help-49

[nova yoke]

yep

[timid tangle]

Ohhh okay thank you guys

.close

[midnight plank]

Channel closed

Closed by @timid tangle

Use .reopen if this was a mistake.

[midnight plank]

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Remember:
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[elder ivy]

I need help making my sign chart

I don't understand why I can't make it proper

My teacher said it's negative from (-infity, -1) U (1/2, + infinity) and positive from (-1,1/2)

Appreciate some help on this

If you can ping me tho

[midnight plank]

@elder ivy Has your question been resolved?

[midnight plank]

@elder ivy Has your question been resolved?

Channel closed

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[midnight plank]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[last slate]

.help

[midnight plank]

Commands:

• clopen: .close, .reopen
• consensus: .poll
• factoids: .tag
• help: .help
• version: .version

Type .help <command name> for more info on a command.

[last slate]

!help

[midnight plank]

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

[wraith bay]

Just say what you need and someone will help you

[last slate]

typing rn

[flint hare]

send it

[last slate]

problem:

or ig could someone jsut help me with it 💀

[merry pewter]

is R(m) the set of residues mod m?

also

!status

[midnight plank]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[last slate]

1

[last slate]

yeah

[merry pewter]

ok then it seems like you should just use the bijection that you have, no?

to make an isomorphism

[last slate]

thanks i didnt think of that

.close

[midnight plank]

Channel closed

Closed by @kindred mesa

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[midnight plank]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[upbeat plinth]

One message removed from a suspended account.

[upbeat plinth]

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[midnight plank]

Channel closed

Closed by @upbeat plinth

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[midnight plank]

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>.
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• 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.

[upbeat plinth]

One message removed from a suspended account.

[upbeat plinth]

One message removed from a suspended account.

[lavish venture]

wait so

[upbeat plinth]

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[fickle oriole]

well well well...

look we have here

[fallow scarab]

How the turns have tabled

[upbeat plinth]

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[lavish venture]

facts

[upbeat plinth]

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One message removed from a suspended account.

[lavish venture]

word

[upbeat plinth]

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[upbeat plinth]

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One message removed from a suspended account.

[lavish venture]

$2xyy’ + y^2$

[grand pond]

knief

[upbeat plinth]

One message removed from a suspended account.

One message removed from a suspended account.

[lavish venture]

machiavelli

[fickle oriole]

how is bro still doing deriatives

wtf

[lavish venture]

word

[upbeat plinth]

One message removed from a suspended account.

One message removed from a suspended account.

[lavish venture]

been like 3 months

[upbeat plinth]

One message removed from a suspended account.

[lavish venture]

what

[upbeat plinth]

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One message removed from a suspended account.

[lavish venture]

y’’ stays on its own side

[upbeat plinth]

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One message removed from a suspended account.

[fickle oriole]

bro has to lock in, 3 months on deriatives is nefarious work

[lavish venture]

😧

[lavish venture]

it is isolated

[upbeat plinth]

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One message removed from a suspended account.

[upbeat plinth]

One message removed from a suspended account.

[lavish venture]

nah

cap

[fickle oriole]

first day or smth

how did you do limits

for over a month

🙏😭

[lavish venture]

huhhh

[upbeat plinth]

One message removed from a suspended account.

[lavish venture]

$y’’ = yaddayadda$

[grand pond]

knief
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[upbeat plinth]

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[lavish venture]

yep

that’s correct

[upbeat plinth]

One message removed from a suspended account.

[lavish venture]

nothing to isolate

you already know dy/dx

you’re looking for y’’

which is on the left

[upbeat plinth]

One message removed from a suspended account.

[fickle oriole]

let u=answer

[lavish venture]

always

[fickle oriole]

answer=u

✌️😹🙏

[lavish venture]

what does bulgogie mean

[fickle oriole]

Bulgogi generally refers to thinly sliced beef marinated in a sauce that is a mix of soy sauce, sugar or honey, sesame oil, garlic, onion, and often pureed Asian pear.

[lavish venture]

ahh

interesting

[upbeat plinth]

One message removed from a suspended account.

[fickle oriole]

arent u vietnamese

the dish is korean

[lavish venture]

yea idk i just eat chicken and steak

[lavish venture]

are you korean

[fickle oriole]

no

im proud american

[upbeat plinth]

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

[fickle oriole]

🦅

[upbeat plinth]

One message removed from a suspended account.

[fickle oriole]

🤯

[upbeat plinth]

One message removed from a suspended account.

[fickle oriole]

????

[lavish venture]

wild

propus is asian american

[upbeat plinth]

One message removed from a suspended account.

[lavish venture]

💯💯💯

[upbeat plinth]

One message removed from a suspended account.

[fickle oriole]

bro stopped studying

[lavish venture]

lacking

[upbeat plinth]

One message removed from a suspended account.

[lavish venture]

i think my class actually spent like the same amount of time you’re spending tbh

[fickle oriole]

idk how youre gonna finish bc topics

[upbeat plinth]

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[lavish venture]

they didn’t get to integration until december

[fickle oriole]

???

