help-0

[tame tangle]

And what do you get when you "open" the brackets?

$\frac{14}{5}i -\frac75 j$

[ocean seal]

Void Walker

[tame tangle]

Wait...

If what I'm seeing is correct, this worked solution is incorrect...

Can you please post the values of both a and b vectors

[proper garnet]

that 3was the question

im doing pt b now

[tame tangle]

pondering music

I believe this is out of my current knowledge; with the only answer I can provide is "the statement which has confused you, is wrong"

If anyone else is reading this channel, I would like to request them to pitch in

I may as well be wrong

[proper garnet]

yea i think the textbook solution is wrong but its been checked over a million times before it was published

thats y im ocnfusedxc

[tame tangle]

I mean, did a math guy check it? And even so, sign mistakes are one of the easiest to miss

Like get past 10 checks miss

[proper garnet]

i have no iea

idea

its jsut my school textbook

[tame tangle]

It probably is right, thus me saying I may be wrong

[lone heart]

@proper garnet Has your question been resolved?

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[chilly idol]

I need help

im not sure how to start off

[fallen verge]

have you tried factoring?

[untold forge]

do you know how to factor a polynomial?

[chilly idol]

yup

[vale wigeon]

6x^4-13x^3-5x^2, 1, 1

[untold forge]

do that

[chilly idol]

ok

[vale wigeon]

actually no there is a way to factor this while maliciously complying

||x, x, 6x^2-13x-5||

[chilly idol]

ok

[gray isle]

is this a multiple choice question

[chilly idol]

nope

[white aurora]

you can take x^2 as common from the equation

[chilly idol]

ya

[white aurora]

that will help

[chilly idol]

makes it much more easier

[white aurora]

ok

[chilly idol]

i got x^2(2x-5)(3x+1)

[untold forge]

Goodjob 😃

[chilly idol]

so this represents it as an expression

so im done

??

.close

[lone heart]

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[thorn fractal]

I am stuck on this kinematics question for my class and I dont even know where to get the information for this question because its not anywhere in my class...

[lone heart]

@thorn fractal Has your question been resolved?

[thorn fractal]

<@&286206848099549185>

[exotic belfry]

i do not even see a question.

[thorn fractal]

its the screenshot

under my text

[exotic belfry]

in the screenshot is a part of a sentence. where or what is the question?

[thorn fractal]

that is the question...

im in the same boat lol

idk like thats it

[exotic belfry]

well, i cant see a question, but its on me. i wish you good luck for someone else to help.

[lone heart]

@thorn fractal Has your question been resolved?

[thorn fractal]

<@&286206848099549185>

[lone heart]

@thorn fractal Has your question been resolved?

[thorn fractal]

<@&286206848099549185>

[lone heart]

@thorn fractal Has your question been resolved?

[tired geyser]

.

[lone heart]

@thorn fractal Has your question been resolved?

[lone heart]

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[charred plank]

Having a better idea of what I'm looking for i'd appreciate any help.
I'm trying to construct $h(x)$ a bijection from $\mathbb N \times \mathbb N \to \mathbb N$ using the following functions:
$f(n,m) = 2^n\cdot 3^m$, $g(n) = (n,0)$ I'm suppose to use some version of the following proof somehow and construct it formally, but not sure how. Like which x should use f and which should use g.

https://www.cs.cornell.edu/courses/cs2800/2017fa/lectures/lec14-cantor.html

[ocean seal]

meitar5674

[wild trail]

that doesn't look like a bijection

ah okay, you're supposed to use those functions

[charred plank]

Yeah

[wild trail]

what have you tried?

[charred plank]

Was trying to construct those chains and somehow get a closed formula for h but got stuck when trying to go left (use the inverses of the functions)

[charred plank]

Sorry forgot to tag

[wild trail]

are you supposed to construct those chains? can't you just use schroder-berstein theorem to show the bijection

In fact I think that's what your supposed to do

[charred plank]

Well schorder-bernstein tells you there is a bijection but they want me to find that h(x)

h(x) - my bijection

[wild trail]

In that case the given functions won't help

[charred plank]

So those chains in the proof are a way to construct h using f,g I think

yet I'm having trouble how to construct it using those two

[wild trail]

Are you supposed to use those to get the function h(x)?

[charred plank]

Yeah

[wild trail]

cause there are much easier ways to get a bijection

bruh

[charred plank]

YEAH

lol I'm supposed to use those

[wild trail]

one last question, is this a homework problem?

[charred plank]

Sort of, not exactly, why? 🙂

[wild trail]

whoever gave is probably an asshole

[charred plank]

lolllll

[wild trail]

anyway, best of luck

[charred plank]

haha thanks 🙂

[flat dawn]

so basically you have to use f and g to construct a new function h that is a bijection from NxN to N?

[charred plank]

Yes

[flat dawn]

hmm

with all honestly the function g seems a bit useless

my intuition is that you should focus on 2^n

[worn fox]

g would probably be the last function in the composite function from NxN to N wires crossed oop

[flat dawn]

in the sense that you can use a sum of powers of 2 to represent a number

[charred plank]

This is the way to construct it from the site I've sent above

But no clue how to find the close formula

[flat dawn]

that's probably not the intended solution, it's literally the proof of the Cantor-Bernstein theorem

unless you are deliberately being asked to convert the solution from the theorem into a function

[charred plank]

Well I think thats what I'm suppose to do honestly

[flat dawn]

note that the Cantor-Bernstein theorem doesn't necessarily provide a closed (arithmetic) formula but rather the mapping from input to output

"I'm suppose to use some version of the following proof somehow and construct it formally, but not sure how. "

hmmm

[charred plank]

According to that proof if I find when a chain stops in B I'm done but no chain stops at B I think? cuz u can always use g

[flat dawn]

so you start with the pair
so let's say x = (a,b)

so a chain would be
x, g(x), f(g(x)) , g(f(g(x))), ...

so the chain would be
(a,b), (a,0) , 2^a , (2^a,0), 2^2^a, ...

