help-23

[lean otter]

it is

[drowsy moss]

,w fundamental theorem of calculus

[flat frigate]

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Requested by Zybikron#5611

[lean otter]

then F'(x) = f(x)

[lean otter]

Ya

wait

im still confused

so it would just be F"(x)?

F'(x)

?

[drowsy moss]

read the last line of this, and look at your question. Do you see what's missing from your equality?

[lean otter]

if this is F(x)

no I dont

[drowsy moss]

FTC says $\int_a^b f(t)\ dt = F(b) \underline{-F(a)}$

[flat frigate]

Zybikron

[lean otter]

yes

and

?

[drowsy moss]

f'(0), where is it?

[lean otter]

its a constant

value

[drowsy moss]

so is F(b) and F(a)

you're not taking a derivative, you're integrating.

constants don't disappear when integrating.

[lean otter]

yeah so wouldn't an integral undo a derivative?

[drowsy moss]

up to a constant, yes

[lean otter]

does $\int :f'\left(x\right)dx=f\left(x\right)$

[flat frigate]

Riemann Zeta Male

[lean otter]

+c

does that not hold

[drowsy moss]

that +c is -f'(0) from your original question

[lean otter]

wouldn't it be

[drowsy moss]

sure

[lean otter]

f'(0)

?

wdym sure

[drowsy moss]

there, fixed it

[lean otter]

theres a minus here

?

[drowsy moss]

so you're adding a negative constant

[lean otter]

ur confusing me so hard

[drowsy moss]

Using FTC, $\int_0^sf''(t)\ dt = f'(s) - f'(0)$

[flat frigate]

Zybikron

[lean otter]

yes

thats what

I said

is that not right

[drowsy moss]

no it isn't

[lean otter]

is it not true

[drowsy moss]

^^^^

no

[lean otter]

if the whole integral was F(x)

and it were equal to F'(s) - F'(0)

[drowsy moss]

?????

[lean otter]

$F\left(x\right)=\int _0^s:f''\left(t\right)dt=F'\left(s\right)-F'\left(0\right)$

[flat frigate]

Riemann Zeta Male

[lean otter]

this isn't true

?

[cosmic grove]

what is F' tho

[lean otter]

Can I just give some context

I feel like that would help so much here

[drowsy moss]

It looks like you're trying to combine both parts of the FTC and they don't work like that

[lean otter]

I was trying to re-write $\left(\int _0^s:f:''\left(t\right)dt\right)\cdot :s$ and go from there

[flat frigate]

Riemann Zeta Male

[lean otter]

but im not really sure if thats the right approach to continuing my solution

[drowsy moss]

So you're just trying to evaluate that first term on the RHS in the last equation?

[lean otter]

no

look at the second picture I sent at the bottom

$\left(\int _0^s:f:''\left(t\right)dt\right)\cdot :s$

[flat frigate]

Riemann Zeta Male

[lean otter]

can this be further simplified/re-written

.close

[safe radish]

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[jade hinge]

anyone know how i can use change of var for 4b)?

[broken yew]

change of var? 🤔

Are you not just supposed to use FTC

[pulsar condor]

You are

[safe radish]

@jade hinge Has your question been resolved?

[jade hinge]

oh ok but how do u do that, cuz dont u need change of var first

cuz ftc has a constant lower bound

[broken yew]

FTC2 might be your friend then

This might be a bit dodgy depending on how you've learnt it... but either bound being a variable shouldn't matter...

Oh right it's a theorem

[jade hinge]

? this

or the other one

[broken yew]

no no go back

FTC1

Like you said, constant lower bound

But there is a theorem you can use to make this not matter

[jade hinge]

split it into 2?

[broken yew]

yes

[jade hinge]

hm ok i tried that for a while, still cant deal with the individual ones

[broken yew]

🤔

[jade hinge]

cuz u got x-sinx

[broken yew]

wait wait wait.

typing

,, \int^{u(x)}_{l(x)}f(x)\dd x=\int^{u(x)}cf(x)\dd x + \int^c{l(x)}g(x)\dd x

[broken yew]

So you have this right?

[jade hinge]

ye

[broken yew]

Can you not the approach as normal?

differentiate both sides

[jade hinge]

sure but the upper bound needs to be x right? to apply FTC

so need change of var

[broken yew]

uhhhhhhhh

[broken yew]

Like I will tell you it won't matter and you don't even need to split like this. You can directly apply FTC2 to variable bounds fine
But this may be a result you haven't seen yet (I'm unsure atm)

[broken yew]

@pulsar condor halp ^

[safe radish]

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[pulsar condor]

chain rule

... is a thing

[broken yew]

@jade hingereopen

[jade hinge]

ok

[broken yew]

you need to .reopen

[jade hinge]

.reopen

[safe radish]

✅

[broken yew]

Is your question

about this basically

[jade hinge]

yea

[broken yew]

that we need exactly this form

[jade hinge]

yea

cuz in pt a) i solved it using change of var to get to this form

[broken yew]

uhhhhhhhhhhhh

So what is wrong with just letting

u = sin x

l = x - sin x

and then proceeding

,, \int^{u(x)}_{l(x)}f(t)\dd t=\int^{u(x)}cf(t)\dd t + \int^c{l(x)}g(t)\dd t

[broken yew]

Cus we had this.

