help-49

[lavish venture]

any ideas

intuition?

looks different than what you're used to probably right

[gritty holly]

ya im not sure how i feel

[lavish venture]

lol

well

[gritty holly]

is this my first time being bulied online

[lavish venture]

experiment a bit with the (-1)^n

like

what does this sort of look like

[gritty holly]

it looks like an alternating series but doesnt the 2exponent on the outside make the -1 always even aka positive?

[lavish venture]

nope

[gritty holly]

damn

[lavish venture]

lmao

well

try ignoring the (-1)^n

what would it be

[gritty holly]

u should also be banned form using "it" because i dont know what u mean

[lavish venture]

$\frac{1}{(n + (-1)^n)^2}$

[grand pond]

knief

[lavish venture]

what would happen if we pretended that the (-1)^n wasn't there

[gritty holly]

then its just 1/n^2 right

[lavish venture]

so you might think we're somehow going to use 1/n^2 right

[gritty holly]

okay sure

[lavish venture]

now

what happens to the (-1)^n if n is even

[gritty holly]

the then denominator increases

[lavish venture]

well

like

what does it become

what number

[gritty holly]

n+1)^2

[lavish venture]

mhm

and what if n is odd?

[gritty holly]

n-1)^2

[lavish venture]

brilliant

now

how can we use this?

which is the larger of the two

[gritty holly]

the n-1 is larger

also do you have a trader joes?

[lavish venture]

yes

never been

[gritty holly]

in the denominator if u have a smaller number doent that make the fraction larger

[lavish venture]

oh you meant the actual fraction

[gritty holly]

i live off trader joes!

[lavish venture]

then yes you're ahead of me

i was getting there

so $\frac{1}{(n - 1)^2} > \frac{1}{(n + 1)^2}$

[grand pond]

knief

[lavish venture]

why is this useful?

what can we stick between the two?

[gritty holly]

i was going to recommend that you get their roasted garlic pesto pizza

this shit is the BEST!

[lavish venture]

man i haven't pizza in like

4 years

no 5

[gritty holly]

what?! how? why?

r u okay

[lavish venture]

in 9th grade i just started eating healthy

[gritty holly]

but no cheat meals

[lavish venture]

nope

[gritty holly]

no pizza ever!

[lavish venture]

never

i haven't had a chip in that long either

i used to do birthday cake once a year

but i stopped that this year

[gritty holly]

i dont think i would be able to survive

[gritty holly]

what do u have on ur birthday then just carrots in stead of carrot cake

[lavish venture]

i had a quality steak

[gritty holly]

(i actually think that joke was really cleaver)

[lavish venture]

i don't think i've had a vegetable since they came out of the jar tbh

lmao

i'm a picky eater

always was

[gritty holly]

wait what? out of a jar?

[lavish venture]

yea like when i was force fed baby food

[gritty holly]

wait r u on that carnivore diet?

[lavish venture]

sort of? not really

[gritty holly]

plz say no

[lavish venture]

i eat apples

like it's not a conscious thing where i only want to eat meat

i just end up eating meat most of the time

i don't mind fruits

[gritty holly]

wow im vegetarian

[lavish venture]

ill eat bread too i guess

[lavish venture]

my condolences

[gritty holly]

i only miss sushi sometimes

[lavish venture]

never had fish before

[gritty holly]

what is ur life

[lavish venture]

i'm weird in some ways

maybe a lot

[gritty holly]

hahah

i havent eaten meat in 3 yrs

[lavish venture]

do you look down upon me for eating cows

[gritty holly]

except ive had fish a few times

[gritty holly]

no but i actually cant help thinking of the environmental impact of a primarily meat diet

[lavish venture]

and what would that be

you mean from the meat industry?

[gritty holly]

its actually the reason im vegetarian

[gritty holly]

ya

[lavish venture]

pesticides?

what impact

[gritty holly]

sure that, and water, and land

[lavish venture]

what about the land

the soil?

[gritty holly]

the land it takes to grow the food for the livestock and the water to grow that food and water the livestock drink

[gritty holly]

i mean large scale aggraculture is really bad for the soil but thats becasue they farm for the crops profit not for the long term success for the land and environment

i can talk about this forever but im not trying to change ur mind!

[lavish venture]

so you're not as concerned with the moral side but more of the environmental effects

i haven't heard that before

do you like peter singer

[gritty holly]

no i dont know who this is

[lavish venture]

bro hes like the number 1 vegan wdym

how many books has he written about this

😭

[gritty holly]

ya no i mean do i think that living things should be treated well, ya but that didnt make me stop eating meat

[lavish venture]

to him im a "speciesist" or whatever he called it

[gritty holly]

honestly i only read 1 non-fiction a year and its usually not about diet

[lavish venture]

interesting

i liked peter singers accent

[tribal temple]

But you're bookprincess false advertising

[lavish venture]

aussie

yea umm

[lavish venture]

you might like peter singer

i liked peter singer

[gritty holly]

nooo! i promis i read

[lavish venture]

but i still love meat

i wasnt convinced

[gritty holly]

i average 60 books a year! plz dont think im a fraud!

