help-0

[rigid smelt]

i guess you can take this decision as experience-wise

[quick laurel]

^

[worthy lily]

well I decided

I would keep going in the class

I registered last minute

[quick laurel]

🥳

[rigid smelt]

i also recommend that you make a good relationship with your teacher, so if anytime that you are struggling with understanding a theory, you can ask for their genuine help

[worthy lily]

think this is better choice than online because I have tutorials they post solutions to

and they post recommended problems and sometimes videos

where the online choice its just 5 assignments and a test

and I think just a textbook

online I have 10 months to complete a course

this is completed in 3.5 months

so it's a lot faster or is that good because it will keep me focused working hard to meet the deadlines

ok well time to get to work

5 / sqroot(36 - 25x^2) - 50x / sqroot(36-25x^2)

so I do u sub for the 2nd one

-50x / sqroot(u)

du = -50x dx

du/-50x = dx

so its now -1 / sqroot(u)

[rigid smelt]

no you are having an extra -1

[worthy lily]

oh right

its +

1 / sqroot(u)

[rigid smelt]

yes, integral of du/sqrt(u)

[quick laurel]

Right, now all you have to do is integrate it

[worthy lily]

isn't that just ln (sqrt(u) )

1 /x the integral is ln(x) right?

[quick laurel]

but its not 1/x

think of it this way

[worthy lily]

oh sqroot x

right

(36 - 25x^2)^(-1/2)

[quick laurel]

$\int{\frac{1}{\sqrt{u}}} \to \int{u^(-\frac{1}{2})$

[worthy lily]

2 (36-25x^2) (1/2) / (-50)

1/25 sqroot(36-25x^2)

[ocean seal]

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

[worthy lily]

yes

[quick laurel]

right so now use the power rule

to integrate

what do you get?

[worthy lily]

so integrate is would be 2u^(1/2)

[quick laurel]

exactly!~

[worthy lily]

w000000000000000t!

[quick laurel]

now all you have to do is sub back in the value of U

[worthy lily]

2sqroot(36-25x^2)

[quick laurel]

Right so now you should have

$-\frac{1}{50} * 2\sqrt{u}$

[ocean seal]

Thasis

[quick laurel]

which becomes

[worthy lily]

-1/25 sqroot(u)

[quick laurel]

perfect

now all you have to do is replace u with its value

and add the constant of integration

[worthy lily]

-1/25 (36-25x^2)^(1/2)

[quick laurel]

$-\frac{\sqrt{36-25x^2}}{25} +c$

[ocean seal]

Thasis

[worthy lily]

right ok

[quick laurel]

Im reposting for convienence

[worthy lily]

yea

I don't know what they are doing there

5x / 6

ok so we are working on the left side now

[quick laurel]

Yes

one moment please

[worthy lily]

5/sqroot(u)

[quick laurel]

before I explain'

do you know anything about trig substitution at all?

[worthy lily]

just that you can do forms like 1 / sqroot(1 - x^2) or -1 / sqroot(1 - x^2)

or you said

sqroot(a^2 + x^2)

in that form

[quick laurel]

I must admit, this is something that is not simple to explain through pure text

[worthy lily]

I see theres a video on it

are you going to be around for a little bit?

I can watch the video

[quick laurel]

I should be

[worthy lily]

can you come back in 10 minutes?

[quick laurel]

Sure, Ill be here

[worthy lily]

thanks

[quick laurel]

but that will save me a lot lol

[worthy lily]

yes I will watch the video

then tell you what I know

[lone heart]

@worthy lily Has your question been resolved?

[quick laurel]

To start, you should factor out 5 from the denominator $\int{\frac{1}{\sqrt{36-25x^2}}} = \int{\frac{1}{5\sqrt{\frac{36}{25}-x^2}}} \Rightarrow \frac{1}{5}\int{\frac{1}{\sqrt{\frac{36}{25}-x^2}}}$

[ocean seal]

Thasis

[worthy lily]

why is it 36/25?

[pine helm]

divide 36 - 25x^2

by 25

and that integral should be familiar to u

[quick laurel]

^

Indeed

[worthy lily]

familiar?

[quick laurel]

So, based on what you told me earlier, you prob wont recognize it

nonetheless

[pine helm]

hint :

int 1/sqrt(1-x^2) = arcsin(x)

[worthy lily]

but 36/25 is not 1

[pine helm]

ok so

[worthy lily]

is it sqroot( anything - x^2) = arcsin(x) ?

[pine helm]

not quite

u could rewrite that as 5/(6(1 - 25/36 x^2))

u can factor out the constant so it becomes 5/6 int 1/sqrt(1 - 25/36 x^2) dx

[worthy lily]

please goto available channel up above

[pine helm]

make a u sub

u = 5/6 x

du/dx = 5/6
du = 5/6 dx

[worthy lily]

sorry hold on

can we go back to the start

[pine helm]

okay

[worthy lily]

1 / sqroot( 36 - 25x^2)

so you wanted the x by itself so you divide by 25

1 / sqroot( 36/25 - x^2)

[pine helm]

yes

[worthy lily]

ok

[pine helm]

after that

[worthy lily]

I am on this point

so the trig sub is a^2 + x^2 right

36 / 25 count as a^2 then?