[charred plank]

oh wait a chain can stop at B cuz we look at the inverse

[flat dawn]

if b!=0, then there's no way to reach (a,b)

[charred plank]

that chain is wrong I believe?

[flat dawn]

if b=0, then we end with (a,0)

and you can only reverse (a,0) if a is a power of 2

until you reach some a that is not a power of 2

[flat dawn]

how so

we start with g not f

actually no you're right mb

apologies

so you do start with
(a,b), 2^a 3^b , (2^a 3^b, 0), 2^(2^a 3^b) , ...

now you can only reverse (a,b) if b=0 because of how g works

and as well only if a is in the very form the "tower" of powers of that specific form

[charred plank]

that's like freakish complex find when giving and (a,b) we won't be able to use g^{-1}

[flat dawn]

yes because g is only onto

then you have 4 types of chains

• The chain forms a loop
• Chains that go "backwards" forever without repeating.
• Chains that stop in NxN , That is, they end on some x with g−1(x) undefined.
• Chains that stop in N

when we are going back with f,
we can only do so when b=0, otherwise we are stuck
and again we can only go back when a is of the very form of the "tower" of powers.
eventually you reach an a that is either 0 or not a power of 2

[charred plank]

But I can't tell using that fact if a,b will end at A or B

[flat dawn]

so in that case

h(a,b) = { 2^a 3^b - when b!=0 or a is not in the form 2^x 3^y for some x,y , log_2(a) - when it's not of the first case (and for the case a=0 we return 0) }

[charred plank]

NxN or N

[flat dawn]

no I feel like I butchered something here

[flat dawn]

it's computable hence you can know whether it will end at A or B

f-^-1 will work if the number is composed of powers of 2,3
g^-1 will work if the number if the tuple ends with 0

so say we start with a pair (a,b)

g^-1 will work only if b=0

if b!=0 we stop at NxN

alright this is too annoying lol

might as well run a program that visualizes this

[charred plank]

Yeah thats my problem 😦

No idea if there's a way to really find the closed solution

[flat dawn]

btw are you from Israel

asking bc you have a Israeli name

[lone heart]

@charred plank Has your question been resolved?

[lone heart]

@charred plank Has your question been resolved?

[lone heart]

@charred plank Has your question been resolved?

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[alpine sable]

Hey there, i want to prove that every 3-cycle is a commutator of An, i found this proof online but i do not understand it properly so i'm looking for an explanation

[mortal trellis]

the idea is that if it worked for this 3-cycle then it will also work for others

cause there is nothing special about the numbers 1 4 3 here

if you switched the roles of lets say 3 and 5 you would get a similar identity for (1 4 5)

[alpine sable]

Interesting, what would be the formal explanation, simply that we can find a similar identity for any 3-cycle?

[mortal trellis]

I mean if you want you can replace 1,2,3,4,5 by a,b,c,d,e and get it that way

but like its just different symbols

[alpine sable]

Ho yeah maybe it'll be slightly more clear

[mortal trellis]

just with variables you kinda have more the feel "I could plug in everything I want"

[alpine sable]

Alright, thanks a lot!

.close

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[unreal valve]

Really quick question

[unreal valve]

Are the two sample hypothesis test (dependent and independent) only calculated using t-test?

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@unreal valve Has your question been resolved?

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[fading plume]

I am really struggling on how to show the F(x) = (1+x+x^2)F(x^2)

I can show the second part of the question given this

Any guidance would be appreciated

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[pearl nacelle]

Can anyone let me know if my answer is correct please.

[sour dove]

,rotate

[sour dove]

looks good! One thing you can clean up for it is rather than doing $x = \frac{\pi}{2} + 2\pi n$ and $x = \frac{3\pi}{2} + 2\pi n$, you can do $x = \frac{\pi}{2} + \pi n$

[ocean seal]

MellowDramaLlama

[sour dove]

Do you see why?

otherwise the pi/6 and the 5pi/6 in their current state are fine

but yes those are the answers, nice work 🙂

[lone heart]

@pearl nacelle Has your question been resolved?

[pearl nacelle]

ty

[lone heart]

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[neat canopy]

I first tried to let z = (x + yi). That gave me terms with and without i, so I collected the like terms and set them equal to 0.
I got two equations, one was quadratic and the other linear, both with two variables, x and y. I tried substituting the linear into the quadratic to reduce it to single variable equation but that quickly grew to a messy equation.

So I scrapped that idea and tried to solve it with the quadratic formula, setting a = 1, b = 2i -3 and c = 5 - i. That gave me -15 - 8i for the discriminant, which I have no idea how to solve.

How should I go about solving this?

[median oar]

If nothing works you can always bash it into quadratic formula

[neat canopy]

Yeah that was my 2nd idea, just didn't know how to continue solving the discriminant.

