help-0

[cinder spindle]

not sure how to do d

[lone heart]

@cinder spindle Has your question been resolved?

[tacit bobcat]

!status

[lone heart]

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

[remote heron]

well the angle is easy enough

you know the relative scale of the components

if you take arccos(.8/1.8)

@cinder spindle

does getting the angle give you enough of a push to get the time?

[cinder spindle]

it gives too much push

[remote heron]

[cinder spindle]

the guy's going too fast

what the fuck am i even saying

[remote heron]

idk

[tacit bobcat]

Can you draw the problem out

[remote heron]

you should know ive taken sleeping pills so i'm pretty sleepy

can you explain anything more about your confusion?

[cinder spindle]

i mean, i just don't really know how to start at all

i've tried drawing diagrams

but i don't know

[tacit bobcat]

What don't you know

I've seen 0 posted diagrams

[remote heron]

The motivation of the diagram is of vectors

a boat moving across the river in the context of the problem has velocity drawn from 2 components

one is the speed of the river, and it pushes directly parallel to the bank

the other is the speed of the paddling, and it pushes directly parallel

the resultant moves from bank to bank

All that babbling to say you should draw a triangle

do you have any triangles?

[remote heron]

yea that looks pretty good

but id add

[cinder spindle]

the final answer won't be a right angled triangle

[remote heron]

it will

[cinder spindle]

hm

[remote heron]

tell me this

lets say that piece you have labelled as 1.8

lets say some time has passed

and its now 3.6

after this amount of time, what has the piece labelled 0.8 become?

[cinder spindle]

1.6

[remote heron]

right

so no matter what length they are

[cinder spindle]

i tried doing

64 / 0.8

[remote heron]

you can write them as 1.8a and 0.6a

where a is just some number that scales them together

[cinder spindle]

right

wait

FUCK

[remote heron]

so you can definitely get the angle now

try adding the a, and using trig functions

or whatever letter you like i guess

[cinder spindle]

you're referring to x in my diagram

?

[remote heron]

x looks like an angle?

[cinder spindle]

right

[remote heron]

my point is

you can write the diagram more generally

ANY triangle for this specific set up can be written as 1.8a and 0.8a

for some a

[remote heron]

right

oh

you mean

yea i was saying this is sufficient to solve for x

i mean it was before but

(since the angle doesnt change)

its specifically the insight that they have to scale together that allows you to get the angle

[cinder spindle]

yea but solving for x rn won't give me the right answer

[remote heron]

use a trig function

[cinder spindle]

yeah ik

[remote heron]

what ratio relates these sides

[cinder spindle]

tan(1.8/0.8)

well inverse tan

[remote heron]

so tan isnt what you want

wait

did i use the wrong one

but i got the right answer

i knew i shouldnt have started helping

but no one else was and i wanted to know the answer

[remote heron]

if you use cosine you get the right answer

so whats wrong with the diagram, then

[cinder spindle]

wha?

you can't do inverse cos(1.8/0.8)

that's undefined

[remote heron]

no, flip em

[cinder spindle]

the fuck

bru

[remote heron]

$\arccos \qty( \frac{0.8}{1.8} ) \approx 63.31$

[ocean seal]

jan Niku

[remote heron]

[cinder spindle]

63.61

but ye

[remote heron]

ah, ye

[cinder spindle]

welp

fuck

[remote heron]

sorry man like i said im a little woozy

but helping with math isnt flying a plane

[cinder spindle]

how old are you btw

[remote heron]

old man

👴

[cinder spindle]

nice

[remote heron]

so cosine of

my guess is

hrm

lemme screw around

if another helper comes, need help with D

[cinder spindle]

i think now's a good time to ping helpers

@mental coyote

for fuck sake

what degenerate named himself helperssss

specifically

to fuck us over

<@&286206848099549185>

lord and savior maximo

[surreal meadow]

it's for when people ping helpers too early i think

[surreal meadow]

also i do not want to think about this problem rn. kind of just annoying trig

[cinder spindle]

aids

[remote heron]

well chromium at the very least ill be able to help once i get some sleep

it may just be 3-12 hours

[cinder spindle]

ah

that's nice

fuck this

.close

[lone heart]

Channel closed

Closed by @cinder spindle

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[pliant nymph]

ii and iv

[lone heart]

@pliant nymph Has your question been resolved?

[gusty gorge]

what about it don't you understand

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[silent sage]

Have inquired regarding this doubt previously; My question is:

How do I prove that |(u-v)/2| = pi/3?

I am not quite sure how to plot it without being aware of the values of the vectors involved. (Have referred to the video previously linked by Mr. Riemann)

[lone heart]

@silent sage Has your question been resolved?

