help-49

[midnight plank]

@hearty vine Has your question been resolved?

[midnight plank]

@hearty vine Has your question been resolved?

[midnight plank]

@hearty vine Has your question been resolved?

[midnight plank]

@hearty vine Has your question been resolved?

[eternal pawn]

you probably mean "if it doesnt then send be to any of the unpaired elements left in C ", then I think it works

[hearty vine]

yea
i kinda switched to thinking of it as, C = A' u B' where A' n B' = 0 and |A'| = |A| and |B'| = |B| which gives me bijections between them, and then i can construct h1 and h2 out of those bijections, where h1 is just the bijection g1: A->A' but with the codomain expanded, so its still injective, and h2:C->B; if x in C is in A', then x=h1(a) for exactly one a in A because of injectivity, so then i send x to f(a); if x in C is in B', then i send it with the second bijection g2: B'->B; h2 will be surjective because for each b in B i can find an element b' in B' so that g2(b') = h2(b') = b

i think this way its more clear how it works
i think id still need to check cases with empty sets involved but i think i can work those out manually

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[still flax]

Hello I'm currently working on this problem and a little confused. I'm wondering if when finding DE cutting the triangle into 2 sections and using trig to find EB would make sense?

actually it wouldn't right? because from E to C is not a straight line 😅 I'm not sure what to do then

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[twilit field]

why is this wrong

oo[s

[lyric charm]

well you have multiple issues with your TeX

[twilit field]

yea, I forgot to re-compile

[lyric charm]

also why 4P(X=4)?

P(X=4)=0 in fact

also your P(X=2) and P(X=3) are both wrong

[twilit field]

that's what I was wondering

why

[lyric charm]

well they don't add up to 1 for one

and second, for 3 holes you want the two balls to land in the same hole

but it doesn't matter which one

[twilit field]

so just 1/4

[lyric charm]

your (1/4)^2 is the probability they both land in hole A

[lyric charm]

yes

P(X=2) will be 3/4 on the other hand

[lyric charm]

your typos look more numerous than a forgotten recompilation would suggest tbh

[twilit field]

how would I get that ( without using total probability)

[lyric charm]

the 2nd ball has 4 equally likely holes to land in, of which 3 are not the same hole as the 1st ball

[twilit field]

got it

tq

[twilit field]

wait, that would be 1/4 * 3/4 then, no

[lyric charm]

no, again, don't force the 1st ball to land in hole A

[placid ridge]

if the first ball can drop in any hole then its probability is just 1

[twilit field]

right

how did I miss that

thanks!

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[fierce canyon]

,rccw

[fierce canyon]

find rectangel area

[last slate]

wheres f?

[graceful drum]

its in the chat

[last slate]

im guessing it's the intersection

[fierce canyon]

mb i didnt put it down yeah

[last slate]

does e bisect the base?

@fierce canyon

[fierce canyon]

not told that

[last slate]

did you find it

[fierce canyon]

all the info is given

[fierce canyon]

not yet

[last slate]

if it bisected it then itd be easier but welp

[fierce canyon]

maybe we can prove it does

i think we needa find the intersection point or something

at F

[midnight plank]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[fierce canyon]

thats how it was shone to me

shown

except the interception is at F

[graceful drum]

bro do you not have the original question

cus theres 2 intersections and we dont know which one is F

[fierce canyon]

BEF

its pretty obvious theres only one F

that can be possible

[graceful drum]

do you have it?

[last slate]

BE can make only join to one unnamed point so

[fierce canyon]

^

[last slate]

what grade?

[fierce canyon]

grade 10 rn

[last slate]

same

i cant solev it wothout e bisecting them though

i dont see any congruency or similarity either

[fierce canyon]

It might be something to do with like coordinates cuz we are doing that rn

[last slate]

but there are no coordinatees

you need a coordinate to apply any formula on it r8

anyway

[fierce canyon]

i meant like B as the origin or something and A is

(0,h)

idk just guessing atp

[last slate]

nah

doesnt add up

for equidistance you need at least one full coordinate or a coordinate which sits right with another constant coordinate

what topic is this from?

[fierce canyon]

Its just a question my teacher showed us

for fun

[last slate]

hmm sorry cant help but lmk if you find it

[placid ridge]

F is where AE intersec BD right

[fierce canyon]

ye

[fierce canyon]

algs ill see

maybe I can ask like gpt or something 😅

[last slate]

try it

[fierce canyon]

$$ (A=(0,h),;B=(0,0),;C=(w,0),;D=(w,h)).

• Let (E=(e,0)) on (BC) (so (0<e<w)). Unknowns: (w,h,e).

Step 1 — area of (\triangle ACE).
Base (CE=w-e), height (h). So
[
[ACE]=\tfrac12\cdot h\cdot (w-e)=9 \quad\Rightarrow\quad h(w-e)=18. \tag{1}
]

Step 2 — find the intersection (F) of line (AE) with diagonal (BD) using line equations (no parameters).
Equation of diagonal (BD) (through (B(0,0)) and (D(w,h))) is
[
y=\frac{h}{w},x.
]

Equation of line (AE) (through (A(0,h)) and (E(e,0))) is found from slope:
slope (m=\dfrac{0-h}{e-0}=-\dfrac{h}{e}). So
[
y = h + m x = h - \frac{h}{e},x.
]

At intersection (F=(x_F,y_F)) these two (y)-values are equal:
[
\frac{h}{w}x_F ;=; h - \frac{h}{e}x_F.
]
Divide both sides by (h) (nonzero):
[
\frac{x_F}{w}=1-\frac{x_F}{e}.
]
Bring (x_F)-terms together:
[
\frac{x_F}{w}+\frac{x_F}{e}=1 \quad\Rightarrow\quad x_F\Big(\frac{e+w}{ew}\Big)=1.
]
So
[
x_F=\frac{ew}{e+w}.
]
Then plug into (y=\dfrac{h}{w}x) to get
[
y_F=\frac{h}{w}\cdot\frac{ew}{e+w}=\frac{he}{e+w}.
]

(So we found (F) by simple line equations — no parameters.)

