help-13

[edgy olive]

Oh ok

[dusk finch]

ew quadratic formula and the question was wrong, it's + x now

and this is true even if the x^2 coefficient is 1 btw, it has nothing to do with the 2x^2

[edgy olive]

So 2x^2+x-45 = 0 ——-> x^2-x-90 = 0

[gray hamlet]

aha with +x its 4.5 and -5

[frail citrus]

$\alpha +\beta=\frac{-b}{a}$ and $\alpha \beta=\frac{c}{a}$ for the roots of a quadatic equation $ax^{2}+bx+c=0$

[wraith dagger]

Dhairya

[dusk finch]

no no no

[dusk finch]

as i said here, it has nothing to do with the 2x^2

if you have x^2 - 2x - 3, the roots will be x = -1 and x = 3. The sum is 2, not -2

[edgy olive]

Ohh ok

Thank you

.close

[cedar kiln]

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[nocturne spear]

how do i do this?

i looked for the name that appears the most, which is rodger

then since most lie about one, i eliminated the statements where rodger is named

and amongst those, sam was the most named

so i picked e, rodger and sam

but it's f, roger and ursula

idk why

[tropic oxide]

i would do it the honest way and think about all cases of "who's the little shit that lied about both"

[nocturne spear]

how do i find that person

it's just someone's word against others

how do i tell if someone lied

[tropic oxide]

i said think about ALL cases. analyze them one by one.

see which ones end up in a contradiction, and eliminate those

assume P lies => Q not on team and R not on team
R not on team => Q's other name is correct => P is on team
Q not on team => R's other name is correct => S is on team
but then S lied about both. can't have TWO double liars as per the question.

therefore P can't be the double liar

this sort of logical deduction

no there's no shortcut to it

you have to do it the honest way

yes even if it takes an hour

[nocturne spear]

i kinda understand this

what do you mean by "Q's other name is correct"

[tropic oxide]

Q says the team members are P and R

she lied about R

and she must have lied about exactly one

therefore the other name that she named is correct

[nocturne spear]

yes

okay

[nocturne spear]

so like assume philip lies, then rodger and qayla are not on the team. qayla says it is philip and rodger, but rodger is defo not on the team - philip is on the team

[tropic oxide]

sure.

[nocturne spear]

so how do i carry on with this to show that philip did not lie twice

roger says that it is qayla and sam, we know qayla is not on the team (per the assumption), so sam is on the team

i understand

.close

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[karmic field]

what happens to the ODE at t=9

[karmic field]

does it not hold anymore or wha?

[upper laurel]

did you solve the IVP?

[karmic field]

nah not yet

i will continue it

[upper laurel]

once you solve the IVP, you can graph y, y', and y'' to see whats happening at t = 9

I have a feeling itll be like a bounce or a knock

[karmic field]

no am asking like in the equation

if at t=9 the right side is infinity does the equation collapse

[upper laurel]

no

[karmic field]

like if initial conditions are at t=9

[upper laurel]

listen

the dirac delta is not supposed to be taken literally

t=9 is at the moment the bounce or knock happens

you can solve the IVP to see what y, y', and y'' are like in the rest of the area surrounding t=9

[karmic field]

so at t=9 is y defined

[upper laurel]

yes

but not directly

[karmic field]

ok

so its the same solution

as any other IVP

or steps

[upper laurel]

it might not be but Ill check

it should only have one solution

[karmic field]

ill do it and tell you if i have a question

[hollow trail]

thinking of it as an ode derived from newton's second law, the delta can be thought of as a collision which happened instantaneously (hence ""infinite force"") but which delivered a finite amount of momentum

[karmic field]

but in collision you dont have infinite force

[upper laurel]

a given acceleration

in an instant

where do you think that acceleration is coming from?

not very finite thats what

[karmic field]

you can actually calculate the force

[upper laurel]

as I said, think about if a ball bounces off the ground

how long does the bounce take?

[karmic field]

depends on the ball

[hollow trail]

a collision delivers a finite amount of momentum; the amount of momentum delivered = impulse = integral of force wrt time = average force * time. if the time of collision = 0, then the force would be "infinite"

[upper laurel]

we are talking about an ideal scenario here

[karmic field]

but time of collision cant be 0

because then it didnt happen

[hollow trail]

like in practice the actual time of collision is not actually 0, but this can be used to idealize a very short collision

[upper laurel]

consider the following

if we had a short collision, we can say it took a small time dt

now this is not convenient for math calculations

so we can take the limit as dt approaches 0

[karmic field]

if the time is 0 then how has it happened

[upper laurel]

are you even listening to me

I am answering your question

[karmic field]

yea

[upper laurel]

with a sentence like that, the time wasnt ever 0 was it

[karmic field]

but in dirac function

its a point

[upper laurel]

limits dont put in 0 directly

[karmic field]

not a dt

[upper laurel]

taebek you can view the dirac function as a limit of other functions

[karmic field]

anyways uhm im not trying to understand the definition

but like

[hollow trail]

the dirac delta "function" also comes out of a sort of limit process, the piecewise 0 and infinity definition isn't really true

[upper laurel]

well you gotta

[karmic field]

if initial conditions are at a

[karmic field]

i liturately dont have the tools for it

[upper laurel]

you really think you can attempt to "break" the physics at play here just because the dirac delta function doesnt act normally?

you dont have the tools, that means your current tools wont tell you what to expect

[karmic field]

yes ik

[upper laurel]

so why push back?

[karmic field]

what

[upper laurel]

Im telling you how you can view it and youre going "but the function definition is telling me this instead"

[karmic field]

what?

