help-17

[velvet zephyr]

no

recheck

2 is not equal to 0.

[lone igloo]

What part is that sorry?

[velvet zephyr]

Last term

[viral copper]

it just needs to be a + 36d^2

other than that you're good

[twin meteor]

argon

[velvet zephyr]

don't make anyone learn formulas. make them prove it.

[lone igloo]

Why is it plus

Isn’t it -6d^2

[viral copper]

expand (a - b)^2

[lone igloo]

Wait sorry

[velvet zephyr]

-ve * -ve = +ve

https://tenor.com/view/fat-codybrown-family-guy-gif-5446404

[lone igloo]

A2 - b2

[velvet zephyr]

No

[viral copper]

you need to distribute properly

(a - b)(a - b)

[velvet zephyr]

(a-b)^2 = (a-b)(a-b) = a^2 - ab - ba + (-b)(-b)

[viral copper]

maybe you've heard of FOIL

[velvet zephyr]

I haven't heard of that.

[lone igloo]

Yea

I did

[viral copper]

it was directed to OP

I think it's an American thing

[velvet zephyr]

okay

[viral copper]

apply that and see what you get

[vast shale]

(a-b)^2 =[a-b][a+(-b)] = a^2 - b^2

[lone igloo]

Ok

[vast shale]

please correct me

[lone igloo]

But why is (a-b)^2 not a2 - b2

[viral copper]

for the same reason (2 - 1)^2 is not 3

[velvet zephyr]

because 2 + 2 isn't equal to 5

[vast shale]

binomial expansion

[velvet zephyr]

Use this.

to expand (a-b)^2

[lone igloo]

Heh

So hard

[lone igloo]

What would ans be?

[velvet zephyr]

n! = n(n-1)(n-2)..... till 1.

[loud walrus]

Dont overcomplicate it for him

Raj

Do you know what does x^2 means?

[viral copper]

Just use foil on (a - b)(a - b)

[velvet zephyr]

x^2 is the area occupied by a square of side lenght x.
Or, it is the slope at a particular point of the function x^3/3

[loud walrus]

I am asking to raj, dont troll please

[lone igloo]

Yes

[loud walrus]

Write here the expression

[lone igloo]

X multiplied by x

[loud walrus]

Ok

So now we are gonna subtitute

(a-b) = x

So x^2 = (a-b)^2

And as we said before x^2 is x times x

We do the same with the right side

[lone igloo]

Ok

[loud walrus]

(a-b)(a-b)

Now

[velvet zephyr]

If you don't understand why we multiply like ths.

[loud walrus]

To expand this, we are gonna multiply each term of the first parenthesis with each of the second and sum them

(a-b)(a-b) will be (a * a) + (a * (-b)) + (-b) * a + (-b) * (-b)

Do you follow until here?

@lone igloo

[lone igloo]

Yes

[loud walrus]

Ok

Now we continue simplifying

What is a * a?

[lone igloo]

A2

[velvet zephyr]

no

a^2

[loud walrus]

What is a * (-b)?

@lone igloo

[lone igloo]

Uh

Idk

[loud walrus]

ok so lets see

Imagine you have a=2 and b = 3

So you have 2(-3)

[velvet zephyr]

[one negative] and [one positive] multipled together make a negative number.

[loud walrus]

What would be that?

[lone igloo]

-6

[loud walrus]

So a * (-b)

Would be equal to

[lone igloo]

Why we this far lol

I’m just confused why it’s + 36d2 instead of - 36d2

[loud walrus]

We are close to that

Finish with the questions

Your question was answered in the very beginning but you did not understand

So we have to do everything now to make sure u know what is this about

[lone igloo]

Ok

This so hard now tho

I’m just g8

[loud walrus]

Do you agree that a * b is =ab?

[lone igloo]

Yes

[loud walrus]

And a * (-b) is equal to a * b * (-1)?

Which is ab * (-1)

Which is -ab

Do you follow here?

[lone igloo]

Yes

[loud walrus]

Ok so

We have so far

a^2 - ab

Now the other is (-b) * a

Which is -ab again

So a^2 -ab -ab

And finally

(-b) * (-b)

[lone igloo]

Ok

[loud walrus]

Do you agree this is equal to (-1) * b * b * (-1)?

And this is equal to (-1) * b^2 * (-1)?

And using commutative you can rewrite as b^2 * (-1) * (-1)

And what is (-1) * (-1)? @lone igloo

[velvet zephyr]

Your brother has opened a channel just above

[lone igloo]

1

[loud walrus]

So do you agree then that

(-b) * (-b) = b^2?

[lone igloo]

Yea

[loud walrus]

So in your problem b was equal to -6d

So (-6d)^2 is

[lone igloo]

Ok

[loud walrus]

(-6d) * (-6d)

Or like we did before

[lone igloo]

Oh shi

That’s why it’s positive

Cuz u multiply it

[velvet zephyr]

(abcdefghijklmnop....)^2 = (a^2)(b^2).......