[lavish venture]

not a utilitarian

you read 59 fiction books a year

are you ok

i havent read a fiction book since percy jackson in middle school

or no

false

i read animal farm like 6 months ago

and 1984 like 3 months before that

[gritty holly]

for school?

[lavish venture]

1984 was for school

animal farm was just for fun

orwell is good

[gritty holly]

ya sure

[lavish venture]

you dont like orwell?

[gritty holly]

to dystopian for me but ya

[lavish venture]

thats the good part

[gritty holly]

i disagree why do i want to read about dispare and the world going to shit

[lavish venture]

,av kniefy

[grand pond]

kniefy's Avatar

Click here to view the image.

[gritty holly]

what is that a pic of

[lavish venture]

no clue

[gritty holly]

but its supposed to be dystopian?

[lavish venture]

that picture?

[gritty holly]

ya

[lavish venture]

i dont see how

[gritty holly]

i dont know i was trying to connect the picture u sent to the conversation we were having

[lavish venture]

lmao i sent it in response to this

im just not interested in rainbows and skittles

[gritty holly]

then i dont get how thats a responce

[gritty holly]

how about fantasy

[lavish venture]

idek what that means

like

lord of the rings?

nope

[gritty holly]

the genre

[lavish venture]

lord of the rings movies were shit

cant imagine how bad the books are

[gritty holly]

but books r always better than movies

[lavish venture]

eh

1984

oh wait

you said books

yea

true

[gritty holly]

i read fantasy

[lavish venture]

so like dr seuss

[gritty holly]

and romance

[lavish venture]

lord

[gritty holly]

omg no

[lavish venture]

ya know what book is fucking terrible

guess

no not quite

the great gatsby sucks

[gritty holly]

ya that was pretty bad but the movie is fun

[lavish venture]

why not?

[lavish venture]

no theyre both horrible

[gritty holly]

because im not a child

[lavish venture]

even if the cast was good

[gritty holly]

no ill watch it every once in a while

[lavish venture]

you wont get those 2 hours back

anyways

$\sum_{n = 2}^{\infty} \frac{1}{(n + (-1)^n)^2}$

[grand pond]

knief

[lavish venture]

you're getting close

[tribal temple]

Hi @prime hornet

[lavish venture]

what happened to ourfallenstars

🤔

[gritty holly]

what?

[prime hornet]

https://tenor.com/view/anime-anime-girls-anime-cute-anime-hug-anime-love-gif-26708157

[prime hornet]

died a horrible death, I hear

[lavish venture]

good for him

[gritty holly]

aw this is cute

[gritty holly]

aw man back to math😭

[lavish venture]

you can take it over the summer then ig

[gritty holly]

nooo i need to pass!!!

okay we were at the part where n-1)^2 was a larger fraction

[lavish venture]

yep

[lavish venture]

what kind of inequality can we get from this

using that fact

[gritty holly]

that this series is between the two?

[lavish venture]

yess

but

[gritty holly]

omg that was a guess

[lavish venture]

with equality of course

$\frac{1}{(n + 1)^2} \leq \frac{1}{(n + (-1)^n)^2} \leq \frac{1}{(n - 1)^2}$

[grand pond]

knief

[lavish venture]

why is this useful??

which part of the inequality do we care about

[gritty holly]

oh of corse

[lavish venture]

because it equals the (n+1)^2 one or is equals the (n -1 )^2 one

kind of like how -|x| <= x <= |x|

[gritty holly]

the n-1)^2 becasue we want to compare that ours is smaller

[lavish venture]

well done

[gritty holly]

😊 thanks

[lavish venture]

do you want more of my exercises or the ones for your class

[gritty holly]

woah i am i done

[lavish venture]

well

[gritty holly]

did we already say that 1/(n-1)^2 is convergent?

[lavish venture]

you've shown its <= something that converges

[gritty holly]

oh i forgot

[lavish venture]

you can show this quite easily

[gritty holly]

can i use the p test?

[lavish venture]

yea you can just shift the indices to make it be of the "proper form"

just note that it doesnt really matter if you shift the indices

like (n - 1)^2 is just n^2 shifted

[gritty holly]

okay cool

dude u could literally be my prof this is basically what u just had me do

[lavish venture]

haha

pay me

tell the uni to hire me

[gritty holly]

ill pay u in trader joes pizza

and with the joy i bring into your life

[lavish venture]

does he give practice exams?

