help-0

[ivory gulch]

it was just sin(x) before

[alpine nacelle]

you just replace all x with x+pi/2

it's a substitution

[ivory gulch]

so you're choosing an arbitrary variable

like y

[alpine nacelle]

yeah you can write it y from this step

if you prefer

[ivory gulch]

and making y = x - pi/2

[alpine nacelle]

yes

[ivory gulch]

ok so then plug in y for every x-pi/2

[alpine nacelle]

as x->pi/2+, y -> 0+

and now it's limit at 0

[ivory gulch]

yeah i have no idea what's going on

i never learned what you're doing rn

$\lim _{x\to \frac{\pi }{2}}\left(-sin\left(x\right)\left(\frac{x-\frac{\pi }{2}}{sin\left(x-\frac{\pi }{2}\right)}\right)\right)$

ok i have this

[ocean seal]

ski

[ivory gulch]

now

$y:=:x-\frac{\pi }{2}$

[ocean seal]

ski

[ivory gulch]

$\lim _{x\to \frac{\pi }{2}}\left(-sin\left(x\right)\left(\frac{y}{sin\left(y\right)}\right)\right)$

[ocean seal]

ski

[alpine nacelle]

you have to replace the x under the limit

and in the sin too

to make it all clear

[ivory gulch]

but im not replacing x

#❓how-to-get-help

read rules and delete pls

[ivory gulch]

but i'm not replacing x

im replacing x-pi/2

[alpine nacelle]

if y = x-pi/2, y+pi/2 = x

[ivory gulch]

how

that's the inverse

[alpine nacelle]

it's an addition

you add pi/2

on both side

[ivory gulch]

this is so confusing

but i think i get it

$\lim _{x\to \frac{\pi }{2}}\left(-sin\left(x+\frac{\pi }{2}\right)\right)$

[ocean seal]

ski

[alpine nacelle]

$\lim_{x \to pi/2^+} -sin(x)\frac{x-pi/2}{sin(x-pi/2)} = \lim_{y \to 0^+} -sin(y+pi/2)*\frac{y}{sin(y)}$

[ocean seal]

Mélo

[ivory gulch]

ok

so now i sub my x value back in

[alpine nacelle]

now you do the sub I just posted

and you calc it

as y goes to 0, y/sin(y) goes to 1

it's a 1

[ivory gulch]

$\lim _{x\to \frac{\pi }{2}}\left(sin\left(\left(x-\frac{\pi }{x}\right)+\frac{\pi }{x}\right)\right)$

[alpine nacelle]

-sin(y+pi/2) goes to -1

I don't understand what you're doing

[ivory gulch]

wdym

[ocean seal]

ski

[ivory gulch]

had a mistake

there

[alpine nacelle]

I don't mean anything, I litterally don't understand

[ivory gulch]

ok

so

[alpine nacelle]

you just have to erase the x-pi/2 and put a y, erase x and put y+pi/2

and tada

[ivory gulch]

idk how the limit switched

[eternal cedar]

(when you are done) how would i do this

[alpine nacelle]

if y = x-pi/2

when x goes to pi/2

y goes to 0

[ivory gulch]

$\lim _{x\to \frac{\pi }{2}}\left(-sin\left(y+\frac{\pi }{2}\right)\right)$

this is right, right?

[ocean seal]

ski

[alpine nacelle]

you have to replace the x, still

[ivory gulch]

i did

i replaced the x with y

[alpine nacelle]

under the limit

y->0

[ivory gulch]

yeah see that part i dont get at all

like i know what you're saying but i dont understand why

[alpine nacelle]

x = y + pi/2

when x -> pi/2

y -> 0

[ivory gulch]

yes i hear that

but idk how

like how do you know that

[alpine nacelle]

because this is an equality

it's our substitution

we're looking at a limit when x-> pi/2

so at a limit when y -> 0

[ivory gulch]

ok i dont want to waste your time

i just do not understand

not your fault

but lets just continue

[alpine nacelle]

I'm sorry but I really don't know how to explain it differently

[ivory gulch]

no its not your fault

i've been doing hw for like 5 hrs now so i am probably just fried

ok so whats the final part look like before you plug in pi/2

[alpine nacelle]

you don't plug pi/2, you plug 0, since now you have y -> 0

y/sin(y) is 1 as y->0

so you get -sin(pi/2) = -1

[ivory gulch]

ok thanks

that's as close as im going to get to understanding

thanks for being patient and trying

[alpine nacelle]

you should take a real break without thinking of math, and read again later

[ivory gulch]

test is in 1 hour

[alpine nacelle]

like tomorrow

[ivory gulch]

yeah i will

[alpine nacelle]

good luck for your test

[ivory gulch]

thank you

[alpine nacelle]

Joey

[velvet condor]

bruh

[alpine nacelle]

cos(2x) = 2cos²(x)-1

[velvet condor]

cos(2x)=cos²x-sin²x=2cos²x-1

in this case cos(θ)=cos(2×θ/2)....

this is supposed 2b θ btw

[velvet condor]

np but next time plz dont ping me

[daring creek]

Hey sorry, but I literally just posted a question lol

[near cove]

Anyone know the answer

[feral crypt]

Could someone help me with this problem?

[red carbon]

I think 88.25

[near cove]

How do you know?

Oh thanks

[feral crypt]

<@&286206848099549185>

[near cove]

Anyone know this?

[velvet condor]

$\frac{d}{dx}(x)=\frac{dx}{dx}=1$

[ocean seal]

Minh Baka

[velvet condor]

easy

:)))

[ivory zodiac]

if it's some online textbook questions thing try copy pasting the question onto google and someone somewhere usually always asks abt it and u'll find a detailed explanation

doesn't wotk 100% of the time tho

[thick flame]

Who you talkin' to?

[near cove]

Me maybe?

[thorny panther]

lets say given sinx = 3/5, 0<x<180deg
in this case cosx can either be positive or negative right? Or am I completely off?

