help-41

[sinful breach]

Setting unknown is an dead end for me

There an elegant observation

[split kraken]

I haven't done linear algebra in a while

[patent raptor]

me too

[sinful breach]

It’s fine think of anything that find diagonalizer instantaneously

Like decomposing the rings

[split kraken]

it kind of shows, because I've been getting burned by Lee's examples for not knowing linear algebra well enough

[patent raptor]

well i can tell it's symmetric

[sinful breach]

Well I felt like maybe I’m most junior

[grizzled pagoda]

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

[sinful breach]

Wrong matrix I think

Should he this one

It has been a year for me too

Even this one it wasn’t easy for most I remember most of classmates failed

[split kraken]

which year of study are you in, out of curiosity?

[sinful breach]

Standard method has a length of 2 pages

3rd

Anyone not curious how to do two line solutions on that beast matrix

[split kraken]

honestly, my interests lie not very much in algebra

[patent raptor]

well it's almost a diagonalmatrix

[split kraken]

so I'm not terribly interested

[patent raptor]

or opposite haha

[sinful breach]

Like how about I let it be $\sigma \otimes A$

[patent raptor]

signa

[grizzled pagoda]

meow

[patent raptor]

what sigma

[sinful breach]

Where sigma is 0 1 \ 1 0

Got it right away right

Omg it’s like trivializing the entire things

[patent raptor]

what are you meowing about

[sinful breach]

Then I know instantly the eigenvalues of pm eigenvalues of A

Like tensor product s property

[patent raptor]

[sinful breach]

Like doing this using standard method you’ll die

I promise

2 pages of length

[patent raptor]

I understood nothing 🔥

[sinful breach]

Tensor product 🤭🤭🤭

[patent raptor]

all i know it's trivial 🔥

[split kraken]

what're your main mathematical interests, meow?

[patent raptor]

why is my hand on your face

[sinful breach]

And for characteristic polynomial I made it even more trivialized

[patent raptor]

now we can also not only denote things trivial

we can trivialize

[sinful breach]

(Me numbers I think) 3 by 3 matrix I used formula x^3-trAx^2+1/2((trA)^2-tr(A^2))-detA

[patent raptor]

how dare I to say you are a cs student

[sinful breach]

This formula is like destroy all sort of 3 by 3 matrix problems

I derived it with newton identity and Cayley Hamilton s theorem

[split kraken]

still asking this

[sinful breach]

Number theory?

arithmetic geometry

[split kraken]

interesting

[sinful breach]

I probably will want to dig some gold too

[split kraken]

what do you mean by that?

[sinful breach]

I want to take elective stochastic process

And go to finance for a couple years

[split kraken]

cool

[sinful breach]

I mean I need money too right?

[patent raptor]

no

[sinful breach]

That characteristic polynomial formula is like insane btw

[patent raptor]

i wish i was as intellectually smart as you

[sinful breach]

That basically destroyed my LA exam

[patent raptor]

you seem to meow, know about alot of stuff

[sinful breach]

Like with direct derivation of eigenvalues what can’t you do?

For LA hahahaha

[patent raptor]

I thought you were pre university

your ass is 3rd year

in theoretical math

[sinful breach]

Can you imagine using cofactor copium

[patent raptor]

I have no idea what that is 🔥

maybe @split kraken knows

[sinful breach]

Cofactor expansion

[patent raptor]

OH

the goat

[sinful breach]

Like that formula I came up with

[patent raptor]

carried me through all these troublesome determinants

[sinful breach]

Directly avoided cofactor copium

Hahahaha

[patent raptor]

Laplace has a special la Place in my heart

[sinful breach]

With that formula I derive characteristics polynomial of any 3 by 3 matrix with ease

In 20 seconds

[patent raptor]

can you derive the world for me in 10 seconds

[sinful breach]

I hate cofactor expansion 😭

[patent raptor]

hahahahahhahaah

[sinful breach]

With that I will fail LA

[patent raptor]

nooo

it's like l'hopital makes your life easier

the two L's create a W

damn i am so cooking wordly

[sinful breach]

I did write principle minor on answer sheet though to show the teacher I did as claimed used “cofactor expansion” not anything else

[patent raptor]

are you afraid of integrals

[sinful breach]

How can you be good with these calculations though

Aren’t they very hard

[patent raptor]

it's not just calculations

[sinful breach]

Yes and no

[patent raptor]

it also requires an abstract way of thinking to solve these

[sinful breach]

I am actually quite good with integral but not computational densed one

[patent raptor]

wth 😂

you and your densed

[sinful breach]

I can solve Cot(arctan(x/b)) something like that

[patent raptor]

oh

[sinful breach]