The upper bound is just u for the left one

the right one, there is a smart trick to do

[jade hinge]

sure yea, so in the end u have to change the ub from u(x) to x right? to use FTC

[broken yew]

whats so special about x though

You can also apply FTC on u being the upper bound

following the exact statement

[jade hinge]

ah

[broken yew]

and as suggested above, the chain rule will do the rest

[jade hinge]

ic ic

ty

[pulsar condor]

$I(x):=\int_0^x f(t)\dd{t} \
F(x):=\int_0^{u(x)}f(t)\dd{t}=I(u(x))$

[flat frigate]

Mosh

[jade hinge]

forgot about that,..

[broken yew]

In the end there is no need to split

its an immediate result you can see

but that depends on what your teacher wants

[pulsar condor]

there is, you can only apply FTC if 1 of the bounds is constant

[jade hinge]

yea

[broken yew]

🤔

[jade hinge]

gotta split

[broken yew]

If both are variable

does this not immediately follow

If f(t) is continuous between the bounds

there should be no problems right?

(if it isn't, then yh)

[pulsar condor]

yeah there's no problems

you cant apply FTC to the LHS of that tho

[jade hinge]

ah

[pulsar condor]

you need to split then apply linearity of the differential operator blahblahblah

[jade hinge]

ic what u mean ok

[broken yew]

but this is a corollary no?

[pulsar condor]

that has nothing to do with the derivative

that's just a property of integrals

[broken yew]

Let me write.

,, \dv x\int^{u(x)}_{l(x)}f(t)\dd t=\dv x\left(F(u(x))-F(l(x))\right)

I'm saying this follows using the above splitting

and is a corollary

(given certain conditions on f)

[pulsar condor]

No...?

Not at all?

[broken yew]

🤔

[pulsar condor]

you'd have f(u(x)) for one

and f(l(x)) for the other

[broken yew]

sorry i wrote that bad lmao

[nova creek]

Well, capital F, I suppose

[broken yew]

I meant this

[pulsar condor]

yeah primitive

then yes

that's FTC2

[broken yew]

As in as soon as you prove the above, then there is no need to split, surely.

[pulsar condor]

well sure, but your method assumes you can even do the integral

[broken yew]

yh ok. something to take care of --- especially when you have something like arcsin(t) as the integrand

[jade hinge]

so u can set the bound as [-1,1] then

[safe radish]

@jade hinge Has your question been resolved?

[safe radish]

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[distant steppe]

can i get some help on this

[distant steppe]

i don't know where to start

is a) D = 1 + 3c?

[solid shell]

Yes

Er

Close

The variables are swapped

[distant steppe]

d = 3c+1?

[solid shell]

You're looking for a function that looks like C = something

[distant steppe]

Ohh

c = 1+3d

[solid shell]

You have the right idea, yup that's oit

So now you can begin constructing a table using the values 1, 2, 3, and 4 as d

[distant steppe]

Does that look right?

[solid shell]

Yup

[distant steppe]

how would I graph this

do I just graph c = 1+3d

[solid shell]

Make a graph where the X axis is d and the Y axis is C, then plot the points in that table

[distant steppe]

Like this?

[solid shell]

Not quite, that graph is saying that at d = 1, C = 0 but the table says that C = 4

[distant steppe]

o

uh

[solid shell]

Try graphing y = 3x + 1

[solid shell]

There you go

[distant steppe]

Thank you !

.close

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[final loom]

show how you found the function

why |x - 2|

why √|x - 2|

why |-√|x - 2| + 2|

no you did not, it's not possible to guess it

I mean sure, you did guess it and guessing was the solution but, how did you conclude what you guessed

how did you arrive at your guesses

why is it not x^3 or x^2

why is it not only -√(x - 2)

that's the working out you need to show

note all possible hints, and the inference you got to arrive at your potential guesses

1. for example

[safe radish]

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[final loom]

you note that f(x - 2) = f(2 - x)

so, you know that this function is even about x = 2

so |x - 2| must be in the function

and so, you only now need to guess what the function is for x > 2, and you'll be done

[safe radish]

✅

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[steep pulsar]

how to simplify (9-7i)-(10-6i)

[steep pulsar]

could i get the answer first then the explanation?

[solid shell]

The same way we discussed before: add/subtract the terms with and without i separately

[steep pulsar]

my issue is

i dont know how far i should simplify

[solid shell]

If you did (8 - 3i) - (10 + 4i) you would get -2 - 7i

You're done simplifying when you have a number that looks like a + bi

[steep pulsar]

so after -2 - 7i

i dont need to go any further?

[solid shell]

Nope

[steep pulsar]

kk

thx

.close

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[solid shell]

Note that that's the answer to my made-up problem, not the one you're trying to solve

[safe radish]

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[marsh walrus]

okay i lied i do need help

[marsh walrus]

its $\int _C Re(z) \dd z$

[flat frigate]

jan Niku (Shuri for Honorable)

[marsh walrus]

along the semi circle radius 4 from z=-4 to z=4

is there a good way to do this that isnt a complete nightmare?