[loud walrus]

(-1) (6d) (6d) (-1)

I am glad u finally understood it

[lone igloo]

Ty am

Tysm

[loud walrus]

Steps are very important

You are welcome

[velvet zephyr]

you should ignore these steps
welcome

[lone igloo]

Ty also

.close

[loud walrus]

!done

[vocal sleet]

If you are done with this channel, please mark your problem as solved by typing .close

Channel closed

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[velvet zephyr]

delay causes defamation

Samuel can you help me in my channel?

Please.

Apparently, no is able to help.

[vocal sleet]

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[untold arrow]

Another quick question, if we have a function G(x) and G(∞)=0, G(-1)<0, then what info can we know from the definition of limit?

[untold arrow]

They said

But idk how does this derived

[tawny hollow]

They pick epsilon = -G(1)/2 > 0

also I think some more context is needed

Since they start talking about x approaching 1?!

I’m guessing they meant infinity, unless again some context is missing

[tawny hollow]

Btw this basically means G is bounded for large enough x

[untold arrow]

Ooh the original question looks like this:

[untold arrow]

This is just the hint of this q

[tawny hollow]

Ok so in the hint, notice how G(1)/2 < G(x) < -G(1)/2

So G(x) > G(1)/2

It seems like that might help in 1)

If that was the intention of the hint

Eh

[untold arrow]

I guess i still need to have a review of the definition of limit, what's M corresponding here

[tawny hollow]

What is epsilon (1, +0 ) supppsed to mean here

[untold arrow]

They just randomly picked a notation

[tawny hollow]

M is just some large number, since we’re talking about the definition of a limit near infinity

[untold arrow]

a is ∞ ?

So L is 0

[tawny hollow]

Yeah sure, but that doesn’t quite make sense for the delta definition, so there’s an alternative for when a is infty

[untold arrow]

I don't understand the x>M>1 part

[tawny hollow]

First off in your textbook, find the appropriate definition

For when we have a limit approaching infinity

I was gonna take a quick shower before I wrote here, so if I’m not active that’s why

[vocal sleet]

@untold arrow Has your question been resolved?

[tawny hollow]

@untold arrow Alright so im back, did you do this?

[untold arrow]

Tbh i didn't find any difference

I feel like they're all the same

[tawny hollow]

This is the same as the one you provided before (almost)

im asking about the one where instead around a point, its when x approaches infinity

Should i just phrase it instead?

[untold arrow]

This way?

[tawny hollow]

Yup

Here im guessing M = N

in our case

[untold arrow]

Ok but still, why x>M>1 ?

Why did they make M in the interval 1,x

[tawny hollow]

I think it might be because they want to use the fact that |G(x)| < -G(1)/2

if M was smaller than 1 and so x too, then that isnt guaranteed

I think it helps if i saw the whole hint, theres probably more context

unless that's all of it

[untold arrow]

Wait

Then they said use Lagrange mean theorem

But they didn't explicitly write how to do that

[tawny hollow]

Well not sure in which way, but i guess i can see a way

so consider f(1) - f(0) = f'(eps)(1-0)

according to the mean value theorem this holds for some epsilon in (0,1)

so we want to show that f'(eps) = f(1) - f(0) > 1

[untold arrow]

Yea

[tawny hollow]

what is G?

since that's not clear to me

[untold arrow]

An auxiliary function they made

[tawny hollow]

And it's left for us to find or?

like do they give an explicit construction?

[untold arrow]

Yes it's just f(x) -|x|

[tawny hollow]

Oh bruh

Ok hm maybe i guess we can use mean value theorem on G instead

Oh wait -|x|?

[untold arrow]

Here too, my typo, sry

[tawny hollow]

Damn

Im guessing you translated this? Are we sure there's not any others typo's?

[untold arrow]

Yes I translated

No

[tawny hollow]

Could you post the exact question for clarity sake?

[untold arrow]

It's handwriting , i checked again I'm sure no😭

[tawny hollow]

Alright im assuming epsilon (1,0) is a typo btw

its surely epsilon in (0,1) right?

and why add plus to 0 ?!

[untold arrow]

1,+∞

[tawny hollow]

Wait.. so it's not (0,1 )but (1,infty)...

Okay yeah that changes it quite a bit

[untold arrow]

i bet it's the last typo😅

[tawny hollow]

hopefully so!

[untold arrow]

Definitely

[tawny hollow]

Alright so in that case i guess we can write the mean value theorem in quotient form if our interval is (1,infty)

[untold arrow]

I don't even know why do they make that G(x)

[tawny hollow]

yeah at this point im not even sure anymore

but it's a hint

so if G(x) = f(x) - |x|

and applying the def. of limit

we see that as they say |G(x)| < -G(1)/2 for large enough x

Hm now let's think about the mean value theorem

For x bigger than 1, we have that G'(x) = f'(x) - 1

So there exists epsilon in (1, infty) such that G'(eps) = lim a -> infty (G(a) - G(1))/(a-1)

Sort of going through this as a sketch so make sure to tighten some loose arguements im making here

It seems G'(eps) = 0 (?) eh

Hm

[tawny hollow]

I think this part is argued carefully with the fact above

[vocal sleet]

@untold arrow Has your question been resolved?

