help-13

[tall hare]

dk about the order of f cl and br tho

[copper crest]

Go accordin to priority and number em ig

[tall hare]

next time ask somewhere else

[copper crest]

Alpha
betical order or whatever

Idk

Guessing

[obtuse frigate]

Oh I thought we were allowed to ask chemistry questions here as well

Sorry

[copper crest]

Wait

[obtuse frigate]

Because I saw a few people post a chemistry question here

[copper crest]

Lemme recall

It's gud u asked

[tall hare]

i personally like physics lol

[copper crest]

I got like a chance to revise it

But yea it's not allowed next time

[crimson sedge]

@gusty vine I wanna know too 😵‍💫

[copper crest]

1-bromo

[crimson sedge]

Also yeah ask in the chemistry server or something, since this is not related to math at all

[obtuse frigate]

Right, apologies

[copper crest]

Wait

Ig I got it

So there are three halogen groups

Bromo

Fluoro

Chloro

[obtuse frigate]

yes

It’s a benzene ring as well

But the numbering makes me confused

[tall hare]

the middle is aluminum?

[copper crest]

It's all substitienys ryt

[gusty vine]

hihii who pinged

oh lexyy HAHAH

[copper crest]

1 bro no?

Bromo

[gusty vine]

1-Bromo-3-chloro-5-fluoro

but ya u shouldn’t ask chem qns here unless it has some calculation stuff iirc

[copper crest]

Yea thus ilwhat I was tryna say
Alphabetical order

[crimson sedge]

Yeah I will stop it now AHAHA I just found it funny how common rhe chemist questions are here

[obtuse frigate]

Got it. Thank you all of you

I won’t ask Chemistry questions here anymore. Apologies once again

.close

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[gusty vine]

HAHAHAH ya I see some here and there usually

[gusty vine]

oh no

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[crimson sedge]

😵‍💫😅

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[rough rune]

I need to find a way to describe the limit within the grey area here.
How should i go doing so?

[crimson sedge]

The limit?

[rough rune]

Something along
-1<=y<=2
something y <= x <= y

[cedar kiln]

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[novel kiln]

Hi Im having trouble understanding example 4 could i get some help?

[rain drift]

unfortunately we can't see the screenshot.... everything is too blurry

can you re-screenshot it?

[novel kiln]

yeah for sure

[cedar kiln]

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[novel kiln]

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[crimson sedge]

given a 4x4 matrix

[crimson sedge]

when selecting 4 cells, what are the odds that the 4 cells are selected from the same row?

is it $\left(\frac14\right)^4$?

[wraith dagger]

metnal

[crimson sedge]

Can you have the same cell selected twice?

no they have to be different

im guessing its $\frac14\cdot\frac13\cdot\frac12\cdot4$?

[wraith dagger]

metnal

[crimson sedge]

wait nvm

idk

im confused

so what do u think @crimson sedge

I haven't done stuff like this in a very long time ahah

I was thinking of something like

$\frac{1}{16} \cdot\frac{1}{15} \cdot \frac{1}{14} \cdot \frac{1}{13}$

[wraith dagger]

♡LexQa♡

[crimson sedge]

hmmm maybe that multplied by 4

cuz there are 4 rows

<@&286206848099549185>

sorry had to lol

[ancient talon]

well the row is chosen by the initial pick

so then, there are 15 entries and 1 specific row that has 3 entries which we want

so for the next pick, there is a 3/15 chance that the row we want is selected

then assuming that happens, we have 14 entries and only 2 in the row we want

so then there's a 2/14 chance

and then finally using the same logic a 1/13

since they're all independent, the probability is 3/15 * 2/14 * 1/13 = .002198

[crimson sedge]

did i misunderstand or did u forget 1/16

[ancient talon]

nope, there's no 1/16

because you're guaranteed to get the row you want the first pick

because you're not looking for one specific row the first time

ist just that all the ones after the first pick have to be in the same row as the first

[crimson sedge]

if you were to explain it formally or idk how to say that i guess in pure mathematical form what would u use? something like combinatorics? conditional probability?

[ancient talon]

combinatorics probably

abstractly, i would represent it like there are 16 total options, and you want to pick 4 that are alike by some metric

[crimson sedge]

alright tysm

[ancient talon]

yeah, np

[crimson sedge]

.close

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[digital bloom]

How is it possible to find a power series solution to y’=1+y^2 where y(0)=0

[digital bloom]

The general closed form that I saw online uses Bernoulli numbers however I’m not expected to know of that

[cedar kiln]

@digital bloom Has your question been resolved?

[cedar kiln]

@digital bloom Has your question been resolved?

[crimson delta]

maybe they just expect you to guess the answer?

it's pretty wellknown

or at least do the first few terms of the power series and then recognize it

[digital bloom]

As in prove that a power series solution exists?

Finding the first few terms and proving it has a radius of convergence?

[cedar kiln]

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[digital bloom]

.reopen

[cedar kiln]

✅

[crimson delta]

does the exercise say that you have to do it with a power series?

[digital bloom]

Yes

[untold glen]

Make a table for f(x) or y, right now you have f'(x),

But instead of f(x) you would do just y

[digital bloom]

I’m sorry I don’t really understand what you mean? Do you mind elaborating onto how?

