help-26

[hearty gyro]

how would one solve this

[hearty gyro]

with a diagram

[wet sun]

What’s the question

[wary tulip]

[hearty gyro]

whats the equation

draw a nth step diagram

[wary tulip]

equation for what? the number of footballs?

[hearty gyro]

yes

not for the box

[wary tulip]

there is 1, then 2 + 1, then 3 + 2 + 1, and so on

[hearty gyro]

ok but how do u write it as an equation

[wary tulip]

what is this question

[hearty gyro]

its a non linear pattern

[wary tulip]

yea the growth quadratic

[hearty gyro]

how would i draw a diagram

[wary tulip]

!original

[topaz sinew]

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.

[hearty gyro]

bruh

[hearty gyro]

here

[wary tulip]

i don't see a question i just see a box with footballs in it

[hearty gyro]

its a visual pattern

its (1,1) (2,3) (3,6) (4,10)

[hasty verge]

yeah

does it have to be an explicit formula

or can it be recursive

[hearty gyro]

wdym by that

[hasty verge]

nvm

do you know the formula for the sum of numbers 1+2+3+...+n?

[hearty gyro]

no

i mean i could probably solve it with a formula

for quadratic pattterns

but my teacher wants me to draw the nth term diagram

like how would i tlook on th enth step

[hasty verge]

wdym draw the diagram

it would just be a 10x10 triangle

[hearty gyro]

idk its some weird concept he made

that works

but its confusing

[hasty verge]

is he asking you to just draw
o
oo
ooo
oooo
ooooo
oooooo
ooooooo
oooooooo
ooooooooo
oooooooooo

or find an equation for the number of footballs at the nth step

[hearty gyro]

both kinda

bro its so hard to explain

what the diagramlooks like

i can draw it

for a different pattern

[hasty verge]

i dont get what u mean

[hasty verge]

the diagram is this no?

[hearty gyro]

itsa visual diagram

[hasty verge]

can i see an example

[hearty gyro]

yes

ill pulll up his slide

[hasty verge]

oh

[hearty gyro]

tops linear and the second one is non linear

[hasty verge]

i mean the nth step diagram would just be a triangle with dimensions n and n

[hearty gyro]

i just draw a triangle

withh the dimensions na nd n?

[hasty verge]

if u catch my drift lol

those are supposed to be footballs but i gave up trying to be neat

[hearty gyro]

wouldnt work

all the ns have to add up tot he formula

like if you put the diagram into an equation

it has to work

maybe its triangle formula

[hasty verge]

its not

it's kind of the triangle formula with a little correction

[hearty gyro]

u get how its 2n x 2n-1 on the diagram

[hasty verge]

yea

[hearty gyro]

it makes the equation

when you simplify it

then you use the equation to see if the amount of (whatever is being is used as a counting block) for that step works with the equation

[hasty verge]

i mean the formula is (n)(n+1)/2

and this is the best i got for you

[hearty gyro]

thanks

[hasty verge]

idk how else you'd do it

[hearty gyro]

actually i think u might be right

i used the quadratic formula

[hasty verge]

oh cool

[hearty gyro]

thanks

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[hasty verge]

yea np!

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[hasty verge]

it says use parameter t

there's no t in ur solution

[neon iron]

I took this screenshot before realizing that

even then its still wrong

[hasty verge]

I assume you did $x+y-7+z=-x+y+7-z?$

[thorny flame]

Vѳrtєx-

[neon iron]

yes

[hasty verge]

or something else

[neon iron]

is that wrong to do?

[hasty verge]

and how did you get to your answer

[neon iron]

wait sorry this is what i did

oops how do i rotate it

[hasty verge]

,rccw

[hasty verge]

for one, (0, -7, 0) does not work in the left side

because the left side is y-7

-7-7=-14

but anyway that doesn't help you solve for the intersection

[neon iron]

how should i go about solving it

<@&286206848099549185>

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@neon iron Has your question been resolved?

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@neon iron Has your question been resolved?

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[chilly walrus]

a bit confused by this proof https://en.wikipedia.org/wiki/Cauchy_product#Proof_of_Mertens'_theorem

[chilly walrus]

how does this follow?

this means $c_i = a_{n-i} B_i$

[thorny flame]

artemetra

[chilly walrus]

$\sum_{k=0}^i a_k b_{i-k} = a_{n-i} \sum_{k=0}^i b_i$

[thorny flame]

artemetra

[chilly walrus]

why is this true?

or am i missing something

[icy sky]

im not proving this formally, but hopefully this helps

[topaz sinew]

@chilly walrus Has your question been resolved?

[chilly walrus]

hmmm

[icy sky]

maybe i drew the lines wrong, but youre basically summing the triangle two different ways

yeah i think the red lines should be horizontal

point still stands

also indexing starts at 0

lmao

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[distant totem]

When dealing with uncertainties, are there some kind of formulas we can use to find the absolute and relative uncertainties of numbers, and if so, can we also find them for compound uncertainties

[topaz sinew]

@distant totem Has your question been resolved?

[gray ridge]

do you have an example? (i'm not sure if i can help, but stating an example might help others to help you)

[distant totem]

Yeah ofcourse.

