help-36

[ornate thistle]

and

$x = 1$

[soft zealot]

Zolo

[mint orbit]

yup

[ornate thistle]

is -6/8 the same as (-6)/8

[mint orbit]

so, if you were wondering before, which numbers add to -1/4 and multiply to -3/4

now you know

[ornate thistle]

Dont we have to check

or smthn

[mint orbit]

we do yea

i mean, these are both roots of 4x^2 - x - 3

[ornate thistle]

But in case one isnt

[mint orbit]

but that wasnt our original problem

[ornate thistle]

or both arent

becuase of no real solutions

[mint orbit]

our original problem was $2x = \sqrt{x+3}$

[soft zealot]

jan Niku

[mint orbit]

what does this tell us about x?

well, actually it says a few things

[ornate thistle]

so $2 * \frac{-6}{8} = -1.5$

[soft zealot]

Zolo

[mint orbit]

yea

is this a problem? not a problem?

or, I could spoil it for you, just thought you might rather think it through

[ornate thistle]

I do

[hexed bison]

Check the domain of each side of the equation

[ornate thistle]

Its a problem

because the right side does not = -1.5

[mint orbit]

well, it cant right

we imagine, square roots are always positive

[ornate thistle]

Yes

[mint orbit]

so for sure, -6/8, that's out

how about 1?

[ornate thistle]

Unless we use 𝓲

√1.5 * 𝓲

?

or not

idk

[mint orbit]

complex square roots end up being a more interesting problem than you'd think

[ornate thistle]

I know 𝓲 = √-1

[mint orbit]

i'd count yourself fortunate to be able to just say, square roots are always positive

[hexed bison]

Only use i if a problem tells you to give imaginary/complex solutions

[ornate thistle]

I dont think they have that on the review for test 1 so

probobly got lucky on that part

But back to our problem

if the left and right done match up then $-\frac{6}{8}$ can't be a solution

$-\frac{6}{8}$

[soft zealot]

Zolo

Zolo

[mint orbit]

yea, we can throw away -6/8

we just have to check x=1

[ornate thistle]

so that leaves 1

so $2 * 1 = 2$ and $\sqrt{4} = 2$

[soft zealot]

Zolo

[ornate thistle]

So $x = 1$ is our final solution

[soft zealot]

Zolo

[mint orbit]

yea

which we can check

,w graph sqrt(x+3) and 2x

[ornate thistle]

They intersect at 1

[mint orbit]

yea

[ornate thistle]

I wasnt tought that

[mint orbit]

to use graphing?

[ornate thistle]

Could you do that on desmos

nah

[mint orbit]

https://www.desmos.com/calculator/3dpvetz01c

purple is our quadratic we got out

blue and red are the original lhs and rhs

[ornate thistle]

lhs and rhs?

[mint orbit]

left and right hand side

[ornate thistle]

Gotcha

[mint orbit]

if you wanna see something really crazy

well, you probably just wanna finish your hw

[ornate thistle]

I have no hw

atm

[mint orbit]

i have a bad tendency to distract people

oh

[ornate thistle]

this is just so i get it down

[mint orbit]

well check this out

your rhs

lets call it $y=\sqrt{x+3}$

[ornate thistle]

what ima do next is the last 3 on my own and give you what i get

[soft zealot]

jan Niku

[mint orbit]

so $y^2 = x+3$ means that $x = y^2-3$

[soft zealot]

jan Niku

[ornate thistle]

I see

[mint orbit]

https://www.desmos.com/calculator/3re6hnz0qy

check it out

two intersections, at x=1 and x=-3/4

if you think thats interesting, if not dont let me distract you any further

[ornate thistle]

it also intersects {1,2}

wow

Wait

could that help me in solving them

well no

[mint orbit]

no probably not

[ornate thistle]

she wants us to show work so using a graphing calc would defeat the purpose

[mint orbit]

this is more of a, hey look the other solution is actually in a pretty sensible place

its right where you might think it is

even though we throw it away

[ornate thistle]

Ima do the next 3 on my own and get back to you

[mint orbit]

[final saddle]

@ornate thistle Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[jagged saffron]

how did the "-" turn into "+"

[peak tapir]

2-x turned into x-2

[barren hound]

which one?

[mint orbit]

looks like the first pink line

the denominator of the final term on the RHS

[jagged saffron]

oh shoot i didn't see that thanks

[mint orbit]

[jagged saffron]

.close

[final saddle]

Channel closed

Closed by @jagged saffron

Use .reopen if this was a mistake.

[night sierra]

your teacher factored out -1 in bottom and so 2 negatives become positive 👍

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sterile pebble]

any reason why only sin = sqrt3 / 2 is a valid solution?

[loud sundial]

What?

$\theta=\frac{\pi}{3}+\pi n$ combines the quadrant I and III solutions

[soft zealot]

Civil Service Pigeon

[loud sundial]

Notice how it’s $+\pi n$ rather than $+2\pi n$

[soft zealot]

Civil Service Pigeon

[loud sundial]

Same for the other branch

[sterile pebble]

ohohhh

pi/3+3pi/3 is 4pi/3

gotchjiu

thx

.c;pse

.close

[final saddle]

Channel closed

Closed by @sterile pebble

Use .reopen if this was a mistake.

[loud sundial]

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[final saddle]

@random vale Has your question been resolved?

