help-49

[lavish venture]

then i can do the same for B

but i was explicitly told "do not try to show that the infimum of the distances between the points in two disjoint closed subsets is positive"

while also being told "first use open balls around points of A and B to construct disjoint U and V and show that their closures are disjoint from B and A"

so how am i supposed to construct balls around points of A and B without my idea

or am i misreading this

[lavish venture]

maybe this is supposed to mean inf{d(A, B)}

in which case that can be zero if the sets get arbitrarily close

but in my case it works because i consider a fixed point a in A

ping me if replying

[midnight plank]

@lavish venture Has your question been resolved?

[midnight plank]

@lavish venture Has your question been resolved?

[midnight plank]

@lavish venture Has your question been resolved?

[midnight plank]

@lavish venture Has your question been resolved?

[wary trail]

@lavish venture if I write in topology terms can you translate into metric space terms

[lavish venture]

uhh perhaps

[wary trail]

ok don't worry I'll write in metric space terms

[lavish venture]

i can't seem to formulate a proof for why the closures of U and V are disjoint

for each $a \in A$ i defined $\delta_a = \inf{d(a, b) \colon b \in B}$ then just took balls of radius delta/3 around each point and took the union to cover A

[grand pond]

knief

[lavish venture]

i did the same thing for B

they are clearly disjoint but im not sure how to put it formally other than its fucking obvious, by construction

[wary trail]

I'm saying if they are not disjoint, that point must be a limit point of both not in either

[wary trail]

starboard moment

[lavish venture]

you mean construct sequences x_n in U and y_n in V such that they both converge to some point x in the intersection of the closures of U and V?

like

let $x \in \overline{U} \cap \overline{V}$ then define $(x_n)$ and $(y_n)$ such that $x_n \to x$ and $y_n \to x$ where $x_n \in U$ and $y_n \in V$

[grand pond]

knief

[lavish venture]

then deduce a contradiction

i was toying with that

[wary trail]

uh let me go back to topology world

[lavish venture]

from this i get something like

what was it

$d(a_n, b_n) < \frac{2}{3} d(a_n, b_n) + \varepsilon$

[grand pond]

knief

[wary trail]

how did you define closed subsets?

just got home

going to write it out

slowly

@lavish venture

[lavish venture]

complement is open

[wary trail]

perfect

[lavish venture]

what did you have in mind

[wary trail]

just writing it down

with my trusty ipad

Not trust iPad

notation for open ball?

[lavish venture]

$B_r(a)$

[grand pond]

knief

[wary trail]

we use $B_2(x;\varepsilon)$ lol

[lavish venture]

maybe the macro doesnt work

type \varepsilon i guess

[grand pond]

Xetrov

[lavish venture]

why 2?

[wary trail]

form of metric

[lavish venture]

oh you mean for notation

[wary trail]

ya

(I'm still here, I'm just in a mess)

$\bar{A} = A \cup {\text{limit points of A}}$

ok?

[grand pond]

Xetrov

[lavish venture]

yes

@wary trail what if we show that $\overline{U} \cap B = \emptyset$ and $\overline{V} \cap A = \emptyset$

[grand pond]

knief

[lavish venture]

then from here we must have that $\overline{U} \cap \overline{V} \subset X \setminus (A \cup B)$

[grand pond]

knief

[lavish venture]

thus if $x \in \overline{U} \cap \overline{V}$ then $d(x, A) \neq 0$ and $d(x, B) \neq 0$

[grand pond]

knief

[lavish venture]

wait but cant d(A, B) = 0

[wary trail]

I’ve proved it can’t since they are both closed

(I think)

[lavish venture]

what if neither are compact?

[wary trail]

Why does compactness matter?

[lavish venture]

my prof said not to do this because apparently theres a counterexample

based on neither of the sets being compact

let me read what you have

[wary trail]

Oh

RIP

Consider R 2

[lavish venture]

yea

[lavish venture]

would this work?

[lavish venture]

^

[lavish venture]

since we already constructed U and V to be disjoint

[lavish venture]

if we show this then the next line follows

[wary trail]

I agree with the logic

Don’t know about the conclusion

[wary trail]

Greater than zero for all a in A

[lavish venture]

yea

[lavish venture]

@wary trail

do you know anything about baire spaces by chance?

Let $(X, d)$ be a metric space and $Y \subset X$; thus, $Y$ inherits a metric $d_Y \equiv d\mid_{Y \times Y}$ from $(X, d)$. Suppose $(X, d)$ is a Baire space and $Y$ is open in $(X, d)$. Show that $(Y, d_Y)$ is also a Baire space.

[grand pond]

knief

[lavish venture]

so i consider a sequence $U_1, U_2, \dots \subset Y$ of dense open sets in $Y$

[grand pond]

knief

[lavish venture]

then need to show $\bigcap_{i = 1}^{\infty} U_n \subset Y$

[grand pond]

knief

[lavish venture]

.close

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[verbal whale]

The ratio of the lengths of the two shorter sides of a triangle is 1:2. The angle opposite the shortest side is 30°. Find the measure of the largest angle of the triangle.