[thin maple]

oh hi

:(

[silent sage]

#discussion / #chill

I may've misconstrued your intentions since you are new to the server; assistance will be appreciated.

[thin maple]

i think its by definition of summing the vectors

as long as |uxv|=sin(theta) is valid you can do this

[silent sage]

My concern is |(u-v)/2|; I need to prove that its = sin pi/3

It's already been proven that |uxv| = sin pi/3

[thin maple]

think abt it geometrically

|(u-v)/2|=sin(theta/2)

[silent sage]

I was linked to this video by Mr Riemann: https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/linear-algebra-vector-examples

But all the vectors were visualised here had values.

[thin maple]

its 1

unit vectors

so throw away the values

theyre just equal length lines

[silent sage]

Facing two arbitrary directions such that the angle between them is pi/3 right?

[thin maple]

sure

doesnt have to be

but in this case yes

2pi/3 right?

[silent sage]

Sin 2pi/3 == sin pi/3 so we can take either?

[thin maple]

theyre vectors

the angle itself cant just

change

they hv direction

even though sine is identical

[silent sage]

Right. It would've altered the value if it was some other trigonometric function.

[thin maple]

yep

[silent sage]

I do need to assume some values for plotting u-v/2 though right?

[thin maple]

theyre 1

it says there

unit vectors

[silent sage]

They're unit vectors so I can only think of (1,0), (0,1) etc. but the angle between these isn't pi/3..

[thin maple]

(rt(2)/2,rt(2)/2)

[silent sage]

😮

[frosty marsh]

Help

[silent sage]

Kindly repost your message in #help-8 or any of the other unoccupied help channels!

[frosty marsh]

Ok

Done

[silent sage]

Kindly delete them from here now. 😅

@frosty marsh

I don't have OCD but this channel doesn't look neat anymore.

[thin maple]

@frosty marsh

[silent sage]

Anyways getting back on track in the meantime; is it possible to predict two vectors in this manner which would have pi/3 as the angle between them?

[thin maple]

uh

just convert between cartesian and polar

[lone heart]

@silent sage Has your question been resolved?

[silent sage]

Trying to figure it out.

[thin maple]

what else btw

[lone heart]

@silent sage Has your question been resolved?

[silent sage]

waaaaaaaaaaaaaaaaaaaaaaaaaaaait a little longer

[thin maple]

oki!

[silent sage]

yass I think I've got it.

I let u = (1,0) v=(1/2,√3/2)
[(1,0) and (1,2pi/3) respectively in polar coordinates first, converted them to cartesian]

(u-v)/2 = (3/4,-√3/4); Its modulus value is √3/2 which is = sin 2pi/3.

Hope everything above is correct.

Had to study what polar coordinates were again (had forgotten about them) so took a while.

[lone heart]

@silent sage Has your question been resolved?

[silent sage]

@thin maple Could I get a confirmation?

[thin maple]

yepp seems correct

[silent sage]

This was my third time inquiring regarding this question; the first two times the bot closed the channel overnight so I really appreciate the help.. Thank you for your time and assistance.

.close

[lone heart]

Channel closed

Closed by @silent sage

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[static mica]

Hey, i need some help again with proving trig identities, i asked a similar question yesterday, and i eventually got it. Ik all the identities and stuff but i dont always catch on what im supposed to do to proceed

[static mica]

this is the question

so what i initially started with was the left side and i converted cos^2t-1 to sin^2t

then i tried breaking down tan or cos

after i did that i realized it was useless

and im debating where its the right side i should manipulate

[quasi vector]

you just multiply the numerator and denominator by tan^2(t)

[static mica]

when?

what

if i do that then i lose than tan^2t on the bottom

[quasi vector]

how?

[static mica]

denominator section

oh wait

u said multiply not divide

[quasi vector]

yep

[static mica]

then it would be tan^2(t) tan^2(t)

[quasi vector]

how

[lone heart]

@static mica Has your question been resolved?

[static mica]

sorry

i got sidetracked for a second

here ill write it and send

thats what i got

when i did that

im gonna start a new ticket

.close

[lone heart]

Channel closed

Closed by @static mica

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[opal topaz]

Can someone dumb down what happened here for me? I'm really lost in what happens even if it's very simple.

[opal topaz]

The internet will tell you power rule but im not sure how to apply that

[alpine sable]

are you confused about the application of the power rule for integrals?

[opal topaz]

yess

[alpine sable]

okay

so

do you know what the power rule is?

first and foremost

[opal topaz]

yeah

[alpine sable]

state it

[opal topaz]

d/dx x^n = nx^n-1

iirc

[alpine sable]

thats for derivatives

i am asking you the power rule for integrals

[opal topaz]

oh then uhh is that

u^n du = (u^(n+1))/n+1

[quasi vector]

[alpine sable]

okay right

so first let's recognise what our n is in your case

[opal topaz]

2

[alpine sable]

no it is not

[opal topaz]

OHHHH

-2

[alpine sable]

yep!

okay

so apply it now

[opal topaz]

okayy

[alpine sable]

so what is your overall expression, now that you have recognised that n = -2?

