help-42

[trail valley]

V≈70.69

[regal geyser]

sakjhdkf

[regal geyser]

yes!!

[trail valley]

😂

[regal geyser]

ok now you have volume in m^3

[trail valley]

Yep

[regal geyser]

and we multiply by the density

[trail valley]

70.69*450?

[regal geyser]

is density 450?

yes ok

[trail valley]

3460.5

[regal geyser]

well that makes sense, in 1 meter cube of wood weights a lot

[regal geyser]

hm i see

[regal geyser]

hm is this?

that doesnt seem right

[regal geyser]

what~

wait

it is giving u the wrong answer lol

[trail valley]

Ohhhh

[trail valley]

There

[regal geyser]

ksaljdh

[trail valley]

Fixed?

[regal geyser]

that is the right answer

yess!

[trail valley]

Ok

Okok

[regal geyser]

remember we could do this now bc

we had meters and meters

if you have inches you need to transform the units

[trail valley]

Now find the mass of the trunk

[regal geyser]

this is the mass

31810.5 kg

which is a LOT btw

almost 32 tons

asdfg

[trail valley]

31810.5?

So i put that?

[regal geyser]

yes ah

that is the final answer, in kilograms

[trail valley]

Ok part B

[trail valley]

The bottom part

[regal geyser]

yeah let me see hm

[trail valley]

👌

[regal geyser]

I don't understand

we don't have the growth rate, do we

?

[trail valley]

I found an example

[regal geyser]

I mean but with the data we are given there, we cannot calculate how much will the tree grow

[trail valley]

Huh?

[regal geyser]

yes, is like

we don't have enough data do we?

[trail valley]

Fine lets skip this question and do

[regal geyser]

I mean now I have to finish my chem hw

kjsahdk

and it is very late : (

[trail valley]

The trunk will gain about 0.71 cubic meters of wood after four years?

[trail valley]

OMG SAME!!!

[regal geyser]

I mean but does the question say that?

[shut sierra]

correct

for part a, the mass of the trunk is 7952 kilograms

i dont know how you got 31810.5kg

[trail valley]

K thanks

[shut sierra]

0.75 is the diameter rather than the radius

[trail valley]

So i did something wrong?

[shut sierra]

yes the both of you multipled by diameter instead of radius

[trail valley]

Ohhh

[trail valley]

So can u help us with part A and B?

[shut sierra]

i just gave you the answer

[regal geyser]

that is right!

I did not read that

you need to divide it by 2!!

to get the radius

[shut sierra]

yup

[trail valley]

What was it?

[shut sierra]

.

[trail valley]

Ok

[shut sierra]

this is your answer to part b which is correct

[trail valley]

Can u gimme this one so i can submit do my last homework then sleep?

[shut sierra]

tell me how you would approach the problem

[trail valley]

Uhh tbh idk im dumb 😂

[shut sierra]

i'll give you the answer if you can figure out the method to solve the problem

save you all the calculation time

[regal geyser]

excuse me but how do you get that?

there is not enough information in the problem right(?)

that sounded mean srry ksadjhlf

excuse my horrible english

https://tenor.com/view/meow-cat-kitty-cute-bye-gif-17017321

[trail valley]

Ohh ohh

[shut sierra]

yes

[trail valley]

Convert the mass of the dish from kilograms to grams:

Use the formula for density to find the volume of the glass:
Density = Mass / Volume.

The dish is modeled as a rectangular prism, so the volume of a rectangular prism is given by:
Volume = Length x Width x Height.
Since the thickness is the height of the glass,

Since the dish is shown to be a square, the Length = Width.

[shut sierra]

you sound like you're just copy and pasting from ai

[trail valley]

😂

Sorry im just tired

I apologize

I apologize im just tired and still have other homework

[shut sierra]

how is the dish even shown to be a square

[trail valley]

Look can u help me

I gottta do other homework then sleep

[shut sierra]

no i will not help you

that was your last chance

[trail valley]

Im sorrry

Look i was doing good the whole time

@shut sierra

I was doing the work myself the whole time

Look bro it was only this one time im sorry

Niwi can vouch for me that i was doing the work myself

[regal geyser]

as a suggestion, it is better to wake up early and do the homework rather than going to sleep super late

it will help u in college, specially if u'll chose a major that needs lots of studying

[trail valley]

@shut sierra

[regal geyser]

brains dont brain as they should if ur tired idk

[trail valley]

I apologize

I wasnt even cheating on my homework

[regal geyser]

you need to find the volume of the thing

right?

[trail valley]

Idk

[regal geyser]

but you have the lengths in inches and the density in kg/meter

[trail valley]

Hey is this correct?

[regal geyser]

you need to multiply base times height

let me check with my best friend

wolframalpha!

[trail valley]

Lol

[regal geyser]

that seems right!

[trail valley]

Thanks

Imma submit

One wrong=80%

Or idk im scared to submit

[regal geyser]

uh that is weird

what r u studying?

[remote mural]

Double check ur work first

[regal geyser]

professors should not mark down that many points

[trail valley]

Is it 2182485 or 2182486?

[remote mural]

Mine do lmao

[regal geyser]

2.18249... × 10^6

grams!!

