help-36

[jade fable]

mutually exclusive mean if event A happens then event B wouldn't happens, if event B happens vice versa...

[rain compass]

yes

[jade fable]

independence for those two events could happens at the same time

[rain compass]

ok, then i'm not sure how to go about this, sorry

[jade fable]

its ok

i think the question is solved cuz im tired

i will try it later

.close

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[jade fable]

.reopen

[final saddle]

✅

[jade fable]

if event A and event B are not related, P(A)=1/2, P(AUB)=2/3 then P(B|A)=?
okay so what is P(AUB)?

P(AUB)= Probability of what?

can someone describe it by words?

[keen prairie]

it's probably A or B

[jade fable]

got you

they has no intersection so => P(A)+P(B)=P(AUB)

[keen prairie]

that's right

also, it's supposed to be they have

[jade fable]

so i put those numbers in, 1/2+P(B)=2/3

and i got 1/6=P(B)

[jade fable]

thank you

[jade fable]

somehow its wrong

but i can't understand why its wrong

[keen prairie]

i think it's somewhere in the P(B|A)

[jade fable]

P(B|A)=P(B) isn't it?

[keen prairie]

P(B|A) is for probability of B given A

it's like

the probability that b happens, if you know that A already happened

[jade fable]

but in this case P(B|A) will be just P(B)

[keen prairie]

no?
why?

[jade fable]

since theyre independent

event A and event B are independence

two independent events

[keen prairie]

oh

[keen prairie]

right

what does A and B are independent events imply?

[jade fable]

"if event A and event B are not related"

[keen prairie]

yes

but if those events are not related

what information do you have?

[jade fable]

given that P(A)=1/2, P(AUB)=2/3

[keen prairie]

right

[jade fable]

god

god

nope

P(AUB)-P(A)=P(B)=P(B|A)

am i right

right

fk

why its wrong?

1/6=P(B)=P(B|A)

[keen prairie]

wait a sec

that's wrong??

[jade fable]

it should be correct but the answer on book got P(B|A)=1/3

[keen prairie]

oh

wait a sec

your book is correct

so

[jade fable]

could you point out the errors i made

[keen prairie]

if A and B are independent events, we actually have P(B|A) = P(B| not A) = 1/2 P(B)

[jade fable]

"P(B| not A)" i cant follow

what is it?

what does it mean?

[keen prairie]

probability of B happening if you know that A doesn't happen

[jade fable]

does it matter if A happens or doesnt happens

[keen prairie]

does what matter?

B?

in this case no

[jade fable]

P(B| not A) = 1/2 P(B) , i cant follow it

it looks like P(A) * P(B)

[keen prairie]

whether A happens or not doesn't affect the probability that B happens

therefore

the probability that B happens when A doesn't happen = the probability that B happens when A happens

we also have the probability of A happening = 1/2

so the probability that B happens when A happens is 1/2

the probability that B happens without A happening is 1 - 1/2 = 1/2

get it?

[jade fable]

i just put it all into the formula

and i got P(B)=1/3

[keen prairie]

wait a sec

which formula?

[keen prairie]

and yes, you're right about that

[jade fable]

im still tryin to find the error

it seems P(B) will be 1/6

[keen prairie]

which formula are you using????

[jade fable]

if event A and event B are independent then P(AnB)=P(A)*P(B)

[keen prairie]

but how would P(AnB) help?

it's just the probability that A abd B both happens

*and, not abd, typo

[jade fable]

P(AUB)=P(A)+P(B)-P(AnB)

then you put those numbers in and heres the answer P(B)=1/3

[keen prairie]

right

[keen prairie]

yep

[jade fable]

but in my mind P(AnB) should be 0

since event A and event B have no intersection

[keen prairie]

ooh
that's where you're wrong

did the prompt explicitly tell you that?

[jade fable]

<@&286206848099549185> if event A and event B are not related(independent), P(A)=1/2, P(AUB)=2/3 then P(B|A)=?

