help-0

[dreamy osprey]

very

[vale wigeon]

i have already had WA calculate the molar mass of Ca(NO3)2 for you

we can now calculate how many moles of Ca(NO3)2 we have in the sample

,calc 35.9/164.09

[ocean seal]

Result:

0.21878237552563

[vale wigeon]

0.22 moles, give or take

and now note that for every calcium ion there are two NO3 ions

[dreamy osprey]

ok

17% of the molar mass if N so do I take 17% of 0.22?

[vale wigeon]

no, you're overthinking it again.

[dreamy osprey]

mk

So how do I find the amount of mols of N

[vale wigeon]

it's exactly twice that of the whole compound

remember moles are a unit of quantity. kind of like dozen but way bigger

[dreamy osprey]

right

[vale wigeon]

so if we have some number of molecules of Ca(NO3)2, and each of these molecules contains 2 nitrate (NO3-) ions,

that means there are exactly twice as many of those ions as there are molecules

hence 2*0.22 moles

[dreamy osprey]

is nitrate No3

NO3

[vale wigeon]

yes

[dreamy osprey]

I get it now ty

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[dreamy osprey]

,reopen

[dreamy osprey]

.reopne

.reopen

WAI

T

[ornate condor]

hi

[dreamy osprey]

i got it wrong

hi

[ornate condor]

lol

this seems like chemistry

[dreamy osprey]

WAIT

[vale wigeon]

you didn't show the directions for sig figs

[dreamy osprey]

i forgot to round

[ornate condor]

but yea u shld find the mass of the bits

[vale wigeon]

that's the only problem

[ornate condor]

and

oh cool alr done eh

[vale wigeon]

circle we already did it

[dreamy osprey]

tysm

soz

.close

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[ornate condor]

lol

[dreamy osprey]

alright hello every were back with more stupidy on how chemicals work

I got this

I got the molar mass of the compound, 414, did that under the mass, got 0.2, multiplied that by avacado's number, then got it wrong

[vale wigeon]

you mean avogadro's number

[dreamy osprey]

avacado

[vale wigeon]

do you mean that you will insist on spelling it that way

,w molar mass C8HF15O2

[ocean seal]

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[vale wigeon]

,calc 82.8/414.07

[ocean seal]

Result:

0.19996618929167

[vale wigeon]

ok, 0.2 it is

[dreamy osprey]

yup

[vale wigeon]

,w avogadro's constant * 0.2

[ocean seal]

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[dreamy osprey]

thats what i got

[vale wigeon]

strange

but this answer is getting rejected for whatever reason...

you even followed the "2 decimal places" directive

[dreamy osprey]

;n;

[vale wigeon]

sounds like an issue with the homework system

do you have unlimited attempts for this?

[dreamy osprey]

2 left

\0/

[vale wigeon]

yuck

[lone heart]

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[vale wigeon]

...what the fuck

[fathom mantle]

wth

hi ANn

🙂

[dreamy osprey]

._.

[ornate condor]

he closed itlong ago lol

[fathom mantle]

Ann we miss you

[vale wigeon]

this was opened in my name by mistake

[silver onyx]

woah

[vale wigeon]

.close

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[fathom mantle]

Complex analysis misses you

[dreamy osprey]

magic

wat

[fathom mantle]

what is your question @dreamy osprey

[dreamy osprey]

its up there

[dreamy osprey]

.

[fathom mantle]

it says report your answer to 1.20 X 10^20?

[vale wigeon]

oh it was milligrams...

somehow that missed me

[dreamy osprey]

I dont like this game

[ornate condor]

why r yall working in closed channels

[vale wigeon]

dunno

[fathom mantle]

because is stil working

.close

[ornate condor]

its just gonna die in a sec

[vale wigeon]

some people just have a fetish for living on the edge

idfk

[ornate condor]

then itll be some random msg that opens it

[lone heart]

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[silver onyx]

the largest set for which the function f(x) = (x sin|x|) /(1- |x|²) is differentiable

[elfin snow]

what are u trying to do

@silver onyx

[silver onyx]

is it R - {-1,1}

[silver onyx]

asking doubt?

[carmine reef]

Any reason it wouldnt be differentiable at -1 or 1?

[silver onyx]

we can split it on 0

it's an even function too

if it's constant at x= 0 xf(x) is continuous at x =0

[elfin snow]

also we say asking a question not asking doubt

[silver onyx]

???

