help-39

[void sandal]

I think

I am getting confused because the same letter is being used here

[shadow monolith]

Like, pick a random element of my set. The probability that that element exists

[void sandal]

okey dokey

(I'm sorry but we may go back over some stuff that was said earlier but we shall see how this goes):

(I'm just working through some examples and ideas)

So in your set you can have some things that may not exist. Gotcha

[shadow monolith]

Maybe this is a good way to explore it. I'm trying to understand the inference from the bottom up. So if we work with the assumption that there are more actually existing things than merely possibly existing things, and assume all outcomes are equally probable, then we're able to derive that the probability of actually existing is less than the probability of not existing. I've got some confusion on how that derivation goes. How would you write out the derivation?

[void sandal]

surely its nonsensical to say that there are more things existing that possibly existing things. When you say that you are saying that your sample is larger than your set which doesn't make sense.

[shadow monolith]

Sample is larger than your set? How do you mean

[void sandal]

You said "if we work with the assumption that there are more actually existing things than possibly existing things.

[shadow monolith]

Yeah

Like unicorns are possibly existing but not actually existing

[void sandal]

ahh ok. So in this case are sample space is infinite?

(I've gone to make a drink but I'll be back haha. I want to answer this question now as well)

[shadow monolith]

Maybe. It might be infinite or finite. Not sure. Sounds like a philosophical question.

[void sandal]

true. Because my reasoning was going to be that if the sample space is infinite then the probabilities become negligible:

So I would say we have to assume that are sample size is finite

[shadow monolith]

Yeah this makes sense. So lets proceed assuming te sample size is finite.

[void sandal]

whooooah. This doesn't check with agreeing with what I said above when quoting you.

Unicorns have a possibiltity of existing but don't. Here, our set is all possible existing things and we are taking samples of what does exist

[void sandal]

Here we are saying that there are more things than could possibly exist

there is quite a difference, do you see?

[shadow monolith]

I don't quite see the difference.

[void sandal]

that's fine, I'll try a different way of explaining

[shadow monolith]

I think we can work with this interpretation & everything should go fine.

[void sandal]

oki. So, our set is all possibly existing things and x is an item in this set. so why does this not work

[shadow monolith]

I guess it's a meta-question. Like why are we setting the sample space as equal to the # of possible existing stuff, and not setting the sample space as equal to the # of possible existing stuff, and the # of psosible not existing stuff. Or another way to put it what are some problems with setting the sample space like the latter. Is it extremely weird to do or unconventional? Is there a reason for selecting the sample space like that? Is it the most representative, or something?

Like what would be wrong with doing this:

P(x exists) = # of total existing stuff / # of total possible not existing stuff.

Or: P(x doesn't exist) = # of total not existing stuff / # of total possible not existing stuff.

[void sandal]

ooo o o o o . We set the sample space as the number of possible exiting things to avoid the infinity issues above. If we make our sample space the sum of possible existing things and the sum of possible non-existing things surley our sample space is infinitley large (jesus this is philosophical). If our sample space is infinite then all probabilities are 0 (or more specifically p(x) = 0 ).

[shadow monolith]

Yeah I gather that. I guess I'm just saying, there are different sample spaces we can choose for p(x exists) that will yield different probabilities for p(x exists). So I'm just trying to figure out why we select one sample space rather than the other. Is it something to do with representative-ness of the sample space, or something? Just guessing here

[void sandal]

ok so, (using your useful assumption of equal outcomes) the first one works. It makes logical sense that the probability that something exists is the ratio of existing things and total possible non-existing things. Now I need to wrap my head around what the 2nd one is saying

[shadow monolith]

This one doesn't make sense? Or: P(x doesn't exist) = # of total not existing stuff / # of total possible not existing stuff.

[void sandal]

I see your stuckness, I think I am on the same page as you know

[shadow monolith]

Oh dope. Lol. But also not dope cos now we gotta brainstorm.

[void sandal]

In this context this does make sense HOWEVER in practice I think there are some issues

[void sandal]

lets take both these statements and say they are both talking about the same data set

and I am some abosulute mad man and have counted everything in the universe

with the second statement, we cannot count the total of non-existing things as we don't really know (assuming finite size) number of things that could be made

ahhhh nnopangnaposagihjol

now I'm going in circles

[shadow monolith]

Yeah I'm not totally following you here

[void sandal]

(I would recommend ignoring that)

hang on

[void sandal]

I want to say that this statement is identical to the previous statement

IF P(x exists) = # of total existing stuff / # of total possible not existing stuff.

then P(x doesn't exist) = # of total not existing stuff / # of total possible not existing stuff.

that is just a fact

[shadow monolith]

Yeah I agree.

Does it also follow here?

IF P(x exists) = # of total existing stuff / # of total possible not existing stuff.
then P(x exists) = # of total existing stuff / # of total possible existing stuff.

@void sandal

[void sandal]

this is slighlty different

[void sandal]

Here, our numerator is changing. What we want to find / know the probability of is changing and that relationship works

[void sandal]

Here, HOW we are finding the probability is changing and these 2 statements are not the same

[shadow monolith]

I see

[shadow monolith]

Right the denomintor is changing in the second, numerator changes in the first.

So now I'm trying to figure out which expression makes more sense:

P(x exists) = # of total existing stuff / # of total possible existing stuff

P(x exists) = # of total existing stuff / # of total possible not existing stuff

[void sandal]

So you need to redirect your question to be what is your sample space?

I would argue in this case your actual sample space is T

[shadow monolith]

Okay. So the actual equality should be:

P(x exists) = # of total existing stuff / # of total possible existing & not existing stuff?

[void sandal]

Not quite with that wording. P(x exists) = # total existing stuff/ # total existing stuff + total non-existing stuff

[void sandal]

of total possible existing stuff IS total existing+ total non-existing

Wow

Formatting

BIG STATEMENT

[shadow monolith]

OHHH

Wait is that true?

Total possible existing stuff = total existing + total not existing?