[opal topaz]

integral x^(-2)dx
= (x^(-1))/(-1)
so u get -1/x^(1) hooray

so jsut x

[alpine sable]

yes! exactly!

you got it, good job!

[opal topaz]

okayy thankss

[alpine sable]

no worries

[opal topaz]

i might ask more questions as im doing an assignment should i close the channel

[alpine sable]

if you have currently, you can ask it right now

you can open more if you have any other

just make sure to close the channel you have open if you don't have any current questions

[opal topaz]

okss

.close

[lone heart]

Channel closed

Closed by @opal topaz

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lone heart]

@river swan Has your question been resolved?

[lone heart]

@river swan Has your question been resolved?

[lone heart]

Channel closed

Closed due to the original message being deleted

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[twin bolt]

hellloo

[small panther]

hi

what your issue ?

[twin bolt]

how do i know to subtract 4-15 and not 15-4?

[carmine reef]

Because the 4 is on the left of the minus sign

and the 15 is on the right

[twin bolt]

so this one is wrong?

[carmine reef]

yeah

[twin bolt]

so left to right then?

[carmine reef]

yeah

[twin bolt]

thanks i have another question

[carmine reef]

<a,b> - <c,d> = <a-c, b-d>

[twin bolt]

for this one

[carmine reef]

but not <c-a, d-b>

[twin bolt]

why is it 3 sqr rt of 2

[carmine reef]

They left out a squared sign in the second to last step

[twin bolt]

wym?

but the answer is correct right?

[carmine reef]

seems to be

[twin bolt]

bet thank you so much man

i appreciate it

how do you become a mod like you?

[carmine reef]

I'm not a mod

but if you help enough people someone will give you a green name

[twin bolt]

ohhh that’s so cool

[carmine reef]

mods have a blue name

[twin bolt]

so your just a helper?

[carmine reef]

yeah

[twin bolt]

that’s awesome mind if i add you as a friend?

you cool fr

[carmine reef]

ah sure

[twin bolt]

your in under grad?

[carmine reef]

yeah

[twin bolt]

that’s awesome

where you go?

ima be in undergrad next year

[carmine reef]

I'm at siu rn

I gotta go atm but I sent a friend request

[twin bolt]

bet see you man

appreciate it fr

[carmine reef]

that's cool, I'm most of the way through now

Np, cya

[lone heart]

@twin bolt Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[faint salmon]

this is super silly but how do you do this operation

[faint salmon]

16/9 - 16/16 = 7/9

i can't find any common factors between these denominators, how was this answer reached?

.close

[lone heart]

Channel closed

Closed by @faint salmon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[ocean seal]

donut

[slate monolith]

its not though

the terms are decreasing not increasing

do you mean -2/3

yes

its the other way around

the ratio is what you multiply to get to the next term, not divide

[ocean seal]

donut

[lone heart]

Channel closed

Closed by @violet ore

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[flint belfry]

i mean you could just say

as n increases the value of 1 will be irrelevant

2^n /7^n
= (2/7)^n
when you raise a fraction to a poitive power it gets smaller

or you could just say the difference between 7^n and 2^n increases as n increases

i dont know if thats enough though

[plain flame]

its probably neater to divide top and bottom by 7^n

[whole shell]

if you are asking, then i assume you dont know how to use lhoptial theorem

[whole shell]

and then yh ^

wait if you know the lhopital theorem

why cant you use it

[flint belfry]

wdym

[whole shell]

(2/7)^n / (1/7^n + 1)

[plain flame]

^

[flint belfry]

why though ?

[whole shell]

you can take the limit of that

1/7^n goes to 0

so does (2/7)^n

[flint belfry]

oh

do you have to break it up like that

[whole shell]

its a more mathmatical way than just saying 1 is irrelevant and 7^n is bigger than 2^n

[flint belfry]

oh okay

[lone heart]

Channel closed

Closed by @violet ore

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[gentle pine]

ok I know how to do this but

how do I find ABC

3x+6+7x-18= ????

wait do I do 3x+6=7x-18

[tacit arch]

also use the definition of bisects

yes

[gentle pine]

bruh I am dumb

thanks

.close

[lone heart]

Channel closed

Closed by @gentle pine

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[gentle pine]

2

very pro

https://tenor.com/view/sweating-nervous-paranoid-gif-4974019

it's this question

[outer lark]

.close

[lone heart]

Channel closed

Closed by @outer lark

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[wheat isle]

Why does the example say the function becomes h(3)

[rustic coral]

For the sake of example ig? Without the diagram being referred to, it's hard to say more.