,w integrate ( 4cos(pi/2 - theta)(-4ie^(i(pi/2 - theta)))) from 0 to pi/2

[flat frigate]

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Requested by jan Niku#2119

[marsh walrus]

i mean like

this is maybe a horrible idea

could i try to show that $Re(z)$ satisfies CR

[flat frigate]

jan Niku (Shuri for Honorable)

[marsh walrus]

then just integrate Re(z) from 4 to -4 along the x axis

then take the negative of that result

?

damn

it doesnt satisfy them

.close

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[safe radish]

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[toxic falcon]

this can be confusing because it's in french

[toxic falcon]

so im stuck with the third question

3)b)

[obtuse jackal]

shall we do this in french ?

[toxic falcon]

u can speak french?

if u want to

[obtuse jackal]

C'est quoi w dans la 3)a) ?

entre français

[toxic falcon]

c'est une règle

attend que je t'envoir

e

[plucky elk]

,rotate

[obtuse jackal]

thx

[toxic falcon]

on a utilisé la règle de rotation

i thought so too lol

[obtuse jackal]

ask in your own channel

[plucky elk]

stop spamming other people's help channels

[obtuse jackal]

<@&268886789983436800>

[plucky elk]

<@&268886789983436800>

good times

[wild cape]

b&

[plucky elk]

👨🏻‍⚖️

[toxic falcon]

now that he left

can u pls help me

xd

[obtuse jackal]

yep

du coup c'est quoi w ? Le centre de la rotation ?

pas que ce soit nécessaire pour la b), mais je suis pas sur de comprendre la a)

[toxic falcon]

w n'est pas le centre de rotation

attent je t'envoir la règle

non tu avais raison w est le centre

XDD

Dsl

[obtuse jackal]

anyways

utilise ae^i(alpha) = -b et passe en polaire non ?

comme ça ça devient une égalité sur les angles

[toxic falcon]

je sais pas i really don't know what to do

bwb

[obtuse jackal]

en fait c'était pas vraiment une question

[toxic falcon]

oh

[obtuse jackal]

même si j'ai pas fais les calculs moi même, je vois pas pourquoi ça marcherait pas

[toxic falcon]

attend une minute que je la fais puis je te montre ok?

[toxic falcon]

oui je comprends mtn mais comment je vais faire pour y arriver a avoir alpha

[obtuse jackal]

c'était une question ? Tu mets tout en une exponentielle puis tu "passe au log" (mod 2pi) et tu obtiens une équation sur les angles

[toxic falcon]

tu veux dire que je passe en forme trigonometrique?

[toxic falcon]

oui je vois

[obtuse jackal]

forme exponentielle, pas trigo

[toxic falcon]

mais "passe au log" veut dire quoi

?

[obtuse jackal]

t'es en maths expertes ?

[toxic falcon]

non

[obtuse jackal]

prepa ?

[toxic falcon]

bac

[obtuse jackal]

spe maths ?

[toxic falcon]

je suis en 2eme année bac

6eme

[obtuse jackal]

wtf

[toxic falcon]

oui je suis très nulle ;-;

[obtuse jackal]

genre bac+2 ?

[toxic falcon]

genre ouais

[obtuse jackal]

c'est quelles études ça ?

[toxic falcon]

je suis en dernier année de lycée

[toxic falcon]

tu veux quelle filliaire?

tu veux dire*

[obtuse jackal]

donc terminale, pas bac+2

tu me rassures

[toxic falcon]

a ouais je sais pas comment ces trucs marche

:,)

je suis marocaine tu vois

[obtuse jackal]

t'es en Algérie ou bien ?

close enough

[toxic falcon]

algerie xf

xD

[obtuse jackal]

j'ai un pote marocain dans ma classe

et un tunisien

[toxic falcon]

les marocains sont cools

:)

tu peux faire l'exercice pour que je comprenne mieux ce que tu veux dire

👉👈

[obtuse jackal]

la 3)b) ?

tu a déjà vu en 2) les angles pour a et b

[toxic falcon]

2)b)?

[obtuse jackal]

pi/6 et -pi/6 si je ne m'abuse

[toxic falcon]

oui c'est vrai mais je sais pas comment lier cetter question avec la 3)b)

[obtuse jackal]

e^i(pi/6+alpha) = -e^i(-pi/6)

[toxic falcon]

oooh c'est ça ce que tu voulais dire dès le début

apres on fait quoi

on passe au log?

[obtuse jackal]

donc e^i(2pi/6 + alpha - pi) = 1
pi/3 + alpha = pi [2pi], je te laisse conclure

[toxic falcon]

alpha = pi - pi/3

alpha = -2pi/3

👏

[obtuse jackal]

Tu comprends bien le passage entre ces deux lignes n'est ce pas ?

[obtuse jackal]

oublie pas le mod 2pi

[toxic falcon]

oui j'ai compris merci infiniment c:

[toxic falcon]

a oui

[obtuse jackal]

On dirait que mon égalité est fausse vu que le résultat est faux

[toxic falcon]

passe à la question suivante puis je te laisse tranquille

;-,

[toxic falcon]

non c'est vrai

le resultat est vrai

[obtuse jackal]

tu remarqueras que t'a fais pi-pi/3 = -2pi/3. Le - est pas sensé tomber du ciel

[toxic falcon]

bah pi-3pi/3 = -2pi/3

c'est faux?!

[obtuse jackal]

ça oui

ça c'est faux

[toxic falcon]

?