[vocal sleet]

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[remote trench]

completed the square

and put it into vertex form

now i need to state the coordinates of the vertex

that would be (h,k)

i dont know how to do that

[timber tartan]

for me

I would have factored out the 2 from the whole polynomial

so

2(x^2 - 2x + 5/2)

[lament linden]

That is not (x-1)² for sure

[timber tartan]

then

[remote trench]

im just following what my mentor says

[timber tartan]

2[(x-1)^2 - (1)^2 + 5/2]

[lament linden]

You need to add and subtract 2 for that.. not 2x

[remote trench]

what

oh

[lament linden]

Google how to complete the square

[remote trench]

i have done it correctly a lot of time

[timber tartan]

2(x-1)^2 -2 + 5

2(x-1)^2 + 3

[remote trench]

you take half of b and then square it and add that

[timber tartan]

that is my final vertex form

[remote trench]

ok let me start again

so far so good?

[knotty lynx]

No

[lament linden]

You dont add a variable, you add a constant

[knotty lynx]

You take half of b (-2) and square it (-1)^2
So you end up with

2((x - 1)^2 - 1) + 5

[remote trench]

but i add the square of half of b no?

ohhhh

[knotty lynx]

Inside the brackets

[remote trench]

i meant 7

like that

[lament linden]

Nah

Not the same thing anymore

[remote trench]

but i added 2

oh

4?

[lament linden]

You added two twice

[knotty lynx]

3

[timber tartan]

I think you need to subtract 1 in the bracket, and add 2 outside

if you approach it like that

[knotty lynx]

Yeah, I recommend factoring out the entire polynomial like Adam said

Less faff

[remote trench]

i have to do this at a later time, my brain cant handle more math

thanks though

.close

[vocal sleet]

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[lyric sluice]

I am looking for intuition as to how the artificial variables (using big-m method) fix the problem with the simplex method (Linear optimisation)

[vocal sleet]

@lyric sluice Has your question been resolved?

[vocal sleet]

@lyric sluice Has your question been resolved?

[vocal sleet]

@lyric sluice Has your question been resolved?

[vocal sleet]

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[lime viper]

how do i do this guys?

[lime viper]

helpers

@help ers

!help

[vocal sleet]

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

[hidden edge]

Consider f(x) = x(x-4)^2. a) Find the critical points of f. b) Determine Intervals on which f is increasing and intervals on which f is decreasing. c) Find all local maximum and minimum values of f if any. d) Find the candidates of inflection of f. e) Determine Intervals on which f is concave up and intervals on which f is concave down. f) Find the inflection points of f.

[lime viper]

??

[vocal sleet]

@lime viper Has your question been resolved?

[dense bison]

Dont know if you still need help for this but try calculating how many balloons remain per sold animal first if you get what i mean by that

Wait that's just the question i realised😓what part of this do you not understand

[vocal sleet]

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[vocal sleet]

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[jagged sky]

6c I have got the wrong answer

[jagged sky]

I did 11.6x12 for top

Front and back I did 5.8^2xpi45/360

Doubled it for front and back

5.8^2

[jagged sky]

Add onto this

5.8^2+5.8^2

Sqrt it Pythagoras theorem

8.2 roughly

Times by 12 to get the bottom

[quaint lance]

You have 2 of them on one side?

[jagged sky]

?

Surface area

[quaint lance]

In the front you have 2 45 degree part-circles, also at the back.

[jagged sky]

Ye I did that doubled it

[jagged sky]

Here

[quaint lance]

You have 4 in total then, right?

[jagged sky]

Ye

[ornate terrace]

wait so you did this, x2 + the pythag and then x 2 again?

ok

[jagged sky]

One sec

Changed it

Got it Ty

.close

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[vocal sleet]

@hushed cosmos Has your question been resolved?

[vocal sleet]

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[bleak prawn]

In part C I found the equation of the line y = x/2 + 4

How can there be a vector representation of a line formula?

A line and a vector are 2 different things...

Does it want me to find the vector at point A or something?

[mellow void]

there a point P on the line, and a direction vector v parallel to the line

so you can write l = {P + tv : t in R}

[bleak prawn]

and a direction vector v parallel to the line
Where? and what is it?

Also why point P? Why not point A? Thats where line l is...

Oh wait nvm

[mellow void]

oh, just find another point Q that lies on the line. then Q-P is hopefully a vector parallel to l

[bleak prawn]

I dont understand sry

Im a little lost

[mellow void]

me neither let me convince myself lmao, it's been a bit

[bleak prawn]

What is Q? And why do we want something parrallel? I thought we wanted the line that goes through A

[mellow void]

Q is just another point on the line

[bleak prawn]

Is the vector were looking for following the momentum of point A? Like the red vector? Or perpendicular to point A like the blue vector?