[gritty holly]

this is the practice exam

[lavish venture]

oh good

how similar are they to the actual test

[gritty holly]

but it only includes chapter 11 stuff

[lavish venture]

right

chapter 11

[gritty holly]

i felt like exam 2 was much harder than the practice exam he gave for it

[lavish venture]

any ideas?

just expose yourself to as many problems as possible

if you can do the hard ones then you're good

[gritty holly]

i only have so much time and so much patients for math

[lavish venture]

you could always take it in the summer

[gritty holly]

my idea is that it converges

[lavish venture]

mhm

and why

what are we going to compare it to

[gritty holly]

u sound like a broken record, we r supposed to be manifesting me passing!

[lavish venture]

lol

its motivation

[gritty holly]

no its putting bad energy into the universe! we only think good thoughts

[gritty holly]

we compare to 1/n^2

[lavish venture]

well

no that wont work will it, like the idea is there

but it is not less than 1/n^2

[gritty holly]

fuck

[lavish venture]

your idea is right

we will use 1/n^2

but how

remember the inequality for sin?

how can we bound the numerator

[gritty holly]

-1<sin<1

[lavish venture]

so 3 + sin <?

[gritty holly]

do i subtract the 3? make it -4<sin<-2

[lavish venture]

why subtract

[gritty holly]

because i want to move it

[lavish venture]

sin x < 1

3 + sin x < ?

[gritty holly]

i still think i would subtract the 3 to move it to the other side of the "<"

[lavish venture]

no

we care about bounding 3 + sin x above

so we don't want to move anything from 3 + sin x

[gritty holly]

umm okay

[lavish venture]

if sin x is at most 1

then what can 3 + sin x be at most

[gritty holly]

4?

[lavish venture]

so how can we use that

[gritty holly]

so its between -4 and4

[lavish venture]

no

[gritty holly]

grrr

[lavish venture]

but we really dont care about the lower bound

$-1 \leq \sin x \leq 1 \implies -1 + 3 \leq 3 + \sin x \leq 3 + 1$

[grand pond]

knief

[gritty holly]

oops its 2

[lavish venture]

but as i said its not important

[gritty holly]

🫡

this is my new favorite emoji

[lavish venture]

so what can we say about $\frac{3 + \sin n}{n^2}$

[grand pond]

knief

[gritty holly]

ummm

[lavish venture]

^

[gritty holly]

but does the denominator effect it

why the thumbs down

[lavish venture]

because it doesn’t

multiplying/dividing both sides of an inequality by a positive number maintains the sign

[gritty holly]

okay

so like this?

tragic

[lavish venture]

multiply/divide both sides

[gritty holly]

so the 4 should have a n^2 denominator

word okay

[lavish venture]

now what can we say about 4/n^2

[gritty holly]

ooo that it converges!

[severe otter]

heyyyyy

[gritty holly]

hey roomie

[severe otter]

hey girl

nice picture

[gritty holly]

this is my roommate😂

[lavish venture]

everyone needs help with calc 2

[gritty holly]

shes in calc1

but ya she has no idea what shes doing either

[severe otter]

actually its calc 1 and 2

[gritty holly]

omg my b queen

[gritty holly]

actually can u help me with one last question before u go to bed?

[lavish venture]

sure

send it

[gritty holly]

nothing i fear

[lavish venture]

what’s the first thing you notice

[gritty holly]

its alternating?

and it starts at 2

and that i hate ln

[lavish venture]

that’s only because you don’t want ln(1) in the denominator

which is 0

[gritty holly]

okay sick soo

[lavish venture]

soo

[tribal temple]

soo

[gritty holly]

okay fam seance at my house

[gritty holly]

thats what this pic gives me

[lavish venture]

james 8th birthday party

[gritty holly]

should i know who that is

[lavish venture]

you just had to be there

[gritty holly]

woah

[lavish venture]

uncultured

https://youtu.be/NgsdTMMUK-I?si=B4NcUCGFRS7__EWn

[gritty holly]

im sry

rn theres 3 of my housemates in my room i cant watch this rn

[lavish venture]

they’ll think you’re cool

[gritty holly]

okay we r wasting precious time u need to sleep soon

[lavish venture]

eyes are shutting

[lavish venture]

alternating series test

enough said

nothing more

[gritty holly]

okay sick

i just hate ln and it scares me every time

[gritty holly]

omg what is that!

[lavish venture]

interesting

namington machiavelli

you haven’t read the prince

[gritty holly]

what?

is that this guy

[lavish venture]

yea

but

machiavelli

[gritty holly]

ya i dont know what that is

[tribal temple]

• checking for absolute convergence too

[prime hornet]

[lavish venture]

🤔

[lavish venture]

oh it does ask for that

true

[gritty holly]

this

[gritty holly]

and this

[lavish venture]

you’ve never heard of machiavellianism?

