help-0

[pulsar delta]

no no

[rapid sundial]

you'll be fine if you passed discrete math

[pulsar delta]

discrete math in college

[hidden fable]

dw, just make sure to study

[pulsar delta]

ug

in undergraduate, this is for pg

[rapid sundial]

Yeah you're fine.

[hidden fable]

this is an entrance test for grad school?

you’re gonna be fine

[pulsar delta]

yes

[lone heart]

@pulsar delta Has your question been resolved?

[lone heart]

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[warm dew]

Hey could someone help me with a quadratic function assignment. i finished it and i just need someone to verifiy my work please send dm

[torpid dirge]

no homework help!

[warm dew]

oh

[tacit arch]

Wrong

[tacit arch]

Show the question and your work

[warm dew]

its an assignment can i send u the docs link in dms

[tacit arch]

Oh no

[torpid dirge]

oh, i mean assignemnt help

[tacit arch]

Help channels are for math questions

[warm dew]

oh i see

i applogize

[lone heart]

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[regal fox]

I need to find the equation of the curve by integration

[vale wigeon]

$x^{1/2} \cdot x^{1/2} \neq x^{1/4}$

[ocean seal]

Ann

[west cipher]

^

[vale wigeon]

also you did some weird shit with notation when integrating.

[regal fox]

oh im stupid it's just X

[vale wigeon]

lowercase x but yes.

[regal fox]

yea I should clear up my workings

lemme solve this rq

it's correct

also is the working better this time around?

@vale wigeon

[vale wigeon]

no, doesn't change the weird integral notation.

your third line should have been: $$\int (x - 3x^{1/2}) \dd{x} = \frac{x^2}{2} - 2x^{3/2} + C$$

[ocean seal]

Ann

[regal fox]

ohhh

oke gotcha

[regal fox]

thansk alot I'll keep that in mind

.close

[lone heart]

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[cinder sundial]

Here's a question:

Given that the spring constant is 10 N/cm

and gravitational acceleration is assumed as 10 m/s^2

[alpine sable]

so what is the question

[cinder sundial]

It asks for the length that the spring would have stretched on such scenario.

[alpine sable]

is the 2 kg box attached to thr ceiling with a spring

or is it just glued there

ok i guess the force is pulling on it

anyways draw a freebody diagram

for each box

[cinder sundial]

I don't think so, we can only know that something provided a force of 75N upward to the box

emm

I would like someone to check my previous approach which leads me to a incorrect answer.

[alpine sable]

ok

[alpine sable]

you forgot the weight

immediately

[cinder sundial]

the weight?

[alpine sable]

oh wait

i see

[alpine sable]

are those forces you listed representing the spring force or thr weight?

[cinder sundial]

the weight

of each box

[alpine sable]

ok so you're missing the spring force

[cinder sundial]

I do

I have a very unique approach

lets continue my approach

So I named the connecting points between one end of the spring to the another as P and Q

Then I just simplified the situation

[alpine sable]

what you're doing is not an ideal way of drawing a free body diagram btw

[cinder sundial]

I know, but i have to understand where im wrong

So

F+F2=75-20=55

F3 is the weight of the 4kg box which is 40

Adding them up we get 55-40 = 15

and that's the force stretching the spring.

[west cipher]

ok

so F=kx?

[cinder sundial]

yes

[west cipher]

ok

[cinder sundial]

15=10*x

[west cipher]

if you found the force correctly then your x=15/10

[cinder sundial]

I suppose not, cause the true x is 5 cm

[west cipher]

ok

[cinder sundial]

I wonder which part of my assumption is wrong

that leads me to a incorrect answer

[cloud nacelle]

can we solve this in the frame of centre of mass

i know there's an external force acting on centre of mass

but we can apply a pseudo force

[cinder sundial]

No, I just wonder where I did wrong in my assumption

[cloud nacelle]

why not

[cinder sundial]

the specific part that leads me to a incorrect answer

[vale wigeon]

an* incorrect answer

[cloud nacelle]

ah this is a complicated question

[cinder sundial]

thank you

[cloud nacelle]

I got a method

to solve

but

how do i explain it

lol

I'd solve it using COM

easier to handle

[cinder sundial]

There's a solution provided in the form of tutorial videos tho

[cloud nacelle]

its going to take way too long for me to type

we can use equations of motion

[cinder sundial]

dont

[cloud nacelle]

on centre of mass

ah yes there's mg as well

[cinder sundial]

you should not provide your solution on this channel, as im not asking how to solve it but someone to check my assumption.

[cloud nacelle]

1. equations of motion on centre of mass
2. work energy theorem

its going to be complicated without centre of mass

the motion is weird

[west cipher]

are you sure your k is correct?

[cinder sundial]

Im sure, it is provided in the description k=10(N/CM)

[cloud nacelle]

they asked maximum elongation right?

You need to use work energy theorem

[cloud nacelle]

what have you done here

[west cipher]

When the string is stretched to its maximum, both blocks will be accelerating at the same rate, right?

[cloud nacelle]

Spring is force is variable

[west cipher]

You can then use 75N=a(net)*(4+2)

[cloud nacelle]

Ah

[cinder sundial]

I know

[west cipher]

Then do FBD on both blocks

[cinder sundial]

but I wonder which part of my assumption is incorrect

[west cipher]

let see

[cloud nacelle]

4+2???

you considered them to be a system.