[pine helm]

i made a mistake on that part hold on

[worthy lily]

ok

[pine helm]

ok so

[worthy lily]

I don't under stand become 5 / sqroot(36-25x^2)

what happened there

[pine helm]

oops

made some stupid mistake

lemme redo it

ok so ur problem was solving int 1/sqrt(36 - 25x^2) dx right

[worthy lily]

yes

[pine helm]

that was a part of a bigger problem

but uh yheah

okay

[worthy lily]

yes

what do you think?

[pine helm]

my brain is forgoring rn my bad

[worthy lily]

ok

[pine helm]

let me think

ok i think i know

sqrt(36 - 25x^2)

sqrt(25(36/25 - x^2))
5 sqrt(36/25 - x^2)

there we go

ok i know how now

anyways u could do that cuz sqrt(a * b) = sqrt(a) * sqrt(b)

1/(5 sqrt(36/25 - x^2))

actually theres a better way

rather than factoring 25

we factor 36

so sqrt(36 - 25x^2) becomes sqrt(36(1 - 25/36 x^2))

which becomes 6sqrt(1 - 25/36 x^2)

so it becomes int 1/(6sqrt(1 - 25/36x^2)) dx

u can factor the 1/6 out so it becomes 1/6 int 1/sqrt(1 - 25/36x^2) dx

now heres the magic

u = 5/6 x
u^2 = 25/36x^2 (the thing inside the sqrt)
du/dx = 5/6
du = 5/6dx

so it becomes
1/5 int 1/sqrt(1 - u^2) du
1/5 arcsin(u) + C
1/5 arcsin(5/6x) + C

1/5 * 5/6 is 1/6 btw thats why it turned from 1/6 to 1/5

@quick laurel could u verify this, ty

[worthy lily]

u = 5/6 x?

[pine helm]

yeah

[worthy lily]

how did we get that

[pine helm]

substitution

(5/6)^2 is 36/25

the thing inside the sqrt

u just have to notice it

so it turns into 1/sqrt(1 - blablabla^2)

which is a well known integrand

[quick laurel]

Looks good to me

[worthy lily]

we can choose what u equals?

I thought u had to sub for something

[pine helm]

that is u sub.

but tbh u can call it whatever

m sub whatever lol

its jsut a substitution

[worthy lily]

I know but 5/6 where did that come from

[pine helm]

by realizing that u need to turn it into 1/sqrt(1 - stuff^2) so it becomes a well known integrand
and that "stuff" is (5/6 x)

[worthy lily]

so you made 36/25x = u?

[pine helm]

no

we turned the integral into 1/6 int 1/sqrt(1 - 25/36x^2) dx remember

[worthy lily]

ye

[pine helm]

the integrand of 1/sqrt(1 - x^2) is arcsin(x) + C

similar to our integral right?

[worthy lily]

yes

[pine helm]

this is where the u sub comes

[worthy lily]

yes I'm trying to figure out the u sub

I can't see the u sub

[pine helm]

u = 5/6x
u^2 = 25/36 x^2

25/36 x^2 is in the sqrt

[worthy lily]

oh ok

so we have u = 5/6x

[pine helm]

yap

[worthy lily]

do we take the derivative?

[pine helm]

mhm

[worthy lily]

usually when I u sub I take the derivative

[pine helm]

thats literally how most usub goes

[worthy lily]

ok

so we make it 1 - u^2

[pine helm]

yep

which is like

arcsin

[worthy lily]

u = 5/6x

so du = -35x / 36x^2?

isn't that the derivative?

[pine helm]

um....

[worthy lily]

hold on

[pine helm]

no

[worthy lily]

u = 5 / 6x right

[pine helm]

yes

[worthy lily]

so that can be 5 (6x^-1)

which is then -30x

[pine helm]

the derivative of 5/6x is 5/6

[worthy lily]

ohhh the constant

[pine helm]

u could interpret it as a line with a slope of 5/6

the derivative of a line is its slope

[worthy lily]

take the constant out 1/6x

[pine helm]

yep

[worthy lily]

then 1 / 6

[pine helm]

yep

[worthy lily]

5/6 = du

5/6 dx = du

[pine helm]

yeah

yep

wait no

[worthy lily]

so du6/5 = dx

[pine helm]

uh

wait

u = 5/6x
du/dx = 5/6
du = 5/6 dx

1/6 dx= 1/5 du * 5/6

so we're left with 1/5 int 1/sqrt(1 - u^2) du

[worthy lily]

1/5 or 5?

k let me do this quickly

is 6xdu = dx correct?

no

6/5du = dx

[pine helm]

lemme just send u this

[worthy lily]

remember we took out 5

and du is 6/5

so the 5 cancels out

6 / sqroot( 1 - u^2)

[pine helm]

forgot the +C but whatever

[worthy lily]

wow

thank you

[pine helm]

yw 😁

[worthy lily]

that is so hard

[pine helm]

it only gets worse 😓 but u can do it!!

[worthy lily]

how did you get so good at math?