[upper laurel]

if you view it as a limit of ever shorter bounces, you never need to consider a bounce that takes 0 seconds to happen

right?

its just a theoretical way to model a really short bounce

[karmic field]

but if i have a limit

inside a function

[upper laurel]

yes or no

[karmic field]

and it goes to infinity

[upper laurel]

can you view ir or can you not

[karmic field]

that infinity is a concept

[upper laurel]

thats not how a limit works

we're not considering the limit of just the function here

we're considering the limit of how the ball would move

at the limit, the ball would take on a particular path

the momentum would be discontinuous

[karmic field]

why is this going towards ball

[upper laurel]

but we dont need to worry about this

[karmic field]

idk what the momentum would be

[upper laurel]

because thats the closest physical example to show you why a dirac delta would be important for physics in the first place

[karmic field]

we have force time and momentum

[upper laurel]

if we were just talking abstractly, that wouldnt resolve your issue

[hollow trail]

the delta function is very carefully defined so that although its value approaches infinity, its integral stays finite

[karmic field]

they all in the same equation

yea i had this question here before

but they told me to not worry about what approaches infinity means

[upper laurel]

have you even solved the IVP?

[karmic field]

because i would need to know measure theory

[upper laurel]

I cant show you the graph of y and such because thats a spoiler

you need to at least solve the thing first so that we can examine it closely

see what happens at t=9 for example

is it discontinuous?

[karmic field]

no because i wanted to solve it but you started explaining

[karmic field]

show the graph

its not like its homework or anything im doing this on my own

[upper laurel]

bro I just told you to solve it first

[karmic field]

well my question is for the initial conditions

[upper laurel]

and I started explaining because you started comaplaining...

[karmic field]

if they are at t=9

[upper laurel]

thats not even relevant to the question right now

Id say y' wouldnt really be defined so it wouldnt make sense to put it there

but Id have to solve the IVP to be sure

[hollow trail]

to do the initial conditions at a discontinuity like that you would specify sided limits rather than values

[karmic field]

that is the question

[upper laurel]

solve the IVP first

to provide extra context for the question

leave the integration constants in,

[karmic field]

ok

there wont be constants

im using laplace transform

[upper laurel]

taebek have you solved a DE before

[karmic field]

obviously

[upper laurel]

the constants inevitably appear for you to be able to insert in the initial conditions

[hollow trail]

laplace transform solves ivp's directly without integration constants

[karmic field]

yea exactly

im finding a particular solution with it

then i solve the homogeneous for the general one

even though

in all examples that is not shown

idk why they decided to forget about the general one after i got to the laplace transfroms

and idk how id solve it without the laplace transform

no idea what type of guess for Yp(t) id take

[hollow trail]

with discontinuous forcing functions like this the laplace transform is the best method

[upper laurel]

the dirac delta is only really defined to be laplace transformed

one of the ways to safely deal with it, the tool, is just the laplace transform

[karmic field]

im just gonna check the solution

cba doing fraction split

does desmos even take heaviside step functions

[upper laurel]

you have to make a version yourself

they do have sign(x)

you can shift that to what you need

[karmic field]

how do i split a function

like 2 formulas

or is there not an option

[upper laurel]

look in the upper-right corner ? for a tutorial on how to use desmos's piecewise feature

the short version is:
{ condition : value if true , value if false }

for example, {x > 0: 1, 0}

sign(x) is the same as {x > 0: 1, x < 0: -1, 0}

[karmic field]

can you just send me it

[upper laurel]

click the ? button bro

[karmic field]

where

[upper laurel]

then choose restrictions

this will give you a tour

[karmic field]

but like this is just restriction

how do i make 2 different ones for the same function

[upper laurel]

oh damn thats no good for a tour

[upper laurel]

I told you up here, but let me repeat it

normally for a piecewise you have

{ formula 1 if condition 1
formula 2 if condition 2
formula 3 if condition 3

desmos wants you to write it down as:
{ condition 1 : formula 1, condition 2 : formula 2, condition 3 : formula 3 }

[karmic field]

y(t) doesnt appear in graph at all

[upper laurel]

bruh

you shouldve taken a screenshot first

x and y are reserved for graphing

you cant use them as functions

[karmic field]

like this ?

[upper laurel]

remove the {}s around the conditions

[karmic field]

oh

[upper laurel]

if you put in x= to the beginning of this, desmos just graphs x = 3y

you can go with something like y_1

[karmic field]

says it doesnt understand the use of :

[upper laurel]

take a screenshot

[karmic field]

oh wait does it not take t as variable

[upper laurel]

wrong removal

the conditions are the t > 9 and the t < 9

the condition isnt the entire thing

[upper laurel]

and remove the {}s around the conditions

thats t > 9 instead of {t > 9}

[karmic field]

ok

yea

its too far down

i cant even see anything

doesnt even look defined at 9

can you somehow scale only 1 axis?

the derivatives arent any better

[upper laurel]

yes, hold shift then drag one of the axes

[karmic field]

it is defined at 5x10^12 at 9

how is that even poossible

all 3 functions are defined at t=9

so if i plug in t=9 at the origal ode

we get that δ(0) = a where a is a real number

isnt this a contradiction

[upper laurel]

as before, avoid considering t = 9 directly

[upper laurel]

this is a floating-point error, dont look at it too hard

[hollow trail]

exponential functions grow reallly fast, is the issue

here is a graph of a more representative example

[cedar kiln]

@karmic field Has your question been resolved?

[cedar kiln]

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[torn marsh]

Do you guys think question six is correct?