?

[west cipher]

yes

4+2

to find net acceleration

[cloud nacelle]

ah

[west cipher]

a(net)=75/6

Looking at the top block,

2*a(net)=sum of forces (incl. spring)

[cinder sundial]

I think I would have close the channel then, it started digressing from the original.

[west cipher]

so

2*75/6=75-20-10x

x is then

[cloud nacelle]

what makes you say that the maximum elongation occurs when the accn is equal

and what about mg

[west cipher]

(2*75/6-75+20)/-10

2*75/6 is the net force

mg is 20

When the first block starts accelerating, the spring will stretch until it creates enough force to lift the second block

then it will continue stretching

due to accelerating the second block

[cloud nacelle]

maximum expansion occurs when the two blocks are at rest wrt centre of mass of the system

so

for this you have to work energy theorem

[west cipher]

what is wrt

[cloud nacelle]

with respect to

[west cipher]

Yes

[cloud nacelle]

First we have to find Velocity of centre of mass

its going to be complicated

[west cipher]

and they are at rest wrt with cm when the velocity of both blockes is equal

[cloud nacelle]

by equations of motion

ah

i cant explain

sorry

its going to take way too long

[west cipher]

But

if the velocity is constant wrt cm for both blocks

then so is a

thus

[cloud nacelle]

but you don't know how much they have expanded

[west cipher]

It doesnt matter

[cloud nacelle]

and there's an external force

[west cipher]

Yes there is

75N

and mg

[cloud nacelle]

what's the max elongation

in tihs case

[west cipher]

max elongation occurs when m1 and m2 have the same speed

[cloud nacelle]

i need answer

[west cipher]

it occurs when m1 and m2 have the same speed, and this occurs when the blocks are accelerating at the same rate

[cloud nacelle]

ok

[west cipher]

i dont see how this is complicated

[cloud nacelle]

i just want answer

maybe your approach

is better

[west cipher]

if the blocks are not at the same a, then there will be oscillation in the spring

[cloud nacelle]

agreed

next?

so

[west cipher]

?

@cinder sundial do you nee help still

[cloud nacelle]

F-kx1 = m2a
kx2 = m1a?

[cinder sundial]

For sure, Im still wondering which part of my assumption is incorrect.

[west cipher]

zerome yes that is correct

though once you find a you only need one eq. to solve for x

[cloud nacelle]

now its correct

elongation's will be different

on both blocks

[west cipher]

elongations will be different?

[cloud nacelle]

yes

[west cipher]

wdym by that

[cloud nacelle]

from initial position

at max elongation
m1 has a different elongation m2 has different elongation wrt initial position

[west cipher]

wdym elongation. do you mean change in position?

[cloud nacelle]

eys

yes

[west cipher]

at max spring elongation, m1 and m2 will have the same speed

[cloud nacelle]

but different elongation

[west cipher]

can you define elongation

im not sure what you mean

[cloud nacelle]

this

x1 and x2 are elongations

[west cipher]

oh

i see now

[cloud nacelle]

yeah

so we cant

use

that's where work energy theorem comes in

that's why we can't directly apply kx = net force

[west cipher]

yes but max elongation occurs when both blocks have acceleration equal to the acceleration of the system

[cloud nacelle]

True

But

[west cipher]

yes

[cloud nacelle]

x1 is not equal to x2

[west cipher]

what does that imply

[cloud nacelle]

that implies

you can't directly use

[cloud nacelle]

this

unknowns

:)

[west cipher]

oh

i see

[cloud nacelle]

yeah

[west cipher]

i misread your equation

[cloud nacelle]

np

[west cipher]

F-kx=m2a

kx=m1a

[cloud nacelle]

no

x is not same

for both

[west cipher]

the force is proportional to the length of the entire spring

that is hookes law

[cloud nacelle]

im not denying

x is the elongation

change in position

[west cipher]

oh wait

im stupid you right

[cloud nacelle]

yeah

[west cipher]

its proportional to k(delta)x

[cloud nacelle]

yeah

and we have no idea about delta x

[west cipher]

if that is the case

then

1 sec

[cloud nacelle]

I had solved this question like months ago

so i do remember this

[west cipher]

F-k(delta)x=m2a
k(delta)x=m1a

delta(x) can still be solved

then it is added to the initial length

[cloud nacelle]

deltax is not same

x1 and x2

two different variables

[lone heart]

@cinder sundial Has your question been resolved?

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[surreal garnet]

Hey there.

[surreal garnet]

Will the angle at exit be equal to 50 degrees?

This here

[cloud nacelle]

use snells law

n1sini = n2sinr

where i is the angle of incidence
n1 = medium in which the incident ray is falling

[surreal garnet]

I need to know what the refractive index of plastic is?

[cloud nacelle]

yeah

[surreal garnet]

but there is no one refractive index for plastic

Can I use this information to find the answer?
that the light ray is aimed at the center of the hemisphere

[hushed locust]

even if you don't know exactly what the refractive index is you do know it's greater than that of air, which tells you something about the angle

[surreal garnet]

It'll bend away from the normal at exit right?

[cloud nacelle]

yeah

and the angle depends on refractive index of plastic

[surreal garnet]

so if the refractive index of plastic is never mentioned in the book, can I assume that this question isn't asking for an angle? that it just wants to know if the ray will bend towards or away from the normal?

