help-10

[restive gorge]

Oh

-inf

But then -inf to 0 the integral would be 0

[zenith raft]

yea

nooooo

[restive gorge]

but the integrand is 0 for -inf to 0

[zenith raft]

it's not

this triangular intersection is the support of f

[restive gorge]

Whats a support now 😭

[zenith raft]

o

just the points that map to something other than 0

[restive gorge]

Achso ok

[zenith raft]

so in this case it's the ones satisfying 0 <= x <= 1 and |y| <= 1- x

[restive gorge]

ok so?

[zenith raft]

so P(X <= 0.5 and Y <= 0.5) is the area of the intersection of that triangle and [-infty, 0,5] x [-infty, 0,5]

but that's not very insightful, it just happens to be that because f is 1 on the triangle

[restive gorge]

,,\int_{-\infty}^{0.5} \int_{-\infty}^{0.5} f(x,y) \dd x \dd y

?

[zenith raft]

[warm shale]

𝔸dωn𝓲²s

[restive gorge]

I may be lost due to sleep of lack but thats what you mean isnt it?

[zenith raft]

yea ig so

[restive gorge]

HUH

,,\int_{-\infty}^{0.5} \int_{-\infty}^{0.5} f(x,y) \dd x \dd y = \int_{-\infty}^{0.5} \left ( \int_{-\infty}^{0} 0 \dd x + \int_{0}^{0.5} 1 \dd x \right ) \dd y

[zenith raft]

[warm shale]

𝔸dωn𝓲²s

[restive gorge]

Then I get 0.5 from -inf to 0.5

[zenith raft]

[restive gorge]

Am I doing something wrong?

[zenith raft]

this diverges doesn't it?

[restive gorge]

Ummm yea

So it doesnt make sense

[zenith raft]

the value of $\int_{-\infty}^{0.5} f(x,y)dx$ depends on $y$

[warm shale]

slayla

[restive gorge]

I'm lost

I think I figured it out

And I can do 0 to 0.5 because -inf to 0 trivially is 0 with integrand 0

fuck sleep

.solved

[obtuse pebble]

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[exotic walrus]

help asap

[exotic walrus]

First off I'm just trying to find the derivative of h(x)

I found the derivative of f and g

f = 1/2x^2+x+3

g=x+1

Does this look correct so far?

[minor pilot]

Hello, did you write this?

It looks correct, yeah

[exotic walrus]

okay great

This is what I ended with

@minor pilot

[minor pilot]

Yes!

It's correct

[exotic walrus]

So now I find the slope by plugging 1 into the derivative function?

then i just get a point on the graph to find b?

[minor pilot]

That's where you find the slope, yes!

[minor pilot]

How do you mean find b?

Oh

Your y-value

Plug in x=1 to the original function

[exotic walrus]

This is what I ended up getting

[minor pilot]

Where did you get 19/8

I see

[minor pilot]

Good

[exotic walrus]

Looks fine?

[minor pilot]

And you inserted it into point-slope form?

It looks wonderful :>

[exotic walrus]

I think it's fine without

[exotic walrus]

Okay thank you so much!

.close

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[atomic orbit]

<@&286206848099549185>

[brazen gorge]

poor soul

you should try simplifying everything in the brackets before differentiating

[heavy shore]

did the author get divorced just before making this?

[obtuse pebble]

@atomic orbit Has your question been resolved?

[atomic orbit]

Nah

I am dying

[obtuse pebble]

@atomic orbit Has your question been resolved?

[drifting wraith]

yea

after 10 years of marriage

[obtuse pebble]

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[heavy shore]

LMAOOO

[heavy shore]

.close

[obtuse pebble]

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[dapper solstice]

i understand in the mark scheme you have to multiply by 0.15cm to the mg, by why would you multiply the force by 0.04?

[obtuse pebble]

@dapper solstice Has your question been resolved?

[dapper solstice]

<@&286206848099549185>

[obtuse pebble]

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[shut citrus]

from 2nd line to 3rd line, how where did that sec^2 theta go??

[dim temple]

cos(x) times sec(x) is 1

[shut citrus]

ohh ok got it, thanks. always missing some sort of trig identity. tyy

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[tame coyote]

What did I do wrong for 14f?
I wrote (2P1)(5P2)(2P1)(3P3) which gave out 480 instead of answer 960

[cunning burrow]

Why don't you just consider each case. It is not clear what you are trying to do from your working out

[tame coyote]

Well I wrote
So assuming the start is either N or D, therefore 1P1
Then I go 5P2 because there are 5 letters left aside from C and D, and there are 2 slots, therefore 5P2
Then this spot must either be Nor D, so 1P1
Then there are 3 remianing letters with 3 slots, therefore 3P3

So say if I put 4P1 also, which are the possible ways for them to be placed

Yeah that's still 480

[cunning burrow]

Why are assuming either start C or D. The question is 14f)

Just to confirm there are no repetitions for 14f)

[tame coyote]

Yeah because it's a sequence, and as the difference in sequence is there it therefores uses permutations

If I use factorial
Say (1)5*4(3!)(4)

Which is just the same

[cunning burrow]

I am still lost

Why don't you consider the case:

N??D???

