help-23

[lean otter]

I think so? 😵‍💫

[junior smelt]

Ah, I'm thinking of the $(f^{-1})'(x) = \frac{1}{f'(f^{-1} (x) )}$ one

[flat frigate]

chartbit

[junior smelt]

You just get it from the above one from chain rule

Was that the one, or some other one?

[lean otter]

Oh yeah that one

[lean otter]

Oh but I guess in reverse right?

Oh wait doesn't matter lol

[junior smelt]

Hmm, I think you just differentiate that first one I said by x, right becomes 1, left becomes something chain rule-y

[lean otter]

Yeah I see it now, I forgot most of the calc 1 stuff so I wanted a refresher, thank you!

[junior smelt]

Ayy no worries, to be fair I have no idea on the multivariate calc stuff these days beyond just taking partial derivatives 😂

I'd be cursed if I ever do a multi-integral over a surface again

[lean otter]

Ohh I am taking the stuff rn and it is uhh

I feel like I'm in a physics class aha

[junior smelt]

Hahah damn, that module was one of the worst 😂

[junior smelt]

Physics, yikes 😷

There was another module we had with planetary motion and all that type of stuff, was actual pain

[lean otter]

Kepler's laws

[devout fossil]

Yo I need help with a question

It’s homework for my AS maths class

On proving identities

[lean otter]

Open

Your own

Channel

[junior smelt]

https://tenor.com/view/crying-cry-crying-face-gif-20235014

Literally opened the notes on that just to see what the module was like

[lean otter]

😭😭

[devout fossil]

I literally have no idea

[junior smelt]

Yea, I think I'm good b

[devout fossil]

I’m new to this

[junior smelt]

Here

#❓how-to-get-help

[lean otter]

How long has it been since u graduated

[junior smelt]

Like a few years time goes by so quickly tbh

[devout fossil]

U guys are graduates

Damn

I just wanna end this AS stuff

[junior smelt]

The first year out went by like a flash, it's nuts

[devout fossil]

Ayt bye

[lean otter]

Oh wow I wonder how it will be by the time I am by that age lmaoo

[junior smelt]

Haha, 'tis all life I guess 😂

Thought by now I'd be over maths, yet here I am somehow

[lean otter]

I am definitely going to try and continue going deeper into math as I go forward. Kind of curious if I will reach the day where I would start talking in the advanced channels and stuff

I think the most "abstract" Concept I have dealt with is graph theory, it definitely is fun times

[devout fossil]

Yo sry I’m back what do I post my question to

[junior smelt]

Any of those you want, provided they're still under that section

[junior smelt]

Ah I'm definitely sure you will, to be fair they're like for higher years right?

That said, some things seem to be on the boundary of "early university" and "advanced", and I guess depending on where you are, you'd come across some things at different times

Like there was a guy I know who basically did rings and modules, but had very little groups and linalg beforehand

[lean otter]

Oh usually catered to like graduate

[junior smelt]

Still managed to smash it tho!

[lean otter]

Oh i see that's fair

[junior smelt]

Ah, for me the line's a bit blurred cause my masters was like joined together with undergrad 🤔

[lean otter]

Oh whaaat

[lean otter]

Seems... Shaky

[junior smelt]

And with mine, many of the courses for masters were also available for later year undegrads

[lean otter]

Oh that's actually amazing tbh, gives u a lot of possibilities

[junior smelt]

Mind you, at least on our side, the module was actually pretty decent, so we suggested to him he do it 😂

Spent some of my first year after helping some peeps with their modules actually, was pretty cool to do!

[lean otter]

I wanna try to TA some first year courses myself if I was able to, it sounds fun and kind of enhancing of your potential

[lean otter]

Hahah that's fantastic lmao

[junior smelt]

It's definitely something to do if you get the opportunity to, if they offer it, I say go for it! As always, teaching others is a pretty good way to enhance your knowledge

Like when I taught people stuff before, I ended up seeing things I didn't notice before, it was like having my eyes opened

[lean otter]

Yeah exactly!

I think teaching, is heavily underestimated. It is way harder to make someone understand a topic than for you to understand it yourself

As they are obviously not you and so on haha

But anyways thank you so much for ur help and it was a nice conversation. I will hit the bed now, but I wish you a great day!

.close

[safe radish]

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[lament wadi]

calculate the power coupling factor of polarization when the angle of the polarizer is alpha, as defined in the figure as the direction of the slot subtended with the vertical. Assuming that the polarizer is large enough to avoid diffraction at its edges. Assuming that the width of the metal part between the slots of the polarizer, like the width of the slots themselves, is infinitesimal. alpha = 52.620 degrees. Answer in units of [W/W].

[safe radish]

@lament wadi Has your question been resolved?

[lament wadi]

<@&286206848099549185>

[lament wadi]

.close

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[muted solstice]

i need help with completing the square for multiple questions

[muted solstice]

x^2+6x=0

[lean otter]

You want to complete the squares?