Let's say we have a uncertainty of

length = 10cm+-0.1

and

width = 5cm+-0.5

Is there any formula to find out the area of it, and the uncertainty

I know we can do 5*10 to find the value on the left so it becomes

50cm^2 +-

But finding the uncertainty is what I have trouble finding

[gray ridge]

ah, as, you can see multiplying would makes the situation much harder, so there will be four cases we should consider
length | width | area
max | max | 10.1*5.5
max | min | 10.1*4.5
min | max | 9.9*5.5
min | min | 9.9*4.5

and finally we shall find the absolute max and absolute min of these extrema from the 4 cases

[distant totem]

Alright I see

[gray ridge]

hope that helps!

[distant totem]

Yeah thank you :)!

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[dusty dew]

Help please hwo do i solve this

[fading owl]

Its a linear equation sequence

Do you know how to add and subtract linear equations?

@dusty dew

Sorry but i gtg

[undone finch]

Are you solving for y or x?

@dusty dew

I'll just put in what I'd do.

-2(2x+3y=7)

• 4x-y=1

---

-7y=-13

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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.

[undone finch]

I'll avoid doing do again.

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[nocturne lake]

Q2c

[nocturne lake]

I dont get how they get the notation in

In question 2c

[gentle night]

Did you solve the question

[smoky sparrow]

you take the intersection of the two solution sets

like this but more complex

you can visualise it by drawing a number line, where the top row is the solution to the 1st inequality, and the bottom row is the solution to the 2nd inequality

then you want the regions where both inequalities are true at the same time

also $\cup$ means union

[thorny flame]

south's secret twin brother

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[dusty dew]

Bothh

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[lyric harbor]

I dont know where I made a mistake evaluating

[lyric harbor]

well, the root I kinda just gave up, I didnt know what to do

[craggy haven]

can you show your work

[lyric harbor]

not rly, left my notebook at home

I just want to refresh before class

[cunning kayak]

what was your approach if you remember?

[lyric harbor]

for the root I did the weird thing to multiply to and bottom

with root

switch signs

so top would be 5x^2-100 -25

smth like that

[cunning kayak]

yup and its called rationalizing

[lyric harbor]

the top would factor to 5(x-5) (5+x)

[lyric harbor]

yuh, that

the bottom tho, idk

I remember I left it as it is

and canceled the x+5

[cunning kayak]

yup

[lyric harbor]

but the root was on the bottom

and there is a -100

so I didnt know what to do

[cunning kayak]

and in bottom it will be:
root(5x^2 - 100) + 5

[lyric harbor]

yeah

[cunning kayak]

and your simplied expression wouldn't be indeterminant form

so just substitute x=-5

and you will good to go!

[lyric harbor]

?

but you cant have negatives in roots

[cunning kayak]

yeah thats x^2

so it will become +ve

[lyric harbor]

but -100

wait

we substituting it with inf?

[cunning kayak]

wait no

wait lemme show u

[lyric harbor]

aight

[cunning kayak]

denominator would become 10

and numerator would 5 * (-10)

[lyric harbor]

I still dont get what you are doing with the -100

root(-75) + 5?? what did you do there?

NO

IM DUMB

AAHHH

[cunning kayak]

uhm

got your mistake

[lyric harbor]

5*25

jesus

[cunning kayak]

yeah

[lyric harbor]

ugh

[cunning kayak]

125

[lyric harbor]

thanks

[cunning kayak]

exactly

np

[lyric harbor]

damn it 😭

[cunning kayak]

i thought you thought

[lyric harbor]

what abt the second problem here, I got -inf

[cunning kayak]

that root(a-b) = root(a) - root(b)
which is false

so i was typing that

[lyric harbor]

oh lol

[cunning kayak]

then i realised you did calc mistake

[lyric harbor]

sleep derivation really does mess you up

being sick sucks

[cunning kayak]

true

[lyric harbor]

what about on the lim x-> -inf?

my answer was wrong

[cunning kayak]

2nd one?

[lyric harbor]

I did a bunch of factoring and then put the -inf and got -inf

ye

[cunning kayak]

x^2 + 13x + 40 = (x+8)(x+5)

[lyric harbor]

yup

oh

just inf

got it

[cunning kayak]

x^2 - 25 = (x-5)(x+5)

[lyric harbor]

yet another calc mistake

wait no

that cancels

so there is a inf/-inf situation

[cunning kayak]

yea its left

wait a bit

[lyric harbor]

oki

[cunning kayak]

i got a phone call

[lyric harbor]

alr

take ur time

[cunning kayak]

back

so

[lyric harbor]

alr

[cunning kayak]

we are left with

(x-5)/(x+8)

take out x common

so x(1-5/x)/x(1+8/x)

[lyric harbor]

ok

yeah

[cunning kayak]

and 5/-inf = 8/-inf = 0-
take it as 0

and you will be left with 1

[lyric harbor]

I did not know it had to be done like that

I thought you would substitute it

[cunning kayak]

that works too

[lyric harbor]

wait

inf/inf

ah

1

oh, I didnt have a negative inf on the numerator

thats where I messed up, calculation error

[cunning kayak]

bro tc of ur calc

[lyric harbor]

yeah 😔

at least I know that it isnt my method

I just need to be more attentive

[lyric harbor]

now for the last one here on the second image

[cunning kayak]

yup thats it

you have suffice knowledge to solve such ques

[lyric harbor]

I've been doing terrible on my tests tho 😭

[cunning kayak]

calc mistake

that one too

[lyric harbor]

bro..