[tame coyote]

Oh fuck

Yeah

Gimme a sec

Yeah 14f

I had a typo

I typed N as C

[obtuse pebble]

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[twilit meteor]

can someone help mee with this

[versed stratus]

!original

[obtuse pebble]

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.

[versed stratus]

please

[twilit meteor]

that is the original question

everything until 'where k = 2root3'

[versed stratus]

is that 11 or 12?

[twilit meteor]

cot-1(11/k)

was that what u were asking

[versed stratus]

yes

hmm

$\operatorname{arccot}\left(\frac{6}{k}\right)+arcor\left(\frac{11}{k}\right)+\operatorname{arccot}\ \left(\frac{18}{k}\right)...$

[warm shale]

ƒ(Why am. I here)=I don't Know

[twilit meteor]

yea

value of that

basically

[versed stratus]

start by grouping terms I guess

[twilit meteor]

just below the question i wrote it in a better way

arctan thing

[versed stratus]

$\sum_{i=1}^{\infty}arcc\tan\ \left(\frac{2\sqrt{3}}{2+\left(i+1\right)^2}\right).$

right

[warm shale]

ƒ(Why am. I here)=I don't Know

[twilit meteor]

u have to use the formula arctan(x) - arctan(y) = arctan((x-y)/1+xy)

[versed stratus]

yeah

[twilit meteor]

(n - (i+1))^2

but it doesnt work

[versed stratus]

,w $\sum_{i=1}^{\infty}arcc\tan\ \left(\frac{2\sqrt{3}}{2+\left(i+1\right)^2}\right).$

[warm shale]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by physicsrocks

[versed stratus]

not sure, sorry

convert it to an integral I guess

a rienman integrak

[twilit meteor]

how

i havent learnt it

@versed stratus

[versed stratus]

I was thinking $\int_0^{\frac{\pi}{2}} \frac{k}{2+x^2}$

,w $\int_0^{\frac{\pi}{2}} \frac{k}{2+x^2}$

[warm shale]

ƒ(Why am. I here)=I don't Know

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Requested by physicsrocks

[versed stratus]

wait

this is wrong

my bad

[twilit meteor]

why is it wrong

actually i havent learnt integration yet either

[versed stratus]

oh

in that case

[twilit meteor]

i have to solve using just ITF

[versed stratus]

this from a coaching book I pressume

[twilit meteor]

most probably

i got it in class

[versed stratus]

hmm

the value of k is causing problems

[twilit meteor]

i was expecting this to work

but it doesnt

can u tell me y

[versed stratus]

https://math.stackexchange.com/questions/2987659/calculate-sum-n-1-infty-arctan-bigl-frac2-sqrt2n21-bigr?noredirect=1

see this

[twilit meteor]

ya but can u tell me why that doesnt work

[versed stratus]

what have you done

[twilit meteor]

the 2 photos i sent

[versed stratus]

no idea tbh

[minor anvil]

what is that supposed to mean

can you maybe explain what you've tried

also i do know how this sum telescopes, so i can tell you that too after you finish explaining your line of thought

[twilit meteor]

wow u m8 have done this question yourself while preparing for jee

[twilit meteor]

because i need the denominator to be a sum of 2 terms + 1 and the numerator to be the difference of the terms multiplied i multiplied the numerator and denominator by a var. x
then i assumed the quadratic in 'n' in the denominator to be of the form (n-a)(n-b) aand the diff of these 2 terms which is b - a is essentially the diff in roots of the quadratic(root of discriminant/mod(a)) shud be equall to the term in the numerator, i think this shud explain what i tried

[minor anvil]

i haven't done this exact problem, but similar ones yes

[minor anvil]

oh the idea is right you do need the difference to reflect in the numerator

im surprised people go out of their way to come up with such amazing ways to execute that idea haha

[twilit meteor]

i mean that is the 'only' way

acc to my teacher atleast

and its very efficient in other problems of the same typee

[minor anvil]

Well what's important is that

Sorry

Wrong emoji

|beta - alpha|

and with this expression in x, you do get the right x value

it is correct so far

[twilit meteor]

i got that biquadratic in x now

and the roots are not ones u can guess

[minor anvil]

biquadratic?

it's a rather simple quadratic

[twilit meteor]

yea the 2nd image'

[minor anvil]