[regal geyser]

hm

but if u are in highschool then idk

[trail valley]

?

[regal geyser]

they should not do that but anyway

[regal geyser]

that is right

the answer is

[trail valley]

What 2182485?

[regal geyser]

2182485.26

yes

[trail valley]

What??

[regal geyser]

you rounded to the nearest intiger

[trail valley]

Is this correct?

[regal geyser]

yes!!

[trail valley]

Oh thanks

Shiit

I got 70% not bad

[remote mural]

What did you get wrong?

[trail valley]

My teacher disabled see what u got wrong

[remote mural]

Dumb

[trail valley]

Idk maybe cause people be sharing there friends the correct answer to get good grade

[remote mural]

I hate it when they do that. How are you gonna learn if you can’t see ur mistake?

[remote mural]

Oh okay makes sense

[trail valley]

Idk

Thats my assumption

[remote mural]

Fair

Good job

[trail valley]

How is this any of this isnt it a square?

[remote mural]

Although next time don’t leave ur hw till last minute. It’s not worth it

[remote mural]

Yeah that’s odd

[trail valley]

I got 8 and 8 correct but the shape?

[trail valley]

My excuse is never learned the lesson

Teacher never taught it

[remote mural]

You should ask ur teacher about that

[remote mural]

If the teacher isn’t teaching you the content you have to teach yourself. YouTube videos are very helpful in that regard.

Anyways, you should get to ur other hw

[trail valley]

Thank god tomorrows friday

[trail valley]

This is my other hw

[remote mural]

That isn’t chemistry

[shut sierra]

cylinder

[trail valley]

Oh thanks!! ^^

[remote mural]

How?

[trail valley]

One again i sincerely apologize for earlier

[shut sierra]

it's not very hard to visualize

[remote mural]

Some of us are mentally challenged misha 😒

[trail valley]

Uhh what is this?

[shut sierra]

this is just a sphere

with radius 5 units

[regal geyser]

semicircle with radius 5

[trail valley]

Sphere or semicircle?

[regal geyser]

oh

around the x axis

then it is a sphere

r u studying solids in revolution?

[trail valley]

Nope my teacher did not teach this

She assigned us 3 lessons to learn on r own cause she had to review with us for end year state exam

[shut sierra]

sphere with radius 2.5

[regal geyser]

we cannot see the full statement

[trail valley]

Ohh my bad

[remote mural]

Is this really 10th grade maths?

[regal geyser]

why?

[trail valley]

Now da surface area and volume

[regal geyser]

hm

[remote mural]

I don’t remember studying this in 10th grade lol

[regal geyser]

of the sphere problem right(?)

the area of the sphere is 4pi r^3 / 3

if I am not wrong

nvm

i am wrong

4πr²

[shut sierra]

the surface area is 78.54 square units, and the volume is 65.45 cubic units

[regal geyser]

why do u give the answer!!

[shut sierra]

because i do not care anymore

[regal geyser]

hm I mean every institution has their own way of teaching

[shut sierra]

he's just going to go to ai even if i don't

[regal geyser]

yeah but let him figure it out by himself

[trail valley]

Im tired im not drawing anything it asks to draw it dosent take points off for drawing

[shut sierra]

he says it's 4am now

[regal geyser]

kslajdhf

well I mean

if you can understand it is enough

i guess

this concepts are very important for advanced math!!

[trail valley]

2:59 am

Both u guys r the best thanks for helping me i appreciate yall verry much ^^

[regal geyser]

hm

[trail valley]

I really mean it i appreciate yaall

[regal geyser]

I mean if you find very difficult try getting a professor

[shut sierra]

cone with radius 8

height 7

[regal geyser]

or extra classes

[trail valley]

Thanks

Surface volume?

[regal geyser]

the volume of the cone is

pi r^2 h /3

[trail valley]

?

[regal geyser]

where r is the radius and h the height

[trail valley]

K

[regal geyser]

the surface area of the con is the circle at the bottom and the arc lenght that is formed by the rest

so it is

pi r^2 + pi r l

[trail valley]

Both yall thank i appreciate both yall @shut sierra @regal geyser thanks for the help

[regal geyser]

where l is the hypotenuse of the cone

[regal geyser]

hm

I am tired

[shut sierra]

the volume is 469.14 cubic units, and the surface area is 468.23 square units

[regal geyser]

https://tenor.com/view/meow-cat-kitty-cute-bye-gif-17017321

[regal geyser]

omg

but...

I mean

as someone that works as a tutor I am dying

[trail valley]

6/11!!!

ALMOST DONE!! #6!!!

[shut sierra]

how much do you charge usually

i'm thinking of becoming one too

[regal geyser]

I mean it depends

[trail valley]

6/11 so far

[regal geyser]

I work on my campus so its like 19 an hour

including drop in hours and everything

[shut sierra]

this is also a cone, this time with radius 3 and height 4

[regal geyser]

so I can get paid by just waiting sakdjhf

[shut sierra]

oh wow

[regal geyser]

I mean

what is your current math lvl?