[upbeat plinth]

One message removed from a suspended account.

[fickle oriole]

we are almost done with ab topics

[upbeat plinth]

One message removed from a suspended account.

[fickle oriole]

we just have one more chapter

[lavish venture]

you’re in ap calc?

[upbeat plinth]

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[fickle oriole]

ye

[upbeat plinth]

One message removed from a suspended account.

[fickle oriole]

same class as kenzo

[upbeat plinth]

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One message removed from a suspended account.

[fickle oriole]

my teacher is just a try hard tho cant lie

[upbeat plinth]

One message removed from a suspended account.

[fickle oriole]

she gets to school at 5 am everyday to check homework

[lavish venture]

yea you’re technically on track

[fickle oriole]

idk why be doing allat

[lavish venture]

like my class was doing series by march ish

[fickle oriole]

she has a porsche 😭

[lavish venture]

maybe february

[upbeat plinth]

One message removed from a suspended account.

One message removed from a suspended account.

[lavish venture]

they only did like 2 weeks of review maybe

[fickle oriole]

no

[lavish venture]

dudes really offended

[upbeat plinth]

One message removed from a suspended account.

One message removed from a suspended account.

[fickle oriole]

im just better

[upbeat plinth]

One message removed from a suspended account.

[fickle oriole]

jokes!!!!

[upbeat plinth]

One message removed from a suspended account.

[lavish venture]

🙈🙈

[upbeat plinth]

One message removed from a suspended account.

One message removed from a suspended account.

[lavish venture]

bruh

[fickle oriole]

bro 🙏😭

just stick to deriatives cuh

[upbeat plinth]

One message removed from a suspended account.

[fickle oriole]

idk the way you learned

[lavish venture]

what has this channel turned into

[fickle oriole]

deraitives was weird

bc we did implicit

early on\

but we didnt do ln deriative or expoential ones

till after we did integration

[lavish venture]

huhhh

[upbeat plinth]

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[midnight plank]

Channel closed

Closed by @upbeat plinth

Use .reopen if this was a mistake.

[lavish venture]

alright

[midnight plank]

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>.
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[drifting root]

for 3c

This is whwt i have so far

How do i continue?

[oak slate]

divide everything by 3 to simplify then find the answer by plugging in some values

[drifting root]

Is there a better way than guess and check or nah

[icy adder]

you can try solving the summation

[drifting root]

Idk how to deal with that tho

[icy adder]

do you know the summation of first n natural numbers

[drifting root]

Uhhh

Probably not?

[icy adder]

can you find sum of an AP

whose common difference is 1

and starting term is also 1

[drifting root]

n/2(1+n)

[icy adder]

yeahh n x n+1 / 2

that is the sum of first n natural numbers right

the sum of series of 1+2+3+4+5....+n

[drifting root]

Ye

[icy adder]

you need to solve both the summation using formulas

the first summation is sum of a GP

the second summation is the sum of an AP

try solving those

[drifting root]

? Wont i just get what i did here

[icy adder]

yeahh correct sorry mb

uhh now you have to do hit and trial

try putting values of n like 1 2 3 4

thats the only possible way afaik

[drifting root]

Ah

Ic

.close

[midnight plank]

Channel closed

Closed by @drifting root

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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>.
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• 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.

[devout harness]

could someone help with this question but dont know its correct

[midnight plank]

Please don't occupy multiple help channels.

@devout harness Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

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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>.
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• 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.

[viral dagger]

status 1

[tawdry laurel]

very random equations

[viral dagger]

ikr

[tawdry laurel]

i've seen ppl use vietas on this stuff b4

[viral dagger]

how tf do you use vieta on this

[tawdry laurel]

let a, b, c be roots of a cubic equation

nvm

[merry pewter]

the sqrt(3) makes me think we should replace b with sqrt(3)b

so that the b^2/3 becomes b^2

then i think it will have something to do with (a+b+c)^2

[viral dagger]

why can we do that

[merry pewter]

well b is real right? im just saying to replace it with a different variable scaled by sqrt(3)

to make the equations nicer

[viral dagger]

ohh

gimme a sec

[merry pewter]

jesus christ

ill do it,
$$a^2+\sqrt{3}ab+b^2=25$$
$$b^2+c^2=9$$
$$c^2+ca+a^2=16$$
$$\sqrt{3}ab+2\sqrt{3}bc+3ac=m\sqrt{3}$$

[grand pond]

Bair

[viral dagger]

D: what did i doo

[merry pewter]

hard to read

[viral dagger]

$$a^2+\sqrt{3}ab+b^2=25$$
$$b^2+c^2=9$$
$$c^2+ca+a^2=16$$
$$ab+2bc+\sqrt{3}ac=m$$

[grand pond]

Skill_Issue (ping when u respond

[merry pewter]

oh

wait no

i guess the thing to notice is that the right side is all perfect squares

[viral dagger]

uhhhh

oh yea

[merry pewter]

i thought it was going to be the factorization of a^3+b^3+c^3-3abc but now i don't think so

