help-0

[terse gull]

and make it

look like this

welk u gotta make it again actually

but since u already made urs

it shouldn’t be too hard

[lone heart]

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[jade mural]

Sam places 2 straws forming angles p and q which are supplementary. Sam moves straw n such that value of q triples. How does value of p change?

[jade mural]

Supplementary means p+q=180

[lone heart]

@jade mural Has your question been resolved?

[mossy niche]

guys helpp

[jade mural]

This channel is occupied

Kindly go to another channel

[marsh gazelle]

so what has been ur approach

are u resolved?

@jade mural

[jade mural]

Its not resolved

I just asummed angles and got the answer

But i cant prove it through algebra

[marsh gazelle]

show me ur work

[jade mural]

Can i type it?

[marsh gazelle]

yeah

[jade mural]

Ok so the proof or assuming

[marsh gazelle]

proof

alg

[jade mural]

Ok so
p+q=180
3q=3(180-p)
3q=540-3p
-3p=3q-540
p=3q-540/-3

I basically tried to compare the og p value and this value

It kept forming quadratics

Which just had root values

Which were useless values

Also i had searched on google

And their solution was this

b=3a
2b=3a+3a
2b=6a
Hence a<2b

They have assumed a=b i am pretty sure and i dont think this is correct

Kindly ignore the diff variables

[lone heart]

@jade mural Has your question been resolved?

[lone heart]

@jade mural Has your question been resolved?

[jade mural]

Can u explain this further

What final asnwer are u getting?

[tiny sky]

so we initially have p and q as our angles

and then after sam moves the straw, let's say the angles are p' and q'

q triples so q' = 3q

then just do the algebra and you end up with p' = 3p - 360

honestly not really sure what format they want the final answer as

[jade mural]

Um so

They want it in terms of p and q

Like for example p is 1/3 of q

Or smt like that

I can tell u the answer if it helps

I just want u to help me arrive to it algebraicallu

*y

[tiny sky]

i mean

3p - 360 is in terms of p and q

or alternatively p - 2q if that looks nicer

[jade mural]

Ok yea thz

.close

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[jade mural]

.reopen

[lone heart]

✅

[jade mural]

I am so sorry how did u get to p-2q

It might be smt obvious

But i cant see it

[tiny sky]

p+q = 180

[jade mural]

U substituted the value of p’ in this equation?

Can u show full working

@tiny sky sry for ping

[tiny sky]

as in p' = 3p - 360

p+q = 180

so p' = 3p - 2(p+q)

[jade mural]

Ok tysm for being patient

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[crude topaz]

can someone calculate this for me i cant find any calculators that do it for me

[static bobcat]

how many sig figs?

[mystic swallow]

use wolframalpha

[crude topaz]

i couldnt format it properly

[crude topaz]

all

[mystic swallow]

,w 1.89/9.8 arccosh(e^{9.8(2)/(1.89)^2})

[pseudo ice]

,w (1.89/9.8) * arccosh( e^( 9.8 * 2 / 1.89^2))

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by justarenegade

[mystic swallow]

dammt

[ocean seal]

Results provided by WolframAlpha

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

Requested by chartbit

[still herald]

,w (189/980)(arccosh(e^(19.6/(1.89*1.89)))

[pseudo ice]

Damn, a second before me

[static bobcat]

is this a physics equation?

[mystic swallow]

nooooo chart got there first D:

[crude topaz]

damn 10 different results

[mystic swallow]

and WA still didn't understand

this is different

[still herald]

fr

mine is correct ig

[still herald]

nvm

i forgot a decimal

[crude topaz]

why does ai tell me its 1.37

[ocean seal]

Results provided by WolframAlpha

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

Requested by anshulyolo121

[static bobcat]

because ai is wrong

[crude topaz]

and why does python tell me other values

[pseudo ice]

(also, which calculator do you have? Some of them have the inverse hyperbolic trig under a menu or something)

[still herald]

this is the correctest

[crude topaz]

ti-84 plus ce-t

[queen wing]

AI is better at explaining maths than at doing it.

[crude topaz]

so what is the right answer

well fuck there goes my research paper down the drain

this fuckin formula

[mystic swallow]

first off

WA is not AI

secondly it is very good for calculations

[mystic swallow]

thirdly

[lone heart]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[crude topaz]

julius ai 🫣

probably gave me monkey formulas that arent even true

[pseudo ice]

Apparently they're in the catalog, it says choose 2nd and then 0 to get to it

[crude topaz]

are you able to tell me if the formula i gave you, that is supposed to calculate the time to reach the ground for a parachute given, the height, drag coefficient(1.75), area of parachute(22.56cm^2), and mass of 9g

is that formula correct?

[lone heart]

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[crude topaz]

.cloe

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[remote gulch]

Suppose there's a machine that can tell me whether any sentence is satisfiable or not but I can only give it one sentence as an input. What I want to know, in one query, is whether two sentences φ and ψ are satisfiable. So I have to construct a sentence π from ψ and φ that let's me know that both are satisfiable. Is it possible to construct such a sentence?

My initial thought was that if there's a set of atomic sentences 𝓜 s.t. 𝓜⊨φ∧ψ, then both φ and ψ are satisfied by 𝓜. But I don't think that's exhaustive because it could be that φ and ψ are satisfied by different models. Unless there's a general way to combine the possible models that satisfy φ and ψ independently s.t. φ∧ψ is satisfied by the combined model, then the conjunction doesn't work.