[median oar]

Just bash through it

What do you have for the discriminant

[neat canopy]

-15 - 8i

[median oar]

Do you know euler’s formula

[neat canopy]

yeah

[median oar]

Hmm but that’ll come out pretty ugly

[neat canopy]

[median oar]

Maybe try something like

Let w = \sqrt{-15-8i}

And then solve for a+ib form for w

So -b^2 +a^2 + 2abi = -15 -8i

[lone heart]

@neat canopy Has your question been resolved?

[neat canopy]

shut I'm trying what they recommended

[lone heart]

@neat canopy Has your question been resolved?

[neat canopy]

i got 1-4i for k=0 and -1+4i for k=1, after solving using De Moivre's theorem. But now idk which to use in the quadratic. With the +/- of the quadratic equation, wouldn't this make it have 4 solutions. The choice given in the question only had 2 solutions.

If the bot closes this, anyone can DM if you have any insight on this.

[upbeat hornet]

If you’re concerned about too many solutions, you can always put them back in to see if they work

[neat canopy]

I found out that when I substitute both values for the discriminant as well as using the + and - values of the quadratic formula (for a total of 4 different equations), I get only 2 solutions. The correct answer according to my working is choice D.

Thanks for all those that gave me ideas.

.close

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[thorn tapir]

I'm trying to prove a result in case of ideals on Commutative Unital Rings.

[ocean seal]

rikusp2002

[thorn tapir]

Now what I tried to do was to apply Strong Induction

So I assumed this is true upto n - 1

How do I proceed from here?

Because afaik I need to show the product of the first n -1 ideals is also coprime with the last ideal

then we can apply the case of n = 2 (I already proved this by Set-theoretic inclusion)

but how do I show that?

[lone heart]

@thorn tapir Has your question been resolved?

[thorn tapir]

<@&286206848099549185>

Let $\mathfrak{\beta} = \displaystyle \prod_{i = 1}^{n - 1} \mathfrak{\alpha}$

[ocean seal]

rikusp2002

[thorn tapir]

We gotta show that

$\mathfrak{\alpha}_n + \mathfrak{\beta} = (1) = A$

[ocean seal]

rikusp2002

[thorn tapir]

then the rest follows

but how do I show this tho

anyone please help 🥲

[velvet remnant]

Hello!

Reviewing the problem…one moment.

Is the $()$ notation correspond to some operation? And how is $A$ defined?

[ocean seal]

stokhosUrsus

[thorn tapir]

That's the principal ideal generated by an element

And A is an commutative unital ring

[velvet remnant]

Gotcha. One moment.

Oh I missed the first statement. Heh/.

[thorn tapir]

it'sokii

[velvet remnant]

Oh boy! Funny enough I just dug out my algebra text today, but I’m quite rusty.

I just need to ask one term: unital?

[thorn tapir]

means it contains a multiplicative identity

here it's denoted by 1

[velvet remnant]

unital ring -> ring with identity?

ok gotcha

[thorn tapir]

yes

my bad my internet is way too bad today

[velvet remnant]

No worries. My brain is pretty fuzzy today. I have my algebra book out refamiliarizing myself.

How about this? Let’s talk it out. Explain your thought process about the problem and the related ideas that come to mind. Sometimes saying things to someone else can help shake loose the ideas you likely already know.

I’ll keep looking at the text and see if we can figure it out together.

[thorn tapir]

ok so

i'll reiterate what I did

I already have proved this case for n = 2

now I'll use strong induction. So let's assume n > 2 and the statement is true for n = 3, 4, .... n - 1.

I'll take the product of these first n - 1 ideals to be beta

If I'm able to show that the last ideal is coprime with the product, then by induction hypothesis, the statement is also true for n.

but that's where I'm getting stuck

I have

all the ideals to be coprime with n

And also that, every element of beta is a product of elements from each ideal.

but can I show that the smallest ideal generated by a_n and beta containing both is the unit ideal, that is, the whole ring? which imples they are coprime

i know it's true but I can't prove it for some reason

I'm stuck

[thorn tapir]

<@&286206848099549185>

[slate monolith]

@thorn tapirearly uni or #get-advanced-access

[thorn tapir]

🥲

.close

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[alpine sable]

i have problem in root operations and rationalization

[sour dove]

[alpine sable]

ok ill find question

[lilac jolt]

[wild trail]

[sour dove]

[lilac jolt]

[sour dove]

lol ok @wild trail it's your turn!

[lone heart]

@alpine sable Has your question been resolved?

[lilac jolt]

(patiently waiting for problems in root operations and rationalization)

[alpine sable]

https://tenor.com/view/furret-pokemon-dance-gif-14704368

The solution ↑

A dancing furret is the solution to everything. Only depends on your ability to draw a gif in an eggjam.

[wild trail]

[lilac jolt]

(the dog has been patiently waiting for problems in root operations and rationalization for 10 years but the food has ran out so the only water source the dog can get is the water dripping from the walls)

they are coming

[lone heart]

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[gaunt turret]

how did it become 2pi/18 ?

[wary stream]

You're finding a common denominator

The common denominator is 18

So you make pi/9 have a denominator of 18 by multiplying by 2

[gaunt turret]

ohh so if the numerator is pi I have to multiply it by 2?

[wary stream]

Yes

[gaunt turret]

Ohh alright thank youu!

.close

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[vast schooner]

How is it wrong?

[versed crater]

you multiplied by -c in line 3 which si wrong

the denominator is 9-c

not -c

[wary stream]

Btw you need to open your own channel

[vast schooner]

So...

What do I do?