[abstract junco]

i am so confused

[velvet condor]

yes

[thorny panther]

Yes to I’m right or I’m wrong? 😂

[velvet condor]

right

ASTC

[alpine sable]

do you know how to find the inverse of a function?

[velvet condor]

let f(x)=y and then express x in terms of y

do it

[abstract junco]

Alright

[abstract junco]

no

[velvet condor]

just do what i say

[alpine sable]

Ok, here's how: replace all x's with y's. and f(x) with x. and solve for y. 🙂

[near cove]

Please I just want a quick answer so I can get a ✅

[velvet condor]

bro u r confusing me too

[abstract junco]

replace all of them??

[alpine sable]

Ok, so replace all x's with y's means, if "x" is in the equation, put "y" down instead

and replace f(x) with x means if you see "f(x)", put down "x" instead.

then algebraically solve for y

[velvet condor]

which is the same as express x in terms of y

your wording is horrible

[alpine sable]

id appreciate some assistance

Okay. Seems straightforward to me.

[alpine nacelle]

2600

[near cove]

That’s the answer?

[alpine nacelle]

yeah

[near cove]

It’s wrong

[alpine nacelle]

yes, I gave a random number because you're not supposed to have someone else do it for you

it's still an answer tho, you should be happy

I answered

am I not really kind ?

[near cove]

Good thing I called your bluff and didn’t put it in 2600 doesn’t make sense

[alpine sable]

There's probably a certain range of acceptable answers, Dallying. Do you know the formula for the mean of a set of numbers?

[near cove]

Nope

[alpine sable]

Ok, the answer is that you sum up all the numbers, and then divide by how many numbers there are. In the problem, it's given that there are 500 houses, so you already have the denominator figured out

[near cove]

So I add everything and divide by 500?

[alpine sable]

Yes, but each house is given as a range, so your software probably allows a range of possible answers

[velvet condor]

have you figured it out?

[alpine nacelle]

the convention is usually to take the midpoint of the range

as the value

[near cove]

Nah I’m confused

[alpine sable]

so since it doesn't give the exact number of square footage for each range, your best estimate is the midpoint

[abstract junco]

watching a video on it right now

https://www.youtube.com/watch?v=j3f88V9M0qM

[abstract junco]

i got it now

[near cove]

Anyone know the answer

[alpine sable]

did you get the previous question right? this looks like the exact same strategy

[jaunty phoenix]

Help

Dis confusing

[alpine sable]

Help please. If someone does 990 hours in a school year but every quarter they do 247.5 hours, how many minutes of instruction per week were done for 1 class. Please help

[alpine sable]

This is a cool question. How would you define 'universal set' to me?

[jaunty phoenix]

I got the answer doe

[alpine sable]

Ambiguous. Are we assuming they're only taking one class? Or are we writing the expression in terms of how many classes they're taking, given that they take equal time? ...

Do you have the original question?

[jaunty phoenix]

its {z | z E multiples of 30}

[alpine sable]

Nice.

whats the problem called when theres like

fractions stacked on top

and you have to keep simplifying till the end

[glass lichen]

Nested fractions

[alpine sable]

right

can you teach me how to solve em

[forest flame]

hey

help me

[alpine sable]

math quiz tmrw

[forest flame]

math

[alpine sable]

its about compound fractions

what

[alpine sable]

do u need help with

[forest flame]

math

[alpine sable]

what math

[jaunty phoenix]

What topic in math?

[glass lichen]

wow, that's so specific and so helpful

[tacit breach]

how 2 do!

gosh this is so hard

[alpine sable]

nested fractions

[glass lichen]

what have you tried @tacit breach ?

[alpine sable]

Oh, nested fractions. Fun!

[tacit breach]

i have tried diving by f(x)

[alpine sable]

more like irritating

[glass lichen]

"diving by f(x)"

[alpine sable]

lol

bruh im focusing on algebra and i have a 54 in ela and i failed a project

[forest flame]

The 21st term of the numbers 5,9,13,17,... is...

[alpine sable]

I promise you this is easier than you think! Simply evaluate the function by replacing all instances of "x" on the right hand side with -3

cause i plaigirised one thing

[forest flame]

The 21st term of the numbers 5,9,13,17,... is...

[alpine sable]

out of 27 things

:(

[glass lichen]

in use.

[alpine sable]

https://tenor.com/view/omni-man-gif-22210485

[forest flame]

can you help me plz

[glass lichen]

no

[alpine sable]

lol

[glass lichen]

I dont help people that feel the need to ping me for no reason

[forest flame]

😢

[alpine sable]

What do you think?

[glass lichen]

• the channel is now in use by web since you opted to waste time and ask to ask first

[forest flame]

87 maybe idk

[alpine sable]

We're assuming this is an arithmetic sequence by the way. It could be 5,9,13,17,0,0,0,0,0,0,... 🙂

[tacit breach]

guys i got -infinity

what happened

[glass lichen]

then you fucked up

[alpine sable]

Can anyone please help me with exponents and powers

[glass lichen]

how did you get -inf

[glass lichen]

in use clearly

[tacit breach]

i got 15

[alpine sable]

Uhh let's say I have a fractional power how do I do it

[forest flame]

The 21st term of the numbers 5,9,13,17,... is...

[tacit breach]

this is too easy bruh

[glass lichen]

IN USE

[alpine sable]

Based on what reasoning?

[forest flame]

arimatika

[alpine sable]

https://tenor.com/view/suicidio-payaso-suicide-clow-gif-14176065

[tacit breach]

its alright mosh i solved it

[glass lichen]

I highly doubt you went from "this is so hard" to "this is too easy" by doing 1 problem, especially when you said -inf as an answer

[alpine sable]

Here's how I would approach it. Write an explicit formula for the nth term, then substitute n=21. Do you know how to do that?

[forest flame]

arithmetic

that

[alpine sable]

what is "d" in this case?

