help-4

[scenic peak]

Right

[tidal moat]

good bit of learning

[scenic peak]

Oop

Yeah sorry, shoudl have had you convert back

Apologies

[tidal moat]

Don't worry about it, I understood that already.

[tidal moat]

https://tenor.com/view/moral-orel-gif-10405045364257293995

[tidal moat]

https://tenor.com/view/moral-orel-clay-puppington-goodbye-slam-door-door-shut-gif-23642600

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[midnight pier]

how exactly does row space correspond with the orthogonal complement

[midnight pier]

i know that given a span of vectors, the orthogonal complement is the null space of the matrix where the vectors are rows

is it just "they work the same matrix where the vectors are rows"

[stark wedge]

essentially yes

[midnight pier]

amazing

that's all I had, writing it out helped me solve it lol

thanks for the confirmation

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[solar flax]

need help idk how to figure which one is smaller like is it 0.008 or 0.304 i know they r dumb question but i really need help to work on my basics for igcse exam

[tidal terrace]

write them as a fraction with the same denominator
would help make it easy to compare

[solar flax]

ill give it a try

304/100 , 20/100 , 8/100 , 57/100

now should i write them sequence wise

[tidal terrace]

0.304 is not 304/100 check again

[solar flax]

30.4/100

[stark wedge]

304/1000

like you're formally right in that 0.304 does equal 30.4/100 but it's a bit silly to only put it over a denominator of 100 since you're still left with a decimal

[solar flax]

then i have to multiply with 1000 to all

ill do it agian

again*

[stark wedge]

you don't "have to" but it can help.

[solar flax]

so 0.008 , 0.2 , 0.304 , 0.57

Is this ans??

[stark wedge]

0.008 < 0.2 < 0.304 < 0.57 yes that's correct

[solar flax]

ok thank bro 🫡 🙃

[stark wedge]

please don't call me "bro"!

[solar flax]

sis

[stark wedge]

... that's better, i guess.

[solar flax]

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[orchid thistle]

hello quick question
x²-1≠0
Is x≠±1?
If it does, in the domain and range part do we write
{x|x≠±1}?

[orchid thistle]

Only a yes or no if possible

[frozen ledge]

!xy

[vale dock]

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.

[frozen ledge]

i’m assuming you have some rational function?

[orchid thistle]

yes

[frozen ledge]

with x^2 - 1 in the denominator

[orchid thistle]

smth like 1/(x²-1)

[frozen ledge]

then yes unless otherwise stated through some piecewise definition where they assign a value at x = 1 or x = -1 then it would be excluded from the domain

[orchid thistle]

;-;

tyvm

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[frozen ledge]

you’re welcome

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[river shale]

not equal

[frank salmon]

Its the thing wich define the order of numbers in R or a set of variable in R

[stark wedge]

like an equation but the equals sign is instead one of > < ≥ ≤

[frank salmon]

Dont we learn inequalities in first grade?

Oooh

I usually imagine any inequality like a function and we need to know at what values x the function will be positive or negative

[frank salmon]

Math jokes never gets old

[stark wedge]

!xy

[vale dock]

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.

[frank salmon]

1.77

[stark wedge]

do you want approximate or exact

[frank salmon]

Wdym exact?

Bro

[stark wedge]

also what does it have to do with the last question about ineqs

[stark wedge]

exact means exact

[frank salmon]

You cant

[stark wedge]

like without any decimal approximations

[frank salmon]

Its an irrational

[stark wedge]

and indeed i was gonna say sqrt(pi) is just sqrt(pi)

[frank salmon]

You’re a genius ig

[stark wedge]

.

[frank salmon]

You forgot the close word

[stark wedge]

i wasn't gonna close

[frank salmon]

Ph

Oh

[stark wedge]

this was just a "..." but shorter

@silver thistle are you just asking random shit that comes into your mind or what.

don't

[river shale]

just go #discussion for these

They are willling to answer u

close the channel 🙂

[stark wedge]

type .close

[frank salmon]

[stark wedge]

....................

well now you're sounding like a troll.

<@&268886789983436800>

[river sequoia]

And a liar

[fresh hare]

ok

[river shale]

.close

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[river shale]

Weird.....

[frank salmon]

.close

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[gaunt fog]

HELP

[gaunt fog]

A

HELLO EVERYONE

HOW TO ANSWER D

JUST to standard form

[river shale]

what is D

[gaunt fog]

in exercises

d.

[river shale]

oh, d

[distant pulsar]

you don’t

[gaunt fog]

i know

but just want the

standard form

how u put it on standard form

i only got to expand the left haand side

and no idea what to do next

should i divide both sides by x

ok actually i have no idea how to do tht

[stark wedge]

hold on a minute

d is an impostor

it can't be expressed as a quadratic

[jovial edge]

I believe the question is not supposed to be x(x+4)=12/x, no way we can get quadratic equation from this

,w x(x+4)=12/x

[lone furnace]

teacher trolling

[rocky lotus]

Results provided by WolframAlpha

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

Requested by yobi_fx.

[earnest ingot]

It might have been x+4 = 12/x, since that has nice roots

[eternal osprey]

You can try to find the cubic equation, and look at the factorization of 12 for possible easy solution.

[lone furnace]

@eternal osprey i dont think this can be factorised nicely.

[eternal osprey]

Yeah, just realized

[lone furnace]

plus there is most definitely a cubic root there

[vale dock]

@gaunt fog Has your question been resolved?

