help-26

[smoky pivot]

Thats... getting concerning...

Ok its back I just had to restart the laptop again

So if domain was all reall numbers then... I believe the range is?...

[acoustic pecan]

hm?

of f or |f|

[smoky pivot]

And that was just the function it's self....

Now I need to search for y=|f(x)|

Domain

[acoustic pecan]

does the absolute value have a restriction on its inputs?

[smoky pivot]

The outcome can never be negative

[acoustic pecan]

sure, but i asked about the income

[smoky pivot]

Can you define what an income is?

[acoustic pecan]

the input

if i have y=|x|, whats the domain of that

[smoky pivot]

|x|= x

[acoustic pecan]

lost me a bit there

[smoky pivot]

I think I am just as lost

So this is what I have

I originally thought I needed to take the given domains and lay them out

[acoustic pecan]

i can tell you that the absolute value has no effect on the input functions domain

because it takes all of R

[smoky pivot]

So (-si,si)?

[acoustic pecan]

but from the graph we can also see that

[acoustic pecan]

aye

[smoky pivot]

The range though...

[acoustic pecan]

of f or |f|

i think you overthink these things a little

[smoky pivot]

I can not tell what number it is

Unless thats just 0

[acoustic pecan]

it is indeed, we know that because f crosses the axis

[smoky pivot]

So the range would be [0,si)?

[acoustic pecan]

that is so

(just to confirm you are using si to mean $\infty$)

[thorny flame]

AℤØ

[smoky pivot]

I cant tell if you were in the Navy or you enjoy talking like a sailor

[acoustic pecan]

just spent a fair amount of time in scotland

[smoky pivot]

Nice👍

Study abroad?

[acoustic pecan]

yes and no

its both a different country, and the same country

im from england

[smoky pivot]

Oh I understand- you are from the UK nice

Ok so I figured out the absolute value of the last one but the domain for this absolute value is... tricky

I could use the given pointz

[acoustic pecan]

what are your thoughts

[smoky pivot]

Well, the function is f(x)=sqr root x

But the line starts from -3

But the absolute value cant be negative

[acoustic pecan]

it still isnt negative

[smoky pivot]

So... would it fold over the y axis?

[acoustic pecan]

are there any negative y values on that graph?

[smoky pivot]

Making it domain for y=f|x| is [3,si)?

[acoustic pecan]

nope

youre confusing the input and output

the absolute value can take negative inputs

[smoky pivot]

So then would it be [-3,si)?

[acoustic pecan]

it would indeed

[ruby wedge]

the absolute value only affects the output

[smoky pivot]

How do I not mix up the two? Know any simple or specific methods?

That might be asking too much belay that...

[ruby wedge]

think of it as the distance from 0 of x

well in this case f(x)

what goes inside of the absolute value is the input right?

[smoky pivot]

Yes

[ruby wedge]

what comes out is the distance from zero of that input

-3 is 3 away from 0 on the number line and so is 3 so |-3| and |3| are both 3

[smoky pivot]

Yes

[ruby wedge]

thats it idk if that helps

[smoky pivot]

It does

[ruby wedge]

great

[smoky pivot]

The input is usually (x +/- a) the output is -/+ b

From what I understand in your phrasing

So in this case the range sqr root function of |f(x)|= [0,si) ?

[ruby wedge]

it shoud be the same

as the original function

[smoky pivot]

I see

[ruby wedge]

because \sqrt{x} never has negative outputs

[smoky pivot]

Aw...

[ruby wedge]

are you talking about this graph

[smoky pivot]

Yes I was

[ruby wedge]

oh ok then it is a bit different

so the absolute value is the same for both functions but the domain is different

that function is \sqrt{x+3)

a sqrt can not have a negative inside therefore the domain should not include any x that make x+3<0

what do you think the domain is then?

[smoky pivot]

It would be [3,si)

[ruby wedge]

close but no

[smoky pivot]

Oh

[ruby wedge]

x+3 can be 0

but not lower

what x satisfies that condition

[smoky pivot]

Hmmm

I do not know... -3?...

[ruby wedge]

yes

so [-3,si)

[smoky pivot]

Ohhhh

Because its a input it stays negative?

[ruby wedge]

yes

|f(x)|=|sqrt{x+3}| not |x|

[smoky pivot]

Ok I understand that one now

[ruby wedge]

good

[smoky pivot]

But...how do I find the correct range for this one?

[ruby wedge]

well first what do we know about absolute value?

[smoky pivot]

It cant end negative

[ruby wedge]

correct whatever goes inside must leave as its positive version

[smoky pivot]

And the range is an output?

[ruby wedge]

in this case f(x) is our input for our absolute value

f(x) has a negative value within its range correct?

[smoky pivot]

Correct

[ruby wedge]

so since f(x) is having the absolute value taken of it, the minimum value of |f(x)| range must be the absolute value of the minimum value of f(x).

which is?

[smoky pivot]

Can we back track a little?...

[ruby wedge]

ok

[smoky pivot]

Is this something to visualize on a graph?

[ruby wedge]

its not necessary

if you want you can

[smoky pivot]

How would that look?

[ruby wedge]

see f(x) has a range of [-1,inf) , f(x) is the input for the absolute value so the range of |f(x)| has to be the absolute value of the range of f(x)

[ruby wedge]

you need a function to use with it we dont have one provided so idk

[smoky pivot]

Soooo [1,si)?

[ruby wedge]

yes

good

[smoky pivot]

Wait- the system says its wrong???

[ruby wedge]

?

[ruby wedge]

hmm it seems to be because since the absolute value make -1 to 1 but also supports 0

that is why

[smoky pivot]

Is this another possible error or is-

Oh you are explaining

[ruby wedge]

no yes they are right

[smoky pivot]

Alright

[ruby wedge]

[0,si)

[smoky pivot]

So say if there was a range of [-5,si) its absolute value would turn to [0,si)?