[mellow void]

also I'm not even addressing the calculus portion of this question so I'm probably missing some insight

[bleak prawn]

Or neither and im just completely misunderstanding the question haha?

[bleak prawn]

I think the only imporant bit is line l is y = x/2 + 4

[mellow void]

ok great

so you can definitely find two points on that line

[bleak prawn]

Oh also we know A is (0, 5)

sry that was important too 😅

[cedar delta]

um

so

here

since the derivative is the slope at that particular point

try finding out the equation of a line for point a

and the get the derivative which will be the slope

[bleak prawn]

Ah

[cedar delta]

and for two perpendicular lines

[bleak prawn]

y = -2x + 5

[cedar delta]

for point A?

[bleak prawn]

Yep

[cedar delta]

so x = 0 at A right

[bleak prawn]

Yeye

[cedar delta]

wait nvm

this equation is of the form

y = mx + c

so m = -2 = slope

[bleak prawn]

Yeye

[cedar delta]

since the product of slopes of two perpendicular lines is -1 the slope of other line is 1/2

and it passes through point A

which (0,5) i think

so now get the equation for the line

[bleak prawn]

Wait sry before we solve, what are they actually asking for?

[bleak prawn]

Blue vector or red?

Sry for shitty drawing

[cedar delta]

this?

[bleak prawn]

Yeah but from this diagram I drew

[cedar delta]

no vectors involved here

[bleak prawn]

Ohhh no

The last question sry

The bonus question

Sorry I didnt say hahaha mb

[bleak prawn]

Yeah this one haha

[cedar delta]

wdym

[bleak prawn]

I finished part a b and c Im doing the bonus question

[cedar delta]

u have the slope of line

[bleak prawn]

yep

[cedar delta]

and also have a point through where it passes

so get the equation now

it is easy

[bleak prawn]

but what does the vector look like sry

[bleak prawn]

Blue or red?

Or neither

[cedar delta]

vector of the line?

[bleak prawn]

Yeah

[cedar delta]

u need the equation to determine that

[bleak prawn]

'Find a vector represantation for line l as well'

[cedar delta]

but I think blue

[bleak prawn]

Ok I see

[bleak prawn]

Which equation sry

y = -2x + 5?

[cedar delta]

the equation of line L

[bleak prawn]

Ah yeah thats y = -2x + 5

or 2x + y = 5

[cedar delta]

the equation of line l is y = -2x + 5

?

[bleak prawn]

Yeye

[cedar delta]

oh

[bleak prawn]

My bad sry im not so good at explaining haha

[cedar delta]

nah its alr

wait

lemme see

[bleak prawn]

Wait

no sry

I got mixed up

[cedar delta]

?

[bleak prawn]

its y = x/2 + 4

is line l

Im so sorry 😂

[cedar delta]

nah its okay

wait

what were the cords for point A?

[bleak prawn]

(0, 5)

[cedar delta]

u made a mistake somewhere

[bleak prawn]

Oh?

[cedar delta]

cuz for the line l

for x = 0

y = 4

[bleak prawn]

Oh fuck yeah

(0, 4)

[cedar delta]

it never interesects point A

[bleak prawn]

Is A

[cedar delta]

yea

alr

[bleak prawn]

Mbmbmbmb

[cedar delta]

no worries

[bleak prawn]

So many silly mistakes 💀

Gotta focus better in my exam lol

[cedar delta]

the vector is the blue one

this is because

in this equation

rate of change of x is double that of y

so it goes more into the x axis then the y axis so its blue

[bleak prawn]

Ok makes sense

Im not sure how to find it tho

[cedar delta]

find what?

the vector?

[bleak prawn]

The vector

yeye

[cedar delta]

umm

lemme see

[bleak prawn]

it say find 'a' vector representation for line l , so im guessing theres a few

[cedar delta]

do u have the answer to this question

[bleak prawn]

Yeye

1 moment

Wtf does that even mean 💀

Idk what that symbol is

The half life symbol 😂

[cedar delta]

wait

what

thats not how I write vectors

I am confused what that even means

[bleak prawn]

You write them like [4, 2]?

[cedar delta]

no

do u know the i cap and j cap method?

[bleak prawn]

no

[cedar delta]

bruh

so basically anything

in the x axis is i cap

in the y axis is j cap

and z axis is k cap

for +ve axis only ^^^^

else it becomes - k cap and - j cap like that

for negative direction in axis

do u understand this?

[bleak prawn]

I think so

[cedar delta]

so in that way

the vector for the line

is

(2t-8) i cap + (t) j cap

where t is time

or wait no

not time

t is any integer

yea

t is an integer

[bleak prawn]

How did you work that out

[cedar delta]

um

[bleak prawn]

Sry if its a dumb question im not too familiar with vectors

[cedar delta]

so the equation is y = x/2 + 4

y = t

and x/2 + 4 = t

too

since they both equal

[bleak prawn]

ok....

