help-17

[leaden crane]

can we go back to this one?

[bitter pilot]

ok..

[leaden crane]

i wanna learn how to do this one with the FTC or whatever, i want to understand it without just removing the integrals and derivative

[bitter pilot]

Now try to rewrite it using FTC

you only know that we call the antiderivative F(x)

so using FTC

[leaden crane]

so we find the anti derivative of sintcost

[bitter pilot]

we simply plug in the bounds

forget the what

we dont care what the antiderivate is

[leaden crane]

[bitter pilot]

we just know there is one and we call it F(x)

Now the first step is to apply FTC which just means to plug in the bounds into the antiderivate F(x)

[leaden crane]

so sin(2)cos(2)?

i'm so lost

[twin meteor]

𝔸dωn𝓲²s

[bitter pilot]

F(x) is my antiderivative and my bounds are 2 and x

[leaden crane]

oh yeah first term is x cus it's on top

[bitter pilot]

that's

it

50%

that's FTC

you plug in the bounds

as usually

[leaden crane]

but like what does F(x) actually mean?

it that just sin(x)cos(x)

or what

[bitter pilot]

F(x) is antiderivative of sin(x)cos(x)

f(x) = F'(x) = sin(x)cos(x)

does this make more sense?

[leaden crane]

kinda

but how would i find the antiderivative of sin(x)cos(x)

[bitter pilot]

you dont need it that's the thing

[leaden crane]

what

[bitter pilot]

because you are differentiating now

X)

[leaden crane]

????

[bitter pilot]

????

[leaden crane]

i dont even know anymore

[bitter pilot]

Don't you want to find F'(x) or am I completely missing the point

[leaden crane]

i have no questions, i'm just lost

i don't know what i need to find

[bitter pilot]

You just posted this

What's like the text

of the task

[bitter pilot]

???????

1st grade shit

reading

[leaden crane]

i understand i need the derivative

but i just don't know what to do to find it

[bitter pilot]

so F'(x)

[leaden crane]

i'm so screwed

[bitter pilot]

BRO

just listen

1st step:

[twin meteor]

𝔸dωn𝓲²s

[leaden crane]

i'm literally trying everything to understand, it's just not making sense at all

[bitter pilot]

Now differentiate both sides

[leaden crane]

i don't understand what F(x) and F(2) are equal to

like what

[bitter pilot]

To the integral

of sintcost 2 to x

[leaden crane]

sin(x)cos(x) - sin(2)cos(2)?

[bitter pilot]

NO

sin(x)cos(x) is not the antiderivative

we dont know the antiderivative and don't need it

[leaden crane]

?????????

we need the antiderivative, then dont?

[bitter pilot]

i suggest to just look

[twin meteor]

𝔸dωn𝓲²s

[leaden crane]

that makes absolutely no sense to me

what the hell

why can't i understand this

you make it sound so simple but god damn

[bitter pilot]

Imagine

f(x) = x²

You only know the antiderivate is called F(x)

[twin meteor]

𝔸dωn𝓲²s

[bitter pilot]

Don't actually integrate

[leaden crane]

i don't even know how to solve integrals anymore my brain is just gone

[bitter pilot]

[leaden crane]

just x^3/3

idk

[bitter pilot]

And I just said don'T actually integrate

Ok you leave no choice

You won't be able to integrate this as e^-x^2 is not integrable

Now what

you are stuck

[leaden crane]

yeah

[bitter pilot]

still there is a way

FTC

actually lemme adjust it

[twin meteor]

𝔸dωn𝓲²s

[bitter pilot]

The only thing that you can do is plug in the bounds

[leaden crane]

put x and 0 in for t?

idk

[bitter pilot]

no

[leaden crane]

im so confused

[bitter pilot]

use the theorem

[twin meteor]

𝔸dωn𝓲²s

[leaden crane]

idk what the theorem means

[bitter pilot]

you have eyes

[leaden crane]

i don't undesrtand the F(x) - F(0)

that makes no sense

[bitter pilot]

dw

just accept it

sometimes you have to keep moving

[leaden crane]

ima accept i fail this class

good lord

[bitter pilot]

no

keep moving

you wanted that A

now you do what it takes

You are literally using it all the times

[leaden crane]

ok so i just do F(x) - F(0)

[bitter pilot]

yes.

