help-0

[empty moth]

so f(8)

[old yew]

217?

[empty moth]

31 divides this surely?

[old yew]

hmm yeah it does

[empty moth]

so 9^3 - 8^3

yeah this problem is kinda trivial

if you know some elementary mathematics

cool trick is you expand the polynomial with taylor around t

[old yew]

oh

out of curiosity why do we do this

[empty moth]

dyk what's taylor expansion

[old yew]

ye kinda

[empty moth]

can you expand f(n) around f(t)

[old yew]

uhhh

[empty moth]

f(n) = f(t) + f'(t)(x-t) + f''(t)/2! (x-t)^2 + ...

[old yew]

i havent done taylor series in forever 😭 so can you show me

oh okay thanks!

[empty moth]

sm like this right

[old yew]

yeah

[empty moth]

now plug in f(mf(t) + t) = f(t) + f'(t)(mf(t) + t - t) + f''(t)(mf(t) + t-t)^2/22!

so we get like

f(t) as a factor of all these terms

[old yew]

ohh

[empty moth]

yeah trivial result

[old yew]

ok thank you :

will this work on any polynomial then?

[empty moth]

no

integer coefs

[old yew]

hmm

[empty moth]

bc we need f(t) to be an integer no?

[old yew]

ohko that makes sense

[empty moth]

smh

b4 you leave @old yew fav lady gaga song

[old yew]

um

shallow

[empty moth]

not bad taste

[old yew]

frr 😭

dont liten to much

[empty moth]

L

that's why you didn't know that thm

[old yew]

😔

thanks tho

!solved

[empty moth]

💀

[old yew]

💀

[echo socket]

It's .close

[old yew]

.close

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[jaunty mulch]

Where the hell did 720 come from

[lone heart]

@jaunty mulch Has your question been resolved?

[pseudo ice]

2 * 360

[fleet dew]

Hi can someone help me?

Pls

I tried it more than once

[pseudo ice]

(i.e. you have $\cos(720 - \beta) = \cos(360 + 360 - \beta) = \cos( 360 - \beta) = \cos(\beta)$, for example)

[ocean seal]

@pseudo ice

[pseudo ice]

And open a new channel if you want help, don't ask in other people's occupied channels

[jaunty mulch]

ooooooo

i thought cos also had 180 intervals though

[pseudo ice]

It doesn't, cos repeats itself every 360, you may be thinking of tan?

[jaunty mulch]

No like

why dont we consider the symmetry properties

[pseudo ice]

That's the cos(360 - beta) = cos(beta) part

[jaunty mulch]

shouldnt it be 180 - beta?

[pseudo ice]

No, you're like reflecting about x = 180, so, like

,w plot y = cos(x), x from 0 to 2pi

fam

[jaunty mulch]

lol

[ocean seal]

Results provided by WolframAlpha

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Requested by chartbit

[pseudo ice]

Annoying

right, if you give me one second

[pseudo ice]

What they're saying, is that, you see the blue line is x = 180, and how it's symmetric about there?

[jaunty mulch]

yahhh

[pseudo ice]

So, for example, 60 and 300 have the same output

[jaunty mulch]

how does that relate to symmetry though

idrk when to consider symmetry

For some reason they made 53.1 degrees

negative here as well

cause of symmetry

in another question

[pseudo ice]

And, to continue, the symmetry basically says the green and orange distances are the same, as are the blue and purple

The blue distance, you can consider as beta, whereas the purple distance is 360 - beta

[pseudo ice]

which leads to this statement here

[pseudo ice]

What does the whole post say here? In general cos is "even" (that means that it's exactly the same if you reflect it about the y axis)

[pseudo ice]

I meant the full picture from what you cropped but anyways, yea, if +53.1deg is a solution for cos, then -53.1deg is a solution too, by being symmetric about the y axis (and ignoring any domain restrictions they give you)

[ocean hawk]

they also missed another solution entirely

[jaunty mulch]

yeah ik

cause they canceld sin

[jaunty mulch]

oh right ok

so Ig I will watch out for

making the solution negative or positive cos x = -cos x or whatever along with the 360 period

thx

maybe i will use cast diagram to double check my stuff

[pseudo ice]

also notice the symmetry about 180 is effectively the same as the symmetry about the y axis (in that if you have one, you can deduce the other, from being periodic)

[jaunty mulch]

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[slate saddle]

Order of Operations question. Supposing n=0, can I write:
12 ÷ 7n = 0
Or do I need to write it as:
12 ÷ 7 • n = 0 ?

Basically, I'm asking if joining the number and variable together in the "7n" format implies that they are inside invisible parentheses, such as when a variable is equal to a negative number, or not.

[round stratus]

there is no objective answer, but from what i've seen 12 / 7n will usually get read like 12 / (7n)

in general the best way to avoid this is to just not write ambiguous expressions like that

[slate saddle]

Fair enough. Thank you.