[near cove]

I did not @alpine sable

[forest flame]

okay

i have a new

The 16th term of the sequence 11,8,5,2 is?
(arithmetic)

[alpine sable]

Use that same formula. What is d?

[tacit breach]

d is common difference

[glass lichen]

clearly wasnt addressed to you

[tacit breach]

1, 3, 5

d = 2

[glass lichen]

so dont give answers, it doesnt help

[alpine sable]

You did not what?

[near cove]

I didn’t get it right

But idc I have someone doing it for me so I’m chilling

[alpine sable]

Prove that if a transversal intersects 2 parallel lines then each pair of the alternate interior angle is equal | how do I do so

[near cove]

@alpine sable

[forest flame]

hey

The 16th term of the sequence 11,8,5,2 is?
(arithmetic)

[alpine sable]

Okay Dallying. I don't mind if you chill lol

[alpine sable]

how do i solve nested fractions :(

[near cove]

Thanks Blake

[alpine sable]

Try working out a specific problem, then let us know of an issue that comes up!

random problem from interne

t

is this a nested fraction

idk

can u find me a problem

You aren't showing the entire question, by the way.

[jaunty phoenix]

https://tenor.com/view/dies-cringe-math-dies-from-math-death-gif-22822700

[alpine sable]

ok.

[modest sky]

hii

i have a test tomorrow and to prepare i made up a random function but I’m confused on how I would do the domain and range with interval notation

this is the function

and this is a picture from desmos. Can somebody help me? Thank you <333

[hybrid plume]

At x=-4 the denominator will equal 0 so it’s undefined

[modest sky]

how would i come up with the domain and range for it? I did mapping and got the points for it

[alpine sable]

This is my own question in my situation. I take 6 classes and each class is 45 minutes long. There’s 47 days in the first quarter. I need to know how many minutes of instruction are in 1 week for 1 class

[modest sky]

all im confused on is how i would format it in interval notation

[alpine sable]

And we assume you attend class five days a week or not?

[modest sky]

I came up with something, but I feel like if I were to write it on a test I would lose marks for bad communication

[alpine sable]

Because in that case, everything else is extraneous except the 6 and 45 numbers

[hybrid plume]

Just write it like this

[alpine sable]

Yes I do

[modest sky]

ty !! if you don’t mind me asking, what application is that?

[alpine sable]

Okay, so then you take 6 classes, that are each 45 minutes long, 5 days a week. So all you have to do is multiply them together:

6 * 45 * 5 = 1,350 minutes of class peer week

[hybrid plume]

Oh that’s just a picture from a website, an example

[alpine sable]

Thank you so so much I needed help on it for so long have a great week

[hybrid plume]

But every time it’s the same. In that picture for the domain you go from the left most point -infinity to the right most point before the gap, 0. Then there’s a gap, you continue from 0 to the right most point, infinity. You add that “u” shaped thing which has a name > “union” in between your “gap”.

[alpine sable]

how to solve nested fraction

or compound

fraction

[modest sky]

that makes sense!! Thank you!

[alpine sable]

(84)½

How do I do this

Sorry if it sounds too simple lol

[alpine sable]

calculator

mathway.com

lol

lmao

lool

Huh

[alpine sable]

"do this" -- what are you wanting to do?

u can just search it up

on mathway.com

(84)^ 1/2

so easy

Lemme

[modest sky]

rude much

[hybrid plume]

@modest sky Edited it a bit to make more sense. Np

[alpine sable]

stfu

[modest sky]

no I

OMG MY AUTOCORRECT

UGH

@hybrid plume would this apply to the function that I made?

[alpine sable]

that is so easy

cringe

[modest sky]

okay roblox boy

jk roblox is fun

[alpine sable]

i dont play roblox

[modest sky]

omg

I used to play

[tardy plank]

where does 2/root(6) and 2/root(4) come from?

[alpine sable]

https://tenor.com/view/finobe-old-roblox-roblox-roblox2012-death-gif-22474654

this is the roblox i played

[modest sky]

yess

ok can u check my work bc it’s so “easy”

😭🤩

[alpine sable]

no

[modest sky]

say yes

[rigid wind]

i'm guessing f'(t) was given or calculated above

[hybrid plume]

@modest sky Range you made a mistake. You need to go from the bottom up to to the top. So it’d be (-infinity, -3] U [-3, infinity)

[modest sky]

thanks !! that’s all I needed. good night !

[hybrid plume]

I’m pretty sure it’s “proper” to go from bottom to top, but u might not get marks taken off for doing what u did. Better safe than sorry tho and np

[modest sky]

okay!

[tardy plank]

@rigid wind calculated below

[rigid wind]

ur screenshot cuts out a lot of context

[alpine sable]

Hey I have a question! Is 1350 the minutes of instruction per week for 1 class? Because I need the minutes for 1 class only

No, for all. I would think about this conceptually. If you're finding it for one class and you're going 45 minutes each day, it's

45 + 45 + 45 + 45 + 45 , or 45*5

but if we're doing for all six classes this becomes messier, but it's good to see it expanded out, as multiplication is just repeated addition

Alright so 225! Thank you so much for the help

(45 + 45 + 45 + 45 + 45) + (45 + 45 + 45 + 45 + 45) + (45 + 45 + 45 + 45 + 45) + (45 + 45 + 45 + 45 + 45) + (45 + 45 + 45 + 45 + 45) = time for all classes in a week, or 45 * 5 * 6

Could you figure out how if it’d equal 247.5 hours at the end of the quarter altogether or no?

[wary stream]

45 * 30 is right too

[alpine sable]

Are we assuming that each quarter is 52/4 = 13 weeks?

[tardy plank]

@rigid windt

[alpine sable]

First quarter starts at September 9 and ends at November 12

Some quarters continue longer than others

hmm, this is not fun but it will take a little work to find the total number of weekdays in that period

if we're assuming it's 2021, then Sep 9 is a Thursday, and November 12 is a Friday. But there are also no breaks in this quarter?