[torn marsh]

The answer key is different to mine

[frail citrus]

correct

[frail citrus]

whats the key then

[torn marsh]

One moment sending it right now

[chrome elk]

You factorized wrong at the last step

[torn marsh]

The second last step or the very last step

[frail citrus]

3x^2 one

[torn marsh]

I got it

But my answer to question eight is incorrect

Circled in red

[sullen cipher]

Check this part again

[sullen cipher]

This should be +

And dont forget the initial denominator

[torn marsh]

I mustve expanded it

wrong

[sullen cipher]

It should be a +
(a+b) portion is the one which is wrong

[torn marsh]

It this better?

Not sure if I am on the right track

[sullen cipher]

Ur initial way was easier and simpler

This is lengthy

Note that e^x .e^-x=1

$e^{-x}=\frac{1}{e^x}$

[wraith dagger]

vικτιμιζερ

[sullen cipher]

This should be negative

[torn marsh]

u mean it shoudve been a minus before the bracket

oh yes

it shoudve been -

[sullen cipher]

Yea

[torn marsh]

but i was on the right track

[sullen cipher]

Both r right

The one u sent b4 is right as well,but there was calculation mistake

[torn marsh]

e^x and e^-x

are not

common right?

[sullen cipher]

Wdym by common

[torn marsh]

they dont have a common factor

[sullen cipher]

$e^x \times e^{-x}=e^x \times \frac{1}{e^x}=1$

[wraith dagger]

vικτιμιζερ

[torn marsh]

yes

I understand that

[sullen cipher]

Then y r u searching for a common factor

When they cancel out each other

[torn marsh]

ahh making more sense

[sullen cipher]

Since this is negative it cancels out so at the last step ur numerator remains as 4.e^x .e^-x

[sullen cipher]

Hopefully

[torn marsh]

so a^7 * a^6 = a^(7+6)

[sullen cipher]

Yes

e^(x+(-x))=e^(x-x)=e^0=1

[torn marsh]

also, should I have expanded the denominator

or

that would provide consequences?

[sullen cipher]

Expanding gets u nowhere

So let it be as it is

Plus ur solution has the denominator in unexpanded form

[torn marsh]

true since its more simplified

alright thank u so much!

Ill open a new ticket for my other question

.close

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[quick inlet]

Hello I was wondering what I did wrong since I’m planning to take this test retake tmrw

[lone slate]

Whats the correct ans tho

Your teacher's notation is questionable

[livid hound]

explain your reasoning for each choice you made

teachers markings are indecipherable and actually look a bit wrong.

[lone slate]

True

[quick inlet]

Wdym?

[lone slate]

The teacher puts checks, circles, crosses everywherd

I don't get what they mean

[slender atlas]

in fact, the last one is a check and a cross.

[livid hound]

especially that cross/tick hybrid

[modern compass]

b) and e) are marked wrong, d is correct.

[lone slate]

What about A?

[livid hound]

dunno why they circled a)

[modern compass]

a) is correct

(supposedly)

[lone slate]

A doesn't look correct to me

[lone slate]

Maybe I'm stupid but no idea

[livid hound]

a) isn't correct

for the same reason e) is wrong

[modern compass]

yeah.... I don't think you can conclude a) is true. If a) was true, then e) would be true.

[livid hound]

but anyway

explain your reasoning for each choice you made

otherwise we don't know what lead to those mistakes

[quick inlet]

I chose b because I thought that segment AB and BC where the radii of the same circle (but I see it’s a little off centered) I said d was correct because ABC is an isosceles triangle and ac and bc are the two lengths that r equal and I said e because I thought it was an equilateral triangle (I know it’s not now) so I chose it because if it was an equilateral triangle it would be correct

[livid hound]

to consider AB and BC to be radii of the same circle, there would need to be a circle centred at B

passing through A and C

[quick inlet]

Alr that make sense

[livid hound]

for e, note that AB is a radius of circle A,
AC is not

[quick inlet]

Alr

[cedar kiln]

@quick inlet Has your question been resolved?

[cedar kiln]

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[silent stratus]

Prove x³+y³+z³-3xyz = (x+y+z)(x²+y²+z²-xy-yz-xz)

[silent stratus]

I am just 9th class so pls do easy one

[carmine yacht]

just multiply them and that's all

[loud gyro]

just multiply the RHS and see how it goes

[silent stratus]

No can't we make LHS like Rhs

[loud gyro]

thats why I said see how it goes

[silent stratus]

In my book they made LHS like Rhs but I didn't understand

[indigo lagoon]

Can you show your book?

[silent stratus]

Ok w8

[loud gyro]

you will need to add and subtract some terms to make both sides have the same terms

[indigo lagoon]

,rccw

[hidden mural]

if you turn the RHS into the LHS (by expanding), you can just reverse your steps to turn the LHS into the RHS

[silent stratus]

How

[carmine yacht]

how have you tried to prove it

[hidden mural]

wdym how

[silent stratus]

I don't know how to , I am just trying to understand what's in book

[carmine yacht]

mb he tried to prove it with geometry

[carmine yacht]

nevermind

[silent stratus]

How we can prove Algebra with geometry

[carmine yacht]

w8 I will try to solve

[silent stratus]

Ok thanks

[carmine yacht]

In fact you can

but rn it's doesnt matter

[silent stratus]

I am just in 9th class

[carmine yacht]

I'm in 10

[hidden mural]

the book's method does seem to be a bit complicated

just expand RHS

[carmine yacht]

this is the easiest fr

[silent stratus]

If we expand rhs then also the , we will get full marks ??