[muted solstice]

yes

[lean otter]

Well lets see

First

do you know the square of sum formula

[muted solstice]

is it something to do with one an umber being a multiple of a number and being the sum of that same number?

[lean otter]

That is correct, but i am not asking that

Im referring to

(a+b)²

Can you work that out

[muted solstice]

(x^2+6x)^2?

[lean otter]

Bro

Try to answer ny question

I want you to expand

This

[muted solstice]

im asking if thats what you mean

ok

(a+b) (a+b)

[lean otter]

Expand

[muted solstice]

im not sure how to expand that any further

[lean otter]

Foil it?

[muted solstice]

o multiply it

[lean otter]

yes

[muted solstice]

a^2 ab ba b^2

[lean otter]

Its a rule, instead of foiling it everytime, you should memorize it

[lean otter]

Simplify

[muted solstice]

a^2 2ab b^2

[lean otter]

Use the + from now on

Okay so basically

You want to write your equation in this shape

you have x² + 6x

Can you choose a and b?

[muted solstice]

x^2 and 6x?

[lean otter]

we need two numbers such that, if we square their sum, we will get 3 terms, one of which is x² and another of which is 6x

One of these two numbers is x

So (x+b) ²

This should make it easier

we get x² + 2bx +b²

[muted solstice]

so b is 6x right?

or just 6

[lean otter]

What we need is

2bx = 6x

Solve for b

[muted solstice]

idk how to do that

[lean otter]

Divide both sides by x

[muted solstice]

2b = 6

[lean otter]

Ok?

[muted solstice]

b is 3

[lean otter]

now plug in the original equation

Not the original, i mean the one we made

[muted solstice]

this one?

[lean otter]

Nope

[muted solstice]

or tthis one

[lean otter]

Above

[lean otter]

Yes this one

But

Better if we plug in

The factorization of it

[muted solstice]

what do you mean by that

[lean otter]

Where did we get this from?

Do you know what step preceded this?

[muted solstice]

by extending this

[lean otter]

Expand*

Yes

That one

Now plug in b

[muted solstice]

x^2 + 12x + 36?

[lean otter]

Nope

b isnt 6

[muted solstice]

oh its 3

x^2 + 6x + 9?

[lean otter]

Yes

Now we had at first

x²+6x=0

What are we missing?

[muted solstice]

now we have this = 0?

[lean otter]

Not yet

[muted solstice]

x is missing

[lean otter]

Think twice before you answer

[muted solstice]

:/

[lean otter]

Where do you see x missing?

[muted solstice]

x²+6x=0

the 2 x's

[lean otter]

Ok?

We have x²+6x+9 in the other equation

The x isnt missing

Something else is missing

[muted solstice]

the = sign?

[lean otter]

x²+6x+9
x²+6x

The answer is in front of you

[muted solstice]

you asked me whats missing and im telling you whats not there

[lean otter]

The 9 is not there

[muted solstice]

ok

[lean otter]

Add a nine to both sides

[muted solstice]

x^2 + 6x+9=9

[lean otter]

Now factor

[muted solstice]

ok

wait im having trouble

[lean otter]

x²+6x+9

Try to un-expand it

Which is called factorization

[muted solstice]

x+x+6x+9?

[lean otter]

Remember when we had something and we expanded it and ended up with this very formula?

Now lets just reverse the process

[muted solstice]

idk how to even try to do that

[lean otter]

Remember when we said that

a²+2ab+b² = (a+b) ²

We wanna do the same thing now

[muted solstice]

so i would do (x+3) (x+3) again?

or a instead of x

[lean otter]

yes

Now

[lean otter]

Plug this into what he had last

[muted solstice]

9?

hello?

[lean otter]

Yes

You get

(X+3)²=9

[muted solstice]

how

oh wait

how do we know its 9 if we dont know the x value yet

[lean otter]

Ask yourself

[muted solstice]

oh right

[lean otter]

Now root both sides

[muted solstice]

square root?

[lean otter]

yes

[muted solstice]

square root the 9 right?

[lean otter]

Both sides

[muted solstice]

both nines?

[lean otter]

x+3=±3

[muted solstice]

where did that come from

[lean otter]

We square rooted both sides

[muted solstice]

it just gave me 3

where did all that other stuff come from

[safe radish]

@muted solstice Has your question been resolved?

[muted solstice]

.close

[safe radish]

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[patent vault]

can i get a hint please?
There are 30 students in a class, all of them girls or boys. They are sitting at 15 two-student desks in such a way that exactly half the girls are sitting with boys. Prove that one cannot reseat the students (at the same 15 desks) in such a way that exactly half the boys are sitting with girls.

[patent vault]

are there 15 girls and 15 boys?

im not sure why its not possible

maybe there arent enough pairs to completely reseat

oh wait i misread

this is a weird question

any hints?

[worthy hemlock]

Not quite

[patent vault]

ye i realized that

[worthy hemlock]

There are 30 students, if half of the amount of girls sit with boys, what does that mean?

