help-10

[desert river]

Methods being what? Substitution?

[dark stirrup]

methods being how you will be proving it. Which properties of calculus or other mathematics are you using to build your proof

[desert river]

Ohh ok. Like the theorems I include later

[dark stirrup]

yeah

It's been forever since I've learned calculus rigorously, but I think this actually needs to be proven

I could be wrong, so maybe someone smarter can weigh in.

[desert river]

It was kinda just skipped in the example I was building this off of

[dark stirrup]

wdym

[desert river]

the professor didnt need me to have my own ideas about proving this from the ground up

so i learned about the few different ways, and one of the proofs that mentioned this just kind of jumped

[dark stirrup]

for sure

If it's already accepted as true, that's fine

But if you have a reference as to where this truth comes from, it's good to cite your source

I'll just assume you plan to do that later

But every fact you write that isn't your own original thought should be cited

Even your historical notes

[desert river]

the whole thing is cited

[dark stirrup]

Your prof may not require that, but objectively it would be necessary in the real world

okay cool

I shall read forward then

[desert river]

just in case you missed them

[desert river]

i think maybe im safe, in reference 1 their proof shows that its a basic operation of integrals

id like to show it better but idk if there is a better way of breaking it down. it was probably the part i felt the most insecure(not emotionally) about so im glad you noticed it too

[dark stirrup]

Oh okay yeah I did miss the sources

I think f(c) approaching f(x) also requires proof.

I think it's a limit theorem

[desert river]

i think its technically part of the squeeze theorem

yah im pretty sure about that

[dark stirrup]

I wouldn't know sadly.

[desert river]

did it not make sense?

[dark stirrup]

Everything else looks solid.

No it makes perfect sense

[desert river]

maybe i can explain it better

[dark stirrup]

Just not sure how rigorous it needs to be

[desert river]

id lean on the side of more rigorous

[dark stirrup]

comes down to audience

[desert river]

its a proof class

[dark stirrup]

I'd def ask your prof to look it over if you can manage that.

[desert river]

not really

[dark stirrup]

shame

[desert river]

i missed his peer review last week

its due tonight

i made it monday-tuesday

[dark stirrup]

Well for what it's worth, I didn't spot any logic errors

[desert river]

NICE!!!!

[dark stirrup]

But I can't say 100% if any info is missing

that's kinda subjective

[desert river]

its fine i think i got the info

[dark stirrup]

You know your audience better than me, so that's your call.

[desert river]

well then i think i only have one question.

do you think i should change the intro at all?

if you look up the article that i cited, its totaly a copy paste

the thing is it's history

idk how to take creative liberties on history

its just history

[dark stirrup]

That's a tough one

I always sucked at that too

It's not "great," but I've read enough papers to realize that everyone basically does it

[desert river]

ok cool. well thank you for your help. i know what i need to do in order to get a decent grade then!!!!! thanks again!!!!

im going to close now, if you have suggestions pls pm me

im going to close now, if you have suggestions pls pm me

.close

[obtuse pebble]

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[obtuse pebble]

@timid silo Has your question been resolved?

[calm quail]

The period of y=cosx is 2π
So you can separate the interval into two ①[-2π,0] ②(0,π]
Interval ① covers one period so in this interval there are A roots
And In interval ② there are B roots
So the answer is A+B

You can draw the graph to check the value

Or you can think in this way:
Because -1<cosx=-0.5<0 so x is the angle in the 2nd quadrant or the 3rd quadrant

In one period,and in every of these quadrant has 1 root
So you just need to check the numbers of the 2nd/3rd quadrant covered in the interval

[obtuse pebble]

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[worldly narwhal]

how do you simplify sqrt of 96 to get 4 sqrt 6

[worldly narwhal]

ik how perfect squares work

just confused

its been a whie since ive done htem myself

[haughty onyx]

$\sqrt{96} = \sqrt{16\cdot{6}} = 4\sqrt{6}$

[warm shale]

Polipoli ❤

[worldly narwhal]

I'm so stupid

Sorry

My brain wasn't working

I was using 4

[haughty onyx]

noooo it’s okay hahah

[worldly narwhal]

It isn't the greatest perf square

[haughty onyx]

happens to all of us

[worldly narwhal]

Thx guys

[tranquil sonnet]

$\begin{align*}
\sqrt{96} &= \sqrt{2^5 \cdot 3}
\sqrt{96} &= \sqrt{4^2 \cdot 2 \cdot 3}
\sqrt{96} &= 16\sqrt{6}
\end{align*}$

[haughty onyx]

no problem!

[warm shale]