[elfin snow]

just for future reference

[silver onyx]

I am asking doubt dude

[elfin snow]

thats not proper terminology, I was just trying to help

[silver onyx]

Okay

please Ping me so I can come and see, thank you

[carmine reef]

I'm not quite sure what this means

But yeah I think 0 is the only point you really need to worry about

Thanks to those absolute value signs

[silver onyx]

it's continuous at 0

[carmine reef]

Ah yeah you can probably show that with the squeeze theorem relatively easily

but is it differentiable

we can at least ignore the opposite value bars in the denominator

[silver onyx]

yes

[carmine reef]

and really the denominator entirely since it's nonzero and differentiable everywhere

so is xsin|x| differentiable at 0

[silver onyx]

it is differentiable at 0

not at + or - 1

that's what I got

so i asked doubt

[carmine reef]

ah yeah ok

[silver onyx]

it is 0 at - 1 and +1

[carmine reef]

Ah

Didn't see the edit

[silver onyx]

oh ok

[carmine reef]

yeah I think you're right then

[silver onyx]

yea

thanks

.close

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[carmine reef]

np

[lone heart]

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[alpine sable]

not sure if this is a dumb question but for example lets say i buy something for 429.23 dollars I pay a equal amount of money every month for 12 months couldnt I use divison to help me solve that easily?

[lilac nest]

Yes, if you want to find how much you pay each month you divide the total you paid by 12

[alpine sable]

Oh ok thank u very much :))

.close

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[proven obsidian]

What did i do wrong? Im trying to calculate the intercepts

[strong compass]

The problem is in your first line

@proven obsidian

[proven obsidian]

wdym

Oooo

Crap didnt see that

Thank uuu!!

Have a good one!

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[left citrus]

Okay so quick question

[left citrus]

Wouldn’t this image be wrong

Because they integrated e^u to be e^u whereas it’s supposed to be (e^u)/u

Or am I missing something

Nvm obv I’m missing something lol

I’m literally integrating in respect to u my bad

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[alpine sable]

need help converting my answer to interval notation

[alpine sable]

(-12, -11) (11, inf)

is my answer

oof thats the answer lol .close

.close

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[stable night]

hi can someone help me with this

a) a = 0, b = 0

[keen plinth]

,w RREF{{a, 0, b, 2}, {a, a, 4, 4}, {0, a, 2, b}}

[ocean seal]

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[stable night]

hi u again

[keen plinth]

hi

i feel like thats a start

[stable night]

[keen plinth]

seeing if you can rref the matrix

[stable night]

oh im doing it without doing that

lmao

i feel that without rref-ing it would be easier tho

[keen plinth]

possibly

havent put pen and paper to this so

[stable night]

for part b i rearranged the matrix to what i wanted

[keen plinth]

¯_(ツ)_/¯

[stable night]

hmm for part c

[keen plinth]

ah i see whats going on

v nice

[stable night]

yes

i got these

c im thinkin

ah sorry i gtg

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@ember stag Has your question been resolved?

[lone heart]

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[left citrus]

Okay

[left citrus]

Quick question again lol

I feel so lost for this

[mellow tusk]

x^2=t

[left citrus]

substitution

Ok so i was on the right path

Yeah so I made x^2 - 2 = u

Kept going but then I found that du/dx was 2x and not x which was the other product

So i just didn’t think about taking 1/2 as a factor out of the integral my bad

I got the answer now though

[left citrus]

Ty

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[hot bison]

how do I do 25a?

[hot bison]

I found that the derivative is 2x

but the tangent line is supposed to be 2x+2?

can someone explain how to get that solution?

[mellow tusk]

u have the slope that is f'(-1), u know 2 points that lie on the tangent, use slope point form to find the equation

[hot bison]

ok so y=mx+b

right?

then f'(-1) is y=-2x+b?

so slope is -2

[mellow tusk]

yes

u can use that

[mellow tusk]

find b by putting x=-1, y=4

[hot bison]

ok

alr so b = 2

that makes more sense

thanks

I understand it now

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[jolly ibex]

Provide acute triangle MNP. Let 3 perpendicular lines MA, NB and PC intersect at H.
a) Prove that triangle MBN similar to triangle MCP ( Done )
b) Prove that: HA/MA + HB/NB + HC/PC = 1

[jolly ibex]

I'm stucking at b)

Anythings relates to orthocenter of this triangle?

Or we have to prove other triangles similarly??

[lone heart]

@jolly ibex Has your question been resolved?

[jolly ibex]

Anyone?

helpp

[lone heart]

@jolly ibex Has your question been resolved?