[keen prairie]

so
right
those events are independent
but that doesn't mean they can't both happen at the same time

[jade fable]

P(AnB) should be 0, can someone explain why it isn't 0

they have no intersection so it should be just zero,P(AnB)=0

[keen prairie]

where did you get that information?

[rain compass]

i'm starting to think this has infinitely many solutions

[jade fable]

from my mind

[jade fable]

help me

[keen prairie]

no
that's wrong

well

A and B are independent

[jade fable]

could you explain why?

[keen prairie]

well
i'll use a counterexample (see next message)

imagine that you flip a coin twice

let event A be "you get heads the first time you flip the coin" and event B be "you get heads the second time you flip the coin"

A and B are independent

but that doesn't mean there's no intersection (if there is actually no intersection, you wouldn't be able to get heads both of the time)

but you can

[jade fable]

so the intersection is first time see the head on the coin and second is also the head

[keen prairie]

yeah (the grammar's a bit bad though)

"the intersection is when you get heads both times" is better

[jade fable]

god, could you fix it

[jade fable]

yes it sounds reasonable

[keen prairie]

right

so

[jade fable]

yes ure right

[keen prairie]

the formula for finding the intersection still works

if the events are independent

am i right?

[jade fable]

yes ure right, the error i've made is i assume that the intersection is 0 without further proving

[jade fable]

i will take it to my note

otherwise i will make the same mistake next time

[keen prairie]

uh
just remember that if two events are independent
it doesn't mean that there's no intersection

[jade fable]

sure, the example you have given is very straightforward

thank you so much

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[pliant fulcrum]

Hello

[pliant fulcrum]

I dont quite understand how to find limits of a rational function

can you please explain to me

thank you

as far as i understand i have to find an asymptote in the first place

but then there are 4 different limits for a rationa; function

which i dont get

ok

thank you

.close

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[bleak robin]

Which area is larger: a circle of radius 3cm or a square of length 5cm? this is my question

[cedar ivy]

Find both

[drifting raptor]

.

[thorny tendon]

^^

[bleak robin]

yeah i did the square root will be 9 or 12

[thorny tendon]

?

[drifting raptor]

wdym?

[bleak robin]

nor right

[drifting raptor]

find area circle

[bleak robin]

will it be 0.98

or 3

[drifting raptor]

no

[final tangle]

will what be 0.98 or 3

[drifting raptor]

where u get 0.98?

[bleak robin]

0.98

[final tangle]

what's 0.98 and where is it coming from

[bleak robin]

its is coming from the area of the circle

[final tangle]

what's the formula for area of a circle and how exactly are you applying it here

[thorny tendon]

^^

[bleak robin]

like e

[thorny tendon]

e is not in the formula for areas here

[bleak robin]

r=0.98

i meant

[thorny tendon]

You just said r = 3

[final tangle]

where's r=0.98 coming from
where even is that seemingly random number 0.98 coming from

[bleak robin]

i rounded up

[final tangle]

rounded what up

[bleak robin]

i rounded the 0.97721 upp

[final tangle]

where's 0.97721 coming from

show all your work

what's the formula for area of a circle and how exactly are you applying it here

[bleak robin]

il take a picture of it

[final tangle]

3cm isn't the area

[bleak robin]

so its wrong

[final tangle]

yes its wrong

[bleak robin]

how can i make sure this formular is right

[final tangle]

what's the basic formula for the area of a circle

(don't overthink this)

[bleak robin]

yeah sorry im having a hard time idk why

[final tangle]

$\text{Area}_{\text{circle}} = , ?$

[soft zealot]

ℝamonov

[bleak robin]

im confused

[final tangle]

don't over think this

what's the basic formula for the area of a circle
A = ?

and if you really don't know it, simply look it up

[bleak robin]

is it this The area of a circle is pi times the radius squared (A = π r²)

[final tangle]

yes

and here you are given the radius

[bleak robin]

which is 3

[final tangle]

apply that formula and get the area

[bleak robin]

so i wil put in 3= π r²)

