help-10

[true granite]

thought you meant equal sides, and equal angle

[wind patio]

nah

[true granite]

there are a few simple ones

[wind patio]

the only one i have found is AED and FEC

[true granite]

if you cut two secant lines with two parallel lines, you’ll get two similar triangles, right?

[wind patio]

secant?

[true granite]

secant means they intersect

[wind patio]

and also we dont have any proof of them being parallel

ok ty but ye we dont know if theyre parallel

[true granite]

oh I didn’t see, no right angle

[wind patio]

and my geo teacher is kinda strict about using the information in there

ye

[true granite]

tempted to use trig

[wind patio]

idk trig tho

[true granite]

but I’m gonna stick to the ratios

[wind patio]

ima learn it soon, but havent yet

[true granite]

yeye dw

[wind patio]

also nice pfp

[true granite]

thanks!

ok I’m gonna try to solve it with you, it looks fun

[wind patio]

k

thats what i thought at first glance, and now it is making my head hurt

[true granite]

so we can get the two other angles

AEB and BEC

[wind patio]

those wouldnt cuz 40 and 20 wouldnt work together

however the top angles

[true granite]

yeye I’m talking about the angles

[wind patio]

are 50 and 70

ye those angles are these

and DEA and FEC are 60 each

and they are the same

[true granite]

50 and 70 add up to 120

[wind patio]

ye then vertical to get 120 on other side

then 360-240 gives 120

and then vertical angles so just divide in half

[true granite]

so the opposite angles at E are 60

[wind patio]

ye

if we had proof of the perpendicular, this thing would be done by now

just use ~AA and boom

[true granite]

yup

[wind patio]

wait i have an idea

if we can find ADE

with BED being 110

[true granite]

reposting so I don’t have to scroll, forgot the command

[wind patio]

ok

and if we find ade we can prove that DAB is 90

and we could also get the 50 from 90-40 and that is angle F

which is the same as AEB

[true granite]

A+D+40+50+90=360

[wind patio]

which would give us the AEB AFC similarity

so EAD+ADE = 180

[true granite]

wait

no

missed something

that’s impossible

[wind patio]

oh ye

[true granite]

missed a 60

[wind patio]

oh we forgot the 60

ye

[true granite]

A+D=120

[wind patio]

so EAD + ADE = 120

ye

[true granite]

if we can get another equation we can solve a system

[wind patio]

but we need those exact variables

ead and ade

[true granite]

yup

and in a different form

Otherwise we’re just finding what we already know

[wind patio]

i was about to do going to 180 w tst but realized that would just get us ead + ade = 120

cuz the other one is 60

WAIT

ADE + EAD + 40 + 20 = 180

shoot

thats just the same

[true granite]

yeah

don’t think this goes anywhere tbh

[wind patio]

this is dificult

ye

[true granite]

still tempted to use trig

[wind patio]

idk if i should email my teacher and ask her if they are perpendicular

i mean if it works and you can explain it to me

[true granite]

wait we’ve already solved the problem

[wind patio]

we have?

[true granite]

the question asks if there are any similar triangles

answer:yes

for example, those two you found

[wind patio]

one of my friends solved it as well

and got 3

[true granite]

oh then we haven’t

[wind patio]

ye

[true granite]

trying to get the technicalities haha

[wind patio]

idk if he made a mistake tho

ye

but

[true granite]

reposting again, don’t mind me

[wind patio]

has to be complete solution

nah ur good

[true granite]

wait

[wind patio]

ye?

[true granite]

maybe we can use the fact that those two triangles are similar

[wind patio]

OOOH

ADE is congruent to FCE

[true granite]

no

[wind patio]

but then we run into the same problem of not being able to define it

the angle is congruent

[true granite]

we can find a relationship between AD and FC

[wind patio]

how?

[true granite]

and try to see if that holds for other sides of AFC and ADC

[wind patio]

we can approcimate the length

we know the proportion is 1 1/3

[true granite]

ok got it

[wind patio]

just remember to flip one

[true granite]

so EF is proportional to which side?

[wind patio]

AE is proportional to FE

and DE to EC

[true granite]

okay

5/2 = FC/AD right?

[wind patio]

wdym by relation ship

i believe so

[true granite]

so FC=2.5AD

[wind patio]

ye ig

[true granite]

If ACD and ACF were similar, then DC/AF would be equal to AD/FC

[wind patio]

shoot where did i get 1 1/3 from

[true granite]

AD/FC is 2/5

[wind patio]

ye

but thats just the rate

cuz we got those numbers from elsewhere

[true granite]

so we just have to check if DC/AF is also 2/5

[wind patio]

ok

[true granite]

,w (1.5+3.75)/7

[warm shale]

Results provided by WolframAlpha

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

Requested by fedeCreeper#7128

[wind patio]

5.25/7 is 0.75

wait waht is taht

[true granite]

magic

[wind patio]

damn my h is really behind

[wind patio]

wait but how does it work

,w3*5

[true granite]

it’s just sending a query to a site called wolfram alpha

[wind patio]

,w(3*5)

[true granite]

put a space

,w 3*5

[warm shale]

Results provided by WolframAlpha

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

Requested by fedeCreeper#7128

[wind patio]

oh thats cool

[true granite]

,w binomial(10,5)

[warm shale]

Results provided by WolframAlpha

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

Requested by fedeCreeper#7128

[wind patio]

whats a binomial

idr if ive learned it yet

[true granite]

dw

[wind patio]

wait what grade r u in

[true granite]

it’s something used to count combinations and to expand polynomials

[wind patio]

ok

[true granite]

and some other stuff probably

[wind patio]

but what grade are u in, if ur still in school?

im in 8th

[true granite]

us?