Step 3 — area of (\triangle BEF).
Base (BE=e) (on the x-axis) and height (vertical) (y_F=\dfrac{he}{e+w}). Hence
[
[BEF]=\tfrac12\cdot e\cdot y_F
=\tfrac12\cdot e\cdot\frac{he}{e+w}
=\frac{h e^2}{2(e+w)}.
]
We are told this equals (3), so
[
\frac{h e^2}{2(e+w)}=3 \quad\Rightarrow\quad h e^2 = 6(e+w). \tag{2}
]

Step 4 — combine (1) and (2).
From (1): (h(w-e)=18). From (2): (h=\dfrac{6(e+w)}{e^2}). Substitute that into (1):

[
\frac{6(e+w)}{e^2},(w-e)=18.
]
Divide both sides by 6:
[
\frac{(e+w)(w-e)}{e^2}=3 \quad\Rightarrow\quad\frac{w^2-e^2}{e^2}=3.
]
So
[
\frac{w^2}{e^2}=4 \quad\Rightarrow\quad \frac{w}{e}=2.
]
Thus (w=2e).

Step 5 — rectangle area.
Plug (w=2e) into (1): (h(w-e)=h\cdot e=18\Rightarrow h=\dfrac{18}{e}). Therefore
[
\text{Area}=w\cdot h=(2e)\cdot\frac{18}{e}=36.
] $$

[last slate]

what the

[fierce canyon]

that is very messy

[placid ridge]

What in gods name

[fierce canyon]

wow

[last slate]

this is not grade 10

my grade 10 brain cannot understand this

ask the teacher and let us know

[fierce canyon]

its like algebra coodrinates

[grand pond]