[random vale]

.close

[final saddle]

Channel closed

Closed by @random vale

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[urban willow]

in this physics problem how does t2 make an angle of 150 degrees with the horizontal?

this goes counterclockwise

they are vectors

[hot lava]

Can u clarify the question a little bit? Where are you getting 150 degrees

[urban willow]

this system is in equillibrium

im asked to find the tension t2

we're using standard notation for angles

so that involves taking the angle it makes with the positive direction of the x axis counterclockwise

[hot lava]

If its counter clockwise wouldn't that make it more than 180

[hot lava]

Ok wait, so we are using coterminal angles?

If that is the case then it would never be 150 because coterminals are always less than 90

[hot lava]

Also skipping into the physics part of it, if T2 is your unknown, you would need to know Fg, T1, and both angles in order to solve, unless you are solving analytically only

[urban willow]

I don't know the angle t2

[hot lava]

Is the question asking for a numerical answer or solving analytically?

[urban willow]

numerical answer

[hot lava]

what does the hon and han mean in this diagram?

maybe that could be what im missing

[urban willow]

40N, 49N

[hot lava]

ooh

[urban willow]

sorry it's my handwriting

[hot lava]

nah ur good I have terrible hand writing too

right

do you know Newton's 2nd law?

[urban willow]

yes I understand equillibrium

I am trying to find it strictly using vectors

so using an x,y coordinate system

[hot lava]

ok so what is the equillibrium of the x direction

[urban willow]

the vector of gravity is 0,-49

?

[hot lava]

Wait I think I learned this a lil differently

F=ma right

Fxtot= 0 since in equilibrium a=0

so uh

T1cos30 = T2cos(theta2)

Does that kind of make sense?

[hot lava]

Is this a limitation that you want or a limitation that the question is asking for

because I never learned how to do vectors...

srry

[urban willow]

.close

[final saddle]

Channel closed

Closed by @urban willow

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[raven loom]

What is this question asking me about?

[raven loom]

I can't decode the language

[rocky tusk]

(x, y) —> (x, -y + 1)

[raven loom]

Still doesn't explain much

[rocky tusk]

what’s confusing

[raven loom]

"Point A' is the corresponding point"

[rocky tusk]

yes

[raven loom]

????

[rocky tusk]

so just at x = 3

[raven loom]

So I keep x here the same?

[runic needle]

A' has the same x-coord as A

presumably

[raven loom]

So anytime they write corresponding it means x stays the same?

[rocky tusk]

the nikola tesla

[raven loom]

Im nigola tesla

[rocky tusk]

alright

[raven loom]

Wait

But I can't solve this

[rocky tusk]

[raven loom]

I don't know what x should be put into the new function

to get

What

[rocky tusk]

just put x = 3 and y = -1 in

[raven loom]

I can't

It won't be equal

[rocky tusk]

f(x) = y

[raven loom]

Yes I can't do that

[rocky tusk]

😭

why not

[raven loom]

Because I can't sovle this equation

I don't have the formula of function

[rocky tusk]

let g(x) = -f(x) + 1

if f(3) =-1 then g(3) =…

[raven loom]

???

[rocky tusk]

have a good day sir

[raven loom]

Ok

Ok why the fuck I am still confused about this shity

It's been going on for 2 days still

[runic needle]

what

[raven loom]

I don't know what happend here

[runic needle]

is there something wrong with the question?

[raven loom]

No, I am wrong

Asking for help here

[bold turtle]

my guy

g is defined RIGHT before that message

[raven loom]

Yes but I don't know like

I don't know what to do with it

[bold turtle]

g is a massive box

you feed x in, it gives you some output we call g(x)

[raven loom]

I don't understand why (3,2) solution makes sense

[bold turtle]

(because its input was x and the box is called g)

First, do you understand this?

[raven loom]

ok

[bold turtle]

That's not a yes or no or not sure

[raven loom]

Yes I understand

BUt it's confusing

[bold turtle]

okay

bruh what is confusing here?

You need to give a more descriptive answer than that

[raven loom]

You said the same thing 2 times in a row

Which makes me assume that you said different things

But that is not true

[bold turtle]

This was all I'd said

[raven loom]

Ok continue

[bold turtle]

g(x), we're actually told what this is equal to

Namely, some -f(x) + 1

i.e. minus the result of putting x into an f-box plus 1

Now if I said that f(3) = 1, then
the result of putting 3 into the f-box equals 1

[raven loom]

So any input will be inverted over x axis and added 1 unit up?

[bold turtle]

How then can we calculate g(3)?

[raven loom]

Why do we calculate g(3)?

[bold turtle]

f(3) is the only value of f(x) we know here

So we want to ensure that the input of that f-box is 3

[raven loom]

What would be the case if they told me find y with this transformation/

IF they only gave me y?

[bold turtle]

Well, two things:
one - find such a question that does that
two - given your OG point is on the graph y = f(x), replace the y to find the x-value that that point has

[raven loom]

So they actually overlap

And im finding the value for x which it will intersect/

[bold turtle]

Okay, you're now talking about some ghost-question that I unfortunately do not possess the superhuman ability of telepathy to read

[raven loom]

No Its the same question

[bold turtle]

Th-

There's no overlapping going on, what?