There are clever substitutions like i let u=icosh^(-1)t e^u du into it

Something like that

But for stuff like ellipsoid surface area I just simply can’t

[patent raptor]

double integrals?

or rather surface itnegrals

[sinful breach]

Like integral in general I just hate computational densed one

I like the one which you solved by one substitution

[patent raptor]

I see you just hate the word computation dense

well most of the time it's so satisfying finding a neat parameterization and everything cancels neatly out

[sinful breach]

Substitution or Euler equation can’t then I try Taylor’s, depending on context I might use tan x/2

If I still can’t see it clearly till the end I give up

[patent raptor]

Surface area of the ellipsoid [ S : \frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2} = 1 ]
[ \iint_S \norm{\mathbf{s}_u \otimes \mathbf{s}_v} : \dd u \dd v ]

[sinful breach]

Don’t let me see this shit

Fuck

[patent raptor]

hhahahaha

we would make a good team

[sinful breach]

I swear this integral will kill human

…

[grizzled pagoda]

𝔸dωn𝓲²s

[patent raptor]

neat maybe i even solved it once somewhere sometime

[sinful breach]

It’s 3 here in holland

[patent raptor]

for the surface?

[sinful breach]

Omg I am having nightmares seeing ellipse integral

[patent raptor]

oh you mean 3 am

yea here too

😂 caught me off guard

[sinful breach]

Dreaming

I mean I had a dream seeing ellipse integral

Got to be not real

[patent raptor]

even though you and me differ, we are isomorph 🔥

[sinful breach]

🫠🫠🫠

[patent raptor]

https://www.desmos.com/3d/gctw7jjusk

this is what you afraid of lmfao

[sinful breach]

You gotta love calculus

Omg 😭

[patent raptor]

I do

I feel like

I am actually doing something

[sinful breach]

I am actually quite grateful that Real Analysis isn’t computationally complicated

[patent raptor]

Do you like coffee?

[sinful breach]

I don’t know I feel like i really needa sleeping 😭😭

[patent raptor]

oh then go to sleep lol

what's stopping you

[sinful breach]

I feel that’s quite unacceptable on a online server 🫠

[patent raptor]

what

[sinful breach]

I don’t know.. anyway

[patent raptor]

yea yu yapped a lot

time to sleep

[sinful breach]

I want to leave a question which I want to see if there’s a solution

[patent raptor]

sure

[sinful breach]

An integral like me type it

$\int\frac{\sqrt{x-1}-\sqrt{x+1}}{\sqrt{x-1}-3 \sqrt{x+1}} $dx$

What’s wrong with it

I double anyone can help me with solving this one

This integral has elegant 5 lines solution btw

<@&286206848099549185> anyone tries this one see if you can solve within 5 lines

[amber wasp]

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

[grizzled pagoda]

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

[patent raptor]

@muted gate it's been hours

[sinful breach]

Tbh this one if you don’t use very conditioning substitution then you can never solve it I think

You two wanna try🤭

[static shoal]

Try Rationalizing it

[patent raptor]

Is this one you came up with?

[sinful breach]

You can try it

This integral if you don’t use a very brilliant substitution you always end up in a dead end

Wolfram has solution but it doesn’t have step by step I’m afraid

[sinful breach]

Kinda since I know the method for it

[patent raptor]

it doesn't look promising

[sinful breach]

I’ll see tomorrow if anyone can ever solve it

A hint

Euler formula

[static shoal]

Euler formula?

[sinful breach]

Combined with hyperbolic functions (another hint)

[patent raptor]

,w Integrate[(Sqrt[x-1]-Sqrt[x+1])/(Sqrt[x-1]-3Sqrt[x+1]),x]

[grizzled pagoda]

Results provided by WolframAlpha

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

Requested by adoniszgks

[sinful breach]

Five line solution I want

I will give it by tomorrow afternoon

[patent raptor]

so much to i hate computational dense

[sinful breach]

But it’s not dense

[patent raptor]

well you will have to convince me haha

[sinful breach]

Last hint

Domain doesn’t matter, the domain will preserve itself

[static shoal]

Why don't you solve the problem instead

[sinful breach]

Well this integral is fun so I share it

This is one of the most elegant integral I have seen in actual sense

[patent raptor]

I wanna give you one too

[sinful breach]

Let me see

Delta epsilon is preferred

that integral I actually have five line proofs

[patent raptor]

show

[sinful breach]

If you’re interested then try it😊

Partially I can

[patent raptor]

No I wont do it

[patent raptor]

,, \int_0^\infty \frac{\ln x}{x^2+2x+4} : \dd x

[grizzled pagoda]

𝔸dωn𝓲²s

[sinful breach]