[leaden crane]

now magic happens and it gives me the right answer

yay

[twin meteor]

𝔸dωn𝓲²s

[bitter pilot]

That's fundemental

we just plugged in the bounds as usual into the antiderivative

[leaden crane]

yes

[bitter pilot]

Now since that is equal

Then that is also equal

[twin meteor]

𝔸dωn𝓲²s

[leaden crane]

indeed

[bitter pilot]

even if it's counterintuitive

Now we differentiate both sides becauseeeee we want to find F'(x)

[leaden crane]

yeah

[severe estuary]

bro

this is still going on?

damn

[twin meteor]

𝔸dωn𝓲²s

[leaden crane]

that makes a tiny bit more sense

[bitter pilot]

yea let that sink in

Because when you do this

[twin meteor]

𝔸dωn𝓲²s

[leaden crane]

i see

[bitter pilot]

But the thing is

sometimes either the antiderivative is too lengthy and complicated to calculate or not even integrable, or you are given 5 minutes which would make it impossible to calculate the antiderivative in the first place, since you are not supposed to

That's why we simply denote the antiderivative as something else, here capital F and just plug in the bounds

it's just a little more abstract but that's it

It's like a definition basically

[leaden crane]

okay so with this one

I just do $F(x^2) - F(\pi)$

[bitter pilot]

integral from a to b of f(x) means to plug in the bounds b and a into my antiderivative F(x)

[twin meteor]

Someone

[bitter pilot]

G* technically but yes

[leaden crane]

screw G

[bitter pilot]

yea ok

[leaden crane]

lmao

[bitter pilot]

now differentiate

to find G'(x)

[twin meteor]

Someone

[bitter pilot]

no

[leaden crane]

fu k

thought i had it

[bitter pilot]

first things first mam

[twin meteor]

𝔸dωn𝓲²s

[leaden crane]

so chain rule that bad boy

[bitter pilot]

yes

[twin meteor]

Someone

[bitter pilot]

OMG

you did it

[leaden crane]

after a hour? and maybe perhaps some tears shed

i finally did it

[bitter pilot]

but you did it straight up

I wanted to do a pre step

[leaden crane]

yeah

[twin meteor]

𝔸dωn𝓲²s

[bitter pilot]

but yea that's the idea

[leaden crane]

this is terrifying with the arcsin

[bitter pilot]

same shit x)

i just burned my tongue fuck tea

[leaden crane]

i literally did that with hot chocolate about a hour ago

😭

still burnt

okokokok F(x) - F(0)

i can ignore F(0) cus that stinks

so

i need to use the product rule?

[bitter pilot]

actually no

[leaden crane]

vcxzsafqwesrdtfygluhi;jokp,[l]

[bitter pilot]

F'(x) is literally the integrand

[leaden crane]

so just

[bitter pilot]

you twerp didn't even use product rule one sinxcosx

[twin meteor]

Someone

[bitter pilot]

yea

[leaden crane]

oh

ima go through a - h 100 times tonight until i get every single one without failure

[bitter pilot]

ok

well now you know the game

it all comes down to applying chain rule or product rule correctly

but yea try

[leaden crane]

do this one is just

$\sqrt{x} \cdot \arcsin(\sqrt{x})$

[twin meteor]

Someone

[leaden crane]

or am i bugging

i am indeed bugging

how in the hell does that magically appear

[bitter pilot]

what

you did it correctly

[leaden crane]

but the 1/2sqrt(x)

[bitter pilot]

derivative of sqrt(x)?

[twin meteor]

𝔸dωn𝓲²s

[leaden crane]

oh so wait

on the previous problem the derivative of x is just 1, so we didn't include that

oh

i se

ee

this one is scary

it's different

lol

i'm going slightly mentally insane

[bitter pilot]

that's the eeasist so far

that's also one where actually calculating the antiderivative may save your ass but dont

apply the game

[leaden crane]

que mi amigo

[bitter pilot]

huuh

[leaden crane]

how do i approach this one

[bitter pilot]

the same way

what is stopping you

[leaden crane]

F(x) - F(1)?

[bitter pilot]

xes

yes

indeed

what'd you get?

[leaden crane]

im confused again

😭

[bitter pilot]

cmon

i am going crazy

[leaden crane]

i am too

[bitter pilot]

what is happening

you did well

the most difficult ones

[leaden crane]

it's no longer multiplication

[bitter pilot]

and now you are failing at this easist

what

[leaden crane]

so my brain went die

[bitter pilot]

ignore

F(x) - F(1)

what is F'(x)

[leaden crane]

$3x^2+2x+1$

[twin meteor]

Someone

[bitter pilot]

that'S it

done

[leaden crane]

but what about F'(1)

[bitter pilot]

If you dont believe the magic

constant

[leaden crane]

oh

[bitter pilot]

if you dont beleive the magic

[leaden crane]

so constant = kill it

[bitter pilot]

you can actually calculate the integral and see for yourself

[leaden crane]

[bitter pilot]

OH NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

WE ARE DOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOMED

NO MULTIPLICATION

😭

[leaden crane]