[raven loom]

Im trying to understand what are they asking me for

Find different y for the same x

But I even can't because I don't know the formula

Oh wait Im stupid

They ask me to invert the y cordinate and add 1 to it

No>?

[bold turtle]

...in essence

[raven loom]

They want something else?

Why is this so complicated this is 6th grade stuff

[proper dagger]

because we don't know how you think about it, and we aren't your personal tutors

[bold turtle]

You've kept the x-coordinate, and changed the y-coordinate

So what're the coordinates of the new point (which we're calling A')?

[raven loom]

I don't know how to think about it in the first place

[raven loom]

(3,2)

But I have no idea how did I get that answer

[bold turtle]

No sarcasm - does your brain turn off when doing a maths question and only turn back on once you've written an answer?

[proper dagger]

your DMs with me tell me another story

as well as what you told littledove

[bold turtle]

Because that's the only way I can imagine you forgetting how you got to that answer literally right after writing it

[raven loom]

I guessed this one

[raven loom]

What does that mean?

[proper dagger]

nvm

[bold turtle]

"Your direct messages to me suggest that it is not true that you 'have no idea how [you got] that answer'"

[raven loom]

I literally guessed, but I can't walk my mind thorugh the steps

It's not logicall

[bold turtle]

No, I'm calling bullshit on that, and to test that:

suppose A were (10, 50). Where is A'?

[raven loom]

(10,-40)

[stone flint]

I believe miss Hanako meant that the helpee has an idea, illogical as it is, contradicting their claim that they do not know how to think about it.

[raven loom]

No I literally don't know what am I doing

[bold turtle]

Not quite

You literally did just say you're negating the y-value and adding 1

So if the original y-value is 50...?

[raven loom]

-49?

[bold turtle]

yes

[raven loom]

Ok I think my brain is done

I think it's time to rest tbh

[proper dagger]

let's not use suggestive language in a server with minors

[bold turtle]

I would strongly advise not using such language

[proper dagger]

esp. not in a help channel of all places

[raven loom]

Ok Im done for today

Im sorry

I don't know what to type

Im tired

.close

[final saddle]

Channel closed

Closed by @raven loom

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[shell plover]

if i have (2+sin(n))/n^3 and i wanna use limit comparison can my Bn = 1/n^3?

[shell plover]

like for a series question

my teacher said it has to be 3/n^3 because 1 is the max of sin

then he like marked me down

i mean it gives the same answer

when I take the lim i get to 2 +sin(n) which will always be greater than 0 right? so then it would converge?

[strange sparrow]

What do you mean by "gives the same answer"?

[strange sparrow]

The comparison test requires that you bound it above with some convergent sequence (if you want to prove that your original sequence converges)

Here (2+sin n)/n^3 <= (2+1)/n^3 = 3/n^3 so your teacher is correct

[shell plover]

oh yea hthat makes sense

idk why i didnt try direct

but then like for 5/(2n-1) i used limit comp again and my Bn was 1/2n, so is it the same issue?

[strange sparrow]

well do you think it converges or diverges

to show that it converges, you need to show that it is termwise bounded above by another convergent series

to show that it diverges, you need to show that it is termwise bounded below by another divergent series

what you use to compare depends on which mode of comparison you want to use

[final saddle]

@shell plover Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rare drum]

Analysis I Excersise 3.6.6

[muted prairie]

What does an element of each set look like?

[rare drum]

like if we talk about set (A^B)^C it will be a function going from C to A^b

like elements are functions

[tired walrus]

it's a function whose input is a point in C and whose output is... another function (from B to A)

[rare drum]

ye

like f(c, (b,a)) type

so like my out put would be an order pair b,a or a function form B to A?

well i dont that matters tho

[muted prairie]

A function

Your output is in A^B

so it's a function from B to A

What about the other set?

[rare drum]

a function

from BXC to A

Takes in ordered pair from BXC and gives a point in A

[muted prairie]

Yeah

So like a multi-input function

[rare drum]

Ye

so what i thought was

to take a function from set 1 to set 2

but then i saw that the function itself takes a function as input

so i got stumped how to prove a bijection

[muted prairie]

It outputs a function

Not inputs one

[rare drum]

ok

[muted prairie]

So we want a correspondence between these two functions

[rare drum]

yes

[muted prairie]

Try seeing if you can find a way to "plug" the input for one function into the other one instead

So like, what happens if you try to plug a pair (a,b) into A → (B → C)

[rare drum]

i think i ll get a point

in C

[muted prairie]

right, so that describes your function (AxB) → C

[rare drum]

ye

[muted prairie]

Then you have to do the other way too

or

otherwise argue that what you've done is bijective between the functions

[rare drum]

like i think

i can put a function in

and get a point

and put that point other way around

and get a function

and prove that an inverse exists

and so there is a bijection

[muted prairie]

Well your bijection will take in a function and output a function

being formal about this is difficult

[rare drum]

ye

[muted prairie]

the hilarity is that what you want is a bijection between function spaces, necessarily a function that outputs another function

And ive described a way to define a function that takes in a pair (f, g) and turns it into the output of your output function

[rare drum]

k

should i close this?

ill somehow manage the rest

.close

[final saddle]

Channel closed

Closed by @rare drum

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[obtuse stag]

The domain of this function is {xER | -8 <= x <= 22} right?

[opal plinth]

Why <= on the left but < on the right?