[lone heart]

@remote gulch Has your question been resolved?

[verbal blaze]

what do you mean by "satisfiable"?

• if you mean "true" or "provable", you can ask "is φ and ψ satisfiable"
• if you mean "cannot be broken into two or more questions", then clearly no.

[remote gulch]

I mean that there exists a truth assignment that makes it true.

And I can't ask meta-level questions, they have to be in the object language i.e. prop logic in this case (sorry, that was not clear from the first msg). So to be clear: the machine takes as an input a proposition in the language of prop logic, and it will output 'yes' or 'no' depending on whether it can be true. For an input φ∈𝓛, ∃𝓜⊆𝓟 s.t. 𝓜⊨φ, where 𝓟 is the set of all atomic sentences and 𝓜 is the set of true atomic sentences s.t. 𝓟\𝓜 is the set of false sentences (𝓜 corresponds to a row in a truth table). But I have two sentences which I need to somehow combine s.t. given the output, I can dicern satisfiability independently for both sentences. This might not be possible but I haven't been able to prove that either.

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[remote gulch]

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[inland anchor]

u guys fw math

[ocean jasper]

hiya math heads

[alpine sable]

why did we join the serv

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[inland anchor]

idk

hope this helps

[daring crater]

thanks

<@&286206848099549185>

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[cyan plover]

need help with if i did this right and what order to list the transformations in (first pic is the example and second is my work so far)

[cyan plover]

<@&286206848099549185>

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[forest coyote]

anyone can help?

[tacit arch]

Pick one and try it yourself first

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[signal ether]

Where did the 1 underlined in the equation come from?

[stark crater]

What do you think it should be

[sharp gate]

From expanding $(x-1)^2$

[ocean seal]

Luca M

[raw jetty]

(x-1)^2=(x-1)(x-1)=x^2-x-x+1=x^2-2x+1

[signal ether]

Wait sorry I meant the -2x not 1
Would it not just be
x^2 + 1
where did the -2x come from

[lunar temple]

What is g(f(3))?

What is f(4)g(4)?

[alpine sable]

from the x multiplying against the -1s

[sharp gate]

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

[raw jetty]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[ocean seal]

Luca M

[sharp gate]

because $(a-b)^2=(a-b)(a-b)$ then you foil

[ocean seal]

Luca M

[alpine sable]

you dont just multiply the x by the x and the -1 by the -1, you multiply the x by the -1s too, and so you get two instances of x * -1, resulting in -2x

[signal ether]

Ahh okay yeah I forgot about that! Thank you guys 🙏

The help is much appreciated!

.close

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[proud moth]

i just need help to prove that Rank(B) = 2r plz

[pallid scarab]

rank(A) is the number of independent columns of A

A* has the same number of independent columns

so if you take a basis of the columns of A, write them f1,...,fr

and a basis of the columns of A*, g1,...,gr

add m zeros in front of the vectors fk

and add n zeros behind the vectors gk

what can you say about the family of fk and gk (with the added 0s)?

[lone heart]

@proud moth Has your question been resolved?

[proud moth]

I’m assuming like linearly independent since their both basis

But would it be linearly independent if one is just the transpose of the other ???

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[silent copper]

help

[silent copper]

<@&286206848099549185>

[gleaming latch]

i was summoned here but idk ehat that is

[flat abyss]

i too was summoned here and yet, don't have a clue on what ur yapping abt

[silent copper]

so everyone are uselsess

.close

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[iron musk]

I did the synthetic division now I’m not sure what the problem is saying to do to write the equation?

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[iron musk]

I did the synthetic division now I’m not sure what the problem is saying to do to write the equation?

[fresh wedge]

Well you got the answer now write it in that
q(x) + r(x)/.... Form

The last 3 line in question is explaining what is q(x) what is r(x)

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[hoary sand]

how to derive all the integration values

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[alpine sable]

Let $i:(Y,\mathscr O_Y)\to (X,\mathscr O_X)$ be a morphism of ringed spaces, and (\mathscr F) be an (\mathscr O_Y)-module, do we have an isomorphism of stalks $(i_*\mathscr F)_{i(y)}=\mathscr F_y$?

[ocean seal]

uop

[alpine sable]

ok, it is not true in general, but https://stacks.math.columbia.edu/tag/00AE seems to be exactly what I want

[ivory pivot]

oo nice

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[limber wharf]

im confused

[limber wharf]

i dont know if what i did is right

[ivory pivot]

,rotate

[strange heath]

i mean

it should be 0

since the numerator would approach zero

[storm marten]

you should try focusing on simplifying the denominator

[limber wharf]

the limit or the denominator

[storm marten]

just simplify the denominator

[limber wharf]

i put it in some calculator on google and got the limit as one lol so i was tryna get there

[limber wharf]

alright

[storm marten]

you can cancel the zero factors

[limber wharf]

okay thank you

.close

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[hard spoke]

<@&286206848099549185> Neuvilette used 220ml of water and 190g of flour to make the dough. Furina made the dough according to Neuvilette's method, but Furina prepared 760g of flour. Calculate the volume of water required by Furina in ml.

[weary stag]

oop

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[alpine sable]

im a new engineering student and i suck at math, any advises?😅

[storm marten]

are you preparing for any entrance exams?

[alpine sable]

no im already in it

[storm marten]

which one?

