help-0

[glass lichen]

you have a leg of 30 and a hypotenuse of 40

assuming the triangle's top vertex is above the midpoint of the base

[sterile thistle]

isnt my base the hypotenuse

[glass lichen]

no

cause 60 40 40 isnt a right triangle

[cursive crescent]

I’m not a LaTex

So take bad handwriting

[raw shard]

handwriting is better than mine

[sterile thistle]

whered you get the 30 from

[raw shard]

half of 60

[cursive crescent]

But your height would equal the sqrt( -(base/2)^2 + (side)^2)

Adjust as desired

[sterile thistle]

so whyd you half 60

[raw shard]

pythagorean theorem only works on right triangles so they had to cut it in half to get a right triangle

[cursive crescent]

If you look at the diagram above, the height is also directly above the center of your base for the triangle

[glass lichen]

pythagorean theorem...

[raw shard]

bruh

[glass lichen]

read if you're going to comment

[sterile thistle]

so

[glass lichen]

so..... what

[pearl wraith]

how do i rationalize C

[raw shard]

channel is occupied bruh

[pearl wraith]

i dont see anyone typing

[sterile thistle]

nah

[wary stream]

But there's a conversation going on

[cursive crescent]

Several people are typing

[sterile thistle]

were ghosts bro

[raw shard]

just because someone doesn’t send a message every second doesn’t mean there isn’t a conversation

i don’t see anyone typing lol what

[sterile thistle]

wouldnt you need the area to find the height tho

[raw shard]

read the rules bruh

[sterile thistle]

a = 1/2bh

you need the height for the area and the area for the height

[raw shard]

did you ever say anything about area?

[sterile thistle]

so confusing

huh

but you need the area to find the height

[glass lichen]

?????

[raw shard]

no you don’t

lol

[glass lichen]

Have you like not read anything we've said

[sterile thistle]

nah

ive been watching youtube

[glass lichen]

Ok, go fuck yourself then

[sterile thistle]

bruh

[raw shard]

seriously @glass lichen

[sterile thistle]

its called sarcasm

[raw shard]

if you don’t listen we aren’t going to talk

[sterile thistle]

bruh

apparently you do

according to google

[raw shard]

well

if you rearrange the equation obviously

[glass lichen]

No

since squaring isnt linear.

[raw shard]

but you usually aren’t given the area and no dimensions

[sterile thistle]

ik

[raw shard]

actually you never are lol

[glass lichen]

tf is a p2

[sterile thistle]

power

[raw shard]

idk

[glass lichen]

^2

[raw shard]

then say ^2

honestly even just say to the power of 2

because that’s less confusing

[sterile thistle]

ok

[glass lichen]

or just make it clear what you're saying, not ambiguous stuff like "40-30 squared"

[raw shard]

a^2+b^2 = c^2 where a and b are legs and c is the hypotenuse

[glass lichen]

the right triangle doesn't have a side of 60

[sterile thistle]

do you always use Pythagorean for triangles?

[glass lichen]

no

[raw shard]

@sterile thistle only for right triangles

[sterile thistle]

ok

[glass lichen]

Pythagorean theorem is only applicable on right triangles

[fast wave]

yo @glass lichen how to find acceleration with mass and v1

[glass lichen]

not sure where you got v1 from

[fast wave]

A sub-atomic particle, mass 1.673 x 10-27 kg, is accelerated from an initial speed of 4.60 x 106 m/s along a frictionless path 2.00 km long. What acceleration would be necessary for the particle to approach the speed of light, 3.00 x 108 m/s?

[sterile thistle]

bruh

[fast wave]

the answer is 25

i got it alr

[sterile thistle]

were kinda occupied right now

[fast wave]

this diff one

[raw shard]

i don’t even know if the channel is occupied at this point

[glass lichen]

flying was using prior to these 2

[raw shard]

that’s the unknown

we know the base and hypotenuse

[sterile thistle]

can you just make it upo

up

[raw shard]

ugh

30^2+h^2 = 40^2

[sterile thistle]

someone said that b4

[glass lichen]

pretty sure mass isn't needed

[fast wave]

whats the formula

[raw shard]

@sterile thistle someone asked an identical question

probably the same thing with cm behind it

[glass lichen]

$v^2-v_0^2=2a\Delta d$

[ocean seal]

Mosh

[fast wave]

?

[glass lichen]

that's the direct kinematics eqn for it

[fast wave]

o ye

[glass lichen]

then just isolate for a

exact height is 10sqrt(7)

10sqrt(7)cm

[fast wave]

v^2 - v_0^2/2d= a

right

[glass lichen]

that's basic math, do it yourself.

[glass lichen]

but yes

[fast wave]

i just plug in numbers den get a

right

[glass lichen]

yes

[cursive crescent]

$$ Height = \sqrt{{-(\frac{Base}{2}})^2 + Side^2 }$$

This took me way too long

[sterile thistle]

$$ Height = \sqrt{{(\frac{Base}{2}})^2 + Side^2 }$$

[ocean seal]

Libster

[sterile thistle]

how do you do that

[wispy olive]

Copypasta.

[glass lichen]

bruh what

how do you do what?

LaTeX?

or basic math?

[sterile thistle]

noo

the formulas

[ocean seal]

Karkess

[sterile thistle]

like type them in

[glass lichen]

Do you just... not know how to ask questions coherently?

[sterile thistle]

???/

breh

[glass lichen]

A good chunk of your questions have seriously been lacking in details

been answered already

[sterile thistle]

BRUH HOW DID KARKESS DO THAT FORMULA

DID HE MAKE IT

OR NOT

WHAT

[glass lichen]

pythagorean theorem READ BEFORE BITCHING

[sterile thistle]

IS THE COMMAND

[cursive crescent]

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[sterile thistle]

,help cmd

[ocean seal]

You really shouldn't take it literally :upside_down:. Please type ,help ping, for example!
The full command list may be found using ,list.

[glass lichen]

It's been explained.

[sterile thistle]

who even are you

like bruh killua?

from animeA?

anime*

,list

[ocean seal]

My commands!