kappa

$\begin{align*}
\sqrt{96} &= \sqrt{2^5 \cdot 3}
\sqrt{96} &= \sqrt{4^2 \cdot 2 \cdot 3}
\sqrt{96} &= 16\sqrt{6} 
\end{align*}$
```Compilation error:```! Package amsmath Error: \begin{align*} allowed only in paragraph mode.

See the amsmath package documentation for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.57 $\begin{align*}
                    
You've lost some text.  Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.```

[tranquil sonnet]

interesting

oh

[haughty onyx]

the bot is confusing to use

[zenith raft]

don't use $ around align 🙂

oh sorry that wasn't your message

[haughty onyx]

oh that wasn’t me hahaha

[zenith raft]

@tranquil sonnet haha

[haughty onyx]

I don’t know how to use those hahah

[obtuse pebble]

@worldly narwhal Has your question been resolved?

[worldly narwhal]

o

No

Can smeone help me

How the fuck do I do this

I get the math but

I don't know how to algebraically bring it down to the point where I can start the solving

[zenith raft]

bring it down to where?

[worldly narwhal]

Like

How do I make it have an A B and C term only

like x^2+6x+8

That format

How do I algebraically do things to the 4 terms

I need to make one disappear

[zenith raft]

is that just subtraction?

[worldly narwhal]

I think so?

WOuld I subtract 10m?

[zenith raft]

subtract 10m + 5m^2 from both sides

or yea you cud do it in 2 moves

[grizzled shore]

look at both sides of the equation

the first thing i notice is there's only 1 variable

2nd thing i notice is the powers of said variable are all integers

and the highest is 2

this means this is a quadratic

and moving everything to 1 side means you get = 0

so we are solving for 0, 1 or 2 solutions for m

[obtuse pebble]

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[rare pelican]

i need help w 2 pls

[rare pelican]

i got

but it don't seem right

[kind hawk]

(a+b)^2 is not equal to a^2+b^2

[rare pelican]

i know, it's a^2+b^2+2ab

but there's no (a+b)^2

only (p-1)^2

and (p-1)^2 = p^2-2p+1

[stable rain]

as in

u got rid of sqrts

u cant do that due to that 1+ on the right

ull also get a

+2 sqrt(stuffs)

[rare pelican]

so i need the +1 on the left or wat

sqrt(p^2+q^2)-1 <= sqrt((p-1)^2+q^2)

surely not tho cause i need it in the form
d(A,C) <= d(A,B) + d(B,C) i can't rearrange yeah

[obtuse pebble]

@rare pelican Has your question been resolved?

[rare pelican]

no i still need help

[tardy epoch]

Then where's your 2ab term on the right side

[tardy epoch]

.

[rare pelican]

can u go thru it i don't know

[tardy epoch]

Why can't you rearrange

[rare pelican]

cause i need to show d(A,C) <= d(A,B) + d(B,C)

i'm not solving for a specific number

[tardy epoch]

Rearrange to this after sketching out the proof

Then write your proof backwards

[rare pelican]

bro wat

pls show the process idk

i don't know the proof

my teacher done nothing on it

[tardy epoch]

Once you have this term on the right, you subtract all your non square root terms to the left and square again

[rare pelican]

idk wat u on bro but is it rihgt now

it's a 2 * not 2x btw

[rare pelican]

ok good help i got it now anyway

.close

[obtuse pebble]

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[bright scaffold]

Hello

[rare pelican]

OH MY

[bright scaffold]

Something is wrong here and i cant figure out what

[bright scaffold]

lmao

[rare pelican]

nah bro u on u own there 💀

[bright scaffold]

Its funny cause my solution pretty much ended up that 5 = 5

[haughty coyote]

Without looking much I can say that always happens if you IBP one way then immediately IBP the other way

Because then IBPs cancel each other out

Instead break the integral a sum
The pure exponential is simple
The other one is a polynomial* an exponential, which can always be solved by IBP

[bright scaffold]

yeah

idk tbh

i look over and over

[haughty coyote]

So once you've committed to a direction for your IBPs, stick to it

[bright scaffold]

i think there is some -/+ that is wrong

[haughty coyote]

Maybe but it doesn't matter, you IBPed both ways and therefore did nothing

[obtuse pebble]

@bright scaffold Has your question been resolved?

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[knotty nebula]

Does it make any difference if I use 1+a compared to 1+|a|

[zenith raft]

yes?

the proof would no longer make sense?

what if a was -2?

then you'd be writing that for all n >= N, |a_n| < -1

which is nonsense

[spiral knot]

|a| = a if a>=0
|a| = -a if a<0

[obtuse pebble]

@knotty nebula Has your question been resolved?

[obtuse pebble]

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[latent mesa]

https://prnt.sc/rEfL6S5l-mIp

[latent mesa]

if radius is given how do u calculate perimeter

[alpine raven]

perimeter of what

[latent mesa]

of the square

actually how would radius of circle even be related to perimeter / area of square

can u explain

[warm canopy]

you need to relate the radius of the circle to the sidelength of the square

stare at the picture for a while

[latent mesa]

The side length isnt given

[alpine raven]

diameter of the circle is equal to the length of the side

[latent mesa]

so 18cm

[alpine raven]

yes

[latent mesa]

so the perimeter is just 18 x 4

and the area is just 18 x 2

or do we involve the circle 2

[alpine raven]

what ?

[latent mesa]

i mean 18 x 18

[alpine raven]

yes

[latent mesa]

Ok so whats simpsons rule

[alpine raven]

google

[latent mesa]

I still dk what it is

[alpine raven]

then you didnt read what it was about tho

[latent mesa]