🤔

[gritty holly]

no

[lavish venture]

stop reading so much fantasy

[gritty holly]

no

[gritty holly]

so would i need to to the ratio or root test

[gritty holly]

stop bullying me

[lavish venture]

no they gave you the inequality for a reason

[gritty holly]

how else would i test for absolute convergence

arent those the only two

[lavish venture]

no

[gritty holly]

wft

[lavish venture]

absolute convergence means you just consider $\sum |a_n|$

[grand pond]

knief

[lavish venture]

which in this case is $\sum \frac{1}{\ln n}$

[grand pond]

knief

[lavish venture]

you still have every test besides alternating

but

there’s really only one you want here

[gritty holly]

but i thoguht that ratio and root where the only ones that told complete covergence

[tribal temple]

(furthermore, ratio test would be inconclusive here I believe)

[lavish venture]

well those alone establish something is absolutely convergent and hence convergent but no this isn’t the only way to determine if a series is absolutely convergent

[gritty holly]

okay so what would i need to do then

[lavish venture]

determine if $\sum \frac{1}{\ln n}$ converges

[grand pond]

knief

[gritty holly]

umm

[lavish venture]

they gave you an inequality

[tribal temple]

[lavish venture]

🗣️

[gritty holly]

sooo ln(n) is not negative and the max is n=infinity?

ya that emoji is how i feel

[lavish venture]

what have we done for the last 4 examples?

[tribal temple]

Nonnegative, sure, but that max statement is sus

[lavish venture]

yep

[gritty holly]

we compared with other series

[lavish venture]

great

and they gave you an inequality

which almost always means we’re doing what

[gritty holly]

comparing?

so ln(n) is less then n

[lavish venture]

meaning

[gritty holly]

that i can compare 1/lnn to 1/n?

[lavish venture]

how

[gritty holly]

r u aksing how can i compare them?

[lavish venture]

i’m asking you

[tribal temple]

Give an inequality that relates them

[gritty holly]

1/ln(n)>1/n ?

[lavish venture]

implying

[gritty holly]

that since 1/n diverges the larger series must also diverge

so i didnt need to do the alternating series test?

or would i still do that

what y?

[tribal temple]

Alternating series test tells you that you converge at least conditionally, but you could converge absolutely

Here we have that the series doesn't converge absolutely, but it might converge conditionally, which is what you're checking now

[gritty holly]

but we found that its divergent

[tribal temple]

"it"

[lavish venture]

you found that it’s not absolutely convergent

since $\sum |a_n|$ diverges

[grand pond]

knief

[lavish venture]

but this does not mean that $\sum a_n$ diverges

[grand pond]

knief

[gritty holly]

ohhh okay

thats enough math now i must learn about evolution

[lavish venture]

yuck

[gritty holly]

its actually a lot more difficult then i was expecting

[lavish venture]

nope

[gritty holly]

the prof is leaning really hard into the biological components of evolution

[lavish venture]

https://tenor.com/view/richard-dawkins-skeptic-atheist-religion-god-gif-14142458

[gritty holly]

me when hes trying to make me understnad how mutated alleles fix under environmental pressures

[lavish venture]

ahh you don’t know who that is lmao

too much fantasy

[gritty holly]

no i dont

but i was talking about my prof when i said he tho

[lavish venture]

yea alleles and shit

[gritty holly]

haha the title of the lecture is "hot or not" and its on sexual selection

i dont know why i think thats so funny

[lavish venture]

ahh yes

birds

very interesting

👎🏻

[gritty holly]

id rather learn about birds than know if a series converges any day!

ive gone to a few santa barbara audubon society meetings and bird people are so nice dont hate!

[lavish venture]

am i a hater

[lavish venture]

no taste

[tribal temple]

But what about learning if series converge or not with us

[lavish venture]

she’s using us chartbit

means to an end

kant is disappointed

[gritty holly]

no i love you guys!

[tribal temple]

Right answer, you better

[gritty holly]

ew i thought i would be able to forget about him after i finished phil

[lavish venture]

"never use people as a mere means"

https://plato.stanford.edu/entries/persons-means/

[gritty holly]

i should have applied to stanford 😭 i mean i LOVE ucsb but i think i would have also really liked it there

[lavish venture]

stanford is hard to get into

what’s the acceptance rate for in state?

is it any better

it’s like fucking 3%

yea they don’t care

because private

tough

[gritty holly]

ya its private

whats the acceptance rate of ur school? i know that u dont share what school it is but im just too curious

[prime hornet]

[lavish venture]

somewhere between 1 and 100%

[gritty holly]

oh no is that an illegal question

[gritty holly]

very funny

[tribal temple]

Plot twist: it's actually 0% and you own the whole school

[lavish venture]

🔥🔥

knief university

[gritty holly]

i just learned that parental care changes the variance of reproductive success between sex (at least in birds)

who knew

[lavish venture]

what’s the difference between hmmcatphone and catphone

🤔

[tribal temple]

The same but in different servers

[lavish venture]

me

no i had no clue

[prime hornet]

are bookprincess channels the new Syrex channels

[lavish venture]

lmao

[prime hornet]

[lavish venture]

until tuesday

unless she bombs it on purpose

[prime hornet]

what happens on Tuesday

test?