😭 that's what my brain was thinking

[bitter pilot]

I would give you a C if I were your prof

😂

[leaden crane]

i would give myself a F if i was my professor

i honestly don't know how i've made it this far

[bitter pilot]

i know

[leaden crane]

it's so sad but it's so true

every test, i spend like 20 hours memorizing the questions on the practice test and pray

[bitter pilot]

that's why the school system is failing

[leaden crane]

same thing as last one but put 4x in for t

[bitter pilot]

same game

but see you made progress so far

[bitter pilot]

mimimimimimiimi

[leaden crane]

wha

thought i was big brain

i am smul brain

[bitter pilot]

same shit

dont look at the sol

yet

try it first

1st step?

[leaden crane]

F(4x) - F(1)

[bitter pilot]

very good

now differentiate

[leaden crane]

oh i did it right, but forgot chain rule

[bitter pilot]

at least you forgot it

that'S better than

"idk what i should do"

[leaden crane]

lol

can't you just write it as (12x+8x+1)(4) then throw the 4 in?

or am i that stupid

[bitter pilot]

4² = 16

16 * 3

[leaden crane]

oh yeah forgot the ^2

[bitter pilot]

so if you write it out then correctly

otherwise

-points

x)

but yea you can

but if you dont have dont

[leaden crane]

192x^2+32x+4

[bitter pilot]

makes it also easier to follow your steps

[leaden crane]

true

ln

[bitter pilot]

but'S that it

[leaden crane]

ok i think i can do this

hol up

[bitter pilot]

OHHHHH LNN

OH NOOO

[leaden crane]

1/x

1/x

1/x

I"M SO SMRT

fr

[bitter pilot]

?

?

?

NO

[leaden crane]

derivative of lnx is 1/x

[bitter pilot]

1st step?

[leaden crane]

F(x) - F(1) 😎

[bitter pilot]

2nd step?

excuse me

algorithm stopped working

i meant

now differentiate

that's how I programmed you

[leaden crane]

im an ai at this point

so it's just 1 + lnx

[bitter pilot]

yes

Let me reprogram you

1st step: Do 1st step.
2nd step: Differentiate.

oh wait

1st is recursive

stackoverflow

[leaden crane]

https://tenor.com/view/broken-the-mitchells-vs-the-machines-malfunctioning-system-down-mitchells-vs-machines-gif-21432279

[bitter pilot]

1st step: Use FTC (Exception if you fail: Just plug in the bounds)
2nd step: Differentiate.

[leaden crane]

gasp tanx

[bitter pilot]

have fun

[leaden crane]

(1+ln(tan(x))) * x

[bitter pilot]

1st step

almost but why * x?

[leaden crane]

cus chain rule

tanx

ohg

1

[bitter pilot]

what is the derivative of tanx mäm

[leaden crane]

im stupid

lmao

uhhhhhh

[bitter pilot]

tan(x) = sin(x)/cos(x)

so tan'(x) = [sin(x)/cos(x)]'

quick quotient rule

[leaden crane]

sec(x)^2

[bitter pilot]

yes

or 1/cos²(x) (ik you looked up)

[leaden crane]

i definietly didn't look it up

[bitter pilot]

https://tenor.com/view/bye-liar-uglass-stupid-you-lying-gif-4115028098834894483

anyway

so

trivially?

[twin meteor]

Someone

[leaden crane]

xD

[bitter pilot]

good

[leaden crane]

why can't latex just automatically do the \ in front when i do just tan

[bitter pilot]

we this we making it outta college

that's what you get from python

kindergarden language

[leaden crane]

😭

[bitter pilot]

everything is automatic with python lmao

print(😭)

[leaden crane]

last few problems before i go die for the night

[bitter pilot]

you got the idea

the game

is this not just difference quotient?

like

Given f with the interval [a,b]

then [f(b)-f(a)] / [b-a]

average value

[leaden crane]

so like

[bitter pilot]

ah no nvm

[leaden crane]

was about to say that's too easy

[bitter pilot]

It's

[twin meteor]

𝔸dωn𝓲²s

[leaden crane]

oh good lord

1/pi-0

[bitter pilot]

You just need to know how to integrate

those are all trivial integrals

for (f) though if you fail

use power rules

[twin meteor]

𝔸dωn𝓲²s

[bitter pilot]

I gotta go sleep x)

But I believe you can do this easily, should be more familar x)

[leaden crane]

yeah doesn't seem to bad

[bitter pilot]

google is also a good friend x)
good night x)

[leaden crane]

good night!!!! tytytytytytyty for the help <3

yeah this problem easy as hell

pog

i did it first time

hell yeah

.solved

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[dim bobcat]

I tried to check this against other proofs online, but they all mention something called an index. Idk what that is but is this proof fine?