Ok whatever but to calculate area with simpson rule it is just h/t * (fo + f1 ... + fn)

what are the x points for h

@alpine raven

should we count even the missing sides like 5m wasn't written many times and on the polar opposite of 7.5m

[alpine raven]

we don't even have the expression of the curve to apply simpson's rule, but anyway I'm not that good in numerical analysis

[obtuse pebble]

@latent mesa Has your question been resolved?

[long plinth]

Do you have a moderation problem?

[latent mesa]

Well it's been 15 mins without an answer from one so yea

[long plinth]

Do not ping moderators for for mathematics answers.

[latent mesa]

I didn't see that rule so i apologize

.close

[obtuse pebble]

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[queen mica]

is this a typo that is meant to be 3x^2? because I'm not sure what 3x2 would mean

[queen mica]

6 a)

,rotate

[wise talon]

Yeah looks like 3x^2 to me

likewise with a)

[queen mica]

Thanks

.close

[obtuse pebble]

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[mighty swallow]

Hello, i needed help with simplifying this

[queen mica]

Wrong chat

[harsh basin]

1^ (whatever) is still 1

[obtuse pebble]

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[floral socket]

can anyone help me with Q15

[timid silo]

,rotate

[digital moat]

ryuga hideki needs help

[floral socket]

sorry what?

[digital moat]

where is your name from

[trail cloak]

You could use binomial distribution

Wait no

Hmm

This feels like it needs a normal distribution curve

[novel knoll]

No setup is binomial so you use binomial

[floral socket]

the topic is binomial, but cant figure out what values to use for the the p,q,k

[novel knoll]

Recall what those represent

[floral socket]

i know n is 30, p should be 0.88? and q should be 0.12. but whats the k?

[novel knoll]

what is k?

[floral socket]

the amount of successes right

[novel knoll]

maybe if we add some notation to this it makes more sense

$\text{Sales} \sim \text{binom}(30,0.2)$, agree?

[warm shale]

ScapeProf

[floral socket]

yeah i would agree with that

if thats the question

[trail cloak]

Hmm

[novel knoll]

And then the question asks to find $k$ such that $$P(\text{Sales}\geq k)=0.88.$$ However as with any discrete hitting exactly $0.88$ is not rly possible so I assume they are asking for the largest $k$ such that $$P(\text{Sales}\geq k)\geq0.88.$$

[warm shale]

ScapeProf

[floral socket]

I wont lie I'm too embarrassed to say I am lost rn.

[novel knoll]

With? Agree this is what the question is asking?

[floral socket]

Oh yeah yeah

Also based on this, are we using the indirect method?

[novel knoll]

So the naive way is just trying. Is k=0 the answer? k=1? k=2? ...

[novel knoll]

what?

[floral socket]

the method of 1-p(0)
like finding out the unsuccessful first then subtracting

from 100

[novel knoll]

thats called the complement

and yes calculating say P(Sales>=1) is easier by looking at P(Sales<1)

[floral socket]

Ahh I think I'm getting it a bit. Would it be something like
1-(30C0)(0.0088)(0.9912)

no thats wrong

[obtuse pebble]

@floral socket Has your question been resolved?

[floral socket]

I think I got it now. got the answer of 4 by the end

@novel knoll thank you so much for your help! I really appreciate it and sorry for wasting so much time on this.

[obtuse pebble]

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[spice sluice]

can anybody explain

how did they get this

?

<@&286206848099549185>

[little warren]

It has to be the equation of lenght of a line in a 3d base ( i might be wrong tho )

[spice sluice]

it isnt explained

in the book

its evan chen euclidean geometry

[obtuse pebble]

@spice sluice Has your question been resolved?

[spice sluice]

<@&286206848099549185>

[haughty swan]

just expand right side

$(x+y+z)(x+y+z) = x^2 + 2xy + y^2 + 2yz + 2xz + z^2$

[warm shale]

rishi e

[haughty swan]

2 I N_0

I is incenter its that cyclic sum

and you were given that N_0 is 1/2(x^2 + y^2 +z^2)

2 times that product

1/2 will cancel

[obtuse pebble]

@spice sluice Has your question been resolved?

[obtuse pebble]

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[weary ginkgo]

i don't understand how we got the second line

[tardy epoch]

expand and group the terms

$\frac{1}{i} = -i$ will be helpful

[warm shale]

riemann

[weary ginkgo]

i tried but i didn't get it

i also used euler formula

[warm canopy]

dont convert the exponentials to trig

just literally expand both those brackets and combine like terms

[warm canopy]

combine the $e^{i\varphi}$ and $e^{-i\varphi}$ terms separately

[warm shale]

ΣAC

[warm canopy]

your second term has the exponentials flipped, either unlfip them or get rid of the negative out front

[weary ginkgo]

alright

i got it

thank you sm

.close

[obtuse pebble]

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[stable iron]

is this true only for $A=\pm I_n$ where $A\in\mathbb{R}^{n,n}$

[warm shale]

ta

[royal basin]

no

there exist other matrices whose square is the identity

[stable iron]

for example

[rigid lintel]

lots of examples

$\left[\begin{array}{cc}
-1 & 0 \
0 & 1
\end{array}\right]$

[warm shale]

Gijs

[rigid lintel]

$\left[\begin{array}{cc}
0 & 1 \
1 & 0
\end{array}\right]$

[warm shale]

Gijs

[stable iron]

oh that makes sense

thanks

.close

[obtuse pebble]

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[long dove]

Show that if $\left( x_{n} \right)$ is sequence of real numbers and $\lim{\left( x_{n} \right)}\neq 0$, then $x_{n}\neq 0$ for all natural number $n$

