help-26

[neon iron]

I did try it but my answer was much larger than the correct answer so i think maybe my logic had some flaws

[pseudo horizon]

yeah it's the ninth tetrahedral number plus the ninth pentatope number plus 1

11C3 + 12C4 + 1

[neon iron]

I need to learn about these numbers then, but is there a way we can solve it without using these pyramidal numbers(tetrahedral) because i am pretty sure this is not in syllabus so there must be some other way to do it, i believe

[pseudo horizon]

hmmm

[long stirrup]

it's stars and bars

you have 10 bins and you distribute 4 digits

[neon iron]

I also think it can be solved using stars and bars too but i don't get how

Could you elaborate pls

[pseudo horizon]

aha

[long stirrup]

like "two 8s and two 7s"

means the number is 7788

[pseudo horizon]

doesn't that overcount?

doesn't that count numbers with decreasing digits too?

[long stirrup]

if you want to

[pseudo horizon]

oh, we don't want to

[long stirrup]

it corresponds to 8877 too

[pseudo horizon]

ohhh

hmm

oh 10 bins and 4 digits... i was thinking the opposite

[stable onyx]

hello

is there person good at math

help me

[pseudo horizon]

just ask a question in one of the available rooms such as #help-4

[neon iron]

I think i still don't get it, maybe it will take some time to dissolve what u just said

[pseudo horizon]

even though the four places are different, they're indistinguishable because they're represented by a canonical form, the sorted order

[neon iron]

T T again a new term canonical form

[pseudo horizon]

i don't really get it either

combinatorics is hard

[long stirrup]

the point is that every awesome number can be described as the amount of digits

one,two fives and seven

it matches one to one

one amount, one awesome number

[neon iron]

so u mean that we just need to find every possible combination of digits since there is just 1 way to arrange it?

[long stirrup]

and that's what stars and bars is for

yes

[neon iron]

ah! I see but the only thing that i don't understand now is how are we going to state the stars and bars equation...like in this way x1+x2+x3+x4=?

[long stirrup]

x1 to x10

=4

or x0 to x9

[neon iron]

ohh i see! I get it now!! i was thinking the opposite

[long stirrup]

this will count from 0000 to 9999

then you deal with 99 separately

i'll see if it matches the answer

[neon iron]

okay I now understand the approach

Thankyou sooo much @pseudo horizon @long stirrup !!

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[long stirrup]

yeah 661

[topaz sinew]

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[young saffron]

Could someone explain how we go from f(x) to this derivative?

When I plotted this in geogebra I got really intriguated

[agile harness]

do you know the derivative of |x|

[young saffron]

isn't it like |1|?

[agile harness]

no

[young saffron]

wait lemme look

[agile harness]

that would just be 1

no don’t look it up

i’ll give you a hint

|x| = sqrt(x^2)

[young saffron]

oki

ohhhhhhh

yeh i get it now

so |x| = sqrt(x^2) that is = x^(1/2)

derivatif of this is 1/2 * x^(-1/2)

so 1/(2*sqrt(x))

correct?

[agile harness]

sure but it’s x^2 inside so you need chain rule and you can’t just have x in the sqrt

[young saffron]

oh right i forgot x is x^2 inside

lemme note this on paper

also THANK YOU

[agile harness]

you’re welcome sir

[young saffron]

how do i close the thread again?

[agile harness]

!done

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[young saffron]

found it

.close

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[lusty cedar]

How did they get that coordinate

I tried setting this to 0

oh wait u take the negative of the modulus innot

wait but how dyu know ur supposed to do that

oh cuse it has neg gradient innit

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[jade knot]

is my work correct?

[jade knot]

assuming I have an initial amount x,

after n years you have x(1.0448)^n amount of money

then do percentage change formula

[(new - old) / old] * 100

which gives around 24.5% increase

idk if thats the right way of doing it tho

[wooden moon]

,calc (1.0448)^5

[thorny flame]

Result:

1.2449898754316

[wooden moon]

yeah, seems right

[jade knot]

ok thank you!

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[serene lion]

Ok

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[lusty cedar]

How do i differentiate this

🙉

is it chain rule

even if it was chain rule

ahhhhh

idk man

[celest charm]

wtf is that

what is the argument of the sin lol

[lusty cedar]

thats what im thinking hahahaha

[celest charm]

is it supposed to be $8\sin(\frac{1}{2}x)-3x+9$?

[lusty cedar]

idek

[thorny flame]

dingus

[lusty cedar]

maybe i should just check the mark scheme

I think its to the power

of

it looks like

but i have no clue what im meant to do with that

[celest charm]

it's incorrectly written i know that much

just don't know what they want it to be

[lusty cedar]

ok ig imma check

so

[lusty cedar]

yeah this was right

thanks

[celest charm]

ofc

[lusty cedar]

got me so lost haha

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[cedar wagon]

What is your question about this ?

[neon iron]

I did this and I’m getting 0.12 instead of 0.2. Yet I cannot find an error in either method

[cedar wagon]

What is B' ?

[smoky sparrow]

oh what the hell is going on in the question

$P(\frac{A}{B})$???