dice

LaTeX source sent via direct message.
```Compilation error:```! Missing $ inserted.
<inserted text> 
                $
l.51 
     
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```

[fierce canyon]

.-.

$$ (A=(0,h),;B=(0,0),;C=(w,0),;D=(w,h)).

• Let (E=(e,0)) on (BC) (so (0<e<w)). Unknowns: (w,h,e).

Step 1 — area of (\triangle ACE).
Base (CE=w-e), height (h). So
[
[ACE]=\tfrac12\cdot h\cdot (w-e)=9 \quad\Rightarrow\quad h(w-e)=18. \tag{1}
]

Step 2 — find the intersection (F) of line (AE) with diagonal (BD) using line equations (no parameters).
Equation of diagonal (BD) (through (B(0,0)) and (D(w,h))) is
[
y=\frac{h}{w},x.
]

Equation of line (AE) (through (A(0,h)) and (E(e,0))) is found from slope:
slope (m=\dfrac{0-h}{e-0}=-\dfrac{h}{e}). So
[
y = h + m x = h - \frac{h}{e},x.
]

At intersection (F=(x_F,y_F)) these two (y)-values are equal:
[
\frac{h}{w}x_F ;=; h - \frac{h}{e}x_F.
]
Divide both sides by (h) (nonzero):
[
\frac{x_F}{w}=1-\frac{x_F}{e}.
]
Bring (x_F)-terms together:
[
\frac{x_F}{w}+\frac{x_F}{e}=1 \quad\Rightarrow\quad x_F\Big(\frac{e+w}{ew}\Big)=1.
]
So
[
x_F=\frac{ew}{e+w}.
]
Then plug into (y=\dfrac{h}{w}x) to get
[
y_F=\frac{h}{w}\cdot\frac{ew}{e+w}=\frac{he}{e+w}.
]

(So we found (F) by simple line equations — no parameters.)

Step 3 — area of (\triangle BEF).
Base (BE=e) (on the x-axis) and height (vertical) (y_F=\dfrac{he}{e+w}). Hence
[
[BEF]=\tfrac12\cdot e\cdot y_F
=\tfrac12\cdot e\cdot\frac{he}{e+w}
=\frac{h e^2}{2(e+w)}.
]
We are told this equals (3), so
[
\frac{h e^2}{2(e+w)}=3 \quad\Rightarrow\quad h e^2 = 6(e+w). \tag{2}
]

Step 4 — combine (1) and (2).
From (1): (h(w-e)=18). From (2): (h=\dfrac{6(e+w)}{e^2}). Substitute that into (1):

[
\frac{6(e+w)}{e^2},(w-e)=18.
]
Divide both sides by 6:
[
\frac{(e+w)(w-e)}{e^2}=3 \quad\Rightarrow\quad\frac{w^2-e^2}{e^2}=3.
]
So
[
\frac{w^2}{e^2}=4 \quad\Rightarrow\quad \frac{w}{e}=2.
]
Thus (w=2e).

Step 5 — rectangle area.
Plug (w=2e) into (1): (h(w-e)=h\cdot e=18\Rightarrow h=\dfrac{18}{e}). Therefore
[
\text{Area}=w\cdot h=(2e)\cdot\frac{18}{e}=36.
]$$

[grand pond]

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

[last slate]

waaittt

[placid ridge]

I mean its probably just because its a bit harder but overall its still using coordinates

[fierce canyon]

bro

this thing

[placid ridge]

And i forgot to press reply

[last slate]

i get it

look at it

e does bisect the line

9×4=36

maybe you missed it?

[fierce canyon]

we werent told that

i think we had to prove it

[last slate]

but this is too bigggg

[last slate]

i dun think you can at least considering grade 10

[placid ridge]

Where do you see it?

[last slate]

the answer

36

[fierce canyon]

i read over it its kinda just like algebra mixed with coordinates

[last slate]

the end of the ai solution

[placid ridge]

Oh yeah w=2e

[last slate]

yeahh but ask your teacher once maybe

[fierce canyon]

probably

[placid ridge]

Ye you had to prove it

[last slate]

how tho?

[graceful drum]

this is setting a bad example on how to solve problems like this

[placid ridge]

Magic or sth idk

[fierce canyon]

I was just tryna see if it could help us in any way since this question isnt really for our level of understanding

[last slate]

real

anyway hands up lmk if you get the answer im friending you

[fierce canyon]

😔

[fierce canyon]

ight

[last slate]

ty

[fierce canyon]

ill look over the ai response for now cuz thats all i have

[midnight plank]

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[twilit field]

I would like to show if $0<c<1$. Then $c^{1/n} \to 1$

[runic hamlet]

well thats false

[grand pond]

wai

[twilit field]

oops, this is better?

[runic hamlet]

yes

[twilit field]

Kind of unsure of how to proceed

My first thought is c <1, so $c^{1/n} = (1-h)^n$ for some $h \in \N$

[runic hamlet]

have you done the c>1 case already?

[lyric charm]

h in R
not specific enough

[grand pond]

wai

[twilit field]

I'll do that after this

[lyric charm]

ok now thats just fully wrong

also how did the 1/n exponent become n

[twilit field]

oops

$c^{1/n} = (1-h)^n; h\in [0,1)$

[grand pond]

wai

[runic hamlet]

wai are you reading what you are writing

[twilit field]

yes

[runic hamlet]

are you sure

[twilit field]

I think this is true

[runic hamlet]

are you reading what ann wrote

[lyric charm]

how did the 1/n exponent become n

[twilit field]

I missed that

[twilit field]

where

[lyric charm]

right here??

wai if you're even REMOTELY unfocused then you should put down the math

go for a walk, go do ANYTHING ELSE that doesnt require mathematical brain effort.

fuck, read a sociology book for that matter.

[twilit field]

I thought I was correcting a mistake when I did that

because the limit. of such a seqeunce is computable using the binomial theorm

[twilit field]

I am focused

[lyric charm]

you're setting c as 1-h, yes?

[twilit field]

yes

[lyric charm]

then, again, how in god's name does the 1/n transmogrify into n?

[twilit field]

I thought there would be such a h , that would make this true, which isn't true in hindsight

[lyric charm]

i mean now you've got h depending on n, which is probably not a great look as far as a rephrase goes

i will say you're gonna need to bust out the epsilons for this

[twilit field]

So this approach isn't optimal?

[runic hamlet]

you can do the c>1 case with bernoullis inequality without epsilons. I assume the c<1 aswell but havent thought about it

[lyric charm]

if you can do the c>1 case then in the case of c<1 take the reciprocal

[lyric charm]

it's not just non-optimal, i frankly just dont see how to continue it at all

[twilit field]

I can do the c>1 cases with that hint. So okay, got it.

Thanks both of you!

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[balmy cypress]

$x^6+2x^5+2x^4-2x^2-2x-1=0$

[grand pond]

Richard Mullin

[balmy cypress]

Pls help

[pearl hull]

What are you looking for?

[balmy cypress]

Solving

[rose pilot]

guess one solution, factorize, repeat

[severe cloud]

[balmy cypress]

Guess?

[pearl hull]

not guess technically

[severe cloud]

educated guess

[pearl hull]

it's more like a trial and error

[pearl hull]

ye

[severe cloud]

Basically try simple small values

Doesn‘t always work but it does here

[balmy cypress]

x=0

-1=0

x=5

Now what do I do?

I want to put in input x = 5

[severe cloud]

try x=1 instead

[balmy cypress]

Ok

1+1+1-1-1-1=0

0=0

So the solution is x = 1?

[steel cedar]

one of the solutions

[runic hamlet]

as a general fact, you only want to guess solutions that are divisors of the last term

[balmy cypress]

x = -1

1-2+2-2-1+2=0

Nice

Finish?

[severe cloud]

Well, you know x=1 is a root, that means x-1 is a factor of your polynomial. So you can divide your polynomial by x-1 and get another polynomial of degree 5. then you can repeat until you get all factors, or something not factorable

[balmy cypress]

$(x^6+2x^5+2x^4-2x^2-2x-1)/(x-1)=0$

[grand pond]

Richard Mullin

[balmy cypress]

How to get grade 5?

[runic hamlet]

do you know how polynomial division works

have you done that in class

[balmy cypress]

Yes

[runic hamlet]

then do it

[balmy cypress]

x^2÷x=x

But here there is also -1