[pliant siren]

Can anybody teach me standard form for 8th grade IGCSE

[alpine sable]

first year we have a Preparatory year with no specific major

its really from the basics

the first chapter is: sets and the real numbers

i feel like i understand it but when i try to solve something it just doesn't

[spring summit]

Yo youre in egyptian engineering school??

unless theres some other arab system that has a preparatory year then i just look stupid😭

[alpine sable]

no saudi uni

[spring summit]

eh close enough

[alpine sable]

close enough

[spring summit]

anyways so my advice for you would depend on some stuff

The main question is any particular topics you struggled with during high school or middle school?

since in mathematics foundations are VERY important, if you fell behind on a certain topic during school it might ruin your mathematical career in college because of how important the topic may be
which is why i think its important for you to go over any material you feel like you dont really understand well if you feel like you suck at math, even if it seems VERY basic, you might have not understood something in it that was important for later more advanced math

and regarding the real number/set stuff if you could itd be helpful to show me your work when you tried to solve a problem on the topic since maybe you do understand but are just using the incorrect method

[alpine sable]

here is the problem i never studied

i dont even know how i got here

[alpine sable]

i saw some of my syllabus with ranak and i noticed it was easy

so i think ill just practice

[storm marten]

yeah that will help, cuz you will get some idea on what you can and can't do rn

[alpine sable]

even though i have a quiz next week but it will do

https://tenor.com/view/daemon-targaryen-house-of-the-dragon-matt-smith-letter-mail-gif-26921562

me studying

[spring summit]

Well then just try to notice what particular topics you struggle with
ie lets say youre doing a math problem, and in the middle you have to factorise, and you get stuck, then you know that you cant factorize well and need to learn/relearn it

[spring summit]

well good thing you find it easy,in that case practicing will help yeah

good luck!

[alpine sable]

thank you

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[shy jolt]

I was looking at some 1q tests and couldn't really figure out the pattern on this particular question

[chrome tiger]

I found 2 explanations why 3rd image might be the answer but they both seem unnatural and I'm not proud of them at all

1. Each row has images with 3, 4 and 5 sticks and at least 1 horizontal short stick in each row. By this logic we need to fit an image with 5 sticks and at least 1 horizontal short stick
2. same but we also note that there're 5 short sticks in the first row, 3 short sticks in the second and we assume that there should be 1 short stick in the 3rd row

[shy jolt]

I see, thank you

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[meager dagger]

Hello, I was learning about Sobol indicies on this site https://towardsdatascience.com/sobol-indices-to-measure-feature-importance-54cedc3281bc and in the article, they said that $var(E(Y|X_i)) \approx cov(Y_A, Y_{AB})$ I don't really see how to get this result

[wooden thicket]

can i occupie this channel pls?

[proven depot]

a question is already posted here

visit #❓how-to-get-help

[ocean seal]

weareinthematrix

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@meager dagger Has your question been resolved?

[meager dagger]

<@&286206848099549185>

[tacit arch]

where exactly is that claimed?

[gleaming latch]

what grade is this mathththththt

[meager dagger]

They say that the first order sobol index is $\frac{var(E(Y|Xi))}{var(Y)}$, later, they say that this index is $\approx \frac{cov(Y_A, Y{AB})}{var(Y)}$

[ocean seal]

weareinthematrix

[meager dagger]

I don't know if that is taught in maths, I'm working on this for an internship

[tacit arch]

where exactly

can you screenshot and be more specific

maybe this paper can help
https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-14/issue-1/Non-parametric-adaptive-estimation-of-order-1-Sobol-indices-in/10.1214/19-EJS1627.pdf

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[feral mesa]

hello

[feral mesa]

"The square root of x4x4 is equal to ∣x2∣ and not to −x2. Explain."

[tacit arch]

$\sqrt{x^2} = ?$ for $x=-3$

[ocean seal]

riemann

[winter light]

!original

[lone heart]

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.

@feral mesa Has your question been resolved?

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[lyric egret]

how do i solve d? idk how to get x2 or how to see when it has a solution and also idk if I have make this into echelon form

[naive valley]

do you know about determinants?

[lyric egret]

yeah

Do I need it?

[vapid shuttle]

[naive valley]

🔥

[naive valley]

you don't strictly need it but it's one way to proceed

[lyric egret]

can you tell me why? I didn't use it in the exercises before 😭

this is hard ngl

this is the awnser but idk how they came to this conclusion:

[naive valley]

you know there's a unique solution if the 2x2 determinant is nonzero

so find out when it's zero

then see if the equations are consistent or not in that case

[lyric egret]

okay

[lyric egret]

but rn its not 2x2 its 2x3 so how do i go from here?

[naive valley]

it's an augmented matrix right?

the non-augmented part is 2x2

[lyric egret]

oh so I take the non-augmented part

got it

so the equation is consistent when 3a-B !=0, then depending on a and B its consistent or not?

right?

[naive valley]

if 3a-B is nonzero then it's consistent and there is a unique solution

if it's zero then try rewriting the matrix in terms of only a or only B

i.e. plug in 3a=B

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[lyric egret]

thanks

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[wary root]

help plz

[wary root]

<@&286206848099549185> plz, idk what i keep doing wrong

or what im even supposed to do

like i turned it into degrees and got 72

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[clever lark]

Hi everyone, I need help with quadratic forms, can you tell me if the procedure is correct? furthermore I am unable to carry out the second point and in general to define when we talk about convex concave almost convex or almost concave, I'm panicking because there are only a few days left until the exam, can you help me? Consider the quadratic form:
Q(x, y) = 3x^2 − (5 + k)xy + 2ky^2
a. Study the definiteness of Q as k varies in R.
b. Are there any values of k for which Q is a concave function?
Can you also tell me what i have to do if the exercise ask me something like: "If k = 7, is Q a quasi-convex function?"