[verbal whale]

where do i write the

1:2

😭

that’s all i need

[sharp coral]

pick a side length for one side and use the ratio to find the other side length

i would also recommend in your drawing that you make more of a distinction between the lengths of AC and BC, they look very similar right now

[verbal whale]

wait so

can u give me example

[verbal whale]

okayy

[verbal whale]

i’m very lost whenever it comes to ratio cause i think that one side is 1 other 2

[sharp coral]

when we have ratios between side lengths, for example let's say AB:BC = 1:2, that means that as a fraction AB/AC = 1/2

you can do a little algebra to solve for one of the sides once you have the equation set up (and you know the other side)

[verbal whale]

ohh

[sharp coral]

it's ok just to pick one of the side lengths in this example, since the angles in a triangle depend only on side ratios, not the actual side lengths

[verbal whale]

okay thank youu!

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[wicked mauve]

this is based on the series for e^(-x^2) ?

[runic hamlet]

yes

can be obtained more easily by plugging -x^2 into the series of e^x

[midnight plank]

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[simple needle]

I’m stuck on parts 3-5. I did parts 1-2 with no issue (part 3 is the third picture so I guess I technically did do it but i don’t know if it makes any sense. I just need help with this to the end if anyone can help walk me through it. This is due tomorrow and determines my grade for the end of the marking period so im really stressed about it :/ )

[midnight plank]

@simple needle Has your question been resolved?

[simple needle]

bruh its been a whole hour and 30 minutes how have i not received any reply yet😔

[coarse sigil]

is the third pic ur work for 3?

[simple needle]

yea but i dont think its right

someone in a different homework server told me to do it

[coarse sigil]

icl im trying to decode what u did so give me a min

[simple needle]

ok

thanks

[coarse sigil]

yah idk whats going on

[simple needle]

its fine

my older cousin is helping me over the phone now

none of the servers have been able to help so i just gave up here anyway

.close

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[magic bough]

Im about to finish Real Analysis I (still got differentiation, integration) and still don't know the derivative of x!

[magic bough]

it was my sole purpose for taking the course

can anyone tell if its differentiable?

im assuming its f: N -> N since I've never seen it take negative or fractions

[tropic vale]

$x!$ is a constant no?

[grand pond]

張嘉棋

[magic bough]

a constant?

I meant the function x factorial

or I guess it behaves more like a sequence

[tropic vale]

well $x!=1234...*(x-1)*x$

[grand pond]

張嘉棋

[magic bough]

right and since I'm assuming the domain cant be the set of rationals then it can't be differentiable since it has to be dense

[tropic vale]

i think there is some sort of sum in the derivative

oh wait in reals

so yhhh cannnot derive

[magic bough]

ah yes, I meant the reals, mb

well at least I know now

[tropic vale]

if u unrestrict it

out of the reals

you can

[magic bough]

unrestrict it out of the reals?

[tropic vale]

yhhhh

what ever reals is a subset of

and beyond

[magic bough]

wait what, I thought reals encompasses everything

oh you mean imaginary

[tropic vale]

could be

after real analysis, you can take complex analysis

[magic bough]

is it worth learning?

[tropic vale]

depends if you enjoy it

[magic bough]

I never do it for enjoyment, more to fill my curiosity and apply to other fields.

This level of math takes too much time and energy

[tropic vale]

me when quant

[magic bough]

I thought about complex analysis but idk if anyone uses imaginary numbers

ive considered topology

[tropic vale]

depends how much u like shapes

[tropic vale]

imaginary numbers make alot of areas in mathematics nicer to work with

[magic bough]

Not at all lol but its useful in some areas in ML I hear

[magic bough]

Thats actually pretty interesting

[tropic vale]

depends on area u wanna look at tbh

if u wanna do ML, don't take maths classes

take ML classes

[magic bough]

gotcha, im still not sure what I will do for my PhD. Im in between Statistics and CS which learning more about functions in RA which has helped me with stats but not CS

[tropic vale]

i made the mistake of taking pure maths classes when i enjoy more quantitative finance

[magic bough]

actually? this is what I was scared of too

[tropic vale]

but i'm lucky in the sense that, quant finance is pretty forgiving in what masters/phd they hire

[magic bough]

lol im know im getting way off topic but I at least want to know, how do you like quant finance?

[tropic vale]

lets move to DMS

[magic bough]

sure

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[wide cedar]

How to get from $f'(x)$ to $f''(x)$?

The answer key says that it is $(x-2)e^{-x}$ not $(x-1)e^{-x}$

[grand pond]

luna-maia

[fallen galleon]

factoring e^-x from the first term leaves a -1

in f'(x)

[cyan inlet]

The last line

You made a mistake jn the last line

-1 - ( 1-x)

= -2 + x

[wide cedar]

Oh!

Right. Thanks

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[reef niche]

u split the contour up

$\gamma_1(t) = it, t \in [0, 1]$ and $\gamma_2(t) = i + t, t \in [0, 1]$

[grand pond]

Charky

[reef niche]

then use the fomrula

$\int_{t_0}^{t_1} f(\gamma_i(t)) \gamma_i'(t) , dt$

[grand pond]

Charky

[reef niche]

u should get the sum of two integrals

[midnight plank]

@molten bay Has your question been resolved?

[molten bay]

How did you get 0 and 1?

[01]

[reef niche]

it doesnt matter, but usually for line contours between point $\mathbf{a}$ to $\mathbf{b}$ u do $(1 - t) \mathbf{a} + t \mathbf{b}$

[grand pond]

Charky

[reef niche]

t in [0, 1]

at t = 0, the line is a, at t = 1, the line isat b

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[twin anvil]

I got the right answer but

act i didnt

the answer key has a negative in front

but i dont

the answer key says this but i have a negative in front of the 3

in the numertor

[polar star]

and your denominator is the same?

