help-36

[ornate token]

Glad to help.

If you are done, type .close by the way.

[final saddle]

@raw patrol Has your question been resolved?

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[chilly granite]

<@&268886789983436800>

thank youu!!

[final saddle]

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[pearl stone]

How do I do this

[night raft]

do you know how to complete the square?

[pearl stone]

No

[raven marsh]

do you know what vertex form is?

[pearl stone]

Yes

[night raft]

https://www.youtube.com/watch?v=2MKigAgPZMQ&pp=ygUUY29tcGxldGluZyB0aGUgc3d1YWU%3D. Here you go

[raven marsh]

Can you tell me what it is?

[raven marsh]

Or alternatively, just watch the video

[pearl stone]

F(x)=3(x-2)^2 +3

[pearl stone]

And ok

[ornate token]

There we go.

[pearl stone]

Ok well I will close this and watch the video thanks

[raven marsh]

[raven marsh]

[pearl stone]

.close

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[brazen breach]

so I integrated and (after a bit of simplification) got ((ln((x^3+1)^n)/(3x+1)))/3 which I assume converges for n values __<__1/3?

[final saddle]

@brazen breach Has your question been resolved?

[kindred mortar]

not exactly. I think the full factorized form is not really helping to see what is happening.

[brazen breach]

wdym

[kindred mortar]

your expression is equal to $n/3\ln(x^3 + 1) - 1/3\ln(3x+1)$ right ?

[soft zealot]

Lin Xia

[kindred mortar]

from here you can develop this way $\ln(x^3 + 1) = \ln(x^3) + \ln(1 + 1/x^3)$

[soft zealot]

Lin Xia

[kindred mortar]

and the second term goes to 0

using this you can show that the solution is $n = 1/3$.

[soft zealot]

Lin Xia

[brazen breach]

ye prolly that's the more right one

thanks

.close

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[sonic crystal]

$$y"-2xy'+y=0$$

[soft zealot]

water beam

[sonic crystal]

Find the general series solution about x=0

[soft zealot]

water beam

[sonic crystal]

this is what i got

i want to check if its right im not sure about the factor of a0 and a1 inside the summations if it needs to be there or not

[runic needle]

you can check ur answer by putting it back in the ode

it makes sense for there to be 2 parameters to your solution (a0 and a1) because it's 2nd order

[sonic crystal]

hm okay

but does a2k / a0 and a2k+1 / a1 look right

like the / a0 and /a1

if i factor it out

[bronze grove]

😂

how the tables have turned

[runic needle]

idk, i mean as long as it matches the first line

[sonic crystal]

?? gtfo vie

[sonic crystal]

alright

[bronze grove]

u used in laugh in my help channels

[sonic crystal]

do not flood my channel with your nonsense

[runic needle]

there is nothing to laugh about

everyone needs help from time to time

[bronze grove]

are u sure about the - in first equation

like after x^2/2

[runic needle]

good question

[sonic crystal]

i think so

[runic needle]

also what if a0 or a1 are 0. ur dividing by 0

[sonic crystal]

but usually we dont choose a0 or a1 to be 0

[runic needle]

alright, well that's an edge case. as long as ur aware

[sonic crystal]

a2 = -1/2 a0

a4 = -1/8 a1

so the negative sign is right im pretty sure

at least for this recurrence the even terms a_2n will be negative

but also

[
\text{Solution:} \quad
y(x) = \sum_{k=0}^{\infty} a_{2k} x^{2k} + \sum_{k=0}^{\infty} a_{2k+1} x^{2k+1},
]

[soft zealot]

water beam

[sonic crystal]

i can write the series like this without factoring which avoids factoring the a0 and a1

[bronze grove]

how is ur next term + then

[sonic crystal]

its just convention i really mean like +....(- insert term) + (-insert term)

[bronze grove]

ohh that confused me

[sonic crystal]

it looks weird if i write it as -....-

@drowsy epoch hello lurker

[sonic crystal]

cuz if i write it as -.....- it might look like im talking about descending powers but im rlly just adding a bunch of negative ascending powers of x

[sullen quail]

difference between + ... + and - ... - ?

[bronze grove]

ur just specifically writing the next term as (- ) not all- the prof may misread it

[sullen quail]

or per notation same

[bronze grove]

but u didnt add brackets for first few terms no

[bold turtle]

If the signs are to flip, the continuation should be made as clearly as possible

So, for instance, a + b - c + d - ... implies the sign flips every other term

But a + b - c + d + e - f + ... implies every third term is negative

[sullen quail]

but for series

they usually use +...

[bold turtle]

If you write a - b - c - ..., you're implying all other terms are negative

[sullen quail]

because it's + other part

and other part contain its own -

inside

[bold turtle]

bruh take some time off the internet for a bit and get some rest

You can write a +... but that's ambiguous

[sullen quail]

i can't go outside sorry

[sonic crystal]

the recurrence relation a_2k already has negative signs encoded into it so i think its fine to keep it as +.....+ ?

[bold turtle]

I said off the internet, not touch grass

[sonic crystal]

if i said -....- that could be mistaken as subtracting my terms in a_2k which will get me positive signs which is not what i want

[glossy zephyr]

you will solve for the general solution and then find the power series

[sullen quail]

they did it

nor?

[bold turtle]

The compromise is to write more terms

Aside from the 1, are all the other fractions here being minus-ed?

[bronze grove]

but if u leave it like that in exam- there is 100% possibilty of prof misreading it and cuting ur marks

[sonic crystal]

yeah because a_2k generates only negative terms except 1

[bold turtle]

Then you need a -...

[sonic crystal]

na my prof would know what im referring to im sure

[sullen quail]

give example where are -

like or + and -

[bold turtle]

Because the series only continues with negative algebra-terms

(by this I mean -x is a negative algebra-term, even if x = -3 say)

[bronze grove]

until the prof knows u personally- aint no way

[sonic crystal]

okay ts sign convention isnt what my doubts was about 😹 my doubts is if i correctly factored out the a0 and a1 here in the series

[sonic crystal]

he does

[bronze grove]

making all the x terms in bracket with - ( x + x + .. ) makes it very neat

[glossy zephyr]

On a serious note, this is correct, but for reference, a_2k and a_2k+1 (completely separate) to each other, form a certain sequence starting from a0 and a1.
a0 associated terms are always negative except for 1

[glossy zephyr]

also, reminder, the 1 and x can be incorporated to the sums

[bold turtle]

Maybe, but the 1 there is positive, so that's less viable

[bronze grove]

we leave 1 out 1 - (x terms)

[bold turtle]

But that's more clunky, esp. when beam's trying to rewrite this as a power series

[glossy zephyr]

Also, doesnt the question ask for the solution at/neighbouring x = 0?

[bold turtle]

(I suppose you could do -(-1 + ...) though)

[sullen quail]

topic about + and - notation is brainrot maybe ignore this

isn't your notation already fine?