[obtuse stag]

typo

[opal plinth]

Ok, sure

[obtuse stag]

Would that be the domain?

[opal plinth]

What you said

[obtuse stag]

huh

[opal plinth]

You asked if it's { x∈R | -8 <= x <= 22 }, I'm saying sure, it is

[obtuse stag]

sweet thanks

[opal plinth]

Is that the entire question?

[obtuse stag]

Yeah I was just uncertain and it would've ruined my entire graph

gotta stop second guessing myself

[opal plinth]

Looking at the expressions you wrote, the domain can be anything you want really

(well, in R)

[obtuse stag]

The assignment was create three functions, two parabolas and one other function that connects them. they need to start at the x axis and end at the x axis

[opal plinth]

Such that they chain together into a continuous piecewise function?

[obtuse stag]

exactly

[opal plinth]

Fair enough

[obtuse stag]

thanks again!

.close

[final saddle]

Channel closed

Closed by @obtuse stag

Use .reopen if this was a mistake.

[obtuse stag]

.reopen

[final saddle]

✅ Original question: #help-36 message

[obtuse stag]

I have a question

This is my graph

It states for functions and domain/range

that we need to find the range of this graph

How would I start that

[thin trail]

Well lets start by first thinking about what really is the meaning of range?

[obtuse stag]

The range is all the possibilties on the y axis right

so like

it confuses me

because its in desmos

this is my first time using desmos

[thin trail]

Ye basically its the values of the y axis which the function encompasses

For example the range for y=x is (-infinity,infinity) cause it covers all the values on the y axis

[obtuse stag]

for the first function

[obtuse stag]

but because on my graph

for the piece that connects the two parabolas

i used a linear function to attach them

and restricted the domain

would that cause it to not be infinity

[thin trail]

Yep

So for example if you restrict the graph y=x to [5,7] the range is also just [5,7]

[obtuse stag]

so ohhh

[obtuse stag]

so the range for the linear equation

would be

{-19.6, 32}

[thin trail]

Ye I think so

[thin trail]

Ye

[obtuse stag]

what would the range be for the parabolas

cause i know the domain for the first one is just

{xER | -8 <= x <= 0}

in set notation

[thin trail]

You need to find the maximum and minimum points of the parabola on this domain

[obtuse stag]

cause it asks for it

[thin trail]

Do you wanna find the domain graphically?

[thin trail]

Yep

[obtuse stag]

it ends at 36

[thin trail]

Thats the maximum

[obtuse stag]

and starts at zero

so

[thin trail]

So whats the range?

[obtuse stag]

{yER | 0 <= y <= 36}

[thin trail]

Yep

Nice

Now for the second parabola

[obtuse stag]

Alrighty

[obtuse stag]

lowest point is -19.6

highest is zero

[thin trail]

Alr

Whats the range then

[obtuse stag]

{yER | -19.6 <= y <= 0}?

[thin trail]

Yep

[obtuse stag]

i always second guess myself like my brain thinks i dont know how to do math

[thin trail]

Its ok by the looks of it you do know how to do maths

[obtuse stag]

thanks a lot for your help!

[thin trail]

Np

[obtuse stag]

.close

[final saddle]

Channel closed

Closed by @obtuse stag

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[worldly hinge]

hello, i need some help

[worldly hinge]

just a sec

here this question

[high jolt]

so $x^3 = 1, e^y = 13.5$ and $x^3 = 7.5, e^y = 0.5$, right?

[soft zealot]

Altanis

[worldly hinge]

uhm

its asking us to show it in the form of y

[worldly hinge]

i think thats correct though

if you get the right equation

[tender pollen]

what does "plotted against" mean

[thin trail]

Like graph

[tender pollen]

are they different functions

[high jolt]

so you know this graph is a straight line function

so that means $e^y = m(x^3) + b$ right?

[soft zealot]

Altanis

[tender pollen]

like x=e^y, x^3=y?

[thin trail]

So like e^y is one axis and x^3 is another axis

[tender pollen]

ohhh

so x=e^y, x^3=y

[worldly hinge]

yes

[tender pollen]

because there's no context

[worldly hinge]

and you find the gradient by the formula

[tender pollen]

wait is there a hidden multivar function f(x,y)

[thin trail]

Nah bro this is just hs maths

[worldly hinge]

this is at the IGCSE 0606 level

[worldly hinge]

yes

[thin trail]

This is basically what its saying @tender pollen

[tender pollen]

as in, context about how the functions are graphed

[high jolt]

plug in your points to find the slope m and intercept b

then just solve

[tender pollen]

i took multivar calc tho

[worldly hinge]

@high joltthank you!

[high jolt]

np

[worldly hinge]

thank you guys

[worldly hinge]

we just sketch them with points

in this question tho, its just as simple as what atlantis said, might be so easy for you guys

[tender pollen]

nah cuz like what does "f plotted against g" mean

does it mean the graph of f(x)=g(y)?

or a linear combination of them

[high jolt]

conventionally, if A is plotted against B, then A is the vertical axis

[thin trail]

Basically e^y is the y axis and x^3 is the x axis

[thin trail]

Ye listen to this guy

[tender pollen]

oh i see now, so like logarithimic scale but for general functions f

OH

so it reduces to linear algebra

[worldly hinge]

also

i have some more questions to ask

[thin trail]

Go ahead

[high jolt]

how would you extract the angle from the vector (5, -12)?