[final tangle]

no

[bleak robin]

or at the end

[final tangle]

why are you replcing A with 3

[bleak robin]

im an idiot it wouldnt make sense if i did

[final tangle]

you are told that the radius is 3
and the radius is represented by the variable r

so the variable you should be replacing with 3 is r

if it wasnt clear, A represents the Area because Area starts with an A

[bleak robin]

sorry where do i get the a in the calculator

[final tangle]

wdym

A is the variable that represents the area

after subbing in the correct value

you'll have
A = some numerical value

[bleak robin]

i got 3.14

[final tangle]

that numerical value will be the area

3.14 is an approximation for pi

,texconfig colour white

[bleak robin]

so i calculated it wront

[final tangle]

i have nfi what you're doing

lets start with the formula for area

A = π r²

you are told that r=3

[bleak robin]

yeah

[final tangle]

can you substitute r=3 into that

and do nothing else

[bleak robin]

yeah

[final tangle]

what do you have after that

[bleak robin]

sorry im looking for the r in my calculaotr

[final tangle]

i didn't say touch a calculator

[bleak robin]

oh okay

[final tangle]

can you substitute r=3 into that
and do nothing else
like literally cross out the r and replace it with 3

[bleak robin]

yeah i did

[final tangle]

and can you show me what you have after doing that

just that

nothing else

[bleak robin]

yeah im taking a pic now

[final tangle]

fml

i'm out

[drifting raptor]

same

[bleak robin]

multiply

[drifting raptor]

uh?

to complicated

[bleak robin]

nah i need to do sum with thr r

[drifting raptor]

circle

[bleak robin]

yeah

[bleak robin]

3

[drifting raptor]

if

[bleak robin]

yeah im starting to get it a bit now

so i will take r=2 away

yeah

so i will take away the 3

r yeah

[bleak robin]

yeah i did the r(3)2

[bleak robin]

yeah i do know that

[bleak robin]

do i need to put in a calculator or do take away

[astral ice]

yes

wait no

forgot you can express it in term of pi

[bleak robin]

wait sorry so the formular is r=(3)

2

[astral ice]

you need an exact answer

just say 9pi

9pi cm^2

wait that’s not even right

how is it 9pi

it should be 4pi

pi*r^2

r = 2

oh

no wonder you were approximating lol

[bleak robin]

so 3cm is equal to 4 4 cm 2

[bleak robin]

im starting to get it a bit no

will it be 6

[bleak robin]

9

so would it be 9 r

[bleak robin]

oh alright

so take away that

and just leave it with 9

[bleak robin]

so dont remove it i should leave it there

[bleak robin]

oh i get you now

[bleak robin]

so its not 9r its the other

[bleak robin]

il show you my work of it

no

its my assignment i have due for friday im just doing it now so i dont have to worry for it

[bleak robin]

so thats right

i think i know how to do that il write out the formular

[bleak robin]

ahh so add the 2cm squared beside it

sorry 2

[bleak robin]

yeah that would be clearer if i write that

[bleak robin]

yeah i realised that

i will just say 3x3 9

r

not r i meant

yeah

so

yeah alright

[bleak robin]

the top one

yeah

so cross that two out

sorry the cm2

beside the pi

[bleak robin]

oh alright did i displayed it wrong

[bleak robin]

yeah im an idiot sorry about that

i confused myself

im not tired i love maths but im just stupid lol

yeah il try do i will take down the square one and show you

[bleak robin]

yeah

[bleak robin]

25

cm

25cm 2

with the small 2 beside it

25 cm squared

[bleak robin]

yeah i know

[bleak robin]

yeah im starting to get an understanding

of i t

[bleak robin]

ohhhhh okay

the 9 (3) is bigger

really

ohhhhh alright

[bleak robin]

yeah i can see how its bigger than it

and can i also give you another question i need help on

yeah but you explained it and broke it down for me soo good

alrifght i will sned you the second qustion

⦁ A rectangle and a square have the same perimeter. If the Length and Width of the rectangle are 4cm and 20cm respectively, what is the length of the square?