[thorny flame]

south

[cedar wagon]

Probably A|B

Also this is very sus

[smoky sparrow]

yeah then how did they come up with P(A) = 0.4 then

bruh

solution is wrong

[cedar wagon]

Maybe a typo and they meant P(A)

[timid flicker]

hey whats up guys can anyone help me solve some of the problems here I solved 1 a and 1 b already

[cedar wagon]

!occupied

[topaz sinew]

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).

[timid flicker]

?

[smoky sparrow]

this is not your channel

[cedar wagon]

Wdym "?" ?

[smoky sparrow]

pls make a new one for yourself

[timid flicker]

sorry i just joined

wich channel should i go to

?

[smoky sparrow]

you can go to #help-35

just ask there

[timid flicker]

thanks

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

Is it?

Where?

[smoky sparrow]

yeah they definitely should be using P(A) = 0.12 instead

then follow the same steps

[neon iron]

Okay good

So I’m not wrong

This question demotivated me

Can you please explain what this question means?

I have trouble with the notation

Reply ping please

[clear lodge]

what is P(A' B') supposed to mean?

@neon iron

[neon iron]

P(A' B') is same as Probability of A' and B' happening simultaneously i.e P(A' intersection B')

[neon iron]

Oh???

Okay

[neon iron]

That was what I was unsure about

Okay I got one more

51. The assertion is false, right?

I cant assume that E1 and E2 are exclusive to prove a “then” statement

[clear lodge]

The assertion can be true, but you're lacking information. The probability of the union can be anywhere between 0.4 and 0.7

honestly, i would not accept any of the 4 options presented as correct

[neon iron]

It can be. But I can’t conclude that it is. So I can’t say blah blah blah, then this is true. It just can’t

[neon iron]

I’ve seen a lot of crappy solutions in this book today

[clear lodge]

you cant say it's false either

(a) is obviously wrong

(b) is not necessarily right, since A is not necessarily right

(c) is obviously wrong

and (d) is, again, not necessarily right, since A is not necessarily wrong

Also, the book answer starts by assuming they are mutually exclusive, which you were never told they were

I would write my own (e) option and contest it with the instructor when asked

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

Yeah

[neon iron]

Would what’s marked be the most appropriate answer considering everything?

[clear lodge]

as i said, *i* would not say either as correct

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@neon iron Has your question been resolved?

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[crimson lagoon]

Hi, im struggling to understand what part b wants from me. my thought would be to get the area from -infinity to the intersection between f and g but the integral would be divergent. So what should the bounds be? the intersection between f and the x axis and the intersection between f and g?

[torpid shard]

My guess is that in reality, they are asking for you to figure the area that also "holds" the y axis in the middle.
The other option is obviously divergent

[torpid shard]

yeah, precisely.

[crimson lagoon]

Okay thank you very much

But I'm not the only who thinks the wording is strange right?

or am i missing something

[torpid shard]

it can be misinterpreted, yeah, but given that it says "Enclosed by the graph of f" you should figure that its fully bounded

if in doubt just do both, lol

[crimson lagoon]

true, although not sure how much my markers will appreciate that

but thank you

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[finite glacier]

Hello,

If I have a joint pdf such that 0<x<y<1, to get the marginal density of x I should integrate y over [0,1] or [x,1]. I know that for y it's x over [0,y]. In addition once i get the marginal densities to get E(X) and E(Y), I just integrate the respective marginal pdf * (x or y) over [0,1] for both?

[topaz sinew]

@finite glacier Has your question been resolved?

[topaz sinew]

@finite glacier Has your question been resolved?

[little ginkgo]

It should be done over [x,1]

[little ginkgo]

You can only do the latter if you define the marginal distribution of e.g. y to return zero if y < x

Otherwise you should again integrate over [x,1] since this is what is defined as the "probability space" of y

[finite glacier]

ok thanks

/closed

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[twilit hemlock]

do i need to use trigo here or..

[restive inlet]

no trig needed

you can approach with partial fractions

[twilit hemlock]

ohh let me try

[twilit hemlock]

thank youu found it but how do we tell when to use trig exactly

[restive inlet]

look up a table of common integrals

[twilit hemlock]

okk

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[left tree]

Help me solve using the method of variation of constants:
(1 + x^2)y'' +2xy' = 12x^3

[thorny flame]

uguu~ba

[left tree]

so far i have only noticed about the left side

[thorny flame]

uguu~ba

[golden blade]

Maybe try the substitution z = y'

[topaz sinew]

@left tree Has your question been resolved?

[left tree]

nah

what next?

$$y_p=\phi_1(x)\arctan{x}+\phi_2(x)$$

[golden blade]

If you used the substitution life would be more abelian

[thorny flame]

uguu~ba

[left tree]

for example?

i dont tried sub.

[left tree]

so, i also didn't look at their intermediate results

[golden blade]

If $u = y'$ then $u' = y''$ so consider now
[ (1+x^2)u' + 2xu = 12x^3 ] and bring that into the form
[ u' + a(x) \cdot u = s(x) ] so that you can use variations of constants.

