help-33

[winged marsh]

nvm coontinue

yes

[cunning oak]

solve where you get a = 2, so a^2 = 4

that means you want x^2 - 4x + 4

[winged marsh]

i see

[cunning oak]

so, to get that add 4 to both sides of the equation

simplify and get (x - 2)^2 = 4

[winged marsh]

wait dont we have to find similar terms first?

[cunning oak]

..?

explain

[winged marsh]

oh ok wait

it was something like this

[cunning oak]

i dont understand what you mean by "similar terms"

but ill continue my answer

[cunning oak]

sqrt, x - 2 = +- 2

ending up with x = 0, 4

[winged marsh]

uh can u explain how to get this?

[cunning oak]

from this

you can split it up into 2 eqs

x - 2 = -2 or x - 2 = 2

[winged marsh]

oh

okay

[cunning oak]

do you understand now?

[winged marsh]

a little

[marsh citrus]

@winged marsh Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[iron ocean]

how to factor trinomials if a>1

[marsh citrus]

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[iron ocean]

how to factor trinomials if a>1

[limber hearth]

You put a(x^2 + b/a*x + c/a) and factor the new one

[iron ocean]

I dont get it

[proud basin]

open a new channel cause this soon will close

but for example if it was like $$2a^3-4a^2+9a-1=0$$
$$2(a^3-2a^2+\frac{9a}{2}-\frac{1}{2})=0$$

[elfin berry]

Skill_Issue

[marsh citrus]

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[graceful rain]

hi! need help with arithmetic sequence

[graceful rain]

The problem is if the first term is 8 and the second is 10, what is the 106th term. using this formula:
a sub n = a sub 1 + (n-1)d

[desert dirge]

what have you tried

[graceful rain]

Ive tried using the formula with:
106 = 8 + (n-1)2
106 = 8 + 2n - 2
-2n = 8 + (-106) - 2
-2n = 220
n = -110

But my classmates answers were 50 🥲

[desert dirge]

106th term doesnt mean the term is 106

it means n is 106

though 50 doesnt seem right either

[graceful rain]

Ive also tried that because thats what my classmates been doing but my answer was 218 🥲

[desert dirge]

,calc 8+105(2)

[elfin berry]

Result:

218

[desert dirge]

from the question you wrote here, this would be the right answer

unless you have the question wrong

[graceful rain]

Okay! Thanks! Sorry for the trouble and confusion!

[brave spire]

u shouldnt be sorry for having a doubt...

[marsh citrus]

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[marsh citrus]

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[cunning oak]

"Find the domain of x which makes (x + 2)^n converge as n aproaches infinity"

[still temple]

what do you think

[cunning oak]

-1 < x + 2 <= 1?

[lyric bay]

Why does that even converge?

[cunning oak]

r^n converges when -1 < r <= 1

lim n -> inf

isnt it?

[spice bay]

yes

[cunning oak]

is this correct?

[spice bay]

yes

but it's not the final form

[cunning oak]

thanks

[spice bay]

isolate x

subtract 2 from left and right

[cunning oak]

-3 < x <=-1

[spice bay]

yes

[cunning oak]

.close

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[fickle shell]

Sry for the bad handwriting

[unreal oxide]

is that a division or a square root lol

[fickle shell]

What do I do here? I cant take -12x away from -3x^2

[fickle shell]

Oops haha was supposed to be long division

[unreal oxide]

u can take -12x away from 0x though, right?

and theres 0x in the original function

[fickle shell]

Ah ok

Yeye I see now

Thank you!

❤️

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[fickle shell]

The question is a little hard to read

So p could be ANY value of x? Even one that isnt on the diagram? Theres no domain right?

[cunning oak]

is the 2 on the top tetration?

[cobalt sedge]

I hope its log to base 2 and not tetration

[unreal oxide]

it must mean the base

[fickle shell]

No idea what tetration is I dont think my course covers that so yeah I think its base

[cunning oak]

tetration of x is x^x

[cobalt sedge]

But, since the distance is vertical, just take the difference g(x) - f(x) = 2

[unreal oxide]

any value in the common domain

[unreal oxide]

coz u r given the functions u can find what their domains are
and the common domain is just the intersection

[cobalt sedge]

this only works if x is in domain of BOTH f and g

[fickle shell]

What is 'common' domain sry

[fickle shell]

the common domain is just the intersection
Intersection of what?

[cunning oak]

of domains i assume

[unreal oxide]

f has a domain
g has a domain

u can find the interscetion of the two

[fickle shell]

Ok I think I get it

Thanks guys!

❤️

.close

[marsh citrus]

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[fickle shell]

.reopen

[marsh citrus]

✅

[fickle shell]

Ok I got another quick question about this one

I did f(x) - g(x) = 2 and solved for x

I got x = 2 and x = -1

Isnt there like some rule where x = -1 cant be a solution?