[cunning kayak]

dw u will get better

[cunning kayak]

it would be
1/((-5) - (-2))

so -5 +2 = -3

[lyric harbor]

DAMN IT

AND I HAD MORE THAN ENOUGH TIME TO CATCH ALL OF THESE

this was an online quiz 😭

[cunning kayak]

:c

[lyric harbor]

yeah :(

this is actually so sad

[cunning kayak]

ik the feeling dw

[lyric harbor]

well wahtever, im ready for the test next week

[cunning kayak]

in one of tests i read prime number as even nos.

[lyric harbor]

just gotta be careful

[cunning kayak]

and messed the shit up

[lyric harbor]

damn bro 💀

[cunning kayak]

yeah...

[lyric harbor]

I mean fair

I can see that happening to me too

ugh

anyway

thanks for your help 💪

ur a real one fr

🔥

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[cunning kayak]

🙂

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[vernal geode]

Find the smallest positive multiple of 84 that has only 6 and 7 as digits

[opal vault]

factor 84 in primes, then find a condition for being a multiple of each prime power

[vernal geode]

emmmmm

i factored it to 3 times 7 times 2^2

[opal vault]

yeah

[vernal geode]

and from here?

[opal vault]

you agree that a number is a multiple of 84 if and only if

it's divisible by 3, 7 and 4?

[vernal geode]

yes

[opal vault]

ok

let's start with an easy one

when is a number divisible by 4

[vernal geode]

sure

[vernal geode]

last two digits...

[opal vault]

ok

[opal vault]

so what are the possible last two digits

of the number you're looking for

[vernal geode]

66 and 76?

[opal vault]

check again

[vernal geode]

oh yh

76

only

[opal vault]

yes

so your number ends in 76

[vernal geode]

fair enough

[opal vault]

next, divisibility by 3

[vernal geode]

ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

and you just continue the trend?

[opal vault]

yeah

[vernal geode]

fair enough give me 5 mins ill try to figure it out myself

ty

having an issue

my number is getting really big really fast

.close

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[mortal heart]

hi guys,

a fair dice is thrown once. find the probability that the score is bigger than 3 or a prime number or both.

is the answer 5/6?

[mortal heart]

3/6 + 3/6 - 1/6 = 5/6

[opal vault]

Yes, 2,3,4,5,6

[mortal heart]

if we apply the formula for not mutually exclusive events:
P (A or B) = P(A) + P(B) - P (A and B), aren't we supposed to add another fraction for the "both >3 and prime" ?

[opal vault]

Isn't -P(A and B) exactly that?

When you're computing probability of A or B

If you just add P(A) and P(B)

You overcounted the instances where both A and B are true at the same time

[mellow breach]

we have to find P(>3 or prime or (>3 and prime))?

[mortal heart]

yes

[mortal heart]

i thought we have 3 events

like P(A) or P(B) or P(C)

[opal vault]

We don't

[mellow breach]

i also thought

[opal vault]

We have two events

[mortal heart]

but isn't "both" an event too 😭

[opal vault]

That can happen simultaneously

[mortal heart]

oh...

[opal vault]

"A OR B" in math is inclusive...

[mortal heart]

wait what is inclusive

i only learned mutually exclusive

is it the opposite of exclusive

[opal vault]

Meaning when you say A or B, both A and B can happen at the same time

[mortal heart]

ohh

i thought it's "and"

[opal vault]

The english language (and most languages) are not reflecting that

[mortal heart]

😭

[opal vault]

No that's not what I meant

When you say "A or B" in maths

Either A happens and B doesn't

B happens and A doesn't

[mortal heart]

yes

[opal vault]

Or both A and B happen

[mortal heart]

wait i still don't understand

why do we not add another fraction

for both 😭

[opal vault]

Bc you don’t need to

"A or B or (A and B)"

[mortal heart]

yes

[opal vault]

Is the same thing as "A or B'

[mellow breach]

now i forgot everything about probability

[mortal heart]

wait so the 'both' there means A and B happen at the same time right

[opal vault]

Yes

When A or B is true, it is allowed for A and B to be true at the same time

[mortal heart]

how do i know that

[opal vault]

How did you define "or"

[mortal heart]

only one is true

oh wait

heheh

i think i'm getting it

[opal vault]

Literally the opposite of what I just said 😭

[mortal heart]

yes

WAIT ok

[opal vault]

Not necessarily only one is true

[mortal heart]

is it like this

[opal vault]

"A or B" means "AT LEAST 1 is true"

[mortal heart]

so both can be true??

😭

OH YES

thats right

thats kinda different with the day to day language

[opal vault]

.

[mortal heart]

i thought 'or' means only 1 is correct

yes

ok so basically "or" adds the probability right

like making the probability higher

[opal vault]

Yeah like

"A or B" always happens in more cases than just "A" alone

[mortal heart]

okok

thank you so muchh

[opal vault]

So whenever it's written something like

"What's the probability that A, B, or both"

It just translates to "A or B"

In maths

[mortal heart]

is it bcs P(A) + P(B) for "A, B" already represents "both"?

