help-0

[pliant charm]

that is just new expression of (x,y) [ x^2 + y^2]

[mighty pasture]

ohh so it doesnt represent a function x^2 + y^2 = k

[pliant charm]

no

[mighty pasture]

its just arbitary x, y on the previous function ?

[pliant charm]

y = f(x)
they just did x^2 + y^2 => x^2 + f(x)^2

[mighty pasture]

ok sure

how in general would i tell the difference for if y = f(x) or g(x)

or is it just a thing of wording

[pliant charm]

yeah

yeah just of wording, in questions they give what is f(x) or g(x)

[mighty pasture]

damn alright thats annoying, thank you for explaining to me though !

.close

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[warm quarry]

for question b

I know that it will be t(n-1)

since V²(n-1)/sigma² ~ X²(n-1)

I know U mean ~ N(0,1)

[void nymph]

tell me thats not gpt

[warm quarry]

i can rewrite $\frac{U\sqrt{n}}{V}$ in : $\frac{U}{\sqrt{\frac{V^2}{n}}}$ but how can I write this down correct or is this enough. Showing how I rewrite this then say U is distributed N(0,1) and V² is distributed X² (n-1)

T = $\frac{N(0,1)}{\sqrt{X/n}}$ t~(n-1)

[warm quarry]

It is to translate the question from dutch to english

[void nymph]

okay

[ocean seal]

Brett

[warm quarry]

Is this enough?

aaah shit U is not N(0,1)

wait let me try again please and ill show and let someone check if they understand it

[lone heart]

@warm quarry Has your question been resolved?

[warm quarry]

Is this good enough?

[warm quarry]

<@&286206848099549185>

[warm quarry]

<@&286206848099549185>

[lone heart]

@warm quarry Has your question been resolved?

[tardy turret]

YES

[warm quarry]

Perfect

Thank you :)

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[topaz grove]

Could someone please look this over and suggest improvements or point out mistakes please?

[mortal trellis]

!nopdf

[lone heart]

Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.

[topaz grove]

Ah, ok. Will fix

i also tried to ask my professor to look it over. his response was that i "have to be more careful!", and nothing else. i asked for elaboration, but received none. for reference...https://www.ratemyprofessors.com/professor/884425

[exotic canopy]

this may be the notation that confuses me but you write
v(x, t) = w(x, t)
so why wouldn't
u(x, t) = 2v(x, t)
?

[mortal trellis]

v(x,t)=u(x,t) aswell

so then you just conclude that everything is zero

so literally the first bullet point is nonsense

[topaz grove]

ah, i put an equals sign instead of a minus sign

so a typo. is there anything else?

if it helps, here it is corrected without the typo:

[mortal trellis]

from a mathematical perspective all domains for everything are missing

from which function spaces are f, A, B, u, v, w? on which domains are we doing things?

[lone heart]

@topaz grove Has your question been resolved?

[topaz grove]

i'm not quite sure i follow. this is a PDE, heat equation, with boundary conditions and an initial condition. i don't recall any discussion of "function spaces" with regards to PDE's?

[mortal trellis]

oh boi

[topaz grove]

looking at the textbook, there appears to be no mention of function spaces in the index

a quick google search looks like you're possibly referring to just the domain and range on which the functions are defined? i'm not sure i understand what you're trying to say. the boundaries are listed, and i imagine it should be reasonably assumed that the domain on which the solution should be defined would clearly be within the boundary conditions listed.

[mortal trellis]

if your course doesnt care about it then I dont want to get into what I mean

[topaz grove]

ok. i appreciate the mention, though. it's something that i can study on my own to prepare for the future at least. other than that, does the work appear to seem correct?

[lone heart]

@topaz grove Has your question been resolved?

[lone heart]

@topaz grove Has your question been resolved?

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[neat wolf]

How could I find the area of the shape ABQR
Given that AB and RQ are parallel and equal in length, (so the shape is a rhombus)?

[merry iris]

doesnt look like a rhombus to me

[neat wolf]

So how would you find its area

[merry iris]

what are you allowed to use

oh abqr not apqr

[merry iris]

do you know how to find the area of a parallelogram

[neat wolf]

Wait so this is just a parallelogram

Yeah I do

[neat wolf]

Length of AB and RQ are both $7sqrt10$

And then multiply it by the perpendicular height right?

[merry iris]

yes

[neat wolf]

W

[merry iris]

w

[neat wolf]

Alright thank you

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[hybrid halo]

Hello

[hybrid halo]

I keep getting this wrong I’m not sure why

Is it the way I’m writing the decimals?

cuz I tried different ways

[merry iris]

how did you get your answer

[lone heart]

@hybrid halo Has your question been resolved?

[hybrid halo]

it was given to me😭

I didn’t reach this part in the lecture so I’m confused

[hybrid halo]

This is probability

“Odd of Events and Basic Rules of Probability”

[lone heart]

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[dapper root]

HELP GUYS

[dapper root]

in algbera

when they put 7x+2

what does that mean

is x like an power?

[solar pebble]

hi bolbol lol

seven times x

then add two

[gray isle]

x is a variable representing some unknown

[shell agate]

x can be any value

[vale wigeon]

do you mean specifically "what does it mean when a number and a letter are put together" or do you mean like "what do all these letters mean in general"\

[lone heart]

@dapper root Has your question been resolved?