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@clever lark Has your question been resolved?

[clever lark]

<@&286206848099549185>

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@clever lark Has your question been resolved?

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[grand hornet]

4 = 4(4b + 6/10) - 2b + 3

[grand hornet]

i got

b = 9.429

can someone verify this

btw 4b + 6 is divided by 10

not just 6/10

[warm stag]

just use mathpapa algebra calculator

[grand hornet]

thanks for helping

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[wicked minnow]

The work already written is what the teacher wrote in the key. I dont understand why the first “X” is added to the equation 6X-43=90. I also dont know why the teacher set it up as 6X-43=90 instead of 6(90-X). This is my first time solving for both measures, not just one.

[wicked minnow]

This is geometry btw

[naive valley]

to answer the first question, look at the definition of complementary angles

[wicked minnow]

Two angles equal to 90 degrees

[naive valley]

well they sum to 90 degrees

[wicked minnow]

right, so the first X is one of the angles, and the 6X is the second angle?

[naive valley]

6x - 43 is the second angle

"43 less than six times..."

and those two added together needs to be 90

which is x + (6x - 43) = 90

[wicked minnow]

oh

well thanks

i have a test tmr

[naive valley]

gl!

[wicked minnow]

this was the last thing i was a tad confused about

[wicked minnow]

thanks

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[stark fjord]

alr so im trying to wrap my head around acceleration

v(t) graph, the particle would be accelerating whenever its pointing away from the x-axis right (circled in red)? and would those same time intervals also be where its speeding up?

[lunar dawn]

it's acceleration when the derivative at that point is not 0

[weak monolith]

There is an acceleration (i.e., a non-null change in the "v" value the more time goes by) whenever there is a slope on the graph - or, conversly, whenever there isn't a plateau.

[stark fjord]

ah

so its always accelerating except for (6,7) and (8,11)

[weak monolith]

Almost!

[stark fjord]

oh (4,5) missed that one haha

alr that clears things up

appreciate it shaleel, carter

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[lament oracle]

i need help with this

how did the first line turn into the second line?

[tight pier]

domain expansion

[weak monolith]

Whenever you have an expression in the following form :

(x - a)^2

You can transform it as such :

(x - a)(x - a)

And then you can multiply them. Try it out and see if you can figure out the rest!

[lament oracle]

okay i see, but how to get that +8?

[tight pier]

,calc -(-7/2)^2 + 81/4

[ocean seal]

Result:

8

[tacit arch]

Expand

[lament oracle]

im so confused, sorry

[tacit arch]

Use foil

[lament oracle]

What am i doing wrong?

[somber eagle]

Should be -49/4

Since you have a negative out the front

[lament oracle]

ohhhh thank you so much

how did it go from line 1 to line 2?

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[ruby elbow]

Idk what to do

No one else in this server seems to know what to do either

.close

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[rugged hedge]

can you please help me find domain and range of these problems

[pseudo ice]

Have you tried any of them? Do you have an idea of how to do any?

[rugged hedge]

i tried to do the first one

but i got too confused

bc of the double radical

i tjink for all of them the radicals are throwing me off

[raw jetty]

notice how sqrt(x)>=0 no matter what x is

[pseudo ice]

How about we start with one of the other ones, as they seem a bit less painful?

Either f or h

[rugged hedge]

for what number

[rugged hedge]

okay

[raw jetty]

all

[rugged hedge]

can we do f

[rugged hedge]

ohhhh

[raw jetty]

sure, for sqrt(x) to be real, x>=0 right?

[rugged hedge]

so if it’s a real number it will be >=0

[raw jetty]

yes

[rugged hedge]

and if it’s not it will be >0

how do u determine if its >= or >

[raw jetty]

that meand x^2+5x-6>=0

[rugged hedge]

got it

[raw jetty]

could you find the range for that?

[pseudo ice]

(values of x that satisfy said inequality)

[raw jetty]

actually i feel bad for taking this channel from chartbit lol

[pseudo ice]

Noooo you're fine I like lurking and supporting in the background

[rugged hedge]

i dont tjink i have learnt how to find the range

domain only

[raw jetty]

wait sorry i meant domain

whoops forgive me

[rugged hedge]

it’s okay

wait

can i show u my work

bc i’m kind of confused on what to do..

[raw jetty]

so the points where x^2+5x-6 intersects the x axis is 1 and -6 correct?

[rugged hedge]

yes

[raw jetty]

could you come to the conclusion that for a quadratic equation, the thing between the two roots is either:
positive, so anything outside of that is negative

negative, so anything outside of that is positive

sorry idk how to explain it to you, basically check for some number between -6 and 1, and check if its positive or not

[raw jetty]

try to remember the shape of the parabola, it might help

[rugged hedge]

okay got it

thank you so much

i will ask my teacher for some help on the others so dw ab it

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[main basin]

What does this mean by the quadraics of a

[gray isle]

you'd consider something of the form
$$a\red{x}^2 + b\red{x} + c$$
to be a quadratic in $\red{x}$
$$a(\red{\this})^2 + b(\red{\this}) + c$$
would be a quadratic in $\red{\this}$

[ocean seal]

ℝαμOmeganato5

[gray isle]

pretty much the variable you're considering with the squared and linear terms
and everything else are consired as constants/coefficients

[lavish turtle]

Yes

[main basin]

but how do we form that to ax^2 + bx + c when there is a whole like a^2+b^2+c^2-ab-bc-ca

and how do we can do the discriminant ?

