help-10

[sweet edge]

is there some kind of fundamental thing I'm missing that can simplify this quite a bit?

[nocturne minnow]

Probably, something like the force is all the same since they all have the same unit vector

[sweet edge]

The more I'm working with vectors, the more I'm realizing that I kinda failed learning about them in-depth

I see

[nocturne minnow]

But do you now understand how to do the rest?

[sweet edge]

Kinda, it's just going to be extremely long

[nocturne minnow]

Just a bit

$T1 \frac{5}{\sqrt{75}}\hat{i} + T2 \frac{5}{\sqrt{75}}\hat{i} - T3 \frac{5}{\sqrt{75}}\hat{i} - T4 \frac{5}{\sqrt{75}}\hat{i} = 0$

[warm shale]

dldh06

[nocturne minnow]

That's the x direction

[sweet edge]

yes

I have this written down so far

I forgot to write the k hat

[nocturne minnow]

You're going to have 3 equations, with 4 unknowns

[sweet edge]

or the RHS

yes

[nocturne minnow]

And you just solve for each tension

[sweet edge]

can i make the assumption that the tensions are equivalent since they're all on the corners of a square?

[nocturne minnow]

Do you have the key to check?

[sweet edge]

Upon submission, it'll tell me if I'm wrong or right

I have 5 submissions

ouch

[warm shale]

Jukelyn

[sweet edge]

a message from my instructor

Which means that I perhaps messed up somewhere else above

[nocturne minnow]

Looks like it, trying to see where

[nocturne minnow]

Just realized, how did you get 2546.11?

[warm shale]

Jukelyn

[nocturne minnow]

If the mag is all the same, what if it was just $\frac{150 \cdot 9.81}{4}$?

[warm shale]

dldh06

[sweet edge]

Uh

Says it's wrong

That statement also doesn't make sense to me tbh

From my professor:

Ig this is just a geometric representation of what we were doing?

but idk

[nocturne minnow]

So obviously, it's going to involve 150(9.81), dividing by 4, and 5/sqrt(75), but I don't recall the proper way

[sweet edge]

hmm

[nocturne minnow]

I think that's just the 2D view of it

[sweet edge]

mmm, shit

[nocturne minnow]

Sorry, I can't be more help

[sweet edge]

It's alright

<@&286206848099549185> any input on this stuff ^^^

[timid silo]

One sec

Brb

[sweet edge]

Okii

[sweet edge]

you alright?

[timid silo]

Yeh

I was helping some people

Before i asked

Just was finishing helping them

So what's the question exactly

[sweet edge]

To find the values for Tension in this scenario:

[timid silo]

Oh this is ok

One sec

U know where this orange plane will intersect the z axis

@sweet edge

[sweet edge]

0,0,0

[timid silo]

Nope

(0,0,5)

Z is not zero

Remove all the 4 T1 ,T2 ... T4

In its place put a single T0

What will be the value of T0

[sweet edge]

yes, true

uh

just 5

[timid silo]

U sure ?

T0 will be equal to the weight hanging from the bottom

So it wil be 1500 N

I assume g to be 10 here

[sweet edge]

alright

that makes sense

[timid silo]

Then u just need to show that the tensions are all equal in magnitude

That shouldn't be difficult

[sweet edge]

we're given that

[timid silo]

Oh lol

Then u get the answer as 15x25

Which is ?

[sweet edge]

375

[timid silo]

Yes

Each of those tensions is 375 newton

U need to show using slope of the two diagonals of the rectangle

That they intersect at (0,0,5)

U get it now ?

Not slope I mean equation of lines

[sweet edge]

nope

uh

[timid silo]

Do u know formula for equation of lines

[sweet edge]

ax+by+c=0

[timid silo]

In 3D

[sweet edge]

nope

[timid silo]

Oomph

I forgot that formula too lmfao

Lemme try

[sweet edge]

xd

[timid silo]

Man i seriously forgot it

[sweet edge]

y=mx+b?

uh

idk

[timid silo]

Not that's for 2D

[sweet edge]

Yeah, no clue

[timid silo]

But it will intersect at (0,0,5)

We can see that

[sweet edge]

yes

[timid silo]

Perhaps someone who knows that formula can help

No wait

I did it wrong

[sweet edge]

rip

[timid silo]

Just a slight modification

Rest is good

Upto T0

We need to use sin(theta)

[sweet edge]

okay..

[timid silo]

Ok finally

This should be it

And it uses cos(theta) not sin(theta) my bad

Finally

This is it

[obtuse pebble]

@sweet edge Has your question been resolved?

[timid silo]

@sweet edge hello u there

[sweet edge]

sorry

yeah

[timid silo]

Did u get it

This one is correct

Hello ?

