help-23

[dusty fable]

Which is 98/7

You need to add decimal points to it

[frozen pivot]

U mean convert to a decimal ?

[dusty fable]

Yes you add a lot of zeros to the smaller number

Like 98 | 7.0000000

By the way 7 | 98 here is fine, you can solve it using long division

[frozen pivot]

Im getting so confused but I understand what u mean for the first one u said

[dusty fable]

Ok I have an exercise book that has a lot of these algebra problems

Ill showcase example of long division

[frozen pivot]

So like for example if there was a question like that in a quiz you could js change it around ??

[frozen pivot]

Oooh so basically numbers that go on and on and on

Continuous?

[dusty fable]

I just gave an example here

Long division is very useful when you're doing Algebra

But with these numbers that are whole numbers

You can just do this method of adding 0s

[frozen pivot]

Yeah that's what my teacher mentioned

So to be clear

The sign thing on top of the numbers, what does it mean?

[dusty fable]

Could you be more specific?

Like in the division?

[frozen pivot]

Like this part

[dusty fable]

That just is a way to highlight the numbers because it links to the question

}

Its a bracket

[frozen pivot]

Ooh I see

[dusty fable]

Ok to see if we are on the same page, could you do 845/7

And show working out

[frozen pivot]

Ok

Waiy

I js add the zeros right ? To the dominator

[dusty fable]

You can do but could you first show your answer please?

[frozen pivot]

That is what I did

[dusty fable]

Your result was?

[frozen pivot]

1.224285714

[dusty fable]

Could you please show working out?

[dusty fable]

Some problems here. First it is 845/7, and because the divisor is 7, you should put 7 on the outside and 845 in the inside

And also can you see how its not 845/7 divided by 100 because you are trying to work out 845/7 originally

That problem results in (845/7)/100

All your math is correct but you are working out the wrong problem

[frozen pivot]

Like am I supposed to use the adding 0s thing?

I am confused

[dusty fable]

Ok Im showing you my working out

For the adding 0s things, you do that when you're doing a small number

[frozen pivot]

Ok

[dusty fable]

Like if I gave you 7/845 you would do that

But for 845/7, a lot of 7s can fit in 845, integers

[frozen pivot]

Noted

[dusty fable]

This is the quick way. Im doing the same calculation in long division but I didnt write it out fully

When you're dividing, you're doing the same tricks. Multiplying. Then adding or minusing till you see that the number fits in (like I did with 120x7)

Oops I meant to allign the digits there

[frozen pivot]

What does the r mean?

[dusty fable]

Remainder

But in problems, always show the decimal or fraction

@frozen pivot Do you see now that long divsion is just showing the mental maths steps?

I knew 12x7 was 84 so I first wrote 12 at the top, then to know my hundreds and ones digit, I minused by 84.

[frozen pivot]

Yeah it is..

[dusty fable]

You just work down digit by digit

Its useful for really long numbers

Like you are working with hundred millions or something

And the reason why long division is so important, the higher you go you need to divide polynomials (like a quadratic)

[frozen pivot]

Yeah I'm gonna have to go through this more this week

[dusty fable]

Here is an example of polynomial division

[dusty fable]

Oh alright. Did I at least help you?

[frozen pivot]

You definitely did help

I have an idea about what it's about now

I js gotta do more problems with it and stuff

[dusty fable]

You alright with me sending some problems you could save?

I got an exercise book on algebra

And have it open on my laptop

[frozen pivot]

Definitely appreciate yes please

[dusty fable]

Ok no problem.

[frozen pivot]

Thanks for questions, that saves up having to search

[dusty fable]

Ok you can save these problems. Have a nice day. Remember to learn things step-wise (step by step) and you realise that everything's alright

[frozen pivot]

I will thank you ben
Take care

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[true peak]

How can I graph x^2 + y^2 <= x???

[fathom adder]

The lhs is a circle with 0,0 as center

[true peak]

Explain your statement.

[fathom adder]

Do you know what is a circle equation ?

[true peak]

Yes.

X^2 + Y^2 = value.

This equation is without including the inside of the circle but you got the point.

@fathom adder So?

[fathom adder]

So what is y = x ?

[true peak]

An equaiton for a linear graph?

[fathom adder]

Which is the right side

[true peak]

Right and going up, and?

[fathom adder]

Have you graph it for now ?

[true peak]

y = x yes.

[fathom adder]

Like both together

[true peak]

I didn't understand why the previous inequality gave me that graph.

What is your point?

[fathom adder]

Its supposed to be centered in 0,0

[true peak]

first of all why? second of all how do you even graph it?

[fathom adder]

First of all, cuz a circle equation is made like (x-a)² + (x-b)² = a value so here a = b = 0

[true peak]

Good.

x is the radius but why does it stop at 0.5?