[cloud nacelle]

yeah they arent asking you the angle of refraction

just show the deviation

[surreal garnet]

Alrighty, tysm ❤️

[cloud nacelle]

have a nice day

[surreal garnet]

you too

.close

[lone heart]

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[dire wren]

Can anybody solve this

[wind cloak]

just sub 4x - π as u or something

[dire wren]

Is it going to be -2 because it wasn’t in the choices

[lone heart]

@dire wren Has your question been resolved?

[cloud nacelle]

You can use L'hospital rule

or as mentioned above

use substitution

[lone heart]

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[alpine sable]

Can someone make the drawing for this? I'm confused how to do it

[alpine sable]

\tikz{
\draw (0,0) -- (32:5) -- ++(317:7);
}

[alpine sable]

it will look like this pretty much

do u know what to do now

yes

thank you so much

.close

[lone heart]

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[alpine sable]

.reopen

[lone heart]

✅

[alpine sable]

wait

can i also ask

where is the angle 317

and nevermind i don't know how to do it :))

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

.close

[lone heart]

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[alpine sable]

How to solve this? I can not even understand clearly 'bout it.....😶

[cerulean junco]

the solid formed is a Cone .

[alpine sable]

how?

[cerulean junco]

if you rotate the 2D figure extremely fast ... taking 1Side as the axis .
you get a 3d figure ....

[alpine sable]

answer would be 240 or 100??

[alpine sable]

in our class there is debate for this..... I am not sure

how 5 as a radius?

[cerulean junco]

that you need to calculate .... with the FORMULA ...to calvulate Volume of Cone .

[alpine sable]

by this is fine

but revolved about the side 12 cm.... can you enlighten me more what is the point?

[cerulean junco]

it is clearly said in the question that you should revolve the figure about the side 12 CM

[alpine sable]

revolve as in?

[cerulean junco]

revolve about the side X mean ... X is the axis

Basically, rotate it with 12 cm side as axis .

[alpine sable]

ok

so length becomes 12

base becomes 5

and 13 becomes hypo??

[cerulean junco]

ya ...

[alpine sable]

ok got it...

so then answer is coming 100 pi

[cerulean junco]

you don't need hypo to calculate the vol of the CONE with length 12cm and base radius 5 cm .

[alpine sable]

yes yes... talking about the triangle

got it nice.... thanks

👍👍

[cerulean junco]

type .close please .

[alpine sable]

ok wait yea

.close

[lone heart]

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[minor hill]

pls help

[lone heart]

@minor hill Has your question been resolved?

[minor hill]

no

<@&286206848099549185>

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@minor hill Has your question been resolved?

[lone heart]

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[minor hill]

no

[minor hill]

plz help

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[cerulean junco]

help me ...
why and how !?

[lone heart]

@cerulean junco Has your question been resolved?

[cerulean junco]

<@&286206848099549185>

<@&286206848099549185>

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[lofty gorge]

What step exactly don't you understand

If it's how did we get subset, it's because we took an arbitrary x of the LHS and showed it's in the RHS, which is the definition of subset

If it's the step after that, the dimension of a subspace can't be bigger than the dimension of the whole space

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@cerulean junco Has your question been resolved?

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[surreal meadow]

@vapid shuttle

[vapid shuttle]

@surreal meadow

[surreal meadow]

we have
[\sqrt{4 + \left[\dv{}{t}\sqrt{2-2\sin\left(2t + \frac{3\pi}{2}\right)}\right]^2}]

[vapid shuttle]

Yes

[surreal meadow]

alright

let me write it out

oh that should be squared

one sec

[ocean seal]

maximo

[vapid shuttle]

Yes

[surreal meadow]

ok let me write it out

we have
[=\sqrt{4 + \left[\dv{}{t}\sqrt{2+2\cos\left(2t\right)}\right]^2}]

[ocean seal]

maximo

[surreal meadow]

do you agree

[vapid shuttle]

Well that certainly simplifies things

Yes

I agree

[surreal meadow]

ok

\begin{align*}
&=\sqrt{4 + \frac{4^2\sin^2(2t)}{4\left(2-2\cos(2t)\right)}}
\end{align*}

let me double check but i think this is fine

nah i fucked something up here let me fix it

there we go

god why cant i derive this. is that right

[vapid shuttle]

Lmao

Me

[ocean seal]

maximo

[surreal meadow]

fuck it i think this is right

anyway

you can divide stuff out

\begin{align*}
&=\sqrt{4 + 2\frac{\sin^2(2t)}{\left(1-\cos(2t)\right)}}
\end{align*}

[ocean seal]

maximo

[surreal meadow]

\begin{align*}
&=\sqrt{4 + 2\frac{1-\cos^2(2t)}{\left(1-\cos(2t)\right)}}\
&=\sqrt{4 + 2\frac{(1-\cos(2t))(1+\cos(2t))}{\left(1-\cos(2t)\right)}}
\end{align*}

[ocean seal]

maximo

[vapid shuttle]

Question

We are integrating from 0 to pi/2

Isn’t that an issue to have 1-cos(2t) in denom

Because at t=0 this is division by 0

[surreal meadow]

what's that thing they teach you with the limits

improper

[vapid shuttle]

Are you saying to do this as an improper integral now?