Use ,ls to obtain a briefer listing, and use ,help <cmd>to view detailed help for a particular command, or ,help to view general help.

If you still have questions, talk to our friendly support team here.

LaTeX Rendering

Render LaTeX code and configure rendering options.
​ ​ ​ ​ ​ ​ ​ ​ ​ ​ tex: Render LaTeX code.
​ ​ ​ ​ ​ ​ ​ ​ ​ ctan: Searches the ctan
​ ​ ​ ​ ​ ​ ​ texdoc: Searches the texdoc
​ ​ ​ ​ ​ ​ autotex: Toggle whether your LaTeX is automatically rendered.
​ ​ ​ ​ ​ preamble: View or modify your LaTeX preamble.
​ ​ ​ ​ texconfig: View or modify your personal LaTeX rendering options.
guildpreamble: View or modify the guild's default LaTeX preamble

Guild Admin

Guild administration
​ ​ ​ ​ ​ ​ ​ ​ config: View and set the guild configuration.
​ ​ ​ ​ ​ ​ ​ ​ rmrole: Deletes the provided role
​ ​ ​ ​ ​ ​ ​ disable: Disable commands in this guild.
​ ​ ​ ​ ​ ​ editrole: Create or edit a server role.
​ ​ ​ ​ ​ autoclean: Automatic deletion of messages in the current channel.
forgetrolesfor: Forget stored persistent roles for one or all members.

Page 1/4

[wispy olive]

Yeas.

[fast wave]

yoo

i got a result thats not available

[glass lichen]

what did you get..?

[fast wave]

this

[sterile thistle]

okok

[glass lichen]

1. v is suppose to be the speed of light, v_0 is initial
2. the speeds are squared

already told you this.

[wary stream]

Is this some broken form of the quadratic formula?

[sterile thistle]

lol @dark compass apparently theyve said it

[cursive crescent]

Courtesy of Symbolab

[glass lichen]

you asked for exact and I gave you exact. If you meant you wanted an approximation, then ask "What's the height approximately?"

Dont ask a question you dont want the answer to

[fast wave]

@glass lichen shiet

[cursive crescent]

Yes

[glass lichen]

the distance needs to be in meters

rn it's 2km

[raw shard]

no @dark compass

[glass lichen]

yeah your question is shitly presented

[wary stream]

Well, you didn't ask a question

[glass lichen]

and this channel is clearly in use

[raw shard]

you have 30^2+h^2 = 40^2, h^2 = 40^2-30^2, h = sqrt(40^2-30^2) = sqrt700

[storm prawn]

teach me how to use three test points

[raw shard]

24.86 is not equal to sqrt700, not even approximately

[glass lichen]

no

stop doing bullshit

you've been told the answer.

many times

[raw shard]

you’re just putting in random numbers

[glass lichen]

Just ignore them at this points

No point in wasting time

[raw shard]

the answer is approximately 26.5

[quartz wraith]

2 perfect squares that are 100 apart?

[dreamy cedar]

what is going on here

[glass lichen]

in use.

[wary stream]

You did not ask a question and you asked in a channel that is busy

[raw shard]

oh my gosh

@dark compass i approximated

[dreamy cedar]

Mosh dont be rude, chiro no one owes you help

[raw shard]

this channel is crazy

[dreamy cedar]

And this channe lsi n use

use one of the other ones

[glass lichen]

we did.

[raw shard]

@dreamy cedar their anger is often unnecessary but here it’s understandable

[glass lichen]

read.

[fast wave]

@glass lichen 3/3 ty

[glass lichen]

np

[raw shard]

this channel is way too active

or it was

too many people sending too many messages

[glass lichen]

??

10sqrt(7)~26.5

done

[raw shard]

i basically made an educated guess

[glass lichen]

the number

[raw shard]

@glass lichen they don’t understand your conversions so probably just don’t do them

[sterile thistle]

no ones as smart as you

[raw shard]

i won’t even explain my process because literally anyone could do it if they got a minute

[sterile thistle]

put it in simplest form

NO WORD

[raw shard]

i don’t even know who’s talking to who

[sterile thistle]

IT

IN SIMPLEST FORM

[glass lichen]

Im just gonna let them handle it themselves tbh

[raw shard]

probably a good idea mosh

[cursive crescent]

It’s entertaining at least. Got some laughs

[raw shard]

you shouldn’t be on here then

[glass lichen]

can't be a worse dumpster fire than it already is

[raw shard]

if you’re in year 6

[sterile thistle]

whats the age limit

to this server

[raw shard]

13

[glass lichen]

13...

[sterile thistle]

im 6

[raw shard]

i hope you’re not serious

i think i’m done

every time i explain something 20 more questions get asked

also if you’re under 13 i literally don’t have to help because you shouldn’t even be on here

[sterile thistle]

killua is 12

so?

[raw shard]

too young

[sterile thistle]

the profile picture says so

[wary stream]

That's against discord's TOS

[sterile thistle]

your photo

i know you irtl

irl

i know you irl

bud

thats why were friends on discord

[glass lichen]

Oh boy, underage and doxing

[sterile thistle]

doxing?

wdym doxing

bruh LMFAO

[cursive crescent]

I’m glad the internet wasn’t such a thing when I was so young.

[wary stream]

Woah, calm yourself there

[raw shard]

@glass lichen i completely believe their ages now

[glass lichen]

<@&268886789983436800>

[raw shard]

if you talk like this you are automatically 12

[sterile thistle]

told you he was 1

12

[raw shard]

lol breaking so many rules

good idea pinging mods

[glass lichen]

ty Nami

[dreamy cedar]

Hurb

[glass lichen]

wb Moth

[dreamy cedar]

I hate it here

[raw shard]

that was definitely interesting to say the least

[dreamy cedar]

[cursive crescent]

[raw shard]

you missed all the annoying stuff @cursive crescent

[glass lichen]

Probably best to drop it at this point

[sterile thistle]

my mans telling me to noose

[raw shard]

true

[cursive crescent]

I liked the diagram at the beginning.

[raw shard]

ok people ask more questions

[glass lichen]

Channel's free.