so i should do the formulas first

how can i do this

wouldnt the square possibly be 20 cm lenth

p=4 a

or p=20 a

yeah okay and sorry if im making it hard for you

no i dont need to rush

p=24 Q= 24

thats wrong

caus ei need to multiply

no

sorry but how can i write the formulas like

1w

or just 1

yeah

ahh so it cant be just 1 it has to be 1w

im starting to get this

yeah correct

yeah

A rectangle and a square have the same perimeter. If the Length and Width of the rectangle are 4cm and 20cm respectively, what is the length of the square?

thats the question its says legnth

[bleak robin]

do i gotta multiply it

no

or do i got to add them togather

[bleak robin]

yeah

yeah

yeah i know like add the legnts of it

ohhhhh

so like 2 is width and 5 w it will be like 2+2+5+5

nah sorry i meant 2 is lenght and 5 is widht

for an example

does that make sense

apple+apple

i would say 2

[bleak robin]

im getting and understanding from it

i can se that slowly

its distributing a to b then c

[bleak robin]

so for example it wil be like t(c+g)=(tc)+(tg)

yeah

so that right

i understand it

[bleak robin]

l+w=(1 l )+(1. w) = (1+1)lw =2l =2 w

i did so wrong

im gonna do it again

l+w=(1 l)+(1 w)= (1+1) l = 2 .w=2l

is it correct or not

oh sorry i just confused myself so hard

let mne try again

l2 +w2

yeah i did

did i get it right

4l and 20w

no i dont know how to replace thing s

sorry

i misread that wrong

i know

i understand it

i got to replace the 2l 2w

Iw

Iw 42

[bleak robin]

is it like this exampke

i=4

4

oh sorry

l=4

becomes 2l+2l=4l

ohhh

2w

it dosent im such an idiot

no

I cm

and yeah i overthink too much when im doing maths#

4=l

OR I

oh its okay thanks for helping me

<@&286206848099549185>

guys i really need help <@&286206848099549185>

.close

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[grizzled swallow]

assuming x and y aren't 0 what is it?

[rain compass]

x^2 + 2xy + y^2

[grizzled swallow]

ah

thanks

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[tranquil pine]

I think I got the top 2 correct. Im not sure about the 3rd one.

[tranquil pine]

Changed

<@&286206848099549185>

Is it (-9sin(3) - 4(3)) - (-9sin(0)-4(0))

[final saddle]

@tranquil pine Has your question been resolved?

[rain compass]

whereas displacement is the integral of v(t) from 0 to 3, distance will be the integral of |v(t)| from 0 to 3

so split the integral whenever it goes from positive to negative or vice-versa and flip the signs

[tranquil pine]

Im not sure how to do this.

How do I split it?

<@&286206848099549185>

.close

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[ivory valley]

can anyone help me with this

[fallow zinc]

<@&268886789983436800>

[sturdy ocean]

banned ty

[final saddle]

@ivory valley Has your question been resolved?

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[tranquil pine]

Any help with q10 pls

[final saddle]

@tranquil pine Has your question been resolved?

[tranquil pine]

<@&286206848099549185>

[final saddle]

@tranquil pine Has your question been resolved?

[weary wharf]

Start by trying to find the time at which pebble A hits the ground

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[tranquil pine]

where have i gone wrong

[tired monolith]

quadratic sequence

write a quadratic formula

[tranquil pine]

an^2+bn+c?

[tired monolith]

actually wait

theres no way that works because of the rate it expands

[tranquil pine]

you are

embarassingly close

to the answer

hmm

[tired monolith]

lol

[tranquil pine]

im not sure what im issing

[slender token]

lol

[tranquil pine]

missing

[main jasper]

aha

[slender token]

just saw it

[tranquil pine]

+c?

it's not what you are missing

wait

is it the +2

to do with that?

idk

[main jasper]

think about ur first term if n=1

[tranquil pine]

ok so basically you ave the second diff of 2

correct?

yes

that means it is going to be a quadratic, so start with n^2

which gives you 1,4,9,16...

yes

omfg, you poor soul

dont i divide by 2

youa re so close

ok

do i - 2

from -1

you have to subtract

the values

-1-1=-2

2-4=-2

7-9=-2

etc

OH.

