help-42

[chrome locust]

ofc it's not

When did I ask thsr

[void umbra]

Then why are you saying these are the same sir

Sir

[chrome locust]

wair

wait

[short salmon]

then if you can accept that, do you see how it applies here?

[chrome locust]

Because bread tastes better than key

[final parrot]

bruh what?

[void umbra]

Yea nevermind actually

[short salmon]

anyways, you should think about it a little more.

[void umbra]

It's fine your teacher can clarify with you

I wish them the best🙏

[chrome locust]

them?

[void umbra]

Hope they get paid well

[short salmon]

referring to your teacher.

[short salmon]

lmao thanks for the diagram hahaha

[vagrant oak]

what you claim is in the form (a+b) * c = a + bc. So what ramonov said is indeed relevant

[chrome locust]

yall prob different

[void umbra]

If you're saying we're different from you

Uh I mean if you wanna say it like that

Then yea I guess

[chrome locust]

no

Ok im an alien then

[short salmon]

here's the thing, you already accepted that it's not generally true that (a+b)c=a+bc. now, we just need you to connect the dots from that to this situation

[chrome locust]

im closing this

[final parrot]

You're not, but it would be better to understand where your mistake is rather than insisting on keeping false information

[chrome locust]

mb brub

[final parrot]

@short salmon Can you close this, he already said that he's leaving

[heavy sundial]

Boiiii ts bussin 😂 ✌️

[vagrant oak]

this is similar to what you're claiming, you can check that it just doesnt work $\left(6+3\right)\cdot\frac{1}{3}=6+\frac{3}{3}$

[potent lotus]

MathIsAlwaysRight

[short salmon]

eh. let him close it himself

(with .close)

[final parrot]

I'm pretty sure they have left

[final parrot]

[vagrant oak]

theyre still in the server, at worst theyll get pinged and either close it or ignore it and itll close itself

[void umbra]

Bro did not infact close this🙏 😭

[short salmon]

who knows. maybe he'll have a change of heart

[primal bear]

https://tenor.com/view/blimey-new10-tenet-robert-pattinson-blimey-new10-gif-19750303

absolute trainwreck

[short salmon]

whaddup nepou

[final parrot]

nah, centuries later for sure

[void umbra]

Maybe this was someone's attempt at ragebait

[final parrot]

I'll close this one since they have confirmed the terminal of the conversation

[untold flint]

.close by OP agreement

[calm coral]

Channel closed

Closed by @untold flint

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[winter elbow]

Bruh

[primal bear]

anyway guys i have a question

$x+1 \ \textbf{\ldots} \ \frac{x^2+1}{x+4}$

im so confused

[short salmon]

unnecessary close imo

but whatever

[final parrot]

I hate Seia sniping me

[potent lotus]

Περσυ

[final parrot]

😢

[primal bear]

yes

thats better

[untold flint]

i'll become the villain this time i suppose

[primal bear]

i think the answer is 3 divided by pi (1)

[calm coral]

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[woven light]

Sigma p=0 to p= infinity 1/(3p)!

[odd fulcrum]

$\sum_{p=0}^{\infty}\frac{1}{(3p)!}$

[potent lotus]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[pseudo wedge]

(3p)!, not 3*p!

[odd fulcrum]

im blind

nvm

[potent lotus]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[calm coral]

@woven light Has your question been resolved?

[odd fulcrum]

So there is a closed form

it’s just not necessarily clean

and I don’t know how’d you even derive it

[calm coral]

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[blazing coyote]

Stupid question, but what does number of cosets of H in G mean

[sour monolith]

the cosets define a partition of the group into disjoint sets

[blazing coyote]

Yes

[sour monolith]

you measure how many sets are in the partition

[blazing coyote]

But those sets need not be a subset of G, do they

[sour monolith]

they are subsets of G

[blazing coyote]

Yea, that's for sure

[sour monolith]

a coset is of the form gH, by closure this is a subset of G

so whats the problem

[blazing coyote]

Ah, makes sense

Sorry

Thanks!

.close

[calm coral]

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[median crypt]

Can someone help me with a question: draw r(t)=(t,2cos(t),2sin(t)) where 0<=t<=2pi

[sour monolith]

draw on paper?

[median crypt]

Yes

Doesn’t need to be exact but roughly

[sour monolith]

3d graphs on paper

[median crypt]

I don’t really see how to find the curve for each plane to draw

Unfortunately

[vagrant oak]

do you know what shape it is?

[median crypt]

No, I want to know the shape

[vagrant oak]

lets look at what happens with y and z coordinate first

(2cos(t), 2sin(t)) what shape / movement does this describe?

[median crypt]

Circle

[vagrant oak]

indeed, and regarding movement, how would the point move? Would it randomly jump around the circle? Or would it cycle through it? If so, in which direction and where would it start?

[median crypt]

Don’t know how to progress

[vagrant oak]

,rccw

[median crypt]

Starts at (0,0,2)

[vagrant oak]

wait u sure?

sin(0) is 0

[median crypt]

(0,2,0)

[vagrant oak]

yeah, thats better

okay and then in which direction does the point traverse the circle, if we ignore x-coordinate for a moment

clockwise or counterclockwise

[median crypt]

Counter

[vagrant oak]

and what will the radius be?