[sweet edge]

it's not right

[timid silo]

Why

What’s the final answer

If u know it

[sweet edge]

I dont

[timid silo]

Bruh

Then why is this wrong

All the cos components of this T1 , T2 will sum upto T0

[sweet edge]

Idk what to tell you

It simply is not the right answer

[timid silo]

How do u know

[sweet edge]

bc it says it

[timid silo]

Oh

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[timid silo]

I feel like I’m making some stupid mistake

[nocturne minnow]

Oof @timid silo

[timid silo]

What am I supposed to do

.reopen

[obtuse pebble]

✅

[timid silo]

Idk how to solve this

I saw that sin(theta) components cancel out

When theta is taken with z axis from all t1,t2,..t4

And the cos components add up

To t0

@sweet edge wait

What does it say in the question to take g

9.8 or 10

[nocturne minnow]

Probably 9.81

[timid silo]

Cause I took 10

[nocturne minnow]

Or 9.8

[timid silo]

Lmao

So that’s where it is

hopefully

I gtg for breakfast

[nocturne minnow]

Physics people don't round g

[timid silo]

Can u help out from here

[sweet edge]

This

[nocturne minnow]

I tried lol

[timid silo]

Been 2 years since I did physics

Lol

Forgot these little details

Do 150 into 9.8

Divide by 4

And multiply by sqrt(3)

[nocturne minnow]

,w (1509.8sqrt(3))/4

[warm shale]

Results provided by WolframAlpha

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

Requested by dldh06#2659

[timid silo]

This

[nocturne minnow]

That?

[timid silo]

Yeh

Yes

Is that right @sweet edge

[nocturne minnow]

@timid silo

[sweet edge]

I’m not sure, I only have one more submission

[nocturne minnow]

If there is tolerance, that is close enough

So shouldn't make a difference, I think

[sweet edge]

I’ll try it

[timid silo]

🤞

Pls pls

[sweet edge]

Wait no

I’m not trying that

[timid silo]

Why

[sweet edge]

It’s the same answer I had earlier and it was wrong

[timid silo]

When

[nocturne minnow]

Previous answer was 636

[nocturne minnow]

And 637 is close enough to 636, site tolerance, would have marked it right

[sweet edge]

what the hell

[timid silo]

Bruh

[nocturne minnow]

I did 9.81

[sweet edge]

oh

true

[timid silo]

I give up

[sweet edge]

tolerance is like < 2% so..

[nocturne minnow]

,w (150*9.8sqrt(3))/4

[sweet edge]

also g=9.8 here

that's

[warm shale]

Results provided by WolframAlpha

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Requested by dldh06#2659

[sweet edge]

dang

[timid silo]

Bruhhh

I give up

[sweet edge]

same

idk

sadge

i guess

I fucking hate physics in math

oh my fucki-

I HATE THIS SHIT

I FUCKING HAD THE RIGHT ANSWER

MOTHERFU-

oh my god I'm so pissed off rn

I hate this stupid ass program

so CRINGE

[tardy epoch]

🫂 I feel the pain

[sweet edge]

I am the pain

I am pain

rn

pain

as fuck

[nocturne minnow]

So that answer we had hours ago was correct? That's unfortunate

And it does say exact magnitude, that's a big oof

And it does say exact magnitude, that's a big oof

[sweet edge]

yep

pain

[nocturne minnow]

FYI, you wrote the same exact thing epsilon had here

Because $\frac{\sqrt{75}}{5} = \sqrt{3}$

[warm shale]

dldh06

[sweet edge]

yeah

I realized

pure pain

[nocturne minnow]

At least now you know how to do it with unit vectors, because that was the unit vector

[timid silo]

I want to talk to the creator of this program

https://tenor.com/view/family-guy-peter-griffin-shoot-him-gif-14044244

I’m pissed rn

[nocturne minnow]

Aren't we all?

[timid silo]

Ik

but I just wanna talk to him

.close

[obtuse pebble]

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[halcyon creek]

So I've been working through with a trig identity the problem of "Find all values of x in between [0,2pi] for the inequality of $$sqrt{2}(sin(2x)) + 1 > 0 $$

[warm shale]

Evitaitini

[halcyon creek]

And I've gotten it down to $$(2sin(x))*(cos(x)) > -(1/sqrt{2})$$
But I don't know how to go further with the 2sin bit since it won't simplify to something neat for the parameters

[warm shale]

Evitaitini

[tardy epoch]

Do you know the double angle formula for sine?

[timid silo]

Leave it as sin(2x)

U get sin(2x) > -1/sqrt(2)

[tardy epoch]

Oh shit they already had the double angle.

Yea listen to epsilon

[obtuse pebble]

@halcyon creek Has your question been resolved?

[halcyon creek]

Ooh

thank you

[obtuse pebble]

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[obtuse pebble]

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[lavish fulcrum]

i am confused on the highlighted part of the question

[faint flower]

is " if gof= g o (f bar) then f = (f bar)" true if g is not injective?

[lavish fulcrum]

i cant seem to figure that out

<@&286206848099549185>

[timid silo]

What does the bar denote

[lavish fulcrum]

f bar is just another function right ?