This one looks so nasty 😭😭

Improper

Maybe feymans

Can you actually which kind of substitution I did for that integral? I will try this one if I have time tomorrow bcs I actually have lectures

It’ll probably take me sometime

[patent raptor]

hahaha

[patent raptor]

complex sub?

would never think of that

reminds me of a double integral

[sinful breach]

Told ya the solution for that integral is almost stunning

[patent raptor]

i am still curious

if you are that stunning

[sinful breach]

I am socially awkward I guess

Have you have any idea of the substitution method

[patent raptor]

[ \iint_S \sqrt{\frac{1-\frac{x^2}{a^2}-\frac{y^2}{b^2}}{1+\frac{x^2}{a^2}+\frac{y^2}{b^2}}} : \dd x \dd y ]
[ S : \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \text{ where } x,y > 0 ]

[grizzled pagoda]

𝔸dωn𝓲²s

[sinful breach]

I hate square root

[patent raptor]

This required me two simple substitions to get me to the answer without actually integrating it

[sinful breach]

Great I’ll see tomorrow

Omg I can’t imagine I will do integral

[patent raptor]

yea fuck epsilon delta

[sinful breach]

They are fun

Omg that’s so rule

Rude

Like without it you can’t even have rigorous definition of limit

I think that puzzle eliminates all candidates of integral bee though

[patent raptor]

yea you are so right

what are derivatives

limits

so

we would be doomed without your delta epsilon

😂

[sinful breach]

The one I posted, if my memory serves correctly, that integral is solved by no body for the integral bee

[patent raptor]

and integrationttoo

[sinful breach]

Precisely

[patent raptor]

i am afraid tho this channel will close by itself until tmrw

[sinful breach]

That’s why analysis is the demonstration of pure art of mathematics

😭

[patent raptor]

integration is also art!

[sinful breach]

I am actually curious who came up with such integral

Proof is an art

[patent raptor]

prove it

[sinful breach]

Without delta epsilon, how can you even say anyone about what is the limit?

Goes to infinity is so vague

Basically what’s the limit

[patent raptor]

idk

tell me

[sinful breach]

With delta epsilon we know

How to show that a set has greatest lower bound?

By definition?

[patent raptor]

infimum?

[sinful breach]

Yek let’s do it by axiom of completeness

Which will make thing a bit more challenging

How to show that 1/n^2 converges and prove it?

To be honest this one I actually don’t know

[patent raptor]

squeeze theorem 😎

[sinful breach]

But with delta epsilon

Btw I will reveal the method for the integral

[patent raptor]

reveal yourself who are you

what is it with you teaching me delta epsilon around 4 am

[sinful breach]

The correct substitution is $e^{i\alpha}$ where $\alpha=\arccos(x)$

This substitution completely trivialized the integral

[patent raptor]

😂

[grizzled pagoda]

meow

[patent raptor]

This substitution completely trivialized the integral

[sinful breach]

Isn’t this elegant enough

Yes it did

[patent raptor]

trivialized is my new favorite word

I will trivialize you

[sinful breach]

I don’t believe there’s more efficient and concise way of doing it

Just that you have to think of it

I have given the correct substitution

Yes

Elegantly

One integral which MIT students can’t solve?

No

You mean substitute with tan^2

It won’t work

This integral is almost notorious

Using trigonometric composition might be a way but direct substitution is impossible

Composition I mean nested trigonometric functions and their inverse

If I remember the standard proof is very densed in term of parts substitutions

This is a well established method I think

But I’m not that into integration though

I know some very elegant ones

I don’t know if I remember the name right this is called auxiliary integral

Expression too long

The one I posted

Still too long

I’ll try to type it fine

$\frac{x-\sqrt{x^2-1}}{4}+\frac{1}{2}\ln\bigg|{\frac{2(x-\sqrt{x^2-1}+1)^{\frac{3}{2}}}{x-\sqrt{x^2-1}}\bigg| +C$

Where’s my expression

Where’s my latex wrong

Finally

It looks different than wolfram alpha s solution but they are equivalent

[grizzled pagoda]

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

[sinful breach]

More appealing

This one looks significantly more concise than the formula from wolfram alpha

And this one is only real but wolfram one takes complex value

Since the complex parts got canceled by integration

Yes

Why

You can try

Let me see

It won’t be simpler very much

This integral is nasty

You see this integral had to be approached initially by hyperbolic substitution

Because of some very important property

Of the inverse of hyperbolic substitution

Which is extremely computational dense

The ln term

But always try! Remember if you can solve this without using that substitution not exaggerating, most of professors won’t do better than you in integration