[ruby wedge]

yes

because the negative values would be mapped as positive and then 0 would be the lowest value for |f(x)|

[smoky pivot]

Ah...

[ruby wedge]

that was my bad, sorry

[smoky pivot]

Its ok

We all make errors no matter skill level

[ruby wedge]

indeed

[smoky pivot]

Ok so dont mind my white board out but

So this one...

[ruby wedge]

ok so first find the minimum value for (x+1)^2-3

[bronze creek]

just graph it

[ruby wedge]

it would be easier to do analytically

[smoky pivot]

Oh- right-

I cant rely on a graphing calculator (not allowed for test) so I want to make sure I understand this

[ruby wedge]

ok good have you found the minimum value

[bronze creek]

well that equation is in vertex form

if u know the vertex then u can find the domain and range

[ruby wedge]

correct

the range should be the y coordinate of the vertex to infinity and domain is -infty to infty

[smoky pivot]

So for my sake- this is is the correct visual right?

[ruby wedge]

this is for (x+1)^2-3

[smoky pivot]

So the domain is (-si,si)?

[ruby wedge]

yes

for both

[smoky pivot]

Ok and the range...

[-3,si)?

[ruby wedge]

for which one?

[smoky pivot]

The function

Not the absolute value

[ruby wedge]

then perfect

yes

[smoky pivot]

The absolute range... eh...

[ruby wedge]

what do you think so far

[smoky pivot]

Does the vertex do this?

The blue is the absolute value

[ruby wedge]

its over exageratted but yes

insted of -3 it is 3

[smoky pivot]

So [3,si)

[ruby wedge]

no

[smoky pivot]

Oh.

[ruby wedge]

range is the minimum value of the function to the maximum

[smoky pivot]

Its unending

[ruby wedge]

so since absolute value only allows the y value to be a minimum of 0

then the minimum is?

[smoky pivot]

0?

So... [0,3]?

[ruby wedge]

yes so the range is [0,si)

[smoky pivot]

Ohhhhh

I might be overthinking this one

[ruby wedge]

your graph is correct

[smoky pivot]

The domain is.... [-6,7]?

[ruby wedge]

yes

[smoky pivot]

The range is... [-6,7]?

Wait-

Nope- yeah

[ruby wedge]

for f(x) yes

[ruby wedge]

but for your coordinate at the bottom (-6,1) its wrong it should be (1,-6)

apart from that so far so good

[smoky pivot]

Yes I did fix it after I noticed

[ruby wedge]

good

[smoky pivot]

Lets seee the domain stays the same

[ruby wedge]

yes

https://tenor.com/view/stressed-out-suspense-eating-popcorn-waiting-to-see-what-happens-gif-14120143

[smoky pivot]

The absolute range is...

[ruby wedge]

....

[smoky pivot]

[0,7]?

[ruby wedge]

https://tenor.com/view/wolf-of-wall-street-lets-goo-gif-11742735383203550293

yesssss

[smoky pivot]

XD

Yeaaaa

[ruby wedge]

good job

[smoky pivot]

On to the next one⚔

[ruby wedge]

https://tenor.com/view/absolute-cinema-raccoon-absolute-cinema-gif-17862327649353748812

yup

[smoky pivot]

Alright!

Oh thats a bad one

[ruby wedge]

much better

[smoky pivot]

Indeed

So the domain of the original function is [-4,0]

[ruby wedge]

yes

graph is good too btw

[smoky pivot]

Thanks

The range is [-4,1]

[ruby wedge]

yuppp

your getting much better

[smoky pivot]

Yeaaaaahhhh

I am understanding- I dont know how long this will last again

[ruby wedge]

keep practicing every once in a while

eventually it will become second nature

[smoky pivot]

Do you know good plaves to practice (that do not cost money)?

[ruby wedge]

Khan acadamy is good

[smoky pivot]

True

Its good my old school account still exists

[ruby wedge]

yeah you can do that

[smoky pivot]

Even though the email is long gone

[ruby wedge]

well you can always make an account

if you don't have any further questions or think you are ok close this channel

[smoky pivot]

I still do

[ruby wedge]

alright bet

[smoky pivot]

Quite a few...

Ok annnd I messed up the range

[ruby wedge]

oh no

mb

its [0,4]

https://tenor.com/view/wipe-off-sweat-bradley-hall-clear-the-perspiration-wash-away-sweat-gif-5666657092934823161

[smoky pivot]

Ohhhhh

So its always low to high?

[ruby wedge]

yes

min to max

[smoky pivot]

Annnnnddd back to zero understanding.

[ruby wedge]

gulp

[ruby wedge]

ok whats up

i dont understand the phrasing honestly

[smoky pivot]

https://tenor.com/view/jumping-rage-black-and-white-yeet-gif-17427380

[ruby wedge]

lol

lets see

we have the points y_1 and y_2

we want them to be equal

[smoky pivot]

Larger graph

[ruby wedge]

thanks

[smoky pivot]

No prob

[ruby wedge]

oh ok very simple

we have the two functions y_1 and y_2

and we want them to be equal what numbers would do that

aka where both functions intersect

[smoky pivot]

Hmm

So......

How do I write this

[ruby wedge]

what x value(s) makes them equal

[smoky pivot]

Ehhh...

[ruby wedge]

they intersect eachother at 2 points so there are 2 answers

what two numbers?

[smoky pivot]

6 and

0?

[ruby wedge]

no, those are y values

we need x values that make the y values equal

[smoky pivot]

Dont tell me... do we have to find slope?...