[wind patio]

ye us

[true granite]

hmm no idea tbh
not from the us

[wind patio]

wait r u in college?

[true granite]

nope

but I love math

[wind patio]

past or b4

like r u done w college or not in yet

[true granite]

before

[wind patio]

ok

wait how old are u

[true granite]

16

[wind patio]

dam ur 3 years older than me and know so much more

im rn in 8th, but you would be in 10th most likely if you were in us

[true granite]

makes sense

[wind patio]

im rlly young for my grade

[true granite]

I study math for fun

[wind patio]

nice

i used to until geometry

[true granite]

it’s great when you’re not forced to do it

[wind patio]

HONESTLY THO

but now i mainly spend my time coding, reading, playing games, or playing percussion

[true granite]

if you wanna know more about this check out combinatorics
it’s a way of counting in how many ways you can arrange objects, or make combinations of them

[wind patio]

ok

ive heard of 5x+4y as a binomial in alg

[true granite]

oh yeah it’s called binomial because it’s part of the binomial theorem

[wind patio]

oh ok nice

[true granite]

it’s a way to expand binomials

(a+b)^2, …^3, and so on

[wind patio]

ok

do yk any good places i could go to learn more?

[true granite]

if you like learning math you can use khan academy, they have some good math content

[wind patio]

ok

ok wait we should get back on track

[true granite]

yeah

HMMM

let me just check if they’re actually perpendicular, then we’ll try to solve it normally

[wind patio]

ok

if its perpendicular its p much done

[true granite]

oops forgot wolfram

,w sqrt(1.5^2+2^2-221.5*cos(60deg))

[wind patio]

https://tenor.com/view/blinking-eyes-white-guy-blinking-meme-what-huh-gif-26334322

[warm shale]

Results provided by WolframAlpha

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

Requested by fedeCreeper#7128

[wind patio]

me rn

[true granite]

,w arcsin(sin(60deg)*1.5/1.8)

[wind patio]

wha-

[warm shale]

Results provided by WolframAlpha

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

Requested by fedeCreeper#7128

[true granite]

,w 0.806 radians in degrees

[warm shale]

Results provided by WolframAlpha

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

Requested by fedeCreeper#7128

[wind patio]

is this just figuring out the 90 degrees?

[true granite]

ok so they’re not perpendicular

the left one is like 89.18 degrees

with some rounding error

[wind patio]

just keep in mind that this is most likely not to scale

[true granite]

they could be perpendicular

wait one sec

[wind patio]

they are most likely intended to b perpendicular

[true granite]

,w arcsin(sin(60deg)1.5/sqrt(1.5^2+2^2-221.5cos(60deg)))

dw

[warm shale]

Results provided by WolframAlpha

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

Requested by fedeCreeper#7128

[wind patio]

what tha hell

bro im so confused

[true granite]

DON’T WORRY

,w 0.804634 radians in degrees

[warm shale]

Results provided by WolframAlpha

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

Requested by fedeCreeper#7128

[true granite]

okay so it’s not perpendicular for sure

sorry about that

it’s like 86.1021 degrees

something random

just ignore all the wolfram queries

[wind patio]

ok

is it just the result + 40

[true granite]

yeah

[wind patio]

oh ye cuz of EAB

[true granite]

I was finding EAD

[wind patio]

ye

[true granite]

with like 2 different trig laws combined

there’s probably a faster way to do it but oh well

letting the computer do the hard work

[wind patio]

lmao

[true granite]

so knowing they aren’t perpendicular, there’s prob no way there are others tbh

[wind patio]

ok

my dad suggested a theorem

but idk what its called

[true granite]

I used the sine law and cosine law

[wind patio]

but basically with a perpendicular line on it

the segments its divided into are proportional

and its prob true

and then u can sas

cuz u alr have 3.75 is proportional to (3.75 + 1.5)

[true granite]

so which segments would be proportional?

[wind patio]

so with the theorem AC would be proportional to BC

and AB to AC

making FAC EAB and DCA ECB possible

it seems likely

using reflexive we have the angles

[true granite]

this is a tough problem

[wind patio]

ye

and they give this to 8th graders

well nr

its meant for 10th and 9th

but its in the geo course

and we are in "advanced" since we skipped 2 grades of math

[true granite]

well uh

I only found the 2 you found haha

just noticed something

[wind patio]

what?

here just reposting

[true granite]

angle ADE is equal to angle ECF right?