[warm shale]

Welf

[daring rock]

What? Am I missing something? This seems obviously false

0, 1, 2, 3, 4, 5, ... is a sequence of real numbers whose limit is not 0, but it contains 0

unless there's something obvious that's going right over my head

[obtuse pebble]

@long dove Has your question been resolved?

[long dove]

by terms given 0, 1, 2, 3, 4, 5, ... \
the sequence is $\left( n-1 \right)$ which is known to be divergent. Hence $ \nexists x = \lim{\left( n-1 \right)$

[twin sapphire]

theres a $ sign

[warm shale]

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

[twin sapphire]

so you meant

if (xn) has a limit

and it is not 0?

[long dove]

yes

[twin sapphire]

yeah you could stilll have

x_0=0

x_n=1

for all n>0

[long dove]

sequence always start from n=1 since n in set of natural number

[twin sapphire]

ok

x_1=0

x_n=1 for all n>1

this has a limit of 1

and still has a 0 in it

[long dove]

you're right. By that, the statement given is false since there is (0, 1, 1, 1, ...) doesn't satisfied.

Thank you @twin sapphire

.close

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[bitter timber]

How do I calculate this? Is there a trick when dealing with fractions?

[twin sapphire]

no

its the same as with any number

[bitter timber]

If I multiplied the first vector with the denominator and the second with the numerator, would the answer just be 1/3 times the vector product?

[twin sapphire]

wtf

why would you do this?

like arre you trying to guess what to do?

[bitter timber]

because I would want the vector in it's most simple form.

No i've just seen people use some trick along those lines

[twin sapphire]

its just regular ol vector maths

[bitter timber]

I would rather deal with integers than fractions when adding or subtracting

[twin sapphire]

just that the cordinates can be fractions

if you dont want to deal with it you can just factorize by 1/3

the whole expression

but i think you can manage

subtratinc 2/3 to integers

[bitter timber]

Alright

.close

[obtuse pebble]

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[patent jetty]

What was vector q

.close

[obtuse pebble]

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[green epoch]

[patent jetty]

Nvm

Wait

.reopen

[obtuse pebble]

✅

[patent jetty]

Have I marked vector q correctly

For the formula
|(b-a). (p×q) |/|p×q|

[obtuse pebble]

@patent jetty Has your question been resolved?

[obtuse pebble]

@patent jetty Has your question been resolved?

[obtuse pebble]

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[haughty onyx]

hi!

[haughty onyx]

need help for part (vi) of the question

my work for the first five parts

[obtuse pebble]

@haughty onyx Has your question been resolved?

[haughty onyx]

oh sorry! I’m not sure where to begin for part (vi)

[limber quartz]

it's ok everyone does it and I'm just extra crusty

[haughty onyx]

if someone could help guide the start it would be really helpful

[haughty onyx]

oh hahaha sorry

[limber quartz]

well

I don't know what Q is

but I can make broad generalizations about dB/dt for certain value ranges

ok, so without this term at all (the one with Q in it), the population is in decline no matter what

eh, let's just solve for > 0

...except you're asking for help with the last one so nvrmnd

@haughty onyx what class is this for?

[haughty onyx]

hi!

oh it’s for my math class

further math

[limber quartz]

Which one

[haughty onyx]

which one?

[limber quartz]

which class?

[haughty onyx]

oh it’s not separated for me

it’s just math

[limber quartz]

well the series expansion is neat

and equilibrium

[haughty onyx]

yes but a little stuck on actually sketching the diagram

[limber quartz]

so I thought maybe this came up in economics or ecological science or something

[haughty onyx]

ohh hahah

[zenith raft]

why was this necessary, she posted work for 5/6 of the problem

[limber quartz]

it's work to read these things

it's nice to know people who post them are still awake

(and she is and she sounds much more patient than me)

I can't solve this one. Dunno what bifurcation is and I can't find a quick lookup. Could you help her?

*"quick" = I can understand it

[zenith raft]

nope

[limber quartz]

@haughty onyx do you have any other examples of bifurcation diagrams from this part of class that we can look at?

[wild swallow]

you're supposed to use that graph to help you

in part iv

[solar trellis]

Intersections in the graphs are stationary points

[haughty onyx]

hi! not really I was only taught a little bit of theory of it

[wild swallow]

it's the intersections or something that you're looking for

yeah

basically the intersections in that graph are when you have dB/dt = 0

[limber quartz]

which one of those equations is the linear y?

[wild swallow]

and you can check the local behaviour by seeing which graph is above

that's enough to get a rough bifurcation diagram

[haughty onyx]

ohhh

[wild swallow]

just think of the plot of two graphs f(x) and g(x) together as letting you work out f(x) - g(x)

because essentially what you have is like

f(x) = g(x) when f(x) - g(x) = 0

so they give the same information

[limber quartz]

ok, then all the linear graphs are the second y for various R, got it

[solar trellis]

Ig the points of bifurcation are the values of R when the number of stationary points (so the number of intersections) changes

[wild swallow]

bifurcation diagram just draws the intersection points

[haughty onyx]

hmmm

[wild swallow]

you might need to know which are attractive fixed points