[patent vault]

what does it mean?

[worthy hemlock]

Say you have a size of 20 students, and half the amount of girls sit with boys. Let's say you have 7 girls, can half the girls sit with boys?

[patent vault]

no

so the number of girls is even?

[worthy hemlock]

If half the amount of girls sit with boys, that means the amount of girls need to be even, right?

So if you split the amount 50- 50, meaning 15 girls, 15 boys, and half the amount of girls sit with boys, is that possible?

@patent vault

[patent vault]

no

[worthy hemlock]

Do you see how you can answer your problem now?

[patent vault]

not really..

[worthy hemlock]

https://math.stackexchange.com/questions/1344136/students-in-a-class-girls-sitting-with-boys-and-boys-sitting-with-girls

[patent vault]

i dont want to look at the solution

[worthy hemlock]

You asked how to solve it, I tried to explain, you didn't understand, so there you go

[patent vault]

this doesnt tell me that they cant be rearranged

this was in one of the solution

Regardless of the relative amounts, the sum of half the boys and half the girls gives half the total number of students.

why is this?

@worthy hemlock

not sure about the second solution either

why would it be a multiple of 4

[safe radish]

@patent vault Has your question been resolved?

[patent vault]

u there?

[hot thistle]

you have half of the girls seating with boys, so then the other half must be all pairs of girls correct?

so then that other half must itself be a multiple of 2, as you have some number of pairs of girls

so then it must be a multiple of 4

@patent vault

[patent vault]

ah thanks

.close

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[muted solstice]

i need assistance with multiple quadradic equations by completing the square

[muted solstice]

x^2+6x=0 is the first one

[slate elbow]

substract x

[worthy hemlock]

by completing the square

[slate elbow]

a^2 + 2ab + b^2

x^2+6x +9 -9=0

[worthy hemlock]

Fyi, don't do the work for people

[slate elbow]

do you see it now?

i aint

[muted solstice]

yeah i got up to that point

and a few minor steps after that

[slate elbow]

.

[muted solstice]

but i keep getting stuck

[slate elbow]

but that is almost

the end then

[worthy hemlock]

You should have something like (x + 3)^2 = 0, if I recall

Solve for x

[muted solstice]

x would be -3 right?

[slate elbow]

x^2+6x +9 write this as (a+b)^2

[worthy hemlock]

Yes, and how many times does that occur?

[muted solstice]

twice?

[worthy hemlock]

Yes

[slate elbow]

but in that example

(x + 3)^2 = 0

you cant get that

[muted solstice]

ok now we solved x now what?

[worthy hemlock]

That's it

You solved the equation

[muted solstice]

so x= -3

thats it?

[worthy hemlock]

Yes

[muted solstice]

hold on

[static vale]

Bro surprised how easy it was

[muted solstice]

i am

ok so if i plug in -3 in the original x^2 +6x=0

it will equal zero?

[worthy hemlock]

I was telling you how to do it before, and you were just overcomplicating it

[muted solstice]

because every video i came across overcomplicated it

and i was just really stressed out aswell cuz of a dead line

why does mathway say x=0,−6

[worthy hemlock]

Oh shoot, hang on, you start with x^2 + 6x = 0, to complete the square you need to add (b/2)^2 to both sides

[muted solstice]

ah yes

[worthy hemlock]

Because if you completed the square on the left side, aka getting it in (x + 3)^2, the sides have become unbalanced

[muted solstice]

ok so would it be (x+3)^2=9?

[worthy hemlock]

Yes

[muted solstice]

so x would be

[worthy hemlock]

Now solve for x

[muted solstice]

6

noo

wait

x would be 0

that makes more sense

[worthy hemlock]

That's one of the solutions

[muted solstice]

0+6*0

[worthy hemlock]

.

[muted solstice]

how would i find the second one

[worthy hemlock]

Well, recall, if you take have to apply the square root, it's a $\pm$

[flat frigate]

dldh06

[muted solstice]

square root (x+3)?

[worthy hemlock]

So when you took the square root of both sides, it's $x + 3 = \pm \sqrt{9}$

[flat frigate]

dldh06

[muted solstice]

ok so x would be 0 and 6

nice

[worthy hemlock]

Not quite

[muted solstice]

wait

[worthy hemlock]

From here, $x + 3 = \pm \sqrt{9}$, what's the next step?

[flat frigate]

dldh06

[muted solstice]

so its x+3= +- 3?

[worthy hemlock]

Then, what's the next step?

[muted solstice]

hold on how did 9 get square rooted

is it cuz we have to do sqr root on both sides?

[worthy hemlock]

$(x+3)^2=9$
If that's the equation, how would you get rid of the power?