[sonic crystal]

wait so what form should i keep it in

should i keep where a0 and a1 is factored or

[bold turtle]

Also, incidentally, googling the question just sent me straight to a video solution lol

https://youtu.be/7w_GdalO9p0 They just left it as an expanded series

[glossy zephyr]

a_2k is always a multiple (one thats predictable) of a0

[sonic crystal]

i stole it off a youtube video

[sullen quail]

okay spoilers

[sonic crystal]

my prof wants me to keep it in a series form tho

[bold turtle]

It's not a spoilers since beam's already got that answer

[bold turtle]

That's literally this message

[glossy zephyr]

Like, i dont want to spoil it, but you can write the sum as

a0 Σ f(k)x^2k

Where f(k) represesnts sequence that arises from the fact that a_2k are all multiples of a0

[sonic crystal]

ohhh wait thats true wait cant i just say a0 ( 1 + sum a_2k*x^2k)

[glossy zephyr]

the 1 can be incorporated btw

[bold turtle]

yeah

[sonic crystal]

i totally forgor a_2k had a0 in every term

lmao

[bold turtle]

You can pull the 1 out entirely, and just have a0 be a separate thing yh

Well not separate, but yk

[glossy zephyr]

Heres a small ex. of wikipedia

Again, we keep the a0 and a1 since these are from IVC

which we dont have

Im not precisely sure if f(k) (a_2k) can be expressed in closed form tho.

[sonic crystal]

hm

$a_{0}\left(\sum_{n=1}^{\infty}a_{2k}x^{2k}+1\right)$

[soft zealot]

water beam

[sonic crystal]

wait so are we allowed to write it as this?

[glossy zephyr]

make the index n = 0 and erase the +1

[sonic crystal]

oh tru

[glossy zephyr]

Notably, its not a_2k, you can write it as a_2k / a0

or "some" f(k)

im not precisely sure that the sequence 1, -1/2, -1/8, -7/240... has a closed form tho.

[sonic crystal]

$a_{0}\left(\sum_{n=1}^{\infty}\left(\frac{a_{2k}}{a_{0}}\right)x^{2k}+1\right)$

[soft zealot]

water beam

[glossy zephyr]

Like, it isnt precisely hard to compute the values from the recursive definition, but it would be neat to have a closed equation for it.

[sonic crystal]

ye would be nice if possible but my prof said for series solutions this is enough for full marks if u can get it down to here

okay anways i think thats all

thank you for the help

.solved

[final saddle]

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[final saddle]

@gentle zephyr Has your question been resolved?

[drowsy epoch]

What's your question

[gentle zephyr]

can i get some help

[drowsy epoch]

You been here for like 2 years, you know how it works

Just state ur doubt and translate if possible

[gentle zephyr]

the doubt is howto integrate this with the given region

the translation is not necessary is just a region in a set and an integral

[blissful meadow]

Hint : ||cylindrical coordinates||

Before you ask:
"Why?" Because the function and region has some x,y circular symmetry (x^2 + y^2) and z has easy bounds.
"How?" Look through your notes for what cylindrical coordinates are, try to write your region R in terms of those coordinates, look through your notes again for how you change from cartesian to cylindrical coordinates in an integral.

[gentle zephyr]

why not polar coord

[blissful meadow]

Polar is 2D. For 3D you either have cartesian, cylindrical or spherical.

[gentle zephyr]

what

why not spherical coordinates then?

[blissful meadow]

Because

z has easy bounds.

[gentle zephyr]

wdym?

[blissful meadow]

Your z is bounded from -3 to 1.

[gentle zephyr]

say I want to use cylyndrical coordinates, how to write the integral with this? and what would be the jacobian @blissful meadow

[marsh mountain]

before you ask, dont you have notes on cylindrical? im sure you've had experience transforming variables

[gentle zephyr]

if I would know everything I wouldn't be asking for help

[marsh mountain]

have you tried anything at all? like show where you're struggling

[gentle zephyr]

Idk how to start

[marsh mountain]

what are your notes on cylindrical coordinates and their transformations?

[gentle zephyr]

im pretty sure cylindrical is just polar but you leave z free

meaning (x,y,z) = (rcos,rsin,z)

idk why you are making a big fuss about it @marsh mountain

[marsh mountain]

never mind

anyways

how would you turn the $1 \leq x^2 + y^2 \leq z^2 + 2$ into polar with this, using $x = r\cos\theta$ and $y = r\sin\theta$?

[soft zealot]

blanketism

[gentle zephyr]

1 <= r^2 <= z^2 + 2

@marsh mountain @blissful meadow

right?

[gentle zephyr]

.

[marsh mountain]

okay, looks fine

do you know how to calculate the jacobian?

[final saddle]

Please do not ping individual helpers unprompted.

[gentle zephyr]

he was asking me a question

[gentle zephyr]

no

[marsh mountain]

do you have notes on the jacobian?

[gentle zephyr]

its the determinant of the transition matrix

[marsh mountain]

okay

[gentle zephyr]

idk

[marsh mountain]

can you calculate the terms?

[gentle zephyr]

no

i need help

[marsh mountain]

okay, what do you know about the jacobian

what do you have on what the transition matrix is

can you start this at all

[gentle zephyr]

if I would know everything i wouldn't be needing help dawg

we would need to see the change of coordinates as a linear transformation

and the jacobian as a matrix representation of change of basis of a linear map

@marsh mountain

[marsh mountain]

im not saying you need to know everything, but you seem like you dont even make an attempt to do things on your own before asking for help

[blissful meadow]

They're not making a big fuss about it and you don't need to know everything. If you ask for help you should have already made a decent attempt at it, and if you really don't know where to start then the least you could do is be aware of the definitions you used in your course, in this instance cylindrical coordinates, how to compute a Jacobian, how to compute its determinant, how to change variables.
If you get stuck doing one of those things, then that's fine but you should say where you're stuck instead of just saying you don't know where to start. Is it with writing the region in terms of cylindrical coordinates? Is it with computing the Jacobian matrix? Is it with computing the determinant of a matrix? Is it with doing the actual change of variables? Is it with computing the iterated integrals?

[marsh mountain]

you're asking basic questions about what a jacobian is, which is strange because you're being given questions about it. you're telling me you have no notes about the jacobian in your book or something where you can try to discern what you need to do before asking here?

but whatever

[soft zealot]

Please give me something to compile, for example latex ,tex The solutions to \(x^2 = 1\) are \(x = \pm 1\).See ,help and ,help tex for detailed usage and further examples!