[lone heart]

@main basin Has your question been resolved?

[main basin]

.close

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[wet magnet]

Can someone help me with 2 i dont udnerstand

[trail jewel]

these questions are bees

[fair parcel]

[trail jewel]

so i think just like try to get both statements to be true

[serene junco]

🐝 ?

[trail jewel]

if both statements cant be tru at the same a value then a cant be any number

but if it uses or then only 1 of them needs to be true

bees = 🇧🇸

aparently

but i just use it

[serene junco]

These questions are great. I'm curious what book this is

[trail jewel]

'bs' i mean

[fair parcel]

All question went above my head

No matter how many times I read it

[trail jewel]

lol

it uses and or and if/then statements

[wet magnet]

Wait

How do i reason for f

And e

[trail jewel]

if 1st condition true then 2nd condition treu

otherwise if 1st condition false then second condition dont matter wether true or false

[serene junco]

in other words, if the condition is false, then the conditional statement is true no matter what

if "P" is always false, then "if P then Q" is always true

[wet magnet]

So if p is false q can be anything

[serene junco]

if p is always false, then yes

[trail jewel]

yes

[wet magnet]

So q can then be a= 7 or any other number

[trail jewel]

and unless it says 'if and only if p then q', but thats a different condition

[wet magnet]

What does that mean

[trail jewel]

if p true then q true, otherwiseif p false then q false too

'if and only if' pretty much spells it out

but u probablly will learn that later

[wet magnet]

Okay thanks i thinks its a bit clearer

[trail jewel]

or u wont cuz it's self explanatory

nice

[wet magnet]

thanks for the help man

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[serene junco]

what is the title and author of this book? if you don't mind

aw man

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[worthy vigil]

So I'm developing a new method for N. betae detection in beetroot seeds. The old method is the WA method, the new method is the PCR method. The main reason for developing the PCR method is because the WA method is unreliable. As the PCR method is not validated yet, I'm also using a third ITS method which gives guaranteed right results (but is too expensive to use for normal sampling).
I want to test the performance of the PCR method compared to the WA method to see if there's a significant difference between the two and to check which one is better by comparing it to the ITS method results.
The results of 80 samples for each of the three methods have been obtained. I was thinking of using a chi-square test and p-value test to determine the significance of the difference between the WA and PCR method, but I'm not sure how to go about this as I can only find examples of comparisons between two scores and I wondered how the ITS results would fit into this calculation.

[sour mica]

imo, the better way is to create a confusion matrix with ITS results as base truth values and computing the relevant scores for both WA and PCR methods
https://en.wikipedia.org/wiki/Confusion_matrix

you might want to reference relevant papers in your domain to check which metrics are relevant in your case

[worthy vigil]

hm alright ill look into this thanks

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[worthy vigil]

.reopen

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✅

[worthy vigil]

I've taken a quick look at the confusion matrix but it seems that its for calculating one method instead of two in comparison to the validated method

[sour mica]

yes. You are supposed to evaluate if some method (WA or PCR) is good enough wrt the other method/base case (or in your case, ITS)

then you can check if PCR performs better (e.g. if the False Positives/Negatives are fewer, True Positives are correct and so on)

[worthy vigil]

so id need to calculate them seperately by comparing them to the ITS method, but how do i then see if the difference is significant or not

in terms of comparing WA and PCR

[sour mica]

difference is significant or not
that is entirely up to your discretion and/or the prevalent standards of academia/industry. Any marginal betterment is also considered good in academia

[worthy vigil]

so theres no way to then determine significant difference like in the p-value test?

[sour mica]

Best way to demonstrate if your method is better is to show that WA has a higher rate of detecting False values than your method

[worthy vigil]

hm as theres no standards for significant difference its going to be up to my discretion then which i dont really like as its hard to defend an opinion 🤔

[sour mica]

If you wait, someone else might have a better suggestion for you

[worthy vigil]

alright

[sour mica]

I mean these metrics give you a number, which you can see as score(PCR) > score(WA). The only thing up to you is how much of the difference is enough for you to declare the method as definitively better. You can still show which method performs better

[worthy vigil]

maybe im thinking the wrong way here but i wanted to first see if theres a significant difference between the two methods and then determine accuracy afterwards

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@worthy vigil Has your question been resolved?

[worthy vigil]

should i perhaps do a chi-square test and p-value test first on just the WA and PCR method, to test for a significant difference between the two methods. then test with a confusion matrix which one is more accurate?

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[torpid dirge]

Show there exist no retraction from X=R3 to A, where A is any subspace homeomorphic to S1.