[hidden mural]

idk ask ur teacher

it is silly if you don't

because it's correct

[silent stratus]

Tomorrow is exam , but in (ncert) school bookin 2-3 ques we just expanded rha and it is correct , this is extra book

[carmine yacht]

after it you just sum it up

and you get x3+y3+z3-3xyz

[silent stratus]

Ok I will ask few of my Friends if we can just expand rhs

Thanks for guidance

[carmine yacht]

np, dm if you have questions

[silent stratus]

.close

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[remote steppe]

I am getting 21 ss the answer

[livid hound]

can you show your work/reasoning

[tropic oxide]

you set aside Rs. 17 for one of each but afterwards you don't need to buy full sets of one of each

you could try to be greedy about it and buy as many of the most expensive ones as possible

(total has to be EXACTLY 120 though)

[remote steppe]

fot

got

it

ans is 17

thank you

.close

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[remote steppe]

.reopen

[cedar kiln]

✅

[remote steppe]

nvm

.close

[cedar kiln]

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[sly bison]

hi guys can anyone help me out

[mild spear]

What have you tried?

[sly bison]

i dont really understand much of anything tbh

im stuck in first question

[mild spear]

Alright,
Do you remember cosine rule?

[sly bison]

uh

whats that again?

sorry 😭

[mild spear]

cos C = (a^2 + b^2 - c^2)/2ab

[sly bison]

ohh yeah i didnt know that

[mild spear]

You could use it to calculate the length of AB, since other sides are the radius of a circle

[sly bison]

ohh okay

can you please guide me through the process?

[mild spear]

Cos 2theta = (r^2 + r^2 - AB^2)/(2 * r * r)
I think you'll also need trigonometry identities like 1 - cos 2theta = 2sin^2 theta.

[sly bison]

okay so cos 2theta just leaves us with -AB²

[mild spear]

You need to simplify it such that AB is in the form of theta and r. Just take everything except AB on one side and AB on the other side.

[sly bison]

so like

AB = √(2r² - 2r²cos2theta)

[mild spear]

Yeah, now take 2r^2 common and put formula for 1-cos2theta

[cedar kiln]

@sly bison Has your question been resolved?

[sly bison]

okay so we get 2r sin theta

thank you sm

[mild spear]

Correct.

Ist is done

[sly bison]

yeah but can you also help me out with part 2

🙏🙏

[mild spear]

Yeah you got the straight length of AB and now you need to find the arc length of AB.

Do you remember the formula to find the arc length given the radius and angle

[sly bison]

π × r × (theta/π)

?

[mild spear]

angle (radians) = arc length/ radius

[sly bison]

so the arc length is r × 2theta

right?

[crimson sedge]

yes

[sly bison]

ooo okok then what?

[crimson sedge]

so arc length is r x 2theta

you found the chord

and their sum is the perimeter right?

[sly bison]

ohh

right

okay i figured out the rest

thank you guys so much for your time and effort

[crimson sedge]

np

gl

[cedar kiln]

@sly bison Has your question been resolved?

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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[twin raptor]

hii can i get help with solving and fact checking my homework cough

[fossil dawn]

sure, just send it over!

[twin raptor]

THANK YOU BRO

hold on

what the freak do you do with chord BR i am so confused

also i dont know if RL is correct

i just assumed they were 6.25 and divided 12.5 by 2 bcuz BA and AL are both 5

[fossil dawn]

i'm not the best at geometry, esp not when power of a point is involved, but i don't see RL = ER anywhere, which you implicitly assumed

[twin raptor]

yepp

[fossil dawn]

then again, you might be saved by power of a point, so i'm going to step back and let someone who actually knows that talk about it

[twin raptor]

the only thing said is that EL is 12.5 unfortunately, same with chord BR

[twin raptor]

no worries

i also have a bunch more of stuff in my homework that im not sure abt

let me send them rq hopefully someone who knows geometry can see

[twin raptor]

can someone help me cough cough its all abt geometry 🥀🥀

[opal hinge]

uhh

which one

[opal hinge]

okay so what do you know about power of a point

[twin raptor]

uh this one first

[twin raptor]

none in our school curriculum i dont think its taught

i live in the philippines so uhm

[opal hinge]

This uses power of a point anyway

[twin raptor]

or maybe i just dont listen to my teachers, but lowkey though i dont think the power of a point has actually been mentioned at all so far

[opal hinge]

oh wait

what about

[twin raptor]

theorems have been introduced though

[opal hinge]

Ptolemy's theorem

[twin raptor]

nope unfortunately, unless its been named diff here in my country

hold on

these are the theorems that were taught to us this week

[opal hinge]

yeah

[twin raptor]

maybe ptolemys theorem was just renamed to be easier idk

[opal hinge]

that's power of a point

[twin raptor]

LEGIT?

[opal hinge]

it is

[twin raptor]

DEAD ASS? bro i swear these things are NOT taught to us

[opal hinge]

https://artofproblemsolving.com/wiki/index.php?title=Power_of_a_Point_Theorem

[twin raptor]

like in depth

stuff is just handed to us but not explained further

[opal hinge]

xD

I had to prove this thing when i was 9th grade

[twin raptor]

bro im grade 10 this is so embarrassing

the stark difference between a 3rd world country's education and im assuming a 1st world country person's educational system?

anyways please continue cough

[opal hinge]

okay just take a look at this

$LR\cdot LE=LA\cdot LB$

[wraith dagger]

Alexis_Fx

[twin raptor]

yeah thats what i did

[opal hinge]

I'm Vietnamese

[twin raptor]

omg asian

hi fellow asian

[opal hinge]

southest asian

just like you

[twin raptor]

idk its just not taught in the philippines man

maybe the vietnamese curriculum is better unfortunately

specifically in the math sector

[opal hinge]

tbh i don't like math that much

[twin raptor]

but yh this is what i did tho, i divided 12.5 in half to get the LR part

[opal hinge]

yeahhh

okay so you have LR

[twin raptor]

thank god its correct lol

although another problem is that WHAT THE FUCK do you do with chord BR

[opal hinge]

xD

BR=BS+SR

right

[twin raptor]

just like me fr!

