help-43

[twin salmon]

What does L(M_k) denote exactly?

[livid spruce]

We denote a Turing Machine M_k if its encoding is the binary string w_k

And L(M_k) is the language of the turing machine

[twin salmon]

Ah so just what it accepts? I don’t have the encoding you are using for the Turing machines (there are many ways to encode them) outside of the fact that M_i corresponds to w_i but I’m guessing a good approach would be to consider the Turing machine that accepts everything. I’m supposing you are using a binary input alphabet as well

[livid spruce]

Yes a binary input, I can show you how we encode it one second

[twin salmon]

From there you can prove this is the smallest one in terms of length of encoding if it works

[livid spruce]

The symbol 0, 1 and B are encoded with 0, 00 and 000 respectively.
• The directions L and R are encoded with 0 and 00 respectively.
• Each state qi is encoded by i consecutive 0s.
• The initial state is q1 (there is no q0... obviously).
• The machine has only one final state denoted by q2 and encoded with 00.
This is always possible with TMs.
• The symbol 1 will be used as separator while encoding a transition, and
the string 11 will be used as to separate between two transitions.

[twin salmon]

And then just the transition function since the initial and final state are fixed (I’m guessing the final state is an accept state)? Try $(q_1, x) \mapsto (q_2, 0, L)$ for each x in the alphabet. the idea is to minimize each component of the Turing machine in terms of encoding

[boreal girder]

Elizabeth

[twin salmon]

You could then try proof by contradiction for a smaller machine and show that due to it being invalid it will have to reject everything

[livid spruce]

the final state is an accepting state, but idk why if I remember correctly my professor just picked the smallest encoding and then concatenated a 1 next to the encoding and changed it from binar to decimal

[twin salmon]

Wdym smallest encoding?

[livid spruce]

the smallest bits

that the machine accepts

[compact pewter]

@livid spruce Has your question been resolved?

[compact pewter]

@livid spruce Has your question been resolved?

[compact pewter]

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[flat inlet]

Question: find all pairs of digits (a,b) for which the number 2a6 divides 9b10. I am looking for alternative ways to arrive at the answer a=6,b=3 that is perhaps more efficient

[hushed magnet]

well if k is divisible by 5 and just from comparing 200 vs 9000 you know k is 40 or 45

or 35

whether the resulting casework is faster than what you have done, dunno

[hushed magnet]

effectively this gives you ell in {7,8,9}. 8 is easy to exclude, 7 was what you did at the end anyway, so then you would have to think about 9

[compact pewter]

@flat inlet Has your question been resolved?

[compact pewter]

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[flat inlet]

Thanks, I'll have a go using that method

[flat inlet]

.close

[compact pewter]

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[rough fjord]

on 3, since a = A and b = B, we prove that (Matrix(A) * Matrix(B))^2 is equal to a^2 b^2 right?

[compact pewter]

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[rough fjord]

isn't (Matrix(A) * Matrix(B))^2 = {{-1, 1}, {0, 1}}?

[rough fjord]

yet according to Quizlet, it is this

I got {{-1, 1}, {0, 1}} and Quizlet got {{-1, -1}, {0, 1}}

I checked mine with a matrix multiplier and mine is right apparently

[short lantern]

show your work because my answer matches the quizlet

they havent squared the matrix yet

thats probably why

[rough fjord]

no

it is my fault

just found my error

thanks anyways!

problem solved

[open girder]

.close

[woeful schooner]

.close

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[open sage]

Question 5

Why +-1 is also in domain? Doesn't it lead y = root(3) which is irrational but x and y should be integers as per given condition.

[balmy dawn]

It's ≤, not =

[spark folio]

you dont need y to be sqrt3, it could be 0

[open sage]

Ah, yes. I'm not use to inequations.

[severe remnant]

domain is the set of all values which R can take

now whats the issue with taking +-1 in either of x or y

[open sage]

Thank you all. I got it.

[severe remnant]

type .close @open sage to close it

[open sage]

.close

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[wary mulch]

is the p correct?

[compact pewter]

@wary mulch Has your question been resolved?

[kind viper]

tons and tons and tons of whitespace in that picture.

anyway, the period of a function ought to be positive, i would think.

but if you correct for that, then you get that the period is 2pi. which is in fact correct.

[wary mulch]

so u cannot have -

period?

[kind viper]

that is what i said

[compact pewter]

@wary mulch Has your question been resolved?

[terse coral]

pretty much

formally, a function is periodic if there exists a positive number T such that f(x + T) = f(x) ∀ x, which means it repeats its values at regular intervals

the smallest such positive T is called the fundamental period

it's also important to understand that the period and the frequency are inversely proportional

[compact pewter]

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[scenic sluice]

Doing group theory and struggling on having a deeper understanding of quotient groups. Ive tried reading my textbook but wondering if some can explain some intuition for it.

I understand quotients groups in the sense of the modulo like Z/nZ

but when it becomes more abstract groups i struggle what makes up the different cosets

[compact pewter]

@scenic sluice Has your question been resolved?

[mild sky]

so you are stuggling to compute quotient groups

?

[compact pewter]

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[scenic sluice]

.reopen

[compact pewter]

✅ Original question: #help-43 message

[scenic sluice]

Yes like given two groups i dont always know what there difference is that will make up the different cosets

[mild sky]

can you give an example? I don't quite understand you issue

[scenic sluice]

ive seen the answer now but GL2(R)/SL2(R)

like identifying that i the two cosets differ by one having det =1 and det = -1

[mild sky]

In this case for example you have a homomorphism $\mathrm{GL}_2(\bR) \rightarrow \bR^*$ given by $A \mapsto \det(A)$

[boreal girder]

ExpertEsquieESQUIE

[mild sky]

this homomorphism has kernel $\mathrm{SL}_2(\bR)$ and its surjective, so by the first isomorphism theorem $\mathrm{GL}_2(\bR)/\mathrm{SL}_2(\bR) \cong \bR^*$

[scenic sluice]

yeah alright

[boreal girder]

ExpertEsquieESQUIE

[mild sky]

and even more explictly, the isomorphism is $A \cdot \mathrm{SL}_2(\bR) \mapsto \det(A)$

[boreal girder]

ExpertEsquieESQUIE

[mild sky]

so what I have shown here that the cosets are determined by the determinant of their elements, so they are of the form of all the matrices with the same determinant

[scenic sluice]

how do i know when given that im considering their determinants

like i know now

[mild sky]

are you asking where does this come from?

a hint about this comes from the definitions of GL and SL

since Gl is all matrices of non-zero det

and SL is all matrices of det 1

[scenic sluice]

yeah

so for the case of C^x/S_1

since S_1 is C^x but restricted to magnitdue of 1 i should be think that the magnitude will be the difference in cosets??

