help-33

[carmine sandal]

so ill give u one of them

for 0.1x^2

the 2 comes down and is multiplied with 0.1

giving 0.2

and 2 in the power

drops to 1

giving u

0.2x

im gonna be honest i can explain it to u

but i think youll understand it more

witha vid or smthng

[plucky trail]

Okay no worries I'll look it up and try to find a video

Thank you for the help!

[proud ice]

You mean $\frac{d}{dx}\left[ax^b\right]=abx^{b-1}$

[elfin berry]

SWR

[carmine sandal]

yes im not sure how to use the Latex bot

thanks 😭

and i forgot to add d/dx

yes

ill delete it to avoid confusion apologies

[carmine sandal]

im so sorry for confusing u further 😭

[plucky trail]

I will look it up and try to find a video thank you both!

That's okay my life is confusion so it's nothing new. 😄

.close

[marsh citrus]

Channel closed

Closed by @plucky trail

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[opal turret]

how can i solve part (c)?

[marsh citrus]

@opal turret Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[hasty hemlock]

taylor series

[hasty hemlock]

i found x^n/2^(n+1)

got interval -2 < x < 2

now i have to check if these value converge or diverge

but if i plug x = 2 in the serie i got 1/2 after cancelation

but what is it than converges or diverge

[brave marsh]

Do the terms of the series go to 0 in that case?

[hasty hemlock]

yeah n = 0 to infinit

[red nimbus]

What sequence do you get in the sum when you plug in x = 2

[hasty hemlock]

.rotate

,rotate

[brave marsh]

What you've done is fine. But the series you get is not just 1/2, it's the series whose terms are all 1/2.

[hasty hemlock]

does it mean that it is diverges or converges for x = 2 ?

[brave marsh]

And if the sequence of terms in the series doesn't converge to 0, so you probably know a test for convergence/divergence that concludes right away.

[hasty hemlock]

so i basically used the divergent test for this right ? so its not equal to 0 so it diverges ? am i right ?

[brave marsh]

Yes

[hasty hemlock]

oke thx a lot

[red nimbus]

You are infinitely adding 1/2 basically

[hasty hemlock]

ow oke thanks guys

.close

[marsh citrus]

Channel closed

Closed by @hasty hemlock

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[alpine basalt]

can i ask DSA questions here

[jagged oracle]

!da2a

[marsh citrus]

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 basalt]

or does anynone have a recommendatino of a better place, like a similar CS server

[tired oxide]

you can ask here

[alpine basalt]

i asked the Q

[jagged oracle]

Sir it's a help channel

You can ask

[alpine basalt]

yeah that was my Q

lol

[tired oxide]

oh

[jagged oracle]

But pls wait if it takes time

[alpine basalt]

data strcture and algorithms

[jagged oracle]

Yes ik that

Wait we have the goat smaych here

She can help

For faster help you can go to specific channel dedicated to coding and ask there

[alpine basalt]

can we make an algorithms channel

[alpine basalt]

where is it lol

[jagged oracle]

#computing-software

[alpine basalt]

i dont uh

[jagged oracle]

Okok

[alpine basalt]

think that's what i'm looking for

that seems like programming

[tired oxide]

just ask your DSA question here lol

[jagged oracle]

Okok sir you can go to
#1207411538650992701

And you can go to the programming thread

[tired oxide]

you can also ask in #computing-software, it's not pure programming

[jagged oracle]

You can find DSA geeks there

[alpine basalt]

something like this

[alpine basalt]

oh ok thanks

didnt know that existde

is that the only cs related channel

[jagged oracle]

You are welcome

[alpine basalt]

all cs related stuff goes inthere?

[tired oxide]

DSA is cs related

[alpine basalt]

ya but like for e.g.

[jagged oracle]

Sir can you check I have written something above

[tired oxide]

yeah

all cs related stuff almost

your questions almost certainly

[jagged oracle]

You can go in general interests and go to the programming thread

[tired oxide]

you can also just ask in the help channels

if you have questions about algorithms

[jagged oracle]

Yes she is right

[alpine basalt]

am i dumb

[alpine basalt]

thanks

[jagged oracle]

Sry for the inconvenience sir

[alpine basalt]

where da programming thread at

[jagged oracle]

Search technology

It contains people interested in programming,hardware etc

If your doubt gets resolved

!done

[marsh citrus]

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

[alpine basalt]

thanx

.close

[marsh citrus]

Channel closed

Closed by @alpine basalt

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[prisma river]

I don't understand why the limit (image below) is equal to -1 (instead of being nonexistent)

[quiet anvil]

It doesn't exist. If your book says it does then there's either a typo in the problem or in the solution

[prisma river]

Let me just send another one for you to check, it's the same issue

[quiet anvil]

lim x->2+ exists

And is equal to -1

[prisma river]

doesn't exist right

[quiet anvil]

It doesn't

The limit from the left is -2 and from the right is 0

So because they aren't equal the limit DNE

[prisma river]

That's wild

Should I make another help or ask here

It's part of the same test prep

[quiet anvil]