[wind patio]

yes

[true granite]

same thing with DAE and EFC

wait

[wind patio]

or, as my teacher would have us say, m<ADE = m<ECF

[true granite]

wrote them wrong

[true granite]

yeah the notation

[wind patio]

ye

[true granite]

maybe knowing that their sum is 120 can give us info on if m<DAC = m<ACF

[wind patio]

wait how we know that

[true granite]

let’s call x the entire interior angle at A, and y at B (I don’t know if this works btw)

[wind patio]

ok

[true granite]

x = 40 + m<DAE

y = 20 + m<ECF

[wind patio]

like this

[true granite]

no

oh, I said B

with y I meant C

[wind patio]

oh

[true granite]

yeah

[true granite]

x+y = 180!

wait wait

[wind patio]

no

x + y = 120

[true granite]

nono

[wind patio]

same as the ADE and DAE from b4

[true granite]

meant the two FULL angles

including eab

[wind patio]

oh

[true granite]

and bce

[wind patio]

like with the 40 and 20

[true granite]

yeah

so you just add 60 and get that they add up to 180

[wind patio]

k

ye

but we alr know where the 40 and 20 go

[true granite]

which means they are parallel

[wind patio]

how

the only parallel proving thing ik is with converse and transversal

[true granite]

if you cut two parallel lines with one line, the angles on the same side add up to 180

since you can just translate the other angle

does it make any sense?

or should I draw it

[wind patio]

draw plz

[true granite]

one sec

[wind patio]

wait so the one line would be the transversal

like this?

x + y = 180?

[true granite]

like that

if they are parallel, they add up to 180

[wind patio]

yes

[true granite]

and we just proved that in our case, they add up to 180

so AD and FC are parallel

[wind patio]

oh so converse of same side alternate interior angle theorem

[true granite]

not perpendicular, but parallel

[true granite]

right

[wind patio]

ok wait then with that we can solve the entire thing

[true granite]

we proved a sort of duality of that theorem

[wind patio]

ye

WAIT

USING THAT

WE CAN PROVE DA IS PARALLEL TO EB

wait can we

[true granite]

I prefer free dart monkey tbh

[wind patio]

lmao

fair choice

allows greed in the early game

with farming early

depends on hero as well

[true granite]

I’m not that good at btd6 though

[wind patio]

i have knowledge, just not much experience, in game or with hotkeys

[true granite]

maybe…

[wind patio]

so i odnt have paragons, or much good boss damage

[true granite]

yeah I don’t have paragons either

I can unlock them, but I don’t have enough xp

[wind patio]

ye same

[true granite]

yeah we can

wait

[wind patio]

wait for what

[true granite]

no, we’ve just proved it isn’t

[wind patio]

wait how

[true granite]

since it’s not perpendicular

and if it were parallel, it would be perpendicular

[wind patio]

no the thing we need perpendicular is DA to AC

and FC to AC

[true granite]

yeah, if da was parallel to eb, then da would be perpendicular to ac

and we know it isn’t

[wind patio]

it isnt?

[true granite]

proved it with trig

a few minutes earlier

[wind patio]

but that requires it to be to scale right

this isnt to scale

[true granite]

let me make a scale diagram

[wind patio]

at least the measurements

ok

[true granite]

wait

that’s much harder than I thought uhhhh

[wind patio]

ye bro

idk how my other friend got it easily

[true granite]

well I can use some construction tools on geogebra

[wind patio]

whats geogebra

[true granite]

an app

[wind patio]

is it similar to desmos?

[true granite]

yeah

ok I’m getting close

give me 2 secs

[wind patio]

ok

just can u explain it to me after ur done

cuz

[true granite]

yeah, I just want to do it to understand how it actually looks

ok I got it

[wind patio]

ok

btw

this is almost definetly not how we are supposed to solve it

[true granite]

not solving it

[wind patio]

lmao ye

[true granite]

just making it to scale to understand what it looks like

then prove what you think is right lol

shortcut!

ok so FC is def parallel to ad

and eb is not

there’s a slight difference

[wind patio]

k ima just ask my teacher tmrw

[true granite]

so i’m pretty sure there’s just 1 pair of similar triangles

and it’s the two top ones

[wind patio]

ill ask my teacher and friends if theres more

if there is, ill lyk

[true granite]

so we had actually solved the problem an hour ago

[wind patio]

ye

[true granite]

great

[wind patio]

sorry if you felt it was a waste of time

[true granite]

not really

[wind patio]

had fun working thru it w u tho

[true granite]

I had fun

it’s 2 am here though

[wind patio]

oh dam

you should prob gts

[true granite]

yup

[wind patio]

ima gts now too

gn

[true granite]

gn!

also

[wind patio]

and lmk if u wanna play btd6 together sometime

[true granite]

I’m happy you haven’t noticed that english is not actually my first language

[true granite]

sure

[true granite]

means I am good at it

heh

[wind patio]

really? you spoke it incredibly well

[true granite]

yeah, I’m from south america

[wind patio]

i honestly thought you were from the US or England

[true granite]

español

[wind patio]

ah nice

[true granite]

I can type the ññññññ

[wind patio]

rn im taking a spanish 2 class lmao

puedo hablar mas o menos espa~nol

pero no estoy muy bueno

[true granite]

soy

[wind patio]

oh ok

[true granite]

yeah ser/estar is prob confusing

[wind patio]

i did estoy cuz im tryna get better

so its not permanent

i heard ser is permanent, and estar is not permanent

[true granite]

ser is like something that you are, something that describes you

[wind patio]

ok

[true granite]

I am nice, I am a man

etc etc

[wind patio]

ah

[true granite]

and estar is something that you are doing or somewhere you are

[wind patio]

soy simpatico

[true granite]

you are at the supermarket

estoy en el supermercado

but you aren’t the supermarket

you are at the supermarket

[wind patio]

ight well i gtg now

[true granite]

that’s basically the difference

[wind patio]

gn

ye ty

ttyl

[true granite]

cya!