May 11, 2026, 6:45 PM

[gentle zephyr]

oof

[marsh mountain]

$$\frac{\partial(x, y, z)}{\partial(r, \theta, z)} = 
\begin{vmatrix}
  \partial x/\partial r & \partial x/\partial \theta & \partial x/\partial z \\
  \partial y/\partial r & \partial y/\partial \theta & \partial y/\partial z \\
  \partial z/\partial r & \partial z/\partial \theta & \partial z/\partial z \\
\end{vmatrix}
$$

[soft zealot]

blanketism

[marsh mountain]

where cylindrical coordinates are $x = r\cos\theta, y = r\sin\theta, z = z$

[soft zealot]

blanketism

[marsh mountain]

can you proceed with this?

[gentle zephyr]

yeah

[marsh mountain]

okay, go ahead

[gentle zephyr]

cos -rsin 0
sin -rcos 0
.0. 0. 1

[marsh mountain]

looks fine

what do you get as the determinant?

[gentle zephyr]

-rcos^2 + -rsin^2 = -r

[marsh mountain]

wut

oh

its not -rcos\theta

should just be a positive

[gentle zephyr]

wat

[marsh mountain]

the derivative

of y = r\sin\theta

is r\cos\theta

[gentle zephyr]

right

[marsh mountain]

you wrote

-rcos theta

negative

[gentle zephyr]

cos -rsin 0
sin rcos 0
.0. 0. 1

[marsh mountain]

okay

rcos^2 - (-rsin^2)

what do we end up with

[gentle zephyr]

r

[marsh mountain]

okay

do you know how to put it all together into the integral?

[gentle zephyr]

no

[marsh mountain]

do you know your bounds for r, z, and theta?

[gentle zephyr]

this is for r

[marsh mountain]

okay

[gentle zephyr]

1 <= r <= sqrt(z^2 + 2)

[marsh mountain]

okay

what about z

and what about theta

then put all together

[gentle zephyr]

-3 <= z <= 1

[gentle zephyr]

hmm

we would need to graph the situation

[marsh mountain]

no, we would not

are we restricting x's and ys?

[gentle zephyr]

[marsh mountain]

except for the radius

like do you see anything on x or y specifically

[gentle zephyr]

no

[marsh mountain]

okay

[gentle zephyr]

0 to 2pi then?

[marsh mountain]

correct

now integrate

[gentle zephyr]

why

[marsh mountain]

if we restricted x or y specifically, then we would need to solve for theta

since $x^2 + y^2 = r^2$, then nothing about theta's restricted

[soft zealot]

blanketism

[marsh mountain]

we just go a full circle

[gentle zephyr]

this is hard

[marsh mountain]

$\int_0^{2\pi}\int_{-3}^1\int_1^{\sqrt{z^2 +2}} ze^{r^2} \cdot r drdzd\theta$

[gentle zephyr]

[soft zealot]

blanketism

[gentle zephyr]

uff

[marsh mountain]

i hope you can handle integration

[gentle zephyr]

we can use fubini

[blissful meadow]

-# that's already Fubini

[blissful meadow]

You can't separate them as a product like this when the bounds depend on one of the variables.

[gentle zephyr]

this shit is hard

does int e^x^2 * x even has a primitive?

[blissful meadow]

Yes.

[gentle zephyr]

,w integral xe^x^2

[soft zealot]

Results provided by WolframAlpha

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Requested by renatoxbz

[drowsy epoch]

reverse chain rule

[gentle zephyr]

u mean u sub

[drowsy epoch]

call it how you want it lol

[gentle zephyr]

yeah I got it

[drowsy epoch]

kind of funny integral cause you encounter twice the xe^(x^2) form

[blissful meadow]

-# (For the record Fubini just says that you can take your integral over are region R with respect to dA or dV and rewrite it as iterated integrals like you have. That's all it says. In the specific case where the region is a rectangle/product of intervals AND the function can be expressed as a product of functions in terms of the respective variables of integration only, then you can just rearrange stuff and it becomes the product of three integrals.)

[gentle zephyr]

oh this shit is tough

@blissful meadow @drowsy epoch

,w 2pi * ((e^3-e^(11))/4 + 2e)

[soft zealot]

Results provided by WolframAlpha

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

Requested by renatoxbz

[gentle zephyr]

can the volume be negative?

[blissful meadow]

You're not computing the volume.

[gentle zephyr]

what am I computing, the center of gravity?

of a particle

[blissful meadow]

In this specific case there is no physical context.
If f(x,y,z) gave some sort of density, then you'd get the mass, just like in your problem from yesterday.

[gentle zephyr]

where is the mistake then

[blissful meadow]

There is no mistake.

The volume can't be negative. The mass won't be negative too, provided the density is chosen such that it's always positive (which is the only way it makes sense physically).

In this case, as I said, there is no physical context. You computed the integral. That's it.

[gentle zephyr]

thanks

.close

[final saddle]

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[sour copper]

Consider the unit circle $C$ defined in the real plane $R^2$ as:

$$C={(x,y)\in R^2 : x^2+y^2=1}$$

Let $T_\theta$ be a rotation of this circle in the counter-clockwise (positive) direction by an angle $\theta > 0$. It is given that $\theta$ is not a rational multiple of $\pi$ i.e. $\theta \notin \pi Q$\par
Let $M (1,0)$ be a point on this circle.

• Prove that $T_\theta^k(M) \neq M$ for all $k \in Z^*$\par
• Use the Principle of Mathematical Induction on $n\in N$ to prove the following statement:
  For every $n\in N$ there exists an integer $m\in N$ such that the length of the arc of the circle extending between $M$ and $T_\theta^m(M)$ does not exceed $\theta\over2^n$\par
• Prove that any segment (arc) of the circle $l$ no matter how small, will contain an infinite number of points from the orbit $l$, where:
  $$l={T_\theta^n(M),n\in N}$$
• If we represent the unit circle in complex form, prove that the orbit L constitutes a subgroup of C

[soft zealot]

Amer

[sour copper]

i am stuck at the last part

here's my work:

[final saddle]

@sour copper Has your question been resolved?

[vital crag]

Can also try #real-complex-analysis or #groups-rings-fields

[sour copper]

ain't got no perms

[vital crag]

#get-advanced-access

[final saddle]

@sour copper Has your question been resolved?

[final saddle]

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[final saddle]

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[ornate token]

Which one?

[final saddle]

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[fluid river]

hello, could someone please help me with these two questions?

Given that:
AB = BC
AF = FE
CD = DE
using point X, where AD = BX and AB = DX, prove that vector BE = AD + CF

must this triangle be an isosceles triangle?

thank you and apologies in advance for the poorly drawn diagram

[brazen breach]

ok I'm not entirely suer on my own logic here

so you have AD=BX so BE=BX+CF
notice that BE=BX+XE, so we have CF=XE which we have to prove
going back we have BE-BX=XE so CF=BE-BX, express BE as the sum of vectors including CF

[fluid river]

so trying to find XE = CF

[brazen breach]

for 2. I have no idea if you can prove it is, maybe consider that centroids don't really move when triangles are changed so no

[brazen breach]

yes, you go back with BE=BX+XE -> BE-BX=XE=CF

[fluid river]

how did you arrive at the conclusion that XE = CF?