12x^2

that's the error

should be 12x^2

[twilit meteor]

no when i square on both sides it becomes 12x^4

[minor anvil]

it was 2sqrt(3)x

if you square it's 12x^2

[twilit meteor]

no i took the x in the denominator to the other side

[minor anvil]

ah there was that too

[twilit meteor]

i did 2 steps iin one so iit m8 not have been understandable

or its just my handwriting

lol

[twilit meteor]

but why doesnt it work

[twilit meteor]

yea either way its all inside arctan so the negative sign if it appears can be taken outsiide

[minor anvil]

yeah still, i like abs value

[minor anvil]

it should, let's see if there's an error, either way I already see the way it's telescoped so let's see if i csn guess the root also haha

oh you did make a mistake

it should be 4x^2 not just 4 inside sqrt

@twilit meteor

[twilit meteor]

oh

thanks

im so dumb

now i get a cubic

[twilit meteor]

3x^3 + 2x -1

[minor anvil]

i dont trust your calc anymore, let me also get that cubic just to be safe haha

[twilit meteor]

yea my weakpoint is calculatiions tbh

its been so since 10th grade

and i stll donno how to get better at t

[minor anvil]

well get back to that soon

but before that

you're trying something like

$\frac{|\alpha-\beta|}{1 + (n-\alpha)(n-\beta)}$

[twilit meteor]

yes

[warm shale]

ginny

[twilit meteor]

what about it tho

[minor anvil]

your work is all over the place

[minor anvil]

you factored it like this

but it should also have x multiplied

[twilit meteor]

and then. i wrote xn^2

[minor anvil]

exactly, you had that

[twilit meteor]

yea i noticed but i cudnt find a way to get rid of it

[minor anvil]

but that is the error lol

that's what you have to get rid of

[twilit meteor]

(xn-a)(n-b)

[minor anvil]

x(n-a)(n-b)

otherwise your root changes from a to a/x

[twilit meteor]

yea

oh ok

[minor anvil]

$(\sqrt{x}(n-\alpha))(\sqrt{x}(n-\beta))$

[warm shale]

ginny

[twilit meteor]

buut now the difference is def gonna have an 'n' term in it right

oh yea

this solves the problem

[minor anvil]

i know

haha

$\sqrt{x}|\beta - \alpha| = 2\sqrt{3}x$ hopefully?

[warm shale]

ginny

[twilit meteor]

yeaa will try and let u know

after which u cud tell me ur method

[minor anvil]

i have no method, i already saw the factorisation

basically it's this, but you can guess how it factors

[twilit meteor]

i tried guessing for half an hour or maybe more

i cudnt

so i thot of this

[minor anvil]

spoiler alert ||its 1 + i/sqrt(3) * (i+1)/sqrt(3)|| after you divide everything by ||3|| once

[twilit meteor]

which has no 'guesses' involved, although if i get a cubic or biquadratic , its essentially useless

[twilit meteor]

im not clickng on that

[minor anvil]

you'll get a quadratic now

[twilit meteor]

thats good to know

but to solve this in an exam seems insane

doesnt it

[minor anvil]

not if you see the factors

[twilit meteor]

especially in jee adv

but i dont thnk its that straight forward

seeing the factors i mean

[minor anvil]

it can be hard

i struggle with this too sometimes

you have to know exactly what you need to multiply/divide

[twilit meteor]

wait i got a llnear

[minor anvil]

show work

[twilit meteor]

and whats worse i got x = -1

[minor anvil]

you should get a Quadratic, with one of its root to be -1 that you'll reject

[minor anvil]

x^2 in the denominator

Not according to your work

okay yeah

[twilit meteor]

oh yea

[minor anvil]

you squared rhs but no x^2

[twilit meteor]

but its stll linear

x^2 on th othe side

yes

[minor anvil]

x^3

x from denominator, x^2 from 12x^2

[twilit meteor]

omg

x = 1/3

am i right

[minor anvil]

yeah

i already knew that, all this time i was working to find the equation that has that root lol

[twilit meteor]

can you pls tell me how i improve my absolute trash calculation skills

it has already cost me so many marks

[twilit meteor]

oh

but how did u see 1/3 was the numbe

[minor anvil]

$\frac{2 \sqrt{3}}{n^2 + 2n + 3}$

[warm shale]

ginny

[minor anvil]

it only makes sense with 1/3 to make the denominator 1 + n/sqrt(3) * (n+2)/sqrt(3)

[obtuse pebble]

@twilit meteor Has your question been resolved?

[twilit meteor]

.close

[obtuse pebble]

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[teal bane]

If tan theta is = -4/3 then why is sin theta = 4/5 and cos theta = -3/5

Like why sin is positive and cos negative?