[lavish venture]

final

for calc 2

[prime hornet]

ah, eek

good luck bookprincess!!

[gritty holly]

no i need to graduate!

[gritty holly]

aww thank you!!

[prime hornet]

I’m rooting for you

[gritty holly]

knief i told u to stop putting bad energy into the universe!

[lavish venture]

my fault

[gritty holly]

it will be if i fail this class

[lavish venture]

right

[gritty holly]

which i wont becase we give off good vibes

but i would definitely blame all my tears on u and come on discord and let u know what u did

[lavish venture]

cry about it on tuesday

💀

[gritty holly]

ive literally cried after every test🥲

[prime hornet]

https://tenor.com/view/hug-warm-hug-depressed-hug-gif-4585064738068342394

[gritty holly]

charbit wasnt it with you that we were working on a problem from like 7pm to 11pm and i was crying and my laptop was dieing and in the end i didnt even get the right answer

no i was a mess! ugly crying it was right before valentines day or something and my house was doing a galentines wine and cheese night and i was in bed crying trying to do that fucking question

all my roommates were coming in seeing asking if i was okay

it was a mess

[tribal temple]

maybe

[gritty holly]

i think it was because u kept sending cats with heats and stuff because i was crying

[tribal temple]

Awwww might have been but I can't seem to find it, digging through my messages

That does sound like a me thing to do though

(and of course, sorry it was that bad )

[prime hornet]

we believe in ya

[gritty holly]

omg it was like right around valentines day but dont even know how u would find it

[prime hornet]

you’ll overcome this test

[normal prawn]

what r v solving today

[tribal temple]

I might have been lurking maybe but may not have typed anything, I'm searching my messages

[prime hornet]

average chartbit help

[gritty holly]

honestly its the best to just see randomly

[tribal temple]

Ah, I think I didn't say anything, I definitely reacted to you around that time

[tribal temple]

Aha, it wasn't me, it was @prime hornet I think #help-46 message

[prime hornet]

ah?

[gritty holly]

ahhhh omg ur right!

[prime hornet]

oh yes, we did get it in the end though

in a different help channel

[gritty holly]

no

[prime hornet]

ah?

[gritty holly]

i put it into the integral calculator

[prime hornet]

did I mess up?

[gritty holly]

turned it in

and only think about it in my nightmares

[prime hornet]

I’m so sorry

I failed you

[gritty holly]

no i was not in a place where i was thinking clearly

i was overwhelmed

and i totally do NOT blame u

[prime hornet]

anxiety is a real monster

I hope you can overcome it one day

I need to sleep now, but I wish you all the best with your studies, with your finals, and with your future endeavours 🤍

[tribal temple]

Goodnight sleep well

[prime hornet]

you’re in good hands whenever you’re in mathcord, so please do come back if you need help

[prime hornet]

https://tenor.com/view/cropped-cat-anime-petting-animal-gif-22258803

[gritty holly]

i should go too! night🥰

[tribal temple]

Awwww, goodnight to you too sleep well too

[midnight plank]

@gritty holly Has your question been resolved?

[tribal temple]

.close

[midnight plank]

Channel closed

Closed by @tribal temple

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[nimble folio]

what year level is this question suppose to be?

just wondering

[thin tree]

I think different countries teach different level

[nimble folio]

what year level is this in Australia?

and how do you solve this?

thxs

[thin tree]

idk about australia

[sage helm]

you can rewrite the left using the product rule

[grand pond]

neon

[sage helm]

so you have xf(x) = x^4 - x + C

or f(x) = x^3 - 1 + C/x

use the initial condition to find C

and then just plug in -1

[nimble folio]

thxs

[midnight plank]

@nimble folio Has your question been resolved?

[midnight plank]

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[lone hound]

a boy stands a certain distance away from the foot of a building and looks at the top of the building. The angle of elevation is 70 degrees. He moves 25m back and looks at the building top once again. This time the angle of elevation is 35 degrees. The height of the boy is 1.6m. Calculate the height of the building.

[lone hound]

My answer is 24.76m

I had to do it by hand

We were given approximations during the exam

tan(70) = 2.7
tan(35) = 0.7

can anyone tell me the real answer? my friend tells me I got it wrong

[vagrant tusk]

It should be approximately 25.1M

[lone hound]

'm' for meters btw

[vagrant tusk]

25.1m

[lone hound]

yeah thats what my friend told me

[vagrant tusk]

That’s the approximation

[lone hound]

wait

my friend told me its 25.25

but anyway

can u tell me how u got there?