[severe cloud]

That is not what polynomial division is

[balmy cypress]

And what would it be called?

[severe cloud]

long division, polynomial division, it depends on where you‘re from. But maybe check your notes or online to refresh on what that is

[midnight plank]

@balmy cypress Has your question been resolved?

[midnight plank]

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[solid pilot]

i got 390 on the psat10. do i have the possibility/chance to improve and get 780? (btw im also an early grad (skipped 11th))

[solid pilot]

ive looked up and seen so many different test prep/study plans but idk which to go with and which ones are actually effective

my SAT is going to be around april 2026

[late rover]

Dw SAT Maths are mostly algebra you can train yourself to get 780 with that much time

[solid pilot]

how should i work up to it?

im so slow when it comes to math 😭

[late rover]

Grinding school math textbook ig, SAT maths are related to ones taught in highshcool. What you've taught in school should be enough

Or use Khanacademy it's quite good

[solid pilot]

did u take the sat?

[gleaming latch]

definitely, even 800 is possible
sat maths isnt "hard" its just a lot of problems so to not screw up any of them is the real challenge
and you can learn most of it before your next test lowk
do what they said and just grind it out

[solid pilot]

Thats reassuring

[late rover]

I will this November but my on my practice one I got 790 so it can't be that hard ig

[solid pilot]

danng gj

and good luck

so, jjust set up a time after school and hw to go over all the basics and fundamentals again and work my way up?

[gleaming latch]

yes you can also just spam past sat/psat questions

imo english is much harder to get 800 on but if youre already solid on that then focus on math 👍

[solid pilot]

i got a 500 on reading

def will polish up on that as well, but i think math should be my priority

[gleaming latch]

yeah math is a lot easier to improve

[solid pilot]

got it, thankss

.close

[midnight plank]

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[white moss]

U = {(x1, ...) \in F^\infty \mid x_k \neq 0 for only finitely many k} How can this be a subspace of F^\inf if it doesnt have a zero vector for the additive identity

[runic hamlet]

why do you think (0,0,0,...) isnt in the set

[white moss]

$$U = {(x_1, \hdots) \in \mathbb{F}^\infty \mid x_k \neq 0 \text{ for only finitely many } k}$$
How can this be a subspace of $\mathbb{F}^\infty$ if $\textbf{0} \notin U$

[white moss]

cuz it says x_k cant be 0

[runic hamlet]

thats not what it says

[robust isle]

0-many non-zero entries is finitely non-zero entries

[grand pond]

Altanis

[lyric charm]

x_k ≠ 0 for only finitely many k

you can't just ignore this bolded part

[white moss]

yeah i understand but doesnt a zero vector have to be completely filled with 0s

[robust isle]

yeah

[lyric charm]

it does

[robust isle]

all entries are 0

so there are no non-zero entries

[lyric charm]

the zero vector does satisfy the condition

there are no values of k for which the k'th component of 0 is nonzero

[white moss]

but the zero vector is (0, 0, ...., 0) with no nonzero constants

[lyric charm]

yeah and "none" is a finite amount

[white moss]

ok wait can you define the zero vector

[lyric charm]

notwithstanding that you're working with F^infty so there's no 0 at the very end (bc there is no end)

[lyric charm]

it already has been defined for you a few times in this chat

[white moss]

is (0, 1, ...., 0) in F^inf a zero vector..?

[lyric charm]

thats a no but also this is poorly notated

you're in F^infty. there is no "last entry"

[white moss]

hm

so can you think of the zero vector in U as (0, 0, ....)

where all the "nonzero" elements are at the "end"

but it never ends so its filled with zeros?

idk much about inf dimensional spaces my linalg textbook hardly covers it

[white moss]

oh wait

i completely. misread this

can i just choose k = 0

then that means there are zero nonzero elements

ok wait im understanding better, U is just the set of elements in F^inf that eventually terminate to 0, 0, .... at the end

and (0, 0, 0, ...) is an element of U

i just didnt understand the def of U

if this is correct ill close the channel

[robust isle]

the question is how many k's exist with x_k != 0

[robust isle]

if there are 0 such k's (a finite amount), then yes you get the zero vector

[robust isle]

that's another way of seeing U yes

[brittle dew]

is SAT math like i see on youtube like there youtuber saying 2^(x+3) = 32 like why i can solve this in my head what hard about SAT? or they jst spreading false info

[gleaming latch]

most of them you can solve in your head, some may require a little work but its at most polynomials and basic combinatorics
the hard thing is getting every single question right without fail
there are also some problems exceedingly harder than others and some problems that may not make sense
these are "experimental" problems and collegeboard uses them to decide what type of questions to use on future tests

[midnight plank]

@white moss Has your question been resolved?

[white moss]

Thx

[white moss]

Yeah cb problems are weird

That's why lots of really good math kids still get 790s

Sat gives some weird math problem and u get cooked

Anyways I'll close

.close

[midnight plank]

Channel closed

Closed by @white moss

Use .reopen if this was a mistake.

[brittle dew]

why in thailand we even doing some complex mobius function in grade 8 :Sob:

[midnight plank]

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[midnight plank]

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

[half idol]

1

North hemis area= south

1:1

[lyric charm]

find the land and water areas in the northern hemisphere as fractions of total SA of the earth

[half idol]

sa mean?

[lyric charm]

SA = surface area

[half idol]

North one has total 5 and earth has 3

hang on

[lyric charm]

not what i ask

[half idol]

I have an idea

Wait

[rough lance]

What's your idea?

[half idol]

Can you explain how we do it?

It was something like i will make it half of earth

[rough lance]

Would you be able to turn the ratios into fractions?

[half idol]

2:3 total is 5 and 1:2 all but 3

[lyric charm]

northern land and water are 2/5 and 3/5 respectively of total northern hemisphere area

so northern land = 2/5 * 1/2 of earth area = 1/5 of earth area

do the same for water

and then do the same for total

[lusty python]

do subtraction

and then you got your ratio

gl

[half idol]

3/5*1/2=3/10 of total water

[half idol]

Total will be 3-1/5=14/5

1/5:14/5

1:14

[rough lance]

3/10 is the water in northern hemisphere right?

[half idol]

Yee

[rough lance]

To find water in southern hemisphere we can do

Total water - Water in Northern Hemisphere

Is that making sense?

[half idol]

Yes

[rough lance]

Let's do that

What do you get

[lyric charm]

...

that looks very wrong to me

[half idol]

I am slightly confused

Let me do it again

And understand

2:3 half of it given ratio and total ratio is 1:2

[rough lance]

Yes

[half idol]

why are we dividing 2/5,3/5

[rough lance]

To convert ratios to fractions