[flat frigate]

dldh06

[muted solstice]

square rooting

and then do the same on the other side

ok i see now

so the 2xs would be

0

and

oh well -6

[worthy hemlock]

Yes

[muted solstice]

wow all that stress and hours wasted over problem this simple

[worthy hemlock]

And you can check the work, by plugging those values into the original problem

[muted solstice]

-6 squared is 36 right?

cuz my calculator said -36

[worthy hemlock]

Because you didn't use parentheses

[muted solstice]

oh ok

alr next question

x^2+8x=2

wait is this the exact way of doingg the last one?

[worthy hemlock]

Same process that you just did, except it's = 2 this time, not 0

[muted solstice]

ok ok

then ill skip that

x^2+12x-5=0

hello?

.close

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[dense wraith]

need help with this

I got the answer

is it 33?

[worldly remnant]

Good job

[dense wraith]

I did 7x-4 = 1/2(38 + 6x - 6)

and then I got 6.5

and then I subbed that in VU

Which gave me 33

is that right?

[frank glen]

Hmm

[dense wraith]

oh no

is that wrong

[frank glen]

I got 5

[dense wraith]

as the final answer?

[frank glen]

X = 5

[dense wraith]

using the same equation?

[frank glen]

Yeah

[dense wraith]

uhhh

ohhh

I just realized

what I did wrong

[frank glen]

What went wrong?

[dense wraith]

I did 19 + 3 by accident

instead of subtracting it

[frank glen]

Alright

What did you get for VU?

[safe radish]

@dense wraith Has your question been resolved?

[safe radish]

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[hybrid narwhal]

can someone help me understand this proof?

[mystic ether]

good luck cuh

[hybrid narwhal]

i'm stuck at the conclusion

[mystic ether]

oh good luck to u too cuh

that looks fuckin difficult

[hybrid narwhal]

[drowsy moss]

what part is confusing you?

[hybrid narwhal]

i just fail to see how they managed to prove that it is continuous and what relevance the algebra of limits theorem has

ok they showed the bottom line which means its continuous but where did they use the algebra of limits theorem

[drowsy moss]

$\lim_{h\to0}\left(\frac{f(x+h)-f(x)}{h}\right)h + f(x) = \left(\lim_{h\to0}\frac{f(x+h)-f(x)}{h}\right)\left(\lim_{h\to0}h\right) + \left(\lim_{h\to0}f(x)\right) = f'(x)\cdot 0 + f(x)$

[flat frigate]

Zybikron

[hybrid narwhal]

i understand that

[drowsy moss]

that's the algebra of limits

[hybrid narwhal]

ohh lmao

ohh i see

ok ok that makes sense

thank you

.close

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[spiral crescent]

how to do this?

[plucky elk]

What does that underline say? 1?

[spiral crescent]

here?

then yes 1

[drowsy moss]

pretty sure it's supposed to be the perpendicular symbol

[spiral crescent]

yes the question asks find perpendicular distance

oh wait i think i got it

[plucky elk]

$\perp$

[flat frigate]

riemann

[plucky elk]

I guess

[spiral crescent]

yes perpendicular

This is a valid way to get the answer right?

[safe radish]

@spiral crescent Has your question been resolved?

[safe radish]

@spiral crescent Has your question been resolved?

[safe radish]

@spiral crescent Has your question been resolved?

[safe radish]

@spiral crescent Has your question been resolved?

[safe radish]

@spiral crescent Has your question been resolved?

[spiral crescent]

.close

[safe radish]

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[runic escarp]

I just need clarification with the wording of the question

<@&286206848099549185>

This is taylor expansion btw

[safe radish]

@runic escarp Has your question been resolved?

[somber otter]

calculate f(pi)/f(e) by putting the values of f(x) and expand by taylors theorem with respect to (x-e) instead of x, write first 2 terms

[runic escarp]

Ah I see... how would you expand with respect to (x-e) ? I think that's what's confusing me

[somber otter]

i think it would be simple if u substitute x-e=t so that way, x=t+e and then expand along t

[safe radish]

@runic escarp Has your question been resolved?

[runic escarp]

Okay so I did some working and it doesn't give me the right answer

[safe radish]

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[viscid grail]

could someone explain to me how this happens?

[viscid grail]

I'm incredibly confused

I just don't understand

on the second row you log with base b both sides

that's how the one above happens

but I have 0 clue how it becomes logax * logba

[stark idol]

log (x^y) = y log x

[viscid grail]

oh

let me do it myself

oh

I see it

ty @stark idol

.close

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[peak estuary]

chill

what is (x+1/x)^3

[heavy minnow]

Don’t ping people randomly

follow the rules

#❓how-to-get-help

I don’t care

don’t do it again

[peak estuary]

that is equal to (a+b)^3

I asked about (x+1/x)^3

ok and now stare at this term. what do we know about it. what do we want to know

[viscid grail]

vistaguy, really pay attention to what Denascite is saying

it makes incredibly a lot of sense

no

think about it

you'll eventually find out

I'm not helping, I have my own problems to study

[peak estuary]

and if we know set z=x+1/x, what do we get

[lean otter]

Yeah about that..