Generally, it's one help thread per question, but if it's another short one it's probably fine

[prisma river]

alrighty

i didn't understand the key

[quiet anvil]

What do you not understand exactly

[prisma river]

idk how the second line works

err I can't figure out latex right now so

Sin(3x) / 3x

[quiet anvil]

So the second line is distribution of the denominator 3 in order to make a second 3x

[prisma river]

How is that equal to 1

When you plug in 0

[quiet anvil]

Lim x->0 sin(nx)/nx = 1 for any non-zero real value n

This is because sin(x)/x goes to 1

[prisma river]

since when 😭

alright uh

[quiet anvil]

And this is just an identity that you probably should know

[prisma river]

i guess no one told me for some reason

[quiet anvil]

It's used to prove the derivative of sin(x)

[prisma river]

oh

well im just starting ap calc

so

we'll see how this goes

thanks for the help

[quiet anvil]

Then you'll run into it!

[prisma river]

yep

.close

[marsh citrus]

Channel closed

Closed by @prisma river

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[humble current]

I do not know how my teacher did this type of problem

Or where he got y1 y2 y3 etc

[rancid geode]

okay, lets start with what euler's method is

euler's method uses linear approximation to get next value

so

${y_1 = y_0 + f'(x)(\Delta x)}$

[elfin berry]

:D

[rancid geode]

@humble current do u agree with this formula for approximation

[humble current]

Yes

[rancid geode]

ok

u can find y_1, using substitution

${y(0.1) = y(0) + 2(7)}$

@humble current do u understand how i got here

[humble current]

Yeah

initial * derivative than initial + whatever i got from initial * derivitiate

i think

or no

not initial * derivative

next step * dervative

[rancid geode]

can u do y(0.2)

[humble current]

Ill try

This is what I got

oh

shoot

oops

wait

[elfin berry]

:D

[rancid geode]

it should be 1.4, no?

[humble current]

for 0.1?

2 + 14*0.1

[rancid geode]

y(0.1)

on year

im high

3.4 is correct

[humble current]

ur good

[rancid geode]

,w [3.4 + (3.4)(9-3.4)(0.1)]

[elfin berry]

Results provided by WolframAlpha

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

Requested by nuclearinteraction

[humble current]

ah

is that y(0.2)

[rancid geode]

ye

[humble current]

I thought y(0.2) is 19.04 * 0.2 + 3.4

[rancid geode]

delta x remains constant

okay, how euler's mthod is

it mvoes right

from the old point

at a distance of h step

[humble current]

oh

shoott

yeah ur right

cuz it moves 0.1

steps

yeah

so is it

19.04 * 0.1 + 3.4

instead

[rancid geode]

,w 19.04 * 0.1 + 3.4

[elfin berry]

Results provided by WolframAlpha

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

Requested by nuclearinteraction

[rancid geode]

yes

[humble current]

ohhhh

ok i think ik how to do the rest of the problem

ty

[rancid geode]

👍

[humble current]

.close

[marsh citrus]

Channel closed

Closed by @humble current

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[cunning oak]

Translation: If there exists smallest integer d1 < d2 < d3 < d4 such that n = d1^2 + d2^2 + d3^2 + d4^2 where n is NOT divisible by d1 d2 d3 or d4. Find all possible n

[cunning oak]

maybe n is prime? idk

i dont know where to start

[teal plover]

what does it mean by smallest integer?

[cunning oak]

smallest set of integers which makes n possible i think

<@&286206848099549185>

[teal plover]

how is smallest defined? from order d1->d2->d3->d4?

[cunning oak]

yeah

[sand fable]

is this problem source reliable?

[teal plover]

is it non - negative integers? or just integer

or positive integers

[sand fable]

integers should be positive only

[teal plover]

maybe could include 0 because there is a theorem that all natural numbers is the sum of 4 squares including 0

[cunning oak]

what do you mean by this?

[cunning oak]

right mb they said positive integers

[cunning oak]

this is for competition math im going to tmrw

[sand fable]

well. usually d means divisor

[cunning oak]

ive never seen d used as that before, this is like 9th grade stuff so letters from a -e are just used as variable (e isnt eulers constant for example)

could anyone help with the question?

[marsh citrus]

@cunning oak Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[dusky island]

hi

[dusky island]

did I do the graph right? specifically the dots

big ups to anyone that can point me to the right direction ❤️❤️

[marsh citrus]

@dusky island Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[wary bluff]

third to fourth line

so I was thinking that

S_xy can be written as B_1hat * S_xx

so we can change that third line to

(S_xx * B_1hat)/sqrt(S_xx * S_yy)

what should the next step be so that I can get the same as them

cant I get rid of S_xx

so that in the num

oh my god

.close

[marsh citrus]

Channel closed

Closed by @wary bluff

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[proud basin]

2 cards are drawn from a deck of 52 cards, find the probability of getting one face card (j,q,k) and a number card larger than 6

[proud basin]

im kinda blanking on this

i think i can divide everytgujg by 4 to disregard suits

[tawdry berry]

so uhh, the sample size is 52 choose 2

[proud basin]

mhm

[tawdry berry]

theres 16 number cards larger than 6, 4 from each suit

12 face cards

[proud basin]

so like 12×16/2?

