi(t-2s, t^2 + s^2 - 2)$ \ Encuentra el plano tangente al grafico de $h$ en $(-1,-1, h(-1,-1)$

[elfin berry]

Renato

[elfin cairn]

I will need translation

[buoyant jetty]

we need to check if F is C1

[buoyant jetty]

Let F ... a)prove that .. .. iff ... in the neighborhood of (1,0,-1)
b)h(s,t) = . . . find the tangent plane to the graph of h at (-1.-1.h(-1,1

hopefully is readable

@\

@elfin cairn are you here?

[elfin cairn]

Yes

[buoyant jetty]

Let $F(x,y,z) = y^2x - e^{yz^2} - 2xz$.

a) Prove that $F(x,y,z) = 1 \iff z = \varphi(x,y)$ near $(1,0,-1)$.

b) $h(s,t) = \varphi(t-2s, t^2 + s^2 - 2)$ \
Find the tangent plane to the graph of $h$ at $(-1,-1, h(-1,-1))$.

[elfin berry]

Renato

[elfin cairn]

For a, the z=phi(x,y) imples F(x,y,z)=1 is easy

The other direction is an application of the implicit function theorem

[buoyant jetty]

care to elaborate?

like we need to check if F is C1 btw

thats the bare minimum to apply the implicit function theorem

there is also another condition that I already forgot

[elfin cairn]

Non zero partial derivative

[buoyant jetty]

for the left direction we need to check if the partial derivative wrt z of F is non zero

[elfin cairn]

Yep

[buoyant jetty]

something like that yea

idk why tho

something like, that z can be expressed as a function of x and y

[elfin cairn]

So F is C1 should be easy

And then you need to comoute the dF/dz

[buoyant jetty]

we need to check if the partial derivative wrt z of F at the point (1,0,-1) is nonzero

[elfin cairn]

And show its not zero at (1,0,-1)

[buoyant jetty]

this near (1,0,-1) thingy troubles me

any idea what the fuck they mean?

[elfin cairn]

By near they mean in a neighborhood. An open set containing (1,0,-1)

[buoyant jetty]

sure but why do they mention

how do I get to know if F is C1 in R3?

or do I just need to know if F is differentiable and the derivative is continous at a point and not in the entire domain

[elfin cairn]

F is C1 iff all the partial derivatives exists and are continouous

[buoyant jetty]

so we need to compute all the partial derivatives

but C1 is in a interval not like in its entire domain

F is a vector field, like F : R3 -> R3

[elfin cairn]

Yes

Only in a neighborhood of our point even

This theorem is local. We don't care what happens far away

[buoyant jetty]

,w partial derivative with respect to z of y^2x - e^(yz^2) - 2xz

[elfin berry]

Results provided by WolframAlpha

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[buoyant jetty]

ok I found all the partial derivatives

now what

[elfin cairn]

Are they continuous?

[buoyant jetty]

how do I know

you mean continous in the neighborhood of a point or continous in all of their domainn

[elfin cairn]

Continuous near (1,0,-1)

[buoyant jetty]

what needs to happen so we can guarantee continuity near (1,0,-1)

[elfin cairn]

The definition of continuity

But this is not the best way to do it

[buoyant jetty]

just notice that the partial derivative wrt x,y,z are sum of continous functions

[elfin cairn]

Yep

Composition not sum

[buoyant jetty]

polynomials, eulers, etc

[buoyant jetty]

sum of continous functions and composition of continous functions

[elfin cairn]

Yep

So they are continuous. Good.

[buoyant jetty]

ye, this F surely is C1

[elfin cairn]

Now about dF/dz. What happens if you plug (1,0,-1)

what is the value

[buoyant jetty]

its non zero

,w partial derivative with respect to z of y^2x - e^(yz^2) - 2xz at (1,0,-1)

[elfin berry]

Results provided by WolframAlpha

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Requested by renatoxbz

[elfin cairn]

Yep not zero

Thats it you are done

[buoyant jetty]

wdym?

what does the implicit function says?

[elfin cairn]

The theorem tells you there is a differentiable function phi defined in a neighborhood of (-1,0) where
F(x,y,phi(x,y))=1

[buoyant jetty]

where is this neighborhood of a point coming from

[buoyant jetty]

we neved used that F = 1

[elfin cairn]

We did kind of use it just that its a constant so it doesn't change any of the derivatives

[buoyant jetty]

you mean we did F - 1 = 0

and took the partial divs

dude this theorem is weird

any idea what is going on?

[elfin cairn]

Because its no use that there is one solution. We get a lot of solution that form a nice curve defined by phi.