It makes a contradiction. OHHH.

[fathom adder]

Hum, i think the value of y can't be anything else than 0

And so x is between 0 and 1

Or no

[delicate bobcat]

You have to complete the square

To solve the inequality

Subtract x first

That will make the center (1/2 , 0)

[delicate bobcat]

This is not the correct form to analyze

Subtract x on both sides and complete the square to get a better idea

[true peak]

Got it.

You get the following:

[delicate bobcat]

That agrees with radius 1/2

So it's

All the points interior to the circle with radius 1/2 and center (1/2, 0)

[true peak]

Btw, is it the only method to approach?

[delicate bobcat]

Probably not

Rarely is something the only way in math

[true peak]

Show me the easy alternatives, please.

[delicate bobcat]

Lol this is probably the easiest xD

Unless you're using a graphing calculator

[true peak]

U know, we must keep a suprise in our pocket if the situation got screwed up 🙂

[delicate bobcat]

Even then the calculator may not help with irrational values

[true peak]

But I appreciate it bro.

[delicate bobcat]

I would say rewriting it in form of the circle is definitely the easiest way in your toolkit

[true peak]

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[still lantern]

Hi, my teacher told me I should have done it to be faster My teacher says to factorize by (n+1)xUn but I don’t see it

[fathom adder]

2eme ligne

Envoie le dénominateur sous n+2

Ça fait (n+2)/(2n+4) * (n+1)un

Et ducoup bah (n+2)/2n+4 Ça fait 1/2

Car n+2 != 0

Donc 1/2 * (n+1)(un)

Et après la factorisation par (n+1)u_n tu as le 0 qui apparaît dans le produit

Et tu as finis

@still lantern

[still lantern]

hmm j'suis entrain de reflechir

jsuis creuvé en plus j'arrive pas a reflechir

merci pour la réponse

[fathom adder]

De rien

[still lantern]

j'essaye de voir

[still lantern]

jcomprend pas ça

[fathom adder]

Une justification qui n'est pas nécessaire après coup, n est entier naturel, donc tu peux oublier

En gros je fais gaffe à pas diviser par zéro

!= signifie different de

C'est le = barré

[still lantern]

je vois

j'viens de me paumer dans mes calculs jpense que dormir me fera pas de mal jvais essyaer de finir ça

la j'ai (1/2)x(N+1)Un

j'arrive pas a me faire apparaitre le 0

[fathom adder]

Et derrière tu as un - 1/2 (n+1)Un aussi

[still lantern]

attends j'ai du sauter une étape

[fathom adder]

Prends à la ligne 2

[still lantern]

a partir de (n+2)/(2n+4) * (n+1)un

?

[fathom adder]

C'est pas que ça la ligne 2

Mais oui

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[sinful iris]

Where did I go wrong?

I got 106 degrees but in the book it says 0 degrees

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@sinful iris Has your question been resolved?

[south phoenix]

Look, I have solved it by completing the square

If it helps..🤔

[sinful iris]

it makes sense

but what's wrong with what i did?

[south phoenix]

What you did is fine; maybe you made a mistake in solving your quadratic

[sinful iris]

lol yea that was it

thanks

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[patent portal]

can i get some help understanding which equation matches the graoh?

[patent portal]

i understand the other ones but having some trouble with those 2

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[patent portal]

<@&286206848099549185>

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[red talon]

the question is whether the variable is discrete or continuous:

X is the useful life of a bridge, as measured in years.

[junior smelt]

"how particular do you wanna be?"

[lean otter]

continuous

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[weak dove]

is the mapping notation to find the parent function like this?

[weak dove]

1a

<@&286206848099549185>

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[weak dove]

help

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@weak dove Has your question been resolved?

[weak dove]

no

<@&286206848099549185>

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[safe radish]

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[tall sphinx]

Theres 2 successful outcomes so its 2/380 which is 1/190

You don’t need to make a new channel each time

They can finish in either order

Nah its the probability you have times two

The. Chance of you getting it right is 1/20 * 1/19

thats the probability of your horsies finishimg in first and second place

Since they can do so in either sequence

The probability is double

Dont overcomplicate this.

[flat frigate]

KFC

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[light shoal]

looks fine to me

[cinder badger]

ty

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[cinder badger]

.close

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[thick dagger]

-sigh- im back and clueless once again

idrk how to do both part a and part b

[mossy thunder]

Square root all numbers that can then for B since I’m guessing..add all of the numbers you see in the same order into your calculator..?

[thick dagger]

wait how would the square rooting work?

[mossy thunder]

Hold on

[thick dagger]

like this-?

[thick dagger]

ok!!

[mossy thunder]

Yep

then idk why it says no but I guess solve it? 😭😭

[thick dagger]

ok after that it becomes thi?