[cedar delta]

and then we get y = t

and x = 2t - 8

so the vector is 2t - 8 for x axis

and t for y axis

where t is any integer

[bleak prawn]

Why

[bleak prawn]

and why

Sry

[cedar delta]

cuz x = 2t - 8

[bleak prawn]

Ah

[cedar delta]

so this is its path in the x axis

like for the line l

it follows x = 2t-8 for x axis

and y = t for y axis

[bleak prawn]

Wait

Why -8 and not -4

[cedar delta]

cuz its x/2

not just x

[bleak prawn]

Ah yeah

sry

[cedar delta]

np

do u understand now?

[bleak prawn]

Ummm

Im figuring it out

[cedar delta]

alr

[bleak prawn]

so we have 2t - 8 i-cap + t j-cap

Right?

so 6 negative i-cap + 1 j-cap?

[cedar delta]

u can put any integer in place of t

even negative ones

cuz a line is infinitely long

so u can

even go

-1 j cap

and -10 i cap

this is the general form I gave u

[bleak prawn]

Ok I see

This all feels really weird haha

But I thiiiink I get it

But how did they get this

[cedar delta]

I don't even know what that even means

[bleak prawn]

Ya me neither

[cedar delta]

cuz I write vector differently

[bleak prawn]

Wtf is that symbol

[cedar delta]

yea fr

[bleak prawn]

Tbh maybe I skip this question for now

Its just a bonus anyways

[cedar delta]

u got the a and b parts done?

[bleak prawn]

When im at a better level of maths I wil come back to it

[bleak prawn]

Yep and c!

[cedar delta]

noice

[bleak prawn]

Thank you for your help with it btw

And thanks for your help with this one to this point

❤️

[cedar delta]

ty for the free practice!

[bleak prawn]

Haha legend 💪

.close

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[finite hatch]

is he saying that spring constnat is = to f = ke

cause i thought

spring constant was k

[sullen shoal]

Yea spring constant is k

F is force

E is extension in spring

[finite hatch]

ohh ok

[sullen shoal]

Or change in length

[finite hatch]

and why in some cases

[sullen shoal]

Yea

[finite hatch]

k is negative?

[lilac bronze]

it's negative because the force acts in the opposite direction as the displacement

[sullen shoal]

No no

[sullen shoal]

Yeaa

[finite hatch]

;-;

[sullen shoal]

Ok so

In simple terms

When u try to stretch the spring

Assume u go to rught

Right*

The force acts towards left right

Opposite to displacement

That's y negative

[finite hatch]

i thought

it goes up or down

[sullen shoal]

Yea sure

[finite hatch]

oh wait

[lilac bronze]

doesn't matter which direction

[sullen shoal]

I mean attach spring to wall and stretch

[finite hatch]

ooohhh

[sullen shoal]

Force opposes stretch

That's y negative

[finite hatch]

can u explain in hang up and down

so we pull it down

[sullen shoal]

Yes

[finite hatch]

force acts down

wait

[sullen shoal]

So what is the force u experience?

[finite hatch]

oh yeah

[sullen shoal]

Up right

[finite hatch]

cause force is trying to get the spring back up?

back to original shape

is that how it works

[sullen shoal]

Yess

[finite hatch]

omg!!

i am smart

jk u are smart

thank u :D

[sullen shoal]

Anytime!

[finite hatch]

did u recently learn this?

[sullen shoal]

I'm done with my 12th

[finite hatch]

bc whenever i learn something i just forget in 2 weeks

omg.

[sullen shoal]

I learnt it in prolly 11th ig

[finite hatch]

am in 10th

ok thx :D

[sullen shoal]

Ohh

Np

[finite hatch]

.CLOSE

um

.close

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[young saffron]

.reopen

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[vast shale]

what does inf, sup, liminf, limsup mean? i googled and stuff but i dont get it

[hybrid flicker]

you know about lower bounds and upper bounds of a set?

[lilac bronze]

imagine an interval of real numbers [1,3]. the minimum is 1 and the maximum is 3. now think about (1,3). 1 and 3 are never in the interval, but are greater than any other lower/upper bounds. like, you can get "infinitely" close to 1 and 3 in the interval, but they still bound the interval without being in it. i forgot limsup and liminf (someone else can probably provide a better explanation)

[hard atlas]

if you have a sequence, there are points you get "infinitely" close to. for example 1/n gets infinitely close to 0 and 1,-1,1,-1,1,-1,... gets infinitely close to both 1 and -1

the limsup of a sequence is the biggest of those points the sequence gets infinitely close to

liminf is the smallest

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[lyric sluice]

In linear algebra I am doing vector spaces. I am just seeking clarification on these notations. Are the top two the same? I understand how the bottom one is different but It is just the top two that confuse me a little.