[buoyant jetty]

how so

[elfin cairn]

Wdym

[buoyant jetty]

like. lets go back a bit

lets rewind for a sec @elfin cairn

STEP 1, WHAT WAS IT, CHECK IF F IS C1

STEP 2, NOW WHAT?

we need that F(POINT) = 0

and that the PDV F(POINT) IS NOT ZERO

@elfin cairn

f(1,0,-1) needs to be equal to 0

[elfin cairn]

Yeah

[buoyant jetty]

but ∂/∂z f(1,0,-1) ≠ 0

[elfin cairn]

Yeah

[buoyant jetty]

ok, I just have z = phi(x,y) now

this definition you send is for like, scalar fields i think

[elfin cairn]

Yeah

Look on wikipedia for the general version

[buoyant jetty]

do you have a link

[elfin cairn]

https://en.m.wikipedia.org/wiki/Implicit_function_theorem

[buoyant jetty]

can you give me a step by step summary of what to do

[elfin cairn]

Check the conditions

Which we already did

[buoyant jetty]

how many conditions

[elfin cairn]

3

[buoyant jetty]

C1

1. F needs to be C1 in an interval of the domain

2. F(x0,y0,z0) = 0 for the neighborhood of (x0,y0,z0)

3. ∂F/∂(the variable such that = phi(x0,y0)) ≠ 0

@elfin cairn

you here?

[elfin cairn]

Yes

In 2 its just that x0,y0,z0 is a solution

But you are right

After proving these 3 things holds you get the conclusion

[elfin cairn]

One thing that is important for this question, is that if
F(x,y,z)=1 then z=phi(x,y)

This follows from the uniqueness of phi

The reason its true is because when fix x0,y0 then the function
g(z)=F(x0,y0,z) is monotone because dF/dz(x0,y0,z0) is not 0. Therefore its injective and we cannot have another solution with x=x0,y=y0 (in some neighborhood)

[buoyant jetty]

true

this is like ivt stuff

or something, that the function is monotonically increasing or decreasing

i mean this is confusing though

[marsh citrus]

@buoyant jetty Has your question been resolved?

Channel closed

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Use .reopen if this was a mistake.

[buoyant jetty]

.reopen

[marsh citrus]

✅

[buoyant jetty]

we still need to apply the theorem of the implicit function

or is it going to be used in b)?

@elfin cairn

like, so far we proved that if F = 1 then there exists a phi = (x0,y0) for the neighborhood of (1,0,-1)

are you here?

[elfin cairn]

The other direction is also true by the theorem

We finished a

[buoyant jetty]

what about b

we still need to use implicit function theorem

no?

[elfin cairn]

We already used it

For b, the implicit function theorem also tells us what is the derivative

Of phi

[buoyant jetty]

yeah

can you give hints for b

there is an equation for the tangent plane

[elfin cairn]

Yes

And it relies only on the values of the partial derivatives

So thats what you want to find

[buoyant jetty]

do you have the tangent plane equation

is like

[elfin cairn]

Yep

So start by finding the partial derivatives

of h

[buoyant jetty]

h is wrt phi dude

correct me if I am wrong but this is crazy

[elfin cairn]

Not crazy

Chain rule

Of course you need to know what is the derivatives of phi

[buoyant jetty]

h(-1,-1) = phi(-1 + 2, 1 + 1 - 2)

h(-1,1) = phi(1,0)

[elfin cairn]

which is -1

[buoyant jetty]

wdym

[elfin cairn]

phi(1,0)=-1

Because F(1,0,-1)=1

[buoyant jetty]

One thing that is important for this question, is that if
F(x,y,z)=1 then z=phi(x,y)

[elfin cairn]

Yes

[buoyant jetty]

z = phi(1,0) => f(1,0,z) = 1

z = phi(1,0) => f(1,0,z) = 1
=> f(1,0, phi(1,0)) = 1

[buoyant jetty]

dude but

[elfin cairn]

And because this phi(1,0)=z=-1

[buoyant jetty]

,w y^2x-e^(yz^2)-2xz at (1,0,-1)

[elfin berry]

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[buoyant jetty]

suppose z = -1

how to find the tangent plane thingy

P = (-1,-1,-1)

[elfin cairn]

You need the partial derivatives of h at (-1,-1)

[buoyant jetty]

z + 1 = fx(-1,-1) + fy(-1,-1)

[elfin cairn]

h!!!

Not f

[buoyant jetty]

also. s and t

not x and y

z + 1 = hs(-1,-1) + ht(-1,-1)

dude

this

is confusing me

[elfin cairn]

Ok

[buoyant jetty]

z + 1 = hs(-1,-1) + ht(-1,-1)

[elfin cairn]

You need to find dh/ds and dh/dt

You can use chain rule for this

[buoyant jetty]

yes but we have phi in the middle

WTF

[elfin cairn]

So the implicit function theorem tells you its derivative

[buoyant jetty]

where

[elfin cairn]

Down

[buoyant jetty]

[elfin cairn]

Now this is dphi/dx

But in the 3 variable case its df/dz in the denominator

[buoyant jetty]

care to elaborate?