[surreal meadow]

you can yes

[vapid shuttle]

Okay

[surreal meadow]

it will cancel out though

[surreal meadow]

as you can see here

[vapid shuttle]

Well

Not if it’s 0

:p

[surreal meadow]

it's a removable discontinuity

[vapid shuttle]

Zero content

[surreal meadow]

\begin{align*}
&=\sqrt{4 + 2(1+\cos(2t))}
\end{align*}

[ocean seal]

maximo

[surreal meadow]

uhhh

this i think

[vapid shuttle]

Uhhh

[surreal meadow]

cancelled out the 1-cos(2t)

now rewrite this as

[\sqrt{4+2(1+\cos^2t -\sin^2t)}]

[ocean seal]

maximo

[surreal meadow]

and 1-sin^2t instead of the cos^2t

[vapid shuttle]

I see

[surreal meadow]

[\sqrt{4 + 2(1+1-2\sin^2t)}]

[ocean seal]

maximo

[vapid shuttle]

Maximo masterclass

[surreal meadow]

so ok you can see we still need to pull out a constant to have the constant term be a 1

so idk what happened there in realtion to your original question

and also, the pic i sent a while back, i fucked up the constant somewhere there or here

[vapid shuttle]

Well we can pull out a constant

[surreal meadow]

that derivative fucked me up

but this is the process

[vapid shuttle]

No worries I’m going to go back through it all anyways

We can write like C*E(something)

To express it in terms of the elliptic integral, even if there is a constant

[surreal meadow]

ah ok nice

[vapid shuttle]

I was very happy just to be able to parametrize that intersection

[surreal meadow]

i thought they wanted E(k) explicitly

[vapid shuttle]

Lol

Felt accomplished after that

[surreal meadow]

yeah im glad you werent asking help with that

cause i was not gonna look at it lmao

[vapid shuttle]

It looks cool

Graphing it

[surreal meadow]

i bet

is it like a sphere and cylinder

[surreal meadow]

oh wow

that is actually pretty neat

[vapid shuttle]

The green is what we want to parametrize but only in the 1st octant

And that makes it tricky

Yeah I have class now

Going to go learn definition of vector space for an hour

Yay me

[surreal meadow]

why are classes already starting

didnt you finish after me

now youre starting before me? did they give you like a single week for break

[vapid shuttle]

Yeah like 1.5 weeks

They started Wednesday for me

[surreal meadow]

damn thats crazy

.close

[lone heart]

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[vapid shuttle]

.coose

[surreal meadow]

i start on the 8th

monday i think

[lone heart]

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[fair musk]

Given a sequence, how would we find the length of the longest strictly increasing subsequence automatically?

Examples:
10, 9, 2, 5, 3, 7, 101, 18 length is 4 since 2, 3, 7, and 101 are the longest increasing subsequence.

0,1,0,3,2,3-> 4
7,7,7,7,7,7,7->1

[vale wigeon]

define "automatically"?

[fair musk]

using a computer

[vale wigeon]

so with a program?

[fair musk]

yeah

[outer lark]

this is a documented problem

[vale wigeon]

why not just scan through the sequence left to right

[outer lark]

there is leetcode practice problems on it and wiki page I believe

[fair musk]

damn, my cover is blown

[vale wigeon]

keeping track of two things: the longest strictly-increasing subseq found thus far, and the start index of the current strictly-increasing subsequence

[fair musk]

it's the practice problem of the day on leetcode

[outer lark]

this approach should get you a nicely implemented solution,

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[warm quarry]

1. dy/dt= 3ty + 6t ( y > 2)

and

2. dy/dt = ty -t² + t + 1 ( y>0)

I dont know when to use y=at+b and dy/dt = a because I have to do that at question 2 but not at question 1

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[patent plinth]

$(x+2y+1)dx - (2x+y-1)dy = 0$
How do I solve this?
This clearly isn't an exact or separable ODE

[ocean seal]

Solitary

[cursive badger]

There’s likely an integrating factor

Ie multiply the whole equation by a term

I know there’s a method precisely for this scenario to obtain it

But I don’t remember it :)

[patent plinth]

yeaah, but the method I know gives this
$P = x+2y+1$, then $P_y=2$ \
$Q=1-2x-y$, then $Q_x=-2$ \
we calculate $\frac{P_y-Q_x}{Q} = \frac{4}{1-2x-y}$ \
So $IF = exp(\int \frac{4}{1-2x-y} dx)$

[cursive badger]

Does that not work? Lemme run the numbers

[ocean seal]

Solitary

[cursive badger]

ugh I haven't done this in too long very sorry ):

if you still need help in a few hours I'll be home and can check my notes but rn I can't recall anything farther and don't remember how to do it myself

wait a second

why do you have negatives in your IF's denominator?

[patent plinth]

thats okay! I'll also give it a try again later. Will update.

[patent plinth]

since Q = 1-2x-y?

[cursive badger]

afaik it's something like Pdx-Qdy = 0 no? I may be wrong but I recall there being something screwy with inconsistent negatives somewhere

I truly can't recall properly ):

[patent plinth]

I'm using notation used here

[patent plinth]

its a +
So Basically the IF is F for FPdx+FQdy=0 such that its exact

[cursive badger]

The line with the (15) has them on opposite sides of the equation though?

[patent plinth]

that's just the condition for the equation to be exact

[lone heart]

@patent plinth Has your question been resolved?