This one is easy

Let x=cosht

dx=sinhtdt

Then we have integral dt = t

Recall that x=cosht

T=arccoshx

By definition arccoshx

$arccosh(x)=\ln(\sqrt{x^2+1}-x)$

Solved

If I didn’t fuck up somewhere

[grizzled pagoda]

meow

[sinful breach]

You see this one you gave me is typical hyperbolic integral

But hyperbola is extremely complicated things

The one you gave me is a trivial integral

And indeed hyperbolic substitution can solve that question

But extremely complicated

[sinful breach]

Good luck

Okay good night I’m gnna sleep too 🥱

That integral is basically just a hyperbolic related something I feel like

You can’t solve it without anything else

Math stackexcange has many people tried it

4

I can’t find the link but this one is famous

Haha study hard integrating fun

Good night

.close

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[exotic olive]

really need help here

[amber wasp]

Please don't occupy multiple help channels.

[exotic olive]

i have to write everything down step by step

can anyone help

[amber wasp]

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

[exotic olive]

please i need help

i asked chatgpt but is it right here

[amber wasp]

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

[exotic olive]

clearly someone has no idea what im trying to say

<@&286206848099549185>

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[exotic olive]

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[light musk]

does someone mind double checking my work for this problem?

its quite a bit different from the books answer, so i assume its pretty wrong haha

[amber wasp]

@light musk Has your question been resolved?

[stable kelp]

your u sub is illegal

[brisk leaf]

Hello @light musk

[brisk leaf]

I think it's correct

What's the book answer

[stable kelp]

oh wait

[brisk leaf]

Can you share

[stable kelp]

yeah im tripping

[brisk leaf]

What?

@light musk

[stable kelp]

the book answer is here

[stable kelp]

i think you have the right answer

simplify it

[amber wasp]

Channel closed

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[light musk]

.reopen

[amber wasp]

✅

[light musk]

wait

why would this u sub be illegal

i have a quiz on this tomorrow and i wanna make sure i understand

[brisk leaf]

It isn't

I have no idea why @stable kelp said that

She said she tripping after

So maybe she said it accidentally

Idk???

[light musk]

alright good to know then

thank you

.close

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[ocean sable]

cos(x+1)=6cos(x)

[ocean sable]

solve for x

how do i do this?

like

cos(x+1)-6cos(x)=0

but what now

[amber wasp]

@ocean sable Has your question been resolved?

[steady snow]

$\cos(a + b) = \cos(a)\cos(b) - \sin(a)\sin(b)$

[grizzled pagoda]

DW1

[steady snow]

$\cos(x)\cos(1) - \sin(x)\sin(1) - 6\cos(x) = 0$

[grizzled pagoda]

DW1

[steady snow]

factor out the cos(x)

[amber wasp]

@ocean sable Has your question been resolved?

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[vast crystal]

the most common triangulation of a torus i see is one in which a square is subdivided into 9 squares and then diagonals are drawn such that each square is divided into two triangles. would it also be correct to subdivide the square into 16 squares then again drawing diagonals to make each square have two triangles?

[vast crystal]

and would it qualify as a different triangulation

because the other triangulations i see online seem ridiculous like how would anyone ever come up with that

[amber wasp]

@vast crystal Has your question been resolved?

[amber wasp]

@vast crystal Has your question been resolved?

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@vast crystal Has your question been resolved?

[vast crystal]

.close

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[meager gale]

am confused on what exactly part b is asking for

saving up for two months = 3028.75

what do i do with this value

[wicked girder]

is that from part a

hi again lol

[meager gale]

nah

part a is

2915.smth

wait a sec

2915.90

oh shit

wait

hold on a sec

[wicked girder]

to find interst accumlated over 2 months, its what u paid (3000) minus the prinpcial (part a)

smt like that

[meager gale]

bro

idk why

[steady snow]

did u get part a

[meager gale]

i thought if i put 1500 in the card itd interest it

[wicked girder]

lol its okay

[meager gale]

yea im good

wow

i saw the 2915 val again and i was like "huh this is sus"

anyway

thanks

.close

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[fallow anchor]

,rotate

[fallow anchor]

Help with 13 question, b

.close

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[keen pawn]

$x^2+y^2+2xy=x^2+y^2 \implies 2xy=0 \implies x=0 or y=0$

[grizzled pagoda]

A dense set(Ping when reply)

[keen pawn]

does this work

for if (x+y)^2=x^2+y^2, then x or y is zero

[radiant pumice]

looks good to me

[keen pawn]

thanks

[radiant pumice]

well done

[viral coyote]

Can't they both be zero too

[radiant pumice]

It's not an exclusive or

[viral coyote]

Ah sorry

[radiant pumice]

no worries, it was a good question

[keen pawn]

I think contrapositive works well here

Wait

$2 \leq n \leq p \implies 4 \leq n^2 \leq p$

mp?