[lone heart]

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[tidal palm]

In question 25 , the answer is C) 14 but why?
f’(3) is 2.. does it become -2 because it’s decreasing at f(3)? If so I don’t get why because the derivative is above the X axis

[tidal palm]

@ me when someone answers thank you !

[shell agate]

What did you do?

[tidal palm]

f(3)=2
f’(3)=2
So I thought 4(2)-3(2)=2 and it’s not in the answers so..

[shell agate]

o

[shell agate]

so why is f'(3)=2

[tidal palm]

I thought u could js tell bcuz that line is f’(x) and at x=3 its output is 2

[shell agate]

We need to find slope

(y2-y1)/(x2-x1)

[tidal palm]

Isn’t that line the slope?

This line

[shell agate]

Yes

The slope is negative

[tidal palm]

Omg wait I get it now

[shell agate]

ok

[tidal palm]

It’s bcuz it’s decreasing at 3 and if we use dis formula we’ll get a negative number

The slope is going down anyway ok ✅ THANK YOU

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[warped topaz]

x'(t) = 3t^2 - 3

3t^2 - 3 = 0

t = +-1

y'(t)/x'(t)

4t/(3t^2 - 3)

4(1)/(3(1)^2 - 3) and 4(-1)/(3(-1)^2 - 3)

But we get 0 for both

I thought it would give us the slopes of the angles at the a tangents

Then I could just do arctan(slope 1) - arctan(slope 2)

[sturdy blade]

velocity vectors are given by P'(t) = v(t) = (x'(t), y'(t))

[sour mica]

uhh, why do you have x' = 0?

[sturdy blade]

then you're just finding the angle between two vectors

[warped topaz]

I thought we had to find the values of t at (0, 6)

[sour mica]

you do

thats just x=0

not x'

[warped topaz]

Oh oops

So t = 0 and t = cubed root of 3

[sour mica]

yea, you got two values of t when it is on y axis

[warped topaz]

4(0)/(3(0)^2 - 3) and 4(cubed root of 3)/(3(cubed root of 3)^2 - 3)

To get the slopes right?

[sour mica]

one of them corresponds to when the particle is at origin

so you gotta choose one that corresponds to when the particle is at S

using y = 6

[sour mica]

not cbrt

[warped topaz]

Ahhh just sqrt

[sour mica]

yea

[warped topaz]

+-sqrt(3)

[sour mica]

yea, one is for v1, and other for v2

[warped topaz]

4(-sqrt(3))/(3(-sqrt(3))^2 - 3) and 4(sqrt(3))/(3(sqrt(3))^2 - 3)

-4sqrt(3)/6 and 4sqrt(3)/6

[sour mica]

why are you calculating dy/dx?

[warped topaz]

y'(t)/x'(t)

[sour mica]

thats just overcomplicating stuff

[warped topaz]

To get the slopes no?

[warped topaz]

Is it?

[sour mica]

You can simply calculate x' and y' and those are the components of the vector

[warped topaz]

Now I just do arctan(4sqrt(3)/6) - arctan(-4sqrt(3)/6)

Right?

Then finished

[sour mica]

then you have x' i + y' j as the velocity vector

yea

[sour mica]

yea

[warped topaz]

98.21

Which is the correct answer 😄

Thank you!!

❤️

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[past knot]

How to prove that if the boundary of a bounded set A has Jordan measure 0 then A has jordan measure

[past knot]

A is from R

[lone heart]

@past knot Has your question been resolved?

[past knot]

<@&286206848099549185>

[lone heart]

@past knot Has your question been resolved?

[past knot]

<@&286206848099549185>

[lone heart]

@past knot Has your question been resolved?

[wispy idol]

https://math.stackexchange.com/questions/213527/closure-interior-and-boundary-of-jordan-measurable-sets

@past knot

[past knot]

@wispy idol the proof is poorly explained and uses some things which i do not know what they are, there should be a more elementary proof

[unkempt quiver]

Yes , thanks for the guidance

Thanks for the valuable information!

[mental terrace]

There's actually a better, MITx version of the whole thing. There's also multivariable part.

https://mitxonline.mit.edu/programs/program-v1:MITxT+18.01x/

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[past knot]

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[dapper root]

ohhh i understand this tyty

[dapper root]

thanks thanks i understand it now

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[main coyote]

help with normal distribution

[main coyote]

I use statistic table, there is no 0.9772 in the standard normal distribution table

i have no idea how to solve this using elimination or substitution method.

my table only has values for P(Z>...)

[wicked helm]

hi

[solemn juniper]

you can make use of the standard normal distribution being symmetric around 0

P(Z>a) = P(Z<-a)

[main coyote]

I don't understand:(

[solemn juniper]

consider this equation

,rccw

[solemn juniper]

you want the value of z such that P(Z>z) = 0.9772

do you suspect this value of z will be positive or negative?

[main coyote]

yup

i want to compare

so there will be 2 equation for me to do substitution or elimination method to find standard deviation and mean

[solemn juniper]

we're getting to that

[solemn juniper]

answer my question please

[main coyote]

wdym

so u want to say 32-M/√var is a positive value or negative value?

[solemn juniper]

sure

including those other symbols doesn't really matter at this step

[main coyote]

tbh idk how to solve this kind of question

[solemn juniper]

there's very little solving involved. You just need to know what the standard normal distribution looks like

what is P(Z>0)?

