help-10

[weary garden]

godbless the folder

[violet vine]

okay, the parabola is flipped around a line

[weary garden]

wait wait can you check 4a

[violet vine]

okay

[weary garden]

i got 2(x+1)^2-8

?

[violet vine]

it's wrong I think??

[weary garden]

what do you think its gonna be

[hushed garnet]

yep

the minima is

-5

[violet vine]

2(x+1)²-5

[hushed garnet]

oh right you can solve using algebra too

[violet vine]

💀

you're not supposed to solve graphically

[weary garden]

how did i get -4

[hushed garnet]

calculus brainrot

[violet vine]

idk how u got -8 LOL

[weary garden]

my tutor doesnt really care

[violet vine]

real

[hushed garnet]

-b/2a, -D/4a

[weary garden]

bruh i done got banned for calling myself the r word

[violet vine]

LOL THEY DONT LET YOU SAY THE R WORD??

[hushed garnet]

the vertex

[violet vine]

parabolas are symmetrical about a line

[misty hearth]

@hushed garnet why are you using desmos and graphing it??

[weary garden]

huH

[violet vine]

^

[weary garden]

wait somebody write the working out that you used

[hushed garnet]

i wanted to confirm my answer

[hushed garnet]

derivative of function = 0

[weary garden]

i thought you didnt know math

[hushed garnet]

for minima

[violet vine]

so to find the minima x value u can just find the x values at a certain y value then take the midpoint

[weary garden]

to get 2(x+1)^2 - 5

[misty hearth]

uh huh...

[violet vine]

STOP LMAO

[hushed garnet]

??

whar

[misty hearth]

i dont

[violet vine]

no derivatives here don't confuse them

idt they know derivatives

[hushed garnet]

oh

ok

[weary garden]

WHO TF THEM

[misty hearth]

i have a learning disablity i was put in special needs i dont know much math

[violet vine]

YOU

[misty hearth]

but even a moron like me would know this

[weary garden]

im NOT A THEY THEM

[violet vine]

why are u here rn lol

[weary garden]

CALL ME HIM

[violet vine]

MY BAD

[misty hearth]

so i can learn math?

[violet vine]

wrong channel

[misty hearth]

why else would i be in here?

[misty hearth]

is this not math?

[violet vine]

this one's to help people

[weary garden]

this is math help

lad

[violet vine]

go to general or something bro

[warm canopy]

dont be rude like this

[weary garden]

not learning math

[misty hearth]

oh sorry

[weary garden]

id rather go to friggin khan academy to learn

[misty hearth]

like rude to my self?

bc i am a moron

[weary garden]

this servers good for 1 on 1 help

[violet vine]

REAL

okok I'm getting off topic

[hushed garnet]

are you in grade 11 rn

[unique torrent]

What going on here?

[misty hearth]

ima go now guys it was nice helping u @weary garden

[weary garden]

nice help man

[hushed garnet]

the guy that needed help

[misty hearth]

best of luck you u @weary garden i hope u get it!

[weary garden]

YO KAI CAN WE DO THIS IN DMS THIS CHANNELS GETTING CROWDED ;SOB

😭

[violet vine]

so all parabolas are symmetrical about their turning point x value

[violet vine]

uhm sure lol

[weary garden]

i hope oyu can learn some math

[misty hearth]

thanks im working on my times tables

i mastered my 6's

[wraith barn]

If its getting of topic just get a mod

Or close this mad move your discussion to another channrl

[misty hearth]

if u want i can add u we can talk in dms

id be happy to help you

[violet vine]

brother I think you're the one that needs help, at least according to you

[misty hearth]

ig

can u teach me?

[obtuse pebble]

@weary garden Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[opal pumice]

Question

[opal pumice]

Just say yes or no

I just did an entrance exam and have to know 💀

Cos^2 x = (1+sinx)/2

In the range of ]-90°, 90°[

What is tanx?

I had -✓3/3

[obtuse pebble]

@opal pumice Has your question been resolved?

[opal pumice]

<@&286206848099549185>

[vital merlin]

what even is the question

[frosty river]

Rewrite the question is not understandable

[vital merlin]

Yeah lowkey cannot understand your question bro

[obtuse pebble]

@opal pumice Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[gloomy vector]

if $3\sqrt{5+k}+2\sqrt{13-3k}$ can be simplified to an integer $a$ or a simplest radical $a\sqrt{b}$. how many such integer's k are there?

[gloomy vector]

whay does this question even mean lmao

[tender tusk]

how many integers,a, are possible when u combine both terms into either a, or a*sqrt(b)

[gloomy vector]

idk

[warm shale]

Skill_Issue

[gloomy vector]

also, sorry i fkrgot its integers k

[tender tusk]

oh

[gloomy vector]

uh

[tender tusk]

well that would make more sense

[gloomy vector]

so like

k=4

[tender tusk]

where did u get that

?

[gloomy vector]

guessing?

[tender tusk]

well guessing isnt a good idea

[gloomy vector]

that gets me 9+2=11

[gloomy vector]

then what do i do

[tender tusk]

well there is one easy one

a*sqrt(b)

this is only possible if both the square roots are equal right?