[ruby wedge]

no no

[smoky pivot]

Phew

[ruby wedge]

yeah

anyway

so we know that both functions equal 6

what numbers make that true

[smoky pivot]

-1 and 2?....

[ruby wedge]

https://tenor.com/view/crushed-it-gif-18087987023179949748

[smoky pivot]

Wait really???

[ruby wedge]

yup

do you know why?

[smoky pivot]

Yesnt

[ruby wedge]

? what

[smoky pivot]

The points are a ray they arent intersecting

[ruby wedge]

the blue and red functions intersect and x=-1 and x=2 making them equal

[smoky pivot]

Ohhhhhhhhh

[ruby wedge]

see how in the coordinates shown they have the same y

[smoky pivot]

I was focused on y2

Uhhhh so this was wrong apparently

[ruby wedge]

those are just the names of the functions y_1 and y_2

[ruby wedge]

you picked the wrong one

there were various

[ruby wedge]

yeah thats wrong

its {-1,2}

because its a set of solutions not coordinates

[smoky pivot]

????

So the { } is used for

Solution set

?

[ruby wedge]

yup

well sets in general

but yeah

(-1,2) would imply the point (-1,2) or a range/domain which neither are solutions

[smoky pivot]

So what would be solution be?

[ruby wedge]

{-1,2}

[smoky pivot]

This one....eh...

Im lost again

[ruby wedge]

show the graph again

pls

[smoky pivot]

Here

[ruby wedge]

thanks

[smoky pivot]

No problem

[ruby wedge]

ok so find the domain where the blue function is less then the red one

[smoky pivot]

How would I write this?

[ruby wedge]

interval notation

[smoky pivot]

Soooo (-1,2)?

[ruby wedge]

yes

[smoky pivot]

So the other stuff is just there to throw it off?

[ruby wedge]

yup

there is one question left

after this one ofc

[smoky pivot]

Yes

[ruby wedge]

they are there because they are an answer to a question but it can throw you off

[smoky pivot]

Eh... y1 > y2 is

Eh...

[ruby wedge]

https://tenor.com/view/excited-hockey-kid-yeah-cheering-gif-4478851357136944344

ik what do you think

[smoky pivot]

I wanna say... D?...

[ruby wedge]

https://tenor.com/view/yup-dale-doback-step-brothers-yes-i-agree-gif-1579811350903017250

[smoky pivot]

I dont fully understand that one but it just occured to me Im at question 12... out of 27...

[ruby wedge]

its important to understand

so

[smoky pivot]

Of 2.4... I havent gotten to 2.6 or the review (approximately 30 questions each)... and I have to take the test tomorrow...

[neon iron]

@ruby wedge i can take over if ur ok with it

[ruby wedge]

@neon iron thanks man

yeah go ahead

[smoky pivot]

Oh shoot- sorry dude

[neon iron]

alr alr i got u

what u need

[ruby wedge]

dont worry about it

[smoky pivot]

Where do I even begin...

https://tenor.com/view/meme-anime-gif-22734101

[neon iron]

ur good dw

[smoky pivot]

What are the odds I finish this all before the test tommorow?

[neon iron]

100%

[smoky pivot]

I mean I can take it at any time- I just have a time limit...

[neon iron]

u can do this

let me try to help?

[smoky pivot]

Sure

Ok eh...

So here we are with this

[neon iron]

ok so we're looking for the graphs intersect right

[smoky pivot]

Yes

[neon iron]

and how many points are there where they intersect

[smoky pivot]

One

[neon iron]

so what choices can we eliminate

[smoky pivot]

A

C

D

[neon iron]

so whats the answer

[smoky pivot]

Wait- do I need to plug in the equation?

[neon iron]

are u looking for the y value

or the coordinate of intersection

[smoky pivot]

Im looking for the solution to y1=y2 apparently

[neon iron]

well yes ik that

but have the previous problems asked for a coordinate

or just a y value

i just searched it up

B is the answer yes

just the x value

[smoky pivot]

Ehhh now I need solution set for y1 < y2?

[neon iron]

send me the problems pls

[neon iron]

alr so we're looking for where y2 > y1

what curve is y2

[smoky pivot]

Its a line ?

[neon iron]

its still called a curve

whcih one

the red or the blue

[smoky pivot]

The red?

Im so confused...

The one with absolute value is the only curve I thought

The blue one

[neon iron]

theyre both curves

but yes red is y2

is y2 ever greater than y1

@smoky pivot

[smoky pivot]

Yes

[neon iron]

where

[smoky pivot]

Where is the y1?

[neon iron]

y1 is the blue function

[smoky pivot]

So Im not trying to simplify y1?

[neon iron]

whyd u do that 🆘

😭

[smoky pivot]

Im going to assume Im over thinking this again💀👍

[neon iron]

yea

why woudl u do that 🆘

😭

look at the graph

[ruby wedge]

you are trying to find what values of x make the blue function greater than the red

im back

[neon iron]

is the red curve above the blue curve

[smoky pivot]

To see if its its then y2???

At least I think my notes say something?

No the blue is above

[ruby wedge]

good

at what values of x

[smoky pivot]

The value of x is... theres no written number

But Im going to say 2?...

[ruby wedge]

there are various values of x where the blue is larger

so it has to be an interval

[neon iron]

well i mean u can sorta look and see that the red is never above the blue

and then use process of elimination

no?

[ruby wedge]

yeah

[smoky pivot]

So 1 and -1?

[ruby wedge]

no

look where is y_1=y_2

you answered it

[smoky pivot]

So its 1 again???