[opal vault]

Ok so just one thing with what you wrotd

Just remember that "A and B" is present once in P(A)

But it's also present in P(B)

[mortal heart]

yes

[mortal heart]

wait what

this doesn't make sense

but my book says so

[opal vault]

Like

[mortal heart]

😭

[opal vault]

If both A and B are true

Then A is true right?

[mortal heart]

yes

[opal vault]

Ok

So in P(A), the elements of "A and B" are already accounted for aren't they?

[opal vault]

Because of this

[mortal heart]

why does P(A) includes B too 😭

i can understand if both A and B are true, A is true

[opal vault]

I never said it includes B

I said it includes the elements of "A and B"

The elements common to both A and B

[mortal heart]

what's the different between element and other things

[opal vault]

It includes "A and B" if you want

The common part of A and B

[mortal heart]

wait ok let me think

[mortal heart]

how do i know this

accounted as in included in the fraction?

[opal vault]

If A and B is true, then A is true

[mortal heart]

yes thats right

[opal vault]

P(A and B) <= P(A)

[mortal heart]

that looks right but i can't understand it somehow

feels wrong

[opal vault]

Why?

Isn't 2 conditions fullfilled at the same time

Less likely

Than 1 condition?

[mortal heart]

like i perceive A as only A, there's no B in A 😭

but i know if A and B are true, then A is also true bcs A was part of those 'A and B'

i think my logic isn't so good

[opal vault]

The left circle is the realm of where A is true

We call it "A"

And the right is the realm where B is true

We call it "B"

[mortal heart]

yess

[opal vault]

Ok

As discussed

There are some things that can live in BOTH A and B

[mortal heart]

yes

[opal vault]

We call that place "A and B"

[wild dune]

<@&286206848099549185> Am I correct A cylindrical tank has a radius of 4 meters and a height of 10 meters. Water is being pumped into the tank at a rate of 2 cubic meters per minute. However, the tank is leaking water at a rate of 0.5 cubic meters per minute.

How long will it take to fill the tank if it starts empty?
What will be the water level in the tank after 3 hours? that is the question this is my answer 270=π(4) ²h=π(16)h h= 270/16π​ ≈ 270/50.27​ ≈5.37 meters

[opal vault]

!occupied

[topaz sinew]

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).

[mortal heart]

yes

[opal vault]

So "A and B" is that shaded place

You can see that "A and B" is inside the realm of A, isn't it?

[mortal heart]

yess

[opal vault]

Because if you live in a place where both A and B are true, then A is true

[mortal heart]

yes

[opal vault]

Then INSIDE of A, there is "A and B"

Isn't there?

[stoic trench]

What’s ur process

[opal vault]

Please I encourage taking this to an available help channel

[mortal heart]

yes!

[opal vault]

Alright

[stoic trench]

@wild dune move to help 17

[mortal heart]

do we ignore the unshaded part of A?

like it has no B

[opal vault]

We don't ignore it no

[wild dune]

ok

[opal vault]

We're just focusing on what's in both circles at the same time for now

So when you compute P(A), which accounts for all instances where A is true

It also accounts for "A and B", the instances where both are true at the same time, doesn't it?

[mortal heart]

OHHH

I GET IT

[mortal heart]

YES

[opal vault]

Yesss

And when you compute for P(B)

It ALSO accounts for those common instances "A and B" doesn't it?

[mortal heart]

yesss

[opal vault]

Alr

So when you compute P(A)+P(B)

You actually accounted for the common instances "A and B" twice right?

[mortal heart]

yesss

[opal vault]

So you're overcounting

[mortal heart]

yes

[opal vault]

Thus subtract the 'population' of "A and B"

To account for everyone exactly once

[mortal heart]

yesss

ohhh

[opal vault]

P(A or B) = P(A) + P(B) - P(A and B)

[mortal heart]

yes!

soo when the question says "both", is it the shaded area?

[opal vault]

Yes

In the english language, when you say "A or B"

You don’t account for the shaded area somehow

While in maths you do

So when you want the maths meaning of "A or B"

In english you have to say "A or B or both"

[mortal heart]

OHH

thats kinda funny 😭

i need a math dictionary

soo "both" was already included in either P(A) or P(B) rightt, soo we don't add another fraction?

[opal vault]

In P(A or B) we account for the "both"

[mortal heart]

yess

[opal vault]

So this formula is enough

[mortal heart]

and we accounted the "both" twice, so we have to subtract it with the shaded area right?

[opal vault]

Yeah, P(A or B) should account for everyone exactly once, while P(A) + P(B) accounts for "both" twice

[mortal heart]

OKIE YAYYY I FINALLY UNDERSTAND IT

[mortal heart]

THANK YOU SO MUCH!!

[opal vault]

No problem 👍

[mortal heart]

yay! okkk i'll close the channel

.close

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[buoyant stirrup]

if you have a sequence of random numbers from 1-100, a_1, a_2, a_3... a_n such that the sequence terminates if a_n is less than a_(n-1), how would you find x such that the probability that x>=a_n is 50%

[hallow depot]

I ask you pronouns

[buoyant stirrup]

He/they

[hallow depot]

can they give an exemple ?