[twin anvil]

Yeah my denominator is the same

same signs

[polar star]

can u show ur working

[twin anvil]

uh

k

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[molten bay]

How can I solve this integration?

[sharp coral]

that integral doesn't make sense

the bounds of integration on an integral with respect to x can't depend on x

[midnight plank]

@molten bay Has your question been resolved?

[astral talon]

are you sure it's not dy dx

[molten bay]

I see

Yeah

[astral talon]

this would make a bit more sense

[molten bay]

But i didn't understand it properly

[molten bay]

What is the difference?

[astral talon]

the first integral is with respect to y

in my case

[molten bay]

Can we not assume it constant?

[astral talon]

in yours it's dx

which cant be possible at least idts

idk what you mean by assume constant

[molten bay]

Why?

[molten bay]

Can we find integration of it?

[astral talon]

lemme check smth rq

gimme a sec

[astral talon]

do you know the answer to this

is it infinity

[molten bay]

Actually no

[astral talon]

because if it's as you stated then it just diverges

[molten bay]

I see

Actually i know to know how limits affects

[astral talon]

see for your question what im understanding after a lot of looking is

The inner integral is:

Since the integrand does not depend on 𝑥 it can be factored out

Thus, the inner integral evaluates to

leaving us with the outer integral

since the integral of an infinite quantity over any nonzero range is also infinite, we conclude that the given double integral diverges

i would look for a second opinion though

[astral talon]

$$\int_{0}^{\infty} \int_{x}^{\infty} \frac{e^{-y}}{y} , dy , dx = 1$$

[grand pond]

Technoblade Never Dies

[astral talon]

since you can write it as $$\int_{0}^{\infty} \int_{0}^{y} \frac{e^{-y}}{y} , dx , dy = 1$$

[grand pond]

Technoblade Never Dies

[midnight plank]

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[molten bay]

Thank you so much

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[last slate]

what do they mean by change of sign

[sterile wadi]

-4 has a negative sign

1 has a positive sign

[last slate]

oh so like different signs?

[sterile wadi]

Yes

[last slate]

different signs proves that they lie between x=1 and x=2?

[sterile wadi]

And that means, geometrically, that between x=1 and x=2 you cross the x axis

[last slate]

oh

thanks

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[last slate]

i dont understand the last part

why did we stop at 0.36

how did we determine 0.36 is the root

[sterile wadi]

Convert every answer to 2DP as you're going. $a_2 = 0.30, a_3=0.38, a_4 = 0.35, a_5 = 0.36, a_6 = 0.36, a_7=0.36$

[grand pond]

Oliver

[last slate]

yea i did

wait

alright

[sterile wadi]

The answer sheet is just saying that you got $0.36$ 3 times in a row, so you can be pretty confident that's the answer

[grand pond]

Oliver

[last slate]

right but why 0.36

[sterile wadi]

This is a convergent method, meaning over time you get closer and closer to the real answer. Once you're getting the same thing 3 times in a row, that probably means it's as close as you're going to get

If you want you can calculate $a_8, a_9, ..., a_n$ and they will get more and more accurate but to 2DP will still be 0.36

[grand pond]

Oliver

[sterile wadi]

So it makes no sense to keep going once you've had the same answer 3 times in a row

[last slate]

okay

but why 0.36

how did we get 0.36

[sterile wadi]

I assume the Newton-Raphson method

[last slate]

whats that?

nvm turns out its because

0.36 was repeated several times

[sterile wadi]

....

What do you think i meant when i said "was the same 3 times in a row"

[last slate]

skill issues

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[last slate]

i did 3(1-e^-p) - p and got 0.254 and -0.149

is it still correct

[lyric charm]

yes

there is still a sign change

[last slate]

alright thanks

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[cedar mason]

hey notation question!

how do i write the chain rule using leibniz notation?

[cedar mason]

i just do $[f(g(x))]' = f'(g(x)) g'(x)$ because it's convenient

[grand pond]

Percy

[cedar mason]

but tbh it took me forever to memorise the chain rule because i couldnt write it in leibniz notation lolol

[astral talon]

is this what you mean

[fresh sparrow]

tbh chain rule is even more obvious in leibniz notation

[cedar mason]

HMMM

[astral talon]

yeah I use this

[cedar mason]

well i get it like that but

[astral talon]

more intuitive

[runic hamlet]

its the reason why you can treat dy/dx as a fraction and it works out

[astral talon]

^

[cedar mason]

when we have f(g(x)) stuff, do i just take the derivative with respect to g(x)?

i mean i know thats the derivation but notationally that's weird as hell

[thin tree]

percy btw u not responding to my dms?

[fresh sparrow]

wut?

[cedar mason]

hold on i didnt see it

[fresh sparrow]

in both cases it's the derivative of the composition w.r.t. x

[astral talon]

if you mean d fg/dx

wait I should

wait

[cedar mason]

I mean.

I know.