[elfin cairn]

$$\frac{\partial \varphi}{\partial x}(x,y) = -\frac{\frac{\partial f}{\partial x}(x, y, \varphi(x,y))}{\frac{\partial f}{\partial z}(x, y, \varphi(x,y))}$$ and $$\frac{\partial \varphi}{\partial y}(x,y) = -\frac{\frac{\partial f}{\partial y}(x, y, \varphi(x,y))}{\frac{\partial f}{\partial z}(x, y, \varphi(x,y))}$$

[elfin berry]

ExpertEsquieESQUIE

[marsh citrus]

@buoyant jetty Has your question been resolved?

[buoyant jetty]

but

[marsh citrus]

@buoyant jetty Has your question been resolved?

[marsh citrus]

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[still temple]

.reopen

wth

[lethal owl]

this is an open help channel now c:

do you have a question?

[past thicket]

uh.

Do you have a question? :3

[ionic ferry]

you can type ".close" if you don't have a question

[ionic ferry]

@still temple

[past thicket]

Aaaand he’s offline

[lethal owl]

any greens that can clopen?

[past thicket]

Let’s summon them

https://tenor.com/view/bop-bop-bop-shoebody-bop-squad-summon-dark-magic-gif-13983602502478731881

[ionic ferry]

ATP we're gonna have to @ the helpers

[cunning fiber]

.close

[marsh citrus]

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[cunning fiber]

.reopen

[marsh citrus]

✅

[cunning fiber]

.close

[marsh citrus]

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[cunning fiber]

cleaning out pins

[marsh citrus]

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[dawn orbit]

Hi

[elfin stone]

brother, I appreciate your courage to claim another one after the mod closed your previous channel 💀

[calm harbor]

.solved

[marsh citrus]

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[wary vale]

can someone help me proof this fourier series?

[wary vale]

i got [-pi * (-1)^n]/n for bn
and for an = [(-1)^n - 1]/n^2

[main idol]

can you show the original question

[wary vale]

This is the question 😭

[main idol]

there's no question there

just the function

[wary vale]

Oh wait

[main idol]

you also need to show your work how you got this

[wary vale]

I do the integrals on another sheet

.close

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[boreal rock]

How to find f(x)

[marsh citrus]

@boreal rock Has your question been resolved?

[boreal rock]

<@&286206848099549185>

[marsh citrus]

@boreal rock Has your question been resolved?

[noble geyser]

Wow

Thats something

Try by simplifying the term first

[marsh citrus]

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[abstract snow]

Is there a typo on the question?

I got 2 c values but the question said that theres only 1 constant

[marsh citrus]

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

[abstract snow]

Or did i do smrh wrong

[brave spire]

alr

lemme check

[abstract snow]

Prob 4

[brave spire]

theres one more condition for both the cases

i think

let me check rq

[abstract snow]

Tyt

[brave spire]

hmm nvm solutions are consistent with range of modulus

[brave spire]

prolly this thn

[ripe dirge]

look at your second case

16 - c^2 <= 0

[brave spire]

yah the solution is valid

-1-sqrt(65)/2 is around -4.5

who square is obviously greater than 16

unless i am tripping

[ripe dirge]

hmm thats right

[abstract snow]

I checked with maple and it gives the same answer too

[brave spire]

yeah then its most likely a typo

[abstract snow]

Wait hold up

Why does maple give me -16 instead of 16 on the 2nd line

Wait nvm its the same

It just ×(-1) on the entire abs for some reason

Anyways thx a lot yall.

.close

[marsh citrus]

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[marsh citrus]

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[abstract snow]

Which part did i do wrong

[lucid zenith]

this is fundamentally not how the chain rule works

[abstract snow]

Isnt it smth like this?

[lucid zenith]

A better way to do this would be to write [ x^{\ln(x)} = \left(e^{\ln(x)}\right)^{\ln(x)} = e^{\ln^2(x)} ]

[elfin berry]

kheer257

[elfin cairn]

What you are missing here is in $\frac{d x^u}{du}$ x,u are dependent so you need to write x in terms of u before using any rules

[lucid zenith]

do you mean they're dependent?

[elfin cairn]

yeah mb

[elfin berry]

ExpertEsquieESQUIE

[abstract snow]

Mmm alr

Ima try that

Anyways thx a lot yall

.close

[marsh citrus]

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[marsh citrus]

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[dusty oar]

i need help for riemann hipepotesm

[stark sandal]

.close

[marsh citrus]

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[elfin stone]

Hi, do you have a specific question?

[stark sandal]

ok was this too trigger happy

[amber birch]

not at all

[dusty oar]

i needed help

[stark sandal]

aighty

[amber birch]

it might even be warranted to call the mods if this continues

[stark sandal]

with what

[dusty oar]

riemann hipepotesm

[stark sandal]

dude at least spell hypothesis correctly

[elfin stone]

@stark sandal just reopen it and see what's inside his sleeves lol

[stark sandal]

aighty

.reopen

[marsh citrus]

✅

[elfin stone]

@dusty oar which part of it?