[wheat isle]

Oh alright

Do you know how I would work out example 4

f o g means f(g(x))right?

[rustic coral]

Yes

[wheat isle]

So would it turn into (2x-1)(3x^2)

[rustic coral]

That would be f(x) multiplied by g(x)

[wheat isle]

so just (2x-1) • (3x^2)

[rustic coral]

That's the same thing you just said.

Do you know what f(g(x)) actually means?

[wheat isle]

The function of G applied by F right?

Or is it the other way around

[rustic coral]

It means you input g(x) into f(x).

In other words, f(g(x))=||2g(x)-1||.

[wheat isle]

Where does the 3x^2 go?

[rustic coral]

g(x)=3x^2

Just substitute it in.

I'm showing you the initial setup

[wheat isle]

Oh

[wheat isle]

I’m a little confused on the part where the 2x-1 gets split into this part

[rustic coral]

Why?

You're not splitting anything, 2x-1=f(x) has an input of x, but you want an input of g(x), so replace x and g(x)

[wheat isle]

Oh alright

So the 2x-1 stays the same but you’re just inputting g(x) into the middle of the equation

[rustic coral]

It's not an equation, it's a function. But yes, you're just taking g(x) as your input into f(x) rather than x.

[wheat isle]

Oh okay

Thanks

[lone heart]

@wheat isle Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lunar lintel]

had a quick question

so the sequence

converges by taking the limit

and an does not = 0

so by divergence test it tells us that the series diverges right?

ok but

why does it go to infinity

or how i suppose

just by taking limit of n as it approaches infinity?

because why cant we do the same thing that we did for the sequence by taking the limit

so i was confused how they got infinity

[pseudo ice]

Well for the sum, you can e.g. find that the terms in the sequence from some point on will be "close" to 9/6

in a way you're kinda adding loads of 9/6's together and all

(well not exactly, that's kind of an oversimplification there - but the best explanation I can think of before going into definitions involving epsilon and etc haha)

[lunar lintel]

confusion is occuring

so if the divergence test says if the sequence is not = to 0 then the series diverges to infinity all times?

[pseudo ice]

If the sequence does not converge to zero, then you could have that:

• the series diverges to ♾️ (e.g. the sequence has a positive limit or diverges to ♾️ as well)
• the series diverges to -♾️ (e.g. a negative limit or diverging to -♾️)
• the series doesn't have a limit (e.g. (-1)^n alternates between -1 and 1, and the sum of that will alternate between values)

[lunar lintel]

i dont think u get my confusion

im saying why cant we do the same thing we did for the sequence for series

like how do you know what it diverges to

like just plug in infinity for n?

[pseudo ice]

What do you mean "the same thing we did for the sequence for series"?

And you're taking sums of multiple terms there so erm

[pseudo ice]

Well the closest you could reasonably do is find an expression for the partial sums and then try and find the limit of that, for which you might be able to do it similar to the sequence way

[lone heart]

@lunar lintel Has your question been resolved?

[earnest spruce]

can't you use l'hôpital's rule @lunar lintel

[cosmic steeple]

$$s_n = \sum_{i=0}^n a_n$$

[ocean seal]

theREALyumdub

[cosmic steeple]

Rewrite the series this way if you wanted to do an actual calculation. But the point is a divergent series won't show you anything - it should diverge

@lunar lintel

You could theoretically get a sum of the sequence a_n but if you evaluate the limit it wouldn't help you calculate the value, just get a divergent value

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[steel temple]

I am having trouble with Question 3. I marked down that the first coordinate is cosine and the second coordinate of P is sine. I know that csc = 1/sin but does that mean that I just flip the value of sine?

[vital epoch]

@lone heart how do u take notes

[steel temple]

By copying them down

I dont use LATED

*LATEX

<@&286206848099549185>

[lone heart]

@steel temple Has your question been resolved?

[lone heart]

@steel temple Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[stoic delta]

Hi

I’m not sure how to do this

This is the answer

[thick grail]

First write it without exponents

[stoic delta]

Ok

[thick grail]

Send the working when you’re done

[thick grail]

Oh …

[stoic delta]

):

[thick grail]

That’s not how you do it

[stoic delta]

Oh

[thick grail]

I’ll send working

[stoic delta]

Ok thank you

[thick grail]

For the fractional and negative exponents, I really recommend looking at videos if you don’t understand

[stoic delta]

Oh

Ok

[thick grail]

Btw, if you have no more doubts, just type .close

[stoic delta]

Oh yea

.close

[lone heart]

Channel closed

Closed by @stoic delta

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[alpine sable]

Calculating the equation of the normal curve with 8 over x

[alpine sable]

Hello!