[wind patio]

.close

[obtuse pebble]

Channel closed

Closed by @wind patio

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[ionic summit]

Hello! So I am doing some practice integrals and this one (the first one lol) threw me off, I got -15/2 instead of the correct answer of 15/2

[ionic summit]

I ended up with 1/2x^2 -3x

[viscid crag]

x²-6x+9 can be factorised to (x-3)²

Then you can remove square root and take absolute value of |x-3|

Take out a minus and you get the integration of -1,2 of |x-3| dx

So now its -x+3

[ionic summit]

wdym take out a minus?

/why?

[viscid crag]

Its absolute value. To remove it, you have to take out a minus

That removes the absolute value

For example

In the case of |x-3|, it becomes -(x-3) and so its -x+3

Alternatively, you can replace x with -x which also removes the absolute value

[ionic summit]

Thats for every case? No matter what kind of function is in the absolute values and limits of integration?

[viscid crag]

Pretty much

You just have to replace x with -x to remove abs

[ionic summit]

what is it was like |sinx|

[viscid crag]

Replacing x with -x here gives sin(-x). Fron trig rules, this is equal to -sin(x). If it was cos(x), from trig rules, cos(-x) = Cos(x)

Are you aware of the unit circle?

[ionic summit]

wow okay I see

thats kinda interesting

right cus like cos is an even function and sin is odd

[viscid crag]

😀

Hmm

[ionic summit]

uhh

[viscid crag]

Yes

[ionic summit]

ok but the "pretty much" answer concerns me

is it like the only case its not

outside of the scope of this

im in calc 2 for reference

[viscid crag]

Lmao i say that sometimes. Although yes, it can be a bit janky when it comes to "e"

Like e^|x| - |x³| for example

You have to separate it into 2 integrals

By finding where it equals to 0

Its hectic

[ionic summit]

okay ima just hope that never happens

idk prof never went over that case and just touched on the abs value thing for integrals

[viscid crag]

Lets hope

[ionic summit]

and trig sub

but thank you so all I gotta do

[viscid crag]

Trig sub is a hard concept at first

[ionic summit]

is pull a negative out

[viscid crag]

Bye good luck

[viscid crag]

Replace with -x

[ionic summit]

okay sorry another example is needed

[viscid crag]

Lmao

[ionic summit]

|x^3 - x^2 +7|

is it just

-x^3 + x^2 + 7

[viscid crag]

Yea so replace x with -x

Yea

Done

[ionic summit]

wait seriously

[viscid crag]

Yep

[ionic summit]

i dont understand abs value

I thought it made things positive

[viscid crag]

Its a bit funky

This method works for most functions

[ionic summit]

oh goodness there it is again

most

the excepting being e?

[viscid crag]

Wait youre making me confused now

[ionic summit]

hahahah

[viscid crag]

💀

There might be more. Im pretty good at this but then again, it won't work for all

Just be careful

[ionic summit]

mann

ok wait what the heck

i threw something random into symbolab

and this appears not to follow that urle

[viscid crag]

One sec

https://www.youtube.com/watch?v=_B34_E-b84E

Watch that

I was slightly mistaken forgive me. Apparently my method only works with linear functions

💀

[ionic summit]

mmmmmmmmmm

wait

but the thing i posted above on symolab

is linear

but that did not work

WAIT

wait no it does I just got confused when it split the integral up

i accidently made an improper integral

sorry one last test @viscid crag

|x- 7|

U said to just make -x

so its -x - 7?

wait nvm I think u were refering to just the trig

u take out a minus for linear functions

sorry for spam ty

.close

[obtuse pebble]

Channel closed

Closed by @ionic summit

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[grand hawk]

how would i go about solving this?

[obtuse pebble]

@grand hawk Has your question been resolved?

[daring rock]

@grand hawk Are you familiar with the remainder theorem?

[grand hawk]

not too well

[daring rock]

It says, if you have a polynomial p(x) and you divide it by (x-t), the remainder is p(t)

[grand hawk]

how do i apply this?