[long peak]

If you don't have g injective then you can have g(x)=g(y) for x!=y

so you could have $g(f(x)) = g(\overline{f}(x))$ for $f(x) \neq \overline{f}(x)$

[warm shale]

Tom

[lavish fulcrum]

i havent been able to think of one tho

[timid silo]

A counter example will work, right

g=x^2
f=x
f bar=|x|

There

[lavish fulcrum]

oh ok my b thanks that works

.close

[obtuse pebble]

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[errant crest]

I have 2/3 = 1/a + 1/3a + 1/(a-1) I’ve gotten that down to 7a^2-4a / (3a^3 - 3a^2) = 2/3 but idk if I’m on the right track

[faint flower]

just cross multiply

one a will cancel out

(check if a=0 satisfies the original question before canceling out)

then just solve the quadratic

[errant crest]

No

[faint flower]

you made things a little harder than they needed to be in taking the LCM, but seems to be right otherwise

[errant crest]

A needs to be a positive integer

[faint flower]

alright then just cancel the a out

[errant crest]

Didn’t I cross multiply though?

!close

Close

/close

.close

[obtuse pebble]

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[timid silo]

HELP. I'm stuck at item #2. Idk how to start it

[vivid lagoon]

i am not full sure on how i would do it either, but if you are allowed I would suggest graphing this and studying it through there

[brittle swan]

slope of line = tan θ

where θ is angle is inclination/depression (θ < 90°)

use this a few times

[timid silo]

Is there a clearer explanation? I don't get it

[obtuse pebble]

@timid silo Has your question been resolved?

[brittle swan]

do you know the relation between slope and angle of inclination/depression of line?

[timid silo]

m = tan Theta???

$$tan theta=- 6/7$$

[warm shale]

Nadz

[timid silo]

Idkkk

[faint flower]

https://www.cuemath.com/geometry/angle-between-two-lines/

[timid silo]

This is what I've got:
$$m2=(168+85√3)/59$$

[warm shale]

Nadz

[faint flower]

I don't have a pen and paper with me rn to solve, but that looks way too complicated for this

[timid silo]

I think so too

[timid silo]

.close

[obtuse pebble]

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[thick python]

Hi, guys, i am looking at this proof, in my mind, non-singular conic C means that for any point on C, there is no point satisfy dC/dx=dC/dy=dC/dz = 0, how can it be related to non-degenerate bilinear form?

[obtuse pebble]

@thick python Has your question been resolved?

[thick python]

.close

[obtuse pebble]

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[earnest shell]

Can someone help explain why right answer here is d?

[spiral maple]

apriori you dont know if BA also gives 3I

[earnest shell]

So since we don’t have any info aboua BA we can’t say anything about it right ?

[spiral maple]

yes

[earnest shell]

Thank you

.close

[obtuse pebble]

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[sonic parrot]

Does this look right

[timid silo]

yes

[sonic parrot]

Thanks

[timid silo]

well done

sure

[sonic parrot]

.closs

.close

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[shadow trellis]

idk how to do this

[shadow trellis]

wait is it that 1/x approaches 0 and cos x will at max be 1? so 0?

[balmy mortar]

Have you an intuitive idea

of what the graph will look like

[balmy mortar]

yes, that's the idea.

[shadow trellis]

ooh nice, thanks

.close

[obtuse pebble]

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[balmy mortar]

@shadow trellis

https://i.imgur.com/ilexF86.png

[shadow trellis]

right, ty

[timid silo]

You may better solve it using squeeze theorem ig.

[balmy mortar]

technically, your idea is squeeze thm

[shadow trellis]

haven’t studied that :((

[balmy mortar]

you are saying the function is bounded by +-1/x

like the graph shows

thats all there is to it

[timid silo]

Well, that's really very easy. You may learn it in less than 10 min.

[obtuse pebble]

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[summer crane]

I am absolutely bamboozled

[timid silo]

The question is confusing.

Can you explain me?

[balmy mortar]

To me, it seems incomplete

I see no restrictions on the side lengths

Can be as long as you like???

[timid silo]

Side length till mars. 😋

[obtuse pebble]

@summer crane Has your question been resolved?

[summer crane]

Sadly that is the entire question that has been asked, that is why I am a bit confused with it as no other context has been provided except for

So if this bamboozles you then heck

It's diffirential calculus

[obtuse pebble]

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[timid silo]

Do I have to move the identity matrix as well in that step

[nocturne minnow]

Are you finding the inverse?

[timid silo]

Or is that fine to swap rows in the beginning before calculations

Yes

[nocturne minnow]

Because yes, you need to do the same steps

[balmy mortar]

every row operation happens to the entire row. Not just the left

[nocturne minnow]

You're treating it like one big matrix

[timid silo]

Yeah but can I swap rows first

[nocturne minnow]

Yes

[timid silo]

Then add the identity matfix

So that's allowed?

[nocturne minnow]

Are you saying swap, before you write down the identity matrix?