[tawdry berry]

so the number of elements in the given event should be (12 choose 1)*(16 choose 1)

[proud basin]

oh

[tawdry berry]

theres no /2 since we're considering every time a card is drawn

[tawdry berry]

just take this and divide by the sample size

[proud basin]

so 12×16/(51×52/2) right?

[tawdry berry]

yeah

[proud basin]

oh alr

.close

[marsh citrus]

Channel closed

Closed by @proud basin

Use .reopen if this was a mistake.

[teal plover]

also make sure you pay attention to wording on these questions since a lot of times they change the wording to make order matter/not matter

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[umbral rain]

for these questions, is it better to do them by expanding out everything or by inspection?

[low ruin]

do the inspection approach

[umbral rain]

how do u do it? I kinda forgot

[low ruin]

Do you know the binomial theorem

[umbral rain]

i think so

[low ruin]

So use that then.

[umbral rain]

isn't that used for expanding out the brackets tho

[low ruin]

no

You can use the binomial theorem to find a particular coefficient

so you can use binomial theorem to find the coefficient of x^3 in (1+x)^4

[umbral rain]

what about the (3-4x)? Do I find coefficient of x^2 in (1+x)^4 and multiply that with the 4x?

[low ruin]

correct

[umbral rain]

alr ty

.close

[marsh citrus]

Channel closed

Closed by @umbral rain

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[small stream]

Given that the function ( f(x) ) is non-negative on the interval ([0,1]) and satisfies ( f(0) = 1 ) and ( f''(x) \leq 0 ) for all ( x \in [0,1] ), prove that
[
\int_{0}^{1} x f(x) , dx \leq \frac{2}{3} \left( \int_{0}^{1} f(x) , dx \right)^2.
]

[elfin berry]

riyobi

[small stream]

My idea is to do IBP for the left side

[marsh citrus]

@small stream Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[orchid merlin]

Can someone give me 10 examples of monomial and binomial

[crystal lintel]

can you give 1?

[orchid merlin]

I can't bro

😭

[tired oxide]

like each? why not
monomials:
1
3
1002345
h
x^2
x^100
-xy
xyz^2w
100xy
these are your building blocks of like polynomials

binomials:
1+x
x+300
200+y
x+y
x^2 y + 3xy
x-4
p-h
3+zx^2
i’m not gonna do the rest but it’s just when you add two monomials together

[marsh citrus]

@orchid merlin Has your question been resolved?

Channel closed

Closed by @orchid merlin

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[exotic wolf]

hi

[exotic wolf]

how do they go from left side to right side?

[vestal geyser]

it is the taylor series definition of e^x

but in this case x is

[exotic wolf]

what...

this is taylor series for e^X

[vestal geyser]

yes

in ur one, n is replaced by x

[exotic wolf]

you are swapping our x with n

[vestal geyser]

and x is replaced by that thing

[exotic wolf]

u cant do that...

[exotic wolf]

here it says n!

[exotic wolf]

here x!

[still temple]

yes u can

[still temple]

since in this its from n = 0

and the other x = 0

so

u can

[eager tinsel]

variable doesn't matter

[exotic wolf]

oh yeah true

but still

how did they get that to e^(u*e^t)

should it not be the sum?

[vestal geyser]

replace the x in this with

[exotic wolf]

very interesting...

okay i understand now

thanks

.close

[marsh citrus]

Channel closed

Closed by @exotic wolf

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[somber vault]

cannot figure out the last one?

[somber vault]

I got one more chance to get it right

the first time i got 54 and the second time i got 72

im getting -27 from x = 21 to x = 27

[still temple]

then its 36+90-27-28

[somber vault]

how did you get -28

[still temple]

i mean

-27-27

mb

36+90-27-27

[somber vault]

huh?

[still temple]

mb its not

[acoustic bramble]

I got 18

[somber vault]

how you get 18??

[acoustic bramble]

What I did was the following:
I counted all the squares.
Then I multiplied that by 9

-# the ones below the x-axis are negative ofc

[somber vault]

so you didnt calculate the area from x = 21 to x =27

[acoustic bramble]

I did

[somber vault]

what did you get

[somber vault]

what i understand the width of (21, 27) is 6 and it height is 3

turning to be -18 because it's below

then there is also a triangle on top with a height of 3 and b of 6

using the area formula for a triangle a = 1/2(h)(b)

i get -9

[acoustic bramble]

I don’t know how you got the height of 3

[somber vault]

because a = 6

so the oppsite of that a =-6

but it is going by 3

[acoustic bramble]

4 squares are 6*6=36, so 1 square is 36/4=9

If you count, there are 5 squares in [21,27]

[somber vault]

yeah but the triangle starts at -6 and ends at -9

do you understand what I'm trying to say?

[acoustic bramble]

We have this right?

Ok I drew the B triangle the wrong way

[somber vault]

yeah your right I was wrong, it goes from 0 to 6 for the height of the square not 3

[acoustic bramble]

I tried to say that, but I might have phrased it in a way you don’t understand.