[hard atlas]

well it depends

the first one is definitely a function

but the second one could either be function notation or it could already be whatever you get after you plug in x into that function

for example if I have f(x)=x^2, then I could either use f(x) to denote that function, or f(x) to denote the real number I get after I plugged some real x into it

[rugged orchid]

I’d rather you call the function by its name “f”

But many people don’t distinguish the difference

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[bleak prawn]

https://cdn.discordapp.com/attachments/1267884548449108080/1267907757730697349/image.png?ex=66aa7e9e&is=66a92d1e&hm=5a2a4f85b43266c2cf5b587a95a2b24be53096c3cfb2a9b29b8e2fa5da8b7ebc&

[bleak prawn]

Part C

I think I know how to do it im just stuck on one bit

[bitter pilot]

area?

washer method is for volumes

[velvet zephyr]

don't encroach multiple channels

[bleak prawn]

I didnt

[velvet zephyr]

.close

jk

[bitter pilot]

💀

[bleak prawn]

Anyways

I have (p-x)e^-x and (-p-x)e^-x

Wtf

Bro

[fervent wasp]

!occupied

[vocal sleet]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[bleak prawn]

Why is everyone using my channels today

Anyways

[bitter pilot]

will you open a new one?

[bleak prawn]

I wanna integrate them both

[fervent wasp]

Plz no

[bleak prawn]

But its not on the x axis

So I cant do integral of ((p-x)e^-x)^2 - ((-p-x)e^-x)^2

Like I cant just do integral of A^2 - B^2

[bitter pilot]

Whats V_p

[bleak prawn]

I have to convert it to y

[bleak prawn]

(p-x)e^-x

[bitter pilot]

ic

no

V_p is region between x=0 and x=1

[bleak prawn]

Oh sry yeah

[bitter pilot]

,,\int_{V_p} f_p = 2

[twin meteor]

𝔸dωn𝓲²s

[bleak prawn]

But my question isnt really about any of that, im just confused about the method of converting a washer to the y axis

[bitter pilot]

what has that to do with washer

[bleak prawn]

Cause it if was just 1 line I could get that in terms of y

But idk how to do it with 2 lines

[bitter pilot]

what

[bleak prawn]

Idk the method thats all

[bitter pilot]

,,\int_0^1 x : \dd x

[twin meteor]

𝔸dωn𝓲²s

[bitter pilot]

for example

thats also between x = 0 and x = 1

so whaaaaat

[bleak prawn]

How do I convert it to y when its a washer

Am I not asking it correctly?

Idk maybe my english is bad

[bitter pilot]

you are asking A and expecting B for an answer

[bleak prawn]

Ok

p * integral of ((p-x)e^-x)^2 - ((-p-x)e^-x)^2

Whats the next step

Easier way of asking

[bleak prawn]

This is for rotating around the x axis, we need it to rotate around the y axis

How do we get it in terms of y

Idk how else to ask 😭

[bitter pilot]

at home

[bleak prawn]

????

What

[bitter pilot]

I am confused cause this has nothing to do with washer method, you should understand that.

So second

It says area not volume

,,f_p(x) = (p-x)e^{-x}

[bleak prawn]

From #rules ... pls dont get angry im just trying to learn

[twin meteor]

𝔸dωn𝓲²s

[bitter pilot]

Why are you projecting your feelings onto me?

Anyway

[bleak prawn]

Ok I understand now

Thank you

.close

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[halcyon oracle]

if you graph ln(y) against ln(-0.0002384x+0.0007494)

and it turns out to be a linear line

can the relationship between y and x be called logrithmic or approximately logarithmic?

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[halcyon oracle]

.close

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[real path]

Are there any proves that a quasiperfect number must be an odd square? There're very limited informations about in online.

[thick shadow]

I don't know about square but we can try different things about the odd part

[real path]

yep that's what im thinking too

[thick shadow]

All I know about squares is that they have an odd number of divisors

[real path]

how do i proof $\sigma(n)=2n+1$ only when $n\equiv 1\mod{2}$

[twin meteor]

Pop

[thick shadow]

since the sum is equal to 2n+1 we can conclude that there are an odd number of odd numbers

hope that this does not sound too confusing

[real path]

yea thats true

odd number of odd factors

[thick shadow]

yeah

[real path]

or is it possible to proof it by contradiction

[thick shadow]

It might be

Good idea

We can try

[real path]

like n DNE when $n=2^nk$

[twin meteor]

Pop

[real path]

Yea this is the furthest I can get to

[thick shadow]

wait, where did $\sigma(n) = (2^{n+1} - 1)*\sigma(k)$ come from

[twin meteor]

Randel_

[real path]

$\sigma(2^u)=2^{u+1}-1$

[twin meteor]

Pop

[real path]

hold up maybe i did smth wrong there

wait no i dont think so

[thick shadow]

No, it could be me - I have just learnt what the sigma function does

Thank you for that btw

[real path]

since the sum of divisor of 2^u is 1+2+4+...+2^u

[real path]

aight np

[thick shadow]

Maybe the way we prove that n is an odd number is by proving that $\sigma(n) = 0 (mod 2)$

[twin meteor]

Randel_

[real path]

but quasiperfect number states that n is a number such that $\sigma(n)=2n+1$

[twin meteor]

Pop

[real path]

instead of 2n

[thick shadow]

true

$\sigma(2^u) = 1 (mod 2)$

[twin meteor]

Randel_

[real path]

yep

actually 2^uk

where k is any possible odd number

[thick shadow]

since k is odd then $\sigma(k) = 0 (mod 2)$ (if it is not a square number)

[twin meteor]

Randel_

[real path]

yea thats true

maybe that's a new thing

i know that divisor sum function is multiplicative

but exponentation is a total new thing

not sure about that tho

oh wait i thought it's 2^k

dang

so that's the k from 2^uk?