[timid silo]

Yes

[nocturne minnow]

No

You can't do that

[timid silo]

Okay I was just making sure 😅

[nocturne minnow]

Whatever operations you do with the original matrix, has to reflect on the identity matrix

That's why you treat it as a whole

[balmy mortar]

You can just reduce the left to the identity matrix... and then add identity matrix at end...?

if you think you're allowed to do that

[nocturne minnow]

But finding the inverse though, that's pointless

[timid silo]

TY very much

.close

[obtuse pebble]

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[timid silo]

Am I doing this right?

[silk galleon]

did you do $(X^T X)^{-1}Xy$?

[warm shale]

xdk1235

[timid silo]

That's the proper xTx

[silk galleon]

yeah thats the right design matrix

[timid silo]

What's the inverse?

46,674

[silk galleon]

you need to find the inverse of $X^T X$ not of $X$

[warm shale]

xdk1235

[timid silo]

Xtx = 46, 674

[silk galleon]

$X^T X$ is a $2 \times 2$ matrix

[timid silo]

Okay I'm messing up there then

Ty

.close

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[timid silo]

i need help with the isomorphism part

sorry i posted earlier but something came up

idk how to find the isomorhpic ones

i cant even visualise what one homomorhpism would be

[balmy mortar]

Can't rlly help with your homework

Perhaps try the question for order 5

or something

[scenic sundial]

@balmy mortar you can maybe give a hint

[balmy mortar]

I think I did

But I don't mind giving some more if that doesn't help much

But should try --- that's what uni problems are more about

Another hint: think about what certain things must map to

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

idk man

this isnt an exam

i need help on the homework hence im here

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[solid gazelle]

2n-9 and 8n+1 are square numbers
n is a natural number
Find n

[solid gazelle]

https://tenor.com/view/stewie-gone-psycho-insane-send-help-family-guy-gif-7916038

[tardy epoch]

what are you allowed to use? can't you just do trial and error?

[solid gazelle]

Uh, how can i use trial and error for solving this?

[raven spire]

How did you attempt to solve it?

[tardy epoch]

oh they don't have to be consecutive squares. that's annoying

||```In [10]: for n in range(5, 100):
...: if (2 * n - 9) ** 0.5 % 1 == 0 and (8 * n + 1) ** 0.5 % 1 == 0:
...: print(n, 2 * n - 9, 8 * n + 1)
45 81 361

[solid gazelle]

i tried to guess n, but after 20 numbers i gave up

[solid gazelle]

https://tenor.com/view/kekw-kek-bttv-twitch-emote-gif-15123134

[tardy epoch]

if this is for a number theory class, this answer isn't gonna cut it

[solid gazelle]

Yea, my teacher won't accept a piece of code

[tardy epoch]

so is this for number theory?

thought it was for high school

there's probably something with modular arithmetic

[solid gazelle]

Idk, the only thing i have is this problem

It's not specified that it is for number theory

[timid silo]

This indeed number theory

Both are square numbers @solid gazelle

??

[solid gazelle]

Yes

[timid silo]

Are they equal by any chance

Jk jk

Here's how to do it

Afaik

[solid gazelle]

https://tenor.com/view/inauguration-cnn2017-trump-donald-trump-cant-hear-you-きこえない-gif-7576947

[timid silo]

Ok tell if u want to write a number as a multiple of 2 or a multiple of 2 plus something , what will it be

The easiest way to write it

@solid gazelle u there ?

[solid gazelle]

Multiple of 2 plus something

[timid silo]

Fine ill cut to short

Do you know modular arithmetic

[solid gazelle]

Not very
||Do i know modular arithmetic ||

[timid silo]

Lol

Do u know it

[solid gazelle]

Yes

[timid silo]

Ok

So u know every number is either 1(mod 2)

Or 0(mod 2)

So let a = 1(mod 2) or a=0 (mod 2)

I don't have congruence symbol only keyboard

Hence using =

[raven spire]

Oof

@solid gazelle ?

[timid silo]

What happen

[solid gazelle]

Huh?

[raven spire]

Write 2n - 9 = A^2 , 8n + 1 = B^2

B^2 - 4A^2 = 37

can you follow from there?

[timid silo]

I bet he can

Thanks ansh

[solid gazelle]

Wait, how did you get b^2-4a^2=37

[timid silo]

He subtracted them

After multiplying a^2 eqn with 4

On both sides to eliminate n

My bad it was subtraction

[solid gazelle]

OOOH

[timid silo]

Then u get this

U know how to solve for a and b from here ?

[solid gazelle]

I'll try to

[timid silo]

Basically factorise LHS

U get (b-2a)(b+2a)= 1 x 37

37 is prime so has only 2 factors

Now can u see which one is which

[raven spire]

simply sum them up, get 2b = 38 :o
subtract : 4a = 36

[timid silo]

Yup

[obtuse pebble]

@solid gazelle Has your question been resolved?

[raven spire]

hmm?