[pine helm]

i dont

i suck at it lol

[worthy lily]

I am in a Calc 2 class right now

[pine helm]

i havent even learned calc in school yet

[worthy lily]

and my options were drop it and study for the next 3 months and come back to school in January for next semester

[pine helm]

dropping classes doesnt sound right ngl

[worthy lily]

do it online self paced and have 10 months to complete but all you get is a textbook

or just keep doing it right now and keep trying

even though it's moving at lightspeed

and I'm so bad at math

you havn't learned calc in school yet?

[pine helm]

yeah im self taught

anyways idk hwo to help here

just practice ig

[worthy lily]

what do you think best option would be?

[pine helm]

practice

it helps u develop a pattern recognition skill

which i think is crucial in calculus

[worthy lily]

but I mean taking the class now without dropping, drop and study and come back in 3 motnhs

[pine helm]

u also need to sharpen ur algebra manipulation

[worthy lily]

or take online self paced so I can take longer

[pine helm]

this is the part where i think most people lack

admittedly me too

[worthy lily]

are you in university

[pine helm]

no

[worthy lily]

or going to university in future?

[pine helm]

high school

first year

[worthy lily]

wow

[pine helm]

yeah

[worthy lily]

can you help me with some more?

[pine helm]

Sure i guess

[worthy lily]

what do you want to take at university?

[pine helm]

Not sure about that

I want to take music but everyone is against it

anyways i think this si getting offtopic, ur free to dm me

but if theres nothing elseu want to ask then u can close this channel

[worthy lily]

I'm going to try one quickly

and if I can't do it can you help me

[pine helm]

Alrright

just ping me

[worthy lily]

so I will keep this open for a while

thanks

[lone heart]

@worthy lily Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[worthy lily]

.reopen

[lone heart]

✅

[worthy lily]

can you help me with this integral

[hollow shale]

I would try multiplying by e^{7x}/e^{7x} and then partial fractions

[echo socket]

Or u-sub

[tawny condor]

Yes multiply by that, and then do u = e^(7x)

Not partial fractions

[hollow shale]

u-sub works too

[worthy lily]

what would that make it

e^(7x) / 64(e + e^(14x)

[echo socket]

With u-sub e^(7x)/64(1 + e^(14x)) = u/64(1 + u^2)

But the u on the nominator will cancel out

[worthy lily]

what do you make u =

[echo socket]

u = e^(7x), just like Redstone said

[lone heart]

@worthy lily Has your question been resolved?

[lone heart]

@worthy lily Has your question been resolved?

[lone heart]

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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>.
• 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.

[marble saffron]

((0,0),(1,0)) = A; V = c(1,0) for any c in R; is "Av = u " a linear operation?

[alpine sable]

I guess you are asking if A is a linear operation over the subspace V?

do you know what conditions you need to check?

[marble saffron]

no not sure, i came up with this question myself, i noticed that the image is not a subset of the domain, which i think should be in the case for operators

but then again it is a square matrix

so not sure

[alpine sable]

yea, AV is not in V. But as your question stands, it doesn't have to be in V

see the linear map definition here: https://en.wikipedia.org/wiki/Linear_map#Definition_and_first_consequences

[marble saffron]

but operators are always from V -> V right

[alpine sable]

you are free to define the codomain appropiately

[marble saffron]

?

[alpine sable]

no

I dont think so?

lemme check

[marble saffron]

operators are more specific than just linear transformations

im pretty sure

[alpine sable]

In mathematics, an operator is generally a mapping or function that acts on elements of a space to produce elements of another space (possibly the same space, sometimes required to be the same space). There is no general definition of an operator, but the term is often used in place of function when the domain is a set of functions or other structured objects.
https://en.wikipedia.org/wiki/Operator_(mathematics)

I guess it does depend on what you are reading too

[marble saffron]

hmm confusing

but then how are operators different from linear transformations

[alpine sable]

I guess you mean linear operators vs linear transformations?

https://math.stackexchange.com/questions/487933/what-is-the-difference-between-linear-transformation-and-linear-operator

[marble saffron]

yes

[alpine sable]

seems like its a personal naming convention

[marble saffron]

yeah

.close

[lone heart]

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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>.
• 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 sable]

how do I approach the last part

[alpine sable]

only the last part

the plot S against alpha

thing

[keen plinth]

do you have an expression for S in terms of alpha?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

well

now i do

cuz i asked in #competition-math

so

got it now

.close

[lone heart]

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• 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.

[acoustic sorrel]

Hey guys, I have a question about my maths assignment

[acoustic sorrel]

This is the harder question, we are meant to self learn row matrix reduction

[pure jungle]

can I find remainder for 128^323 divided by 9

by congruence modulo

[acoustic sorrel]

open this again after I close it

.close

[lone heart]

Channel closed

Closed by @acoustic sorrel

Use .reopen if this was a mistake.

[hollow inlet]

#❓how-to-get-help

[acoustic sorrel]

.close

why does this show me twice?

???

[lone heart]

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

[lucid aurora]

. If 𝑎 = (1, 3, -3), 𝑏⃗ = (- 3, 6, 12), and 𝑐 = (0, 8, 1), determine the magnitude of 𝑎 +1/3𝑏⃗ − 𝑐

ive tried every way i know and cant get the answer

[lucid aurora]

but the answer should be 3

if you can tell me how that would be great thanks

[chrome plank]

What have you tried?