[opal hinge]

And we want BS*SR

[twin raptor]

hell yeah bro

[opal hinge]

so

$BR=BS+SR \Rightarrow BS=BR-SR$

[wraith dagger]

Alexis_Fx

[twin raptor]

how do you cut BR's value(which is 7) in parts

[opal hinge]

$BS\cdot SR = SR\cdot (BR-SR)$

and what's BS*SR equal to

[wraith dagger]

Alexis_Fx

[twin raptor]

but how do you subtract BR with SR though when you dont know how to put 7 into parts

because BS and SR value overall is 7

[opal hinge]

well, B,S,R should be collinear

[opal hinge]

yeah

BS+SR=BR

=7

[twin raptor]

ooo so i should divide 7 by 2 then?

[opal hinge]

nah

[twin raptor]

explain this is baby goo goo ga ga terms

[opal hinge]

BS and SR aren't necessary equal

I mean BR is cut into to part BS and SR which we don't know the length of both

but since it cut from it so BR=BS+SR

like

5 is cut into 2 and 3

[twin raptor]

yeah thats honestly the problem lmao so im kinda stumped on what im going to do with chord BR aka value 7

[opal hinge]

so 3+2=5

[opal hinge]

yeah this's what you do

[twin raptor]

so you're saying the value of 7 when cut into parts might be 4 + 3

[opal hinge]

yes

or 2+5=7 or smth like that

[twin raptor]

oofff this is hard ngl bcuz like which order

ngl i might need to fuck around and find out w this

[opal hinge]

<@&268886789983436800>

[fossil dawn]

<@&268886789983436800>

[opal hinge]

uhh you don't need order

[opal hinge]

but yeah you should try first

[twin raptor]

7 = SR(7-SR)? SR is unknown

[opal hinge]

yeah

We solve for SR

[twin raptor]

im just plugging in values meow

[twin raptor]

alright i'll try it lmao

tysm!

[opal hinge]

hey,...would you mind taking my place helping her

I suppose to study for the SAT

[twin raptor]

gl on ur sat g

alr im done w the math number 4 thing im lowkey needing a person to fact check stuff on my homework bcuz i am NOT confident in my own work

can someone fact check this please fkrbtjebdwkadb

wait nvm i think i got it

ty everyone that helped meow

.close

[cedar kiln]

Channel closed

Closed by @twin raptor

Use .reopen if this was a mistake.

[grave osprey]

r≠7

oh it's closed

[twin raptor]

wait

pray tell

what do you mean by that

[grave osprey]

.reopen

[twin raptor]

.reopen

[cedar kiln]

✅

[grave osprey]

i might be wrong but don't u use the same thing w tangent to the secant r?

[twin raptor]

fr?

[grave osprey]

$6^2=(r-5)(r)$

[wraith dagger]

Kaladin.

[grave osprey]

#help-13 message check the one w tangent

[twin raptor]

OHHHHHH SO I CANT USE THE 3 I USED IN THE TANGENT/FINDING Q PART IN THE FINDING R PART?

so like 3 shouldnt be used in the secant part then

but then what will i use if theres no 3?

wait im so confused hold on

[grave osprey]

there are two secants; one that is q+3 and the other is r

3 is the part of the former secant

[twin raptor]

whats the former secant?

[grave osprey]

q+3

[twin raptor]

so the finding q part?

sorry for the dumb questions btw i suck at math so please bare with me cough

[grave osprey]

well translating it to ur q, we get AB =R , AD=R-5, DB=5, and AC=6

[twin raptor]

im kinda confused hold on

let me make

a diagram

im getting confused by the line names like A and etc. bcuz my copy doesnt have a name for the lines

[grave osprey]

u can label them

[twin raptor]

like this

[grave osprey]

mhm

[grave osprey]

can you label the first intersection of the secant r with the circle?

both actually

[twin raptor]

wait how im kinda confused because intersection would be like four lines crossing each other or like roads meeting at a point

unless my understanding is wrong

bro im so fucking confused i hate math sm 💔💔💔💔

[grave osprey]

well not necessarily lines

[twin raptor]

what do you want the label to be and can you point out the intersection

[grave osprey]

D and C are the points where the lines intersect the circumference of the circle

[twin raptor]

okay so you mean touch when you say intersect lmao

[grave osprey]

well yeah

kinda

[twin raptor]

okay i got confused there lmao

okay so what do you want me to label them as?

[grave osprey]

whatever

F and G or smth

[twin raptor]

wait its already labeled with a letter though

C and D are the labels

[grave osprey]

well there is another line

R

[twin raptor]

OHHH

alright makes sense mbmb

[grave osprey]

buddy there is one more😭

in AE line

[twin raptor]

OH YEAH wait hold on

there

[grave osprey]

okay

[twin raptor]

also please bare with me im not that good with math AT ALL

[grave osprey]

AE+EF=AF right?

[twin raptor]

yep

[grave osprey]

AE=AF-EF hence is also right

AE=r-5

[twin raptor]

yeah, but the problem is that i dont know what i can subtract with 5 to get the missing external/outer segment and THEN get r

unless theres an easier way that i dont know

[grave osprey]

Now, applying the power of a point theorem we get $\
AC^2=AF \cdot AE \implies \
6^2=r(r-5)$

[twin raptor]

omg wait thank u

holy fuck i made it harder for myself lmao

[wraith dagger]

Kaladin.