[gaunt fog]

how

tell me

[stark wedge]

tell you what

did you mean: "how can it happen that this thing can't be expressed as a quadratic?"

multiplying by x gives x^2(x+4) = 12 which becomes x^3 + 4x^2 = 12

and this is a cubic

and it does not have any nice roots to knock down the degree

@gaunt fog does this answer your question?

[gaunt fog]

what

i expanded mine

so its x2 + 4x = 12 over x

i dont get it

[stark wedge]

x^2 + 4x = 12/x

this is not quadratic

@gaunt fog i feel like we are speaking over each other, and at least one of us is not hearing or not listening to the other.

$x^2 + 4x = \frac{12}{x}$ is not a quadratic equation. you can't have division by $x$ in a quadratic equation.

[rocky lotus]

Ann

[gaunt fog]

so

how u do it

[stark wedge]

you don't.

[gaunt fog]

ye but gotta need atlest

solution

[stark wedge]

you talk to your teacher and say something like "this nice lady on the internet told me this is actually a cubic equation. can you double-check to see if there's any typos in here?"

[gaunt fog]

😦

[vale dock]

@gaunt fog Has your question been resolved?

[swift magnet]

cubics are solvable but definitely more complicated than quadratics

[vale dock]

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[light egret]

Hi! I don't understand what d/dx means. I get it stands for the derivative, but what does it mean? What does that dx is like a infinite small rectangle in a function, but I don't understand what the d above means

[eternal osprey]

d itself has no meaning. Only the whole expression $\frac{\text{d}}{\text{d}x}$ have meaning, which is to derive the following expression.

[rocky lotus]

Xwtek

[light egret]

Oh okay

Weird

[stark wedge]

yeah dont question it

[eternal osprey]

Well, there is a justification, but that involves advanced calculus.

[stark wedge]

sometimes math notation has some historical relics/fossils

[light egret]

So does the dx still mean the infite small rectangle in this expression or not?

[eternal osprey]

$\text{d}x$ just means that we operate the derivative/integration on the variable $x$

[rocky lotus]

Xwtek

[light egret]

okay

I think I get it more or less

thank you

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[light egret]

Hello, it is me again. Which integration techniques do I need (to know) to solve this?

[light egret]

hi, this channel is occupied please post somewhere else

[vagrant ether]

Do you know how to integrate 1/x ?

[light egret]

yes

hold on

[vagrant ether]

Can you see wat you need to do ?

[pastel oyster]

which one

[light egret]

never mind, I dont know how to

[light egret]

help 14 for example

anything in math (available)

[vagrant ether]

If u split it up into two fractions

Because it’s one denominator

[light egret]

I don't understand what you mean, do you mean that the x becomes x^-1?

Oh no I understand

[vagrant ether]

Nice

[light egret]

So I make the integral of 1/x + 3. 4thsqrt(x)/x?

[vagrant ether]

Yeah

[light egret]

ok i got it thank you!

.close

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[gaunt fog]

Sur

[gaunt fog]

What is that move called

Never heard of that before

Like where u multiply the denominator

Of 12

And why we do that anyways

[tidal swift]

because we want all the x on one side

[turbid valve]

Even simpler than that

[drowsy kraken]

Are u taught cubic equations??

[turbid valve]

The way I describe it is, you wanna avoid handling fractions in your arithmetic if you can avoid it

Multiplying through by the denominator means you no longer have to deal with a fraction

Algebraically speaking there's nothing more to it than that

[drowsy kraken]

U can find roots to the cubic question

But there will be 3 factors

Instead of 2 like there is in quadratic

By chance do u have answers to the questions

[vale dock]

@gaunt fog Has your question been resolved?

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[midnight pier]

Uh

So

Anyone gonna help ?

[icy sigil]

What's the question

This is just a circle equation?

What is this

@midnight pier

[midnight pier]

Wtf

Why isn't it laoding

Its like

H=-g/2

K=-f/2

[icy sigil]

What is f and g

[midnight pier]

Centre ?

U don't know the equation

[icy sigil]

The centre is h and k and it's (2,4)

Wdym f and g is the center

[midnight pier]

X²+y²+2gx+2fy+k=0 ?

[icy sigil]

Ah

[midnight pier]

I figured this one out but idk what k is.

Only radius is given

[icy sigil]

I learned it differently I get what you mean now

[midnight pier]

And if I have to find out k using Centre like substituting radius

It'll be pain in ass

[icy sigil]

Okay so g and f is not the center

[midnight pier]

They are

But

H=2g

Where as k=2f

It's like

To find k

We have to divide g/2

So I wana take this h and k to g I have to multiply by 2

[icy sigil]

What is the question

[midnight pier]

To find equationb

[icy sigil]

That's what I am not understanding

[midnight pier]

Having centre _2,4

And radius 4

[icy sigil]

Do you know expansion of (a-b)²

[midnight pier]

Yes

A²+2ab+b²

[icy sigil]

That's all you have to do then join like terms

[icy sigil]

-2ab*

[midnight pier]

But I need k aswell

[midnight pier]

Forgot k ?