[daring rock]

Well, for your first polynomial

You're told that if you divide $x^4+5x^3-ax+b$ by $(x+1)$, the remainder is 7

[warm shale]

tatpoj

[daring rock]

So the remainder theorem tells you that if you evaluate that polynomial at x=-1, you get 7

[grand hawk]

so

p(-1) is 7

oh wait lol i got it\

ty for the pointers @daring rock

.close

[obtuse pebble]

Channel closed

Closed by @grand hawk

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[next reef]

The sample space consists of all the numbers from 000 to 999, both inclusive

[obtuse pebble]

Channel closed

Closed by @queen flax

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[viscid crag]

what is meant by A

[pastel meadow]

A denotes that matrix here

[viscid crag]

oh ok

thanks

.close

[obtuse pebble]

Channel closed

Closed by @viscid crag

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[somber zealot]

how would i integrate this?? i thought the derivative and integral would cancel each other but there is an upper and lower bound?

[timid silo]

um

seemingly you don't have to integrate anything

since they are asking you to take the derivative

Apply the Fundamental Theorem of Calculus of
[
\dv{x} \int_a^x f(x) \dd{x} = f(x)
]

[somber zealot]

PFFF

idk why i keep forgetting fundamental theorem of calc

thanks!

.close

[obtuse pebble]

Channel closed

Closed by @somber zealot

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[obtuse pebble]

Channel closed

Closed due to the original message being deleted

[vivid edge]

just want to make sure

x=2.4 or x=-1

[timber fox]

plug the values you get back into the original equation and check if you get 0=0

[vivid edge]

wdym?

[timber fox]

if u got x = (-1)

check if 5(-1)^2 + 17(-1) - 12 = 0

[vivid edge]

i got -24 so im guessing its wrong

how can i fix it?

[obtuse pebble]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[vivid edge]

.close

[sour lantern]

I want to calculate inverse laplace and this is what I got

this is what the internet says should be the answer

is my answer also right or did I mess something up?

[obtuse pebble]

@sour lantern Has your question been resolved?

[obtuse pebble]

@sour lantern Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[whole dock]

Why does the electric field does not add to the force on the charge due to gravity aren't they both opposing the repulsive force due to the negative charge?

[obtuse pebble]

@whole dock Has your question been resolved?

Channel closed

Closed by @whole dock

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[timid silo]

Anyone able to explain how this equals a circle???

[lone jetty]

|z - z1| = r

is a circle radius r centered at z1

| (x + iy) - (x1 + iy1) | = r

((x + iy) - (x1 + iy1))^2 = r^2

you can have the fun of expanding it out and proving it to yourself @timid silo

it works out exactly the same as the cartesian equation of a circle

[timid silo]

Thank you very much

Now I understand it

[timid silo]

Tyty 🙂

.close

[obtuse pebble]

Channel closed

Closed by @mighty junco

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[elfin abyss]

if something is not a divisor of 0 in a ring, is it not necessarily invertible?

[elfin abyss]

Can you give me an example

[royal basin]

are you sure about the order of words in that question?

oh, nevermind, i misread.

no, a non-zerodivisor is not necessarily invertible. and even Z has examples aplenty

such as the number 2

[obtuse pebble]

@elfin abyss Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[harsh crow]

I understand this but how u even get the number of 50 cent coins idk

[obtuse pebble]

@harsh crow Has your question been resolved?

[harsh crow]

No

[lost tree]

what have u tried

[harsh crow]

The obivous parts

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[hard whale]

I have a further question about the scalar product

[hard whale]

Isn't n . p =0 since p the position vector on the plane is also perpendicular to the plane

So shouldn't n .p =0

Instead of d

[obtuse pebble]

@hard whale Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[edgy whale]

i know how to make y subject of l2

but i dont know how to find y-intercept of equation. (high possibility chance of miss counted question)

[high lily]

after isolating y, the equation will pretty much be in slope intercept form from which the slope and y-intercept (as the name suggests) can be easily identifiable

[edgy whale]

Oh ok i see, and how do you "isolate" the y. (this is last year exam paper)

[high lily]

you said you did that

[edgy whale]

oh ok i see

[high lily]

i know how to make y subject of l2

[edgy whale]

so not using the y subject

[high lily]

making y the subject, isolating y, solving for y

are different ways of saying the same thing

[edgy whale]

ok ill try that and see how it goes

[high lily]

with the goal of getting an equation in the form
y = stuff without y

supposedly you have that already

[edgy whale]

great explanation Thank you!

[uncut vault]

HElp

Rewrite x1/2 in radical form.

c)√x

not getting it

[high lily]

channel is occupied. please read #❓how-to-get-help and claim your own under the available section @uncut vault

[uncut vault]

ok

[edgy whale]

how may i close the occupied channel so nobody come here?

[uncut vault]

but i dont have permision to it

[high lily]

if you're done type .close

[uncut vault]

i dont have permision to it

[edgy whale]

Perfect.

[high lily]

if you can send stuff here, you definitely have the perms to send stuff in an available one

[edgy whale]

.close

[obtuse pebble]

Channel closed

Closed by @edgy whale

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[proper ivy]

why cant we write this as: 1/3 + (2/3 * 1/3) + (1/3 * 1/3)

i get it its easier with finding the opposite first, but why does my method give a wrong answer

[drifting wraith]

1/3 + (2/3 * 1/3) + (2/3 * 2/3 * 1/3)

[proper ivy]

ohhh right

thanks a lot man

sorry if i came off as a little bit racist

.close

[obtuse pebble]

Channel closed

Closed by @proper ivy

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[rancid leaf]

I'm trying to solve the exercise a) I have to determinate if the set V is a subspace of R^2, I’m trying to use the gen but I'm not sure how it can say that is a subspace or not

[obtuse pebble]

@rancid leaf Has your question been resolved?