[obtuse jackal]

0 = -2pi/3

[toxic falcon]

mais d'où

je comprends pas

[obtuse jackal]

c'est pas des pi/6

j'ai oublié le -

-3/2

donc c'est des 5pi/6

[toxic falcon]

A OUI

[obtuse jackal]

donc e^i(10pi/6 + alpha - pi) = 1
5pi/3 + alpha = pi [2pi]

la c'est bon

[toxic falcon]

a = racine de 3 e^(5pi/6)

[obtuse jackal]

désolé

[toxic falcon]

je l'est deja fais mais j'avais rien remarqué

xd

[toxic falcon]

non c'est pas grave t'exuse pas

[toxic falcon]

oui c'est bon

je suis très heureuse merci bcp bcp

[obtuse jackal]

tu sais faire les c) et d) ?

[toxic falcon]

je suis en train d'y reflechir

comment je fais pour w?

[obtuse jackal]

perso je l'aurais calculer directement mais visiblement le but est de ne pas le faire

utilise la a), t'as besoin de rien d'autre

i.e. pas de la 3)b), la 2) est évidemment utile

[toxic falcon]

3)a)

?

Photo de Hafsa👺

c mieux

[obtuse jackal]

la méthode attendue (je pense) est de réarranger ces égalités et de passer au module

[toxic falcon]

on calcul module de a puis de w?

[obtuse jackal]

tu passe au module dans l'égalité

après avoir réarrangé un peu

[toxic falcon]

arg(a-0/w-0)= arg( conjugué de a -0/w-0)?????

[obtuse jackal]

pourquoi arg ? C'est || ici

[toxic falcon]

AWI

TU DISAIS MODULE

[obtuse jackal]

évidemment avec arg c'est faux car l'un est > 0 et l'autre < 0

[toxic falcon]

mais w c'est quoi

c'est le centre oui

mais

[obtuse jackal]

lmao

[toxic falcon]

j'abondonne tu peux fermer channel

[obtuse jackal]

non attend

[toxic falcon]

🙂

oui?

[obtuse jackal]

juste tu développe, tu réécris (a-w)e^i(alpha) = -w e^i(alpha) et tu passe au module

d'où la d)

en utilisant b=a barre tu obtiens l'autre égalité à |w|

[toxic falcon]

attend je crois comprendre ce que tu dis

montre moi comment on passe au module

[obtuse jackal]

tu prend le module de chaque coté. Les exponentielles imaginaires ont pour module 1 donc elles disparaissent

[toxic falcon]

|a-w|= |-w|

apres

je met la regle et je la racine?

je met *

[obtuse jackal]

la notation du module est la même que celle de la valeur absolue pour une raison

[toxic falcon]

|a-w|= |w|

:)

ça fais 3 mois que j'ai pas touché le math

j'ai mes.raisons

;-;

[toxic falcon]

|a-w/w|=1

mais ça na aucun sense ce j'ai fais

[obtuse jackal]

je sais pas où ça mène je t'avouerais

mais pour la c) il n'y en a pas besoin

[obtuse jackal]

tu fais juste ça sur la 2e égalité pour obtenir un résultat similaire, et tu les combine

[toxic falcon]

(b-w)e^i(alpha)=-we^i(alpha)

[obtuse jackal]

réfléchis un peu. La même méthode, pas la même expression

réarranger puis passer au module et simplifier

[toxic falcon]

j'ai utilisé la même methode ce qui differencie des deux c'est a barre non?

[toxic falcon]

ce ne serait pas la meme chose? just a barre serait b?

[obtuse jackal]

cf question 2) oui

[toxic falcon]

donc mon expression etait juste

?

;_;

je vais pleure

XD

je rigole

[obtuse jackal]

.

[toxic falcon]

bah

[obtuse jackal]

je te l'avais déjà dis

[toxic falcon]

j'ai pas compris ce que tu veux dire

[obtuse jackal]

du coup on a les égalités des questions c) et d)

[toxic falcon]

j'admire ta patience

[obtuse jackal]

je sais, c'est fou. Ma productivité en souffre cependant

mais c'est un choix

[toxic falcon]

oui c'est vrai

d c'est confirmé

mais c

[obtuse jackal]

les deux sont égaux à |w|

[toxic falcon]

et comment on fait pour montrer que w=-1

[toxic falcon]

c'est le cas

[obtuse jackal]

passe à la définition avec la racine. C'est une équation de degré 2 (le signe de w est évident)

[toxic falcon]

je vois tu peux fermer mtn

[obtuse jackal]

mon .close est sans effet ici.

c'est le demandeur qui peut fermer (ou les modos)

où le bot dans longtemps

[toxic falcon]

avant de fermer je veux te remercier infiniment :D

voila

.close

[safe radish]

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[obtuse jackal]

de rien

[safe radish]

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[foggy python]

what does {a, b E(euro) R & a +/- bi} mean

[queen parcel]

Send a picture if you can - I can't easily understand that

[winter pivot]

Euro

[stoic dune]

Euro

[stoic dune]

∈ means "in"

a,b are elements of the set R

[foggy python]

I get that part, but what does a+/-bi mean

[stoic dune]

I actually have no clue lol. That's not standard

[winter pivot]

It means z and/or conj(z)

[foggy python]

https://tenor.com/view/xqc-xqcl-xqcow-streamer-stare-gif-23495711

[queen parcel]

I think it wants a and b where a and b are the components of the imaginary number

[foggy python]

what does that mean

[winter pivot]

no wait they wrote that weird

it's only half of a boolean

there needs to be an equal sign

a+-bi is what?