[somber vault]

Yeah I didn't so you what do you get for your answer?

because i get 54

[acoustic bramble]

I got 18

by just counting the squares

[somber vault]

well if we know all the areas do we just add them up

to get the total

[acoustic bramble]

I think you forgot something

You counted an area twice

[somber vault]

how so? wouldn't I just add the bottom areas together to get the total area for the bottom?

[acoustic bramble]

You added the areas of a,b and c together and subtracted it by 45. However, the area of a is also included in the area of b.

[somber vault]

nope I see Im wrong

yeah I see

i just noticed

I apperciate your help

.close

[marsh citrus]

Channel closed

Closed by @somber vault

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lucid turret]

find 5 postivie integer pairs that satify:
2n^2 + 1 = m^2

[lucid turret]

give, if possible, the general solution

a question made by me

i got by trial and error n = 2, m =3

[stoic slate]

n=12; m=17

[jagged relic]

n=835002744095575440, m=1180872205318713601

[lucid turret]

bruh

how are you finding them!

[jagged relic]

By hand obviously

[lucid turret]

are you brahmagupta?

i don't want specific vlaues

wait

just help me with this condition

give steps to find find p and m:

p^2 - 1 = 2^m
p = odd and of the form (3q)
m = odd

[sacred idol]

maybe modulo artithmetic again???//

[lucid turret]

,w 2*835002744095575440^2 + 1 = 1180872205318713601^2

[sacred idol]

wait

[elfin berry]

Results provided by WolframAlpha

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

Requested by anshulyolo121

[sacred idol]

2^m??

[lucid turret]

eya

[sacred idol]

https://tenor.com/view/black-guy-shcoked-gif-27654754

[lucid turret]

lol

[sacred idol]

project euler looking ass problem

hey maybe python can help

will come back in one mon

[lucid turret]

k

[jagged relic]

You know, WolframAlpha can give you a closed form

No need for Python

[sacred idol]

interesting

[sacred idol]

oh

theres very limited solutions

very interesting 🤔🤔🤔🤔🤔🤔🤔🤔🤔

ph wait

never mind

this is it

cant seem to find any pattern

[lucid turret]

n = 2378, m = 3363

nice

[grave dove]

but some of these are not 100% correct

[lucid turret]

n = 2, m = 3
n = 12, m = 17
n = 70, m = 99
n = 408, m = 577
n = 2378, m = 3363
n = 13860, m = 19601
n = 80782, m = 114243

wait

[grave dove]

cuz of m%1<0.001 instead of m%1==0

[lucid turret]

n = 470832, m = 665857
n = 2744210, m = 3880899

how did nel find?

he must a super computrer

[sacred idol]

yeah

[sacred idol]

wolfram alpha

[lucid turret]

,w substitute n = 2744210, m = 3880899 in 2n^2 + 1 = m^2

[sacred idol]

maybe

[elfin berry]

Results provided by WolframAlpha

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

Requested by anshulyolo121

[lucid turret]

👌

[lucid turret]

yes as he was talking about 'wolf' ram 'alpha'

ima come back after 10 min after exercizeing

[marsh citrus]

@lucid turret Has your question been resolved?

[lucid turret]

ok#

im back

found two mroe solutins

n = 15994428, m = 22619537
n = 93222358, m = 131836323

i need to remove my helpers role'

<@&286206848099549185>

[cyan peak]

What's the activity?

[lucid turret]

2n^2 + 1 = m^2

find the general solution in positive integers n and m

n - > odd

m -> odd

[grave dove]

i dont think you could find a general solution to this

this problem requires the square root of perfect squares, in order to have integer values

but, there is no known closed form formula for the perfect squares

random fashion

[jagged relic]

I might be misunderstanding... wat?

[grave dove]

its like the same thing with prime numbers, you know them, but if you try to find a general formula for them, you cannot find

we know the perfect squares, but we dont have a general formula for them, i mean

[jagged relic]

... what about

$n^2, n \in \mathbb{N}$

[elfin berry]

Nel

[grave dove]

haha, i mean a function f(n) such that:

f(1) is the first perfect square "1"

f(2) = 4

f(3)=9

[jagged relic]

That's literally f(n) = n^2

[grave dove]

i really have an idea, i think i saw this on YT

i just fail at conveying it

english not my 1st lang

[quaint elm]

uh if you want to talk about that grab a channel of your own or go to some appropriate topic channel, to avoid derailing this one

[quaint elm]

this is likely not reducible any further, though it does remind me a little bit of the Pythagorean theorem

[smoky plover]

pells equation

[marsh citrus]

@lucid turret Has your question been resolved?

Channel closed

Closed by @lucid turret

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[quiet ingot]

is this valid?

[quiet ingot]

taking a differentiated function outside?

[eager tinsel]

no

that's not how you do it

[quiet ingot]

ight ty

[eager tinsel]

you may use IBP here

[quiet ingot]

whats that?