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[rose sigil]

but then how will we make facebook image math questions

[small lance]

LOL

[torpid dirge]

lazy notation

[torpid dirge]

extra work

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[fringe eagle]

i need help

can someone solve the d

<@&286206848099549185>

[vestal stag]

do you know how to make the equation of y to become f(x)?

adjust the equation of y to make it become f(x), you will see another equation (of straight line) pops out at the other side

[vestal stag]

(with the equation of straight line at that side to be =0)

that is the equation of straight line you need to draw

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[grizzled heron]

hi, thats the question. Im pretty sure the answer is supposed to be B

[grizzled heron]

but I dont know how to get to it

honestly I dont even know where to start, B just looks correct

[slate vortex]

f of what x value gives you 2

[dusky sentinel]

sorry to burst in but isnt it like the f to the power of minus one the opposite of f?

[whole fable]

it's an inverse function

[slate vortex]

$f^{-1}(x)$ generally denotes the inverse of $f$. You might be thinking about $f(x)^{-1}$.

[ocean seal]

Ari

[whole fable]

it is

so in an inverse function you just reverse the values of y and x

so find when y = 2

[sage jacinth]

Assume $f(x) = a$, where a is some constant
$f^{-1}(f(x)) = x = f^{-1}(a)$, so
$f^{-1}(a) = x$
When a = 2, $f(x) = 2$, so x = 4.
$f^{-1}(2) = 4$

[ocean seal]

a guy

[grizzled heron]

ah i see

thats smart actually

thanks

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[quick gulch]

i'm learning differential equations on Khan Academy, but I can't quite understand how he got to the solution on the left. Was I supposed to take a different course before this to understand that? can someone please explain?

[glacial raptor]

Have you leanrt about Complementary function and particular integration?

Cf pi

[quick gulch]

I don't think so, should I start there?

[glacial raptor]

Yes

[quick gulch]

Alright, thank you:)

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[hidden pecan]

How can I solve this trig equation:
$\sin(\pi\sin(x))=\cos(\pi\cos(x))$

[ocean seal]

Stef

[lethal belfry]

hint:- sin and cos differ by a phase difference of $\frac{\pi}{2}$

[ocean seal]

ƒ(Why am. I here)=I don't Know

[hidden pecan]

I haven’t found any info about solving this in my textbook

[hidden pecan]

Ok

So I should make the inside of the sine and cosine a sum?

[lethal belfry]

$\sin(\pi\sin(x))=\sin( \frac{\pi}{2}-\pi\cos(x))$

[ocean seal]

ƒ(Why am. I here)=I don't Know

[lethal belfry]

what does this tell you ?

[hidden pecan]

Shouldn't this be for the outside sine?

[woeful scroll]

?

Why

[hidden pecan]

$\sin(x)=\cos(\frac{\pi}{2}-x)$

[ocean seal]

Stef

[hidden pecan]

How does this help?

It still doesn't make sense

[kind crater]

hello
does anyone know a youtube channel for probability and statistics course

[tepid drum]

#book-recommendations

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@hidden pecan Has your question been resolved?

[ripe warren]

the answer is 10.8 nut how do i get there

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[pine escarp]

Ik this is a stupid and easy question but if the run in the slope is X2 - X1 and you’re going from 3 to -3 that’s a run of 6 yet when you do 3-3 it’s 0 how can that be, are you just not allowed to cross number lines with slopes?

[maiden glen]

you should open a new channel if you have a question of your own, but the run is 3 - (-3) = 3+3 = 6

[maiden glen]

I don't think you can answer this without more information on the variable

if it's linear/uniform you can interpolate

but that isn't given

[ripe warren]

if its given then what do i do

[maiden glen]

you can figure out how much the variable changes between the 3rd and 8th decile, then divide by the distance between the deciles, then add it up until you get to the 5th decile

(I don't work much on data science/stats, so I would check over that with some more detail)

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[silent tinsel]

Where did I go wrong?

[silent tinsel]

Needed to put in the form Ax=b

[alpine sable]

im assuming those 1, 2, and 3 on the x's are subscripts?

[silent tinsel]

yes

[alpine sable]

ill be real, its probably easier for you (visually) to swap x2 and x3 with y and z

[alpine sable]

you made an augmented matrix

[silent tinsel]

I was just going based off the book

[silent tinsel]

true

[alpine sable]

so you have
-x + 0y + 2z = 1
x - y +0z = -2
0x + y + z =-1

correct?

[silent tinsel]

Yes

[alpine sable]

and you're just supposed to put that into AX=B form?

[silent tinsel]

Yes

[alpine sable]

or are you also supposed to solve it

[silent tinsel]

Solve

Actually I’m not sure

[alpine sable]

A is a matrix of coefficients, X is the var matrix, and B is the "equal" matrix

let me make picture

[silent tinsel]

Right

[alpine sable]

one sec my screenshot function is very unhappy rn

ok got it

[silent tinsel]

right

[alpine sable]

that is what AX=B form looks like

[silent tinsel]

right

[alpine sable]

for any system of equations

so yeah it looks like you just have to put it into AX=B form (which means I just gave you the answer for that one, which I'm technically not supposed to do... but I think you can do the others now)

[silent tinsel]

don’t think it’s asking me to solve

[alpine sable]

agreed

[silent tinsel]

I knew how to do that

Just assumed I had to solve

but I do think I made an error for my rref

[silent tinsel]

thanks

[alpine sable]

given AX=B do you know how to solve it?