[thick shadow]

yeah

[real path]

lmao

sorry mate it's 5 in the morning here

just woke up an hour ago

wait

[thick shadow]

dw about it

[real path]

if $\sigma(k)$ is an even number

[thick shadow]

then k is a square number

[real path]

$\sigma(k)\nmid 2^{u+1}k+1$

[twin meteor]

Pop

Pop

[real path]

sorry even number here

wait no 💀

[thick shadow]

hold on bro

is that some kind of a theorem or sth

[real path]

2k+1 is still an odd even tho k is odd

im exploding

[thick shadow]

Same right here

[real path]

doesnt work

[real path]

for what

yuh

[twin meteor]

Randel_

Randel_

[real path]

how is that?

[twin meteor]

Randel_

[real path]

doesnt that mean $(2^{u+1}-1)\sigma(k)=2^{u+1}k-1$

is this valid

[twin meteor]

Pop

[thick shadow]

I am sorry for having to leave you like this but I really have to go

[real path]

yeaa its fine ill wait for someone else

at least there's progress

[thick shadow]

Hope you find the solution

<@&286206848099549185>

[real path]

thanks mate

[vocal sleet]

@real path Has your question been resolved?

[real path]

<@&286206848099549185>

[vocal sleet]

@real path Has your question been resolved?

[real path]

dang i gotta go

.close

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[lusty salmon]

Not a specific question but I'm entering the ninth grade so I'd like to have some algebra or geometry related tips to keep in mind

[lusty salmon]

Or just in general any questions that you think would be good for a ninth grader (14 year old)

[hallow plover]

Start learning about analytical geometry, the sooner the better, play around in desmos with coordinates of points and curves and stuff, trust me, having intuition with this early on will help a lot

[lusty salmon]

I'm interested in maths and really enjoy it so don't think youre bothering me by asking harder questions

[oak magnet]

https://discord.com/channels/268882317391429632/326138737606262786 its probably more like a subject to a discussion too !

[lusty salmon]

I have mastered linear equations but never have I actually studied anything with curves will keep that in mind

[hallow plover]

The sooner you realize that all equations have a geometric counterpart, the better, trust me, the intuition helps so much in the long run

https://www.desmos.com/calculator

Use this

[oak magnet]

You can find all type of equations online tho

Like for lines,ellipses

Circle

[lusty salmon]

Alright do you recommend any YouTube videos or articles that would give me an introduction

Yeah I've heard circles are really important next year

[oak magnet]

Who have you watched already ?

[lusty salmon]

I also have a different question

[hallow plover]

Also go watch everything from 3blue1brown

[lusty salmon]

This year I studied triangle congruence theorems and postulates (hs, HL sas, sss, etc) but I have heard older kids talk about the sas similarly theorem and other similarity theorems so any idea on what those are?

[lusty salmon]

Not yet I'll give it a look tomorrow

[oak magnet]

Blackpenredpen pretty cool too

[lusty salmon]

Ok ok

[hallow plover]

congruence and similiarity are not the same, you'll learn about similiarity later on

[lusty salmon]

Id like to have a head start on similarity so could you give me an introduction or possibly a few YouTube videos

@oak magnet I'd like to stay in touch could you please send me a friend request

[oak magnet]

I let all math stuff on the server sorry, ill stay here tho, and if you have any questions youll get help dw

[lusty salmon]

Alright alright

[lusty salmon]

.

[mental falcon]

go on khan academy and look at topics you are interested in

[lusty salmon]

Ok got it

Any other topics I should keep in mind?

[oak magnet]

https://youtu.be/BI-rtfZVXy0?si=H_UNkh5Tdt3tqWTA

[mental falcon]

sounds like algebra, geometry, trigonometry would be at an appropriate level for you

[lusty salmon]

Tysm

[oak magnet]

(It was 16y ago xd)

[lusty salmon]

Yeah I'd like to also learn sine and cosine before I learn them in school

I have no idea what they are but I know they are under trigonometry

And that I'm going to take them the following year

Is there anything I should keep in mind here

[mental falcon]

khan academy has video lectures and exercises on all the high school topics you could want, go through what you want on there and if you have questions you can post here

[oak magnet]

All videos on ytb tho

[mental falcon]

https://www.khanacademy.org/profile/me/courses

[lusty salmon]

Do you think there are any highschool topics that I should learn

Like topics that would be somewhat easier for highschoolers and won't be covered in middle school

[oak magnet]

Some functions

[mental falcon]

common high school topics are algebra, geometry, trigonometry, precalculus, calculus, not everyone does the same at same time kind of depends on your current math level and varies by country, so did you just finish middle school? what classes have you finished?