[stoic dune]

So there are complex solutions for a, but the a ∈ R makes me think you shouldn't include them

[winter pivot]

no it's saying that a,b are real numbers

but a+-bi on its own is not a boolean you can't evaluate it to be true or false

[safe radish]

@foggy python Has your question been resolved?

[safe radish]

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[broken yew]

draw

[lean otter]

I did

[winter pivot]

Let G' = g

[lean otter]

what I understood from this question was basically that you're trying to prove that if you have some function g(x) that is being integrated from a to b that would be equal to the integral of the midpoint of a to b and then g(a+b-x) is sort of "counting the area" backwards from b to the midpoint if that makes any sense.

I can show u my drawing but it’s on my iPad

And I’m in bed rn

$\int_{a}^{\frac{a+b}{2}} g(x)dx + \int_{\frac{a+b}{2}}^b g(x)dx$

[flat frigate]

Riemann Zeta Male

[lean otter]

Am I on the right track?

@broken yew

[broken yew]

Why would you ask ME

oh nvm u said u drew it

💤

idk i havent actually done the Q

I can see that it almost certainly can be solved from the geometry involved, that is all.

[winter pivot]

Let G'(x) = g(x) then just write out the definite integral

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

Idk how this helps

[broken yew]

Does the picture realllllly not help

mystified.

[lean otter]

It doesn’t

I’m not that smart @broken yew

[safe radish]

@lean otter Has your question been resolved?

[plucky elk]

Just make a substitution on the right integral and you're done. The information is in the limits

[safe radish]

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[sly elm]

Hello? Anybody know how to factor trinomials?

[sly elm]

2x^4 - 20x^2 - 78.

is the problem im working with

[upper folio]

sub u=x^2

then you have 2u^2 - 20u - 78 which you can solve

[sly elm]

Wait so

Wait i mightve learned a tad bit different than that

having a memory problem rn

but i remember my teacher doing it like 2(x^4 - 10x^2 - 39)? And then doing something from there

wait sorry that was the product

just the equation divided by the GCF then do something else after thst

my bad im talking too much

[upper folio]

oh yeah

ummm

so 39 has factors 13 and 3

so they are potential solutions to x^4 - 10x^2 - 39

[sly elm]

Oh wait

so should i replace 10 with something like -13 + 3?

[upper folio]

no no

[sly elm]

ohh

[upper folio]

just let x=13 and x=3 and see if x^4 - 10x^2 - 39 = 0

if x^4 - 10x^2 - 39 = 0 then x=a is a soln, so x-a is a factor of x^4 - 10x^2 - 39

and you can do polynomial division to factorise it

[sly elm]

Ohh okay

uhm real quick

whats a soln

[upper folio]

solution

i'm just lazy

[sly elm]

OHH

Bruh sameee but I want to make use of my brain because I cant sleep

and i got a lot of missing math

[upper folio]

yeah same, well good luck, do try and get some rest though it's hard to think when you're exhausted

[sly elm]

Okay thanks for your help!

.close

[safe radish]

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[lean otter]

So

[lean otter]

$\int_{a}^{\frac{a+b}{2}} g(x)dx + \int_{\frac{a+b}{2}}^b g(a+b-x)dx$

?

[flat frigate]

Riemann Zeta Male

[lean otter]

Is this rightV

?

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[ruby cloak]

Help me please I need to see if this is right angle triangle or not

[queen parcel]

Post the image with your first message

[safe radish]

@ruby cloak Has your question been resolved?

[ruby cloak]

Is a not a right angle triangle

<@&286206848099549185>

@plucky elk

@queen parcel

@upper folio

[queen parcel]

Don't ping random people.

[ruby cloak]

@sly elm

Oh okay

Please help me it’s urgent

[queen parcel]

If you read #❓how-to-get-help

[ruby cloak]

Dude bro I literally applied for help

[queen parcel]

Wym you "applied"?

[ruby cloak]

Yes

[queen parcel]

Lol

[ruby cloak]

Please see if what I did is correct

[queen parcel]

What have you tried?

[ruby cloak]

This

[queen parcel]

You haven't tried anything

[ruby cloak]

Is a not the right angle

[queen parcel]

Read this: • Show your work, and if possible, explain where you are stuck.

[ruby cloak]

It’s asking which one is not the right angle triangle

The answe is A right

[queen parcel]

I know what it's asking. I'm reading what you're saying. You're not reading what's sent right above your message for help

[queen parcel]

Why do you think it's A?

[ruby cloak]

First of all it’s a ablisque

Second of all it’s acture

Acute

It has a weird slope so it makes it an oblique

Am I correct

[queen parcel]

How do you define "weird"?

[ruby cloak]

It’s not constant

[queen parcel]

"weird" doesn't give any information

[ruby cloak]

It’s not constant

[safe radish]

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[queen parcel]

Slope is constant along a side length

[ruby cloak]

What the answe r

[safe radish]

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[cerulean wadi]

$I_n=\int {-1}^0x^n\sqrt{1+x}dx:for:n=0,1,2,3...,:show:that:I_n=-\frac{2n}{2n+3}I{n-1}:for:n=1,2,3,....:$

[flat frigate]

Hamburglers

[cerulean wadi]

my first step was

[flat frigate]

Hamburglers

[cerulean wadi]

then by parts

[flat frigate]

Hamburglers

[cerulean wadi]

then did some rearranging and not getting original integral

[feral linden]

I let x=sin^2(t)-1 t from 0 to π/2, so it became (-cos^2(t))^nsin(t)dt= (-u^2)^ndu u from 0 to 1, the result I got (-1)^n/(2n+1). Is there something wrong so far?