[thick dagger]

idk guys

all ik is that its possible for part a ;-;

[thick dagger]

ok wait idk what to do after this

[mossy thunder]

yeah keep solving until your equation is equal

[thick dagger]

so erm idk how to progress ;-;

[mossy thunder]

so 20.8=2a+2ab+9b

oops forgot squared

[thick dagger]

oh wait how does become 2sqrt2 + sqrt3?

[mossy thunder]

ACTUALLY ur answer should be a=1 or a=-1

[thick dagger]

ohh ok

wait i got to go to be rn

[mossy thunder]

wait lemme explain how LOL

Oh okay

[thick dagger]

tysm for ur help szerpplx!!

i think i have somewhat of an understanding on what to do now! ❤️

[mossy thunder]

Basically yes multiply to remove both root by parentheses

[thick dagger]

ohh ok!

tysm!

have a good day kind sir!

[mossy thunder]

and then $$a^{2}(11 + 4\sqrt{6}) = 11 + 4\sqrt{6}
$

Ahh

$a^{2}(11 + 4\sqrt{6}) = 11 + 4\sqrt{6}
$

[thick dagger]

lmao its ok!!

[mossy thunder]

😢😢😢😢😢

Okay bye!!!!

[thick dagger]

gn or good morning or good day

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[safe radish]

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[wicked hull]

<@&286206848099549185>

[wicked hull]

Why can the expression be rearraned?

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[wicked hull]

.close

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[finite igloo]

Visualization of Wave Motion:\
The general form of a wave motion is $y(x,t) = \sin(\kappa x \pm \omega t + \phi)$. This is one of the solutions of the wave equation. How do I visualize such a graph mentally during the exam?

[flat frigate]

k

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[sullen pelican]

It's not completely about maths, I am struggling with a few chapters in high school maths even though i know the concepts but cannot apply them.
pls help me find out the problem and also how to solve it

[finite igloo]

ja?

[sullen pelican]

pls read it once

[finite igloo]

do more problem

more practices

[sullen pelican]

ok whats the most efficent way to do this

[finite igloo]

get problem sets for ur topic

[sullen pelican]

i dint get that wdym

[finite igloo]

there are always online sources for practice problems

for me, i have textbooks

[sullen pelican]

yes

[sullen pelican]

me too

by any chance are you also in 10th grade?

[finite igloo]

sadly, no

[sullen pelican]

dang

np

alr thanks

[finite igloo]

do u want some refs?

[sullen pelican]

for?

[finite igloo]

for problems

[sullen pelican]

ok sure that would help

[finite igloo]

https://www.stanfordmathtournament.com

this is extremely hard

[sullen pelican]

oh

also do you think it would be even better if i maybe saw youtube videos b4 practicing so i can have stronger foundation of concepts?

[finite igloo]

maybe look up problems from ur national exam

[finite igloo]

yes

[sullen pelican]

ok

[sullen pelican]

alr

[finite igloo]

try proving equations urself too

to be able to use it, u have to understand it

like really understand it

[sullen pelican]

ok

[sullen pelican]

so like understanding the proofs for theorems etc?

[finite igloo]

yes

[sullen pelican]

ok

[finite igloo]

that's my approach

but others may have different ideas

[cobalt iron]

The main idea about doing things like this is to abstract real world scenarios and search for relevant concepts

Cut the unnecessary informations out and try to find where to apply

[sullen pelican]

ok

alr thanks guys

i will start now

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[acoustic kestrel]

hint: exponent laws

[stiff cape]

x=3

[acoustic kestrel]

specifically the fact that $a^c b^c = (ab)^c$

[flat frigate]

lily

[acoustic kestrel]

!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.

[versed wave]

!nosols

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As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[acoustic kestrel]

Great

thanks Fungor

[versed wave]

no problem lilor

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[odd crest]

x/y dy/dx = ln(x/y) -1

let y= vx

dy/dx = v + xdv/dx

1/v (v+xdv/dx) = ln (v)-1

x/v dv/dx= ln(v)-1

i hopeyou can do the rest

[modern bloom]

why did you do this substitution

[odd crest]

homogenous

in x and y

[glacial meadow]

Lnx+lny=lnxy not ln x/y though?

[odd crest]

oh

i saw it as ln x- ln y

oopa

v=xy should work

[glacial meadow]

Also don't see how it is homogeneous (though this could be a lack of knowledge)

[odd crest]

its not

[glacial meadow]

A constant term exists

And ln is not a homogenous function

[glacial meadow]

Aren't substitutions supposed to break on non homogeneous equations?