[brazen breach]

AD=BX

AD=BX, BE=AD+CF => BE=(BX)+CF=BX+CF

[brazen breach]

BE=BX+XE
hmm isn't that familiar

[fluid river]

sorry gimme one second im trying to visualize this

mb

[sullen quail]

AB=BC, AF=FE, CD=DE tell you that B, F, D are midpoints of AC, AE, CE respectively

also that does NOT force triangle ACE to have two equal sides, so large triangle need not be isosceles

[fluid river]

ahhh, after writing it down it makes sense!

and we dont know it must be isosceles?

[fluid river]

yeah, i understand theyre midpoints, just wondering how to use that to prove q1

[sullen quail]

i think 1 pretty much implies 2

or you need to prove 2 too somehow?

[fluid river]

as in question 1 proves question 2 or the fact that their midpoints proves question 1?

[fluid river]

nono, that im just curious about

so triangle ACE DOESN'T have to be an isosceles?

[sullen quail]

proof should vector ?

[fluid river]

wdym?

[sullen quail]

or go with undesirable say

[fluid river]

wdym by proof should vector or go with undesirable say? as in does it have to use vectors to prove it?

[sullen quail]

should vectors be used in the proof, or is that, say, undesirable?

[fluid river]

it doesnt really matter, the second part of the question im just curious about. you dont have to use vectors, I just want some sort of explination to whether or not AE has to equal CE

[sullen quail]

i mean there are vector proofs haters exist

just in case, i asked

[fluid river]

sorry for the ping, I have a follow up question

you say that BE = BX + CF and BE = BX + XE, therefore CF = XE

but we dont know whether or not BE = CF + AD is true or not, so doesnt that mean we cant compare the two? because although we know that BE = BX + XE is true, we dont know that BE = BX + CF is true or not?

[fluid river]

oh yeah, nw. just want some sort of explination

[sullen quail]

name explanation of what, maximally concretely

[fluid river]

just an explanation of whether triangle ACE has to be an isosceles triangle with AE = CE

[fluid river]

and this^

[final saddle]

@fluid river Has your question been resolved?

[fluid river]

<@&286206848099549185>

[fluid river]

pls help with this

[sullen quail]

counterexample
A=(0,0) C=(2,0) E=(0,3)

then B=(1,0) F=(0,1.5) D=(1,1.5)
so
AB=BC=1
AF=FE=1.5
CD=DE=√(1²+1.5²)=√3.25

and in triangle ACE
AE=3
CE=√((2-0)²+(0-3)²)=√13

equalities only tell you that B F D are the midpoints of AC AE CE resp.

(triangle is isosceles only when it has two equal sides)

[fluid river]

sorry, let me draw this out to visualize

[sullen quail]

(my bad counterexample is worst way to state something, but anyway may be helpful a bit still)

[fluid river]

sorry im currently really confused
you just solved for CE & CD, but you didnt prove that BE = AD + CF. didnt you just- create a triangle? you know that BFD are midpoints, but you never proved that BE = AD + CF?

[fluid river]

also, could you explain whether this is correct or not? Im still not sure that I understand the first part of the question

[fluid river]

someone please help, I'm still so confused🙏

[sullen quail]

you mean vectors?

[fluid river]

yeah, how vectors BE = AD + CF

[sullen quail]

both equations must already be proven, if you asking this, then, yes

[fluid river]

Im trying to figure out how I can prove that BE = AD + CF, and the person ealier used BE = AD + CF to solve for CF = XE. but since we dont know whether BE = AD + CF is in fact true, isnt the whole proof invalid? we cant say that CF = XE useless we state we know that BE = CF + AD, which is what were trying to prove.

right......?

i feel like im more confused than when we started
if it helps, can we go from the top again? how does vector BE = AD + CF?

[sullen quail]

im not sure even in what i myself sayin

i tried to help

i don't saying proof itself tho

i also think that your proof may be better than mine, so i will refrain, sorry

i think i helped at least btw, sorry

[fluid river]

um, its ok, thanks for trying though, appreciate it

----------------------------------------------------------------------------------------------------------------------------------------------------------
just gonna copy and paste my question again, clean slate, someone please help me, I feel like I havent gotten anyway in the past few hours

Given that:
AB = BC
AF = FE
CD = DE
using point X, where AD = BX and AB = DX, prove that vector BE = AD + CF

must this triangle be an isosceles triangle?

[ornate token]

Well, let's define B,F,D are midpoints.

Then AF =?

[fluid river]

FE?

[ornate token]

AF = 1/2 AE.

Do the same, AB = 1/2 AC.

DE = 1/2 CE.

Now, BE = BC + CE.

Which is?

[fluid river]

BE = BC + CD + DE?

or BC + 2 CD

[ornate token]

BE = BC + CE.

Similarly, CF = CA + AF.

You want the mid segments.

Then since CA = -2AB, AF=FE, as well as BC=AB, you can adjust those 2 equations.

[fluid river]

so CF = -2AB + FE and BE = AB + CE?

[ornate token]

We also want to show AD + CF = BE.

But AD = BX.

Then triangle law somewhere here.

[fluid river]

triangle law? so like BC + CE = BE?

[ornate token]

Something like that

Well try a bit here.

[fluid river]

well

AD = BX, so we need to check if CF = XE

so if CF = XD + DE

CF = CB + BF

so does BF = DE

BF = FE

but FE = DE only if triangle is isosceles right?

[fluid river]

@ornate token?

<@&286206848099549185> someone please help explain, I havent gotten anywhere in the past few hours 🙏 . I'm sorry for pinging a second time, but idk what else to do.

[weary cosmos]

Is anything else given ? Like BE being perpendicular to AC or any other info?

[fluid river]

nope

just that FBD are midpoints

do you have to assume that theyre perpendicular? that would make it isosceles right?

[weary cosmos]

Wait listen

Let's assume some vectors

Say that AB vector is a

And then BC vector is in same direction

So BC vector would be ?

[fluid river]

a as well

[weary cosmos]

Yes good

Now say that BE vector is some b

Okay ?

Ok so

AE vector

If we would write it

It would be ?

[fluid river]

2AF?

or a + b?

[weary cosmos]

a+b yes

Beacuse we have info about them only rn

And then CE vector?

[fluid river]

-a+b

[weary cosmos]

Yes good

Now what is AF vector

[fluid river]

(a+b)/2?

[weary cosmos]

Yes a+b /2

And

Then CF vector would be ?

[fluid river]

-2a+b/2?

wait

-3/2 a + b/2

[weary cosmos]

Yes good

Can u do the same stuff for AD vector?

[fluid river]

AD = 3/2 a + b/2

[weary cosmos]

Yess very good very nice

Now what do we have to prove ?