that was rather embarassing

makes sense?

yes

im stressing cuz i have exams tmrw

and i havent completed the algebra list

don't overstress yourself, focus on the fundamentals of what you have learned. A little stress is good to keep you on your feet but too much will cause these slip ups

[tranquil pine]

i did the set work but i realised it didnt include alot of the topics

only today

i realised

so im not sure how to work this out

i can send you the work for this one

actually i found an explanation

of this problem

which might clear a few things up

i know how to work the question

just the topics

wait actually one thing

when do i include "+ n"

i have all these topics

im going to be honest, if i tried to explain, you probably wouldn't understand half of what i said

[tranquil pine]

oh

i would use yt or khan academy

ok thank you

they should have those covered in very good detail

i think i clicked on the wrong video

or is this normal

thank you for your helo

help

i will continue

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[tranquil pine]

search quadratic sequences

[final saddle]

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[opaque ember]

b&

@slender token pls dont delete modpings

[slender token]

oh

sorry didn't know that

a Ye i know why

ghost pings

[opaque ember]

ye

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[rancid mica]

We have that sqrt(400) is 20 and sqrt(100) is 10 soo it must be between those numbers try squaring some number.

Factorize 196 could help to.

[final saddle]

@tranquil pine Has your question been resolved?

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[acoustic galleon]

i just apwanted to make sure fbg was 35 and abc 180

[tranquil pine]

Correct

[acoustic galleon]

thanks

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[steel talon]

12 people sit around a table and each person knows 4 others. how many ways can they be arranged so no one sits next to someone they know?
here is my thought process: it should be 11!-(2*7!)
is this acceptable?
i get 39906720

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[steel talon]

<@&286206848099549185> please

[steel talon]

anyone?

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[jolly tapir]

Here is my interpretation

[grim badger]

What exactly are you trying to do?

[jolly tapir]

Of question 7

My internet's weird, I don't know why it's not sending some pictures first

Anyway. Volume of solid of revolution.

[grim badger]

I don't recall how to do that stuff, sorry

[jolly tapir]

Need some help with understanding this problem: Question 7

[jolly tapir]

Mainly I am confused by x>=0. Surely it cannot mean everything to the right of x gets rotated and counted as the volume? That'd be infinite

<@&286206848099549185>

[crude garden]

So what if it is infinite?

[mortal wadi]

they just mean this area

[jolly tapir]

that's probably not the aim of the problem then? and i'm probably understanding it wrong, that's what

[jolly tapir]

why would it be x>=0 though, that'd encompass every intersected area where x>=0 no?

[mortal wadi]

no because the rest of the graph isn't bounded

[crude garden]

How would you rotate around the x axis in 2D?

[jolly tapir]

this is a calculus problem

it's 3d

[crude garden]

Aight

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[jolly tapir]

Oops

Meant

.close

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[median scaffold]

ur just posting a bunch of random problems without saying anything and ur still expecting me to answer u? lol

[astral compass]

#help-8, ty

[icy glacier]

#❓how-to-get-help read the rules buddy

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[viral swan]

@tranquil pine Have you tried logarithmic differentiation?

Or the fancy dumb name for rewriting it with e^ln()

And using log rules

I've never seen something like that

These problems don't usually cause too many problems as logarithmic differentiation though

So you could like uhhh

$f(x)=7x^{3e^{5x}}$

[soft zealot]

PapaBread

[viral swan]

Oh wait this is harder than I thought

Maybe

[soft zealot]

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

[viral swan]

$f(x)=e^{\ln(7) + (3e^{5x}) \ln(x)}$

[soft zealot]

PapaBread

[viral swan]

Would this be easier to differentiate

I would think so

It hurts my head but

I think it'll work

Np

Say .close

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[crimson scarab]

please someone respond this time

.close

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[leaden trail]

https://media.discordapp.net/attachments/882634549178273853/920804071865221160/IMG_3680.png

[leaden trail]

Can someone help?