[eager tinsel]

integration by-parts

[quiet ingot]

oh ye

its a question from https://discord.com/channels/268882317391429632/373217754666500097

ty

.close

[marsh citrus]

Channel closed

Closed by @quiet ingot

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[storm swift]

can someone help with d and e please

[fathom ridge]

binomial

[storm swift]

hm?

what do u mean

[grave dove]

what happens to the ratio y0/x when |x|>>|y0|

[storm swift]

gets very small

[grave dove]

yes, close to 0, negligible compared to the 1

[storm swift]

yeah

[grave dove]

and thats about it, you can deduce C and D

[storm swift]

ohh, so i don’t have to do any taylor expansions 😭

[grave dove]

i dont think its necessary

they intentionally wrote V in that form, in my opinion, with the ratio y0/x being so clear

[storm swift]

so like this?

[grave dove]

no, what, y0 is not 1

[storm swift]

i’ve subbed the |x| back in

[grave dove]

you said y0/x gets very small, 0

[storm swift]

ojhhhhhhh yeh

[grave dove]

so replace the ratio with 0

[grave dove]

the line just before the last is fine

why did you split the fraction 😛

[storm swift]

i don’t know, where does the |x|^3 come from

[grave dove]

D=0, thats the thing!

[storm swift]

oh

that’s horrible

[grave dove]

no, its actually better, simpler!

[storm swift]

yeah but i would so think that i had got that wrong looking for an x^3 term, and think i needed to do a series expansion becuse there was an x^3 term lol

[grave dove]

i understand xD

who knows, i might be wrong

this is how I would do the approx

they intentionally wrote V in that way

with the ratio y0/x CLEAR

[storm swift]

yeah fr

[grave dove]

they could have wrote it otherwise

[storm swift]

yeah

oh well

thanks 🙂

.close

[marsh citrus]

Channel closed

Closed by @storm swift

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[silk aspen]

I understand the sequence of the steps but why is it that average temp of insulation is 25 - T but the average temp of polywood is T - 4

[lucid turret]

actually no odd n is possible 😛

[lucid turret]

this

wait

no way

I set the condition of n being odd 😛 😛 :p

😛

bozo

jk

a guy said to me bozo i.
i never used this word but now in front you i am using it.

i have become a bad boy

jk

.close

[silk aspen]

what .close

non replied to me yet

[marsh citrus]

@silk aspen Has your question been resolved?

[marsh citrus]

@silk aspen Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[oblique field]

Explain how you would simplify the following expression using exponent laws and then evaluate
for when n = 12. Your answer should contain only positive exponents.

[oblique field]

Can someone double check

Idk if I did it right

Ping me when reply

[marsh citrus]

@oblique field Has your question been resolved?

[oblique field]

<@&286206848099549185>

Another way to do it

[round furnace]

In the first picture you take the sqrt over only the top part of the fraction and in the second you take it over the entire fraction?

Which is it supposed to be or am I missing something?

[oblique field]

Idk either which one is correct

Because it’s two ways

[round furnace]

Well I do not even know what the original equation was because you are solving 2 different ones

Another difference is that in the second picture the upper part of the fraction has an exponent while it is a linear function in the first picture?

[marsh citrus]

@oblique field Has your question been resolved?

Channel closed

Closed by @oblique field

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[oak bloom]

i want to isolate for L

could i first divide by sides by L?

[calm harbor]

I suggest you move H to the left side

[oak bloom]

wait is this right?

[calm harbor]

Correct

✅

[oak bloom]

thanks!

.close

[marsh citrus]

Channel closed

Closed by @oak bloom

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[oblique field]

can someone help with this i am so confused

[oblique field]

I dont know where to start

[brave marsh]

You should plug the points they are giving you inside the equation.

[oblique field]

wait let me write it out

im still stuck

@brave marsh

[brave marsh]

Ok let's do some work before that then.

Generally, for an exponential that is increasing like that, what is the asymptote on the the bottom as x goes to the left?

This gives a few pieces of information:

• since the exponential usually has a horizontal asymptote at y=0, it seems like it's been translated up by a certain number here...

[marsh citrus]

@oblique field Has your question been resolved?

Channel closed

Closed by @oblique field

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[cunning oak]

find the amount of all possible integers k, if
a) k + 28 is a perfect square
b) k + 2800 is also a perfect square

[cunning oak]

idk where to start

[past atlas]

wait it is the uhhhh
you want the uhhhh

repeating arithmetic formula

i forgot the name of it

a_n = a_1 + (n-1)d

or something

rbit if im wrong im ready to be super wrong

just give it to me straight

[hollow glen]

assign n² to the first one and m² to the second one and look at m² - n², thats at least my first idea

[past atlas]

recursive arithmetic formula

oh

right it uhh has to be a perfect square

[past atlas]

listen to him

ignore me i was never here

[marsh citrus]

@cunning oak Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[marsh citrus]

Please don't occupy multiple help channels.

[elder grotto]

No way this is wrong

sorry its been a long day

its asking for x

my bad

its 43 questions so yk im gonna tweak out a lil

thx I was gonna delete it

[past atlas]

oh yeah camarozzz to close a channel you type .close

[elder grotto]

.close

[marsh citrus]

Channel closed

Closed by @elder grotto

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[azure flare]

How can i calcualte whether this converges or diverges when x = 5?