[raw shard]

@cursive crescent same with the impossible triangle

[sterile thistle]

@dark compass

[raw shard]

ok seriously stop lol let people ask questions

[hoary laurel]

Hi I’ve got a few questions for an open book assignment I’m doing

Unit is solving polynomial inequalities

[wary stream]

Post the specific question you have

[hoary laurel]

Alright

This is the first one

Sorry for bad lighting

So I know i have to get the X-intercepts first which for this inequality is, x=1, -2, and -3

But I'm not sure what to do after that

[placid zinc]

-3 isn't an x-int

Once you have the x-ints, then test the points between them to see what their signs are

[hoary laurel]

Would the x- int be 3 then?

Since you reverse the sign out of the bracket

[alpine sable]

is a=1, b=5, c=2, so a+b+c is 8?

[hoary laurel]

hey this ones occupied rn man

[alpine sable]

oh sorry

[placid zinc]

If you're unsure, try plugging -3 and 3 in

Then to actually check the signs, plug a few points in between in.
x = 0 is an easy point here

[tranquil tulip]

is this right?

that it’s impossible

[wary stream]

Similar triangles

[sterile thistle]

https://cdn.discordapp.com/attachments/490557019623915520/894392930998038608/unknown.png

howwwww

[tranquil tulip]

Use similar triangles

[sterile thistle]

the impossible triangle buzz

[mellow anchor]

ok

[dusk girder]

Can somebody help me with some linear algebra

I’m not sure if I did 4b correctly

[elder glacier]

@sterile thistle

bro did you make another account just to join this server again lmfao

[astral stump]

How do you find the scaling factor

[raw shard]

don’t you just do something like 57/43

[astral stump]

i should add you only know 1 image size

[raw shard]

and that’s how much bigger the second one is than the first?

[wary stream]

It'll be different for each one

[tranquil tulip]

$width of small square/length of small square= width of big square/length of big square$

[astral stump]

these were taken at different resolutions 4:3 5:4 19:9 21:9

[raw shard]

well that doesn’t matter because we still have the side lengths

unless i understand horribly incorrectly

[ocean seal]

beautyiskeytosuccess

[astral stump]

say you only have the data 19:9 and 60x60 then you trying to find scale factor for 5:4 (but you don't know 57x57)

[tranquil tulip]

$(width of small square/length of small square)= (width of big square/length of big square)$

[ocean seal]

beautyiskeytosuccess

[tranquil tulip]

Whatever

Jus do 57/43

[astral stump]

i can't do 57/43 becasue i don't know about 43

[wary stream]

$\frac{\text{width of small square}}{\text{length of small square}}= \frac{\text{width of big square}}{\text{length of big square}}$

[ocean seal]

dldh06

[tranquil tulip]

Huh? what is there to know about 43

[wary stream]

That's what you wanted, right?

[tranquil tulip]

Yes ty i did it way wrong

[astral stump]

nope lol , say we know width and height of big square and that it somehow tied to screen res 19:9 we need to find scale factor to lower it to 5:4 (57x57) or 4:3 (43x43) but we don't know the width and height of these small squares only that some how tied to 5:4 and 4:3

[tranquil tulip]

oh i don’t know then sorry

[brave thicket]

hi, i just learned about f(x) = ax + b. does anyone know what a & b represents here (in simple terms)?

[wary stream]

Slope and y intercept

[sterile thistle]

@elder glacier what

[fierce linden]

A refers to slope and b refers to the y-int if ur confused about which is which

[brave thicket]

ok thanks a lot

[celest anvil]

how do

[amber iron]

So

If you have something like z = y^3+x^2. x, y, z are all variables.

and x is a function of y and z

then how do u find partial derivative of x wrt y

[jaunty root]

Does the gregory-newton formula also works for non-integers outputs?

[amber iron]

yeah

<@&286206848099549185>

f(x,y,z) = z-y^3-x^2 = 0

so if youre finding partial of x wrt y, how would you do that

[cursive crescent]

Take the standard cubic formula and evaluate the derivatives in symbolic form, and once you get to the third derivative you can set f’’’(-2)=12, and then work your way backwards

Once you get started it should start to be apparent :)

[celest anvil]

for f'''(x), i got 6a=12, a=2?

[cursive crescent]

If that’s how it worked out. I can’t work it out right now, but that work make sense to me.

AX^3 => 3X^2 => 6X => 6, seems right,

[celest anvil]

then i work up to 6ax+2b=-24?

and x is -2?

[alpine sable]

Axis

[cursive crescent]

Yep, and you have a

[alpine sable]

Axis 2

I did this by my own

Actually taking a revision in this class

[wary stream]

What exactly do the arrows denote?

[alpine sable]

The arrows denote the lines (axis)

[alpine sable]

Did this help you @wary stream?

[wary stream]

Not exactly

Like the arrows point in different locations

I understand the quadrants thing but the arrows, not really

[upbeat gorge]

The arrows point towards the x-axis i guess?
Truth be told you can forget the arrows

[cursive crescent]

I agree I think the arrows might confuse things a little bit.

[foggy acorn]

How do i show that f is not differentiable at (0,0)?

[harsh belfry]

I keep getting a different answer to the key

Any chance someone could tell me how come the sin and cos become squared?

[raw shard]

derivative of sin is cos and derivative of cos is -sin, so they just multiplied them together and said it was squared

so like d/dx (sin(x)cos(x)) = cos(x)cos(x)+-sin(x)sin(x) = cos^2(x)-sin^2(x)

[high palm]

Is this channel occupied?

@raw shard apologies for the ping

[raw shard]

let me see

@harsh belfry do you still need help?

[harsh belfry]

Ah

Sorry I stepped away.

Second I'm reading it.

[shrewd tundra]

For the whole numbers 6, 10 and 14, check the associative property of the subtraction
of whole numbers.

help

pls

[harsh belfry]

Go ahead quantum.

[raw shard]

@shrewd tundra don’t post that in every single channel

[harsh belfry]

I'm good here.

[raw shard]

@high palm if you’re still here you can ask

[harsh belfry]

Channel occupied by quantum.