[thin tree]

Using tan

[vagrant tusk]

I used variables first by calling height h

[lone hound]

i did the same

[thin tree]

There is a formula for this btw but since you don't know that just take tan twice

[vagrant tusk]

X = the horizontal distance between

[lone hound]

i also took the same variable

distance between boy and building when angle of elevation is 70 deg right

is x?

ok

so look

[vagrant tusk]

Yes

[lone hound]

heres what i DID

x tan(70) = (x+25)tan(35)

$\frac{2xtan(35)}{1-tan^2(35)}$ = (x+25)tan(35)

[grand pond]

bagelguy3

[vagrant tusk]

Looks right from what I see

[lone hound]

divide both sides by tan(35)

[thin tree]

Woah u didnt need to use that formula

[vagrant tusk]

Wait

I don’t think you needed to use that formula

[thin tree]

yea

[lone hound]

we haven't been taught this yet

double angle formula

but i knew it

so i just decided to use it

[vagrant tusk]

Something just doesn’t seem right

[lone hound]

the tan(35) cancel out

e

[thin tree]

Its 25.225

[lone hound]

nooo

[thin tree]

Is it

[lone hound]

thats what my friend said

I got 24.7

[thin tree]

Yea I got that

so basically do this

[lone hound]

ok

[thin tree]

x tan 70 = 25+x tan35

[lone hound]

k

[thin tree]

tan 70/tan35 =25+x/x

And cross multiply

You will get x

[lone hound]

2x = 25(0.7)

BRUH

ARE U KIDDING ME

[thin tree]

multipy by 10

[lone hound]

OMG

[thin tree]

to remove decimal

[spring wave]

why dont you jusr subtract 1 from both sides and then invert?

[thin tree]

idk

[vagrant tusk]

I’ll leave this to you guys

[thin tree]

I just do cross multiplication

[thin tree]

Did you get value of x

[lone hound]

sadly yes

[thin tree]

what

[lone hound]

oh wait

i got it

now i realize how he did it

and how he got it

thx

[thin tree]

yea

[lone hound]

.close

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[molten socket]

what should be the first step

[sick fossil]

Expand both sides

After that, comparing coefficients gives you some equations you can solve, and then you'll have your answer

[molten socket]

ok

ty

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[grave kernel]

i could check for continuity but im confused about the other 3 options

option 2 i can kinda figure out cuz the greatest integer will create a problem with differentiability in -1,0,1

[supple abyss]

its 3

[grave kernel]

how do i prove that

[sick fossil]

Check the left derivative and right derivative, or sketch it out

[grave kernel]

sketching this will take a lot of time

😭

[grave kernel]

and taking the derivative too

i mean

derivative is still doable

but what about option 3

[sick fossil]

you don't need graph paper, just make a rough guess at what it looks like

[sick fossil]

or try translating the points of discontinuity and non-differentiability

[steel rivet]

Guys where can i ask my doubts related to calculus?

[grave kernel]

i know that but if i take x to be 1.5
its kinda hard to imagine how 1 + sqrt(0.5) and so and so forth will be like

[grave kernel]

i got that they are continuous at integer points

to me it seems option 4 is the incorrect one

[sick fossil]

discontinuous?

[grave kernel]

continuous

[sick fossil]

I just graphed it using desmos and it seems you're right

[grave kernel]

right thank you

just eliminated the options

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[molten socket]

i keep getting 18deg

what did i do wrong

since apb:bqc is 2:3 i let cdb be 3x and adb be 2x

so cbd would be 90-3x since semicircle

and then vertically opposite angle of that and also angles in alternate segment to get angle bae= 90-3x

and then angles in alternate segment again, bae = adb = 2x

so 90-3x = 2x, 90 = 5x, x =18

wiat bruh

sorry

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[glossy pagoda]

Im trying to prove that any two numbers from the set of rational numbers multiplied together will be the same in the other way round, like this, a x b = b x a

[glossy pagoda]

I used chatgpt to do the proof. And im not sure if this is how you do proofs

it seems that the whole proof just relies on the fact that multiplication of integers is commutative there the rational number a x b will be equal to b x a

[midnight plank]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[midnight plank]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[last slate]

@glossy pagoda

https://www.hamilton.edu/documents/Writing Mathematical Proofs1.pdf

if you want to learn how to do proofs ^

[midnight plank]

@glossy pagoda Has your question been resolved?

[glossy pagoda]

ngl i know how to write proofs

just dont know how to prove the commutative

imma just write its commutative

as the general proof. so its chill

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[steady trail]

Why if u<0 ->-u

Example |-5|-> 5 not -5

[glass dome]

by definition

| | is a function

absolute value

the absolute value of something can be something else

why is sqrt(5) not 5

why is |-5| not 5

same reason

[steady trail]

But it is written that if x <0 the module gives me -5

does not make sense

[glass dome]

i don't know what that means

look

[steady trail]

If

[glass dome]

if u >= 0

then |u| = u

[steady trail]

u = -5

[glass dome]

so for example |1| = 1

|2| = 2

|4| = 4

however

if u < 0

then |u| = -u

for example |-5| = -(-5) = 5

|-3| = -(-3) = 3

[steady trail]

5

Thank you all, Clear

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[keen pagoda]

what theorem is this

[solid iris]

clairaut

[lyric charm]

clairaut

[solid iris]

or equality of mixed partials

[lyric charm]

pronounced /klero/ because French

[keen pagoda]

ohh i see

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[twilit field]

Trying to find $\pdv{z}{x}$

[grand pond]

What a wonderful world !