[thorny flame]

𝔸dωn𝓲²s

[golden blade]

You can first get the homogeneous solution and then based on that find the particular so you get u = u_h + u_p in the end

[left tree]

i don't understand

can you send full

[topaz sinew]

@left tree Has your question been resolved?

[left tree]

<@&286206848099549185>

[neon iron]

I am here

@left tree

[left tree]

is it 12x^3

?

[neon iron]

let me see

nononoon

you r incorrect

[left tree]

im correct i think

[neon iron]

look this.

[left tree]

wth

[left tree]

isnt just

way faster isnt it?

[neon iron]

please understand that pic

and solve

[left tree]

im sure i sended some already

so i need particular y

i found it already

then variation of parameters

[neon iron]

??

[golden blade]

just dont help if you have no idea instead of sending chat gpt stuff

[left tree]

yeah

[neon iron]

lol

I solved so much problem

and just now, I need to send fast

so I used chatgpt

but that way is true

[golden blade]

real

[neon iron]

I learned so

Do you know about differential and partial differential equations?

[left tree]

i need find phi 1 derivative

and phi 2 derivative

then phi 1 and phi 2

[neon iron]

so u want entire solution?

[left tree]

i need help on exact method

this may be the complete solution but i'm sure i've already reached half of it

[neon iron]

ofc

[left tree]

i need calm down

and stop be toxic

sorry 😔

i just dreamed that here would help me and solve equations for me

maybe i'm behaving wrongly, but only you and one other person really helped me in these two days

maybe this server is not meant for this

but i almost don't see anyone here

[neon iron]

If you finish the first half and send me a screenshot, I'll finish it for you.

@left tree are u there?

[left tree]

yeah

[neon iron]

solved?

[mystic jay]

What is method of variation of constants? I have a method to solve this, but osk if it follows that

[mystic jay]

Integrate this to get
(1+x^2)y'=3x^4+C

[neon iron]

nonono
u solved this?

[left tree]

for why?

[golden blade]

From here you can derive if $s(x)$ = 0 the homogenous solution $u_h = Ce^{-A(x)}.\$
Then the particular solution is $u_p = C(x)e^{-A(x)}.\$
You would next calculate $u'_p$ and plug in both into the differential equation to solve for $C(x).\$ Then you get the solution $u = u_h+u_p = y'$ and you can integrate simply to get $y$.

[left tree]

yeah

[thorny flame]

𝔸dωn𝓲²s

[mystic jay]

You can integrate (3x^4+C)/(1+x^2) to get y?

[left tree]

but i already have check

[left tree]

.

[mystic jay]

Why did you equate it to 0?

(Second step)

[left tree]

yeah

but i sended it earlier

lol

[left tree]

chatgpt

[neon iron]

why don't use matlab?

[neon iron]

because I am busy

but that way is true

[left tree]

okay man

[neon iron]

as u know, i am a programmer

and i have to work

now, for a few hours, I don't work because of u

[left tree]

unfortunately is not reason why im ask here

[neon iron]

what?

[left tree]

i sincerely don't want to distract anyone, forgive me

[neon iron]

np

dw

[left tree]

i think that if this coincides, then there will be other non busy people

[mystic jay]

@left tree that is incorrect?

[left tree]

this is method

[neon iron]

hm...

[left tree]

from ru wiki

[neon iron]

this is solution?

lol

[sweet shard]

<@&268886789983436800>

[left tree]

this is a more specific than the one on the english page

https://ru.m.wikipedia.org/wiki/Метод_Лагранжа_(дифференциальные_уравнения)
https://en.m.wikipedia.org/wiki/Variation_of_parameters

[neon iron]

nnoo

that is so complex

[left tree]

i think i need f(x)/a_n(x) on end

not just f(x)

[neon iron]

now u want me to solve your problem entirely.
that is bad.

[left tree]

😳

[golden blade]

I literally sent a blue print and y'all still keep philosophizing about this

[left tree]

idk

[golden blade]

Literally this

[sweet shard]

maybe uguu doesn't want hints and just wants the answer

[golden blade]

maybe

[left tree]

isnt this right method?

if so

I already forgot 1/a(x)

because before the highest derivative I have a(x)=1+x^2

[empty spoke]

if you're going to send GPT screenshots you are not able to explain it's honestly best that you don't reply at all.

[topaz sinew]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[neon iron]

kidding me?

i only use that i am so busy

if u dont know about me, dont say so!

@empty spoke when u r a kid, I solved those

[empty spoke]

I don't care. If anyone can go and do the same then it adds nothing to the convo

[sweet shard]

but not too busy to copy paste questions and answers into/from chatgpt

[empty spoke]

this seems to be variation of parameters in the general case. After doing a change of coordinates as in #help-26 message it reduces to applying variation of parameters for a linear first order equation

[left tree]

yeah

integration by parts, sec

or no idk

[left tree]

it is

[neon iron]

as i said, that is incorrect

u make me so disappointed

@left tree perhaps, I will remove u

gl!

[lean pebble]

Are you kidding ??? What the **** are you talking about man ? You are a biggest looser i ever seen in my life ! You was doing PIPI in your pampers when i was beating players much more stronger then you!