But

okay

write me the chain rule for $\frac{d}{dx} \sin(3x)$ in leibniz form

[grand pond]

Percy

[cedar mason]

(this is totally googleable im just bored apparently)

[astral talon]

let y = sin u and u = 3x so that y = sin 3x

sorry idk latex

[thin tree]

I know

Just put the words in $ $

[astral talon]

dy/dx = dy/du * du/dx

that's how I would do it

[fresh sparrow]

$\frac{dy}{dx} = \frac{dy}{du}\cdot \frac{du}{dx}$

[grand pond]

artemetra

[fresh sparrow]

it's the same formula

[thin tree]

u just said u didnt know latex

[astral talon]

gpt

$\textbf{Step 2: Differentiate } y \text{ with respect to } u: \[1mm]
\frac{dy}{du} = \cos u$

[grand pond]

Technoblade Never Dies

[cedar mason]

yes but 👀 how do i write the sin(2x)

[astral talon]

and then substitute

[thin tree]

Uh Percy r u talking about chain rule differentiation?

[cedar mason]

ah so its just inconvenient af

[thin tree]

Just differentiate from outermost function to innermost

[cedar mason]

isnt that hwat i said

[thin tree]

So for sin(3x)

[cedar mason]

i know how it works

[thin tree]

Ok

[cedar mason]

im asking leibniz notation for it

[thin tree]

oh u mean substitutions

[fresh sparrow]

sorta, this really only works well when you make the substitutions technoblade never dies mentioned

[fresh sparrow]

these

[cedar mason]

hmmm yeah thats fair

[astral talon]

to be fair i was taught trig differentiation conceptually like differentiate the trig func with the same angle repeated, and then multiply by derivative of the angle

I was never told it's chain rule

I only found out recently

[fresh sparrow]

because the dy/du would then be derivative of sin(u) which is cos(u), as you can see u did not change

[astral talon]

i should nick

nvm I cant

I should ask a mod to nick me

[fresh sparrow]

so it says as cos(3x)

and the du/dx part would be the derivative of u w.r.t. x, which is 3

[fresh sparrow]

why not? /nick

[cedar mason]

Oh

wow.

that sucks so much

[astral talon]

doesnt work

i dont have perms

[fresh sparrow]

it does not

[astral talon]

eh personal preference

[fresh sparrow]

i think the question of "write this in leibniz notation" doesn't make sense in the first place

[astral talon]

for rate of change qsses I find this notation so manageable

[fresh sparrow]

regardless of notation the derivative would be the same function

[cedar mason]

i replied that to techno telling us about the trig thing but slow net lol

[fresh sparrow]

oh woops

[astral talon]

oh

yeah

it does suck that we were taught to memorize rather than the concept

fire isnt it

[cedar mason]

yeaaaah

anyway

.close

[midnight plank]

Channel closed

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[zenith mirage]

so im trying to get the inverse of the first line but i did it totally wrong

[silent compass]

It seems like you cubed the equation and missed a term or two

[brittle grotto]

$(a+b)^3\neq a^3+b^3$

[grand pond]

00100000

[zenith mirage]

well, yes, iwould cube the equation

[brittle grotto]

so 2->3 is wrong

[zenith mirage]

okay, so what does the term change into?

[brittle grotto]

precisely, 2 terms

[brittle grotto]

this is binomial theorem with n=3

[zenith mirage]

i am not sure what that is or means

[brittle grotto]

that's fine too

just multiply it out manually

[zenith mirage]

whats the theorum?

[zenith mirage]

thats what i tried

[fallow breach]

pascals triangle

[zenith mirage]

okay, what is it?

[brittle grotto]

$$(a+b)^3=$$
$$(a^2+2ab+b^2)(a+b)$$

[grand pond]

00100000

[fallow breach]

give me a sec

[zenith mirage]

oh good lord

absolutely not

[zenith mirage]

im notdoing that 😭 no way

[fallow breach]

soo it adds the top 2 terms

[slender walrus]

its not ideal to cube both sides of the equation in its current state
as it'd generate more undesired terms

[brittle grotto]

and then you can see that it equals $$a^3+2a^2b+2ab^2+b^3$$

[lyric charm]

line 3 is wrong

[slender walrus]

also (1/2)^3 isn't 1/16

[silent compass]

Yeah better to take the 5 to the LHS

[grand pond]

00100000

[silent compass]

Then cubing the equation

[lyric charm]

btw do we even need to do any cube of a sum expansion

[zenith mirage]

Readabove, theyve already told me that

[lyric charm]

cause i think we do'nt

don't

[zenith mirage]

ann dni

[brittle grotto]

definitely not

[slender walrus]

ideally you'd want to first isolate $\cbrt{y-3}$

[grand pond]

ℝαμOmeganato5

[brittle grotto]

wait actually, you do

[zenith mirage]

buti need to

make x y

and y x

[fallow breach]

what's the problem

[zenith mirage]

first

[brittle grotto]

you'd either have to do it on the left or right

[silent compass]

I think you gotta cube one way or another to isolate the y?

[brittle grotto]

because there will always be a binomial term

[astral talon]

i think OP should post the full qs

[brittle grotto]

I already said that 😐

[slender walrus]

the question is fine

[brittle grotto]

no this is fine

unlike the cocaine guy

[zenith mirage]

i already did, i said im finding the inverse of the firstline

[astral talon]

(there was more to the qs they sent this before in a diff chat and raged)

[zenith mirage]

dni sami

[zenith mirage]

i didnt rage

omg

.close

[midnight plank]

Channel closed

Closed by @zenith mirage

Use .reopen if this was a mistake.

[brittle grotto]

ohhh, I see

[astral talon]

;=;

[lyric charm]

grah

[brittle grotto]

💀

[fallow breach]

I sorry

[zenith mirage]

Donot fucking talk tome anymore if youre gonnaspout bs like that. I am just trying to fuckingleanr but apprently thats not okay

[brittle grotto]

ok woah

[astral talon]

.