[untold glen]

Like do a taylor series for it, or in your case a maclurin series, which is just a taylor series centered at 0

[cedar kiln]

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[jolly sage]

I need graphic visualization for all Z; |z+i|>=|z+1| in Complex plane, thanks for helping

[mighty drift]

You may try to work it out algebraically. Or you can do it intuitively by thinking it terms of distances (reminder: |x - y| is the distance between the points x and y)

[jolly sage]

i would be grateful for help with intuitive solution

[mighty drift]

Reformulating, this is asking about the points that are farther away from -i than from -1

[jolly sage]

Oh, thanks

.closed

[mighty drift]

.close

[cedar kiln]

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[jolly sage]

.close

[mighty drift]

Helpful people have the right to close channels themselves in case you didn't know (not that you shouldn't do it yourself ofc)

[cedar kiln]

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[toxic moat]

lhop

[gleaming schooner]

that would give -1/e^x

ah makes sense i am so dumb

[toxic moat]

yes

[gleaming schooner]

thanks @toxic moat

[toxic moat]

np

[gleaming schooner]

.close

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[toxic moat]

fast

gj

💕

[gleaming schooner]

love u 💕 , can i get ur ig?

[toxic moat]

wow

no

[gusty vine]

omgggg

[gleaming schooner]

😂 😂 😂

[gusty vine]

@toxic moat ur getting hit on :0

[gleaming schooner]

my rizz failed

[gusty vine]

#queen

[toxic moat]

ikr

hahaha

rizz?

[gleaming schooner]

my bad, i apologize

.reopen

[cedar kiln]

✅

[gleaming schooner]

.close

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[hollow minnow]

[toxic moat]

LOL

[gusty vine]

I can’t find snow

😭

[magic saddle]

my bro got the anti rizz

[hollow minnow]

It’s a secret organisation

[magic saddle]

worst rizzler in history

[gusty vine]

add me 🥹

[hollow minnow]

[cosmic steppe]

I want yogurt

[gusty vine]

yum

Yoghurt

[gleaming schooner]

u win sometimes, u lose sometimes

[hollow minnow]

Acceptance Rizz

[gusty vine]

what’s a fizz?

rizz*

[magic saddle]

ur flirting ability

[hollow minnow]

One's ability to seduce a potential (usually female) love interest.

[gusty vine]

who creates these words

[magic saddle]

if you have mad rizz it means u can pull anyone

[gusty vine]

USUALLT FEMALE

[magic saddle]

16 year olds on tiktok

[gleaming schooner]

which does not depend on drip

[gusty vine]

drip?

is that like your attire

[magic saddle]

drip increases rizz though

[gleaming schooner]

yes

[magic saddle]

ye

[toxic moat]

same lol

[hollow minnow]

I just copied from wiki haha

[toxic moat]

we all love our wiki

[gusty vine]

HAHA

[gleaming schooner]

yet i have been single forever, friendzoning & suffering is the only constant

[magic saddle]

Also lightskinned people tend to have more rizz due to something in their genes

[gusty vine]

uhhhh

no comment 😶‍🌫️

[gleaming schooner]

nah

[hollow minnow]

[cosmic steppe]

What the fuck is this

[gleaming schooner]

she's lightskinned

[hollow minnow]

Lmao

[gusty vine]

yoghurt

[magic saddle]

the lightskin stare multiplies your rizz by miles

[gleaming schooner]

idc

[gusty vine]

okie y’all should move to #discussion hahah

[hollow minnow]

More like

#chill

[gusty vine]

YESH

I forgot that was a channel

[gleaming schooner]

i hv finals next week

no one will give me their ig so it's a waste of my time

[hollow minnow]

Do you have that intelligent rizz

[gusty vine]

[hollow minnow]

What was dat

[rain drift]

I saw that

[gleaming schooner]

my first impression to people is i am nerd

[gusty vine]

HAHAHAH

smth I learnt from my friends

am not proud of it

[gleaming schooner]

i learnt that from ur mom

[gusty vine]

okie before the mods kill us y’all shd move to #chill

[hollow minnow]

It’s calm

[gusty vine]

calm

[gusty vine]

very original

[rain drift]

it's okay, I'm ready to die by mod

[cedar kiln]

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[sullen tundra]

Need to use integration here

I did v(t) = 1/4t ^4 - t^3 + C

But dont know how to use the distance of 10 cm in 2 seconds

[cedar kiln]

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[crimson sedge]

Okay so if i know a rectangular room is 11 square meters big and that the "ratio" is 4.5 x 8.5 How do i calculate the dimensions of the room (? x ?) if i dont have them. It's like calculating the area in reverse i guess?

[cosmic steppe]

Let "x" be the scalar multiple of the ratio

[crimson sedge]

I'm class 8 math so this is kind of overclass for me

[cosmic steppe]

Then $(4.5x)(8.5x) = 11$

[wraith dagger]

Umbraleviathan

[cosmic steppe]

I'm assuming the "ratio" refers to the dimensions' ratios?

[crimson sedge]

Yes but not the dimensions itself thats why this is a bit hard for me

[cosmic steppe]

Well they have to be multiplied by some scalar multiple to achieve that area. Multiplying the ratio by that scalar multiple doesn't change the ratio

[cosmic steppe]

Hence this

"x" is gonna be this scalar multiple

If you can find x, you can find the physical dimensions of the paper

[crimson sedge]

Yes i think you have to multiply the ratio by something but i dont know where to find what i need to multiply it by?