[tender tusk]

this is also a correct solution

[gloomy vector]

yea

[timid silo]

K belongs from -5 to 4

[gloomy vector]

i mean not really

if one of them was for example sqrt8 it could still work if the other is sqrt2

[timid silo]

Just check them manually

[tender tusk]

hmm yes, i didnt consider that

[gloomy vector]

fair

k=2 works

[timid silo]

It have a little domain of only 10 numbers

K can be -5,-4,-3,-2,-1,0,1,2,3,4

[gloomy vector]

-1 works

[timid silo]

-5 also works

[gloomy vector]

-4 works

-5

ok thx voth of you

.close

[obtuse pebble]

Channel closed

Closed by @gloomy vector

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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

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

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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.

[neon oar]

guys blud came with 1 million

[untold badge]

what are u confused on

[neon oar]

Im not

I just want to know

is this right?

11,000x+22,000\le1,408000

[untold badge]

whats "\le"

oh

[neon oar]

how does texit work?

[untold badge]

less than or equal

idk

[neon oar]

yeah

[untold badge]

theres supposed to be a vairable next to 22,000

[neon oar]

there is y

[untold badge]

where

[neon oar]

oops

I forgot

but I wrote it

[untold badge]

oh well then its correct

[neon oar]

ok thx

.close

[obtuse pebble]

Channel closed

Closed by @neon oar

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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

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

[storm jewel]

i got how they got all the data, but now im confused as to how to derive the law from here

[obtuse pebble]

@storm jewel Has your question been resolved?

[obtuse pebble]

@storm jewel Has your question been resolved?

[obtuse pebble]

@storm jewel Has your question been resolved?

Channel closed

Closed by @storm jewel

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.

[misty finch]

algebra

[misty finch]

yo

can someone help i got some basic highschool math

<@&286206848099549185>

[velvet rover]

send the question

[timid silo]

Hi

[misty finch]

not really sure how to start

[strong sentinel]

Go from the inside

[velvet rover]

pedmas

[misty finch]

k so -2(3+a3-4)

[strong sentinel]

Yes

9

Not 3

-2(3a +9 -4)

[misty finch]

oh thx

[strong sentinel]

[misty finch]

k

1 sec

[strong sentinel]

Yes

......

[misty finch]

so -2(3a+5)

[strong sentinel]

Yes

[misty finch]

what do i do abt the -2

[strong sentinel]

Multiply

With those inside the bracket

[misty finch]

oh so both

[strong sentinel]

Yes

Both

[misty finch]

thx

[strong sentinel]

Seperately

[misty finch]

so its -6a-10

[strong sentinel]

Yup

That's right

[misty finch]

thx

btw

howd you get the 9 at the start

[strong sentinel]

3×3

[misty finch]

oh wait 3x3

yeah lmao

thx

btw

[strong sentinel]

Yup

[misty finch]

one more thing

[strong sentinel]

Yes?

[misty finch]

how can i solve these

lke the method

like question A for example

[strong sentinel]

Take them to the same side

That's the first step

[misty finch]

so they change operations

[strong sentinel]

Or you can just cross multiply

[misty finch]

that sounds easier lol

[strong sentinel]

Yes that they do

Cross multiplication is the simplest

Fastes

Fastest*

[misty finch]

so

[strong sentinel]

.......

Yes?

[misty finch]

3x+9

4x-8

[strong sentinel]

6x + 9

[misty finch]

mb

[strong sentinel]

The other one is correct

The denominators will be both 12

[timid silo]

-6a-10

[strong sentinel]

So they go away

[strong sentinel]

That question was solved

[misty finch]

k so now its 6x+9/12 = 4x-8/12

how can i solve

[strong sentinel]

Yes

You cancel the 12s

Or multiply 12 on both side

That would cancel it out

That's the logic behind it

[misty finch]

how would i apply cancelling it

[strong sentinel]

Multiplying 12 on both sides

That would take out the denominators

[misty finch]

ah i see

so 12 x 6x+9 = 12 x 4x-8

then solve

[strong sentinel]

No

You don't need the 12 now

Take the 12 out

Keep it simple and solve

6x+9= 4x -8

[misty finch]

mb

[strong sentinel]

[misty finch]

is there a step after this

[strong sentinel]

Yes

Take the x variables on one side

And integers on the other

[misty finch]

move them over and they switch operations

then sum

[strong sentinel]

2x = -17

Yes that's it

[misty finch]

epic

thx dude

[strong sentinel]

Alright

[misty finch]

would you have time for

one more question

[strong sentinel]

Yes

[misty finch]

how would i solve A

or check with ls/rs

because ik how to do distributive property but i forgot abt ls/rs

[strong sentinel]

Divide both side by 2

First you solve for x

After getting the x value

You substitute

In the ls and rs seperately

You must get the same answer

On both the sides

[misty finch]

1 sec sry

alr i solved it and got -16

like the question

[strong sentinel]

????

You got x as -16?

????