[jolly ibex]

hello

[lone heart]

@jolly ibex Has your question been resolved?

[jolly ibex]

Can I be supported???

Hello there?

Don't ignore me please

[jolly ibex]

<@&286206848099549185>

[tawny condor]

Multiply HA/MA by NP/NP

And try to see what geometric meaning this product has. Look at the numerator and denominator separately

[tawny condor]

@jolly ibex

[jolly ibex]

Yes I'm here

[tawny condor]

do you need any more hints?

[jolly ibex]

Wait let me do some steps

If i need i will tell you

Just a minute

[tawny condor]

no it doesn't

HA/MA isn't 1

[jolly ibex]

no no wait

I got wire crossed

[tawny condor]

You have HA * NP and MA * NP

tell me what those mean

[jolly ibex]

hmmm

[tawny condor]

What does HA * NP / 2 mean?

[jolly ibex]

areas of perpendicular triangle

[tawny condor]

what triangle?

which vertices?

[jolly ibex]

triangle HNP

[tawny condor]

Okay good

so what is HA * NP?

[jolly ibex]

oh oh

Is that called " Formulas of perpendicular triangle" ?

like

[tawny condor]

HA * NP is just 2 * area of triangle HNP

right?

[jolly ibex]

yes

[tawny condor]

do that with the rest of ratios

?

[jolly ibex]

no sorry

[tawny condor]

you have HA/MA + HB/NB + HC/PC

[jolly ibex]

yup

[tawny condor]

if we take the ratio HA/MA

and multiply it by NP/NP (which doesn't change its value, since NP/NP = 1)

we get

HA * NP / MA * NP

[jolly ibex]

Oh I understand

[tawny condor]

which is 2 * area of HNP / 2 * arena of MNP

which is

area of HNP / area of MNP

now do the same to the other ratios

[jolly ibex]

HNP / MNP

[tawny condor]

and simplify

[jolly ibex]

ok

Got it

Thanks for your explaination Red

.clos

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[plain nexus]

What does it mean for a game to be "impartial"?

[plain nexus]

Let's say I play nim: I have n piles of stones and players alternate in moves. Players can take 1, 2, ..., k stones from a single pile (assuming there is enough stones)

number of stones removed in move has to be less than or equal from last move (so e.g. if first player removes 10 stones then second one cannot remove 12 but only 1, 2, ..., 10)

Is this impartial game?

[lean spire]

each player has the same options at each position

yes that game is impartial

[plain nexus]

ummm... well if k=10 then on first move p1 can choose to remove e.g. 5 stones (he could remove 1, 2, 3, ..., 10) but second player will be able to remove only 1, 2, ..., 5 stones so those options aren't the same? or maybe i didn't understand it

[lean spire]

but if p2 makes the first move, then the exact same sequence of moves can be made, but by the opposite player

[plain nexus]

oh

so like

impartial means that moves only depend on position, not on player?

[lean spire]

yes

usually the two players are labeled left and right

either one can start

[plain nexus]

so if e.g. p1 could remove numbers from 1, 2, ..., x and and p2 could remove 1, 2, ..., y for x != y then it wouldn't be impartial?

oh

[lean spire]

yes

[plain nexus]

oh okay, it makes sense

[lean spire]

it would be partisan

[plain nexus]

Thanks!

[lean spire]

yw

[plain nexus]

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[alpine sable]

is it 0?

[next pulsar]

write out f(g(x))

[alpine sable]

okay and then

i did that and replacest the x with the chioices

choices*

fg(x)= -3-2(-x^2/6)

now what

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

simplify this and then equate the expression with all the values given in the options one by one, if there exists a value of x for which the expression is equal to that value then it means that value is part of the range, if for a certain value you get no solutions for x then that value does not lie in the range of f(g(x))

so which one of the choices is it? They all Gave solutions

[alpine sable]

show your work when you equated the expression with -4 i.e. the first option

-25/3

b)-13/3

c)-3

d)-5/3

-3 + x^2/3 = -3 + (-25/3)^2/3
-3 + 625/18
this does not look equal to -4 to me

[sullen iris]

You can also use derivative technique

[alpine sable]

ooooooh 2

[sullen iris]

So you can find at what x point f'(g(x)) = 0

[alpine sable]

gotcha guys thanks for the help

.close

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[mint shoal]

Not sure what im doing wrong

The answer is in terms of e

So definitely not 1

[void niche]

Your antiderivation is incorrect

Try differentiating what you claim to be an antiderivation to see

[mint shoal]

Not sure i follow we are just starting this stuff are u on about the t terms derivative?