[west girder]

lmao kookie

[rugged pond]

I'm getting my threads stolen all the time

[alpine sable]

do i ask here

[rugged pond]

you can

[alpine sable]

oh my bad

[west girder]

yea go ahead

[alpine sable]

i have a very stupid question

so

for calculating the equation of the normal to the curve
y = 8 over x-x+3^2

I know how to solve it and find y, but i’m getting stuck with 8 over x

do we need to simplify it first?

Differentiation ^

i’ll send a photo

for example if it was just y = 8x - x + 3x^2
it would be f(x) = 8 - 1 + 6x

correct me if i'm wrong

in other words idk how to work with the 8 over x

[granite pike]

Do you mean to ask you dknt know how to differentiate 1/x?

[alpine sable]

8/x, would differentiate to what exactly, is what i mean

• x + 3x^2 = - 1 + 6x

8 over x = ?

[granite pike]

1/x^n = x^(-n)

Hopefully you know that the derivative of x^n is n * x^(n - 1)

[alpine sable]

Thank you!!

[granite pike]

Np

Please type .close if you're finished

[alpine sable]

.close

[lone heart]

Channel closed

Closed by @bleak flax

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[teal shale]

is there anyone here in french

[lone heart]

@teal shale Has your question been resolved?

[molten pivot]

No

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[spare fern]

Could anyone help me out with a physics problem?

[spare fern]

My assessment is tomorrow I really have to learn how to do this

It would mean a lot if someone could help me out

[quasi vector]

i think you'd be better off asking this question in a physics server

[spare fern]

I've already tried

no luck

[quasi vector]

https://discord.gg/physics

you tried asking here?

[lone heart]

@spare fern Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lone heart]

@lucid yoke Has your question been resolved?

Channel closed

Closed by @lucid yoke

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[thorn tapir]

I'm having a problem solving a particular indefinite integral.

[thorn tapir]

$\int \frac{x^6 - x^3}{(2x^3 + 1)^3} dx$

[ocean seal]

rikusp2002

[thorn tapir]

Someone suggested Ostrogradsky's method, but I was looking for any simple ways like substitution or similar ideas.

[strange meadow]

u=2x^3?

Are there bounds

[vapid shuttle]

you will get a replacement for dx that includes 1/(3x^2) so that wouldn't work

its an indefinite integral

[strange meadow]

But sub x for that

[vapid shuttle]

?

[strange meadow]

x in terms of u

[vapid shuttle]

you're going to further complicate the integral that way

[strange meadow]

don’t think so

The denominator being a linear thing cubed is easier

[vapid shuttle]

it won't be linear

[strange meadow]

Maybe trig sub?

Yes it would?

[vapid shuttle]

it would include the 1/2x^3 with x in terms of u..

as a factor

[thorn tapir]

Nvm, dividing by x^6 in both numerator and denominator solves the problem

[strange meadow]

What reallyb

[thorn tapir]

Tru

Yes

[strange meadow]

Omg

That’s crazy

[thorn tapir]

Yeah

Thanks for the help btw

.close

[lone heart]

Channel closed

Closed by @thorn tapir

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[raw apex]

Prove that { n/5, n belongs to Z } is a group with respect to addition.

[raw apex]

It's my channel

It's occupied

Alright

[rose sigil]

what do you need to do to show it's a group?

[raw apex]

Yea

[rose sigil]

wat?

[raw apex]

Yes I need to prove that its a group

[rose sigil]

i wasn't asking that loll

[raw apex]

Heh

I don't get it

[rose sigil]

you need to show the addition associates, there's an identity element, etc

[raw apex]

Yes

But how

[rose sigil]

can you list all the things you need to show first?

that's pretty important haha

[raw apex]

1. Closure property
2. Associative property
3. Identity property
4. Inverse property

[rose sigil]

ok good

any progress at all?

[raw apex]

Hmm I kinda get it how to do it

But idk how to

[rose sigil]

???

[raw apex]

Fractions aren't integers right

Like 1/5

[rose sigil]

no, 1/5 is not an integer

but { n/5, n belongs to Z } contains all the integers

[raw apex]

What if n is 1

And 1 belongs to Z

But 1/5 doesn't

And it's not closed

So it doesn't satisfy the closure property

Hence it is not a group

Is it?

[rose sigil]

that makes no sense

[raw apex]

This whole group theory doesn't make any sense

Ughhh

[rose sigil]

:c

closure means if you take two things in { n/5, n belongs to Z } and add them, you get something in that set

[raw apex]

@rose sigil see

If you take two elements

Suppose n and m

And we get n/2 + m/2 under addition

We get n + m/2

[rose sigil]

n/2 and m/2 what where did those come from??

n + m/2??

[raw apex]

Two things

(n+m) /2

[rose sigil]

what are n/2 and m/2 for?