[icy sigil]

When you join like terms you will get k

It's the term with no x or y

[midnight pier]

Wdym

Like u mean

Since I have radius

Do I

R=root underg²+f²+k

-k

And

Just

U know

Value here and there

[icy sigil]

When you expand (x-h)²+(y-k)² you'll get x², y², -2hx, -2ky, h² and k² terms

[midnight pier]

Bor

[icy sigil]

Since h² and k² are just numbers you can join them together

[midnight pier]

But

The k is constant

K is c here

[midnight pier]

This k is constant

[icy sigil]

Bro

Yes

It is constant

[midnight pier]

I don't have constant

I only centre

And radius

[icy sigil]

Do you know how to turn (x-h)²+(y-k)²=r² into x²+y²-2gx-2hy+k=0

[midnight pier]

+c

It's not k

Irs c

X²+y²-2gx-2fy+c=0

[icy sigil]

Same thing, it's just a different name

Do you know how to turn it into that

[midnight pier]

Hes

[icy sigil]

Because if you do you'll get c after the process

[midnight pier]

Using whole square gormula

(A+b)²

[icy sigil]

What is your question again?? You want to find the x²+y²-2gx-2fy+c=0 equation for that specific circle right

[midnight pier]

Yes

[icy sigil]

Okay so. You have (x-2)²+(y-4)² = 4² right

What is (x-2)²

[midnight pier]

Thanks

.close

[vale dock]

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[icy sigil]

Okay, then you just do the same for y-4

And then subtract 4² from both sides

Np

[midnight pier]

Bro.

.close

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[somber flicker]

@glass kelp here

[somber flicker]

?

[glass kelp]

Post your problme.

[red tulip]

What do you need help with

[lyric sundial]

Here is ok, yes

[somber flicker]

evaluating functions

[lyric sundial]

???

[red tulip]

Whats the function

[noble coral]

What is the function

[somber flicker]

here sorry for ur time

[red tulip]

You insert -2/3 for x

[lyric sundial]

Would you be able to calculate f(0)?

[noble coral]

I mean just replace x with -2/3

And add

[somber flicker]

okay imma try

okay I wrote -2/3 + 2 (-2/3)

is that correct?

[red tulip]

-2/3 squared

[somber flicker]

okay I wrote it na

the suqared

squared

[red tulip]

Yes now you can evaluate it

[somber flicker]

how do I do that with "/"

[red tulip]

Its a fraction so you just multiply -2/3 by -2/3

Numerators multiply together and denominators multiply together

[somber flicker]

ah okay

[lyric sundial]

,rccw

[lyric sundial]

Never forget brackets! @somber flicker

[red tulip]

I was waiting for him to accidentally make the square negative lol

[somber flicker]

is it 4/9

[lyric sundial]

Yep good 👍

[somber flicker]

how do I multiply 2(-2/3)

I suck at math sorry

[lyric sundial]

The exact same way you multiplied (-2/3)•(-2/3)

[final adder]

take 2 as 2/1

[somber flicker]

bear with me uhm is it -4/6

[final adder]

close!

if you take 2 as 2/1, the denominator gets multiplied by 1, not 2

[somber flicker]

owh

and what would it be?

[final adder]

well you would have $\frac{2}{1}\cdot\frac{-2}{3}$

[rocky lotus]

Frances

[final adder]

so therefore you get...?

[somber flicker]

2 and -6

am I right

[final adder]

what would the new numerator be? (its the product of the two numerators)

[somber flicker]

it would be 2 over 1 and -6 over 1

?

Bear with me😭

[final adder]

ok wait how are you getting that?

[somber flicker]

idk too tbh

[final adder]

when you multiply fractions, say $\frac{a}{b}\cdot\frac{c}{d}$, you get $\frac{ac}{bd}$

[rocky lotus]

Frances

[somber flicker]

owhhh

[final adder]

thats like a general formula

[somber flicker]

so it would be 4/9 over 2/-6

?

[final adder]

in this formula, you take a=2, b=1, c=-2, d=3 right

if you plug in the values of the original equation

so what would be ac/bd?

[somber flicker]

2,-2 and 1,3

?😭

[final adder]

yeah, now multiply the pairs together

(because ac is just shorthand for a * c)

[somber flicker]

so it would be 3-6

?

and answer would be 3?

No i mean

2

and -6

?

[final adder]

how did you do (-2/3)*(-2/3)?

bc that part was correct

you just apply the same logic here

[somber flicker]

4 and 9?

[final adder]

but how did you do it? how did you get 4 and 9?

[somber flicker]

ok lemme write it in a formal way I think it might be the best for me wait...

wait...

[final adder]

mhm take your time

[final adder]

yep thats right!

[somber flicker]

tyy

soooooo muchhhhhh

🥹🥹

[final adder]

mhm no problem!

@somber flicker dont forget to close this when you're done!

[somber flicker]

how do I close

Im new here

[final adder]

just type .close

[somber flicker]

oh alr

.close

[vale dock]

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[alpine island]

im getting 8 and -8

but ans is 8

why not -8?

nvm got it

.close

[vale dock]

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[lime bone]

I'm baffled that people here do not allow robot being put on used to solve math questions. May I ask why?

[river shale]

[final adder]

like chatgpt?

[sleek nebula]

[lime bone]

yes

[final adder]

their math skills are...

interesting

[stark wedge]

!nogpt

[vale dock]

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).

[sleek nebula]

inaccurate + bad

• misleading at times

[stark wedge]

you cannot trust AI to do math correctly

[lime bone]

I mean they are advertised as capable of math.

[sleek nebula]

advertised \neq good at

[river shale]

Nope

[stark wedge]

and viagra is advertised as giving you a 24 hour long erection, so?