[solar trellis]

I don't think bifurcation diagrams typically contain info about the stability of fixed points

[wild swallow]

depends ig

when i studied this stuff the unstable ones were drawn as dashed lines or something

[limber quartz]

why isn't that diagram what they are asking for? Isn't R the parameter?

[unreal musk]

Out of curiosity A Level further maths yea? Which exam board/level is this?

[haughty onyx]

A Level H3 math

https://drive.google.com/file/d/1Opl2Lqs_7V3OlFC-euh6vEz7N60xwc3K/view?usp=drivesdk

[unreal musk]

Rarely ever checked some of the higher level modules they have

[haughty onyx]

this is the paper

[wild swallow]

cool stuff

[limber quartz]

you got good school

[zenith raft]

[wild swallow]

[haughty onyx]

it’s hard 😭

[wild swallow]

fun tho

[solar trellis]

Wait if you open that can they see your Gmail account

Idk

[haughty onyx]

kind of yes

[zenith raft]

i doubt it

[wild swallow]

you can open it without an account too

[zenith raft]

even if you open something that displays the viewers at the top right you're still anonymous unless your acc is an editor or something

[solar trellis]

Kk

[wild swallow]

dw you won't get unexpectedly doxxed this time

[limber quartz]

@wild swallow does she just need to draw vertical lines demarcating the intervals for B?

[wild swallow]

not sure what that means

[haughty onyx]

hi! I think there’s a new bifurcation at 0.384?

so a tangent there?

[haughty onyx]

ohh my teacher sent us that file

don’t worry hahaha

[solar trellis]

Yea

Also at 0.560

[solar trellis]

But here they merge I think

Not bifurcate

[rugged wind]

yoo wtf is this paper man

[haughty onyx]

oh it’s my school one

hi! I think I’m going to have to skip this question 🥲

[solemn trout]

I did a project on that exact question in HS. Spruce budworms.

[haughty onyx]

if anyone knows how I can start sketching the (vi) pls do ping ty!

[haughty onyx]

ohh

what’s HS?

[solemn trout]

High school.

[haughty onyx]

ohh you did this question in high school?

[solemn trout]

As part of a differential equations class, and as a group project.

[haughty onyx]

ohh! do you know how I can start sketching the graph?

[solemn trout]

Let me pull up the paper first.

[haughty onyx]

okay!

[solemn trout]

https://i.imgur.com/byqxm9U.png

The paper I used used μ rather than B.

I can't say why this is what you are supposed to do, since that was 4 years ago.

But basically you solve for R and Q in terms of μ, then plot the points parametrically.

Wait, that might not be what your paper wants you to do.

@haughty onyx

[haughty onyx]

hi!

[haughty onyx]

I found tangents at R 0.384 and 0.560

but overall I’m not sure how to begin sketching it

[solemn trout]

Here is the bifurcation diagram my group computed. Though this is for R and Q varying.

Ak, I have something to do, so I'll have to head off.

[haughty onyx]

how about B against R?

[haughty onyx]

ohh okay! tysm for helping! :D

[solemn trout]

No problem. Sorry I could not help further. Good luck!

[obtuse pebble]

@haughty onyx Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[obtuse pebble]

Channel closed

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[timber fox]

[timid silo]

,calc 9-9/9+9-9/9

[warm shale]

Result:

16

[timid silo]

another episode of social media refusing to accept the concept of fractions!

[royal basin]

9 - 1 + 9 - 1

[timber fox]

ive seen quiz website math questions, roblox math questions, and now tiktok math questions

[royal basin]

there is only the order of operations to get

and here it is unambiguous

[timid silo]

are you in grade 1

[royal basin]

https://en.m.wiktionary.org/wiki/unambiguous

[timid silo]

u said grade 6 like 5 minutes ago

whatever

[timber fox]

[timid silo]

peak math education courtesy of K12

[green epoch]

[royal basin]

i don't know if you asked "what does the word 'unambiguous' mean?" or "what does your use of 'unambiguous' refer to"

what is your native language?

[timid silo]

oh nice i can speak a bit

[timid silo]

don't ask questions like "are you in grade 1" towards people who are trynna learn

[royal basin]

hm. i can't find the Arabic translation for the word

[timid silo]

it translates to something like uhh

like ive seen you say similar remarks in other channels

hmm

but it's just unnecessary 🤷

[royal basin]

anyway

in the expression 9 - 9/9 + 9 - 9/9, you do the division first

[timid silo]

"خالية من الغموض" معنى الكلمة على ما اعتقد @cerulean sequoia

[royal basin]

order of operations says so

[timid silo]

but anyways

[royal basin]

multiplication and division come first

then addition and subtraction

[wise talon]

there's that thing called BODMAS

[timid silo]

PEMDAS

[wise talon]

or whatever

[royal basin]

BODMAS or PEMDAS or some more regional variations.

[timid silo]

basically pemdas but british

lolmao

[wise talon]

brigham young university moment

[timid silo]

bodmas >

Bedmas sounds lamer

[royal basin]

😒

[wise talon]

yeah I did GCE A Levels so

[royal basin]

you all have silly attachments to particular acronyms

[timid silo]

no

[royal basin]

if y'all wanna argue order of operations acronyms then take that shit to #chill

[wise talon]

whatever the binary op x is performed first yeah

[royal basin]

:?

...

<@&268886789983436800>

[timid silo]

sigh

always has to turn out like this huh

.close

[obtuse pebble]

Channel closed

Closed by @native knoll

Use .reopen if this was a mistake.

✅

[timid silo]

what do you need the channel open for?

[timber fox]