[crimson sedge]

Yes

[cosmic steppe]

You legit can

It's just a quadratic

[crimson sedge]

I don't know how

[cosmic steppe]

Simplify (4.5x)(8.5x)

[crimson sedge]

Yes

[cosmic steppe]

Go simplify it

I'm assuming you've done some variable multiplication before

[crimson sedge]

$38.25⋅x2$

[wraith dagger]

Castella

[crimson sedge]

that?

im pretty lost sorry

english isn't my main language either so i don't understand all the terms i apologise

or 29627.015625?

[cosmic steppe]

x^2?

Let me check

Yeah

[crimson sedge]

so the short corner is about 3m?

wait

[cosmic steppe]

$$38.25x^2 = 11$$

[wraith dagger]

Umbraleviathan

[cosmic steppe]

Solve for x

[crimson sedge]

im pretty bad at algebra

[crimson sedge]

x = 0.536266?

or 0.287581699?

[cosmic steppe]

,w Sqrt[11/38.25]

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Umbraleviathan#3607

[cosmic steppe]

The 0.536

[crimson sedge]

:]

so do i do

for example

4.5 x 0.536266

then?

[cosmic steppe]

The dimensions are 4.5(0.536) and 8.5(0.536)

[crimson sedge]

so the dimentions are roughly 2.4 x 4.5?

right?

[crimson sedge]

i think that is right

in that case it's solved

[cedar kiln]

@crimson sedge Has your question been resolved?

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[rotund plaza]

if the roots of $z^6 + z^3 + 1 = 0$ are also the roots of $z^9 - 1 = 0 $ Identity which of the roots of $z^9 - 1 = 0$ are the roots of $z^6 + z^3 + 1 = 0 $

[wraith dagger]

vertify

[south tundra]

Factor

[rotund plaza]

the answers are

$cis\frac{2\pi}{9}, cis\frac{-2\pi}{9},cis\frac{4\pi}{9},cis\frac{-4\pi}{9},cis\frac{8\pi}{9},cis\frac{-8\pi}{9}$

[wraith dagger]

vertify

[cedar kiln]

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[rotund plaza]

.close

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[crimson sedge]

<@&286206848099549185>

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185>

<@&286206848099549185>

[keen elbow]

@crimson sedge is is precalc.?

[crimson sedge]

yes

[cedar kiln]

@crimson sedge Has your question been resolved?

[grand raft]

Do u still need help

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[sly canopy]

can someone explain how to factor this

[hushed spoke]

Factor whats common first

[rare schooner]

take y common?

then ull get a quadratic, and then youll know how to factor a quadratic

[sly canopy]

ahh okay ill tr y that

[warm charm]

how do i open a channel

[hushed spoke]

#❓how-to-get-help

[sly canopy]

ahh i got it

thank you use much

.close

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[topaz imp]

can anyone tell me what does this mean

[topaz imp]

like how come λ^2 = 2λ + 1

[crimson delta]

well lambda^2+lambda+2=0

[topaz imp]

that I got it

[crimson delta]

therefore lambda^2=-lambda-2

and then in characteristic 3 you get lambda^2=2lambda+1

[topaz imp]

I am a little new to this topic can you please tell what's characteristic 3?

[crimson delta]

the characteristic of a ring is the minimal number n so that 1+1+1+...+1=0

have you not seen that before?

[topaz imp]

ah I did

[crimson delta]

here we are working over F_3 = Z_3 = Z/3Z (not sure about your notation)

clearly 1+1+1=0 in F_3 so its characteristic is 3

[topaz imp]

oh

got it

thanks

.close

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[crimson sedge]

How to solve this

<@&286206848099549185>

[split jetty]

Pythagorean theorem

[crimson sedge]

Yes

[split jetty]

Do it

[rare schooner]

you know whats a pythagoras theorem? @crimson sedge

[crimson sedge]

6+8

[rare schooner]

uh no

write it down if you havent, a^2 + b^2 = c^2

[crimson sedge]

For future reference please remember

Idk am stuck

,!15

ok

Oh well

[rare schooner]

c being the longest side

[crimson sedge]

Just don't ping at least after 15 minutes

[rare schooner]

a and b being the other sides

[crimson sedge]

ok

[rare schooner]

so substitute the 6 and 8 into a and b

and do the maths

@crimson sedge

[crimson sedge]

I square them?

[rare schooner]

yes

what do you get?

[crimson sedge]

And add them?

[rare schooner]

yes

[crimson sedge]

OK answer is 100?

[rare schooner]

bo

no

you forgot to squareroot

[rare schooner]

because thats c squared

to remove to squared just squareroot

[crimson sedge]

So 10?

[rare schooner]

yes

[crimson sedge]

thx

You are better than my teacher

[rare schooner]

haha thanks

btw if u need more explanation

[crimson sedge]

No thank you I appreciate you helping me

I feel like am smart

[rare schooner]

https://youtu.be/AA6RfgP-AHU

[rare schooner]

ok lol

close it if ur done

do .close ty

[crimson sedge]

ok

.close ty

[cedar kiln]

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[half crescent]

Help

[split jetty]

Can you use lhopital?

[cedar kiln]

@half crescent Has your question been resolved?

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[autumn notch]

$B,C \in \mathbb{Z}$

[wraith dagger]

Oskar AC

[autumn notch]

B and C are 3X3 matrices

[tropic oxide]

do you mean they are 3 by 3 matrices with integer entries?