[amber birch]

okay so this is the Riemann zeta function right

[dusty oar]

zeta and omega

[stark sandal]

i spit out my coffee.

fuck

[stark sandal]

(literally.)

gotta clean this up

[dusty oar]

sorry😭

[stark sandal]

'zeta and omega' 😭

ok

great laughs

but dont troll in help channels

[amber birch]

there's no omega

[dusty oar]

there is omega in this?

my homework literally says that

[calm harbor]

lol

[stoic saddle]

<@&268886789983436800> troll suspected

[stark sandal]

ok this is getting boring now

[calm harbor]

This is what I'm looking for

[dusty oar]

im not trolling

[stark sandal]

id have let it continue if it was at least funny

[stoic saddle]

!xy

[marsh citrus]

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.

[vernal mantle]

Can you take a picture of your homework

[pallid jolt]

catbit is speedy

[glass silo]

.close

[marsh citrus]

Channel closed

Closed by @glass silo

Use .reopen if this was a mistake.

[stoic saddle]

ggs

[glass silo]

The first one I've managed to get so far

[stark sandal]

i got here much quicker

shouldve let it be lmfao

[calm harbor]

that way you don't get a chance to spill your coffee

[stark sandal]

hmm

fair

'zeta and omega'

https://tenor.com/view/spit-take-laugh-lmao-gif-17027890749900710490

literally me

[cobalt sedge]

budget george dantzig

[marble gazelle]

bro i wont spare you ever

[marsh citrus]

Available help channel!

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

hi

[balmy shadow]

is it to be done using synthetic geometry

[verbal iron]

<@&286206848099549185>

[balmy shadow]

!15min

[marsh citrus]

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

[harsh scroll]

bro calm down

[verbal iron]

sorry

[harsh scroll]

do you have a diagram?

[verbal iron]

yeah

[harsh scroll]

send it here

[verbal iron]

it is drawn by me

is it ok

[harsh scroll]

yeah

[marsh citrus]

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

[verbal iron]

👆👆

[harsh scroll]

hmm

[verbal iron]

what can we do

[harsh scroll]

AFE and ABC should be similar why in the diagram seems kinda weird

[verbal iron]

it is just flippe

[harsh scroll]

It would take me a bit to do this, if any helper can help atm feel free to

[verbal iron]

atm ?

[wheat quarry]

at the moment

[verbal iron]

oh

[verbal iron]

can u?

[wheat quarry]

no

[harsh scroll]

Do you know cyclic quadrilateral

[verbal iron]

yeah

[harsh scroll]

so do you agree with me AFE and ABC are similar

[verbal iron]

no

i can see they are

but

cant show

[weak surge]

Do you know BCEF cyclic?

[verbal iron]

AFHE will be cyclic na

opp angles 180]

[harsh scroll]

yeah

[weak surge]

Yes

But BCEF cyclic

Do you know that?

[verbal iron]

how

opp angle are not 180

[weak surge]

Angle BFC is angle BEC

[weak surge]

Thats not the only way

[harsh scroll]

that one angle & chord theorem

What's it called

[weak surge]

Alternate segment theorem

[verbal iron]

if BFC = BEC then how do we know that BFEC is cyclic

[harsh scroll]

okay so

actually...

[weak surge]

Search it up

@verbal iron

[verbal iron]

ok

[harsh scroll]

https://www.cuemath.com/geometry/alternate-segment-theorem/

[weak surge]

oh damn

[harsh scroll]

btw you don't have to use it

BFC and BEC are right triangle with the same hypotenuse

[weak surge]

Ah indeed

That might be harder to see

(that the center is midpoint of BC)

[verbal iron]

BTW @weak surge

[harsh scroll]

yeah the circumcenter of both triangle is midpoint BC

and they have the same radius

[verbal iron]

the yesterdays sum i got ans as 256/17

one of my friend also got the same answer

[weak surge]

Cool

[harsh scroll]

and so did i

[verbal iron]

do u want to see it ?

[harsh scroll]

nah

I used another method tho, only 1 variable

[verbal iron]

oh

can u dm me that one variable solution

i want to see

[weak surge]

@harsh scroll You can send it here if you want

I would also be keen to see

[harsh scroll]

hmm okay gimme a min

could you send the problem...