[mild sky]

what is C^x

[scenic sluice]

can i just think of it as , an elemtn of C^x will have form re^itheta and element of S_1 will have form e^i*theta, si what is left is just the magnitude of each element

the complex not including 0 my bad

[mild sky]

oh right

yep this seems right

[scenic sluice]

so think about what makes the subgroup different and use that quality to figure out what the different cosets would be

[mild sky]

quotient groups in general are characterized by the equivalence relation $$a \sim b \iff ab^{-1} \in H$$

[boreal girder]

ExpertEsquieESQUIE

[scenic sluice]

lovely

[mild sky]

so for |ab^-1| to be in S1, a and b must have the same magnitude

[scenic sluice]

ohhh

[mild sky]

this works nicely again because |?| is a homomorphism

[scenic sluice]

wait that makes sense

thank you thank you

[mild sky]

nice

[scenic sluice]

.close

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[hoary cradle]

how to prove this

[kind viper]

come up with a combinatorial interpretation for that fraction, i guess?

[hoary cradle]

??

[kind viper]

come up with a permutations and combinations question that would have this as an answer

[compact pewter]

@hoary cradle Has your question been resolved?

[hoary cradle]

wait

im here

now what

[winged lion]

that doesnt seem right

[hoary cradle]

yes

so what should i do instead

[hushed magnet]

one option is to let f(n,m) be that thing and then work out a recurrence

[hoary cradle]

i dont know what that is

[hushed magnet]

another is to consider how often a prime p divides denom and numerator and show that it divides the numerator at least as many times as the denom

[hoary cradle]

,,\frac{\binom{2m}{m}\binom{2n}{n}}{(m+n)!} = = \binom{2m+2n}{m+n}.

,,\binom{2m}{m}\binom{2n}{n}}= \binom{2m+2n}{m+n}.

,,\binom{2m}{m}\binom{2n}{n}} =\binom{2m+2n}{m+n}

[hushed magnet]

its an old imo problem so you will need more than just simple rewriting

[hoary cradle]

which year

[hushed magnet]

1972

[hoary cradle]

ohh

ok fine thanks

.close

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[flint wing]

im confused how we get m<=n

[urban kindle]

(n+1)/2<=n

[flint wing]

huh

[urban kindle]

n is at least 1

[flint wing]

ye

[open girder]

n+1 = 2m implies m = (n+1)/2 so when is (n+1)/2 <= n?

And it should make sense intuitively why m<=n

[flint wing]

oh so u subtitute

[open girder]

If m = n+1, then 2m = 2n+2 which is clearly greater than n+1.

[flint wing]

i see

thanks

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[lofty mountain]

need help

Time speed distance is the topic

[kind viper]

let's recast the same problem with the same numbers but an entirely different setting.

Cities A and B are 819 km apart. Two high-speed trains leave the stations in each city at the same time.

The train headed from A to B is moving at 200 km/h. The train headed from B to A is moving at 150 km/h.

How far from city A will the two trains pass each other?

[lofty mountain]

root (Time 1st × Time 2nd)

[kind viper]

??

[lofty mountain]

or 819 / 200+150

[kind viper]

where is any of this coming from

it sounds like you just tried to guess a formula

twice

[lofty mountain]

that's what the teacher taught me

[kind viper]

just magic formula with zero explanation got it

[lofty mountain]

first one is the formula to find the meeting point

[kind viper]

,rccw

[kind viper]

can you un-crop this

i want to see entire question that this came from

i for one have no idea why you even would have roots in the question you sent originally

[lofty mountain]

wait i am sending

1st statement is another meething point concept

i know i am wrong

but after reading the question..only these came to mind

@kind viper

[kind viper]

does t1 mean time for B to cover segment BP?

oh, no

apparently T1 and T2 are the times taken for each train to reach their destination after meeting.

this just means nothing for us at all.

completely irrelevant to the question.

[lofty mountain]

oh

[kind viper]

so all formulas involving T1 and T2 that you sent also are useless for us right now.

[kind viper]

this is simpler: the trains are approaching each other at a combined speed of (200+150) km/h. use this to figure out the time until they meet

and then how much the train from A travelled in that time

it is simple distance-speed-time concept, no roots necessary, none of this fancy shit that applies only in questions designed specifically for these formulas.

[lofty mountain]

819/350

[kind viper]

if you say number only i will PURPOSEFULLY understand it in wrong way to force you to explain yourself.

[lofty mountain]

do i have to divide it...and change it inti points

[kind viper]

no you have to say what this 819/350 represents.

[lofty mountain]

time they meet

[kind viper]

right.

"time to meet is 819/350 hrs"

is how i expected you to say this

not very long to type unless your fingers fall off

[lofty mountain]

they asked for the page no.

@kind viper

[kind viper]

no they asked for line no.

no pages.

[lofty mountain]

yes..i mean

[kind viper]

any case i told you what to do afterwardxs.

reread what i said earlier

or should i repeat?

[lofty mountain]

?thus

this

[kind viper]

maybe i should learn hindi so you understand better.

[lofty mountain]

haha...i understand basic english

[kind viper]

igure out the time until they meet
and then how much the train from A travelled in that time

[lofty mountain]

A wrote 370 pages

right?

[kind viper]

did you mean 370 LINES not pages? why do you keep saying pages?

[lofty mountain]

oh sorry

my bad

i was going to write line

[kind viper]

anyway how did 370 come

[lofty mountain]

BAD INT

wait

oh...it will be 200

its 468

[kind viper]

every time you give a new number i will always ask how it came

[lofty mountain]

i am making lot of mistakes

[kind viper]

you can say 5824 or 82342 or 83582 or 1818283 or 5821823 or 7819999999

but with no calculation to show how you got it it will be useless EVEN IF right answer

[lofty mountain]

sorry..i noted

[kind viper]

ok yes 468 is correct

A wrote 468 lines from start

[lofty mountain]

what if i write B's speed

there

what is going to be found

[open sage]

Find it and add it to 468

You'll find a known no. given in question

[kind viper]

the number of lines written by B

[lofty mountain]

the question didn't tell about from first or from last

[kind viper]

yes it did

it says the boy writing 200 lines/hr went from start and other went from end

read it again

[lofty mountain]

at the end
?

ok

nvm

thank you ann

.close

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[round pier]

im confused how this is wrong

[barren horizon]

where does cos(√...) come from?