Let's say 2:3

[half idol]

2:3 are not fractions?

Ohh they are not

[rough lance]

We can have two outcomes 2/(2+3), 3/(2+3)

[half idol]

True

[rough lance]

Is this alright to you?

[half idol]

Yes

[rough lance]

Nice

[half idol]

5 is half of it

[rough lance]

Let's start from the start

First is total land and total water on earth that's 1:2

Make them into fractions please

[half idol]

1/3,2/3

[rough lance]

Absolutely

Now do the same for northern hemisphere

[half idol]

We did already?

[half idol]

.

[rough lance]

Yes, the next step will be

Because it's the half of it

[half idol]

Yeah

This is very i am stuck

[rough lance]

2/5 and 3/5 both will be divided by 2

[half idol]

2/51/2, 3/51/2

[rough lance]

Because Northern hemisphere is half of the total earth

[half idol]

1/5,3/10

[rough lance]

Yes

Yes

You're correct

[half idol]

Rest is simple thanks

I will minus

[rough lance]

Yes then find the ratio

Do tell me what you get

If any issues arise let me know

I'll assist you

[half idol]

1/3-1/5=2/15

[rough lance]

Yup

[half idol]

2/3-3/10=20-6=11/30

4/30 14/30

2:11

[rough lance]

Here is some calculation error if I'm correct

Should be 20-9 instead of 20-6

[half idol]

Ohh

[rough lance]

Is it understandable

Or may I elaborate more?

[half idol]

No no

[rough lance]

Oh okay

So what did you get

2/3 - 3/10 = (20-9)/30 = ?

[half idol]

I got 2:11

[rough lance]

Did you?

[half idol]

Yeah

[rough lance]

I think it'll be 4:11

[half idol]

Why

[rough lance]

Let's recheck it a bit

Land on sothern hemisphere

Is

2/15

[half idol]

Yes

[rough lance]

Water on southern hemisphere is

[half idol]

4/30

[rough lance]

11/30

Yes

[half idol]

Ohh

Yes

[rough lance]

Yes exactly

You got it

Great work

[half idol]

.close

[midnight plank]

Channel closed

Closed by @half idol

Use .reopen if this was a mistake.

[half idol]

Thanks

[midnight plank]

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[twilit field]

How many times would you expect to roll a fair die before all 6 sides appeard atleast once

[keen saddle]

6 times lmao

[hard shard]

P(X=x)=p => E(X=x)=1/p

[twilit field]

hmm?

[hard shard]

have you taken a second to understand what i said?

[twilit field]

I'm trying to

You're saying P(X=x)= E(X=x)=1/p?

how

[dawn dagger]

implies not equal

[hard shard]

if the probability of an event occurring is p, it will take an expected 1/p attempts for it to occur

[twilit field]

hmm, how

oh, I see

follows assuming unifrom distbution?

[hard shard]

wdym uniform distro

this can work for weighted dies, unfair coins, etc.

[twilit field]

I don't get how

[hard shard]

say you flip an unfair coin with 80% prob of landing heads

1000 times

about how many are heads?

[twilit field]

800?

[hard shard]

yes

now we define a "run" to be the flips up to and including a heads

e.g. THTTHHH would have runs TH TTH H H

notice that each run has exactly how many heads?

[twilit field]

4

[hard shard]

just a single run

[twilit field]

2

[hard shard]

no it has one

just heads at the end

[twilit field]

oops, read it wrong

wait, isn't a run the flips upto an including a heads

so TH is 2

[hard shard]

sorry the definition is bad

count a run as a set of unfavored events after the last favored event up to and including the next favored event

heres the fun part: whats the average legnth of a run in the 80% heads 1000 flips case?

[twilit field]

2

[hard shard]

how did you get that?

[twilit field]

1/(1/2)

[hard shard]

the coin is unfair

[twilit field]

then it should be 1/0.8

1.25

[hard shard]

why did you calculate 1/0.8?

youre right, im just wondering how you got there

[twilit field]

this

[hard shard]

im trying to give you the intuition, dont just apply formulas randomly

lets go back to the idea of how many heads in one run?

[twilit field]

1

[hard shard]

yes one

so what can we say about the number of runs?

[twilit field]

count a run as a set of unfavored events after the last favored event up to and including the next favored event
there will be 4?

[hard shard]

what can we say about the approximate number of heads? (80% heads 1000 flips)

[twilit field]

800

[hard shard]

yes and theres a 1-1 correspondence from heads to runs

so what can we say about the runs?

[twilit field]

There are half as many runs as heads?

[hard shard]

1-1 correspondence aka bijection

[twilit field]

so 800

[hard shard]

yes

so we can count the average number of flips per run

[twilit field]

got it

[twilit field]

MSE says ||14.7||

[keen saddle]

MSE?

[twilit field]

Math Stack Exchange

https://math.stackexchange.com/questions/28905/expected-time-to-roll-all-1-through-6-on-a-die

[keen saddle]

But whenever I play ludo I never get the number i need

Even after like 50 rolls

[twilit field]

I'll close this now?

[midnight plank]

@twilit field Has your question been resolved?

Channel closed

Closed by @twilit field

Use .reopen if this was a mistake.

[midnight plank]

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[neon geyser]

haai im in the 9th grade rn and im having trouble rationalizing this radical can someone teach me 😣

[lyric charm]

image incoming?

[neon geyser]

yess

gime a sec

the video told me i couldnt have a radical on the denominator

[lyric charm]

is the stuff in the box what you need to rationalize

[neon geyser]

yess

[lyric charm]

$\frac{5x^2z^3\sqrt{3}}{2y^2\sqrt{2}}$

[keen saddle]

You can have it

[grand pond]

Ann

[lyric charm]

this thing

[keen saddle]

It's just better to have it in the numerator

[neon geyser]

ohh rlly

[keen saddle]

Easier to do stuff with it

[lyric charm]

yeah having radicals in denom is not illegal

it is just simpler when they are in num

[neon geyser]

oh okayy thanks for letting me knowww

[lyric charm]

now, let me ask you this: what would you do if all you had was $$\frac{1}{\sqrt{2}}$$ and you were told to rationalize it?

[grand pond]

Ann

[neon geyser]

uhhh

i actually have no idea how to start im sorryyy

[lyric charm]

https://www.youtube.com/watch?v=5j8a75aHaSE

[neon geyser]

oh do i watch this then get back to you or is that it?

[lyric charm]

thats what i would say you do, yes

[neon geyser]

which onee

[lyric charm]

wdym "which one"

if you aren't sure which timestamp in the video to look at, then watch the whole thing -- it's like 10 minutes long.

[neon geyser]

oh no im sorry i meant do i watch the video then get back to you or after watching it i close it

[last slate]

Just watch the video.

Come back if you have questions.

[neon geyser]

i am rn ^_^

[neon geyser]

why did he put squares where did the squares come from?

[lethal path]

do you understand how $\sqrt[3] {5^3} = 5$, firstly?

[grand pond]

south

[neon geyser]

yaa

[lethal path]

right, so we need to find a number x

if we multiply 5^(1/3) by x, we need to get 5

so that's just $\sqrt[3] {5} \cdot x = \sqrt[3] {5^3}$

[grand pond]

south

[neon geyser]

huh whats a number x?

[lethal path]

we need to find x, and x is a number

[neon geyser]

ohhh

right

[topaz cypress]

25 ?

[neon geyser]

what 25?

[lethal path]

and then $x = \frac{\sqrt[3] {5^3}}{\sqrt[3] {5^1}} = \sqrt[3] {5^{3 - 1}}$ (rules of indices)