[zenith mirage]

I got frustrated because someonetold me that its simple math when im strugglingith it

[slender walrus]

$$x = \frac12 \cbrt{y-3} + 5$$
one of your first goals would be to first get \
$\cbrt{y-3} = \what$

[brittle grotto]

uhhhh... look, your question was well-defined and fine

[zenith mirage]

Thats pretty much just callingme dumb. I know its simple. I struggle with it anyways (THATS WHY IM HERE)

[grand pond]

ℝαμOmeganato5

[brittle grotto]

we're all at different stages of our math education; don't listen to people putting you down for not having had the time or experience to study something that they're already learned

[fallow breach]

you are not dumb

let's create the idea

[zenith mirage]

No bc both him and some otherperson are trying to make me look bad and thats notokay

When i react to that im somehow wrong!!?!

ive already closed the channel. Its not worth it

[brittle grotto]

you're not wrong, it was just surprising

feel free to reopen it; we'll finish helping you with the question

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[brittle grotto]

oh, it's too late now

[brittle grotto]

oh wait oops

[zenith mirage]

it doesnt matter

have a good day, yall

[brittle grotto]

actually, while I have this channel, can someone explain to me the general approach for finding the phase portrait of an ODE that's not in $Ax=0$ form?

[grand pond]

00100000

[brittle grotto]

I know that you can take eigenvalues of a matrix when it's a nice $Ax=0$ equation

[grand pond]

00100000

[zenith mirage]

Yes, and i didnt ask that this time. So butt out (and i then changed my question to asking howtofind theinverse. so like bro)

[brittle grotto]

ok I guess I give you guys permission to talk in my help channel lol

no no it's alright

[slender walrus]

i don't see why you think there's anything hidden behind what was being asked.

[brittle grotto]

I'm just asking kind of an open question

[thin tree]

lalnashef is mad

[brittle grotto]

I'm just confused on what's going on with this whole thing to be honeset

[brittle grotto]

were you the second person she was referring to??

[thin tree]

No

I don't call people dumb

[brittle grotto]

ok anyways, my textbook shows examples like this diffeq

[zenith mirage]

rightfully so

[fallow breach]

stop

[brittle grotto]

which clearly can't be expressed as $Ax=0$ (I haven't looked at the non-homogeneous cases)

[grand pond]

00100000

[thin tree]

Don't worry everyone has their own pace of learning , just learn ignore those who call you dumb.

[brittle grotto]

and of course, finding critical/equilibrium points is easy

[slender walrus]

@zenith mirageif you feel like you are being mistreated by users, you can raise a ticket with @shadow scaffold.
you have the option to block them, but it is also not productive to just leave as there are others present that would be willing to help if you have the patience

[zenith mirage]

itsevery timei try to learn. how do i ignore the majority of people anytime i try to be better

[thin tree]

Hey a lot of people I have seen here are genuinely nice

[zenith mirage]

ive already blocked them and toldthem to dni

[brittle grotto]

but figuring out how to draw the phase portrait by hand (without graphing the vector field) is very confusing

[brittle grotto]

yeah, this community is mostly great

[fallow breach]

do you need all solutions

[brittle grotto]

no

just the phase portrait

or like, a general strategy to approach ones where I can't find the eigenvalues for a matrix of the system

and also, ways without finding the explicit solution of the ODE

I can find more explicit examples

[fallow breach]

sorry I can't do that rn I'm dumb

[brittle grotto]

chatgpt basically just told me "well, guess the solution"

and then when I told it "how do I do it without guessing?"

[fallow breach]

I would do derivative operators

[brittle grotto]

it told me "lmao turn it into a PDE"

[fallow breach]

and substitute

sooo

[brittle grotto]

and of course, I don't think turning it into a PDE would help me too much... 💀

[brittle grotto]

what's a derivative operator?

[fallow breach]

d/dx

or D

[brittle grotto]

you mean, like, a linear combination of $\frac {d}{dx}$?

[grand pond]

00100000

[brittle grotto]

ohhhhh, ok I see I see. I'm a little stupid about the words

[brittle grotto]

but this is really hard to do by hand, right?

[fallow breach]

I mean lemme try

[brittle grotto]

no but

[fallow breach]

hold up

what is x derivative of

x prime

[brittle grotto]

I need ones at this level of general detail

[fallow breach]

is it of t

[brittle grotto]

and plugging in points would be really hard

[brittle grotto]

yes

sorry; I should've clarified

[robust isle]

well one way to get a good enough idea of what's going on is to linearize the system around equilibrium points

https://www.d.umn.edu/~mhampton/ODELA/#Nonlinear

[brittle grotto]

linearize it? now that sounds hot

[brittle grotto]

you're telling me I can turn this linear?!?!

that's awesome!

and this should generally work?

I think for another set of examples in the book, it talks about different strategies for phase portraits of conservative equations

1.5.3. Conservative equations. In this section we consider the particu-
lar case of the di!erential equations conserving a given function. We first
introduce the notion of conservative equation.

and it mentions using level curves

but honestly, I am really bad at multivar

and don't understand that either

I'll ask about it some other time tho

[robust isle]

the idea is that around equilibrium points the system behaves roughly like a linear system

[brittle grotto]

wdym by that?