[silent tinsel]

I’d do rref

[alpine sable]

there is an easier way

way easier

have you learned about inverse matrices?

[silent tinsel]

yes

but only for 2x2

[alpine sable]

oh yeah

yeah 3x3 inverse is janky

[silent tinsel]

not sure how’d I do 3x3

[blazing stump]

Hi

[silent tinsel]

how janky?

[silent tinsel]

howdy

[alpine sable]

honestly now that I say that I think I only know how to find the determinant not the inverse LOL

[silent tinsel]

lol

[alpine sable]

so your best bet there would be RREF most likely

[silent tinsel]

thought so

[alpine sable]

(if you have a ti-84 you can also have the calculator do it)

[blazing stump]

Как вы

[alpine sable]

i would assume server is english only m8

[silent tinsel]

true I have an 84 CE and an Nspire

can’t use either in this class

[alpine sable]

ah rip

but yeah thats what AX=B is

[silent tinsel]

fr

[alpine sable]

now

if it was a 2x2 system of equations

if you multiply both sides by the inverse matrix of A

you will get X = B(A^-1)

A times its inverse cancels out

[silent tinsel]

From what I did most is correct

but I’d get 7+8

which does not equal 1

do you think it’s solvable?

I got it

I missed a negative when swapping

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[fallow marten]

This is the exact same style as the other question you posted

Your problem is identifying what f and g are

[quasi sonnet]

f is sin

[fallow marten]

#help-5 message

[quasi sonnet]

and g is the bracket.

[fallow marten]

right

this is in fact, just one more level of nesting

in this case you have f(g(h(x)))

can you tell me what f, g and h are?

[quasi sonnet]

No I don't

tell me

[fallow marten]

can you guess?

[quasi sonnet]

sin is f

[fallow marten]

not quite

f is the thing you do last

[quasi sonnet]

I really don't know

plese tell me

h is sin

f is the bracket

and g is 5x?

[quasi sonnet]

?

[fallow marten]

do you know how function composition works?

if I said calculate f(g(x)), what would you do?

I give you x, then you...

[quasi sonnet]

Use the chain rule

[fallow marten]

no no

stop

I'm just asking you to calculate a number

I'm not asking you to differentiate anything

even simpler

let's say you know what f is

I give you an x

and I ask you to calculate f(x)

what do you do?

[quasi sonnet]

I dont know

[fallow marten]

go study function composition

you shouldn't be differentiating anything if you don't know how to compute basic input-output

[quasi sonnet]

But I don't know what answer you're expecting

[fallow marten]

there's only 1 answer

[quasi sonnet]

And that is?

[fallow marten]

bruh I'm not teaching you what a function is

other people have helped you on the other 2 or 3 help channels you made today

similar questions but your foundations are simply not good enough to be doing them

if you don't even know what f(g(x)) is, then how are you supposed to know what the chain rule even means?

[quasi sonnet]

So what's the answer?

I can't find it.

[quasi sonnet]

.

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[crimson cape]

Suppose that the production Q of a company, as a function of the amounts of invested capital K and employed labor L, is given by the Cobb-Douglas production function

Q:RxR → R :

What is the minimum amount that the firm must spend on capital and labor to achieve output q if a unit of capital costs k euros and a unit of labor & euros? This amount will of course depend on the numbers q, k and l which we assume are strictly positive.

Note: To answer this question, you will have to find the minimum of a function under a boundary condition. If you find only one candidate minimum, you can assume that it is indeed a minimum without checking further.

For the function see the photo please

So the problem here is that a langrangefunction is not enough I think I should use the implicit theorem somewhere

This is with Lagrange it’s unsolvable

<@&286206848099549185>

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[uneven palm]

how can i find this where gama is e^(i2t) from 0 to 2pi

[uneven palm]

i thought using cauchy interal formula

but i am not sure how in this casee

if i do a normal line integral i get -2

[left wharf]

what is that symbol in the numerator

My complex analysis is hella rusty but iirc you have Log(z) as the antiderivative if z is not on the negative real axis and Log(z) = iAngle(z)+ln|z|

so you do a limit trick to conclude that you get i(2pi) from the integral if you go around the unit circle once and presumably if you go around it twice you'd get i(4pi) and then when the dust settles you get 2

but that could be wrong idk

presumably you'd get the same result from Cauchy's integral formula

and I mean kinda the whole idea behind Cauchy's integral formula, or at least the way I understand it, is that you abuse the fact that throughout most of the path you have a valid antiderivative and you do some clever limiting analysis to deal with the rest

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[nocturne sage]

I need help with this

[worthy maple]

How is this wrong? I dont get it. Calc 2

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[foggy nest]

Can u follow bro?

[limpid turret]

<@&268886789983436800> spam

[clever folio]

Don't spam here.