[lucid aurora]

i tried adding all the vectors up

for example for a 1+3+(-3)

so a would equal 1

then do the same for b and c

[chrome plank]

But that's not how sums of vectors work

[lucid aurora]

do i have to add the x from a b and c

then the y den the z

[chrome plank]

You have to find the magnitude of a + 1/3 b - c

[lucid aurora]

yea

[chrome plank]

So start by finding that vector

[lucid aurora]

how

[chrome plank]

The very first step should be to find 1/3 b, and then you can just sum each individual components of all vectors

[lucid aurora]

ok

so b is -1,2,4

[chrome plank]

that's 1/3 b

But yes, it's correct

[lucid aurora]

If 𝑎 = (1, 3, -3), 𝑏⃗ = (-1, 2, 4), and 𝑐 = (0, 8, 1) now this is what i have

[chrome plank]

that's 1/3 b, not b

[lucid aurora]

yea

[chrome plank]

But now all that's left is to sum/subtract them

[lucid aurora]

so we multiply it by 1/3 at the end?

[chrome plank]

wdym

[lucid aurora]

for a i got root 19

b root 21

c root 65

shits confusing

[chrome plank]

I meant the vectors, do you know how vector sum or subtraction works?

https://www.youtube.com/watch?v=8QihetGj3pg

[lucid aurora]

yes ik how to do that

so i would do a and b first then - c

[chrome plank]

yes

But again, 1/3 * b

[chrome plank]

which is the vector you found here

Let us know what you get

[lucid aurora]

-2,1,8

[chrome plank]

I don't understand how you got that, can you show your work?

[lucid aurora]

well i added vector ax with vector bx and - with vector cx

and did the same for the y and z

ok look

so a is (1,3,-3)

i added those together to get 1

so that vector a

[chrome plank]

why? That's not how it works

[lucid aurora]

den how does it work

can you show me because im lost

[chrome plank]

The sum of vectors works like this, N and M are unrelated, general vectors
N = [n₁, n₂]
M = [m₁, m₂]
now,
N + M = [n₁ + m₁, n₂ + m₂]

[lucid aurora]

ur trying to find the magnitude of a b and c so you need and x y and z to sub in

hold up

i got 0,-3,0

[chrome plank]

Yes that's it!

And now you can find the magnitude of that

[lucid aurora]

oh

thanks

i see noe

now

[chrome plank]

So what do you get?

[lucid aurora]

3

[chrome plank]

nice :)

[lucid aurora]

thanks!!!

[chrome plank]

[lone heart]

@lucid aurora Has your question been resolved?

[lone heart]

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• 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 sable]

hi

[alpine sable]

i need help

[chrome plank]

[alpine sable]

i dont understand math

i can someone help me with that

[chrome plank]

yes, just ask your question

[alpine sable]

wait

in sending the pic

im*

[hollow inlet]

👌

[alpine sable]

bro help me

[wise thistle]

is that a video

[alpine sable]

im too lazy to open my past paper book

SOMEBODY HELP ME

AH!!!!!!!!!!!!!!!!!!!!*&&

WHY I DONT UNDERSTAND ,ATH!/

[chrome plank]

what is the question lol

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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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 sable]

Simplify n2 x n5

[prisma zephyr]

hey I have a question regarding manifolds.
A quiet elementary question.
Can I understand local coordinates just as the space the charts map the Manifold patches to?

[hollow inlet]

@prisma zephyr this channel is already grabbed, #❓how-to-get-help

[prisma zephyr]

oh sry

[alpine sable]

Wdym

[wise thistle]

can you elaborate

[alpine sable]

I’m so confused

[ornate condor]

the person was an invader

[hollow inlet]

@alpine sable Do you know a^m * a^n = a^m+n

[prisma zephyr]

a sec ago it still was in availabe

[alpine sable]

No:(

[prisma zephyr]

ima head out bye good luck^^

[alpine sable]

Ty!

[wise thistle]

did you mean n^2 x n^5?

[alpine sable]

Ya

[wise thistle]

add up the powers

[alpine sable]

Lemme send the question

[wise thistle]

since it’s both n

[hollow inlet]

Do you know what are laws of exponents.

[alpine sable]

No

😭😭

Can u give me an example and like u solve it

And then I will try to do on mine

[wise thistle]

$a^m • a^n = a^{m+n}$

dont mind the slip ups

[alpine sable]

It’s Ight

[wise thistle]

its very ugly forget that

[alpine sable]

ITS OKAY ISTG

I JUST NEED TO UNDERSTAND

[ocean seal]

gracialglacier

[wise thistle]

get it?

[alpine sable]

OHH

So my answer will be

[hollow inlet]

So, 2^1 * 2^2 = 2^(1+2)

$a^m \cdot a^n = a^{m+n}$

[ocean seal]

Srijandev

[alpine sable]

So my answer will be the (n2 x n5)

Is

[wise thistle]

what is your answer

[alpine sable]

N2 . N5 =

[wise thistle]

yes continue

[alpine sable]

n 2+5

[hollow inlet]

🎉

[wise thistle]

yes

[alpine sable]

Right?