[median crypt]

2

[vagrant oak]

Alright,, so the point which traces out the curve moves ccw on a circle of radius 2 on the yz-plane if we ignore the x-coordinate

so now its time to put the x-coord back in

x = t, what kind of movement does this represent if we ignore yz coordinates now

[median crypt]

Moves right to 2pi

Or postive

[vagrant oak]

at what speed? Constant? accelerating? deccelerating?

[median crypt]

Constant

[vagrant oak]

alright, so the point is moving at constant speed along the x-axis and at the same time making a circle in yz plane (or planes parallel to it)

can you visualize the shape now? If not, you can try doing it with your hand. Start by circling your hand on the table and then start lifting your hand up at constant speed

[median crypt]

Issa spiral

[vagrant oak]

yep, its a spiral

so now you just need to draw it. Try drawing the endpoint and startpoint, and then just connect them with a single-twist spiral, making sure it spirals in the right direction

if u want ur sketch to be more precise, you can add few midpoints

such as the values at pi/2, pi, 3pi/2

[median crypt]

Alright, thanks 🙏

[vagrant oak]

np

[median crypt]

.close

[calm coral]

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[calm coral]

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[still terrace]

Thomas is an enthusiastic dart player and goes to an Irish pub. He meets up with Nicole and Rebekka and likes to have one or more Guinness beers. In a sober state, Thomas hits the bullseye with a probability of 90%. His hit probability, however, drops by half after each Guinness.
a) Calculate the probability that he hits the bullseye at least once when he throws three times: once sober, once after one Guinness, and once after two Guinness.

[still terrace]

so

im confused with the atleast

so his first throw is 0,9

his 2nd throw is 0,45

and his 3rd is 0,225

im confused

<@&286206848099549185>

[sour monolith]

the probablity he hits at least 1, is 1 - (probablity he doesn't hit anything)

[quick talon]

It’s easier to compute the probability that he doesn’t hit at all and use it as your opposite case

[still terrace]

ohhh

[still terrace]

hmm okay

man where are my thoughts going

so 1- probability that he doesnt hit anything

is a guranteed hit?

[sour monolith]

yeah

if he doesn't miss he hits at least once

[calm coral]

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[still terrace]

okay so i can just like memorize the fact that

whenever something says atleast in the problem

its always 1- the probability

of the thing

and stuff

[calm coral]

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[limber veldt]

I am working on a 2D physics engine in Rust and I just can't solve this problem I'm stuck on. The problem: 2 lines are traveling at 2 different speeds and angles (you can also define the angle and speed with 1 line of travel for each). They also travel proportionally of course (in the same time), so I have to know where is the first point the bodies will collide and after how much traveling, which is described with some variable t. For instance, a 12 speed line and 4 speed line collide at t = 0.5, then the first line traveled by 6 and the second by 2. Here is the visualized problem and 2 math equations I came up with but can't finish (I am doing it separate from school and learning programming on my own, I am 17):

[calm coral]

@limber veldt Has your question been resolved?

[limber veldt]

<@&286206848099549185>

[bright tree]

can you post this in latez

LaTeX

[calm coral]

@limber veldt Has your question been resolved?

[limber veldt]

t is amout traveled

So I want to get first t(if they can colide)

[blazing pagoda]

Firstly I would like to state that calculating this is bit too much most of the time for programming. (You want the exact point right?)

[limber veldt]

Yea

Its before touch colision

And its not

It kinda jsut works

When it works

[blazing pagoda]

I can't see how it is useful but still a problem is a problem.

Does the 2 lines represent objects(center of mass) or just lines that will collide and go back(like a point particles)

[limber veldt]

2 lines represent part of the body

So it kinda goes in for loop and checks witch line conctacs first

[limber veldt]

It stops tuneling

[blazing pagoda]

yeah there was that I just never seen a reason to fix it but for a better look and for high speeds alright.

[limber veldt]

Yea idk tried the non tunel proof but idk I ended up with this one

I cudl do the non tunel proof one but I am already here

So

[blazing pagoda]

So ok the last image got into my mind I think but if I am right with what I understood you want the point that the 2 lines intersects.

First the time of the collision.

[limber veldt]

Look I have school tomorow its 11 pm to me

I got o sleep

2 points go at 2 dif direcrions

First time they touch thats it

And dif speed

[blazing pagoda]

Ok sorry.

[limber veldt]

Gn go now sleep

Ther eis alweys

A bigger nerd

He will come here laugh at this problem and solve it in 2 seconds

[blazing pagoda]

Alright gn

May you close it then and come back later if needed.

[calm coral]

@limber veldt Has your question been resolved?

[calm coral]

@limber veldt Has your question been resolved?

[calm coral]

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[formal zephyr]

Can someone tell me why I got marked down on part a? Thanks

[desert relic]

Wait so g(3) is 0

Now you've gotta find f(0)

And when x is 0, the function doesn't exist

See how the graph is open when passing through the y-axis

That means it doesn't exist at x = 0

[formal zephyr]

Ik it doesnt exist but I think I can still find the limit

[mossy furnace]

f(0) = 2, no?