[cursive badger]

yup, the image you shared is how you derive the formula for the integrating factor from that

notably, however, that means the the two lines before (15), in reverse order, are
[FPdx=FQdy]
[FPdx-FQdy=0]

[ocean seal]

Astral

[cursive badger]

hmmm wait maybe not

AH yeah I see what I mixed up you were right

Yeah I have no idea, I last did dfqs two years ago and it's clear that I am not capable of helping you enough

consider #odes-and-pdes btw if this channel takes too long

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@patent plinth Has your question been resolved?

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[prime seal]

what is some more clever way i can find determinant of this matrix other than pascal's expansion

[limpid turret]

It's almost a lower triangular matrix

[prime seal]

how can i transform it into ltm?

could i do it such that ill take it into blocks first one will be on top left 2x2 second one top right 2x3 third bottom left will be 3x2 and last one 3x3

and then ill transopose those blocks

and ill get lower triangular matrix

[unkempt citrus]

convert it into a lower triangular matrix through elementary operations and then the determinant is the product of the elements of the diagonal

[prime seal]

alright but then i have to find its inverse and spectrum

[prime seal]

will this be the least labour intensive way?

[unkempt citrus]

I think so. Just subtract $R_ 1 -R_3$ and then $R_ 3-R_4$ to obtain a lower triangular

[ocean seal]

José

[unkempt citrus]

matrix

Sorry, $R_1 - 4R_3$*

[ocean seal]

José

[prime seal]

i did it like this

$3R_1+4R_2,R_3-R_4,R_4-R_5$

[ocean seal]

Slowaq

[prime seal]

but now determinant is -3 and it is supposed to be -1 @unkempt citrus

[unkempt citrus]

multiply $R_2$ by $\frac{1}{3}$ and gives -1

[ocean seal]

José

[prime seal]

but why wolfram yields different numbers?

,w lower triangular matrix {{3,4,0,0,0},{-2,-3,0,0,0},{2,1,1,1,1},{5,-2,0,1,1},{-2,3,0,0,1}}

[ocean seal]

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Requested by slowaq

[prime seal]

,w determinant {{3, 0, 0, 0, 0}, {-2, -3, 0, 0, 0}, {2, 1, 1, 0, 0}, {5, -2, 0, 1, 0}, {-2, 3, 0, 0, 1}}

[ocean seal]

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[unkempt citrus]

(multiplied by the same number)

It's because when you multiply a row by a number, the determinant is also multiplied by that number*

I had gotten confused with the other property haha. It only changes sign if you swap rows

[prime seal]

yes and i multiplied it by 3,4,-1,-1

but when i multiply my det by 12 i dont get -1

[unkempt citrus]

only for 3

the others were to subtract/add rows, which does not change the determinant

[prime seal]

ah alright i get it now

[prime seal]

but how can i write this matrix into block matrix?

[unkempt citrus]

I don't understand your question, what is a block matrix?

[prime seal]

https://en.wikipedia.org/wiki/Block_matrix#Block_matrix_determinant

this

ill split my original matrix into blocks

and then i can find determinant by finding determinant of block matrices on the diagonal

in this case i think i can do it this way

,w det({{1,0},{-Divide[2,3],-1}})det({{1,0,0},{0,1,0},{0,0,1}})

[ocean seal]

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[prime seal]

these two matrices are on diagonal with 0 being over diagonal and other number being under it

[unkempt citrus]

According to what I saw, you just have to make a proper subdivision, whatever you want.

[lone heart]

@prime seal Has your question been resolved?

[prime seal]

yes but now i have to find inverse

do i have to do Gauss-Jordan method?

beacause formula using determinants will take too lond to do i think

[unkempt citrus]

Yep. It's a bit long, but it works

[prime seal]

ah crap xd

[prime seal]

.close()

.close

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[alpine sable]

1. Prove that the only even prime number is 2.

[alpine sable]

Is this proof fine

[torpid dirge]

that's long..

[alpine sable]

yeahh i was yapping way too much

[torpid dirge]

can't you just say that it can be expressed as 2n thus it has a non zero prime factor 2

non one or itself*

so it's not prime

idk how you got 12 lines

[alpine sable]

Oh

that is way more simpler than whtai was saying

[torpid dirge]

maybe. i didn't read all

[alpine sable]

nah it is

ok then

thanks

[torpid dirge]

meow

[alpine sable]

.close

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[viscid lynx]

how to solve this?

[viscid lynx]

https://cdn.discordapp.com/attachments/1126206229350453409/1192994866536382616/image.png?ex=65ab1a0c&is=6598a50c&hm=c9740cf280e0024d60991372a2cbb72fab86aa67cfe3c89504c11ba2dce5e0ed&

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@viscid lynx Has your question been resolved?

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@viscid lynx Has your question been resolved?

[rustic coral]

https://math.stackexchange.com/questions/1724348/what-is-arctanx-arctany

[lone heart]

@viscid lynx Has your question been resolved?

[lone heart]

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[crisp hill]

8.3.1 I think my answer is sketchy

[crisp hill]

Can someone check it?

[clever linden]

I aint doin allat

[crisp hill]

Then why r u here...