[autumn notch]

$det(A), det(b) = -1 \or 1$

[wraith dagger]

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

[autumn notch]

yes

[tropic oxide]

so then you mean $A, B, C \in \bZ^{3 \times 3}$?

[wraith dagger]

Ann

[tropic oxide]

you're being sloppy with notation

[autumn notch]

yeah sorry

let me rephrase

B, C is 3x3 with integer entries, they have either -1 or 1 as determinant, now show that the product BC has integer entries and has determinant .-1 or 1

hope thats better 🙂

[tropic oxide]

surely the only nontrivial part of this is that det(BC) = det(B)det(C)?

[autumn notch]

but what abour the integer entires

[tropic oxide]

if you know how matrix multiplication works then you should know that each of the entries of BC is obtained from some entries of B and C by means of multiplication and addition

and integers are closed under both

unless you deem that to be non-obvious enough to warrant a 3 page proof

[autumn notch]

ah, so the entires are given from B, and C therefore BC has the same entries

nah i think thats all right

i feel stupid now, that was so easy, well thanks Ann, have a nice day.

.close

[cedar kiln]

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[autumn notch]

.reopen

[cedar kiln]

✅

[autumn notch]

nvm

.close

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[ember plaza]

How would I proof this statement with a direct mathematical proof?

[cedar kiln]

@ember plaza Has your question been resolved?

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[crimson sedge]

Have i done this right?

Trying to find the linear equation

[cedar kiln]

@crimson sedge Has your question been resolved?

[autumn notch]

har du fundet ud af det

@crimson sedge

ellers har jeg løsningen, du mangler lige lidt

du bruger

til at finde hældningen

hvilket giver -1/3

[crimson sedge]

oh shii

[autumn notch]

så sætter du dette ind i y_1=-1/3(x_1)+b og isolerer for b

hvilket giver 4/3

dette samler du så på formen y = mx+b

y=-1/3x+4/3

giver det mening william

[crimson sedge]

kan you write that in english 💀

[cedar kiln]

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[dire turtle]

i have got some issues with this system even though i solved it once

[dire turtle]

<@&286206848099549185>

[valid yacht]

why do I think that they're the same equations nvm idts now

anyway, have you tried squaring the first one on both sides?

[dire turtle]

yea

[valid yacht]

what did you get?

[dire turtle]

$\frac{x}{y}+\frac{y}{x}+2(\frac\sqrt{x}{y}+\sqrt{y}{x}= 100/9$

just

x/y+y/x+2(sqrt/x/y*sqrt/y/x)=100/9

[valid yacht]

and the $\sqrt{\frac{x}{y}} \sqrt{\frac{y}{x}}$ becomes $\sqrt{\frac{xy}{yx}}=\sqrt{1}=1$

[wraith dagger]

n11

[valid yacht]

Thus we have $\frac{x}{y} + \frac{y}{x} = \frac{82}{9}$

[wraith dagger]

n11

[dire turtle]

82/9?

thats like 100/9

[valid yacht]

(100/9)-2

[dire turtle]

and what about the 2

$(a+b)^2$

[wraith dagger]

Kssenia

[dire turtle]

i mean like 2ab

[valid yacht]

Thus we have $\frac{x}{y} + \frac{y}{x} + 2= \frac{100}{9}$. Or $\frac{x}{y} + \frac{y}{x} = \frac{100}{9}-2$. i.e., $\frac{x}{y} + \frac{y}{x} = \frac{82}{9}$

[wraith dagger]

n11

[dire turtle]

ohhh yea

[valid yacht]

now how can we proceed further with this

Using both equations we get $9xy+25=\frac{82xy}{9}$

[wraith dagger]

n11

[valid yacht]

,w solve{x^2+y^2=9xy+25}

[wraith dagger]

Results provided by WolframAlpha

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

Requested by n11#1655

[valid yacht]

🦧

[dire turtle]

answer key

[dire turtle]

find common denom

9xy

9x+9y=82xy

not even that

look

x^2+y^2+2xy/xy=100/9

x^2+y^2= 9x+25

[dire turtle]

9xy+25+2xy/xy=100/9

11xy+25/xy=100/9

9(11xy+25)=100xy

99xy+225=100xy

xy=225

x=225/y

no?

[cedar kiln]

@dire turtle Has your question been resolved?

[crimson sedge]

Hi hi @dire turtle

Seems like u r still doing this?

I will write it out for u this time on paper

[dire turtle]

thanks i have got it

[cedar kiln]

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[crimson sedge]

Oh okay nice

[dire turtle]

took some while but yea

its aight now

[crimson sedge]

Yep that's gucci

[dire turtle]

🙂

im still in geo tho

half way there

[crimson sedge]

Oh yea

I saw ur q yesterday

With like the bi sector thingy

[dire turtle]

wasnt so hard compared to now

[cedar kiln]

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[dire turtle]

yee

[dire turtle]

whoops

[crimson sedge]

Oop

.close

[cedar kiln]

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[crimson sedge]

What do u have now tho lol

[dire turtle]

just some geo question u wanna see it?

[crimson sedge]

Sure just DM me I guess because this is closing

[dire turtle]

aight

[cedar kiln]

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[cosmic steppe]

W = FΔx

F = ma

[wraith dagger]

donut

[cosmic steppe]

Maybe

I'm not too keen with physics so I can't assess whether it's correct

[cedar kiln]

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[cedar kiln]

@bold mauve Has your question been resolved?