What's wrong @solid gazelle ?

[solid gazelle]

wait how

[raven spire]

You got this?

*understood this?

[solid gazelle]

Yes

[raven spire]

Then factorise L.h.s. and r.h.s.

[solid gazelle]

I also understand (b-2a)(b+2a)=37

But how did you get 2b=38

[raven spire]

(B+2A)(B-2A) = 1 x 37

Do you understand that 37 is a prime and the only way to write it as a factor is 1 x 37?

if yes, then either of the factors (B+2A) or (B-2A) from L.H.S. should be 1 and the other should be 37

[solid gazelle]

OOH, understood

I completely forgor 💀 about prime number

[raven spire]

Yeah, now since (B+2A) > (B-2A), (B+2A) = 37 and the other one is 1

solve for A, B

then plug in for n

[solid gazelle]

So a=9,5 and b=20?

Wait

[raven spire]

a = 9, b = 19

[solid gazelle]

Is there something wrong?

Wait

I'm stupid

YYEEES

N = 45

FINALLY

Thank you so much

@timid silo @raven spire thank you

[raven spire]

:)

[solid gazelle]

.close

[obtuse pebble]

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[obtuse pebble]

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[clever nacelle]

Hi, what is a surjective function?

[clever nacelle]

I mean I've read the definition but still don't really understand it

[hazy marlin]

well , given a certain domain and an range

the function is surjective if for ever element in its range there is such x from its domain that f(x)=y

take for example y=x^2 so that f : R -> R

the function isn't surjective, because there is not a real number x so that if you square it you get a negative number right?

so for example if you take -1 , an element of our range, (R) you can't find real number x such that x^2=-1

[clever nacelle]

ok so the domain must go to all the values of the co-domain?

[hazy marlin]

on the other hand, if you redefine the function so taht it maps f:R->[0,+infinity) , it is surjective now

[hazy marlin]

yes exactly

maybe it will be more intuitive to think about it the other way around
each value in the co domain has a value in its domain that is mapped to it.

[clever nacelle]

ok

[hazy marlin]

made a small correction on the codomain definition

[clever nacelle]

so the domain can have values not mapping to anything as long as some of the values map to all of the values of the co-domain

[hazy marlin]

yes

that is correct

however do notice that it can only be surjective if the group of the co domain is smaller in its cardinality then the domain

like, if you have 4 values in your domain and 4 values in your co do main,
then each value in your domain HAS to be mapped to a corresponding value in the co domain for it to be surjective

[clever nacelle]

OK I understand, but why do I not understand the first example you gave

[hazy marlin]

if the co domain is smaller, say 3, then you can map 3 valued from the domain to the 3 values of the codomain , thus achieving surjectivity

[hazy marlin]

what exactly?

[clever nacelle]

what does this mean

the r -> r part

set R to set R

I mean its the function notation

[hazy marlin]

it just means that function f maps values from domain R to co domain R

[clever nacelle]

okay

and R is not a set

right

[hazy marlin]

it is a set

[clever nacelle]

because then it would map set R to set R

[hazy marlin]

it's the set of all Real numbers

yea it would

[clever nacelle]

oh ok

[hazy marlin]

you can map a set to itself after all

you can also map a function this way :

f: N -> R

aka a sequence

[clever nacelle]

huh

I'm lost

[hazy marlin]

N->R means mapping natural numbers to real numbers

a seuqnece a1,a2,a3...an is a function that takes a natural number, being the index and maps it to some real number

a1=3.14 is essentially the mapping 1->pi

[clever nacelle]

ok

and bijective is when each value in the domain maps to a unique value in the co-domain

?

[hazy marlin]

what you described is injectivity

a bijective function is one that is both Injective and surjective

[clever nacelle]

ok

so both domain and co domain have the same cardinality?

since for it to be injective, it has to for each input have a unique output

and if the co-domain was larger, it would not be surjective

?

[hazy marlin]

well yes but not exactly
a more precise definition would be that if for values a and b f(a)=f(b) then a=b

the codomain must be of equal size or smaller then the domain

[clever nacelle]

how

[hazy marlin]

you can map a domain of 4 values to a co domain of 3 values so that the mapping is bijective

[clever nacelle]

won't that mean that its not surjective anymore

[hazy marlin]

say your domain is 1 2 3 4 and co domain is 1 2 3

[clever nacelle]

oh wait no

[hazy marlin]

I can map 1 -> 1
2->2
3->3

[clever nacelle]

ok so 1 element maps to 2 things

[hazy marlin]

the function I defined is both injective and surjective, and thus bijective

having an element map to 2 things defied the definition of a function

[clever nacelle]

so not all values of the domain have to be used?

[hazy marlin]

Nope

I mean

take for example 1/x

the value 0 in the domain is never used

such a point would be an incontinuity point

for example

[hollow plank]

Wait, no; the domain of a function is exactly where it is defined

A bijection between sets indeed imposes that the sets are of same cardinality

Partial functions exist and are useful, but when talking about injection, surjection or bijection, this is for non-partial functions.