[ruby wedge]

no

wait

[neon iron]

but at 1 theyre equal

not greater than

[ruby wedge]

so at every other point it is greater

[smoky pivot]

https://tenor.com/view/why-persian-room-cat-guardian-but-why-trendizisst-anyaboz-gif-2156104475561014590

[ruby wedge]

what answer encompasses every x value except 1

[neon iron]

what does greater mean

[ruby wedge]

@neon iron lowkey this is becoming a two person job

[neon iron]

yea yea ik 😭

im down for it tho

[ruby wedge]

yeah fs

i was just helping someone else

[smoky pivot]

https://tenor.com/view/long-tears-gif-11087877242190144149

[ruby wedge]

lol

anyway you didnt answer my question

[smoky pivot]

The example is no help either

[neon iron]

alr arl rainbow

calm down

what does greater mean

[smoky pivot]

It means y1 is less then y2

[neon iron]

yes

[ruby wedge]

https://tenor.com/view/pesado-dios-mio-stressed-problematic-oh-no-gif-12622815322168322147

[neon iron]

so on a graph how would that look

[ruby wedge]

yes but not what i was lookin for

its okay tho

[smoky pivot]

I wanna just say theres no solution

[ruby wedge]

there is

[smoky pivot]

But its probably A?...

[ruby wedge]

yes

but lets undertsnad

[neon iron]

umm yk what A means?

[ruby wedge]

yeah lets not guess

[smoky pivot]

I dont understand how its 1 and 1 when then line isnt even on the orgin

[neon iron]

what does that have to do with the origin

[neon iron]

thats not the origin

[smoky pivot]

HOW IS THAT 1

[neon iron]

ummm look at the x axis

[smoky pivot]

...

[ruby wedge]

it goes by 2

so half is 1

lets go back to the basics you have a function right? the function has an input and output essentially the input (x) value dictates the output (y) the height of the function so if the height of the blue function is higher than red one there are x values that make that true you want to find those

x values that make the blue function greater than the red which is all of them except for 1 because they are equal to eachother at that point

[neon iron]

@ruby wedge u got this

im not quiite the teacher u are 😭

[ruby wedge]

lol

its okay

[smoky pivot]

Thank you for trying💀⚰😭

[ruby wedge]

i have taught before so

[smoky pivot]

@neon iron I appreciate it

[ruby wedge]

alright you and me again

[smoky pivot]

Ok ok maybe A visual would help?

[ruby wedge]

alright let me make one real quick

[smoky pivot]

Or maybe I should get back to this question later

[smoky pivot]

Ok

[ruby wedge]

nah i just need you to understand why it is a

[smoky pivot]

I want to as well but the puzzle is not piecing

[ruby wedge]

did you read my explanation

[neon iron]

its not a 😭

[smoky pivot]

I did

I do

And I will do

[ruby wedge]

the range is that one

maybe its the wrong letter mb

[smoky pivot]

But its not... I need a visual

[ruby wedge]

but its the one that excludes 1

[neon iron]

ummm yea ur right

mb mb

[ruby wedge]

ok ok

[neon iron]

im tuned to domain for intervals 😭

[ruby wedge]

lol its okay

[smoky pivot]

Ok

So...

Are we sure we shouldnt simplify the absolute value?

[neon iron]

how would u do that

[smoky pivot]

Probably not

[neon iron]

how is that even possible 😭

[smoky pivot]

Hold on its in my notes

[neon iron]

💀

[ruby wedge]

https://tenor.com/view/pesado-dios-mio-stressed-problematic-oh-no-gif-12622815322168322147

icant make a visual

plus im more of an analytical person

anyway you dont need to do anything to the function

[smoky pivot]

I am also analytical... in the most useless way right now

[neon iron]

its literally graphed 😭 why would u want to work with the actual equations

[ruby wedge]

we found out that when x=1 , y_1 is equal to y_2

[neon iron]

yes

[smoky pivot]

I dont know maybe it would give me a sense of control or something 💀

[neon iron]

yea but hows that hlep

[ruby wedge]

so at every other x the blue function is larger than the red

[smoky pivot]

I cant figure out where the negative one is from

[ruby wedge]

so there are two intervals where the blue is larger (-infty,1) and (1,infty)

[smoky pivot]

Ohhh...

[ruby wedge]

if you combine them (union) then you get the answer a

[smoky pivot]

So the answer is A....

[ruby wedge]

yes

do you somewhat understand

[smoky pivot]

I was focused on the numbers and point its self

[ruby wedge]

i think thats your issue

you need to be holistic

[smoky pivot]

Computer saying incorrect

[ruby wedge]

really?

show me

[ruby wedge]

oh so we are looking for the opposite mb

[smoky pivot]

https://tenor.com/view/ron-swanson-gif-26420349

[ruby wedge]

lol

which one is y_1

[smoky pivot]

The opposite makes more sense then this one

[neon iron]

It’s indefinite 😭

Istg I said this

[smoky pivot]

I just wanna put no solution so bad

[ruby wedge]

if the blue one is y_1 then it is no solution

[smoky pivot]

Because tell me where a -1 just appears from

[neon iron]

Rainbow what grade r u in

[ruby wedge]

prolly highschool

[smoky pivot]

College algebra

[ruby wedge]

thats a class

so you are implying you are in college

[smoky pivot]

Yes

[neon iron]

Well I’d think so

[ruby wedge]

okay probably a freshman

[smoky pivot]

I havent done math since I graduated school 4 years ago 💀

[ruby wedge]

damn

[neon iron]

Oh 4 gal yrs?

Gap yrs?

[ruby wedge]

@neon iron what was the highest math you studied or studying

[smoky pivot]

I failed the first test because it started with a camera looking at me a timer and a white screen - suddenly all that I spent weeks learning just- poof...