Because its a negative and we cant have negatives inside logs?

Or something like that?

Or am I thinking of something else...

[whole quiver]

the input of log shouldn't become negative OR zero after you keep x=(-1) in f(x) or g(x)

[marsh citrus]

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[marsh citrus]

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[idle vessel]

What does this mean?

[spark otter]

the number on the left is i*(a real number)

meaning pure imaginary

[idle vessel]

oh

thank you

.close

[marsh citrus]

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[fathom ridge]

what a stupid way of writing that

[valid cape]

[marsh citrus]

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[final hinge]

confused as to what answer i would choose

[final hinge]

same thing shows up on my graphing calc

[golden dove]

@final hingeOn the first one

[cobalt sedge]

check the signs of the coefficients and the closest values to the a and b

[golden dove]

Try the values

What do you get if you use x = 2?

[final hinge]

if i use x=2 for the equation i got from the calcuulator, y is 17.7

[golden dove]

y = 0.5 * 2 - 15
y = 1.5 * 2 + 15

And so-on, which one gives y = 18?

[final hinge]

ok

so see which one is closest

[golden dove]

Not closest, but exact

[final hinge]

but why wouldn't the calculator give me one of those answer choices?

[golden dove]

Because you chose the wrong equation

[final hinge]

wdym?

[golden dove]

you chose a=1.35 and b=15

not a = 1.5

[final hinge]

i didn't choose those

[golden dove]

oh

[final hinge]

the calculator gave me those values

both of them

both desmos and my ti-83

[golden dove]

Well you shouldn't use a calculator here, because it's not giving exact values, but yeah it's the closest

[final hinge]

ok so the answer's just 1.5x+15

thanks for your help

have a good rest of your day

.close

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[marsh citrus]

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[exotic wolf]

Hi

[exotic wolf]

What am I doing wrong here?

[tawdry stag]

Hey, do u have a problem?

[idle vessel]

lmao

[eager tinsel]

in the second step

denominator

[sharp vessel]

You suddenly have a minus in front of the x squared

[exotic wolf]

I substitute t = -x^2

because i want the form

1 / 1 - t

[exotic wolf]

Wdym?

[eager tinsel]

this thing

[sharp vessel]

I dont see any t

You didnt make any substitution

[exotic wolf]

let x^2 = -t

i get

1 / 1-t

and then i use taylor expansion formula for 1 / 1-t

[sharp vessel]

So you meant to write 1 - (-x^2)

[exotic wolf]

Yea

[sharp vessel]

#❓how-to-get-help @frosty minnow

[exotic wolf]

I misspelt, should be - not +
But the rest doesn’t change

I computed the rest thinking it was a -

.close

[marsh citrus]

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[marsh citrus]

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[still temple]

Me 2nd time posting this

Answer-62

explain pls 😭

[lucid zenith]

$\frac{(1+l)^3}{1+l^3}=\frac{(1+l)^2}{1-l+l^2}=\frac{(1+l)^2}{1+l^2}\frac{1+l^2}{1-l+l^2}=\frac{13}{37}\frac1{1-\frac{l}{1+l^2}}$

[elfin berry]

kheerii

[lucid zenith]

now you just need to find that last ratio

which shouldn't be too bad

[marsh citrus]

@still temple Has your question been resolved?

[still temple]

I think i did this few hours ago

my answer didnt match

[lucid zenith]

you must have found the ratio wrong

simplifying the expression given, we get $$12l^2+37l+12=0$$ which gives the required ratio as $-\frac{12}{37}$

[elfin berry]

kheerii

[lucid zenith]

which seems to be giving us 13/25 as the answer

hmmmmmmm

[lucid zenith]

are you 100% sure about this answer?

[still temple]

i think soo

[lucid zenith]

oh wait this is supposed to be a plus

[still temple]

i got it from a math olympiad

[elfin berry]

kheerii

[lucid zenith]

which does give us the correct answer yeah

[still temple]

uh i think soo

yeah

.close

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[amber birch]

I got an alternate way using https://brilliant.org/wiki/componendo-and-dividendo/

[marsh citrus]

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[eager tinsel]

!status

[marsh citrus]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[eager tinsel]

you agree that working with cosine is easier than working with secent?

that's ballzy statement

!noans

[marsh citrus]

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.

[eager tinsel]

I am sorry but we can guide you to the solution but not give it

All I can advice is to reciprocate the general term and convert it to cosine

It will be easier to handle

[eager tinsel]

remember this statement

it is in the rules of this server

Nothing my friend

[eager tinsel]

follow this advice

it will help you

okay so you know the formula for 2cosAcosB

?

nice

so use that here

forgive me I can't maybe wait for someone else

[calm harbor]

Stop

Be nice, not toxic

[desert dirge]

the point of the server isnt to pump out solutions, its to help you achieve them yourself

[calm harbor]

It’s not their mandatory to assist you with your Math problem. Furthermore, it’s normal to make mistakes

If you’re looking for exemplary and flawless advice, I suggest you get a tutor.