[grand pond]

south

[neon geyser]

where did the denominator come from?

[topaz cypress]

x = $$\sqrt{25}$$

[grand pond]

AmIra

[lethal path]

from here, divide both sides

[topaz cypress]

is it true ?

[neon geyser]

oh okay

[neon geyser]

ya i think its right he reacted with a thumbs up

[lethal path]

yeah, so I'm trying not to give you an answer which is like 'you instantly see it works'

imagine you don't know what number to multiply the top and bottom by

this is how you could find out

[neon geyser]

ohh

[topaz cypress]

wait . it is $$\sqrt[3]{25}$$

[grand pond]

AmIra

[lethal path]

also it's the cube root of 25

yeah they typed it wrong

[neon geyser]

ohh

[neon geyser]

right i see

then whattt

[lethal path]

once you've figured out that the cube root of 25 is the number you should multiply on top and bottom

I think the working explains itself here

$\frac{\sqrt[3] {25}}{5}$ is the final answer

[grand pond]

south

[lethal path]

5 = 5/1 is a rational number, so the denominator is now a rational number

[neon geyser]

yaaa

[neon geyser]

ohh

[neon geyser]

how would i do this with a square root though?

instead of a cube root

[lethal path]

note that $\sqrt{2} \cdot \sqrt{2} = 2$

[grand pond]

south

[neon geyser]

ohhhhhh

so it would be 1/2?

[topaz cypress]

soooo simple

[neon geyser]

yaa its 9th grade math n i cant keep up so im asking abt it here 😓

[lethal path]

no!

[neon geyser]

oh

[lethal path]

you need to multiply top and bottom by the same number

[topaz cypress]

I am Arab btw

[lethal path]

you said 1/sqrt(2) = 1/2 but I'm not going to hound you on that

[neon geyser]

is this right? or do i have to add squares asw

[topaz cypress]

true

It's like you multiplied the number by 1.

[neon geyser]

huh

[neon geyser]

ohhhh

[grand pond]

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

[neon geyser]

ohh like this right?

[topaz cypress]

😭

[topaz cypress]

yesssss

[neon geyser]

okayy

[neon geyser]

how am i supposed to rationalize this then

and when do i know when im supposed to add squares when multiplying stuff

[neon geyser]

like on here

[lethal path]

the only surd in the denominator is sqrt(2)

hence you can multiply the entire fraction by sqrt(2)/sqrt(2)

(it doesn't matter at all if there are any square or cube roots in the numerator: the point is to 'get rid of them' in the denominator)

[lethal path]

you have to read the question and check if it wants you to rationalise your answer

[neon geyser]

but on some problems i can rationalize without the squares

[neon geyser]

like this one

so idk when i should add them bcs there are also problems that have them

[neon geyser]

like on here

[lethal path]

yes, cause you only need the squared numbers for cube roots

[neon geyser]

ohhhhhhh

[lethal path]

the square root case is the simplest one

you always have $\sqrt{5} \sqrt{5} = 5$

[grand pond]

south

[neon geyser]

okayy

[lethal path]

but for cube roots, you could either have $\sqrt[3] {2} \sqrt[3] {4} = \sqrt[3] {8}$

[grand pond]

south

[lethal path]

or $\sqrt[3] {4} \sqrt[3] {2} = \sqrt[3] {8}$, so that one with the 2 isn't squared

[grand pond]

south

[neon geyser]

okayy

[neon geyser]

okie tysm!

.close

[midnight plank]

Channel closed

Closed by @neon geyser

Use .reopen if this was a mistake.

[midnight plank]

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[proud abyss]

i do not know where to start from

[tall bronze]

Hello

Soo

@proud abyss you need to show that

where the sum is over all nonempty subsets of the set ({1, 2, \ldots, n})

[grand pond]

YZYBlueBoy22

[proud abyss]

right

[tall bronze]

Understand the sum.

For each subset ({a_1, a_2, \ldots, a_k}) you take the product of its elements.

[grand pond]

YZYBlueBoy22

[tall bronze]

Then you sum up the reciprocals of these products.

You have to expand the product.

Do you have a clue how to do it?

[proud abyss]

so, for instance, if n = 2 then its subsets would be {1}, {2}, {1, 2} and then we do 1/1 + 1/2 + 1/1.2?

[tall bronze]

Exactly!!

[
\frac{1}{1} + \frac{1}{2} + \frac{1}{1 \times 2} = 1 + \frac{1}{2} + \frac{1}{2} = 1 + \frac{1}{2} + \frac{1}{2} = 2.
]

[grand pond]

YZYBlueBoy22

[tall bronze]

@proud abyss

The product is

[
\prod_{i=1}^n \left(1 + \frac{1}{i}\right) = \left(1 + \frac{1}{1}\right)\left(1 + \frac{1}{2}\right) \cdots \left(1 + \frac{1}{n}\right).
]

[grand pond]

YZYBlueBoy22

[tall bronze]

This equals.

[proud abyss]

n+1

[tall bronze]

[
\frac{2}{1} \times \frac{3}{2} \times \frac{4}{3} \times \cdots \times \frac{n+1}{n} = \frac{n+1}{1} = n + 1.
]

[grand pond]

YZYBlueBoy22

[tall bronze]

Correct!

Relate the sum of the subsets

[proud abyss]

does this give a sum of terms of the form 1/(a1.a2.a3....ak)? (a1, a2, ..., ak) is a subset of {1, 2, ..., n}

[tall bronze]

Exactly

[
\frac{1}{a_1 a_2 \cdots a_k},
]

[grand pond]

YZYBlueBoy22

[proud abyss]

yeah

[tall bronze]

({1} \rightarrow \frac{1}{1})

[grand pond]

YZYBlueBoy22

[tall bronze]

({2} \rightarrow \frac{1}{2})

[grand pond]

YZYBlueBoy22

[tall bronze]

({3} \rightarrow \frac{1}{3})

[grand pond]

YZYBlueBoy22

[tall bronze]

({1,2} \rightarrow \frac{1}{1 \times 2} = \frac{1}{2})

[grand pond]

YZYBlueBoy22

[tall bronze]

({1,3} \rightarrow \frac{1}{1 \times 3} = \frac{1}{3})

[grand pond]

YZYBlueBoy22

[tall bronze]

({2,3} \rightarrow \frac{1}{2 \times 3} = \frac{1}{6})

[grand pond]

YZYBlueBoy22

[tall bronze]

({1,2,3} \rightarrow \frac{1}{1 \times 2 \times 3} = \frac{1}{6})

[grand pond]

YZYBlueBoy22

[tall bronze]

All these terms gives n=3

[proud abyss]

right

[tall bronze]

[
\sum_{\text{all subsets}} \frac{1}{\prod a_i} = n + 1.
]

[grand pond]

YZYBlueBoy22

[tall bronze]

Removing the empty subset's contribution (which is 1).

[
\sum_{\text{all nonempty subsets}} \frac{1}{\prod a_i} = (n + 1) - 1 = n.
]

[proud abyss]

it becomes n

[grand pond]

YZYBlueBoy22

[proud abyss]

all right, got it! thank you

[tall bronze]

My pleasure

[proud abyss]

.close

[midnight plank]

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[last slate]

yoyoyoo

[last slate]

when finding triangular form of a matrix to find its determinant easier, is that the same as dont elementary row operations?

like guassian elemination?

[abstract birch]

wdym

you can transform a matrix to upper or lower triangular form by doing elementary row operations

which is the same as gaussian elimination

if thats what your asking

[spiral rock]

there is also triangulation

which is finding a triangular matrix that is similar to your matrix

in C its always possible to do that

and its not the same as doing row operations

[last slate]

yes

my book was facotring put numbers

out*

[spiral rock]

yeah this is the same as gaussian elimination, but you keep track of changes to the determinant as you do the row operations

[midnight plank]

@last slate Has your question been resolved?

[midnight plank]

Channel closed

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[midnight plank]

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[jovial hound]

How would I go about integrating the second part? Was it a good idea to split it or