[desert relic]

Oh wait

Yeah, insane dude mb

[formal zephyr]

oh wait you're right

bro that image is so terrible its impossible to see

how is this fair

[desert relic]

Even I made the same mistake as you, the image sucks dude

[old sonnet]

These are the axes lol

f(0) = 2

[mossy furnace]

schools investing in a decent printer challenge: impossible

[formal zephyr]

bruhh

thanks i can do my test corrections now

.close

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[still terrace]

so the laws of de morgan

[still terrace]

its basically

A U B is the same as A and B?

or only if they both got the line above the head

[warm warren]

I have a feeling that’s not what de morgan says

What does de morgan say?

[still terrace]

im not sure what he says bro

fuck math

but

[warm warren]

Where did you encounter the words de morgan?

[still terrace]

here

[warm warren]

Good god

[velvet osprey]

half of these are confusing or wrong or both

[warm warren]

No wonder you’re confused

This is just on Wikipedia

[old sonnet]

"Break the line and change the sign" is how I remember them

[thorny stump]

Wth

[old sonnet]

That's wrong

[warm warren]

I mean

It’s true

But like

I’m having a headache understanding it too

[thorny stump]

No it's not

[warm warren]

Oh no it’s not

Yeah idk

This is just cursed

[calm coral]

@still terrace Has your question been resolved?

[still terrace]

yo

im back

[still terrace]

help

[still terrace]

bro wtfff

this doesnt make sense

also what can i use the inverse tree for

like what is it useful for

[old sonnet]

It does, come on

[still terrace]

it says

for the upper pne

[warm warren]

Did you read it

[still terrace]

Everythhing thats not A and B

and the values that they hold together

they should be highlighting

not A and B both

or is blue the highlight color

[warm warren]

Look at the caption…

[old sonnet]

Lmao

[still terrace]

ohh

yeah

but the 2nd one

[warm warren]

Attention span so short reading 2 sentences is hard

[still terrace]

everything thats not A and B

but the A circle isnt A

its not not A

[warm warren]

But it’s in not B

[still terrace]

wait

[warm warren]

You need to write what you’ve written with brackets

Not A and B is different to not (A and B)

[still terrace]

howw

wtf

so the long bar isnt the same as individual var

bar

for A and B

bro i might just skip these problems

[warm warren]

Not ($A$ and $B$) is $\overline{A \land B}$

[potent lotus]

frosst

[warm warren]

Not $A$ and $B$ is $\overline A \land B$

[potent lotus]

frosst

[warm warren]

The idea of demorgan laws is if you distribute the Not, the and becomes or

And if it were an or inside it because an and when you distribute

[still terrace]

oh

yeah but

A and B with a merged overline

is the same as A and B with individual overlines right

[still terrace]

also what can i use the inverse tree for

[warm warren]

No!!

It’s not the same

De morgan tells you exactly how different they are

[still terrace]

ohh

shit

what does the line even mean then

it just means „not“ for both right

like the long line

[mossy jetty]

this is ~(A and B).

[mossy jetty]

this is (~A) and B.

if that is your confusion.

[still terrace]

ik

but these r the samev

?

[mossy jetty]

no.

[still terrace]

what the fuck man

[mossy jetty]

~(A and B) means that you do (A and B) first, then you flip the truth value of the result.

[still terrace]

hm okay

[mossy jetty]

~A and ~B means that you flip the truth values of A and B individually first, then you AND them together.

[still terrace]

oh

and the U flips everytime

you change the lines or something

[mossy jetty]

not always (look at line 1 here).

[still terrace]

it flips everytime

the u or v

[mossy jetty]

oh, sorry. I misread it.

yes, looks like an accurate summary.

[still terrace]

ty

also whats the inverse tree diagram useful for

[mossy jetty]

I have never heard of an "inverse tree diagram". I know what tree diagrams are, but not inverse tree diagrams.

[still terrace]

hm okay like a flipped one

[mossy jetty]

do you have an example of usage?

[still terrace]

yeah wait

i cant find one

[calm coral]

@still terrace Has your question been resolved?

[calm coral]

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[fleet onyx]

Is this correct for number 11?

Ahh i draw the diagram wrong

Wait a sec

[calm coral]

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[calm coral]

@fleet onyx Has your question been resolved?

[calm coral]

@fleet onyx Has your question been resolved?

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[clear fable]

Hi

[clear fable]

how to write well in math ?

[hollow lion]

Read more maths

[clear fable]

Yes , but in exam

to have complet mark ?

[hollow lion]

Look at model answers for past papers and copy the structure of the answer

[clear fable]

Thank's but : can you give me models ?

[clear fable]

how did you structure you're answers , can you synthetise what you learned from

?

[hollow lion]

It depends on the level you’re at. But generally, you can ask your teacher for marked, old exam papers and just read the answers there

You can also ask for a mark scheme, which tells you how marks are awarded for each question

[clear fable]

Second year of university

[hollow lion]

At my uni, we could find past papers on the uni site used by lecturers and students

[calm coral]

@clear fable Has your question been resolved?

[amber bay]

na just write whatever is needed

in presentable format

like not over cutting and clearly stating and proving claims , conjectures etc

most profss dont mind handwriting

[clear fable]

so to introduce problem and give a demonstration

[amber bay]

ok

[clear fable]

But for demonstration

What's you're method to structure It's propositions from macroscopic to microscopic

[mossy jetty]

probably a better way is to show a question you have trouble answering?