[final adder]

i would say thats false advertising then

[sleek nebula]

ann what

[stark wedge]

(i don't know if they actually advertise it that way)

(but i deliberately went for an exaggeration)

[safe fulcrum]

woah Ann

[sleek nebula]

i was going to sleep in 2 minutes and then saw ann message

[safe fulcrum]

I wouldn't trust it
GPT doesn't understand what it's saying, that's the problem
everything it knows is based on processing the reasoning made by actual humans (so GPT doesn't know how to reason by itself, cause it literally can't)
the thing is that maths is like a stack of bricks
if you learn one thing incorrectly, suddenly everything above that brick needs to be relearned

that's why I'm trying to get you to move away from using GPT whenever you don't understand something in maths
cause it's the people who know the least that get tricked the most by GPT

[craggy girder]

most gpts are made to be able to predict the next token (or letter)
they can only reproduce what is already fed to them or like take diff ideas and display them together

[sleek nebula]

but hope that answers your qn @lime bone

[craggy girder]

this is why its dangerous to use it for maths as they dont know what is going on, they just see that after this token most ppl use this token so they do too
they are not trying to solve your problem

[final adder]

they also may give you a response that "sounds correct" but in reality its just a bunch of bs

[safe fulcrum]

#help-22 message

here's an instance where I was helping someone after they used GPT

as you can see, GPT did steps 1, 2, 3, 4 correctly

[distant pulsar]

in this context, the people are students

there are two cases:

• case a: AI is correct
• • student copies ai work and doesn't learn how to do math
• case b: AI is wrong
• • student is confused by wrong answer

[safe fulcrum]

but instead of admitting it couldn't progress past those steps, GPT literally started guessing numbers and arrived at a wrong solution

[distant pulsar]

i've seen some students use ai to learn in a manner i'd consider fairly responsible, so it depends. but discouraging ai tools in general is not a particularly bad idea on the educator's part

[safe fulcrum]

(it said because we assumed r = 5, r^2 = 25 so r = 5)

[final adder]

this is why i use chatgpt when im too lazy for latex (oops) but not for actual math

[safe fulcrum]

that's literally circular reasoning

[limpid raft]

chatGPT often hallucinates esp when asked things about math

[safe fulcrum]

most students who know how to use AI responsibly also know how to properly study and ask questions from actual humans

[limpid raft]

this is why it is against our policy to use to help other people

[distant pulsar]

yes that is definitely true

[limpid raft]

you're welcome to use whatever you'd like in a personal capacity

[safe fulcrum]

our server is based on humans helping other humans

not robots helping robots

[limpid raft]

either way, this is not the intended usage of help channels. if youd like to inquire more about policy, please DM ModMail

[stark wedge]

@lime bone Has your question been resolved?

[lime bone]

yes

[rare dragon]

AI is best way to learn

[lime bone]

I'm convinced to not use AI to solve math questions

[stark wedge]

!nogpt

[vale dock]

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).

[limpid raft]

it absolutely is not, but use whatever you want

[safe fulcrum]

and Ohio is the worst state in existence

[stark wedge]

you got some balls saying this in THIS CONVO of all places

[final adder]

ann's the bot now 😭

[rare dragon]

for the general concept, yes, but for actual problem solving no

[limpid raft]

if you have further questions, DM ModMail

[rare dragon]

AI is bad at math and makes mistakes

[limpid raft]

.close

[vale dock]

Channel closed

Closed by @limpid raft

Use .reopen if this was a mistake.

[rare dragon]

but its good at teaching concept

[vale dock]

Available help channel!

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[wraith lagoon]

i don't understand where to start with the numbers given to me in this problem

[safe fulcrum]

this is the proportions z-test for 1 sample

[wraith lagoon]

is this calculus i've never taken a calculus class in my life

[safe fulcrum]

bruh that's statistics

[wraith lagoon]

what do the numbres n and x mean in the problem though and where do i plug them into this formula

[safe fulcrum]

ah, actually for this problem you don't have p-hat = the proportion that the researchers claim to be true

so we need something else here

[safe fulcrum]

can I see parts b, c, d?

[wraith lagoon]

i can't look at them because i have to answer the first part before the rest show

[safe fulcrum]

oh well the wording of part a is a bit convoluted

in reality they're just asking you for 563/924, as a decimal

[wraith lagoon]

what is that number called

[safe fulcrum]

the question tells you that number is called p

[wraith lagoon]

so the population proportion is equal to x/n

[safe fulcrum]

so the idea behind statistics is, we'll never be able to know the true percentage, cause we can't go and interview all 8 billion people on Earth

[safe fulcrum]

no

[wraith lagoon]

now it wants the margin of error E

[safe fulcrum]

the sample proportion is x/n

[safe fulcrum]

the population proportion is unknown

[wraith lagoon]

thats why its asking for a point estimate drawn from the sample instead of the real number right

[safe fulcrum]

yes, cause we can only get an estimate by interviewing a sample

a point estimate means the answer is just a single number

not a range or anything else

[wraith lagoon]

part b is asking for the value of the margin of error, is that the complement of the confidence level

[safe fulcrum]

okay so it's the 2nd formula in the box

yeah so you can just use p0 = 563/924 here

[wraith lagoon]

what does the 0 mean

[safe fulcrum]

do you recall how H0 means the null hypothesis?