[harsh scroll]

$\frac{FM}{AM}=\frac{[FBC]}{[ABC]}$

[elfin berry]

Alexis_Fx

[harsh scroll]

now we have [ABC]

just subtract the rest

to get [AEFD]

[verbal iron]

i will try to digest it

[harsh scroll]

@weak surge if you interest

[verbal iron]

_______

[weak surge]

i am viewing

[verbal iron]

nice emoji

[weak surge]

yea thats similar to his original metjod

thanks

[harsh scroll]

tbh I didn't understand the original

why does it has 2 variable

anyway let get back to the problem we're doing

[harsh scroll]

okay so do you agree that BFEC is cyclic

[verbal iron]

let it be igtg sorry

.close

[marsh citrus]

Channel closed

Closed by @verbal iron

Use .reopen if this was a mistake.

[harsh scroll]

[marsh citrus]

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[daring spire]

Is question resolved?

[harsh scroll]

yes, now do you need anything?

[daring spire]

Ah ok no i don't need anything tyfa

[harsh scroll]

.close

[marsh citrus]

Channel closed

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[odd agate]

. @little drift you may have this channel

[little drift]

can you tell me factors of 25&55

[umbral folio]

!nosols

[marsh citrus]

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.

[odd agate]

!noans for helpees

[marsh citrus]

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.

[odd agate]

nosols is for helpers

[umbral folio]

woops sorry

im new 😔

[late geode]

what have you tried?

[sick walrus]

do you know how to prime factorize a number?

if so, you may apply that directly here.

[little drift]

i know 5 and 1

[sick walrus]

1 is not a prime number. if you are asked to list factors, you are allowed to list 1 as a factor, but be wary when asked for prime factors.
either way, are you just looking for a list of factors of both numbers?

if you are, start with 25 first.

[little drift]

tell me i have one mit to sumbit

[sick walrus]

I can guide you there, but I can't feed you the answer, I'm afraid.

[little drift]

piz

[sick walrus]

you're right that 1 and 5 are factors of 25. you're missing just one more.

!noans

[marsh citrus]

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.

[sick walrus]

hint: 1 * ? = 25

also, I implore you not to DM me.

[little drift]

5

[little drift]

ok

[sick walrus]

1 * 5 = 5, though.

you want 25, not 5.

(what do you recall about 1 times a number?)

[little drift]

idk

[sick walrus]

um.... I kind of gave away the relationship for 1 times a number here.

[little drift]

piz can you alllow lute to answer

[sick walrus]

it is this server's policy to not allow direct answers. if you wish, you could take it up with the moderators.

[next ivy]

that's just a bot

either way, we are here to help you learn, not to freely give out answers, I'm afraid

[marsh citrus]

@little drift Has your question been resolved?

[willow rampart]

Oh sorry I sent it wrong

I got the answer to be 0
But in answer key it's 2

[elfin stone]

,rccw

[marsh citrus]

Channel closed

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

Problem associated with topic: Heights and Distances.

[glass silo]

,rccw

[still temple]

Thanks for the help, I was not able to rotate it

[sick walrus]

do you have a sketch of the problem?

[still temple]

This much was I able to solve.

Wait

[glass silo]

,rccw will rotate the last picture in thread countercclockwise for you, ditto ,rcw rotates clockwise for you

[still temple]

I'm on the last part of this problem

To find AD

Please forgive me because of my handwriting 💔

Can anyone help me or they are working with this?

[maiden edge]

find bd?

[still temple]

AD

[maiden edge]

gimme few mins i can try

no first step

[still temple]

I've found the first two answers

I need guidance for the third issue

and the first two answers are correct, so no need to start it freshly

[maiden edge]

I NGOTNIT]

i got it wait

[still temple]

You got it?

[sudden mulch]

Try applying pythagoras to find the diagonals

[still temple]

What would that lead to?

[maiden edge]

yes can we attach images here when u are new

[livid wren]

can anyone help me with a recurrence relation question 😔

[sick walrus]

!occupied, sorry. please use a channel like #help-49.

[marsh citrus]

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).

[still temple]

Did not understand.
Did you get it anyways?

[faint pine]

you can use length of AC and cosine of 60 to find length of EC

[sudden mulch]

See if you find bd using pytha you can then use trigo

[still temple]

You have reversed my diagram, anyways let me check

[elfin stone]

,rccw

[still temple]

Aha

Thanks once again

BD is 16m, but how would that help?

[maiden edge]

just find x and then apply trigno on ade?

my ans is coming 16 root 3 but im not sure

[still temple]

x is 8 x sqroot(3)

[still temple]

Sadly it's wrong, you can try again.
The fact is if you can somehow prove that Triangle ADE is a right angled triangle, everything is set

[maiden edge]

oh wait

[still temple]

Or triangle ADC

[maiden edge]

? the angles u wrote arent given?

[still temple]

Not all of them

[sudden mulch]

Hn you can do that since angle aed is 90

[still temple]

How is Angle ADE 90 degrees

[sudden mulch]

Aed

[still temple]

Oh I mean, I need angle DAE or angle ADE

not to prove that it's a right angled triangle, because it already is

I wonder how did the ones who were giving CBSE board exam 2023 solved it.
Big brains

[sudden mulch]

Well its actually easy I have lost in touch with it so

[still temple]

Not all questions are really easy, because some problems consist of angles out of the regular Trigonometry table such as 15* , 43* , etc.