[left tree]

omg

[neon iron]

lol

perhaps, u r a faker!

[left tree]

so am even worse

[neon iron]

anyway, in here, let's stop such that

[left tree]

cant solve ez things myself

[neon iron]

if u have any words, dm me

[left tree]

i need close this sorry

[neon iron]

okay

.close

[lean pebble]

.close

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[mystic jay]

Do you know vieta?

[wicked mist]

nope

[mystic jay]

So this is of the form

3(x-x1)(x-x2)(x-x3) right?

And we want

[wicked mist]

yes

[mystic jay]

2(x1x2+x1x3+x2x3) right?

[wicked mist]

yes

[mystic jay]

The expansion of this is
3(xxx-(x1+x2+x3)xx+(x1x2+x1x3+x2x3)x-x1x2x3)

Right?

[wicked mist]

yes, but is there also not a quicker way to solve this by a formula?

[mystic jay]

Wdym?

This is quick?

[wicked mist]

like i thought were a formula for finding product of roots

[mystic jay]

There is

Vieta

[wicked mist]

could you not use that to find surface area?

ohh

thats what vieta is

[mystic jay]

That is what I am doing?

[mystic jay]

So we want 2/3 times the coefficient of x, right?

[wicked mist]

i thouht vieta was just taking the 3rd term and dividing by the 1st term

[wicked mist]

yes

[mystic jay]

Any term divided by first term

[wicked mist]

o

.close

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[sharp chasm]

Calculate the limit in the sense of distributions of:
[ T_n = \sqrt{n} \delta_n ]

[thorny flame]

jandro0103

[sharp chasm]

Hint?

[topaz sinew]

@sharp chasm Has your question been resolved?

[sharp chasm]

<@&286206848099549185>

[pseudo sonnet]

perhaps you'll find help more quickly in #advanced-analysis?

[odd pagoda]

also what is delta_n

[sharp chasm]

Dirac delta function

[sweet shard]

if you know fourier transforms, you could try to find the fourier transform of the product then inverse fourier transform of the convolution

https://math.stackexchange.com/a/4117943 for fourier transform of the sqrt(n)

[odd pagoda]

but whats the n doing

[sharp chasm]

Yes i know the FT

[odd pagoda]

!original

[topaz sinew]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[sharp chasm]

But it's a very long text, I don't understand where to look exactly

[odd pagoda]

I doubt that delta_n is the dirac delta function, cause then they would have just written delta and T_n would obviously not converge

[sharp chasm]

Yes it is the Dirac delta concentrated in n

[thorny flame]

jandro0103

[sharp chasm]

<@&286206848099549185>

[thorny flame]

jandro0103

[sweet shard]

Then it's not the delta function!

[sweet shard]

Do this

[sharp chasm]

But in reality this problem was written in pen, I'm sending a similar one but clearer

[thorny flame]

jandro0103

[sharp chasm]

Maybe the previous one was written badly, but I would need a hint here too

This one was definitely well written

@sweet shard

[noble lily]

@sweet shard $\delta_n$ converges in distribution to the dirac delta. Maybe it's arbitrary? Idk. But canonically, something like $\delta_n(x)=ne^{-(nx)^2}$ works. I can't work through this rn bc I'm busy, but the suggestion for Fourier transform is what I'd go through as well if that's the sequence we're working with

[thorny flame]

kirby

[noble lily]

But like has been discussed here, post the original problem and any relevant context because we don't know what the question has you assume or not @sharp chasm

[icy rapids]

Are you here @sharp chasm

[patent light]

I think this is the exercise now

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@sharp chasm Has your question been resolved?

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[neon iron]

Apart from the typo where they changed the question to write the solution

Isn’t the solution incorrect

They opened absolute sign with zero respect to what values of x we can have

According to which we should make cases

[topaz sinew]

@neon iron Has your question been resolved?

[burnt badger]

Do you mean an absolute value in the original expression?

Or one that would appear later in the algebra

[neon iron]

When they were evaluating LHS. from 2 to 3 step. There should be absolute sign

[neon iron]

Later I think

[burnt badger]

From the radical signs?

If you have a question about signs of things, cos2theta is something between -1 and 1

So 1 + cos2theta & 1 - cos2theta are necessarily >= 0

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@neon iron Has your question been resolved?

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[tired terrace]

There is this question given $2x+3y=14$ solve for min of $8/x+3/y$, and the values of x and y when min occurs.

The solution as of in attached image shows only the ineq is right but provides no information of infimum. All I could find was this identity https://math.stackexchange.com/questions/2267660/supremum-and-the-cauchy-schwarz-inequality but neither $\sqrt{2x}$, $\sqrt{3y}$, $\sqrt{\frac{8}{x}}$, $\sqrt{\frac{3}{y}}$ is bounded everywhere.

So what are the prerequisites of using Cauchy ineq to determine the infimum here?

[thorny flame]

Cro

[topaz sinew]

@tired terrace Has your question been resolved?