[amber bay]

i have no idea wht that measn

[clear fable]

Like how did you create the map of demonstration in paper

Like introduce what there's and for what and the plan , then execute in middle of space , then conclude

And in the plan how you structure the steps etc?

[amber bay]

write wht is given to u

wht do u have to prove

start by observing sample cases

genralize

simplify

write and prove any claims u may be using

then just write QED at the end if its a proof based problem

or box ur final answwrr

[clear fable]

Yes

[amber bay]

ok

[clear fable]

Thankyou so much

Professional disco

[amber bay]

ok bro

[clear fable]

and thanks for @hollow lion

[clear fable]

But the question is still open

For others to give theirs methods .

[calm coral]

@clear fable Has your question been resolved?

[clear fable]

how to write math well for complet mark , tell me you're knowledj of solving problems?

[calm coral]

@clear fable Has your question been resolved?

[sly brook]

the same doubt?

weird man

[final parrot]

@clear fable How long do you plan to keep this channel? It'll be better for you to move it to #1021175428326633542 if you're looking for a thread without time restriction. Just a suggestion for you.

[clear fable]

ok

[upper sparrow]

In fact this is more suited for #study-discussion, I would think, rather than help channels or the forum

[calm coral]

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[steel ember]

what is arbiturary constant

ph its js

the C

but here why is it modulus on v but not t?

[upper sparrow]

"You don't wanna start going back in time now, do you?"

(time will always be positive, so you can ignore the possibility of it being negative, which the absolute value is meant to deal with for you )

[calm coral]

@steel ember Has your question been resolved?

[calm coral]

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[steel ember]

oh

[steel ember]

im goofy asf lol

thank you

.close

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[blazing coyote]

So I assume $Y(x) = e^{e^{-x^2}}$ here?

[potent lotus]

wai

[sour monolith]

Y = e^X

[blazing coyote]

what

but X is the normal distribution

which is e^{-x^2}

[sour monolith]

its pdf is 1/sqrt(2pi) * e^{-x^2}

[blazing coyote]

right

so that too, right

$e^{\frac{1}{\sqrt{2π}} \cdot e^{-x^2}}$

[potent lotus]

wai

[sour monolith]

what you are missing is that the pdf is not the value of the variable

it helps you describe its distribution

[blazing coyote]

I know

but I was asked for its PDF

[sour monolith]

yeah so its not just plug in

because the integral from -inf to inf should be 1

[blazing coyote]

Fair enough. But $X$ is a normal distribution

[potent lotus]

wai

[blazing coyote]

I think I should revise the theory once

I"m clearly missig something

Thanks

.cose

.close

[calm coral]

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[calm coral]

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[quaint venture]

Ik it’s long but if anyone could tell me the answer . It would be appreciated

[dim hornet]

do you want the answer?

[crisp sphinx]

,rccw

[quaint venture]

Yh

[teal drift]

!status

[calm coral]

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

[teal drift]

!noans

[calm coral]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[dim hornet]

That is why i’m explaining mr bot

[quaint venture]

I’m on 3

[teal drift]

What answer did you get?

[quaint venture]

A=0.7 and b=0.3

[crisp sphinx]

did you get that by expanding, or by another method?

[quaint venture]

Expanding

[teal drift]

!show

[calm coral]

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

[quaint venture]

Ok but it’s all messed up and confusing

[teal drift]

Then you should do it again on a neater way

Or just send it as it is, even if it's messy

[quaint venture]

Here

[dapper sable]

You need parentheses.

(x^3 + 6x^2 + 5x - 12) - (x^3 + 5x^2 - 4x - 12)

The reason is because you're subtracting the whole thing after the -.

So, if you have something like x^3 + 5x + ... for the part after the -, you want to subtract that whole thing, not just the x^3 part.

[quaint venture]

Oh ok

Ty

[dapper sable]

No problem.

Also, your expansion is wrong, I think.

[quaint venture]

Yh I think I definitely made a mistake

[dapper sable]

(x + 4)(x + 3)(x - 1) = (x^2 + 7x + 12)(x - 1) = x^3 + 7x^2 + 12x - x^2 - 7x - 12 = x^3 + 6x^2 + 5x - 12

[quaint venture]

Ty , your great

[dapper sable]

So, that part is good.

(x + 2)(x - 2)(x + 5) = (x^2 - 4)(x + 5) = x^3 + 5x^2 - 4x - 20

That part is a little mistaken.

[quaint venture]

Yh the -12 at the end . I see now

I rushed it so i probably confused the 5 with the 3 and ended up with -12 instead of -20

[dapper sable]

Oh, OK.

There are ways to do it without expansion.

[quaint venture]

Oh

[dapper sable]

For example, the equal sign with three lines means that it's an identity (true no matter what x is).

So, the coefficients on both sides will be the same.

So, if you look at the constant term, it's ab on the right side.

[quaint venture]

Yh

[dapper sable]

What is it on the left side?

[quaint venture]

-12-20

?

[dapper sable]

Almost.

Don't forget the minus in between.