Top right

[void niche]

No

When your integral went away

And instead you had brackets with the things to substitute in

This is the incorrect step

[mint shoal]

Oh so i integrated wrong

[void niche]

Yes

[mint shoal]

Lol

What about now?

[lone heart]

@mint shoal Has your question been resolved?

[mint shoal]

<@&286206848099549185>

[lone heart]

@mint shoal Has your question been resolved?

[lone heart]

@mint shoal Has your question been resolved?

[real gazelle]

,w integral from 1 to 2 of e^(2x)/(e^(2x)-1)^2 dx

[ocean seal]

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[real gazelle]

hmmm I think your answer is right

you can simplify it more though

yea your answer is right

[lone heart]

@mint shoal Has your question been resolved?

[mint shoal]

how?

[real gazelle]

first you can turn the double negative into a plus

and then you can make the fractions have a common denominator

(note that e^4 - 1 = (e^2 - 1)(e^2 + 1))

and then you just subtract the two fractions

[mint shoal]

thanks

[real gazelle]

no problem!

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[bold zephyr]

Howdy all, I have just tried to sold this long division question and they want you to show the remainder. My awnser was 137 however the awnser in the book is -7. Could someone help me find where I went wrong?

[bold zephyr]

.close

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[cyan ingot]

uhhhhhh

[cyan ingot]

is this 90 or 0 orrrr

[slow hound]

neither ;)

use the dot product formula

[lone heart]

@cyan ingot Has your question been resolved?

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[kindred crater]

I need help with this problem

[kindred crater]

I am using the shell method to find the volume

I'm not sure if I did the integration right

This is how I set the problem up:

[lone heart]

@kindred crater Has your question been resolved?

[kindred crater]

<@&286206848099549185>

[lone heart]

@kindred crater Has your question been resolved?

[cold hinge]

why did you put 2pi in front of the intrgral?

and also why is there an x right after the integral

volume? aren't you trying to find the area?

[kindred crater]

it was the format for the volume

[lone heart]

@kindred crater Has your question been resolved?

[kindred crater]

.close

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[pseudo igloo]

hi

[pseudo igloo]

im not getting it

[native cloud]

What have you tried

[pseudo igloo]

ive tried doing the formula this : (f(x)-f(a))/x-a

and the alternate one thats similar

[neon scarab]

You have a point, and derivative can help you get the slope on that point, then you can apply the point-slope form to obtain the equation 🙂

[pseudo igloo]

ive been getting it wrong and it seems that im doing something wrong

[native cloud]

Did you learn quotient rule?

[pseudo igloo]

i remember it but we are very early in calc

[native cloud]

I mean, you have to use y - f(n) = f'(n)(x - n), right?

[pseudo igloo]

yes

but thats for the end

i have a hard time understanding text

[native cloud]

I wouldn't know how else to solve this without using quotient rule

[pseudo igloo]

can you show me?

[native cloud]

$\frac{f'\left(x\right)g\left(x\right)-f\left(x\right)g'\left(x\right)}{\left(g\left(x\right)\right)^2}$

[ocean seal]

AirToastie

[pseudo igloo]

this is the example the program uses

for a diff numbered question

[native cloud]

Your f(x) = x + 1 and your g(x) = x - 7

[pseudo igloo]

but the derivatives would just be 1 and 1

[kindred crater]

you don't need quotient rule for this. You just need to do it how this example showed you. a = x coordinate. So the f(a) which is the function of 'a' = -8 because when a (or x) is 7, y (or f(a)) is -8

once you plug everything in, you get the slope of the tangent line, then you plug it into the point-slope formula

[pseudo igloo]

what would be a simpler way of solving this though?

[native cloud]

?

[kindred crater]

I don't recall a "simpler" way. It's making you do it this specific method anyway

[pseudo igloo]

would the rule given by the other guy work
?

[native cloud]

Yes

But I don't think your professor wants you to use that rule

[pseudo igloo]

i vaguely remember it

he said it was fine

[native cloud]

Oh then

It will be

((x + 1) - (x - 8))/(x - 8)^2

[pseudo igloo]

will the denominator become g?

[native cloud]

Wdym it becomes g?