[main coyote]

0.5?

[solemn juniper]

indeed

now if P(Z>z) = 0.9772, is z greater than, less than, or equal to 0?

[main coyote]

lemme think

greater than 0?

[solemn juniper]

what makes you think so?

[main coyote]

idk, if P(Z>0) = 0.5 and P(Z>z) = 0.9772 then z must be more than 0 lol

I have no idea 😭😭😭😭

[solemn juniper]

must it?

what is P(Z>0.5)?

[main coyote]

oh 0.4801

so less than zero

bruhbruhbruh

[solemn juniper]

ok so the value of z we're interested in is less than 0

[main coyote]

so the higher z value means the lower 0.whatever value

[solemn juniper]

sure

[main coyote]

so

[solemn juniper]

so

[main coyote]

how can I compare 32-M/√var with something so I get 2 equation

[solemn juniper]

z = (32-mu)/sigma, so finding z is how we get those equations

[main coyote]

how to find the z value

[solemn juniper]

that's what we're doing right now

[main coyote]

for P(x>45) = 0.1056, after those workings I got P(Z>1.25) using table

but things like P(x<32) = 0.0228, idk how to do it

[solemn juniper]

again, that is what i'm trying to explain at this very moment

[main coyote]

how

[solemn juniper]

so we're solving for z (which is [32-mu]/sigma) in P(Z>z) = 0.9772

[main coyote]

okay

[solemn juniper]

we know that z is negative, yet your table only deals with positive z values

[main coyote]

but 0.9772 is not in the table

[solemn juniper]

how can we adjust that equation so it instead involves positive numbers?

if only there was a transformation that uses the symmetry of the standard normal distribution around 0

[main coyote]

my brain isn't functioning 😭

[solemn juniper]

if only it was literally the second message I sent in this channel

[main coyote]

So P(Z<-32-M/sigma) = 0.9772?

[solemn juniper]

P(-32-M/sigma) doesn't parse

[main coyote]

I miss that Z<

[solemn juniper]

better

so you have something of the form P(Z<...) while your table gives values pertaining to P(Z>...)

how can we make everything match up?

[main coyote]

wait is the value still 0.9772?

[solemn juniper]

yes

that's why it's symmetric

[main coyote]

ummmmm

idk

[solemn juniper]

well that's a problem

how do you normally transform P(Z<...) statements into P(Z>...) statements?

[main coyote]

So 1 - P(Z<-32-M/sigma) = 0.9772?

[solemn juniper]

no

[solemn juniper]

typo, fixed

[main coyote]

uh mybe if P(Z<11) then to make it greater than symbol 1 - P(Z>11)?

[solemn juniper]

alright

now apply that to your problem

[main coyote]

there is only P(Z>...) value in the table

then how

oh make it P(Z>-(32-M/sigma)) = 0.0228?

[solemn juniper]

yes

that's something you can solve

[main coyote]

oh thats legal

[main coyote]

so after all of these I actually have the answer here lol

[solemn juniper]

there's a reason why i started with that

[main coyote]

SO THATS IT

that easy 😭

tysm Steakanator

cool ppl fr

[solemn juniper]

ezpz

[main coyote]

.close

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[drifting tapir]

my brother came home after driving my car. my tank was full and now its that. how much $$$ did he use?

[shell agate]

Troll?

[true phoenix]

??????????????

[shell agate]

Call mods or what

[dry sleet]

You will need to give a lot more info, mainly what car you driving but oke

[random cypress]

lol

[small lance]

probably his entire bank account

[drifting tapir]

whatbdo u need?

[shell agate]

0

[sour mica]

Well, clearly 0 bucks. He stole the fuel from you

[drifting tapir]

lol i wish

he drove 2 hours maybe 3

[drifting tapir]

audi a4

[pseudo ice]

• the cost of the fuel per unit?

[sour mica]

Just go to the gas station or whatever you call it, and see how much you need to pay to refill it

[shell agate]

lol

[drifting tapir]

3.95

[drifting tapir]

I was going to but he might say no and not pay for what i just paid that hes supposed to pay

[wet gazelle]

someone help me.
Given 2 points A(0,-3), B(4,1) and point M on circle x^2 + (y-1)^2 =4. Find the smallest value of MA + 2MB

[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).

[shell agate]

No

[small lance]

it's much faster to call the gas station than asking strangers in a math server.

[drifting tapir]

its a math server where volunteers help and my question is math related.

“Than asking strangers in a math server” Uhh Yeah the whole purpose of this server?

its ok nvm

.close

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[mossy lion]

I’m working on my Grand Oral, a French final exam where we talk about a topic we choose. I’m thinking about doing it on How do logarithms help solve problems that would be impossible to do by hand?
Do you think that would be a good and interesting topic?

[lone heart]

Please don't occupy multiple help channels.

[shell agate]

Close your other help channel

[mossy lion]

how?

[shell agate]

#help-15 type .close

[mossy lion]

do any of you think ‘How do logarithms help solve problems that would be impossible to do by hand?’ is a solid topic for a final oral exam in maths?

[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).

[tulip bone]

it depends upon how u make it interesting

if ykwim

anything can be interesting

[patent vale]

im thinking and it sounds like it could be quite interesting but atleast for me it depends on if you touch on the practical uses of logarithms

[lone heart]

@mossy lion Has your question been resolved?