[robust isle]

so it gives you a rough shape of the trajectories of the system but it's not perfect obviously

[brittle grotto]

is it good enough to generally draw a convincingly accurate phase portrait?

say, on an exam or something?

lol

[robust isle]

go check out the page, it's gonna do a better work than me

[robust isle]

yeah

that's prolly the best you can get away with without literally plotting the vector field

[brittle grotto]

ok, I'll give it a read. thanks for the resource! this phase portrait stuff has really been killing me

[brittle grotto]

sounds good

thanks everyone :^)

.close

[midnight plank]

Channel closed

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[midnight plank]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[molten socket]

\frac{a^2-8a-20}{a^2+5a} > 0

[molten socket]

\frac{a^2-8a-20}{a^2+5a} > 0

$\frac{a^2-8a-20}{a^2+5a} > 0$

[grand pond]

꧅

[molten socket]

ok consider positive case first both denominator and numberator > 0

i get a> 10 or a <-2 from numerator

and a> 0 or a <-5 in denominator

so how do i know the priorities of and or

which do i take first

[lyric charm]

do you have to do it with casework?

there is an easier way to do this entire problem if not

[molten socket]

whats casework

[lyric charm]

like this "consider positive case first, then negative case"

[molten socket]

dont have to but i still want to understand if im supposed to take and first or or first

[lyric charm]

well

[verbal pumice]

wavy curve

[lyric charm]

ok like

you get

(a>10 or a<-2) AND (a>0 or a<-5)

[molten socket]

yes

[lyric charm]

if you really want to

you can distribute the and over both ors in a sort of FOIL-like way

and get

(a>10 & a>0) or (a>10 & a<-5) or (a<-2 & a>0) or (a<-2 & a<-5)

2 of these and-clauses will collapse into falsehood and you can apply the identity law FALSE or P = P

thus being left with (a>10 & a>0) or (a<-2 & a<-5)

a>10 & a>0 then simplifies to just a>10, because any number greater than 10 is also automatically greater than 0

by the same token a<-2 & a<-5 simplifies down to just a<-5.

so you get a<-5 or a>10 for this.

i definitely recommend against this method though!!!

[molten socket]

whats this not casework method then

[lyric charm]

well, you still factorize num and denom as you would otherwise

so $\frac{(a-10)(a+2)}{a(a+5)} > 0$ yes?

[grand pond]

Ann

[molten socket]

ye

[lyric charm]

then you know the number line is broken up into 5 intervals by the points 10, -2, 0 and -5

so... well ok it still kind of looks like casework except that you no longer need to fuck with ands and ors

but basically you can make a sign table

[molten socket]

ok good

[lyric charm]

Interval | a<-5 | -5<a<-2 | -2<a<0 | 0<a<10 | 10<a
---------+------+---------+--------+--------+-------
a-10     |      |         |        |        |      
a        |      |         |        |        |      
a+2      |      |         |        |        |      
a+5      |      |         |        |        |      
---------+------+---------+--------+--------+-------
Product  |      |         |        |        |      

like this

and fill out each row with "+" and "-" signs accordingly

and then multiply those

[molten socket]

damn ok how u make that table

thank u very much anyways

[lyric charm]

triple backticks to enter code-block formatting

and then i just manually entered | and - symbols

with some copy and paste

[molten socket]

ok tysm

.close

[midnight plank]

Channel closed

Closed by @molten socket

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[midnight plank]

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Send your question here to claim the channel.

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[dark locust]

herplp is the "claim" alwyas Ha?

[dark locust]

asoruru its 2 am idk if im making sense

[verbal pumice]

Sure I guess?

[dark locust]

really? okayygh

thank youu

[verbal pumice]

I think the "claim" thing is something your instructor would have made up though

[dark locust]

OH AHHAHAAHAH

[verbal pumice]

you generally just deal with the null and alternate hypotheses

[dark locust]

I SEE I SEEE

[dark locust]

okayokay tyyy can i ask one moreee?

[verbal pumice]

maybe

it's been a while since i've done this

[dark locust]

normally we would diivide for level of significance andik that two tailed = one of each 0.05 becomes 0.025

but like when writing the final level of significance wiill it be 0.05 or 0.025..

wht i noticed from my teacher is at first its 0.05 but then when shes in step 5 she changes it to 0.05 which kinda makes me confusedd

[dark locust]

yes no problemm

dwww

[verbal pumice]

the level of significance doesn't change

[dark locust]

this is my last question 💟

[dark locust]

ohh it will stilll be 0.05?

and 0.025 is just the idea?

[verbal pumice]

we split the confidence in two because we have a two tailed test

but it's still the same significance

(as asked for in whatever problem you're solving)

[dark locust]

okayokay gotchuu thank you!!!!

i cna sleep now hahhashhahd

[midnight plank]

@dark locust Has your question been resolved?

[midnight plank]

Channel closed

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[midnight plank]

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[kind ledge]

!help

[midnight plank]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[kind ledge]

i need to find (h,k) for -3x^2 +7x -2

for now i did h = -b/2a

h= -7/2(-3)

h = -7/-6

h = 1.66666666666667 or smth

idk if thats good

[wet pollen]

That is correct.

[kind ledge]

alright ty

and how do i find K?

and how do i write h

1.67?

[wet pollen]

Just plug that into the original equation and solve for y.

[kind ledge]

or 1.66

[wet pollen]

y = -3(7/6)^2 + 7(7/6) - 2

[kind ledge]

that will give k?

[wet pollen]

It better.

[kind ledge]

alr ty

[kind ledge]

wait but

its not 7/6

its -7/-6

[wet pollen]

And the negatives cancel out.