So, you'll negate everything after the main -.

-12 + 20.

Like before with the parentheses thing I said.

[quaint venture]

Ok

[dapper sable]

So, ab = 8.

[quaint venture]

Oh

[dapper sable]

Does it make sense why?

[quaint venture]

Yh but the only confusing part is where did +20 come from . Wasn’t it -20

[dapper sable]

Well, you have (x + 4)(x + 3)(x - 1) - (x + 2)(x - 2)(x + 5).

Notice the - in the middle.

[quaint venture]

Yh

[dapper sable]

So, you need to subtract the whole right part from the whole left part.

So, you get -12 for the whole left part.

You get -20 for the whole right part.

So, -12 - (-20).

[quaint venture]

Oh now it makes sense . Ty

[dapper sable]

No problem.

So from the constant terms, you get ab = 8.

What about the coefficients of x?

On the right side, what do you get for the coefficient of x?

[quaint venture]

-4x

[dapper sable]

How did you get -4x?

Oh!

Sorry.

I meant the right side of the equation.

Not the right side of the -.

[quaint venture]

5x

[dapper sable]

Well, the right side of the equation is (x + a)(x + b).

[quaint venture]

Oh the whole equation

So it’s bx+ax?

[dapper sable]

Yes, so the coefficient is a + b.

[quaint venture]

Yh

[dapper sable]

Now, what is the x coefficient on the left side of the whole equation?

The way to find that out is:

[quaint venture]

5-(-4)?

[dapper sable]

(x + 4)(x + 3)(x - 1)

Let's look at that.

If you take the first part of each factor, you get x * x * x, right?

[quaint venture]

Yh

[dapper sable]

That's because you pick out three xs.

That helps us to get the x^3 coefficient.

But we want the x coefficient.

That means we can only multiply in one x.

Does that make sense?

[quaint venture]

Yep

[dapper sable]

So, let's do that. Here's one:

(x + 4)(x + 3)(x - 1)

So if we multiply those three parts together, we get -3x, right?

[quaint venture]

Yhh

[dapper sable]

OK, what's another way of picking one thing from each factor where we only pick one x?

[quaint venture]

I understand but idk how to word it out

[dapper sable]

OK, so we got -3x for mine. What do we get for yours?

[quaint venture]

For my coefficient of x?

[dapper sable]

Yes.

[quaint venture]

9

[dapper sable]

How did you get 9?

[quaint venture]

Wait wrong click

8

[dapper sable]

How did you get 8?

[quaint venture]

No I meant 5-(-4) =b+a

[dapper sable]

Sure, but I'm showing you a quicker way if you want me to.

Where you don't need to fully expand.

We can do just expansion if you want to.

[quaint venture]

Oh sorry I need to go sleep I’m exhausted and I probably won’t understand

[dapper sable]

Oh, OK.

[quaint venture]

Ty for helping tho

[dapper sable]

So, we have 5 - (-4) = a + b.

Which means that a + b = 9.

So, we have ab = 8 and a + b = 9.

[quaint venture]

Yh so b is 1

A is 8

[dapper sable]

Yes, that's right.

[quaint venture]

Finally

Tysmmm

.close

[dapper sable]

You're welcome.

[calm coral]

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[calm coral]

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[vivid cypress]

hello

[vivid cypress]

plotting straight line graph

with a table of values

[stoic crater]

I advise you to just assume the values of x and y, it really helps. all you have to do is mark the points and join them to form a straight line

for eg. say ur equation is x+y=7, put x=0 then u find that y=7 and put y=0 u find that x=7. now u have to mark these 2 points (7,0) (0,7) on graph and join them to form a straight line

this method works for every equation

also its not necessary to put x,y = 0, you can assume any value you want but try to keep calculations easier @vivid cypress

[vivid cypress]

ok thanks

the questions look something like this right

[stoic crater]

see here you are limited with values of x and y you can put

the question has restricted you that you can only put values from 0 to 6 of x and -5 to 14 of y in the first equation

[vivid cypress]

yeah

i understand

[stoic crater]

yup

[vivid cypress]

but can u give me a question like this

and then you can see if its right or not

i have a test on this tomorrow

[stoic crater]

okay i’ll give u a question

[vivid cypress]

ok

[stoic crater]

solve this eq

y=4x-u

[vivid cypress]

whats u

[stoic crater]

y basically

no

y=4x-9

mb

[vivid cypress]

aight

can you include something limited as well

limit the values of x and y

[vivid cypress]

like this

[stoic crater]

-10<x<10
-15<y<20

[vivid cypress]

ty

,rotate

[vivid cypress]

do these x values seem right

[dim hornet]

Brodie

[vivid cypress]

what

@dim hornet

[potent lotus]

xfilin
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[vivid cypress]

why did u choose -6

u can choose the first number brodie

-10

[potent lotus]

xfilin

[vivid cypress]

ight

.close

[calm coral]

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[quiet island]

Let $f: [-1,1] \to \mathbb{R}$ defined as:

[potent lotus]

Halex

[quiet island]

Show f is RIemann-Integrable

$f \in R$ iff for all $\varepsilon > 0$ there exists a partition $P_{\varepsilon}$ of $[-1, 1]$ such that $U(P_{\varepsilon}, f) - L(P_{\varepsilon}, f) < \varepsilon$

[potent lotus]

Halex

[quiet island]

Thing is, I'm not sure how to deal with discontinuities

[sleek vessel]

Well you can just create partitions for each of the segments

Individually

And then by combining them you get a partition for the whole domain

@quiet island can you do this

[quiet island]

How about the discontinuities?