[lone heart]

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[lone heart]

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[dusk thicket]

Can someone help please?

Oh man

[vale wigeon]

!msgdel

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The original post of this help channel has been deleted, and it will abruptly close and possibly lock. (This is irreversible.) Please claim a new channel, and don't delete the first message of any future channel you claim.

[dusk thicket]

I never knew this was a thing

.close

.close

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[alpine sable]

can anyone help me in determinants question?

[alpine sable]

question is theoretical i wanna discuss

[vale wigeon]

too vague then

you have to narrow it down to some specific doubt or problem

[winter light]

Start by searching "determinant of matrix" in YouTube
Or google it or, even better, take a linear algebra book and read/study it

[ancient temple]

What is the question?

[alpine sable]

question is logical but a very long , i have a doubt and i wanna discuss

[ancient temple]

So please ask the doubt

so we can discuss

[alpine sable]

this

can you accept a video call now?

can you accept a video call now?

why?

why?

[winter light]

And don't write each message twice

[winter light]

Also because you might get a positive answer by a scammer that can rob your data, since you're in a server with hundreds thousand people

[alpine sable]

i wanna free help

[winter light]

Exactly

[ancient temple]

what is the doubt regarding this?

[alpine sable]

i wanna discuss on a call . cna you accept a call now?

[ancient temple]

can you discuss your question here in text?

[ancient temple]

@alpine sable

[alpine sable]

can you accept a call or not @ Asteroid

[ancient temple]

i cannot

[proven ridge]

No reason to be like that
You could just
Politely tell him why it's weird to ask for a video call from strangers

[wheat isle]

they did

[alpine sable]

but i didn't understand

[winter light]

Why?

If English is not your native language, you can use, say, Google translate

[alpine sable]

I can speak english and english is my native language

[winter light]

Then what's the issue?

[alpine sable]

please firstly accept a video call and i sent the question before

[winter light]

...

<@&268886789983436800> how else to explain him??

[wheat isle]

@pseudo ice catbit

[patent vale]

call me maybe etc etc

[wheat isle]

hes gonna actually call u dont tempt him

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[jolly notch]

<@&268886789983436800>

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[real gazelle]

Please don't ask for video calls here, practice online safety

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[trail oasis]

uh...

[forest marsh]

you have a math question ?

[trail oasis]

Yes

So

x^2 + y^2 + 1/x^2 + 1/y^2 = 4

Find x and y

[forest marsh]

so

x² - 2 + 1/x² + y² +1/y² -2 = 0

proceed to complete the square

ok but so does x = y = -1

[nocturne sandal]

just notice all the answers, ez

[forest marsh]

x² - 2 + 1/x² + y² +1/y² -2 = 0
(x-1/x)² + (y-1/y)² = 0

now see that a sum of square is zero only if the thing in it are 0

solve for x and y

[forest marsh]

surprisingly theses are the two among the four solutions kekw

[trail oasis]

a

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[woeful cloak]

I need help

[woeful cloak]

I need to find AB

Is it Tangente that I have to use?

tan52x2?

[gray isle]

yes

[woeful cloak]

Oh ok cuz I tried using chatgpt and it used Cosinus

LOL

[gray isle]

don't use chatgpt for math

[woeful cloak]

Kk thanks

[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).

[woeful cloak]

MNO is similar to KLO

I need to find PK

I found KL, 8.8

and I have no idea what to do next

hello??

.close

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[slender cairn]

hello

[slender cairn]

can someone help me with 43

[reef wren]

could you factor 24 ?

[slender cairn]

8 and 3

[native lagoon]

Well, |hint: 24=3×8=3×2^3|

[reef wren]

yep and what's the cube root of 8 ?

[slender cairn]

2

oh heah

i got confused

i keep forgetting to make it to a cube root when its like a fraction exponent

[reef wren]

you don't really have to

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[lime patrol]

i have a ap calculus ab exam coming on may 12 is there a website that will give me past paper questions from a certain unit then after you answer it a explanation also i really need help with frq i honestly dont know how im ment to answer it

[cerulean tangle]

what are the questions that you need help with?

[lime patrol]

i mainly struggle w the hardest questions from each unit and unit 8 i was sick so didnt even watch one class

but if i gotta choose its 5,6,7,8

[cerulean tangle]

is there any exercise that you need help with?

which website are you referring to? what kind of questions does each unit have? which one do you need help with? @lime patrol

[lime patrol]

no im asking if anyone knows a website for my situation

[cerulean tangle]

to solve your exercises or help you with them

[modern sedge]

khanacademy has some exercises, not sure if it has past exams as well

[lime patrol]

sadly it doesnt also they are too easy compared to the exams

[modern sedge]

https://www.savemyexams.com/ap/maths/college-board/calculus-ab/past-papers/

maybe this

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[lime patrol]

life saver

[lone heart]

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[modern sedge]

,Haha, nice, btw it's the first thing that came up when I googled "Past calculus AB exams" or sth like that, so maybe try googling next time

[modern sedge]

.close

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[modern sedge]

accidentally used , instead of .

[lime patrol]

i googled that i swear to go i didnt get that

[ancient spire]

is madasmaths good

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[alpine sable]

I need help with a trig problem

[lone heart]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[nocturne sandal]

can you put z1 and z2 into polar form first?