[versed crater]

open your own chanel

first

[vast schooner]

Bro the dude closed the channel

.reopen

.close

just tell me the answer

[versed crater]

ok its fine

you forgot to multiply both sides by 9-c

rather than just -c

you cnat do what ytou did

[vale wigeon]

we don't give out answers

!nosols

[lone heart]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[vale wigeon]

!volunteers

[lone heart]

Helpers are just people volunteering their time to help you. Be polite.

[vale wigeon]

!help

[lone heart]

Please read #❓how-to-get-help

[vast schooner]

Ik

I was asking to help me here

Cause the other dude closed the channel anyways

Also so -144c?

[vale wigeon]

you should use a channel that doesnt have someones name on it...

[vast schooner]

BRO THWY CLOSED THE CHANNEL

And I had this one open before and went to try and slive the problem

And came back and just posted my problem

[lone heart]

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[gray isle]

its still marked as closed,
hard to spot the op
if it abruptly locks then it doesn't work out well for anyone involved
please try to abide by the rules

[gray isle]

.close

[lone heart]

Channel closed

Closed by @gray isle

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[vast schooner]

Ok anyways

[gray isle]

reminder, to claim a new one if you want help

for the reasons i've just typed above

[vast schooner]

This correct?

[vale wigeon]

open your own channel

[vast schooner]

So no?

[gray isle]

doesn't matter if its right or wrong because noone will look

[vast schooner]

Hmm

[gray isle]

if you don't have your own channel

[vast schooner]

Is this how to do it?

[wary stream]

Please read #❓how-to-get-help

Open your own channel

This channel will close and possibly lock up

[vast schooner]

Stop crying

[wary stream]

If you want proper help, that's what you need to do

[vast schooner]

Cry babies

[gray isle]

last try, or we won't bother

[vast schooner]

DONT

[gray isle]

(or at least i won't)

[vast schooner]

Please don't

You r ANNOYING

[vast schooner]

Again?

[wary stream]

You realize that when this channel fully closes, and possibly locks up, you're going to need to open your own channel

[night geyser]

the reason people are asking you to follow the rules is because the bot system literally breaks if you dont

as in like

youll be cut off from the channel abruptly

insulting people trying to tell you how NOT to get cut off by the bot

is not a good move

mute lasts for 30 minutes

[lone heart]

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[proper garnet]

how do you distinguish which one has mu and which one doesnt

[wind cloak]

If the net force in one direction is less than μN, then the friction adjusts itself to equal that force, else it just equals μN

[proper garnet]

but for this its in equilibrium

so wouldnt the net force of the entire tihing be 0

[wind cloak]

Yup

So balance the force along the incline and perpendicular to the incline

Assume friction at its maximum value

It will even be in equilibrium for values of the coefficient over the minimum value ofc

[proper garnet]

and why are they both denoted as normal in the diagram

i thought the normal was only the force holding up the object

[wind cloak]

Is there some sort of external force on the block

[proper garnet]

nope

everything is at equilibrium

[wind cloak]

The friction seems to be in the wrong direction

[proper garnet]

yeah tahts what im thinking

wait

ill show u the quesdtion

[wind cloak]

Yes but that doesn't mean there can't be an ext rnal force

Like the purple arrow to the right

[proper garnet]

i think thats just to show that its at equilibrium

[wind cloak]

Friction should be acting in the opposite direction

[proper garnet]

yea thats what im saying

but if we calculated the right side it would equal to the left side as well right?

since its at equilibrium

[wind cloak]

Yes

You would equal the friction to the component of the gravitational force acting on the block

[proper garnet]

wait im still kinda confused on how do u know which one the coefficient of friction is on

[wind cloak]

For a moment imagine there is no friction

And think of where the block would slide

Friction acts opposite to that direction

[proper garnet]

ohh ok

wait why tf is friction on the left side in the diagram then

oh and why are they both denoted as normal in the diagram

[wind cloak]

It's incorrect

[proper garnet]

oh ok

[wind cloak]

Which both?

[proper garnet]

why does the mu move from the 50gsin10 to the 50gcos10

[proper garnet]

like on the inclined and normal

y aixs

.close

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[hollow thicket]

How is the area of the trapezium found?

[lone heart]

@hollow thicket Has your question been resolved?

[sharp panther]

Shall I tell?

[hollow thicket]

yes pls

[sharp panther]

Okay I'm

And then area of trapezium= 1/2 × height × ( sum of parallel sides)

Here height = 2sin(theta) and parallel side 1 = 2m
Parallel side 2 = 2m + 4sin(90-theta) which is equal to 2m + 4sin(theta)

[lone heart]

@hollow thicket Has your question been resolved?

[hollow thicket]

wait so how is cos (theta) acheived?

oh yeah complementary angles nvm lol

thanks

.close

[lone heart]

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[molten sky]

check if the results are right

[chrome topaz]

For 16 how did u get x to be 2? That would make 2^x = 4

[vale wigeon]

he did not?

i see x ∈ (2,3) written down

which is correct

[molten sky]

so i take the smallest value and the largest value

[molten sky]

so for 16 its right?

and the results right?

[vale wigeon]

yes looks like it

[subtle birch]

Yes it is correct

[chrome topaz]

I'm so confused

[molten sky]

what about this

[chrome topaz]

Is the 2^x = 5 irrelevant then or smth

[vale wigeon]

the blue text should have (-3**)**^2 + 1

[vale wigeon]

no, it's how we get that 2 < x < 3 (which is the most you can get with mental math)

[molten sky]

it is
-3^2 +1

its will be 9 +1

right?