TYSMMM OMG

[wise thistle]

nice bro

[alpine sable]

TYY

[wise thistle]

np

[hollow inlet]

lmao great!

If you're done close this!

[alpine sable]

Okkk

[wise thistle]

nice @hollow inlet

[hollow inlet]

breh wot?

😒

[wise thistle]

good work

[alpine sable]

How do I close it

[wise thistle]

.close

[hollow inlet]

wait @alpine sable

[alpine sable]

I might still have questions

[wise thistle]

aight

[alpine sable]

I have a quiz tmwr and i barely know shit

[hollow inlet]

uh whatver

[wise thistle]

know your exponent rules

[hollow inlet]

lol no cheating 😛

[wise thistle]

and youll be fine

[alpine sable]

I will try

[wise thistle]

lmao

[hollow inlet]

cheating?

for sure, go ahead.

No one provide any help 😦

[wise thistle]

when you cheat, youre just cheating yourself of knowledge broskie

trust

[ornate condor]

HAHAHA

[alpine sable]

Mamas words

[ornate condor]

[hollow inlet]

mam ;/

[wise thistle]

its dadas words now

[alpine sable]

Sadly..

[wise thistle]

LMAO

[hollow inlet]

cheating is good, but later you should review your cheated questions

anyways, pls don't cheat.

good bye 👋🏻

[alpine sable]

I promise i will try

[hollow inlet]

wait wot

[hollow inlet]

mods may ban yu.

[alpine sable]

Why

What did I do

[hollow inlet]

cuz cheating not allowed.

You will cheat, as you said?

[alpine sable]

I HATE U 😭

Dw i won’t

[hollow inlet]

🎉

honesty is the best policy 😛

[alpine sable]

This

[wise thistle]

what is a square number

[alpine sable]

The answer

[hollow inlet]

breh

[wise thistle]

meaning

i want the meaning

you know it?

[alpine sable]

It’s the answer

Ya

But what about the

[wise thistle]

aight whats the meaning of a square number

[alpine sable]

ITA THE ANSWER

[wise thistle]

bro

fk the answer

[alpine sable]

😭😭

[wise thistle]

im asking for the definition

[alpine sable]

Idk

[wise thistle]

it’s a number squared

[alpine sable]

So like

[wise thistle]

1^2

2^2

[alpine sable]

Oh

[wise thistle]

3^2

4^2

what is 4^2

[hollow inlet]

it has even powers of its factors.

[alpine sable]

No the teacher told us something else

I’m so confused

[wise thistle]

what

did

your teacher

sah

[hollow inlet]

what did your teacher taught?

[alpine sable]

It’s the answer

So like

[hollow inlet]

sigh

[wise thistle]

fk your teacher

[alpine sable]

For example

[wise thistle]

BRUH

AYO

[alpine sable]

Anyways

[wise thistle]

SUS

[alpine sable]

Ya you not me

[hollow inlet]

this is weird and offensive?

[wise thistle]

@alpine sable

[hollow inlet]

isn't

[wise thistle]

sry bro

@alpine sable

[alpine sable]

2 x 2 = 4

[wise thistle]

what’s 3^2

yes

[alpine sable]

4 is the square

Number

[wise thistle]

so 4 is a square number

[alpine sable]

Yup

[wise thistle]

what is 3^2

[alpine sable]

Idfk

[wise thistle]

mf

3x3

[alpine sable]

Oh right I forgot

WIAT IM SORRY

[wise thistle]

its aight

ITS AIGHT

[alpine sable]

ok so I’m right?

RIGHT?

[wise thistle]

no

youre left

[alpine sable]

.

[wise thistle]

you didnt answer my question

[alpine sable]

😭😭

[wise thistle]

and asked if youre right

[alpine sable]

shut up

[wise thistle]

bro im shutting down

u know what a $\sqrt$ is

[ocean seal]

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

[alpine sable]

Ya that thing

[wise thistle]

ye

when you take square root of a squarw number

youll get a whole number

[hollow inlet]

$\sqrt{4}$

[ocean seal]

Srijandev

[alpine sable]

Mhm

[hollow inlet]

^^?

[wise thistle]

look at your paper now

[tranquil gazelle]

It’s 2

[wise thistle]

what number when you take square root

gives you a whole number

[alpine sable]

11?

[hollow inlet]

scroll less

[wise thistle]

explain to me

why u chose 11

[alpine sable]

Idk I guessed it

[hollow inlet]

how?

[wise thistle]

detailed

[alpine sable]

It seems right

[hollow inlet]

breh

[wise thistle]

are you willing to learn

or nah

[alpine sable]

Yes

[wise thistle]

aight

[alpine sable]

I want to pass life

[wise thistle]

exactly

[hollow inlet]

breh

[wise thistle]

math gonna come with u bro

[hollow inlet]

||troll||

[wise thistle]

you gotta do good in it

[hollow inlet]

come on topic.