[sly sierra]

yea this seems fine

the key facts are that the cosets partition G and are all the same size

[dim bobcat]

alright cool

[sly sierra]

the index is n in this case, btw

[dim bobcat]

I did that proof earlier but I actually don't know if I did it correctly though

[dim bobcat]

oh that helps a lot

I see

this is what I did for that proof

5.12 was showing $\phi: H\to aH; \phi(a)=ah$ is a bijection

[sly sierra]

yep as long as you have that there's a bijection, that gives you that they're the same size (cardinality)

[twin meteor]

Juke | ping me if no response

[dim bobcat]

alright

nice

Lastly, I think this is fine but

any thoughts?

for injective, idk if I can add them like that actually

I might do = and then multiply inverse on the right instead...

[sly sierra]

you're using additive notation, but G isn't assumed abelian

[dim bobcat]

one moment then

[sly sierra]

actually you're mixing product and additive notation

with ah - bh

[dim bobcat]

i see

and these aren't even rings so idk how that makes sense

[sly sierra]

i would just do ah(bh)^-1

[dim bobcat]

what about this

[sly sierra]

sorry i actually have to take off, i have something in the oven and the timer just went off haha

[dim bobcat]

No prblem

[sly sierra]

you can ping me if you want and i can take a look later

[dim bobcat]

alr np

I think it's fine tbh

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[thin bramble]

I don't know where to begin.

[thin bramble]

is there a way to calculate that by hand?

[heavy yoke]

do you know what kind of sum this is?

[thin bramble]

its the sum that I got by doing a AR model

[heavy yoke]

there is a name for this type of sum, of a constant raised to the power of the index variable

[thin bramble]

sorry I didn't know

[heavy yoke]

it is called "geometric"

we have a formula for geometric sums

[thin bramble]

oh could you tell me? sorry im really stuck

[heavy yoke]

,, \sum_{k = 0}^n a r^k = a \ab(\frac{1-r^{n+1}}{1-r})

[twin meteor]

pnoןɔ

[heavy yoke]

so you just need to find what $r$ and $a$ are for this particular sum

[twin meteor]

pnoןɔ

[vocal sleet]

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[ornate marlin]

how do i convert this into a definite integral? i have the answer but i just don’t know the process :d

[ornate marlin]

i know the formula

[finite mist]

Then just substitute them in

[ornate marlin]

thats the part i cant seem to do

[finite mist]

Hmm

you have the answer right

[ornate marlin]

yeha

i tried reversing it too

[finite mist]

one way to learn is to try to reversing it

can u send the answer here

[finite mist]

The answer is 2x/(1+x^2) ?

Hmm, my answer doesnt match it

[azure viper]

log(1+x^2)

And is log2

[ornate marlin]

i need help w this one

not that

[finite mist]

@ornate marlin

This?

[scenic ravine]

hmm, maybe divide by n^2

[ornate marlin]

why is the n in (i/n)^2 squared as well

isnt it i^2/n

since u only took one n out

[ornate marlin]

but if i do then wont the delta x will be weird

4/n^2

[scenic ravine]

true

that's what's troubling me too

[ornate marlin]

[left lichen]

yup

its right

[ornate marlin]

what happened to the n

[left lichen]

hold on

[ornate marlin]

okay

[left lichen]

Thats what he did

@ornate marlin

[ornate marlin]

ahhh i see

thank you so much!

[left lichen]

:)

[ornate marlin]

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[opaque grotto]

no idea

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@opaque grotto Has your question been resolved?

[opaque grotto]

<@&286206848099549185>

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[short notch]

If tan 4 theta can be expressed as 4tan theta - 4tan^3 theta / 1 - 6tan^2 + tan 4 theta

What are the roots are y^4 + 4y^3 -6y^2 - 4y +1 =0

I'm so confused not sure what to do

[vocal sleet]

@short notch Has your question been resolved?

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@short notch Has your question been resolved?

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[woeful tinsel]

So I got

1-(x^3)/2 but apparently it was wrong

[pale perch]

show your work

[woeful tinsel]

@pale perch ^

[pale perch]

thats not how multiplying things works

is (a+b+z)(c+d+w)=ac+bd+zw?

[woeful tinsel]

No

How do u multiply (n!) (2n!)

Yeah I’m lost idk how to multiply them

[pale perch]

well you want to be sensible in how many terms you look to

[woeful tinsel]

Oh wait do I just list out terms for each of them

And then just distribute?

[pale perch]

(1-1/2 x^2)(1+x+1/2 x^2+1/6 x^3)

just expand, yeah

ignore anything higher than x^3

[woeful tinsel]

Got it! Thanks!!