I can give u some contacts

[shut sierra]

i live in asia so i don't think it would be relevant

😭

[trail valley]

I had a 2 tutors before when i was younger one was a short fat girl i think she had migit decease forgot what called and i dont remember the other one but he was a white guy young who bit his nales and ate a sandwitch front me once he was nice

[regal geyser]

aw but u still can!

[regal geyser]

...

I mean

[shut sierra]

💀

[regal geyser]

💀

what the hell

[remote mural]

This was so unnecessary to say 💀

[regal geyser]

It is not cool to call people like that

[trail valley]

That one thingy where ur like short

Like an elf

[regal geyser]

stop!!

[shut sierra]

im dead 💀

[trail valley]

Im sorry i just didnt know what it was callled

[regal geyser]

what do you mean "it"

[trail valley]

The name of the thingy

[regal geyser]

wrong gif

[shut sierra]

HAHAHAHAHHAA

[trail valley]

When ur short

[regal geyser]

https://tenor.com/view/poop-cat-meme-dark-fnaf-gif-2491098315710587638

oops

[remote mural]

LOL

[shut sierra]

NO WAY U USED THAT LAUGHINT GIF

[remote mural]

I saw that

[regal geyser]

KSDAJHFGSA

[trail valley]

Like abnormally short

[regal geyser]

IM SORRY OMG

wrong gif

[shut sierra]

https://images-ext-1.discordapp.net/external/G3a2MTdGcDusfWRiD6_dJswgkrkJFGBjSQFKeIlJcuk/https/media.tenor.com/aSkdq3IU0g0AAAPo/laughing-cat.mp4

[regal geyser]

I missclicked

https://tenor.com/view/poop-cat-meme-dark-fnaf-gif-2491098315710587638

I wanted to use this one!!

well I finished my chem hw

[shut sierra]

this is no longer a math channel

[regal geyser]

https://tenor.com/view/shocked-shocked-cat-silly-cat-cat-kitten-gif-7414586676150300212

[shut sierra]

this is a comedy channel

[regal geyser]

maybe

I mean it is late...

I had a long day so

[regal geyser]

I guess ill just go now ah

[trail valley]

See

[shut sierra]

where are you from

[regal geyser]

...

[trail valley]

I forgot what it was called

[regal geyser]

complicated ah

in a nutshell

I was born in Peru, but my parents are from italy and arabic, and now I am living in california

and I study and work here ah

[shut sierra]

that is rather complicated

[trail valley]

Idk y this problems so big

[regal geyser]

hm to some extend

[shut sierra]

bigger than the girl with dwarfism?

[regal geyser]

OMG

[trail valley]

Oh nah

[regal geyser]

guys may I ask how like

[trail valley]

https://tenor.com/view/owm-midget-running-gif-25005046

[regal geyser]

for how long have u been living in this world

give your answer in years

https://tenor.com/view/poop-cat-meme-dark-fnaf-gif-2491098315710587638

[trail valley]

16

[remote mural]

-3 years

[regal geyser]

-273.15 ?

[shut sierra]

8.935e+6 minutes

[regal geyser]

omg

[trail valley]

Alright imma skip this question

[regal geyser]

16 years

[regal geyser]

hm I feel old

[shut sierra]

17

[regal geyser]

(I'm 18)

[shut sierra]

wow you are old

[regal geyser]

lol

[trail valley]

Lol 16 17 18

[hot bone]

high five

[regal geyser]

aww

I mean but you do feel old

[shut sierra]

this is a cylinder with radius 2.5

[regal geyser]

and I'll be 19 soon

https://tenor.com/view/cat-kitten-cat-crying-kitten-crying-05starrynight-gif-10141647709992578610

my roomate started snoring

[trail valley]

Height?

[shut sierra]

slap his ass

[hot bone]

it's okayy

[trail valley]

https://tenor.com/view/cool-fun-white-cat-dance-cool-and-fun-times-gif-16435335956387921912

[hot bone]

nineteen could be good

[regal geyser]

5''

[hot bone]

I am excited for it tbh

[shut sierra]

height is 2.5

[regal geyser]

IM NOT

[hot bone]

why not

[regal geyser]

I want to not age

[hot bone]

eighteen is good to me too

more than expected

[regal geyser]

I mean I'm surprised I'm still alive as well but

[hot bone]

well that's boring

[regal geyser]

imagine being young forever....

and not having to stress over college

[trail valley]

9/11 questions

[hot bone]

yes, what's your problem?:D

[regal geyser]

(I hate chemistry)

[shut sierra]

two cones

[hot bone]

high five again

chem suckss

like

ughh

[trail valley]

Wait OMG I JUST RELIZED!!

[regal geyser]

whenever I hear the word "cone" I get a heart attack

[hot bone]

why

[regal geyser]

In advanced physics there are the classic problems

[trail valley]

Hight?

[regal geyser]

"pump water out of the cone", and we need to find the work done

[hot bone]

conic

[regal geyser]

and you need integrals for that, and many differentials

and it is just a mess

[hot bone]

mmhm

[shut sierra]

3

[hot bone]

calculus isn't easy

[shut sierra]

i assume

[hot bone]

tho Iam pretty new in it

[regal geyser]

the worst thing is that it is actually a thing, because the shape of the cone is the best one to pump things out of it

[trail valley]

Radius surface area volume?