[misty finch]

k so

2(3x-4)=-4(x+6)

6x-8=-4x-24

2x/2=-32/2

[strong sentinel]

3x -4 = -2x -12

It changes operations

Change it you'll get different answer

5x = -8

X = -8/5

[misty finch]

wait so how did you get this

[strong sentinel]

Its literally what you told, but simplified

Divided both sides by 2

The answer still won't change

[misty finch]

lol

k

so

oh i see what you did ok

ill fix it

i messed up lol

[strong sentinel]

Yup

Work more on alg

[misty finch]

true

[strong sentinel]

Which grade math is this?

[misty finch]

im in gr10 im in canada academic

we just gotta do some review but i was kinda trash at math in gr9

[strong sentinel]

Woh

[misty finch]

so i like forgot everything 💀

[strong sentinel]

This is grade 10!?

[misty finch]

gr9

review

[strong sentinel]

Alright

You'll be good as you practice

De

Dw

[misty finch]

thx

[strong sentinel]

[misty finch]

1 sec

[strong sentinel]

Yes?

[misty finch]

im js solving it but i think i messed up

[strong sentinel]

!show

[obtuse pebble]

Show your work, and if possible, explain where you are stuck.

[misty finch]

2(3x-4) = -4(x+6)
6x-8 = -4x -24
2x/2=-12/2
x=-6

[strong sentinel]

Change operations on the 4

4x

6x+4x = -16

[misty finch]

sry im js kinda confused

[strong sentinel]

Alright

You got it??

You there??

[misty finch]

yep

i just realized where i went wrong

[strong sentinel]

Good job

[misty finch]

thx for ur help

[strong sentinel]

Np

.close

.close

[obtuse pebble]

@misty finch Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[unkempt lotus]

How do I find concavity from this graph of f’(x)?

[unkempt lotus]

Is it slope of f’ ?

[keen quarry]

it f’ is increasing, f is concave up

if f’ is decreasing, f is concave down

[obtuse pebble]

@unkempt lotus Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[spice kiln]

I dont know how to find z

[harsh remnant]

Should we use sine law or cosine law?

[spice kiln]

wait i got it thanks

.close

[obtuse pebble]

Channel closed

Closed by @spice kiln

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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

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

[vernal acorn]

is 65 right?

[obtuse pebble]

@vernal acorn Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[vernal acorn]

is my answer choice correct?

[wet moss]

yes

[vernal acorn]

another question, is my work for this right?

[civic socket]

are you doing a test or smth?

[vernal acorn]

it’s a practice for the final but it’s weighted almost the same so i wanna make sure i’m getting everything right

[civic socket]

it looks fine

[obtuse pebble]

@vernal acorn Has your question been resolved?

Channel closed

Closed by @vernal acorn

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.

[waxen fossil]

Is the second answer correct

[tranquil geyser]

So what is the straight line test?

[waxen fossil]

The vertical line test to see if the equation intersects at only one point

I got 22 minutes to answer

[tranquil geyser]

Intersects what line the x axis?

Ok so what you need to do is find out which graph has more than 1 value for f(x)

For the same x value right?

[waxen fossil]

the second option was correct thanks for trying to help me

[tranquil geyser]

Lol

I was about to explain 😞😣

😣

[obtuse pebble]

@waxen fossil Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[timid silo]

Hello, when trying to solve this logarithm, I got 2.5 and I can't find another solution to it. I plugged it in for x in the equation and it doesn't come out to two. I know the answer is 5 since I used desmos to solve it but I cant get to 5 algebraically. I was wondering if someone could help me figure out what I did wrong. (Ignore the circle)

[fallen pine]

When you square rooted both sides, it should be $10=2x$

[warm shale]

Ari

[fallen pine]

Since $\sqrt{4x^2}=2x$ not $4x$

[warm shale]

Ari

[timid silo]

omg thank you so much ! went over my head to square root the 4.

.close

[obtuse pebble]

Channel closed

Closed by @lusty topaz

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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

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

[opaque bronze]

I'm currently struggling while learning functions. The question I'm stuck on is "Sketch a graph that is not a function and has a domain of {xER} and a range of {yER, y-3}"

[dark vector]

sorry, by {xER}, do you mean $x \in \mathbb{R}$?

[warm shale]

Out Of Nosh

[opaque bronze]

Yes

[dark vector]

wdym by {yER, y-3}?

[opaque bronze]

Sorry, the symbol didn't show up. Meant {yER, y ≥ -3}.

[dark vector]

ah

gm

*hm

okay do you remember the definition of a function?

[opaque bronze]

Yeah, a relation where every input (x value) can only have one output (y value)

[dark vector]

right

so you'd want a graph where there's more than one y-val for at least one x-vale

*x-val

i'd suggest just sketching both sin(x) and -sin(x) on the same graph and calling it a day

[opaque bronze]

hmm

Does that count as two functions or should it count as an answer anyway?