[amber iron]

Could I get some help after this channels available

[raw shard]

this channel is available

[shrewd tundra]

ahh

[shrewd tundra]

For the whole numbers 6, 10 and 14, check the associative property of the subtraction
of whole numbers.

[raw shard]

read the rules bruh

[amber iron]

f(x,y,z) = z-y^3-x^2 = 0
so if youre finding partial of x with respect to y, how would you do that if x is a function of y and z

[raw shard]

oh my god

some people

my god

[harsh belfry]

https://tenor.com/view/face-palm-no-nope-cant-frustrated-gif-8484257

[amber iron]

lmao

[shrewd tundra]

For the whole numbers 6, 10 and 14, check the associative property of the subtraction
of whole numbers. - help

pls

[harsh belfry]

no body reads the rules....

[raw shard]

@amber iron you can delete and repost your question

ok dude actually stop

you’re basically not listening

[shrewd tundra]

me?

[harsh belfry]

very annoying

[high palm]

I'm here all day I got a pile of questions

[shrewd tundra]

ahhhhhhh

[high palm]

So is it okay if I post it?

[raw shard]

i literally don’t know at this point

[high palm]

If not I can just go to another channel

[raw shard]

probably do that

[high palm]

It's really not a big deal

[amber iron]

the dude is probably trolling

[cursive crescent]

Maybe swap to a different channel and let ykj3 use this one

[raw shard]

@amber iron unfortunately i don’t think they are

[harsh belfry]

I think hes foreign or something and wasnt reading the messages.

[raw shard]

ok guys stop talking let people ask questions please

mini modding time

[amber iron]

yeah

[harsh belfry]

👍

[amber iron]

so how would you be able to find partial of x with respect to y for that function

[raw shard]

@amber iron you can repost your question

[amber iron]

f(x,y,z) = z-y^3-x^2 = 0
so if youre finding partial of x with respect to y, how would you do that if x is a function of y and z

[verbal bloom]

can someone tell me this answer please

[cursive crescent]

[raw shard]

bruh

[verbal bloom]

im sorry but i really need it

sorry

[rocky atlas]

Do u understand roaster form?

[amber iron]

go to another channel lol

[cursive crescent]

Anyways, isolate y and do the derivative with respect to x, and treat everything that is not x as a constant

[verbal bloom]

im new and idk anything bruh fr but the teacher wants me to answer olease help

[amber iron]

@cursive crescent its not dy/dx

[raw shard]

@cursive crescent they are making it like x = something though

[amber iron]

its partial of x with respect to y

[raw shard]

that won’t work

[amber iron]

aka dx/dy

[rocky atlas]

Server rule can't tell answers

We don't work

[raw shard]

if you try to do x = something, you’ll be excluding some solutions

[cursive crescent]

Oh maybe I flipped it

[verbal bloom]

can u dm?

[raw shard]

like in the case of isolating x or y in x^2+y^2 = n

[verbal bloom]

i really need it ugh

[raw shard]

pay attention in class next time

[amber iron]

its math, the world is not gonna end if you dont do it

actually maybe the world does end

[raw shard]

@amber iron did you read what i said? i’m not an expert in partial derivatives but it seems right

idk why i answered if i don’t even know how to do it really lol

[amber iron]

i didnt read where you said it

Problem is x is not independent as well

[cursive crescent]

Would you not just take care to be sure to include both the positive and negative solutions of the root and get the solutions, or am I confusing something?

[amber iron]

x is a function of y and z

so its a bit of a chain rule usage too, but i dont know how to use it

[raw shard]

@cursive crescent well would you combine them after taking the derivative?

maybe you could do x^2 = something idk

and divide by 2 afterwards?

ugh that sounds wrong

[amber iron]

you can't treat x as a constant here

x and y, both are not constants

[cursive crescent]

Yeah yeah, I had the thing flipped. So it’s partial x / partial y?

[amber iron]

yes

and x is defined in terms of y and z

[raw shard]

how would you even do that lol

i guess chain rule?

[cursive crescent]

I’m like 90% sure you isolate x and the do the derivative with respect to y and treat z as a constant.

[rocky atlas]

z is a variable

[cursive crescent]

Right but this is the partial, not implicit differentiation.

[amber iron]

like if it was asking for dy/dx instead of dx/dy, and x was a function of y and z, im pretty sure i'd be able to do it

[acoustic mirage]

can someone pls tell the anser to these quesions

[raw shard]

bruh

channel is occupied

[amber iron]

#help-3 @acoustic mirage

[wary stream]

Also, we are not here to give you answers

[acoustic mirage]

then ?

[raw shard]

probably at least 10% of the time that i say bruh is in this kind of context

[acoustic mirage]

explain them atleast

[amber iron]

channel is occupied tho

[raw shard]

talk about this in a different channel

[amber iron]

is it possible to just find partial y/partial x and then its reciprocal?

[raw shard]

i think so

[amber iron]

does it work like that

cool

damn, my teacher expected me to do all that in the exam

[raw shard]

woah this is a homework question?

[amber iron]

no it was on the test

on the test it was harder, involving ln and cos and such

[cursive crescent]

Okay, so what was the question? I’ll write it on paper to see if I get what’s going on/what you’re looking for

[amber iron]

z = ln(10-x^2-cos(y)). given x is a function of y and z, find partial x / partial y

[cursive crescent]

Gotcha

[foggy acorn]

how do i show that f is not differentiable at (0,0)

[amber iron]

whats f

well, the work wasn't as hard as i thought looking back

i completely zoned out

[cursive crescent]

Don’t quote me on this

[raw shard]

@cursive crescent is that a total derivative?

[cursive crescent]

It’s implicit partial derivatives using the chain rule to evaluate for each variable, or something.

[foggy acorn]

can we proceed to #help-2 for convenience

[cursive crescent]

I looked back at old notes and just slammed down variables

[raw shard]

@cursive crescent woah

[cursive crescent]

But does that seem familiar at least?

[amber iron]

sure @foggy acorn

wtf, the teacher actually made this easy

[raw shard]

something else that sounds interesting that i gotta look up and forget about a minute later

[foggy acorn]

oh wait someone occupied it .-.