That was rlly helpful I was stuck for a while!

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[brisk moss]

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[jagged rivet]

help

[glacial crane]

Here's a link to demos of each of the algorithms mentioned in the homework

https://math.libretexts.org/Bookshelves/Applied_Mathematics/Math_in_Society_(Lippman)/06%3A_Graph_Theory/6.06%3A_Hamiltonian_Circuits_and_the_Traveling_Salesman_Problem

Look over that first, and if you have any questions let me know

Does that help at all?

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[granite kettle]

Hello I have a question about physics

[granite kettle]

Btw this is a lab activity, Ive already conducted the lab and now I got the data which I inputted into spreadsheets and I got the graph and stuff

Now it's just Q9 and Q10 in which I kinda have no idea how to do

This lab is to find the coefficient of static friction and it looks like this

My teacher gave me a hint for Q9, and he gave me this equation:

y * g = μs * x * g

y represents hanging mass, x represents wood block mass

It says express slope in terms of other variables and I did:

μs = y * g / x * g
= (151)(9.8) / (504.142)(9.8)
= 0.2995

Q10 is really confusing me i dont know where to start

[near tartan]

linear regression in physics

[granite kettle]

Any help will be appreciated

[near tartan]

you just have to pick a slope where line is closest to those 4 points

5

[granite kettle]

line of best fit right

[near tartan]

yea

there are mathematical ways to do this but i think they want you to eyeball it

[granite kettle]

google sheets actually has a feature

under the title it is the trendline which is basically like line of best fit

y = 0.111x + 82.8

[near tartan]

then 0.111 is your answer

[granite kettle]

Wtf

wait

let me show a picture of my previous question work

cuz im confused why the coefficients are different

it sideways but at the bottom my answer for coefficient of static friction is 0.2995

how come its different i thought it was supposed to be the same

i think my teacher made the question unclear lol

[near tartan]

,rotate

[granite kettle]

or maybe im overthinking

[near tartan]

yeah cuz that line will never get us an exact coefficient of friction

there are inaccuracies

[granite kettle]

oh i see, so for Q10, i just state the line of best fit, then state the coefficient is 0.111

i mean it doesnt say show your work which I assume there isnt any calculations needed

do you think Q9 is correct?

My teacher gave me a hint for Q9, and he gave me this equation:

y * g = μs * x * g
y represents hanging mass, x represents wood block mass
It says express slope in terms of other variables and I did:

μs = y * g / x * g
= (151)(9.8) / (504.142)(9.8)
= 0.2995

honestly its only work 2 points each question so i also assume its not to be overthinked

so ima just use that as my answer

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[near tartan]

a or b

solve the 2 equations together

that's how you find intersections between 2 graphs

because that's how circle works

plug in y= 3x-5 in the circle

x^2 + (3x-5)^2 = 36

this will be a quadratic equation in x

you can find the 2 x values which will be your answers

[near tartan]

by this

y is that

so y^2 will be that

simple

first expand that square

,w expand (a+b)^2

[twin meteor]

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Requested by ankitwa

[near tartan]

9x^2 - 30x + 25

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[silver viper]

what substitution can i make on this limit??

[lone linden]

I'd just recognise it as the def of the derivative

or if you can't use that, try factoring the denominator using ||difference of squares||

[silver viper]

Yeah I was thinking about using the difference of squares but it seems like too much work. So I thought that maybe there is a trick

But it doesn't seem like there's gonna be an easy way

[lone linden]

the difference of squares is pretty fast tbh

you can do this in ~ 2 lines

[wraith venture]

yeah it's not much work at all

or you're doing it wrong

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[placid osprey]

AnX should contain 1, 2, 6, 7
BnX^C should contain 0, 9

But I don't know how to go about it

[edgy sapphire]

also check what it shouldn't contain

like X can't have a 5 or else AnX has a 5 and the union has a 5, but C doesn't

[placid osprey]

so i need to list all possible subsets

?

[edgy sapphire]

yes

[placid osprey]

how many such subsets are there

and what's the best approach as a first step

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[vast shale]

Can anyone tell me approach to solve this question

[vast shale]

Question is part of chap relation and functions

[scenic ravine]

is this a test?

[vast shale]

Ya , mock test

[scenic ravine]

wait, you're giving it right now?

[vast shale]

Given

No looking for answer

[scenic ravine]

ok, in that case start by finding the range of $3-sin(4x)$

[twin meteor]

ƒ(Why am. I here)=I don't know

[scenic ravine]

this is a mock CUET test?

[vast shale]

Han

Are u Indian?