[clever linden]

https://media.discordapp.net/attachments/741945274901200897/1185175256307077230/IMG_6446-1.gif?ex=658ea778&is=657c3278&hm=8a357907b21748669c0c2c1d46be54f9204722eb7a3785f1906d3fd9cb0cc922&

[crisp hill]

:/

If ur not gonna help me then just leave lmao

[azure frigate]

can you write down the points in question 8.3.1 so they are clear

[torpid dirge]

seems right

[crisp hill]

Thankss

Aops gives rlly weird answers sometimes

[crisp hill]

It's all in the ss lil

Lol

[torpid dirge]

aops?

[crisp hill]

Yes

It's a type of textbook

And there's math competitions

Lol

[torpid dirge]

oh

sorry i didn't read the question

i just jumped to your equation

[crisp hill]

Oh lol

Pls read it

😅

[torpid dirge]

you solved your thing right but you formed the equation wrong lol

like you formed it with the assumption the line passes through the origin

[crisp hill]

Oh

Wut

I did it using slope

😅

It's all on the same line

So it has to all have the same slope

I used the first complete coordinate and filled it in with a

[torpid dirge]

oh

[crisp hill]

And since both of those are slopes both are the same

[torpid dirge]

my bad it's right

[crisp hill]

Oh

Lol

[torpid dirge]

brainflop

[crisp hill]

It's okk

I do that all the time

That's why I'm on thus server

Lol

[torpid dirge]

👍

[crisp hill]

Tyy

:D

[torpid dirge]

np

[crisp hill]

.close

[lone heart]

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[alpine sable]

I don't know how to solve this question but the answer was given to me and it was 8(x-1/x²)...etc

[azure frigate]

can you take a clear image of the question ...is it some differential equation or somthing ?

[alpine sable]

Yes

(x²+2/X)⁴ is the question

Differentiate with respect to x

[azure frigate]

oh i am sorry i thought its a differential equation its just a question of derivative

[alpine sable]

Huh

[azure frigate]

ok how do you differentiate f(x)⁴

[alpine sable]

Uh I don't know sorry I don't use f(X)

Oh wait that's y right

[azure frigate]

yeah okay go ahead name it Y

[alpine sable]

4y³

[azure frigate]

no not necessarly ...if you are doing x⁴ thats when its 4x³ because we are differentiating with respect to x

[alpine sable]

Oh okay

[hidden fable]

tip: chain rule!

[alpine sable]

I mean I got Dy/du= 4u³ and du/dx= 2x -2x-²

[azure frigate]

so y⁴ would actually give 4×y³×y' or in different notaion 4×y³×(dy/dx)

[alpine sable]

Yeah

Thank you!

.close

[lone heart]

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[azure frigate]

okay now what if we replace y with (x²+2/x) then we would have 4×(x²+2/x)³× d(x²+x/2)/dx

oh

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[alpine sable]

Oh wait sorry

[alpine sable]

You gave me a hint and I got it already thanks!!

.close

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[solar finch]

yo guys

[solar finch]

can you give me an infrastructure that has 5 conic sections? ToT

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[alpine sable]

Help me guys

[alpine sable]

Check my part 1

Can this be fine?

[lone heart]

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[somber minnow]

obviously the power rule doesn't always work

i guess?

blue and purple are happy

but green and red are not happy

i used the power rule on both and one of them works and the other one doesn't

is this a case where you would have to use the chain rule first?

[hidden fable]

you have to use the chain rule to differentiate sqrt(3x-5)

you have to multiply by the derivative of the "inner" function (3x-5)

[somber minnow]

is that also the case for sqrt(x)?

do you have to differentiate the inner x first?

[hidden fable]

you could! but the derivative of x is just 1

and multiplying by 1 does nothing really

[somber minnow]

wow chain rule is actually pretty interesting

[hidden fable]

so the derivative of sqrt(3x-5) is 3/(2sqrt(3x-5))

[somber minnow]

it's the coolest derivative rule i think

[hidden fable]

if you add that 3 it should work

[hidden fable]

it really is! it's hard to get the idea at first

but with practice it becomes more intuitive

[somber minnow]

it is prolly the hardest rule too

in ap calc ab

[somber minnow]

chain rule kinda goes against the other rules if that makes sense

that's what makes it different

all the power, quotient, product rules go together and can be used interchangeably but chain rule is kinda different

[lone heart]

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[torpid dirge]

a vector space V has a nonzero element v. show that there exists a linear functional phi such that phi(v) is nonzero

[torpid dirge]

ive no idea wher to start :<

[lone heart]

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[torpid dirge]

.clos

.close

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[vestal canyon]

Is the following a valid proof? :

To proof:
[
f\Big[ \ f^{-1}[K] \ \Big] = K
]

The proof:
[
f\Big[ \ f^{-1}[K] \ \Big] = image( \ { x \in X \ | \ f(x) \in K } \ ) = { f(x) \in Y \ | \ f(x) \in K } = K
]

[ocean seal]

Tobi

[vestal canyon]

It kinda feels wrong and right at the same time xd.

"The image of the preimage of a set K is again set K"

[echo socket]

Is K a subset of the image of f? The equality may not be true otherwise

[vestal canyon]

Why?