The domain of 1/x is not R, it R* (R without 0)

[clever nacelle]

ok right, so let me get this from the start, injective means that all the values in the domain map to a UNIQUE element in the co-domain

[hollow plank]

yes

[clever nacelle]

and surjective means that all the values of the co-domain have a mapping

[hazy marlin]

yes yes yes you're right
otherwise an inverse function could never be surjective

my mistake matas

[hollow plank]

yes

[hazy marlin]

a bijective function imposes equal cardinalities of both sets

[clever nacelle]

its fine, this is helping 🙂

ok

let me draw 2 functions

[hollow plank]

(to be pedantic: it's even actually how "having the same cardinality" is formaly defined)

[clever nacelle]

this is bijective right

[hazy marlin]

fair point heh

[hazy marlin]

yes

[clever nacelle]

and this is not injective as 0 and 2 map to 1 and also not surjective as nothing maps to 2

[hazy marlin]

Exactly right.

[clever nacelle]

thus also not bijective

ok, thank you very much guys :))

[hollow plank]

no problem 🙂

[hazy marlin]

you're welcome ! and thanks @hollow plank

if you're willing you can help me out on help-15 channel

[obtuse pebble]

@clever nacelle Has your question been resolved?

[obtuse pebble]

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[timid silo]

Someone ping 1mbibe please? Dude just blocked me and i have no clue why

[timid silo]

Xd

[brittle swan]

?????

wtf is this request

this is a math server

[flat anvil]

stop trolling

.close

[obtuse pebble]

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[timid silo]

Ya du français ici??

Shit wrong channel

.close

[obtuse pebble]

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[pseudo mural]

i need help with d

[pseudo mural]

i got 8/7(2^n) but the pattern doesn't hold

[worthy drum]

Isn't it just dividing by 2?

[obtuse pebble]

@pseudo mural Has your question been resolved?

[timid silo]

https://tenor.com/view/eminem-job-for-me-gif-10358335

@pseudo mural

11,18,37…

Hmmm

[obtuse pebble]

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[timid silo]

Bruh

.reopen

[obtuse pebble]

✅

[timid silo]

Nvm I guess u solved it

.close

[obtuse pebble]

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[flat anvil]

so first you wanna set that to zero

and notice that you can divide everything by 2 to make your life easier

[timid silo]

Yup

[flat anvil]

then you must use the rational roots theorem and synthetic diviosn

a lot

[timid silo]

He can’t do long division ?

@flat anvil

[flat anvil]

he can

it just takes longer

[alpine raven]

long division by x-10

[balmy mortar]

what.

[flat anvil]

(more writing)

[timid silo]

Then that’s easier

[balmy mortar]

long division is just 1 line of working

[flat anvil]

what

[balmy mortar]

and then quadratic

[timid silo]

Long division by x-10 is easier

[alpine raven]

it will just be f(x)/2

[balmy mortar]

what what.

[flat anvil]

wait

long division is more writing

i thought

[balmy mortar]

that depends on HOW you do it.

[flat anvil]

how are you doing it?

[balmy mortar]

term by term.

I can show.

[flat anvil]

yeah so in that case

synthetic is just as fast

(if not fasteR)

[balmy mortar]

2x^3 - 24x^2 + 44x - 40 = (x - 10)(???)

[flat anvil]

synthetic divison is a shortcut for long division

[balmy mortar]

2x^3 - 24x^2 + 44x - 40 = (x - 10)(2x^2 ???)

wait is what im doing synthetic?

[open sentinel]

set f(x) to 0?

[flat anvil]

nah its not

[flat anvil]

yes

[balmy mortar]

I see I have a -20x^2 term

so to balance, I need to make +4x^2

2x^3 - 24x^2 + 44x - 40 = (x - 10)(2x^2 + 4x + ???)

I now have a -40x term

to balance i make +84x

which means ive made a frigging mistake

[timid silo]

That’s synthetic division

What ure doing

[flat anvil]

rlly?

[open sentinel]

this is a synthetic division problem

[balmy mortar]

uh heck did i do wrong

2x^3 - 24x^2 + 44x - 40 = (x - 10)(2x^2 - 4x + ???)

kk

2x^3 - 24x^2 + 44x - 40 = (x - 10)(2x^2 - 4x + 10)

😅

@flat anvil what is synthetic to u

[timid silo]

Bruh

This is synthetic division

What you are doing

[alpine raven]

just do it like this and you are done

[open sentinel]

i think its basically dividing but the division sign is flipped over and you move everything a place down

yea

basically

[balmy mortar]

yh well mine is 1 line of work

as long as u dont f up

[flat anvil]

man i dont even know what synthetic division is anymore

[open sentinel]

should i go to the next problem

[flat anvil]

yes

[open sentinel]

this one just stumps me

like i have no idea what to do

[royal basin]

if the question asked for the value of g(5), would you be able to do it?