.close

[obtuse pebble]

Channel closed

Closed by @timber fox

Use .reopen if this was a mistake.

✅

[timber fox]

if you dont have a question to ask then close the channel

[wise talon]

Please don't hog the channel

[royal basin]

#chill and #discussion exist for that

[timid silo]

neither of them care, they both said the N word and continue to do whatever they are doing right now

oh the other guy is already banned

nice

How did that one dude get banned when alenciaga posted a video of someone screaming the N word

not sure

also had a PP being flashed

there is only one moderator on

but will ping again

<@&268886789983436800>

tfw mods have logs

okay finally

.close

[obtuse pebble]

Channel closed

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[whole dock]

How do i solve this

[timber fox]

might have to elaborate a bit unless im missing something

[whole dock]

this is the formula for the electric field due to a dipole on the axis

Here p is the unit vector

From -q to q

[timid silo]

That doesn’t answer the question; what are you trying to solve?

[whole dock]

I want to simplify this

[timid silo]

There you go

That makes more sense

So, what have you tried?

[timber fox]

looks really simple to me tbh, you have removed the constants and are left with the variables inside/

[whole dock]

Yeah but idk how they simplfied it in the book

[timber fox]

so you want to simplify the original equation to what you posted?

[timber fox]

ah I see

yeah I mean the just factored the constant out

and then common denominator stuff

of the inside

to get 4ar

[timber fox]

yep

looks goodo

[whole dock]

Thankss

.close

[obtuse pebble]

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[timber fox]

looks similar to perihilion and aphelion velocity equations O_O

weird how everything is similar :DD

[obtuse pebble]

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[dawn vigil]

I realized when proving things, when we have for every e > 0, a <= b + e, then a <= b, can we just say "since e > 0 is arbitrary..." we have a <= b + e implies a <= b instead of having to prove why this is the case?

[wise talon]

Hmm

So your given is

[dawn vigil]

@wise talon There's a theorem from Abbott I found

[wise talon]

Oh show me

[dawn vigil]

kk

[wise talon]

I'm familiar with that book

[dawn vigil]

Let me screenshot it

[wise talon]

or you could give me the theorem number too

i have the book right on my desk

[dawn vigil]

Don't have it on top of my head, but it's definitely in there. But, the theorem was exactly this: https://math.stackexchange.com/questions/2496174/what-does-epsilon-0-is-arbitrary-mean

[wise talon]

Ah

epsilon > 0 arbitrary means

we can literally just pick anything

for example I can choose eps = 1

or eps = 23918408230480238423

or eps = pi

as long as it's > 0

are you talking about theorem 1.2.6

[dawn vigil]

Yeah

[wise talon]

$a = b \iff \forall \epsilon > 0 |a-b| < \epsilon$

[warm shale]

DerpZ

[dawn vigil]

Right, does Thm 1.2.6 apply here?

Could I just use Thm 1.2.6 here?

[wise talon]

that's sort of what we're doing here

with that contradiction just now

so the gist is that U - L < eps means that

U >= L

[dawn vigil]

Yeah, so instead of having to do that contradiction, once we proved it, can we just say "Since e > 0 is arbitrary..."

[wise talon]

Well you need to check with your prof if they're okay with you skipping steps

If you understand it I don't see why not

The contradiction we showed was because you were asking why we can just directly conclude it

We filled in the missing steps

[dawn vigil]

Alright, yeah, that is my question. Like I understand the proof, but I was just wondering once you proved it, if it's okay to go from point A to point B instead of having to fill in the gaps. I'm self studying this btw so I can get ready for analysis when I have to take it

[wise talon]

Yeah sure

But you need to be able to fill it in

[dawn vigil]

Because it seems like a lot of proofs don't explain how they go from point A to point B as we discussed because they already proved it somewhere else

[wild swallow]

you prove it then quote the result later

[wise talon]

If you're taking an exam you could probably

[dawn vigil]

Alright, just quote it

[wild swallow]

well if you're writing a book that's what you'd do

prove it once and then quote it in all subsequent uses

[wise talon]

or:

"exercise for the reader"

"trivial"

[wild swallow]

[wise talon]

"convince yourself"

"the reader is asked to verify"

[wild swallow]

if you're writing a good quality book*

[wise talon]

btw if they do ask you to verify you should verify

[dawn vigil]

That part where they go from e > 0 is arbitrary, to this proves that U <= L, did they not quote it because it was really trivial?

[wild swallow]

well depends on the level of rigour you're aiming for

[wise talon]

yup that is trivial

[wild swallow]

you might say "ah that's a trivial property of the real numbers ofc that must be true"

but then at the same time it really isn't a trivial result

because once you leave the reals it might no longer be true

[wise talon]

luckily it's real analysis but yes

[dawn vigil]

yup

[wise talon]

also

interesting that you are at integration

doesn't real analysis go like

sequences serieses functional limits

etc

[dawn vigil]

I actually took real analysis awhile back and studying for real analysis II. real analysis I was a huge struggle so that's why I'm studying it early before I take the class

[wise talon]

ah

[lost badger]

Hi

[wise talon]