[worldly hinge]

NO NO

sry,

you dont do that

[thin trail]

I think theres an easier way

[worldly hinge]

yeah

a much easier one guys

[high jolt]

oh oops yeah

[reef depot]

Whats the question?

[worldly hinge]

y'all are so smart, you're complicating easy stuff

[thin trail]

Rtoc fan in the wild

[tender pollen]

yeah, normalize vector, multiply by 26, and integrate

[worldly hinge]

how do you find the velocity vector

[reef depot]

What nadat said

[worldly hinge]

is there a formula for this

[reef depot]

Normalize means divide by the size of the vector

[worldly hinge]

wait

[reef depot]

Doing that gets the direction in an easy form and you can apply speed 26 to that direction

[tender pollen]

velocity?

(10,-24)

[high jolt]

you don'tneed to integrate anything

[worldly hinge]

i'll send the solution, and you guys explain me the solution, because what nadat said maybe true, but i'm still young for that 💀

[reef depot]

No need to integrate

[tender pollen]

yeah im dumb, it's not asking for position

[reef depot]

No not too young

[high jolt]

when you change the length of a vector or scale it, it's direction is preserved, correct?

[thin trail]

Look basically what you can obtain is that the ratio of the velocity on the x and y axis are 5:12

[tender pollen]

by pythagorean triple (5,12,13), normalized vector is (5/13,-12/13)

[high jolt]

speed at an instant is the magnitude of velocity, and you're given the direction. so you try to make your given direction vector have a magnitude of 26, noting that changing the length of a vector preserves its direction

[tender pollen]

multiply by 26 to obtain (10,-24) <- solution

[thin trail]

Oh yeah that method is best

[worldly hinge]

can you explain what this mark scheme says

what is it trying to imply

[reef depot]

Velocity is speed and direction.
Speed is the length of the vector and direction is given by any vector parallel to it.

So you take the unit vector in that direction and multiply by speed to get the desired velocity vector. The desired velocity vector will have the correct direction and length.

[tender pollen]

yeah 👍

[reef depot]

[tender pollen]

normalize * 26

[worldly hinge]

so basically

speed multiplied by the vector?

[reef depot]

To illustrate lets work a small example backwards

[worldly hinge]

yes please

[reef depot]

Say someone gives you a velocity vector (1,1)

[worldly hinge]

mhm

[reef depot]

Whats the speed? Its the length of the vector

[worldly hinge]

yeah, you can find that with a formula

[tender pollen]

||(a,b)|| = sqrt(a^2 + b^2) is the formula

[reef depot]

Whats the direction? Well we could say (1,1) is the direction, so is (2,2) but to keep things easy and standard we normalize it so we get a unique direction being (1,1)/length(1,1)

[worldly hinge]

yess

[tender pollen]

where ||(a,b)|| is the magnitude

[worldly hinge]

absolutely

[tender pollen]

and then, after normalizing, we multiply by n to get a vector of magnitude n

[reef depot]

So the direction(normalized) * speed = velocity since

((1,1)/length(1,1) )* length(1,1)=(1,1)

[worldly hinge]

hmm

what did you get as the asnwer though?

[tender pollen]

(10,-24)

pythagorean triple (5,12,13)

ok something's wrong with that

bro

you used the 12-adic norm???

[worldly hinge]

guys, im sorry but i dont understand

[tender pollen]

ok

so

i have vectors (x,y) right

and the magnitude is given my the formula

but sometimes

you want the magnitude to be n

the intuition behind normalized vectors

is that the normalized version of (x,y) (call it n)

satisfies ||n||=1

AND angle(n) = angle((x,y))

so what we get

when doing M*n

is a vector with magnitude M

and angle of (x,y)

[reef depot]

You gotta work with us. What part do you misunderstand

[worldly hinge]

OH, but then why do we find the sin of the ansgles

[worldly hinge]

this part

[tender pollen]

we don't care about sine

you find more beautiful solutions, not bashy solutions

[reef depot]

The reason the solution here has sine is because they are writing the direction in terms of the angle about the x axis. But this is extra work

[worldly hinge]

really

ok

so i get that we can find the magnitude of the vector

similar to this:

[tender pollen]

yeah

magnitude is 13

[worldly hinge]

ok, after this, we find the angle of the vector?

[tender pollen]

extra work

[worldly hinge]

ok ok

so then?

[reef depot]

Unnecessary but might be helpful for another question

[tender pollen]

normalized vector is 1/13 * (5, -12)

which is

?

[reef depot]

Well you dont need to worry

These are nice fractions

And 26/13 is 2

[tender pollen]

yup 😁😁😁

so our velocity is 2 * (5, -12) = (10, -24)

[worldly hinge]

yes @tender pollen

so its moving by a factor of 2?

[tender pollen]

no, by a factor of 26

[tender pollen]

bump

[worldly hinge]

oh

ok ok

yes got it

so, now

we have the magnitude

and the factor of direction or sum shit

[tender pollen]

(10, -24) has the exact same direction as (5, -12)

[worldly hinge]

mhhmm

[thin trail]

So does (100,-240)

[tender pollen]

in general, for vector A and scalar b>0, b * A has the same direction as A

[worldly hinge]

yes

bro wait

what if there is just a simple formula for this

its for two marks 😭

[tender pollen]

yeah

the simple formula is

[\frac{a(x,y)}{\sqrt{x^2+y^2}}]

[soft zealot]

nadat12

[worldly hinge]

wait, can we use this?

p = u + tv, where p is the position vector, u is the unit vector, and v is thevelocity?