I forgot to mention, asking or providing full solution to the question are prohibited from this server

All we can do is guide you through the process.

Sure

I can’t, but the mods can

<@&268886789983436800>

[quaint hill]

.close

[marsh citrus]

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[calm harbor]

Ty

[marsh citrus]

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[thorny latch]

i need clarification

is this asking for the value of X or the value of the other missing side length

[sand fable]

if this is a question you're submitting i would just find both

but it should mean find the side length labeled x

[thorny latch]

okay thanks

[calm harbor]

Find x

[thorny latch]

wait is it sayign to find X by using the missing side length

[calm harbor]

It means you need to present x on your answer sheet

[thorny latch]

oh its just saying find x by solving for the side it represents

[sand fable]

who knows? you can guess what the problem means but i don't think it matters much

[marsh citrus]

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[hybrid root]

how would you get the x intercept in terms of parameter c from this cubic? $t^2(t-1)-c$, where t=x-c

[elfin berry]

Jake The Human

[sand fable]

by using the cubic formula

[hybrid root]

this long boy?

shit, img quality is bad sry

this one?

[limber hearth]

There is only three different expression

[hybrid root]

You mean there are only three terms in my cubic case?

[limber hearth]

But if you have y = t^2(t-1) -c

[limber hearth]

Three different

[hybrid root]

What's your point? I can see I have three different terms, but do you mean this will simplify the usage of the formula? Or something else?

[limber hearth]

Let y = 0

t^2(t-1) - c = 0

t^2(t-1) = c

(x-c-1)(x-c)^2 = c

(x-c-1)(x^2 -2xc + c^2) = c

(Im trying)

[sand fable]

if that's the cubic formula then yes

[limber hearth]

(x^3 -2cx^2 + xc^2 -cx^2 +2xc^2 -c^3) - x^2 + 2xc -c^2 = c

Avoid

xd

[hybrid root]

Yeah it seemed like a tricky one

Well if I have no other option I’ll use the cubic formula, as horrendous as it looks

Thank you

[sand fable]

you can plug it into a calculator

[hybrid root]

Oh wow, lmao

thanks

I had hoped for a cleaner result, but the math doesn’t lie

thx

[limber hearth]

The fact that there is a 4th degree ones xd

[marsh citrus]

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[boreal panther]

According to the projected growth rate, how will these regions rank from largest to smallest populations in 2015?

[boreal panther]

how do i set this up

[cobalt sedge]

calculate it similar to a compounding interest problem

interest rate = projected annual growth
principal = 2000 population
time = 15 yrs

So, Pop at 2015 = P * (1+r) ^ t

[marsh citrus]

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[frosty bronze]

does anyone know why this is wrong?

[marsh citrus]

@frosty bronze Has your question been resolved?

[coral shoal]

What angle are you trying to find here?

I might be blind but I don’t see an alpha on the diagram

[marsh citrus]

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[marsh citrus]

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[ancient vine]

Hi can you try find DEF, i feel like my answer of 67 degrees is wrong as when I use sine rule for DF its inconsistent on the side I use

[novel juniper]

045 is just 45deg, right?

[ancient vine]

yes

wait let me send my working out

[novel juniper]

Hmm, so angle EDF=45 deg

[ancient vine]

yes i got that

and then i made a right angle triangle

[novel juniper]

And DFE is?

[ancient vine]

split down the middle of e

[novel juniper]

Why do you need that

[novel juniper]

,rotate

[hushed egret]

this is false

[hushed egret]

why do you think that

[ancient vine]

i thought itd form a 90 degrees

then 90-45

[hushed egret]

why would it form 90

does it look like 90 in the diagram you were provided?

you think the blue angle is 90?

[marsh citrus]

@ancient vine Has your question been resolved?

[marsh citrus]

@ancient vine Has your question been resolved?

[marsh citrus]

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[small stream]

Any quick way to compute the partial deriavative

[fading shore]

I don't think so

Other than that the x partial and y partial should be similar looking

Same as any other partial derivative I guess, a combination in this case of the product and chain rules

What do you mean

[small stream]

I mean idk how to calculate in this way

[fading shore]

Are you comfortable doing normal derivatives?