[vestal hawk]

hey guys how would u integrate something like 1/(5-2.5x)

[alpine sable]

Do you know how to find the integral of 1/(x-a) where a is a constant?

[vestal hawk]

hm

i know that its ln(x-a)

[alpine sable]

Okay, so all that's left is algebraically manipulating your expression

or actually u-sub

[vestal hawk]

whats u sub

[alpine sable]

I’m homeschooled I have no breaks except weekends

[alpine sable]

Actually just use this. u-sub is something you will learn later

[hearty jay]

pls can someone help me with this

[alpine sable]

Looks like 47 days (45 days + Columbus Day + Veterans Day). so 47 * 45 * 6 / 60 to get the hours

[alpine sable]

Yes. make sure the functions are equal at the end points of the intervals. so you'll need to compare the first part of the piecewise to the second at x=0, and the second and third part at x=1. it will end up making a system in terms of a and b, which then you will solve

[leaden sundial]

Is the conditional statement ¬(p → q) → p a tautology?

[alpine sable]

Do you know how to figure out if something is a tautology using truth tables?

[oak chasm]

@leaden sundial Turn the outer → into ∨.

[worldly lava]

hm

[oak chasm]

(p → q) ∨ p

Now, if p is true, then the right side of the ∨ is true, so the entire expression is true.

If p is false, then the left side of the ∨ is true, so the entire expression is true.

[vestal hawk]

guys how do i find particular solution for y'+4y=0, y(0) = 2 ?

so far i got y+2y^2 + c = 0

[alpine sable]

assuming that's correct, use the initial condition

[vestal hawk]

how do i use it in this case these 2 y's got me confused

[placid zinc]

y' means dy/dx
It looks like you've integrated in terms of y

[alpine sable]

that's not correct btw

[placid zinc]

When you want to integrate in terms of x

[alpine sable]

first, separate the equation and integrate both sides. you've made an error for your general solution. it's in terms of e

[forest flame]

hey you bitch ass

[vestal hawk]

so

dy = -4y dt

[alpine sable]

yes, but make sure that all y's are on the same side

so dy/y = -4 dt

[vestal hawk]

yup

got it thx

i forgot about the rule of y to one side

[wintry oyster]

hey guys, im doing some starter stats work and for some reason the books answers are always off by like either the last digit or the last 2 digits can anyone explain to me what im doing wrong to get such a weird output?

This is what my book says is the correct answers

i am using the normalcdf func on my calculator for this problem as well

[alpine sable]

I'm getting your number

0.9568

[wintry oyster]

right!?

[alpine sable]

bad error on their part, I guess

[wintry oyster]

hmm maybe the book is wrong... just never seen it

thanks for confirming im doing it right was getting frustrated

[pallid folio]

hello guys pls help me with dis question

[reef pebble]

need someone to answer my whole math test

one page

[wintry oyster]

ion think thats how this discord works pal

[tardy plank]

where do you find textbook answers to even numbered question

s

[wintry oyster]

i dont think you can unless that book is really popular most books will only give you only 1 set of answers for either even or odd to stop you from just getting every answer

[elder crag]

hi, can someone help me?

[wintry oyster]

just ask, dont ask if you can ask.

[elder crag]

i am lost

its due in an hour and im just trying not to fail the class

40 minutes

[reef pebble]

fuh

[elder crag]

ikr

i come back to this discord after a whole entire year and theres no trustworthy friendly nerd to help me with my troubles

[wintry oyster]

you intersection is empty so 0

sorry

[pseudo orbit]

Hi

I wanted to know if someone could guide me on this problem?

[harsh silo]

anyone know how to change this to a transformed function?

[wintry oyster]

wait like 15 mins and @ the helpers im sure if they are able to they will help

[harsh silo]

like y = a(square root) [k(x+d)] + c

[pseudo orbit]

It says write an algebraic equation I wrote the equation but how will I solve it

[elder glacier]

@pseudo orbit whats the equation

[pseudo orbit]

200L + 6m = 500L - 6m

[elder glacier]

you can't solve that

im assuming

[pseudo orbit]

Yes...

😭

[elder glacier]

are both L and m variables

[pseudo orbit]

Oops l is for liters

Don't mind the L

Mb

M is variable

[elder glacier]

yea so its 12m = 300

m= 25

why is u wrong?

[pseudo orbit]

@elder glacier

[elder glacier]

yes?

[drowsy remnant]

does anyone know how to solve this?

[crude nest]

help me

[wintry oyster]

https://tenor.com/view/memes-meme-lois-falling-down-stairs-falling-down-stairs-gif-16921703

[crude nest]

[fickle dock]

<@&268886789983436800> spam preventing people who need help from getting help

[elder glacier]

<@&286206848099549185>

why is my u wrong?

[tame falcon]

Don't step over other questions. Read #❓how-to-get-help . Also, is this is a legitimate question?

[crude nest]

sorry

[crude nest]

also yes

go to #help-3

[rigid wind]

can you post the whole thing?

[tame falcon]

How did you find this u?

[elder glacier]

@tame falcon y intercept

[elder bloom]

can anyone help

<@&286206848099549185>

[alpine sable]

Have you tested the base case?

[craggy fossil]

1+1

[inner sentinel]

when i do this one i keep getting a different answer

[alpine sable]

first option

wait

not sure actually

[signal bone]

hi i have question about finding distance of moment arm.

from axis of point to B = 0.5m and N=100N, how do you get .433m for moment arm?

[alpine sable]

ratio of the sides is constant as you go from left to right

so 0.173 / 0.2 = x / 0.5

x = 0.4325

[signal bone]

i'm sorry but .173 and .433 was not given

[alpine sable]

how about theta?

[signal bone]

not given

[alpine sable]

what is given

[signal bone]

only .2m and .5m and 50 N , 100N

[alpine sable]

I think there has to be more info to know that

[signal bone]

oh actually sry, i found out that the angle is 30 for both

so i guess i can use cos to figure it out?