[odd crest]

wym

[glacial meadow]

I may be misremembering, but fairly sure substitutions in DEs work precisely because of the homogeneity of the functions

That is, the property that f(kx)=k^nf(x) for some real n

[odd crest]

i hope this works

[odd crest]

yeah well ln(x) + ln(y)-1 = ln(xy/e)

[glacial meadow]

But that distributes to a sum, not a product

Also, k's supposed to be a constant

[odd crest]

i dont understand

i just see "xy"

so i intuitvely subsitute it

[glacial meadow]

Welp, forget it, again I may be wrong

I just recall reading something along those lines

If your method works, it works

[odd crest]

i havent gone through a proper course in DE so i do not know

[safe radish]

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[brazen pagoda]

could someone help me with this?

[brazen pagoda]

i found the answer on the internet but it is way too weird
i dunno how the line 1 turned into line 2

[digital sparrow]

do you know the expansion of sin(a+b)?

[hasty marsh]

this is sine compound angle

[brazen pagoda]

yea sin(a+b) = sinacosb + cosasinb

[digital sparrow]

ok and sin2x

cos2x?

they just used these identities and skipped over the steps

[brazen pagoda]

sin2a = 2sinacosa
cos2a=cos^2 a - sin^2 a = 2cos^2 a -1 = 1 - 2sin^2 a

[digital sparrow]

yess

[digital sparrow]

^

[brazen pagoda]

okay let me figure it out by that

[digital sparrow]

ping me if you dont "figure it" out

[brazen pagoda]

sure

[digital sparrow]

[safe radish]

@brazen pagoda Has your question been resolved?

[brazen pagoda]

@digital sparrow i think ive gone on wrong way
It is being more and more complicated

[digital sparrow]

hmm

lemme read

bro substitue the value of sin pi/4 and cos pi/4

[brazen pagoda]

👀

i forgor

it is now 2sinxcosx + cos2x = 3sinx + cosx + 2

which one of cos2x should i change into?

[digital sparrow]

^

i think you will understand this now

[brazen pagoda]

oh yea

i see i see

i did it
tysm

.close

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[lean otter]

I'm having some trouble with this, here's the thing:

To prove
arcsin(3/5) - arccos(12/13) = arcsin(16/65), let each be A, B and C respectively, then we have to show that A - B = C, the book I'm studying from proves that sin(A - B) = sin(C) and then concludes A - B = C, but isn't it the case that arcsin(sin(x)) = x iff x is between 90 and -90 degrees, how do we know here that arcsin(sin(A - B)) = A - B?
As I understand it, this fact is clearly what we are using in the proof.

[prime yacht]

arcsin is defined as the inverse of the sin function.. i don't think i really understand your question here either..

[lean otter]

Em

Sin(npi + (-)^n×a) = sin(a) but the angles aren't equal.

Nevermind

Ok, my question is why can't A - B exceed 90 degrees?

[prime yacht]

maybe this will help

[lean otter]

How so?

[prime yacht]

sin(2pi) = sin(0) but 2pi≠0

[lean otter]

Yeah exactly that's my problem.

[prime yacht]

instead we think of it as 0=0

here is the graph of arcsin (x)

Domain of sin(x) = [-infty, infty]
Range of arcsin(x) = [-1, 1]

[lean otter]

My question is why arcsin(sin(A-B)) = A - B here?

A - B can be greater than 90 degrees, can't it?

[prime yacht]

ohh i see. you are asking if there is a case where A-B is not in the range of the principle values of sin(x)?

[lean otter]

The book doesn't mention explicitly that A - B is in [-90, 90] so I assume I must be missing something obvious.

[lean otter]

Yeah

[lean otter]

You sure?

[prime yacht]

i meant the range of sinx = [-1, 1]

but i was trying to say that arcsin sin x = x is only true for x = [ -pi/2, pi/2 ]

i'll graph arcsin(sin(x)) = x for you

[lean otter]

(I'm sorry if I'm being a little opaque, English isn't even my third language)

[lean otter]

That's what I'm trying to say.

How do we know A - B lies in that range?

[lean otter]

Correct me if I'm wrong,
Aren't we using this in the proof?

[prime yacht]

ok

[lean otter]

You can tell me why you think that A-B lies in that range (if you think it does). That will clear it.

There?

Hello?

[prime yacht]

i think that arcsin and arccos are both (0, pi/2), right?

because it is assumed that for arcsin x or arccos x, x is positive and x<1

?

[lean otter]

Arccos is (0, pi)

Arcsin is (-pi/2, pi/2)

[lean otter]

Seen examples with negative x.

<@&286206848099549185>

[fathom jewel]

Whats the q Euler

[prime yacht]

😭 wait im so dumb

ok goodnight. sorry

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

No

[lean otter]

Sorry I got disconnected.

[lean otter]

Here

[fathom jewel]

but isn't it the case that arcsin(sin(x)) = x iff x is between 90 and -90 degrees
that's right

[lean otter]

What do you mean?