So eventually I_n=(-1)^n/(2n+1) so I_n=-(2n-1)/(2n+1)I_ (n-1)

(2n-1)/(2n+1) which isn’t 2n/(2n+3) but I can’t find my error 😂

[safe radish]

@cerulean wadi Has your question been resolved?

[safe radish]

@cerulean wadi Has your question been resolved?

[safe radish]

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[compact needle]

hey uh

[safe radish]

Please don't occupy multiple help channels.

[compact needle]

hi

is this occupied

i'm wondering how to solve equations like

i'm not sure what to do with the denominator or the numerator in these situations. Any help is appreciated :]

[tall bough]

since rh is 0

de om will go away

so it's only num

then solve for x

[compact needle]

ok

[tall bough]

$\qed$

[flat frigate]

The Fractalogist

[safe radish]

@compact needle Has your question been resolved?

[compact needle]

hmmmm yes

[safe radish]

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[willow cloud]

you guys do physics grade 9 ?

[last dagger]

just send the question

[tacit fog]

hold on

[tacit fog]

i think this is math server not physics

i mean the subjects are closely related tho

[stoic dune]

So you can't lose by sending the question. If nobody wants to attempt, then nobody wants to attempt.

[last dagger]

yea most people here can do physics anyways

well at least i can

[stoic dune]

You can definitely be more on topic with the physics server in #old-network though.

[tacit fog]

i dont think we should post it i am new so i will go with the flow ig

[stoic dune]

But yeah, especially at that level, math and physics are pretty similar

[last dagger]

newtons law of gravitation

F=GMm/r^2

just sub the values in and you get the answer

[willow cloud]

yea I did that but I don't get the answer the answer is 3.6 x 10 raised to the power of 22

[last dagger]

if you sub it in correctly you will get the right answer, check your terms

the question gave it in the correct units as well so theres no need to convert it

[stoic dune]

I assume you have a calculator? You don't need to carry this out manually

[last dagger]

just punch the values into a calculator from the first step

[stoic dune]

The E button is very helpful for these

[willow cloud]

well calculator not allowed sadly

[last dagger]

uh for gravitation calculator is always allowed

i dont see why it shouldnt be

[willow cloud]

Indian problems

[last dagger]

you cant do harder gravitation questions without calculator though

[willow cloud]

yea am in 9th grade

[last dagger]

yea i got my calculator in the 5th grade

anyways your first step is right so just check your arithmetic

no way im doing that without calculator, its a waste of time imo

[willow cloud]

true

[last dagger]

questions should test your concepts, not how well you can do powers of 10 in your head

[willow cloud]

I got the concept down in an hour but been doing this for last 5 hours and still haven't got how to do this life kinda sad when country dont allow calculator sad

[last dagger]

yeah that is just really odd

[willow cloud]

this goes till grade 10th

[last dagger]

i have no idea how you would move on to harder gravitation questions like this

you will have formulas like T=sqrt((4pi^2 r^3)/GM)

where r G and M are really huge/small numbers which are in multiple magnitudes of 10

so

[willow cloud]

we just use exponents for that and write it like that

for now

like from eleventh grade we get calculator

cuz thats just inhuman

[last dagger]

this is news to me, i never knew a country which disallows calculator for physics, and gravitation specifically

well without a calculator theres only so much you can do with the formulas so it really limits what you can learn

[willow cloud]

yea anyways bye peace

.close

[safe radish]

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[rich badge]

Need help with c I don’t understand where the points a b and c and d are

[rich badge]

I don’t know how to use what they give to get a rough shape of the quadrilateral and bame it

Nvm I just made a = 1 and b is 2 and drew it out

Can someone confirm if this correct and I didn’t do soemthing random

[safe radish]

@rich badge Has your question been resolved?

[safe radish]

@rich badge Has your question been resolved?

[safe radish]

@rich badge Has your question been resolved?

[jade gust]

,rccw

[safe radish]

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[tall bough]

https://gyazo.com/82fea9b7235bba2c333e41b89fd06e0c

fourier transformation

i did it with changing cosx to ((e^ik+e^(-ik))/2

doing that i will get 2 integrals and the final answer will be sin(2k)/2

but its wrong idk why

i think actuall solution is done with integral by parts then forming the exponential terms into trigonometric terms and with calculator i get sin(1-k)/(1-k)-(sin(1+k)/(1+k)

theres a hint that says use product rule of fourier transformations, idk what that is

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@tall bough Has your question been resolved?

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[safe radish]

@lean otter Has your question been resolved?

[unkempt belfry]

can you zoom in its hard 2 read

thx

reading

ok is ur picture right do you think

have you done part a

surface area of a cone is

[safe radish]

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[latent eagle]

struggling with this integral

i can think of a way to express it in terms of a gamma function

but to get an exact answer would be quite difficult by hand

when i plug it into an integral calculator i get an erfi function

and i have no fucking idea what that is and i dont think thats what my professor is looking for

[queen parcel]

You need some u-sub

Do you have any ideas for a u-sub?