[blissful pier]

v^5/v^3=v^2

then power rule would be best

[jovial hound]

OH LMAO

[blissful pier]

sorry forgot how to do algebra for a sec

[jovial hound]

IM SLOW

Thank u I was NOT thinking

[blissful pier]

yeah also on the first one you could've just one v^2/v^3=1/v, and obviously int 1/v=ln|v|+C

[jovial hound]

.close

[midnight plank]

Channel closed

Closed by @jovial hound

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[midnight plank]

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[last slate]

yo

[last slate]

is this right

[waxen musk]

you know you can check your work with rref on a calculator

[blissful pier]

appears to be, but probably not the most efficient way to RREF this matrix

[last slate]

do i have the concept right

like did i understand what they meant

[waxen musk]

oh column operations?

youre doing row ops here

[last slate]

thing is there are multiple ways to do this

either find cofactors

turn it triangular

or make a column all 0s except for 1

do all of them work the same?

and used in all cases?

[last slate]

well no

theyre saying to clear out a23 and a33

so i just did row operations

[waxen musk]

oh ok

[last slate]

is that what they wanted?

[waxen musk]

they want det here

[blissful pier]

nvm I did not read the instructions of the problem

[waxen musk]

neither did i completely lol

[blissful pier]

I thought they wanted you to get it in RREF lmao

[last slate]

@waxen musk btw is this observation correct?

[waxen musk]

i believe so

or make a column all 0s except for 1
though this only tells you if det=0

[last slate]

wdym?

i thought that

[waxen musk]

well hold on

on the cofactor expansion? maybe
in general? its for det=0

[last slate]

you could find the determinant like that

by just taking 1 column

[waxen musk]

i realize its not entirely clear what you meant

[waxen musk]

so, your rref works here, but you need to be clearer about how youre using it to find the determinant

[last slate]

like what they did here

does this work on all 4x4 matrices if i wanna find their determinant?

[waxen musk]

oh this is just the standard method to finding det, and you dont need rref for it

actually, rref will lose the scales here

[last slate]

i can manually make a column have 0s to make it look like their matrix?

like is that what this question wanted

[waxen musk]

i think it wants you to do this by cofactors

for example, here is one cofactor and its relevant matrix

[last slate]

but theyre saying make 0s..

[last slate]

and making a column 0s looks like this

or is it not the same cause this is 3x3 and that is 4x4?

i honestly dont know at this point

[waxen musk]

hold on

theyre saying that we can take advantage of the 0s to make det easier

because 0 C = 0

because there are actually several ways you can expand cofactors

what theyre doing is picking on way which makes the most 0s immediate

which cuts down on how many cofactors you have to write out

make sense?

[last slate]

so like i would still do cofactors but im ignoring the ones multiplied by 0s for obvious reasons

is that what you meant

[waxen musk]

yes, if i understood you correctly

[last slate]

so basically, creating the 0s is just a way to make expanding co factors easier

but its technically the same process

because youre just rewriting the equations they still hold true

[waxen musk]

we arent creating 0s per se, were just noticing 0s

[last slate]

wdym? we are doing row operations no?

[last slate]

wait thats if its already there right

[waxen musk]

not here

[last slate]

but say you have a matrix with no 0s

and you know roiw operations can give you 0s

ah alright

[waxen musk]

yeah, if det=0, then rref has to also give you det=0

[last slate]

wait what

thats a seperate point right?

[waxen musk]

yeah

other than finding 0 determinants, row ops arent super helpful in finding det because they allow arbitrary scaling

[last slate]

are you saying that without modifying the matrix if i take a regular determinant by cofactor expansion and i get 0 then i dont have to worry about rewriting anything cause the det will just be 0?

is that what youre sayin g

[waxen musk]

more like, if you have a matrix A and det(rref(A)) = 0, then det(A) = 0

and thats really all we use rref for in finding determinants

[last slate]

ohh

well yeah

i mean yeah

[waxen musk]

what they want you to do is find the nice cofactors of the matrix to make it easy

[last slate]

throguh doing an operation with this concept right

[waxen musk]

yeah, this is cofactor expansion

[last slate]

but the 0s part

this isnt RREF

but there are 0s

[waxen musk]

exactly

they chose these cofactors

[last slate]

generally speaking, is choosing any row/ any column and doing its cofactor expansion give us the determinant?

[waxen musk]

yeah

[last slate]

in all matrices

[waxen musk]

every cofactor expansion has to work

[last slate]

ah okay

[waxen musk]

it has to do with alternating products, which is a bit technical of a proof for these purposes lol

[last slate]

is det(RREF(A)) the same as the triangular process?

[waxen musk]

actually kind of

its involved

i forgot about this one lol

[waxen musk]

this has to do with the fact that either det(rref(A)) = 1 or det(rref(A)) = 0

[last slate]

is having a matrix in a lower triangular pattern the same as RREF

[waxen musk]

no, the rref should be the indentity or have 0 rows at the bottom

these are called triangular matrices

and because of how cofactor expansion works, the det of any triangular must be the product of its diagonal

[last slate]

ah i see

i was thinking of that too

[waxen musk]

yeah triangulars happen to be very nice matrices for a lot of things

[midnight plank]

@last slate Has your question been resolved?

[midnight plank]

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[pearl hull]

If I wanna find the negation of this statement, can I say
$\exists x(x \le -2 \vee x \ge 3)$?

[grand pond]

🌙 ЅκψΑиdΝιɡħτ

[scenic wyvern]

looks correct

[pearl hull]

Alright, lemme do the rest

$\exists x(x \le -2 \vee x \ge 3)$\
$\exists x (x < 0 \vee x\ge 5)$\
$\forall x (x < -4 \vee x> 1)$\
$\forall x (x \le -5 \vee x\ge -1)$\

[grand pond]

🌙 ЅκψΑиdΝιɡħτ

[scenic wyvern]

all correct, nice

[pearl hull]

appreciate it

.solved

[midnight plank]

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[midnight plank]

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[last slate]

yo

[last slate]

this is on matrix column operations, they factored out a 2 from the first column, but then doesnt the 2 just multiply into the whole matrix??

[sharp coral]

not in determinants

[last slate]

wdym

[sharp coral]

2 * det(matrix) = det(that matrix with one of its columns multiplied by 2)

so multiplying the determinant of a matrix by 2 is not the same at all as multiplying the matrix by 2

[last slate]

but thats not a determinant being multiplied its just a cilumn operation

like theyre just saying factor out a 2

they havent taken the det yet

[sharp coral]

the vertical bars mean determinant

[last slate]

oh..

[last slate]

same for row operations right

like the factoring thing

[sharp coral]