[fathom jewel]

But I dont think that helps much proving

arcsin(3/5)-arccos(12/13)=arcsin(16/65)

[lean otter]

You mean it's useless?

[fathom jewel]

Yes, how would you want to use this here with arccos especially

[lean otter]

Waity waity

[lean otter]

Here

[fathom jewel]

,w arccos(x) = pi/2 - arcsin(x)

[flat frigate]

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[fathom jewel]

That might help more for the proof i think

[lean otter]

But did you have a look at mine?

[flat frigate]

bacc the sigma😔🤞

[lean otter]

Is that the case here?

I mean is that demonstrably the case here.

[fathom jewel]

For what

[lean otter]

To use arcsin sin(A-B) = A-B we must have A - B between 90 and -90 degrees, the proof in my book uses this fact but doesn't show how A-B lies between the required limits.

Can you give a reason why A-B indeed lies between 90 and -90?

[fathom jewel]

sine is bijective in that interval

[lean otter]

I know that, but I must know why A-B lies in that interval!

[fathom jewel]

therefore the inverse function was defined with range between -90° to 90°

If A-B is not within that interval then the equation is not true

,w plot arcsin(sin(x))

[flat frigate]

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Requested by adoniszgks

[lean otter]

Which equation, the one we ought to prove?

Ah you mean this one

[fathom jewel]

arcsin(sin(x))

[lean otter]

So I just have to assume that it's indeed the case? That doesn't sound right.

It's been more than an hour now.

Ok just tell me whether my question makes sense.

[fathom jewel]

Nothing makes to me sense right now

[lean otter]

Or am I hallucinating

[fathom jewel]

You wanna prove this
arcsin(3/5) - arccos(12/13) = arcsin(16/65)
using arcsin(sin(x)) = x iff |x| < pi/2

[lean otter]

Yes

[fathom jewel]

3/5 < 1

[lean otter]

F the book, show me your way please.

[fathom jewel]

which means

[lean otter]

Yes

[fathom jewel]

sin(x) = 3/5 then there exists an x between 0 and pi/2

[lean otter]

Yes

[fathom jewel]

same with 16/65

[lean otter]

Hm

[fathom jewel]

0 < 16/65 < 1 = 65/65

[lean otter]

I see that

So?

[fathom jewel]

yea i was explaining to you

why it's between 0 to 90°

[lean otter]

I know that already

My question is why must the difference be between 90 etc...

[fathom jewel]

because arcsin(sin(x)) = x not for all values of x

if you now x = A-B same must hold for A-B

[lean otter]

Nevermind, either I am hallucinating or you don't get me.

[fathom jewel]

I don't get you

[lean otter]

Let's call it a day then, it will come to me in my sleep.

I'm deeply indebted to you for your time

Thanks

.close

[safe radish]

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Use .reopen if this was a mistake.

[lean otter]

. reopen

.reopen

[safe radish]

✅

[lean otter]

.close

[safe radish]

Channel closed

Closed by @stiff echo

Use .reopen if this was a mistake.

[fathom jewel]

arcsin(3/5) - arccos(12/13) = arcsin(16/65)
A-B=C
|C| < pi/2 which is the case because arcsine's range is between -pi/2 and pi/2
assuming the equation is true (but you are ordered to prove it anyway, so we can assume it holds)

[lean otter]

Yeah, I saw it for C (that's why I didn't talk about it), but what do you mean by the statement in the bracket.

.reopen

[safe radish]

✅

[shadow sparrow]

sigma

[fathom jewel]

i meant that you can assume this equation to be true, since they ask you to prove it

[lean otter]

I'm not in an exam though, I need to know why it is true, without any gaps in my reasoning.

[fathom jewel]

or rather assume if it was true, then A-B must be withitn [-90°,90] because A-B = C

i tried to answer your question as well as i could, i still dont know how you would actually prove especially using "the hint" your book suggested

[lean otter]

I agree with you, the problem is probably because I can't express myself properly.
Thank you very much.

.close

[safe radish]

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[shy verge]

i need help with this

[shy verge]

.close

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[sweet prawn]

I dont know where to start for this

[digital sparrow]

this is basically chain rule

[sweet prawn]

Yeah i understand how chain rule works but im still super confused

[digital sparrow]

tell me what dy/du is

[sweet prawn]

uhm

is it f'(g(x)) x g'(x)

?

[digital sparrow]

yes

but that is way too complicated to look at

think of chain rule as first doing dy/du

then du/dx

then multiplying them

[sweet prawn]

thats more complicated huh

[digital sparrow]

hmm

[sweet prawn]

id rather stick with f'(g(x)) x g'(x)

but could you tell me how to start this?