[dark vector]

well, it's two functions making one graph

and you're asked to sketch a graph, which that would be

[opaque bronze]

yeah makes sense

for some reason i was thinking i had to make it one function

but wait, shouldn't it go upwards for it to count as yER?

this covers the domain but not the range

[dark vector]

not necessarily

wait

hm

ye i see wht u mean

ok new plan

y = x^2-3 and y = 1 on the same graph

bada bing bada boom

[opaque bronze]

that does the trick

hope this counts as a valid answer, thanks for the help

[obtuse pebble]

@opaque bronze Has your question been resolved?

Channel closed

Closed by @opaque bronze

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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

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

[grizzled shore]

im a little confused

[grizzled shore]

so i want to prove that the set of all derivations of A denoted Der(A) is a vector space

but im not sure what do i write after C^\infty

does the f,g come from U? or R^n?

[polar fossil]

f,g are functions on U that are C^\y

[grizzled shore]

so i dont need them to be smooth R^n functions

[polar fossil]

not on all of R^n just on U

[grizzled shore]

but shouldn't this proof of closure for X and Y have to be fulfilled everywhere on my manifold?

or is it because this is a sort of differentiation that's "a local property" (im hearing people say this a lot) and so it's fine if the properties we require of it only are satisfied in some local neighbourhood for every point

but that reasoning seems a bit handwavey

[polar fossil]

having trouble keeping track of this but i think in your case you care about the entire field K

[warm canopy]

the thing you are trying to prove is not about manifolds just about linear maps on algebras

[grizzled shore]

I know that’s why I’m a bit confused where these functions come from

Or do I not even need them as I’m being K-linear

[warm canopy]

C^inf(U) will be an algebra

[grizzled shore]

And not C^\infty linear

No why am I showing linearity

I’m not

I’m showing closure under addition of derivations and K-scalar multiplication

[warm canopy]

yeah you are already given that D is K-linear

[grizzled shore]

Although doesn’t it sound like it should be C^\infty-scalar multiplication

Well Der(A) being a k-vector space is that what I want?

I’m not sure because the text doesn’t say what field it’s a vector space over

But the smooth functions aren’t a field so I don’t think I have another choice but K

Ah I see now

I can’t really show that the addition of derivations is still a derivation without applying it to some product of smooth functions

[warm canopy]

im confused on what you're trying to show. are you trying to look at the particular example of the vector field X on U, or are you trying to prove it for a general derivation on an algebra

[grizzled shore]

Oh a general derivation

I’m trying to prove that Der(A) is indeed a vector space

[warm canopy]

then there is no concept of smooth functions here, just elements of A, and a derivation A -> A

[grizzled shore]

So first I’ve got that Der(A) ⊆ End(A) so I just need to show that Der(A) is closed under the operations

But how do I know that X + Y is still in Der(A)

Where X and Y come from Der(A)

[warm canopy]

that is precisely what you have to prove

prove the derivation property for X + Y

[grizzled shore]

Yes but how would I do it without something to apply the derivation to

[warm canopy]

X + Y is a map from where to where?

[grizzled shore]

They would just be elements of A?

Oh

[warm canopy]

yeah

[grizzled shore]

Ah

No smooth functions required

We know not even what smooth functions are here

We have only linear algebra

[warm canopy]

X (vector field) : C^inf(U) -> C^inf(U) is playing the role of D : A -> A in the specific case of manifolds

[grizzled shore]

Aha

[grizzled shore]

That makes this make more sense

[warm canopy]

yeah the point will be that once you've proven the D : A -> A case, whenever you see a collection of derivations you can just know they form a vector space

[grizzled shore]

Yep

And that’ll be the vector fields

[warm canopy]

yup!

[grizzled shore]

Tyty!!

.close

[obtuse pebble]

Channel closed

Closed by @grizzled shore

Use .reopen if this was a mistake.

[grizzled shore]

.reopen

[obtuse pebble]

✅

[grizzled shore]

(kX)(ab) = X(kab) since X is K-linear

=(X(ka))b + (ka)(X(b)) since X is a derivation

=((kX)(a))b + (ka)(X(b)) since X is K-linear

=((kX)(a))b + a(kX(b)) since A is an algebra over K

=((kX)(a))b + a((kX)(b)) by definition of scalar multiplication

Hence kX is a derivation?

[warm canopy]

made things harder for yourself

(kX)(ab) := k*X(ab)

[grizzled shore]

That would’ve been most helpful

For some reason I wasn’t sure if I could do that

But I argued the addition of derivations directly from pointwise addition

But didn’t do it for the scalar multiplication

Ok thank you

.close

[obtuse pebble]

Channel closed

Closed by @grizzled shore

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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

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

[restive rapids]

Let's say I have the basic operations (+-*/) as well as nth roots, and decimal precision goes to the hundredth place. What would be the simplest, fastest, and most accurate way to calculate exponents (including decimal exponents like 0.5 and 1.5)?

[drifting wraith]

can you calculate (1/3) root?

[restive rapids]

As in like square root but the square is 1/3?

Bc if so, no I cannot calculate that

[cyan forge]

probably newton-raphson method for radicals

would work pretty well

[drifting wraith]

well power of 0.943 is 1000th root of x^943

as far as i know

[restive rapids]

Ahh you mean that

[drifting wraith]

no i meant what you said

[restive rapids]

I can do that but what about powers over 1

[drifting wraith]

it's the next thing

[restive rapids]

To do power of 1.5 you would have to do the 0.5th root of x^15?