[regal geyser]

the only cones I like are the ones with chocolate icecream

[hot bone]

I love your pfp btw
how about chatting in #discussion ?

[regal geyser]

it is the best thing ever!!

[regal geyser]

hm sounds good

[regal geyser]

aww thanks : )

[trail valley]

Yeee rest?

The rest?

JUST 2 MORE AFTER THIS AND IM DONE!!!

@shut sierra

[shut sierra]

too lazy to find

[trail valley]

Ok

Shiit

[shut sierra]

just use cone volume calculator online or something

[trail valley]

These last 2 r short

[trail valley]

I mean 2 wrong out of 11 not bad

No thats a C i want a B

[shut sierra]

this is a cone

with a height

6

and a radius 9

[trail valley]

Ok

Im only missing the surface aread @shut sierra

What is it?

[shut sierra]

where is the solid

i cant even see it

[shut sierra]

isnt that a different question

[trail valley]

Im just missing the surface area on that question

[shut sierra]

rotating this solid doesn't produce a cylinder

nevermind

[trail valley]

Well i got it correct

[shut sierra]

i saw wrongly

let me see

[trail valley]

And lastly these 3 and im done

Lastly these 3 blank ones after that question and im done

@trail valley

@shut sierra

[shut sierra]

surface area 414.69

[trail valley]

I GOT 83% on my homework

[trail valley]

I kinda submited right before u saif that but thanks

[shut sierra]

is that good or bad

[trail valley]

Thats a B

[shut sierra]

bad

[regal geyser]

Hm

Not enough...

[trail valley]

Im happy with a B

[regal geyser]

Nah I'm joking u did a good job!

[trail valley]

Fuck that

[regal geyser]

And looked for help, and got a 86

[trail valley]

Ill do my chemistry homework tomorrow in lunch and in my buisness class cause she wont be there

[regal geyser]

I mean if I get that my parents kill me

[trail valley]

I already have the answers my friend and some girl lemme tske a picutre there papers its just copying them down and the question

[regal geyser]

(I had 110% grade in Calc 2)

[regal geyser]

💀

[trail valley]

They both googled the answers so ik its correct

I might not even go school idk

[regal geyser]

Never skip school!

[trail valley]

My mom asked me if im doing snything in school tomorrow so im thinking she taking me surprise?

[regal geyser]

Fr is a very bad decision

[trail valley]

When i asked y she said nothing?

[regal geyser]

I mean

At the end u know it better

[trail valley]

She asked that to my brother sister too

[regal geyser]

U know how your school is and everything but I never recommend skipping school

[trail valley]

Buisness she not gonna be there she testing and she leaves no assignment english he just gonna put movie on cause we reading the tempest by shakeshare st the same time he puts some play version on it he got on amazon prime

I think only 2 classes doing stuff is intensive math and chemistry

[regal geyser]

😥

I mean

Is on you

[trail valley]

Idk

[regal geyser]

And if you think ur mom will take u somewhere

I mean it is always good to go out sometimes akhrkaba

I'm not encouraging you but I don't want to make u feel bad either

[trail valley]

Idk bro im tired

I was doing homework fell asleep woke up randomly and started continuing my homework

[regal geyser]

Hm school stress

Go get some sleep!!

[trail valley]

I cried on the inside doing homework i tried crying out loud but couldnt but was stressed cause me my friend were stressed cause my teacher didnt teach the homework

One My friend has the same teacher but different class period

Gn im tired going sleep

[shut sierra]

what about chem homework

[regal geyser]

Chem = bad

[trail valley]

Like i said i can do it in lunch and my buisness teacher not gonna be there so i can do it there

It wont be long my friend and a girl looked up the answers and wrote em and let me take a pic all i gotta do it copy the question and the answer

[shut sierra]

how about do chem now and sleep in lunch

[trail valley]

Me tired

Me sleep now

Its 3 54 am

[remote mural]

Yes go to sleep

[trail valley]

Bro why is there a guy in tiktok live rn awake rn tryna look at star wars fortnite

[remote mural]

Go to sleep sonic 💀

[trail valley]

The fact i follow him on tiktok

[remote mural]

You’re gonna be so dead in the morning

[trail valley]

And another tiktoker i follow doing 3 am asmr

[remote mural]

Time difference?

[trail valley]

CASEOHS AWAKE RN!!!

[trail valley]

No its night time for him to he in the dark

WHY TF IS CASEOH AWAKE!!

[remote mural]

Maybe he also had hw to do last minute

Jk

[trail valley]

Caseoh on minecraft rn

He always streaming in the dark

[remote mural]

Aren’t you gonna sleep now?

[trail valley]

https://tenor.com/view/case-oh-elbow-drop-sped-up-gif-3857149809924349837

[trail valley]

Yea yea gn

Got distracted for few mins

[remote mural]

Oh that’s his name

[trail valley]

https://tenor.com/view/caseoh-cat-kitty-case-oh-caseoh-kitty-gif-10158875947500614550

[remote mural]

I only know his face

[trail valley]

I unironically like watching him on youtube

[remote mural]

Lmao noice

[trail valley]

Ok well goodnight guys

[remote mural]

Goodnight

@trail valley type .close when ur ready

[calm coral]

@trail valley Has your question been resolved?