[fluid river]

BE = CF + AD
b = 3/2a + b/2 -3/2a + b/2
b = b
OHHHHH

[weary cosmos]

Yesssss !

[fluid river]

hmmm, i wonder why x is included then

[weary cosmos]

I haven't thought about the isosceles condition yet

Probably there it has some use

[fluid river]

hmm ok

but from what i just proved, it seems like it doesnt have to be an isosceles

[weary cosmos]

Yeah

It doesn't need to be

[fluid river]

now i wonder if there is a way i can use x in my proof

[weary cosmos]

There would be but

I don't think we should be bothered about it

[fluid river]

okok

thank you so much

ive been suck here for like 3 hours

trying to do this

i really appreciate it

[weary cosmos]

My pleasure!

[fluid river]

.close

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[hot owl]

can someone help me with part g i have no idea what im doing

[modest sequoia]

it is asking you to graph g(x), using the info you get from parts a-f

[late gazelle]

Using the information from the previous parts, we should have all defining features of the graph, x,y intercepts, maxima / minima, etc.

Just put it all together to sketch the graph

[hot owl]

i have no idea how to sketch a graph

[late gazelle]

Plot the points we do know first

[modest sequoia]

https://www.youtube.com/watch?v=JTVNUdL7sWs

take a look at this, a visual representation will probably help you better than just words

[hot owl]

so like (2,-16) etc

[hot owl]

thanks

[late gazelle]

Yea

And just “connect the dots” in smooth way

Making sure that:

You have the concavity of each part correct

[modest sequoia]

for a small interval like this just connecting may or may not work, but for larger intervals you'll definitely want to make sure of your concavity and intervals of inc/dec as the other helper mentioned above

and well you'll get all that information from parts a-f, of course.

[hot owl]

i think i get it

my graph looks stupid though

[late gazelle]

It’s a “sketch”

So it doesn’t have to look perfect

[modest sequoia]

show what you have right now, it definitely won't ever be perfect but it'll get better as you practice it

[hot owl]

hold up all i have is the x and y axis

😭

[modest sequoia]

no worries go ahead and make a rough sketch of what you think it'll look like to the best of your ability and send that

[hot owl]

sorry for the erease marks i was stressingout

[modest sequoia]

that looks very good actually, just try to make it a smoother curve going from (0, 0) to (3, -27)

but you got the basic idea right

,w graph x^4-4x^3 from x = -1 to 5

[soft zealot]

Results provided by WolframAlpha

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

Requested by diamondbtw

[hot owl]

okay will do

thank you very much

[modest sequoia]

ofc! your sketching will get better as you go on, just keep up the practice :)

[hot owl]

ayeee #kingshit

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[lime crest]

A round robin tournament has $2n+1$ competing teams, in each game the outcome is always a win or a loss. For teams $X,Y,Z$, call the set ${X,Y,Z}$ "circular" if $X$ won against $Y$, $Y$ won against $Z$, and $Z$ won against $X$. Determine $\$ $(a)$ the minimum amount of circular sets in the tournament $\ (b)$ the maximum amount of circular sets in the tournament

[soft zealot]

Copter

[lime crest]

how would i do this?

by the question they mean every possible pair of 3 teams, btw

[ionic venture]

Did you finish the geo?

[lime crest]

which one

[ionic venture]

The one with the rectangle

And similar lengths

[lime crest]

i gave up on it

ill retry later tho

[ionic venture]

It's not that difficult

[lime crest]

can you dm me?

[ionic venture]

You just need to look at something

[ionic venture]

Ofc

[lime crest]

^

[ionic venture]

Complete Directed Graph?

[lime crest]

wuh..

[ionic venture]

Are you familiar with graphs?

[ionic venture]

The teams are the nodes and the games are the edges

[final saddle]

@lime crest Has your question been resolved?

[lime crest]

uhhhhh

[ionic venture]

Might've overflown you with information my bad

What do you think about the problem tho?

[lime crest]

no idea man

[ionic venture]

Hmm...

We should try looking at small cases

Maybe we could find some patterns in the results

[lime crest]

n=1?

[ionic venture]

Sure, it's the simplest one

n = 1 --> 2n + 1 = 3 So we only have teams {X, Y, Z}

[final saddle]

@lime crest Has your question been resolved?

[final saddle]

@lime crest Has your question been resolved?

[cerulean epoch]

you should think about small cases for (a) because there is a construction

hmm you haven't answered Erebus for 2n + 1 = 3

is there something that's confusing you

[final saddle]

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[final saddle]

@mossy chasm Has your question been resolved?

[mossy chasm]

.close

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[pearl stone]

I need help understanding how to get the points for this -1/3 (x-5)^2 +1/2

[drowsy epoch]

wdym points

[pearl stone]

So far I have the point (5,0.5)

[pearl stone]

For graphing the coordinates

[brazen breach]

substitute values of x into the expression

that's it

y=-1/3 (x-5)^2 +1/2

[pearl stone]

I know but I get confused midway through

[modest sequoia]

you got your vertex (5, 0.5)

[wet crater]

can you show where you worked up until?

[modest sequoia]

now just find values around it and plug them in

if you have the point 5 as your vertex, that means the parabola either goes up or down around it with that point as your minimum or your maximum. so if you have 5 as your "midpoint" then plug in values like 4 and 6, then 3 and 7, etc. into your function

[pearl stone]

Ok .close

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[keen hare]

is this reasonable or did i miss the point or do somethin weong

[keen hare]

this question felt very easy and i feel like somethings wrong

[tiny gorge]

you seem to be assuming that P is linear instead of affine

in general, can't it also change F?

[keen hare]

well but a line after an affine is still a line

i just dont know how to show it

[keen hare]

i dont know

[tiny gorge]

what's your definition for affine transformation?

[final saddle]

@keen hare Has your question been resolved?

[keen hare]

when you multiply a solution of a differential equation by a matrix P (made up of eigenvectors) to get a simpler equation with the same shape

[tiny gorge]

isn't that a linear transformation?

an affine transformation is more general, it's a translation composed with a linear transformation

[keen hare]

then i guess i dont really understand affine transforms

[keen hare]

how would you start with this problem

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[lime crest]

im only stuck on a very small part in this

Let QK intersect RM at F.
im trying to show that QMFA is a rhombus

i know that DEM is equiv to QAM, and NEQM is a kite, all is left is to show that <QMA = <AMF

[final saddle]

@lime crest Has your question been resolved?

[lime crest]

<@&286206848099549185>

[sterile marsh]

bmo?

[lime crest]

wuh

[final saddle]

@lime crest Has your question been resolved?