[neon iron]

I’m uhh doing abstract algebra rn… I’m at a private hs and they let me do classes at a local community college

I’m actually doubling

[ruby wedge]

me too

[neon iron]

Abstract with discrete math

Fun stuff

Not a fan of discrete icl

[smoky pivot]

Long story went to military had medical discharge yada yada

[neon iron]

As in ur doing abs algebra as well

[smoky pivot]

I used to be good at this...

[neon iron]

Or as in ur hs let’s u take classes at a local college

[smoky pivot]

I did dual enrollment

[ruby wedge]

topology

[smoky pivot]

But in my final year (because transportation issues)

[ruby wedge]

as in dual enrollment

[smoky pivot]

Also covid did a number

[ruby wedge]

yeah

I graduate this year

[neon iron]

That’s cool

Oh I’m a sophomore 😭

[ruby wedge]

applied to MIT a few days ago

[smoky pivot]

Oh my gosh there it no solution this entire time...

[neon iron]

Nice nice

That’s where my dad went… before he dropped out

That’s the dream tho

[smoky pivot]

Congrats

[neon iron]

Mit or caltech

[smoky pivot]

Hope you get in

[ruby wedge]

yeah wish me luck

[neon iron]

Good luck man

[ruby wedge]

MIT

[neon iron]

Nah I’m saying those are the dreams

MIT caltech or Stanford

[ruby wedge]

oh yeah fs

[neon iron]

My brothers at Princeton for physics rn

That’s sick asf icl

[smoky pivot]

I should have just put no solution from the start💀

[ruby wedge]

yeah

[smoky pivot]

This entire time I spent...

[ruby wedge]

your family is intellectual asf

[neon iron]

Umm great parents

[ruby wedge]

im the outstadning one in my family

[neon iron]

Yea

[ruby wedge]

gotta represent

[neon iron]

It’s hard to be outstanding here

In comparison 😭

[ruby wedge]

lol i have fun with it, its competition

[neon iron]

Hey but pressure makes diamonds

[smoky pivot]

I have a diagnosed learning disability:D

[neon iron]

Pressure is a privilege

[neon iron]

😭

[ruby wedge]

oh

[smoky pivot]

Maybe 2.. other ones

[ruby wedge]

holy bomb drop

[smoky pivot]

But thats not offical yet

[neon iron]

@ruby wedge can I friend u

[ruby wedge]

fs

[smoky pivot]

You guys have no learning struggles? If so, I'm glad for you

[ruby wedge]

i dont

well kinda

i have autism but it actaully helps me

hyperfixiation

[smoky pivot]

I might have autism- I mean everyone seems to ask me if I do (and its never jokingly) buttt its a shame the possible benefits are cancled out by the Adhd._.

I get the hyperfixations - but only if they give a LOT of dopamine

Anyway back to math

Im now dealing with... this.

Oh wait I might-...

Nope.

@ruby wedge @neon iron sorry for getting off topic

[ruby wedge]

your are good

[neon iron]

Rainbow

Do yk how to solve abs value inequalities

[smoky pivot]

I believe so but let me just test this one and if I do I will skip and work on this specific part tomorrow

[neon iron]

Alr alr

[smoky pivot]

I think I do something like...this

[neon iron]

Alr alr

[smoky pivot]

Now I think I gotta check

[neon iron]

Good job

[smoky pivot]

x can technically be both

After checking

So would that make the solution set (6,-12)?

[neon iron]

Yea

[smoky pivot]

Im going to guess its not points so its the finite number set with these{} instead of ()

[neon iron]

Yea

[smoky pivot]

Ok so... apparently thats wrong

What did I do wrong here?...

[ruby wedge]

lowkey i havent done this in a while so idek

[neon iron]

Show me the answer choices

[smoky pivot]

Im wondering if I should try to finish this tonight or if I should pick it up tomorrow with a fresh mind- even though well- the test is tomorrow.

[neon iron]

Ok did u solve all 3 inequalities

Or just the first one

[smoky pivot]

I wish at the very least we could keep basic formula notes next to us

Ah- the first one.

I see

Hm...

[ruby wedge]

i would say pick it up tmrw

[smoky pivot]

Yeah I feel like the later it is the more things are... slipping like... sand perhaps

I'm just nervous

I didn't anticipate that my plan to work on the second chap through the week would get interupted by 4 days sick

[neon iron]

It’s alr u got this

[smoky pivot]

Thank you

It is 01:30 right now

[ruby wedge]

yout welcome

[smoky pivot]

Maybe its is best to pick it up early tomorrow

[ruby wedge]

yup

[smoky pivot]

Thank you so much for the help

I imagine I took up alot of your time

@neon iron @ruby wedge Hope you have a good day/evening

I should probably close this up for now right?

[ruby wedge]

yup

goodluck

[smoky pivot]

Thanks

.close

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[sturdy fulcrum]

Hello. I wanted to solve Hatcher's Algebraic Topology exercise 1.1.1.

[clear python]

Send an image of the question please

[sturdy fulcrum]

It says, show that composition of paths satisfies the following cancelation property: If $f_0 * g_0 \simeq f_1 * g_1$ and $g_0 \simeq g_1$ then $f_0 \simeq f_1$

[thorny flame]

Gol D Roger

[sturdy fulcrum]

I need to construct the homotopy, but Idk where to begin

To be more precise, the question is this:

[sturdy fulcrum]

<@&286206848099549185>

[elfin bridge]

Well you can compose with the inverse path of g0 on the right of both sides

[sturdy fulcrum]

Like $ f_0 \circ g_0 \circ g_0^{-1} \simeq f_1 \circ g_1 \circ g_0^{-1}$?

[elfin bridge]

Ye

[sturdy fulcrum]

Ok, I suppose the left side is homotopic to $f_0$. What happens to the right side?