[cedar kiln]

@bold mauve Has your question been resolved?

[cedar kiln]

@bold mauve Has your question been resolved?

[cedar kiln]

@bold mauve Has your question been resolved?

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✅

[cedar kiln]

@bold mauve Has your question been resolved?

[eager sparrow]

@bold mauve for 1, define first delta x and x_i

delta x = b-a/n

a= 40, and b=110

so x= 70/n

then for xi = a + i(delta x)

so xi = 40 + i(70/n)

Let me get back here in about 25 minutes I still have a job to do

[eager sparrow]

Ok I'm back

So have you finished any work now @bold mauve ?

Bring out a piece of paper and try to write my messages.

So that I can sure you're doing the right thing

So multiply delta x and xi

(40 + 70i/n)delta x

[eager sparrow]

@bold mauve Sorry about that

The inside is 0.7 (110-x)

Little busy today rn

[eager sparrow]

Delta x = b-a/n

So 40-0/n

delta x = 40/n

And xi = a + delta x times i

so xi = 0 + (40/n)i

xi = 40i/n

We know that work is equal to fd

And we know that weight = mass times acceleration

so Work = integration of (0.7(delta x))

so f(x) = 0.7 x

Let x = xi

f(xi) = 0.7 (40/n)(i)

Find the summation of i = 1 to n

Sum of (f(xi)(delta x))

(0.7 (40/n)(i))(40/n)

Since i is just multiplying other numbers, according to the summation rule, you can just factor the other terms

Summation of i

And we know that the summation of one number is the arithmetic series

so sum of i = n(n+1)/2

(0.7(40/n)(40/n)(n(n+1)/2)

try to simplify it

You will get (800n + 800 )/n

Try to make it in a form where the denominator n is alone with only one number

800 + 800/n

and we know that everything divided by infinity is 0

so 800+0

800

same can be done with question 2

just make delta x = (20-0)/n

since delta x = b-a/n

[cedar kiln]

@bold mauve Has your question been resolved?

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[oblique loom]

]

[oblique loom]

no idea where to start

.close

[cedar kiln]

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[short token]

in ideal generated by a subset of commutative ring with unity is given as

[short token]

here

we dont know about the order of A

[tropic oxide]

what is your question?

[short token]

do we use all of elements of A here

[tropic oxide]

not necessarily

tbh i think this would've been better written as $$\curly{\sum_{k=1}^n a_k r_k \mid {\color{red} n \in \bN}, a_k \in A, r_k \in R}$$

[wraith dagger]

Ann

[tropic oxide]

the ideal generated by A consists of all finite R-linear combinations of elements of A

if A itself is finite, you might as well take the whole lot, but if A happens to be infinite, you don't want to allow yourself to take infinite sums lest convergence bullshit get in the picture

[short token]

but i dont get why (A) is ideal

or

if a,b is from (A)

[tropic oxide]

would you like me to check it against the formal defn of an ideal in front of you?

[short token]

why a-b is also in (A)

because lets say

|A| = 8

[tropic oxide]

A = {8}, you mean?

okay, A has eight elements

[short token]

then (A) can be linear combinations of 4 elements of A

but what if we take

different 4 elements

2 times

[tropic oxide]

bad wording

[short token]

yeah ik

😄

wait

[tropic oxide]

i mean like

the sum of two finite R-linear combos is itself another finite R-linear combo

perhaps with more terms than the former two

something like $(a_1 + 6a_2 + 3a_3 - 6a_4) - (a_4 + 4a_5 + 10a_6 + 3a_7)$

[wraith dagger]

Ann

[tropic oxide]

where a_1 through a_7 are members of A

[tropic oxide]

no

if A = {a, b, c, d} then (A) = {r_1 a + r_2 b + r_3 c + r_4 d | r_k in R}

(also you missed an opening curly brace)

[short token]

so linear combination using all elements

[tropic oxide]

the ideal generated by A consists of all finite R-linear combinations of elements of A
if A itself is finite, you might as well take the whole lot,

but if A happens to be infinite, you don't want to allow yourself to take infinite sums

[short token]

oh

[tropic oxide]

any linear combination can be "padded" with zero-coefficient terms w/ the "missing" elements of A

[short token]

yes

so what if A is infinite then

infinite sum

ok

😄

or maybe

[tropic oxide]

am i getting through at all

feels like i'm not

you're compelling me to repeat myself a 3rd time here

[short token]

i didnt see the "dont"

[tropic oxide]

that's a pretty crucial word to just not see

[short token]

im trying not to waste time 😦

ok i got it ty

.close

[cedar kiln]

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[late lintel]

I need help.

Lesson is Quadratic functions System equation, (Finding the values of A,B,C)

[tropic oxide]

,rccw

[late lintel]

oo thank you!

[tropic oxide]

okay, so that is a system of linear equations

do you know how to solve systems of linear equations in general?

[late lintel]

sadly i do not

[tropic oxide]

do the names of methods such as substitution and elimination ring any bells?

[late lintel]

yes i do remember the teacher discussing those methods however i still do not know how to solve for any of those 2 methods

[tropic oxide]

so you remember the teacher discussing these methods, but you do not remember the methods themselves?