[grave osprey]

okay it's fine

[twin raptor]

so wait all this time they were all tangents

[grave osprey]

np

[grave osprey]

only AC

[twin raptor]

yeah but like i didnt think enuff

that i could actually use AC once more

[grave osprey]

you can do it w secants as well!

q=9

[twin raptor]

instead made it harder for myself by using secant secant power theorem after 🥀🥀🥀🥀

the power of the point in my country is differently named btw if ur confused on what im yapping abt

TYSM AOJGWJGBJGNE

thanks jinx never knew jinx from arcane was actually goated in math

.close

[cedar kiln]

Channel closed

Closed by @twin raptor

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[opaque sedge]

can someone verify this in 2x2 matrix because i am getting |AB| not equal to |A||B|

[chilly warren]

What matrix A B such that
|AB| ≠ |A| |B|

[opaque sedge]

i don't know

oh

i know actually

[opaque sedge]

there are infinte solutions to not equal to

[chilly warren]

Can you show me one?

[tropic oxide]

show at least one

[chilly warren]

In fact, a relatively short algebraic manipulation shows that in at least 2x2 matrix, the equation holds.

At least in element being part of commutative rings, which is more lax than the usual matrix requirement that the elements are a part of a field.

[opaque sedge]

|AB| has 6 terms
and |A||B| has 4 terms
equating those two will cancel 4 terms
and we will left with 2 terms = 0

[chilly warren]

|AB| has 6 terms?

[opaque sedge]

yeah for 2x2 matrix

[chilly warren]

Show me the terms

[opaque sedge]

oh sorry it has 8 terms

[chilly warren]

And you should notice that some or them are actually identical, with opposite signs.

[opaque sedge]

,r

,rotate

[chilly warren]

,rccw

[chilly warren]

And $a_{11}b_{11}a_{21}b_{12} - a_{11}b_{12}a_{21}b_{11} = 0$

[opaque sedge]

ahh

u r right some terms |AB| canceled with itself

[wraith dagger]

Xwtek

[opaque sedge]

wait a minute

$|AB|=|A||B|\newline$
$|A||B|=|B||A|\newline$
$|B||A|=|BA|\implies |AB|=|BA|\implies AB=BA?$

[wraith dagger]

Aditya

[last apex]

the last implication is false

[chilly warren]

Nope, determinant function isn't one-to-one

But, yes |AB| = |BA|. It just doesn't imply AB=BA

[opaque sedge]

ok

[rugged sluice]

hi

[opaque sedge]

hi

.close

[cedar kiln]

Channel closed

Closed by @opaque sedge

Use .reopen if this was a mistake.

[rugged sluice]

hru

:3

[cedar kiln]

Available help channel!

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• Show your work, and if possible, explain where you are stuck.
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[opaque sedge]

im good

[opaque sedge]

oops

.close

[cedar kiln]

Channel closed

Closed by @opaque sedge

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[tranquil oracle]

!status

[cedar kiln]

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

[remote steppe]

no idea what to do

[tropic oxide]

speed = step size * step rate

[tranquil oracle]

you need to compare speeds, there's a natural unit of time and unit of distance to use to compare to

[tropic oxide]

step rates ratio is 5 : 6 : 7 as given directly by the question but you have to think a bit more about the step size ratio

[tranquil oracle]

(or for the method I'm suggesting)
for time, you have "amount of time cat A takes 5 steps"
for distance, you have "distance of 6 steps for cat A"

[frosty creek]

Comparison of step lengths and number of steps are given

Can find distance using the 2 values

And then compare to get ratios

[remote steppe]

!?

[tropic oxide]

ok so maybe you should name 1 person whose instructions you want to follow and listen to that person only

what is wrong?

[tranquil oracle]

don't worry about the other two of us, we probably can find other things to do if you don't need us

[remote steppe]

let me google

[frosty creek]

Dont worry bro

[remote steppe]

there you go

[frosty creek]

@tropic oxide @tranquil oracle can you see the spain im feeling with s silent

[tropic oxide]

.......

[remote steppe]

lol

[tropic oxide]

this was not Google

this was chatGPT

[remote steppe]

yes its gpt..
i just wanted to randomly select one

[frosty creek]

All for one, one for all

[tropic oxide]

you do not need gpt for that

[tranquil oracle]

you know what, just go with Ann ig

at least there was a selection

[frosty creek]

Atleast chatgpt was clear about the person

😔

[remote steppe]

sorry

[frosty creek]

The only thing that matters is understanding the solution

[tropic oxide]

ok like look

do you want to go along with my suggestion or not @remote steppe

[modest escarp]

lmao not good practice for selecting randomly

[tropic oxide]

yes or no question

[wicked mantle]

[remote steppe]

yes go

[frosty creek]

I would’ve asked chatgpt for the solution instead

[tropic oxide]

speed = step size * step rate
step rates ratio is 5 : 6 : 7 as given directly by the question but you have to think a bit more about the step size ratio

[tranquil oracle]

!noai

[tropic oxide]

!nogpt

[cedar kiln]

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

[tranquil oracle]

||oh wait it's called nogpt oof||

[frosty creek]

Alright lets stip

Stop

Let her explain

[modest escarp]

assign each person a number from 1-3, randomly generate integer from 1-3, and then you can be much more confident in the randomness of the selection

[remote steppe]

i thought it selected a random person..i didn't speak and read correctly

go ann

now i am fully there

?

[tranquil oracle]

basically do this

[remote steppe]

can you give me an example

i don't get it

[tropic oxide]

i walk at a rate of 2 steps per second and each of my steps is 0.8 meters long, therefore my walking speed in m/s is?

[remote steppe]

ok..
2×0.8 =1.6 m/s

[tropic oxide]

yeah see. so you understand the principle?

difference is that we are not given step rates or sizes in any familiar unit but only their ratio relative to each other.