[heavy minnow]

man

muted for 3 hours

follow the rules

[lean otter]

I don't think you saying that repeatedly will make you get help any faster

[lean otter]

Lmao rip

.close

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[heavy minnow]

Thanks

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[gaunt raptor]

Check this pls

[sand minnow]

,rccw

[sand minnow]

$\dv{x}xe^x\neq xe^x$

[flat frigate]

Duh Hello

[sand minnow]

first line

you need to use product rule

[gaunt raptor]

Yeah i used in the next step

[sand minnow]

ah, well you didnt distribute the ln(x) to it after

$\ln x \dv{x}(xe^x)=\ln x(e^x+xe^x)=\ln (x) e^x+\ln (x) xe^x$

[flat frigate]

Duh Hello

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[somber comet]

may ik what comes next

[thin bridge]

do something to both sides of the equation to get
stuff = 0

[safe radish]

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[somber comet]

okkk

ty

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[safe parrot]

How do i go about solving this?

[raw pivot]

so first of all you can simplify

[safe parrot]

x^2 - 3^2 = 2^2

?

[raw pivot]

so the first thing you should do is put all your known terms to one side and all your unknowns to the other

[slow fern]

Is 6 the answer?

[raw pivot]

ye but dont give out answers like that

[slow fern]

You can find the answer just by looking

[safe parrot]

,rotate

[safe parrot]

These are the formulas provided but i'm having some trouble understanding it

The top one, does it mean:
a^x can be written as xloga

[compact ferry]

relate them to exponentials

a^x is not xlog(a)

but log(a^x) = xlog(a)

[safe parrot]

ugh i really dont understand

everyone in my class says its super easy just follow the formula but i dont even understand the formula provided

[safe parrot]

its honestly aggravating

[safe parrot]

#❓how-to-get-help

[safe parrot]

Can someone please explain these so i understand them

[safe radish]

@safe parrot Has your question been resolved?

[safe radish]

@safe parrot Has your question been resolved?

[safe parrot]

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[static yacht]

Is this move allowed / correct?

[static yacht]

(new help channel with clearer question)

[pseudo scroll]

yes

[static yacht]

.close

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[lean otter]

A box has 4 marbles carrying the number X, and 5 marbles carrying the number Y

What is the chance that, when randomly pulling 3 marbles from the box, they all have the same number

[lapis shadow]

whats the probability u take 3 marbles all with X on them?

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

yes, or Y

either 3 Xs or 3 Ys

[lapis shadow]

no im asking u what the value is

what is the probability that u take 3 marbles will X on all of them

can u find it

[lean otter]

oh

lets see

i can get to an answer, but im not sure how to put it mathematically

at first,

we have 4/9

we take one X

we get 3/9

which is 1/3

we take another X

thats 2/8

which is 1/4

we multiply these

4/3* 4 *9

should be 1/27

is this correct?

[dire hound]

Shouldn't it be 3/8 instead of 3/9?

[safe radish]

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[dire hound]

Because u take a marble out decreasing the total number of marbles

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[safe radish]

Please don't occupy multiple help channels.

[carmine vessel]

how to do this

[little parrot]

do u still need help with this?

[safe radish]

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@carmine vessel Has your question been resolved?

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[main lynx]

Can someone help me with this ?

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[vocal spindle]

i got (12-x)/12

first

[elfin thicket]

I can help

[vocal spindle]

yeah

[elfin thicket]

if you typed that into a text

please

[vocal spindle]

how?

[elfin thicket]

The equation

[vocal spindle]

in text?

[thin vessel]

you should multiply it with the common denominator

[vocal spindle]

i did

i got

(3(3x-2)-4(2x-5))/12=(1+6)/6

[elfin thicket]

Check your dm

[thin vessel]

then multiply by 12

the whole equation

[vocal spindle]

$$\frac{3x - 2}{4} - \frac{2x - 5}{3} = \frac{(3x - 2) \cdot 3 - (2x - 5) \cdot 4}{12}$$

Simplify the expression on the left side by performing the multiplication and addition.
$$\frac{9x - 6 - 8x + 20}{12} = \frac{1+x}{6}$$

Combine like terms to get:
$$\frac{x - 26}{12} = \frac{1+x}{6}$$

[flat frigate]

KING TEE

[vocal spindle]

Multiply both sides of the equation by the common denominator to eliminate the fractions.
$$x - 26 = (1+x)$$

Combine like terms to get:
$$x - x - 26 = 1$$

Solve for x by adding 26 to both sides and moving all terms to the left side:
$$-26 = 1$$

Solve for x by subtracting 1 from both sides:
$$x = \boxed{-27}$$
This is the solution to the given equation.