[late lintel]

technically yes, i remeber the teacher discussing them but i dont remember how to solve with those methods i wasnt really paying much attention at the time

[tropic oxide]

not sure why you say "technically" but ok

ok, so let's first write our system of equations clearly:

100a + 10b + c = 23
400a + 20b + c = 22
625a + 25b + c = 40

so there are a few different ways we could proceed here

[late lintel]

mhm?

[tropic oxide]

here's one i think could be least error-prone

take the first equation and subtract it from the other two

do you understand what that means or should i spell it out

[late lintel]

no worries i follow

[tropic oxide]

okay

in this case, do as i told and tell me the equations you end up with.
if you do it correctly (and don't jump the gun), you will have the first equation (100a + 10b + c = 33) left intact, and the other two equations should contain the letters a and b only.

ping me when you are done with this step - we are not done yet. i will instruct you on the next step afterward.

[late lintel]

@tropic oxide heres what i got 300a + 10b +c=1 and 525a+15b+c=17

[tropic oxide]

incorrect. show your work so that i may correct your mistakes.

[tropic oxide]

ok so no work to speak of

you tried to do it in your head and messed up in several places

first off, 22 - 23 is -1, not 1

and second, the c's should have cancelled out

(400a + 20b + c) - (100a + 10b + c) = 400a - 100a + 20b - 10b + c - c = 300a + 10b

not 300a + 10b + c

[late lintel]

ohh

[tropic oxide]

generally, you should not do things in your head unless you are 100% confident that you could do them correctly if you were woken up at 3 in the morning and made to do them at gunpoint.

[late lintel]

should i end up with 2 equations left?

[tropic oxide]

three equations, but the next step will only involve two of them.

[late lintel]

so will the first equation still be there, even if its not used?

[tropic oxide]

we will use it later.

[late lintel]

alright im ready for the next step :>

[tropic oxide]

okay, so you should now have:

300a + 10b = -1
525a + 15b = 17

this is a 2×2 system, in case this makes it more familiar to you

[late lintel]

famillar but still kinda off

[tropic oxide]

well, just to give you some perspective

what we've done so far is we have eliminated c (from all equations except one - the one we'll use to solve for c later)

we can now keep going in almost the same fashion to eliminate, say, the variable b

[late lintel]

do we divide it with its GCF?

[tropic oxide]

but this time we will need to adjust things a little

before we can subtract one equation from the other, we need to make sure that the coefficient on b is the same in both - that'll ensure that cancellation happens as we want it to

dunno what "it" means

[late lintel]

and how would that happen?

[tropic oxide]

well, the coefficients on b right now are 15 and 10

we could of course multiply the top equation by 1.5 but that would introduce decimals

which we don't want since decimals are harder to work with than integers

(or more error-prone rather)

so instead we can multiply by 3 on the top equation and by 2 on the bottom, yielding this:
900a + 30b = -3
1050a + 30b = 34

and now we can subtract one from the other

do you understand how to continue from here?

[late lintel]

what was the reason why we picked 3 and 2 as numbers to multiply these equations?

[tropic oxide]

the lowest common multiple of 10 and 15 is 30

30 = 10*3 = 15*2

i picked the multipliers so as to make the coefficients of b the same - and the common coefficient i chose to make is 30

[late lintel]

OHhhhhh that makes more sense

[late lintel]

so that would allow us to eliminate variable b?

[tropic oxide]

yes

mind you, we could have instead gone on to eliminate a - the reason i went with b instead is because its coefficients are smaller and easier to work with

[late lintel]

so we would be left with 900a=-3 and 1050=34?

[tropic oxide]

no. bad.

elimination does not mean just striking things out like you did...

[late lintel]

so what should i do??

[tropic oxide]

we can now keep going in almost the same fashion to eliminate, say, the variable b
but this time we will need to adjust things a little
before we can subtract one equation from the other,

[late lintel]

-150-37=0?

[tropic oxide]

are you just blurting numbers out at random?

[late lintel]

No? Y?

[tropic oxide]

well it sounds like you're doing just that

instead of placing pen to the paper and like

actually going through carefully with what i told you to do

[late lintel]

Im sorry i honestly dont know where i went wrong i subtract 900 with 1050 and -3 with 34

[tropic oxide]

you do not just subtract numbers from numbers

that's how you make a number smoothie

[late lintel]

i dont?

[tropic oxide]

well like

if you were a surgeon and this problem was a patient, then "i subtract 900 with 1050 and -3 with 34" sounds like "i rip out all of their organs and mash them together with my own two hands"

[late lintel]

can you point out whats wrong with my answer?

[tropic oxide]

everything

there's a more fundamental misunderstanding going on than just an algebra or arithmetic mistake.

ok, look. here are our equations again:

1050a + 30b = 34
900a + 30b = -3

subtracting the first equation from the second equation

first and foremost

means doing this

(1050a + 30b) - (900a + 30b) = 34 - (-3)

do you understand what just happened Y/N

[late lintel]

i sort of follow

[tropic oxide]

there's no "sort of", either you know what it means to subtract one equation from another or you don't.

[late lintel]

im kinda confused, do i add 900 and 30 or do i like subtract them by colum?

[tropic oxide]

no, you do not "add 900 and 30" for fucks sake they arent ISOLATED

stop making gore out of every equation you see

they dont appear in the equation as just the number 900 and just the number 30 they are MULTIPLYING some letters

would have to actively not look at the equation to not see that

simplify the left-hand side

do it CAREFULLY

ON PAPER

WITH YOUR PEN

AND HANDS

[late lintel]

150a=34-(-3)?