[rich plume]

quadrants

[teal bane]

I know tan is negative in 2nd and 4th

Sin is positive in 2nd and cos is positive in 4th

[high lily]

insufficient info to determine whether sin or cos is the negative one

[rich plume]

oh yeah

[teal bane]

It is the slope of the line

4x + 3y + 2 = 0

[high lily]

angle of inclination is usually taken to be positive

0° < theta < 180°
and for the case of negative slope
90° < theta < 180° (Q2 where sin is positive and cos negative)

always post the full context of the problem

[obtuse pebble]

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[slate crater]

Hello

[slate crater]

How to prove unimodality?

For example i have some polynomials on the interval [0,1] and they all have one single extrema

how to prove this

[obtuse pebble]

@slate crater Has your question been resolved?

[obtuse pebble]

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[sudden axle]

: a sinsousadal function has an amplitude of 3 units a period of 180, and a max at (0,5). represent the function as a sine function and cosine functino

[sudden axle]

Can someone help me with this

?

[obtuse pebble]

@sudden axle Has your question been resolved?

[obtuse pebble]

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[dry horizon]

how do I start this guys

[final tangle]

i dont know how to solve this

do you know how to solve it

[dry horizon]

no

thats why im asking

[rich plume]

omg its albert einstein

[final tangle]

but i dont know what the answer is

@rich plume do you know the answer

[rich plume]

maybe

[dry horizon]

so I tried integrating to get the 2 position equations

[rich plume]

you only need the three eqations of motion

idt integration is required here

v=u+at
s=ut+(1/2)at^2
v^2=u^2+2as

[dry horizon]

it should be since i know that acceleration is -32ft or gravity

not completely sure though

[final tangle]

yeah im pretty sure is integration is needed

[final tangle]

i think so too

[dry horizon]

💀

[dusk ruin]

these formulas are just integration P:

[dusk ruin]

you can plug the values into the formulas beard provided if you wish

or use the more aptly named $x(t) = v_0t+\frac{1}{2}at^2$

[warm shale]

Astral

[dusk ruin]

which, while derived from integration as well, and in fact exactly the same as the formulas above, is much easier to understand

[dry horizon]

yeah I got that part

so if I have the ball thrown 2 seconds after

do I plug in (t-2) for it

[dusk ruin]

yes

[dry horizon]

for t*

so I tried that

[dusk ruin]

exactly, you do understand

[dry horizon]

and my solution did not work

[dusk ruin]

what equations did you get?

[dry horizon]

so I have $s(t) = -16t^2+20t+380$

[warm shale]

albert einstein

[dusk ruin]

also make sure you're using the right value for gravity

since the values provided are in m/s

and gravity is 9.81 m/s^2

[dry horizon]

oh shoot

[dusk ruin]

fyi note that start height is completely irrelevant

[dry horizon]

that must be why since in another problem they gave gravity in feet

[dusk ruin]

since both balls start with the same offset

[dry horizon]

ah

one sec

[dusk ruin]

yeah that's probably your issue if you otherwise thought you knew how to do this

[dry horizon]

ah

thank you so much

[final tangle]

oh

thank you

.close

.close

.close

.close

[dry horizon]

💀

thanks again

.close

[obtuse pebble]

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[dusk ruin]

you can't close other people's help channels lol

[obtuse pebble]

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[obtuse pebble]

Please don't occupy multiple help channels.

[timid silo]

This is what ive tried but ive been doing it wrong

[crude solar]

In the second line it’s in addition, so you will have to cancel out the + 10^100 as well

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

take common

YEA IM HERE SORRY

10?

🥲

[obtuse pebble]

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[sweet sparrow]

I'm confused about the difference between partial sums and the general formula

[velvet falcon]

Can you clarify what you mean? Maybe provide an example?

Maybe like the partial sum of an arithmetic sequence, you mean?

[sweet sparrow]

Yes

Sn and An

[velvet falcon]

And by general formula you mean just a standard sum?

[sweet sparrow]

.close

[obtuse pebble]

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[obtuse pebble]

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[sturdy siren]

Can someone please help me try to understand and get thru the steps to solve this problem

[sturdy siren]

all i know what to do is bring the 5 to the right side

then ^2 both sides to take out the square root in the front of the equation

then i get lost

[dark stirrup]

so far so good

you'll end up with a quadratic

factor it or use quadratic formula

[sturdy siren]

alr ima keep going and ill let you know what i get

is the equation u use to plug into the quadratic formular $-x^2+11X-24$

[warm shale]

0

[dark stirrup]

looks good

[sturdy siren]

alr

im going to plug it into the formula

then lyk my answer

i got

x=-11±5/-2

it looks wrong

idk what i did wrong🥲

[dark stirrup]

show how you plugged it in

[sturdy siren]

alr

this is my work

[dark stirrup]

Oh

That is correct

I thought you wrote $-11\pm\frac{5}{-2}$, not $\frac{-11\pm5}{-2}$

[warm shale]

SWR

[dark stirrup]

[sturdy siren]

ooo

is that the answer?

like now i can put it into my math work

to check if its correct

or is there another step

[dark stirrup]

simplify it

calculate both $\frac{-11+5}{-2}$ and $\frac{-11-5}{-2}$ and see if either work as solutions

[warm shale]

SWR

[sturdy siren]

oo

i got

3,8

is that correct?