[obtuse pebble]

@rancid leaf Has your question been resolved?

[unreal musk]

One way that might help and be a bit more intuitive is to show it is a subspace directly: if you have $(x_{1}, y_{1}), (x_{2}, y_{2}) \in V$ (so $x_{1} = \frac{4}{3} y_{1}$ and $x_{2} = \frac{4}{3} y_{2}$), then show their sum also "looks the same", and that if you have a scalar $\alpha$, that $\alpha (x_{1}, y_{1})$ "looks the same" too

[warm shale]

chartbit

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

Channel closed

Closed due to the original message being deleted

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[blissful bane]

Given 13% of people are left-handed. What is the probability the first left-handed person will be the sixth person polled?

[obtuse pebble]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[blissful bane]

I'm trying to figure out which distribution does this belong to

[trim portal]

Same as the probability that first 5 persons will be right handed, and the 6th left handed

Probability questions usually just need to be rephrased

[blissful bane]

so a geometric distribution, with 5 failures and 1 success?

[trim portal]

Sorry, Idk to what distribution does it belong. I just know how to calculate the probability

But according to probability formula for geometric distribution, you are right

[blissful bane]

the required probability by multiplication theorem is (0.87)^5(0.13) right ?

thanks a lot.

I wasn't able to comprehend that sixth person is the only success

i thought there was a chance of combination

have a great day.

[trim portal]

u2, bye

[obtuse pebble]

@blissful bane Has your question been resolved?

Channel closed

Closed by @blissful bane

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[timid silo]

Let $X$ be a normal space and $Y \subset X$ a linear subspace. For $x_0 \in X \setminus Y$ we define
[
f: \cmap{\spn}{Y,x_0} \longrightarrow \K, \map f{y+\lambda x_0} = \lambda, \quad \forall y \in Y, \forall \lambda \in \K
]
a) Prove that $f$ is well defined and linear

\vs{3 mm}
b) Prove that $f$ is continuous if and only if $x \notin \overline{Y}$

\vs{3 mm}
c) Prove that $\overline{Y} = \bigcap\set{\ker x^{\ast} \where x^{\ast} \in X^{\ast}, Y \subset \ker x^{\ast}}$

\vs{5 mm}
\textbf{My attempt:}

\vs{3 mm}
a) We start by noticing that
[
\cmap{\spn}{Y, x_0} = \set{y + \lambda x_0 \where y \in Y, \lambda \in \K}
]
To show that $f$ is well defined, we can show that
[
(y+\lambda x_0 = y' + \lambda ' x_0) \implies (y = y' , \lambda = \lambda ')
]
And assuming that $\lambda \neq \lambda '$. Then;
[
x_0 = \f{y-y'}{\lambda - \lambda '} \in Y
]
So since $y, y' \in Y$ and $Y$ is a linear subspace; this results in a contradiction. Thus,
[
(\lambda = \lambda ' ) \implies (y = y ' )
]

\vs{3 mm}
b) We can start off by supposing that $f$ is continuous. We will then prove that $x_0 \notin \overline{Y}$. Assume, for the sake of contradiction, that $x_0 \in \overline{Y}$.

\vs{2 mm}
Then there is a sequence $y_n \subset Y$ such that $y_n \to x_0$. Since $y_n , x_n \in Y, y_n \to x_0$ and $f$ is continuous, then $\map f{y_n} \to \map f{x_0}$.

\vs{2 mm}
By the definition of $f, \map{f}{y_n} = 0, \quad \forall n \in \N$. It follows that $\map f{x_0} = 0$ which is false, since by the definition of $f$, we have $\map f{x_0} = 1$

\vs{2 mm}
Suppose now that $x_0 \notin \overline{Y}$, for example, $x_0 \in \comp{(\overline{Y})}$, which would be open. Then
[
\exists \epsilon > 0 : \map B{x_0; \epsilon} \subset \comp{(\overline{Y})}
]
This inclusion would then be equivalent to $\overline{Y} \cap \map B{x_0; \epsilon} = \emptyset$. Let $x = y + \lambda x_0 \in \cmap{\spn}{Y, x_0}.$ If $\lambda = 0$, then
\begin{equation}
\abs{\map f x} = 0 \leq \f{\norm{x}}{\epsilon}
\end{equation}
if $\lambda \neq 0$ then $\f{y}{-\lambda} \in Y$ so $\f{y}{-\lambda} \notin \map B{x_0; \epsilon},$ for example, $\norm{-\f{y}{\lambda} - x_0} \geq \epsilon .$ Therefore,
\begin{equation}
\norm{x} = \abs{\lambda} \norm{-\f{y}{\lambda} -x_0} \geq \epsilon \abs{\lambda} = \epsilon \abs{\map f x}
\end{equation}
Then, both cases of (1) and (2) should show that $f$ is continuous

[timid silo]

Hey guys are the way a and b were done correct? I mainly followed the lecturer's method but I want to double check

[timid silo]

i dont think (2) is true anymore

i am really suspicious of the last quarter of that to be honest

[heavy siren]

Can you solve this kenken

And this

[timid silo]

sigh

.close

[obtuse pebble]

Channel closed

Closed by @brave kite

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to the original message being deleted

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[magic tinsel]

We have 16 buckets b_1, ... ,b_16. They contain w_1,...,w_16 balls respectively.
How many ways can I make groups of 10 balls such that no more than 3 balls are from the same bucket?