[scenic ravine]

yeah

[vast shale]

Ah

[scenic ravine]

a lot of people here are

[vast shale]

Didn't knew that

[vast shale]

Can u explain how?

Will we equate it?

[scenic ravine]

do you know how to find the range of a function?

say sin(x)

can you find the range of sin(x)?

[vast shale]

It forgot the answer

Preparing chap one 😭

[scenic ravine]

$- 1 \leq sin(x) \leq 1$

[twin meteor]

ƒ(Why am. I here)=I don't know

[vast shale]

So we need to find it using inqualities

[scenic ravine]

now what's the range of $sin(4x)$

[twin meteor]

ƒ(Why am. I here)=I don't know

[vast shale]

In place of sinx we need to keep that terms from question

[vast shale]

Help me bro

[scenic ravine]

$-1\leq sin(4x) \leq 1$

[twin meteor]

ƒ(Why am. I here)=I don't know

[scenic ravine]

can you do it from here

I have to go now, have some work to do

@vast shale

[vast shale]

let y = 1/3-sin4x

now find sin4x in terms of y

[vast shale]

and apply this

[hollow heron]

wild guess
but A is the answer

[scenic ravine]

!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.

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[wispy finch]

how is this 2/PI

it should be -2/PI right??

[winter thistle]

2/pi is correct, why do you think it is -2/pi?

[wispy finch]

cos pi is -1 and cos 0 is 1 so -1-1 is -2

[winter thistle]

but what is the integration of sin

[wispy finch]

omggggg

-cos

[winter thistle]

😉

[wispy finch]

I AM STUPPIIIDDDDDDD
'

i did derivative

[winter thistle]

happens to all of us

[wispy finch]

it took me 20 min

thank you so much

[winter thistle]

np

[wispy finch]

.close

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[wispy finch]

How do I integrate this

[wispy finch]

So cos^2 kt^2 first term correct

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[rustic lagoon]

I need some help with constructing a Voronoi diagram without having to manually place every line and perpendicular bisector

[rustic lagoon]

I read some things on Delaunay traingulation, but from what I could tell it would not help me that much?

<@&286206848099549185>

[pale swan]

hello, help me with this:Let us now consider a non-uniform thin rod with a length of 𝐿2=6 m with a linear density depending on the length according to the law 𝜆(𝑙)=𝜆0(1+𝑘𝑙), where 𝜆0=2 kg/m is the value of the linear density at the left end (i.e. 𝑙 is measured from the left end), 𝑘=0.2 m−1 - proportionality coefficient.

2. Determine the mass of rod 𝑀2. Give your answer in kilograms to the nearest tenth.

[tepid plinth]

!15m
In future, wait 15 minutes after posting to use that tag...

[tepid plinth]

You please request a new channel. This one is already occupied. Read #❓how-to-get-help

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[daring marsh]

I don't understand one x to y = function of x

but says this is wrong so I am not sure

[heavy yoke]

x is the input, and f(x) is the output

for a relationship between x and f(x) to be a function, each input must correspond with only one output

[daring marsh]

so then why is table 2 is wrong

table 2 should be the only corerct answer then

[heavy yoke]

why should table 2 be the only correct answer?

[daring marsh]

table 4 two inputs with different outputs table 3*** two inputs for same output

table one two inputs with different outputs

tabe 2 one-one

[heavy yoke]

what about table 3?

[daring marsh]

i mean table 3 after 4

[heavy yoke]

remember that x is the input and f(x) or g(x) (or similar) is the output

[daring marsh]

Idk what you mean

[heavy yoke]

a function can have two different inputs give the same output

what a function can't do, is have the same input give different outputs

[daring marsh]

each input must correspond with only output

[heavy yoke]

each input must correspond with only one output, but each output does not need to correspond with only one input

[daring marsh]

Okay I don't see what's wrong with one and two

[heavy yoke]

let's go one at a time then

In table 1, is it a function? If not, why isn't it?

[daring marsh]

Yeah the output is unique each instance with two similar inputs

If two inputs can have different outputs then it's a function according to what you told me

[heavy yoke]

every function must associate one, and only one, output to every input

the same input cannot produce two different outputs

two different inputs can produce the same output

[daring marsh]

I'm confused because you just told me the opposite

[heavy yoke]

that's what i meant to say

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@daring marsh Has your question been resolved?

[daring marsh]

yeah idk still confused two is the answer then

its telling me 4 is right

but that would mean 1 is valid

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@daring marsh Has your question been resolved?

[vocal sleet]

@daring marsh Has your question been resolved?