[alpine sable]

They are already in polar form

@nocturne sandal

[tacit arch]

use exponent rules to multiply them then

,tex .exp rules

[ocean seal]

riemann

[nocturne sandal]

i meant a form like $r e^{i \theta}$ which makes it easier imo, but not required

[ocean seal]

mono

[lone heart]

@alpine sable Has your question been resolved?

[ocean seal]

HitenTandon

[lone heart]

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[alpine sable]

what did i do wrong

part b

it makes no sense

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[winged sun]

hey people what's the best channel to do relations and functions? i have done it tons of time but still suck at it

[tacit arch]

#proofs-and-logic maybe ?

[winged sun]

why is the 3rd option not correct?

[thin meadow]

Uh

Cause 1,1

Makes it have two ones on the same column

Which doesn't follow rref

@winged sun look at these rules for rref

[winged sun]

oh got it thanks , i was applying the scalar property that's why

[thin meadow]

ah

alr

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[latent belfry]

im learning how to solve integrals. With u substitution, i made u = (x^3+1) and du = 3x^2, but du doesnt match u at all.

so, I rewrote du as x^3 + x^2 dx

x^2 dx = 1/3du but what do i do with the x^3?

[solemn juniper]

x^3 looks pretty closely related to u

[latent belfry]

so will it be u-1?

ohh

thank you

[solemn juniper]

[shrewd eagle]

hey team

sry i thought this was discussion

[solemn juniper]

https://tenor.com/view/cat-skate-board-gif-778367011615093516

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[tepid lodge]

no idea where to even start

I know point slope form but that's about it

[buoyant saddle]

L(x) = f(a) + f’(a)(x - a) is the tangent line to f at x = a

find h(pi/4) and h’(pi/4)

[tepid lodge]

what does h' do?

like what is it meant for

[buoyant saddle]

idk what that means

it’s the slope

at the particular point

remember y = mx + b

[tepid lodge]

oh ok sorry xD

[buoyant saddle]

it serves as m here

[tepid lodge]

h'(pi/4) is 0 so m = 0?

[buoyant saddle]

idk how you got that

your h’ is wrong i think you confused it with h

[tepid lodge]

oh I confused it with x sorry

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[sharp stag]

why did gpt do all this? can you not just use $log_b u = (1/u(lnb))*u'$

[ocean seal]

Paul04

[proud obsidian]

yea thats how its derived

[sharp stag]

interesting

yeah I didn't bother looking into all that but I'll do so now that it came up

thanks

.close

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[elder iris]

not exactly math but anyone able to help?

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[jovial stratus]

is this correct, i think g would be only 2 but i may be very wrong

[alpine sable]

No

B intersection C is {2}

What does that have in common with {1, 3, 5, 7, 9}

[jovial stratus]

apologies, would G. be {} ?

or null or however i would notate it

[alpine sable]

Yes

Empty set

[jovial stratus]

ok, for the others set would i repeat numbers or no

[alpine sable]

What do you mean?

[jovial stratus]

like for a how i put { 1,2,2,2 etc} could i change it to just 1,2,3 and so on ?

[alpine sable]

Yes

A set can only have one of each element

[jovial stratus]

thank you jd vance’s couch

i get it now

[alpine sable]

i.e you must

[jovial stratus]

ok thank u im gonna close it now

.close

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[verbal kindle]

So I calculated this limit in my calculator.

specifically this part as l approaches infinity

What I got was the answer of "2"

My professor did this and it seems like he got 1/2

[uneven isle]

no he got 2 as well? assuming u mean the entire hting inside []

[verbal kindle]

I calculated the part where he had the red part and still got 2.

oh my god

[uneven isle]

they wrote 1/sqrt(1/4)

[verbal kindle]

what is wrong with me

i didnt register the 4 on the bottom becoming a 2 after the 2 went on top

omg

im sorry

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[alpine sable]

Hi I would like help

[lone heart]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[alpine sable]

<@&286206848099549185>

[tacit arch]

!da2a

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No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[alpine sable]

Can anyone check my equations to see if there are any mistakes

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[cerulean ridge]

consider prime numbers (greater than 3) p, q and r that form an arithmetic progression where q=p+d and r=p+2d

prove 6 divides d

[vale wigeon]

!occupied

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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).

[cerulean ridge]

i figured d === 0 mod 2 since both p and q must be odd

not sure how to prove it’s divisible by 3

[vale wigeon]

suppose d isn't divisible by 3

p, q and r are in AP. what can you say about their residues mod 3?

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@cerulean ridge Has your question been resolved?

[cerulean ridge]

oh

i’m stupid

thank you

[lone heart]

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[high zealot]

did I do this right?

[high zealot]

evaluate this intergral

[woeful granite]

looks good

[high zealot]

lets go

thanks

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[raw jetty]

given positive integer $k\geq 2$, prove there exists an infinite amount of positive integer $n$ such that both
$$kn+1 \quad\quad (k+1)n+1$$ are squares

[ocean seal]

skissue.in.a.teacup

[raw jetty]

my best guess is to assume its finite, then pick the largest one and prove a larger one exists, but i have no idea how to do it

well for labeling sake
$$kn+1=x^2$$
$$(k+1)n+1=y^2$$

[ocean seal]

skissue.in.a.teacup

[proud obsidian]

this reminds me of pells equations..