[raw apex]

n and m belongs to Z

And to satisfy the closure property

[rose sigil]

do you mean n/5 and m/5?

[raw apex]

No /2

Not 5

[rose sigil]

and you did mean /5 here? not /2?

[raw apex]

Oh frick it's /5

Shall I ping helpers

Been like 15 mins already

[rose sigil]

idk about pinging helpers but i'm gonna let someone else help

[raw apex]

Alright

<@&286206848099549185> help

[lone heart]

@raw apex Has your question been resolved?

[smoky hedge]

?

[true epoch]

Whats your doubt may i know?

[smoky hedge]

Just check the properties

[peak umbra]

hello

can you guys help

im in middle school

and im so confused about math right now

[true epoch]

what help would oyu like?

algebra calc geometry

[peak umbra]

so like my family moved to another country and i didnt go to school for 1 year and when i did i went to language school for 3 years currently its years 4 and i have no idea what im doing

[true epoch]

ohkk

[peak umbra]

yeah

[true epoch]

so u need help

for understanding

the whole shiut

[peak umbra]

yeah

its so confusing

[true epoch]

then have to approach moderators for support

coz we only help for doubts

[peak umbra]

like i have NO IDEA why theres letters in math now algebra is fucked

[true epoch]

basically

imma tell you

stop associating things with maths

see it as something new

like u have never seen a letter

letter are a medium of seeing algebra

to solve unknown shit

for eg: Sam has 10 apples he gave 4 how many left?

[peak umbra]

6

[true epoch]

good

in algebra

u would say

x=10-4

which also six

[peak umbra]

oh

so its like a place holder?

[true epoch]

but u dont need variables like apple and shit

yeahhhh

exactly

[peak umbra]

huh

another thing im confused about division cause i almost did like none in elementery because of language school

[true epoch]

like the decimal one

?

[peak umbra]

yeah

[true epoch]

ok

so imma send you a one shot video

watch it

[peak umbra]

wait but whats the point of a place holder when you can just write a number?

[true epoch]

definitely u will solve all of those

[true epoch]

its uses are in physics

[peak umbra]

oh

[true epoch]

like to calculate speed

from distance and time

when we reach higher class

we see that we dont even use the terms speed and distance

we write u = x/t

and others

so algebra is infact very important

[peak umbra]

whats x/t?

is it x=speed and t=distance?

[true epoch]

x=dist. t = time

u = speed

[peak umbra]

oh

[true epoch]

its written for convinence

its not necessary to write only x , t

write anything

but its like a tradition

to use them

[peak umbra]

oh ok

[raw apex]

Prove that { n/5, n belongs to Z } is a group with respect to addition.

[peak umbra]

wait can you explain division to me because any youtube video i see doesnt explain it well

[raw apex]

My problem isnt solved yet

[true epoch]

its not possible coz i need a laptop and i dont have one currently

[true epoch]

lets have a look

[raw apex]

Alright

[peak umbra]

oh ok

[true epoch]

what is a group

[raw apex]

A group ( G, • ) or ( G, *) is called a group when it satisfies following properties:

1. Closure property
2. Associative property
3. Identity property
4. Inverse property

[true epoch]

ohk

then whats the issue u encountered

[raw apex]

Idk how to make the given problem satisfy closure property

[true epoch]

how do you think we can do it

express your thoughts

so that we see where u are wrong

[raw apex]

I think we are going to suppose two elements n and m which belongs to the set Z

[true epoch]

flawless till here

[raw apex]

And by question we can do n/5 + m/5

[true epoch]

yes

[raw apex]

Which should belong to the same set but it doesnt

Right

[true epoch]

it will my dear

when u add both

the numerators add while the denominator

is 5

dont reduce the fractions

two integers give an integrs on addition

[raw apex]

Wait does fractions belong to integer?

[true epoch]

n+m = k

[true epoch]

they never said that

they said that n belong to integer

not n/5

[raw apex]

Oh yes

[true epoch]

so now ig its done

[raw apex]

So how can we show it

[true epoch]

just write every step and explain it

and ye

you can tell

that two integers sum up to give an integer

say like as we know

[raw apex]

It becomes n/5 + m/5 = (n+m)/5 right

[true epoch]

yes

[raw apex]

And how does the result belong to the same set

[true epoch]

well

assume n+m to be K

then it become k/5

[raw apex]

Yes

And

[true epoch]

where K belongs to Z

and is of the form n/5

both satisfied

[raw apex]

Oh

I somehow get it but im still confused

[true epoch]

yes

[raw apex]

Alright im gonna try

I’ll close this channel

.close

[lone heart]

Channel closed

Closed by @raw apex

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[alpine sable]

pls someone help ive been trying to answer this for the past 3 and a half hrs and my brain hurts so much already

[alpine sable]

<@&286206848099549185>

[strange meadow]

!15m

[lone heart]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[strange meadow]

!status

[lone heart]

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

@alpine sable Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[valid merlin]

Can someone help me with this question??