[wraith lagoon]

no

[safe fulcrum]

you sure sound like you've never studied a day of stats in your life

anyways

[wraith lagoon]

this is the first math class ive taken in three years

so that checks out lol

i don't know what the null hypothesis is that sounds like a cool album name but aside from that i'm clueless

i don't think my professor has talked about it

if the 0 is not being used to change the value why is it there

[safe fulcrum]

okay, so in statistics we do a lot of experiments

so like if I want to test if giving a certain medicine will reduce someone's chance of getting brain disease or whatever

we always want to assume that the drug has no effect

cause maybe the patients got better on their own: that's just what happens when you have a large number of patients, through random chance

so you can't assume that the drug is doing the healing

[wraith lagoon]

yeah thats why you use a control group right

[safe fulcrum]

yep!

that's why we need to account for the placebo effect

for one group of people, give them a medicine that does nothing (that's the placebo)

then for the other group, give them the real medicine

then you can see that the medicine is causing the difference in the disease rates

instead of just being related to by coincidence, by correlation

(so correlation does not imply causation: this is what people mean when they say this)

[wraith lagoon]

i understand that

for the margin of error i plugged the numbers into the formula and got 0.000258

which is wrong

then it told me this

i did a question like this earlier with the confidence level of 94% and found za/2

anyways that would be 0.975 which using the table would give me a z score of 1.96

so it would be 1.96 times the square root of p hat and q hat over n

but how do i find p hat and q hat

[safe fulcrum]

ah, you need to multiply by the critical value of z

I actually didn't know what they meant by 'margin of error'

but that formula clears it up

[safe fulcrum]

yep, this part is correct

[safe fulcrum]

so for p you just do 563/924
and q = 1 - p

[wraith lagoon]

so q is the complement of p

[safe fulcrum]

you can use those values, p and q, in place of p-hat and q-hat

[safe fulcrum]

yes, that's just a general naming convention for all of stats

[wraith lagoon]

and n is 924 right

[safe fulcrum]

yep

[safe fulcrum]

maybe try using the exact value 563/924 instead

to avoid rounding errors

[wraith lagoon]

so itd be 1.96 times the square root of 0.000257704545455

[safe fulcrum]

I'm not sure how it's marked oh well

[wraith lagoon]

lol

which is equal to 0.031

wow i did it

[safe fulcrum]

nice!

[wraith lagoon]

ive been on this question for an hour and i have two more chapters to do, this is question 5 of 20

lol

[safe fulcrum]

bad teaching is universal sadly

[wraith lagoon]

once i understand this though i think it'll get easier to do the rest of them

now its asking for the confidence interval

[safe fulcrum]

ofc! yeah it's just about using the right formulas in all honesty

[safe fulcrum]

okay so now this is the easy step

so you have your point estimate 563/924

and then you do (563/924 - margin of error, 563/924 + margin of error)

(lower bound, upper bound)

that's literally it

[wraith lagoon]

and so this interval is estimating the population proportion with the given margin of error at the confidence level of 95%

[safe fulcrum]

yes, cause we specifically used the number from the table, 1.96

which corresponds to a probability area of 95% in the middle

another convention in statistics is that we use the area starting from the left

so middle area = 95%
2 tails = 100% - 95% = 5%, so each tail is 2.5%

then 2.5% + 95% = 97.5% from the left

so yes we needed the z-score = 1.96

[wraith lagoon]

i tried doing this one on my own and i messed up the margin of error

so 99% confidence would be 1 + 0.99 / 2 to equal the area

i think i got the z score wrong and found the z score for 0.9995 instead of 0.995

i hate this chart lol

so the z score is 2.58 then i think

[safe fulcrum]

,w z score 2.58

[rocky lotus]

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Requested by sooouth.

[wraith lagoon]

which would mean the margin of error is 0.026 when rounded to thre decimal points

[safe fulcrum]

yep so that's the right z-value

yeah and then it's the same steps as part b in the previous question

you got this bro!

[wraith lagoon]

i learn pretty quick huh check me out

[safe fulcrum]

yeah it's actually not that hard once you know the procedure

[safe fulcrum]

I think the most annoying thing is just learning all the different standard errors, so the 2nd formula in this will always be different

but throughout all of stats, you always have margin of error = z-score for the confidence value * standard error

[safe fulcrum]

and you always have confidence interval = (point estimate or mean - margin of error, (point estimate or mean + margin of error)

so it gets repetitive yes

[wraith lagoon]

this is just asking me to do the same thing i did the last two questions but with less steps before right

[safe fulcrum]

hmm let me see

[safe fulcrum]

oh yes that's the same as the other two

now you just have to remember all these steps and do them in one go

[wraith lagoon]

,w z score 1.65

[rocky lotus]

Results provided by WolframAlpha

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Requested by fragby

[wraith lagoon]

i did the math and i got a z score of 1.65

and an E value of 0.063

so it should 36/135 +- 0.063 right

[safe fulcrum]

did you try checking yourself? I can't be bothered to go through all the calcs, sorry

[wraith lagoon]

yeah i think the problem is that it wants me to give them a percentage and i have it as a decimal

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[vale dock]

@wraith lagoon Has your question been resolved?

[wraith lagoon]

<@&286206848099549185>

[tidal swift]

more info needed for future helpers

!xy

[vale dock]

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.

[tidal swift]

is this a PISA past year question? if it is, give full context from all relevant previous steps

this alone is not sufficient to answer the question.