[void sandal]

I would say so yes

[shadow monolith]

How are you reasoning to that

[void sandal]

Unfortunately intuition ATM but I'll try it with some actually reasoning. In this case our sample space is everything, all objects. An object can either exist or not. There is no probability in an objects existence at a given moment. Since an object can either exist or not it must fall into either of those categories and so all objects is the sum of those categories

[shadow monolith]

Yeah I agree with that.

All objects is the sum of the total existing & total not existing. But how are you getting to the further step of saying total possible existing stuff = all objects?

Total not existing might include an object that's impossible to exist

Right?

[void sandal]

At that point it is a philosophical question

[void sandal]

But I could say that if you take this to be true then surely we have infinite objects

[shadow monolith]

Looks like it. Is there a way to get to Total possible existing stuff = total existing + total not existing avoiding any philosophical question.

[void sandal]

^. And this would break our assumption that the set is finite

But bare in mind, just because the Probability of something is 0 doesn't mean is can't happen.

(if we accept infinity)

[shadow monolith]

Yeah. Should keep that in mind

[void sandal]

So the assumption is really quite important for it to all work. If we don't allow the assumption then we get the problems

I need to go to sleep but I've read this again:

Basically summarising: the "of Possibly existing stuff" gives the whole set T (sum of non existing and existing). The bottom equation saying "of possible stuff" is more ambiguous about it's set and says that we must consider things that are possible but can't exist which I would argue is contradictory to the definition of possible

[shadow monolith]

I agree it's contradictory to the definition of possible. I don't exactly know if T is equal to possibly existing stuff. I'd have to think about that more.

[pearl pond]

@shadow monolith Has your question been resolved?

[pearl pond]

@shadow monolith Has your question been resolved?

[pearl pond]

@shadow monolith Has your question been resolved?

[shadow monolith]

My question is:
Given all outcomes are equally probable,

I'm trying to figure out why this equality is correct:

Pr(x exists) = # of actually existing stuff / # of possibly existing stuff

Rather than this other equality:

Pr(x exists) = # of actually existing stuff / # of possibly not existing stuff

In other words: Which is the correct sample space to use for this calculation?

[wide stream]

I.... don't get the question. Is this your own hypothetical question?

What are the 'outcomes that are equally probable'?

[shadow monolith]

Yes it's my own hypothetical question. Maybe 'outcomes that are equally probable' is improper language.

[shadow monolith]

Really what I'm trying to do is figure out how this inference works, under the stated assumption. How would you guess this inference formally follows?

[wide stream]

I think they are saying that if you think of some random thing, for example an animal with a crocodile's head and a cow's body, and assuming you are sufficiently imaginative, it would be more likely that you think of something which doesn't exist.

[shadow monolith]

Not sure I follow. How'd you write that out in a more formal way if you had to?

[wide stream]

I'm not sure I can, sorry...

[spiral pivot]

I thought I answered this question a few days ago

[shadow monolith]

It's a distinct deeper question #help-46 message

[feral sedge]

This really isn't formalizable

As for your original question I don't think there's a difference really between "possibly existing" and "possible"

[shadow monolith]

I'm thinking about it like "possible" includes "possibly existing" & "possibly not existing". To make my question concise: How are we deriving this equation?

p(x exists) = # of existing stuff / # of possibly existing stuff

OP seems to assume this equality & I don't understand how we're getting to this equality.

[feral sedge]

What's something in the set "possibly not existing" but not "possibly existing"

[shadow monolith]

Married bachelors.

[feral sedge]

Really it's whichever one you want it to be

As far as which set is the universal one

Whether you want to allow logically impossible things or not

[shadow monolith]

Don't the two ratios yield different probabilities?

[feral sedge]

One could argue they both yield 0

[shadow monolith]

Oh cos the denominator's infinity. I guess.

Is it more proper to have the universal set be the union of possible existing things, and possible not existing things?

[feral sedge]

Depends on what your goal is ig

If it's to make statements about the probability of a "possibly existing" thing actually existing then no

In this context, maybe a thing is an arbitrary combination of descriptors/properties?

[shadow monolith]

Sure.

[feral sedge]

Then as defined yes

[shadow monolith]

Ah, I see. So if we're interested in the probability of something existing conditional on it possibly existing, then we'd wanna find the ratio of actually existing things to possibly existing things.

But if we're interested in just finding the probability of something existing, then we'd wanna find the ratio of actually existing things to the total number of possible worlds (which includes possibly existing things & possibly not existing things)?

[feral sedge]

Yeah

[shadow monolith]

Dope. Last question. So to get the equality:

Pr(x exists | x possibly exists) = # of existing stuff / # of possibly existing stuff

Do we need to assume all outcomes are equally likely?

[feral sedge]

yeah

that would be the assumption being made

[shadow monolith]

So "all outcomes are equally likely" would be like all the possibly existing entities have equally likelihood of occuring?

[feral sedge]

yeah

[shadow monolith]

.close

[pearl pond]

Channel closed

Closed by @shadow monolith

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[dapper thistle]

whats happening here

[next trellis]

they're basically doin the same thing again tbh

the goal of all the subsitution technique qs is to substitute the appropriate thing, and find a derivative which is basically rearranged and is in the question

so that you work it easily

[dapper thistle]

this one looks sm harder

[next trellis]

yeah true

they just took the bigger one and substituted it

and found its derivative

[dapper thistle]

why do u need to find its deriv

[next trellis]

then made the du / 2 look in such a way that they can rearrange it to replace (x+2) dx

[dapper thistle]

but i thought that came from the big one

[next trellis]

they find the derivative so that they have a 'du' in the equation to integrate bc we substituted the big one to 'u'

[next trellis]

yeah it did, it just became smaller when they found its derivative, and then they rearranged

[dapper thistle]

whyd they make it like that tho

does it make the question easier

[cosmic garnet]

yes

[dapper thistle]

how?