[native cloud]

$\frac{9}{\left(x-8\right)^2}$

[ocean seal]

AirToastie

[native cloud]

It will result this

[kindred crater]

well if you did this example, you would have (x-7)(1)-(x+1)(1) / (x-7)^2

[pseudo igloo]

yeah

[native cloud]

Oh I was using the wrong question lol

[pseudo igloo]

lol

[kindred crater]

bottom would be difference of squares, so you would get -6/(x+7)(x-7)

[pseudo igloo]

ah i see

thank you i got it

[kindred crater]

sorry, it'd be -8/(x+7)(x-7)

[pseudo igloo]

thank you

[kindred crater]

despite being able to use quotient rule, I would still try it the way it showed you just in case you have to use a specific method on an exam

[pseudo igloo]

the professor said use whatever gets you the answer

[kindred crater]

That's good. My prof made us use the f(x) - f(a) method for just one question on one of the exams just to prove we could do it

quotient rule is easier to remember though

[pseudo igloo]

yeah

.close

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[short bobcat]

Can someone determine the vertex of the first equation

And show me how

[neon scarab]

Check “completing sqaure” on web or on your textbook. I am sure they can already provide detailed explaination on what you need to do to obtain the vertex for quadratic equation graph. 🙂

[short bobcat]

It’s just a sheet of paper…

I don’t have the text book

.close

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[upbeat shadow]

Why does the anti derivative of y” turn 1 into (x-2)

[upbeat shadow]

For i

[lone heart]

@upbeat shadow Has your question been resolved?

[rigid smelt]

The antiderivative of x^2+x+1 is x^3/3 +x^2/2 + x + c_2, which is also equivalent to x^3/3 +x^2/2 +x-2 + c_2, considering c_2 is just an arbitrary constant

[slender gull]

Basically you're playing with the constant.

[rigid smelt]

Here it might be better if you differentiate between the constants a bit if that's what are confusing you

[upbeat shadow]

Is there a reason they chose -2?

[rigid smelt]

Idk, they probably thought since they are plugging in 2 they might as well make that term be 0

[slender gull]

Yeah that seems like it.

[upbeat shadow]

Oh yea I see

[rigid smelt]

Or unless there is more context to this which you are not showing

[upbeat shadow]

Nope that makes sense

Thanks guys

[lone heart]

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[digital forum]

How do I solve b and c

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@digital forum Has your question been resolved?

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[modern topaz]

@slow hound

[modern topaz]

@keen plinth

Can u guys go over that question again

im seriously not gettin it

[slow hound]

yo

repaste it

[modern topaz]

u guys were talking and overlapping

[slow hound]

snow's a gigachad

[modern topaz]

so it was hard

to comprehend

snow is dead and doing his homework

[slow hound]

🤣

anyway, first i established a recurrence relation

[modern topaz]

okok

[slow hound]

lemme find the SS's

[modern topaz]

alright

[slow hound]

its a nice problem honestly

[slow hound]

that leads to this

[modern topaz]

bro how??????? ???

how did u get that???

[slow hound]

ok lemme hit you with the intuition

i observe that as you take successive powers of n, the coefficients are related to each other

so i try and define a relation between them

[modern topaz]

ok

u mean when you expand

the thing

[slow hound]

ye

[modern topaz]

the coefficients

are related?

[slow hound]

i pair up the things

let's expand it together

[modern topaz]

okok ur so patient

[slow hound]

,w (a+bsqrt(2))*(1+sqrt(2))

[ocean seal]

Results provided by WolframAlpha

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

Requested by S̨̥̫#8871

[modern topaz]

what is wolframalpha?

btw

[wary stream]

WolframAlpha is a computational knowledge engine and answer engine developed by Wolfram Research. It answers factual queries directly by computing the answer from externally sourced data

[slow hound]

LOL

[modern topaz]

oh lol cool

[slow hound]

legendary response

[modern topaz]

what does this exactly show? ur expanding the

[modern topaz]

this thing?

[slow hound]

yeah im expanding it, it should be this

hold up

[modern topaz]

ok

[modern topaz]

hey snow

crap lol

not snow

but fairy

are u saying that the coefficient of a binomial theorem

times the thing inside the bracket

equals its expansion right?