[wraith lagoon]

this is all that was provided to me

i don't know what its from it's just listed on my homework

[tidal swift]

then unfortunately this problem cannot be solved. you are told to find the sample size needed for estimation, but there's no mean, no variance, no other statistical values

[wraith lagoon]

so when i use the tool that the homework gives me to help me answer the question it says this

the reason i haven't used it until now is because after using it, it changes the question the next time i go back to it

but i still don't understand what im supposed to do

i have found the area as 1.65 but i don't understand what to do with that value

do i square it then multiply it by 0.25

[tidal swift]

yes

then divide by the square of the margin of error

[wraith lagoon]

okay so i got 0.680625 / 0.0016 which works out to 425.390625

but that seems to be incorrect

[tidal swift]

round up

[wraith lagoon]

i answered 425 and it said the correct answer was 421

okay so they used an area of 1.64 instead of 1.65

,w z score 1.64

[rocky lotus]

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Requested by fragby

[tidal swift]

oh rounding errors

[wraith lagoon]

i hate statistics lol

[tidal swift]

yeah it happens

guess whenever a z-score calculation is involved be prepared to peek +/-.01

or +/-.001

[wraith lagoon]

yeah

[tidal swift]

you never know which values are in use

[wraith lagoon]

the next portion it gives me a percentage of adults that can wiggle their ears at 24% and wants me to find the sample size

so i did the math and i ended up with 0.49058304 / 0.0016

which works out to 306.6144

rounded up is 307 which is correct whoop whoop

since i used that tool it changed the question

i got a z of 2.58

,w z score 2.58

[rocky lotus]

Results provided by WolframAlpha

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Requested by fragby

[wraith lagoon]

what are you saying i should do though

try 2.57 and 2.59 too?

i got the answer 2353 but it was incorrect

i found the z score of 2.58 and did 2.58 squared to get 6.6564

and i did 6.6564 (p hat)(q hat) and got 6.6564 (0.0367)(0.9633)

0.0367 x 0.9633 comes out to 0.03535311

and 6.6564 x 0.03535311 comes out to 0.235324441404

so i did 0.235324441404 / E^2 which is 0.1 squared, equal to 0.0001, and i got 2353.24441404

which rounded up is 2353

but its still incorrect

does anyone know what step i messed up on

the correct answer was 957

[wraith lagoon]

i don't understand how to do this because there's no p value given

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[swift barn]

Is this right?

[sick sparrow]

$R = \frac{\rho L}{A}$

[rocky lotus]

Triaxyz

[swift barn]

@sick sparrow you are right but I cannot use it for this problem

[sick sparrow]

why

[swift barn]

I have to find resistivity @sick sparrow not resistance

[sick sparrow]

yes I was just putting it here for reference

I know ρ is resistivity in this case

so it would be (0.04 * 1.4x10^-6)/2

[swift barn]

So the answer is right or wrong?? @sick sparrow

[sick sparrow]

let me check

your decimal is right but it's supposed to be 10^-8 not 10^-10

[swift barn]

So the answer is 2.8×10^–8 @sick sparrow

Why not 2.8×10^–10

[sick sparrow]

because I don't know how you got that

[swift barn]

28/10 = 2.8

[sick sparrow]

I plugged in the second line of your image on my calc and it gave me the same thing as me

[swift barn]

Look @sick sparrow

[sick sparrow]

I'm aware of that mathematical statement

but that's not what the calculator shows dawg

do the calculation yourself in desmos or something and you'll see

everything is in SI units already too so there is no unit conversion at play

[swift barn]

I am not converting unit btw

[sick sparrow]

I know x2

do you have your calculator with you?

[swift barn]

Yeah! so what?

[sick sparrow]

plug in what you have in the second line of this image and post what the calculator says

[swift barn]

Ok

You are right but why 28/10 doesn't work in that case

@sick sparrow

[sick sparrow]

because I have no idea where you got it

[swift barn]

28/10 = 2.8 that's how I thought

[sick sparrow]

actually yes I do

let me type this out

you got what looks to be 28x10^-9 in the third line so you converted it to 2.8 which is good

but you messed up in that step

28 = 2.8x10^1

you were supposed to add 1 to the powers of 10, but you subtracted 1 which led you to 2.8x10^-10

[swift barn]

Yess so that's where I messed up

Thanks for the help buddy

.close

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[crude peak]

how to integrate $\int_{0}^{1}\frac{\left(3x^{3}-x^{2}+2x-4\right)}{\sqrt{x^{2}-3x+2}}dx$ ?

[rocky lotus]

woxke amxur zoypg qwzaa fjebh

[silver oxide]

Complete the square in the denominator then use substitution.

[crude peak]

alright thnaks

Im trying to see if I can go with this
$\int_{0}^{1}\sqrt{\frac{x-1}{x-2}}\left(3x^{2}+2x+4\right)dx$

[rocky lotus]

woxke amxur zoypg qwzaa fjebh

[crude peak]

like is it possible to move from this

[distant pulsar]

this integral is quite bad no matter how you do it

[crude peak]

wdym

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@crude peak Has your question been resolved?

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[cosmic crest]

let R be the region bounded by y=8x^2 y=2x and x=0. find area wrt to x and then wrt y

[cosmic crest]

okay so I drew the region I think correctly

now wrt x and y is the confusing part for me

so wrt x means formula is like y=mx+b

so for wrt x the bounds for the integral are the max and min y values right?

and we use dx

.close

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[raven lake]

I'm learning about Fourier transforms. I'm seeing that the factor in brackets is a "rectangular pulse". I cannot find that in my books, or in other pages. Can someone tell me more about them, and how I'd solve them? Be it directly or more thoroughly? Because I thought I just had to distribute the 4 among the two u's, but apparently it's not so

[gloomy harness]

start another channel
this one’s taken up

[faint tendon]

sorry

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[jade ivy]

You can just distribute the 4 in if you want, but it should be clear that this isn't helpful since integrals are linear functions and you will just want to factor out the 4 anyway.