[azure flare]

when I put 5 there, it doesn't remove the n in the denominator when i let n go to infinity, then don't i get both infinity in the numerator and in the denominator?

[cunning fiber]

Yes, that’s an indeterminate form.

If you want to be a bit hand wavy, appeal to orders of growth

[azure flare]

the problem is that i really have to prove it in the exam

they don't accept that

[cunning fiber]

Then just calculate it rigorously - showing that the sequence is always increasing and unbounded isn’t too hard.

[azure flare]

oh

okay then

.close

[marsh citrus]

Channel closed

Closed by @azure flare

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[wooden bear]

currently doing question C,

1. my first derivative is correct. but is my second derivative correct?
2. also for the red question mark in the problem, what do i put up there now after making the fraction -2/9. Does the fraction power just dissppear?

[wooden bear]

did i do the product rule right? besides where the red question mark is?

<@&286206848099549185>

[marsh citrus]

@wooden bear Has your question been resolved?

[wooden bear]

.close

[marsh citrus]

Channel closed

Closed by @wooden bear

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[spiral stratus]

can someone explain to me why the rotation vector changes?

[spiral stratus]

isnt the unit circle always the same?

[whole sleet]

Can you show us the "original" and "changed"?

[spiral stratus]

oh sorry

in the image the point 1,0 rotates to cos(theta) and sin(theta)

but then for the second vector its -sin(theta) and cos(theta) for 0,1

im confused why the vectors seem to rotate by a different amount despite them both being on the unit circle

[marsh citrus]

@spiral stratus Has your question been resolved?

[whole sleet]

They are rotating the same amount

Just their start is different, so their end should be too

[marsh citrus]

@spiral stratus Has your question been resolved?

Channel closed

Closed by @spiral stratus

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[dapper escarp]

Part (ii) pls...

[marsh citrus]

@dapper escarp Has your question been resolved?

[dapper escarp]

i know how to get the unit vector to AB direction

[vivid chasm]

can only give quick hint cause i have to go

[dapper escarp]

k

[vivid chasm]

the vector from part a is very important

[dapper escarp]

oh

[vivid chasm]

also, a + b bisects the angle between a and b

hope you get it 🙂

and gl

[dapper escarp]

k ill try

anyway thanks

<@&286206848099549185>

[marsh citrus]

@dapper escarp Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[sharp raptor]

is this correct

[sand fable]

u can delete this line

everything around this is right

[sharp raptor]

oh okay

[still temple]

pls tell me this isnt grade 12 math

[fathom totem]

Look like intro of 11th

[still temple]

thats gonna start for me this year 😭

[sharp raptor]

look it’s not that hard

that question is asking for x not that much unless its something like this

[still temple]

how u go from 10g9^x = -1 to 9^-1 = -1 ☠️

[still temple]

log????????????????

[sharp raptor]

is that a real question or did u just made it up

[still temple]

https://tenor.com/view/iwakura-lain-suicide-thinking-gun-gif-11659613

[sharp raptor]

do u really tried to say log in numbers

[still temple]

log3

gello

[sharp raptor]

[still temple]

hello

[still temple]

huh

wtf is log

log 3

is there log 2

[sharp raptor]

u really wrote 10g as log

[still temple]

logarithm

[sharp raptor]

[still temple]

WTF IS F

G

[still temple]

yes

it is correct

I JSUT REWROTE UR SHI

[still temple]

hi pls

help me

stop helping women and help me

jk

✌🏽😛

can you chill

[marsh citrus]

@sharp raptor Has your question been resolved?

Channel closed

Closed by @sharp raptor

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[still temple]

1. A triangle ABC is taken in the plane with ∠B = 40° and ∠C = 60°. For a point D taken on the side BC, let E be the perpendicular leg lowered from D to AB. |AC| = 2 (|AE|+|DC|)

If the condition is met, what is ∠DAC?

[marsh citrus]

Please don't occupy multiple help channels.

[zealous idol]

20 degress

degrees

im on pc so ill send a detailed solution when i get my phone

[still temple]

The answer is 10 degrees 😦

[marsh citrus]

@still temple Has your question been resolved?

[idle ridge]

It seems like you already have a channel here #help-0 so I'm closing this one so that helpers don't get confused by there being two channels

.close

[marsh citrus]

Channel closed

Closed by @idle ridge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[umbral rain]

how do u do this

[still temple]

binomial theorem

consider which terms in (b+c)^n are divisible by c^2 (and which aren’t)

[still temple]

@umbral rain

[umbral rain]

nC2b^(n-2)c^2, nC4b^(n-4)c^4 etc?

[still temple]

note that c^3 is as well

in fact, anything that has a c^n term where n>1 will be divisible by c^2

[umbral rain]

ohh yp

how do i proceed from there?