[visual tiger]

minus over minus

[kind ledge]

wait

what if its -5/-9

then its 5/9?

[visual tiger]

yes...

[wet pollen]

Yes, the negatives cancel out.

[kind ledge]

oh ok nvm

i get it

ok

im asking dumb questions

my fault

[visual tiger]

$\frac{-a}{-b} = \frac{(-1)a}{(-1)b} = \frac ab$

[grand pond]

rafilou is not not born in 2003

[kind ledge]

ill do this

[kind ledge]

👌

i got

-4 1/2 + 8 1/6 - 2

but i dsont think im supposed to have those entire numbers

-4 and 8

[wet pollen]

,calc -3*(7/6)^2 + 7*(7/6) - 2

[grand pond]

Result:

2.0833333333333

[kind ledge]

do i write 2.083 or just 2

[wet pollen]

I would write the fractional form.

[kind ledge]

alr well its -4 1/2 + 8 1/6

the fraction forms

then

i gotta addition those two

[wet pollen]

,calc -4.5 + 8 + 1.6

[kind ledge]

it gives 5.1?

then its 5.1 - 2?

[wet pollen]

,calc -4.5 + 8 + 1/6

[grand pond]

Result:

3.6666666666667

[wet pollen]

Wrote that wrong.

[kind ledge]

crap wait

mb

its -4 1/12

not -4 1/2

[wet pollen]

,calc -4 + 1/12 + 8 + 1/6

[grand pond]

Result:

4.25

[kind ledge]

it gives me 4.08333333

[kind ledge]

its doing a mistake

this one is -49/12

[wet pollen]

Yes, you see that on the next line.

[kind ledge]

oh

ty

[wet pollen]

Do you see where you possibly made your mistake?

[kind ledge]

which mistake

[wet pollen]

Well, you got the wrong answer.

[kind ledge]

for k?

i never found k yet

[wet pollen]

What do you think plugging 7/6 into the equation was doing?

[kind ledge]

replacing x

to find k

[wet pollen]

Yes. And you were getting the wrong result.

[kind ledge]

oh

i didnt put it into like

the big form fractions

49/12

and not 8/1/12

im not understanding whats happening here tho

[wet pollen]

,calc -4 - 1/12 + 8 + 1/6

[grand pond]

Result:

4.0833333333333

[kind ledge]

oh wait

u put it to 12

ok lemme do that

where did 73 come

[wet pollen]

-49 - 24 = -73

[kind ledge]

-49

its -?

oh yeah

it is

k gave me

25/12

but do i write it lik that

because the coordinates

dont have fractions

like (h,k)

[wet pollen]

I would leave it in fraction form, but that's me.

(7/6 , 25/12)

[kind ledge]

but what if i gotta draw it on the like thing

the graph

[wet pollen]

You can estimate where the point should be if you want to plot it.

[kind ledge]

so do i just like put it into decimal to draw the point

then when im writing h,k

i put it into fraction

[wet pollen]

On a graphing program?

[kind ledge]

its on paper

[wet pollen]

On paper, I would use fractional form.

[kind ledge]

ight

[wet pollen]

Unless your teacher explicitly tells you write an approximate answer to n decimals.

eg. Accurate to the hundreths would be 2.08.

[kind ledge]

alr

well

i used decimal to find where the point is located

but then i wrote it into fraction

to locate it

like

if im writing an equation

im typing it into fraction

but i turned it into a decimal

to know where it is in the graph

cuz idk how to find it if its 7/6 25/12

[wet pollen]

You could also write 2.083 with a bar over the 3.

[kind ledge]

yeah

ty my guy

.close

[midnight plank]

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[empty ivy]

Hi how do you start

[midnight plank]

@empty ivy Has your question been resolved?

[woeful turret]

we need to get a quadratic in tan theta

im not getting how to do that tho

[midnight plank]

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[leaden seal]

can someone help me answer this please

[hearty rune]

what have you tried

[leaden seal]

Ill show now

is this correct so far

[hearty rune]

should be 3t but otherwise sure

[leaden seal]

oh

sin3t

[woeful turret]

dont do this

[woeful turret]

use vectors

[hearty rune]

starting with 15sin(3t)+20cos(3t)

do you know how to find R

[woeful turret]

or just listen to this guy

im out

[leaden seal]

yeah im trying

ill show u after

[hearty rune]

there is a formula for it if you know it

[leaden seal]

this is what I did

whats the formula?

[hearty rune]

the formula is what you did just without the steps in getting there

[leaden seal]

shall I open a new channel for the rest?

or just carry on?

[woeful turret]

shit i deleted it

[leaden seal]

lmfao I saw it

[woeful turret]

okay did u understand?

its the correct answer as well

[leaden seal]

it went before I could interpret it

[woeful turret]

ok one second ill type it again

[leaden seal]

Thank you baby Yoda

[woeful turret]

d =15 sin 3t - 20 sin (3t+pi/2)
d= 15i - 20 j
d = root 15^2 + 20^2
tan alpha = -20/15 = -4/3

@leaden seal

[leaden seal]

uve used vectors

[woeful turret]

yes

[woeful turret]

if u do it like this u are so cooked

[leaden seal]

ummm

its the way I've been taught

.close

[midnight plank]