[flat frigate]

KING TEE

[vocal spindle]

it isnt -27

.close

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[crimson steppe]

need explanation of how to do that

[grizzled pasture]

💀

[wheat cave]

which of them

[crimson steppe]

all of them kindly

[wheat cave]

where exactly are you stuck

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[serene pine]

How should I integrate this

[obtuse plover]

Try a u sub

[solid shell]

Yeah you can do u-substitution

[obtuse plover]

Don’t forget ur “dx”

[serene pine]

Could any of you write it down on paper please

I really dont understand it

[flat frigate]

Stephen

Stephen

[serene pine]

I still don't understand it but thank s 🙂

.close

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[obtuse plover]

https://youtu.be/sdYdnpYn-1o

This vid may help

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[slow seal]

how do i do this?

[marsh walrus]

calculus?

[slow seal]

yeah

[marsh walrus]

related rates

[slow seal]

i believe so

[marsh walrus]

no i mean use related rates

[slow seal]

i don't know how to get started

what do i do with the 32 revolutions per minute?

[marsh walrus]

first you have to kinda build a roadmap of related quantities

so you are interested in x

but x depends on theta

but theta depends on t

[slow seal]

not following to be honest

[marsh walrus]

what is $\dv{\theta}{t}$

[flat frigate]

jan Niku

[marsh walrus]

use this

remember we want radians

not revs

[slow seal]

i feel like im just forgetting some formula

thats the issue

[marsh walrus]

its no formula

you have 32 revolutions per minute

so how many radians per minute

[slow seal]

oh

2pi yeah?

[marsh walrus]

theres 2pi rads in one rev

so youre doing 32 rotations in a minute

and each one of those is 2pi radians

[slow seal]

yeah 64pi

but im still lost lol

tantheta = x/4? then take derivative?

oh wait

i think i got it?

i got it

thank you

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[slim walrus]

Hello I need help with this math problem:

[slim walrus]

We want to move a box over a distance of 13 m in the direction indicated by the vector d by applying a force of 400 N corresponding to the vector f. The work W (in J) corresponds to the scalar product between the force and the displacement. Determine the force necessary for the work to be equivalent to that done by a force having the same orientation as the displacement if the angle φ formed between the force and the displacement is 20 degrees.

[stray socket]

You wanna project f onto d?

[slim walrus]

I don't really know. I don't even understand the question that well

It's a question in my math book

[obtuse plover]

W1 = W2. Fdcos1 = Fdcos2

I’ll be back

[safe radish]

@slim walrus Has your question been resolved?

[slim walrus]

I understood

Thx you anyway

.close

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[viral current]

can someone please help me on this problem?

[safe radish]

@viral current Has your question been resolved?

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[viral current]

.reopenm

.reopen

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✅

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[willow steppe]

how to obtain equation of ellipse where a=Acosθ and y=Bsinθ, θ is parameter

[untold sky]

recall the trigonometric identity cos²θ + sin²θ = 1

[willow steppe]

ok then

[willow steppe]

how to eliminate A and B

[safe radish]

@willow steppe Has your question been resolved?

[safe radish]

@willow steppe Has your question been resolved?

[lapis shadow]

u cant eliminate A and B

you are looking for an equation relating a and y

[willow steppe]

x and y

[lapis shadow]

so maybe u meant to write x = Acostheta here

still

[willow steppe]

i mean the eq which i need is x^2/a^2+y^2/b^2=1

@lapis shadow

[lapis shadow]

yeah

[lapis shadow]

use this identity

[willow steppe]

how to get a^2 and b^2 as denominator

[lapis shadow]

okay if x = Acostheta

what costheta = what?

[willow steppe]

??

[lapis shadow]

sorry i mean if x = Acostheta

can u find costheta in terms of x

so move everything other than x to one side of the equals sign?

[willow steppe]

ookkkk gotcha

thanks alot

[crimson steppe]

i want the steps for this maths

[lean otter]

Sat?

[safe radish]

@willow steppe Has your question been resolved?

[crimson steppe]

yes

[versed sand]

hey i am Indian of class 8th

[willow steppe]

.close

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[inland grove]

ho

[inland grove]

i need help but im just a seven grader so dont be mad at me

[crimson nacelle]

if you are in 7th grade aren't you under 13

but anyways, what's your problem?

[safe radish]

@inland grove Has your question been resolved?

[dusky escarp]

ask

[inland grove]

wait i hve to check

ill take that back

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[smoky hatch]

i have a question are you here?

[smoky hatch]

hello?

[real swan]

Just ask the question

[quasi bison]

who's this "you" that you, @smoky hatch, are trying to reach?

[smoky hatch]

okay

i have a problem

so

there is a teacher who has 24 students, and he has to correct the tests from them

he has 6 options, really bad, bad, normal, good, very good and super good

how many possibilities are there?

??

[quasi bison]

well, there's 6 options for each student with 24 students

so surely you would want to multiply that many copies of 6 together

[dusky escarp]

basic multiplication

24X6 = 12 X12 = 144

[safe radish]

@smoky hatch Has your question been resolved?

[smoky hatch]

i have another question

there are 6 men and 5 women, you have to form a group of 5 peope, what is the chance that the majority are men?