[mystic jay]

assuming x and y are positive

we could do this

but this is not neccessarily true

this has no infimum

ot minimum

[tired terrace]

hmm let me check

[tired terrace]

uhm with calculus i find x=4 or 28

[mystic jay]

take x = -0.0000001

[tired terrace]

By taking y=(14-2x)/3 and solve for d/dx(8/x+3/((14-2x)/3))=0

oh right

so first x>0 y>0

I think I get it.

.close

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[slender musk]

integration by parts

[neon iron]

If I'd continue this, I would have to do another integration by parts right?

[desert atlas]

+1 -1

[slender musk]

the integral after integration by parts is supposed to be $\int\limits_{0}^{1}\frac{x^{3}}{3(x^{2}+1)}dx$ not what you wrote

[thorny flame]

如月あやみ　Kisaragi Ayami

[neon iron]

wow

stupid mistake

thx

[slender musk]

afterwards do long division

[cinder sequoia]

you can also just differentiate the x^2 and integrate the arctan

[ionic oar]

or just sub x^2 + 1

[cinder sequoia]

and you get something that can be done by u sub

[neon iron]

was just looking through all you guys' answers

but this isnt possible right? substitution for u = x^2 +1

[slender musk]

the integral of arctan is $x\arctan x-\frac{1}{2}\ln(x^{2}+1)$ so im not sure how that helps actually

[thorny flame]

如月あやみ　Kisaragi Ayami

[neon iron]

becasue then you get du = 2xdx

[ionic oar]

here I meant

[ionic oar]

yeah

[slender musk]

then +1-1 yea

[neon iron]

but where do we find 2x in the function

[ionic oar]

write x^3 as x*x^2

[slender musk]

\begin{align*}
\int\limits_{0}^{1}\frac{x^3}{x^{2}+1}dx&=\frac{1}{2}\int\limits_{0}^{1}\frac{x^{2}}{x^{2}+1}d(x^{2})\&=\frac{1}{2}\int\limits_{0}^{1}\left(1-\frac{1}{x^{2}+1}\right)d(x^{2})\end{align*}

[thorny flame]

如月あやみ　Kisaragi Ayami

[lapis badger]

Hi, could someone help me understand Taylor’s theorem, especially the Taylor polynomial, please?

[neon iron]

oay

i understand what u are trying to say

but now i get this

[slender musk]

open a different help channel

[neon iron]

.rotate

,rotate

[neon iron]

oh wait

i have to substitute x^2

lemme see how i do that

OHHHHH

[ionic oar]

lol

[neon iron]

,rotate

[ionic oar]

yeah

[neon iron]

now integrate by parts again?

[ionic oar]

nah just split the fraction

1/6 - 1/(6u)

[neon iron]

ahh partial fraction decomposititon

oh

nvm

thats it 😂

[ionic oar]

yep

[neon iron]

think i still made a mistake

,rotate

[neon iron]

answer should be this

[ionic oar]

you never added the initial integration by parts part

[neon iron]

yeah cause its 0

wait lemme send

,rotate

[ionic oar]

huh?

pi/12 I think

[pallid hinge]

arctan1 is not 0

,w arctan1

[neon iron]

for real? but arctan(0) = 0

[thorny flame]

Results provided by WolframAlpha

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

Requested by _rysel_

[neon iron]

and 1/3 * 0^3

is also 0

so if ud fill in x = 1 or x=0 one of them would be 0

im stupid

nvm

i understand

[pallid hinge]

graph of arctan looks like this

[neon iron]

1/12pi indeed

yeah ty

[pallid hinge]

rest should be pretty straightforward

[neon iron]

theres still something wrong

[pallid hinge]

(u-1)/6u

[neon iron]

my final answer is

[pallid hinge]

is just 1/6 - 1/6u

[neon iron]

pi/12 -1/3 + ln(3)

[neon iron]

yeah i did that

here

[pallid hinge]

isnt upper bound 2

for u

[neon iron]

hmm

bruh

ur correct

[pallid hinge]

yeah lmao

[neon iron]

tysm

[pallid hinge]

and i think things work from there

[neon iron]

finally

[pallid hinge]

allg

[neon iron]

i got it 😭

tysm for all your help

.close

[pallid hinge]

np

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[worn bison]

The grid below represents part of a nautical chart. The squares are equal and the scale used on the map indicates that each 1 cm corresponds to 1000 m. A cargo ship leaving A traveled along the route ABCD.

[worn bison]

Knowing that 1 nautical mile is equivalent to 1,852 meters, we can say that on this route, from point A to D, the ship traveled in nautical miles approximately:

sqrt(2) = 1,41
sqrt(5) = 2,23

[fervent ferry]

Yes, and what exactly are you stuck on?