[small stream]

There're lots of ways after all

I only want to know how can i calculate this one

[fading shore]

Well I don't know how to give examples without solving the derivative for you sorry

Here's the definition for the product rule: $\frac{\partial }{\partial x} f(x,y)g(x,y) = \frac{\partial f}{\partial x} g(x,y) + f(x,y) \frac{\partial g}{\partial x}$

[small stream]

but we dont know if f is differentiable or not

[elfin berry]

MasoKiffles

[fading shore]

Sorry I didn't get the whole problem but it looks differentiable everywhere except for (0,0)

[small stream]

ooh

ok so as the pic said, how did they know the partial d are not continuous at (0,0)？ I should calculated the expressions of these partial d out ?

like this?

[fading shore]

That looks pretty right, I haven't worked it out myself

The function isn't differentiable at any point where the derivative is discontinuous

[small stream]

hmmmm

you mean function f(x,y)?

[fading shore]

Yeah f won't be differentiable at any point where the derivative is discontinuous

[small stream]

ooh so their logic is

since f is not differentiable at (0,0), its derivative at (0,0) must be discontinuous?

[fading shore]

f isn't differentiable at any point though

Yes

[small stream]

hmmm i still feel so confused

[marsh citrus]

@small stream Has your question been resolved?

[marsh citrus]

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[obtuse plume]

When drawing a graph from a function such as

f(x) = x^(2)-6x+8

how do i know on what x coordinates i have to draw a dot?

[obtuse plume]

nevermind, its still morning

[limber hearth]

You mean where it intersect the x-axis ?

[obtuse plume]

yes lol

[limber hearth]

Roots :D

[obtuse plume]

thank you lmao

.close

[marsh citrus]

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[ancient vine]

.reopen

bruh

[marsh citrus]

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[idle vessel]

What the sigma???

[limber hearth]

Sigma ?

[idle vessel]

Why does my Wolfram Alpha say it’s not 0?

[limber hearth]

Why would it be zero ?

[idle vessel]

Cuz w^2+w+1=0

[copper raven]

the result is essentially 0 tho

it's prolly some floating point crap

[idle vessel]

Idiot

.close

[marsh citrus]

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[marsh citrus]

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[novel juniper]

Can you express $y$ in terms of $x$?

[elfin berry]

🏳🌈f(why am i here )= idk

[prime yoke]

does this mean that x^2 + y^2 = 144

[prime yoke]

i did that initially

y=x-12

[proud basin]

wrong

[prime yoke]

im slow

12-x

[novel juniper]

Cool, $y=12-x$

[elfin berry]

🏳🌈f(why am i here )= idk

[proud basin]

can you do am-gm here tefhnichallt

[novel juniper]

Now, do you know calculus?

[prime yoke]

yes

[prime yoke]

??

[proud basin]

uh

lemme try with am gm

[prime yoke]

i can use derivative

=0

to get a turning point

idk

[novel juniper]

so can you minimise $x^2+(12-x)^2$?

[prime yoke]

findwhich is minimum

[elfin berry]

🏳🌈f(why am i here )= idk

[prime yoke]

wdym minimise

find the minimuym

im not sure

does it equal anything

wait

do i find derivative

[young dirge]

its i

cool

[prime yoke]

i got x = 6

i got answer

lol

[novel juniper]

,w minimise x^2+(12-x)^2

[elfin berry]

Results provided by WolframAlpha

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

Requested by physicsrocks

[novel juniper]

cool at x=6 indeed

[prime yoke]

i got a turning point at x = 6 and technically i should check if its minimum or max right

actually its not a negative function or a cubic

[proud basin]

ow amgm doesent work

wait

[novel juniper]

I mean you should but it's obvious this is an UP parabola

[prime yoke]

yea

[prime yoke]

what is amgm

[proud basin]

its an inequality

[prime yoke]

impart your wisdom

math olympiad

[novel juniper]

Arithmatic mean- geometric mean

[proud basin]

$\frac{a+b}{2}\geq\sqrt{ab}$

[prime yoke]

ah

[elfin berry]

Skill_Issue

[prime yoke]

and what relevance does this have to the mathematical world

why did u try and use it

dont go too deep i dont wanna waste ur time

[proud basin]

sometimes you xan use it to get a min/max without calculus

[prime yoke]

ohh ok

but we like calc

anyway thanks guys

.clode

[proud basin]

please do waste my time

im bored

[prime yoke]

unfortunately i cannot

im studying

for calculus application SAC

try this one

if ur bored

[proud basin]

oh wait

am gm works here

woohoo

[prime yoke]

imma get stuck on thsi too

actually might not

i just picked the last one for u to do

assumed its the hardest

is a asking for the minimum radius and height which will still guarantee 500cm^3 volume