[jagged cobalt]

what have you tried?

[lone heart]

@valid merlin Has your question been resolved?

[valid merlin]

well, by putting 2 in the middle of the two inequalities then subtracting the (a+2b)^2/blah from everything. Gets me pretty close. But I run into an issue with the direction of the inequalities.

[jagged cobalt]

i suppose you can do it like that - the way i first thought of was to move everything to a single side for both inequalities - which pulled the answer out almost immediately

However, if we continue the way you were going - could you show me what you have atm?

[valid merlin]

oop, nvm. got it. Thanks for the help anyways ig.

.close

[lone heart]

Channel closed

Closed by @valid merlin

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[pseudo ore]

guys what is 1+1=? 🤓

[mortal trellis]

17

dont troll

.close

[lone heart]

Channel closed

Closed by @mortal trellis

Use .reopen if this was a mistake.

[keen pasture]

11

[ocean seal]

MathIsAlwaysRight

[keen pasture]

First and second one for bingo

[modern sedge]

Yay

[mortal trellis]

well I'm just working mod 5

[modern sedge]

Javascript?

[keen pasture]

Python

[pseudo ore]

thanks bb gril 🤓 🤓

[modern sedge]

"1"+"1"

[keen pasture]

Yeah

If you forgot that you're inputing numbers as variables this can happen

[modern sedge]

I would consider this as a proof of minn being underage

[pseudo ore]

.close

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[high palm]

how do i factorise this

[alpine sable]

set x^2 = t

[high palm]

OHHH

thanks so much

[alpine sable]

No wait

[high palm]

wait

[alpine sable]

That doesn't help much

[high palm]

not

yeah it's still unfactorisable

lol

[modern sedge]

It's full of golden ratios

[alpine sable]

You probably have to rewrite that x^2 term into two terms that can be factored nicely

Don't see what it can be right now though

[high palm]

if it helps the topic difference of two squares and perfect squares

[modern sedge]

This is difference of squares

[alpine sable]

Oh yeah

I see it now

You can get a nice perfect square by rewriting that x^2 term

[high palm]

lemme see

[high palm]

how would i do that?

[silent dock]

Need help witht tgis

H*

[high palm]

i don't see anything

[high palm]

get another channel

[nimble fern]

!help

[lone heart]

Please read #❓how-to-get-help

[silent dock]

!help

[lone heart]

Please read #❓how-to-get-help

[modern sedge]

x^4 + 1 + sth is perfect square

[high palm]

sth?

[modern sedge]

it means something

you have to determine the "something" and then then split the x^2 term to get "something"

[high palm]

oh

[alpine sable]

Honestly might still help to write t = x^2

To see it better

[high palm]

ok so

after putting in t = x^2

you get t^2 - 3t +1

now t^2 + 1

is in (t+1)^2

t^2 + 1 = (t+1)^2 - 2t

but you still get 1 extra t?

oh wait t is x^2

so can u difference of 2 squares that

[modern sedge]

You still didn't rewrite t^2 - 3t +1

[high palm]

hang on

[modern sedge]

you will get t^2 - 3t +1 = (t+1)^2 - 5t, so the (t+1)^2 might not be the best perfect square. Can you think of other perfect square that will contain these 2 terms?

[high palm]

how about (t-1)^2

[modern sedge]

try that

[high palm]

(x^2 - x -1) (x^2 + x -1)

i don't think t is the best way to do this

cuz in the second term "x"

u have to divide t

[modern sedge]

It's the best way I guess

[mossy gust]

You just need to factorize it into something like (x+a)(x+b)?

[modern sedge]

It's possible

a and b will be golden ratios

[mossy gust]

I'm asking if there's anything else that is required.

[ocean seal]

MathIsAlwaysRight

[modern sedge]

But I dont think that this is the best looking result

(That's just factorization of one of the factors)

[high palm]

anyways thanks

for the help

i appreciate that you didn't just give me the answer

otherwise i probably would've just copied it and moved on forgetting the reasoning

[mossy gust]

@high palm You did factorize this into 4 different roots, right? If so, be sure to close the channel.

[high palm]

roots?

i remmeber that in polynomials

remind me please

[mossy gust]

The "r"s in things that look like (x-r), where you multiply them together and recover the polynomial. They are where a graph of the polynomial cross the x axis.

[high palm]

not sure what you mean

you mean the zeroes

maybe im tripping

but i did get the answer

so yeah im done

.close

[lone heart]

Channel closed

Closed by @high palm

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[fierce lark]

Some of the derivative proofs in my textbook are pretty bad ngl, esp quotient rule. Do you think Id be able to use sum like this over the quotient rule proof in my textbook?