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[woeful turret]

ok it is a huge process and i was particularly taught never to do this lol

but if u want to u can 👍

[hearty rune]

this isnt how ive seen it taught

typically you find R

then you have

d=R[ 15/R sin(3t) +20/R cos(3t) ]

then solve cos(a)=15/R, sin(a)=20/R for a common a,

should only take like 3 lines or so

[leaden seal]

.reopen

[midnight plank]

✅

[hearty rune]

that whole middle section could just be skipped

if you have Asin(t)+Bcos(t)

then R=sqrt(A^2+B^2), i havent seen someone have to write a derivation

[leaden seal]

Oh okay isee

[leaden seal]

is this correct for this

[hearty rune]

did you mean npi rather than n/pi

[leaden seal]

ohhhh

yh

is the rest correct

[hearty rune]

seems okay

[leaden seal]

okay thanks

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[midnight plank]

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[winter forum]

hey

[winter forum]

im kinda of confused how did we get e^-2/3?

[placid spoke]

yeah that's actually not correct

if you started at n = 0 it would be right

[winter forum]

how tho

[placid spoke]

$e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}$

[grand pond]

doaby

[placid spoke]

so they replace x with -2/3

but if you start at n = 1 instead,

$e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} = \frac{x^0}{0!}+ \sum_{n=1}^{\infty} \frac{x^n}{n!}$

[grand pond]

doaby

[winter forum]

and how do they end up with e^-2/3?

[placid spoke]

this formula

if you replace x with -2/3 on both sides

[winter forum]

oh mb i didnt see that

ok

thanks

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[teal solstice]

How do you do this? I was going to use the Trapezoidal rule because that's what this lesson was about. But the intervals aren't equal.

[rose cobalt]

You don’t necessarily need equal intervals for estimating

[midnight plank]

@teal solstice Has your question been resolved?

[lyric charm]

it says

use 6 right rectangles

they explicitly want you to use the right-endpoint rectangle rule

and yeah the intervals are not equal but thats ok

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[sour sierra]

How to find theta

[cedar mason]

....what

[sour sierra]

Idk I am not sure how to do it

[cedar mason]

more info?

!xy ?

[midnight plank]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[sour sierra]

I lost the original question paper

But the line that pass through origin is a tangent

[woeful turret]

Original

[sour sierra]

Sorry typo

[woeful turret]

Y=mx

3=4m

M = 3/4 = tan theta

Theta is 37

[sour sierra]

Ohhh thank you

Wait I think there is part 2

To find the radius of corcle

Oh I think I see how to do part 2 now thank you for the help guys

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[dry ore]

Hihi for (b) can I check ik area is area of y+2x=17 from pt q to o- area of B which is x^+2-(17-2x) and integrate
But can I check how do we know if it's x^+2-(17-2x) or (17-2x)-(x^2+2) I can't differentatite between which to minus clf one explaining and why can't I do integral of A-B to find the area? Like in one step not total area - off

[tiny moon]

Have you found P Q R?

[unique juniper]

Can you just explain(differently) what your problem is? Because A-B doesn't give you what you think it gives.

[dry ore]

No I alr got A

[dry ore]

I know we need to integrate A and sub in coordinates - the area of interaction between the curve and line

[unique juniper]

uhm, you say you have A

[dry ore]

But for the area of intersection how do we know if it's curve -line or line - curve that's the thing im confused abt

[dry ore]

Hmm I did alr get the area of A

[unique juniper]

what?

area of intersection?

[dry ore]

,rotate

[dry ore]

This is the to find the area of B right

[unique juniper]

uhm, no

[dry ore]

Thing is I'm confused about which day to do it

[dry ore]

Oh really am I getting smth wrong

[unique juniper]

you have to realise that A + B = area under the line

so... think...

[dry ore]

U mean A+b is area from pt Q to O of y+2x=17 right ?

[unique juniper]

think... because saying more will be condmened by helpers as spoon feeding just think about it...

[dry ore]

Tks for help

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[dark locust]

The computed value of the Pearson’s r from the sample, (r = -0.01) is relatively greater than the critical value (±0.361), and therefore do not fall within the critical region. In this effect, we FAIL TO REJECT the null hypothesis (H₀: ρ = 0), and REJECT the alternative hypothesis (H₀: ρ ≠ 0). With that said, it can be concluded that there is no sufficient evidence that the amount of study time in hours affects the grades of Liceo G11 ABM students in General Mathematics.

Guys is the mean symbol correct? My teacher only taught as us to use the u symbol but i feel like rho/p matches this more.

[polar star]

any symbol is fine if you define it

i could use as my mean symbol

[dark locust]

HASHAHAHA OKK thanksss

ill use u to be safee

[dark locust]

ttytyty

[cedar mason]

$\mu$?

[grand pond]

Percy

[cedar mason]

mu is the standard symbol for mean

[dark locust]

yesss! i will use thiss

but mu and rho are practically the same right its just a matter of preference?

[cedar mason]

yeah wel call mu mu

its not u

[dark locust]

asuahsha okayy!

[cedar mason]

ive never seen $\rho$ used. you can if you wanna i guess.

[grand pond]

Percy

[cedar mason]

i see rho and i think like density and stuff.

[dark locust]

oh gosh i used rho for pmy previous scaffold i probably got wrong there 😭

anyway, thank you!

[reef meteor]

Hiii everyone, I plan to take the edX MITx Micromasters in Probability and Fundamentals of Statistics and was wondering if someone here would take it too. I have 3 years of not doing math at all and wanted to practice with someone.

My name is Laurent and I'm from Panama. Best!