[amber iron]

lets discuss in dms then

its just dx/dy = -siny/(2x)

[foggy acorn]

i placed the question in #help-3

[cursive crescent]

Well it seems easy. Just take the partial of the function with respect to y and again with respect to x, and divide them with a negative sign maybe

[raw shard]

maybe

[cursive crescent]

A lot of maybes here. I don’t remember this really at all.

But that’s what my notes made it seem like B)

[amber iron]

i just did it directly, and the whole denominator didn't matter cause there was a 0 on the other side

[cursive crescent]

What do you mean did it directly?

[amber iron]

heres my work

thanks for the help guys

[raw shard]

@amber iron do you still need help on the first question?

[cursive crescent]

Gotcha.

[amber iron]

i'm fine, thanks

[raw shard]

ok

[waxen spruce]

question

how to solve jump discontinuities by hand

[vagrant sluice]

Hey guys, I just wanna double check out whether my answer is correct or not.

Is there anyone who can check out whether my answer is correct or not for the conditional probability problem in a below image?

[vagrant fractal]

is this the final answer or do I need to solve some more?

[fast shuttle]

Can anyone tell me how do i evaluate limits?

[paper canopy]

@vagrant fractal

[fast shuttle]

I don’t need the solution, can just someone tell me if its the same as finding the limits or its a whole different process

[cursive crescent]

This I believe would be an application of L’hopital’s rule

If my mental math is correct this evaluates to 0/0

[fluid loom]

Using appropriate identity evaluate 30.8 ×29.2.

pls tell

Using appropriate identity evaluate 30.8 ×29.2.

Using appropriate identity evaluate 30.8 ×29.2.

[fast shuttle]

Thanks for the help!

[cursive crescent]

Of course :)

[paper canopy]

can somebody help me

[cursive crescent]

It seemed like you already had that worked out

[paper canopy]

i think its wrong

[versed mica]

it looks right…?

wait actually

i kinda forgot calc stuff, but a way to be sure ur second derivative is correct is by doing Lo D Hi minus Hi D Lo over Lo squared

and then subbing in the first derivative where necessary

[paper canopy]

👍

[dreamy bone]

bruh what did my teacher do?

I'm confused can anyone pls help?

like why did she make xlnx into lnx/(1/x)?

[jagged imp]

you can write $x\ln(x)$ as a fraction $\frac{x\ln(x)}{1}$ and divide the numerator and denominator by $x$ to get $\frac{\ln(x)}{\frac{1}{x}}$

[ocean seal]

Sneaky

[dreamy bone]

first of all damn bro

you really know how to operate this thing

like is it matlab thing?

[jagged imp]

? its LaTeX and I didn't misoperate anything

[rigid wind]

tex?

[dreamy bone]

anyway, thanks a lot for the help. I actually understand what you meant!

[jagged imp]

oh

[dreamy bone]

ohhh right Latex my bad

[jagged imp]

i misread your message

lmfao

tahnks

[dreamy bone]

not matlab

[jagged imp]

i thought you said you really dont know how to operate it

[dreamy bone]

lol ya nw

but thanks for the help. idk why It didn't click to me

[oak jewel]

How does pascal's triangle work?

is n=3?

[lapis valley]

n = 3 will be 1 3 3 1

[oak jewel]

oh so its the row

n=1 is 1 1?

[lapis valley]

i think

[oak jewel]

makes more sense now thanks

[lapis valley]

yes

[hollow pelican]

hi guys does anyone know how to differentiate this

[eternal osprey]

If you take derivative from left side and derivative from right side using limits can you say that derivative is the same?

For piecewise question

[hollow pelican]

not using limits

normal derivatives only

[eternal osprey]

Limit as x approach a?

[hollow pelican]

no

[eternal osprey]

So if i calculate the derivative from the left and right

If they evualte the same then its f

G*

Or do I have to take derivative of actual function

Cause i end up with 0/0 for that

[hollow pelican]

yea actual function

[eternal osprey]

Shit

Could i send the question

[placid zinc]

Derivative in terms of θ?
dr/dθ = 2sin(5πθ)cos(5πθ)5π

Note the triple chain rule here

Take the derivative of the outer function, keeping the inner intact, then multiply the derivative of the inner

[eternal osprey]

first i made f(x) continuous

But using definition of derivative my shit ends up being 0/0 for my middle function.

[hollow pelican]

ok

[placid zinc]

Well, 0/0 means you haven't found the answer yet

[eternal osprey]

I get A - A/0

[wispy solar]

how do i pay taxes

[eternal osprey]

A-A / X

And x is zero

And A is zero

And when I plug it into a graph it literally looks like the derivative from the left and right

But your saying it cant be?

[placid zinc]

You're saying a lot of things

So yes, you can prove the limit exists by checking the left/right sides

[eternal osprey]

Why cant i use definition of derivative tho?

Cause its just a fancy limit

And treat limit from left equal to limit from right

Boom

Heres my work if anyone could give me a hand

<@&286206848099549185>

[crisp grove]

looks ok to me

[lapis hedge]

What do you need clarification of?

[placid zinc]

See YouTube if you haven't yet. Some of the best tutorials there

Take any two sets, I'll call them A and B.

Put some arrows between these sets. Every arrow has to start at some element of A, and end some element in B.

All of these arrows are their own set, called a relation between A and B.

[lapis hedge]

All functions are relations but not all relations are functions. This is due to the fact that functions are relations that have one output for an input. A relation shows the relationship between inputs and outputs and do not necessarily only have one output for one input.

[rocky atlas]

I see

There is clear difference between function and relation

Let's understand this difference from example

Not for u

Not for me

This is a clear difference in math

In existence

Our job is to understand them

No no this is very normal to student

[lapis hedge]

input x and output y

[rocky atlas]

Y is the output of a relation or function

x is the input of a relation or function

For any value of x you get specific y

[placid zinc]

Take a relation (that is, a set of arrows)
This relation can also be called a function if every element in A has exactly one arrow leaving it.

[rocky atlas]

If there is a element in (input) that doesn't have a arrow leaving then it's not a function

In y=5x function can you tell me a value of x that gives 2 values of y?