[still temple]

so if you take (b+c)^n and subtract off the two terms that aren’t divisible by c^2, the rest is divisible by c^2

[still temple]

this is the first half of the problem

for the second half, let a=5, b=2, n=42 and c=3 and it should just work

[umbral rain]

ohh ok tyvm

.close

[marsh citrus]

Channel closed

Closed by @umbral rain

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[rotund burrow]

How do i do this?

[knotty trellis]

Have you drawn a diagram?

[rotund burrow]

I think i have to like diff something right but idk what

Yeah its just like a triangle

[knotty trellis]

does your diagram look like this?

[knotty trellis]

differentiate?

[rotund burrow]

Since i need to find a maximum or something

[knotty trellis]

right, we can do it that way

[knotty trellis]

?

[rotund burrow]

Ye

[knotty trellis]

cool

so now we need to express α

in terms of x

[knotty trellis]

How would you find the angle α?

[lucid turret]

is the angle below alpha fiexd?

[knotty trellis]

Not really, it depends on x

but we only need an expression for alpha in terms of x

Here is a hint: try finding the orange and green angle instead

[marsh citrus]

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).

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[rotund burrow]

Orange is just like tan(orange) = 0.9/x right

[knotty trellis]

correct

so arctan(0.9/x)

orange =

[rotund burrow]

So green is tan 0.6/x

[knotty trellis]

*arctan

but yes

so what is alpha?

[rotund burrow]

Orange - green?

[knotty trellis]

correct

arctan(0.9/x) - arctan(0.6/x)

and this is the expression we need to maximize

now there are 2 ways to go, either use formula for difference of arctangents, or differentiate the above (and set the derivative = 0)

[rotund burrow]

I think diff

[knotty trellis]

okay

So start by finding the derivative of that expression

it should be just chain rule and derivative of arctan

if you need help with that, lemme know

[lucid turret]

is it around 39 deg - 40 deg?

[knotty trellis]

slightly higher

but not too mcuh

[knotty trellis]

+- 3 deg

[lucid turret]

hmm ok

[knotty trellis]

Btw it's quite tedious and the result should be a fraction

if you wanna save some work, you can ignore the denominator

because you are gonna be setting the fraction = 0

so you only care about the numerator

[rotund burrow]

Welp my fraction was long

[knotty trellis]

it is long

,w d/dx arctan(0.9/x) - arctan(0.6/x)

[rotund burrow]

But is the numerator -0.3x^2 +0.162

[elfin berry]

Results provided by WolframAlpha

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

Requested by methisalwaysright

[knotty trellis]

Correct

so now it's sufficient to just set whole that fraction = 0

and fraction = 0 iff numerator = 0 (and denominator is not 0, lest it would be division by 0)

so 0.162 - 0.3x^2 = 0

solve this and you will get the distance for which the angle is maximal

[knotty trellis]

Oh wait

it will be lower

by a lot

I accidentally looked at distance instead of angle lol

[lucid turret]

wait

the question is asking the value of x

not of angle

[knotty trellis]

yes

I'll dm you my results

@rotund burrow have you got the answer?

[knotty trellis]

it suffices to solve this now

[rotund burrow]

Is it just like +- sqrt0.54

But like positive only

[knotty trellis]

yep

and that's the distance which makes maximal angle

[rotund burrow]

Thank you very much bro

.close

[marsh citrus]

Channel closed

Closed by @rotund burrow

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lucid turret]

. yeah i got 11 deg too

[dull sable]

How to show this is true

[cunning fiber]

Hint: Note that the summand is equal for k=1 and k=-2, for k=2 and k=-3, and so on

[silent marten]

i dont know if it heps , but maybe split the right sum into -inf to 0 , and 0 to + inf

[cunning fiber]

If you start from the right hand side and combine it with this, it would

[dull sable]

I’m still a little confused is this similar to splitting a sum into even and odd parts

[marsh citrus]

@dull sable Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[past atlas]

Hi, what is the law of universal linearity?

[amber birch]

https://math.stackexchange.com/questions/630339/pedagogy-how-to-cure-students-of-the-law-of-universal-linearity

are you talking about this

[past atlas]

Yes I think so I was reading that on google but I couldn't understand it on my own except that I seem to fall into the category of students using the law of universal linearity

or like committing a fallacy of some sort

I am sorry I didn't understand it

[amber birch]

yeah basically a lot of students who aren't that good at maths

[past atlas]

I know it isn't a good thing and want to stop

[past atlas]

sounds like me

[amber birch]

think that 1/a + 1/b = 1/(a + b) for some reason

[past atlas]

yes I used to think so too but now I know better

[amber birch]

with all kinds of operations, like logarithms, exponentials, trig functions

cool

[past atlas]

it seems I still have some problems similar to that

[lucid zenith]

Making the error once is fine, making it more than once isn't

[amber birch]

https://tutorial.math.lamar.edu/extras/commonerrors/algebraerrors.aspx

[past atlas]

If I feel like I am slowly but surely phasing them out of my errors, should I be worried?