[tender pollen]

uh

[worldly hinge]

oh

[tender pollen]

the only problem is that you don't know the initial position

[worldly hinge]

yeah ik we cant use mine

in the next part we do

[worldly hinge]

but for this, this formula is fine

[tender pollen]

it's the velocity, given that it's moving at a speed of a and direction (x,y)

[worldly hinge]

OHHH

guys i think i got it

so, find the magnitude

ok, divide the speed on the vector by its magntidue

then, multiply that by the vector

right?

[tender pollen]

yeah you got it 👍

[worldly hinge]

let me solve once

on paper then ill show

this right?

but whhy cant we take the root of 169 as -13 also?

i mean its possible right

[opal pelican]

By definition sqrt(x) is the unique function g:R->R that satisfies g(x^2)=|x|

[worldly hinge]

@tender pollen

@reef depot

[tender pollen]

because magnitude is positive

[worldly hinge]

@thin trail

[opal pelican]

So while -13 is a solution to x^2=169 you generally take the positive one

[tender pollen]

no the reason is that magnitude is positive

[thin trail]

Ye I kinda need to go sleep so I cant help but Im hurt that Im your third pick

[reef depot]

Distance is positive

[opal pelican]

Oh is this the modulus of a complex number?

[reef depot]

Length is also positive

[opal pelican]

Well, that's a more intuitive explanation if so

[tender pollen]

close enough, the magnitude of a vector

[reef depot]

If you disagree that length is positive then give another definition and maybe we can come to some agreement

[opal pelican]

Alright, my bad then

[reef depot]

Yeah its the same thing

[worldly hinge]

thank you @tender pollen

[final saddle]

@worldly hinge Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[umbral jay]

x – y/5 – 10 = 0

[final saddle]

Please don't occupy multiple help channels.

[proper dagger]

!close, stay within one channel for the same question ( #help-6 )

.close

[final saddle]

Channel closed

Closed by @proper dagger

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fallen valve]

Why is the radius of convergence obtained by using the ratio test $|a_k/a_{k+1}|$ the same ions obtained by the root test? $(\lim_k |a_k|^{1/k})$?

[soft zealot]

LXDL

[lapis wedge]

https://math.stackexchange.com/questions/761262/question-about-the-radius-of-convergence-and-the-ratio-test

This might answer your question

[final saddle]

@fallen valve Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fallen valve]

ah okay, but I think Im tryign to show this agrees with the radius of convergence provided by the root testr

[fallen valve]

test*

[final saddle]

@fallen valve Has your question been resolved?

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[noble marsh]

hi there. It's akind of meme that i saw on the internet, but if we take it seriously, is it even possible, to solve this problem?

[dense coral]

numerically? yeah
analytically? I severely doubt it

[olive lantern]

Probably yea

[vital crag]

Don't do random problems from the internet

[spare summit]

doubt this thing even has a closed-form solution

esp. not with the gamma function in the way

[noble marsh]

i tried to get an assist from Ai, but he said that "Leave me alone brotha ".

[spare summit]

meme problems deserve meme answers lol

[frail oyster]

I'd assume the integrand becomes an odd type complex oscillatory function over a symmetric interval, and real part cancels. So the answer should be zero?

Probably not tho 🤔

[spare summit]

this is complex-valued alright but it's very unlikely to be 0

my verdict is that this is as meme-y as you claimed it to be so I'm noping out of this without there being a clear goal to this integral.

[noble marsh]

ChatGPT says:
"Because the factor creates complex oscillations, and over a symmetric interval these oscillations can cancel out when multiplied by a continuous real function, making the integral equal to zero."

[noble marsh]

Casual math problem in a valentine's day.

[spare summit]

"the factor". what factor?

[noble marsh]

factor over the euler function.

[frail oyster]

Yea this is what I think would happen too but what can we take away from a meme?

[noble marsh]

a cup of coffee.. i think .

[spare summit]

I don't quite buy what it's saying, but again to me this is a rather bs question in the first place

[tired walrus]

!noai

[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).

[spare summit]

oh this factoid exists. very convenient then

[noble marsh]

[proper dagger]

!done?

[final saddle]

If you are done with this channel, please mark your problem as solved by typing .close

[noble marsh]

.close

[final saddle]

Channel closed

Closed by @noble marsh

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[void python]

can anyone explain how is A*2E (E matrice or I, elementary matrice)
is same as: 2A ?
it makes no sense, becuase that 2 will not multiply each element in matrice by 2, instead of just diagonally

[void python]

or am i overthinking and its ok

A*2E = 2A?

[thorny canyon]

it does multiply each element by 2

[thorny canyon]

that's right

you can consider an arbitrary nxn matrix and try multiplying it out ifw

it'll work

[void python]

yay alrighty, thankies

.close

[final saddle]

Channel closed

Closed by @void python

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pastel fable]

75

my answer

is it correct?

i did not use any circle's identity

[radiant igloo]

Yep ✅

[pastel fable]

ty ❤️

.close

[final saddle]

Channel closed

Closed by @pastel fable

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[magic flume]

I'm lost.