[dark stirrup]

plug them both in and verify

[sturdy siren]

to the original?

[dark stirrup]

yes

[sturdy siren]

alrr

8 is the answer

[dark stirrup]

correct

good work

[sturdy siren]

Thank you!!

.close

[obtuse pebble]

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[flat wharf]

is omega a number or not?

[flat wharf]

literally that simple

[trim portal]

omega?

[flat wharf]

yes

[trim portal]

omega can refer to a lots of things

[flat wharf]

as in that O

[trim portal]

in what O?

[flat wharf]

the number

well not number

like infinity

[teal turret]

$\Omega$ and $\omega$

[teal turret]

thats omega

[flat wharf]

yea

that one

[trim portal]

omega is a letter

do you mean this one?

in context of set theory?

[flat wharf]

it said this

[trim portal]

hmm

omega is countable afaik

the big omega then?

anyway

[flat wharf]

idk

[trim portal]

it's ordinal number in both cases

[flat wharf]

it's a project I'm working on

[trim portal]

not a traditional natural or real number

it's ordinal number

[flat wharf]

bcse there's this big question we are made to ask

and mine was

can everything be described in numbers

[trim portal]

huh

that's interesting question

[flat wharf]

yea

[trim portal]

more of a philosophical one tbh

[flat wharf]

yea

but theres this one specific bit

[trim portal]

you'll need to get some definition of number for that

there are plenty of them

[flat wharf]

we did like

[trim portal]

(non mathematical usually)

[flat wharf]

all like

ones that exist

like

it could be a temperature

idk how to describe that

[trim portal]

Anything describable in finite amount of finite words of finite alphabet should be describable with natural numbers

because you can just encode it in some way

[flat wharf]

That's kinda like cheating tho

almost like making new letters

[trim portal]

basically

but if you have object such as "cat" you cant simply say, oh cat is just 2646135136

so if you think that it's cheating, you should probably accept that some things cannot be described purely in numbers

[flat wharf]

so far what I've got is

[trim portal]

or you have to broaden the definition of number by a lot

[flat wharf]

for the tangible

u can describe every atom

but I got stuck

bcse

idk if u can describe its position in an infinite universe

[trim portal]

with real numbers definitel

(also technically the universe is not infiniteú)

[flat wharf]

say it was tho

[trim portal]

(also technically, its divided to units of finite length)

[flat wharf]

and u had a theoretical object

[trim portal]

Then it's a space R^3

meaning every point can be described with a triplet of real numbers (r1, r2, r3)

[flat wharf]

infinitly far away

[trim portal]

infinitely far away?

huh?

[flat wharf]

yea yea i'm a coder, I get that

[flat wharf]

like

in theory

[trim portal]

this is not a common thing, even in infinite universe

[flat wharf]

say in your imagination

in an infinite universe

[trim portal]

in R^3, which is essentially infinite, every 2 points have finite distance

the fact that the universe is infinite doesnt imply that there can be 2 things infinitely far away

[flat wharf]

but that object can be infinitely far away from u?

surely?

like

realisticly it wont

but in a theoritical world

bcse however far away u can put it

[trim portal]

even if the world is infinite, it doesnt mean that there can be object infinitely far away

[flat wharf]

U 100% sure

bcse I watched some like

chess video on this

and it was very similar

and said something with

omega

[trim portal]

yes, im quite sure as I have an example. R^3. World where every point can be described through 3 coordinates

in this world of R^3, you can get as far away as you want

you can get 1 unit away

10 units away

or 10^10^10^10 units away

but you cant get infinitely many units away

the distance from center and any other object will always be finite

but it can get as large as you want

it's like saying that because the set of natural numbers is infinite, there must be infinite number in it

but there is no infinite natural number

[flat wharf]

ohhhh

[trim portal]

the set contains all natural numbers 1,2,3,4.... but it's still infinite set

although all of the numbers inside are finite

[flat wharf]

ok

so its possible to describe everything tangible?

[trim portal]

hmm

technically it should be, in the sense that with a number you can refer to unique tangible object

[flat wharf]

like how

[trim portal]

Every tangible object should be describable as a set of points

[flat wharf]

like positions of atoms

is a point

[trim portal]

you wanna work with atoms?

that simplifies it a bi

ibt

[flat wharf]

well obv u can join the atoms

[trim portal]

there are finitely many atoms in every tabgible object, right?