[cosmic garnet]

will you expand the whole function and integrate all of them or use a substitution that converts the integral into minimal form and lets u integrate quickly

i'd choose the latter

[pearl pond]

@dapper thistle Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[narrow steeple]

.close

[spring falcon]

So you have a weight call it w and its remainder is 2 when divided by 5, so you can write w=5x+2, similarly w = 7x+5

[spiral goblet]

this would give a negative weight which is impossible

[spring falcon]

this is a chinese remainder theorem problem, do you know how to apply it?

the x's are not the same that was my bad, use thee fact they are both equal to W so you have sosmthing of the form 5a + 2 = 7b +5

then rearranging youll get 5a - 7b = 3

yes crt is nothing but a linear combination of congruences

which is what we are constructing from the infomation given

our linear combination is now 5a - 7b = 3

we just need to solve for a and b simultaneously

and since we are living in modulus land we know we are specifically interested in integers, so my wisdom to you is to focus on a and plug and chug until an interger for a yields an integer for b when solving

these numbers are nice enough where you can do that

yeah its following the crt formally using the derived equations, crt can be applied to as many congruences as you want, in this case it is just 2 congruences

yeah

im gonna use = as congruent btw

if you have p = ai mod ni which is just i number of congruences youll want to follow these steps

also as a prereq you should know how to find multiplicative inverses

but anywaay given p = ai mod ni, youll first wnt to calculate the product of all of your moduli which is N = n1 * n2 * ...

next youll need to find Ni = N/n1 so baasically N1 = N/n1, N2 = N/n2, ...

this is where youll find the multiplicative inverses

call it yi = (Ni)^-1 mod(ni)

where each yi is the multiplicative inverse of each N/ni = Ni

its handy to make a table to organize all of these values

but then our solution p from earlier is just a linear combination of
p = (b1N1y1 + b2N2y2 + ...) mod N

where b is the remaainder from the original congruences, that will be given from the problem, and then you calculate each Ni as N/ni and lastly yi is the multiplicative inverse of each Ni mod ni

so b wil, be given thats a W, Ni is easy to calculate its just a product of each modulus, the only problem child is finding each multiplicative inverse

yes, try it yourself and we can compare answers, like most things with number theory its all just an algorithm

start with w = 2 mod 5 and w = 5 mod 7

yeah the multipllicative inverse is just an application of the euclidean algorithm, it is called the extended euclidean algorithm

yeah so lets do the example y1 = N1 mod n1 which is y1 = 7^-1 mod 5

are you following that?

yeah so basically what we are trying to do is solve 7x = 1 mod 5

we want to find an x such that when 7 is multiplied by x and divided by 5 the remainder is 1

well lets start with yi = (7)^-1 mod 5, if we multiply both sides by 7 we get 7yi = (7)^-1 * 7 mod 5 = (1/7)*7 mod 5 = 1 mod 5

so 7yi = 1 mod 5

yeah from what i said ealier to this example x = yi

just a palce holder for a variable

so we now want to solve 7yi = 1 mod 5, we can use the definition of mod to reqrite this as 7yi = 1 + 5k

now, what i did in undergrad was i would rewrite this as yi = 1+5k/7 and i would just plug in integers starting from 0 for k and see which k value gave me an integer solution for yi

so start at k=0, k=1, ...

you hsould find at k = 4 you get yi = 3

thus the multiplicative inverse is 3

so what we saaid earlier when we multiply 7 by 3 and divide by 5 our remainder should be 1

and 7*3 = 21/5 yields a remainder of 1

so we are good to go

oh you bet

so now youre solving 5x = 1 mod 7

sounds like a plan

yes but in this case i =2 since this is the second congruence

then multiply both sides by 5

so we haave 5y2 = 1 mod 7

i keep using x as a force of habit hahah myb if its confusing you

i got y2 = 3

k = 0 y2 = 1/5, k = 1 y2 = 8/5, k=2 y2 = 3

cause 5*3 = 15/7 yields remainder 1

so now we have b1 = 2, b2 = 5, y1 =3, y2 = 3, N1 = 7, N2 = 5

we are now ready to construct our answer in the form
w = n1y1N1 + n2y2N2 mod N

the original remainders from the problem statement

2mod5 and 5mod7

its the 2 and 5 respectively

yes sir

w = 117 mod 35 but we can simplify this down to w = 12 mod 35

well letss focus on 12

lets take 12 for w and see if it satisfiess our two other congruences

12 = 2 mod 5, 12 = 5 mod 7

12/5 yields remainder of 2, 12/7 yields remainder of 5

well we have 117 mod 35

117 mod 35 = 117 - 35 mod 35 = 117 -35 -35 mod 35 = 117 - 35 -35 -35 mod 35 = 12 mod 35

just reducing

yes

so 12kg is our answer

and we checked it by plugging it back in to the other equaations

but you asked for the answer of the form nk+a so it woukd be

w = 12 mod 35 => w = 35k + 12

but the questsion is asking for the weight in kg and it would be 12kg

yeah unfortunately so

its the same type of problem

like the exact saame aapplication of the theorem

yeah he is applying other theorems from number theory

sure

im not sure where youre starting at in this problem

[pearl pond]

@midnight haven Has your question been resolved?

Channel closed

Closed by @fathom jackal

Use .reopen if this was a mistake.

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[waxen smelt]

for this question

the solution says this:

but for delx/del t

shouldnt it be this:
af'(u) - ag'(v)?

[pearl pond]

@waxen smelt Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[celest onyx]

Im doing critical points and i dont understand where in what order should i detect those p1 p2 p3 p4

[pearl pond]

@celest onyx 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[waxen smelt]

i dont really understand whats happening

here

[waxen smelt]

i found delz/del r which is:

Z_xcos(theta) + Z_y sin(theta)

now i have to differentiate this again

[viscid sierra]

saul

[waxen smelt]

but I dont get how to do it

[pearl pond]

@waxen smelt Has your question been resolved?

[pearl pond]

@waxen smelt Has your question been resolved?

[pearl pond]

@waxen smelt Has your question been resolved?

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[green ibex]

I need help

[green ibex]

<@&286206848099549185>

[tall flint]

!15m

[pearl pond]

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

[green ibex]

Oh sorry

but please

Help

@sharp tree

?

I have tried nothing

[violet tundra]

what don't you understand specifically that is stopping you from trying something?