[alpine sable]

Yes

[signal bone]

thank you

[alpine sable]

yw

No problem

[quiet crown]

i = sqrt(a/p) * 100 - 1

something like that

[fresh wigeon]

is the normal line just the tangent line but m is the negative reciprocal?

[vale wigeon]

you could say that.

[gentle reef]

does anyone know how to do this question

[fresh wigeon]

damn bruh this is like what im learning rn

find the derrivative of it when its all on one side then consolodate dydx then thats your derrivative then your derrivative is m and then you have the other points

so you are just solving for dydx in that i think

@gentle reef

[gentle reef]

i did that but im getting the wrong answer

https://media.discordapp.net/attachments/486841085210132490/890831595672576000/PXL_20210924_052634223.jpg?width=507&height=676

[toxic zephyr]

your first step is incorrect?

you cant just square everything out

[gentle reef]

im not allowed to square everything?

[fresh wigeon]

yeah

[toxic zephyr]

im pre sure thats wrong

[gentle reef]

dambbbb fr

[fresh wigeon]

you need to find the derrivative of it using one half

first step is wrong

[toxic zephyr]

its implicit diff

[fresh wigeon]

and then when you find the derrivative of it all go one function at a time

[solemn juniper]

Freshman's dream

Sadge

[toxic zephyr]

but you have to do it with the square roots

[fresh wigeon]

aye im a junior and im learning all of that rn

shits hard

[gentle reef]

damb can one of u help me real quick then, this the last thing i was stuck on and its due in 10 mins lol

[fresh wigeon]

its 11 and i got a quiz tmrw on chain rule, trig fxns, and tangentnormal line

I can try solving it

[gentle reef]

thanks bro

im trying as well but im probably going to screw it up

[fresh wigeon]

its chain rule and product rule im pretty sure

[gentle reef]

did u get an answer

[fresh wigeon]

still solving

is 3ydydx+3ydydx

what is that

what is 3ydydx+3ydydx

@gentle reef

[fresh wigeon]

what is this

nvm

[humble yoke]

I calculated ACS but what now

[tardy plank]

if f(x,y) is undefined than the domain doesn't exist there right

like for certain values of x, and y

is it the same rule for f(x) ?

[split oriole]

Domain are the points where function is defined.

[tardy plank]

ok so for an f(x,y) function where the domain is zero it would be undefined there just like an f(x) function right

like f(x,y) = 1/x+y would be undefined at x = 0 and y = 0?

this is multivar stuff

[split oriole]

No it will be undefined when x=0 and y=0

Basically what is your question?

[alpine sable]

bring 1/x terms and constants to opp sides

so 2/x > -4

bring 4 to lhs

(2+4x)/x > 0

so either 2+4x and x both > 0 or < 0

[alpine sable]

6y dy/dx

[fresh wigeon]

yeah i figured that out

i was just being stupid

[alpine sable]

Oh ok sorry

XD

[fresh wigeon]

all g

[alpine sable]

anyone know why in implicit differentiation,
differentiating x gives 1, as usual, but differentiating y gives dy/dx

like I know it does that but why

[fresh wigeon]

because you want to find the derrivative which is yprime but since y is inside of the equasion for example you have to like simplify for dydx

something like that

[tough coral]

sdll

well

think of it as this

[alpine sable]

so basically d/dx * y = dy / dx

[tough coral]

the derivative of y = 2x

y' = 2

not y' = 2x'

its the same in implicit differentiation

[alpine sable]

elaborate ?

phh

oh

I see

thanks

[tough coral]

ye

as to why

honestly idrk

but that's just how it is

[alpine sable]

I think its because
y = x²
d/dx(y) = d/dx(x²)
dy/dx = dx²/dx
dy/dx = 2x

as dx²/dx means differentiate x² in respect to x

@tough coral

or atleast its a way to remember it idk

[placid zinc]

So when you do implicit differentiation, you are differentiating both sides in terms of x

Note that the derivative of y, in terms of x, is dy/dx by definition.

[alpine sable]

Yes

[placid zinc]

That's a handy way to think of it

Except not *

[alpine sable]

but it only works that way when y is on its own

if we have y² then we gotta use product rule to think about it that way

[placid zinc]

It's more like a function application. d/dx acting on y

[alpine sable]

Yea

[placid zinc]

For any function of y, you can always
-Take the derivative of it, as if it were x
-Multiply it by dy/dx

The derivative of y² is 2y dy/dx

[alpine sable]

Yes

because y² = y × y so we use product rule and get 2y dy/dx

as ydy/dx + ydy/dx = 2y dy/dx

[placid zinc]

That's true too, but I'm talking much more general.
The derivative of sin(y) is cos(y) dy/dx

[alpine sable]

Yea

I get u

[placid zinc]

Okay lol I'm a step behind. You've mastered this already

[alpine sable]

sometimes I just like to see the proof of stuff before I use it so I can understand why I use it

[reef pebble]

oh sorry, my mistake if this channel is busy

[placid zinc]

I think we're just wrapping up

[alpine sable]

ur good

its free

[reef pebble]

ok so

ho am i supposed to turn that into venn diagram

I literally didn't understand it

[placid zinc]

Everything in the left circle (including the middle) adds to 45

Everything in the right circle (including the middle) adds to 32

There's 12 in the middle

How many are in the left circle, but not in the middle?

[reef pebble]

?

45

[reef pebble]

hmm, so (45)(12)(32)?

hello?

[modest yew]

Hey

I think I can help here too

The first question on there asks how many people only like math

Why did you put 20?

[reef pebble]

Wild guess

[modest yew]

Alright no worries

[reef pebble]

😭

[modest yew]

Oh no actually

You are right I read the question wrong

It should be 20

You subtracted 12 from 32 to get 20 right?

That's my bad

Yeah good job on the first two

Here I'm gonna try to draw a diagram real fast

[reef pebble]

thanks

[modest yew]

Right so this is what we have so far right?