[worn bison]

i don't know how to start

i THINK we can do a Pythagorean theorem

[pallid hinge]

yep

[fervent ferry]

sqrt(2) is the digonal of a square, sqrt(5) is the diagonal of a 2x1 rectangle

this is just pythagoras

so you count how many of each diagonal the path is and multiply

[pallid hinge]

keep everything to meters for now and then convert it at the end

[worn bison]

thanks all you guys

i will try now

[pallid hinge]

you need to find how much the cargo ship travelled

[worn bison]

ok

so

wait

[pallid hinge]

if you know how many "squares" the cargo travelled, you can convert it to meters, to miles, to nautical miles, to anything

[worn bison]

so

i still unsure about the BC line

[pallid hinge]

what does pythagora say

[pallid hinge]

consider this triangle

[worn bison]

ohhhh

[pallid hinge]

tall 2 squares and long 4 squares

[worn bison]

ignore the bottom

[pallid hinge]

dw

[worn bison]

so

the image is a little bit confunsing

but

i think you can understand

[pallid hinge]

its root 20

but yes

you also need to find the other lenghts of the other 2 segments ab and cd

same process

and you sum all of the distances at the end

to get the total distance travelled

and those would be your cms travelled

then you can convert it into anything

[worn bison]

wait, so AB = 2^3?

[pallid hinge]

nope

you know that AB^2 = 4^2 + 4^2

so AB^2 = 16 + 16

AB^2 = 32

you take the root

AB = root32

32 can also be rewritten as 2^5

which can also be rewritten as 2^4 * 2

you can take the 2^4 out of the root

and it becomes 4root2

not sure if you have to do this part

depends if the teacher asks you

[worn bison]

it's not my homework or something like that

but

[worn bison]

oooohhh

okok

thanks

[worn bison]

sooo

its basically 32⋅1,41?

[pallid hinge]

no

its 4 * 1.41

[topaz sinew]

@worn bison Has your question been resolved?

[worn bison]

Wait

It wasn’t 2^5?

[pallid hinge]

its all under the root

[worn bison]

Sqrt(2^5)

[pallid hinge]

yes

[worn bison]

So

[pallid hinge]

$sqrt(2^5)$

sad

[worn bison]

You remove 2 powers of 2, isn’t it?

[pallid hinge]

yes imagine i only had 2^4

(which is technically 16)

taking the square root is the same as elevating to the power of 1/2

by applying the power of a power rule

2^(4 * 1/2) gives 2^2

[worn bison]

Ok so

it gives me AB value of 5,64

so

now

we have this weird CD

[worn bison]

.

that

apparently

have

5+0,5

of height

ok

i solved

thank you guys i love you all

,close

[worn bison]

thankyou very much

.close

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[reef hatch]

I know now that I chose the wrong terms for u and dv, but is there another reason why I got the problem wrong?

[cedar wagon]

always choose u as ln

will get you something easier in the second integral of the ibp

[reef hatch]

but is there another reason why I got the problem wrong?
choosing the wrong variable on its own shouldn't make it wrong right?

[sweet shard]

Your uv term on line 2 is incorrect

[reef hatch]

oh thx

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[leaden phoenix]

I’ve been stuck on this question for a while can’t seem to find out the issue, i calculated the domain using the denominator and where it’s undefined then tested each set but it’s partially correct

[sweet shard]

There's only one x value where the function is undefined

[visual sparrow]

the first one is wrong as -7/2 (-3.5) is within that interval

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[grim sable]

prove that there is no integer n such that $3^n \equiv 99 \pmod{100}$

[thorny flame]

Dork9399

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[noble pier]

can someone help out here? chatgpt can’t help with an actual proof and we’re stuck

[noble pier]

the partial sums series is not n=1^inf it just says it goes from n=1 to inf, same for a_n sequence

translations a bit off but that’s about it

[topaz sinew]

@noble pier Has your question been resolved?

[lean pilot]

s_n is sum of a_n from 1 to n?

[topaz sinew]

@noble pier Has your question been resolved?

[noble pier]

yes

i know the statement is true, but i don’t know how to write the proof for it

<@&286206848099549185>

[lean pilot]

I think maybe try to prove the sequence is monotone

And bounded(?)

Then apply monotone convergence theorem

I believe monotone is not so hard to prove

[noble pier]

yea i think that works thanks

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[agile shell]

Hi,
PI_1 : 5x-2y-z=-2

I wanted to understand why i cannot find the normal to pi_2 by doing the cross product of
(1 4 -3) x (5 -2 -1)

[agile shell]

i thought that the line of intersection is paralllel to the normal of the two normals of the planes

[topaz sinew]

@agile shell Has your question been resolved?

[finite storm]

1. What do u know about the relationship between normal vectors of the two planes and the intersecting line.
2. Using the points, can u find the normal vector of one of the two planes?

[agile shell]

1, well i know the line of intersection of parallel to the normal of the two normals of the planes, ie :
if the line is: r = a + tb
then b = n1 x n2

[agile shell]

2, i know how to do the question using the two given points, use (1,1,1) and (0,0,2) to get a direction vector on PI_2 then cross that direction vector with (1 4 -3) to get n_2

Im just confused on why (1 4 -3) x (5 -2 -1) doesnt give me a correct normal vector

[topaz sinew]

@agile shell Has your question been resolved?

[sonic escarp]

as you know one point on the intersection line, and as you know the direction vector of the intersection line, you know all (=infinite) points of the intersection line. so you know enough points of the plane.

(0,0,0) on the plane -> 2c = d
(1,1,1) on the plane -> ...
take another point of the intersection line -> ....