[drifting wraith]

x^56.93 is 100th root of x^5693

[restive rapids]

Ohh ok

It makes sense

[restive rapids]

Thanks!

[restive rapids]

Why is it 56.93 and not 569.3?

The root is 100

And the total length is in the 1000ths

@drifting wraith wait but I can't use exponents...

So I can't use the method that you are listing

[obtuse pebble]

@restive rapids Has your question been resolved?

[plain charm]

I assume you are working with bitshifts, so ill just drop: $a^b=2^{log_2(a)b}$

[warm shale]

NulledOutChicken

[restive rapids]

I can't use log sadly

[plain charm]

you can write your own log_2 though

you just abuse that $x=m2^p$ in floating point repres

[warm shale]

NulledOutChicken

[plain charm]

then $log_2(x)=log_2(m)+p$

[warm shale]

NulledOutChicken

[plain charm]

so you only need to find $log_2(m)$, where m is between 1 and 2

[warm shale]

NulledOutChicken

[plain charm]

This can be easily approximated with an quadratic or even linear polynomial

[restive rapids]

I am not using bit shifts btw

[plain charm]

Yeah do not worry you can also do it with floating point tricks or even multiplication

[restive rapids]

How would I go about doing the approximation?

And even if I do find $log_2(m)+p$ I still need to find $2^(product)$

[plain charm]

$log_2(x) \approx m-0.9707 +p$

[warm shale]

NulledOutChicken

V1ewsh0t

[plain charm]

So you have $a^b=2^{b log_2(a)}=2^{b(m_a+p_a-0.9707)}$

[warm shale]

NulledOutChicken

[plain charm]

lets define the exponent as a variable $\phi := b(m_a+p_a-0.9707)$

[warm shale]

NulledOutChicken

[restive rapids]

Ok

[plain charm]

$\phi$ is a real number and can be written as: $\phi = int(\phi) +(\phi - int(\phi))$

[warm shale]

NulledOutChicken

[plain charm]

So as a whole part plus a fractional part

Where the whole part is just the integer cast

[restive rapids]

So you are turning ø into an integer

[plain charm]

Not exactly

I just say that it can be written as an integer plus a real number between 0 and 1

So basically $\phi= int(\phi)+ \epsilon$

[warm shale]

NulledOutChicken

[restive rapids]

And how does this help?

[plain charm]

Well we already know that $a^b=2^\phi$

[warm shale]

NulledOutChicken

[plain charm]

And it helps because now we write $2^\phi=2^{int(\phi)}*2^\epsilon$

[warm shale]

NulledOutChicken

[restive rapids]

Ahh

[plain charm]

or more descriptive

$2^\phi=2^n*2^\epsilon$

[warm shale]

NulledOutChicken

[plain charm]

And I can get $2^n$ with just multiplying 2 by itself

[warm shale]

NulledOutChicken

[restive rapids]

what does $epsilon$ mean?

[plain charm]

$2^\epsilon$ I can get with square roots since $0<\epsilon<1$

[warm shale]

V1ewsh0t

NulledOutChicken

[plain charm]

it is the fractional part of $\phi$

[warm shale]

NulledOutChicken

[plain charm]

$\phi=n+\epsilon$

[warm shale]

NulledOutChicken

[restive rapids]

So how would you get €

[plain charm]

$\epsilon=\phi-int(\phi)$

[warm shale]

NulledOutChicken

[restive rapids]

What does int mean and what does it do to the function ø?

[plain charm]

int(1.5)=1

int(-3.4)=-3

[restive rapids]

Ahhhh

Ok so epsilon is the decimal part of the product of the function!

[plain charm]

sooo

should I put everything together for you now

My fellow student

[restive rapids]

Yes sir

[plain charm]

$a^b=2^{b(m_a+p_a-0.9707)}=2^{int(b(m_a+p_a-0.9707))}*2^{frac(b(m_a+p_a-0.9707))}$

[warm shale]

NulledOutChicken

[plain charm]

if you use bit shifts, you are as fast as the c standard library

but do not tell anyone

[restive rapids]

But how do you bitshift a fractional number?

[plain charm]

Why do you think I extracted the whole number part 😉

[restive rapids]

Ahh ok

One question, what is ma and pa?

[plain charm]

$a=m_a*2^p_a$

[warm shale]

NulledOutChicken

[plain charm]

$a=m_a*2^{p_a}$

[warm shale]

NulledOutChicken

[restive rapids]

So how would I find both ma and pa?

[plain charm]

Good question

$log_2(a)=log_2(m_a)+p_a$

[warm shale]

NulledOutChicken

[plain charm]

therefore: p_a=int(log_2(a))

and: $m_a=\frac{a}{2^{p_a}}$

[warm shale]

NulledOutChicken

[plain charm]

Where $p_a$ is a n

[warm shale]

NulledOutChicken

[plain charm]

whole number+

[restive rapids]

Ahh ok!