yes, the same applies to row operations

[last slate]

but then when you just put the number on the outside its not clear from where you factored out

and even when you find the determinant

like you multiply that number you factored out by it?

[sharp coral]

does it matter which row/column you factored it from?

[last slate]

yes

its like a system of equations right

i dont see how factoring like that makes sense

[sharp coral]

yes, the equation is saying the original determinant = 2 * this new determinant, so to calculate the original determinant you end up multiplying the new one by 2

[last slate]

but again i dont understand why that kind of factoring is valid

like mathematically

[sharp coral]

the column operation of multiplying a row by 1/2 would produce a determinant which is 1/2 of the original. so we cancel out the effect of that by multiplying it by 2

[last slate]

you lost me here tbh

all what its in my brain is whats factored out on the outside

[sharp coral]

the same logic can be applied to columns

[last slate]

wait so determinants in general is just factoring out a value in some row / column?

thats literally what it is?

[sharp coral]

that's one of the properties that the determinant has

[last slate]

so whenever i see that a row or a column in any matrix can have a number factored out i just factor it out and thats my determinant??

[sharp coral]

well you still have the rest of the determinant to compute

it just is now an easier determinant to compute than before

[midnight plank]

@last slate Has your question been resolved?

[midnight plank]

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[keen seal]

why did they suggest k and k+1? what if its the squares of two odd numbers or two even numbers intsead of having dfferent parity

[keen seal]

wouldnt two even numbers squared give an even number

[lyric charm]

have you actually tried following the hint

like sure, the difference of two squares of the same parity will only ever give you even numbers,

but you should read carefully what they ask you to prove

you're asked to prove

every odd number is a difference of squares
and NOT asked
every difference of squares is an odd number

[keen seal]

whats the

difference in this

can i put both as 2k + 1 = a^2 - b^2

[twilit field]

what if one is odd and one is even

[lyric charm]

well a^2+b^2 is a sum of squares...

[keen seal]

sry i meant

[lyric charm]

"all A are B" and "all B are A" are logically speaking converses to each other.

"all Harvard students are geniuses" and "all geniuses are Harvard students" are two very different statements, do you agree?

[keen seal]

yea

its different

but how could i write it down differently

[lyric charm]

write what down differently from what

[keen seal]

so like every odd integer is diff of two squares (2k + 1 = a^2 - b^2) and every difference of square is odd number ( a^2 - b^2 =2k + 1 =)

[lyric charm]

let's backtrack.

have you actually tried following the hint that they give you here?

[keen seal]

yea ik it gives odd

but i dont get why this

taht they suggest

[lavish venture]

when a problem starts off by showing something holds for all … it’s a good idea to consider an arbitrary thing satisfying that

start off with an odd integer and show it is the difference of two squares

[keen seal]

Yes. K and k + 1 are arbitrary but when the two squares are even it gives an even and I’m confused here

[lyric charm]

ok so

$(\forall k)(\exists a)(\exists b)(2k+1=a^2-b^2)$

[grand pond]

Ann

[lyric charm]

this is the statement which you have to prove

[keen seal]

ohhh okkok

now it makes sense ty

.close

[midnight plank]

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[midnight plank]

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[foggy inlet]

anyone know how to do circuits

[midnight plank]

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

[sharp coral]

what about it?

[foggy inlet]

i need help finding the answers beow

below

but idkd where to start

[midnight plank]

@foggy inlet Has your question been resolved?

[sharp coral]

can you find the open circuit voltage and short circuit current?

[midnight plank]

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[vast glen]

I need help doing a not very nice integral

[lusty furnace]

what have you tried

[vast glen]

One sec

and i want to see if $|z_2|<1$ where $z_2=-\frac{ai}{b}+\sqrt{1-\frac{a^2}{b^2}}$

[grand pond]

Alrik

[vast glen]

And i know it is, because if not the integral will be zero. I just dont know how to show it

[vast glen]

Its not a great argument for exams

[vast glen]

all i need is this

If i get this i can find the order of the pole (1), residue and wham bam we're done

[midnight plank]

@vast glen Has your question been resolved?

[vast glen]

lets break it up in smaller problems. First, if a>b>0, then a-sqrt(a^2-b^2)<b

i want to show this

<@&286206848099549185>

[midnight plank]

@vast glen Has your question been resolved?

[vast glen]

:c

.close

[midnight plank]

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[near brook]

i need help with finding range and increasing and decreasing intervals

[near brook]

like it fr does NOT make sense esp the intervals

theres NO points

[shell wigeon]

... did you forget to post f(x)?

[near brook]

oh mb

@shell wigeon

[frozen talon]

what do you mean by this?

[shell wigeon]

What exactly is your question?

[near brook]

okay look so

i just dont understand how to get the increasing and decreasing intervals

it doesnt make sense

[frozen talon]

what is an increasing interval?

[near brook]

above the 0

[frozen talon]

huh, I would've said it's an interval where the function is increasing

you can be above the y=0 line and going down

[near brook]

but its hard to tell because theres arrows going left and right

[shell wigeon]

Why are there multiple colors? Who wrote what?

[near brook]

that was my teacher lmao

[shell wigeon]

All of it?

[near brook]

yes

[frozen talon]

did you differentiate f yet?

[shell wigeon]

Damn, your teacher is wrong on the range

[near brook]

wdym

[frozen talon]

lmao true

[frozen talon]

do you know the derivative of f yet?

[near brook]

bruh im in adv func and shes out here selling my grade

[near brook]

i dont recall

[frozen talon]

or are you just supposed to be eyeballing a graph

[near brook]

honestly i think so

[shell wigeon]

For a simple function like this I guess that's fair

[frozen talon]

so you don't know derivatives?

[near brook]

nope

[frozen talon]

ok

[near brook]

i have like a quiz on a chart similar to that but i just cant wrap my head around these random intervals

[shell wigeon]

This is f(x)

[near brook]

and like test values? What do test values gotta do with this lol

[near brook]

yes thats how i wouldve done it

[shell wigeon]

Would you know how to find the intervals with this graph?

[near brook]

can i tell u what would I think the intervals would be

[shell wigeon]

Of course

[near brook]

Increasing Int : ( -4, infinity) u - Infinity, 2) (-infinity, -1)
Decreasing Int : (- infinity, -4) u (-1, infinity) u (2, - infinity)

[shell wigeon]

Why -4?

[near brook]

for which

[shell wigeon]

Any