[raw jetty]

elaborate?

topic is pythag triples and pells equation so it could be a good lead

[woeful zenith]

from what i can gather the second condition is unnecessary

wait

no

i confused myself

[proud obsidian]

well from some algebra i have that (k+1)a^2 - kb^2 = 1

[raw jetty]

what is a and b supposed to represent?

[proud obsidian]

oh wait you used x and y here

replace a with x and b with y

[uneven isle]

cant u just algebra this

[uneven isle]

this rearranges to k = y^2-x^2

[proud obsidian]

yea i saw that

[raw jetty]

not n=y^2-x^2?

[uneven isle]

o sorry i meant n

n = (y-x)(y+x)

if y^2 > x^2, y-x bigger positively necessarily

addition and substraction of integers is closed under integers so you know n is sitll an integer

this necessarily means u can pick infinite amounts of n

as long as it satisfies (y-x)(y+x)=n

[plush wing]

but then kn+1 is not always square, or im missing something?

[uneven isle]

it will be square for any times u pick n to be (y-x)(y+x)

[plush wing]

sounds wrong for me

[raw jetty]

say k=2, pick y=2 x=1 <=> n=3, 3×2+1=6=/=x^2=1

i think its like if both solutions of x and y exist, then that implies n is in the form of (y-x)(y+x) but not backwards

[uneven isle]

o yes u are right

its not an iff

its just an implication

my fualt

[raw jetty]

by contradiction, for some k let m be the largest n that holds, that implies x and y are the maximum,
(k+1)x^2-ky^2=1
(im not sure about this but i know pell eqs have inf solutions, but not sure about generalized pell eqs)
thus you can pick a larger (x,y) then contradiction? or does this fall into the same problem as before

[plush wing]

how you are picking larger (x,y) ? also you actually need to get larger y^2-x^2

[lone heart]

@raw jetty Has your question been resolved?

[raw jetty]

do pell eqs in the form ax^2-by^2=1 have infinite solutions given a and b?

[plush wing]

in this form not for all a and b, for example if a and b are not coprime then it has no solutions at all

[raw jetty]

damn

[lone heart]

@raw jetty Has your question been resolved?

[plush wing]

and yeah this will have same problem this will only guarantee that both conditions are equivalent (now necessary true)

after putting n=y^2-x^2 in first eq you can use y = x+a this way kx^2 will go away and you will have x^2 without coeff, after that you just can transform it to Pell's

[lone heart]

@raw jetty Has your question been resolved?

[raw jetty]

$$ky^2-kx^2+1=x^2$$
$$kx^2+2akx+ka^2-kx^2+1=x^2$$
$$2akx+ka^2+1=x^2$$

hm?

[plush wing]

you have mistake at a^2

[raw jetty]

o

[ocean seal]

skissue.in.a.teacup

[plush wing]

for $x^2-2akx$ you get $x^2-2akx+a^2k^2-a^2k^2$ replace $x^2-2akx+a^2k^2$ with new variable and you can transform it to Pells, you will also need to ensure that backwards transformation will give you integer values

[ocean seal]

ViNton

[raw jetty]

uhh so $a^2k^2+ka^2+1=(x-ak)^2$

[ocean seal]

skissue.in.a.teacup

[plush wing]

yeah make substitution ant try to get Pell's

[raw jetty]

erm substitution?

[plush wing]

x-ak = t

[raw jetty]

$1=t^2-(k^2+k)\cdot(a)^2$?

[ocean seal]

skissue.in.a.teacup

[raw jetty]

like that?

[plush wing]

yeah you got Pell's, but you also need to check that doing backwards transformations will lead to x, y, n be integers

[raw jetty]

whats backwards transformations

[plush wing]

Pell's will only guarantee that t and a are integers you need to get back to x, y, n

[raw jetty]

ah

t=x-ak, t and k and a are integers, thus x must be an integer, and since y=x+a then y is also an integer

hm for n integer...

btw whats the end goal with getting it to a pell eqn?

[plush wing]

Pell's guarantee that t and a are integers and there are infinite such pairs

[raw jetty]

hm how do you actually prove n is an integer?

am i dumb

[plush wing]

for example we did x-ak = t just find x from here and you will realize that its integer

[raw jetty]

huh

wdym?

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[raw jetty]

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[alpine sable]

whats the fastest way to multiply matrices like these? i know the standard way but it gets pretty annoying to add and multiply that many times

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

would really appreciate a response if anyone knows a shorthand or faster method of multiplying such matrices

[tribal geyser]

I think there’s really no easier way

[crude shadow]

its you that gets faster, when u get used to them u can just calculate them mentally

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[steady thorn]

hey guys, anyone got some tips to how i should approach these questions

[steady thorn]

or can someone help explain the question in the first place i dont really understand it 😭😭😭

[zinc bolt]

Do you know the first principle definition of derivatives?

[steady thorn]

not really

is it not just finnding the first derivative or something like that

yo man come back

its just this right

so what is the forward difference and backward difference

oh and the centered difference

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@steady thorn Has your question been resolved?

[brisk ruin]

what is your question lol?

[steady thorn]

good question

can anyone help me explain like the first few sentenced of this

[steady thorn]

this

like what is forward backward centred difference

or straight up explain what is mesnt by first and second order approximations

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[tame nebula]

need help with the using the trapezoid here

its using this right

[pale swift]

log
?