[buoyant stirrup]

There's a ttrpg I'm designing a "dungeon" for and when you finish killing a wave if enemies, you get to scavenge, and you get to continuously roll the dice until uou get a number less than your previous, so I need to find what number has a 50% chance of the number or something higher being rolled

[hallow depot]

I think x depends on n...if n=100 then there is no such a x

if n=1 then I think x =50 could work

[topaz sinew]

@buoyant stirrup Has your question been resolved?

[buoyant stirrup]

Ok, but what if n is anything else, I'm assuming there's some smooth distribution that describes the probability of x being in the given range of [a_n, 100], but how would I find it or something akin to it?

[topaz sinew]

@buoyant stirrup Has your question been resolved?

[topaz sinew]

@buoyant stirrup Has your question been resolved?

[topaz sinew]

@buoyant stirrup Has your question been resolved?

[odd pagoda]

if you have some programming experience, its probably faster to just run a monte carlo experiment instead of modeling this precisely mathematically

[buoyant stirrup]

I will try, yes

.close

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[valid brook]

Hello everyone! I'm learning vector calculus, and right now I'm trying to figure out how to calculate flux integrals. I'm really confused by all the different changes of measure, from dS to dA to dudx, and I'm not sure if I solved my problem correctedly.

[valid brook]

Given this example, can someone look over what I did and tell me if I set up the problem correctly?

(I already double-checked on my own using WolframAlpha to make sure that the cross product and the definite integrals are evaluated correctly, I just need to make sure that conceptually I used the right approach)

\textbf{Evaluate the flux integral (\iint_S \mathbf{F} \cdot \mathbf{n}\ d \mathbf{A}) where (\mathbf{F} = \left[e^y, e^x, 1\right]) and the region (S) is given by (S: x+y+z=1) such that (x\geq 0, y \geq 0, z \geq 0)}

[thorny flame]

RiverineDolphin

[valid brook]

That's the problem statement

And here's my attempt at a solution:

As I understand, in order to evaluate a flux integral there are three steps:

1. First, find a parameterization r(u,v) of the given surface S in terms of u and v
2. Find the surface normal vector N, given by N = r_u \times r_v
3. Set up and evaluate the double integral

I'm pretty sure I did steps 1. and 2. correctly (indeed for the cross product I double-checked with WolframAlpha)

But I have no idea if I did 3 correctly. In particular, I'm not sure if I used the correct bonds for the definite integrals. Can someone double-check if I set up the boundaries correctly?

And I'm not sure if the integral is supposed to look so "messy" 😭

Please somebody help me!

<@&286206848099549185> Hi there, kindly asking for help.

[topaz sinew]

@valid brook Has your question been resolved?

[valid brook]

No

[valid brook]

<@&286206848099549185> Hi , can someone take a look?🥺

.close

[topaz sinew]

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[minor fable]

Looks right

I could try this myself but i am lazy right now

[valid brook]

Hi there

.reopen

[topaz sinew]

✅

[valid brook]

@minor fable I'm just getting really confused about the double integrals, really 😦

I ended up putting the whole expression into WolframAlpha, and it gave a different answer

So I'm not sure what to do anymore 😦

I'm okay with finding the parameterization function r(u,v), and with calculating then normal vector

I just don't know how to set up the double-integral with the correct bounds.

Can you show me just for that part?

Given the problem statement:

\textbf{Evaluate the flux integral (\iint_S \mathbf{F} \cdot \mathbf{n}\ d \mathbf{A}) where (\mathbf{F} = \left[e^y, e^x, 1\right]) and the region (S) is given by (S: x+y+z=1) such that (x\geq 0, y \geq 0, z \geq 0)}

Ignoring the F \cdot n d A part

Can you just show me how to manipulate the inequalities to set up the boundaries for the double-integral? Please? 🥺

<@&286206848099549185>

[timid junco]

Bluds been trying to get help for two hours now 🤣

[minor fable]

i just put that in gpt as i aint calculating that myself

So i guess youre right with your approach, the only difference is getting the integral

i think the issue lies ln chatgpt

Not at your approach

[valid brook]

Thank you for your effort, but unfortunately chatGPT isn't really helpful for me. I've been trying to debug myself with ChatGPT, and I've gotten multiple different responses each time.

[minor fable]

Yeah

[valid brook]

That's why I'm turning to people here 😅 --- because at least people aren't hallucinating here.

[minor fable]

gpt aint good at maths (instead of gpt o1) for example

But your approach seems right

[valid brook]

I've been just really struggling with setting up the integrals for all any of my double integral problems.

[minor fable]

As you used the usual steps of how to evaluate this

[valid brook]

😭

Alas, the approach being right won't help with the assignment.

The answer has to be right.

[minor fable]

Yeah

[valid brook]

Honestly, I would be very grateful if you can work out the problem for me, so at least I have an exemplar.

[minor fable]

I am just confused why e^(1-v)

[restive inlet]

Do not use chatgpt output when assisting.

[valid brook]

That doesn't look right

Ugh

I think I'm just wrong somewhere, unfortunately.

I'm now trying to do easier problems in the textbook, and still struggling significantly.

[minor fable]

Yeah i know that it has its issues.

I just use it to have better overview of the used techniques/approaches

and no one helped that guy

[restive inlet]

It's in the rules and guidelines of the server to not use it due to its unreliability.