[proud basin]

i have no clue how to do it

erm

[prime yoke]

thought u were a math olympiad

[runic temple]

do you know the surface area of a cylinder formula

[prime yoke]

yea of course

[runic temple]

we want to minimize that

what else do we know

[prime yoke]

u asking me

[proud basin]

the equations would be like
pix^2y=500
minimum of 2pix^2+2pixy

[runic temple]

yes

[prime yoke]

or do u not know

[runic temple]

i know

[prime yoke]

yea so find the minimum

i was rightt

[runic temple]

be confident then

[prime yoke]

but wait

[runic temple]

it seems like you know what youre doing

[prime yoke]

the show is not over

kinda

we got 2 variables dont we

[runic temple]

well yeah

but what happened last time

[prime yoke]

$2\pi r^2 + 2\pi r h = 500$

does this work

yep nice

[runic temple]

4

[elfin berry]

Lebob

[runic temple]

we dont know the surface area

[prime yoke]

wait i need volume formula

did u not say surface area of cylinder tho

[proud basin]

my brain is going for am gm knowing fullly well it wont work

[runic temple]

it could, but its not the best course of action

[prime yoke]

$\pi r^2 h = 500$

[elfin berry]

Lebob

[proud basin]

i mean what, you want me to do derivatives 😭

[runic temple]

i said we want to minimize it

[prime yoke]

.

[proud basin]

sart

sqrt

[prime yoke]

wait i did wrong

why is this so weird

[proud basin]

is this what people call multivariable calculus

[runic temple]

its annoying to solve

[prime yoke]

$r = \sqrt{\frac{500}{\pi h}}$

[elfin berry]

Lebob

[prime yoke]

cooked

what tf do i do now

[proud basin]

plug in

[runic temple]

personally i wouldve solved for h, but this works

you plug that in for r into the second equation

[prime yoke]

we have a second equation

orh

oh

surface area

yeah

[proud basin]

dummy

[prime yoke]

i type without thinking sometimes

but not everyone is a math olympiad

ykw i cant be stuffed doing all the steps in my head and then latexing

plug in

[proud basin]

bruh you think being a math olympiad suddenly makes me know multivariable calculus?? 😭

[prime yoke]

i do

plug that in

eliminate r

then u have a equation

that u can derive

set = 0

solve

find min

[proud basin]

without my own curiosity olympiad brings me to basic trig

[runic temple]

yup

[prime yoke]

then do f(that) to get y value

wait am i finding y and then solving x

ive done the worst way

[runic temple]

youre finding h and solving for r

[prime yoke]

tjos

this

i mean

[proud basin]

i wanna suffer with questions but dont have any

[prime yoke]

i did it backwards

make it annoyinb'

[proud basin]

wait i do

[prime yoke]

how do i even do olympiad

how do u even go down that path

not that i want to but yk

[proud basin]

err

[runic temple]

practice

[prime yoke]

im barely surviving school whilst still being sane guys

i lock in every night for hours on end

[proud basin]

i liked math as a child so i joined a math extraculicular, as luck would have it my teacher was a math olympiad teacher which brought me into math olympiads

[runic temple]

if youre crazy enough to like math, olympiads could be fun

[prime yoke]

i dont really like like

but i dont hate

some topics i do (probability)

[runic temple]

liking math? couldnt be me lmao

[prime yoke]

i wouldnt take it over playing videogames

but i dont mind it

[proud basin]

i liked math until i was thought probability and combinatorics

jk i hate that topic but i still like math

[prime yoke]

probability is so shit

[proud basin]

real

oh and also geometry

[prime yoke]

nah geometry good

[proud basin]

oh yes so fun reading a 30 page essay about a single question

[prime yoke]

u talking about angles and shit

nvm i got it all wrong

what can be so hard about it

seriously what does the 30 pages do

[proud basin]

its a hyperbola

lemme give you question one from a hard paper my teacher gave me

[prime yoke]

ok

[proud basin]

its given triangle ABC with AB=AC, angle bisector cab and abc intersect bc and ac at D and E, K is the incenter of ADC, if BEK=45° find angle CAB

trig is explicitly not allowed

[prime yoke]

nah wtf

[proud basin]

ikr

[prime yoke]

lemme try

[proud basin]

gl

[prime yoke]

am i using similar and congruent triangles or some shit

@proud basin

i think i sold pretty hard

i cant go any further

my lines are off

[runic temple]

||60||?

[proud basin]

idk

why ask me

[prime yoke]

is my drawing right

[runic temple]

you gave the problem

i figured youd have the answer

[proud basin]

idk the solution

[runic temple]

open another help channel and ill explain

[proud basin]

i dont :3

i was thlold tge sul but i forgor

[prime yoke]

anyway thanks for the help giuys

gotta lock back in

.close

[marsh citrus]

Channel closed

Closed by @prime yoke

Use .reopen if this was a mistake.