That's why a function can't have more than 1 outputs or 2 arrows in 1 input

[rocky atlas]

There can be many inputs but output is 1 value only in a function

[placid zinc]

Can see the problem with the second relation, that two arrows are leaving from 5. Can't call that a function.

[rocky atlas]

Like in quadratic function 2 values of x can have 1 value of y but there can't exist 2 or more y who will have one x

Yup

Though there might be case where 2 value of x can have same y

But there can't be 2 unique value from one x

Yes

Like in quadratic equation

X has 2 values but y is one value

x^2+5x+4=0

[woven idol]

maybe this will help idk

[rocky atlas]

You really research deep lol

I guess

I mean try to think of a example

Where power is 1 and u have 2 values of x for one unique value

Np

[scarlet leaf]

I want to write a quadrantic equation that has a zero in the equation from the picture, but I don't know where to start.

[alpine sable]

@scarlet leaf conjugate roots (if you know of them)

z = 1 - 2i, 1 + 2i

multiply the roots and you have the quadratic equation

$z^2 - 2z+ 5$

[ocean seal]

omsai

[alpine sable]

should be the thing ig

[scarlet leaf]

so (1-2i)(1+2i) -> z^2-2z+5?

[alpine sable]

ugh no

z is a root of the equation we want

[scarlet leaf]

nevermind

yeah

[honest lagoon]

can anyone help me??

[scarlet leaf]

i missread lol

[alpine sable]

so you know how the answer came, right?

[scarlet leaf]

not entirely sure no

[alpine sable]

okay so

you know of the theorem that states that if a quadratic has a imaginary root

then the conjugate of that root is also a root of the equation

[scarlet leaf]

hmm

[alpine sable]

so you have the roots, multiplying the factors of the quadratic gives you the quadratic

so the factors of the quadratic are? @scarlet leaf

[scarlet leaf]

I don't know man, english isn't my native tongue so math termonology is kind of hard to grasp at times

[alpine sable]

your english is pretty good tho

[scarlet leaf]

so I conjugate the rootz and get z= 1-2i and 1+2i?

[alpine sable]

yes

[scarlet leaf]

and then I multiply the roots

[alpine sable]

not really

[lapis hedge]

The factors

[scarlet leaf]

isnt that what you said above tho?

or am i tripping

[alpine sable]

I said the factors

[scarlet leaf]

oh mb

still don't understand how multiplying the factors gives me

$z^2 - 2z+ 5$

[ocean seal]

wsnd

[lapis hedge]

(x-1+2i)(x-1-2i)

notice you can group x-1

[scarlet leaf]

so should I move over z to the other side initially to get 1-2-i-z = 0 or where did you get x from?

[lapis hedge]

I'm pretty sure z was for 'zero'

[scarlet leaf]

so how did you get x into the two roots?

[lapis hedge]

Factor theorem

[scarlet leaf]

what?

[lapis hedge]

here from wikipedia... : The factor theorem states that a polynomial f(x) has a factor (x-k) if and only if f(k) = 0 (k is a root)

(x-k)(x-k) = (x-(1-2i))(x-(1+2i))

[scarlet leaf]

as I said above, my understand for english mathematical terms are incredibly flawed, I think I'd find it easier if you showed me the steps on how you solved it, or something like that

so you insert the function into k in this case then?

[lapis hedge]

the roots

[scarlet leaf]

so 1-2i is the roots?

1-2i and the conjugate*

is that correct?

[lapis hedge]

right, 1-2i and 1+2i

[scarlet leaf]

So by knowing that, we can refer to the factor theorem which gives: (z-k)(z-k) = (z-(1-2i))(z-(1+2i)) in our case

[lapis hedge]

correct

[scarlet leaf]

and what would be the easiest method of epxanding (z-(1-2i))(z-(1+2i))?

does foil work in this instance?

[lapis hedge]

easiest to group

[scarlet leaf]

like how? find it difficult since they're multiplied

[lapis hedge]

Using associative property,
(x-1+2i)(x-1-2i)
((x-1)^2+2i*-2i)

[still violet]

Hello, I would appreciate if someone can tell me what the "hat" above the Beta exactly means, in terms of AI?

[thorn kindle]

Beta hat is the coefficient vector of the least squares hyperplane

[still violet]

Yes, so in terms of terminology, the hat what does it mean then? Thank you for your response

[thorn kindle]

Hats are typically used to say that this quantity is the estimator

[still violet]

Oh okay, I get it. Thank you! May I ask another thing? This is the formula of the ridge regression. Do you know what I need to change to get the lasso regression formula?

Typical multi linear regression formula

Ridge Regression

And the lasso? 🙄

[foggy acorn]

how do i differentiate with respect to x and with respect to y?

[fickle rain]

There is no closed form solution for lasso

[rigid wind]

#help-2 message

[sand geode]

hi guys.. can anyone please help with this?

why are they making reference to "even integers"?

<@&286206848099549185> any fella available?

[glass lichen]

Cause they're arguing why a isn't surjective

No even number is mapped to by a, so it's not surjective

[glass lichen]

Just apply chain rule

[olive sentinel]

Is there a known algorithm to factorize a polynomial of degree 4 into the products of 2 polynomials of degree 2?

@glass lichen , anyone available

[lone dawn]

Are you able to demonstrate? I’ll send a pic of my attempt and you’ll be mortified

[gray isle]

show how you proved the first line

i guess you could also consider
e^(kx + n) = e^(kx) * e^n

[lone dawn]

I’m aware the mistake I’ve made must be extremely stupid, but I don’t see it

[glass lichen]

The inside function is kx+n, the outside is e^x then evaluated at kx+n

[lone dawn]

U able to show using the wolframalpha stuff please?

[glass lichen]

d/dx e^(kx+n)=(k)e^(kx+n)

[lone dawn]

Yea I know that but I don’t understand why

How do I prove it with the chain rule?

[glass lichen]

What's derivative of the inside?

[lone dawn]

What do you mean when you say inside? I was taught the chain rule by substituting with u and then multiply dy/du with du/dx

[glass lichen]

Yeah... u's the inside function

So u=kx+n here.