[remote steppe]

speed = Distance/Time

is that needed here?

i think yes

.close

[cedar kiln]

Channel closed

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[tranquil oracle]

are you replying to someone

[frosty creek]

Side effects of perma studying, nothing else

[tranquil oracle]

yeah larger than equal would be more likely

what's the problem?

[odd verge]

Are you asking for the probability to roll higher than 1?

[tranquil oracle]

what are the two dice

[floral arrow]

Show your calculation

[tranquil oracle]

are both fair dice with 1-20 on the faces?

[floral arrow]

Can

you

[tranquil oracle]

until 0/20

[floral arrow]

please

make

full

sentences

[tranquil oracle]

no, probability does not work like that

[slender atlas]

there's immediately a problem after the first two fractions. you will find that the first two fractions sum to 37/20, which is more than 1.

[floral arrow]

I think it's fine for now

Unless that's the end of the argument

[tranquil oracle]

let me guess what happened ||average out to get 10/20 mistakenly multiply by 20 terms when there's only 19, and put in a divide by 20 and get 1/2 exactly||

is it resolved?

[floral arrow]

No

[tranquil oracle]

where did you get 9 from

[floral arrow]

1+2+...+19 = 190

[tranquil oracle]

9 pairs means 18 terms

1 to 19 has 19 terms

also why 9 * 9.5?

no it isn't, the left is an integer and the right isn't

[floral arrow]

Remembering the triangular number formula would make your life a lot easier

Yes

[tranquil oracle]

yeah

faster way

1/20 chance of same roll
otherwise P(i roll strictly higher) = P(you roll strictly higher)

[floral arrow]

Instead of doing 1+...+18 + 19 = 9*19 + 19 = 10*19 = 190
just do 1+...+19 = 19*20/2 = 19*10 = 190

[tranquil oracle]

P(you roll strictly higher) + P(i roll strictly higher) + 1/20 = 1
2*P(you roll strictly higher) + 1/20 = 1
solving, you get 19/40

[cedar kiln]

Channel closed

Closed by @austere garnet

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[slender atlas]

hi, this channel is not yet open, by the way.

[cedar kiln]

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[cedar kiln]

Channel closed

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[fervent arch]

i have a question about bayesian stats

[indigo lagoon]

yes post plz

[fervent arch]

If I have a coin and I say, 'I think the probability of heads is 50% and tails is 50%', and then I toss the coin and observe the sequence H H H H T, what is the updated probability of heads and tails?

Is this question different from the following: 'I think the probability of heads is 50% and tails is 50%', and I know that in a series of tosses I got 4 heads and 1 tail?

Basically, my question is: in the first case, we shouldn’t include the binomial coefficient in the likelihood function, but in the second case, we should, right? Because in the first case we observed an exact sequence.

[slender atlas]

from my very limited knowledge, it sounds correct.

[indigo lagoon]

If I have a coin and I say, 'I think the probability of heads is 50% and tails is 50%', and then I toss the coin and observe the sequence H H H H T, what is the updated probability of heads and tails?
I'm not sure if you wanna determine the probability solely by the result of these 5 cases, but if you wanna do it and there could only be H or T two consequences, the probability would be 80% of head and 20% of tail.

Generally we don't determine, take this case for example, the coin's probability with just 5 flips.

[flint cape]

The search term for what I think you're trying to describe is "hypothesis testing"

[indigo lagoon]

There is no trace of that in this question

[fervent arch]

i want to determine the posterior probablity of getting heads, knowing that the posterior probability is 50%, knowing that i got H H H H T..

[slender atlas]

I think OP is referring to this in the context of Bayesian statistics, which has a little bit of a different set of rules.

[flint cape]

oh wait Bayesian, well shit

[fervent arch]

and i also want to determine the posterior probablity of getting heads, knowing that the posterior porb is 50% knowing that in a sequence of tosses i got 4 H and 1 T ( in no particular order ) i just know that

[slender atlas]

doesn't it depend on what prior you are using? sorry if I'm not being insightful here.

[lyric plank]

the prior they indicated was Bernoulli(.5)

[lyric plank]

it might not seem like it, but you actually get the exact same result whether or not you add them together

P(that sequence |p) = p^4 (1-p)

P(4 heads and 1 tail |p) = 5C4 * p^4 (1-p)

up to a proportionality constant, these are the same

P(p| data) = P(data |p) P(p) / P(data), where P(data) is simply a normalizing constant that absorbs constants from the top

[slender atlas]

sorry for intruding again, but doesn't using a Bernoulli prior mean that the posterior probability still takes the coin as fair?

[lyric plank]

the posterior is proportional to p^4 (1-p)

on (0, 1)

so the posterior takes p as Beta(5, 2)

ah wait my bad

you're right

the prior is perfectly deterministic

i misread the question

i guess let's pretend the prior is nondegenerate

regardless, it doesn't matter if we take the data as a sequence or use the sum of the data, because the sum is a sufficient statistic

[fervent arch]

Ok thank you to both of you!!!

so it is a different question but the result will be the same

[lyric plank]

yes, for any prior

[fervent arch]

thank you!!!

[lyric plank]

just in general though make your priors non degenerate

or else like Lute pointed out its pointless

[cedar kiln]

@fervent arch Has your question been resolved?

[cedar kiln]

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[wide sequoia]

Hey, This is probably going to be a weird request sorry in advance.

I am struggling with Algebra 2 and a bit of Algebra 1. If I can get some help to comprehend it better it'd be much appreciated.

[slender atlas]

this is a rather broad request. are there specific questions you're struggling with?

[wide sequoia]

I don't have a specific question I am struggling with.