[flat wharf]

wait

what if in theory u had an object with infinite atoms

or is that also not possible

[trim portal]

thats essentially possible

not in this universe (as far as we know/think/believe), but in R^3 it is

[flat wharf]

ohhhhhh

ok that causes a few problem

[trim portal]

as long as its countably infinitely, it should be okay

and if we work with atoms, which occupy finite amount of space (which cannot get arbitrarily small), there can be at most countably many of them

in R^3

[flat wharf]

what does that mean

[trim portal]

it means that we can somehow count it

you can for example count natural numbers

simply 1, 2, 3, 4, 5, 6...

you can also count the integers, you can list them in following order and then count them:

0, 1, -1, 2, -2, 3, -3...

[flat wharf]

yes

[trim portal]

you can even do this with rational numbers

here is the way to do it

you start and go through the arrows and count

[flat wharf]

ok

[trim portal]

and you will eventually get to any rational number

[flat wharf]

ohhh

[trim portal]

but the next step is a problem

[flat wharf]

I see

[trim portal]

it's the reals

reals are uncountable

[flat wharf]

what are reals

[trim portal]

there is no way you can start counting them in a way, you will eventually get to every single one of them

[trim portal]

real numbers

[flat wharf]

which are

like non

sqrt(-n)

sort of stuff

[trim portal]

sqrt(n) sort of stuff mostly

[flat wharf]

like a number that could be a temperature

[trim portal]

sqrt(2) is not rational, but its real

[flat wharf]

is pi and all included

[trim portal]

there are also some reals that cannot be descrive

described

not even with finite amount of words

[trim portal]

yep

pi is included

[flat wharf]

ok

so like a temperature

[trim portal]

you could say that

[flat wharf]

one sec I gotta ask if emotions are tangible in some philosophy server

[trim portal]

lol

that would make it a bit harder

[flat wharf]

wait

apparently I have to fill in an intro

for it

nvm then

bcse aren't emotions just the electronic signals

from the brain

[trim portal]

it depends

emotions are caused by the neural system and all those signals

probably

possibly hormones play a role too, but the point stays

but can you really say that emotion is nothing but those signals?

emotion is more like a feeling, concept or state

it can be described through those signals, sure

but it doesnt mean its the same thing

it'd be like saying that cat and 6361351513515134135134 are the same thing, because through some encoding we could map the number into the cat

[flat wharf]

hmmm

yea

[trim portal]

this is all a matter of opinions though

[flat wharf]

idk

philosophy server is kinda a headache to use though

[trim portal]

its probably because philosophy isnt like math

math is precise, philosophy is mostly matter of opinion

[flat wharf]

yea

I have to agree

[trim portal]

for this task, just make some opinion and then argue why did you make the opinion and why do you think it's correct

you can present examples of how some object can / cant be described

etc

[flat wharf]

yea fair enough

teacher decided to make our life a headache though

by making us include scholarly research

[trim portal]

huh

was this from math lesson?

[flat wharf]

no no

we just chose a question to do with numbers

[trim portal]

what subject is this?

[flat wharf]

for some dumb reason

[flat wharf]

just a club

in school

[trim portal]

ah ic

[flat wharf]

what should I add to this

Just summarise what u said plz

I'm way too tired rn

[trim portal]

Even in sufficiently small infinite universe, we can describe positions through a triplet of numbers

[flat wharf]

ok thank u

can u just say what that means

as we may get asked on it

how can infinite be small

@trim portal

ok it doesn't matter...

.close

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[silver torrent]

im a bit confused what the d in the context of derivatives means. For example, if you have df, is the d a prefix to indicate that df is a very small change in f or is d some constant that f gets „multiplied“ with?

[lapis charm]

Are you comfortable with delta x meaning change in x

dx is the same except for infinitesimal delta

[silver torrent]

yes I know that (from physics I think lmao)

but then what does the d mean? Im not talking about dx or dy or df or anything, just talking about the d

[obtuse pebble]

@silver torrent Has your question been resolved?

[lapis charm]

Afaik it doesn’t really mean anything by itself

What does a negative sign mean by itself?

[silver torrent]

yeah

so its just a prefix

.close

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[frosty river]

sin is not injective

There are infinitely many angles whose sine is 0.897...

You need extra info to determine the angle. In this case, I'm pretty sure you have these data:

sin(x)=0.897...
x is between 90° and 180°

The method is called reduction to second quadrant

It's doing the "inverse" of the method "reduction to the first quadrant". (It is actually reduction to the first quadrant).

You reason on the goniometric circumference to find an angle in the second quadrant (90, 180) whose sine equals the sine of the value that the calculator gives

Since the calculator gives 64, the angle you are looking for must be 116 because...