[calm coral]

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:
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• Show your work, and if possible, explain where you are stuck.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fiery nova]

i have no idea how to go about integrating this expression, can somebody help?

[fiery nova]

the question asks to use the substitution x = 2 tan θ

[short prawn]

Do it, then

[fiery nova]

i did, but i don't know how to proceed

[fringe reef]

show your work

[hallow loom]

is anyone here good at analogy reasoning

[short prawn]

#❓how-to-get-help

[hallow loom]

My bad thanks!

[fiery nova]

I foiled the denominator and substituted tan θ and ended up with 5 / (tan⁴θ + 8tan²θ + 16) * 2 sec²θ dθ

[short prawn]

Pro tip: I know PEMDAS, but it's much nicer to write those as 5 * 2 sec²θ / (tan⁴θ + 8tan²θ + 16) dθ

[fiery nova]

yeah ur right

mb

[short prawn]

Also, yeah that's wrong. It looks like you're substituting x=tan θ + 4, which is not the hint says

[fiery nova]

the denominator is (x^2 + 4)^2

i expanded that

[short prawn]

Don't do that

[fiery nova]

Oh

[short prawn]

It's much nicer not to expand first

[fiery nova]

what's the correct approach then?

[short prawn]

Just plug in directly without expanding the denominator

Also a nice hint: tan^2 θ + 1 = sec^2 θ

[fiery nova]

I'm at 10 sec²θ /(tan²θ + 4)² dθ

how do I proceed from here on?

[short prawn]

No, the denominator is incorrect

[fiery nova]

isn't the original expression 5/(x^2 +4)^2?

i just substituted tan θ into that

[short prawn]

No, 2tan θ, not tan θ

[fiery nova]

ohh right

mb mb

ok

i can see where this is going

is it 2.5x?

the final integral, i mean

nvm i got it

thank you

.close

[calm coral]

Channel closed

Closed by @fiery nova

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

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[tawdry mason]

how should i approach this?

using trig

[left sorrel]

uh the line with magnitude x is a perpendicular bisector

[tawdry mason]

so

can u just assume that

[left sorrel]

you can just go full trig route ig

[tawdry mason]

wdym

[left sorrel]

do you know sine rule?

or law of sines

[tawdry mason]

uh

sin is = o / h

[left sorrel]

no the one that holds even for non-right triangles

[tawdry mason]

oh

no

how would that work though

how does that help at all

[left sorrel]

u said you don't know it right?

[tawdry mason]

yeah

[left sorrel]

you can find green with it

then you can find x with it trivially

sin(50 degrees) = x/l

[tawdry mason]

ohhh

i get it now

tysm

.close

[calm coral]

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[left sorrel]

np but are we sure you're allowed to use this?

[tawdry mason]

idk

[left sorrel]

bruh

[tawdry mason]

i havent learnt it yet

so

[left sorrel]

then u shouldn't use it (i guess)

[tawdry mason]

oh

but

how woudl u solve it without it

[left sorrel]

call the yellow leg n

call the orange leg 100-n

so you have tan(60 degrees) = x/n and tan(50 degrees) = x/(100 - n)

[tawdry mason]

ohh

[left sorrel]

express each one in terms of x then equate and bla bla

[tawdry mason]

is ee

i think that s how they wanted me to do it

[left sorrel]

so can you finish the thought?

if u can't then you should probably .reopen

[tawdry mason]

yes i think i can solve it now

ty!

[left sorrel]

[calm coral]

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[trail valley]

Hi

[short prawn]

!da2a

[calm coral]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

@trail valley Has your question been resolved?

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[tawdry mason]

im still stuck on the question above

[tawdry mason]

im stuck at finding n

oh nevermind

.close

[calm coral]

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[calm coral]

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[snow hare]

find if it exist, the limit of the recurrent sequence:
$\a_1 = 5, \quad \frac{a_{n+1}}{a_n} = \frac{n+1}{3n}$

[potent lotus]

milanesa de pollo

[short prawn]

You know how to find the exact formula for $a_n$, right?

[potent lotus]

Xwtek

[calm coral]

@snow hare Has your question been resolved?

[atomic palm]

use the idea of a sequence being bounded and monotone implies convergence

[snow hare]

how to find an formula?

[short prawn]

$$a_n = a_1 \prod^{n-1}{k=1} \frac{a{k+1}}{a_k}$$

[potent lotus]

Xwtek

[short prawn]

Telescoping product

[calm coral]

@snow hare Has your question been resolved?

[snow hare]

i need more tips

[atomic palm]

this is a very nice way to do it

[snow hare]

i dont know that symbol

[atomic palm]

what is the product of a collection of numbers all less than 1/2?

[snow hare]

like product sum or whatever that means

[atomic palm]

yeah, it just means product

[snow hare]

0

[atomic palm]

for $n \geq 2$, $a_{n+1} \leq \frac{1}{2} a_n$

[snow hare]

,w (1/2)^100

[potent lotus]

AlphaNull

[atomic palm]

exactly

[potent lotus]

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[snow hare]

very smoll

[atomic palm]

indeed, it tends to 0

[snow hare]

so what?