[lusty salmon]

I'm entering the last year of middle school where I begin with trigonometry

I have no previous information about trigonometry

[oak magnet]

Is trigo all about soh cah toa ?

[mental falcon]

cool, then i'd say you could go through the trigonometry class on khan academy and get a headstart, learning trig deeply is invaluble as it's something that you will keep using in any other future math class. it also involves working a lot with triangles, circles which you said you were interested in so it will also help solidify your geometry skills

[lusty salmon]

If you want to know my level I would say I'm pretty outstanding in mathematics I got a 97/100 in my maths average last year

[lusty salmon]

Ok ok

[mental falcon]

https://www.khanacademy.org/math/trigonometry

[lusty salmon]

Thank you all so much for your help if you don't mind staying in contact within the next school year feels free to add me

[mental falcon]

great then you should be able to self-study well and you always have resources like this discord if you need clarification on something

[lusty salmon]

Yeah I don't use this server too often but it really helps when I'm struggling with a concept

Alright that's it?

[oak magnet]

If you good we are good

[lusty salmon]

Alr how do we end this again

[oak magnet]

.close

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[oak magnet]

.reopen

[lusty salmon]

Ight thanks

[vocal sleet]

✅

[oak magnet]

Do it

[lusty salmon]

See y'all thanks for the help

.close

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[gray escarp]

hello, i've done this problem and found the first 4 answer but those circled in red, i was not able to find

i did cos2theta = -1/2 for 0<= theta <= 2pi & 4pi

i found 2pi/6 , 4pi/6, 8pi/6, 10pi/6

how i went about this was: alpha = 2theta, cos(alpha) = -1/2 and I looked at the unit circle for the values, then i divided the 2 values obtained by 2

please ping if you respond

& this is in stewart's early transcendentals, calculus with polar section

nvm i got it

.close

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[heady quest]

find the results using de movire's

[heady quest]

Hey so how did this turn into z^3+8i=0

Isnt the theta supposed to be pi/2

Since its 90 degrees?

i thought it would be x^3 = 27i

[lone linden]

$2z^3+16i=0 \implies z^3+8i=0 \implies z^3=-8i$

[twin meteor]

Civil Service Pigeon

[heady quest]

So is it like wrong

[lone linden]

Positive arguments are taken anti-clockwise from the positive real axis

[heady quest]

cause the question says 27

[heady quest]

what does that mean

[lone linden]

Yeah ig so

[heady quest]

okie

.close

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[lone linden]

They’re taking two vectors that lie in the plane. The cross product gives a vector that is perpendicular to these two vectors, and is thus the normal vector.

Regarding your second question, (a,b,c) is the general form for the normal vector in its Cartesian representation, but it doesn’t even tell you that much by itself tbh

[tender isle]

so what is n=(a,b,c) used for then?

[lone linden]

(a,b,c) is the general form for the normal vector in its Cartesian representation

Although you could represent any vector like that

So it’s not particularly useful

The only real use in writing it like that is so you can say the equation of the corresponding plane is ax+by+cz+d=0

[tender isle]

Oh ok.

Just to make sure I understand, a x b aka the cross product of a and b always gives us a vector that is 90 degrees on both a and b?

[lone linden]

Yes

[tender isle]

Perfect, thank you 🙂

.close

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[fluid comet]

How to do this.

1. It is reported that out of the 3000 applicants being accepted to the Univerity, 20% of them are accepted to the Buiness course. Out of thase being accepted to the Ruined course, 10% of them are offered a scholarship. What is the percentage of the students being accepted outride Business course and get the scholarship, provided there are only 15 scholarships to be offered to whole applicants?

2. 40% of Class 3A are female students. If the female students in that dass have 80% chance to puss a math test and the male students have 75% chance to pass a math test. What Is the over all chance of the whole class to pass a math test?

[sly sierra]

Ruined course?!

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@fluid comet Has your question been resolved?

[mellow wyvern]

what have you done so far

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[fallen iris]

How do I even start bro

[mild rapids]

do you have some paper to draw?

try drawing in the same plane the following:

when all the functions are in the plane, just look for the domain (all x values with a real answer in y)

[fallen iris]

So just union?

A

???

Wit

E

E???

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[tepid sable]

How do I solve this

[vocal sleet]

@tepid sable Has your question been resolved?

[tepid sable]

No

[calm light]

first try to isolate the sin(theta)

[tepid sable]

Yeah

Sin = 3/4

[calm light]

sin = -3/4

[tepid sable]

Yeah

[calm light]

do you need to solve for all possible solutions or just the solutions on an interval?

[tepid sable]

All possible solutions

Or well

In between 0<=2pi

[calm light]

so let’s first use inverse sine to find one of our solutions

[tepid sable]

-48.59

[calm light]

we need our answer to be between 0 and 360 degrees

how can we do that?