[runic temple]

youre welcome

[prime yoke]

wait

was my drawing righjt

@runic temple

[proud basin]

err

[runic temple]

it was close

[prime yoke]

what did i miss

[runic temple]

you know CK goes through the incenter of ABC

[proud basin]

my teacher gave me this drawing but idfk why E' and I was there

[runic temple]

because same angle bisector

[prime yoke]

so mine was flipped

ok thanks

will open agian if i require help

.close

[runic temple]

alright

[marsh citrus]

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[drifting pollen]

hello im tryna do this question but im not sure how the sin becomes a negative after taking the inverse of it

[eager tinsel]

sine becomes negative?

elaborate what you mean\

[drifting pollen]

Wait let me show you an image of the solution

@eager tinsel

[eager tinsel]

hey

sorry for the waiting

[drifting pollen]

eyah alg

[eager tinsel]

ah so you mean how did they got pi-arcsine right?

[drifting pollen]

yeah idk the algebra behind it

[eager tinsel]

see, you know the range of arcsine function?

like how we generally define it

[drifting pollen]

i get the standard range of arcsin which is pi/2 and -pi/2

and the doman is -1 to 1

[eager tinsel]

yeah

but see in the question we are given pi/2 to 3pi/2

okay?

[drifting pollen]

yes

so you gotta move up the whole graph by pi

to satisfy the inverse range

[eager tinsel]

yeah I'm coming

[eager tinsel]

yup

since arcsine belongs to {-pi/2, pi/2}
pi-arcsine will belong to the {pi-pi/2, pi-(-pi/2)}

which is {pi/2, 3pi/2}

[drifting pollen]

yes alright

[eager tinsel]

since we wanted this range instead of the the general arcsine range we subtracted pi from it

any doubt?

[drifting pollen]

wait didnt we add pi

not subtract it?

[eager tinsel]

you literally confused me for some minutes

but anyways

[eager tinsel]

see, in pi/2 to 3pi/2 value of sine function goes from what to what?

[drifting pollen]

my bad i thought

we added it

because in the solutions we added pi

[eager tinsel]

oh. no

it is a wonderful doubt

[eager tinsel]

answer that

first

[drifting pollen]

well if we are talking about the inverse than the range becomes the domain of the inverse

and vice versa for the domain

[eager tinsel]

I was just asking value like from -pi/2 to pi/2 it goes from -1 to 1

like that

[drifting pollen]

oh yeah i got that

since arcsin is -1 to 1

the domain that is

mb if im a little confusing not the best at math

but tryna improve

[eager tinsel]

okay see, this thing goes from 1 to -1 right?

[drifting pollen]

yes

[eager tinsel]

yes, but since arcsine is defined to get values only from -1 to 1

we subtract it form pi

[drifting pollen]

ah yes yes got it now

because the domain of the original starts at pi/2

[eager tinsel]

if we add it in pi, the range of sine will go to fourth quadrant

mb

[drifting pollen]

yeep

[eager tinsel]

3pi/2 to 2pi

got it?

[drifting pollen]

yes

[eager tinsel]

perfect

[drifting pollen]

so far what i got rn is that we subtracted pi so we can follow the domain of arcsin

[eager tinsel]

yeah

[drifting pollen]

and we add pi in the y axis to satisfy the range too

since the new range of arcsin is pi/2 and 3pi/2

[eager tinsel]

subtract the whole thing form pi

but yeah

you're getting it

[drifting pollen]

aight

its now how the arcsin has a negative

is the only thing i am very lost

[eager tinsel]

?

$arcsine{\in}[\frac{-\pi}{2},\frac{\pi}{2}]$ \
$\pi-arcsine{\in}\pi-[\frac{-\pi}{2},\frac{\pi}{2}]=[\frac{\pi}{2},\frac{3\pi}{2}]$

[drifting pollen]

ah alright i get it now thanks

[elfin berry]

77²

[drifting pollen]

ty got it now

[eager tinsel]

!done

[marsh citrus]

If you are done with this channel, please mark your problem as solved by typing .close

[drifting pollen]

thanks again @eager tinsel

.close

[marsh citrus]

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[marsh citrus]

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[glad wagon]

circle geometry

[versed birch]

name the center point of that circle O, connect OP, OQ, OR

apparently OP⊥BC, OQ⊥AC, OR⊥AB

[glad wagon]

yeye

[versed birch]

so, S_△ABC = S_△AOB+S_△BOC+S_△AOC

[glad wagon]

sorry what is the S b4 the triangel symbol

[versed birch]

the area of that traingle

[glad wagon]

oh alr

[glad wagon]

wait so from there where do i go

[versed birch]

...

[glad wagon]

OH BRUh

sorry

its late here in aus

[versed birch]

list S△AOB S△BOC and S△AOC accroding known conditions

add them up

[glad wagon]

yea

tysm

.close

[marsh citrus]

Channel closed

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[glad wagon]

.reopen

[marsh citrus]

✅

[glad wagon]

@versed birch sorry could you quickly help me with another circle geo question?