[tawdry laurel]

i didnt see that

[crude jungle]

RHS got all perfect squares

[tawdry laurel]

yeah ikik

[crude jungle]

smth we can use it

uh

[tawdry laurel]

i just didnt see it when i first looked at qn

[viral dagger]

$$a^2+\sqrt{3}ab+b^2=a^2+b^2+c^2+c^2+ac$$
$$\sqrt{3}ab=ac+2c^2$$

[grand pond]

Skill_Issue (ping when u respond

[crude jungle]

ok i think i got smth

so first of all

we can get c^2 = 9 - b^2 from eq 2

and substitute in eq 3

and uh, after simplifying, im getting

$$ca+a^2-b^2=7$$

[grand pond]

Baizhi

[crude jungle]

from eq 1, we get

$$b^2 = 25 - a^2 - \sqrt{3}ab$$

[grand pond]

Baizhi

[crude jungle]

put this

[crude jungle]

in this

by which we will get

$$ca + 2a^2 + \sqrt{3}ab = 32$$

[grand pond]

Baizhi

[crude jungle]

now rearrange eq 1 by shifting all terms to RHS except root 3ab

$$\sqrt{3} ab = 25 - a^2 - b^2$$

[grand pond]

Baizhi

[crude jungle]

...

ok i messed up ;-;

[midnight plank]

@viral dagger Has your question been resolved?

[midnight plank]

@viral dagger Has your question been resolved?

[graceful drum]

wait

does this work

let x = b/sqrt(3)

then for the first equation

a^2 + x^2 + sqrt(3)ax = 25

for the second one x^2 + c^2 = 9

[viral dagger]

this you subtitute b=sqrt3b

the same

[graceful drum]

ok but i found something with a similar substitution

for the 3rd one c^2 + a^2 + ac = 16

rewritten as (c-a)^2 + 3ac = 16

we now that 25 - 16 - 9 = 0

therefore (a^2+ x^2) - (x^2 + c^2) - (c-a)^2 + sqrt(3)ax - 3ac = 0

or (a^2 + x^2) + sqrt(3)ax - 3ac = (x^2 + c^2) + (c-a)^2

this implies that (a^2 + x^2) + sqrt(3)ax - 3ac >= 0

therefore 25 - 3ac >= 0

therefore 3ac <= 25

Thats the first part

next

[viral dagger]

how does it imply that

[graceful drum]

cus sums of squares of real numbers are always postiive

[viral dagger]

its (x^2+c^2)-(c-a)^2 thats not sum of squares

[graceful drum]

now we rewrite this as (x-c)^2 + 2xc = 9

[graceful drum]

mb both are positive, ill edit that

now we know that 9 + 16 = 25

therefore (x-c)^2 + (a-c)^2 + 2xc + 3ac = 25

or 25 - 2xc - 3ac = (x-c)^2 + (a-c)^2

therefore 25 - 2xc - 3ac >= 0

or 25 - 2xc >= 3ac

but we know 25 >= 3ac

therefore -2xc >= 0

[viral dagger]

contradiction then?

[graceful drum]

no

then 2xc <=0

[viral dagger]

a,x,c are positive reals

[graceful drum]

is zero positive?

then i made a mistake probably

[viral dagger]

i dont think so?

[graceful drum]

can u even add inequalities together

[upper crag]

0 is not positive or negative

[feral sedge]

0 is 0

[graceful drum]

but ig it has something to do with inequalities

[graceful drum]

this step is wrong though

u cant add inequalities like that

rather we can

but the application here is wrong

[midnight plank]

@viral dagger Has your question been resolved?

[feral sedge]

where is this q from lol...

a^2 + ab + b^2 / 3 = 25
b^2 / 3 + c^2 = 9
c^2 + ca + a^2 = 16

from equation 1 = equation 2 + equation 3, derive this: ab - ac - 2c^2 = 0. continue,
substitute a = tc into ab - ac - 2c^2 = 0 to get b = c(1 + 2/t)
substitute b = c(1 + 2/t) into equation 2 to get c^2 = 27t^2 / 4(1 + t + t^2)
substitute a = tc into equation 3 to get c^2 = 16 / (1 + t + t^2)
hence, t = a/c = 8sqrt3 / 9, or a = (8sqrt3)c / 9
substitute t = 8sqrt3 / 9 into b = c(1 + 2/t) to get b = (3sqrt3 + 4)c / 4
substitute b = (3sqrt3 + 4)c / 4 into equation 2 to get c^2 = 432(91 - 24sqrt3) / 6553
substitute a = (8sqrt3)c / 9 and b = (3sqrt3 + 4)c / 4 into ab + 2bc + 3ac to get (72 + 91sqrt3)c^2 / 18
substitute c^2 = 432(91 - 24sqrt3) / 6553 into (72 + 91sqrt3)c^2 / 18 to get 24sqrt3
hence, m = 24