[torpid dirge]

how do i start this question, what do i have to do to show to a retraction can't exist?

hi sloth!

yes it is

how does them having different homology groups imply no retraction can exist?

is there a theorem about it?

because any space has a retract to a point but can have a different homology to a point right?

this is retraction not deformation retraction

its hatcher pg 39, 1.1.16

whats the theorem?

no but same issue, why does two spaces having a different fundamental group imply there cannot be a retraction from one to the other?

like all spaces have a retract to a point

but S1 clearly has a different fundamental group than a point

i thought all spaces could?

its just that they can't deformation retract to it

so

retraction preserves fundamental group and homotopy groups?

no theorem about it?

i see

well i understand it intuitively so ill go with that for now

thank you

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[keen plinth]

this is only for homotopy btw

what on earth is that edit

you can definitely inject 0 into Z

Z cant be injected into 0

[keen plinth]

ig the same proof works for homology

[torpid dirge]

hiiiii

hi snow sloth

[keen plinth]

if this is from the fundamental group chapter, thats enough

idk where you got this problem from

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[snow bear]

r

[snow bear]

why

when i move y left or right answer different

[forest marsh]

What is 2y - 7y ?

[snow bear]

when i move Y left, answer is negative

when i move Y right, answer is positive

• and + answer

i dont know why

[forest marsh]

Theres no difference between first and last lines

Multiply by -1

And you have the same thing

[snow bear]

3,9 and -3,9 is difference

[forest marsh]

So

You have in the first line -5y = something

And in the last

You have 5y = -something

[snow bear]

y = -3,9 and y = 3,9 is both right?

[forest marsh]

Without the context of equation yes it is

[forest marsh]

?

You have 5y = 19.5 in the last

[snow bear]

when y = -3.9 or y = 3.9 is it the same or what?

[snow bear]

1y = 3,9 or -3,9

[forest marsh]

You don't have the negative sol

Solve the two equations

[snow bear]

okay i understand

[forest marsh]

y = 3.9 cuz the only difference between 1st and last equation is that you mulitply by -1 on both sides which change absolutely nothing to the result

[snow bear]

so when i moving x left answer changes

[forest marsh]

Youre doing it wrong on the second time

Its -2x

Not 2x

And its -18

Not +18

[snow bear]

okay i understand

[forest marsh]

So youre supposed to have -5x = -25

So x = 5

Once again

[snow bear]

This okay?

[forest marsh]

Oula

Wait

Then there is no solutions

Since 0 is different than -23

Erase the two last lines

Never write a division by zero

[snow bear]

Good

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[devout creek]

I'm using Gaussian method on this Matrice, to find x1, x2, x3.
It's the first time I get the answers in fractions, so I don't know if it is done right

Does this look somehow right? 😵‍💫

[tight pier]

yes vegeta

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[alpine sable]

can anyone explain this to me

[lone heart]

@alpine sable Has your question been resolved?

[unkempt harness]

I don't understand doctor' handwriting.

[alpine sable]

lol

wait

do you understand this?

@unkempt harness

[unkempt harness]

what is (x_1-x_2)(x_1+x_2)=0
x_1=x_2,-x_2
[______]
2 images, hence not ome-ome?

[alpine sable]

ONE ONE

[unkempt harness]

or is that θme-θme

[alpine sable]

ONE-ONE

injectivity

[unkempt harness]

I think it should be correct as long as x≠0

[alpine sable]

bruh

[alpine sable]

i think you have not studied this thing

[alpine sable]

actually it can be equal to 0 too

i got it, found my mistake

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[fallow socket]

I have no idea how any of this works

[tacit arch]

start here:
https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/a/review-summation-notation

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[thin saffron]

how do you do this??? i dont understand

[azure needle]

Have you learned sine rule

[thin saffron]

yea sina/a=sinb/b=sinc/c

[tardy stag]

can you apply it here?

[thin saffron]

how thought like "sin60/18=sinabc/20"??

[tardy stag]

ye

[thin saffron]

what does angle abc mean??

[thin saffron]

ohh ok that what i was confused about

thanks

so i do 20*sin60/18?? as the reverse to find angle abc?

[tardy stag]

i suppose so yes

[cerulean crescent]

angle abc is arcsin(5/3*sqrt(3))

[tardy stag]

there are actually two possibilities

[cerulean crescent]

https://tenor.com/view/batman-thinking-thinking-about-you-think-thinking-of-you-gif-20503421

[tardy stag]

arcsin is not the inverse of sine ;)

[cerulean crescent]

it is

[lone heart]

@thin saffron Has your question been resolved?

[pseudo ice]

There’s an important caveat to that though…

[cerulean crescent]

what?

[lunar dawn]

yeah yeah, domain range restrictions bla bla it's the inverse

[pseudo ice]

,w arcsin(sin(pi))

[ocean seal]

Results provided by WolframAlpha

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Requested by chartbit

[pseudo ice]

It’s only inverse when sin is between -pi/2 and pi/2 inclusive, using arcsin gets you one possibility but you then need to find the other ones

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[night jackal]

im kinda confused on how it wouldn't be -74/5. i even went on desmos and it doesn't appear to be wrong. on top of that, im honestly not sure what goes in those red boxes to the left lol

[hushed locust]

each of the different segments/sub-definitions of f(x) will be used for the different sided limits

they are asking you for the relevant part of the function

[night jackal]

so i shouldnt be plugging 3 into that bottom function?

[lone heart]

@night jackal Has your question been resolved?

[night jackal]

im also p confused on this part. not sure where to go after x^2 gets introduced

[waxen flame]

The next step says to multiply through the inequality by x^2.

-1 * x^2 and 1 * x^2

[night jackal]

ohhhh

appreciate that

[night jackal]

would u happen to also know abt this one as well ? @waxen flame

[waxen flame]

For the boxes on the left, they just want you to enter the expression that corresponds with the appropriate interval.