[subtle birch]

He took a range
x must lie between 2,3 (there could be more precision but not required, just simple math)

[vale wigeon]

you're missing the (), is what i'm saying.

[chrome topaz]

Oh I c ty

[molten sky]

haa so the - have the ^2

but the results are right?

[vale wigeon]

your calculations are right yes

[molten sky]

okay thank u

.close

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[proper garnet]

could i get some help

should i draw a diagram first?

[tulip prism]

Yes

Take tensions as T1 and T2, Then simply resolve into components, and also take that the system is in equilibrium and solve for T1 and T2

[lone heart]

@proper garnet Has your question been resolved?

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[honest oxide]

can someone tell me how to do this? the instructions says to collect like terms, and to not factorise the answer

[honest oxide]

i know 4f^2/2f is 2f i think

but i don't know if i'm meant to do g/2 + 11fg

if this is how you're meant to do it

[subtle birch]

use BODMAS

[honest oxide]

so

division first

[subtle birch]

yes

[honest oxide]

5.5g?

[subtle birch]

yes

Better write as 11/2

[honest oxide]

and then left to right

[honest oxide]

oh yeah

uh so then 4f^2 - g/2

[subtle birch]

They said do not factor

just take g common

[honest oxide]

oh

wait so is the answer 4f^2 - g/2 + 11/2

[honest oxide]

sorry i dont understand what common means

[subtle birch]

11/2g

[subtle birch]

both the terms -g/2 and 11/2g contain g as a variable
So you can do g(-1/2+11/2)

[honest oxide]

oh yes i can

[honest oxide]

is that the answer

i'm so bad at math

[subtle birch]

no

[honest oxide]

the rest of the questions were like so easy and didn't need special tricks

[honest oxide]

wait so -g/2g + 11g/2g

[subtle birch]

How man

Try writing on a paper

[upbeat hornet]

,rotate

[subtle birch]

where did the g go?

[honest oxide]

i just wrote down what i could understand up to

we dealt with the 11g getting divided by 2

basically the end is simplified already i guess

[subtle birch]

$4f^{2}-\frac{g}{2}+\frac{11}{2}g=4f^{2}+g\left(-\frac{1}{2}+\frac{11}{2}\right)=4f^{2}+5g$

[ocean seal]

B-eard

[honest oxide]

OH there was a g

Yooo i understand

tysm

.close

[lone heart]

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[edgy olive]

hello

[lone heart]

Please don't occupy multiple help channels.

[edgy olive]

`This question concerns a game called Families.

The game is played by three players, each starting with a hand of four cards. There are three families in the game: α, β, and γ, and each family contains four cards.

The game proceeds with players asking questions of the form: Player A asks Player B, "Do you have any cards from family β?" Player A can only ask this question if they already hold some β cards. If Player B has any β cards, they must answer "Yes" and give one of them to Player A. We notate this question and answer as (A, B)β₁. If Player B has no β cards, they must answer "No," and we notate this as (A, B)β₀.

If a player receives a card after a positive response and ends up holding four cards of the same family, they must declare the family they constitute, and those cards are removed from their hand and the game. We notate this as (-, A)γ₄, for example, when Player A declares a family of four γ cards.

A player continues to make moves until they receive a negative answer. Then, play passes to the next player in alphabetical order (A-B-C-A).

If a player declares a family of cards and holds no remaining cards in their hand, they have won the game, and the game stops.

If a player lies about their hand or makes a statement that creates a logical contradiction, they have lost the game, and the game stops.

To prevent trivial wins, no player may start with all four cards of the same family.

In the examples that follow, each move in the game is separated by a dash, —.

(A,C)α₁ — (A,B)α_ — (B,A)β₁ — (_,Α)α₀
what should be in each blank space? Explain your reasoning carefully.
`

im totally confused, spent hours on this question

gonna pay to whoever solves it

<@&286206848099549185>

[gray isle]

don't multipost

[lone heart]

@edgy olive Has your question been resolved?

[lone heart]

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[teal robin]

how is this not one to one

[slender gull]

Is [] supposed to be floor function

[teal robin]

oh i see
thanks

.close

[lone heart]

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[upbeat hornet]

What are f(1) and f(2)?
edit: already answered

[lone heart]

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[cosmic crow]

Can someone please double-check this for me?

[lone heart]

@cosmic crow Has your question been resolved?

[cosmic crow]

<@&286206848099549185>

Just double check the image above

Thanks

?

Umm ok

Thought asians were like calculators or smth

[languid bolt]

brooo don't just randomly ping me

[cosmic crow]

You're 7?

Idk

Oh.

I'm 14 but I'm in 9th grade?

Okie

[languid bolt]

let me rewrite it, tell me if it's wrong

[cosmic crow]

Turned 14 this Jan smh

[cosmic crow]

ok

[languid bolt]

x = 2 + 4\sqrt{5}
15(x^2 + 1/x^2) - 10(x + 1/x) + 9

this?

the question

[cosmic crow]

Uhm yes

[languid bolt]

,,15(x^2 + \frac{1}{x^2}) - 10(x + \frac{1}{x}) + 9

[ocean seal]

help

[cosmic crow]

Ye

[languid bolt]

something gone wrong

hold up

[cosmic crow]

?

[languid bolt]

latex, it's a math syntax

or something

i forgot the terminology

[cosmic crow]

The whay

What*

Byee

[languid bolt]

the 1/x is correct

x + 1/x is correct

[cosmic crow]

ok

wait, kirito????

[languid bolt]

4830 correct

wait... 10(18)??