[alpine sable]

Ik I’m gonna fail it

So ain’t picking it

[wise thistle]

you have a calculator with you

[alpine sable]

Ya I do

[wise thistle]

you dont get to pick lmao

[wise thistle]

aight

you see the square root symbol

[alpine sable]

Will in uk yes u gotta pick

Mhm ya

[hollow inlet]

$\sqrt{8} \sqrt{9}$

[alpine sable]

I do that?

[hollow inlet]

Which of the following is a perfect square?

[alpine sable]

9

[ocean seal]

Srijandev

[alpine sable]

9

[hollow inlet]

👏🏻

[alpine sable]

NO WAIT 8?

HOW

WAI

BRO

[hollow inlet]

breh, you are right?

are u sure.

[alpine sable]

uh alr hood

Good

Yea I’m sure

[tranquil gazelle]

wait can a square number be 8? bc its factors aren’t the same they’re 2 different numbers.

[hollow inlet]

cool.

[wise thistle]

bro u not picking math?

[hollow inlet]

perfect square

[alpine sable]

Yes but I gotta pass this year if i ddi i would choose whatever uni I want

Rlly hope i pass

Back to math

[wise thistle]

https://youtu.be/B-Sfvry_h3Q

watch that bro

you need it

[alpine sable]

I don’t have time watching something

[wise thistle]

aight your choice

[alpine sable]

I’m about to go to sleep I gotta finish

[wise thistle]

alr bye bro

[hollow inlet]

If you do not get it, ask @wise thistle

[alpine sable]

Byee tysm

Should I close?

[wise thistle]

your choice bruv

[alpine sable]

I will keep it might need it

[wise thistle]

aight

[hollow inlet]

ping us

[alpine sable]

Okkk

@hollow inlet @wise thistle

[hollow inlet]

@alpine sable do you know the prime factor of 99?

in previous quest

[alpine sable]

No

I already know I’m failing so I’m skipping stuff so it’s Ight

[hollow inlet]

@wise thistle ^^^^

[alpine sable]

He passed away:(

Srsly where did he go

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

.close

[lone heart]

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[lone heart]

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[nimble fern]

you can use a table if you want

if you dont mind, you can check this website about how to plot straight lines on a graph

https://thirdspacelearning.com/gcse-maths/algebra/straight-line-graphs/

[lone heart]

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[proper jasper]

Can someone please help me understand how to solve this?

[proper jasper]

I know I can simply graph it but I believe the teacher wants me to use math.. somehow

And I also think the teacher meant on an interval, so that the answer isn't just infinity

[gray isle]

they probably should've said local max

or had boundaries

[proper jasper]

There's only 2 "turns" so I'm assuming that too

[gray isle]

are you doing a calculus course atm?

[gray isle]

so yeh

they probably should've said (meant) local max

[proper jasper]

I am but we haven't covered this specifically. So, I don't know how to apply calculus to solve the problem

I set f'(x) to 0 and get 1

Don't know where to go from there

[gray isle]

note that 1 isn't the only solution to
3x^2 - 3 = 0

[proper jasper]

• 1 too

[gray isle]

yes

these will be the locations of your stationary points

from the general shape of a cubic, you should be able to deduce which one will be your local max

if you aren't allowed to use that approach, you could use the second derivative

[proper jasper]

I may be interpreting the question wrong, but what I think I'm trying to do is get the answer (1, 2)

I don't know how to do that without graphing or with a second derivative

Set f'(x) to 0, solve for x.. Then plug x back into f(x)?

Yeah I reckon that's it, but if I'm wrong please save me 💀
Thanks for the help!

.close

[lone heart]

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[sharp sentinel]

How would you write out the following English sentence in a logical statement: "If Grizz is hungry, then he will bite Nate, but if he is not hungry, then if he’s awake he will bite Nate" where S = Grizz is asleep, R = Grizz is hungry, and V = Grizz bites Nate. And only using ~, ^, v, and -->?

[sharp sentinel]

What I tried so far was (R -> V) v (~R -> (~S ^ V))

[tawny condor]

"if he is not hungry, then if he’s awake he will bite Nate" can be interpreted as if he is not hungry and he is awake then he will bite Nate.

So ~R and ~S

I'm not sure how to express the "but" though.

You used v, which I guess makes some sense. The R -> V part seems fine aswell

[sharp sentinel]

okay thank you

[tawny condor]

@sharp sentinel .close if you don't need anymore help.

no problem!

[sharp sentinel]

.close

[lone heart]

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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[neon perch]

hi

[neon perch]

Is a^2Π the same as Πa*2

[rustic coral]

If you mean is $a^2 \pi =\pi (a\cdot 2)$, then no.

[ocean seal]

enclave wangedrocht

[rustic coral]

it's only true for $a^2 =2a \implies a=0, 2$

[ocean seal]

enclave wangedrocht

[neon perch]

no like

no like is $a^2 \pi = \pia^2

uhm

bot

not

ok

[rustic coral]

then yes, multiplication is commutative.

$a^2 \pi=\pi a^2$

[ocean seal]

enclave wangedrocht

[neon perch]

Yes

Thank you

[neon perch]

what grade are you?

wait

u might be american

nvm

[rustic coral]

10th

[neon perch]

Ah ok

[rustic coral]

yeah I am

lol

[neon perch]

thank you though

[lone heart]

@neon perch Has your question been resolved?