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[past saddle]

can someone help? how do I start solving this

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[tight pier]

cant you take both sides to x-4

[small lance]

@past saddle

[tight pier]

tho the approach would work out only for x > 4

and x != 5

[past saddle]

sorry had a mighty cockroach invade my personal space

I've defeated it

tbh I don't really know how to work with equalities of logarithms

the assignment is due tomorrow and I had no time to learn it because of other subjects

well technically it's due today

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[past saddle]

yeah.. I think this one is gone unless by sheer luck the assignment is postponed, I've asked my professor to make it longer and we'll see how they answer

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[bleak wadi]

need help on a statistic homework assiment

[bleak wadi]

i dont get it

i get the first part

dont get the second

new problem

two problems

anyone?

SOMEONE!

<@&286206848099549185> i need da help

BRUUUUUUUH.....someone

PLLEEEASSE

[lone heart]

@bleak wadi Has your question been resolved?

[bleak wadi]

NOOO

IT HASNT

NO ONES HAVE

[alpine sable]

Guys i need help

[bleak wadi]

https://tenor.com/view/bruh424019499-gif-25675566

[steady dock]

for the 2nd one on frequency and relative frequency, i dont know much ab stats but i hav some memory of frequency being the times x is mentioned, and relative frequency being the times x mentions / total number of values , although i'd check ur notes if u have them and see if this matches with it bc im not entirely sure, sorry

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[quasi sonnet]

How do I solve the 2nd one

[boreal jetty]

i can not read what you have written:

is that a 1?

[hot hatch]

$\log_2^3 x^5$

[ocean seal]

Monarch of Eternal Night

[swift ledge]

Bro

I’m cooked

I can’t even complete this simple question (I need help my homework is due later today)

[hot hatch]

!help

[lone heart]

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

[hot hatch]

Send your question there

[quasi sonnet]

That’s the sign of derivation

We use

And I already got it

But

What formula do I use in this bracket?

[coral flower]

Log rule?

Also u do know that
$$log a^n = n log a$$

[ocean seal]

JustToPro

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[alpine sable]

tan(A + B) = (sin A cos B + cos A sin B) / (cos A cos B − sin A sin B)

tan(A + B) = [sin A/cos A + sin B/cos B] / [1 − (sin A/cos A)(sin B/cos B)]. How is this correct? Something seems wrong about it

[gray isle]

divide numerator and denom by
cosAcosB

[alpine sable]

tan(A+B)= sin(A+B)/cos(A+B)

and

for second one convert tan(x) in sinx by cosx form

the second is supposedly derived from the first

this confuses me

[alpine sable]

no

that is what my resource claims

what is tan(A+B)

[gray isle]

my messages are invisible

[alpine sable]

tan(A + B) = (tan A + tan B) / (1 − tan A tan B)

the econd to this makes sense

not first to second

https://brownmath.com/twt/sumdiff.htm

[alpine sable]

yup

just take a quick look

i dont understand how you could just divide by cos

cosa

and b

[gray isle]

basic fraction manipulation

[alpine sable]

hmm

guess im just unframiliar w that

[gray isle]

how would you simplify
4/12

[alpine sable]

1/cosA.cosB

1/3

[gray isle]

how

did you get 1/3

[alpine sable]

12 div 4

[gray isle]

its more or less the same idea,
you can divide the numerator and denominator by 4

$\frac{4}{12} = \frac{4/4}{12/4} = \frac13$

[ocean seal]

ℝαμΩℕωⅤ

[gray isle]

same idea applies here

[alpine sable]

oh

[gray isle]

dividing numerator and denominator by the same amount

[alpine sable]

would you mind putting this tan(A + B) = (sin A cos B + cos A sin B) / (cos A cos B − sin A sin B)

tan(A + B) = [sin A/cos A + sin B/cos B] / [1 − (sin A/cos A)(sin B/cos B)] in latex rq

hlo everyone I am new here prolly younger than everyone since I am in 7th grade lol

[gray isle]

$$\tan(A+B) = \frac{\sin(A)\cos(B) + \cos(A)\sin(B)}{\cos(A)\cos(B) − \sin(A)\sin (B)}$
$$\tan(A+B) = \frac{\frac{\sin(A)}{\cos(A)} + \frac{\sin(B)}{\cos(B)}}{1 - \frac{\sin(A)}{\cos(A)}\cdot\frac{\sin(B)}{\cos(B)}}$$

[ocean seal]

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

[alpine sable]

thank you

that helped alot thank you thank you

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If your question has been answered, please type .close to allow other people to use the help channels.

[alpine sable]

.close

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[verbal shuttle]

i need to convert the rectangular coordinates (-3, 4) to polar coordinates.
the answer i got was (5, -0.927), by using pythagorean theorem for r and arctan(y/x) for theta. the provided/correct answer for the question is (5, 2.214)
-0.927 plus pi is 2.214. why do i add pi to the result of arctan?

[fallen verge]

be careful with which answer you get

arctan has the range (-pi/2,pi/2)

but if you graph the point (-3,4), you see that its outside of that range

[verbal shuttle]

so since it is out of the range of arctan, that makes it okay to add pi?

[fallen verge]

if you remember from solving equations like tan(x)=-3/4, you get solutions of the form arctan(-3/4)+npi for integer n

[verbal shuttle]

right

[fallen verge]

you have to make sure your answer agrees with the original solution, so you have to add pi

and usually they constrict the range betwee [0,2pi), so you only get one answer

[verbal shuttle]

makes sense. thank you for the help!