[edgy sapphire]

these are what make 1 and 4 not a function, whenever an input splits into two possibilities

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[open coral]

Can someone please help me with e(ii)

[open coral]

I foudn the first solution but I forgot how to find the second

.close

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[upbeat flax]

I am having problems with a step of finding the absolute max/min values.

f'(x) = (25-2t^2) / sqrt(25 - t^2)

When looking for a critical value where f'(x) does not exist, why does it call for the DNE to become an inequality?

[hybrid wind]

So like you need help finding where f'(x) = undefined?

[upbeat flax]

I am following along with a video on showing where f'(x) is undefined, I am just trying to understand the steps the video is taking.

https://www.youtube.com/watch?v=3aje1L3WtCQ&list=PLl-Np5U6u5E54PygbTaBsSzpSmVQVeJHq&t=190

Demonstrates it here 🙂

[hybrid wind]

So you need to know why f'(x) = und is a crit point?

[upbeat flax]

I am trying to understand why you need to set [ sqrt(25-t^2) ]

to an inequality --> [ 25-t^2 <= 0 ]

in order to obtain f'(x) = undefined

[hybrid wind]

I have no idea

Seems redundant to me

[raven owl]

Becuase if 25-t^2 = 0 then it is undefined (dividing by 0) and if 25-t^2 < 0 then ur sqrting a negative number

[upbeat flax]

Square rooting a negative number would just result in an imaginary number right? And those aren't being covered... yet o>o

[raven owl]

Yeah that wouldn't be undefined but they probably wan't you to ignore that for now (and probably a long time)

[upbeat flax]

.close

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[hybrid wind]

Why would is the first reason valid?

Isn't the whole point for a crit point to be undefined as well?

[raven owl]

We are looking at values where the derivative is undefined but the original function isn't so we can independently check if those points are the max

(not sure I understood your question fully)

[hybrid wind]

Wouldn't 25-t^2=0 be sufficient

[raven owl]

yeah it would

cuz we already know the domain is [-5,5]

[hybrid wind]

Alright

Just gotta make sure I wasn't tweaking 😅

Ty

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[atomic lance]

So I know since the events are independant, I use this formula: P(A and B) = P(A)P(B)

[iron parrot]

yes

so adding on to that, P(A and B and C and D) = ?

[atomic lance]

And since the probabilities of each sever being congested at some point in the next hour is pi

Therefore the probability that each server not being congested at some point in the next hour must be 1 - pi

[iron parrot]

nice

[atomic lance]

So since we want to know the probability that the whole connection is slow at some point in the next hour: P(slow) = P(atleast one server is congested)

So the P(a given server is congested) must be 1 - P(server is not congested)

Is this correct?

[iron parrot]

yes

[atomic lance]

So how would I find the probability that a server is not congested?

I know the for P1, P2, P3 and P4 it is 1 - pi

Therefore the probability that all four servers are congested is: (1 - pi) * (1 - 1pi) * (1 - pi) * (1 - pi)

Where would I progress from here? @iron parrot

[iron parrot]

we would want to find the probablitity that none of the servers are congested

not the probability that they are all congested

[atomic lance]

So would the probability of none of the servers being congested be: 1 - P(all servers congested)?

[iron parrot]

no

because by subtracting, you don't consider the cases where 1 is congested, 2 are congested, and 3 are congested

[iron parrot]

here, this is wrong

we are given that p_i is the probability of a server being congested

so it is actually the probability that none of the servers are congested

[atomic lance]

?

Oh I see

So the probability that none of the four servers are congested is: (1 - pi) * (1 - 1pi) * (1 - pi) * (1 - pi)

[iron parrot]

yes

[atomic lance]

So to find the probability that all four servers are congested I would do this: [1] - [(1 - pi) * (1 - 1pi) * (1 - pi) * (1 - pi)]

[iron parrot]

exactly

gj

wait

not all four servers

[iron parrot]

the probability that at least one of the servers is congested is this

but the probability that all of them are congested is p1 * p2 * p3 * p4

also you might want to replace the i's with 1,2,3,4

[atomic lance]

Oh ok

[atomic lance]

Why is this the probability of at least one the servers being congested?

Isn't the compliment of none of the servers being congested, all of the servers being congested?

<@&286206848099549185>

[iron parrot]

that is correct

however, the complement of P(A and B and C and D) is not P((not A) and (not B) and (not C) and (not D))

[atomic lance]

Why?

I mean, then what would the compliment of P(A and B and C and D) be?

[iron parrot]

P(A') U P(B') U P(C') U P(D')

[atomic lance]

Oh I see, and 'U' means Or right?

[iron parrot]

yes

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[grizzled frost]

i dont even know how to do this problem at all

dont even know where to start

1/5

4

would it be like 1/5^4

?

[twin meteor]

Ransik

[grizzled frost]

yes

you can get rid of the two possibilities

1/3

?

1/3 x 1/3

?