(i cannot find a nice way to do this)

the values of a, b, c (which happen to unique) are not nice either

$(a, b, c) = \left(32\sqrt{\frac{91 - 24\sqrt{3}}{6553}}, 36\sqrt{\frac{\frac{2185}{48} + 24\sqrt{3}}{6553}}, 12\sqrt{3}\sqrt{\frac{91 - 24\sqrt{3}}{6553}}\right)$

[grand pond]

Mqnic_

[viral dagger]

my teacher posted it on their story and i just took it :p

[feral sedge]

:/

[viral dagger]

cmon free question that i found cant blame me

[feral sedge]

then ig. there is no reason to assume this question has a clean solution. if that is where it came from

[viral dagger]

man this is horrifying

spooky

[feral sedge]

it is cursed

[viral dagger]

spooooooky

alr im gonna open this till night if its not solved (hopefully elegant in the slightest) ill close this

maybe ill ask on mathexchange or smth

[feral sedge]

well there is a solution here. but it is not nice is all

[cunning dragon]

i had to solve first but it seems to be easy ig

[viral dagger]

what?

[cunning dragon]

yupp m=16 ig from my step

[viral dagger]

how did you get that

[cunning dragon]

bro first take express b^2 from second equation and then substitute into first equation you will get 16 and then and get c^2 which equals a^2 + ab - 16 and substitute it in 3rd equation and u get 2a^2 + ab +ca = 32 and when you get b^2 express it as c^2 and then we solve 2a^2 + ab +ca = 32 and c^2 = a^2 + ab - 16 and use c^2 from c^2 = a^2 + ab - 16 and take a=4, b= 3, c=1 as it is complex to me and solve ab + 2bc +3ac = 30 = m(3^1/2)

m= 10*(3^1/2)

lol i had done mistake m doesnt equals to 16 but equals to 10*(3^1/2)

@viral dagger yoo i had solved

[viral dagger]

erm

lemme repost

[cunning dragon]

is my answer correct

[viral dagger]

what do you mean "when you get b^2 express it as c^2 then ..."

[viral dagger]

idk

[cunning dragon]

bro u get b^2= 27-3(c^2) u have to express it in c^2

[viral dagger]

oh thats what you meant

why a=4 b=3 c=1

[cunning dragon]

yupp and u know this gave me the idea to finding a general way to solve these types of equations and i m 13 yrs old kid and i will research on this thhing

[viral dagger]

this sesms like a random choice?

[cunning dragon]

bro u have to first getting all the value of a and b and c by solve 2a^2 + ab +ca = 32 and c^2 = a^2 + ab - 16

[viral dagger]

quite literally (4,3,1) does not work

[cunning dragon]

you get

[cunning dragon]

ohh so i have to do more work on it

btw where u get this question

[viral dagger]

😭

[cunning dragon]

@viral dagger where u get this question

[viral dagger]

a

[cunning dragon]

it seems like mathematical analysis

@viral dagger what r u expecting from a 13 yrs old kid

[viral dagger]

nothing?

[sinful trout]

"skissue?"

[viral dagger]

no offense :p

[cunning dragon]

ooh

[viral dagger]

short for skill issue :p

[cunning dragon]

but it seems like mathematical analysis

[sinful trout]

yeah ik

[sinful trout]

probably isn't

and "mathematical analysis" isn't very specific?

there are several fields of analysis

[viral dagger]

my friend calls me it so i just changed to it so i can shorten my name

[sinful trout]

what subs have you tried so far

[viral dagger]

b=sqrt3b to simplify to this

then uhh idk

[sinful trout]

???

[cunning dragon]

systems of nonlinear equations ig

[viral dagger]

idk what to sub

it seems like if i sub its going in circles

[sinful trout]

a(a+b) = 16

[viral dagger]

huh

[sinful trout]

well we aren't exactly going to be using algebraic geometry here are we

oops nvm

[cunning dragon]

but it like university levels questions

[sinful trout]

$$\frac{b^2}{3} = 9 - c^2\to\frac{b^2}{3} + 7= 16 - c^2$$
$$16 - c^2 = ac + a^2 = \frac{b^2}{3} + 7$$
$$a^2 + ab + \frac{b^2}{3} = 25\to a^2 + ab+\frac{b^2}{3} + 7 = 32\to 2a^2 + ab + ac = 32$$

[grand pond]

ren

[sinful trout]

dude
it's not a uni level question

[cunning dragon]

olympiad?

[sinful trout]

*sighs*

i don't know man

i'm just trying to help skill here solve this question

[cunning dragon]

ok i wont know much and i m studying maths myself so i dont level of this question i just trying to solve

[sinful trout]

skill any constraints?

[viral dagger]

uhh gimme a sec

[sinful trout]

*sighs*

"positive real numbers"

very helpful lmao

[viral dagger]

mk no problems yet

[sinful trout]

?