[lilac jolt]

dude. not true!!!!

[languid bolt]

wait i think i did something wrong

[languid bolt]

i agree

almost every anime watcher knows kirito

https://tenor.com/view/kirito-gif-19215815

[lilac jolt]

yeah but this is a help felix channel

[languid bolt]

wait yeah 180

[cosmic crow]

Help me when?

[lilac jolt]

LOL

[cosmic crow]

It's fine sao is good

[lilac jolt]

see even Felix knows

[cosmic crow]

Too much bullshit in the gun Gayle part tho

[languid bolt]

should be correct

yeah

it's correct

[cosmic crow]

Okie thanks

[lilac jolt]

lots of people hated it

[cosmic crow]

how do I end this

Like the channel

[lone heart]

Channel closed

Closed by @tiny laurel

Use .reopen if this was a mistake.

✅

[cosmic crow]

Okie dokie

.close

[lone heart]

Channel closed

Closed by @cosmic crow

Use .reopen if this was a mistake.

[cosmic crow]

byee

Time to skedadle

Dms

Study and skip 8th grade

Become a true asian or smth

Idk what you mean

You said you were in 7

hmm

Idk

imma get the heck outta here

[lone heart]

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[scenic falcon]

what formula do i use? i forgot sorry

[unique trout]

Find the base of the triangle

Then since the altitude is in the exterior part of the triangle you have to draw it

It has to be perpendicular to the base

So like this

[unique trout]

Then the angle adjacent to the 120 degree angle is 60 degrees

Then use 30-60-90 triangle ratio

To find the side length

And then just use bh/2 formula

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@scenic falcon Has your question been resolved?

[lone heart]

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[delicate kernel]

How to get the blacked out triangles surface?

[alpine sable]

You mean area?

Also this image is so low quality x what are the sides for the right square?

Is that a 1 ?

@delicate kernel

[vernal thunder]

It’s a 3

[delicate kernel]

Yes

[delicate kernel]

3

left square is 7x7 and the right one is 3x3

[upbeat hornet]

What have you tried so far?

[delicate kernel]

Getting area of 7x10 and cut it in half to get 35

[upbeat hornet]

What is 35 the area of?

[delicate kernel]

Full big triangle

[upbeat hornet]

From there, can you see the next step to get the area of the smaller triangle?

[delicate kernel]

Nah

[upbeat hornet]

Hint: similar triangles

[delicate kernel]

3:10=x:7?

[upbeat hornet]

What is x?

[delicate kernel]

Unknown side

[upbeat hornet]

And can you use this to get the area of the triangle?

[delicate kernel]

I can use Pythagoras to get all sides

[upbeat hornet]

What about the area?

[delicate kernel]

Get if by formula

it

This one

Sry for inverted image

[upbeat hornet]

,rotate

[upbeat hornet]

Using this formula, what is the area of the triangle?

[delicate kernel]

Give me a min so i can calculate

I got 3.15cm2 so its probably wrong

[upbeat hornet]

do you have an exact value?

[delicate kernel]

You mean when its not rounded up?

Because I rounded up 3.15 from 3.14978

[upbeat hornet]

Did you use exact values when you calculated the square root?

[delicate kernel]

Nah

I rounded up everything beforehand to 4 decimals

[upbeat hornet]

And there is a simpler way to find the area than heron’s formula: you can use bh/2

[delicate kernel]

h is height?

[upbeat hornet]

yes

[delicate kernel]

So it is 3.15

?

[upbeat hornet]

Why is it 3.15?

[delicate kernel]

(3x2.1)/2

[upbeat hornet]

Where did 2.1 come from

[delicate kernel]

this

[upbeat hornet]

Then 3.15 is correct

If you don’t have any other questions, you can .close this channel

[delicate kernel]

Actually

I have

If you dont mind

The guy yesterday couldnt figure it out and me neither for the last 2 hours

How do i get lenght DE

[upbeat hornet]

can you send a clearer image

[delicate kernel]

I dont have clearer

I can draw it on paper if you want

give me a sec

The top corner is not 90 degrees so Pythagoras is out of the question

[upbeat hornet]

Hint: similar triangles

[delicate kernel]

Yes man i tried so i can get constant but idk how that helps me with those that i have no info on

if i had AB i would put 3:8=DE:AB

or no

4/8

And then DE is 0.5 AB

[upbeat hornet]

have you missed some important information that you might not have seen?

[delicate kernel]

Probably

And I still not see it

Hint?

Wait you teasing me the answer or you seriously asking for more info?

Because that is all I am provided with

[upbeat hornet]

I am seriously asking because I overlooked something just now

[delicate kernel]

Nah man thats all I have

That is the only info

[upbeat hornet]

And as I see it now, if that is all you are given, then all you can tell is that DE = AB/2

But I think that it’s likely the questioner forgot to mention that angle ACB is 90°

[delicate kernel]

Nah our teacher said it is not 90

[upbeat hornet]

I think you should ask the teacher then

[delicate kernel]

We already did in class, she just said we'll figure it out

[upbeat hornet]

Could you try asking again, this time saying “we have tried everything and still can’t figure it out”

[delicate kernel]

I dont think so because the test is in 2 days and we wont really have time for her to explain anything to us

I can ask thursday when we have her second time but i think thats kinda useless then

[upbeat hornet]

It looks like this question is wrong, so you might want to focus on other ones to prepare for the test

[delicate kernel]

Ye

But this one is defo on the test because she told us she is just going to change values but the same exact triangles will be there

[upbeat hornet]

Try messaging her because this question actually doesn’t seem to make sense

[delicate kernel]

Ionno man

Ive been trying forever to figure it out

Tried everything

Thx for help man

.close

[lone heart]

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[haughty gale]

Hi can someone send me a video link where they teach how to use integration by parts on problems like these?