[green ibex]

Everything

[violet tundra]

do you understand how multiplication and substitution works?

[green ibex]

Nope

[warm current]

If I told you to evaluate $x+y$ when $x=1$ and $y=2$, then you start with the expression $x+y$, and you replace $x$ with 1 and $y$ with 2. So you just need to evaluate $1+2$, which 3, and that would be your answer.

[jolly parrot]

SWR

[warm current]

That is the concept of substitution

[green ibex]

Ohhh

But it’s gonna be 3-5

[warm current]

I was just giving you an example

[green ibex]

Well

uhh

I don’t understand the part

3x x=-5

that becomes 3x-5

[warm current]

where are you seeing this?

[green ibex]

negative

[green ibex]

Here

[warm current]

Oh you mean $3x^2$ when $x=-5$?

[jolly parrot]

SWR

[green ibex]

Yes

that’s what I mean

[warm current]

Say you had $2x$ when $x=-1$, then you just do $2\times -1=-2$

[jolly parrot]

SWR

[warm current]

2x means you are multiplying 2 and x

[green ibex]

Ohh

Alr ty

Thank you so much

.close

[pearl pond]

Channel closed

Closed by @green ibex

Use .reopen if this was a mistake.

[warm current]

and in your $3x^2$ problem, you are multiplying $3$ and $x^2$

[jolly parrot]

SWR

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[steady walrus]

A chocolate is wrapped in a box shaped like a triangular right prism. The end surfaces are equilateral triangles with sides of 50 mm. The box is 300mm long. How much chocolate is there room for?

[steady walrus]

<@&286206848099549185>

[tulip musk]

!status

[pearl pond]

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

[steady walrus]

3😔 🙏

[tulip musk]

Lemme see what you've tried!

[steady walrus]

oh i did it in my head

let me write it down

[steady walrus]

first i used pytagaros to find the height and got 43 and than i took 4 x 50=2150 2150 x 43

[tulip musk]

Mmh okay

Do you know how to calculate the volume of the prism?

[steady walrus]

V= A x H

[tulip musk]

Yeah

How will you find the base area?

[steady walrus]

g x h/2

[tulip musk]

It's an equilateral triangle

[steady walrus]

ye

[tulip musk]

Try again

[steady walrus]

🤔

[tulip musk]

[ \text{Area} = \frac{\sqrt{3}}{4} \times s^2 ]

[jolly parrot]

Gaza

[tulip musk]

Where s=50mm

[steady walrus]

we have not learnt that formula

this is the conclusion in the book

but i dont understand how they got that

but why do they use the lenght as the height

[tulip musk]

$\frac{1}{2} \times \text{base} \times \text{height}$
It's this formula then

[jolly parrot]

Gaza

[tulip musk]

It's equilateral

[tulip musk]

This is the base area

[steady walrus]

but they said that 300 was the lenght not the height

[tulip musk]

The height it's equal to the length of the box

[steady walrus]

.close

[pearl pond]

Channel closed

Closed by @steady walrus

Use .reopen if this was a mistake.

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[weary holly]

find k so that the function is continuous on any interval

[weary holly]

i dont know where to start

[fossil jewel]

Try to imagine what this would look like on a graph

[weary holly]

the second would be a horizontal line

first one a diagonal one

[earnest stratus]

Horizontal line? Not really.

[rough forge]

what is the critical value of x in the interval where it might not be continuous

[weary holly]

-3?

[rough forge]

-3 is not even in that interval

you know for sure x+3 and kx are continuous functions, if you look at them separately, but if you define a piecewise function, then the only x value that is critical is the one, where you change functions

so at what x are you switching the from kx to x+3

[weary holly]

1

[rough forge]

yes!

what you wanna want to do now

what is h(1)?

[weary holly]

4

[rough forge]

yes!

now you want

[jolly parrot]

𝔸dωn𝓲²s

[rough forge]

If x approaches 1 from the left side

what has k to be

[fossil jewel]

Overkill

I don’t think he knows likits

Limits

[weary holly]

i do

[rough forge]

it's a trivial limit

[fossil jewel]

My bad

[rough forge]

and i am trying to show the concept on how to approach these piecewise function tasks

[weary holly]

4?

[rough forge]

yes

and then they are continuous because LHS limit = RHS limit

[weary holly]

understood

thanks

[pearl pond]

@weary holly Has your question been resolved?

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[torpid nova]

can someone help me setup the integral

[torpid nova]

I think i have the first two bounds

z goes from 0 to r

r goes from 0 to sqrt(2)

but not sure how to bound theta? My first thought was from 0 to pi/2 but i feel like thats wrong

[pearl pond]

@torpid nova Has your question been resolved?

[acoustic path]

it helps to consider what the graphs y = sqrt(2 - x^2) and y = |x| look like

[acoustic path]

(also x^2 + y^2 = r^2 not r)

[torpid nova]

semi circle and like a v shape

intersecting at x = -1, 1

with the inside of the v and circle being what we're integrating in the original integral

[pearl pond]

@torpid nova Has your question been resolved?

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[lyric helm]

x^2 - 12x + ? = (x - ?)(x-?)

[lyric helm]

how do i find out what the question marks are

[hot lodge]

Factorise the left hand side

[lyric helm]

how

[tropic saddle]

are the question marks all intended to be the same thing?

[lyric helm]

no

[tropic saddle]

then this isnt solvable

(uniquely)

[lyric helm]

well im not completely sure abt this

bc i did anotehr one and it was two different numbers

[proven elm]

the perfect square thing

divide the center term by 2

[lyric helm]

center term?

[midnight haven]

you can complete the square

[lyric helm]

12?

[proven elm]

square it to find the first question mark

b term

[proven elm]

yes this is what i'm talking about

[tropic saddle]

(on second thought, even if this was true then it wouldnt work either)

[proven elm]

(x-6)(x-6)

[lyric helm]

ohh

[lyric helm]

im not working on that question anymore but can you tell me if (x-3)(x-4) is the same as (x-4)(x-3)?