[latent eagle]

ive tried that. I tried subbing u = x^500, so du = 500x^499 dx

or including the negative in that usub

so i get either e^u^2 du or e^-u^2 du

[queen parcel]

That's right

$\int_0^{\infty} e^{-u^2} du$ is a fancy integral though

[flat frigate]

Shen

[latent eagle]

i can see lol

[queen parcel]

Times some constant

[latent eagle]

yeah

[queen parcel]

Because x^499 dx ≠ du

[latent eagle]

yeah youre right i just dropped the constant for the moment to worry about the integral

[queen parcel]

Ye

[latent eagle]

Im not quite sure how to evaluate this new integral by hand if im being completely honest

[queen parcel]

You can't using just single-variable calculus

e^(-x^2) has a non-elementary antiderivative

Have you heard of the Gaussian integral?

[latent eagle]

im familar

[queen parcel]

It uses that integral in here

[latent eagle]

im about to say something that might be completely wrong so bear with me

This looks like a useful identity. Since the bounds are 0 ----> Infinity and this is an even function, can i say that the final result for that would be sqrt(pi)/2?

[queen parcel]

I'm impressed you got that

Not gonna lie

But you couldn't be more correct

Yup

[latent eagle]

oh alright cool, thanks a lot for your help

[queen parcel]

np np

[latent eagle]

https://tenor.com/view/gman-gif-18029042

[queen parcel]

Dividing by the 500 from the u-sub gets you:

[latent eagle]

oh neato

thanks again!

.close

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[queen parcel]

np np

[safe radish]

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[lean otter]

hi, I'm trying to do the mean of excel cells with this formula =B2:M9/36 but i get a value error ! i dont understand

[ancient escarp]

=AVERAGE

[lean otter]

i get another error

[ancient escarp]

google

[lean otter]

oui

ah bah oui je suis con

merci !

bonne journée à toi

.close

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[lean otter]

I need help w circle theorem

[safe radish]

@lean otter Has your question been resolved?

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[native pagoda]

Can you guys help ?

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[safe radish]

Please don't occupy multiple help channels.

[solid vigil]

For 2a) is it (P(sick female) + P(sick male))/ (P(sick female) + P(sick male)+(P(healthy female) + P(healthy male))

so (0.5+0.003)/(0.5+0.003+31.8+30.3)

[orchid lava]

anyone here did CEMC grade 11 contest ready to discusss?
ready to discuss all 25 questions for checking

[safe radish]

@solid vigil Has your question been resolved?

[fossil orchid]

P(X=f_s)=p_11

[unkempt belfry]

which part are you stuck on?

[solid vigil]

all good now

thanks

.close

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[still acorn]

i have a question (combinatorics)

we have a ticket from 000000 to 999999
if the sum of the first 3 digits is equal to the sum of the latter 3 digits, it would be a lucky token
if the sum of all digits is 27, it would be a good token
now, which one has more ticket, and find the difference of amount of both ticket

they said to use bijection, but i do not understand lol

[stoic dune]

For every lucky token, you can assign a three digit number. Likewise, for every three digit number, you can assign a lucky token. See how?

[still acorn]

uhh i kinda get it, but what kind of 3 digit number tho

[safe radish]

@still acorn Has your question been resolved?

[still acorn]

<@&286206848099549185>

[safe radish]

@still acorn Has your question been resolved?

[still acorn]

<@&286206848099549185>

[feral linden]

Same many

There are two maps, f from lucky tokens to three digit numbers, g from good tokens to three digit numbers. f(abcdef)=abc, g(abcdef)=abc. For example f(084715)=084, g((769320)=769

Notice that f and g are surjective

So the number of lucky tokens is $$|\cup_{m} f^{-1} (m)|=\sum_{m} |f^{-1} (m)|$$

Similarly the number of good tokens is $$|\cup_{m} g^{-1}(m)|=\sum_{m} |g^{-1}(m)|$$

[flat frigate]

Cogwheels of the mind

Cogwheels of the mind

[feral linden]

Now for any three digit number m, |f^-1(m)|=|g^-1(m’)|

Where for any m=abc, m’=(9-a)(9-b)(9-c) for example (472)’=527 so |f^-1(472)|=|g^-1(527)|

So when you take sum, you can pair m and m’, |f^-1(m)|+|f^-1(m’)|=|g^-1(m’)|+|g^-1(m)|

Therefore they are equal

(Where m=m’ |f^-1(m)|=|g^-1(m)|, when m doesn’t equal m’ you pair m and m’ that’s what I meant )

[still acorn]

where is 9-a, 9-b, 9-c from

[feral linden]

I thought you could figure it out yourself…

[still acorn]

oh damnnnn

[feral linden]

For a three digit number m, I use S(m) to denote the sum of three digits, for example S(042)=6

Then (m,n) from f^-1(m) iff S(n)=S(m)

Like (024 312) from f^-1(024) because S(024)=6=S(312)

On the other hand, (m,n) from g^-1(m) iff S(m)+S(n)=27

But 27-S(m)=S(m’) right

So iff S(n)=S(m’)

So (m,n) from g^-1(m) iff (m’ n) from f^-1(m’)

Where m=100a+10b+c then m’=100(9-a)+10(9-b)+(9-c)

You can easily see that S(m)+S(m’)=27

[still acorn]

alright lol

[feral linden]

#❓how-to-get-help

[still acorn]

thanks for your help, this really meant to me, now I am still stucking a lot with bijection problems

[feral linden]

Sure just ask, when you can’t figure out

[still acorn]

😄 once again thanks

👋

.close

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[young moon]

The question

The attempt

[safe radish]

@young moon Has your question been resolved?