[haughty gale]

especially like this one

[haughty gale]

I can find a video where they teach how to use integration by parts on problems like this

<@&286206848099549185>

[lone heart]

@haughty gale Has your question been resolved?

[haughty gale]

[lone heart]

@haughty gale Has your question been resolved?

[plain raptor]

https://www.youtube.com/watch?v=sWSLLO3DS1I

would this help?

[lone heart]

@haughty gale Has your question been resolved?

[lone heart]

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[stone gulch]

[stone oxide]

i gotu

[stone gulch]

They gave you the formula, what to do here?

What did you do till now?

[stone oxide]

just plug in 9 for 4pir^2

oh

he delete

d

[stone gulch]

Read the Guidelines.

"We're not here to do your homework", but to help you understand the concepts

[lone heart]

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[steady basin]

in this example, why did they use the gran schidmt process to find another eigenvector to create the change matrix? why couldnt they have just used the three eigenvectors they originally found?

because when i did diagonalising endomorphsisms in the previous chapter, i just used the three eigenvectors i orginally found

[merry depot]

eigenvectors from different eigenspaces are orthogonal, not necessarily ones from the same space

so the two vectors from h = -1 are not orthogonal, they do the orthogonalization to make those two vectors orthogonal, making an orthogonal basis

[steady basin]

yh yh i get that but what im asking is, why didnt they just use the same three eigenvectors they orginally found to diagonalise the matrix?

why did they find another one

like what was the point in that

[merry depot]

the two vectors from the h = -1 space are not orthogonal.

[steady basin]

ik

[merry depot]

therefore they cannot make an orthogonal basis

[steady basin]

but why do they need to be orthogonal

but

i used the three eigenevctors

we originally found

and they diagonalise the matrix

the same way

i used this as my change matrix

and the matrix was still diagonalised

with -1 -1 1

[merry depot]

you probably can? I don't know what exactly they're trying to do.

[steady basin]

nah it works

[worn fox]

they want C to be orthogonal

[steady basin]

is that a must for self adjoint endomorphisms?

cuz i never did that for normal endomorphsims

[worn fox]

no but it is desirable

[steady basin]

i see

[worn fox]

it also asks for it in the question

[steady basin]

yh yh

i just was confused

why

[worn fox]

albeit it in a weird way

[steady basin]

like whats the point

ok

cool thanks for ur help guys

[worn fox]

orthogonal matrices are nice:)

[steady basin]

true

[wary stream]

Orthonormal matrices are nicer

[worn fox]

orthogonal matrices have orthonormal columns

dont ask why the terminology is dumb

[wary stream]

Not always

That's why Gram Schmidt exists

[wary stream]

What I'm saying is that not all orthogonal matrices are orthonormal but all orthonormal matrices are orthgonal

But I could be wrong

[worn fox]

orthogonal matrices and orthonormal matrices are two names for the same thing

[wary stream]

I just know that I was taught that orthogonal matrices have vectors that are orthogonal but not always normalized

[worn fox]

yeah thats just incorrect

by definition orthogonal matrices satisfy QQ^T = I = Q^TQ

which immediately implies its cols and rows are orthonormal

[steady basin]

did u guys enjoy linear algebra as a module

i find its kinda meh

sometimes good

sometimes abstract and kinda nasty

[wary stream]

I think the confusion comes, because I was taught orthonormal matrices have orthogonal vectors and magnitudes of 1 while orthogonal matrices do have orthogonal vectors but it's magnitude isn't always 1

[worn fox]

yeah i think thats just non-standard

i agree the actual terminology is misleading/confusing

[wary stream]

not all orthogonal matrices are orthonormal but all orthonormal matrices are orthogonal
Which leads back to this, orthogonal matrices can be orthonormal but not always
But that does lead to terminology being confusing

[lone heart]

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[dark pelican]

Can someone guide me through this questions

[surreal meadow]

which one

have you done a) yet?

[dark pelican]

@surreal meadow no

[surreal meadow]

try a u substitution

[dark pelican]

im confused about the table values

[surreal meadow]

what about them confuses you

[dark pelican]

how would i integrate f'x and fx

[surreal meadow]

first do the u substitution

[dark pelican]

would would i even sub out 😭

[surreal meadow]

u = 3f(x)

in the future, if you're not sure what to sub then just try some stuff out

that's how you learn

[dark pelican]

@surreal meadow

[surreal meadow]

what's the derivative of 3f(x)

[dark pelican]

f'x

god damnt

wait no thats what i did

now im confuse

wait no actually would f(x) be a constant itself?

@surreal meadow

[surreal meadow]

no

it's 3f'(x)

@dark pelican

[dark pelican]

would it be (2(e^6-e^4))/3

@surreal meadow

[surreal meadow]

yeah looks good

[dark pelican]

ite lemme try b and c on my own

ill be back!

@surreal meadow i dont need +C for a right

[surreal meadow]

is the integral definite or indefinite?

[dark pelican]

definite

[tacit arch]

That should answer your question

[dark pelican]

So these should be right?

[tacit arch]

Doesn't look like you changed your limits with the u-sub

[lone heart]

@dark pelican Has your question been resolved?