[thorny flame]

Gol D Roger

[sturdy fulcrum]

Since $g_1$ and $g_0$ are fundamentally distinct

[thorny flame]

Gol D Roger

[elfin bridge]

Well theyre given to be homotopic here

Since theyre homotopic endpoints are fixed right

[sturdy fulcrum]

Yeah

[elfin bridge]

Idk if this was mentioned in the text also but if g_0 homotopic to g_1, then g_0, then g_0 o f is homotopic to g_1 o f

So therefore g_1 o (g_0)^-1 (using this inverse notation) is homotopic to identity

I dont have the latex off the top of my head sorry

[sturdy fulcrum]

Don't worry, I think I understood what you mean

[sturdy fulcrum]

But, do I have to specify why the first part of this works?

Since I think is using what I need to prove

Like, the composition property

Of homotopic paths

[elfin bridge]

This one isnt too bad, you just find a homotopy X x I -> Z given f: X->Y and a homotopy H: Y x I -> Z (between g_0, g_1)

Namely you take H and you precompose it with a function f x Id_I: X x I -> Y x I, (x, c) |-> (f(x), c)

So H o (f x Id_I) is a homotopy X x I -> Z (you can verify this)

[sturdy fulcrum]

Ok, I'll write it then. If I conclude it I will close. Thanks for the idea

[elfin bridge]

Theres a similar one but with postcomposition which you might need to finish the proof too

[sturdy fulcrum]

Which one is that?

[elfin bridge]

Like f o g_0 is homotopic to f o g_1

If g_0 is homotopic to g_1

The proof is entirely analogous you just postcompose with f

[sturdy fulcrum]

So, what you say is to prove composition left and right are the same?

[elfin bridge]

No so like what im thinking here is

We have that id is homotopic to g_1 o (g_0)^-1

Thus using that, we would have that f_0 homotopic to f_1 o g_1 o (g_0)^-1 is homotopic to f_1 o id -> f0 homotopic to f1

You'll need to check this is true by verifying the endpoints are the same

Which should be true by defn of homotopy anyways

[sturdy fulcrum]

Oh I see

But, checking that would mean giving the homotopy?

[elfin bridge]

So from this you could construct an explicit homotopy sure

But you dont necessarily need to write out the homotopy to show things are homotopic (this method doesnt really require an explicit homotopy to be constructed)

[sturdy fulcrum]

Wow, that's really nice to read

Ok, I'm going to fill the details on what you've told me.

I will close as soon as I'm done

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[red sky]

<@&286206848099549185>

[finite storm]

nah

[red sky]

Too early?

[finite storm]

first send problem

second wait 15 min

[red sky]

,rccw

[red sky]

45

How many positive numbers are in the arithmetic progression

[left juniper]

!status

[topaz sinew]

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

[red sky]

2

[left juniper]

Send us your best attempt

[red sky]

,rccw

[red sky]

Absolute nonsence

[late aspen]

it's a sequence of odd numbers starting from 175 and going backwards

[red sky]

Yes ik the answer but I need a way to write it

[late aspen]

T(n) = 175 - 2(n - 1)

positive so T(n) > 0

175 - 2(n - 1) > 0

175 - 2n + 2 > 0

177 - 2n > 0

2n < 177

[red sky]

Thank you

[late aspen]

n < 88.5

[late aspen]

np

[left juniper]

Don't give full answer, please? Give hints instead

[red sky]

Also the answer is 88, but I get 88.5 so yea

Don't know if that counts

Bc 89 is also an option but it's wrong

[left juniper]

What is the value at index 89?

[red sky]

I imagine a negative number

Bc it's n<88.5

[left juniper]

Yes. So you know that the number at index 1 to 88 is positive

[red sky]

Oh

Okay thank you

Have a nice day man

.close

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[dark quest]

can someone explain to me how you are supposed to get the x = expression please?

[dark quest]

@haughty drum

[opal vault]

well you want some irrational number between a/b and c/b. So let's try to find an irrational number between a/b and (a+1)/b

so, we only need to find an irrational number between a and a+1, because then dividing by b makes it an irrational number between a/b and (a+1)/b

so, we only need to find an irrational number between 0 and 1, because then adding a...

so... pick your favorite irrational number between 0 and 1

any will work (so 1/sqrt(2) = sqrt(2)/2 works for example)

[opal vault]

also for future reference, it's @ Helpers, not @ Helper (you pinged a specific person)

(and wait 15min before using that ping)

[dark quest]

ah ok thank you for answering back I thought there was a special reason for picking sqrt2

also i didn't realize i pinged the wrong ping sorry

[dark quest]

why is it a+1/b though? where is the a/b

[blissful needle]

try splitting the fractions into two parts

[dark quest]

split it into numerator and denom?

[opal vault]

(a+1)/b, not a + (1/b) jic

and (a+1)/b = a/b + 1/b

if we want an irrational $I$ such that $\frac{a}{b} < I < \frac cb$

[dark quest]

why is it important to make the distinction of (a+1)/b

[thorny flame]

Raphaelisius Maximus MMIII

[opal vault]

since we have $\frac{a}{b} < \frac{a+1}{b} \leq \frac cb$

[thorny flame]

Raphaelisius Maximus MMIII

[opal vault]

if we manage to find an irrational $I$ such that $\frac{a}{b} < I < \frac{a+1}{b}$

[thorny flame]

Raphaelisius Maximus MMIII

[opal vault]

then we win

is this ok so far?