[plain charm]

So $2^{p_a}$ is just multiplication or bit shifts 😉

[warm shale]

NulledOutChicken

[restive rapids]

Is it 2pa or 2^pa

[plain charm]

2^pa

[restive rapids]

Ok!

[plain charm]

$p_a=int(log_2(a))$

[warm shale]

NulledOutChicken

[plain charm]

buuut

you can find it a bit easier 🙂

if you are working with floats you can immediately extract the exponent

[restive rapids]

How would we do that?

[plain charm]

Okay

I thought about it

To get $p_a$ you just divide a with 2 until you get a number less then 2

[warm shale]

NulledOutChicken

[plain charm]

the number of divisions is $p_a$

[warm shale]

NulledOutChicken

[plain charm]

the number you end up with is $m_a$

[warm shale]

NulledOutChicken

[plain charm]

Okay

I will put it together once more

We wanna write $a^b=2^{log_2(a)*b}$

[warm shale]

NulledOutChicken

[restive rapids]

Yes

[plain charm]

for that we write $\phi=log_2(a)*b=(log_2(m_a)+p_a)*b$

[warm shale]

NulledOutChicken

[plain charm]

where $p_a$ is the number of times you can divide $a$ by two until you get a number less then two

[warm shale]

NulledOutChicken

[plain charm]

and $m_a$ is the resulting number

[warm shale]

NulledOutChicken

[plain charm]

and $log_2(m_a)=m_a-0.9707$

[warm shale]

NulledOutChicken

[restive rapids]

🤏🕶️😮

[plain charm]

$a^b=2^{b(m_a+p_a-0.9707)}=2^{int(b(m_a+p_a-0.9707))}*2^{frac(b(m_a+p_a-0.9707))}$

[warm shale]

NulledOutChicken

[plain charm]

$p_a = #: \frac{a}{2}<2$

[warm shale]

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

[plain charm]

$m_a=\frac{a}{2^p_a}$

[warm shale]

NulledOutChicken

[plain charm]

I compressed it into three lines, hopefully you get me

[restive rapids]

100%

This has been extremely helpful

Like more helpful than you think

$And just to make sure, pay is the number of divisions by 2 and ma is the answer from that$

[plain charm]

Well I wrote my own math library so I had my fair share of encounters with those problems

[restive rapids]

Seriously impressive

[plain charm]

exactly

100% correct

[restive rapids]

I'm trying to make a raytracer in geometry dash and I needed to do this for specular highlights

[plain charm]

haha, if you need inspiration check out my github https://github.com/Ultiminer/CONSTEXPR_MATH

So far I have one star and that one is from me 😦

[restive rapids]

Not anymore

[plain charm]

Omg. Two stars. I am rich

[restive rapids]

For real though, thank you so much, this was a very helpful and informative "lesson" and you did a great job teaching!

I'll do you if it works!

@plain charm you have a wonderful day!

.close

[obtuse pebble]

Channel closed

Closed by @restive rapids

Use .reopen if this was a mistake.

[plain charm]

tysm

have a great day

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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

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

[narrow nexus]

in need of assistance to find the exact value of tan[cos^-1 (2/3)]

[cyan forge]

draw a triangle for reference

[narrow nexus]

i dont have my book on me so i gotta use my laptop

[cyan forge]

you have a right triangle with angle θ

the side adjacent to θ is 2

the hypotenuse is 3

we can deduce this from the ratio inside the arccos

[narrow nexus]

im a bit lost 😓

[narrow nexus]

ohhh

[cyan forge]

do you see how $$\theta$$ is $$cos^{-1}(2/3)$$

[narrow nexus]

yea

[warm shale]

aZxc

[cyan forge]

so to find tan theta

we need to find the lenght x

whic his opposite to θ

right?

[narrow nexus]

yea

[cyan forge]

how do we find x?

[narrow nexus]

cross multiply?

[cyan forge]

think again

we have a right triangle

we know two sides

we have to find the third

what's a useful theorem about the sidelengths of right triangles?

[narrow nexus]

im not sure

[cyan forge]

a^2+b^2=?

[narrow nexus]

ahh

[cyan forge]

yep

in this case we know the "c" and "a"

so we can plug those in and solve for "b"

which in our case is x

[narrow nexus]

alrighty

so do i multiply the a^2 x c^2?

[cyan forge]

not quite

[narrow nexus]

i mean add

[cyan forge]

again

the sum of the squares of the sidelengths is the square of the hypotenuse

what is the hypotenuse in our triangle?

[narrow nexus]

3?

[cyan forge]

yep

what are our sidelengths? note that we're calling the one we don't know x

[narrow nexus]

x and theta?

[cyan forge]

remember theta is our angle

[narrow nexus]

ur right

[cyan forge]

our adjacent side was 2

remember?

[narrow nexus]

ah yes

[cyan forge]

so our sidelengths should be 2 and x

while our hypotenuse is 3

so using pythagorean's theorem, can you fill in the blanks for [ ]^2+[ ]^2=[ ]^2

[narrow nexus]

a^2 + c^2 = b^2?