[slow hound]

ok wait gimme 2 min

ill clear everything up

[modern topaz]

ok

[slow hound]

someone's blowing up my dms rn 😂

[modern topaz]

okok

snow unrelated question

this works because everything is squared right?

and it's multiplying negative numbers so the sign changes

[modern topaz]

answer this too

[slow hound]

yeah once you pile up all the terms

[modern topaz]

ohh ok

[modern topaz]

answer thsi briefly

too

emergency

[slow hound]

but anyway once you get here, you basically split it into it's integer and rational parts

[slow hound]

yep

[modern topaz]

this is not the same

as the previous one u sent

the right side

has so many more things

[modern topaz]

this

lol

u just expanded

the left side

i just realized

[slow hound]

yeah, now we pile it up

[slow hound]

we see the root 2 part aka b_n = a_n-1 + b_n-1

[modern topaz]

latex plz

[slow hound]

forgive me christina i will need 10 min

i will type out a beautiful explanatoin for you after 10

[modern topaz]

yep no worries

@keen plinth do u do abstract algebra

@slow hound do u do Lie algebra

[slow hound]

heard of it, no idea what it is tho lol

okay i think im in the clear now 😂

[modern topaz]

okok

[slow hound]

right, so here i just expanded the LHS

[modern topaz]

yep

[slow hound]

that make sense?

[modern topaz]

wait is it bn?

[slow hound]

wdym?

[modern topaz]

this?

why is it bn>

an-1+bn-1=bn?

[slow hound]

yep ^^

bn is the sum of the coefficients of the terms with sqrt attached

[modern topaz]

why is that the case?

oh

ok

im dumb lol

i got it

[slow hound]

cool cool

[modern topaz]

yes thats clever

yes

yes

[slow hound]

now we get this in terms of one variable

cuz rn it's 2

an and bn

so how do we do that?

[modern topaz]

ok? maybe i get it, can u actually do it

[slow hound]

yea

[slow hound]

i used those 4 equations above

try and see which substitutions i made if u want

[modern topaz]

OMG this is so clever

shit

ok go on

[slow hound]

oh just you wait

[slow hound]

let's not forget that

[slow hound]

lets look at the first equation

[modern topaz]

okok

[slow hound]

so our ratio now becomes

[modern topaz]

HOLY

MAGIC

[slow hound]

now, let's take a detour

[slow hound]

remember our key facts, first being this

[slow hound]

so now detour time!

[modern topaz]

ok

whats detour

[slow hound]

we are going to go to an intermediary place first

this should make intuitive sense

[modern topaz]

actually not quite.,,,? can u explain one liner

[slow hound]

well the LHS goes to infinity

and the RHS also does

[modern topaz]

also didn't u flip the two thing

[slow hound]

yeah i did, but you'll see why

[modern topaz]

ohok ig

[slow hound]

let's call this limit x

so that stuff is x

now, the main attraction

we are gonna do some manipulations

remember that as we do this, the limit is always in the background

im just choosing to hide it for the sake of convenience

[slow hound]

here i divided top and bottom by bn

[modern topaz]

ok

[slow hound]

now we will focus on the bn-1/bn part

i just substituted the definition of bn in

now im gonna do the same thing on the RHS

i'll divide by bn-1

[slow hound]

see how this can come in handy now?

[keen plinth]

are we suffering through this pain

[slow hound]

hey its snow

yep

[modern topaz]

SNOW

[slow hound]

do the thing, solve for x

[slow hound]

plug it back in here

and winner winner chicken dinner

[modern topaz]

so solve this?

[slow hound]

yep

[modern topaz]

how do u do it😭

[slow hound]

ok so bn-1/bn is x

and so is bn-2/bn-1

so just replace those with x

\color{marigold} $x = \frac{1}{2+x}$

[ocean seal]

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

[modern topaz]

ok

oh

WOW

[slow hound]

christina have you guessed my timezone yet

[modern topaz]

what is it

def not mid night

[slow hound]

GMT + x

[modern topaz]

just tell me the exact time at ur palce

i dont know gmt

lol

[slow hound]

4:07

[modern topaz]

afternoon?

[slow hound]

morning

[modern topaz]

bro

did u sleep

[slow hound]

i dont sleep i grind

[modern topaz]

nice rise and grind

[slow hound]

https://tenor.com/view/l-lawliet-death-note-stare-eyes-anime-gif-17559982

[modern topaz]

snow snow,

so putting it back to the main equation

1/1+1/2+x?

like that?

[slow hound]

did you solve for x

[modern topaz]

yay

so

-1/sqrt 2

[slow hound]

uh

should be positive

the ratio cant be negative since the terms are increasing

[modern topaz]

oops

nvm

[slow hound]

snow did it in their head

[modern topaz]

what

[slow hound]

bro

,w x = 1/(2+x) + zeta(2)

[ocean seal]

Results provided by WolframAlpha

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

Requested by S̨̥̫#8871

[slow hound]

ah crap

that aint lookin too good

we might need a specialist to look at this

[modern topaz]

ok snow but is the idea basically solve x and plux it back to the main, 1/1+x

and get the limit?