.close

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[runic dome]

Assume Set Z to be {1 < z < 50}

Subset D = {Multiples of 4}

Subset E = {Prime numbers}

Subset F = {Perfect squares}

d) Find the harmonic mean of the elements in Subset F that are also multiples of 3, then determine the number of elements in Subset E that are greater than this harmonic mean and are palindromic primes.

[runic dome]

the answer I got is 1 but my teacher said it was 0

[limpid turret]

!show

[lone heart]

Show your work, and if possible, explain where you are stuck.

[runic dome]

okay wait

i forgot about that

euhh wai ti did the harmonic mean wrong 😭 😭 😭 😭

.close

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[heavy vapor]

Is this proof ok?

[lone heart]

@heavy vapor Has your question been resolved?

[lone heart]

@heavy vapor Has your question been resolved?

[lone heart]

@heavy vapor Has your question been resolved?

[tidal mural]

Its not clear what the a_n are

[heavy vapor]

Elements of some group

[tidal mural]

Your last line is written badly then

And your line starting with "Then" kinda does two steps at once, so you might want to split it up

[heavy vapor]

Why is the last line badly written?

[tidal mural]

An element of a group cannot be true

[heavy vapor]

ohhh I see it now. I should write $(a_1 ... a_n)(a_n ... a_{n+m}) = a_1 ... a_{n+m}$ for all $m \in \mathbb{Z}$ then?

[ocean seal]

juand8

[tidal mural]

Yes

[heavy vapor]

Thanks

.close

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[sudden bloom]

Number 1 ☹️

Idk what to do 😭😭

[cinder sundial]

Would you take the hand of a loyal servant of Mickey Mouse

[sudden bloom]

Uh

Yea

[cinder sundial]

Then I will take a look at this question

[sudden bloom]

Thank you 🙏

[cinder sundial]

The intersection upon the line with respect to their position

[sudden bloom]

The only number I have is 9 😭

But the teacher said that you don’t acc need algebra to answer it and you could use graphs or illustrations and I’m just more confused

[cinder sundial]

Yes

He’s right

It is two

[sudden bloom]

How could I graph it?

[sudden bloom]

Can you explain pls?

[cinder sundial]

Sure

[sudden bloom]

Wait if the very end should be counted do I add one so it is three?

[cinder sundial]

It said after they “start traveling”

[cinder sundial]

You can assume my two fingers as the two fellas mentioned in the question

With one’s traveling way more faster than the other

[sudden bloom]

So they only intersect once then again at the end?

[cinder sundial]

Yes

[sudden bloom]

OHH SO ONE IS STILL GOING AND THE OTHER MADE JT THATS ONE INTERSECTION

and going back wouldn’t he pass the other guy again and they meet again at the end?

[cinder sundial]

I cannot understand your question

[sudden bloom]

okay so they both start

(Imagine this btw)

One guy is going slow and the other is going fast

oh wait nvm

Sorry I’m tired and I forgot since one is going fast they don’t meet

[cinder sundial]

It’s okay

[sudden bloom]

But after the faster guy turns and makes it to the end he passes the guy who is still walking once

[cinder sundial]

Yes

[sudden bloom]

Then they meet again at the end as the are both done?

Why the heck is it so simple

[cinder sundial]

Yes, exactly

[sudden bloom]

I love you thank you

I can sleep peacefully tonight

[cinder sundial]

Glad to hear that

[sudden bloom]

Thank you so much 😭 🙏

Nighty night now

.close

[lone heart]

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[sudden bloom]

WAIT HOLD UP THE WUESTION SAYS “Mike rides an e-bike back and forth until Ian returns to the starting point” SO DOESNT THAG MEAN HE JS STILL KOVING?

.reopen

[lone heart]

✅

[sudden bloom]

^

[cinder sundial]

Shit, you’re right

[sudden bloom]

The one time I wish I wasn’t 🥲

[cinder sundial]

It can still be solved tho

[sudden bloom]

Yea but it’s tough

[cinder sundial]

It’s not

[sudden bloom]

Kinda

Well for me it is

[cinder sundial]

By the relation V_mike=9V_ian, we can notice that the ratio of periods for the twos is 9/1.

[sudden bloom]

Do you think I should use the s = d/t equation

[cinder sundial]

No

[sudden bloom]

Okay

[cinder sundial]

I mean you could, but it makes a lots of effort

[sudden bloom]

Ah alright I see

[cinder sundial]

I have to wash some plates

But you could you illustrate the situation using your imagination and hands

[cinder sundial]

Given the ratio of the twos

[sudden bloom]

So I’ll create some type of visual to help

[cinder sundial]

I think it would be possible to calculate the time of their encounter during the trip

[sudden bloom]

So Mike is always 9 units ahead of Ian?

[cinder sundial]

No, and you can find an counter example for this

[sudden bloom]

(Mike is the one who is 9 times the speed of Ian)

[cinder sundial]

Like they do encounter with each other, so Mike is not always 9 units ahead

[sudden bloom]

Wait shit that’s right cause it’s back and forth that wouldn’t make sense

[cinder sundial]

I think I can make another illustration using my hands

[echo imp]

imma look at ur illustration cuz im stuck on this question as well 😄

[sudden bloom]

ARE YOU ALSO DOING THIS PROGRAM?