[round pier]

sinx derivative

[slate sand]

Look at the first time on the top

-cos sqrt …?

[round pier]

yeah

sinx derivative

chain rule

d/dx root(1-sin) = 1/2(1-sinx)^-1/2 * -cosx

= -cosx/2rt(1-sinx)

i then bring the 2sqrt term to the denominator

then quotient rule says denominator

-cos *g(x)

and i STILL got it wrong?

[slate sand]

Why is there sqrt inside the cos..

[round pier]

this?

i just explained it

[round pier]

^

[slate sand]

What??

Look closely

Isn’t there supposed to be an x

[round pier]

how

oh wait

its still wrong

it gave me a new question instead lol

what was the correct answer to the previous one @slate sand

i still dont get what i did wrongf

[wicked pelican]

how did you solve this question

i bet its not mental math
So i need the steps you do it

[compact pewter]

@round pier Has your question been resolved?

[round pier]

i can just send the pic if you want

well, if youre still here

[wicked pelican]

Yep please

[round pier]

okay

Only look at the first 4 lines of the page

What I like to do with weird derivatives is to find the derivative of each component

The answer is incomplete on my book though

But essentially I found f’, g’ and plugged it in

[wicked pelican]

Its 7-sinx not 1-sinx

[round pier]

i thoughtbyou meant for this

my bad

well, i left the new one for later since it was stressing me out

but if i can solve the old one i can do the new one

[wicked pelican]

misread ah

Sorry

Lemme check

[round pier]

its ok

[compact pewter]

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[round pier]

.reopen

[compact pewter]

✅ Original question: #help-43 message

[round pier]

also for this derivative,

i keep checking it over

it keeps marking it wrong

[wicked pelican]

👍

[round pier]

like how is this wrong

[wicked pelican]

So you mean the answer in the box is wrong

[round pier]

yeah

when i simplified

mayube its because i didnt put parenthesis on it

on the denominator

[wicked pelican]

No

Not the bracket matter

[round pier]

yeah then i dont know lol. i assume its at least correct

if its correct i wont worry about anything else

[wicked pelican]

You might did something wrong in product rule

Like you missed something out

Answer is close

[round pier]

but even when i asked ai it had the same answer

its fine tbh ill just ask in office hours

thanks for the help. appreciated @wicked pelican

.close

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[vocal matrix]

Is there any short way to do this?

[vocal matrix]

My proof ended up taking a couple pages and I'm not sure it's airtight

Basically I reasoned that some series of elementary matrices could transform A into U, the upper echelon form

[swift sun]

Using Laplace expansion this would be a one-liner

[vocal matrix]

haven't learned that 😭

[vocal matrix]

and every single one of these elementary matrices had some corresponding elementary matrix for the augmented matrix

[swift sun]

In general though, if you have a block diagonal matrix (which you do here), a nice result is that the determinant is equal to the product of the determinants of the blocks

[vocal matrix]

hm, that's interesting

just found out about the term

[swift sun]

It even holds in a stronger way:

If the matrix is upper-triangular with block diagonal matrices, then the determinant is still the product of the determinants of the blocks

$\det \left(\begin{matrix}A&B\ 0&D\end{matrix}\right) = \det(A)\det(D)$.

[boreal girder]

Kepe

[swift sun]

Well anyways that's just for the more general case lol

[vocal matrix]

yeah it would be very helpful if I managed to learn why that was true

[short ferry]

do you know some thms about determinants already?

Like the computation thingy when you expand along some row and write it as sum of determinants of smalelr matrices

[vocal matrix]

some, just learned it recently

[vocal matrix]

not yet

[short ferry]

then maybe the elementary matrices, it doesnt look so bad

maybe your prof just included quite a lot of details

if you look at it intuitively, you can do exactly the same row operations (just shifted one row down) and it'll bring the A part to row-echelon, while not changing the first row and column

[swift sun]

IIRC the proof uses the Schur complement

[vocal matrix]

basically what I did, I just used a lot of paper since it took a lot for me to write this out formally

[short ferry]

yeah, the proof in its essence is quite elegant and simple, it's just tedious to fill in all the little details

[vocal matrix]

proving this happened to be my exact next question so I would appreciate if you could help me here

steps I have thus far

[swift sun]

Something along the lines of this: \ \li \ Say we have $\mathbf{M}=\left(\begin{matrix}\mathbf{A}&\mathbf{B}\ \mathbf{C}&\mathbf{D}\end{matrix}\right)$ and $A$ is invertible (don't worry this won't impose a restriction later, we can use limits). Then [\mathbf{M}=\left(\begin{matrix}\mathbf{I}&\mathbf{0}\ \mathbf{CA}^{-1}&\mathbf{I}\end{matrix}\right)\left(\begin{matrix}\mathbf{A}&\mathbf{0}\ \mathbf{0}&\mathbf{D}-\mathbf{CA}^{-1}\mathbf{B}\end{matrix}\right)\left(\begin{matrix}\mathbf{I}&\mathbf{A}^{-1}\mathbf{B}\ \mathbf{0}&\mathbf{I}\end{matrix}\right).] Now hopefully you know that $\det(AB) = \det(A)\det(B)$. Then we get [\det (\mathbf{M})=\det \left(\begin{matrix}\mathbf{I}&\mathbf{0}\ \mathbf{CA}^{-1}&\mathbf{I}\end{matrix}\right)\det \left(\begin{matrix}\mathbf{A}&\mathbf{0}\ \mathbf{0}&\mathbf{S}\end{matrix}\right)\det \left(\begin{matrix}\mathbf{I}&\mathbf{A}^{-1}\mathbf{B}\ \mathbf{0}&\mathbf{I}\end{matrix}\right).] Now if you set $\mathbf C = 0$, then the first determinant is just $1$. The second stays like that and the third is $1$ again (just by multiplying it out, it's a bit tedious but you can actually write out the large matrix and see that the only summand that will be $1$ is the diagonal one, every other one contains a $0$). \ \li \ And so we reduced the entire thing to just a block diagonal matrix

[boreal girder]

Kepe

[vocal matrix]

what is S?