[slow hound]

yeah

the limit disappears

[modern topaz]

but x has 2 values??

so

two limits?

[slow hound]

what does x represent?

[modern topaz]

bn-1/bn?

[slow hound]

it represents the ratio between bn-1/bn

can that ever be negative?

[modern topaz]

no

[slow hound]

so we take the positive solution

[modern topaz]

AHHH

okokokokokokokofksdofkosdafkodsfk

okasdofkaodsfkosadfkoasdfkasodfkoaskf

bro ur so smart dkfjnasdfkjsandfdsaf

[slow hound]

nah

https://tenor.com/view/nice-the-rock-sus-the-rock-sus-meme-louis-thrane-gif-25854498

[modern topaz]

OK THX DUDE< BIG HELP BIG HELP BIG HELP

.close

[lone heart]

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[neon scarab]

You may want to try rewriting this using sec and tan

[lone heart]

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[lone heart]

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[past bloom]

anyone has youtube links for this topic?

[past bloom]

what should i search?

[lone heart]

@past bloom Has your question been resolved?

[past bloom]

.close

[lone heart]

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[solar trail]

whats meant by a "pair of linear equations"?

[noble sinew]

There are written 2 equations

They form “a pair”

[solar trail]

are they like the same equation? like the same value or something

how do i solve them

[noble sinew]

Its a system of equations

So the solution must be a pair (x,y) that solves both equations at the same time

[solar trail]

oh

do you have any yt references that can help me with this whole thing

ive never heard of this

[noble sinew]

Just google solve system of equations

[solar trail]

okay thanks

.close

[lone heart]

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[cinder rampart]

how can i find instantaneous rate of change when x=2 and f(x)=x^2?

[high rapids]

Derive f(x)?

[cinder rampart]

what is that mean

idk what derive is

[carmine reef]

so as an idea

[cinder rampart]

do i find a point like (2,4)

plugging in 2 to x^2

[carmine reef]

what's the slope of a line going through y=x^2 at x=2 and x=2.01

[cinder rampart]

uhh

(2.01-2)/something idk

[carmine reef]

the 2.01-2 would be on the bottom

[cinder rampart]

okayyy

what do i put on top?

[carmine reef]

slope is ∆y/∆x

[cinder rampart]

x(x)

[carmine reef]

rise over run

[cinder rampart]

oo

idk about rise

[carmine reef]

The amount the function increases by

[cinder rampart]

is it 4?

[carmine reef]

Nah

It's gonna be something really small

The rise

[cinder rampart]

0.01

0.1

[carmine reef]

f(2.01)-f(2)

[cinder rampart]

oh i have to put it like that?

[carmine reef]

see how that's the difference in y value between the 2 points

[cinder rampart]

yeah

0.01

[carmine reef]

which is = .0401

[cinder rampart]

wait

oh is it cuz i square it

[carmine reef]

you do 2.01² - 2²

since f(x) is x²

[cinder rampart]

oh and bottom is the 2.01-2

[carmine reef]

yeah

[cinder rampart]

is there any method i can use without calculator

[carmine reef]

well this only got you the approximate slope anyways right

The answer is 4.01

Once you do the division

[cinder rampart]

ok

[carmine reef]

So to change this into a method to get the exact slope

And one that wouldn't require a calculator

[cinder rampart]

so if x=3 i do f(3.01)/f(3) over 3.02-3?

[carmine reef]

How well do you understand limits?

[cinder rampart]

pretty well

[carmine reef]

over 3.01-3 but yeah

Ah

So

Step one

[cinder rampart]

can i just do like 3.00001 and get 6 as answerr for that

[carmine reef]

We want to find the line going through y=f(x) at x=c and x=c+h

[cinder rampart]

yeah

[carmine reef]

Well

Specifically the slope of the line

Using rise/run, can you find a formula for that?

[cinder rampart]

y2-y1 over x2-x1

[carmine reef]

right

good start

[cinder rampart]

yess

[carmine reef]

x1 is c though in this case right

[cinder rampart]

yeah

[carmine reef]

then x2 is?

[cinder rampart]

h

[carmine reef]

c+h

[cinder rampart]

c+h

the h is 0.01?