[echo imp]

yeah

[sudden bloom]

WHAT

THATS CRAZY

I cooked on the quiz ngl

Ima get cooked by the assignment though

[echo imp]

lol

[violet jetty]

It's actually simpler than it looks. Think of IVT

[sudden bloom]

Number 2 is easy it’s like one of the things from the lessons where they replaced the number with n and got the equation f(n) = f(n - 1) + f(n - 3)

I forgot where it was though

[echo imp]

i looked at the lessons for 5 min and decided it was boring

😐

[sudden bloom]

Fair enough

[echo imp]

so i just went right to the quiz

[sudden bloom]

What’s that?

[echo imp]

they explained it in the lessons?

[sudden bloom]

Some of them

[echo imp]

o

[sudden bloom]

Not all though, one of the quiz questions was straight out the lesson but the numebrs were slightly different

[violet jetty]

For every half-lap Mike does, they have to meet once. Since Mike does 9 half-laps by the time Ian does his first half-lap, they have to meet 9 times in the first half

[sudden bloom]

So since Ian goes from start to end and end to start they meet 18 times in one lap?

Would you add/subtract one bc the end also needs to be counted

[echo imp]

what did u get for question 2 ❓

[sudden bloom]

I didn’t do it yet but once I do I’ll show u

[cinder sundial]

I think the answer is 17

[echo imp]

k thx

[cinder sundial]

That they encounter each other on the road

[sudden bloom]

Okay so you subtract one then

[violet jetty]

I believe you don't need to add one, the 18 laps figure already counts the final position

[sudden bloom]

Read this Incase you missed it grammar guy ^

[sudden bloom]

I see

[violet jetty]

But you do need to subtract, because them both starting from the same place doesn't count as a "meet", so they never meet in Mike's very first half-lap

so itds 8+9

[cinder sundial]

Yes

[sudden bloom]

So 17

[violet jetty]

oui

Euclid was fun

[sudden bloom]

Thank you all sm 😭😭

[cinder sundial]

You can actually

Make a model

[sudden bloom]

Really?

[cinder sundial]

That is more simple for you to observe

So that you can have a a grasp of the question

[sudden bloom]

Do you know how?

[cinder sundial]

I think the models composed of our hands is quite an example?

[sudden bloom]

I’ll draw stick men instead of hands for the middle

Model

[cinder sundial]

But they are static

[sudden bloom]

Like multiple to show it

[cinder sundial]

I see

The key for this question is that once ian finished one lap, mike would be done 9 laps

And then you can kind of think up the situation in your mind or your realistic model for sure

[sudden bloom]

Like done going from start to end

[cinder sundial]

You should be able to find the number of their encounter

[sudden bloom]

Then end to start

Is total 17 bc u subtract 1

[cinder sundial]

Yes

[sudden bloom]

Or basically do 8 + 9

Got it got it 😁

[cinder sundial]

I believe you would done better during question in the future

[sudden bloom]

Huh?

Sorry I’m a bit dyslexic that sentence confused the hell out of me 💀

[cinder sundial]

I mean once you have done a lot of similar questions, you would be able to imagine stuff in your mind, and solve it within a whip of lightning

[sudden bloom]

Ohh

I feel like if I did physics it would help with the speed and distances and all that

I just finished grade 10 so I haven’t done physics yet

[echo imp]

same

[sudden bloom]

Did you do functions? The grade 11 math?

[echo imp]

i finished grade 12 math but i forgot like 60 percent of it

[sudden bloom]

How?? Didn’t you just finish grade 10?

[echo imp]

yeah

[sudden bloom]

I’m confused?

Did you do it in summer school or something?

[echo imp]

i was in accelerated class so i did math 11 this year and math 12 outside of school

[sudden bloom]

Oh

IB?

[echo imp]

math 12 wasnt for credit tho i just know it

[echo imp]

nah

[sudden bloom]

Oh

[echo imp]

my school isnt good enough

D:

[sudden bloom]

😭😭

[echo imp]

wanna help me with # 2

[sudden bloom]

I did pre-IB grade 9 and 10 so I did the grade 11 math second sem of math and some of the grade 12 math with logs and radians

Yea I’m doing it rn

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[hollow vapor]

??? mate why

[fallen verge]

lol

<@&268886789983436800>

[real gazelle]

This is not an appropriate use of a help channel.

Please do not do this in the future.

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[umbral arrow]

can someone explain to me what epsilon does here in this NFA?

[sour verge]

What does epsilon do in general?

[umbral arrow]

Empty strin g

[sour verge]

So it's a free transition, you can take it or not.

[umbral arrow]

so is it like we are in q0 and q1 at the same time?

like how to draw computing tree

[sour verge]

Yes that's the idea.

You're in both at the same time, and each computation tree follows along.

If a single one of those trees ends up on an accepting state, then the string is accepted.

So what are string that would work here?

[umbral arrow]

0*, 1*? so regex is 0* U 1*?

i am not sure on if the regex is correct though.

[sour verge]

What about a string like 01?