The 75 at the bottom is total number of students

[reef pebble]

huh

yes

75

[modest yew]

But the problem is that when you add the left and right circles (kids that only like math and kids that only like English, you get something less than 75

So you found number od kids that only like math and only like English right?

In questions 1 and 2

So add them

What number is that?

[reef pebble]

I didnt get this

[reef pebble]

add 45 + 32?

[modest yew]

No, I'm saying to add 20 and 32

But... I think I may be wrong? Or the question is screwed up? Because 20 and 32=52

[reef pebble]

where do i get 20?

[modest yew]

From there I would subtract 52 from 75

[reef pebble]

where did you get 52?

@modest yew

;-;

I should quit osu

[modest yew]

I'm still here, just seeing if mélo can provide insight lol

[reef pebble]

and start learning math

[modest yew]

I'm def not doing this right either

Ah I feel

I'm also struggling with math, tho it's a different type

[reef pebble]

ok

@modest yew ||what you know about rolling down in the deep||

[modest yew]

@reef pebble || iknow that when your brain goes numb you can call that astro freeze||

[alpine nacelle]

Let A the set of people who like English, B math
You have the number of elements of A, B, and A inter B
Q11 asked for card B\A = card B - card A inter B = 32-12 = 20
Q12 asked for card A\B = card A - card A inter B
Q13 asked for card E\ (A union B) = card E - card A union B = card E - (card A + card B - card A inter B)

Be careful of the answer you picked for Q12

[reef pebble]

hm

[somber osprey]

glhi

[reef pebble]

lemme process this

[tough coral]

STATS SUCKS

stats is the worst

[reef pebble]

what card means

[alpine nacelle]

cardinality

the number of elements in a set

card A = number of elements of A

[reef pebble]

what does \ mean?

[alpine nacelle]

A\B are the elements of A which are not in B

[reef pebble]

hm

[reef pebble]

can i ask for the formula instead

[alpine nacelle]

$A \setminus B = A \cap B^c$

[vale wigeon]

\setminus

[ocean seal]

Mélo

[alpine nacelle]

thanks

[reef pebble]

ahhh

[reef pebble]

E?

[alpine nacelle]

your set as a whole, the 75 students

[reef pebble]

ok

[reef pebble]

am i allowed to ask for answers?

sorry if I'm annoying

[alpine nacelle]

It would be better if you give it a try and post some answer in case you're right

[reef pebble]

:((

[alpine nacelle]

I mean I've written the formulas, if you need the answer so much you can just use them even if you don't see the steps you know

I just told you card E = 75 so it's just additions and subtractions

[alpine sable]

melo

could u help me with a surds question

[reef pebble]

ok

[alpine nacelle]

post it in some free channel xae, and wait for help, like everyone else

[alpine sable]

kk

[reef pebble]

by inter you mean Subtract?

[alpine nacelle]

the intersection of sets A and B is A inter B: $A \cap B$

[ocean seal]

Mélo

[torn cedar]

Hello I needed some help on this problem

its related to a subject i have in engineering called "Linear Systems"

i believe this should be an unoccupied channel

[stoic epoch]

hi i need some help in class

[alpine sable]

can anyone give me a set with 15 proper subsets

[alpine nacelle]

any set with 4 elements

[torn cedar]

hello

it says this channel is unoccupied

can i type my question?

[alpine nacelle]

yes

[torn cedar]

Here

:3

[alpine nacelle]

U is rank 2 (at most), so you can see it as a morphism which removes one dim from your space, any element in his kernel maps to 0

[torn cedar]

could you elaborate a bit i couldnt understand

[alpine nacelle]

Because the last row of U is full 0, the last coordinate of Ux is necessarily 0

[torn cedar]

got it

[alpine nacelle]

You map to a subspace of dim 2 (at most)

[torn cedar]

so 3x2 matrix? how do i find the x such that is gives me null

should i consider 0 as 3x3 with all elements 0?

[alpine nacelle]

x = (m, n, p)^T
Ux = (am+bn+cp, dn+ep, 0)

3 unknown, two equations, so an infinity of possible sol for x

[torn cedar]

yea

[alpine nacelle]

the solutions are a subspace of dim > 0

[torn cedar]

thats the problem :/

is it fine if i write the solution as such?

cause i was thinking of a more specific answer

[alpine nacelle]

you need to find a specific x for (A)

[torn cedar]

yea, been a while i worked on matrices

god damn it 😐 thanks for your help tho

ill try to work on this

[alpine nacelle]

I mean, you have dn+ep = 0, so it should be kinda quick to find such a x

[torn cedar]

i need to brush up

on concepts

its just been a while

how did you assume x to be 3x1

[alpine nacelle]

isn't x a vector ?

[torn cedar]

they didnt mention

am i allowed to assume that?

[alpine nacelle]

I mean, you can take x=(x1, x2, x3, x4) but Ux will be 3x1 anyway

[torn cedar]

actually

your right

fuck

[undone isle]

👍

[alpine nacelle]

actually you can't but you understood what I meant

[torn cedar]

yea

i did

thanks

[alpine sable]

wait so

1 2 3 4
12 13 14
23 24
34
1234

[alpine nacelle]

the full set is not a proper subset (of itself)

the empty set will be, in a non empty set

[alpine sable]

can i ask what part the proper set is

example p'4=32

like that

[alpine nacelle]

a proper subset is a subset which is not the full set

[alpine sable]

wha?

but

i dont get it now

my teacher told us a proper subset is

a

i cant explain it but its like equal set i think

same elements

[alpine nacelle]

The only set equal to the full set would be the full set, you would always have only 1 proper subset

I doubt your teacher would say something so absurd without thinking for 3 sec

[alpine sable]

idgit

were reviewing this subject next week i should be fine

and she might be more specific next week

can anyone help me with number 5?i just need to know how to do it then I'll do the rest :<

what grade is that its familiar

grade 11

thought it was ours last year

💀

[brisk flume]

does anyone know this?? pls help

[tawdry sphinx]

You know the formulas right?