[digital sparrow]

but because im helping

we will use dy/du

lol

[sweet prawn]

ok

[digital sparrow]

so wht is dy/du?

hint: y = 2u^3 + 1

[sweet prawn]

2(-3^2)^3+1

[digital sparrow]

where did 'u' go?

[sweet prawn]

isnt g(x) = -3x^2?

[digital sparrow]

yes

[sweet prawn]

so yeah

[digital sparrow]

where is x then?

[digital sparrow]

no x in this

[sweet prawn]

ohh

[digital sparrow]

lol

[sweet prawn]

uhm

i dont understand where i am wrong

[digital sparrow]

y = 2(-3*x^2)^3 + 1

you just forgot the x

[sweet prawn]

ohhh

[digital sparrow]

but this isnt how we will do this

[sweet prawn]

lmao yeah

[digital sparrow]

tell me dy/du

it isnt that hard

[unkempt meadow]

Don't you just got to find the derivative of both then multiply them

?

[digital sparrow]

for some reason he doesnt want to!

[unkempt meadow]

Huh

[sweet prawn]

uhm is it 6(-3x^2)*-6x?

[digital sparrow]

^

[unkempt meadow]

But you would do that

@digital sparrow

[sweet prawn]

avg math proffesor mentality </3

[digital sparrow]

YES BUT THAT ISNT WHAT I ASKED

bro

what is dy/du

[sweet prawn]

I am just going by the book

[digital sparrow]

NOT Y IN TERMS OF X

[sweet prawn]

uhh

[digital sparrow]

do you know what dy/du means?

[sweet prawn]

nope !

[unkempt meadow]

LOL

[digital sparrow]

oh

[unkempt meadow]

😭💀

[digital sparrow]

lol

[sweet prawn]

if your wondering the way im being taught derivatives is f(x) to f'(x)

so thats prob why

[digital sparrow]

dy/du is that same as f'(u)

[sweet prawn]

oh

[digital sparrow]

cause y = f(u)

dy / du = f'(u)

u = g(x)
du / dx = g'(x)

get it now?

[sweet prawn]

uhm

[digital sparrow]

what is f'(u)?

[sweet prawn]

its 6u^2

[digital sparrow]

yess

so what is dy/du?

[sweet prawn]

is it the same so 6u^2

[digital sparrow]

yess

lesgoo

[sweet prawn]

ohhh okkk

[digital sparrow]

ok what about g'(x)

or du/dx?

[sweet prawn]

is it -6x

[digital sparrow]

yes

so what will be dy/dx?

[sweet prawn]

wait im sorry dy/dx is the same as f'(g(x))?

[digital sparrow]

dy/dx is the same as dy/du * du/dx

[stable kestrel]

free nitro?

[digital sparrow]

here you go

[stable kestrel]

thank you

[digital sparrow]

[stable kestrel]

😍😍😍

[digital sparrow]

f'(g(x)) * g'(x)

chain rule

[sweet prawn]

im sorry im confused

:(

i know the chain rule but in this question is confusing me on how to use it

[digital sparrow]

gimme a min

or just watch a vid on chain rule on yt

[sweet prawn]

oh i did but this questions weird

[digital sparrow]

its hard to explain just via typing lol

[sweet prawn]

here gimme a min

[digital sparrow]

yes but that -6 is being multiplied

not subtracted

[sweet prawn]

oh yeah my bad forgot to add the multiplication symbol

[digital sparrow]

ill write and send how to do this via du

[sweet prawn]

so im right here?

[digital sparrow]

yess

[sweet prawn]

yayy

[dapper star]

padhle bhai

[digital sparrow]

thik h bhai

aur bhi kucch karu kya?

[sweet prawn]

would this be right?

[digital sparrow]

,rotate

[digital sparrow]

yeah

[sweet prawn]

Ahhh yayy

thank you again !!

[digital sparrow]

this is prob the way the ques expects you to do

but yeah do it your way lol

[safe radish]

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[earnest sluice]

did I do this perfect cubes correctly?

[earnest sluice]

sum of perfect cubes

[lean otter]

you mean 3^3

[earnest sluice]

ohhh

okay

what a silly mistake 😭

.close

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[lean otter]

hi

[lean otter]

wait

AD = 2cm

ADCB is a square

AH = HD = ED = EC = GC = BG = FB = AF

find the area of the inner square

I wannna know the best methid

[digital sparrow]

use similarity

and midpoint theorem

you in 10th?

i remeber this question lol

[lean otter]

im in 9th

[digital sparrow]

oh lol

[lean otter]

i haven't learnt it yet

[digital sparrow]

then dont use similarity

yeah

midpoint will be anough

[lean otter]

okay

thanks

what about this

A triangle has side lenghts 18cm, 24cm and 30cm. Find the area of the triangle whose vertices are the incenter, circumcenter and centroid of the orignal triangle.

is there anything else I can do apart from using coordinate geo?