[versed birch]

√

[glad wagon]

part B

[runic temple]

draw the circumcircle of ATB

[versed birch]

hm

[runic temple]

where is its center?

[versed birch]

A, B and T are on the same circle whose diameter is AB

[glad wagon]

its not given

[runic temple]

it can be deduced

[versed birch]

accroding part A

[glad wagon]

idk

all i can think of is proving congruency

[runic temple]

where the a circle is defined such that all points are equidistant from the center

excuse my typing its late

[glad wagon]

all good

[runic temple]

remember that a circle*

[glad wagon]

well like

i feel like if i use that way my tutor will mark me down

like drawing another circle

is there another?

[runic temple]

i dont see why you would get marked down

[glad wagon]

true but if i get a q wrong i have to redo the worksheet

[glad wagon]

wait would it be approprirate

construct diameter AP on the first circle

then angle ATP = 90 degrres

then ATB is just 180-90

[marsh citrus]

@glad wagon Has your question been resolved?

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[small stream]

I really need someone explain this to me, i dont understand the linear map part

[desert dirge]

it means J has the properties
J(x+y)=J(x)+J(y), where x and y are from R^m
and J(ax)=aJ(x) where a is from what is likely R here, a scalar

[still temple]

in other words, J is an R-linear map from the vector space R^m to R^n

I like to think of J as a "linear approximation" of f

[marsh citrus]

@small stream Has your question been resolved?

[red nimbus]

you should ping snow

[marsh citrus]

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[small stream]

@hushed egret (sry for interrupting

[graceful mesa]

@small stream, you opened the channel under your name now 😭

(inevitably)

[broken dome]

Now you have become the helpee

[graceful mesa]

😳

[iron marlin]

basically differentiable functions are locally affine

[small stream]

affine?

[iron marlin]

Ax+b

[small stream]

how, i mean, how DIFF related to AFFINE

I know them seperately but i canot wrap my head around the connections between them

[iron marlin]

f(x+h) is roughly [f(x)-Ax]+A(x+h)

[small stream]

what's A

[marsh citrus]

@small stream Has your question been resolved?

[slim surge]

A is the matrix of a linear map probably.

[slim surge]

My rough intuition for differentiability is that a function differentiable around x_0 looks like an affine (linear but not passing by the origin) function if you zoom in far enough on x_0. A better way to say this is If you zoom in far enough on x_0, then around that point the function changes linearly with some small error. The big definition is a formalisation of this for general mapping from R^m to R^n.

[small stream]

i just dont understand that why cannot it just be

[slim surge]

If J was not there the limit wouldn’t be = 0 all the time like (do x dot product x as an example). diffentiability is not a generalization of the derivative it’s a property of a function, namely the way it change is locally linear.

[small stream]

(do x dot product x as an example
could u elaborate

[slim surge]

give me a minute

[marsh citrus]

@small stream Has your question been resolved?

[small stream]

how did you calculate this?

[slim surge]

For a function f of R^n to R it’s the gradient of f transposed, for R^n to R^m it’s a matrix called the jacobian matrix J(x)

these things are the representation of the linar function such that x_0 + J(x)x “approximate f the best” around x_0

[small stream]

Also why do they have | | .... | |

what does || indicate

[slim surge]

the norm

like vector length

[small stream]

if i only talk about one or two dim, do i still need this sign?

[slim surge]

yeah for dimension 1 it reduce down to absolute values

but i think you still need it

[slim surge]

do you have a good feel for what is alinear map?

[small stream]

im not sure but i think i have a general feeling for it

also i want to ask what's this notation

[slim surge]

lol that’s me being lazy to write the word But with my t that looks like a p

https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/tangent-planes-and-local-linearization/v/what-is-a-tangent-plane

this guy can explain it better than me with nice visuals go there

wait that’s not the right one this is sorry : https://youtu.be/VmfTXVG9S0U

[small stream]

This is fabulous, tysm

I'll watch them first then if i still get questions again i'll ask here

Thank you !!

.close

[marsh citrus]

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[limpid bison]

what have I done wrong here

[unborn condor]

you need to write a lot more clearly, that is unreadable

[marsh citrus]

@limpid bison Has your question been resolved?

[silent marten]

Sorry my handwritting is bad

1/2 * r^2 * angle in radians = Area of circular sector

and the arc lengh = angle in radians * r

[limpid bison]

thats 4 right?

the denominator

[silent marten]

Yes

[limpid bison]

ok cool

thank you

.close

[marsh citrus]

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[marsh citrus]

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[exotic wolf]

hi

[exotic wolf]

how do i prove

p(A) * P(B|A) = P(A∩B)

P(B|A) means the possibility that B happens if A already has happend...