[sleek vessel]

If you partition [-1,0], [0,0.5] and [0.5,1]

You can combine them to partition [-1,1]

The discontinuities don't affect the partitioning at all

[quiet island]

Could you help me to choose such partition?

[calm coral]

@quiet island Has your question been resolved?

[sleek vessel]

Well the function is essentially constant in those intervals

What partition do you choose for such functions

[quiet island]

one that somehow includes the points of discontinuities?

[sleek vessel]

Let's forget about the discontinuities

Let's only work on the intervals

[quiet island]

only the end points then

[calm coral]

@quiet island Has your question been resolved?

[calm coral]

@quiet island Has your question been resolved?

[calm coral]

@quiet island Has your question been resolved?

[sleek vessel]

Good

Now does combining this partition work for the entire domain

[calm coral]

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[calm coral]

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[calm coral]

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[calm coral]

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[latent gulch]

guys i need help for 3(iii)

[latent gulch]

i truly do not understand the logic

[velvet osprey]

did you find dy/dx

[latent gulch]

yess

[velvet osprey]

yeah now just consider it as a function in its own right

and find its min

[latent gulch]

ohhhhh

let me tryy

[latent gulch]

guys i got the answer already

[latent gulch]

does gradient at least here means the stationary point?

like dy/dx = 0?

does that mean the stationary point always has the least gradient?

[upper sparrow]

Not always, but here the gradient is nonnegative, and finding its minimum value is relatively easy (which is why it's only 1 mark and a "state..." response)

(also there's where the derivative of a function is zero, which tells you where the original function may have a maximum or minimum, and there's this question, which is instead asking you where the derivative takes its minimum value )

[latent gulch]

ohhhh so is it bcs of gradient is nonnegative so the least value it has is 0? that's why we put m = 0?

[latent gulch]

ohhh i seee

[upper sparrow]

Well, it's more that the gradient is nonnegative, and the least value it can take is 0 (by -1 + tan(x) being zero), in other settings it may be a little bit different (you could for example have had the derivative being e^{-2x}(-1 + tan(x))^2 + 3 or something, a made up example, and that would have a minimum value of 3 instead, still where tan(x) = -1)

[latent gulch]

alrighttt thankuu sm!

[upper sparrow]

Always a pleasure you're happy with everything now?

[calm coral]

@latent gulch Has your question been resolved?

[calm coral]

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[final parrot]

Hi, which question do you need help with?

[warm warren]

You didn’t draw anything

I mean they look right

Try draw it

What about the previous questions

Use those to help you

No I mean the previous parts

I disagree…

What are a h k

What did they tell you it was?

I’m only guessing but i would assume you’ve done it right

We’ll look at the previous parts

Start with what |x| looks like

Can you plot |x|?

[cedar oyster]

do you have any examples of a function you've successfully drawn?

[wide chasm]

.close

[calm coral]

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[west mist]

Ciao! Ho fatto questo esercizio, ma sicuramente ho sbagliato qualcosa.. qualcuno può aiutarmi? Se in italiano ancora meglio.. grazie!
Vorrei che l'esercizio mi venga spiegato, non risolto e basta

[final parrot]

Ciao! Ho fatto questo esercizio, ma sicuramente ho sbagliato qualcosa.. qualcuno può aiutarmi? Se in italiano ancora meglio.. grazie!
Vorrei che l'esercizio mi venga spiegato, non risolto e basta

Hi! I did this exercise, but I definitely did something wrong. Can someone help me? If it's in Italian, even better. Thanks!
I'd like the exercise explained, not just solved.

Hai detto tutto troppo in fretta e in una botta sola, non ho capito niente
You said everything too quickly and in one go, I didn't understand anything.

Questo è sbagliato, dovresti includere 1 tra parentesi

@west mist

Ci sono tre termini nell'equazione sopra, quindi tra parentesi dovresti averne tre anche secondo la legge distributiva

[west mist]

Quindi mettere tra parentesi (3^(-2)+3+1) ?

[final parrot]

Sì, sai perché?

[west mist]

Ho capito perché, ma non capisco da dove esce l'1

[final parrot]

Bene, andiamo con calma. Come hai fatto a ottenere questa staffa in anticipo?

[west mist]

Avevo tolto tutti i 3^(×) mettendo ciò che rimane in parentesi

[final parrot]

Sì, ma hai dimenticato questo tizio

$3^x = 1\times 3^x$

[potent lotus]

This is sad 😢

[west mist]

Ahhh, okay okay capito fin qua

[final parrot]

Ecco un altro problema

Dovrebbe esserci un segno negativo prima di 3^-2

C'è un segno negativo qui, e non puoi abbandonarlo

[west mist]

Quindi sarebbe -3^(-2) ?