[echo socket]

E.g., let f: [-1, 1] -> [-1, 1] be given by f(x) = x^2

And let K = [-1, 1]

Then preimage of K is [-1, 1]

But the image of [-1, 1] is [0, 1]

[vestal canyon]

True. xd

Okey how can I make the statment right. Injective seems good

[echo socket]

Injectivity is irrelevant

Surjectivity would make the statement always correct because K would always be a subset of the image of f

But a stronger statement would simply require K to be a subset of the image of f instead

[vestal canyon]

Oh yeah actually I implicitly stated that :

[
f : X \to Y \hspace{1cm} K \subseteq Y
]

[ocean seal]

Tobi

[echo socket]

Y is the codomain, not the image

[vestal canyon]

True so$K \subseteq image( f )$ would be required

[ocean seal]

Tobi

[echo socket]

Yeah

In general the image of ${ x \in X \mid f(x) \in K }$ is only a subset of $K$

[ocean seal]

A Lonely Bean

[echo socket]

And the requirement makes K be contained by the former

So that equality of those sets holds

[vestal canyon]

So the last equality should in general be a subset. Thus:

[ f\Big[ \ f^{-1}[K] \ \Big] = image( \ { x \in X \ | \ f(x) \in K } \ ) \subseteq image ( K ) ]

[ocean seal]

Tobi

[echo socket]

Subset of K

Not subset of image(K)

[vestal canyon]

So :

[ f\Big[ \ f^{-1}[K] \ \Big] = image( \ { x \in X \ | \ f(x) \in K } \ ) \subseteq K ]

[ocean seal]

Tobi

[echo socket]

Yeah

[vestal canyon]

And the other direction needs that : $K \subseteq image( X )$ because we then have :
[ K \subseteq image( X ) ... f\Big[ \ f^{-1}[K] \ \Big] ]

[ocean seal]

Tobi

[vestal canyon]

hum

Okey so in generall for the one direction we have:

[
f\Big[ \ f^{-1}[K] \ \Big] = image( \ { x \in X \ | \ f(x) \in K } \ ) = { f(x) \in K } \subseteq K
]
Because the last set may be empty or smaller then K as in your example with $x^2$ where $[0,1] \subseteq [-1,1]$

Now for the direction in reveres we need:

[ { f(x) \in K } \supseteq K ]

[ocean seal]

Tobi

[vestal canyon]

Ye with $K \subseteq image( X )$ this last is just equality xd thanks

[ocean seal]

Tobi

[vestal canyon]

.close

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[patent prairie]

can anybody help me in this area and perimeter question

[patent prairie]

Asmita and Rasmita each have ropes of the same length. Asmita makes a circle with her rope, and Rasmita makes a square with the rope. If the area of Rasmita's square is 196 square meters, compare the areas of the square and the circle.

how do i find the area of circle and compare the area of square and circle

[dusky shale]

Do you agree that perimeters of both square and circle will be same?

[patent prairie]

idk

[dusky shale]

Dude think a little

[patent prairie]

yes

[dusky shale]

If they both have ropes of same length, then regardless of the shape they make, their perimeter will be equal, no?

[patent prairie]

yes they will have the same perimeter

[dusky shale]

Do you know the formulas to find perimeter of square and circle?

[patent prairie]

ys

[dusky shale]

Whats formula of area of square?

[patent prairie]

l^2

[dusky shale]

So you will get the length of one side of square?

[patent prairie]

yes its 14m

[dusky shale]

So what will be the perimeter of square?

[patent prairie]

56m

[dusky shale]

Do you agree that the perimeter of circle is also 56m ?

[patent prairie]

yes

[dusky shale]

Lol why

How is perimeter same, can you explain

[patent prairie]

nono

idk i cant think

[dusky shale]

Do you know what is perimeter of a shape?

[patent prairie]

which shape?

[dusky shale]

Any

[patent prairie]

we have to add all sides

[dusky shale]

Yes you are supposed to know it by now 😭...perimeter is the boundary of shape...like in square its the sum of 4 sides same as in rectangle, in circle its the total length of boundary, in triangle it is the sum of 3 sides

Area is the region inside the boundary

[patent prairie]

i k now

i just forgot

[dusky shale]

If the 2 girls have ropes of same length then regardless of any shape they make, their boundaries will always be equal...but area may vary

[dusky shale]

Can you explain this now?

[patent prairie]

because the rope is of the same length

[dusky shale]

So do you now have the total length of rope?

??

[patent prairie]

how do i find the total lenght of rope

[dusky shale]

The first girl made a square with it, right?

[patent prairie]

yes]

[dusky shale]

So its boundary should be equal to rope of length?

[patent prairie]

its 14m

[dusky shale]

Thats the length of only 1 side of square

The total boundary, what is it?

[patent prairie]

56m

[dusky shale]

So what will be the length of rope

[patent prairie]

56m

[dusky shale]

And will it be equal to boundary of circle? Think before answering

[patent prairie]

yes maybe?

[dusky shale]

It will be since rope length is same for both circle and square..so their boundaries will be equal..so equate 56m with formula of perimeter of circle..get radius and put it in formula of area of cirxle 👍

[patent prairie]

ok thakyou i found the area of circle ,its 2744/11

.close

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[spare badge]

So the chance of hitting a 6 0 time in 10 rolls is close to 0.0000017%? Assuming to figure this out would be using Binomial distribution (please correct me if i'm wrong there)
How would you calculate the chance of not hitting any number once in 10 rolls? because surely that'd be a higher chance? would it just be multiply by 6?