[minor fable]

okay noted it

wont use chatgpt

it wasnt my intention to assist with thaz

[valid brook]

Still hoping that someone will help me with the probleem 😦

[minor fable]

Its just to provide better overview over the approach

As i didnt look up this topic

[valid brook]

Unfortunately, I don't need a better overview over the approach.

I already know the approach

[minor fable]

For me i mean

[valid brook]

I need some help with the actual minuiate

[minor fable]

But your approach seems right

[valid brook]

Which is mostly how to determine the boundaries.

[minor fable]

Whats your problem

also the solution

[valid brook]

My problem is that I'm not sure how to determine the boundaries for the double integral using the constraints given for x, y, z.

I'm trying to set up the integral, but I don't know how.

[minor fable]

I mean it looks right in your exercise

But as i said i didnt do flux integrals

I understand the approaches

i think there MIGHT be errors while setting up the integral. But the first steps are right. You used the cross-product correctly etc

[minor fable]

For example why 1-v?!

Maybe i am wrong with that

It seems right, as you checked with WA

e^v(v-1)+ e^(v-1) + v

Thats what i got

@valid brook

[valid brook]

Wtf?

[minor fable]

And why “-e^v”

[minor fable]

Damn i am just joking

my humor is dumb

[wooden osprey]

???????????/

[valid brook]

That's so out of line.

I'm not sure if I need any help on this problem anymore.

I'll give it another attempt tomorrow.

[wooden osprey]

@minor fable please do not help if you don't know what you are doing

[minor fable]

Man

He didnt get any answer for like many hours at least

I was sorry for this guy

so i tried my best

but as I said he seems right

[minor fable]

But yeah thats the only message you see ofc

[restive inlet]

Stuff like that is uncalled for.
At this stage I'm going to direct you to #rules and #❓how-to-get-help and give you time to read up on how to behave here.

[minor fable]

Yeah yeah

[valid brook]

.close

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[ashen cave]

would remainder theorem still apply here?

x^3-1 = (x-1)(x^2+x+1)

but idk what else to do besides long division (which is kinda tedious)

[mellow breach]

use synthetic division....

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[autumn plaza]

how do i find range

[signal plover]

if a>0, y> y value of vertex, if a<0, y<y value of vertex

[autumn plaza]

um

[reef fjord]

the range is all the possible 'output' values of the function

[pure talon]

OMG I LOVE PRECALC

[autumn plaza]

whats precalc

[reef fjord]

you know that f(x) is an upward facing parabola, so it has a minimum y-value (output), correct?

[pure talon]

oh americans call the class before calculus pre calculus because it’s the class before calculus

[autumn plaza]

oh what

im already doing calculus

[pure talon]

YOURE LYING THESE ARENT DERIVATIVES 😭😭😭

[autumn plaza]

oh..

[signal plover]

thats definitely precalc

[autumn plaza]

is this

[pure talon]

oh yeah nvm this is calculus

[signal plover]

wait nvm

[pure talon]

ik how to do this

[signal plover]

did you not learn parabolic functions in algebra?

[autumn plaza]

wut

idk im in 10th

wait

yeah i learnt min max and stuff

but ages ago

...

[signal plover]

oh ic

[autumn plaza]

im studying for my exam

in 5 weeks 🥲🥲

[pure talon]

find the derivative of the function and set that derivative equal to zero. solve for the x of that derivative and that should be where ur critical points are. critical points are points that show the local minimum and local maximum points of an equation within a given interval, but because this equation is a parabola and its positive, there should only be one critical point and it is a minimum.
once u find the critical point (x=??), u put that x value u have found into the original equation. then u get the y value, so u now have all h need to find the range

@autumn plaza

[autumn plaza]

stationary points?

oh ok i see

can i ask one more question

[pure talon]

yeah

[autumn plaza]

can u help me draw this diagram

[pure talon]

omg idk how to do this one 😭😭

[autumn plaza]

😢

[pure talon]

i’m taking calc ab as well

[autumn plaza]

whats that

ab?

[pure talon]

calculus 1

[autumn plaza]

oh

[pure talon]

america is just weird

[autumn plaza]

i have 2 math course

one is more proof based and one is more straight forward

[autumn plaza]

oh america

[pure talon]

chemistry?

physics?

[autumn plaza]

huh

yea i also do chemistry and physics

[pure talon]

those two classes are basically second math classes 😭😭

[autumn plaza]

wait what

what u mean

chemistry is so much theory

[pure talon]

chemistry uses math to find moles and convert units

[autumn plaza]

oh yea

but organic chemistry

and stuff

[pure talon]

physics uses math to find torque, acceleration, speed, etc.

[autumn plaza]

and then u have to explain so much

[pure talon]

i hate science 😭

[autumn plaza]

i hate proof math

i am bad at vectors lol

[pure talon]

proof math?

is that similar to like trigonometry identities?