[viral dagger]

this :p

i still dont know where you get a(a+b)=16 from

[sinful trout]

i didn't

that was mb

a(2a+b+c) = 32

is what i have on hand

working on it

2c^2 + ac = ab

wut

i don't know where you got those from

[viral dagger]

wait

[sinful trout]

but i trust you

[viral dagger]

nah nvm

[sinful trout]

ooooooookay

if ur wondering

i had a(2a+b+c) = 32

and from the third one we have 2c^2 + 2ac + 2a^2 = 32

so 2a^2 + ab + ac = 2a^2 + 2ac + 2c^2

therefore, 2c^2 + ac = ab

[viral dagger]

the thing is all this time bc has not showed up at all

[sinful trout]

ikr

it's so annoying

maybe just multiply stuff randomly with b or c lmao

$$a^2c + abc + \frac{b^2c}{3} = 25c$$
$$a^2b + abc + bc^2 = 16b$$

does that help in any way

[grand pond]

ren

[viral dagger]

what if you square everything

ok this is starting to borderline joke

icl but this form looks really nice

[sinful trout]

??

where'd the sqrt three come from what

[viral dagger]

this but replaced the x with b

[sinful trout]

don't

do that

that's

[viral dagger]

idk im scared this is like a red herring or smth

[sinful trout]

really confusing for me

[viral dagger]

ig but it gets rid of fractionssss

ok fin

[gilded rock]

Can someone please please help me with fpm I have exam tmr

[midnight plank]

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).

[midnight plank]

@viral dagger Has your question been resolved?

[viral dagger]

.close im gonna go to sleep, gn

[midnight plank]

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[viral dagger]

https://cdn.discordapp.com/attachments/469869606018744340/1303845073900933190/image0.gif

[midnight plank]

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[gaunt nimbus]

Let ${a}$ be a real number and ${p(x)}$ be a polynomial such that ${p(a) \neq 0}$. If ${q(x)= (x-a)^np(x)}$ for each and every positive integer ${m \leq n}$, there is a polynomial ${p_m(n)}$ such that
[ q^{(m)}(x) = (x-a)^{n-m} \left( (x-a)p_m + \frac{n!}{(n-m)!p(x)} \right) ]

I found this from a solution from a high school math competition that I took two days ago. Idk where this is taken from or is there a name for this and where else I can apply this in the future.

[grand pond]

k
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

k

[wicked trench]

This sounds very specific ngl

[gaunt nimbus]

wait

lemme drop the question

[grand pond]

k
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[gaunt nimbus]

@wicked trench

[midnight plank]

@gaunt nimbus Has your question been resolved?

[midnight plank]

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[upper cairn]

This is potential on my test tomorrow how the hell do I even start it 😭😭

[chilly cobalt]

do you know the definition of pi?

[midnight plank]

@upper cairn Has your question been resolved?

[midnight plank]

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[gaunt nimbus]

How does one perform well on all math topics? What do these people have in common to be able to know tips and tricks and everything? Like I can do calculus but I can’t even do geometry.

Is there like a thing u should know that underlies all the math topics?

[midnight plank]

@gaunt nimbus Has your question been resolved?

[olive matrix]

my dad kept saying "neatness and practice" and i think that definitely applies

[patent glen]

We all dont know anything, most of us usually help with something we have recently worked with, say through hobbies or school.

While others just help for fun and practicing

[gaunt nimbus]

i see

so it boils down to having fun and practices

[midnight plank]

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[lusty pike]

hey there

[lusty pike]

I have the answer to this question but I don't know why it worked

the matrice P is part of an earlier question

and so by multiplying 24 by the determinate of P you get $\frac{24}{5}$

[grand pond]

sealpup321

[lusty pike]

which is the answer

but why does that work?

I would get it if you were multiplying by P' but this is just det(P)

<@&286206848099549185>

[midnight plank]

@lusty pike Has your question been resolved?

[lusty pike]

<@&286206848099549185>

[manic cave]

what is this, i did'nt understood the question.

basically what is to be proved is true for any circle irrespective of the figure.

[twilit cypress]

is this a cambridge question?

the font looks familiar

[midnight plank]

@lusty pike Has your question been resolved?

[manic cave]

2nrsin(pi/n) < 2pi*r<4rsqrt(3) where the 1st and the last term are the perimeter of the incribed and circumscribed hexagon. By keeping n = 6 and solving we will get the required inequality.

[midnight plank]

@lusty pike Has your question been resolved?

[upper cairn]

edexcel higher question from 2024

[upper cairn]

dont worry i know how to do it its fairly easy

[midnight plank]

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[flint anchor]

find v.a and h.a

[flint anchor]

h.a doesnt exist

and i have found the v.a but it is wrong

[untold fern]

you have factored correctly right? one sec ill do it

[flint anchor]

i found v.a with the help of the discriminant

[flint anchor]

u can factory it too

but you will get 1 and 5

[ripe gulch]

-1

[flint anchor]

thing is 1 isnt included

only 5

[flint anchor]

u have to do the opposite of the factorised

[ripe gulch]

Nevermind u right

[untold fern]

so its just 1

yea

wait mb I tweaked

5

[flint anchor]

so why not 1

[untold fern]

at x = 5, there should be a VA

[untold fern]

it cancels

with the numerator

if you factor the top, you get x(x+1)(x-1)

the bottom you get (x-1)(x-5)

therefore, the x-1 cancels and creates a hole

[flint anchor]

ohhh but when doing it with discriminant u wont be able to find it

[untold fern]

im sorry what?

im not quite sure i understand

[flint anchor]

you know you could find the v.a with discriminant right?