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[raven lake]

I supposed so. I wanted to make sure since frequencies are a new territory for me, thank you

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[steady flicker]

You have any progress?

[west cloud]

!15min

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[tacit sentinel]

hi

[final adder]

beat me to it lol

[tacit sentinel]

What do you need help with

oh god

im on mobile ts is pain

uhh

summarize everything cuz stuff isnt trying to load lol😭🙏

ill try to help w/ but my internet is in an absolute dog state

[steady flicker]

Probably you can do is show A + B is subring of R

Alr

What did you get?

Nvm

Alr after that you need to show now that A ∩ B is an ideal of A

After you show that you can proceed to defining homomorphism and prove isomorphism

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@jade ibex Has your question been resolved?

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[faint ravine]

quick question(I hope)

[faint ravine]

we are trying to find all natural numbers such that n2+25n+19 is a square

and it says that the equation is "bounded" with (n+4)2<n2+25n+19<(n+13)2

i understand the (n+13)2 part

but not the (n+4)2 part

where do we get (n+4)2 from?

[ebon glade]

can you multiply out (n+4)^2 ?

[faint ravine]

n2+8n+16

[ebon glade]

can you see how thats smaller than n^2+25n+19 ?

[faint ravine]

yes

bit so is (n+3)2 and (n+5)2

[ebon glade]

well (n+5)^2 is n^2+10n+25. you cant compare that easily to n^2+25n+19

the 10n is less than 25n but the 25 is bigger than 19

[faint ravine]

i understand

[stark wedge]

you should use the symbol ^ for exponents btw.

on english layouts it's shift+6

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[faint ravine]

.close

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[solid turret]

How do I get the area of triangle ADE?

[manic cairn]

are AB and CE parallel?

[solid turret]

Yes

[river shale]

is it a 2D graph?

[solid turret]

Yes 2d

[river shale]

anymore information?

[solid turret]

Not really

Except that AB and EC are parallel

So I did something like this and know that DFC ∽ HEF. But I don't know the ratio

[vale dock]

@solid turret Has your question been resolved?

[vale dock]

@solid turret Has your question been resolved?

[solid turret]

<@&286206848099549185> ?

[glossy dove]

are BD and AE parallel?

[strong granite]

@solid turret is it 10.5

[glossy dove]

!nosols

[vale dock]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[solid turret]

Okay, thanks. But why?

[strong granite]

ABCF is a parallelogram

So DF=3

DFC~HEF

Wait I think I messed up somewhere

Ok so EH=FH=x

Now if we take triangle AEH and BDC
(X+7)/7=x/3
X=21/4

Therefore EH=21/4

Now the area of ADE=(1/2)4(21/4)
Equals 10.5

[solid turret]

Okay, thank you

[vale dock]

@solid turret Has your question been resolved?

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[faint cave]

So I understand the solution:

But . . . Can’t I construct a triangle like this?

And clearly 53 < 82 ????

[charred lily]

do you know that the length of the median AD is 5?

[distant pulsar]

in a triangle with lengths 2-7-8, the median of A is about 4.66369, not 5

[faint cave]

Yes,

[faint cave]

Oh?

[slate folio]

Use apollonius theorem

you'll get AB^2 + AC^2 being a constant

the solution is basically just proving that theorem

[faint cave]

Ohhh, so the length of a median is fixed by the length of the sides of a triangle?

[slate folio]

no

[faint cave]

Or like a range?

As in if I have a triangle with a known median length, the side lengths cannot be whatever I want it to be,

They have a range of lengths or something?

[slate folio]

yea

if you know the median and the length of the base

in this case, AB^2 + AC^2 = 2(AD^2 + BD^2)

[faint cave]

Wait so given a a median and two sides I can find the lengths of the third side???????

[slate folio]

correct

[faint cave]

AAAAAAHHHHHH

THAT MAKES SENSE

THANK YOU A LOT :DDD

[slate folio]

you're welcome

!done

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[faint cave]

.close

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[silent dune]

Uh trying to show the Hausdorff maximal principle, assuming Zorn’s lemma but am stuck at a specific step. Let me set it up:

[silent dune]

the Hausdorff maximal principle (HMP). Every poset has a maximal linearly ordered subset.

Zorn’s lemma. If X is a poset and every linearly ordered subset of X has an upper bound, then X has a maximal element.

So to reiterate, trying to prove that: Zorn’s lemma => the (HMP).

The idea is to apply Zorn’s lemma to the collection of linearly ordered subsets of X. This collection is partially order by inclusion.

I’m stuck at showing that every linearly ordered subset of this collection has an upper bound

Bcuz if it did, we’d show that X has a maximal linearly ordered subset.

[silent dune]

Would appreciate any hints on this specifically!! Thx!

My attempt before (from a dream today lol) was to consider the union of the collection; but that failed miserably

[vale dock]

@silent dune Has your question been resolved?

[vale dock]

@silent dune Has your question been resolved?

[wicked zenith]

Define $\mathcal{C} \coloneq { C \subseteq X : C ;\mbox{is a chain in}; X }$ partially ordered by inclusion. You want to prove every chain in $\mathcal{C}$ has an upper bound in $\mathcal{C}$. Consider a chain of chains $\mathcal{L} \subseteq \mathcal{C}$ totally ordered by inclusion. Let $U \coloneq \cup_{C \in \mathcal{L}} C$. See ||$U$ is itself a chain in $X$|| and therefore ||$U \in \mathcal{C}$||. See ||$U$ is an upper bound of $\mathcal{L}$||. Apply Zorn's Lemma to $\mathcal{C}$.