[cyan forge]

no, for our triangle specifically

[narrow nexus]

oh

[cyan forge]

so our lengths our 2, x, and 3

how should we apply pythagorean's theorem with these 3 numbers?

[narrow nexus]

2^2 + 3^2 = x^2

[cyan forge]

look back at this diagram

3 is our longest side: the hypotenuse

so it should go on the right side of our equation

[atomic niche]

please tell me what step the error is in. i think its a simple problem but im not sure if its step 3 or 4

[cyan forge]

this channel is occupied

you can use one of the open channels

[atomic niche]

I can't access them for some reason

And I've been looking for the answer to this problem for over 2 hours

[narrow nexus]

soo its 2^2 + x^2 = 3^2?

[cyan forge]

yes!

now simplify this

[cyan forge]

?

show me your channels bar

[narrow nexus]

4 + X^2 = 9

[cyan forge]

mhm

now isolate the variable

[narrow nexus]

4 + 9 = X^2?

[cyan forge]

try again

say what you're doing step by step

how did you get from 4+x^2=9 to 4+9=x^2?

[narrow nexus]

i just thought thats what u had to do

[cyan forge]

well let's start again from here

try subtracting 4 from both sides

what do you end up wtih?

[narrow nexus]

sides as in the equation?

[cyan forge]

yes

since both sides of the equation are equal, if you subtract 4 from both of them they will still be equal

does that make sense

[narrow nexus]

i think so

so that would be 9 - 4 = X^2
and X^2 - 4 = 9?

[cyan forge]

9-4=x^2 is correct

im not sure how you got the second one but just focus on 9-4=x^2

what is 9-4?

[narrow nexus]

5

[cyan forge]

yes

so x^2 is 5

right?

[narrow nexus]

yes

[cyan forge]

hten what is x

[narrow nexus]

the square root of 5? since its x^2, so that would mean 5 x 5.

or is it just 5

[cyan forge]

sqrt(5) is correct

remember what we were trying to find in the beginning tho

[narrow nexus]

oh yes

so tan = sqrt(5)/2?

[cyan forge]

yes

you got it

[narrow nexus]

so thats it?

[narrow nexus]

is that all i needed to do?

@cyan forge thank u for ur help, even tho i was very slow 😭. i appreciate it

.close

[obtuse pebble]

Channel closed

Closed by @narrow nexus

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[timid silo]

Question 31: Two villages are 4,360 km apart. The road connecting the two villages is lined with trees on both sides. The trees are spaced 15 m apart, and the first tree is 200 m from the exit of each village. How many trees are there on the road connecting the two villages?
A. 264

B. 265

C. 528

D. 530

[brazen gorge]

4 thousand kilometers?

or 4360 meters

[timid silo]

Yeah

[brazen gorge]

that gotta be a typo. none of the answers work then

pretty sure it should be 4360 meters

[brazen gorge]

regardless, what have you tried?

[timid silo]

I did tried to do it wirh miles but not getting the correct answer

[brazen gorge]

wdym with miles

[brazen gorge]

show your work, then

[timid silo]

Like 15 miles or 200 miles apart

[timid silo]

In my mind don't have a paper pen

[brazen gorge]

m stands for meter, not mile

mi is for mile

[timid silo]

Yeah but I translate the question from French

[brazen gorge]

ah okay

[timid silo]

Could it be the teachers fault in asking wrong question

[brazen gorge]

pretty certain C is the answer

[timid silo]

How

[brazen gorge]

so this question is at least answerable

[brazen gorge]

consider the whole distance that the trees cover (from one side)

it's 4360-2*200 = 3960
why? because of the 200 meter offsets for both villages

[timid silo]

Ummm correct

[brazen gorge]

then, divide by 15

[timid silo]

Hmmm

[brazen gorge]

in this case it's pretty straightforward to do it in your head (hint: divide by 3 and then divide by 5)

[timid silo]

Wallah my mind is like not working

I'll do it again but thanks buddy

You give the huge hint

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

No

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[mystic snow]

What type of maths goes 1,1,2,3,5,7,12 ?

[marsh geyser]

What kind of question is that? Make a proper question that makes sense

[violet dune]

yeah, this question doesn't really make sense on its own, but if you're trying to find a sequence it's probably best to try throwing it out on https://oeis.org/

[mystic snow]

It's resolved it was fibbontachi

[wet moss]

Are you sure your sequence is correct then?

[fallen pine]

3+5=7 😳

[daring sorrel]

no no he did not say fibonacci he said fibbontachi

[untold scaffold]

my favorite math goes that way

[obtuse pebble]

@mystic snow Has your question been resolved?

Channel closed

Closed by @mystic snow

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.

[tired fiber]

@obtuse pebble help

[tired fiber]

if z1 = 2+ 5i, z2 = 3 - i, then the value of sqroot(z1 * z2 + z2 X z1) is equal to?

[obtuse pebble]

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.

@tired fiber Has your question been resolved?

[tired fiber]

<@&286206848099549185>

[tired fiber]

anyway i know the answer, this was just a test to know how competent you guys are..... i don't want to waste this channel

.close

[obtuse pebble]

Channel closed

Closed by @tired fiber

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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

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

[fallen inlet]

Hey
Is there a name for a situation like when angle 5 becomes 53 degrees bc it’s the same in the other side?