[safe radish]

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[stoic dune]

Have to click the checkmark to keep the channel open haha

Make a new channel if you are still struggling with it

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[harsh tiger]

I know that the geometric multiplicity is equal to the dimension of the eigen spaces. But how do I relate this to the equations given? I can find the eigen values from the equations but idk what to do next. Can anyone tell me how to go about it?

[compact ferry]

$1 \leq m_g(\lambda) \leq m_a(\lambda)$

[flat frigate]

Gijs

[compact ferry]

m_a and m_g being the algebraic and geometric multiplicities

[harsh tiger]

So, do i find the roots first and then put it in this inequality?

does 3 roots mean the diagonal has 3 elements?

[compact ferry]

3 equal roots means that root has algebraic multiplicity 3

16a) for example

$\lambda = 0$ is a root with $m_a(0) = 3$

[flat frigate]

Gijs

[harsh tiger]

thanks!

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[fickle trail]

I have asked thus a few times but I’m still not clear about this question.. some say that 0, 90, 180, 270, 360, etc. degrees does not fit in a quadrant (1-4) because it sits on the line.

But Google is telling me quadrant 1 is 0-90 degrees, not 1-89 degrees

Do we call these straight angles that sit on the line “quadrant angles”? And are they still part of their quadrant 1-4 respectively?

I think 90 degree would be quadrant 2, yeah?

Or is this where they overlap

[lean otter]

It lies on the border of quadrants I and II so it can treated as belonging to, and also having the properties of, either and both of them

[fickle trail]

Hmmm so 90 degrees is both quadrant 1 and 2?

We can say quadrant 1 angle for 0 degrees? Quadrant 2 angle for 90 degrees?

Or it could go both ways

For 90

[lean otter]

okay so i think you are thinking semantics a bit too much here

forget about quadrants

think of the unit circle instead

[toxic stratus]

it really doesn't matter

[fickle trail]

Oh OK

[lean otter]

"Quadrants" are just things they teach u to make u learn the thing easier

but all you need to know is given to you in the unit circle, if you understand how that works

[fickle trail]

So these angles that sit on the line are less relevant to quadrants.. it’s only the ones that fall within them

[toxic stratus]

it's just an edge case

[fickle trail]

Like 361 degrees would be quadrant 1

But 360 degrees would be quadrant 1 or 4 depending on how you want to look at it

[toxic stratus]

whether or not they belong to a quadrant really doesn't matter

[lean otter]

why do quadrants matter this much?

[toxic stratus]

you would just say it lies on the axis

[lean otter]

like, what does an angle being in quadrant 2 tell you?

[fickle trail]

Hmmm really? Because using the quadrants is how it’s being taught lol

[fickle trail]

Maybe the end behaviour

[lean otter]

again this tbh

[fickle trail]

Oh OK, so for 360 degrees it tells us that it’s on the positive x axis

[lean otter]

yes

just think that instead

[fickle trail]

Alrighty

I will remember that for anything 0,90,180,360, etc. in 90 degree intervals.. just state the axis behaviour instead of the quadrant it falls into

Thank you!

.close

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[wind robin]

.

[wind robin]

why was it changed here

and how

[lean otter]

,rotate

[faint hornet]

i can answer one of those questions off the top of my head,
why - to get it in the form of beta function

[wind robin]

how can i do it ?

[wind robin]

how

[safe radish]

@wind robin Has your question been resolved?

[spiral crescent]

Ok i think i get it

[wind robin]

how?

[spiral crescent]

Fiest sub x=pi-p

Ill just show the way i did it was pretty lengthy tho

[wind robin]

its fine i need to understand it

[wind robin]

can you explain it real quick

[spiral crescent]

Ok so first on the top right you see

[wind robin]

ye

[spiral crescent]

x=pi-p

dx=-dp

[wind robin]

what are those?

[spiral crescent]

What are what

[wind robin]

like why did you make x= pi-p

[spiral crescent]

It was making one of the bounds 0

[wind robin]

ah i see

[spiral crescent]

And it wouldnt change the original integrand

[wind robin]

yes yes

[spiral crescent]

So in the 3rd step what i used was something from periodicity of functions

sinx ^6. cosx^7 has period 2pi

[wind robin]

ye

[spiral crescent]

So you can seperate it like that

Then in the 0 to 2pi bounds integration

I manipulated the area

[wind robin]

ye

[spiral crescent]

"area"

Gives 0 to pi, the thing added to itself

Then took it was W, and used kings rule, and ull find w=0, so I=0+0=0

And you get what you wanted to see

[wind robin]

but you replaced x with p?

[spiral crescent]

Do a substitution

x=p

[wind robin]

How on earth did my teacher do all that in one line

[spiral crescent]

Idk💀

Maybe theres a better way

[wind robin]

ill think of a better way

hopefully

thank you

[safe radish]

@wind robin Has your question been resolved?

[safe radish]

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[lucid grotto]

Determine the value of the parameter a for which the tangent line to the graph of y = x^2 + 2ax + a^2?
in the point with x-coordinate 2 is orthogonal to the straight line y = 3 - x.