[midnight haven]

is 2*1 the same as 1*2

[pearl pond]

@lyric helm Has your question been resolved?

[lyric helm]

yes

[pearl pond]

Channel closed

Closed by @lyric helm

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[sly elm]

Chapter of "Espece Vectorial", Couldn't understand How he could reach this result:

<@&286206848099549185>

[merry carbon]

Expand this out and see what it becomes - you should be able to identify the basis elements from there

[merry carbon]

!15m also

[pearl pond]

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

[pearl pond]

@sly elm Has your question been resolved?

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[weak cipher]

i sortve understand it but keep getting them wrong. any help?

[warm current]

what're you getting for each one?

[weak cipher]

for x->0- = -6, x->0+ = inf, x->0 = inf, f(0) und

is my best guess

[warm current]

Explain $\lim_{x\to0^+}f(x)=\infty$ to me

[jolly parrot]

SWR

[weak cipher]

yes i dont understand

[warm current]

But it was your answer. How did you get it?

[weak cipher]

oh, since it is positive 0, it goes up into the infinite function?

idk

[warm current]

Oh. So your understanding is that you start at 0, and keep going right (because its 0+), and keep going until the infinite part?

[weak cipher]

right

[warm current]

Okay. At least now I understand your thought process. So let me correct it for you.

[weak cipher]

the examples dont make sense

[warm current]

$\lim_{x\to 0^+}f(x)$ is the value that $f(x)$ approaches as $x$ approaches 0, but only from the right side of 0. That is, you would consider what $f(x)$ approaches from the positive $x$ axis.

[jolly parrot]

SWR

[weak cipher]

so + is the right side and - is left?

[warm current]

yep

[weak cipher]

ok, so 0+ would be -6 then?

[warm current]

yup

Exactly right

[weak cipher]

and 0- would be 0?

or -4

[warm current]

Neither.

$\lim_{x\to0^-}f(x)$ is what $f(x)$ approaches as $x$ approaches zero from the left side. $x$ is going toward zero again, but you're only looking at the left side now, instead of the right.

[jolly parrot]

SWR

[weak cipher]

yes, and its expressed at 0 no?

i cant tell

[warm current]

expressed at 0? What do you mean?

[weak cipher]

on the left the only function i see could have the answer -4

[warm current]

nah its like you're going like this

[weak cipher]

omg

i completely forgot at the one on bottom

lmao

so 0- is also -6, then x 0 is inf?

[warm current]

How're you getting $\lim_{x\to0}=\infty$? What's your thought process?

[jolly parrot]

SWR

[weak cipher]

i dont know

how is different than the others

[warm current]

$\lim_{x\to 0}f(x)$ is what $f(x)$ approaches as $x$ approaches 0, regardless of the direction. As you get really close to $x=0$, what is $f(x)$ getting really close to?

[jolly parrot]

SWR

[weak cipher]

-6

[warm current]

yup

there you go

[weak cipher]

-6 for all besides f(0) which is und?

[warm current]

yup. $f(0)$ is undefined

[jolly parrot]

SWR

[weak cipher]

ty!

[warm current]

Another important note: for any value $a$, if $\lim_{x\to a^-} f(x)$ exists and $\lim_{x\to a^+} f(x)$ exists, and $\lim_{x\to a^-} f(x)=\lim_{x\to a^+} f(x)$, then $\lim_{x\to a} f(x)$ exists and $\lim_{x\to a} f(x)=\lim_{x\to a^-} f(x)=\lim_{x\to a^+} f(x)$

[jolly parrot]

SWR

[warm current]

Also, if $\lim_{x\to a^-} f(x)$ exists and $\lim_{x\to a^+} f(x)$ exists, but $\lim_{x\to a^-} f(x)\ne\lim_{x\to a^+} f(x)$, then $\lim_{x\to a} f(x)$ does not exist.

[jolly parrot]

SWR

[warm current]

just good stuff to know

[weak cipher]

ok

[pearl pond]

@weak cipher Has your question been resolved?

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[summer imp]

What have you tried?

[cobalt mural]

i dont think theres enough info idk

[summer imp]

They give you the radius.

[cobalt mural]

how do i find area with just that

which is?

3

?

[summer imp]

Yes

[cobalt mural]

ohh

ok

so whats the fpormula

[summer imp]

If the angle is 84, then the area corresponds to 84/360 of the disk's area

[misty gorge]

the formula for the area of a circle is pi * r squared

so because we're given r = 3, the area = pi * 3 squared = 9 * pi

[cobalt mural]

so the are of the circle is pi times 6

?

[misty gorge]

you then try to see what percentage or what fraction of the full circle that shaded area is by looking at the degrees

[misty gorge]

pi times 9

[cobalt mural]

how

[misty gorge]

because 3 squared is 3 * 3 and not 3 * 2

[cobalt mural]

if radius is 3

[cobalt mural]

OHH

mb

[misty gorge]

Yeah you're good

[cobalt mural]

so the answer is like a ?

[misty gorge]

so the percentage of the full circle that 84-degree section makes up would be 84/360 because the full circle is 360 degrees

yes

[cobalt mural]

yeah so the are of the cirlce is like 27 ish

divided by around 4

is around that

got u

[misty gorge]

around that yeah

it's best to keep the numbers exact until the end to round them but yeah

[cobalt mural]

so a squares are is also diameter times pie right

area

[misty gorge]

not exactly

radius * radius * pi

or radius squared * pi

[cobalt mural]

i see

[misty gorge]

usually notated as $pi*r^2$

[cobalt mural]

so if radius is 5

then 25 times pie

[misty gorge]

yes

!

[cobalt mural]

got u

u can close this now

[pearl pond]

@cobalt mural Has your question been resolved?

Channel closed

Closed by @cobalt mural

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[midnight haven]

why are the signs cancelled

[vital verge]

.help

[pearl pond]

Commands:

• clopen: .close, .reopen
• consensus: .poll
• factoids: .tag
• help: .help
• version: .version

Type .help <command name> for more info on a command.

[midnight haven]

????