[lone heart]

@umbral arrow Has your question been resolved?

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[vagrant token]

Hi

[lone heart]

@vagrant token Has your question been resolved?

[left isle]

if you had a question I would recommend posting it, otherwise please close the channel using ".close"

[small lance]

What’s the question?

[lone heart]

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[pearl kraken]

#help-14 message

[pearl kraken]

@real gazelle i have tried factoring it

and i did get what u got but idk how that helps to get the answer

I keep getting Arg(z) is -pi/2<x<pi/2 but thats wrong

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@pearl kraken Has your question been resolved?

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[vague cloak]

.close

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[trim cedar]

Calc 1 help
I don't understand how to do this. How do I find the f'(1) and g'(1)? I used the product formula, but I think I have the wrong values.

[pearl kraken]

f' and g' can be found using rise/run

cuz its linear

[trim cedar]

doesn't that make f'(1) = 1/4?

but when I plug that is it doesnt work. It isnt right

[pearl kraken]

what did you get for g'(1)

[trim cedar]

for u'(1) I got 7/4

so I got
f(1)=2
f'(1)=1/4
g(1)=3
g'(1)=1

[narrow scaffold]

2*1 + 3*1/4 = 11/4

[pearl kraken]

^

[trim cedar]

... why am I getting a different answer I wonder

[narrow scaffold]

u' = f'g + g'f

plug in the values you found

[trim cedar]

oh wait... I think I mathed wrong...

I plugged everything in right... I added my fractions wrong...

I hate fractions...

I even double checked on the calculator... but I must have input it wrong idk. Sorry lol, I'm just a dumb

oh and thanks btw!

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[pearl kraken]

you can simplify it with algebra 👍

-p^2/2-3

because 3/6 is 1/2

and 3/6 is not 1/3

[lone heart]

@naive grove Has your question been resolved?

[pearl kraken]

how does it get -2p^2/6

isn't the 3 outside of it

p^2/x is different to p^2/6

Idk how you're getting -2p^2/6

[wooden bolt]

you are correct tho. it's -(p²/3) - 3.

can you show the whole problem? @naive grove

how about this: (-p²-9)/3

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[scarlet oriole]

How to calculate this sum?

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[scarlet oriole]

.close

I've found out, nevermind

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[uncut tide]

could i please get help with part c and d

[uncut tide]

ive done a lot of working but its quite messy and i need help precisiely understanding whats going on as its quite a large topic of what i need to know, any help greatly appreciated

hi?

.close

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[patent swallow]

How can I start?

[lone heart]

Please don't occupy multiple help channels.

[patent swallow]

I tried doing f(r) = f'(r) but got nothing

[mortal trellis]

you could try computing the gcd of f and f'

[patent swallow]

how didnt I think abt that 😭

yeah that'll probably help

thanks

[neon adder]

!noans

[lone heart]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[neon adder]

!noans

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The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[patent swallow]

lmao

#bots

[patent swallow]

,w gratest common divisor between x^12-3x^4+2a and 12x^11 - 12x^3

[ocean seal]

Results provided by WolframAlpha

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Requested by chuti

[patent swallow]

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@patent swallow Has your question been resolved?

[mortal trellis]

it probably thinks a is another variable, not a parameter

do it by hand

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@patent swallow Has your question been resolved?

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@patent swallow Has your question been resolved?

[wraith jacinth]

and also give me the types of skills to interpree these word problems

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[patent swallow]

.close

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[teal fable]

find the circumcenter orthocenter centroid and nine points for the triangle whose vertices are ( -5 ,-7) , ( 13,2 ) and ( - 5,6 )

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[alpine sable]

how does einstein summation convention apply here, does the "if an index appears twice its a sum over that index" rule also apply to derivatives?

[alpine sable]

for context im doing a fluid dynamics course and i had to speedrun learning about tensors and index notation i would apppreciate it a lot if someone could send me short resources on that stuff so i can parse index notation better

in the notes this is what the notation for divergence should be so did my lecturer just make a mistake or is there a way im meant to just know that its divergence in the above pic

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[alpine sable]

.close

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[alpine sable]

How do i get the angles and when i have the angles do i add them up to find angle BDE, ABF and BEF??

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[worldly mortar]

hold up lemme see if i can figure it out

i forgot im stupid

sorry

[alpine sable]

no worries

[gray isle]

consider angle sums on lines
in triangles
parallel lines theorems

[alpine sable]

what does that mean

[alpine sable]

.close

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[toxic fable]

hi

[toxic fable]

i have no clue how to approach this

[pallid scarab]

ok

let $y = \sqrt{x^2+2x+24}$

[ocean seal]

rafilou2003

[celest obsidian]

take x^2 +2x +24 to be u, then the equation becomes u +8*sqrt(u)-65

oh wow

[pallid scarab]

and try to rewrite the LHS in terms of y

[toxic fable]

ok let me try

thats what gpt said but it didnt seem to work but ill try one more time

thanks

[gray isle]

don't use gpt for math

[toxic fable]

yeah that was a last resort 😦

before coming here

[gray isle]

don't use gpt even as a last resort

[toxic fable]

alr

guys

can i also solve by finding vertex then zeros?