Think why, if you don't know why, I help you

Not really in this caze

Think of how the sines in the second quadrant relate to those in the first one

If x is in (0,90) then sin(180-x)=sin(x)

If you draw the triangles this is clear ↑

What is the result of 180-64?

[obtuse pebble]

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[mighty portal]

somebody help please

[mighty portal]

what is the curved suface area of one frustum

[obtuse pebble]

@mighty portal Has your question been resolved?

[mighty portal]

<@&286206848099549185>

@analog vault How do i find it

I got 5π - 5/√6 (π)

<@&286206848099549185> please

[obtuse pebble]

@mighty portal Has your question been resolved?

[mighty portal]

<@&286206848099549185> plz i need help on this project

[gray sun]

its 1:30 am.

im eepz

eppy

eepy

[mighty portal]

for u

for me its literally 6 30

[gray sun]

and i dont even know math idk why i have this role

[gray sun]

nicee

[obtuse pebble]

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.

[gray sun]

sorry

[mighty portal]

nah i accidentally did the ! no sol thing

[obtuse pebble]

@mighty portal Has your question been resolved?

[obtuse pebble]

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[visual pulsar]

can someone help me visualise this

plane being normal to axis

they gave this as the diagram but i dont see how the plane is normal to the axis

normal means it has to be perpendicular right

[coral plank]

yeah

as its perpendicular its normal to it

by def

[obtuse pebble]

@visual pulsar Has your question been resolved?

[visual pulsar]

ahh it would be better if they said axis normal to plane

got it

[obtuse pebble]

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[sharp hare]

,rotate

[sharp hare]

im not sure

that i did the concave upward part correctly

or the second derivative

[tranquil ginkgo]

$\frac{d^2y}{dx^2}$=$\frac{\frac{d{\frac{dy}{dx}}}{dt}}{\frac{dx}{dt}}$

[sharp hare]

i know i messed up the first derivative actually

it should be 2t+1/(2t)

$\frac{2t+1}{2t}$

[warm shale]

ram

eurgene114514

[sharp hare]

i see

wait

how do i find dy/dx

[tranquil ginkgo]

you already have it above

[sharp hare]

oh right

how do i find dx/dt

i know d (dy/dx) = 1

[obtuse pebble]

@sharp hare Has your question been resolved?

[obtuse pebble]

@sharp hare Has your question been resolved?

[sharp hare]

@analog vault

[obtuse pebble]

@sharp hare Has your question been resolved?

[sharp hare]

😦

[teal bane]

First

Take derivatives of x and y

Dy/dt and Dx/dt

Then divide them to get Dy/Dx

Then take 2nd derivatives in dy/dt and dx/dt

and do the same

For d^2y/dx^2

[obtuse pebble]

@sharp hare Has your question been resolved?

[obtuse pebble]

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[old coral]

Hi, I was doing a recurrence relation question by using eigenvalues and eigenvectors. I was able to find a solution containing matrix. But is there a way to just find the general solution without any matrices? I’m trying to find the equation Xk

[old coral]

If i were to just use only first value in the matrix, i won’t be able to get X1 = 3 and X2 = 4

So i’m kinda confused

[obtuse pebble]

@old coral Has your question been resolved?

[obtuse pebble]

@old coral Has your question been resolved?

[red ice]

There is a way using the characteristic polynomial: move all the terms to the left and you get $r^3 + 5r^2 - r - 5 = 0$

[warm shale]

south

[red ice]

,w r^3 + 5r^2 - r - 5 = 0

[warm shale]

Results provided by WolframAlpha

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Requested by sooouth.

[red ice]

That suggests you have done something wrong with the eigenvalues

,w a(k + 3) = -5 a(k + 2) + a(k + 1) + 5a(k)

[warm shale]

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Requested by sooouth.

[red ice]

Yep and subbing in k = 0, 1, 2 will give you 3 linear equations in c1, c2, c3

Evidently this is not how your assignment wants you to solve the question, so this is just for your information

[obtuse pebble]

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[still badger]

writing $\sqrt{11}$ as continued fraction

[warm shale]

babario

[still badger]

.close

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[exotic locust]

.close

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[teal bane]

Hello

[teal bane]

I had a doubt related to circles

Theoritical doubt not a numerical

the formula xx1 + yy1 + g(x+x1) + f(y+y1) + c = 0

Represents a tangent to a circle from external point x1,y1

And also the chord of contact of two tangents from the same point

How is that possible?

Nevermind got it figured thanks

.close()

.close

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[daring burrow]

Is the answer not understoood due to my constant sign? Not sure if they want a small c or not

[high crater]

probably they want small c

[daring burrow]

It still says it cant be understood haha

I notice the c is bolded

do I need to treat it as a vector?