AlphaSigmaNullable any hints?

[short prawn]

Have you tried my telescoping product formula?

[snow hare]

well

can you help me understand it

im new with this product notation

also I sent my work with a alternative but more simplistic approach but dunno if its correct

[short prawn]

It's the same as sigma notation, but with multiplication instead of summation.

Your idea looks like the same, but done manually, and has some incorrect steps. Also, doing what you're doing right now requires infinite steps

Think
$$\prod^n_{k=1} f(k) = f(1)f(2)...f(n)$$

[potent lotus]

Xwtek

[short prawn]

We have some properties about this notation, which is familiar if you know the corresponding sigma notation:
$$\prod^n_{k=1} af(k) = a^n \prod^n_{k=1} f(k) \text{(if a does not depend on k)}$$
$$\prod^n_{k=1} f(k)g(k) = (\prod^n_{k=1} f(k))(\prod^n_{k=1} g(k))$$
$$\prod^n_{k=1} \frac{f(k)}{g(k)} = \frac{\prod^n_{k=1} f(k)}{\prod^n_{k=1} g(k)}$$
$$\prod^n_{k=1} k = n!$$
$$\prod^n_{k=1} \frac{f(k+1)}{f(k)} = \frac{f(n+1)}{f(1)}$$
The latter is also called telescoping product.
I think the properties I gave should be enough to deduce the formula for $a_n$

[potent lotus]

Xwtek

[short prawn]

I thought you should have been taught about this, right?

After you did this manipulation, determining the limit of the sequence is simply a manner of plugging the value.

You can prove all but the fourth formula by induction. (The fourth one cannot be proven because it's the definition of factorial)

[calm coral]

@snow hare Has your question been resolved?

[snow hare]

I havent been introduced to sigma nor the product symbol

but

if its similar to sigma should be multiplication instead of sum

[snow hare]

mmm

okay

[snow hare]

idk what telescoping means tho

I haven’t been introduced to that term

does it mean divergence?

[short prawn]

Google it

In general it's a bad etiquette to ask what a term means unless you have googled it first.

Since, the google search gives this as the first hit:
https://en.wikipedia.org/wiki/Telescoping_series

[snow hare]

my bad

what does it mean?

that is a sequence or series with a recurrence relation?

in mathematics, a telescoping series is a series whose general term

also you sent me a link for telescoping SERIES

but this is a recurrent sequence

will it still work

thats the fibonnaci

a telescoping sequence prolly

maybe?

[short prawn]

The task is to turn recurrent sequence to a product series

[snow hare]

how is one to two happening

what is this factorial stuff you placed in here

[short prawn]

Normal factorial.
1! = 1
2! = 2
3! = 6
4! = 24
...

The last one is the definition of the factorial, so you can't prove it.

[snow hare]

?

definition of the factorial?

[short prawn]

Yes

[snow hare]

isnt n! = n * (n-1)!

[short prawn]

Yes, but that's a property of factorial, not the definition

[snow hare]

so confusing

https://cdn.corporatefinanceinstitute.com/assets/factorial3.png

[short prawn]

The same, I just used k as the label instead

[snow hare]

im new to math and you throw me this factorial notation

how is third happening tho

is that true?

[short prawn]

Yes. You prove it by induction

[snow hare]

also I dont get the second step

[short prawn]

I told you that's the definition of factorial

[snow hare]

i know that now

but how is 1 going to 2

or is 1 going to 3 ?

and 2 is a formula

[short prawn]

No, I just listed the properties of product notation, not that I'm implying the first implies the second.

[snow hare]

okay

I see it nos

now

you mean this step

,rotate

[snow hare]

where first numerator is divided by last denomi

I think I get it now

but you want me to induct that?

[short prawn]

Yes

[snow hare]

what is my inductive hypothesis

n = 2?

[short prawn]

Also:

1. You forgot to raise 1/3 to the power of 3
2. You need infinite steps right now

[snow hare]

yeah sorry

yeah but infinite terms I need induction

[short prawn]

Or you can use my product formulas

[short prawn]

Yes that.

[snow hare]

you mean to assume this is true for all n

[short prawn]

That's true for all n. It's a theorem

[snow hare]

theorem?

[short prawn]

Yes, it's a theorem.

[snow hare]

called?

[short prawn]

telescoping product.

[snow hare]

my question arises because I dont know what telescoping means

I havent been introduced to the term, only to sequences

[short prawn]

So, you didn't get taught what is a series?

[snow hare]

I mean I didnt knew we needed to convert to a series, this is from my sequences problemlist

series are being taught in a couple weeks

[short prawn]

Wait, so you're learning limit first and then series?

[snow hare]

yeah

is that bad?

[short prawn]

No, I'll have to adjust

[snow hare]

I mean I can deal with it but lemme research about telescoping definition

[short prawn]

In this case, the only thing I know to solve this by limit only is by doing ansatz

[snow hare]

ansatzs

?

[short prawn]

ansatz = assuming the answer and then proving it afterwards

[snow hare]

ahh

got it

assuming is true, what was the followup reasoning?

[short prawn]

Plugging the ratio you're given to the formula.

[short prawn]

Wait, do you know L'Hopital yet?