[autumn plaza]

hmm i did that for like 2 days

wait lemme find example

[pure talon]

😨

how tf u go from trigonometry to calculus in 2 days 😭😭

[autumn plaza]

its in teh same course

is this the trig ur talkign about

[pure talon]

i lowk don’t know anymore 😭😭

[autumn plaza]

i hate quetions like this

wait can someone pls help me with it

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[junior gust]

And I love science

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[deft holly]

why is it that when i use the function squared and find its derivate, it gives the same min and max pts

[deft holly]

like

this is a question finding the minimum value of PQ

i can use D^2’ and it gives me the same ans as if i were to do D’, but its probs easier to do this way

why does it work tho

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[deft holly]

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[neon iron]

\textbf{Problem:} Let $f\in\6{L^2}\R$ and let $\6{\hat f}{\xi}$ be its Fourier transform. Consider the Sobolev space $\6{H^1}\R$ defined as the space of functions $f\in \6{L^2}\R$ such that $f'\in \6{L^2}\R$.

\vs{5 mm}
Prove that $f\in \6{H^1}\R$ iff: \[
\int_{-\infty}^\infty \8{1+\abs{\xi}^2}\abs{\6{\hat f}\xi}^2 \dd \xi < \infty
\]
\textbf{My Progress:} I am kind of new to Sobolev spaces, so bear with me. I understand how Parseval's theorem connects $\int\abs{\6fx}^2 \dd x$ to $\int \abs{\6{\hat f}\xi}^2 \dd \xi$, but I am stuck on handling the $f'$ condition. I proved prior that $\6{\widehat{f'}}\xi = 2\pi j \xi\6{\hat f}\xi$ with $j = \3{-1}$, but I am not sure how to combine that with $f\in \6{L^2}\R$ to show that the integral is finite. Also, I don't really see why adding 1 to $\xi^2$ should appear naturally?

[pseudo jetty]

,, \int \abs {f'}^2 = \int \abs {\widehat {f'}}^2 = \int \abs {2\pi i\xi \widehat f}^2 < \infty

[pseudo jetty]

so $f, f' \in L^2(\R)$ is equivalent to
[ \int (\abs f^2 + \abs {f'}^2) < \infty ]
is equivalent to
[ \int (\abs {\widehat f}^2 + C \xi^2 \abs {\widehat f}^2) < \infty ]
where $C$ is a constant

[neon iron]

Oh so thats how you characterise the membership of f and its derivative in L^2(R)

[pseudo jetty]

well individually theyre L^2 so the sum of their norms is still L^2

im just going to sweep under the rug the entire question of how you take derivatives of L^2 functions

[neon iron]

I didnt realise that I can check whether $f\in \6{H^1}\R$ just by looking at $(1+\abs{\xi}^2)\abs{\hat f(\xi)}^2$ instead of directly checking the integrals of $f$ and $f'$ in the spatial domain

[neon iron]

but thats cool i guess

so 1 + |xi|^2 is because its not just about the function being square integrable but also how it behaves at infinity

thonk

[ocean terrace]

hi snow

hi kilo

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[shadow nymph]

When we say “The sum of successive integers is necessarily even”
Do we say that Q is a sufficiency condition for P?

[shadow nymph]

I'm trying to translate this sentence in math

[glass maple]

i might just be picky but im finding some of the characters hard to read

[shadow nymph]

yes

let me rewrite it

[hasty arch]

i feel bad for ur teacher 😭

having to grade your paper

[glass maple]

damn bro getting roasted for no reason

[shadow nymph]

I did get roasted by a old student just this moring

[glass maple]

is that a k

after n

[shadow nymph]

Dang sometimes my Autism just cook me up

[shadow nymph]

yes

any easier way to draw k

[shadow nymph]

Wallahi im finished

[hasty arch]

yes

[glass maple]

for all n, where k is an integer squared, there exists an integer, gamma, such that 2 * gamma implies the sum of successive integers from k to n

[glass maple]

although the implication here doesn't really make sense

[shadow nymph]

not bad

thanks

[shadow nymph]

Fr... but the exercices say "Study the implication ..."

else I would just write

equal instaid of implies

u know wut fuck it

it doesn't make any sense

[shadow nymph]

wait wut

no n and k is an integer

hello ?

@glass maple

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@shadow nymph Has your question been resolved?

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[fleet zenith]

Good day to you, I just need help in simplifying the 1st expression and if it's the same as the second expression Thank you and God bless \ ^o^/

[acoustic pecan]

what do you think

[fleet zenith]

Well no lol

Did I get it right?

[thorny flame]

amitt

[fleet zenith]

Thank you!

So it's not the same right?

[mellow breach]

no

[fleet zenith]

no as in it is the same or no, it isn't the same?

since the second expression involves an exponent and the first one is just a fraction, am I getting this right?

[lucid junco]

no

[fleet zenith]

No?

[mellow breach]

u know logarithm identity?

[fleet zenith]

u mean the rules and stuff?

ye kind of...

is it this?

[thorny flame]

Edmund Cloudsley

[twin junco]

Rule 3 might be helpful 👀

[neon iron]

yup yup

[fleet zenith]

Oh thanks! so expression 1 and 2 are not the same

[twin junco]

depends on the value of x maybe

[neon iron]

you can try plotting them

[fleet zenith]

wdym?

[twin junco]

(but in general, as functions, no)

[fleet zenith]

oh

[neon iron]

,w plot y = log_2 (x/3), y = 3log_2 (x)

[thorny flame]

Results provided by WolframAlpha

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

Requested by alison_burg3r5

[neon iron]

they do intersect at x = 1

[fleet zenith]

oh u can plot logarithms? I didnt know that 😭

[neon iron]

you can plot whatever

well not whatever

but yeah most functions

are plottable

[fleet zenith]

Ig im not in that part yet, but the questions basically ask if its tru or not that expression 1 n 2 are equal/same

[fleet zenith]

Thank you everyone! (´▽`ʃ♡ƪ) Have a wonderful day!