[swift sun]

Ok and now we still need that the det of a block diagonal matrix is the product of the dets

[vocal matrix]

if I never learned it before, could I assume you could treat blocks like scalars?

[swift sun]

That's the D - CA^(-1)B thing

We care about C = 0 anyways though so S = D

[vocal matrix]

I see

pretty clean chain of logic

[vocal matrix]

assuming this is true

[swift sun]

Yep, you can actually write out every block and do the whole multiplication but as I said it's tedious

But lets you confirm this

[vocal matrix]

alright thanks, I'll open a new ticket if I run into issues

best, thank you both

.close

[compact pewter]

Channel closed

Closed by @vocal matrix

Use .reopen if this was a mistake.

[compact pewter]

Available help channel!

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[modern arch]

Number a6)

[chilly basalt]

,rccw

[chilly basalt]

Right, what’s your doubt?

[modern arch]

How do I find the consecutive numbers between 3(pie)

[chilly basalt]

Can you assess the number of pi?

[modern arch]

3.141592654

[chilly basalt]

Right, times three then you’ll get the result you want

If you’re having problem with how to do it in general, here’s a rule for you

[modern arch]

9.42477961

But how do I use this

[native shard]

without using a calculator

[modern arch]

🥀

[chilly basalt]

That number is between 9 and 10

[chilly basalt]

^^ wanna check it out?

[native shard]

your idea should be to bound 3pi between two numbers whose difference is at most 1

[modern arch]

Yes

[modern arch]

How do I bound it

[native shard]

so here we know that 3 < pi clearly but also pi < 3.2.

[modern arch]

Wdym also pie

I don’t get it

[chilly basalt]

Look, we already know that pi =3.14XXXXXXXX

Do you agree with this?

[native shard]

its pi, not pie

[modern arch]

Yes

[modern arch]

Mb

[kind viper]

.. but also, pi < 3.2

[chilly basalt]

So we assess the value of 3.2x3 and 3.1x3, because they’re the number on 3pi’s left and right

[kind viper]

\*

[kind viper]

you mean 3pi's left and right

[chilly basalt]

Right 😔

[kind viper]

3.1 < π < 3.2
therefore
3×3.1 < 3π < 3×3.2

@modern arch does this make sense to you

[modern arch]

How did u get 3.1

[native shard]

i mean you can just use 3

[kind viper]

how many decimals of pi do you know

[native shard]

both work

[modern arch]

Oh it’s less

[chilly basalt]

We’re just looking for their neighbors

[modern arch]

Ic

[kind viper]

we are looking for some numbers close to pi yeah

there is some freedom of choice there

[modern arch]

So 3x pi?

[native shard]

$3 < \pi < 3.2 \implies 3 \cdot 3 < 3\pi < 3 \cdot 3.2$

[boreal girder]

knief

[kind viper]

this is also exactly what i said.

[kind viper]

right here

[native shard]

im aware ann

[kind viper]

well ok

not exactly

you use 3.0 instead of 3.1

but the idea is the exact same

[native shard]

yes because they asked about 3pi

[native shard]

^

idk i think its more natural

🤷‍♂️

[modern arch]

Wht does this mean

[native shard]

secret code

anyways do you get the inequality

either anns

or mine

[modern arch]

No

[native shard]

tough

[kind viper]

ok let's start again then shall we?

if i say that
pi lies between 3.1 and 3.2

do you understand that

[modern arch]

Yes

So something slightly higher and lower than pi

[kind viper]

so then, based on that,

we can say that 3pi lies between what and what?

[modern arch]

2 and 4?

[kind viper]

how tf did that happen

[native shard]

maybe you confused it with pi lies between 2 and 4?

[modern arch]

So something between 3.1

[kind viper]

how did the numbers 2 and 4 come about

[kind viper]

no you're thinking in the wrong way i think

[modern arch]

Lie between 3?

[modern arch]

Oh

[kind viper]

ok

forget pi

just forget pi entirely for now until we come back to it

[modern arch]

Ok

[kind viper]

imagine there's a certain gizmo that you remember seeing at the mall, and you don't remember how much it cost exactly

but you remember that it cost more than €50.

[modern arch]

Yes please

[kind viper]

then you can say with certainty that

4 gizmos cost more than _____.

fill in the blank

[modern arch]

50

[kind viper]

i mean yeah duh, but you can put a bigger number than that.

[modern arch]

60

[kind viper]

ok no stop guessing

[modern arch]

It like 55

[kind viper]

1 gizmo > 50
4 gizmos > ?

[modern arch]

Like this?

[native shard]

where did 30 come from

[kind viper]

you kinda overthought this again even tho now it's vaguely on the right track

[modern arch]

It’s 50

[kind viper]

bad handwriting for sure

[modern arch]

💔

I was writing fast

[kind viper]

well don't write fast then

this isn't a speedrun

[modern arch]

Yes please

[solemn matrix]

it does not take you a whole minute to write a digit

just write normally

[kind viper]

you should have said that

4 of these gizmos cost more than 4×€50

do you understand

yes or no

[modern arch]

Yes

[kind viper]

ok

let's try a similar thing again...

if some other thing at the mall was sold for something less than €70 per unit,

then you can be certain that 5 of those things will cost less than _____.

fill in the blank again

this is like, basic multiplication with inequalities that you have to really just not overthink

i don't know how to put it any other way

[modern arch]

I got 350

Bc I mupltied it

[kind viper]

that spelling is a bit 🥀

[modern arch]

Multiplied

[kind viper]

yes so

[modern arch]

I’ll type slower too

My bad

[kind viper]

if x<70 then 5x<350

good

ok

now we come back to the extremely scary case when there's not one inequality but two

3.1 < π < 3.2

do you agree or disagree with this inequality firstly

do you understand pi lies between 3.1 and 3.2 yes or no

[modern arch]

No

[glossy steppe]

Pi=3.14159265359

Skittle ^^^

[modern arch]

Ok

[kind viper]

let's not pretend pi stops at eleven decimals tho

[glossy steppe]

ok then buddy

[kind viper]

@modern arch do you know how to compare decimals

[glossy steppe]

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679

[kind viper]

as in how to tell which one of two decimals is bigger

[modern arch]

Kind of

[kind viper]

there's no kinda, you either do or you don't.

[modern arch]

Then no

[kind viper]

you are being obstructive.