[lucid grotto]

help

[alpine adder]

Orthogonal?

[lucid grotto]

yes

90 degrees

[alpine adder]

Oh perpendicular

[lucid grotto]

yeah

[alpine adder]

Take the derivative

[lucid grotto]

of the straight line?

y' = -1

[alpine adder]

No the x²+2ax+a²

[lucid grotto]

aah okay

can't

[alpine adder]

Have you learnt derivatives yet

[lucid grotto]

yes

[alpine adder]

Hmm then what's the problem

[lucid grotto]

how do I derivate a?

i havent done that yet

x^2 would be 2x

and then?

[alpine adder]

Wait sorry my battery is almost finished and will go off in a min and I can't get the charger rn sry ask someone else for help

[lucid grotto]

okay no problem

thanks

<@&286206848099549185>

[junior smelt]

...what does the 2ax become?

[junior smelt]

a is a constant

[lucid grotto]

so a = 0

[junior smelt]

(i.e. you treat it like any other number, like 4, 20, 69, etc)

[lucid grotto]

alright

[alpine adder]

Lol

[lucid grotto]

so the final derivative would be 2x

ryt?

[alpine adder]

2a

[junior smelt]

Not quite, you start off with $x^2 + 2ax + a^2$

[flat frigate]

chartbit

[junior smelt]

$x^2$ becomes $2x$ as you rightly said, but $2ax$ becomes...

[flat frigate]

chartbit

[junior smelt]

This

[lucid grotto]

2x + 0 + 2a?

okiee

2x+2a

what do I do after taking derivative?

[junior smelt]

Basically, you would substitute x=2 into that, and figure out that it's equal to something

[lucid grotto]

4 + 2a = 0

a = -2

[junior smelt]

Hmmm not quite

[junior smelt]

Remember that you want the gradient out of this to be something that'll be perpendicular to that line, yea?

[lucid grotto]

yeah

[alpine adder]

What would be the line that is perpendicular to 3-x

[junior smelt]

(gradient of the line)

[lucid grotto]

negative reverse?

[junior smelt]

Right idea...

Think you know how to get it...

[lucid grotto]

but I dont know how to get that?

[lucid grotto]

no

how do I get it with the derivative that i just found?

just plugging it?

[junior smelt]

Substitute the answer to our question to be equal to 4 + 2a

[lucid grotto]

2x+2a
y=3-x

[junior smelt]

You know that the gradients of perpendicular lines multiply to -1 (hopefully), or something similar...

[lucid grotto]

yes

[junior smelt]

So then the gradient of a line perpendicular to the line y = -x + 3 is...?

[lucid grotto]

x-3

[junior smelt]

I'll take that - the answer to my question was "the gradient is 1"

Now, set 4 + 2a = 1 and solve for a

[lucid grotto]

i am so sorry, i just dont get it

[lucid grotto]

could you please help with this?

[junior smelt]

All we asked for here is the gradient of perpendicular lines

[lucid grotto]

yes

[junior smelt]

You want the line y = -x + 3 to be perpendicular to the tangent you get out of here

Assuming you're familiar with finding the equation/gradient of tangent lines?

[lucid grotto]

yes I do know how to find equations

[junior smelt]

Cool, so basically, with $y = x^2 + 2ax + a^2$, we find the derivative $\frac{dy}{dx} = 2x + 2a$, and evaluate it at $x=2$ (giving $\frac{dy}{dx} = 4 + 2a$)

[flat frigate]

chartbit

[lucid grotto]

yes

[junior smelt]

We could find the equation of the tangent line (by e.g. substituting x=2 into y=...), but then that line we get, we know it to be perpendicular to the line y = -x + 3

And the gradient of that tangent line would be $4 + 2a$, so we know e.g. that $(4 + 2a)(-1) = -1$ (that's restating "product of the gradients of perp lines is -1")

[flat frigate]

chartbit

[junior smelt]

Does that help any more?

[lucid grotto]

yesss

thank you so much

[junior smelt]

Anyways, from there, it's just solving for a, and you're done!

[lucid grotto]

thanks

🙏

.close

[safe radish]

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[ember sphinx]

https://gyazo.com/ff4a2c9d0d40889cd7baf3a263b8ad94

[ember sphinx]

what is the condensation method

everytime i search it up it comes up with chemistry

[plucky elk]

https://en.wikipedia.org/wiki/Cauchy_condensation_test

[ember sphinx]

omg

thank you

.close

[safe radish]

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[safe radish]

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[brittle lantern]

How do I determine whether this is true or false?

[brittle lantern]

I get a parametric form of line L

Oh wait dw

.close

[safe radish]

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[vapid vortex]

How do I go about finding all possible integer combinations of the dimensions of a rectangular prism where SA = V?

[safe radish]

@vapid vortex Has your question been resolved?

[vapid vortex]

<@&286206848099549185>