As far as -74/5, that should be correct. You may want to ask your teacher about that one. It's entirely possible the website has the wrong answer set for that question.

[night jackal]

oh when i filled in the rest, -74/5 turned green

[waxen flame]

Weird that it was fine for the first one. 🙂

[night jackal]

fr

thanks for the help man!

[waxen flame]

yw

[night jackal]

.close

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[novel remnant]

How do I do this one?

[winter light]

You shall multiply numerator and denominator by 4

[fickle musk]

4

its a standard limit

sinx/x is 1 when x approaches 0

a good question i did recently was

floor(sinx/x) X->0

and the reciprocal of it

[novel remnant]

I have no context for that haha😅

Why do we multiply by 4?

To get rid of the sin?

[fickle musk]

its a derived result

[tacit arch]

https://www.youtube.com/watch?v=l22G37FOn7I

[fickle musk]

see how they almost are similar in neighbourhood of 0

as they approach 0

[static bobcat]

proof by graph

we love that

[fickle musk]

real

i mean y=x is tangent to sin x at origin

[novel remnant]

Where does the 4 takes play in the graph🫠

Hold on I’ll watch the video

[fickle musk]

it doesnt

u make the bootom x 4

so u get the same x form

and u need to multiply 4 above

basically manipulate the limit to ur needs

[static bobcat]

let us know once ure done

[novel remnant]

I feel like I need hours of context to understand that video where tf did circles and triangles come from🫠

[fickle musk]

what do u

know in math

so far?

[novel remnant]

I’ll give up on the proof lol I just want to know what is the action of multiplying by 4 doing

[static bobcat]

thats fair

[novel remnant]

I finished a precal course and I just started calculus

[fickle musk]

i mean at least watch that

i guess

and see if u find something useful

[fickle musk]

hmm

[novel remnant]

I can’t comprehend what’s happening tbh, that looks nothing like the sin graph I know

[static bobcat]

do u know the joke that sinx=x

[novel remnant]

Nope haha

[fickle musk]

sinx is always like that unless u multiply

factors

with or smth

[novel remnant]

Yes this so the triangles don’t look anything like that

It’s all straight lines

Besides the circle

[static bobcat]

honestly just take a graphical view

[fickle musk]

just think that

[static bobcat]

here, around 0, what do u notice?

[fickle musk]

as sin x

and x

approach 0

both are very similar

and we know that similar/similar = 1

for ur understanding

[novel remnant]

Ohhh okay that makes sense when you put it that way

[fickle musk]

remember than

for tanx /x its similar

but there is a difference here that

in nbd of 0

tan x >x

[novel remnant]

But if you multiply these by 4 don’t you get 16/4

Which isn’t similar

[fickle musk]

but sinx < x

so if u see floor function

pay attention

[static bobcat]

u do that for this

[fickle musk]

umm

[novel remnant]

What does floor mean

[fickle musk]

no?

[static bobcat]

we want it in sin(u)/u form

let 4x=u in this case

[fickle musk]

didnt u say u took precalculus

[novel remnant]

Wait when you multiply sin 4x by 4 what do you get

Not sin 16x?

[static bobcat]

4sin(4x)

no

[novel remnant]

I didn’t hear that word once there idk

[sleek nest]

can someone go to my help channel i just wanna see if i did things right

[fickle musk]

no?

sin is a function

which when taking 4x parameter gives output to a value

u are multiplying 4 to the value essentially not to the parameter

unless u are changing the definiton of x

[novel remnant]

Ohh, you multiply the result of 4x?

Like after the function does its thing

That’s when you apply the times 4?

[fickle musk]

ywa

u are essentially doing that

[novel remnant]

I see so basically to get 4x on the bottom you multiply by 4 so then you have it both on top and bottom

[novel remnant]

And then you cancel them out?

[fickle musk]

yup same form

[fickle musk]

not cancel

use the standard result

[novel remnant]

How do I take the sin of 4x

Or do I plug 0

[fickle musk]

wait

credit to chatgpt

[novel remnant]

You use the known limit so you don’t have to prove another one?

[fickle musk]

yes

always

there are certain u need to memorise

[static bobcat]

or just cheat ur way (falsely) with lhopital rule

not falsely but yeah it insights circular reasoning

[novel remnant]

What’s lhopital

[static bobcat]

dont worry about it right now

after uve done derivatives return to it

[novel remnant]

I got lost at step 3

Since u equals 4x then we have x equals u over 4?

U equals 4x cuz of the previous line but how does x equal u over 4

[fickle musk]

umm u = 4x

divide both side by 4

u/4 =x

i think u might wanna revisit pre calc a lil more before derivative and integrals

[novel remnant]

Why do you divide both sides by 4??

[novel remnant]

We learned none of this in precal

[fickle musk]

i am pretty sure

they taught

linear equations

[novel remnant]

Not with sin

[fickle musk]

are u stuck at that step 3

when we have sin u/(u/4)?

[novel remnant]

Ohh you divide both sides by 4 to isolate the x??

Why this time the action does affect the 4x??

When you multiply by 4 it stays 4x but when you divide by 4 suddenly it can be divided

I thought you only divide the result after taking the sin

Wait no it didn’t affect the 4x

It affected the 4 that was before the sin

So the point of multiplying it by 4 in the first place was only so you can divide it by 4 afterwards after adding that other function so that that function’s denominator would be u over 4???