[drifting wraith]

there's no trick for this, sounds like a programming question

[magic tinsel]

it kind of is, it's related to a project im doing in python i just wanted to count to see if it'll be faster than the previous method

the hope is that if all w_n are equal to about 20 than the result would be less than 86 choose 10

[drifting wraith]

do the balls have identity or not?

[magic tinsel]

um hm not sure i get what you mean

[drifting wraith]

like if you have 2 buckets of 20 and the rest have no balls what's the answer

uh

and you can have any number not just 3

[magic tinsel]

right it can't be done for less than 4 buckets

since we'll need at least 10 balls

[drifting wraith]

but if you can have all 10 from the same one

like it's either (40 choose 10) or it's just 11

[magic tinsel]

right i think that would be 40 choose 10

[drifting wraith]

all right

@magic tinsel

from math import comb
from functools import *



@lru_cache(999)
def count(a,w):
   if not a: return 1
   if not w: return 0

   r = 0
   for i in (0,1,2,3):
     r += comb(w[0],i) * count(a-i, w[1:])
   return r


w = 23,23,21,23,19,23,18,20,21,22,18,23,21,18,18,18

print(count(10, w))

[magic tinsel]

oh thank you um

[drifting wraith]

the result is more than 86 choose 10 apparently

i don't know what's 86 choose 10

[magic tinsel]

function is a bit confusing

what does comb do

[drifting wraith]

choose

[magic tinsel]

like about 3.5 trillion iirc

[drifting wraith]

i meant why 86

[magic tinsel]

oh it's the number of magic series of order 4

just some stuff im working on, not really relevant

what about exactly 3 or 1

from each

do i just set i in (1,3)?

[drifting wraith]

yeah

[magic tinsel]

aight thank you so much for the help

deeply appreciated

have a nice rest of your day frownyfrog

!close

.close

[obtuse pebble]

Channel closed

Closed by @magic tinsel

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[analog harbor]

whats the 0 thing means

[native cove]

It's called theta, means angle

Just think of it as X, there's no difference if you call it a or x

[analog harbor]

ok got it

.close

[obtuse pebble]

Channel closed

Closed by @analog harbor

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[feral siren]

How do i find the minimum value of
CosA + CosB + CosC
Given that A + B + C is 2π

[feral siren]

i think that the question itself is incomplete ?

[lost tree]

can u try using cosA + cosB = 2cos(A+B/2)cos(A-B/2) ?

and replace A+B with 2pi-C

[feral siren]

yea i did all that stuff but i can't simpify further then

[ruby path]

Is there perhaps a geometric answer?

[feral siren]

yea original question is of geometry

[ruby path]

Have you tried drawing a unit circle perhaps

[feral siren]

ye=\

[ruby path]

,w cos (2pi/3)

[warm shale]

Results provided by WolframAlpha

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

Requested by NEONPerseus#2128

[ruby path]

Is the answer -1.5

[feral siren]

ye

[ruby path]

Hmm

So at the point where A = B = C

Our math teacher did tell us about these "equilibrium points" but I don't remember the context of the relation to minimas and stuff sorry

[feral siren]

.close

[obtuse pebble]

Channel closed

Closed by @feral siren

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[buoyant void]

The question says to approximate the answer

[buoyant void]

<@&286206848099549185>

[obtuse pebble]

@buoyant void Has your question been resolved?

[obtuse pebble]

@buoyant void Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[obtuse pebble]

Channel closed

Closed due to the original message being deleted

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[weak mauve]

hi im pretty weak on vectors could someone help me with these two questions

[obtuse pebble]

@weak mauve Has your question been resolved?

[obtuse pebble]

@weak mauve Has your question been resolved?

Channel closed

Closed by @weak mauve

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[uneven ravine]

@bronze sky

[uneven ravine]

LAMo

why u here

[sharp pecan]

what is the question?

[gloomy canyon]

dont use the channels like this please

[uneven ravine]

mbmb

[gloomy canyon]

#discussion exists for a reasons ksksks

[uneven ravine]

he is my boyfriend

mb

[sharp pecan]

.close

[gloomy canyon]

ye ye

[obtuse pebble]

Channel closed

Closed by @sharp pecan

Use .reopen if this was a mistake.