.close

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[eager harness]

i need help with this

the first picture is a description

the second picture is the graph i drew

[eager harness]

i need help with these 2

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@eager harness Has your question been resolved?

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[radiant ruin]

do i use lhs-rhs to prove 4a?

[grave oracle]

u can start wid a gen stuff like a perfect sqr is greater than or equal to 0

from that u can reach to a concl

for 4a

[radiant ruin]

i squared both sides and then subtracted rhs from the lhs

[grave oracle]

ya that is also a method

after that ?

[radiant ruin]

idk what to do from there

[grave oracle]

u got ?

kk

I'll tell both ways

[radiant ruin]

i got a^(2)/4 + b^(2)/4 ≥ 1/2(ab)

but idk what that proves

[grave oracle]

understood ??

[radiant ruin]

OHH i have to get rid of the fraction

thank you so much

i get it now

[grave oracle]

np np

[iron breach]

Satisfying math!

[radiant ruin]

.close

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[grave oracle]

feel free to dm if u get doubts on this

[radiant ruin]

thank u so much :)))

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[solemn maple]

I did what I thought was a similar question to this but when I saw that this equation had cos and sin in it, I wasn't sure how to do this probelm

the question I was able to complete was solving for sin^2x= 3/4

[grave oracle]

I got only sinx 2 values
one x I got other idk angle value

[solemn maple]

I don't really understand what you mean

[grave oracle]

I got sinx = a,b

can u find x ??

[solemn maple]

that's what I'm confused with, I'm not sure how to solve for x because I'm not sure what the angle is

should I be shifting some of the equation to the right?

[grave oracle]

this is what I got
x=arc(-1/5) , (150,30)

[tranquil pine]

cos(x)^2 = 1 - sin(x)^2
and for comfort say u = sin(x)

[solemn maple]

is this from the double angle formula?

[grave oracle]

I'm adding 10 and subtracting 10

in the pic

[tranquil pine]

No it's from
sin(x)^2 + cos(x)^2 = 1

[solemn maple]

where do you get the - 1 from? in the question it says +9

[grave oracle]

@solemn maple I did it in a better and a understanding way see can u understand

[solemn maple]

ohhh, alright

thank you @grave oracle

[grave oracle]

Np if u still get doubt feel free to dm

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[sick musk]

can someone explain this to me. im confused please

[iron breach]

SSS Congruence Rule
The Side-Side-Side congruence rule states that, if all the three sides of a triangle are equal to the three sides of another triangle then the triangles are congruent.

[sick musk]

.close

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[sick musk]

.reopen

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✅

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[calm socket]

How would I use the $25 off in this question?

[calm socket]

nvm figured out the answer, just had to subtract 25 from the answer I got

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[little sedge]

How to solve this using gauss Jordan elimination?

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@little sedge Has your question been resolved?

[little sedge]

<@&286206848099549185>

[gusty drift]

To perform Gauss-Jordan Elimination:

Swap the rows so that all rows with all zero entries are on the bottom
Swap the rows so that the row with the largest, leftmost nonzero entry is on top.
Multiply the top row by a scalar so that top row's leading entry becomes 1.
Add/subtract multiples of the top row to the other rows so that all other entries in the column containing the top row's leading entry are all zero.
Repeat steps 2-4 for the next leftmost nonzero entry until all the leading entries are 1.
Swap the rows so that the leading entry of each nonzero row is to the right of the leading entry of the row above it.

So basically, you should just be able to apply this algorithm

[little sedge]

Thank you ! But I've been trying for more than an hour and I still can't get the answer

[cedar ivy]

You can show what you did

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[lyric sandal]

Im wondering if someone can further explain on how i can solve this problem

[lyric sandal]

What is the domain of h ( x ) = | x |, if range is { 0, 1, 3 } ?

[gusty drift]

So because |x| is not injective (ie one-to-one), we have several options for the domain

What have you tried?