[tropic oxide]

ok great

now simplify the right-hand side

[late lintel]

150a=37?

[tropic oxide]

yes...

ok, now you should be able to solve for a

then solve for b and c using the previous equations we had

[late lintel]

A=0.246 B=30 C=1?

[tropic oxide]

is there a reason why you wrote the letters a, b and c in uppercase?

because you shouldn't do that.

and no, 37/150 ≠ 246/1000, so your value of a is wrong.

[late lintel]

oh No reason So after determining "a" does that sums up everything?

[tropic oxide]

no, you need to find b and c too

[late lintel]

so does that mean a=37/150, b=30 and c=1?

or is there a more further answer, if so can you explain i don't know how to further answer if there is a more further answer

so sorry if im giving you a hard time

[cedar kiln]

@late lintel Has your question been resolved?

[tropic oxide]

,w 100a + 10b + c = 23, 400a + 20b + c = 22, 625a + 25b + c = 40

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Ann#0413

[tropic oxide]

it looks like your values of b and c are wrong

[late lintel]

can you tell me how did b=-15/2 and c=220/3?

[tropic oxide]

well

maybe

you have the equation:

900a + 30b = -3

and you have your value of a, which is 37/150

are you able to find the value of b, given that a = 37/150 and 900a + 30b = -3?

if YES, then do it, write ALL steps on PAPER and send me a picture here.

if NO, then tell me "No, I am not able to solve for b" and i will walk you through it.

[late lintel]

No, I am not able to solve for b

[tropic oxide]

ok

are you able to replace a with 37/150 in the equation 900a + 30b = -3?

[late lintel]

222+30b=-3?

[tropic oxide]

,calc 900 * 37/150

[wraith dagger]

Result:

222

[tropic oxide]

ok, great

now, are you able to solve for b in the equation 222 + 30b = -3?

[late lintel]

252b=-3?

[tropic oxide]

no

222 + 30b is not the same as 252b

[late lintel]

-15/2

[late lintel]

can the value also be in decimal form?

[tropic oxide]

would rather you didn't do decimals.

would also rather see you do all steps on paper.

but i guess i'm not going to get that.

[late lintel]

oh was i suppose to put that on paper?

sorry my bad.

but what do i do for c?

[tropic oxide]

well, i asked you to do that, yes.

[tropic oxide]

now remember this.

100a + 10b + c = 23

this equation now comes back into the picture.

[late lintel]

mhm?

[tropic oxide]

you know the values of a and b

are you able to find the value of c?

[late lintel]

yes

[late lintel]

@tropic oxide sorry tp ping but can i ask what method did we use to answer? was it Elimination of Substitution

[tropic oxide]

assuming you meant "or" and not "of",

given that i have used the word "eliminate" several times during our convo and never said "substitute", i think it should be pretty clear that we in fact solved this system by elimination

[cedar kiln]

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[ocean scroll]

“Brooke plays volleyball and also plays the trumpet in the middle school band. Brooke spends two hours after school participating in volleyball activities. At home, Brooke practices playing her trumpet for 1/8 of the time that spends on volleyball activities at school. How long does she practice the trumpet?”

[cedar kiln]

@ocean scroll Has your question been resolved?

[ocean scroll]

<@&286206848099549185>

[tall hare]

she plays volleyball for 2 hours

but she practices trumpet for 1/8 that time

i suggest you to convert the hour in to minutes and then calculate

[ocean scroll]

120 times 1/8?

[tall hare]

exactly

that would be how many minutes she practiced the trumpet

[ocean scroll]

So 15 is my final answer then?

[tall hare]

15 minutes yes

nicely done

[ocean scroll]

Okay, Thankyou very much!

[tall hare]

have a nice day

[ocean scroll]

You too.

.close

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[ivory finch]

What is this?

What does it mean?

[tropic oxide]

do you mean "I cannot understand the meaning of the string of symbols |a+b| ≤ |a|+|b|" or do you mean "I understand this inequality as-is but not why it's called this way"

[ivory finch]

Both

Is that just <= sign?

Idk why it calls that "traingle inequality"

[tropic oxide]

yes, ≤ means "less than or equal to"

it has two different typographical variations, $\leq$ and $\leqslant$, which mean the same thing

[wraith dagger]

Ann

[ivory finch]

Wait is it just talking about if a or b are negative?

[tropic oxide]

no,

the inequality is true for all values of a and b

[ivory finch]

oh wait i think i get it

if a is 2 and b is -1

then the left side would be lesser?

[tropic oxide]

|2 + (-1)| is strictly less than |2| + |-1|, yes.

[ivory finch]

And then if it is both positive then it will be equals

[tropic oxide]

yeah, sure.

[ivory finch]

So this is just general statement

about absolute values

[tropic oxide]

yes

yes, this is a property of absolute values.

an important property, mind you.