[sudden mulch]

Such questions generally do not come in exams

[still temple]

I would still atleast expect one

nevermind, did any of you get to a conclusion?

[sudden mulch]

Height 8 aaya tower ka ?

[still temple]

Ha

[maiden edge]

32? lmao

whole no is weird ans

[still temple]

Distance between them is 8 root 3

[sudden mulch]

Is the ans 21.16

[maiden edge]

just apply pyth

[still temple]

Nahi

[maiden edge]

if x is 8 root 3

h is 8

[sudden mulch]

See i subtracted your tower ka height and x hai and i applied pytha

[maiden edge]

then thst part will be 16

[sudden mulch]

Ya

[still temple]

,rccw

[still temple]

21.16 aapko kaise mila

O wait

This does not require trigo but rather pytha

[sudden mulch]

Yaa

Check the ans though

[still temple]

8root(7)

Did you get this @sudden mulch ?

[sudden mulch]

Ya

[still temple]

Let's go, it's correct

[sudden mulch]

Yayy

[still temple]

How did I miss this

[sudden mulch]

Happens

[still temple]

That was so simple

Thanks alot bhaiya

.close

[marsh citrus]

Channel closed

Closed by @bold fjord

Use .reopen if this was a mistake.

[marsh citrus]

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Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[compact dust]

is the answer for 9 1/square root of 2x+1? i alr answered 8 its 4

[main idol]

!show

[marsh citrus]

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

[compact dust]

uhh idk how to use that bot😅

[stoic saddle]

you should use sqrt() to type roots.

like, not in TeXit but just plain text.

[compact dust]

oh ok

[stoic saddle]

as for showing your work:

paper and photo

[main idol]

,w diff sqrt(2x+1)

[elfin berry]

Results provided by WolframAlpha

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

Requested by rie.mann

[main idol]

looks right

[compact dust]

YAY

THANK YOU

.close

[marsh citrus]

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[marsh citrus]

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[tidal charm]

I'm learning to decompose things, is it necessary for the Ax+B to be above the x^2 + 1? Or could it be above the x+1? I tried switching the Ax+B and the C to see if I could do it but I couldn't solve for A, B, or C in the same way. Not sure if that's because you have to always have the Ax+B over the higher order factor or just because of this question.

[devout blaze]

It has to be above x^2+1 to satisfy the degree

[tidal charm]

Oh okay, so do I always have to have a form of the decomposition up top that's exactly 1 degree less than that side's denominator?

[woeful whale]

You can do Ax+B/x²+1 + Cx+D/x+1
and get C=0

so there is no point in doing the extra work

[woeful whale]

yes

[tidal charm]

Thank you! Great succinct answer

.close

[marsh citrus]

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[gaunt lynx]

what did i do wrong?

[pallid tapir]

check for sign errors

[gaunt lynx]

wdym

like

• • errors?

[pallid tapir]

say you multiply a whole expression by (-1)

make sure you do the distribution part right

[gaunt lynx]

i did bro

i think its right idk what i did weong

[pallid tapir]

$-2p^2+p-\frac{77}{32}=0$ looks fine; the line afterwards is not

[elfin berry]

Flip

[pallid tapir]

thank you

(rotate wouldn't work anyway, it'd rotate the 2nd image)

[noble geyser]

bruh

[gaunt lynx]

ohhhh shit

its -p

[pallid tapir]

ye

ignore the typo in my tex, forgot the 2 lmao

[gaunt lynx]

i got an exam tomorrow man im so done

[pallid tapir]

glhf!

[gaunt lynx]

yeah?

[queen sun]

Just rotated it*

[gaunt lynx]

ty

it still doesnt work

on the calculator

help @pallid tapir

[pallid tapir]

so cross-referencing with the problem as stated now... you sure you meant to write 77/32?

also, the odds of interest are in getting two wins or two losses. what you've written on the left-hand side is the odds of getting a win and a loss, or a loss and a win (they're the same). it is salvageable in this position, but you need to adjust the number on the right

[gaunt lynx]

17/32

my writing is bad

[pallid tapir]

ack you're right, you dash your sevens and I do too, that's my bad

[gaunt lynx]

so

[gaunt lynx]

so win^2 + loss^2 = 17/32

[pallid tapir]

are you asking for confirmation?

[gaunt lynx]

uhh

yeah i guess

like whats the correct thing then

@pallid tapir

[pallid tapir]

in preparation for an exam, you should start generating your own thought process, and justify your own answers

[gaunt lynx]

yeah man

but is it correct what i thought or no

cuz im geniuenly like confused

[pallid tapir]

instead, pretend I don't know, and explain why you think your model is correct

[gaunt lynx]

so like u pull twice

and thats the explanation for the ^2

[pallid tapir]

pull?