[twilit field]

I was thinking $yz+ xy \pdv{z}{x} = -\sin(x++z) ( 1+ \pdv{z}{x})$

[grand pond]

What a wonderful world !

[twilit field]

so $yz+ \sin(x+y+z) = \pdv{z}{x} (xy - \sin(x+y+z)) \implies \pdv{z}{x} = \frac{ yz+ \sin(x+y+z)}{ xy - \sin(x+y+z)}$

[grand pond]

What a wonderful world !

[twilit field]

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[long lotus]

uhh how do i solve this integral?

[fallow scarab]

,w int 0 to 1/2 sqrt((1+x)/(1-x))

[grand pond]

Results provided by WolframAlpha

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

Requested by rie.mann

[fallow scarab]

fascinating

[long lotus]

[fallow scarab]

clicking the wolfram link tells you to try u = (1+x) / (1-x)

[polar mortar]

you can multiply by the conjugate of the denominator and turn it into a trig sub problem.

actually, not even a trig sub. Just a trig integral and a u-sub

[midnight plank]

@long lotus Has your question been resolved?

[long lotus]

ohh okay i got it, thanks!

[midnight plank]

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[crisp obsidian]

I’m kinda lost for part 2 of this problem. Not sure how f being differentiable helps here

[midnight plank]

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[last slate]

Hello! I think I am going to need your help. So my problem is:
I am writing a program to display a function's graph. So I am going to need help with bezier curves. Right now I am stuck at quadratic function, I have been withing about it for so long right, now and I found out I am going to need someone's help. So basically when I have:
y = ax^2 + bx + c
So I can basically calculate every point on the curve. I feel its so obvious when I have that much information 😄
Okay so I think I should use Linear interpolation, but I guess I can't find correct sources to understand it properly or idk.
I will be grateful for your help.

[fallow scarab]

can you show what function you're trying to work with

[last slate]

any, so right now
y= x^2

I am trying to make the simplest version first

[fallow scarab]

the graph of y = x^2 is the set of points (x, x^2)

what are you stuck on?

[last slate]

so I am programming an svg to make the graph. So basically I get the user input. I have to choices calculate big amount og points, hoping that it will look like clean curve, or use bezier curves.
SO basically from them point on the curve I want to calculate the quadratic bezier curve. this vide explains it.
https://www.youtube.com/watch?v=emFMHH2Bfvo
1:50
I have watched longer materials, but basically I need reverse the proces.
Svg calculates curve from points and control points. But I need to calculate the control points with points and curve.

uhh

I am so bad at explaining. I am sorry, I hope this will help

[fallow scarab]

nah it doesn't

and i don't think anyone's gonna watch a video to help you

[last slate]

ohhh okay, Thats unfortunate. Thank you for your time anyway

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[dusty portal]

filler

[grand pond]

;(

;(

[dusty portal]

This is the problem

[dusty portal]

Is this just linearity of cross product?

I forgot

[fallow scarab]

!1c

[midnight plank]

Please stick to your channel.

@dusty portal Has your question been resolved?

[dusty portal]

<@&286206848099549185>

Please, this is like the hardest problem in the chapter

I'm so close to solving it

[sharp verge]

@fallow scarab cant you help

[dusty portal]

?!

Don't tell me you're talking about the other question bro

[terse knot]

oh ooops

[dusty portal]

<@&286206848099549185>

Bro

[dusty portal]

If anyone has an alternate solution please provide so

[fallow scarab]

!noping

[midnight plank]

Please do not ping individual helpers unprompted.

[dusty portal]

:despair:

[sharp verge]

🙄

[dusty portal]

<@&286206848099549185>

[midnight plank]

@dusty portal Has your question been resolved?

[midnight plank]

@dusty portal Has your question been resolved?

[dusty portal]

Are you kidding me

Get the fuck out of my thread

Now

I think you’ve been told several times, unless you’re blind, to post in your own channel

[solid iris]

@gilded lotus dont post in an occupied channel. see #❓how-to-get-help

[dusty portal]

.close

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[dusty portal]

I’m probably gonna solve it tonight anyways, I don’t care

It’s been exactly 3 hours

[simple field]

i think this, no?

where did you get stuck w this

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[minor spoke]

Just need a simple explanation, do I need to multiply 7.4*7.4 because of the power of 2 or do I keep it like that

[minor spoke]

Anyone !

?