[tame nebula]

?

i mean calclulating this part

i see two trapezoids

[tacit arch]

trapezoid could work for some part of the integral yes

[tame nebula]

and i want to know how to use the 2 trapezoids and add them to get the area

[tacit arch]

area of two trapezoids = area of trapezoid 1 + area of trapezoid 2

[tame nebula]

how do i get the area of a trapezoid

[tame nebula]

with the numbers here

[tacit arch]

find the lengths of the trapezoid you need

use the information in the function h(x)

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[atomic shore]

If anyone want to enlighten me on error propagation I would be delighted.
Let say I have two measured values, 100 and 25 both with an error margin of 1.

If I would subtract one from the other one how big would the error margin be?

In my head it make sense that they would add.
(100+-1)-(25+-1)=75+-2

Tho some sources I find seem to construct some sort of function to determine the value of the error margin like taking the squareroot of the sum of the error margins squared.

[atomic shore]

So if anyone has an easy answer/resource to turn towards that would be great

[placid zinc]

There's no single way to do error analysis. One resource may be different from another

From my eng courses, we would add like you suggested. I don't know what your prof may personally want, though

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@atomic shore Has your question been resolved?

[atomic shore]

Ahh, well that sucks

Thanks, I will check with her and see then

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[worn bane]

can anyone suggest an easy way of doing this...

[forest marsh]

,rccw

[tight pier]

maybe write 945 as factors or prime factors

2x+3 and 2x+5 would imply some odd number

[waxen elk]

Ich bin grad fertig und es war der horror

[tight pier]

du kannst mir hier nicht schreiben lol

[worn bane]

?

[waxen elk]

Oopp

Mbmb

[worn bane]

.close

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[worn bane]

i am skipping this question...that's why close

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[formal hornet]

Last problem, I’m not sure how to evaluate it?

I know the integral converges but the result I got seem to be infinity

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[formal hornet]

<@&286206848099549185>

[wind cloak]

you can't use the geometric series expansion on this integral

since x is from 0 to infinity

try splitting it from 0 to 1 and 1 to infinity

and on the second integral sub x --> 1/x

then you can do what you are doing

[formal hornet]

ahhhh i see

thank you very much

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[lofty crystal]

Sorry, this question was asked earlier by me, but i didnt undertood, plus i went afk 😭 How do you even approach this problem?

[north rover]

Try to see where each one is positive and determine if the other graph is increasing/concave up on that interval.

If concave up, then your “positive” one is your g’’, and the concave up will be g.

If increasing, you’ll have either the pair g’ and g or g’’ and g’.

[lofty crystal]

so first should i look for the concave thing or the positive slope?

[north rover]

Concave

It gives a direct answer

[lofty crystal]

i dont understand, you're relating the "concave up" thingy to the slope being positive, right?

[north rover]

No, concave up implies the second derivative is positive

[lofty crystal]

So in that case, the third one has a concave up like structure, and as well has the positive stuff

[lofty crystal]

Yeah

[lofty crystal]

so is the third one having positive second d?

dang, im not able to undestand it 😭

[tribal geyser]

I would look at the points where the slope = 0, and see if it coincides with roots of another graph.
THEN, I would slope with sign

[lofty crystal]

what do you mean by roots of another graph??

[tribal geyser]

For example, between II and III. When III = 0, slope II= 0

[lofty crystal]

yeah

thats what

then?

[tribal geyser]

What does it mean yo have this ?

[lofty crystal]

well i think it does mean that its the derivative of that graph, like III being the derivative of II

[tribal geyser]

Exactly, now you can confirm with increase / decrease of II coinciding with sign of III

[lofty crystal]

so like, when the II graph is moving in the positve area, the III graph is moving in the negative area, but as the II graph approaches to the X axis, the III graph too approaches to X axis

[tribal geyser]

Rather when graph III is positive, graph II increases and vice versa

[lofty crystal]

but when graph II is postive, graph III decreases

am i correct?

[tribal geyser]

The sign of graph III is correlated with the slope of graph II.

We’re not talking about the sign of graph II

That means III =(II)’

[lofty crystal]

yes

okay

oh my god, why do i feel this is so much complex!

[tribal geyser]

That’s Why I told you try to find of the zéros of a graph coincide with a flat slope of another

[lofty crystal]

well, then II and III are doing so

yeah just like thay

[lofty crystal]

when the II is approaching the valley, the III one touches the X axis

wait so does that mean, I is the main function, II is thefirst derivate, and III is the second derivative?

[tribal geyser]

If the zéro coincides of a graph coincides with max or min from another graph. Then the first graph is probably a derivative

[tribal geyser]

No

What’s the relationship between I and III ?

[lofty crystal]

oh so is it like this: If the slope of the graph is 0. A flat line, then the coincinding graph would touch X axis to return 0?

AND

that the Coinciding graph is the derivative of that first graph who has a flat line on it

[lofty crystal]

that when the I touches X axis, the slope of the III graph at that point becomes 0

[tribal geyser]

Yes ! This allows you to spot quickly a good candidate for derivative. But you still need to Check the signs after Sporting the candidate

[lofty crystal]

okay I understood that

but then how shud i check the signs to confirm it?

[tribal geyser]

So can you confirm that the slope of III (increasing/decreasing) coincides with sign of I ?