What are we even solving for anymore I’m so lost

For u for x for the limit what’s going on

Then I have this too

And this

[fickle musk]

i think u need to ask ur teacher to help u

if u are having troubles like that

[lone heart]

@novel remnant Has your question been resolved?

[novel remnant]

He sucks thats why im here

He doesn’t explain anything, he just goes over the material and explains stuff assuming we have context

Can you tell me the answers for the last two I gave up on trying to understand this

[novel remnant]

<@&286206848099549185>

[rustic coral]

Both of these rely on the common limit $\lim_{\theta \to 0} \frac{\sin \theta}{\theta}=1$

[ocean seal]

Civil Service Pigeon

[rustic coral]

Proof here: https://math.stackexchange.com/questions/907362/why-the-limit-of-frac-sinxx-as-x-approaches-0-is-1

[rustic coral]

For this one, consider rewriting the limit as a product

[rustic coral]

For this one, use the ||sine double angle formula on the numerator||

[novel remnant]

I have no context to any of this

No idea what all of that means, I just want the answers please🫠

I ended up not understanding the simple one so I’m definitely not understanding the later two

[novel remnant]

<@&286206848099549185>

[slender forge]

the proof for this is sick

[novel remnant]

Can you tell me the answers please lol

[slender forge]

im working on it 😛

[slender forge]

is it both these

[novel remnant]

Yes the last two

[slender forge]

excuse my terrific handwriting btw

[novel remnant]

I have no context to any of that tho like I’ll need to ask tons of stuff to understand what’s going on

So I gave up

[novel remnant]

I didn’t even understand the simple one

[novel remnant]

This one

I don’t get this

[slender forge]

small angle approximation gives sin(x) = x, so you have 4x/x = 4

its not harder than that

this is standard for limits and continuity problems

[novel remnant]

Is that an alpha or a zero

[slender forge]

what the other ones wrote is just unnecessary info for this problem, but really good to know

[slender forge]

doesnt matter

its a constant

[novel remnant]

I feel so confused after all of that

[slender forge]

its very interesting math so read up on it. but for now you can ignore it

[novel remnant]

You need to know radius for this??

The professor never said anything about tadius

I can’t believe I’m paying over a grand for that useless professor

[slender forge]

writing in radians is so much easier than in angles since theres always a chance for the answer to be a fraction

and radians are much easier to calculate with

[novel remnant]

Oh it’s radians

[slender forge]

yeah

its habit for me sorry

i cant remember the last time i wrote in angles

[novel remnant]

No the professor said anyway that we have to use radians

He said no more angles lol

But if I tried to understand now how th 1 over x squared got us infinity it’d take hours and destroy my brain

[slender forge]

professor?

ive never heard of angles being used in a high level maths class

[novel remnant]

We got to use it in precal

Cal1 now it’s gone lol

[lone heart]

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[alpine sable]

HI

[alpine sable]

so my problem is this:

and my approach was, if that set exist then in order to prove it we should use the subset scheme axiom

so, we start searching for the least set which we can take the elements and does not assume analitically the set we are trying to show existence (for example, thinking in the set of all functions + some relations wont work because it is assuming the existence of the set of all functions)
so for this search in every step I must prove the existence of the least set, and at the end I conclude this requires the existence of the set of all sets , so the set that contains all functions cannot exist.
is this reasoning correct?

(for example the least set which we can apply the subset axiom for the set that contains all functions is the set that contains all relations and so on)

[sour verge]

If you assume that this set of all functions exists, then using the subset axiom you can restrict this set to show the existence of some subset (with a well chosen predicate) which is more or less equivalent to the set of all sets.

I'm not sure about going one step above, since I feel like you're trying to make the set of all functions into the comprehension of some other set (especially in your last line). The set f is already big enough to create problems on its own.

[alpine sable]

oh thanks, I will check that way

[alpine sable]

that's what I was thinking at the beginning , but since I could not find that especial subsub set, I tryied the other way.
but I will search for that

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[lone heart]

@wind zephyr Has your question been resolved?

[wind zephyr]

.close

[lone heart]

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[tulip marsh]

Can someone explain how to do part a?
I got it into ref & got the corresponding column vectors but I’m struggling with getting the basis

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[tulip marsh]

.close

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[cinder sundial]

Bull!

[cinder sundial]

Mickey!

Given <a_n> is an arithmetic sequence

Minnie is Mickey dressing like a girl

[cinder sundial]

And 0<a_1<2, a_3=4

Let b_n=2^(a_n)

Is (b_2) >4, true

Am I wrong

Why?

Mickey Mouse!

Mickey Mouse!

Free Mickey Mouse!

Let me do the reasoning

<a_n> is a sequence in ascending order

[vapid shuttle]

Free him ⚔️⚔️

[buoyant saddle]

preach

[cinder sundial]

Hence b_3 should be bigger than b_2. Because they are both possess a base number of 2 but the former has a bigger index

That implies b_3 > b_2

I see my wrong

My flaw

My ignorance

[buoyant saddle]

you’re welcome

glad to help

[cinder sundial]

Thank you lord Mickey for once again guiding me towards the truth.

[warped marlin]

i found it, but you gotta follow step by stp

since b2 = 2 ^ a2

lets first find a2

[cinder sundial]

Do you agree with my statement

[cinder sundial]

^

[warped marlin]

no no, i dont agree, what :p