[vital verge]

sry wrong channel

[midnight haven]

its ok

[midnight haven]

the negative signs are cancelled because there are two negatives

[midnight haven]

but why

why do samw things get cancelled

whenever you are dividing or multiplying two negatives, they cancel out

why

[midnight haven]

because thats how it works

buT wHyyy

[midnight haven]

just say u dunno smh

[waxen ore]

its so easy

[midnight haven]

dont ask irrelevant questions. the sign just moves in a different direction.

[waxen ore]

when you divide or multiply two negatives with each other they become a positive

[midnight haven]

literally what i said

[waxen ore]

when you divide or multiply one negative with a positive it will always be a negative

[steep saddle]

dont worry about that until you have to prove that a negative times a negative is positive in uni

[midnight haven]

qhy

[waxen ore]

yeah idk why they are saying we dunno

[steep saddle]

it just is.

[waxen ore]

mane idk

i did this in 7th grade

[midnight haven]

aigh

[waxen ore]

it just kinda works like that

[midnight haven]

ikii

[midnight haven]

math = math

[waxen ore]

so this would be 6

if it was -12/2 it would be -6

[midnight haven]

ikik

[steep saddle]

https://youtu.be/x_xxxvCJjBo?si=2enOC1H2WlmS32-a

[midnight haven]

they didnt har divison mann

but tysm

.close

[pearl pond]

Channel closed

Closed by @junior atlas

Use .reopen if this was a mistake.

[warm current]

Division is just solving for multiplication. The same rules apply.

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[vital verge]

.help

[pearl pond]

Commands:

• clopen: .close, .reopen
• consensus: .poll
• factoids: .tag
• help: .help
• version: .version

Type .help <command name> for more info on a command.

[vital verge]

69?

i cant do

anyone?

[acoustic path]

rewrite (sect)^2 using an identity

[vital verge]

and?

i am stuck at sin^t - cos^t

[acoustic path]

how did u rewrite (sect)^2

[vital verge]

1 + tan^t

[acoustic path]

ye ok 1 + (tant)^2

and after that u r very close to completing the proof

it helps to notice the similarities between the left side and right side

[vital verge]

man i am stuck thats why

[lavish portal]

What have you done with the numerator

[vital verge]

i did (1 + tan)(1-tan)

and stuck

[vale sentinel]

Isn’t that for 1-tan^2(x)

[lavish portal]

Yes the numerator

[vital verge]

typo error sry

[lavish portal]

Actually instead of that

Rewrite everything in terms of sin and cosine

[vital verge]

yeah i did (tan+1)(tan-1)

at last i got sint)^2 - cost)^2

[lavish portal]

This is further from the solution

[lavish portal]

^

[vital verge]

idk mann

[lavish portal]

you don’t know how to do that

?

[vital verge]

yea

[vale sentinel]

tan is sin/cos

[vital verge]

no i mean i cant get the answer

[lavish portal]

Tan^2-1 / tan^2 +1

rewrite in terms of sin and cos

remember sin^2 + cos^2 is 1

oh wait maybe I don’t know the solution 😭 but I’d do that anyways

[vital verge]

i got a test tmw 😭

[lavish portal]

are you trying to do anything with the problem

[vital verge]

im trying to prove

the left side is equal to right

you know

[lavish portal]

Yes so

Are you trying to manipulate the expression

[vital verge]

kinda?

i aint pro

[lavish portal]

This is probably closer btw

[vital verge]

but trying to practice

can you like find the solution?

[lavish portal]

rewrite in terms of sin and cos

If you want to practice you gotta do it yourself

without us just giving you the solution

I still thinking rewriting is a good step have you even tried it 😭

[vital verge]

yea ofc man

[lavish portal]

Can you send it

[vital verge]

ive tried it

this is another way i tried it

but didnt go well

[lavish portal]

Isn’t sin^2-cos^2 kinda close

Let me get paper

[vale sentinel]

I got that

Too

From right side

[pearl pond]

@vital verge Has your question been resolved?

[lavish portal]

Oh wow the solution is a lot easier than it seems

Uhhhh my hint is dividing by tangent

somewhere

[vital verge]

alr

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[abstract fox]

How do I answer this?

[pearl pond]

@abstract fox Has your question been resolved?

Channel closed

Closed by @abstract fox

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[bold wigeon]

I have no idea how to solve this, where do i start?

[versed mica]

well what is required for f(x) to be differentiable

what are the necessary conditions

[pearl pond]

@bold wigeon Has your question been resolved?

[bold wigeon]

continuous

and no sudden change in gradient like cusp

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[exotic scaffold]

if i had to represent this as a power series

could i just split it up into 3 * 1/(x+2) * 1/(x-1), and then turn the two fractions into power series and represent the final answer as a product of 2 power series

i know i can do it using partial fraction decomposition but just asking

[hollow cobalt]

You will need to rewrite that product as a power series

[exotic scaffold]

wouldnt that just be multiplying both the sequences of the series together

or

[hollow cobalt]

What do you mean exactly

[exotic scaffold]

like if im multiplying 2 power series

both going from n = 0 to inf

wouldnt i just multiply whatevers inside each of the power series together

[hollow cobalt]

Multiply each term? No, that's not it

[exotic scaffold]

if one series were to be like 3x^n

and another series were to be like 5x^2n

would the product of the 2 series be (3x^n)(5x^2n)

[hollow cobalt]

Like I said, it's not just multiplying each term

[sinful stream]

if you would multiply those two series together you would need 2 different indexes i believe

[hollow cobalt]

[ \left(\sum_{n=0}^\infty a_nx^n\right)\left(\sum_{n=0}^\infty b_nx^n\right) = \sum_{n=0}^\infty\left(\sum_{i=0}^na_ib_{n-i}\right)x^n ]

[sinful stream]

since its like multiplying polynomials, so you get a bunch of middle terms

[exotic scaffold]

oh shoot

i see

[jolly parrot]

A Lonely Bean

[sinful stream]

this you should probably approach with partial fractions

[exotic scaffold]

so going back to this if theres like a polynomial in the denominator i should go for factoring and partial fraction decomp

[sinful stream]

yes

[exotic scaffold]

are there any other techniques to use if there are polynomials in the denominator

[hollow cobalt]

If the polynomial is of the form 1 - x^n, then you don't need to factor

[exotic scaffold]

yeah i know but like if there are multiple terms with x

[sinful stream]

there are taylor series i suppose

[exotic scaffold]

alr

thanks

.close

[pearl pond]

Channel closed

Closed by @exotic scaffold

Use .reopen if this was a mistake.