[celest obsidian]

let $u=x^2+2x+24\ \therefore$ equation is $u +8*\sqrt{u}-65 =0\ \Rightarrow \sqrt{u} =\frac {(-8\pm\sqrt{8^2-4(-64)}}{2}\ $Calculate u from that and solve for x

[ocean seal]

Sly

[celest obsidian]

probably not

[toxic fable]

i see

thank you all for your help

[toxic fable]

hwo did u go from the therefore statement to the next line

[gray isle]

quadratic formula but they messed up a number

[celest obsidian]

oh sorry it should be 65

[toxic fable]

i got it now

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[hard tartan]

I tried to solve it in various ways but I couldn't. Could someone help me? the question is: Consider x such that 9 sin x + 3 √5 cos x = 11 with sin x > 0 and cos x > 0. What are the two possible values for tg x?

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@hard tartan Has your question been resolved?

[celest obsidian]

i solved the equation and got sin x = 2/3 and 19/21

x = arcsin(2/3) and arcsin(19/21)

[hard tartan]

Oh ok, thank you very much! Now I understand

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[ruby elbow]

always need someone to double check with

because sometimes I make the dumbest mistakes

[sharp gate]

Looks good to me

[ruby elbow]

kool

thank you

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[wet pewter]

How do I go about this algebraically?

[cinder sundial]

Find the zeros

[wet pewter]

but isnt that just when it touches the x axis

what importance does it have here

hello again lol @sour verge

[sour verge]

Points of inflections happen when the derivative goes from increasing to decreasing or vice versa

[wet pewter]

so positive or negative?

[sour verge]

Wait

Not true

[wet pewter]

when it goes from either dec. to inc. or vice versa

[sour verge]

One sec

[wet pewter]

ok

[sour verge]

So you want to know when the derivative is increasing/decreasing. How do you think you can go about that

[wet pewter]

find the 2nd derivative?

maybe

then plug in each value

i honestly have no clue here

[dull lintel]

I think this is correct

[wet pewter]

oh

let me try it

2x -2

but

[cinder sundial]

It is1!

[wet pewter]

how do u know its 1?

OH

cuz it would equal 0?

because its a point of infliction

right?

[cinder sundial]

First

First

[dull lintel]

you are finding extremum point

[wet pewter]

but at the point of infliction does f'' (x) = 0?

oh

that helps significantly

[cinder sundial]

If you know there’s only one point of inflection point

[sour verge]

Wait

This is a parabola

It does not have a point of inflection.

The second derivative is constant

[cinder sundial]

Fuck

[cinder sundial]

It is not

It is not

Excuse me

[dull lintel]

what is not

[wet pewter]

wait so its not 1?

[cinder sundial]

Check the degree

It is not a parabola

It is a function with a degree of 3

[wet pewter]

oh yeah

[sour verge]

It is a parabola?

[wet pewter]

its a function with the degree of 3

no its not

[dull lintel]

oh it gives us the definition of f' not f

[cinder sundial]

It is not

[wet pewter]

ohhh

[cinder sundial]

Hello

What the f

[sour verge]

It is lol it's degree 2

[cinder sundial]

^

[sour verge]

Ok I am an idiot mb

[dull lintel]

f' is 2. degree
f is 3.

[sour verge]

Fine then

[cinder sundial]

Damn

[wet pewter]

oh

so if its a parabola

[cinder sundial]

Let me finish my words

[cinder sundial]

Then it would not

[wet pewter]

ok

[cinder sundial]

Has a inflection point

[wet pewter]

it would not have*

ur name is please correct my grammar

[cinder sundial]

Thank you

[wet pewter]

np

ok so

since its not a parabola

[cinder sundial]

I think you only have to find the x where f”(x) in this question

[wet pewter]

then i can set f'' = 2x - 2

[cinder sundial]

Then you can determine the x would be the inflection point

[wet pewter]

0 = 2x - 2

o0h

oh

[cinder sundial]

As you already know

3 degree function always has a inflection point

[wet pewter]

anything 3 and above always has inflection point right

[cinder sundial]

“Above”

[wet pewter]

always has an inflection*

[cinder sundial]

You mean degree

[cinder sundial]

Thank you

[wet pewter]

oh

np

anything with the degree 3 or above

any function*

base function

not derivative

[cinder sundial]

It is not true

[wet pewter]

o

[cinder sundial]

Only thing that’s assured is

3 degree function has an inflection point

[wet pewter]

because of how the graph looks

ok that makes sense

[cinder sundial]

If you do not know whether a function has an inflection point

Then you have to check the “sign”

[wet pewter]

using your method?

which you showed me earlier

[cinder sundial]

Because f”(x)=0 doesn’t necessarily means x is where the inflection occurs

[cinder sundial]

Yes

[wet pewter]

ahh okok

[cinder sundial]

That I wrote on the paper

[wet pewter]

thank you very much

[cinder sundial]

No problem

You can actually justify my statement

[wet pewter]

may i ask 2 more questions

[cinder sundial]

Using the definition of second derivative

[wet pewter]

i only have 2 more homework questions left

[wet pewter]

oh

the second derivative is exponential increase

right?

i think i get it

.close

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