[glossy steppe]

im sorry but i was trying to help you started iit

[kind viper]

ok, do you know how to compare integers

[modern arch]

Yes

[kind viper]

ok

so how do you tell which of two integers (numbers without a decimal) is bigger

[modern arch]

CAn u give an example

[modern arch]

Their value

[kind viper]

sure i guess.

35358 vs. 1154

who is bigger and how can you tell

[kind viper]

mmmm that's gonna be a no

[modern arch]

Oh

[kind viper]

there's gonna be another example coming

but for now tell me how we can tell which of the numbers

35358 and 1154

is bigger just by looking at them on the page

[modern arch]

35358

Has more numbers

[kind viper]

has more digits.

[modern arch]

Digits

[kind viper]

ok.

what if the amount of digits is the same for both numbers? what do you do then to compare them?

[modern arch]

The first digit

[kind viper]

and if the first digits also match?

[modern arch]

Second

Or Ty r following digit

[kind viper]

ok and can you say it more generally

[modern arch]

The next digit

[kind viper]

when two numbers have the same amount of digits, we start at their leftmost digits and go left to right until we find a pair of digits that aren't the same.

[modern arch]

Oh yes

[kind viper]

this is the same logic that also works for comparing decimals

• are the integer parts (before the decimal point) the same? if not, compare those. if yes, continue.
• if the integer parts are the same, compare the decimal parts digit by digit, left to right. if one of the decimals stops, all of its digits from then on are 0.

do you understand this

[modern arch]

Yes

[kind viper]

ok let's try this then. round 1

a = 7.3563
b = 7.3502

who is bigger?

[modern arch]

A

[kind viper]

ok good

would prefer lowercase a bc it IS possible to turn off auto capitalization but ok

round two

[modern arch]

sorry

[kind viper]

c = 0.6
d = 0.11

who is bigger?

[modern arch]

c

[kind viper]

why?

[modern arch]

Bc the second digit of c is greater than the second digit of d

[kind viper]

right

i would say the first digit after the decimal

but yes that's correct

now

3.1 = 3.1000
pi  = 3.14159...
3.2 = 3.2000

[modern arch]

3.2

[kind viper]

i didnt ask you to say who is biggest among these

[modern arch]

Oh

[kind viper]

even though 3.2 actually is

but now that we have gone over how to compare decimals

do you NOW understand that 3.1 < pi < 3.2 ?

[modern arch]

yes

[kind viper]

ok

now what i want you to do is

take this inequality i just wrote

and multiply everything by 3.

[modern arch]

ok

[kind viper]

good ok.

we got to here.

... if you're writing by hand you should use the π symbol but like. ok. whatever.

so now 3pi lies between 9.3 and 9.6.

[modern arch]

ok

[kind viper]

can you show this on a number line with integer points marked on it

it doesn't need to be to-scale but it does need to be accurate

[modern arch]

I don’t think I can

[kind viper]

mmmm.

well

if a number lies between 9.3 and 9.6, between what two integers will it be?

[modern arch]

Are they suppose to be in decimals?

[kind viper]

who are "they"

[modern arch]

The number between

[kind viper]

.........

an integer is by its nature without a decimal part.

[modern arch]

Ic

[kind viper]

ok look

9.3 lies between ___ and ___.

fill in the blanks here with two consecutive whole numbers.

[modern arch]

8 and 10?

Idk how to do this

[kind viper]

8 and 10 aren't consecutive

[stable viper]

Close but make the numbers consecutive (Like 1 and 2; 3 and 4)

[modern arch]

9 and 10

[kind viper]

right

in fact here, let me show you what i meant with the number line thing.

[modern arch]

yes please

Ty

[modern arch]

Ohhh

Could I ask for help w another thing

[kind viper]

well you just did but sure ig

[modern arch]

I don’t rlly get the arrows

[kind viper]

they are drawn in weird places

but they're supposed to signify that the sets continue off to the left or to the right respectively ig

[modern arch]

Ohhh

Tysm Ann

I’m so sorry for being dumb

[kind viper]

...i outright refuse to attach or confirm any such labels.

[modern arch]

Oh

Ty

Also

for the example b

Why is 1 like a line

Instead of a spot

[compact pewter]

@modern arch Has your question been resolved?

[modern arch]

.close

[compact pewter]

Channel closed

Closed by @modern arch

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[regal mango]

I have a doubt about power rule

[dull moon]

just post the doubt. you need not ask before posting

[chilly basalt]

Right, what is your doubt? Could you be more specific?

[chilly basalt]

,rccw

[regal mango]

This is the rule Right

[chilly basalt]

mhm

[regal mango]

Then how does this under line eq come out?

[storm tusk]

This is by application of chain rule

[regal mango]

How

[storm tusk]

What does chain rule state?

[regal mango]

Let me check

Idk 😐

[kind viper]

https://www.youtube.com/watch?v=0T0QrHO56qg

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

[regal mango]

Why we have to take another darivative

Why we have to take another darivative of inner eq

[storm tusk]

Well, chain rule says so

I’m not sure I understand

[regal mango]

@storm tusk Thanks for trying to help!

@kind viper @storm tusk @severe remnant Thanks for helping me but now my confusion is clear by this video

Check this

[severe remnant]

thats the very definiton of chain rule

u HAVE to keep differentiating until the inner fxn has been differntiated fully

[regal mango]

.close

[compact pewter]

Channel closed

Closed by @regal mango

Use .reopen if this was a mistake.

[compact pewter]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[trail sluice]

Can someone give me an oppinion on this. Does this sound interesting?

[rigid perch]

uhh that sounds like misunderstanding the complex numbers

[trail sluice]

yes, indeed. Hi Cloud. Thanks for your time. Let me post the rest. Then it should make more sense to you

[rigid perch]

so like $i = \sqrt{-1}$ is just an informal definition we give to students for intuition. it's not the actual definiton of $i$

[boreal girder]

cloud ☁

[kind viper]

nobody actually defines i as the result of applying the square root function to -1.

[trail sluice]

so to what is i defined then?

[kind viper]

there are several ways to construct C which are internally consistent

all of them of course contain an element whose square is equal to -1, and this element thus deserves to be named as "i"

there are 3 constructions i can think of off the top of my head:

• ordered pairs with explicitly defined + and * operations
• quotient ring (a.k.a. modular arithmetic on polynomials)
• matrices

which one would you like to hear

[trail sluice]

it doesn't really matter how many layers you put on top. In the end, you end up with something that is the square root of -1, don't you?