[lofty crystal]

well, when the slope of III is increasing the sign of I becomes negative

atleast thats what i made out

[tribal geyser]

Really ?

[lofty crystal]

here;s the thing: Im not understanding how do i handle the sign

i got it how to check for the slope and the 0 over the X axis

(also sorry im troubling you 😭)

[tribal geyser]

Im just saying, check this again

[tribal geyser]

No worries

[lofty crystal]

so

yeah, so when the slope is increasing in III graph, the I graph stays above the X axis

so i think its positive?

[lone heart]

@lofty crystal Has your question been resolved?

[timber wigeon]

@sudu still need a hand?

@lofty crystal

[lofty crystal]

yeah please

😭

[timber wigeon]

I think an easier way to look at this question is to look at turning points

You know that if f(x) has a turning point at x=a, then f'(a)=0 right?

@lofty crystal

[lofty crystal]

yeah just a sec

i was downloading the img

[lofty crystal]

yeha

turning point in the sense that it forms a flat line

right?

[timber wigeon]

Yes at that point the curve is "flat"

[lofty crystal]

hmm

[timber wigeon]

So we can use this to check which curves are the derivatives of the others

[lofty crystal]

okay

[timber wigeon]

eg. I has a 0 at the origin and III has a turning point there

[lofty crystal]

so like for i see the 1st graph, the 3rd one directly relates with it

[timber wigeon]

Suggesting that I is the derivative of III

Yes exactly

[lofty crystal]

wait, so like the III one is the derivative graph right?

Like the III one gives the information aboput the slope of the 1st graph

so if graph 1 is g, then the 3rd one is g'?

[timber wigeon]

Check the turning points, if there is a turning point at the one you think is g, is the one you think is g' at 0?

[lofty crystal]

oh actually no

cuz its like somewhat behaving like this

[timber wigeon]

mhm, so what does this suggest

[lofty crystal]

but from what i cud see here, is that the II and III are going well together

[timber wigeon]

And which is the derivative of the other

[lofty crystal]

that maybe the III is the second derivative of I one?

[timber wigeon]

Maybe, and what about II?

[lofty crystal]

So i think its like I is g, II is g' and III is g''?

[timber wigeon]

Not quite

[lofty crystal]

but see, the 1st one is directly relating with the 2nd one

[timber wigeon]

It must "relate" at all points remember

What about the other points where II is 0?

[lofty crystal]

yeah but

then how do you identify the raw function?

[timber wigeon]

The same idea we've been using but remembering it must hold for all points

So according to your answer, at all points when II is 0, I must have a turning point

[lofty crystal]

yeah thats where im getting wrong

failing to relate it with all of them together

[timber wigeon]

Do it one step at a time

It's much harder to do all 3 at once than 2 at once

[lofty crystal]

well, whats this then? I mean, the other two sections have a slope and the graph at 0, but this has nothing

will it be zero when the first one is zero as well?

[timber wigeon]

Not necessarily

Remember, derivatives only relate the gradient, not actual value

[winter light]

It means that graph II is not the derivative of graph I

[timber wigeon]

Hopefully from this you can see that neither I is the derivative of II or vice versa?

[lofty crystal]

yeah!

[timber wigeon]

Good, so what do you think is best to check next?

[lofty crystal]

so lets check I and III?

so like which area is the slope positive

[winter light]

Usually it's better if you start from max/min and roots

[timber wigeon]

Best to check turning points as you have no scale on the y-axis

[lofty crystal]

okay

[timber wigeon]

But yes this is good

[lofty crystal]

guys uk what, i shud just take a break from this

i really really appreciate you guys for trying to help me

but for some reason its just going above my head

Sorry, and thank you so much!

.close

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[sharp iris]

hello

[sharp iris]

can we calculate the kernal of a linear map using carmer mehtod

[vale wigeon]

what's a carmer method?

[sharp iris]

determinant method

[vale wigeon]

oh Cramer's rule?

[sharp iris]

to solve a linear system

[vale wigeon]

no. unless the kernel of the map is just {0}, it won't work.

[sharp iris]

yees

[vale wigeon]

and if det(A)≠0 you do not need to do any more calculation anyway bc then you will know there and then that the kernel is trivial

[sharp iris]

ah okay so i only need to calculate the det if its not equal to 0 then the map is injective and the ker is trivial

but how is that

and why

[vale wigeon]

mmm no

like, if det=0, you still need to do some other work to actually calculate the kernel

which is most likely gonna happen with like, row reduction or something

[sharp iris]

yeah i know that

but when det(A)≠0 i can solve the system normally

using cramer’s rule

then when i find the unknowns

[vale wigeon]

yeah and get that the only solution is 0

so it is pointless

finding the kernel means solving Ax=0

[sharp iris]

the value of the unknowns

yees

[vale wigeon]

so if you know what you're gonna get

there's no point to doing it

[sharp iris]

oh okay

i was verifying if we can calculate it using the method

also what can the teacher ask me about it

[vale wigeon]

no we can't

[sharp iris]

i talked about everything in the homework but i don’t know if its enough or not

[sharp iris]

alr

why

i didn’t get it

[vale wigeon]

because the method fails for det(A)=0 and gives no info about what the kernel is

[sharp iris]

okay

and not in the kernal

when we solve a system using the rule

and the det A=0