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[chilly hollow]

#1 please help

[chilly pike]

do you know what type of function it would be?

@chilly hollow

[chilly hollow]

idk

[chilly pike]

like

linear function, step function, piecewise function

etc

[chilly hollow]

we have to figure it out, but i think its a linear or quadratic

[chilly pike]

well

[chilly hollow]

help me make the equation based off the given info

[chilly pike]

it's not a linear or quadratic function

do yk what a piecewise function is

[chilly hollow]

yes

[chilly pike]

here

would you be able to write the conditions as a piecewise function

[chilly hollow]

idk, can you just give me the domain and range and i will figure it how you got it?

work myself backwards

[chilly pike]

i can't do that

I can't directly give you the answer

but here

[chilly hollow]

its a practice sheet

read the title

i will prepare me for my test!

[chilly pike]

you can make a variable a equal to the order weight

[chilly hollow]

it*

[chilly pike]

still

if a<100kg, y = 4x; if a>= 100kg, y = 3.5x

makes sense?

[chilly hollow]

yes

what is the next step?

@chilly pike

[chilly pike]

thats your function

you should be able to figure the rest out

[chilly hollow]

ohh

yeah

i can figure the domain, but what's the range?

[chilly pike]

can you explain to me what the range is?

[chilly hollow]

the y-values (up and down)

what the y-values can be; yer

explain why this is a function?

@chilly pike

[chilly pike]

calculate the lowest and highest y value you can possibly get from the function

that's how you find the range, right

[chilly hollow]

explain why this is a function?

will i get 2 different lines if i graph this?

[sonic ridge]

each piece of the function will have its own slope if thats what u mean

[fallow grove]

so it is a function?

[sonic ridge]

yes. a function is when each input has only one output, which is the case here

[lone heart]

@chilly hollow Has your question been resolved?

[chilly hollow]

Determine the domain and range

?

[lone heart]

@chilly hollow Has your question been resolved?

[lone heart]

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[vivid bane]

How would you write this in text?

[dense sleet]

Wdym by write this in text

[vivid bane]

sorry not text, latex

[dense sleet]

You cant really draw triangles in latex as far as i know

[dawn hamlet]

maybe ppl will know in #latex-help

[vivid bane]

well really just the expression

Oh theres a dedicated channel for that

[dense sleet]

Find $$cos(\theta)$$

[ocean seal]

Pluton

[dense sleet]

And you have $a = 13$ and $b = 3\sqrt{3}$

[ocean seal]

Pluton

[alpine sable]

,tex {\textbf{\color{pink}Definitions of sin/cos/tan}}\[3pt]
%v1_050822_764959481070616617
\colorbox{gray}{\begin{minipage}{.05\linewidth}{\phantom{.}}\end{minipage}\begin{minipage}{.45\linewidth}\phantom{.}\
$\sin\theta=\frac{\text{\color{yellow}Opposite}}{\text{\color{orange}Hypotenuse}}$\
$\cos\theta=\frac{\text{\color{lime}Adjacent}}{\text{\color{orange}Hypotenuse}}$\
$\tan\theta=\frac{\text{\color{yellow}Opposite}}{\text{\color{lime}Adjacent}}$
\end{minipage}\hfill\begin{minipage}{.45\linewidth}
\begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-1,xscale=1]
\draw (33.7,6.14) -- (220,112.6) -- (33.7,112.6) -- cycle ;
\draw (33.7,102.51) -- (43.79,102.51) -- (43.79,112.6) -- (33.7,112.6) -- cycle ;
\draw (164.88,113.13) .. controls (155.37,102.56) and (159.07,87.77) .. (176.51,88.3) ;
\draw (142.87,84.84) node [anchor=north west][inner sep=0.75pt] [align=left] {$\displaystyle \theta $};
\draw (81.33,10.23) node [anchor=north west][inner sep=0.75pt] [rotate=-29.88] [align=left] {\color{orange}Hypotenuse};
\draw (10.99,98.99) node [anchor=north west][inner sep=0.75pt] [rotate=-269.68] [align=left] {\color{yellow}Opposite};
\draw (80,114) node [anchor=north west][inner sep=0.75pt] [align=left] {\color{lime}Adjacent};
\end{tikzpicture}\end{minipage}}

[ocean seal]

Toby

[trim wagon]

,tikz \draw [thick]
(0,0)-- (0,-5.5) --(-13,0)--(0,0);

[ocean seal]

Deep. (kawaiiCat for emoji)

[alpine sable]

you can use --cycle

[trim wagon]

hmm 🤔

[dense sleet]

You can do that???