[grizzled pagoda]

A dense set(Ping when reply)

[keen pawn]

*no?

[radiant pumice]

that's a valid inference yes

assuming p>1 and n>=2

[keen pawn]

one minute

We can show that the biggest factor of a number is $\floor { \sqrt{p}}$

[grizzled pagoda]

A dense set(Ping when reply)

[keen pawn]

well, $\sqrt{p}$ rather

[grizzled pagoda]

A dense set(Ping when reply)

[keen pawn]

well, other than p

I'll have to prove this now

oops

that's false

[cunning birch]

yeah not necessarily

only show that if p had a factor > sqrt(p)...

then p = nk

where do n and k lie?

[keen pawn]

Let there exist a factor greater than $n$, let this be m

[grizzled pagoda]

A dense set(Ping when reply)

[pseudo crescent]

If and only if btw, its a detail but an important one

[keen pawn]

then have have $p=mk \implies k= \frac{p}{m}$.
But we know that $ m>\sqrt{p} \implies \frac{1}{\sqrt{p}} > \frac{1}{m}$, so $\sqrt{p} > \frac{p}{m}$

[grizzled pagoda]

A dense set(Ping when reply)

[keen pawn]

But no number less than $\sqrt{p}$ divides it, we've thus arrived at a contradiction

[grizzled pagoda]

A dense set(Ping when reply)

[keen pawn]

.close

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[broken latch]

am i wrong?

[mint nacelle]

,w 75.41 = 3.142 (x + 5)^2 - 3.142 * 5^2

[grizzled pagoda]

Results provided by WolframAlpha

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Requested by sooouth.

[mint nacelle]

that's correct

[broken latch]

alright

ty

.close

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[split sail]

Can someone help me with this

[split sail]

Can someone help me with this

Question 5

Ghe one I have crossed is what I did

Ok

So the 22.5 is not correc5

Why doesnt the angle divide into two since there are 2 triangle

Oo ok so I just leave it at 45

Then whats the next step

How do I find h

20? Cus the 2 sides are equal

Ohh. Then where does 45 go to

The yellow one

45?

25

Ohhhhhhhhhhhh

So h also =25

Ohhhhh

Thank u very much

Have a nice day

.close

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Channel closed

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[untold torrent]

!help

[amber wasp]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[untold torrent]

In have a test in 20 miniutee

I need help with 2

[split sail]

ok

well, it is not D, F, A, B, C

what's left?

[untold torrent]

So im just supposed to find out what its not?

[split sail]

see that E has only a cube root

[split sail]

you can use this to win marks

but you should be able to do this

[untold torrent]

What if i have ti show my work

I dont get it

[split sail]

Do it yourself and you'll get it

[untold torrent]

Do i need to simplify cubroot 24x^11

[little widget]

$$
4x\sqrt[3]{24x^11} \
= 4x \sqrt[3]{3 \cdot 8 \cdot x^{11}} = 4x \sqrt[3]{3 \cdot 8 \cdot x^9 \cdot x^2} \
= 4x \sqrt[3]{3 \cdot 2^3 \cdot \cdot (x^3)^3 x^2} \
= 4x \sqrt[3]{2^3 \cdot (x^3)^3} \cdot \sqrt[3]{3 \cdot x^2}
$$

damn latex

$$
\begin{align*}
4x\sqrt[3]{24x^{11}} \
= 4x \sqrt[3]{3 \cdot 8 \cdot x^{11}} \
= 4x \sqrt[3]{3 \cdot 8 \cdot x^9 \cdot x^2} \
= 4x \sqrt[3]{3 \cdot 2^3 \cdot (x^3)^3 x^2} \
= 4x \sqrt[3]{2^3 \cdot (x^3)^3} \cdot \sqrt[3]{3 \cdot x^2}
\end{align*}
$$

[grizzled pagoda]

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

[little widget]

yep good enough

then you cancel out the cubes with the cube roots

do you understand the steps?

[untold torrent]

Kind of

I dont get how the second last step become the last step

[little widget]

if you have a root of a product, you can take the cube root of each term, $\sqrt[3]{a \cdot b} = \sqrt[3]{a} \cdot \sqrt[3]{b}$

[grizzled pagoda]

kaue

[split sail]

well cuberoot(x^3 y^3 ................) = xy..........

[untold torrent]

I didnt know you can do that

[little widget]

this is a property of radicals

[amber wasp]

@untold torrent Has your question been resolved?