[dark pelican]

?

sorry im kinda stupid

@surreal meadow

[slate monolith]

if you substitute some x with u

then the integral is in terms of u

so you need to change the bounds, which were originally in terms of x, to be in terms of u

[dark pelican]

I am so confused can u point out my error

@slate monolith

[surreal meadow]

they just did haha

[slate monolith]

i'll elaborate

[surreal meadow]

if we make the substitution u = 2x, then the bounds need to change to u = 2(4) and u = 2(0)

[slate monolith]

when you write a number next to the integral symbol

it doesnt just mean plug in that number into the variable in the integral

it means that some variable is equal to some upper and lower bound

so there your bounds are x = 2, x = 6

when you do a u sub and get a function in terms of u, you cant plug in x = 2 for u

cause x isnt u

at least not in your case here

so you need to find u such that x(u) = 2, and x(u) = 6

[dark pelican]

Bruh

How did I even do that

[surreal meadow]

your bounds are x = 4 and x = 0

your sub was u = 2x

so your upper bound is now u = 2(4) = 8

[dark pelican]

No I know I’m just calling myself stupid

[surreal meadow]

and u = 2(0) = 0

oh

i read that as "how do i even do that"

my bad

[dark pelican]

Correct?

[surreal meadow]

1 - 15/2 = 13/2?

[tacit arch]

More reading and examples about substitution
https://tutorial.math.lamar.edu/Classes/CalcI/SubstitutionRuleDefinite.aspx

[dark pelican]

1=2/2

15-2

[surreal meadow]

2 - 15

[dark pelican]

Jesus Christ bruh

Who let me take calc 2

Thanks for the help 💀💀💀💀💀

[tacit arch]

Learning curve is high from precalc to calc

[lone heart]

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[lone heart]

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[keen orbit]

I started off by realizing that there are like 4 cases where there are 2-steps

2
2,2
2,2,2
2,2,2,2

so in the first case, a double step will be taken, and the rest will be single steps

I believe that correlates with C(8,1)

n=8 possible positions to take the double step

and r=1 being one double-step to take

the rest would be single steps, and there would only be one way to do the remaining single steps

then for the next case...

I thought it would be: C(8,1) * C(6,1)

but I'm not sure that's right

oh, maybe that is right, haha, I think I just screwed up when I was entering it into the desmos calculator

damn, I still got it wrong

how is that not right

son of a bitch, I think I see what I did wrong

nope, still wrong

[rustic coral]

You should add the number of cases for each case (the cases based off the number of double steps)

[keen orbit]

oh, instead of multiplying?

[rustic coral]

Yeah

[keen orbit]

damn, thanks haha

huh, still getting it wrong

[rustic coral]

Send your working

[keen orbit]

I think it is rule of product for each tier

[rustic coral]

What?

Just send your setup

[keen orbit]

so let's say you have 9 steps

S S S S S S S S S

D = double
S = single

D S S S S S S S

is that different from S D S S S S S

[rustic coral]

Your setup for 0 double steps is correct.

Your setup for 1 double step is incorrect because there will only be 8 total steps, not 9. This means that there are ||(8 choose 1)|| possibilities.

Your setup for 2 double steps is also incorrect because once you choose where to place the double steps, you also already choose where to put the single steps. Hence, the total number of possibilities is ||(7 choose 2)||

[keen orbit]

8 possible choices for a double step?

when there is 1 double step?

[rustic coral]

8 total steps, of which you choose 1 of those to be a double step.

[keen orbit]

what if you're on the ground initially

like you don't start out on a step

I guess the problem assumes that you start from the first step, like you're standing on it?

you're standing on the first step before you move anywhere

[rustic coral]

I think the problem assumes you’re traveling 9 steps in total

So I assume you’re on the ground initially

[keen orbit]

oh, I see, if you're taking one double step, you will have 8 total steps

oooh, okay, I think it's starting to make sense

so you essentially count how many steps you would be taking total

if you were to count a 2-step as a single step

and then you choose r 2-steps

out of n total steps

[rustic coral]

I think you have the idea

[keen orbit]

awesome, got it, thx

[lone heart]

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[lone heart]

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[shy skiff]

how to solve this? gotta find a and b

in terms of theta

[shy dove]

with trigonometric functions

[shy skiff]

mhm 😅

[shy dove]

Does "SOH CAH TOA" ring a bell?

[shy skiff]

si

yeah I know how to rotate those around but there's only one variable

[shy dove]

?

What do you mean rotate "those" around?

[shy skiff]

hypo is 20, a and c are ?

so sin = ?/20

[shy dove]

sine = opposite / hypothenuse. Can you give me the sine of theta in your drawing?

[shy skiff]

no cus I don't know the opposite

again, ?/20

[shy dove]

that's the letter a if I'm not mistaken

so $sin\theta = \frac{a}{20}$

[ocean seal]

imTyp0

[shy skiff]

oh well yeah I get that. so ?/20

[shy dove]

not ?/20, a/20

yes you don't know the value of a, but that's fine

the question asks you to find the value of a represented with theta

[shy dove]

so taking this equation, what would a be?

[shy skiff]

no clue

the opposite?

csc

[shy dove]

just take what I sent above. Do you remember in algebra how to isolate a variable?

[shy skiff]

kind of your solving for a

20sin

[shy dove]

yeah! Because the question asks for a, but written only with theta's

20sin(theta) that's right. Now you can do the same for b by using a different trigonometric function

[shy skiff]

20cos

[shy dove]

yup

[shy skiff]

what now lol