[open sentinel]

probably not

this is all new to me

[royal basin]

so you don't know how to read the graph of a function?

[open sentinel]

i skipped a year of math

[flat anvil]

you go to where x = 5 and you look at what the y-value is (and we know b/c y = g(x) that the y value is g(x))

[royal basin]

consider that y = g(x) isn't just an arcane equation we write as part of some sort of ritual

you should look at the point on the graph of g whose x-coordinate is 5

that point's y coordinate will be g(5)

do you at least understand the concept of coordinates in general?

[open sentinel]

no

is anyone still here?

[flat anvil]

you uh

dont understand coordinates?

[forest sinew]

you may wanna just like

[flat anvil]

https://www.khanacademy.org/math/pre-algebra

[forest sinew]

im sure we can find a short video

[flat anvil]

do some khan acadmey pre algebra

[forest sinew]

3-8 minutes

probably on the lower end of that

[open sentinel]

im just gonna skip it ig

trying to go to bed as quickly as possible

[royal basin]

well sooner or later you will have to learn this again

your lack of knowledge can and will bite you in the ass later, multiple times

[forest sinew]

you could just watch a 5 minute video then go to bed and let it simmer

[open sentinel]

everyone in my class is like 3 years older than me. worst comes to worst, i fail the class and have to take it again

im smart

kinda

not really

do u know how good triple advanced math looks on your college aps?

[forest sinew]

https://www.youtube.com/watch?v=9Uc62CuQjc4

it will not matter since graphs are one of the few things that never go away

like algebra

in general

not even worth arguing since youll motivate yourself eventually

good luck

[open sentinel]

u r right, and i will invest time later, but right now, i still have 20 questions to answer that i probably dont know how to do

[forest sinew]

idk what to tell you

the problem is as easy as understanding coordinates

you watch a a short video

you understand

theres nothing to really debate about there

[open sentinel]

i know

.close

[obtuse pebble]

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[marsh shadow]

pls help guys

[obtuse pebble]

Please don't occupy multiple help channels.

[twilit loom]

do you know what conditions are necessary to construct a triangle?

[marsh shadow]

yaa

asa sas sss rhs

[junior inlet]

try drawing a diagram, i guess

[marsh shadow]

of every part?

[junior inlet]

*i mean diagrams

[twilit loom]

this is for congruency, not construction

[marsh shadow]

so wht do i do

[twilit loom]

what is the sum of internal angles for a triangle?

[marsh shadow]

like the sum shud be 180*

[boreal vale]

x^(2)+5x=36

in CAS

[twilit loom]

stay in your channel

[boreal vale]

oh shit sorry

[twilit loom]

so the sum of any two angles has to be less than 180, yes?

[marsh shadow]

ok

[twilit loom]

which options does that rule out

[marsh shadow]

bro in 2 options the angles sum to be more thn 180

[junior inlet]

(also: the sum of 2 sides' length of a triangle must be less *more, sorry than the other side's length)

[marsh shadow]

but how do i do other 2?

[marsh shadow]

ok

ty

ty

.close

[obtuse pebble]

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[elder trellis]

Please someone solve this

[raven spire]

WHATTTT

A + B < C?

[tardy epoch]

Do you have a Fourier transform table somewhere

[elder trellis]

Like the formulas?

Would this do?

[obtuse pebble]

@elder trellis Has your question been resolved?

[obtuse pebble]

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[elder trellis]

Did someone get it?

[timid silo]

help

[obtuse pebble]

@elder trellis Has your question been resolved?

[obtuse pebble]

@elder trellis Has your question been resolved?

[obtuse pebble]

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[wanton dagger]

How do I do these questions I’m new to it.

[timid silo]

https://youtu.be/Kz_reJgi_Rg

[wanton dagger]

Okay.

[timid silo]

Your about me is a die?

[wanton dagger]

A yeah, just random.

[timid silo]

Cool, I'll steal it.

[wanton dagger]

Ok lol

[timid silo]

XD

[wanton dagger]

Okay I think I should get it from this video thanks.

.close

[obtuse pebble]

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[tardy vector]

A scale model is built from a sailing ship with the scale of 1 : 200. What is the area of the ship's sails when the true area is 2800m^2?

[obtuse pebble]

@tardy vector Has your question been resolved?

[obtuse pebble]

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[grand obsidian]

how to get x

[sage geode]

Have you tried anything so far?

[grand obsidian]

nope cuz im not even sure if that line is diameter

[sage geode]

Alright so first you need to notice that the angle x is the same as sum of angles SQT and TQV, right?

Let's start with solving for the angle SQT

Since the triangle that this angle is in is a right triangle, so 50 + angleSQT = 90 obviously

Therefore the angle SQT is 40

You can now solve for the other angle similarly

And just add them up

[grand obsidian]

ahhh now i got it

thankyou very much

have a good day !!