well it's real anal

[dawn vigil]

lmao yep

[wise talon]

if you're about to ask for help

[lost badger]

What , you're having sex?!

[wise talon]

please do not

[dawn vigil]

@wise talon @wild swallow thank you! 🙂

[warm shale]

Dream

[dawn vigil]

.close

[obtuse pebble]

Channel closed

Closed by @dawn vigil

Use .reopen if this was a mistake.

[wise talon]

LOL

[wild swallow]

[lost badger]

.reopen

[wild swallow]

gottem

[wise talon]

that is such a good one

[lost badger]

So sad that math is ligma

[wild swallow]

[obtuse pebble]

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[wide star]

if 0/0 is 0, is 0^0 also 0?

[sage geode]

0/0 is not 0

Nor is 0^0 anything

[slim basalt]

k^0 = k/k, therefore 0^0 = 0/0. but you arent allowed to divide by 0, so 0/0 or 0^0 are not defined

[wide star]

Not what I asked

[sage geode]

Well

"If 0/0 is 0, is 0^0 also 0"

False implies false

So yeah

[wise talon]

Ok maybe let's try to entertain this

Let's suppose 0/0 = 0

[wide star]

Not all false implies all other false

[wise talon]

now

[wide star]

3+3=5 dosnt means 5*58=8

[wise talon]

what

[sage geode]

Let me demonstrate?

3 + 3 = 5
6 = 5
0 = 1

5 * 58 = (1 + 1 + 1 + 1 + 1) * (8 + 1 + ... + 1) = 1 * 8 = 8

[wise talon]

easier way:

[sage geode]

Idk which class of formal logic you've gone through

[wise talon]

let M be a system of arithmetic such that 3+3 = 5

then define 5*58 = 8

[wide star]

Anyways back to the topic

Would 0/0=0 means 0^0=0

[sage geode]

Yes, 0/0 = 0 -> 0^0 = 0

[wide star]

So 0^0 would not be 1?

[sage geode]

You could also prove that 0^0 = 1 I believe

If 0/0 = 0

Should be a way

[wide star]

Make up your mind

If 0/0=0, 0^0 would still only have one answer

[wise talon]

no...

[sage geode]

Well, no
Again, since false implies false you can have
0/0 = 0 -> 0^0 = 0
0/0 = 0 -> 0^0 = 1

[wise talon]

since your system of logic is inconsistent

0^0 could be 1 or 0

[wide star]

0/0=0 for a reason

Not that the reason it self is relevant

[sage geode]

There's no proof for 0/0 = 0

[wide star]

0/0=0(1/0)=0z=0

[timid silo]

but if you limit 1/x when x go to 0 it goes to infinite

[slim basalt]

xD

[wide star]

0/0=0 in a extension of the complex numbers I’m working on

[sage geode]

Similarly you can say that 0/0 = 1 because a/a = 1

[wide star]

That’s just a factual statement

Not arguable

[sage geode]

Again, you're forgetting to account for the fact that you can't divide by 0

[wide star]

Not in the complex numbers

That’s why I’m extending them

[sage geode]

You have it defined?

Division by 0

[wide star]

Yes

But that’s not too relevant

[sage geode]

It is

Show it

[unreal musk]

Right, how exactly are you defining division by zero such that you don’t force 0=1?

[wide star]

0/0=0, 1/0=z, 2/0=2z 3/0=3z etc

With z being a new dimension & number

But again this isn’t too relevant

[unreal musk]

0=0, 1=0, 2=0, 3=0 etc

…or?

[wide star]

I literally just said 1/0=z

z≠0

z*0=0

Now can we get back to 0^0

[warm canopy]

[wide star]

No?

[night igloo]

https://en.wikipedia.org/wiki/Vacuous_truth?wprov=sfla1

Long story short: it does, you can derive anything, true or false, when you assume a falsehood to begin with

[wide star]

But in this extension of complex numbers

0/0 factually is 0

[night igloo]

You can stipulate whatever you want in your own number system, but I don't think anyone would be familiar with it as to help you answer anything

That's not the purpose of these help channels

[warm canopy]

It doesn't help that your number system is not and will never be well defined

[wide star]

I mean I told you the only relevant part of the question

[night igloo]

If you want to derive something in math, every step of the way of your reasoning is, or should be, relevant

[wide star]

My reasoning z*0=0

[night igloo]

What's z?

Moreover, do multiplication (*) and the symbol 0 carry any special meaning that is unconventional?

These are all very important things to know

[wide star]

It’s a new number

That happens to also be a unit of a new dimension (kinda like i)

[wide star]

I don’t think so

[balmy mortar]

0^0 is 1,

cus i said so

[night igloo]

Ok, what are other properties of this z? Right now it doesn't seem very special, since I can come up with other numbers that do the same thing: 1 * 0 = 0 for example, or 69420 * 0 = 0

[warm canopy]

This also would imply z = 0/0 but you've decided its 0 and only 0

So z=0 wow!

[wide star]

How so?

[wide star]

z is 1/0

[warm canopy]

Divide both sides by zero, which you are supposedly allowed to do in your number system

[wide star]

Not valid because 0/0≠1

[warm canopy]

That does not invalidate the ability to divide by zero in your system

It bewilders me that you can hold so many contradictory ideas in your head

[wide star]

No but it dose invalidate that dividing both sides by zero keeps the value the same on both sides

It would be like saying 1=5 because 1•0=5•0

[night igloo]

The symbol "1 / 0" doesn't make sense in our conventional number system. Can you please make clear what you mean with this?

[wide star]

one divide by zero

[unreal musk]

…but that’s exactly the point that’s been made throughout, you won’t have some properties like that

[wide star]

But this wasn’t true for multiplying by zero

So I don’t see what we are loosing

[night igloo]

Does the symbol "1 / 0" indicate an object, such that you multiply it with 0, you get 1?

[wide star]

No

[night igloo]

Interesting

Then please elaborate

[wide star]