[untold fern]

discriminant? of what

[flint anchor]

discriminant of denominator

[oak slate]

isnt that a matrix thing

[flint anchor]

how?

factorising i guess is more precise

[untold fern]

well

yeaaa I guess you can

but it can be inaccurate

[flint anchor]

yeah that is what im saying

[untold fern]

because if you plug in the answer it will cancel the top and it would be irrelevant

in the future, I would avoid using discriminant

stick with just factor and standard

[flint anchor]

ohhhh i guess you could always plug in the x's and see if it makes sense in the function

alright that was it thanks

.close

[midnight plank]

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[untold fern]

np 😄

[midnight plank]

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[last slate]

Find the force acting on each member

[midnight plank]

@last slate Has your question been resolved?

[steep brook]

i can't help with this, but you'll typically get a better response if you show some of your work or explain where you're stuck

[midnight plank]

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[vagrant mica]

What power makes it equal to zero?

[rose trout]

None

[vagrant mica]

wait whatt

what do I put for my answer then?

[keen herald]

Any you've tried?

[vagrant mica]

It's not possible though

right

[keen herald]

It's not

Just trying to reinforce the idea lol

One might assume 1 or 0 would elicit silly behavior like that, but 36^1 is 36, and 36^0 is 1

[last slate]

^

LOL

[vagrant mica]

Yeah, thats what I did

and it wasnt 0

[last slate]

x does not exist

[vagrant mica]

https://tenor.com/view/fade-away-oooooooooooo-aga-emoji-crumble-gif-20008708

[last slate]

Actually said what I was thinking but it’s not possible as n^0 =1

[last slate]

put -infinity if you’re that pressed for an answer

or DNE

[vagrant mica]

Imma just put no solution

[keen herald]

If you want something more rigorous, we can try taking the natural log of both sides

[vagrant mica]

What's that

[keen herald]

$ln(36^x) = x, ln(0) = \text{DNE}$

[grand pond]

m. frost

[keen herald]

It's the opposite of exponents, basically the function that gets the X in 36^x

[last slate]

Well ln(0) is undf btw

[vagrant mica]

Thanks guys

[keen herald]

But ln(0) is undefined so a^x = 0 can't exist

[last slate]

So technically even if you performed the nat. Log you would get DNE

[vagrant mica]

.close

[midnight plank]

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[keen herald]

Exactly my point

[midnight plank]

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[obtuse willow]

How come 19 is a relatively simple antiderivative?

But why is this asking me for finding the n on the selected interval?

[elder zephyr]

it is not asking you to find n, but just saying that the integration constant depends of n

[obtuse willow]

Can you explain that further for me?

I don't get it.

Why is it for 21 and 23 but not 19?

[midnight plank]

@obtuse willow Has your question been resolved?

[midnight plank]

@obtuse willow Has your question been resolved?

[brazen moth]

Hi @obtuse willow

[obtuse willow]

Hello!

[brazen moth]

What you need to observe here is that at npi + pi/2

Tan and sec is undefined

That's why they have open brackets on such numbers

At these number that anti derivative and for this case the derivative will also go undefined

So they have excluded

[brazen moth]

Even if they wrote this

This would be fine too

Hope this helps

[obtuse willow]

So whenever I have an anti derivative that includes tan or sec.

[obtuse willow]

I have to take that into account?

[brazen moth]

Yup

Any function including tan or sec

Also for csc and cot

[brazen moth]

This has to taken into account

[obtuse willow]

I see.

But sin and cosine don’t need that right?

[obtuse willow]

Wait the answer to this includes sec.

Why doesn’t it include the pik thing @brazen moth?

[brazen moth]

Yup

[obtuse willow]

No I mean…

[obtuse willow]

Why doesn’t 19 use this?

[brazen moth]

For that I have genuinely no idea

Maybe they forgot or something

But 19 will undefined at the same points aswell

See it's simple logic

Tan is sin / cos

Sec is 1/cos

Where cos goes to 0

Tan and sec get undefined

[obtuse willow]

Okay.

[brazen moth]

And that occurs at npi + pi/2

So we excluded those points

Similarly for csc and cot

Sin and cos themselves are always defined

They got nothing in the denominators to make them undefined

That's all

Do you get it now @obtuse willow

?

[obtuse willow]

Yes.

Hmm…

Question.

[brazen moth]

Yeah sure

[obtuse willow]

Is it possible that cos and sec are “balancing” each other?

Since Sec is 1/Cos?

[brazen moth]

Can you please try and specify what you mean by balancing

@obtuse willow

[obtuse willow]

Oh.

I dunno how to describe it.

But could it be possible that the one Cos lets Sec be defined somehow?