[kind viper]

you end up with something that solves the equation z^2 = -1

which, sure, is "a square root of -1" by any other name.

only that's not a starting point

it's a consequence of whatever construction you use

[trail sluice]

I think you're just contradicting yourself. Here's a question: what's the square root of -25? can you calculate it?

[kind viper]

where am i contradicting myself exactly?

[hushed magnet]

in the natural numbers 7/2 is also not allowed

but so what

we extended from the natural numbers to a system where you can do that

[kind viper]

once C is constructed, in whatever fashion you like, the two square roots of -25 are going to be ±5i.

[trail sluice]

you see, that's a little bit overkill. because it's easy to say that the result is simply +- 5. No i required here.

I just seems to be like an unncecessary helper, like I introduced in my paper. A very contradicting one at the same time.

See, in basic math, we can take the sqrt of 625. we end up with +- 25. So -25 is a valid result of a square root operation.

So if I am asking, what happens if you take the square root of a negative number, a positive and negative number will both be valid candidates.

Maybe this helps

[kind viper]

because it's easy to say that the result is simply +- 5
no, these guys give **+**25 when squared, not -25.

I just seems to be like an unncecessary helper, like I introduced in my paper. A very contradicting one at the same time.
you keep yapping about a contradiction yet you're not pointing out where the contradiction is in what i have said

[trail sluice]

That's the trap, I claim your falling into. See the addendum

[kind viper]

ok so now multiplication produces something that smells vaguely like an ordered pair, and also isn't commutative...

what is {+5, -5} * {+5, -5}?

jeez ok yknow what

<@&268886789983436800> we got a potential crank over here, can y'all have a look

[trail sluice]

I like your question, let me think for a second

[zealous rune]

The help channels are not really for this kind of thing. I can assure you that Ann, Denascite, and Cloud know what they're talking about. Please be polite if you are looking for genuine guidance, otherwise please go elsewhere than a help channel.

I'll keep an eye out, Ann.

[trail sluice]

Ok, there are multiple solutions.
First of all, in case 1, there's 5 * 5 = 25
second case: -5 * -5 = -25
third case: +5 * -5 = { 25, -25 }
case 4: -5 * 5 = { -25, 25 }

now this basically means your input was case 3.

meaning, you will also multiply with case three. meaning you get { 625, -625(see case 2) }

it's fine, we can end this conversation at any time. I was just asking for another oppinion. I knew that it wasn't easy to understand what I was trying to say

[kind viper]

do you have a full definition of the number system which you are proposing, yes or no

emphasis on the word "full"

[hushed magnet]

I can imagine what you are trying to say. but you just have simply completely misunderstood what sqrts and complex numbers are

[trail sluice]

What if not? What if it were you who did? Did you try and read my draft including the addendum? Because I rather think that common math is overlooking something

[kind viper]

you gave only part of your draft, & i dont see anything resembling the full definition that i asked for

[trail sluice]

case 1: 5 * 5
case 2: 5 * -5
case 3: -5 * 5
case 4: -5 * 5

two results: +25 and -25

sorry, there is a loss of information!

All I'm trying to do is to preserve it

[trail sluice]

If you wouldn't fight against me, you could easily follow my tracks and complete what you're looking for, or ask a question, like you did earlier, which I answered

[kind viper]

im not fighting against you

im trying to understand what this {x,y} notation is supposed to mean

right now it sounds as if you are making things up on the spot and dont have a defn you could point me to

[zealous rune]

Ann is being very patient. If you feel no progress is being made, we could simply close this help channel if you'd like?

[kind viper]

if im right about this then the convo is kinda pointless

[trail sluice]

thanks, let me help you. If you look at my last post, it's supposed to indicate the ordering, and the sign of the numbers used to create the result

[trail sluice]

it's just bouncing, like any proper discussion, no bad feelings here

[kind viper]

so {x,y} notation is only meaningful for you if x and y have the same magnitude? is that correct? yes or no.

[trail sluice]

yes, it has to be, because we're essentially still talking about squares and roots. So basically, the input is a starting number, which is squared, but there are 4 situations. However all 4 outcomes have the same magnitude, yes. They are just created by different sign combinations

[kind viper]

ok

so let me just say this for the record: the notation {x,y} only makes sense when x and y are real numbers of the same magnitude.

my next question:

in your number system, what is {5, -5} + 1

[trail sluice]

let me put it this way: the notation {x,y} applies when two equal numbers or two numbers of the same magnitude are multiplied, in order to preserve their sign

[kind viper]

idgaf when it "applies" or not

you have just confirmed to me that a notation like {5,-5} is meaningful but {3,7} is not.

also you're avoiding my question of

in your number system, what is {5, -5} + 1

[trail sluice]

"only makes sense" and applies - is one and the same thing to me. Something can not make sense and at the same time not apply

[kind viper]

in your number system, what is {5, -5} + 1

[trail sluice]

it's {6, -4}

[kind viper]

the notation {x,y} only makes sense when x and y are real numbers of the same magnitude.

and now you are giving me {6, -4}

6 ≠ 4

[trail sluice]

it's obvious, isn't it?

[kind viper]

girl you have just contradicted yourself

first you say {x,y} requires |x| = |y| then you're saying the result of some calculation is {6,-4}.

this is quite an overt contradiction.

[trail sluice]

aaah, language barrier, sorry, magnitude was confusing. because it means sign and amount at the same time.

[kind viper]

no

magnitude means absolute value

what's your native language?

[trail sluice]

German

[kind viper]

magnitude = Absolutbetrag

= |x|

[trail sluice]

yeah, but we're not talking about absolute values here, maybe my bad. We're talking about equal numbers, given no sign, that include a sign.

so basically +- |x| and +-|y|

This magnitude is absolutely confusing in what we're doing here.

Always remember the 4 cases.

Let me try again. If you allow me.

Give me 5 minutes, it's really difficult to explain, as it's contradicting the classic oppinion so much

[kind viper]

its not about contradicting the "classical opinion"

it is that you cannot express yourself clearly

and you obviously dont have a full definition of this {} number system written anywhere, in english OR german

otherwise you could have pointed me to it long ago

[trail sluice]

The {x, y} notation is all about preserving the sign. Aren't the examples I gave enough in my original draft.

This one.