[barren hound]

and your target is $\f1{x(x+1)}$

[soft zealot]

schrödinger's kitten

[barren hound]

so you know that $A(x+1) + Bx = 1$

[magic flume]

Yes

[soft zealot]

schrödinger's kitten

[magic flume]

Indeed

[barren hound]

you found A but idk if you found B?

[magic flume]

Yes

I didn't

[barren hound]

we know A = 1

so then we just have (A+B)x = 0

so B = -1

[magic flume]

I'm so stupid

[barren hound]

no self deprecating

[magic flume]

Ty you can close this now

[barren hound]

you can! type .close

[magic flume]

.close

[final saddle]

Channel closed

Closed by @magic flume

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rotund pewter]

so I got this question and I think I'm missing some important insight on how to solve this?
Not necessarily that I'm missing any formulas or how to convert them, it's just I can't really wrap my head around what the hell is going on or what move would I even do

Here's the question:
$n,m \in \mathbb{R}, \log_{3}{3-x} \leq 3, \log_{3}{x-n} \leq m$
There is only one x that satisfies the first inequality while not satisfying the second inequality, and there is only one x that satisfies the second inequality while not satisfying the first inequality.
What's n+m?

[soft zealot]

Be not afraid.

[rotund pewter]

i couldve better formatted

havent used latex since like

6 months

$n,m \in \mathbb{R} \ \log_{3}{(3-x)} \leq 3 \ \log_{3}{(x-n)} \leq m \$
There is only one x that satisfies the first inequality while not satisfying the second inequality, and there is only one x that satisfies the second inequality while not satisfying the first inequality. $\$
What's n+m?

[soft zealot]

Be not afraid.

@icy current

[final saddle]

@rotund pewter Has your question been resolved?

[rotund pewter]

well i did that

it didn't help a lot

it is still as confusing as it used to be

the issue isn't with the log or readibility

i cant get my head around that

theres one tat satisfy the first and one that satsify the other

but doesnt satisfy the other etc.

so that implies

every other answer either satisfies or doesnt satsify both

considering i can find other answers

every other answer satisfies both

i dunno where i look for 2 missing answers

its really confusing there's like 5 inequalities

and i cant convince myself i can just

multiply or add them together and get an answer

[icy current]

Ok, can you show how far you got?

[rotund pewter]

nowhere

i'm baffled

i dunno how i'd compare the things

[icy current]

Just show your work, we'll go from there

[rotund pewter]

i don't have work its just

what i said

it's that

i can't screenshot the page

because i dont have a phone

yeah thats crazy

i have a phone but it doesnt have internet or online its old

i typed the problem out perfectly and i have 0 clues or 0 things

i mean i can play around w the inequalities

i've gotten them out of the log

i also know x < 3 and x > n because the thing in log > 0

but like i cant make sense of the information they gave

only 1 x satisfy the first but not the second and 1 x satisfy the second but not the first

[icy current]

I'd just eliminate the x by adding the inequalities

[soft zealot]

@icy current

[final saddle]

@rotund pewter Has your question been resolved?

[rotund pewter]

there's only one n and one m as an answer

huh

n + 3^m >= -24

what's n + m

hows that related

you need the x

it's just really stupid where you gotta somehow restrict the inequalities

because you js gotta somehow argue

if there's only 1 x that satisfies one by doesnt satisfy the other

then adding or removing epsilon which is very small lets sayy

should give you no other answer where it satisfies one and doesnt satisfy the other

using that insight you gotta conclude some n and m restrictions

but i js cant wra my head around the amount of inequalities and bs happening

[icy current]

Hint: This means $n < -24 \because \forall m \in \bR, 3^m > 0$

[soft zealot]

@icy current

[icy current]

I recommend playing with this condition and seeing where you get

[rotund pewter]

i dont see how that helps really

yeah thats irrelevant

i solved it

geniunely tbf

i just didnt wanna give it a real try

[rotund pewter]

this was totally irrelevant to my solution though

-21

is the answer i got

im not sure if thats right though

bcuz theres no answer sheet

its an exam question that i couldnt solve on the exam

its just 3 > x >= -24 and 3^m + n >= x > n and for the conditions where only 1 answer satisfies both and the other it doesn't you gotta have it so that n = -24 and 3 = 3^m + n

okay

,close

however the

hell

.close

[final saddle]

Channel closed

Closed by @rotund pewter

Use .reopen if this was a mistake.

[wild rune]

.reopen

??

is it open?

[proper dagger]

it's not

it's still in occupied for this very reason

grab an available channel like #help-27

[wild rune]

have you given any mathematics olympiad?

can someone provide me how to prepare for IMO?

[strange sparrow]

#❓how-to-get-help

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ocean jacinth]

Can anyone explain the derivation of the formula for the sum of squares of first n natural numbers?
This is the formula:

n(n+1)(2n+1)/6

[ocean jacinth]

THIS was the og problem and I got stuck on the first step

[spare summit]

there is a great post on MSE about this that may help you much better than I can think of at the moment.

sorry if linking to MSE is not allowed - just lmk and I'll nuke

[tired walrus]

linking to MSE is perfectly kosher

[spare summit]

ah alright, thank you

[tired walrus]

anyway do you know how to find the sum of the first n natural numbers (without square)? @ocean jacinth

[ocean jacinth]

Thank you sm

[tired walrus]

or in fact the sum of an AP in general

[ocean jacinth]

Yes

[spare summit]

glad to help!