[final parrot]

YESSSSSSSSSSS

[west mist]

Finalmente hahah, sono peggio di un parto questi esercizi, ci metto troppo a farli e domani ho verifica hahaha
Da qui riesco ad andare avanti da sola, grazie mille

[final parrot]

Nessun problema, c'è altro?

@west mist

[west mist]

Mhh, per il momento non credo.. in caso posso lasciare questo canale occupato così mi aiuti se ho bisogno? Che sicuramente avrò bisogno di qualcos'altro tra poco hahah
Così almeno non entro ed esco in vari canali

[final parrot]

Quanto tempo ci vorrebbe?

[west mist]

Boh un minuto credo, il tempo che finisco di provare questo esercizio e sicuramente verrà sbagliato
Già vedo un paio di difficoltà, ma provo a farlo da sola in fretta se non riesco ti chiedo sennò esco dal canale tra poco

[final parrot]

Ok, I'll wait for you

Ok, ti ​​aspetto

[west mist]

Ho finito un paio di esercizi e per miracolo sono esatti hahaha, farò una pausa adesso.. quindi esco dal canale, grazie mille ancora dell'aiuto

[final parrot]

No worries

[winter elbow]

.solved

[calm coral]

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[remote mural]

yo

[remote mural]

what do they mean by "how close to eacother do the insects get?

like which point can they get the closest to one another?

or

[chilly marten]

closest distance between their locuses

[granite brook]

yes

at what points are the lines closest to eachother

[chilly marten]

can you write their locus as an equation

they prol skew lines (guess)

[remote mural]

what does locus mean btw

[chilly marten]

set of all points which satisfies a given set of conditions

so like for a point P
where
x = h ,
y = 5h^2

Locus of P :
y = 5 x^2

similarly i was wondering if you could eliminate the parameters from each equation to form a equation in x,y,z

it will give you an idea of the path of the ants are moving on if they were on a 3d space

[remote mural]

i still have no idea what this means tbh

[chilly marten]

"i was wondering if you could eliminate the parameters from each equation to form a equation in x,y,z"
this

[remote mural]

ohh

like a symmetrtic equation

but what does that do

[remote mural]

why is that helpful

[final parrot]

[chilly marten]

no?

[final parrot]

not necessary

Sorry for disturbing, I'll let you finish

[chilly marten]

yeah but i was thinking it will give them an idea on what topic the question is asking , as they were unable to understand the question , rather solve it

[chilly marten]

na na thats fine , i understand the ask-up its valid

[final parrot]

I would start by asking a few simple questions as prompt such as "Do you agree those parametric forms of function can be represented as the coordinates of the ant", or even smth board like "What have you observed in these parametric form".

It's a matter of opinion :))

[chilly marten]

Oo yeah thats fair , maybe i am missing context of what they know, which will stop me from explaining clearly

[chilly marten]

@remote mural im sorry if i confused you more ,
can you just read out his msg!

[calm coral]

@remote mural Has your question been resolved?

[remote mural]

yea

i know the parametric equations we have are endpoints of vectors that are scaled along the line

and i know setting a value for t will scale the vector in a unique way thatll give you unique end points

and that end point

is the point

on the line

[final parrot]

Sure

[remote mural]

yea

[final parrot]

So do you agree that regardless of what t we input, the point will be on the line?

[remote mural]

i agree

[final parrot]

Alright, so the same idea can be applied to another function

right?

They're both in parametric forms

Fam, I really need you to stick with me....

It's not the first time I get ghosted like this, and I believe it would be more effective for you sticking with me from the beginning to the end

[remote mural]

im not ghosting

im just thinking of what youre saying

[final parrot]

I see

[remote mural]

im just thinking what this means

or how it relates to your initial question

that any t would give us a point on the line

[final parrot]

Alright, sorry for the false accusation

I'll ask if you're still here next time

[remote mural]

its okay no problem

[remote mural]

so im at this point

idk what to do next

i understand any t gives a different point on the same line

[final parrot]

yes

So for convenience, let's call them line A and line B

This is Line A, do you agree that (6+t, 7-t, 2+t) is on the line?

[remote mural]

well

yeah

yes

[final parrot]

This is Line B, do you agree that (1+t, 4+t, 4t) is on the line?

[remote mural]

terms with the t are the components of the direction vector scaled

right

[final parrot]

I know what you're talking about, but I still need a clarification. Do you mean "the coefficient of t"?

[remote mural]

yea?

[final parrot]

Like the numbers beside t

[remote mural]

yea

[final parrot]

then this is yes

[remote mural]

like this

as an example

[final parrot]

that's correct

[remote mural]

alright

[final parrot]

^^

[remote mural]

yup

yes

i doi

[final parrot]

Alright, now we can cook

[remote mural]

for sure

[final parrot]

Let's say (1+t, 4+t, 4t) is the point on line B and (6+t, 7-t, 2+t) is the point on line A

How would you find the distance between them?

[remote mural]

terminal - initial

that would be after i have a value for t though

[final parrot]

not really if I ask you to include t in your answer

[remote mural]

but t being unknown can represent all possible points on the line

right?

[final parrot]

yes

right

[remote mural]

yeah so

cause i imagine we need a well defined point to find the distance between

[final parrot]

I partially agree with this, you need two well-defined points to find the distance between them, and the distance between them does not include any variables.