The idea is as follows: we say: 5 *5 = 25, we ignore, that it could maybe be -25. Yet we know, that 5 * -5 is -25. I'm just trying to say, that it matters a lot what sign the number has. the number is equal, just the sign matters. the word magnitude has no sign, it ignores it, and explicitely gets rid of it.

So we say, we can do: 5 * 5 = 25 * 5 = 625 - all positive numbers, classic square
but on the way back, the square root, gives two results, plus and minus...
yet we also know, that we could do 5 * -5 to get a negative value after a "square" operation

I'm just trying to say, that like the square root operation which has two results, the common square operation should also have two outcomes. And to note them, I introduced this { x, y} notation

That's it. Got it now

[kind viper]

ok so this is all just pure nonsense and you're using notation that you yourself have no idea how to handle and you obviously have no rules set out for it.

so im sorry but theres no way this could even be examined.

im out and im gonna alert <@&268886789983436800> again

[sullen merlin]

I have been summoned

[brazen quiver]

Huh?

[trail sluice]

alright, wow. well then... thanks for your time I guess

[zealous rune]

OK, I can see that there's no actual question here

Since this seems to have met its end naturally, let's close the channel.

Please use help channels for help in the future.

[trail sluice]

well, maybe, could I get something else than anna to have a look at it?

[zealous rune]

.close

[compact pewter]

Channel closed

Closed by @zealous rune

Use .reopen if this was a mistake.

[zealous rune]

Maybe you could talk about it in #discussion or a similar channel instead.

[kind viper]

something else 💀

[pastel sapphire]

Heeeeelp

[trail sluice]

then it's going to really explode ....

[kind viper]

!occupied

[compact pewter]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[ashen crown]

Can I get some help at 8

[compact pewter]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[pastel sapphire]

Fine 😪

[zealous rune]

.close

[compact pewter]

Channel closed

Closed by @zealous rune

Use .reopen if this was a mistake.

[kind viper]

ok now the chann-

wa

ok fuck it whatever

@pastel sapphire do you have a question to ask

the channel opened in your name

[verbal kiln]

ended before it even started lmao.

[pastel sapphire]

Yes

[zealous rune]

Sorry, I assumed badly

.reopen

[compact pewter]

✅ Original question: #help-43 message

[pastel sapphire]

Wait lemme send pic

[kind viper]

ok

in the future you can (and should) begin by sending the pic of your question

[pastel sapphire]

K

[vague seal]

Why does one side have lengths and the other angles

Am I tripping

[pastel sapphire]

Idk ask the one who made it

[kind viper]

i think on the rhs it's about arcs

[pastel sapphire]

BC and AD are arcs im sure

[kind viper]

have you made any progress so far

[pastel sapphire]

Well... no

[kind viper]

you may have some circle theorems at your disposal...

ok, do you know the inscribed angle thm

[pastel sapphire]

Hmm

Ye I do not know them with names

[pastel sapphire]

And probably not im assuming

I searched it up and I do NOT know it 🙁

[kind viper]

you do not know this theorem?

then you do not have the tools to prove that one.

[pastel sapphire]

Mf I damn know this theorem lol

Mb

Again I do not know their names

[kind viper]

i dont have the energy to give you the entire proof but the idea is going to be to draw the lines AC and BD and look at some angles you can form this way

[pastel sapphire]

Well is BC arc twice as big as AD or not cuz im tweakin rn

Wait nah nvm

What am I yappin

[kind viper]

we dont know their ratio at all

[pastel sapphire]

Well if I draw a shape that connects BC and AD it shall be a paralellogram

I couldnt even get ChatGPT to help bruh

[ashen niche]

Yo this is 9th grade am i wrong

[pastel sapphire]

Nope youre not

[ashen niche]

U indian ?

[pastel sapphire]

Nah

[ashen niche]

Ahit

[pastel sapphire]

We dont even learn this in school

[ashen niche]

Oh

Which country?

[pastel sapphire]

Albania

Balkan vibes ig

[ashen niche]

This was taught in school to us like this exact question

[ashen niche]

Ah k

[pastel sapphire]

Lol

Well any way you can help?

[ashen niche]

Lemme see

I should remember it

bc and ad are the arcs right?

[pastel sapphire]

Btw I got this from school olympiad past papers

The teacher didnt even prepare us about anything

[ashen niche]

Lmao

[pastel sapphire]

She just said olympiad on monday

[ashen niche]

Haha

[ashen niche]

?

[pastel sapphire]

Mhm

They are the arcs

[ashen niche]

Completely forgot

In my defense it has been 2 years

[pastel sapphire]

Its alr

Whats the percentage of the filled part?

This is also in old olympiad

Options are 80%, 82%, 84%, 86%, 88% and 90%

[vague seal]

88

Use this foruma-

Area = absinC

C is the angle between sides a and b

[pastel sapphire]

We havent even gotten the tring functions yet we get them in 10th grade

But ive studied them myself lol so thx

[vague seal]

What about heron's formula

[pastel sapphire]

Im not sure bout that idk

[vague seal]

you can use heron's formula to solve this as well, but it will take more time

[pastel sapphire]

Nope I also dont know that

[vague seal]

You can also use geometry but that will be tedious

[pastel sapphire]

Well lets go step by step using a formula

[flat inlet]

Similar triangles

Ratio of small to big is 1/5 so area is 1/25=4%

100-4x3=88

[vague seal]

This solution is much better

[pastel sapphire]

Very snart

Smart

So I just imagine triangles to assume the ratio?

[flat inlet]

You don't imagine

[vague seal]

Take the ratio of their side lengths

[flat inlet]

Theyre in front of you

[pastel sapphire]

Oh yeah

Mhm now I got it

But why 100-4x3?

[flat inlet]

100 is big triangle and 4 is small triangle

Whole part take away unshaded=shaded

[pastel sapphire]

Oh 3 sides 100/25 is 4 and the 100- is 100%

Ye I got it thx

[pastel sapphire]

Is it possible if you can help me with this?

BC and AD are arcs

[flat inlet]

What is m()?

[pastel sapphire]

Just ignore it

Country stuff

[flat inlet]

By arc you mean the angle the arc makes with the origin?

[pastel sapphire]

Yes

So when I say BC i mean the arc BC not a segment BC

Kinda goofy

[flat inlet]

Okay i finished it

You want some hints or

@pastel sapphire

[compact pewter]

@pastel sapphire Has your question been resolved?