[lone dawn]

Ah ok

Ah I see

O I PUT U AS THE POWER not as e^x

Should be able to do it now, thank you.

Thanks

[olive sentinel]

Is there a known algorithm to factorize a polynomial of degree 4 into the products of 2 polynomials of degree 2?

[small bear]

Answered in another channel, ferrari's method is a well-known one

[sharp urchin]

<@&286206848099549185>

[small bear]

Don't ping helpers that early, see #❓how-to-get-help
Anyway, think of a way to write m<FEK in terms of x

[sharp urchin]

is this server only for one type of mathematic

?

[small bear]

No

[alpine sable]

guys i ran into this in my homework is it solvable?

[quartz oxide]

What are you trying to “solve”

You mean “simplify”?

[still violet]

Thanks for your answer! I really appreciate it. Then, if I want to do lasso regression, I need to do it with the Sum of the Squared Errors + lasso formula (lambda * |w|
if I remember correctly) and then the gradient descent?

[fickle rain]

Yes

[still violet]

Understood. Thanks a lot!!

[scenic musk]

Hellpppp badly needed. Thank you

[rigid kiln]

Does this make sense?

(I need to prove f is injective)

Am I allowed to assume that f(x,y) = f(a,b)?

[magic plank]

yeah i would write something like "Assume there exist x,y,a,b \in R, such that..."

[alpine sable]

Hey, I've got a question about game theory, specifically about the Nim game. Consider any position with 3 heaps where only one heap has one token. I would like to get all the loosing positions.

Ping me, whoever has ideas about this

[blazing rose]

Anyone know how I do simpsons rule here

i dont understand how to do it about the y-axis

[sudden dawn]

what's the first and second derivative of (x+2)^2 (2x-1)^3?

[wary stream]

Product and chain rule

[lapis valley]

I need help with b ii) and iii)

my method didn't work

@everyone

[blazing rose]

lmao

[lapis valley]

hey

can u help a girl out

[alpine sable]

-2x - (3y + 5) + 3x ?

[forest sage]

commutative law, expand the bracket by multiplying in -1 to all the terms in it

$-2x -1*(3y+5)+3x$

[ocean seal]

Bagel

[forest sage]

$-2x-3y-5+3x$

[ocean seal]

Bagel

[forest sage]

add the -2x and 3x

$-3y-5+x$

[ocean seal]

Bagel

[alpine sable]

2x^2 = 1/3

[blazing rose]

<@&286206848099549185>

[velvet condor]

given 2022 real numbers $x_1\leqslant 2x_2\leqslant ...\leqslant x_{2022}$ such that $x_1+2x_2+...+2022x_{2022}=0$
prove that for some arbitrary t,
$x_1 \floor{t}+x_2 \floor{2t}+....+x_{2022} \floor{2022t} \geqslant 0$

[ocean seal]

Minh Baka

[half epoch]

Everyone burying poor @blazing rose ‘s question 😛 Do you know simpsons rule?

[wary stream]

I don't recall much about Simpson's rule but I used this resource a lot for calculus
https://tutorial.math.lamar.edu/classes/calcii/approximatingdefintegrals.aspx

[lapis valley]

can someone help me here too

: )

[velvet condor]

me 2....

ill just wait

[half epoch]

Just get a new channel? We have 10 of them you know

[velvet condor]

bruh

[forest patrol]

wait guys how many lines of symmetry does a pyramid with a square base have?

It's 3 yeah?

[half epoch]

Well since josh seems gone, I guess we can do the next one

[velvet condor]

i just realized that he pinged everyone but i think the mods fixed it so that no one will get pinged

bruh

[lapis valley]

it doesnt work lol

[velvet condor]

you should have been banned

if it worked

😉

[lapis valley]

i know it doesn't work thats why i did it

why are u so mean to a girl 😦

[forest patrol]

help

[half epoch]

So what did you find w to be?

[lapis valley]

$cis(\frac{2\pi}{7})$

[ocean seal]

hduxueiwkwnxudi

[lapis valley]

im bad at latex

[lapis valley]

is it this?

[half epoch]

Yep

[lapis valley]

What I tried was connect the two vectors

[copper wedge]

4x2yz3+5x3y2z2

[lapis valley]

so I drew $cis(0)$ and then connected $cis(\frac{2\pi}{7})$ on its tip

[ocean seal]

hduxueiwkwnxudi

[copper wedge]

would adding polynomials do i also add the numbers in front

[lapis valley]

so then I have an isosceles triangle

If I conect the tips

do u get me @half epoch

[copper wedge]

like 4x^2yz^3 + 4x^3yz would equal 8x^75y2z

[blazing rose]

yeah ik the formula but idk how to use it when i have to rotate around y axis

[blazing rose]

thanks. looking now

[velvet condor]

?

[copper wedge]

polynomials

[half epoch]

Yes, but don’t think this will get you an answer really

[velvet condor]

i dont get what you are saying

[lapis valley]

why not

[copper wedge]

do u not know what 4x^2 means

[lapis valley]

it doesnt work like that

?

[half epoch]

I mean you can draw the resultant like that, surely. But I doubt that’s the answer they expect

[lapis valley]

oh

ok

😦

[half epoch]

They want the new argument in terms of pi

[lapis valley]

i got in terms of pi

Should I send a pic

one sec

[wary stream]

Reformat this using parentheses, for readability

[forest patrol]

How many lines of symmetry does a pyramid with a square base have <@&286206848099549185>

and does anyone have a diagram for 3d shapes with their symmetry lines

[lapis valley]

what the fuck

i got the answer

[copper wedge]

(4x^2yz^3) + (2x^yz^2) = ?

[wary stream]

I mean around the exponents too

[copper wedge]

yes but thats how the question is formed

[wary stream]

Like (4x^2)(y)(z^3)

[copper wedge]

yes but in the equation they aren't seperated

[forest patrol]

bro please someone?

[velvet condor]

do you even know what you are writing

i need explaination

because i

do not get it :/

[wary stream]

Because it's text formatted it looks like $4x^{2yz^{3}}$

[ocean seal]

dldh06

[wary stream]

Which is probably not what you meant

[copper wedge]

ohyea no

[wary stream]

So $4x^{2}yz^{3}$?