[ivory finch]

i still dont get why its called "Triangle Inequality"

[tropic oxide]

right

well, you know that absolute values can be seen as distances, yes?

|x| is the distance between x and 0, or alternatively |x-y| is the distance between x and y

[ivory finch]

Yeah

[tropic oxide]

right

so then

you know the triangle inequality from geometry, yes?

that the sum of any two sides of a triangle is always longer than the third

[ivory finch]

Sure

[tropic oxide]

if you imagine a "triangle" with vertices x, y and z, the triangle inequality for it becomes |x-y| ≤ |x-z| + |z-y|

or, |(x-z) + (z-y)| ≤ |x-z| + |z-y|

[ivory finch]

can u draw that? i dont get it

all these terms confusing me

[crimson delta]

have you seen vectors?

in one dimension (aka just numbers) the triangle inequality is slightly harder to see cause triangles are 2-dimensional things

[cedar kiln]

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[night marsh]

Don't understand how my original integral could be simplified like this. What's meant by putting terms over a common denominator

[violet night]

$y+\frac{1}{y}$ all multiplied by y

[wraith dagger]

Clarkie

[violet night]

and to keep the equation the same

[night marsh]

Can I just do that

[violet night]

you have to multiply the top by y as well

because y/y is just 1

[night marsh]

ahaaa

lol

thank u, was too tired to see it

gonna close this now, arigato

.close

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[cosmic coral]

Hi guys need some help please. I have learning Disabilities sorry if spelling is bad am useing speech to text.

When i say COMMAND i mean that i press on my android calculator so i can learn what to press if you could please reply by saying what part for example
[ PART 1 100 X 10 = 1000] for each one below i would be turely grateful.

PART 1: Lets assume i want to BUY FC. I want to know how to use a calculator to work out Coreign Currency exchance rate and what i would get from UK POUND to EURO / USA

LART 2: Lets now assume I want to SELL EURO to pound how do i work that out useing a calculator because I know i would be getting a diffant lower amount so i dont know the calculation command as in what i would press on a calculator on my phone as i want to be able to do it.

PART 3 how do I calculate percentage of a certin amount of like $ / £ and

PART 4 also lets assume i want to get something on lease and i was charged a certin percentage per day or month how do i work that out and the intrest

PART 4: also how to i calculate fraction on a calculator please.

PART 5: lets assume a partliment has X number of seats how do i work out what two-thirds is.

PART 6: how do i work how intrest on X amount for X days or months.

[bitter reef]

1. You want euro / pound ratio, so you can do pound * euro / pound to get pound into euros.
2. You want the inverse, so the pound / euro ratio. Similar to part 1 you do euro * pound / euro.
3. To get the percentage from a ratio you multiply by 100. So 1 / 2 as a percentage is 1/2 * 100 = 100 / 2 = 50 so 50%
4. See the first image for interest formula. Fractions are just division represented in a better way. "÷" or "/" is used on most calculators.
5. Two thirds of a number is 2/3 times that number.
6. See part 4.

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[final gorge]

how did they get f(x)=x+f(0) from f(x+1)=f(x)+1

[final gorge]

<@&286206848099549185>

[cedar kiln]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[crystal raptor]

Give context

[crystal raptor]

Ah so you just need to follow the chain down

f(x+1)=f(x)+1 = f(x-1)+1+1=...

[final gorge]

oh

thanks

<3

.close

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[drifting solar]

Kinda confused on the partial derivatives here

This is what I'm working with atm

[cedar kiln]

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@drifting solar Has your question been resolved?

[drifting solar]

.close

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[wild karma]

How is it possible that the divergence of my vector field is zero, but yet the flux across a sphere with its normal vector is not zero? According to divergence theorem the flux across the sphere should be zero if the divergence of vector field is zero.

[cedar kiln]

@wild karma Has your question been resolved?

[wild karma]

The area is between a sphere centered at origin, and some object object which surrounds the sphere. The vector field is not differentiable at origin, but would divergence theorem still be usable for the area between the sphere and the other object?

[cedar kiln]

@wild karma Has your question been resolved?

[cedar kiln]

@wild karma Has your question been resolved?

[cedar kiln]

@wild karma Has your question been resolved?

[dire geode]

probably have a mistake. just show all your work

[cedar kiln]

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[upbeat mirage]

hello

[crimson sedge]

yo

[upbeat mirage]

i ave this problem for a practice quiz

this is what i think i need to do & what the notes say but i can’t figure it out

when i put it in the calculator it doesn’t come up with the right answer

[crimson sedge]

should be 0.06 i think

[shut idol]

Are u missing a bracket

[upbeat mirage]

the answer says 16,418.71

[shut idol]

Is correct

Ur missing a bracket

When using calculator

8500 x (1+ (6%/12))^(12x11)

[upbeat mirage]

ok i’ll try that cus when i put it in it says error

[shut idol]

And 6 percent is 0.06 not 0.6

[upbeat mirage]

omg it worked

thank you so much

am i allowed to ask multiple questions

[toxic moat]

lol

yes

feel free to ask it here

or close it and ask again

[upbeat mirage]

this one my friends helped me with & they say the answer that is marked correct is wrong is this true?

[crimson sedge]

,w simplify (4)/(root(14) - root(13))

[wraith dagger]

Results provided by WolframAlpha

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

Requested by hibyehibye#9497

[crimson sedge]

no its correct

[upbeat mirage]

woah that’s really cool

[buoyant latch]

I mean technically line 2 is wrong

[upbeat mirage]

i think that’s what they meant maybe i don’t really get how to do it after getting rid of the bottom stuff

[buoyant latch]

Do you know what you did from line 1 to line 2

[buoyant latch]

But why

[upbeat mirage]

no i have no clue

[buoyant latch]

Let’s look at this expression (a - b)(a + b)