[amber birch]

https://www.siue.edu/~zagusti/Math150F08/Common_Math_Errors.pdf

oh there's a longer version here

[amber birch]

nope! that's a good sign

[past atlas]

let me open it

I would definitely say I make the same error more than once though, but it stops

I might slip up every once in a while after but that's usually a face palm moment

[lucid zenith]

Happens to the best of us sometimes

[past atlas]

I think working with SI units in physics and rigorously converting units from one to another helped me a lot

[amber birch]

definitely I'd advise you to be gentler to yourself

[amber birch]

oh that's good practice

yeah maths is all about exposure, so when you're doing science, even if it's just things like that, it can be very useful for your mathematical understanding in general

[past atlas]

But this Law of Universal Linearity thing, what is it exactly, is it just common math errors

[lucid zenith]

If you can get to the point that on getting a wrong answer you can easily spot the mathematical error in your working then that should be a good sign

[past atlas]

the likes in those two lists you linked?

[amber birch]

in physics there's also working with proportionalities

[amber birch]

yeah

[past atlas]

I haven't totally understood proportionalities yet tbh

[amber birch]

they're all symptoms of assuming f(x) + f(y) = f(x + y) is true for all functions f

[past atlas]

It didn't click

[amber birch]

that's okay

like just practice

[past atlas]

I get that for F=ma, I think F is proportional to m

or a

or both

like if a becomes twice as big

F becomes twice as big

but then I started hearing stuff like

[lucid zenith]

Assuming the mass stays constant yeah

[amber birch]

the important thing is that if F is proportional to m, you're assuming a stays constant

[past atlas]

inversely proportional

[amber birch]

oh yeah ofc

[past atlas]

ohh

so the proportional guys are not constant

[amber birch]

https://www.youtube.com/watch?v=AWH6wQBbpo0

there's this video and more generally this channel that breaks things up into digestible chunks

if this is the right level of maths for you

[past atlas]

i will check maybe

idk what GSCE is tho

[amber birch]

cool

[amber birch]

it's a British curriculum

[lucid zenith]

Math is math

[amber birch]

doesn't matter it covers a lot of algebra 1 stuff

a lot of people recommend org chem tutor as well

[past atlas]

Would F=ma mean that F is directly proportional to a?

if m is constant

[lucid zenith]

Yes

[past atlas]

Sorry for brazing past the video

but just to go back to the original question again

[past atlas]

in this link/forum

a guy commented saying

"maybe you should introduce them the “Law of Universal Linearity”. In my opinion, it's a funny "law" and students(age dependent) love funny stuff, it helps them, in some sort, remembering things."

and if I understood things right, the Law of Universal Linearity is synonymous to common math errors

a very broad definition

Someone said something about it being too early to introduce the concept of “Law of Universal Linearity” but I don't understand why it would ever be too early to say people make common math errors?

Maybe I have totally misunderstood something

[amber birch]

yeah, it just happens to be the case, that a lot of mistakes students make are from assuming f(x) + f(y) = f(x + y) for all functions f

[amber birch]

there are other kinds of maths errors here

lik erounding too early

does your final answer make sense?

this is a very similar kind of error in calculus

square root only has one value, the positive one

[past atlas]

and that's because if you had to multiply two numbers with one another you could only get a positive one

the cubic root could be negative right?

[amber birch]

yep!

[amber birch]

that doesn't really explain it though

for example, -2 * -2 = 4, but 2 * 2 = 4 as well

[past atlas]

true

how would you explain it properly?

[amber birch]

it's sort of a definition

if we solve $x^2 = 4$, we write $x = \sqrt{4}, -\sqrt{4}$

[past atlas]

is it the sqrt(a^2) = |a|

[amber birch]

oh that's very related, correct

[elfin berry]

south

[past atlas]

but that doesn't explain it by itself either, sorry i will let you explain now

[amber birch]

$y = \sqrt{x}$ is a function, so we cannot get more than one $y-value$

[past atlas]

im just trying to follow along

[amber birch]

vertical line test and all

[past atlas]

sorry but im swedish so

[elfin berry]

south

[past atlas]

vertical line test doesnt tell me anything 😦

[amber birch]

interessant

this is not a function

so to make it a function, we either have to take the bottom half or the top half

[past atlas]

that's two functions

[amber birch]

so that it follows the vertical line test

[amber birch]

exactly!

[past atlas]

i must have not been paying attention in school

when we went over this

i vaguely remember seeing it

but i never engaged or applied myself

why does the vertical line explain that it is not 1 function

if they intersect

sorry if the vertical line

intersects the proposed "function" twice at the same x value

it cant be a function?

if a horisontal line intersects a function twice at the same y value it is still a function isnt it?

[amber birch]

yeah, that's the definition of a function

that 1 x-value always results in 1 y-value

the converse isn't true, for 1 y-value, there can be more than 1 x-value

for example if we have y = x^2

y = 4 gives x = -2, 2

[past atlas]

i dont want to be annoying

[amber birch]

that's still a function

[past atlas]

but

[amber birch]

yeah?

[past atlas]

why is that

super vague and

not focused

but just why is that true, that an x value can only produce one y

is that just the definition of a function like you said

like we decided it is that way

[amber birch]

that's the definition of a function

yep