[gloomy canyon]

no prob

[uneven ravine]

anyone knows why dividing by 0 is undefined

give me a detailed explaination

[sharp pecan]

.reopen

[obtuse pebble]

✅

[sharp pecan]

is that your actual question?

seems like a google search, the answer depends on your knowledge

[zenith vale]

cavendish your pfp looks cute

[tawny fog]

You can give a logical explanation for that but I like to explain it by limits
You know that
$\lim_{x\to c^+}f(x)≠\lim_{x\to c^{-}}f(x)$ then the limit dosen't exist

[warm shale]

Arnab

[tawny fog]

The limit $\lim_{x\to c}f(x)$ dosen't to be more specific

[warm shale]

Arnab

[tawny fog]

So in the graph

,w plot y= 1/x

[warm shale]

Results provided by WolframAlpha

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

Requested by 𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛#6985

[gloomy canyon]

approaches both negative and positive infinities

[tawny fog]

Oh sorry forgot to mention that

[tawny fog]

Here when c is 0^+ the limit is

Ufff

$\lim_{x\to 0^+}\frac{1}{x}=\infty$

[warm shale]

Arnab

[tawny fog]

And when c is c^-

$\lim_{x\to 0^-}\frac{1}{x}=-\infty$

[warm shale]

Arnab

[gloomy canyon]

what arnab said is basically correct

[tawny fog]

And yeah apply that logic

[tawny fog]

🥲🫂

[gloomy canyon]

though another way to look at is that
for 1/0 =x
x is valid for every value

i forget exactly what the proof if is, but basically if 1/0=1, then 1/0=2, and also -2, or 10^100

thats another reason why its undefined

[sharp pecan]

I believe that cavendish207 is not actually interested in this and just said that to make it seem like they had a question

[obtuse pebble]

@uneven ravine Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[silver plover]

need some help with this please

im new to this Kernel terminology

CHARTBIT

LONG TIME NO SEE

as u can see

im back

[unreal musk]

Read my mind

[silver plover]

semester 2 has commenced

[unreal musk]

Welcome back!

[silver plover]

and im back to learning again

[unreal musk]

Assuming by the kernel of that matrix $A$, they mean the kernel of the linear map $f : \mathbb{R}^{2} \to \mathbb{R}^{2}, f(x) = Ax$?

[silver plover]

lemme send u my definintion

[warm shale]

chartbit

[unreal musk]

Ah yea same thing haha

Might help to find the determinant of that matrix (why?)

[silver plover]

r we trying to find the 'x' in Ax = 0 ?

[unreal musk]

Well that is what we want to do of course, ideally

But here it's a nice square matrix that we have

[silver plover]

i was thinking writing 2x +4y = 0 and 3x -2y = 0

then maybe solving for x and y?

wont x and y just be 0 lol

hence is the kernel just the trivial solution?

[unreal musk]

Also, are you familiar with the fact that a linear map is injective (one-to-one) if and only if its kernel is trivial?

(similar with group homomorphisms too )

[silver plover]

i am not , no

[unreal musk]

Oh, well then, exercise for the reader to do both

[silver plover]

lmao

[silver plover]

going back to what u said here

the determinant is -16

hence that shows that A is invertible

so for invertible matrices, will the kernel ALWAYS be the trivial solution?

interesting

[unreal musk]

[left multiply by the inverse matrix]

[silver plover]

ofc

ye this makes sense now

thanks chartbit

[wise talon]

beat me to it

bleh

[silver plover]

DERPZ

[wise talon]

hey

[silver plover]

havent seen u in ages as well

im in semester 2 now

[wise talon]

nice

[silver plover]

back learning again

[wise talon]

so that kernel definition is shockingly close

in fact its not just close

its the exact one as in group homomorphisms

[silver plover]

lmao

[wise talon]

so let f be a homomorphism from G to H

the Ker f = {g in G | f(g) = e_H}

so here you think of e_H as the 0

[silver plover]

i see

btw i havent done homhphpophposiissm groups before

[wise talon]

ah okay

its fine

its a nice way to think about it tho

[silver plover]

i just started 2 days ago

😭

[unreal musk]

You'll get to them soon enough

[silver plover]

im about to move onto gaussian elimintation

[unreal musk]

Nice nice

[wise talon]

vector spaces are just abelian groups under +

[silver plover]

for this module

my lecturer has a 'flipped classroom strategy'

so i have to learn the content

[unreal musk]

Modules are like generalisations of vector spaces over arbitrary rings

[silver plover]

before the lecture

we only have 1 lecture a week for this

...

[unreal musk]

Oh, damn, I see 🤯

[silver plover]

thats why im learning this all now

since my first lecture for this module

is

tmr

...

😂

[unreal musk]

Oh damn, fair enough! Best of luck for it

[silver plover]

learning is so much better than revision

too much pressure when revising

[wise talon]

take group theory

real fun

[unreal musk]

Awww I see, for me it's the other way around

[silver plover]

im doing groups and rings next year

[wise talon]

noiceee

NOICE

idk why no fields but its probably included

[unreal musk]

Well, actually, can't lie, I'm just a nerd

[silver plover]

... INSTEAD of real analysis 2

[wise talon]

[wise talon]

NO

NO

no

no

[silver plover]

mate i aint doing that shite

[wise talon]

do both

[unreal musk]

https://tenor.com/view/red-card-referee-red-sent-off-dismissed-gif-21029120

[wise talon]

not allowed

if you do not take analysis 2 you will be forced to wait

69mins for help