[neon iron]

they are equal

for a single value

[fleet zenith]

ok now im more confused

[neon iron]

There is a difference between equality

and identity

[fleet zenith]

o

[neon iron]

lemme give you an example

[fleet zenith]

aight

[neon iron]

let's say I have the equation

y = 2x + 3

and

y = x + 4

and I have the value of x = 1

what would the first equation equal to?

y = 2(1) + 3 = 5

and the second one would equal to

y = 1 + 4 = 5

so they are equal!

but

[fleet zenith]

o

[neon iron]

let's say I had a different value of x

let's say I had x = 2

2(2) + 3 = 7

but

2 + 4 = 6

here, they aren't equal

therefore they aren't identical

if two equations are equal for ALL values of x, they are identical

[fleet zenith]

ohhh thank you! I get it now, though I have another question how about this?

[neon iron]

how about you try this one ;)

and I'll guide you through wherever you get stuck

[fleet zenith]

no I just need to know how to simplify expression 1 or can it not be simplified?

[neon iron]

hmmm doo you reall need to simplify expression 1

or expression 2?

[fleet zenith]

not rlly lol

its just to review since I have an exam

😭

[neon iron]

okay

[fleet zenith]

anyways is this the rule for expression1?

[neon iron]

yup

[fleet zenith]

Ohhh

so if it has a variable then its a product rule?

and if its fraction its quotient rule

ok thanks!

[neon iron]

not exactly

no

[fleet zenith]

hm?

wdym

[neon iron]

It can be either a variable OR a constant

the rule would apply nevertheless

to give you an example

[fleet zenith]

oh

[neon iron]

$$\log_b \left( \frac{x}{y} \right) = \log_b x - \log_b y \$$
$$\log_2 \left( \frac{8}{4} \right) = \log_2 8 - \log_2 4 \$$
$$\log_b (xy) = \log_b x + \log_b y \$$
$$\log_3 (6 \cdot 2) = \log_3 6 + \log_3 2 \$$

[fleet zenith]

but for the expression 1, I realized it's not multiplying 2 and x so they're one um what do you call it

[thorny flame]

Edmund Cloudsley

[fleet zenith]

OH

[neon iron]

2 and x are being multiplied

[fleet zenith]

Ohhhh

[neon iron]

yup yup

okay wait

[fleet zenith]

oki

[neon iron]

$$\log(2x) = \log 2 + \log x$$

[thorny flame]

Edmund Cloudsley

[neon iron]

this is expression 1

[fleet zenith]

Thank you!!!

[neon iron]

with the base being 3 obviously

[fleet zenith]

I'll fr ace that test fr 😩😩🙏🔥

[neon iron]

so they can be equal for some value(s) of x

but they aren't identical

[fleet zenith]

thanks for clarifying it to me. (´▽`ʃ♡ƪ)

[neon iron]

,w plot log_3 (2x), log_3 (2) - log_3 (x)

[thorny flame]

Results provided by WolframAlpha

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

Requested by alison_burg3r5

[neon iron]

so if you had to say, they are equal, would you say they are equal?

[fleet zenith]

not really since expression 2 is subtraction

if we're following the product rule it's supposed to be addition

so the answer is false 😩

[neon iron]

they can be equal. They can't be identical

[fleet zenith]

Yeah in that concept so thanks!

https://tenor.com/view/cat-kiss-gif-25376137

[neon iron]

Good luck with your test

[fleet zenith]

Enjoy your day lol

[neon iron]

you too

[fleet zenith]

thanks 🙏🔥

.close

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[prime oxide]

7th question pls anyone

[topaz sinew]

Show your work, and if possible, explain where you are stuck.

[cunning kayak]

hint: apply point-line disn formula with x-axis & y-axis
take locus as (h, k)

[prime oxide]

Then

Could u pls send a more elaborate solution

pls

[cunning kayak]

!nosols

[topaz sinew]

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.

[cunning kayak]

can u solve it further?

[prime oxide]

it aint a homework

am doing it for practice

[cunning kayak]

can you?

[prime oxide]

got it thank u bro

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If you are done with this channel, please mark your problem as solved by typing .close

[prime oxide]

.close

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[astral monolith]

I don't know how to find x and y

[astral monolith]

urm hello

[neon iron]

,rotate

[neon iron]

fitzee right? which class?

[prime oxide]

10

[neon iron]

ok

online or offline?

[prime oxide]

integrated

[neon iron]

k

[neon iron]

have you tried anything

?

@astral monolith

[astral monolith]

i just need the answer step by step to recall it, cz i actually forgot to deal with it

this one is based on google helo but at the end it is stuck there

[neon iron]

,rotate

[topaz sinew]

@astral monolith Has your question been resolved?

[astral monolith]

I don't know how to find x and y

,rotate

[thick lily]

try multiplying by the conjugate of 2+i. This is nearly the same as multiplying by the inverse

[topaz sinew]

@astral monolith Has your question been resolved?

[topaz sinew]

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