[lyric sandal]

i haven't tried anything yet, im new to this type of math and im having trouble on figuring out where to start

okay

okay

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[tranquil pine]

Hi could someone help me with 7 b I’m confused on how to solve it I found the derivite 4x^3+12x+12x+4

[hard vapor]

send teh question

ok

if the tangent line is horizontal, what is the slope of the tangent line?

[tranquil pine]

It’s 0 if I’m correct

[hard vapor]

correct

[tranquil pine]

So what do I do with it?

[hard vapor]

and what is the slope of the tangent line at any given point?

[tranquil pine]

1 I think

[hard vapor]

no

you should already know the answer to this

(you yourself gave it)

[tranquil pine]

0

[hard vapor]

no

it is the derivative

the derivative tells you the slope of tangent line of a point

[tranquil pine]

So do I set the derivative equal to 0?

[hard vapor]

and I believe that your expression for derivative is incorrect

[hard vapor]

yes

[tranquil pine]

Oh ok

Oh thank you I figured it out the correct derivative is 2(x^2 + 2x+1)(2x+2)

And I got x=-1

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[warm solar]

Could someone please check problem number 8?

Did I do it right?

Are there more steps too it?

[frail flax]

looks good to me

but ur adding 90 to 252 not 9

[warm solar]

Thanks just wanted to make sure I found AB

Ik

I did 90

I just put 9

[frail flax]

yeah

thats the only problem xD

[warm solar]

I also put x instead of ab

Thanks man @frail flax

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[keen prairie]

(Krull's theorem in Noetherian rings.) My attempted proof is weirdly simple, so I automatically assumed that it's somehow wrong. Is this correct?

Take an ideal I. If I is maximal, we're done. If not, it's contained in another ideal. Call it J. Repeat this process.
Since there are no infinite ascending chains, we will eventually reach a maximal ideal.

[keen prairie]

(and also how can i prove this for non noetherian rings)

[keen prairie]

neko?

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@keen prairie Has your question been resolved?

[keen prairie]

<@&286206848099549185>
btw join the abelian revolt

[keen prairie]

nvm i figured it out

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[soft grove]

i have to find all of the angles and i do not knowhow

[soft grove]

for the last one it is COD not CAD

[iron breach]

@soft grove Is O the center of the circle by chance

[soft grove]

i dont think so i think its just an angle

[grim badger]

You should get clarification on if O is the center or not because that problem applies inscribe and central angles

[soft grove]

ok let me ask

it is

the teacher said

o is the center

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[grand thistle]

can someone explain the scalar product also known as the dot product?

[final saddle]

@grand thistle Has your question been resolved?

[modest crystal]

It's an operation inside a vector space that holds certain properties

For example, <au, v> = a * <u, v> where <*,*> is inner product

the dot product is a specific inner product

say u = (u1, u2... un) and v = (v1, v2... vn)

then the dot product of u and v

<u, v>

is u1 * v1 + u2*v2 ... +un*vn

[grand thistle]

it gives a scalar product right but that what does that number represent

[modest crystal]

u= (1, 2, 3), v = (4, 5, 6)
<u, v> = 1*4 + 2*5 + 3*6

ah

well, it's used for projections, degrees between vectors, etc

which is also used to find orthonormal vectors

[grand thistle]

true

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[fiery beacon]

.open

.reopen

<@&286206848099549185> my help channel got taken I been waiting for 15 minutes btw

[fallow zinc]

Ask a question, and don't ping helpers right away

[fiery beacon]

@fallow zinc has it been 15 minutes?

[fallow zinc]

No, you just opened this channel

[fiery beacon]

oh it has been 8 minutes sorry

[fallow zinc]

more like 2

[fiery beacon]

I was in the previous channel in #help-28

[fallow zinc]

You also still haven't asked a question

[fiery beacon]

this is wat I am confused about I tried putting in both methods yet neither of them worked

[final tangle]

the question is cut off

[fiery beacon]

alright I will show more on sec

[final tangle]

and also you're not being asked for the solid of revolution

[fiery beacon]

oh wat is it asking

[final tangle]

read the question carefully

[fiery beacon]

oh it is the base of a solid object

Im still not entirely sure what that would mean

like would it extrude in a different place

[fallow zinc]