[flat inlet]

Ok whatever here goes:

Construct Q as the intersection of AC and BD. Fix m(BC)=2a, m(AD)=2b, APD=p. By inscribed angle theorem ACD=a and BDC=b. Similarly ABD=a and BAC=b. So BDP=CAP=180-b. Use angle sum of quadrilateral to get AQD=2b-p. Finish by equating (ACD+BDC) and AQD by exterior angle of triangle, which simplifies to the problem statement

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[spice flicker]

im a bit confused

[spice flicker]

im given a matrix A = [1 1; 2 2], and its rref = [1 1; 0 0]

What does it even mean for a column space to have a basis?

wait, a column space is the span of all of the column vectors

but there's dupes? (1, 0) = (1, 0)

[timid lodge]

in that case the column space is just the span of (1,0), which is just a line

[spice flicker]

but doesnt [1 1 | a; 0 0 | b] have an inconsistency when b != 0, therefore it can't span, since span requires consistency?

in fact if I rref it, I'll get [1 1 | a; 0 0 | b-2a]

oh but if I rref it, it'll show me that I need to discard the second column vector when constructing the set to make it linearly depending, and therefore form a basis for the column space

[rigid perch]

yeah so because the first column alone forms a basis of the column space of rref(A), correspondingly the first column of A forms a basis of the column space of A

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[lean sky]

im not sure if im really on the right track here with these limits or how to even sketch the graph

[lean sky]

what's confusing me the most is how I'd graph the middle to fulfill 6 but i could be overthinking it

[lean holly]

TRİGONOMETRİ

[lean sky]

elaborate

[lime shale]

wherever the both sided limit doesn't exist, there is either a vertical asymptote or a jump discontinuity in the graph

if the one sided limits exist but are unequal, theres a jump discontinuity

[kind hollow]

you basically want f to run from left to right taking all values of x, but having the jumps where the jumps are needed

[lean sky]

so something like this? but wouldn't it not fulfill 6 because of the 2 points at x=-3 and x=3

[kind hollow]

all you need is for x to take the values of all real numbers. f(x) is defined at x=-3 but not continuous

you painted one of the two lil circles black on -3 right?

[lean sky]

yup

also did on 0 and 3

[kind hollow]

gut gut

[lean sky]

there's so much leftover shit from erasing my bad 😭

[kind hollow]

lol its alright still visible

im pretty sure your shapes correct

[lean sky]

oh so is that it? it was that simple?

[kind hollow]

unless your function is not extending to +-infty for x it should be good yea

[lean sky]

I forgot to add arrows but yeah it is

thanks a lot!

[kind hollow]

ur welcome

[lean sky]

.close

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[sharp herald]

Im wondering, my prof said, that even within the same SCM, if its cyclic, there can be multiple solutions to the same counterfactual. I dont understand how to get to that point. Ive been trying to build examples, but its not working out for me.

[sharp herald]

(based on the work of judae pearl)

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[drowsy cedar]

OK so I'm doing quadratic equations and I understand how to do them just fine it's just the one part is I don't know which order the factors go in when you do the x bracket stuff

[native shard]

multiplication is commutative

[drowsy cedar]

Like the question I'm doing is 8x²-2x-15=0
So I put (2x+3)(4x-5)=0
And then I got x = -3/2 x= 5/4

But the actual answer is x=-5/4 x= 3/2

[native shard]

how did you get -5/3 and 4/3

[drowsy cedar]

Hold up wrong numbers

Wait

[native shard]

and you mean 5/4 and -3/2?

[drowsy cedar]

yea I looked at the wrong question lol

I just don't understand which order to put the stuff in the x brackets

[native shard]

wdym by order

like (2x + 3)(4x - 5) vs (4x - 5)(2x + 3)

or something else

[drifting flax]

We have $8x^2 - 2x -15 = 0$

[boreal girder]

USS-Enterprise

[feral flicker]

You mean the diamond method for finding roots?

[drowsy cedar]

Like idk if it would be (4x +3) (2x -5) or (2x +5) (4x-3)

[drifting flax]

No I am pretty sure he means how to know which sign

Yes

[drowsy cedar]

It dosent make it clear what goes where

[drifting flax]

Well

[drowsy cedar]

And that's where I'm messing up

[drifting flax]

Multiply the brackets out

And see what you get

[native shard]

i don't know what method you're using for factoring

[drowsy cedar]

It's just called factorising method in my books idk

[feral flicker]

Can you draw an example of the x brackets you are talking about?

[native shard]

yea but are you using some organizational tool like a diagram

me personally id factor this by grouping

[drowsy cedar]

These

Like (x- ) (x+ )

[native shard]

right but how are you getting these numbers

[drowsy cedar]

Factors of 15

[native shard]

if you use an approach that isnt just guessing then it wont be a problem

[drowsy cedar]

I multiply it out in my head to see if I can make -2x

[native shard]

write $8x^2 - 2x - 15 = 8x^2 - 12x + 10x - 15$ then factor by grouping

[boreal girder]

knief

[native shard]

i got -12 and 10 from two numbers that multiply to 8(-15) = -120 and add to -2

[drowsy cedar]

I don't think we're doing the same method here

[native shard]

yea but then you're just doing an unnecessary amount of guess work

[drowsy cedar]

It's not really guess work it takes 2 seconds

[native shard]

then how come you can't find the order

[drowsy cedar]

Because I don't know where to put what

[native shard]

if it takes 2 seconds you should have no issue

[drowsy cedar]

Because each question does it differently

And the notes don't say anything about it

[feral flicker]

Regardless, both of your answers are incorrect. Why did you swap the coefficients of the x variables?

[native shard]

i mean correct me if im wrong but it seems like you're just looking for factors of the constant term then making that your constants in the two factors but then you also have to go back in each of those cases and consider possible factorizations of the leading coefficient

this is highly inefficient

[native shard]

do this

[drowsy cedar]

I don't understand that at all

[native shard]

ok ill show you

[drowsy cedar]

I'm just doing it the way I was taught I don't think ill be allowed to do that in the test

[native shard]

do you agree that the left hand side equals the right hand side

lets start there

[native shard]

?

why wouldn't they allow this

the question is just going to say "factor ..."

not "factor by this method only"

anyways

you group the two pairs of terms here

[drowsy cedar]

What I'm trying to ask is how do I know which one is right

[feral flicker]

,rotate ccw