[gaunt lynx]

and that goes for win and loss

spun*

[pallid tapir]

no no, like, pretend you're the teacher, I'm a student, you're going through this example with me because I've never seen something like this before

what even is the problem statement? what parts matter?

[gaunt lynx]

ngl i feel like i should include the 40 some where

[marsh citrus]

@gaunt lynx Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[warm sandal]

I really need help guys

[marsh citrus]

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

[warm sandal]

Dont know how to begin

[marsh citrus]

@warm sandal Has your question been resolved?

[hoary sapphire]

what have you done

i have experience solving biharmonic stuff

[cunning fiber]

Subbing ||x = e^t|| should work

[hoary sapphire]

well i should first ask what you have donw

because these are kinda essential problems you'll learn solving ordinary odes

okay how would you have begun

[marsh citrus]

@warm sandal Has your question been resolved?

[marsh citrus]

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[buoyant jetty]

I dont understand the implicit function theorem

I have a Elementary understanding of it though

there is a consecuence of the implicit function theorem that will be used like in b)

[marsh citrus]

@buoyant jetty Has your question been resolved?

[buoyant jetty]

is something like there exists some z = phi(x,y) such that F(x,y,phi(x,y)) = 0 around the point (x0,y0,z0)

there is a bunch of conditions that have to happen before we can use it i think, like F being C1 and the derivative wrtz of F not being 0 at the point (x0,y0,z0)

we also need that F(x0,y0,z0)=1

all of them apply, is just that

the theorem itself is confusing

[still temple]

hello guys

https://www.youtube.com/watch?v=ysoV7uqffbE

I made a video

Proof that every positive real number has a square root

[buoyant jetty]

isnt it equivalent to proving square root is surjective

[still temple]

yes just skipping the case y=0

[buoyant jetty]

I gave it a like btw, seems interesting

.close

[marsh citrus]

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[marsh citrus]

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[deep ginkgo]

can someone help me solve thios

[deep ginkgo]

ik the top is a difference of cubes

but idk the formula for it

[static quarry]

do you know one of the factors for the numerator?

[deep ginkgo]

do u mean 3?

3^3 = 27

[static quarry]

yea so you know the numerator can be factored as (t-3) times something

(times a quadratic)

[deep ginkgo]

wdym

do u mean (t-3)^3

[static quarry]

no

(t-3)(t^2 + ...)

what's the ... part, can you work it out?

[deep ginkgo]

would it be 9

[static quarry]

no there's also a term involving t

t^2 + at + b is the form

can you find a and b?

one way is to just plug in a couple of values for t

or you could carry out the polynomial division (t^3 - 27) / (t - 3)

[deep ginkgo]

ohh i see

i understand it now

okay thank you

.close

[marsh citrus]

Channel closed

Closed by @deep ginkgo

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[next owl]

Guys what’s this

Help ✌️😭

[past thicket]

Claim a channel

This is technically open, but I’m not sure you’ll receive great help
Here

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
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[past relic]

hey so im trying to do this problem and i tried everything and my professor's substitution method but his didn't have decimals so he did everything cleanly, and i can't even get an answer to input cuz everything's not lining up. Does anybody have any idea what's wrong i spent the last idk 3 hrs on this problem w no avail and even chatgpt is crashing out over it and i can't buy the pro version cuz its too expensive ngl

[marsh citrus]

@past relic Has your question been resolved?

[trim stratus]

You've assumed 3 unknown variables (I_1, I_2, and I_3); you'll need three equations to solve the problem.

[ionic ferry]

Also why is I1 flowing from negative to positive, it just makes it more difficult IG

Just make I1 flow in the direction of loop (from positive to negative), and write I3 as I1 + I2

@past relic you still here?

[trim stratus]

He could've very well reduced the number of variables too.

[ionic ferry]

Yeah exactly, I3 is just I1 and I2 together, also IG I1 should flow from positive to negative anyways

[trim stratus]

Can't really say without calculating

[ionic ferry]

Yeah but current flows from positive to negative, he might still get an answer but it's better to not take a risk

[trim stratus]

Not always, the V_1 cell could be getting charged if current gets pushed through its positive terminal due to the V_2 cell.

[ionic ferry]

Yeah but in basic circuit diagrams unless he's taken a loop for the entire circuit where it includes both the voltage differences, that shouldn't matter much

[past relic]

sorry was busy w smthn but uhm i mean my teacher said that we could orientate the loops however we want and it'd be like the same i think?

at least

[ionic ferry]

That's not wrong, still it'd be easier if you fix it in one way, that'd prevent confusions

[past relic]

oh so ur saying i should orientate both clockwise?

or counterclockwise

and then i'll get my right answer?