The object extends along the z-direction

[fiery beacon]

I notice this alot

it seems that a lot of the questions I get wrong are due to misinterpretation of the question being ask

Im still trying to figure out how far it will extrude in the z direction

[fallow zinc]

The question tells you the height (Hint, given where you are along the x axis)

[fiery beacon]

oh so 9-4

[fallow zinc]

no

at each x value, the vertical cross section is a square

[fiery beacon]

OH

idk I think I almost got it

[fallow zinc]

And final hint: $V=\int\dd{V}$

[soft zealot]

Mosh

[fiery beacon]

it is like extruding at the x axis?

like I multiply the length by 2

[fallow zinc]

at each x value, you picture a square that's coming out of the page

where the side length of each square is given by the gap b/w the functions

[fiery beacon]

I might have to restart the question it was too many tries

it will be the same concept just different numbers

[fallow zinc]

Yeah

[fiery beacon]

I got it

I square the whole thing

[fallow zinc]

Yes, so your infinitesimal of volume is $\dd{V}=A(x)\dd{x}$

[soft zealot]

Mosh

[fiery beacon]

this reminds me of how I was trying to figure out the volume of triangle and I split up the length and the width into two functions

and I took the lenghts and divide it by the height to get different slopes

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@fiery beacon Has your question been resolved?

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[forest osprey]

i have no idea how to do this

[coral ravine]

What have you tried so far

[forest osprey]

the furthest i got up to was 11-3 and 20-4

after that im lost

[wind glacier]

What does 11-3 represent

[forest osprey]

isnt it the distance between the x axis

[wind glacier]

You mean x coordinates?

[forest osprey]

oops yes

[wind glacier]

It is that but what else can it represent in terms of the rectangles

[forest osprey]

honestly im not sure

[wind glacier]

How about now?

Remember that the rectangles are identical

[forest osprey]

oh so

yeah

so if the distance is eight

then its 3 and 3

i mean

4 and 4

[wind glacier]

You havent subtracted the yellow bit

[forest osprey]

so then its 3 and 3

yellow bit being 2?

[wind glacier]

3 + 3 - 2 = 4

[forest osprey]

no i mean

[wind glacier]

Don't try to do this using numbers

[forest osprey]

alright

[wind glacier]

Use placeholders and algebra

Let's say the longest side of the rectangle is called l and the shortest side or width is w

So Red = l
Yellow = w

[forest osprey]

yeah

[wind glacier]

We can see in that picture that the distance is actually the same as

2l + w = 8

Do you understand that?

[forest osprey]

yes

[wind glacier]

Now what about the y coordinates

The difference is 16 but how can we get it in terms of w and l

[forest osprey]

2l-2=16

[wind glacier]

Oops sorry I made a mistake before

It shouldn't be 2l + w should it

What should it actually be

[forest osprey]

2l - w ?

[wind glacier]

Yes

[wind glacier]

This isn't quite right

[forest osprey]

okay so we have 2l

[wind glacier]

Use the colours if you have to

Yes we definitely have a 2l

[forest osprey]

2L + w = 16

[wind glacier]

Thats exactly right

So now we have two equations
2l - w = 8
2l + w = 16

[forest osprey]

so its a simultaneous equation

[wind glacier]

Yes

So can you solve this

?

[forest osprey]

l = 6

[wind glacier]

Good

[forest osprey]

w = 4

[wind glacier]

Yep and im pretty sure thats the answer

[forest osprey]

so c is (6,4)

[wind glacier]

Close

Sorry what I said was misleading

Remembering C is further on than A

[forest osprey]

so what do i do next

[wind glacier]

Look at where A is

You need to get from A to C

How do you do it

[forest osprey]

im not sure what you mean by that

[wind glacier]

A is at (3, 4) right

[forest osprey]

the distance between them?

yeah

[wind glacier]

And we know that the distance to C is 6 along and 4 up

So what will be the coordinate of C

[forest osprey]

yeah

oh

3,4+6,4

its 9,8

thank you