[brazen moth]

Are you trying to say that does cos fill spaces sec doesn't and vice versa?

I Mean Thiers a lot of cool things about it

That I have stumbled upon while learning trigonometry

Give me a moment I will draw out some of them

[obtuse willow]

But it ain’t it?

Should I ask my teacher this tomorrow?

[brazen moth]

I Mean I will try to give you something to work with

Like look at this

[brazen moth]

Sec covers parts of the graph

That cos can't

And it's true the other way around

[obtuse willow]

I see.

[brazen moth]

Another one is that principle brach of cos graph

And sec graph

Fit perfectly

Together

Honestly one of the beautiful things I have seen

A graph do

[low hull]

Very

[brazen moth]

Cos x^2 and secx ^2

They fill each other out

To perfection

Covering all of infinity

[low hull]

The reason why i love math

Unrelated but https://www.desmos.com/calculator/6ut1a9ljy7

[brazen moth]

Cool

Anyways @obtuse willow

I hope that's enough to satisfy your questions needs

Anything else I can help with?

If not please .close the channel

[obtuse willow]

Yee I'm done.

Thank you!

.close

[midnight plank]

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[weary flare]

Would this be correct? I don’t know how it will have a sum.

[midnight plank]

@weary flare Has your question been resolved?

[rose trout]

It's not that the terms diverge, it's that they don't converge to 0.

But yes, you're right

[weary flare]

Thank you

.close

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[cosmic tiger]

Help pleaseee only the first one

[polar socket]

function is increasing and decreasing is when theyre talking abt slope no??

[daring bison]

when it goes up its increasing

when it goes down its decreasing

[cosmic tiger]

i think so

[polar socket]

so like you just need to figure out when the slope is negative and when its positive

[cosmic tiger]

so were lookign at both axis or...

[polar socket]

awm no??

idk wym by axis, u just look at the slope

rise over run

[cosmic tiger]

x and y both negative and positive

[polar socket]

??

[cosmic tiger]

is the first one like...-2.5

[polar socket]

u dont have to determine the exact slope, u just have to identify if the slope is negative or positive

[cosmic tiger]

oh sorry i meant like this

ermmm

negative..

i think

[polar socket]

okay negative

from where to where tho

[cosmic tiger]

yaaaaaaaaaaay

i-

uhm

i just look at the arrows...

[polar socket]

okay domain wise 😭 😭

the x values, x-axis

is that what u meant earlier

[cosmic tiger]

yaaaaa

[polar socket]

aurrrr

[cosmic tiger]

my eyes arent really all that good but ill tryy

[polar socket]

u look at the x-values or x-axis to determine the intervals

[polar socket]

its okay, an estimate is an estimate

unless if u estimate like

234892 when the x-value is 4

then ill be like sideeying hardcore

[cosmic tiger]

i-

cry

is it the same -2.5

and uhm

omy

i think im stuck

[polar socket]

what

why is it -2.5

[cosmic tiger]

im not suree

i saw it kinda cuts thru

im not suree

[polar socket]

are u looking between -2 and -1 or smth

[cosmic tiger]

uh huh

[polar socket]

oh

gurl thats -1.5

[cosmic tiger]

or its -3

...

[polar socket]

okay let’s

divide this function into different sections

so it’s easier to visualize

[cosmic tiger]

oki

[cosmic tiger]

ahhh i thought as muchh

[polar socket]

the function is divided into 3 sections, cut twice

bc u can see there’s a hill and a trough right??

1 hill, 1 trough

or trench

[cosmic tiger]

uh huhhh

[polar socket]

or whatever u wanna call the lowest point is

okay SO

[brazen moth]

A crest?

[cosmic tiger]

is it like the minimum and maximum thingy...

[polar socket]

sort of

so yk this is negative right

[polar socket]

oh is it called that

honestly I blocked that out bc of physics trauma

[brazen moth]

Yeah the bottom things

[brazen moth]

Lol it's alright

Ik you thinking about wavelengths

[polar socket]

EW WAVELENGTHS

censor it for me 🥰🥰

w*v#l#ngths

[polar socket]

anyways @cosmic tiger ^^

[cosmic tiger]

yaaaaa

[polar socket]

u just need to figure out the interval part

or the domain

or the x-values

[cosmic tiger]

-1.5, 2

[cosmic tiger]

waaaaa

[polar socket]

this is technically correct but for smth else

that’s the increasing part

[cosmic tiger]

omg...

[polar socket]

look at the first section of the graph

ur almost there gurlie

if u can get the increasing part

u can get the decreasing parts

PLURAL

[cosmic tiger]

-3...

idkkk

[polar socket]

oh gurl

[polar socket]

u see the arrow at the left end of the function right

[cosmic tiger]

o

infinity..

idkkk

neg and positive

wait

[cosmic tiger]

isnr both negative...

[polar socket]

okay UR GETTING CLOSE

what infinity

[cosmic tiger]

pos

[polar socket]

awm

positive infinity??