[ionic ferry]

Well TBH that's not very important, you might face issues with plus minus though if you're not careful

The main thing was that I3 is just a relation between I1 and I2

[past relic]

wdym you mean? i thought I2 and I3 was a relation to I1

[ionic ferry]

Are you aware of Kirchoffs laws

[past relic]

yh the amount entering a junction is the same as the amount leaving a junction

[ionic ferry]

Yes, so let's say I1 and I2 are both entering a node, then the currect flowing out would be I1 + I2

[trim stratus]

It's best to use nodal analysis here if you want to avoid variables (if you've learned it)

[past relic]

lemme show you so basically the red dot is the node, I3 goes into it, I2 goes into it, and I1 comes out

so its I3 + I2 = I1

[trim stratus]

Yes

Were you able to write the equations for the two loops?

[past relic]

its these 2

i did two circuit equations

one goes counterclockwise so you get the first

i mean clockwise

the second goes counterclockwise and you get second

[trim stratus]

Now try eliminating I_2 or I_3 from both the equations

[past relic]

you can't elimnate i3, i'll try i2

cuz there's 1

one min

oh

that's what i did

[trim stratus]

You can write I_3 as (I_1 - I_2)

[trim stratus]

So what do you've now?

[past relic]

its hard to understand cuz my writing is basd but basically i2 = i1 - I3

and then you sub i1 - i3 into i2

then you need to like do the whole thing where you find common factors so you can cancel out I3 to get I1

but then i ran into the issue

you can't multiply by anything to get 0.70I3 to be the same as 3i3

so the problem's basiclaly impossible

[trim stratus]

$$21-0.70I_3-2.30I_1=0$$
$$10-3I_3-1.40I_1=0$$
Are these your equations?

[elfin berry]

Will

[past relic]

yeah that's right ye

this is the same way my professor solvwed a similar problem

but his problem was ez cuz

it was all whole numbers

he threw out decimals at us

he could easily cancel it out

[trim stratus]

It would be really nice if you could write both the equations in terms of I_3

[past relic]

wdym in terms of i3, how do i do this? like take out i3?

from both

[trim stratus]

Isolate I_3 to the LHS for each equation

[past relic]

ohhhhh wait

so ur saying isolate i3 for both equations

[trim stratus]

Yes

[past relic]

then set them equal to each other?

wait

[trim stratus]

Yep

[past relic]

that might be a strat

hollup

[trim stratus]

There you go

[past relic]

there's still two variables 😭 do you think i should email my professor there's smthn wrong w the problem?

[trim stratus]

I thought you'd be using

[trim stratus]

These equations

[past relic]

OH

I USED WRONG EQUATIONS

ONE MIN AGAIN

[trim stratus]

Lol

[trim stratus]

Btw, your equations are wrong

I just noticed

[past relic]

HUH

what happen

why is it wrong

where

why

how

[trim stratus]

What's the sign convention that was taught by your professor?

[past relic]

what does sign convention mean

you mean

[trim stratus]

When to take - and +

[past relic]

OH

ok so basically when you go from + to - its like - and when you go from - to + its + !

[trim stratus]

Huh

[past relic]

like i2 goes from + to - so its - I2?

i think

uhm idk acc

i forgot lemme check my notes again

ok yh + to - is -

and - to + is +

das what i did in dis example

now idk if im right but i think that's what my recitation dude said

and he was an applied mathematics major so i beleived him although he does fk up on concepts ngl

so im not entirely sure now

but i'd say

im around 90% sure

why do you need physics to be a doctor anywawy

[trim stratus]

Okay so, this is the sign convention which I personally follow:

For battery:

• If you leave the battery from the positive terminal while moving in the loop, take it as +V
• If you leave the battery from the negative terminal while moving in the loop, take it as -V

For resistor:

• If current is in the opposite direction to your loop, take it as +IR
• If current is in the same direction to your loop, take it as -IR

[past relic]

what does current being in opposite direction of loop mean? do you mean if we set it as clockwise and counterclockwise direction

[past relic]

ohhhhhhhh

i see

so according to this

i1

is negative!

[trim stratus]

Try to write the equations

[past relic]

wait

[trim stratus]

Using the convention

[past relic]

i wrotei t as negative

[past relic]

ngl i got the same thing as i got before

is it the same?

[trim stratus]

It's not

[past relic]

but both voltages come from + terminal so they positive, and I1 current goes opposite and and oh wait i see it that's supposed to be positive

wait

so does this mean

that we switch

all the signs

to positive instead

cuz their all opposite?

[trim stratus]

Do it with the convention in mind

[past relic]

so i did the first circuit clock wise and I3 goes opposite and i1 goes opposite so

they're +

[trim stratus]

Yep!

[past relic]

and the second circuit is counterclockwise and I2 goes right and i3 goes up

so their also positibe

life is all positive

no negatives

someone could turn that into a haiku

[trim stratus]

I_2 and the clockwise loop have the same direction, it should be negative