[lime crest]

i got it, i think

Let H be the foot of the atitude dropped from R to BC. Let RH intersect QM at G.
i claim that R,G are reflections of eachother on MB

and rhen you can just angle chase, i think

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[lime crest]

also BN, MQ intersect on (RHB) which is cool

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[modest sequoia]

<@&268886789983436800>

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[ember peak]

how can i fill in the variables such that F become fields (not sure that's the right translation for körper) ? i know the solution but i don't understand how to get there. the only thing i can understand is how to get that in 𝔽₃ a is not equal to 1

[ember peak]

?

[olive osprey]

Do u like my edits

??

[ember peak]

the spam today is so strange, there are places where you could ask where people care about such edits, why do you ask in random maths help forums instead

[compact laurel]

This is not the place for that

[gritty kiln]

nice

[olive osprey]

Thx

𝚈𝚘𝚞𝚝𝚞𝚋𝚎

[ornate token]

Please delete.

[olive osprey]

You

Ok

[ornate token]

Do not spam please.

[olive osprey]

@olive osprey

[ornate token]

!redir

[final saddle]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[drowsy epoch]

Hmm, b would just be 2+2 but what's that mod 3

[ember peak]

"but what's that mod 3" i'm not sure what you mean by that. i mean, i know what mod 3 is but i don't see why you bring it up

wait, no, i only know mod with two parameters but mod 3 only has 1 parameter

[drowsy epoch]

modular arithmetic

Like think of Z/3Z

[ember peak]

that sounds familiar but i don't remember that.
i thought i should somehow use the qualities of fields to figure out a solution

[drowsy epoch]

Well you only need commutativity and that each element appears once per row and col

[ember peak]

i don't know why each element only appears once per row. for plus i know there must be an inverse element so there must be 0 somewhere. for * i know there must be an inverse element as well so d must be 1

like, talking about F3 for now, i want to get that done before moving to F4

[drowsy epoch]

Because when you add and multiply u want the result to be unique

[drowsy epoch]

Yeah

[willow cliff]

you can think of the elements of F_3 as being the remainders of numbers when you divide by 3

so then $\mathbb{F}_3 = { 0,1,2}$, since those are the only remainders that can result from dividing by 3

[soft zealot]

TestTickler

[willow cliff]

and so addition respects the fact that these are the only possible "outputs" over mod 3 ($\mathbb{F}_3$)

[soft zealot]

TestTickler

[ember peak]

so, any time i have the same thing twice i could do something like for example
0+1=1=1+1, therefore 0=1 which contradicts that F has 3 elements ?

[willow cliff]

well 1 + 1 is just 2 right, but 2 divided by 3 just leaves a remainder 2

so it still stays the same

but when we do 1 +2 = 3, 3 is a number that when divided by 3 leaves 0 remainder , so then 1+2 = 0

you essentially just compute the operation like normal, and then look at what remainder is left with respect to dividing by the size of your field

that is your answer for the variables

[bold turtle]

-# Randomly jumping in, but yes, field is the correct translation for Körper here

[drowsy epoch]

This won't work nicely with F_4 however

Since Z/4Z isn't a field

[ember peak]

so, this would be enough for F3 ?

how did that get there

[drowsy epoch]

Yeah should work

[late spade]

can anyone give me the full pic of this problem plssss

[drowsy epoch]

However ur reasoning for d is weird

We know it has an inverse, the question is what the result would be applying it

[ember peak]

my thinking was 2*x = 1 and we know it's not 2*0 or 2*1 so it has to be 2*2

[drowsy epoch]

Either you do that by mod 3 or rule 2 out by the uniqueness property

[drowsy epoch]

Why 2x=1?

[ember peak]

because there exists some inverse element for 2 for *, otherwise it wouldn't be a field

[drowsy epoch]

Yeah I had a brain lag for a sec

I thought u did something circular

[ember peak]

i mean, that does happen to me more often than i'd like so it was a fair assumption

[drowsy epoch]

I was js 2nd guessing myself

[drowsy epoch]

IF_4 is a bit tricky because there is not really a natural choice like before

[ember peak]

those should be all the possible cases for a,b,c, if i'm not mistaken, i'm trying to see how that interacts with d,e,f right now

[drowsy epoch]

Why would c be 4 not 0

Or 4 at all

[ember peak]

typo

[drowsy epoch]

I am not quiet sure on this one, there seem to multiple choices possible?

[drowsy epoch]

-# Jump back

[ember peak]

i'm pretty sure those are all possible options

[drowsy epoch]

What does the solution say

[ember peak]

the second option from the top, a=0,d=0

i'm assuming there is only one solution but i just noticed i don't actually know if that's the case

[drowsy epoch]

Hmm

Even if we said 1+2=3=b then the choices for a and c need something too

Guess you can choose a=0 instead of 2 because we don't want to do mod 4 here since Z_4 isn't a field

But that's circular idk

Z_2 x Z_2 would make sense for the + table

[final saddle]

@ember peak Has your question been resolved?

[drowsy epoch]

I am sure that the choices for IF_4 are based on Z_2[x]/(x²+x+1)

[ember peak]

i am considering going to sleep. luckily the task is just to find some solution, not to explain it, so i would be fine with figuring out the reason at any point between now and next week at this same time

[drowsy epoch]

Ok

[ember peak]

unless you had some train of throught going that could help here ?

[drowsy epoch]

fwiw I don't think it helps since it would dive too deep into abstract algebra

[ember peak]

what does fwiw mean ?

[drowsy epoch]

for what it's worth

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[quiet garden]

can someone explain what these B and D stuff r i dont get linear transformations

[quiet garden]

its something like i plug B into T and then idk after

[formal trail]

In matrix notation
[ \begin{bmatrix} 1 & 2 & -1 \ - 1 & 0 & 1 \end{bmatrix} \begin{bmatrix} a \ b \ c \end{bmatrix} = \begin{bmatrix} d \ e \end{bmatrix} ]
corresponds to the function
[ T\big(a(1) + b(x) + c(x^2)\big) = d(1,1) + e(0,1) ]

[soft zealot]

clôud

[formal trail]

so the idea is that you do a matrix multiplication with column vectors, but those column vectors are really just "coordinates", i.e. coefficients of a linear combination of the given bases

[quiet garden]

what about B

in all these problems they all got diff stuff and sometimes u use them sometimes u dont i dont get it

[formal trail]

if the vector spaces are the same then you can use the same basis for both the input and output

so you always multiply a vector representing coefficients of a linear combination of B by the matrix to get out a vector representing coefficiennts of a linear combination of D

[quiet garden]

i dont get it so i plug each thing in B into T?

[formal trail]

to be honest i'm not sure what they actually mean by "action of T", does your textbook define it somewhere?

[quiet garden]

i dont either but i mean in general for linear transformation problems how do i do them

[formal trail]

what textbook is this?

[quiet garden]

nicholson-2023A.pdf

[formal trail]

well from reading the textbook they actually do seem to want it something like this

but you actually do the matrix multiplication to find a formula for d and e in terms of a, b, and c and then simplify

because by "action of T" they seem to mean "formula for the output given a generic input"

[quiet garden]

but for linear transformation r all of them pluging B into T, and then plugging D into those answers?