[dire geode]

do problems then

[wide sequoia]

That's the issue it doesn't click.

[lost wigeon]

[slender atlas]

then do you have examples of questions where it doesn't click?

[dire geode]

what is "it"

[lost wigeon]

🪱

[wide sequoia]

alge 2

[chrome elk]

We are happy to help you with specific problems

[lost wigeon]

Worm

[chrome elk]

But we can't exactly help you with the entirety of alg2

[dire geode]

see
#help-13 message

[lost wigeon]

I like worms

[chrome elk]

!redir

[wide sequoia]

tha's-nice

[cedar kiln]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[wide sequoia]

np

[chrome elk]

For that you could hit up the topic specific channels

But if you have questions we can help you with those

[wide sequoia]

Thanks.

[slender atlas]

so is there anything else we can help you with?

specific questions only, please.

[wide sequoia]

No, there's no other questions I have.

[slender atlas]

alright. please remember to close this channel when you're done.

[wide sequoia]

How-do-I-do-that?

[dire geode]

!done

[cedar kiln]

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

[wide sequoia]

.close

[cedar kiln]

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[cedar kiln]

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[round willow]

Can someone tell me how to obtain the function of this tan graph?

[slender atlas]

what have you tried, since the screenshot says that the answer is not correct?

[round willow]

I tried working it out with the y=Atan(Bx - C) + D but im pretty sure im doing it wrong

[slender atlas]

for future helpers: please show what your previous answers/attempts were.

maybe others could help diagnosing the issue with your approach.

[gray hamlet]

why try to do it

[round willow]

wdym

[gray hamlet]

i mean it should be hard

there is no c and d

only a and b

[round willow]

Yeah and somehow im still getting it wrong

[gray hamlet]

B is easy

try to find out the period

[round willow]

Got it

pi

[gray hamlet]

yea

[round willow]

ok thank you

.close

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[crimson sedge]

Hi. Would the answer for part 1 a simply be Binomial Distribution?

[ancient lodge]

Yes

they may want you to specify n and p though

[crimson sedge]

Oh, like X follows a Binomial Distribution(31, 0.447)

[ancient lodge]

good

[crimson sedge]

The question asks us to do it in R. I am wondering if it is that I should graph it

I may have to ask the teacher

[ancient lodge]

[crimson sedge]

Thank you. I am going to work on them now

.close

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[torpid ginkgo]

if you see a symbol on both sides of an = sign you can cancel it out?

[hard thistle]

usually lol

[oblique flare]

Depends

[hollow trail]

context?

[long swan]

Like α = α implies 1 = 1 so that's correct, you can cancel it. But if you have dy = dx you can't really cancel the d's and say y = x (actually you can, but it's not dividing)

[oak anchor]

what do you mean

like $a+b = a+c \Longrightarrow b = c$ ?

[wraith dagger]

Médicis

[silk gust]

another example is if you have sin(x)=sin(y), x can equal y but that isn't the only solution

[cedar kiln]

@torpid ginkgo Has your question been resolved?

[torpid ginkgo]

Give me a sec I have to read

[night wedge]

Do you have a question in particular where you want to cancel out both sides?

[cedar kiln]

@torpid ginkgo Has your question been resolved?

[torpid ginkgo]

depends on what

here is an example

[night wedge]

Is mu_k a function?

If so then you can’t cancel m

[torpid ginkgo]

what is the underscore for?

[night wedge]

$\mu_{k}$

[wraith dagger]

BBMaths

[night wedge]

Subscript

Lower down text

[torpid ginkgo]

that's the coefficient of kinetic friction

[night wedge]

Then the brackets here are not needed, so you can cancel out the m’s

[torpid ginkgo]

what determines whether or not they can be cancelled out

[night wedge]

When you “cancel out”, you could be meaning many different things.
In the example you gave above, cancelling out the m’s is fine because one thing we can do to an equality of numbers is divide both sides by the same thing.
So if we divide both sides by m, we end up with the equation without m’s

So cancelling out is just like adding/subtracting/multiplying/dividing, squaring, square rooting etc. both sides of the equation

Although if you square both sides, you might get extra unintended solutions to equations

[torpid ginkgo]

give me a sec

one more question

6.89=2.13-Ff

how do I isolate Ff

im rusty on the algebra and keep making these kinds of mistakes in my studying

[night wedge]

Add Ff to both sides

[torpid ginkgo]

and then what do I do with the 6.89

subtract it?

I kept doing that and getting the questions wrong

[cedar kiln]

@torpid ginkgo Has your question been resolved?

[night wedge]

Then the equation you gave was wrong

[torpid ginkgo]

I did that and it worked

[cedar kiln]

@torpid ginkgo Has your question been resolved?

[north wyvern]

if and only if its an injective function

https://en.wikipedia.org/wiki/Injective_function

and to show its injective, we essentially just assume f(x_1)=f(x_2) and we prove x_1=x_2

[north wyvern]

to be precise, this happens because there is a left inverse, but thats a bit abstract

to clarify, there is some other function g which has: g(f(x))=x

then we can 'cancel' the f

[pastel vault]

these are all numbers, so talking about functions isn't relevant

so you can divide m on both sides, as long as m is not 0

but in the context of physics, you can't have mass = 0

so $a = \mu_k g$ is perfectly valid

[wraith dagger]

south

[cedar kiln]

@torpid ginkgo Has your question been resolved?

[cedar kiln]

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[carmine sorrel]

Can someone please explain me why my method is wrong?

Answer given is 6

I got 6 from a diff method(integrating factor method)

[sour tundra]

$\frac{d}{dx}{\int_1^x f(t) dt}$ is $f(x)-f(1)$ instead of $f(x)$