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[wind meadow]

What do I do wrong here?
i set u = cos(41x)
du = -41sin(41x)dx
sin(41x)dx = -(1/41)sin(41x)
and then its -1/41 int(1/(1+u^2))du
and then its -1/41 ln(|1+u^2|)+C
and then i geet -1/41 ln(|1+cos^2(41x)|)+C

[tepid ether]

Int of 1/1+u^2 is not ln|1+u^2|

[warm current]

I do not believe $\int\frac{du}{1+u^2}=\ln|1+u^2|$

[jolly parrot]

SWR

[wind meadow]

...oo

how would you simplify that then?

or integral that

[tepid ether]

Well you sort of have to know this one

[sharp vigil]

reach back into the recesses of your memories of previous calculus classes to recall the derivatives of inverse trig functions (or google them)

[tepid ether]

Try taking the derivative of arctan(x)

[wind meadow]

ooooh i see i see

OOH THAT

tan

[warm current]

arctan

[wind meadow]

oh

so it'd be -1/41atan(cos(41x))+C

[warm current]

yes, which you can simplify

wait

I lie

[wind meadow]

. . . into -1/41 cos(41x)^2/sin(41x) +C

[warm current]

https://tenor.com/view/ignore-me-the-venture-bros-grand-galactic-inquisitor-ignore-gif-18430223

[wind meadow]

ty for the help!

.close

[pearl pond]

Channel closed

Closed by @wind meadow

Use .reopen if this was a mistake.

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[bold wigeon]

how would i solve this for N^2x?

[tropic saddle]

N^2x =N*(Nx)

and Nx you already computed

[bold wigeon]

ye

wait

oh

no i dont get it

[tropic saddle]

Nx is <0,-2,2,2>

so N^2x is N*(Nx)=N*<0,-2,2,2>

[bold wigeon]

ohhh then u just do it again ok thank u

.close

[pearl pond]

Channel closed

Closed by @bold wigeon

Use .reopen if this was a mistake.

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[sage patrol]

can someone explain how to solve this

[pearl pond]

@sage patrol Has your question been resolved?

[sage patrol]

<@&286206848099549185>

[pearl pond]

@sage patrol Has your question been resolved?

[hasty osprey]

For x < 1, draw a line with an open dot at 1 and an arrow moving left

For x > 3, draw a line with an open dot at x = 3, and with an arrow right

As this statement is “or”, these two arrows should represent the answer

[pearl pond]

@sage patrol Has your question been resolved?

[winged flare]

@midnight haven and I am

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[whole oak]

Is there any necessity to move left to the left-most zero after changing a 1 to x?

or can the process just be "Move to 1, change to x, move to next 1, change to x, move to next 1, change to x, accept"

and anything outside that is rejected

More officially

1. Move right until the first 1. Change to X. If none, REJECT
2. Move right again until the next 1. Change to X again. If none, REJECT.
3. Move right until next 1. Change to X. If none, REJECT.
4. Move right to next 1. If none, ACCEPT. Else, REJECT

or do i have to move left to the left-most non-blank every time?

[unborn abyss]

you can do whatever you want

you don't even really have to change to x as far as i can tell

[whole oak]

i guess since it's the practise we're taught, it'd be good to maintain consistency

[unborn abyss]

there's no reason to do it

[whole oak]

so just move right 3 times to a one

no changing

no moving left

?

[unborn abyss]

yeah

this is a regular language so like

the turing machine is going to be very simple

[whole oak]

for the transition diagram, do i just do for each step something like 1 -> 1, R

i just never added the writing to it yet

[unborn abyss]

yeah that's how i'd draw it

you need to encode the information (state, value) -> (state, value, direction)

so that works

[whole oak]

okay, so then for each reject it'd just be

wait i can't do the symbol

[ but flipped, basically blank space symbol

[ -> [, L

is this okay for each reject (apart from the last one)

[unborn abyss]

doesn't really matter which way you move

but yea

[whole oak]

I'd have to add a direction though right?

[unborn abyss]

yeah

[whole oak]

okay thanks lemme fill this out rq

[unborn abyss]

although, why space and not 0?

is space your "wildcard"?

[whole oak]

for which part exactly

or all spaces

[unborn abyss]

all spaces

[whole oak]

because I don't want it to reject a string that has 0s in it

it can have infinitely many 0s

[unborn abyss]

oh ok space is your end of string

[whole oak]

just has to have three 1s exactly

[unborn abyss]

that makes sense

[whole oak]

yeah

sorry

[unborn abyss]

and implicitly 0 transitions to itself?

or rather each state transitions to itself on 0?

[whole oak]

erm

this is where my understanding isn't great, because I'm following some examples our lecturer gave us

I'll send one

[unborn abyss]

okay, that doesn't bother to define all possible transitions -- for example, what if it's at i and sees an X?

that's impossible because of the way the machine works

in your case though, you definitely have the chance of seeing the symbol 0

[whole oak]

oh so i have to add another state in between i and S1?

i see what you mean now

i > S1 is the starting value only

[unborn abyss]

well even in their example, what if they're in S1 and see an X

again, it won't because of how the algorithm proceeds

but the point is that you need to define what happens, in your case, if you're in any of your states and you see a 0

[whole oak]

something similar to this?

every blank arrow is just bc too lazy to write [ -> [, L

it's an untidy version ik

just a quick sketch

[unborn abyss]

yeah (why not just use i as s1 though?)

[whole oak]

like, just loop through zero at i?

I'm not even joking when i say that my understanding of these rely on the visual examples because her notes don't explain them well

[whole oak]

i felt like it was an illegal move lmfao

okay neater and updated one

good?