[silent dune]

Plz give hints and not direct solution :d

[wicked zenith]

I've hinted too much, sorry

[silent dune]

I.e what direction should I go? Did you read my attempt?

[wicked zenith]

I missread your attempt. I think you've basically tried what I suggested, just got stuck on either the "union of a chain of totally ordered chains is itself a chain" part, or the "union of a chain of totally ordered chains is an upper bound"

Have I interpreted correctly?

[silent dune]

I conjectured that the union of the collection, i.e the union of the chains (to X) is a itself a chain and also thus a good candidate as an upper bound for a chain of the collection of chains.

But I realized that (unless I’m missing something) that the union is not a chain.

[wicked zenith]

Are you taking the union of a total order of chains of X, or a total order of elements in X?

[silent dune]

Just the union of the collection of chains of X

[wicked zenith]

just for clarification, by "chain" I mean "a subset of a poset forming a total order"

[silent dune]

Mhm

As an upper bound for a chain of the collection of chains of X is an element in the collection of chains of X; the upper bound must be a chain of X. But this fails miserably unless I’m missing something

[wicked zenith]

I think you're on the right track

you've shown the union of chains is itself a chain?

[silent dune]

I’ve found that it’s not a chain by a simple example

[wicked zenith]

What's the example?

[silent dune]

Let X = {a,b,c} and R = {(a,b), (a,a), (b,b), (c,c)}

Then R is a partial order on X if I’m not missing anything

Let F be the collection of chains of X, that is,

F = {{a,b}, {a}, {b}, {c}}

Do u see the problem?

(the defn. of poset I’m using doesn’t care about empty sets incase youre wondering)

It would make sense that the upper bound depends on which chain it concerns

Which happens in this example

and the union fails miserably here unless of course I’m missing something

[ebon glade]

of which chain in F are you saying the union is not a chain?

[wicked zenith]

Both {a,b} and {c} are maximal. Suppose we take L = { {a}, {a,b} } totally ordered by inclusivity, the union of which is {a,b} and is indeed a chain and an upper bound.

[ebon glade]

we arent just randomly unioning chains together

we are only unioning chains that "fit"

[wicked zenith]

We could also take L = { {c} } and the same argument would apply

Do we require a least upper bound?

[silent dune]

Hm, so it’s a different union that I had in mind?

[ebon glade]

in general the union of chains is not a chain, thats correct

but here the chains themselves form a chain

they are subsets of another

[silent dune]

Hm

Ah

[wicked zenith]

We're just looking for maximal elements, not necesserily supremums.

[silent dune]

I’m currently not in a good environment to think this through, I’ll come back in a bit. Thx people for the help so far

[wicked zenith]

Your proof is definitely on the right track.

[vale dock]

@silent dune Has your question been resolved?

[viscid lodge]

How can I solve x2+x=1?

[charred burrow]

i assume you mean $x^2+x=1$

[rocky lotus]

DaveyLovesSocks

[charred burrow]

do you know the quadratic formula?

@viscid lodge

[charred burrow]

@viscid lodge $\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

[rocky lotus]

DaveyLovesSocks

[charred burrow]

if you dont know it theres really no reason that you could do it

[turbid valve]

[... you know completing the square is a thing, right?]

[charred burrow]

forgot about that

[final adder]

@viscid lodge @charred burrow Welcome to the mathcord!

but i believe @silent dune isn't done with this channel yet

[vale dock]

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).

[charred burrow]

👍

[vale dock]

@silent dune Has your question been resolved?

[vale dock]

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[fair wing]

can you explain how did they take common factors and simplified calculation in the bottom part

=> 22b = 61x59 - 48x61-11^2

.close

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[north scarab]

do u guys know why and how I got this wrong

Q3

B)

[jovial edge]

How can you get from the first line to the second line?

[north scarab]

.rotate

which part

could u circle it

[jovial edge]

$\frac{x^2+1}{x^2+5}=(x^2+1)(x^2+5)$ this is what you wrote right?

[rocky lotus]

Alexis_Fx

[north scarab]

yea

then I expanded it

[jovial edge]

How can you even get that

$\frac{x^2+1}{x^2+5}\neq (x^2+1)(x^2+5)$

[rocky lotus]

Alexis_Fx

[north scarab]

I had to

get the differentiation

of u and v

in order to use the product rule

right

I just used u and v

[jovial edge]

you can write it as $\frac{x^2+1}{x^2+5}=(x^2+1)(x^2+5)^{-1}$

[rocky lotus]

Alexis_Fx

[jovial edge]

to use product rule

[north scarab]

u forgot the ^-1 in the first term

[stark wedge]

no, a/b = a * b^-1 not a^-1 * b^-1.

alexis didn't forget anything. you forgor the ^-1 (and it is a pretty serious thing to forget...)

[north scarab]

u’v + v’u

is the product rule

right

[stark wedge]

yes but we aren't talking about that yet.

(tbh for differentiation there's a better way to do it anyway)

[north scarab]

Ok I’ll come back to this later (I’ll take a note of it)

I wanna go through another problem I’m stuck with

,rotate

[rocky lotus]

Couldn't find an attached image in the last 10 messages.

Jul 30, 2025, 4:27 AM

[north scarab]

,rotate

[north scarab]

is this simultaneous questions

[jovial edge]

Yes and no

[north scarab]

am i on the right track?

[jovial edge]

if you want it to be a simultaneous problem you have to have 2 independent equation, you can't just create one from the other