[snow hare]

I havent learn differentiation nor integration we still on limits

[short prawn]

Then forget my method. In the end, you'll need to apply L'Hopital.

[snow hare]

ratio is $\frac{n+1}{3n}$

[potent lotus]

milanesa de pollo

[snow hare]

i mean it will be introduced next class but does the ratio is in inf/inf form?

ah it is

1/3

[short prawn]

Well, I don't mean this ratio, but the one that appeared much latter.

[snow hare]

what is this $\a_n = a_1 \prod^{n-1}{k=1} \frac{a{k+1}}{a_k}$

[short prawn]

Now, for something that you can so with only sequences property, prove that the limit is zero.

[potent lotus]

milanesa de pollo

[short prawn]

The same thing, but rearranged.

[snow hare]

if its less than 1

nah I dont get it

which sequence property what do you mean

that if two limits of subsequences are different from each other the original sequence is divergent?

[short prawn]

Let's go back to this. The limit is zero. Now prove it.

First prove that the sequences are strictly positive.

[snow hare]

exactly how do I prove its increasing or decreasing

[short prawn]

No, strictly positive means > 0

[snow hare]

first

I need to know if its bounded

how do I prove that the sequence is strictly positive?

all elements in the sequence must be positive

tbh im taking engineering course this is way out of my league

i didnt knew what telescoping or telescoping product meant

.close

[calm coral]

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[calm coral]

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[eager token]

Hii how would i do this

[dusty crescent]

Hi mommy

[eager token]

Hello child!

[dusty crescent]

So you got the sin right?

[ruby skiff]

Sorry I was late

[eager token]

Yeah but its wrong 😭

[dusty crescent]

Ah you see

[upper sparrow]

Hi everyone

[dusty crescent]

sec is not the inverse of sin

[eager token]

HI CHARTBIT :DDD

[eager token]

OH

OH

BRO

💀

OMG

[ruby skiff]

@Everyone what is 2 + 2 X 2

[dusty crescent]

At least you read the question this time

[calm coral]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[eager token]

😭😭😭😭

[remote mural]

6

[eager token]

SEE IM IMPROVING

[ruby skiff]

Correct

[dusty crescent]

Can you solve it now?

[eager token]

Lemme tryy

Wait why is the csc wrong

Is sin supposed to be -sqrt(21)/5?

[upper sparrow]

Cause similarly cosec is not 1/cos

[remote mural]

what quadrant does x lie in based on the given conditions

*edit

[eager token]

But i did 1/sin for csc

[eager token]

3?

[remote mural]

why's that

[dusty crescent]

Some sadistic mathematician decided to give wrong names to the inverse function

[eager token]

OH SO CSC IS POSITIVE?

[remote mural]

yeah but, why

[dusty crescent]

It's probably best if you sketch the unit circle for this

Just in case

[eager token]

Cos tan is positive in the third and first quadrant

[eager token]

Okkk 👍

[upper sparrow]

Alongside the aforementioned sign issue though…

[remote mural]

yes, right

wait cos isn't positive

ok coz

because

ok

[eager token]

Ueah 😭

Sorry

[eager token]

Wait what?

[dusty crescent]

I nominate this as the most confusing sentence in all of math discord

[eager token]

😭😭😭

Oopsie

[dusty crescent]

Ok to summarize, did you calculate the sin now?

[eager token]

Ok i got this

Wait

Wrong thing

[dusty crescent]

How did you calculate sin?

wait

you got csc right

and sin wrong?

[eager token]

Wait is sin positige

Im so cofnsuf

Confused

[dusty crescent]

sin = 1/csc

just inverse it

tan is less than 0

so it's either quadrant 2 or 4 right?

[eager token]

But i thiught it was quadrant 3

Cos tan is positive

[dusty crescent]

... is it?

Mommy are you reading the question?

[eager token]

OH

OH

OH

💀

Why is reading the hardest part of math

[dusty crescent]

@upper sparrow she's at it again

[eager token]

😭😭😭😭😭

[dusty crescent]

So tan is in quadrants 2 or 4

but since cos is negative

we know it has to be 2

in which sin is positive

[eager token]

Okok so

[upper sparrow]

Another one

[dusty crescent]

I want to see

how you calculated that sin

[eager token]

Flip the csc

[dusty crescent]

But where's the 5?

[eager token]

Uh

When i ratiobalize it do i just multiply by sqrt(21)?

[dusty crescent]

yes

[eager token]

OH

[dusty crescent]

ratiobalize lmao

[eager token]

😭

So

[dusty crescent]

this is correct, but the answer sheet probably isn't expecting you to be rational

to rationalize*

[eager token]

Oh its ok 😭

[eager token]

THANK YOUT HO

<33333

THANKS GUYS

.close

[calm coral]

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[green night]

are these two inequalities not the same?

[green night]

sorry if its a dumb question I'm just a bit confused rn

if someone can clear it up for me

[dry garnet]

well if you multiply both sides by 2, it should be 100,000 no?

how did you get 25k?

[green night]

right holy shit

u just had to say it and i see it

I was following along with something another classmate did

[dry garnet]

ah lmao

[green night]

and it just messed me up

its so obvious but I was for like 10 minutes not getting it

been studying too long, thank you.