[digital sparrow]

is that a right angles tri?

18, 24, 30?

it is

[lean otter]

yea

[digital sparrow]

do you know where in, circ, and centroid lies for right tri?

[lean otter]

yeah

in the center

nvm

mid point of the hypotenus

[digital sparrow]

https://tenor.com/view/galaxy-galaxy-brain-perndorfer-meme-uw-u-gif-26321098

yeah

that is?

out of circ, in and G

[lean otter]

what?

[digital sparrow]

mid point of hypotenuse is which point

I, C or G

[lean otter]

G?

[digital sparrow]

nope

[lean otter]

C?

yeah

[digital sparrow]

i dont remember

lol

[lean otter]

it's G

[digital sparrow]

what are the other 2 points

[digital sparrow]

def not g

[lean otter]

wait

wait

you talked about the circumcenter

that is O

[digital sparrow]

that isnt a right traingle lol

[digital sparrow]

we call it C usually

[lean otter]

okay

[lean otter]

centroid and incenter

[digital sparrow]

location

in a right tri

[lean otter]

wdym

[digital sparrow]

like that is mid of hypo

what about these

[lean otter]

oh

inside the triangle

[digital sparrow]

lmao

incenter is at the point where the right angle is

[lean otter]

no?

that is the orthocenter

[digital sparrow]

oh dam'

lol

[lean otter]

coordinate geometry is the best option here right?

[digital sparrow]

i guess but you cant use that in 9th

[lean otter]

mhm atleast not for school exams!

[digital sparrow]

yeah

btw its super late for you lol

should go to sleep

[lean otter]

yes tmr is my school

bye thanks you

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[olive vault]

given a sequence a_n > L, a_n -> L. does that imply that a_n is monotone decreasing?

[peak estuary]

no

try finding a counterexample

[olive vault]

i cant think of one

maybe an oscillating sequence?

can we say anything about the limit of a_n+1 / a_n?

[peak estuary]

you can for example take two sequences with a_n > L and then alternate between them

[olive vault]

oh yeah duh

[olive vault]

what about this?

[peak estuary]

limit of quotient is ... ?

[olive vault]

is what?

[peak estuary]

quotient of limits

of course you want L nonzero

[olive vault]

ah

what if L is zero

because it is in my case lol

[peak estuary]

then I dont think it has to converge

something like 1/n and 1/n^2 alternating?

[olive vault]

oh yeah right

so what im trying to prove is

[olive vault]

given L is 0 here

prove that this converges

[peak estuary]

am gm

[olive vault]

whats that

[peak estuary]

an inequality

[olive vault]

ohh

totally forgot about this

[safe radish]

@olive vault Has your question been resolved?

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[true peak]

In the following question,

I got asked about finding the bornes of the double integral, draw the graph and changing the order.

So,

First of all, why the union of D1 and D2 does equal to the values shown in D'?

like from 1 to 2 in x-axis? isn't supposed to be from 1 to 4?

y^2 part below the surface why is it on the top and y is in the buttom?

<@&286206848099549185>

[safe radish]

@true peak Has your question been resolved?

[true peak]

<@&286206848099549185>

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[prisma helm]

can sm1 tell me how to approach this prolbem

[prisma helm]

because when there isnt a coefficient I just multiply ihside the root and go from there

[mellow cypress]

Everything is multiplied and since multiplication is commutative you can do it in any order

So you can just rearrange it to be
(2x)(2x)(root)(root)

And simplify them

[prisma helm]

what if I try simpligiying the roots first

[prisma helm]

would that be wrong or just harder

because when adding thats what I do

[reef cave]

I mean you must simplify inside if you are adding, since you can't distribute the root

[mellow cypress]

I would multiply the roots together first

Then it will be easier to simplify the final product

[prisma helm]

ok thank you

/close

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[sand gate]

HELPO

[sand gate]

PLEASE

proof is making me lose my braincell

😭

did I use it wrong

no one is here

.close

[safe radish]

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[sand gate]

bruh what

[lyric blaze]

u said .close

[mossy fractal]

You typed to close the chat, so it closed

[lyric blaze]

so it closed

[sand gate]

uhh

huh

DID I BREAK IT

[safe radish]

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[jaunty owl]

Find a function whose level curves are the same as in f(x, y) = max{|x|, |y|}. , but rotated π/4 counterclockwise

ow come i can rotate (x,y) first and then apply the function
and get the desired function
i thought the order of functions in general matter

[jaunty owl]

@left gyro ik its reversed in this case but why does it still result in a valid result

like i thought you would have to apply the function first and then apply the rotation