[fallen inlet]

Congruent? Reflexive?

[dark stirrup]

Congruent

If two triangles are congruent, then their corresponding angles are equal

[fallen inlet]

Ohhh

CPCTC

Corresponding parts of congruent triangles are congruent

?

[dark stirrup]

Sure

[obtuse pebble]

@fallen inlet Has your question been resolved?

Channel closed

Closed by @fallen inlet

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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

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

[stray python]

is this correct

[stray python]

is this correct

is this correct

<@&286206848099549185>

[obtuse pebble]

@stray python Has your question been resolved?

[fallen pine]

this interval isn't even written correctly lol

Oh nvm I see they mean -infinity not positive

idk why they omitted the -

yeah it's right

[fallen pine]

yes

yeah these are all good

[stray python]

are these correct

<@&286206848099549185>

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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

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

[dire jackal]

I used the slope formula and concluded that every 10 years it grows 0.1 inches

I don't know the final answer though, and I don't have a clue if I did it right\

[pulsar cloud]

thats correct if its varying linearly, we just know the initial and final diameters we dont know how the graph is

[dire jackal]

Oh, so do I just not answer what the diameter of the tree is gonna be in 2065?

[pulsar cloud]

it can not be varying linearly right so thats just one of the cases

but i think you have to go with that since no other information is given

[dire jackal]

Okay, thank you

.close

[obtuse pebble]

Channel closed

Closed by @dire jackal

Use .reopen if this was a mistake.

[dire jackal]

.reopen

[obtuse pebble]

✅

[dire jackal]

Okay, so I applied the 0.1 every 10 year thing to double check

I got the answer of 147 \

For 2065

.close

[obtuse pebble]

Channel closed

Closed by @dire jackal

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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

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

[ancient bluff]

i am cooked for this question

[upper shuttle]

what is a rational function

[obtuse pebble]

@ancient bluff Has your question been resolved?

[cyan forge]

start from a parent function

like sin(x)

this doesnt like thag bad u got this

[ancient bluff]

how can i start w the rational one

[upper shuttle]

write down the properties it has

[ancient bluff]

for the y-int is it b/d

in ax-b/cx-d

[upper shuttle]

a rational function f(x) = g(x)/h(x) where h and g are polynomials.

f(0)=-2, from a

try to write out the other properties that the rational fn has

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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

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

[daring steppe]

Hi These look like they are vector spaces, where am I going wrong?

[daring steppe]

the book shows this answer which doesn't make sense to me either:

Zero is in the set of R^3, right?

[orchid sand]

the proprty they're referring to in (a) is the fact that vector spaces have to satisfy the distributive property

[daring steppe]

i think the answer might be from another edition probably - edit same edition

[orchid sand]

i.e. for scalars a and b and a vector v, we have (a+b)v = av + bv

but this doesnt hold, as they show

[daring steppe]

im confused

[grizzled shore]

are you doing a or b

[daring steppe]

lets start with a

[grizzled shore]

let's start with the +

what does + need to satisfy

[daring steppe]

I thought by definitivon Vector*1 = vector

[daring steppe]

"the set V is closed under vector addition, that is,v +w ∈ V"

[grizzled shore]

no

you know not yet it's a vector addition

[grizzled shore]

this has to do with the set

[daring steppe]

ah

[grizzled shore]

not with the operation

[orchid sand]

by definition a vector space has to have some multiplicative identity. this is usually 1, but b is an example where this isn't the case

in fact, b has no multiplicative identity which is a problem

[daring steppe]

isnt r*0 = 0

and 0 is in set R^3

[orchid sand]

i think you're getting the definition of a vector space confused with the conditions of a subspace

this is the definition of a vector space

[daring steppe]

is itnot associative?

[grizzled shore]

it is associative

(x+y) + z = 0 + z = 0 = (y+z) = x + (y+z)

[daring steppe]

yeah

ok

im lost then

[grizzled shore]

that's because the addition is fine

[daring steppe]

it is communitive, associative, it passes closure

[grizzled shore]

closure has to do with the set

not with the operation

we say the set is closed under <operation>

the operation itself can't be closed

[daring steppe]

ok

so if its multiplicative that is the issue

i dont see it

[grizzled shore]

let's look at the scalar-multiplication operation now

[daring steppe]

r*x = rx .... looks fine

[grizzled shore]

what does this need to satisfy

[daring steppe]

looks like scalar multiplication to me

if r = 1

[grizzled shore]

.

[daring steppe]

we get. <x,y,z>

[grizzled shore]

forget your intuition

look only at the definitions and axioms

[daring steppe]

Multiplicative identity "1v =v

[grizzled shore]

we're dealing with a strange addition here, your intuition will be off

[daring steppe]

r = 1 -> <x,y,z>

how does that not pass?

[grizzled shore]

well it's not the only thing it needs to pass

[daring steppe]

1v=v

[grizzled shore]

but it does pass having a multiplicative identity