[thin pawn]

Have you used this site before? And if so, did they accept the exponents in this form? Usually exponents are represented using ^

Or they could want all the constants before the t

[daring burrow]

I havent needed to use it for vectors before

[thin pawn]

C is not a vector

Wait i,j,k.. are you doing vector calc actually?

[daring burrow]

Yes its a calc 3 course

Just started using vectors actually haha

I figured it out, it was supposed to be a vector

.close

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[teal bear]

hey i need help woth what this code is doing

[teal bear]

i have some knowledge about how python works, but i really dont understand how this exact code works

the task is to create a code that decides the area in the case that a person chooses to have 6000 rectangles in a function

thats what the task looks like

[tame narwhal]

it's calculating sum of the areas of 6000 rectangles under the curve from 0 to 6

[teal bear]

could you explain part by part on the code?

why is it doing x-max minus x-min?

[tame narwhal]

because that is the width of the whole interval. in this case 6

[teal bear]

ohh

but whats the difference between putting width as x-max and not the minus x-min? x-min is 0?

i dont see the point of that line being written like that

[tame narwhal]

what if someone wanted a different x_min? better to code it explicitly

[teal bear]

ah okok thanks, but anyways moving forward to the part i find most confusing, the area at the bottom, whats being calculated in the area = area + width * f(x)

what value does f(x) hold?

[tame narwhal]

the function value

same as in math notation

[teal bear]

so its just multiplying that whole thing with 1/9 etc…

?

[tame narwhal]

yeah, whatever f(x) is

[teal bear]

the value never changes does it?

oh wait

it does fuck

the loop

[tame narwhal]

x changes

[teal bear]

why does it change though, why does it do x = x + width?

[tame narwhal]

because you want the area of each rectangle

if you don't change x, you don't change rectangles

[teal bear]

ah ok i sort of understand it, thanks

.close

[obtuse pebble]

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[obtuse pebble]

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[deep ravine]

Why is v’(4) multiplied by 0.2?

[obtuse pebble]

@deep ravine Has your question been resolved?

[obtuse pebble]

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[spice chasm]

why does $\dv{x}\sin^{-1}(\cos x)\neq-1$

[warm shale]

Jash

[spice chasm]

?

u get $\frac{-\sin x}{\sqrt{1-\cos^2 x}}$

[warm shale]

Jash

[spice chasm]

1-cos^2 is sin^2

sqrt is sin

-sin/sin=-1

[marsh geyser]

What do u mean by this

[spice chasm]

sqrt of sin^2 is sin

[warm canopy]

$\sqrt{\sin^2(x)} \neq \sin(x)$ in general

[warm shale]

ΣAC

[marsh geyser]

No it is not

[spice chasm]

how

if u do substitution with like u=sinx then sqrt{u^2}

=u

[warm shale]

nyxie9151

[warm canopy]

what if u = -1?

[spice chasm]

1

[marsh geyser]

So you deleted one solution

Imagine sqrt(x^2) = 1

[spice chasm]

so do u do like $-\frac{\sin x}{\abs{\sin x}}$

[marsh geyser]

Now this can be true when x=1 but also when x=-1

[warm shale]

Jash

[spice chasm]

wait

isnt that a known function

i forgot the name

its like

[modest ingot]

sgn

[spice chasm]

ye

so $-\text{sgn}(\sin x)$

[warm shale]

Jash

[spice chasm]

oh ok ty

.close

[obtuse pebble]

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[slate crater]

Hello, how would this formula look for t^(k-1)?

[tired shell]

you can replace the three k's with k-1 and it works

[obtuse pebble]

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[open spoke]

Given a connected graph G with n vertices, why will there always be a connected subgraph of G with n-1 vertices?

[obtuse pebble]

@open spoke Has your question been resolved?

[tired shell]

you'd split it into cases, either it's a tree with leaves, or has a cycle

or use spanning trees since those always have leaves

[obtuse pebble]

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[obtuse pebble]

Please don't occupy multiple help channels.

[ashen iron]

Can I just get the answer to this

I don’t have time to sit and talk about the steps

Can u just send what to write

In school rn btw

[fresh pebble]

just sub the area that was given into the area of triangle formula and isolate for h

[ashen iron]

I got 10 mins to turn this in

[ashen iron]

And how do I do that?

[fresh pebble]

whats the formula of a triangle

[ashen iron]

A=bh/2

[fresh pebble]

yeah

area and base are already given so we can just substitute that into the equation

[ashen iron]

Ok

So what is the area and base?

[fresh pebble]

136.5 = 21h / 2

the area given was 136.5 and the base of the traingle was 21 right?

,rccw

[warm shale]

Couldn't find an attached image in the last 10 messages.

May 7, 2024, 10:18 PM

[ashen iron]

Looking for this?

[fresh pebble]

,rotate

[fresh pebble]

thanks

[ashen iron]

Yes

[ashen iron]

He

*yw