[trim wagon]

yes sir

[alpine sable]

ye tikz op

[trim wagon]

tikz can do all sort of stuff

maybe not here

[earnest garden]

SOHCAHTOA

[trim wagon]

there you go

[ocean seal]

Deep. (kawaiiCat for emoji)

\begin{tikzpicture}
\node [scale=2] (a) at (-6,1) {13};
\node [scale=2] (a) at (1,-3) {$3\sqrt3$};
\node[scale=1.5](a) at (-0.3,-4.8) {$\theta$};
\node [scale=3](cos) at (-15,2) {$\cos \theta$};
\draw [red](0,0)rectangle (-1,-1);
\draw [thick]
(0,0)-- (0,-5.5) --(-13,0)--(0,0);
\end{tikzpicture}

[trim wagon]

@vivid bane

[alpine sable]

nice!

[ocean seal]

Deep. (kawaiiCat for emoji)

[lone heart]

@vivid bane Has your question been resolved?

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[peak silo]

Hello, I have a question for you, I don't know, you will probably understand, but I would like to calculate the force on the ball. I know its density after compression and its weight and I am trying to calculate the force acting on the ball.

[peak silo]

<@&286206848099549185>

.close

[lone heart]

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[alpine sable]

been banging my head against the wall on this one for 20 minutes

can't figure out why the answer isn't this

approximating with x=7, y=5, and z=70

[slate jolt]

what formula do u get for the linear approximation of f around the point (a,b,c)

[alpine sable]

f(a, b, c)+fx(a, b, c)(delta x)+fy(a, b, c)(delta y)+fz(a, b, c)(delta z)

[slate jolt]

alright

and in this case?

if u compute the partial derivatives?

[alpine sable]

partial derivatives are x/sqrt(x^2+y^2+z), y/(x^2+y^2+z), and 1/2sqrt(x^2+y^2+z)

plugging in a b and c, you get 7/12, 5/12, 1/24

[slate jolt]

ok that seems right

and so you get your result

[alpine sable]

given answer is 12.146

[slate jolt]

and the actual value is not that far is it?

[alpine sable]

OH

the textbook had it backwards

[alpine sable]

nvm that's not it

looks like my estimate is too accurate then

but i'm using the right method

[slate jolt]

i'm double checking the calculations on my own

[alpine sable]

this is directly from the book

[slate jolt]

but it seems good at first glance

yeah the formula is right

yeah i get the same thing

i would have answered what you have

[alpine sable]

weird

well i have to go now

thanks for trying to help

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

Channel closed

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[mint estuary]

.reopen

[lone heart]

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[edgy crag]

I've got this question, but I could only found one answer out of two

[edgy crag]

I found z = -2 (z = -2 +0i)

But apperantly, there's also z = -10 (z = -10+0i)

[lone heart]

@edgy crag Has your question been resolved?

[rare gale]

@edgy crag I think you need to rework the problem and be more careful of your algebra

this jumps out as an initial mistake

there may be others but im going to stop there since that carries through all the way to the end

[edgy crag]

Owww thanks!!!

.close

[lone heart]

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[soft sinew]

Hi Im in grade 11 rn and I was having trouble grapghing y=xsquared -4x

[soft sinew]

ive used desmos but I dont know how to grapgh this equation

[slate jolt]

do you need to graph it by hand?

[wary stream]

y = x^2 - 4x?

[soft sinew]

yes

[soft sinew]

yeah there are going to be others like this that i need to grapgh by hand

[slate jolt]

ok so do you know how to graph x² first?

[soft sinew]

yes

I also know how to graph with relfections and tranlsation but otherwise I dont

[wary stream]

The other thing is, do you know how to make a table of values to plot?

[soft sinew]

yes but that i cannot do due to time restraints it is too slow

[wanton tusk]

also have u tried to find x and y int

also min point

[soft sinew]

how would I do that?

[wanton tusk]

at an x intercept

what’s the y coord?

[soft sinew]

y = x^2 - 4x? is the only equation im given

[wanton tusk]

yes

but

ok

if you’re on the x-axis

what will the coordinate of y be

do u see the red points

ignore everything else HAHA

[ornate condor]

here u r

[soft sinew]

0?

[wanton tusk]

yes

ya

[wanton tusk]

QUEEEEN

[ornate condor]

QUEEN

[wanton tusk]

so to find x-intercept

y=0

so x^2 - 4x = 0

u can factor and find ur x values

[soft sinew]

I think I get it thankyou

[wanton tusk]

🥳

welccc!

[sinful cloak]

triangle MNP: MN=a,angle MNP=60,angle MPN=40.calculate the area of ​​triangle MNP in terms of a

help me pls

[lone heart]

@soft sinew Has your question been resolved?

[lone heart]

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[dense moon]

hey

[dense moon]

how yall do that?\

[vague coral]

domain : all the values that x should take such that f exists
range : all the values that f can take

[dense moon]

this right before I submit?

[vague coral]

domain is wrong

[dense moon]

do I assume it goes thru -2,2

cuz it doesnt stop at 1?

[vague coral]

no

f exists for all real values

[dense moon]

so what do i put for the domain

[vague coral]

R

the range is also wrong

[dense moon]

can u get in a call, so u can explain?>

[vague coral]

no sorry

Like I said, the domain is the set of all possible values such that f exists, which means all the possible values of x that can return a value of f

for example f(x) = 1/x
1 is part of the domain becuz f(1) exists, but 0 is not part of the domain cuz 1/0 doesnt exist (you cant divide by 0)