[olive yarrow]

assuming you're talking about a six-sided dice, that probablilty doesnt seem right

that looks like the pr0bability of hitting a six (or any one number) 10 times out of 10

[spare badge]

I got 0.0000017% from having the chance be 83.33% and "fail" 10 times in a row

[lament forge]

...well (5/6)^10 is around 0.1615, not 0.0000017%, so idk how that happened

[spare badge]

So you wouldn't use binomial distribution?

[olive yarrow]

you could but you dont need to

its straightforward

[spare badge]

regardless, that's not the main part of the question

[lament forge]

the chance of a given roll not being a 6 is 5/6

for that to happen 10 times in a row is (5/6)^10

what you have seems more like (1/6)^10, which is the chance of getting all 6s when you roll a dice 10 times

[spare badge]

Ah i see what i did wrong

I was looking at the chance to fail 83.3% 10, when i needed to look at succeeding it 10 times

But the 2nd line of the question still stands

[lament forge]

...by "not hitting any number" i assume you mean "there's some number that it doesn't hit" and not "you roll the dice and no numbers happen"?

multiplying by 6 is... close, but you'd have some problems with double counting, since if two numbers both don't happen you'd count that possibility twice

so you'd need to subtract (4/6)^10 multiplied by the number of ways to choose two numbers, which is 15

but then in the case where three numbers are missing, you count it three times and then uncount it three times so we need to count it again

and then probably that causes problems with the case where four numbers are missing

idk if there's an easier way than this

[lone heart]

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[hollow vapor]

Hi can I have help with h

[gray isle]

apply factorisation identity for difference of odd powers

[hollow vapor]

Yea im kinda stuck on what to put there

Like i know what to do idk how to do it

[gray isle]

what does the identity i mentioned say?

[alpine sable]

isnt that just the derivative?

[hollow vapor]

(X-Y)(butidkwhattoputhere)

[alpine sable]

[
\m{f'}c = \lim_{x\to c} \f{\m fx - \m fc}{x-c}
]

[alpine sable]

its the definition of the derivative

[hollow vapor]

O

I understand what all these are

Its applying it which is hard for me

[alpine sable]

what is ur f(x) here? in relation to the formula i posted

[hollow vapor]

f(x)= x^2n+1?

[alpine sable]

yeah

f(n)?

[hollow vapor]

f(n)= n^2n+1

[alpine sable]

amazing

so what is f'(x)

[hollow vapor]

Uhh gimme a minute

Yea uh

Idk

My main problem is idk what the hell to do with the numerator

I mean idk how to do it

[hollow vapor]

Im so confused on how to do it cause the only thing i can get is infinity

[alpine sable]

how do you get infinity in differentiating x^(2n+1)

[hollow vapor]

Oh

Whoops

Not infinity

Isnt it just the starting question?

[alpine sable]

wot?

[hollow vapor]

Im sorry

Ignore what ive said

F’(x) means that something is approaching 0 right?

Sorry i was taught to do it this way, but the problem is idk what to do with the 2n+1 as the indice

.close

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[wise tinsel]

hello hello I need some help, im wondering if you can solve the length width of the rectangular box in the middle with only the height and volume given

[vale wigeon]

volume?

is this actually meant to be a 3D shape...?

!xy

[lone heart]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[wise tinsel]

yes

hold on

i only got a picture of from a very weird angle

[vale wigeon]

take a pic of the whole problem with the text

[wise tinsel]

here

trying to do pool c since i was assigned to do it

[cinder tundra]

The reason why you don’t take a proper picture and you do from that weird angle is because you are in class?

[wise tinsel]

nope it was my friends laptop

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[rich fern]

why is -10 rejected here

[golden canyon]

If n = -10, then the factorial isn't defined

[vale wigeon]

what is (-9)! ?

[rich fern]

huh?

[vale wigeon]

you ask why n=-10 is rejected

[rich fern]

if you solve the quadratic you get n-9 or n+10

i want to know why n+10 is rejected

[rich fern]

yea

[vale wigeon]

i, in turn, ask you what happens when you plug n=-10 into the original equation

specifically the left

[rich fern]

oh i see

ah my bad you cant have negative factorials

[distant heath]

how to ask for help

[echo socket]

#❓how-to-get-help

[vale wigeon]

!help

[lone heart]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

@rich fern Has your question been resolved?

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[raven crag]

What does it mean, that the partial sums of the series 1/2 + 1/4 + 1/8 + 1/16 + ... = 1 are generated by the discrete function 1-(1/(2^n)), where n takes the integral values 1,2,3,4,5...?

[raven crag]

Oh wait, I'll edit the question

[golden canyon]

If you plug in n into the function you get the sum of the first n terms

1-(1/2^1) = 1/2, 1-(1/2^2) = 1/2 + 1/4, ...

[raven crag]

Oh I see, thanks!

Awesome

.close

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[tired sparrow]

hello I need help

I have 0 knowledge over stat but I do know what the 3 ms are

[hard patio]

3ms?

[wispy ether]

mean median and mode?

[hard patio]

ah

[crystal berry]

I assume you don't know what a grouped mean is

[lone heart]

@tired sparrow Has your question been resolved?

[tired sparrow]

yh

yep

das all I rlly know

otherwise im clueless

[hard patio]

that is when you have to find mean in a distribution where the variables(any parameter you are finding frequency for, in this case time in hours) is a range i.e for example 2-4 (2 to 4) as opposed to just one value like 2hrs or 4hours or 3hrs etc.