[agile shell]

yes yes i know how to solve the question using that method

[agile shell]

my main question is this

[sonic escarp]

whats you result?

[agile shell]

if i do (1 4 -3) x (5 -2 -1)

i get

(5 7 11)

if i use (1,1,1) i get the equation 5x + 7y + 11z = 23

if i use (0,02) i get 5x + 7y + 11z = 22

[sonic escarp]

why should this calculation should help you to solve the question?

[agile shell]

my reasoning is that

the intersection of the planes

that lines direction vector is perpendicular to both n1 and n2

right?

[sonic escarp]

the intersetion line is in both planes.

[agile shell]

yes

im saying its perpendicular to the NORMALS of the plane

so if the line is perpendicular to the normals

then if i find the perpendicular of the line and one of the normals

should i not get the other normal ?

[sonic escarp]

PL_1 isnt given in your exxample, but i am pretty sure that your equation for PL_1 is wrong (and therefore your normal vector for PL_1 is wrong).

[agile shell]

PI_1 is right

[sonic escarp]

the cross product is normal to both vectors, so if you take the cross product of the normals of two planes you get the direction vector of the intersection line. so far, so ok.

you wanna calulate the cross product of a normal to a plane and the direction vector of the intersection line. yes, this vector would be normal to the direction vector of the line, but why do you expect that the normals from the planes should be normal to each other?

[agile shell]

ur right

this would work if

PI_1 and PI_2

[sonic escarp]

what you are calculating is a vector which is normal to the intersection line (yes, ok) and it is normal to the normal of plane 1, so it is in plane 1

[agile shell]

are perpendoicular

right?

but if they arent it wont

cause n1 and n2 arent perpendicualr

makes sense

[sonic escarp]

you could take the direction vector of the intersection line (is in the plane) and the vector between the two given points (is in the plane) - if they hopefully are not parallel. so you can get the normal of plane 2.

[agile shell]

yep makes sense

thanks!

how do i close it?

[sonic escarp]

type .close

[agile shell]

ok thank u

.close

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[leaden phoenix]

What about the others?

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[coral night]

Introducing with the set $\mathbb P$ a prime number is rigorous ?

[thorny flame]

Aquamy

[chilly walrus]

what?

[coral night]

I don't know if this set is common for English people, in France, it's known.

[chilly walrus]

you can write "Let $\mathbb{P}$ be the set of prime numbers" and that'll suffice

[thorny flame]

artemetra

[humble schooner]

There is no prime numbers set

[chilly walrus]

what?

[coral night]

But not $\forall p \in \mathbb P$ ?

[thorny flame]

Aquamy

[coral night]

Automatically

[chilly walrus]

yea but then you'll have to say that p is a prime number

ahah

sometimes using a couple words instead of symbols makes the text clearer

[coral night]

So it's useless

[cedar wagon]

Ça dépend ce que tu veux faire

[cedar wagon]

Pour une phrase quantifié comme ça on peut s'en passer

Par contre si tu veux calculer un produit/somme de termes avec un p qui se balade dans l'ensemble des nombre premiers la c'est beaucoup plus utile de marquer p in P

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@coral night Has your question been resolved?

[coral night]

Ok je vois

mrc

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[neon iron]

Completely lost here

[tough nest]

AB is i think the length

of the segment between A and B

[neon iron]

I don't even know if it wants AB as a length or A*B

Cause it doesn't have that little line above it

[tough nest]

you can easily try both no?

[neon iron]

I don't know how to get A and B

[tough nest]

ah ok

[neon iron]

😭😭

[tough nest]

well you have a line

with 3 equations

and a plane

in which you can plug in 2 of the 3 to find what value x or y or z has to be for the intersection point

so

take the plane 2x + 3y - z = -13

you can plug in 1 - z into it

to get rid of z

for example

(x - 2) / 3 = 1 - z

so then the plane equation becomes

2x + 3y + (x - 2) / 3 = -12

using (x- 2) / 3 = (y + 1) / 2

you can find either x or y

and plug it into this

[tough nest]

this one

to find the other

etc

and the same for the other plane

to get A and B

[neon iron]

Ahhhhhhhhh

Ty ty 🙏🙏🙏

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[jolly root]

hello

[jolly root]

i checked 2 helpers before this one and i didn't even get a respond

so here it is without further ado

translate it if you don't speak french.
it is rather simple

i am somehow supposed to use the mean value theorem or rolle theorem

[opal vault]

qu'as-tu essayé?