[dark quest]

uh

i see than we reduced the scope of our problem to between a and a+1

[opal vault]

well first between a/b and (a+1)/b

[dark quest]

yeah

[opal vault]

and then between a and a+1 as we multiply by b

[dark quest]

yeah

[opal vault]

(and then between 0 and 1 as we subtract a)

[dark quest]

wait what

what's between 0 and 1

and why are we subtracting a

[opal vault]

if it helps you we can do it

since a is rational (an integer)

if we have an irrational I between 0 and 1

then a + I is an irrational between a and a+1

and we win

[dark quest]

then why is c

why is there a a<c

and c/b?

[opal vault]

c/b ?

ok wait

remember we forgot about c?

[dark quest]

yeh

[opal vault]

when we said we only need an irrational between a/b and (a+1)/b

it's this portion that explains it

[dark quest]

why do we need to metion c if all we need is a+1 and a

[opal vault]

because we need to prove that we don't need c

[dark quest]

whut

if we don't need c we need to prove that we dont need c by saying c exists?

im very confused

[opal vault]

let's start from the beginning

we want to show there is an irrational between any two rationals

so... take a/b < c/d any rational numbers

"d" isn't needed, because we can take a common denominator

so take a/b and c/b with a < c

[dark quest]

yes

[opal vault]

since we have $\frac ab < \frac{a+1}{b} \leq \frac{c}{b}$, we can be even pickier and ask to find an irrational between $\frac ab$ and $\frac{a+1}{b}$

[thorny flame]

Raphaelisius Maximus MMIII

[opal vault]

because in that case it'll be between $\frac ab$ and $\frac cb$

[thorny flame]

Raphaelisius Maximus MMIII

[opal vault]

so we don't need "c/b" anymore

see how this lets us simplify the problem step by step

[dark quest]

ok

[opal vault]

we needed to justify every step

but now we don't need "d", and now we don't need "c" anymore

now let's push this further

saying we don't need "b", because if we find an irrational between a and a+1, then just divide by b

but we don't need "a" either, because if we find an irrational between 0 and 1, then just add a

[wintry meteor]

-# Side discussion: Is the wording in the question is wrong? I think it should say “Between every two distinct rational numbers”

[opal vault]

(it's implied, let's not be that picky about the wording)

[opal vault]

@dark quest is there something you want to go over from those last two steps?

[dark quest]

no i think i get it now

my only problem with reading the solution was like

[opal vault]

alright

[dark quest]

trying to figure out how I'm supposed to come to the proof by myself

im studying for a exam and i am not very confident in proofs

and its very late at night lol

[opal vault]

it's not easy but yeah simplifying helps

[dark quest]

i get the problem now though tyvm

[opal vault]

less variables = easier problem

[dark quest]

ok i will try to remember that for tomorrow

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[graceful cove]

I see that 10! is the total amount of outcomes and somewhat see that 4!3!2!1! represent the amount of repeats we have but since there are four different nationalities shouldn't there be 4! ways of getting these extra counts so shouldn't it be 10!/4!4!3!2!1! instead of 10!/4!3!2!1!

[topaz sinew]

@graceful cove Has your question been resolved?

[craggy haven]

i think the assumption is that the outcome is like

  1 Russia
  2 United States
  3 United States
  4 United States
  5 Russia 
  6 Great Britain
  7 Brazil 
  8 Russia
  9 Great Britain
 10 Russia

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[rancid laurel]

hi, why is this k value not a solution?

[rancid laurel]

thanks in advance.

according to the conclusion in my book, only k = 1.975 is the right answer

[fallow heart]

Because that basically corresponds to k = 0, which would give you the function f(x) = 1. But the integral of this between 0 and 1 doesn't equal π

k being something like 10^-15 is very likely an index of a numerical error

[rancid laurel]

ohh i see

[rancid laurel]

understood

thanks

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[autumn timber]

can someone give me introduction into proving things in maths with short example?

[topaz sinew]

@autumn timber Has your question been resolved?

[topaz sinew]

@autumn timber Has your question been resolved?

[junior scarab]

What is the problem?

[topaz sinew]

@autumn timber Has your question been resolved?

[autumn timber]

i dont think I understand how you can prove something in maths and if you can add some simple example

[quasi depot]

A proof is a sequence of logical steps that start from axioms, and use what you already know to make logical implications

An example that you should be familiar with is solving equations

lets say you are given the equation x^2 - 2x + 1 = 0

by solving the equation in the real numbers (and providing all of the steps) you prove the statement "if x is a real number, then x^2-2x+1=0 if and only if x=1"

[autumn timber]

so i dont have to write the fancy stuff for everything?

[quasi depot]

wdym?

[clear lodge]

define "the fancy stuff"?

[topaz sinew]

@autumn timber Has your question been resolved?

[autumn timber]

for example take a look at the proof of 1 + 1 or golbach's conjecture

[inland mica]

it depends on your level of math

usually when you learn math, there will be assumptions you need to make, so as not to prove everything from the ground up every time you want to use a result

for example, you will never have to prove that 1+1 = 2 when taking calculus courses because it is accepted as true, and because the point of the course is not to prove it again

in short, you don't need any fancy stuff to write a proof, it just needs to be logically sound

[autumn timber]

well I need to learn something more for one competition, its like 4x harder than math at normal school and they require a lot of proving, example from last year is that you have some 4 letter number and prove that there is ab + cd = sqrt n; cd - ab = 5

or smth

more like how many exist and find something

also there were a lot of geometry proof, so yeah

[clear lodge]

as bloubb has stated, it really depends on what you're allowed or assumed known at that point.
You usually prove stuff not from ground up, but from what is assumed known.
In geometry, for example, you'd be allowed to use pythagora's theorem, without any need to prove it, because it's assumed known

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[true fulcrum]

.rotate

[hardy wing]

,rotate

[true fulcrum]

ok so im at the last step but im a lil confused

why is x =4 or =0? its not exactly clicking

btw hello

forgot to be polite

[hardy wing]

$f'(x) = 3x(x-4)$, a critical point is when $f'(x) = 0$, so you find the values of x where $3x(x-4) = 0$

[thorny flame]

Stitches

[hardy wing]

Or do you not understand why 3x(x-4) = 0 when x = 0 or 4?