[carmine sigil]

@minor spoke

The ^2 is on the units. yd^2

In other words, the value 7.4 has already been squared at some point in the past.

(and so it represents an area, one square yard is an area that is the same size as a square with side length 1 yard. That is 1 yard long and 1 yard wide)

Hope this helps.

[minor spoke]

Ohh okay because I already multiplex 7.4*7.4- will it come out the same correct solution or nah?

[carmine sigil]

I think you're confused

That's ok

[minor spoke]

Uh a bit

My bad-

[carmine sigil]

No biggie

I'm here to help

So do you remember the formula for the area of the circle?

[minor spoke]

So basically do I do 7.4 times 7.4 then divide that by pie. After square root it to get the radius

Yeah I know

[carmine sigil]

Can you state the formula?

[minor spoke]

Radius to the power of 2 times pie?

[carmine sigil]

A = π r^2

This is correct

[minor spoke]

Yeah that

[carmine sigil]

Ok

[minor spoke]

But for finding the radius?

[carmine sigil]

So 7.4 yd^2 is which value in that equation?

[minor spoke]

The area

[carmine sigil]

Ok so we have 7.4 yd^2 = π r^2

[minor spoke]

Mhm

[carmine sigil]

Can you solve for the radius?

[minor spoke]

I got 4.17 as the radius but not I’m unsure if it’s right-

I rounded up to the hundredths btw

So it’s approximate

[carmine sigil]

This doesn't sound correct, but can you show your work?

[minor spoke]

Uh

I kind of erased it but I’ll do it again lol

There

[minor spoke]

Is it correct?

[carmine sigil]

No

You don't multiply 7.4 by itself

It just is 7.4

[minor spoke]

Ohh my bad

Okay

It’s cause the power of 2 got me confused

So just

7.4

[carmine sigil]

Yes, then divide by pi and take the square root

[minor spoke]

Divided by pie the square rooted?

[carmine sigil]

Yup

[minor spoke]

TYSM

SAVIOR

[carmine sigil]

Wait one sec

[carmine sigil]

Ok, that's cute as hell haha

There's something that I want to make sure you understand before you go though

And it has to do with units

And why the units are squared.

So let's say I have a circle with a radius of 2 yards

[minor spoke]

Yeah

[carmine sigil]

A = π r^2

A = π (2 yd)^2
A = π (2^2 yd^2)
A = 4π yd^2

When we square the value with a unit, the unit get affected by the square too, it remembers it's been squared

[minor spoke]

Ohh okay

[carmine sigil]

Similarly, if we have 4π yd^2 = π r^2

We divide by π to get 4 yd^2 = r^2

Then take the sqrt:

[minor spoke]

Yeah so that the pie isn’t in the way?

[carmine sigil]

√(4 yd^2) = √(r^2)
√(4) √(yd^2) = √(r^2)
2 yd = r

Again the unit is also affected by the operation

[minor spoke]

👍

[carmine sigil]

Thanks for sticking with me

[minor spoke]

Tysm for the help

Ofc Omg I wish I had someone like you help me all the time

Tysm for all the help

[carmine sigil]

I'm glad you found me helpful 🙂

[carmine sigil]

You're very welcome

[minor spoke]

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[median ridge]

for

[median ridge]

,tex $y = log_2 (\sqrt{x^2 -4})$

[grand pond]

suds

[median ridge]

first of all

this is for domain

i did $x > \sqrt{4}$ so $x > 2$

[grand pond]

suds

[median ridge]

but would it be x > -2?

[twilit field]

almost

[median ridge]

because its +- sqrt 4

[twilit field]

x>2 or x<-2

[median ridge]

how come?

why does the sign flip

because we arent dividing by a negative?

[twilit field]

Okay, so first , let's get one thing out of the way

$\sqrt{x^2-4} >0$

right

[grand pond]

What a wonderful world !

[median ridge]

yes

well no

yes

no

because log_2 (0) is a thing

[twilit field]

remember the domain of the log function

[median ridge]

so >=

[twilit field]

no

[median ridge]

oh but no

because there is no power to get there

[twilit field]

the log function's domain is (0, \infty)

[median ridge]

okay yes

got that

im a bit rusty lmao

[twilit field]

okay, cool

so $x^2>4$

[grand pond]

What a wonderful world !

[twilit field]

Intutively , what does this mean

[median ridge]

oh x could be positive or negative

[twilit field]

yes!

[median ridge]

(+- x)^2 > 4

ah so if u do the two different sets

of -x and x

u do divide by negative

[sage helm]

yes

[median ridge]

ok thank you!

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[queen bane]

Hello can anyone help me with this please..?

I have a hard time figuring it out

[midnight plank]

@queen bane Has your question been resolved?

[carmine sigil]

@queen bane it sounds like the idea behind this problem is measuring the angle between A and B from X and figuring out how close you can be before you're in the danger zone

But I'm not entirely understanding where exactly the danger is