[sage geode]

You too

[raven spire]

@grand obsidian

actually

Lmk if you wanna know sth nice about this problem

there's actually a simpler equation that goes 70° + x + 50° = 180°

[obtuse pebble]

@grand obsidian Has your question been resolved?

[grand obsidian]

yes i do wanna know

the more i know about this question the better it is

[raven spire]

XD

[grand obsidian]

can you explain why it must = 180?

[raven spire]

Do you know about the alternate segment theorem?

[grand obsidian]

not really

[raven spire]

Okay

so

Alternate segment theorem states that... if DE is tangent to the circle at point C

then angle DCA = angle ABC and angle ECB = angle BAC

[obtuse pebble]

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[grand obsidian]

.reopen

[obtuse pebble]

✅

[grand obsidian]

aighttt now i understand it even even better

[raven spire]

Can you see that? or wanna try to prove it?

Oh

Yep

So in your question

[grand obsidian]

i understand it perfectly

[raven spire]

angle PQS = angle STQ and angle RQV = angle VUQ

[grand obsidian]

oh my, my mind is blown away right now

it is that easy

gotta remember this concept

so hopefully i got this right, the answer is 60

[raven spire]

Yes

[grand obsidian]

aight thankyou

you too sir have a good day

[raven spire]

50 + x + 70 = 180, cause straight line angle... x = 60°

[grand obsidian]

yep

.close

[obtuse pebble]

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[obtuse pebble]

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[ripe fern]

what ive done is put it into a calculator

[ripe fern]

and spammed until i got the answer to only 5 repletely

do i have to prove by induction?

<@&286206848099549185>

[novel knoll]

prove monotone and bounded

now you have a theorem that says limit exists

[novel knoll]

try and use that to set up an equation and solve for the limit

[ripe fern]

im not too sure how to do that >_<

[novel knoll]

induction is 1 way

[ripe fern]

ok ok, ill try

im sure ill get lost but ill try 😂

[obtuse pebble]

@ripe fern Has your question been resolved?

[obtuse pebble]

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[magic blade]

can someone explain or link me something that explains vertex and standard form for parabolas?

[sage geode]

So the standard form for a parabola is usually y = ax^2 + bx + c, where a,b and c are simply called coefficients

And the vertex form is y = a(x - h)^2 + k

What makes the vertex form useful is that

You can clearly see that the minimum/maximum of y is achieved at x = h

[magic blade]

I only know (x-h)^2=4p(y-k) and (y-k)^2=4p(x-h) what form is that?

[sage geode]

And that the minimum/maximum value of y is k

[timid silo]

For a parabola, whose vertex is at origin (point V is vertex), it's equation is y² = 4ax. F is the focus of the parabola. Coordinates of F are (a, 0).

[sage geode]

The 4p(y - k) = (x - h)^2 is equivalent

You can see that by isolating the y

And the 2nd form is the same thing but with x and y axis switched

In both cases the vertex is at (h, k)

[magic blade]

doesn’t one mean vertical and one mean horizontal (pointing up or down and right and left)

[sage geode]

Yes

[magic blade]

what forms can I switch between

[sage geode]

The (x - h)^2 = 4p(y - k) is the vertical parabola

And the (y - k)^2 = 4p(x - h) is the horizontal one

[magic blade]

so if the x is on the 4p side it’s along the x axis and if the y is on the 4p side it’s along the y axis

[sage geode]

If I were to memorise which one is which, I'd take a look at which of the x or y is being squared

If x is being squared, then it's a vertical parabola

If y is being squared, then it's a horizontal parabola

[magic blade]

I see

so what’s that form called

oh is that standard form only when the vertex is at origin?

[sage geode]

I guess it can still be called the vertex form

[sage geode]

No

You can write any vertical/horizontal parabola in either of the forms

It's just that standard form has coefficients of x and x^2

[magic blade]

is there another type of vertex form?

[sage geode]

Not sure

[magic blade]

ok so what about switching from vertex to standard or whatever

when do I have to do that

[sage geode]

Idk I don't think it's always necessary

Unless the question itself is asking you to do that lol

[magic blade]

I see

If i’m not mistaken the questions we usually get is find the directrix focus etc

do I just need the vertex= whatever letters correspond to the number in the equation thing

are you guys active on VC

if so I’ll come on later

[sage geode]

Not me

[magic blade]

do you know if there’ll be anyone active there in a few hours

[sage geode]

idk

[magic blade]

alright i’ll be closing this and come check then thanks for the help man means a lot

.close

[obtuse pebble]

Channel closed

Closed by @magic blade

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[obtuse pebble]

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[fresh fulcrum]

My solution:-

I just need a hint on how to approach the problem

[obtuse pebble]

@fresh fulcrum Has your question been resolved?

[fresh fulcrum]

<@&286206848099549185>

[timid silo]

Post it in #help-11 or #help-20

[obtuse pebble]

@fresh fulcrum Has your question been resolved?

[fresh fulcrum]

.close

[obtuse pebble]

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