[amber wasp]

Channel closed

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[fierce edge]

is it basically just saying a 180 degree rotation from M (from O) sends you to N

and a 180 degree rotation of B (from O) sends you to D?

same logic with X and Y?

hmm interesting solution

makes sense i guess

[amber wasp]

@fierce edge Has your question been resolved?

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[swift spoke]

how can I solve this

[crisp stratus]

hint: 8 = 2^3, 27 = 3^3

[swift spoke]

i did 3^x * 2^-x = 2^3 * 3^3

then what

[swift spoke]

ik

then what do i do

[zinc sapphire]

are you learning logarithms?

[swift spoke]

i still didnt lern them

learn

[zinc sapphire]

Just want to make sure

What methods are you being taught in class

I don’t want to give you something irrelevant to your class

[swift spoke]

just learned exponents today

i learned that "a" needs to be the esame

same

like 3^x = 3

x = 1

[zinc sapphire]

Ok, what exponent can represent the numerator and what exponent can represent the denominator

for the right hand side

[swift spoke]

i did this

[zinc sapphire]

Sorry missed it

You missed the negative on 3^-3

Answer should be more or less clear after

[swift spoke]

yes true

ok what do i do next

[zinc sapphire]

Can you rewrite with the fix just so I can see

I’ll just do it

3^x * 2^-x = 2^3 * 3^-3

[swift spoke]

my answer key says the answer is -3

[zinc sapphire]

Yes

Look at the equation

If we’re given some base to the power of x, and it equals the same base to a real number power, what does that tell us about the x?

Let me write it even more simply

If 3^x=3^-3, what does x equal?

[swift spoke]

-3

[zinc sapphire]

Yep

[swift spoke]

but what happened to the 2^-x

and 2^3

[zinc sapphire]

and if 2^-x=2^3, what does x equal?

[swift spoke]

then shouldnt it be 3/3

=1

[zinc sapphire]

Well… look again

Remember before we said the x in the exponent was equal to the number of the exponent on the right

so if -x=3, what is x?

[swift spoke]

-3

then it should be 9?

[zinc sapphire]

Yeah, so we get -3 in both cases

[swift spoke]

-3 * -3

[zinc sapphire]

Not yeah to what you said

[swift spoke]

wdym

[zinc sapphire]

I said yeah and I wasn’t agreeing it was 9

We’re finding out what x equals, not the total value of the expression

[swift spoke]

oh so the total value of the expression is 9

?

[heady willow]

I think the method you’re doing is too complex

A general rule in maths is any number to the power of -1 means 1/that number

so 5 to the power of -1 is 1/5

[zinc sapphire]

He knows this

[little widget]

the way to go is to just re write the RHS as a power of 3/2

[zinc sapphire]

He’s been using negative exponents to transform the fracs throughout

[zinc sapphire]

I like this better

[heady willow]

so now he’s figuring out how to cube 3 to 27?

[zinc sapphire]

So we get 2^3/3^3, now swap them and pull out the exponent

then we have the same form as (3/2)^x

to swap them you make the exponents negative because we’re moving the numerator to the denominator and vice versa

Both ways work

This is probably simpler and more intuitive like kaue said

[swift spoke]

wut

[swift spoke]

can u like show me in text

so i understand it

[little widget]

$\frac{8}{27} = \frac{2^3}{3^3} = \left(\frac{2}{3}\right)^3 = \left(\frac{3}{2}\right)^{-3}$

[zinc sapphire]

Thanks

[grizzled pagoda]

kaue

[zinc sapphire]

2^3 moved to the denominator will be 2^-3

and likewise for 3^3, if we put it in the numerator it’ll be 3^-3

so 3^-3/2^-3

which is just (3/2)^-3

[swift spoke]

but

if we flipped that bat

part

we need to flip also the other side

so it doesnt work

[amber wasp]

@swift spoke Has your question been resolved?

[amber wasp]

Channel closed

Closed due to timeout

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Available help channel!

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[exotic olive]

so this is my question

[exotic olive]

and i answered this for f(x)

i didnt do g(x) yet but wanted to know if i did everything correctly for domain and range of f(x)

my graph

[exotic olive]

<@&286206848099549185>

[little widget]

,w graph x⁴ - 2x³ - 39x² + 40x + 400

[grizzled pagoda]

Results provided by WolframAlpha

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

Requested by wkaue

[little widget]

the range does not include negative values

[exotic olive]

wdym??

this is my graph

[little widget]

range means all possible outputs

you put (-inf, 0]

[exotic olive]

y values

yeah

[little widget]

there is no negative output

[exotic olive]

OHHHH

okay hold on

sorry im dumb

wait positive inifnity then

so positive +inf, 0 right

[little widget]

other way around

smallest value goes first

[exotic olive]

wait why other way?