.close

[calm coral]

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[dry garnet]

nw

[green night]

.reopen

[calm coral]

✅

[green night]

.close

[calm coral]

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[bronze adder]

it does?

,w sum from n = 1 to infinity (3 + sqrt(n))/(2n - sqrt(n))

[potent lotus]

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[bronze adder]

right uh

I just went by the degree at the bottom being 1/2

it doesn't

[remote mural]

its a sequence tho not a sum

[bronze adder]

oh

[remote mural]

irs just ur standard limit

then

[bronze adder]

yeah

[potent lotus]

snow

[bronze adder]

as n --> infinity

yeah this

[calm coral]

@remote mural Has your question been resolved?

[calm coral]

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[winter nebula]

Can anyone help me with part b please?

[calm coral]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[winter nebula]

<@&286206848099549185>

[calm coral]

@winter nebula Has your question been resolved?

[winter nebula]

<@&286206848099549185> anyone please?

[grim stratus]

try law of total probability

P(B' n C) = P(B' n C n A) + P(B' n C n A')

you can find P(B' n C n A) and P(B' n C n A') with Bayes and the given data

[winter nebula]

Oh wow thats a rule?

How is that

Shit there’s a lot of rules i gotta memorise or understand

[calm coral]

@winter nebula Has your question been resolved?

[winter nebula]

no idea

[winter nebula]

sorry but how did you come up with this rule?

[calm coral]

@winter nebula Has your question been resolved?

[winged fjord]

The idea is that probability of union of disjoint events is the sum of the probabilities

So write B' n C = B' n C n U where U is the set containing all events

Now notice U = A u A'

Then:
B' n C n U = B' n C n (A u A')

And now use distributive law of sets

B' n C n (A u A') = (B' n C n A) u (B' n C n A')

Notice that the union is disjoint because the expressions to the left and right of the union are contained in A and A' respectively, so they can't intersect

Now since B' n C = (B' n C n A) u (B' n C n A') and the rhs is a disjoint union, when taking probability you can turn the disjoint union into a + sign

[winter nebula]

yh yh i think i got it

i also drew a venn diagram

it helped a lot

thanks a lot @winged fjord

.close

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[winged fjord]

Let $g,g_n\in L(\mathbb{R}^d)$ such that $g_n \to g$ a.e and $\int_{\mathbb{R}^d}g = \lim_{n\to \infty} \int_{\mathbb{R}^d} g_n $. Let $f_n, f$ be measurable functions such that $f_n \to f$ a.e. and $|f_n|\leq |g_n|$.\
Prove that $\int_{\mathbb{R}^d}f = \lim_{n\to \infty} \int_{\mathbb{R}^d} f_n $.

[potent lotus]

Casiel368

[winged fjord]

I'd like to use dominated convergence but I can't find any function that dominates all the f_n at once

On another thread I was wondering if sup g_n would work but it turns out it isn't necessarily integrable so I ran out of ideas

[dreamy marten]

Given that (g_n) converges to (g) almost everywhere and (\int g = \lim_{n\to\infty} \int g_n), and for each (n), (|f_n| \leq |g_n|), we need to prove that (\int f = \lim_{n\to\infty} \int f_n).

Step 1: Apply Fatou’s Lemma Since (|f_n| \leq |g_n|) and (g_n) converges to (g), we can apply Fatou’s Lemma to the sequence (|f_n|). This gives us: [ \int \liminf_{n\to\infty} |f_n| \leq \liminf_{n\to\infty} \int |f_n| ] But since (f_n) converges to (f) almost everywhere, (\liminf_{n\to\infty} |f_n| = |f|) almost everywhere. So, we have: [ \int |f| \leq \liminf_{n\to\infty} \int |f_n| ]
Step 2: Apply Dominated Convergence Theorem Now, we know that (|f_n|) is dominated by (|g|) and (|f_n|) converges to (|f|) almost everywhere. So, by the DCT, we have: [ \lim_{n\to\infty} \int |f_n| = \int |f| ] Combining this with the inequality from Step 1, we get: [ \int |f| = \lim_{n\to\infty} \int |f_n| ]
Step 3: Apply Dominated Convergence Theorem again We know that (f_n) converges to (f) almost everywhere and (|f_n|) is dominated by (|g|). So, by the DCT, we have: [ \lim_{n\to\infty} \int f_n = \int f ]

[winged fjord]

Stop trolling please

<@&286206848099549185>

[dreamy marten]

it isnt trolling bro, i answered your question

[remote mural]

nerd

[winged fjord]

That is not correct

[upper sparrow]

And is probably GPT generated, a bannable offence...

[calm coral]

@winged fjord Has your question been resolved?

[calm coral]

@winged fjord Has your question been resolved?

[calm coral]

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[hybrid flint]

I haven’t really learned calculus yet but I kinda need to solve this problem 💀

[hybrid flint]

How should I start

I feel like getting d^2y and dx^2 but I don’t think dividing it is right

[bright lagoon]

is this an Examination?

[hybrid flint]

No lol my mom just asked me this

[bright lagoon]

your mom?

[hybrid flint]

Yea

[bright lagoon]

is this a test?