Well thats because if you have zero zeroths you have nothing

[night igloo]

That is unrelated to what I was asking

My question is: If I multiply 0 with "1 / 0", what would be the result?

[wide star]

0/0

Aka zero zeroths

Thats why I said that

[night igloo]

So it's just another symbol, "0 / 0"?

[unreal musk]

Think most of us are familiar with what happens when you ask Siri that question

[meager swift]

📠

[wide star]

No 0/0 is zero

Because you have no zeroths

[meager swift]

0/0 is zero?

[wide star]

That’s the first thing I said lol

[meager swift]

U said if that was that

If

[unreal musk]

…

[wide star]

Well yes because most people are working in the complex numbers where that’s not true

I’m working in number space (my extended version of complex numbers) where it is true

[meager swift]

But complex numbers contains any other kind of numbers

[wide star]

Ah yes

5+z+7q my favorite complex number

[meager swift]

If you ignore those other wonky complex complete numbers or whatever it's called

[wide star]

(q is i/0)

[unreal musk]

…can’t lie, this 0/0 argument has “we put man on the moon, so we can put man on the sun” energy, I’m just watching for the amusement

[meager swift]

Okok so 0/0 is 0 right

You know what else is zero

2 * 0 is zero

[wide star]

Ok…

[meager swift]

$\frac{0}{0} = \frac{2\cdot0}{0} = 2$

[warm shale]

edwardborn

[meager swift]

Qed

2=0

[wide star]

No

[meager swift]

Yes!

[wide star]

Do the math

(2•0)/0

[night igloo]

I'm starting to think that the object we're exploring is similar to the Riemann sphere

[wide star]

0/0

[meager swift]

You do the math! (╯°□°)╯︵ ┻━┻

[wide star]

Not even close

[night igloo]

https://en.wikipedia.org/wiki/Riemann_sphere?wprov=sfla1

[wide star]

In that sphere 2/0=1/0

But in number space (my system) 1/0≠2/0

[unreal musk]

Can you then explain to us which step in that calculation is a false assumption?

[night igloo]

Hmm ok, so what would be the reciprocal of z?

[wide star]

The idea you can factor out 0

Because again 0/0≠1

[meager swift]

Ah fair

[night igloo]

1 / (1 / 0) = 0?

[wide star]

Let me check my notes on that one

[wide star]

Yea

[night igloo]

Ok... And 2 / (2 / 0) = 0 also?

[wide star]

Yes

[night igloo]

Do you agree that 1 / (1 / 0) * (1 / 0) = 0 * (1 / 0) = 0 / 0 = 0?

[wide star]

Yes…

[night igloo]

But do you also agree that 1 / (1 / 0) * (1 / 0) = 1?

We're just multiplying and dividing by 1 / 0

[wide star]

No

1/(1/0)=0

0*z=0

[warm canopy]

Just because there are two valid ways to evaluate an expression doesn't mean you can reject one

[night igloo]

Here you're saying that 1 / z = 0, so does that mean 0 * z is actually 1?

If we multiply both sides with z

[obtuse pebble]

@wide star Has your question been resolved?

[meager swift]

Well it's oddly hard to think of a counterexample for 0/0 = 0

Maybe it actually doesn't break math if you define it that way

[meager swift]

So I guess the answer to this is

Probably

[wide star]

No

[wide star]

Thanks

[meager swift]

[obtuse pebble]

@wide star Has your question been resolved?

Channel closed

Closed by @wide star

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

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[wild orbit]

So for y lower limit shouldnt it be ,-square root of (4-x)
But in the solution ,why is the lower limit 0?

[obtuse pebble]

@wild orbit Has your question been resolved?

[obtuse pebble]

@wild orbit Has your question been resolved?

[obtuse pebble]

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:
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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.

[obtuse pebble]

@limber eagle Has your question been resolved?

[drifting wraith]

yeah

one of this is possible

the rest have too many handshakes, more than it's possible

just check every one

[whole dock]

I think 2nd is possible

4th as well

3rd too

[drifting wraith]

very good

[whole dock]

We use permutations here right

[drifting wraith]

that's the exact opposite of what it is, that's very accurate in some math sense

[whole dock]

Well what i did was

12P2

And divide by 2

[drifting wraith]

yeah

that's good

[whole dock]

Same for all

Really?😭

[obtuse pebble]

Channel closed

Closed due to timeout

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

[timid silo]

Hello

[timid silo]

I need help

Similarity math

@fallow wharf

[proven zephyr]

you need me?

awww

btw just post the question

no need to wait for someone to come

[timid silo]

Can u do similarity maths? Similarity Geometry

Class 9

[proven zephyr]

just post the question

[timid silo]

@proven zephyr

[proven zephyr]

,rccw

[timid silo]

Find the unknown areas

Similarity maths

Let me write the question

In this , Find the unknown area A

I mean in the first rectangle we need to find the A

[teal turret]

Trapezoid?

[timid silo]

Yes

[teal turret]

Do u know if they’re similar trapezoids

[timid silo]

Areas of Similar shape

[teal turret]

Ok

[timid silo]

I dont think they r

[teal turret]

Wat

Then how u supposed to compare

[timid silo]

The answer is 12cm²

In the book

But I need to do it, its my homework

[proven zephyr]

they should be

[timid silo]

Yes the answer is 12cm²

[proven zephyr]

otherwise you can't do anything to it

[timid silo]

Yes

But how to do it plz help

[proven zephyr]

isn't it just

what is the side called i forgot

base right?

ok

[timid silo]

Yes

[proven zephyr]

(smaller base/bigger base)^2 = area small/area big

isn't it just that?

[timid silo]

Yes yes