[carmine reef]

In the example we did before yeah

That's good

[cinder rampart]

okk

[carmine reef]

So now y2 and y1

[cinder rampart]

f(x) and f(x+h)

[carmine reef]

Exactly, though reverse order

[cinder rampart]

yes

[carmine reef]

So now we have the slope is this

Oops

[carmine reef]

This

Doing the substitution, that's [f(x+h)-f(x)]/(x+h-x)

[cinder rampart]

yes

[carmine reef]

and the bottom simplifies a bit

[cinder rampart]

o wait

2x+h

[carmine reef]

[f(x+h)-f(x)]/h

[cinder rampart]

oo

oh yes thats minus

[carmine reef]

one of the xs is subtracted there

[cinder rampart]

yes

[carmine reef]

So that's our generalized approximation formula

Ah maybe I should replace the x with c or something but

I don't really need to I don't think as long as you understand

[cinder rampart]

ok

2.01^2 plus 2 divided by 0.1

[carmine reef]

So the cool thing about this formula is we can try it with any function, any x value, and any h value

AND

the real magic is

The smaller the h value is the closer our formula is to the true instantaneous rate of change

Does it make sense why?

[cinder rampart]

yes cuz if its really small yhen it will eventually be nothing

[carmine reef]

You're basically drawing a tangent line at that point

[cinder rampart]

cuz its almost yhe same point

[carmine reef]

Yeah exactly

The average slope between 3 and 3.001 is very close to the slope at 3

So here's where the real genius part comes in

We take the limit as h→0 of [f(x+h)-f(x)]/h

[cinder rampart]

why do u make it 0?

[carmine reef]

Well our points are x and x+h, right

[cinder rampart]

yeah

[carmine reef]

So we're trying to make them as close together as possible

[cinder rampart]

oh ok

[carmine reef]

If we just make h=0, then we get 0/0 in our formula and that doesn't help

[cinder rampart]

yeah

[carmine reef]

but if we take the limit as h->0 instead it actually works

[cinder rampart]

do i simplfy

[carmine reef]

Lim h→0 [f(x+h)-f(x)]/h

[cinder rampart]

ok

[carmine reef]

That's the final formula without knowing a specific function

[cinder rampart]

ok

[carmine reef]

It's called "the definition of a derivative"

[cinder rampart]

what do i do after?

[carmine reef]

Choose f(t) = t^2

As your function

And x=2

you don't actually have to set an x value if you don't want either

[cinder rampart]

where did t come from

[carmine reef]

I didn't want to use x to define the function since we were already using it

[cinder rampart]

ok

[carmine reef]

t isn't important, I'm just using it to show what f does

[cinder rampart]

t is the x+h right

[carmine reef]

well you can think of the function as an abstract object itself

it takes in inputs and returns their squares

so whatever you input is the "t"

for the f(x+h), the input is x+h

for the f(x) the input is x

[cinder rampart]

ok

[carmine reef]

but yeah so if we let f be the function f(t)=t²

we can plug it in our derivative definition

and we'll be able to make progress with the result

[cinder rampart]

ok

[carmine reef]

probably you should do that part

Lim h→0 [f(x+h)-f(x)]/h

I also might fall asleep soon

2:30 here lol

[cinder rampart]

oh

ill go on resarch with dervative definition

u can go to sleep

[carmine reef]

good luck

[cinder rampart]

thx for alll this

[carmine reef]

If you understood most of what I said you probably understand the definition of a derivative better than almost any calc 1 student

hopefully

putting it into practice is it's own challenge

[cinder rampart]

yeah ill do lot of that

[carmine reef]

good night :)

[cinder rampart]

u2

[lone heart]

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[silver onyx]

Anyone know phy?

if so, can anyone tell why y coordinate became 0?

[tacit bobcat]

Apply the Lorentz force properly

[lone heart]

@silver onyx Has your question been resolved?

[silver onyx]

can you help, I am just confused in this part

[tacit bobcat]

Do you have the formula for it?

Write it out

[silver onyx]

F= qvb sin theta

@tacit bobcat I got

.close

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[quasi kraken]

Is the following Relation symmetrict
R = {(a,a), (b,b), (c,c)}

[lone heart]

@quasi kraken Has your question been resolved?

[worthy relic]

symmetrical relative to what?

like what line does it flip across?

[silver onyx]

yes it's symmetric, reflexive and transitive too

[silver onyx]

symmetric relation

[worthy relic]

ok maybe i dont know what im talking about sorry

[quasi kraken]

Ah thanks!

[silver onyx]

no sorry lol