[formal trail]

well you always plug in an arbitrary linear combination of B into T, do the matrix multiplication to find the coordinates of the output given the coordinates of the input, and then turn those coordinates into a linear combination of D

[quiet garden]

can u give an example i cant find any

[quiet garden]

where did the 4 matrices from B go. it became v? i dont get what T, M_DB ,C and all these letters stand for

[formal trail]

all of this notation is explained in the textbook but C_B is the coordinate vector representation of a vector with respect to B

that means if a vector $\vb v$ can be written as $$\vb v = \bmat{ a & b \ c & d }= a \bmat{1 & 0 \ 0 & 0} + b \bmat{0 & 1 \ 0 & 0} + c \bmat{0 & 0 \ 1 & 0} + d \bmat{0 & 0 \ 0 & 1}$$ then it's coordinate vector representation is $$C_B(\vb v) = \bmat{ a \ b \ c \ d}$$ (note how it's just the coefficients of the linear combination)

[soft zealot]

clôud

[formal trail]

$M_{DB}(T)$ is the matrix defined so that multiplying the coordinate vector representation of $\vb v$ wrt basis $B$ gives the coordinate vector representation of $T(\vb v)$ (the output of the transformation given input $\vb v$) wrt $D$

[soft zealot]

clôud

[quiet garden]

is this even english im so cooked

[final saddle]

@quiet garden Has your question been resolved?

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[short ore]

I don’t understand how to do this

I get that you make the diff=0 for k

At x=1

[sweet imp]

When the global minimum is satisfied, what is the value of f'(x)?

[short ore]

But how do you find range of k

[short ore]

I got this but I don’t think it’s correct

[ruby crypt]

its correct

u can try plotting the graph online to double-check

[short ore]

But it asks for the range of k

[short ore]

Oh I think the range of k values is for the other parts

Alright all good thank you

[short ore]

these are the answers @ruby crypt

dont know how they got less than

@sand barn can u help pls man

[ruby crypt]

I misunderstood the question sorry, the question is asking values of K which has global minimum at x = 1

so its not limited to -2e^2

[final saddle]

@short ore Has your question been resolved?

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[tired iron]

A block of wood of mass 10kg floats on water density of wood is 600 and that of water is 1000 find the buyount force acting on wood block
So i calculated the upthrust using the formual row g V that resulted in 163.33N and the book says the answer is 98 N is there sm issue or point i am missing

[eternal saffron]

The block of wood is in equilibrium, because it's has not net force acting on it. For the buyount force must just counteract the weight force

Given that is floats, but it does because its less dense then water

[tired iron]

But upthrust can be more than its weight?

[eternal saffron]

No, or else it would shoot off into the sky

[tired iron]

Oh

Alr ty

[eternal saffron]

np!'

[tired iron]

.close

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[static oak]

I’m confused by the answer key for 21 because I got <-2/SR20, 4/SR20> and why is it U/|U| and not just |U|

[sonic crystal]

normalize

thats how u turn it into a unit vector

[static oak]

I’m not sure what that means

[sonic crystal]

youre just dividing by the magnitude/length of the vector

[static oak]

Oh kk

[sonic crystal]

like a unit vector is just the vector itself divided by how long the vector is

[static oak]

I’m not sure how to do the a part of this question

Because where not given an angle

[sonic crystal]

do you know what component form is

[minor field]

you can work with the X and Y singh I guess?

they are both positive so the must be vector in the first quarter

🤷

[final saddle]

@static oak Has your question been resolved?

[late laurel]

Try writing them in i,j form

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[cinder vapor]

Hey <@&286206848099549185> I am having hard time getting the logic behind it

[final saddle]

Please do not ping individual helpers unprompted.

[sterile marsh]

!15m

[final saddle]

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.

[cunning ridge]

oops wrong command

[cinder vapor]

What ?

[sterile marsh]

read the bot's message

[cunning ridge]

if your q remains unanswered for 15 mins then you can ping helpers

[cinder vapor]

Oh sorry

[sterile marsh]

What's the issue in this problem

[cinder vapor]

Oh I m having problem on creating equation for this prob

[sterile marsh]

what do you understand from the first sentence?

[cinder vapor]

Nothing like I m trying understand what it is saying but I m just getting zoned out

[cinder vapor]

This question is in my native language but still I can't get it for some reason

[sterile marsh]

Hindi?

[cunning ridge]

has to be hindi

[cinder vapor]

No

[cunning ridge]

nvm

[sterile marsh]

I see.

Let's consider Nabil's present age to N, and Shuvo's present to be S. The question begins when Nabil's age was the same as Shuvo's.
"was" So, we are talking about N−S years ago.

[cinder vapor]

But it belong to same language family

[sterile marsh]

Do you get this much?

[sterile marsh]

Bhojpuri?

[cinder vapor]

Bengali

[cunning ridge]

oh cool indian

[sterile marsh]

Ah. I see

[cinder vapor]

Erm m not indian

[cunning ridge]

well nvm again

not an indian

[cinder vapor]

Why N minus S

If we are talking about them being same

[cinder vapor]

Oh now I get it

Okh continue

[sterile marsh]

No wait. This question seems wrong

There's a contradiction

[cinder vapor]

Where?

[cunning ridge]

where

[sterile marsh]

Suppose Nabil is 30, and Shuvo is 20.
So when Nabil was 20, Shuvo's age must be twice of 30.

So Shuvo must be 60

Which is not possible

fit in with any age

[cinder vapor]

Wait so is the problem with Google translate

Call this is my question from my like government textbook

[cunning ridge]

if u still solve it u get an answer

cuz i got an ans

[cinder vapor]

To be honest I didn't get the question

[sterile marsh]

Let Nabil's present age be $n$ and Shuvo's present age be $s$.

Assume first that Nabil is older, so $n>s$.

The statement says that when Nabil's age was equal to Shuvo's present age, that was $n-s$ years ago.

At that time:

$$
\text{Nabil's age} = s
$$

$$
\text{Shuvo's age} = s-(n-s)=2s-n
$$

According to the condition:

$$
2s-n=2n
$$

$$
2s=3n
$$

$$
s=\frac{3n}{2}
$$

This implies $s>n$, contradicting the assumption that Nabil is older.

Now assume that Shuvo is older, so $s>n$.

The statement requires a past time when Nabil's age was equal to Shuvo's present age $s$. But if $s>n$, then Nabil has not yet reached age $s$, so such a past time cannot exist.