[left gyro]

youre thinking of plotting points like a parametric, this is not that situation

imagine you have the graph x^2 + y^2 = 1

now if you replace x with 2x, you get this:
(2x)^2 + y^2 = 1

the reason is that by replacing x with 2x, youve essentially done this to your graph

[jaunty owl]

right

[left gyro]

youve modified x in advance, then the circle is drawn on this modified graph

now youll notice there the opposite effect happened

had you had (2 cos t, sin t), the circle is horizontally stretched

[jaunty owl]

interesting

my like intution is somewhat failing me here just because we did the linear transfomraitons in lin alg so its a bit hard to visualize for me lol

i can see it with the examples youve given though

[left gyro]

hold on I gotta do something but thats the general effect

in general, if you have f(x,y)^2 + g(x,y)^2 = 1, the seemingly "opposite" change gets applied to x and y before the circle is graphed

[left gyro]

in this case, that change is to rotate by 45 degrees before considering max

I can elaborate later

[jaunty owl]

alright ill think on it in the mean time

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@jaunty owl Has your question been resolved?

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@jaunty owl Has your question been resolved?

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[jovial sentinel]

undefined because it doesn't cancel?

[twilit moat]

Are you sure you have your derivative correct

?

[jovial sentinel]

pretty sure its right

[twilit moat]

Shouldn't it be 2/3(x-6)^-1/3?

[jovial sentinel]

at 6?

[twilit moat]

The general derivative

[jovial sentinel]

i need to do it in the alternate form

someone told me its because theres a 0 in the denominator

.close

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[rough briar]

can someone explain this solution to me. Particularly the part when they use the rank nullity theorem. I dont understand how there is n - p on the LHS while p is still on the right side. Shouldnt dimV been substituted with just n, and dimnullT would have + p?

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[gilded pine]

trying to do 34b. rn and this is my work so far

[gilded pine]

dont know how to progress from here

Nvm i got it :)

.close

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[lean otter]

yo is this accurate for wahts normally covered in linear algebra

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[feral beacon]

only need help turning this into the equation for a sphere

[feral beacon]

sorry for the horrendous handwriting it looks a lot better on my tablet than my pc

i can clarify anythbing as well

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[devout peak]

not sure how to approach this one

this is what i have so far

[covert yoke]

Good start. So what is the probability that it is specifically fixed by Donald?

[devout peak]

0.26

[covert yoke]

And by Joe?

[devout peak]

well thats dependant on donald no?

[covert yoke]

Yes

[devout peak]

joe's only exists IF donald cant

[covert yoke]

Yes exactly

[devout peak]

which is where im stuck

xd

[covert yoke]

So the probability that it is fixed by Joe is the probability that Donald doesn't fix it AND the probability that Joe does

How do you handle AND in probability?

[devout peak]

x

multiplication^

[covert yoke]

Ok

Giving what for the probability Joe fixes the cell phone?

[devout peak]

p(D^c) p(J|D^c)

?

[covert yoke]

Yes

[devout peak]

but over total probability

[covert yoke]

Well, P(J|D^c) is just P(J)

Because these are independent events

[devout peak]

so i wouldnt ahve to use bayes thm here?

[covert yoke]

In the sense that, Joe always has a 0.38 chance of fixing the phone regardless of if Donald has a shot at it or not

You don't, no

Well, actually

I guess it's a little more subtle

And I'm incorrect

[devout peak]

0.285

[covert yoke]

P(J|D^c) is the value you want to compute, but it is also the value actually given in the problem.

[devout peak]

yeah

[covert yoke]

"If Donald cannot, then there is a 38% chance..."

,w 0.74 * 0.38

[flat frigate]

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Requested by omnipotententity

[covert yoke]

0.285 is close, but something is wrong

Typo?

[devout peak]

i input 0.75 by mistake

[covert yoke]

Ok

So now "if it is fixed, what is the probability that it is fixed by Joe?"

How would we find this?

Hint:

[devout peak]

so i hjave to find P(fixed)

or

[covert yoke]

Yes

[devout peak]

1-P(unfixed)

so 1-(0.74*0.64)

[covert yoke]

Well, maybe, but it's easier to use a different method

Imo

P(fixed) = P(fixed by Donald) + P(fixed by Joe)

We already have both these values

[devout peak]

i see

[covert yoke]

(we can add these to probabilities because they are mutually exclusive)

[devout peak]

and then P(J)/P(fixed)

[covert yoke]

Yup

,w 0.2812 / (0.2812 + 0.26)

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Requested by omnipotententity

[covert yoke]

Seems reasonable

[devout peak]

do you mind if i ask you another question

regarding probability

@covert yoke

sorry for ping

[covert yoke]

I don't mind, but no promises I can help

[devout peak]

this one