[lean otter]

lemme try it'll take time but yeah wait

you still need the solution or is it solved?'

[sharp wharf]

That’s not how trigonometric manipulation works, have you learnt double angle formulae

[lean otter]

angle can not be added there is separate formula for it

you need to understand the graph

[young moon]

Nvm i got it thank u !

.close

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[golden acorn]

As x approaches a, do i just write infinity? +- infinity? Or just simply does not exist?

[golden acorn]

From left, right and both sides.

[split ether]

Wdym, there's no graph of a function here

[golden acorn]

That's also why I'm confused. That's the question, so i just write does not exist for everything?

[split ether]

Of a well-defined function at least

[tall cobalt]

The function is only defined on x = a so f(x-a) does not exist

[split ether]

And if this is the graph, then it looks like it's not even defined around a

So the limit wouldn't exist

[tall cobalt]

also f(x) is not a function at all bc it fails the vertical line test

pretty badly

ITs a relation and a relation defined on a single point

[golden acorn]

Ohh i see, so just write dne for everything then

.close

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[lean otter]

can someone check over my work here?

[plain lion]

Seems right to me

[lean otter]

sorry, i don't understand the graph

could you explain what im looking at and how it shows that the question is correct?

[plain lion]

I mapped the term as points and now you see that when d =10/3 (I used d instead of x) the points line up

[lean otter]

oh i get it now okay

sick man thanks alot, appreciate it

.solved

oops

.close

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[lean otter]

Please can someone check this question for me? I think I have done it wrong

[cursive spindle]

Seems fine to me

,w integrate 1/(2(5-3x)^3)

[flat frigate]

Results provided by WolframAlpha

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

Requested by pepper#3419

[lean otter]

yeah i got that when i used wolfram too, but it has confused me as its not the same as my answer

pls help!

[cursive spindle]

How is it not the same?

Wait

[lean otter]

oh wait am I being dumb

[cursive spindle]

Why is your integral sign remaining after the fact

Your 3rd line onward does not make sense

Write it properly

[lean otter]

ohhh

[cursive spindle]

Write the dx for the first two lines too

[lean otter]

how would I do that?

okay!

[cursive spindle]

It's just writing

Take out the curly thing at the start once you integrate

[lean otter]

right!

[cursive spindle]

Before you integrate, you need that thing, along with dx

It tells readers what you are integrating with respect to

[lean otter]

okay! wait on sec, I'm just writing it

so after the 3rd line, it doesn't make sense?

What should I do after the (1/2) (5-3x)^-2?

oh sorry, did you mean after (1/2) (5-3x)^-3?

[cursive spindle]

Yes

[lean otter]

So how should I do it? 🙂

[cursive spindle]

$$\begin{aligned}&\int\frac{1}{2\left(5-3x\right)^{3}}\dd{x}\=&\frac{1}{2}\int\left(5-3x\right)^{-3}\dd{x}\=&\frac{1}{2}\left(-\frac{1}{3}\right)\left(-\frac{1}{2}\left(5-3x\right)^{-2}\right) + C\
=&\frac{1}{12\left(5-3x\right)^{2}}+C\end{aligned}$$

[flat frigate]

pepper

[lean otter]

Ohh right! I see where I went wrong

Thank you for your help!!!

.close

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[safe radish]

Please don't occupy multiple help channels.

[ancient escarp]

submit it and find out

[toxic stone]

no it has ended ald

[ancient escarp]

what

[toxic stone]

and it wont show the answer coz is final

[ancient escarp]

it won't show the answer because it's a test?

[toxic stone]

no coz it is final exam

[ancient escarp]

<@&268886789983436800>

[toxic stone]

final exam they wont show results

[ancient escarp]

that's unfortunate

[toxic stone]

the exam is ald over

why are u tagging moderator loll

im just trying to know if i have done it right

[hushed mirage]

moderator here. you;re; in big trouble mister

[wild cape]

[safe radish]

Channel closed

Closed due to the original message being deleted

[ancient escarp]

so you can still see your answers on the screen? your buddy also posted a question in #help-8

and it doesn't look like it's over for them

[wild cape]

odd

ic

[solid field]

not sure why u r creating trouble @ancient escarp

[broken yew]

They are just following the rules

[ancient escarp]

because academic dishonesty isn't tolerated

[broken yew]

And your post is a bit sus

[solid field]

sorry for that

[wild cape]

i find it very weird that 3 ppl post the same q at the same time

[ancient escarp]

you can also edit anything on html pages

[wild cape]

sure but i tend to give benefit of the doubt when it comes to that lvl of manipulation

[toxic stone]

.close

i gueeseed u cant edit the time

.close

[ancient escarp]

it's already closed since you deleted your original message

speaking of deleted messages, i was talking about editing the text on the screenshot you sent and now deleted, not your computer time

[broken yew]

Lets just drop it

[safe radish]

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[timber atlas]

Shouldn’t the answer for this question be 2(3 root 5 divided by 5) or am I wrong?