[ocean seal]

dldh06

[copper wedge]

yea

[wary stream]

Do you have a screenshot of the actual problem?

[indigo storm]

How to make n subject?

[glass lichen]

Logs

[indigo storm]

(xii) question

Can someone help me

[wary stream]

Mosh just answered your question

Use logs

[magic warren]

i have no idea how to find z

[half epoch]

Or you can do something more useful, z are the points that are 2 away from the complex number 2 + 2i

[magic warren]

ok

[blazing rose]

Learath do you mind helping me with the Simpsons rule problem?

[half epoch]

Sure, write out simpsons law and the integral we want to calculate using it

[blazing rose]

this?

this is for revolving around the xaxis which i also need help with since i got it wrong

[crisp grove]

u r doing the integration wrong

u hv the square on f not the entire intefral

[blazing rose]

so im confused

what do i put the power of 2 over

[crisp grove]

over f(xi)

take $G(x) = f(x)^2$ then your problem becomes $\int G(x)$. use simpson's now and see where u did wrong

[ocean seal]

Ryuzaki

[blazing rose]

nvm i got it for the xaxis

but i still dont know what to do for the yaxis

original problem

[crisp grove]

for y u need to consider the point 0-4

& do the appropriate subtraction

[vestal hollow]

Can anyone check my work for the first half (the line integral) and then help me with the second half?

So let's begin with the line integral

z is only defined when $1-x^2-y^2 \geq 0$, so it forms a natural boundary when $1-x^2-y^2 = 0$

[ocean seal]

feather

[full linden]

Anyone here good at stats for data science ?

[vestal hollow]

That is, its boundary is the unit circle

Which we can parameterize as $\vec{r}(t) = <\cos(t), \sin(t)>$

[ocean seal]

feather

[vestal hollow]

Then $F(\vec{r}(t)) = <-\sin(t) + 0, \cos(t) - 0, \cos(t) - \sin(t)>$

[ocean seal]

feather

[vestal hollow]

and $\vec{r}'(t) = <-\sin(t), \cos(t)>$

[ocean seal]

feather

[vestal hollow]

Now since we want the integral over the entire circle, we'll integrate over 0, 2pi

So $\int_{0}^{2\pi} F(\vec{r}(t)) \cdot \vec{r}'(t) dt = \int_{0}^{2\pi} dt = 2\pi$

[ocean seal]

feather

[vestal hollow]

holy fuck what is that awful formatting with the derivative of r(t) ._.

anyways yeah that's my line integral

So now for the surface integral we evaluate the curve

idk how to tex determinants so skip skip but I got <-1, -1, 2> for the curl

Now the problem I'm having is parameterizing z so I can find dS and finally take the dot product

And normally I would use the z = f(x, y) formula with dS = <-f'_x, -f'_y, 1> but here since it's a square root that's gonna be really ugly to integrate

[blazing rose]

what do i subtract from?

[crisp grove]

think

[blazing rose]

y axis?

[crisp grove]

(a to b) = (0 to b) - (0 to a)

[blazing rose]

i dont understand

[gritty geode]

Find the sum by suitable rearrangement. State the properties used. 253 + 352 + 347 + 648 . Is it Umm Associactive property?

[bitter turtle]

@acoustic sable

[raw nexus]

the answer is 0.160 but im not sure how to get the answer

please can somone help me?

[solemn juniper]

What did you choose as your substitution?

[raw nexus]

i dont know where to start tbh

[solemn juniper]

You want to look at your integrand for two pieces, where one looks like the derivative of the other

Take a moment, see if you notice something that looks like that

[raw nexus]

not sure, (4t) and (πt^2)

[solemn juniper]

You're on the right track

What's the derivative of t^2?

[raw nexus]

2t

[solemn juniper]

So if you let u = 2t^2, then du = 4tdt which is part of your integrand

[raw nexus]

okay

[solemn juniper]

Make that substitution, and try to solve from there

[raw nexus]

i have no idea

[solemn juniper]

[raw nexus]

can you guide me through it?

pls

[solemn juniper]

You don't know how to make a direct substitution?

[raw nexus]

i dont know what u mean

[solemn juniper]

Make these substitutions into your integral

[raw nexus]

i dont know how

[solemn juniper]

Then you need to look at your notes for integration by substitution

[raw nexus]

i am at the moment

[solemn juniper]

Because this is the easy part, it's finding the correct substitution that is supposed to be the "hard part"

[raw nexus]

so i have u =2t^2 and du = 4tdt

do i need the inverse of du to get dt?

[solemn juniper]

No

4tdt already exists in your integrand, it's just a straightforward plug in

[oak chasm]

253 is 3 above 250. 347 is 3 below 350, so 253 + 347 = 250 + 350, which is easier to add together.

[raw nexus]

i still dont get it

2t^2-4tdt

[solemn juniper]

$\int_0^{0.48} \sin(\pi t^2) \underbrace{4t \dd t}_{\dd u}$

[ocean seal]

Steakanator

[raw nexus]

okay

channel occupied pls move to another channel

[raw nexus]

what do i do from there

[solemn juniper]

You make the substitutions

Turn your integral into one that is based on u

[raw nexus]

how do i do that

[solemn juniper]

Your notes hold the answer to that question

[raw nexus]

im looking at my notes now

[solemn juniper]

Do they have an example in there?

[raw nexus]

thats the example

[solemn juniper]

Does it make sense?

[raw nexus]

kind of

does it make sense to you?

[solemn juniper]

They set u = -t^2, so every instance of -t^2 in the integrand is replaced with u

Yes

[raw nexus]

okay

im not sure

[solemn juniper]

What are you unsure about?

[raw nexus]

so i need to replace something in this equation with u

[solemn juniper]

Don't overthink it

You have a t^2 in your integrand, and you know exactly how u is related to t^2

[raw nexus]

*2

i have the notes and everything i just dont get it

this is so hard

[solemn juniper]

It's not sin(2pit^2), it's sin(pit^2)

[raw nexus]

this is so fustrating

what do i do