[fierce lark]

this is whats in my textbook btw

I got no idea whats going on lmao

[vale wigeon]

are you planning to rederive the quotient rule from scratch every time...?

if not then wdym by "use"

[fierce lark]

I doubt id be asked to show prove it from scratch to be honest

id probabily be given a function and then get asked to prove it

[ornate condor]

um

do u mean find the derivative?

[vale wigeon]

i mean...

what's your problem here

it's a little unclear what you want to ask or know

[fierce lark]

1.Is the first proof that I showed valid? 2.Do yall think it would be fine to use on a midterm 3. Id appreciate if you could explain exactly whats happening in the textbook version of the proof

[keen pasture]

1. Assuming that you already know product rule and the derivative of 1/g, I'd say yes. 2. You can use it once it has been proven in lecture 3. They proved the 1/g derivative rule in your 2nd picture

[lone heart]

@fierce lark Has your question been resolved?

[fierce lark]

hes only used the textbook proof in lecture 😭

[fierce lark]

Im not sure what im doing wrong/how to keep going after this step in the proof

[keen pasture]

You're trying to unserstand the textbook proof?

[fierce lark]

yes

[keen pasture]

You added the fractions wrong

[fierce lark]

is it just the signs in the numerator or have I completely messed it up

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[fierce lark]

.reopen

[lone heart]

✅

[keen pasture]

a/b+c/d = (ad+cb)/(bd)

Not b+d

[fierce lark]

yea but arent there 1s in both the numerators?

[keen pasture]

I mean the denominator

[fierce lark]

ah I see

lemme try again 😓

yep got it to work

thanks!

just also wanna make sure, normally when were working with rationals we arent able to just seperate the fractions like we did here (were allowed because the h is approaching 0 or somehting like that?)

over here

[lone heart]

@fierce lark Has your question been resolved?

[keen pasture]

What do you mean with seperate the fractions? Rewriting like you did here? You can do this with rationals, too

[fierce lark]

ok ty, guess im totally lost gotta go prac

.close

[lone heart]

Channel closed

Closed by @fierce lark

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[gusty coral]

hi

[gusty coral]

could anyone help me w this q:

Suppose that T: R2 → R2 is the transformation that first performs a horizontal shift that moves ⃗e2 to ⃗e2 − 0.5⃗e1 (while leaving ⃗e1 unchanged) and then reflects the result around the x2-axis. Knowing that T is linear, find its corresponding standard matrix

i messed up my signs idont understand why

[rocky grove]

Okay so

Let's say e1 is "i" and e2 is "j"

So you're saying that j becomes (j-0.5i)?

Or is it like

Let's say your vectors are mi + nj

Oooo wait

So like

So is it like this?

Red = after and dotted black = before.

@gusty coral

[gusty coral]

Yes i think thats it for j

oh wait is the x2 axis the y axis ?

[rocky grove]

Yeah

This is what the matrix transformation will look like

Purple is the target

So the j becomes negative

Since it got reflected about the y axis

Wait

Yeah

[gusty coral]

ithought the purple would be on the left side since its reflected around the y-axis no?

[rocky grove]

Yeah I corrected it

[gusty coral]

oh yes

yes thats it ithink

thanku🥺🥺🥺🥺

[rocky grove]

So yeah you flip all the positive i values into negative ones

Which is supposed to be the first row

I think

[gusty coral]

yep i got it now:) thanku again!

.close

[lone heart]

Channel closed

Closed by @gusty coral

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[glass crest]

so we need to solve this indeterminate form and i'm so lost idk what to do 😔 thank u in advance!

[quasi vector]

l'hopital's rule

[sharp thorn]

too complicated

[glass crest]

unfortunately that hasn't been taught to us yet so rip

[quasi vector]

which is why I crossed it out

[heady void]

do you have the answer

[sharp thorn]

divide the numerator and denominator by x

or take the x out common

so it is

[heady void]

idk tho I would split the tanx into fractions

[thick grail]

you would have a cosine to deal with tho?

[sharp thorn]

$\lim_{x \to 0} \frac{x(1-\frac{tan x}{x})}{x(\frac{\sin x}{x} -1)}$

[ocean seal]

bettim

[thick grail]

this is way better because you can actually apply the identities

btw this is doesn't work with cosine

[sharp thorn]

it doesnt have to

[thick grail]

yeah

[sharp thorn]

$lim_{x \to 0} \cos x =1$

[ocean seal]

bettim

[heady void]

yeah

[sharp thorn]

messed up the command ignore

[thick grail]

ah

[heady void]

I was thinking of using this

as if that might help