[unique ingot]

Where did this 1 come from?

[stray estuary]

put parentheses between the 1 and x^3

it should be factored as

$(x^3+1)(x^3+8)=0$

[unique ingot]

Did I copy the answer wrong

[ocean seal]

blanket

[unique ingot]

It looked kinda confusing

[stray estuary]

whoever wrote that up wrote it incorrectly

[unique ingot]

I see, thanks!

[stray estuary]

the solutions are fine but the display of it is not right

ye no worries

[alpine sable]

i'm not sure how to find instantaneous Velocity , i'm in 9th grade so no need to bring any calculus in this

[stray estuary]

the only methods i know of are using the definition of a derivative (limits) or estimating the instantaneous velocity via points

[alpine sable]

what does ⇒ mean

[stray estuary]

implies!

[alpine sable]

[alpine sable]

well , go ahead and show me how to estimate the instantaneous velocity via points

[stray estuary]

so p ⇒ q would be read as "if p then q"

@alpine sable

[alpine sable]

ah

[stray estuary]

well if we were testing say the instantaneous velocity at x=1 for x^2, then we could test

$$\frac{(1.00001)^2-1^2}{1.00001-1}=2.00001$$

where we have x=1.00001 as a super close number to 1

[ocean seal]

blanket

[alpine sable]

sure but how do we get the at x=1 for x^2

[stray estuary]

well that's deciding what point you want to find your instantaneous velocity at

i just so happen to ask for an estimate for the instantaneous velocity of x^2 at x=1

[alpine sable]

hm

[stray estuary]

yes

that's why i chose 1.00001 because it's close to 1

to more rigorously show that the instantaneous velocity at x=1 is 2, then i would have to use limits

and im not sure if you know what limits are

[alpine sable]

i dont think so

[jade birch]

How did you find instantaneous velocity in class?

[alpine sable]

the teacher didnt show us how , he posted some powerpoints stuff to revise from

[jade birch]

pathetic

Anyway, do you know now?

[alpine sable]

no not really

[jade birch]

Hmm...

[stray estuary]

yeah i find it insanely weird that your teacher would show instantaneous velocity without teaching at least a little bit of calculus or discussing limits

because... it doesn't make sense to learn about instantaneous stuff where you're discussing infinitesimal quantities without knowing at least limits

[jade birch]

I'm not sure what I can say that blanket hasn't already explained above

You know what a slope is right? @alpine sable

[alpine sable]

yeah the rise over run ?

i just studied it

[jade birch]

Yep

So you usually calculate the slope by being given two points

[alpine sable]

not studied it , just watched some videos about it and got it down

[jade birch]

point A and point B

[alpine sable]

here is what i've done os far

[jade birch]

And it's super easy to find the slope then

[alpine sable]

hm

[jade birch]

right?

[alpine sable]

so instantaneous velocity would equal the slope of a certain point ?

[jade birch]

Exactly

But you cant technically calculate the slope using only one point r

[alpine sable]

so i pick a point , draw a tangent line and find its slope

[jade birch]

So we need a second point

[alpine sable]

yeah

[jade birch]

Now we can choose that point to be super close to the point A that we want to find the instantaneous velocity at

using blankets example

Point A(1, 1)
Point super close to A(1.00001, 1.00001)

Now when you find the slope of these two points

You can say, without a problem, that the slope you found is the instantaneous velocity at A

[alpine sable]

it would be A over point super close to A which would equal around 1 over 1 which is 1

[jade birch]

It's be this

Rise over run

[alpine sable]

thats it ?

[jade birch]

Yeah

You found the slope at point A

And that slope is the instantaneous velocity

[alpine sable]

fair enough

lets say i got the instantaneous velocity , how would i write it ? 1 speed unit ig /time unit/direction ?

[jade birch]

Velocity is distance over time

so if distance is in meters and time in seconds

m/s

[jade birch]

what?

[alpine sable]

oh its like what you said , but i couldnt explain it well

[jade birch]

Right

[alpine sable]

oh thanks really much

mind if i ask about the instantaneous acceleration

[jade birch]

Np

Sure

It is the slope of velocity-time graph right?

[alpine sable]

isnt it displacement-time ?

why is -2 correct but 2 wrong?? how is pic2 different from pic2.

[jade birch]

Uhhhh let me google it, i dont remember physics

[alpine sable]

Complicated stuff

[stray estuary]

the slope of a displacement vs time graph is velocity

[jade birch]

[stray estuary]

$x'(t)=v(t)$

[ocean seal]

blanket

[stray estuary]

or however physics students would denote displacement

[jade birch]

Man, english terms make little to no sense ;- ;

[alpine sable]

i agree since english isnt my first language , but its a bit easy to say the least

[jade birch]

This is instantaneous acceleration

You want the change in speed (velocity) during a very very tiny change in time

[stray estuary]

^

[alpine sable]

so its just like the instantaneous velocity , but we'll find the velocity - time ?

of a certain point and get its slope

[jade birch]

Yeah

Just

You'll find the change in velocity over change in time

not velocity-time (??? what's this)

[alpine sable]

oh i thought it meant velocity over time

[jade birch]

remember, change in velocity (rise) over change in time (run)

[ocean seal]

.itsjustnai

[alpine sable]

so finding the instantaneous acceleration would be finding a slope of a A and a point thats super close to A

[jade birch]

Sure, you can think of it like that

[stray estuary]

also you're not finding instantaneous acceleration

you're estimating it

to actually find it you'd need better tools than what you have access atm

[jade birch]

True

But nonetheless, the error is negligable

[stray estuary]

if their teacher makes them learn instantaneous velocity without limits or derivatives, i dont know what else they'd slip up on

[alpine sable]

a bit sad

😔

but i was sick for a day so maybe he gave it to them in that day

let me ask my classmates ig

[stray estuary]

i definitely would

to be fair, it's enough to just pick points really close to some other point to estimate your instantaneous velocity

but to actually find the exact value, maybe your teacher went over a concept in class that you just werent there for

[jade birch]

What concept?

limits and derivatives in 1h?