[soft zealot]

TheAstorPastor

[cinder vapor]

Like I have done other math like linear algebra or like quadratic formulas I can get that but I can't get like questions that are in like constructed with linguistic logic

[cunning ridge]

well even if it isnt valid we get the answers that balance those equations even if it isnt logical

[cinder vapor]

Okay then I will give the question with my native language you guys translate it because this question is from my government text book

[cunning ridge]

ok

[sterile marsh]

chatgpt says,
When Nabil's age was equal to Shuvo's present age, Shuvo's age was three times Nabil's present age. When Shuvo's age becomes equal to Nabil's present age, if the sum of their ages is 63, what are their present ages?

[cunning ridge]

uh

[sterile marsh]

gemini says "When Nabil's age was equal to Shuvo's current age, Nabil's current age was double the age Shuvo had at that time. When Shuvo's age becomes equal to Nabil's current age, the sum of their ages will be 63. What is the current age of each?"

[cunning ridge]

and thats copilot

[cinder vapor]

Ok

[sterile marsh]

2:1 rules. that translation is correct i think

do we have bengali helpers here?

[cinder vapor]

So is still the answer illogical

[sterile marsh]

lemme read it

[cinder vapor]

I can get the answer from YouTube but they will not like tell me the logic behind it so I am here to understand a logic actually

[cunning ridge]

rather than error in the q its prob error in the translator

[plucky rover]

Uh do we need a translator for bangla here

Give me a moment

[modest sequoia]

i can read hindi its a little different though

[sterile marsh]

yes please

[modest sequoia]

zavier locked in W

[cunning ridge]

yess

new info : zavier is from wb

[sterile marsh]

lmao

or bangladesh

[cunning ridge]

oh yea bangladesh too

my geo sucks holy

[modest sequoia]

google translate says this

[sterile marsh]

#help-36 message

[modest sequoia]

oh nvm that was the original post lol oops

[plucky rover]

Yeah that's correct

[cinder vapor]

Ye

[sterile marsh]

ok thanks

[plucky rover]

Cute didn't know I was being regionally profiled

Anyway leaving this to the helpers who were here already 🌺

[cunning ridge]

yea

[cinder vapor]

So the question is contradictory enough to be wrong as a answer?

[sterile marsh]

so. @cinder vapor let's suppose nabil's age is x, and shuvo's is y. let's take the first condition to be z years behind

[cunning ridge]

pastor can do the rest

[cinder vapor]

Okh

Then ?

[sterile marsh]

so. can you convert "Nabil's current age was double the age Shuvo had at that time." into an equation

[cunning ridge]

its a joke 😔

[plucky rover]

-# so was mine lmao

[cunning ridge]

fair

[cinder vapor]

So x = y- z?

[sterile marsh]

what are the present ages of nabil and shuvo?

[cinder vapor]

X and y ?

[sterile marsh]

then what will be their ages z years ago?

[cinder vapor]

X-z, y-z?

[sterile marsh]

ok great. now the question reads when nabil's age was equal to shuvo's current age.
so nabil must be older right?

[cinder vapor]

Yea

[sterile marsh]

what will be the difference in their age?

[cinder vapor]

X - (y-z) = z years

[sterile marsh]

huh? the age of nabil is x. age of shuvo is y
so difference should be x-y

[dawn tide]

2x = y+z

[cinder vapor]

Oh

[sterile marsh]

Nabil's current age = $x$
Shuvo's current age = $y$
The difference in their ages = $z$ (where $x - y = z$)

[soft zealot]

TheAstorPastor

[cinder vapor]

Okh now I get it

[sterile marsh]

"When Nabil was Shuvo's current age ($y$)," the time passed was $z$ years ago.

[soft zealot]

TheAstorPastor

[modest sequoia]

<@&268886789983436800>

[sterile marsh]

<@&268886789983436800>

snipeed

[cinder vapor]

Okh

[modest sequoia]

mrbeast aint getting to us that easy

[cinder vapor]

Go it

[sterile marsh]

can you convert the condition, which is "Nabil's current age was double the age Shuvo had at that time." into an equation now?

[dawn tide]

Mrbeast will receive $10,000 if they solve this question.

[cinder vapor]

2y =x-z?

[sterile marsh]

not quite.
what's nabil's present age again?

[dawn tide]

2y = x+z because they need to be equal.

X+y = 63

[cinder vapor]

Y

[cinder vapor]

Oh

[sterile marsh]

hmm. well, yeah that's correct as well. can you pick from here. i guess that's an easier way to approach the problem

i gotta go

mum's calling me. prolly for dinner

https://tenor.com/view/i'm-out-i'm-out-1-3-seconds-1-3-seconds-meme-sliding-gif-18353827383643920094

[cinder vapor]

Okh bye

[dawn tide]

2y = x is also possible.

according to me

x+y = 63

2y+y=63

3y=63

y=21

x=42

[cinder vapor]

Wait how if x is nabils current age and y is shuvos current age

Wait imma come back after 10 minutes ig

[dawn tide]

Let me think about it for a while during that time.

I didn't fully understand the question.

[final hedge]

why we using ai bro 🥀

[tropic crest]

<@&268886789983436800> using ai to help

[dawn tide]

I don't understand the question.

[tropic crest]

Then just dont help

Its that simple

[final hedge]

then js let some1 else take over

dont use ai

[final saddle]

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).

[dawn tide]

Is using AI prohibited?

[tropic crest]

Yup

[final hedge]

yeah

[tropic crest]

Yes

If to help

[steep hatch]

Yes and is usually a bannable offence

if users want to see an LLM's output they can open chatGPT themselves

[dawn tide]

I'm new to this server, so I didn't know what I was doing, and I apologize.

[final hedge]

its alright

dont use it again

[dawn tide]

ARROW

[steep hatch]

Dw, just don't do it again or else you might get a less nice mod responding

[final hedge]

lance goat

[dawn tide]

😄

[final hedge]

@cinder vapor you there?

[cinder vapor]

I m back

[leaden moon]

let me see

[cinder vapor]

Yes

[final hedge]

see 2nd pin

not first

[final hedge]

ight

[leaden moon]

yea i saw that

[final hedge]

let N be nabil's current age and S be shuvo's current age

[leaden moon]

Shuvo's present = Nabil's then
Nabil's present = 2(Shuvo's then)
(Nabil's present) + (Nabil's future) = 63

[final hedge]

so @cinder vapor what were their ages (N-S) years ago

[leaden moon]

so basically this is the info

[leaden moon]

is that what im understanding correctly?

[final hedge]

not fully correct

[leaden moon]

like what the hell are the timestamps 😭

[final hedge]

3rd line seems wrong

to me

[leaden moon]

shuvo's age in the future + nabil's in the future = 63

[final hedge]

yeah

[cinder vapor]

Okh

[leaden moon]

but since shuvo's age in the future = nabil's present

[final hedge]

ngl this q hella confusing

[leaden moon]

yea ngl

[final hedge]

@cinder vapor

[cinder vapor]

Fr trig seems less confusing

[leaden moon]

this thing algebra

[cinder vapor]

Wha?