oh okay

[exotic olive]

okay okay is that my only error

hold on lemme take another ss

does everything here look good

[little widget]

0 is included and infinity is not included

[exotic olive]

like this

@little widget are you here

[little widget]

hi

no

[ means included

( means not included

(0, inf] would mean 0 is not included and infinity is included

you dont need to say infinity is not included

[exotic olive]

[0, ∞) so like this

[little widget]

yeah

[exotic olive]

okay okay

[exotic olive]

got it everything else looks fine right

im going to do the g(x) rn can i tag you to check everything once i'm finished

[little widget]

yeah if your teacher accepts graphing as justification

[exotic olive]

im following a vid my teacher sent all of us and shes doing it similarly with a diff polynomial fucntion

[amber wasp]

@exotic olive Has your question been resolved?

[exotic olive]

@little widget is this good for g(x)

my graph

[little widget]

the first segment is not [-1, inf)

0 is the lowest y-value, not highest

the range is incorrect

you dont need an union, and you cant put a higher value (inf) before the smaller (0)

[exotic olive]

without a union how would i do it

[exotic olive]

yeah i get the higher value part ill change that

so [0, inf) right

[little widget]

yeah

[exotic olive]

so do i just remove the union

[little widget]

yeah

[exotic olive]

so its 0, inf?

[little widget]

you do need a union for the domain

just look at the graph and see where it is defined

[exotic olive]

i thought for domain it was x vlaues

[little widget]

it is

[exotic olive]

so why is this wrong

[exotic olive]

ok

[little widget]

[-1, inf) includes the hole in the middle

[little widget]

this is the domain

(where the line continues infinitely on the left and on the right)

it includes all values <= -1

so you should have a negative infinity

[exotic olive]

ohhhh yeah okay

okay sorry i was confused

[exotic olive]

okay so [-1, -inf)

[exotic olive]

is this better

@little widget dont want to bother are you still here

[exotic olive]

<@&286206848099549185>

[little widget]

-inf is smaller than -1

[exotic olive]

oh yes let me do that

[exotic olive]

okay how is this

[little widget]

for the range you just removed the union symbol, its supposed to be a single interval

[exotic olive]

oops yeah like this right

[little widget]

yeah

[exotic olive]

everything else looks good right? i just have to compare the two now

[little widget]

it's a bit informal but it's alright

[exotic olive]

thank you i wrote their comparison

theres just two more parts left

[amber wasp]

@exotic olive Has your question been resolved?

[exotic olive]

.closoe

.close

[amber wasp]

Channel closed

Closed by @exotic olive

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

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

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

[exotic olive]

this was my question i had to find domain

and this was my answer

[tranquil shale]

ok

why are you doing this in notepad

[exotic olive]

does everything look good

[exotic olive]

lmaoo i mean i dont feel like writing

<@&286206848099549185>

[exotic olive]

did you check it

[tranquil shale]

yes its correct

even if the parts disagree at -1

it would still have domain R

it just wouldnt be continuous

[exotic olive]

thank you

i didnt give you the graph but u didnt need that right

[tranquil shale]

no

[exotic olive]

okay

[amber wasp]

@exotic olive Has your question been resolved?

[amber wasp]

Channel closed

Closed due to timeout

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Available help channel!

Send your question here to claim the channel.

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

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

[keen pawn]

Consider $T(u+w) = 3(u+w)$, this proves that 3 is an eigenvalue of T.

[grizzled pagoda]

A dense set(Ping when reply)

[keen pawn]

We now consider $T(u-w) = -3(u-w)$, this proves that $-3$ is an eigenvalues of T

[grizzled pagoda]

A dense set(Ping when reply)

[robust isle]

you've managed to prove both

but the question says or

isn't that a little bit concerning to you

[keen pawn]

that is a bit concerning, yes

[robust isle]

but what could go wrong?

[keen pawn]

it doesn't have to be an exclusive or though

[robust isle]

it does not, but it's certainly not always both

[gloomy tide]

overachiever

[keen pawn]

T(u) = 3w
T(-w)=-3u

[robust isle]

the question you should be asking yourself is the following: could one of u + w or u - w fail to be an eigenvector

[keen pawn]

well, u+w certainly doesn't

[robust isle]

are you sure

what is an eigenvector?

[keen pawn]

when both are non-zero

[robust isle]

define it for me

[keen pawn]

A non-zero vector such that $T(v) = \lambda v , \lambda \in \mathbb{F}$

[grizzled pagoda]

A dense set(Ping when reply)

[robust isle]

aha

so there's the word

non-zero

is u + w non-zero?