[unborn abyss]

you're basically giving instructions for this machine

[unborn abyss]

nahhhh you're free to go back to the initial state

just as long as it's clear where the start state is

which your incoming arrow does a good job of that

yes this one looks good

if you blur your eyes you can probably see the FSA hiding in there

[whole oak]

aha yeah

is there a way to show the process, or does anything go really?

[unborn abyss]

the process of evaluation?

[whole oak]

yeah, if you see i have to show how it processes an empty string, 01, 101, 01101, 0110110

[unborn abyss]

right yeah

[unborn abyss]

this way is decent i guess? but it's missing state information

sometimes i've done something like this

[whole oak]

lemme quickly do the first two

are they okay

[unborn abyss]

seems fine, i'd say that that's a partial trace because in the case of 01 you don't show the first step of seeing the 0 and moving to the right while staying in s1

but full traces are annoyingly long

[whole oak]

yeah i dont know if they want it annoyingly long

there's another question on this that I've already answered, and just want to make sure that I've said enough for it

just want to see is my answer sufficient, then i'll finish up the processing of the strings and submit it

ok finished strings

[unborn abyss]

side note how is your handwriting so good

yeah that seems fine

[pearl pond]

@whole oak Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[whole oak]

aha idk but thanks for the compliment but most importantly for the help!

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[cursive belfry]

Q15

What do I do from here

I can’t factorise because of Y

@versed remnant

We haven’t covered that in class

Ohhhhhh

I didn tveen@

See that@

Omg

[pearl pond]

@cursive belfry Has your question been resolved?

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[nocturne urchin]

can anyone help me with this problem

[nocturne urchin]

the topic is QUARTILES FOR GROUPED DATA

<@&286206848099549185> help me out please

[pearl pond]

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

[nocturne urchin]

oh mybad

can you help me out?

but still can you help me out?

<@&286206848099549185> can someone help me out please

[nocturne urchin]

pleasee help me out <@&286206848099549185>

<@&286206848099549185> anyone pleaseee

.close

[pearl pond]

Channel closed

Closed by @nocturne urchin

Use .reopen if this was a mistake.

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[wind linden]

where does he find the 8/3 from

[pearl pond]

@wind linden Has your question been resolved?

[wind linden]

.close

[pearl pond]

Channel closed

Closed by @wind linden

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[sour tiger]

really a physics problem but yeah

where did xm1 and xm2 come from

also ycm1 and ycm2

[sharp tree]

Come from this

[sour tiger]

ahhh

thanks!

.close

[pearl pond]

Channel closed

Closed by @sour tiger

Use .reopen if this was a mistake.

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[somber hazel]

Is this correct?

[somber hazel]

translation:

[rough forge]

ja...

[somber hazel]

really?

[rough forge]

ja...

[somber hazel]

thank you

[rough forge]

😂

[somber hazel]

xd

xd

.close

[pearl pond]

Channel closed

Closed by @somber hazel

Use .reopen if this was a mistake.

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[cerulean echo]

Hey was wondering how to do part (iii) of this question

[warm current]

Which one did you get as the partition?

[cerulean echo]

y=(2^k)(x)

The other one isnt symetrical for any integer k

[warm current]

Can you start by building one class?

[cerulean echo]

2^0?

[warm current]

1?

What are the elements in the class?

[cerulean echo]

{1,2,4,8,16}

[warm current]

Cool. You have created one class. Can you do another?

[cerulean echo]

maybe {3,6,12}

[warm current]

Hm?

Looks good.

[cerulean echo]

and {5,10}

[warm current]

Yup

[cerulean echo]

ahh i think i get it now

Thank you so much

[warm current]

Good work

[cerulean echo]

.close

[pearl pond]

Channel closed

Closed by @cerulean echo

Use .reopen if this was a mistake.

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[hoary meadow]

bit confused on how to do this

[hoary meadow]

i differentiated and ended up with x = theta(k - 1) but i dont think it's right

[pearl pond]

@hoary meadow Has your question been resolved?

[pearl pond]

@hoary meadow Has your question been resolved?

[pearl pond]

@hoary meadow Has your question been resolved?

[tropic saddle]

why do you think its not right

[hoary meadow]

nvm it is

it's cz i was reading the markscheme wrong lol

.close

[pearl pond]

Channel closed

Closed by @hoary meadow

Use .reopen if this was a mistake.

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[abstract fox]

Is this correct?

[pearl pond]

Please don't occupy multiple help channels.

[merry carbon]

.close (duplicate of #help-37)

[pearl pond]

Channel closed

Closed by @merry carbon

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[weary holly]

estimate f’(2) for f(x)=3^x . explain your reasoning

[wet osprey]

have u done anything similar before?

[weary holly]

this is how far ive got

[weary holly]

ive also used my calculator to compute this for small values of h like .003 etc

[midnight haven]

What kind of indeterminate is that?

[wet osprey]

and what did you get

[weary holly]

≈ 9.89

i think ive got it

.close

[pearl pond]

Channel closed

Closed by @weary holly

Use .reopen if this was a mistake.

[pearl pond]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[thorny jetty]

d/dx (sin x + cos x)/sin x

[thorny jetty]

The book has some long answer by using quotient rule

And my question is

Can't you jsut cancel out the sin x and be left with 1 + cot x, or is that wrong because we have to worry about when sin x = 0?

sin x = 0 when x = 0 (0≤x<360) but in the limit definition of a derivative x tends to 0

[fluid axle]

cot is just cos/sin, you still have the problem of cot not being defined when sin is 0

[fluid axle]

in the limit definition of a derivative x tends to 0
not in general no

[hasty osprey]

Yes, you can cancel out

[thorny jetty]

oh sorry i forgot

it tends to h

not 0

i mean

h tends to 0

[fluid axle]

yeah the difference in x's goes to 0

[thorny jetty]

ok that makes sense

thanks

.close

[pearl pond]

Channel closed

Closed by @thorny jetty

Use .reopen if this was a mistake.