1/5^4

?

oh wait they are the same still

so 1/3 x 1/3 x 1/5 x 1/5

?

[twin meteor]

Ransik

[grizzled frost]

ohh i see now

hmm

2

1?

4

?

2/3 x 2/3 x 4/5 x 4/5

?

64/225 then

ooo nice

yes

1?

yess

64/225

1 - 64/225

??

oh wow i understand it now

wow thank you so much

!

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[mighty vapor]

when a car is on a circular curve, the car will lose contact with the ground when normal force is zero right?

[edgy sapphire]

yes

[mighty vapor]

can i ask why? @edgy sapphire

[edgy sapphire]

when the normal is really small that means you're barely pressed into the ground

if you flip that around, when the normal goes a bit beyond zero you're going a bit away from the ground

it's kind of a like the sensation in an elevator

[mighty vapor]

what about weight though?

isnt the car accelerating downwards now and still touching the ground if normal force is 0

[edgy sapphire]

what's the exact problem?

normal force gives you your feeling of weight so when it's zero you're essentially floating

idk if this is a toy car on a circle or like racecar on a sloped track

[mighty vapor]

looks like this

for the free body diagram i did weight pointing down 2 blocks and then normal force pointing up 1 block

[edgy sapphire]

oh maybe this is a little different

yea it's weight and normal on the dot

one fact is you need a total force of mv^2/r to go in a circular path

and if you can't achieve that force you'll fly off the circular path

either way though at the critical point where it's about to go airborne, N=0

[mighty vapor]

why is n=0 though w hen its about to go airborne?

doesnt weight make it stay to the ground

[edgy sapphire]

weight is trying to, but when you go really fast you need a ton of weight to keep going along a circle
if you're not heavy enough you'll curve at a smaller angle which means airborne

like when you're going so fast, there's no time for the weight to pull you down that far

[mighty vapor]

ohhhh that makes sense

[edgy sapphire]

like as an extreme example if you have what's almost a cliff, usually you'll go airborne at the edge. but, if gravity is super high near infinity you'll just stick to the track

[mighty vapor]

ohh okok

tysm!!

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[hollow acorn]

Given that g is the inverse function of f, find each of the following:
a) f(x)=a
b) f’(x)
c) g’(a)

[hollow acorn]

I tried solving for x to get f^-1(2) but I didn’t know how…

[hollow acorn]

By making the equation equal to the given a value

[vocal sleet]

@hollow acorn Has your question been resolved?

[hollow acorn]

<@&286206848099549185> please help 😭 im going crazy

[crude arrow]

lmao

x^5 - x^2 + 2x = 2

[hollow acorn]

Huhhh

[crude arrow]

which part are you on

rn

[hollow acorn]

I gave up because i was gonna do the next questions but then i realized they were all like that one

Like

I tried solving it

[crude arrow]

goddamn 😭

[hollow acorn]

But the way i did it with easier questions DID NOT WORK w that one

[crude arrow]

are you allowed to use a calculator

[hollow acorn]

And now im actually going crazy

[hollow acorn]

No

[crude arrow]

x(x^4 - x^2 + 2) = 2

lmao

[hollow acorn]

Like my teacher did one example and ive been going off of that for all the questions but idk how to apply whatever he did to the harder ones

[crude arrow]

the answer is kinda in ur face for this one

[hollow acorn]

Yeah

I got to that

But

What else

Am i supposed to do

[crude arrow]

I mean if it has an inverse, the function should be 1-1

so we see that when x = 1

trivially

it works

[hollow acorn]

😅

[crude arrow]

f(1) = ?

[hollow acorn]

Uhhh

😅

[crude arrow]

😭

[hollow acorn]

Im giggling omg its over for me

[crude arrow]

ngl

it's not over

IF

you tell me what f(1) is

[hollow acorn]

IM actually laughing okay lemme look

[crude arrow]

otherwise it's so over 😭

[hollow acorn]

Uhm…

😅

Wait

Omg

2 = 2 😭😭😭 IDK

PLEASE

[crude arrow]

yeah

[hollow acorn]

Omg

[crude arrow]

so like since f(1) = 2

g(2) = ?

[hollow acorn]

.

[crude arrow]

remember that g is f inverse

[hollow acorn]

One over 2!

[crude arrow]

you cannot sell here

[hollow acorn]

😅

IM laufhing

Omg

Help

[crude arrow]

it's 1

[hollow acorn]

IDK WHATS GOING ON

OH MY GOD

IM AN IDIOT

[crude arrow]

it's the inverse lmao

[hollow acorn]

Is it over for me?

[crude arrow]

depends

[hollow acorn]

Its over.

All i know is that the final answer is 1/4