Let's lay emphasis on

does not include any variables

[remote mural]

yes

but here you wanna include the variable to see which variables gives you the shortest distance?

[final parrot]

Let's say (1+t, 4+t, 4t) is the point on line B and (6+t, 7-t, 2+t) is the point on line A
And finding the distance between these coordinates basically tells you the distance between the two points on the line with a given t input

[final parrot]

Yes!!

This is the way

[alpine cobalt]

lol

[final parrot]

Let's see how would you convert this, any idea in advance?

[remote mural]

but to find the distance including the variable is like finding all possible distances

you dont get 1 specific one

[remote mural]

not sure tbh

[final parrot]

You're right

100% and I'm not gaslighting you

[remote mural]

😂

[final parrot]

So basically after you apply a "secret formula", you'll get an ugly compund

and that ugly compound represent the distance between two points with different input

what you're looking for is: what t input will yields the greatest result.

So far so good?

We can have a 3 minutes recess for you to absorb what have been taught here.

[remote mural]

wdym by secret formula

[final parrot]

I'll leave it as a prompt, not gonna reveal it since you're supposed to know what it is

[remote mural]

uh

is it the terminal - initial

on each component with t?

[final parrot]

Can you elaborate this?

[remote mural]

wait i think i know what you mean

the symmetric equation right?

[final parrot]

idk honestly

[remote mural]

not that symmetric equation?

[final parrot]

No

How do you find the distance between two points?

For example, (1, 1, 1) and (2, 3, 1)

[remote mural]

terminal - initial

so

<1, -2, 0>

[final parrot]

good start

[remote mural]

i assume you apply the same thing on the components with t

[final parrot]

yes, but I'd like you to finish this first lol

[remote mural]

finish what?

ohhh

yeah well okay

you basically found the components of the line connecting the 2 points

the distance is just how long that line is

which is

magnitude

which is sqrt(5)

[final parrot]

Fantastic

Do that to the ugly stuff up there

i assume you apply the same thing on the components with t
Yes, for sure, certainly, absolutely, undoubtedly

[remote mural]

okay ill write it out

[final parrot]

it's kinda messy here, let me pin a few important information

[final parrot]

This must be one of the time that I use multiple pins in a single thread lol

Ping me when you're back

[final parrot]

(1+t, 4+t, 4t) (6+t, 7-t, 2+t)

[final parrot]

good, continue

[primal bear]

wtf is this

[final parrot]

incorrect simplification

try again

[primal bear]

why the fuck is the actual question not pinned

@winter elbow shoddy work

demoted

[final parrot]

That would be 4 pins in a row

[primal bear]

theres no limit

[final parrot]

x term incorrect in the first step; z term incorrect in the second step

[final parrot]

4t -3t = t not -5t for z term

[final parrot]

Looks pretty decent

Can you expand those brackets and simplify?

[final parrot]

The constant looks a bit off

Might double check it

what is 9+4+25?

[remote mural]

oops

no way i did that

[final parrot]

still wrong

,w calc 9+4+25

[potent lotus]

Results provided by WolframAlpha

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

Requested by huntiebounty

[final parrot]

.........

[remote mural]

wai its just 25 + 9

ohh i forgot to add the 4

yeah thats 38

we want

the shortest distance

[final parrot]

Now you have those cool guys under the roof, any ideas?

[remote mural]

so the shortest this whole thing can be

[final parrot]

yes

[remote mural]

how can i know that

[final parrot]

You're looking for the Min of the value

[remote mural]

when t doesnt make it negative ?

[final parrot]

think

Revealing it here ruins the fun

[remote mural]

okay wait

so this is literally the distance between all possible points

[final parrot]

Hint #1: ||What function is this?||
Hint #2: ||What's the characteristic of this function?||
I leave some hints on the board, only when you're about to give up do you open them.

[final parrot]

yes

cool guys and their roof means the distance

[remote mural]

line function?

its a point

[final parrot]

Is this a line function??

[remote mural]

point function

no

lmao

[final parrot]

no, I mean what function is $f(t) = 13t^2 -24t + 38$

[potent lotus]

This is sad 😢

[remote mural]

quadratic?

[final parrot]

You 100% have seen this somewhere before

yes

[remote mural]

ohhhh

[final parrot]

Open the second hint

[remote mural]

you need to solve for roots

[final parrot]

no, that's not what we are looking for rn

unfortunately

[remote mural]

38 + 13t^2 -24t is essentially a point right

any point on the line

[final parrot]

how come?

You don't even have the bracket anymore

[remote mural]

well we are taking the magnitude of a hypotnuse rn

if we knew the points

[final parrot]

Yes

[remote mural]

we would be doing sqare root those components

[final parrot]

Absolutely

[remote mural]

so were looking at arbitrary hypotnuses

[final parrot]

Let's not call it that way

it makes things complicated

[remote mural]

arbitrary distances

or lines

connecting arbitrary points

[final parrot]

We're looking for a certain t that makes the shortest distance

Is that correct?

[remote mural]

yes

[final parrot]

and this stuff is the distance

[remote mural]

we need the shortest points

so we wanna know those points via t

[final parrot]

So we're basically looking for the Min value of this stuff

[remote mural]

yes

i agree