[cosmic tiger]

no neggg

[polar socket]

yas queen

bc we’re on the negative side of the x axis

[cosmic tiger]

its on the negative sideee

[polar socket]

so u found a part of one interval

-infinity

so the function is decreasing from negative infinity to what

[cosmic tiger]

pos infinity...

nooo

but its going down

[cosmic tiger]

the other arrow

wait nu

[polar socket]

look where is it cut off

[cosmic tiger]

o#

[polar socket]

you already figured out the function is increasing (-1.5, 2) right

[cosmic tiger]

the intervals

[polar socket]

so where’s it’s decreasing

[cosmic tiger]

-1.5

[polar socket]

YASSS

(-infinity, 1.5)

OKAYYYY

THATS ONE OF THE DECREASING INTERVALS

there’s still one more

[cosmic tiger]

do we use union

or..

[polar socket]

yas

always union

unless the problem uses the word “or” always use union

[cosmic tiger]

2ohhh

ohhh

so after union is

2

sorry bracket 2

[polar socket]

bracket??

wait

r u Canadian or American

or non American

[cosmic tiger]

(2

[polar socket]

okay

[cosmic tiger]

neither

[polar socket]

(2,

2 to what

[cosmic tiger]

im from pluto

uhm

infinity

[polar socket]

YASSSSSSS

[brazen moth]

🎊 🥳

[cosmic tiger]

yaaaaaaaaaaay

[polar socket]

me after getting over with my calc quiz tmrw

[polar socket]

tell me u now know what to do

[cosmic tiger]

uhmm

i did

[brazen moth]

Go on.....

[cosmic tiger]

(-infinity,1)

[brazen moth]

Good start

[polar socket]

yas

[cosmic tiger]

union

[polar socket]

uh huh

[cosmic tiger]

(4,positive infinity)

[brazen moth]

It was going so well

[cosmic tiger]

uhh

uhm

two arrows

[polar socket]

this is when the function is what

[brazen moth]

4 arrows

[cosmic tiger]

ye 4

[cosmic tiger]

uh,

cant remember

is it like the or thingy

[polar socket]

THE FUNCTION??

[cosmic tiger]

ian know

[brazen moth]

https://tenor.com/view/let-him-cook-cook-cookin-big-wok-gif-141999319614473134

" The or thingy "

[cosmic tiger]

ohhh

[brazen moth]

The function go up then down then up then down

It go up from
(-infinity, 1] U (3,4]

[cosmic tiger]

3,,,

how comes

[brazen moth]

And go down from
(1,3)U(4,infinity

[cosmic tiger]

oh

[brazen moth]

Is the function not approaching -infinity at 3

[cosmic tiger]

maybe i have eye problem so i can barely see

[brazen moth]

I think @polar socket has just left

[brazen moth]

Nah it's alright

You new to this

Jokes aside

It takes everyone time

So nothing to be embarrassed about

[cosmic tiger]

oki oki thanks for the help

.close

[midnight plank]

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[midnight plank]

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[mighty tree]

,rotate

[grand pond]

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

Nov 13, 2024, 5:58 AM

[mighty tree]

I don't know how to approach this qn

,rotate

[last slate]

First find y',which gives us the slope of the tangent in terms of x.

[wheat steppe]

what have you done so far

[last slate]

:p

[mighty tree]

Hmm done got -x/x+1

[mighty tree]

At first I thought of getting y' and then comparing graident but I have no idea what to do aft y'

Only thing I know is that all the tangents would have the same graident

[last slate]

Hint:y-y1 = y'(x-x1)

[mighty tree]

Hmm I got this

,rotate

[mighty tree]

Hmm I suppose this is the eqn of the line that the tangents pass through that are also points on the curve ?

[last slate]

You also know that the points that you have to find are supposed to be on the curve y=x/1+x

[mighty tree]

Hmm I equate the 2 eqns?

[last slate]

❌

[mighty tree]

Oh

[last slate]

Wait

Yeah lop

Lol

[mighty tree]

Oh Alright lemme try it

[last slate]

I meant to say substitute but both lead to the same result

[mighty tree]

Ahh alright

I. Got a quadratic

The solutions for x are long demical places tho

I feel I might have made a mistake somewhere

What the

Ok nvm ans key also have weird demcimal places lemme try

[mighty tree]

Wait I don't understand smth this gives u the eqn of a line so by using the graident and the coordinate don't u only get one solution for the tangent ?

[last slate]

No

For example

[midnight plank]

@mighty tree Has your question been resolved?

[mighty tree]

Ohh okay

Aight I understand now thanks!

[midnight plank]

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[limber acorn]

Did I setup the integral correctly?

[midnight plank]

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[limber acorn]

<@&286206848099549185>

[midnight plank]

@limber acorn Has your question been resolved?

[limber acorn]

.close

[midnight plank]

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[midnight plank]

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[half meteor]

Calculus 2

I dont get how to do this, i was thinking y = t and then parametrize, t € [0,5].

But it would be two equations

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[twilit field]

So I'm trying to prove this version of FTC