[tired walrus]

ok, do you wanna read the MSE post first or should i yap

[ocean jacinth]

Yap on please

[bold kettle]

But tbh knowing the derivation is not much beneficial bro

But your wish

Try doing some problem on telescopic series

[tired walrus]

so you can rewrite 2^2 as 2+2, 3^2 as 3+3+3 and so on

[bold kettle]

And then try to solve it on your own

[tired walrus]

and you can arrange the terms of the sum of the first n squares as follows:

1
2 2
3 3 3
4 4 4 4 
....
n n n ... n

with me so far?

[ocean jacinth]

Yepp

[tired walrus]

right

...ok hang on

i have a suspicion that this might be a bit circular

in that it won't actually help you figure out sum[1,n] k^2 without already knowing sum[1,n] k^2

[winter dagger]

Ig u can prove it by using that

(1+2+3...+n)^2 = sum of squares+ 2 * summation of 2 numbers at a time

[tired walrus]

"summation of 2 numbers at a time"
and how are you gonna find that

[winter dagger]

It would form a AGP if ain't wrong

[tired walrus]

where would the 'geometric' part come from

[winter dagger]

Huh?

[tired walrus]

if you claim it is AGP then some geometric progression factor has to come

[ocean jacinth]

It won't be a gp cuz the ratios will differ with each term no?

[tired walrus]

anyway hm i think my idea of reading this array vertically won't help much

i dont think i have anything better rn than "guess that it is a cubic then work out coeffs"

or "look at summations of k^3 - (k-1)^3"

[ocean jacinth]

Alrr

Thanks for trying tho!!

.close

[final saddle]

Channel closed

Closed by @ocean jacinth

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[winter stag]

from pinter's abstract algebra

[winter stag]

heres an attempt of mine on question 3

anything wrong with it?

[final saddle]

@winter stag Has your question been resolved?

[strange sparrow]

it looks ok

i would add that you needn't consider negative powers of a (why?)

[winter stag]

i actually had a previous iteration where i didnt consider negative powers

didnt look right to me after i noticed the "product of a negative number of f(a)s" thing

[strange sparrow]

Wait nvm for some reason I thought your G was finite

[winter stag]

yeah i only noticed aswell after my 1st try

k thamks for the help

.close

[final saddle]

Channel closed

Closed by @winter stag

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tiny kraken]

<@&268886789983436800>

[final saddle]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fallen valve]

why are we allowed to just set $a_k$ = 0 when k is odd? i.e. how is $sum_{k=0}^\infty a_k z^k = \sum_{k=0}^\infty \frac{z^{2k}}{5^k}$? like it semes one is always "double" the other, i.e. $\sum_{k=0}^{2N} a_k a^k = \sum_{k=0}^N \frac{z^{2k}}{5^k}$

[soft zealot]

LXDL

[final saddle]

@fallen valve Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[shadow marlin]

How to calculate the determinant of $\left(\frac{1}{1 + |i-j|}\right)_{1 \leq i, j \leq n}$?

[soft zealot]

bloubbloub

[shadow marlin]

I tried row operations but to no avail

[winter lava]

Do you know the definition of determinant that uses permutations?

I wonder if we can find pairs of permutations that cancel

[final saddle]

@shadow marlin Has your question been resolved?

[winter lava]

Hmm maybe not

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[shadow marlin]

.reopen

[final saddle]

✅ Original question: #help-36 message

[shadow marlin]

oh I got it

thanks

wait

[winter lava]

it didn't work like i thought

[shadow marlin]

previous question was $det((t^{|i-j|})_{i, j})$ for $0<t<1$

[soft zealot]

bloubbloub

[shadow marlin]

so it looks like integration maybe

except each coefficient needs to be integrated so it's tricky hmm

i thought I had it but no

I only need to prove that the determinant is positive so maybe that helps

[final saddle]

@shadow marlin Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[earnest shuttle]

how to do this question

[final saddle]

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

[earnest shuttle]

2. I have begun but got stuck midway

[barren hound]

can you show what youve done?

ultimately this is going to be epsilons and deltas and stuff

probably

[earnest shuttle]

i tried to find f' by starting on Left side limit but i can cancel out h in denominator

can't*

[barren hound]

hint: if youre on the left side you can assume x < 0

which has implications for |x|

[earnest shuttle]

-x

[barren hound]

yes

[opaque ember]

i think we dont have to look at one sided limits?

[final saddle]

@earnest shuttle Has your question been resolved?

Channel closed

Closed by @earnest shuttle

Use .reopen if this was a mistake.

Available help channel!

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lapis wedge]

Can someone let me know if my example works

[lapis wedge]

The mersurable space is (Z, {emptyset, Z})

the function is f : Z to R defined f(x) = -1 if even, 1 if odd

|f| would then be the costant function 1

so if B contains 1 then |f|^-1(B) = Z

if B doesnt contain 1 then |f|^-1(B) = emptyset

so |f| is S-meseruable

f is not S measurable since if B = {-1}, then f^-1(B) = 2Z which is not in S

I think this example is good but can someone let me know if im missing something