[nova sierra]

a formal proof? I am not sure about one

You could use a Venn Diagram to get a meaning of it though

[exotic wolf]

ahh im stupid... i can just use the formula for P(B|A)

[nova sierra]

yeah

[exotic wolf]

P(B|A) = P(A∩B) / P(A)

[nova sierra]

yep

[exotic wolf]

oh well...

thanks anyways

[nova sierra]

probability of B given A, then just multiply both sides by probability of A

[nova sierra]

no problem, very little help, but whatever lol

[exotic wolf]

.close

[marsh citrus]

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[twin arch]

What do I do 😭

[nova sierra]

maybe try some trigonometric substitution

[twin arch]

Idk how do the finate ones

I need help

[nova sierra]

Look at the denominator of the fraction

It is 4 - x^2

[twin arch]

(2-x)(2+x)

[nova sierra]

And look at the trig identity $$sin^{2}(\theta) + cos^{2}(\theta) = 1$$

[elfin berry]

Adam

[twin arch]

Where did you get that from

[nova sierra]

It is a trigonometric identity which comes from the Pythagorean theorem and the unit circle

[twin arch]

How does it relwte

To the question

[nova sierra]

Well if you rearrange the formula

we get $cos^{2}(\theta) = 1 - sin^{2}(\theta)$

[elfin berry]

Adam

[nova sierra]

and if we multiply by 4 on both sides

we get $4cos^{2}(\theta) = 4 - 4sin^{2}(\theta)$

[elfin berry]

Adam

[nova sierra]

And with 4 - x^2

we could make a substitution for x

So we apply a trigonometrix substitution to simplify the integral

[still temple]

I would have used partial fraction and logarithm, though I suspect it is the same as using trig

[nova sierra]

then we will have new bounds and evaluate the integral at those, and see what happens

[nova sierra]

this is also a good method

[twin arch]

Wait

Hold up

Can I do some of it and show you guys my work

[nova sierra]

sure

[twin arch]

@nova sierra @still temple

[nova sierra]

Approaching it like this is good too

So for the partial fractions, what do you do next?

[nova sierra]

Hmm

[nova sierra]

For the second coefficient B

Check the work again

[twin arch]

Why

[nova sierra]

Here you substituted -2, yes?

[twin arch]

Ye

For B

[nova sierra]

Original form

[twin arch]

Oh sh

It’s +4

Do I do power rule

@nova sierra

[nova sierra]

Sorry

[nova sierra]

For which part?

[twin arch]

The square

[nova sierra]

Here with the logs?

[twin arch]

Yeah

Idk what to do next

[nova sierra]

Ah

I would keep it separated

It's tricky with the absolute values

now you evaluate the integral at the limits of integration, 1 and 2

[twin arch]

Which one

I kinda uhh got rid of it

[nova sierra]

wait

for the integral of 2 - x

I believe it is -ln(2-x)

when you integrate those types of functions

you multiply by the derivative of the bottom

[twin arch]

Huh

@nova sierra

Wdym

[nova sierra]

Wait

sorry

I think I am wrong

[twin arch]

Why

[nova sierra]

ignore that

[twin arch]

Ok

What do I do next

Do I just do this

[nova sierra]

wait no

you do

[nova sierra]

when you use u-sub for an integral like that

you end up with the negative sign

[twin arch]

Ye

[nova sierra]

so $\int {\frac{1}{2-x} d{x}}$

[elfin berry]

Adam

[nova sierra]

is -ln(2-x)

yeah

[twin arch]

ye

[nova sierra]

sorry

I misread my work

[twin arch]

But what do I do for the answer

[nova sierra]

okay

now just substitute the limits of integration, and subtract

so if F(a) is the integral, do F(b) - F(a)

where a and b are the limits of integration

[twin arch]

Where do I use u substitution

U= 2-X

[nova sierra]

here

[twin arch]

Or U=2+X

[nova sierra]

go back when you were computing the indefinite integral

[nova sierra]

well, when you integrate them separately, you need to use the substitution for u = 2 - x, and when you integrate the second function, u = x + 2

[twin arch]

Like this

[nova sierra]

yep

[twin arch]

What is AI doing then

When it says X=1, U=1

[nova sierra]

Oh yes

[twin arch]

and X =2, U=2

[nova sierra]

forgot about that

bounds will change

[twin arch]

Huuuuh

[nova sierra]

just substitute the bounds to get the bounds for u

[twin arch]

Wdym

Substitute

[nova sierra]

because we have changed the nature of the integral

so for example

in the first integral

u = 2- x

so when x = 1 (the first limit of integration), u = 1

we just do 2 - 1

because we are integrating in the u-world now

[twin arch]

Yes

[nova sierra]

and so when x = 2, u = 2 - 2