[keen pawn]

not always

[robust isle]

so we've found our point of failure

now the follow up question is: why can't both fail?

[gloomy tide]

the T in T(v) stands for Too big to fail

[keen pawn]

Let u+w=0 and u-w=0

then that would mean both u, w are zero

[robust isle]

very good

and that's why there's an or in the question

[keen pawn]

I see

thanks

[robust isle]

[keen pawn]

.close

[amber wasp]

Channel closed

Closed by @keen pawn

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

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

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

[exotic olive]

i had to answer for Part B, i already did part A

[exotic olive]

did i do everything correctly

here's my graph

<@&286206848099549185>

[split sail]

I gotchu, let me look

[gray linden]

i believe so

[exotic olive]

thank you so much

[exotic olive]

the left one is -1 right

[gray linden]

yes

[split sail]

I agree with ziming

[gray linden]

but I believe it does touch -1

[exotic olive]

yeah thats what i did

thank you guys

[gray linden]

maybe reword this

but the graph is good

[exotic olive]

am i wrong there

[tranquil shale]

it does not touch -1

[tranquil shale]

thats just floating point imprecision

[exotic olive]

it does eventually no?

[gray linden]

oh

[tranquil shale]

$3^{x+3} - 1 = -1 \implies 3^{x+3} = 0$

[grizzled pagoda]

rain

[tranquil shale]

no solution for x

[soft comet]

Yes

[tranquil shale]

you can't use desmos for everything 😄

[exotic olive]

so its 0?

[tranquil shale]

so whats 0

what r u asking

[exotic olive]

wait is -1 right

[tranquil shale]

$\lim_{x\to-\infty} 3^{x+3} = 0$

[gray linden]

does it not converge?

[grizzled pagoda]

rain

[tranquil shale]

dawg u dont need mathematica for this

it does converge

[gray linden]

nvm

mb

oops

[exotic olive]

do i have to change something i'm confused

[gray linden]

nah ur good

im slow tdy

[exotic olive]

oh okay lmao

[amber wasp]

@exotic olive Has your question been resolved?

[amber wasp]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[verbal lark]

One message removed from a suspended account.

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[quick ridge]

this is tough

[verbal lark]

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[quick ridge]

did you just use x for multiplication

[verbal lark]

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[verbal lark]

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[quick ridge]

looks like $\cross$

[grizzled pagoda]

knief

[quick ridge]

for multiplication

please don’t use that

use a dot

or parentheses

[verbal lark]

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[quick ridge]

then explain this

[verbal lark]

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[quick ridge]

oh

wait

the problem had an x

[verbal lark]

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[quick ridge]

you did product rule

[verbal lark]

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[quick ridge]

i didn’t even notice that

[quick ridge]

you did product rule

[verbal lark]

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[grizzled pagoda]

Kenzo

[verbal lark]

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[quick ridge]

also why are you writing?

you know latex

also

[verbal lark]

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[quick ridge]

instead of * use \cdot

[quick ridge]

write it in latex then print

[grizzled pagoda]

Kenzo

[verbal lark]

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[verbal lark]

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[quick ridge]

weird guy

yea sure but you have a product of two functions

[verbal lark]

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[quick ridge]

no i meant originally

[verbal lark]

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[quick ridge]

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

[grizzled pagoda]

knief

[verbal lark]

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[quick ridge]

lol

[verbal lark]

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[quick ridge]

bro what

[verbal lark]

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[quick ridge]

🥱🥱

perhaps, but it’s due friday

[verbal lark]

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[quick ridge]

yea but wtf is the 2 doing

get rid of him

fuck that dude

[grizzled pagoda]

Kenzo

[quick ridge]

yep

[verbal lark]

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[quick ridge]

set = 0

[verbal lark]

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[grizzled pagoda]

Kenzo

[verbal lark]

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[quick ridge]

not really

[verbal lark]

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[grizzled pagoda]

Kenzo

[verbal lark]

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[quick ridge]

continue on

[verbal lark]

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[grizzled pagoda]

Kenzo

[verbal lark]

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[grizzled pagoda]

Kenzo

[verbal lark]

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[grizzled pagoda]

Kenzo

[verbal lark]

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[quick ridge]

daniel

[verbal lark]

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[quick ridge]

fire

[verbal lark]

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[quick ridge]

yep

[verbal lark]

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[quick ridge]

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[quick ridge]

tbh, don’t give a fuck about classifying it

just compare the y values

when you plug those in it’s obviously zero

oh wait no interval is given

[verbal lark]

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[quick ridge]

what is

[verbal lark]

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[quick ridge]

yea i know but they didn’t restrict it

[quick ridge]

first derivative test

or second derivative test

[verbal lark]

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