[true fulcrum]

so this is saying that hwen the derivative of a function is = 0 meaning 0 slope meaning 0 change we must find the values of x this happens at?

[true fulcrum]

the latter

i get the factor

the the derivative

and the derivative

[hardy wing]

Yes. The derivative of a function being 0 means that the slope is 0. This might correspond to a maximum (thing tip of a parabola), a minimum (think bottom of an upside down parabola, or an inflection/saddle point (ie. neither, think x^3 at x = 0)

[true fulcrum]

what exactly is an inflection - a kind of center on the parabola?

its just why is x = 0 or 4?

[lucid junco]

It is where concavity changes

[true fulcrum]

sure that makes sense

but how do you arrive at x=0 or x= 4

[lucid junco]

so you’re not confused about how to get f’(x) itself just why x=0,4 ?

[true fulcrum]

yes

[lucid junco]

if a*b=0 then either a=0 or b=0

It’s called the zero product property

[true fulcrum]

right

ah

ah

yes i see now

[lucid junco]

You have done quadratics before ? It is the same thing as that

[true fulcrum]

thanks

[true fulcrum]

not really

but i understand now thanks

.close

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[winged basin]

I am preparing for a linear algebra test, where I am allowed to use python. I have a problem with linear codes.

import numpy as np 

def p1_of_list(bits):
    return (bits[1]+bits[0]+bits[2])%2

def p2_of_list(bits):
    return (bits[1]+bits[0]+bits[3])%2


def p3_of_list(bits):
    return (bits[0]+bits[3]+bits[2])%2

def generate_paritycheck_matrix(n,k):
    A = np.zeros((k,n-k))
    index = 0
    for bits in np.identity(k):
        A[index][0] = p1_of_list(bits)
        A[index][1] = p2_of_list(bits)
        A[index][2] = p3_of_list(bits)
        index = index + 1
    return A

def generate_generator_matrix(n,k):
    return np.hstack((np.eye(k), generate_paritycheck_matrix(n,k)))

#from here it does not make any sense
n,k = 7,4
data = np.array([[0,0,1,1]])
hamming = np.dot(data, generate_generator_matrix(n,k))


parity_check_matrix = np.hstack((generate_partycheck_matrix(n,k).T,np.eye(k-1)))
np.dot(parity_check_matrix, hamming.T) 

[winged basin]

The result of the last line is:

array([[2.],
       [2.],
       [4.]])

Which makes no sense to me, this should give index of the column that contains the error, no?

or in this case it should be 0, no?

[zinc holly]

Ayo

[winged basin]

I am super afraid I don't get the theory

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@winged basin Has your question been resolved?

[topaz sinew]

@winged basin Has your question been resolved?

[sweet shard]

just show the actual question

[winged basin]

This isn't an exercise, but I guess the question would be: Implement a linear Code System, which can generate the generator matrix, parity check matrix and check sent hamming codes.

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@winged basin Has your question been resolved?

[topaz sinew]

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[grand solar]

have a question about these two questions

[grand solar]

why does one specify prime power order and the other doesnt

also can it be done without a calulcator

I was just going to find the orders of most of the elements to elminate which groups its not isomorphic to

for 27 G can be isomophic to either $Z_{16}$ or $Z_8 \oplus Z_2$ or $Z_4 \oplus Z_4$ or $Z_4 \oplus Z_2 \oplus Z_2$ or $Z_2 \oplus Z_2 \oplus Z_2 \oplus Z_2$

[thorny flame]

Branshi

[grand solar]

this is from a chapter about the fundamental theorem of finite Abelian groups

.close

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[topaz sinew]

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[pulsar forum]

Hi, I'm Italian, I need help with maths, anyone speak Italian?

[spare smelt]

Mama mia

[pulsar forum]

Are u italian?

[drifting swift]

inappropriate to say in this context, innit 😭

[drifting swift]

we got at least one Italian speaker among helpees and i can probably call him over but you should send your question(s) in Italian and then do your best to translate if needed

[pulsar forum]

Uhm, ok, I'm not good speak english, but i can try. Where do i send a question?

[grand solar]

here

[pulsar forum]

I have a rational function x^3+x/3x. I can study the limits, but I can’t find the first and second derivatives, and I can’t plot it on the Cartesian plane.

[whole slate]

what’s bothering you?

[pulsar forum]

When I get to the first derivative, I can’t go any further. I could try to send a photo, but I’m not sure if you can read my writing.

[whole slate]

please send

[topaz sinew]

@pulsar forum Has your question been resolved?

[clear python]

Could you turn on the lights and send another picture

,rccw

[pulsar forum]

There are limits shown at the top of the page, but please ignore them

The sign study is wrong, ignore that too. I corrected it on another page.

[topaz sinew]

@pulsar forum Has your question been resolved?

[topaz sinew]

@pulsar forum Has your question been resolved?

[shy wolf]

I'm sorry I can't really speak italian, but in that problem you can cancel the x in the denominator and numerator, when $x\neq 0$, so it should be easier to calculate the derivatives that way. If you choose to use the quotient rule anyways, you've made some mistakes while substituting the derivatives in the formula, it should end up being $\frac{(3x^2+1)(3x)-(x^3+x)(3)}{(3x)^2}=\frac{2x^3}{3x^2}$

[thorny flame]

KonoEmllikDa

[topaz sinew]

@pulsar forum Has your question been resolved?

[topaz sinew]

Channel closed

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[topaz sinew]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.