[stray estuary]

idek

i could see limits

derivatives hell no, but limits are pretty easy if you dont discuss delta epsilon

like

$\lim_{x\to a}f(x)=f(a)$

[ocean seal]

blanket

[jade birch]

Even derivatives are if you don't discuss limits though

[alpine sable]

he said that we did

[stray estuary]

true but what kind of self respecting teacher doesnt discuss limits if you're talking about derivatives

[alpine sable]

well either ways thanks

[stray estuary]

no worries, i hope it helped

[alpine sable]

it really did

[stray estuary]

it's not a full answer but i hope its enough to get you through for now

[jade birch]

[stray estuary]

welp its 4 am

time to pass out now

[alpine sable]

thats what we might get , i could send some worksheets he gave us , just some True or False questions

well that was weird

[alpine sable]

you should really get some rest

[jade birch]

Did mods ban or did he delete?

[alpine sable]

i think he deleted it

forgot his name since i was typing

try to ping him

[amber urchin]

I guess he is asking for his friend

[unique ingot]

Is this correct?

[jade birch]

Yes

[unique ingot]

Bruh my textbook answers are full of typos

[jade birch]

How so?

[unique ingot]

They never give the correct answers lol

Oh well

[thorn dust]

so if a person has a 70 meter rope and they wonder how many 5 meter ropes they can make out of them its just 70 / 5 or?

[jade birch]

Yep

70/5 is just asking how many 5's are in 70

@thorn dust

[thorn dust]

ok ty

[bronze temple]

Let 𝑓(𝑥) = 𝑥 + 1 and ℎ(𝑥) = 2𝑥
b. (𝑓 − ℎ)(𝑥 + 1)

[pearl musk]

θ is the angle b/w b and c. φ is the angle b/w the cross product of (b and c) & a. my teacher said sin(θ) cos(φ) = 1 implies the three vectors are mutually perpendicular, but I don’t understand how. why can’t θ and ɸ be any other complementary angles?

[bronze temple]

good day to all of you,i need help with this math homework. idk if the +1 in letter b is a typo, but I'm stuck. my answer doesn't match the answer key

[cerulean kelp]

Hello

I am struggling to calculate eigenvectors from a matrix using the eigenvalues

Please can someone help me ❤️

[glass lichen]

what dont you get?

[cerulean kelp]

I've come across various processes of trying to calculate eigenvectors and am just trying to follow the process I found on a website (which I will paste shortly after this message) but I can't seem to figure it out... It's the same matrix btw, I'm just attempting the different eigenvalues that were discovered.

https://www.mathsisfun.com/algebra/eigenvalue.html
Ctrl+F: "Example (continued): find the Eigenvector that matches the Eigenvalue −1"

[glass lichen]

Yeah so you want to solve the system $[A-\lambda I|0]$

[ocean seal]

Mosh

[cerulean kelp]

Matrix minus the eigenvalue * identity matrix equals 0

[glass lichen]

ie find the kernel/nullspace of A-lambda I

[cerulean kelp]

I kind of did that but unsure what to do to derive the eigenvector from that

Apparently some people transform is to REF

[glass lichen]

yeah... you find the nullspace

[cerulean kelp]

But I think that's a very long winded way of doing it

What's the nullspace

[glass lichen]

set of solutions to [A|0] is the nullspace (or kernel) of A

you want to find the nullspace of $A-\lambda I$

[ocean seal]

Mosh

[alpine sable]

A)    True
B)    False
``` can someone explain how is this false ? ![aPES_Think](https://cdn.discordapp.com/emojis/493353113332219924.webp?size=128 "aPES_Think")

[glass lichen]

if acceleration is 0, what's velocity

[alpine sable]

0 ?

[glass lichen]

no

[cerulean kelp]

Acceleration would refer to it speeding up from what it's velocity is wouldn't it? I'm no expert though

[alpine sable]

ohh

makes sense

[glass lichen]

any constant velocity will have a=0.

[alpine sable]

its alright , i got it

thank you

[glass lichen]

also next time dont post in an in use channel.

[alpine sable]

my bad

[cerulean kelp]

I'll do my best to derive what that is, thanks

[glass lichen]

Ok.

[runic void]

Can someone help me with derivatives?

[wary stream]

No, no one in a math server can help you with derivatives \s

[runic void]

I'm just asking for help

[wary stream]

#rules and #❓how-to-get-help

[glass lichen]

Yeah... don't waste time with asking to ask

[runic void]

Sorry

[undone river]

I need help with the 7th word problem PLEASEEEEE

[wary stream]

,rotate

[cerulean kelp]

How do I do that

[wary stream]

There are tons of resources that you can Google, like Khan Academy

[cerulean kelp]

I went through that guide and it didn't make sense to me

He went through a different, long winded process that seemed really confusing. - e.g. Reduce matrix to ref then somehow derive x,y,z from that

[wary stream]

You do $$A - \lambda \cdot I = 0$$

[cerulean kelp]

Ngl, when I figure this out, I'm making the most concise guide for calculating eigenvalues and eigenvectors

Yep

[ocean seal]

dldh06

[wary stream]

That's it

[wary stream]

I recall helping you with this, did you watch the Khan Academy video I linked?

[cerulean kelp]

Yeah

I went through that guide and it didn't make sense to me
He went through a different, long winded process that seemed really confusing. - e.g. Reduce matrix to ref then somehow derive x,y,z from that

[wary stream]

He as in the guide or video?

[wary stream]

Subtract $\lambda v$

[ocean seal]

dldh06

[wary stream]

Then row reduce

[cerulean kelp]

video

[cerulean kelp]

I will reduce as best as I cna