[jolly root]

j'ai posé l'ensemble A des pts ou f s'annule
j'ai supposé par l'absurde que f ne s'annule pas sur cette ensemble

autrement dit , je veux trouver un c dans A ou f'(c)=0

puisque A est infini et f ne s'annule pas sur A
je voudrais discuter si f s'annule un nombre fini de fois sur I
ceci peut aider à trouver un voisinage entre deux reels ou f s'annule mais ou elle est strictement monotone

on est supposé à utiliser le TAF mais je n'arrive point

je peux aussi facilement trouver un c ou f=f' et un c ou f'=0

il existe une infinite ou f=0

ce qui est delicat s'agit de quoi poser ou faire intervenir pour qu'on obtienne les 3 egalites

[opal vault]

est-ce que tu peux montrer que pour tout epsilon il existe x tel que f(x) = 0, y tel que f'(y) = 0 tels que |x-y| < epsilon?

le théorème de Rolle va beaucoup t'aider pour montrer l'affirmation ci dessus

(premier indice : ||A possède une suite convergente (pourquoi ?)||)

[jolly root]

A est bornée

theoreme de bolzano -weiestrass

il existe une sous-suite a elements dans A tq cette sous suite converge

[opal vault]

ok

notons cette suite x_n

(d'ailleurs que peut-on dire de la limite de x_n?)

[jolly root]

la limite de xn est un element de A

cad f(l)=0

notons l la limite

[opal vault]

ok

maintenant

TAF

sur [x_n,x_n+1]

[jolly root]

il existe yn dans cette intervalle tque f'(yn)=0

yn est comprise entre xn et xn+1
donc yn tend vers l aussi

donc cette limite l est celle qu'on cherche

[topaz sinew]

@jolly root Has your question been resolved?

[topaz sinew]

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[quiet flume]

how do you do this?

[topaz sinew]

@quiet flume Has your question been resolved?

[topaz sinew]

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[tawny axle]

Why is this not -91

[neon iron]

ok so here's how you solve it

1. find g(x)

2. find f(x)

3. find g inverse (x)

4. find f . g inverse (x)

[storm hearth]

Dont even need to try that much

[neon iron]

that's how I solved it 😢

[tawny axle]

I reversed that function

[storm hearth]

You are given like a minute to solve it so

[tawny axle]

but still

It became g(f-1(13))

[autumn geode]

can you translate the original question 😭

[storm hearth]

Well you let 2x = 13 which is wrong

[tawny axle]

but f(13) gets in

[storm hearth]

Question doesnt really need a translation

Just says, given that find g()

[autumn geode]

does it ask for f-1(13)

[tawny axle]

asks for (fog-1)-1 so I did (gof-1)

[storm hearth]

I will show you a quick tech to find the inverse fastly

[tawny axle]

wait is it 2/x

No

[autumn geode]

first of all

isn't fog = f(g(x))

[tawny axle]

yeah

[storm hearth]

To solve a + 3 = a + b you add -a to left side of a right,

But notice function composition is NOT commutative. We say an operator * is commutative if
ab = ba

[autumn geode]

first of all

simplify

f(x) = 3x+4/2

g(x) = 5 - 4x - 2

[storm hearth]

To find inverse of f, on each side with composition operation so f^{-1} • f = I
Where I is the identity function I(x) = x

[autumn geode]

find fog first

then inverse of fog

then inverse again

[storm hearth]

So you quickly get f^{-1}(3x+4) = 2x

[autumn geode]

a better idea would be

turn fog into a new function

j(x)

it should make things easier

[storm hearth]

Then let 3x+4 = 13 to find f^{-1} (13)

[neon iron]

The answer I got

doesn't seem to match the options here :(

[tawny axle]

so f-1(x) is (x-4)/3 right?

then I need to find g(9)

[autumn geode]

-7?

[tawny axle]

isnt it -33

[storm hearth]

Did you get the fast tech

[neon iron]

I got the same answer

[tawny axle]

fast tech?

[neon iron]

technique

[storm hearth]

You will have 1 min in YKS so might as well learn the fast way too

[tawny axle]

oh yeah

[tawny axle]

wait a minute you know YKS?

[storm hearth]

Yeah, if it wasnt trivial enough, i am a turk as well

[tawny axle]

lol

still wondering why is it not -33

[autumn geode]

f(x)=3x+4/2
g(x) = 7 - 4x
fog = f(g(x))=
k = 3(7-4x)+4/2
2k = 3(7-4x)+4
2k = 21-12x + 4
2k = 25-12x
k = 25-12x/2

[storm hearth]

What is your answer?

Options dont have to be correct all the time , yknow

[autumn geode]

y = (37 - 3x) / 8
x = (37 - 3y) / 8
8x = 37 - 3y
3y = 37 - 8x
y = (37 - 8x) / 3
(fog^-1)^-1(x) = (37 - 8x) / 3

[tawny axle]

wait now I found it 1?

[autumn geode]

that's my answer

wait

[autumn geode]

it's 22 for me

wbu

-22.33

[tawny axle]

OMG its 3

so if f(2x) = 3x + 4 and it asks for f(13)

x should be 13/2

and f-1(x) is (x-4)/3

f-1(13) = 3/2

x+2 = 3/2 x = 1/2

then 5 - 4 x 1/2

which is 3

did I do it right?

[storm hearth]

I believe its -11 tho

[storm hearth]

Nope its 6

[storm hearth]

Why calc f(13)

[tawny axle]

cuz its reversed

so I should start with f

and I calculated f-1 there

mb

[tawny axle]

this part

[storm hearth]

Wanna save yourself all the work?

[tawny axle]

started with f-(13)

[storm hearth]

And some energy