help-0

[zinc turret]

I m thinking to made this by writting full part 2x+1/3 =0

And full part of 3x+1/4 =0

So that the equality is true

[cerulean garnet]

are you tryna find x?

or what

[zinc turret]

Yes

[cerulean garnet]

ok go ahead

[zinc turret]

I need to find x

[cerulean garnet]

continue expanding on this

[alpine sable]

@zinc turret use that [t] <= t < [t]+1

[cerulean garnet]

,turn

how do you turn this around ;-;

[zinc turret]

,turnr

[vale wigeon]

,rccw

[zinc turret]

Thanks

[vale wigeon]

this is the command for "rotate counterclockwise"

rotating clockwise is ,rcw

[zinc turret]

Is this corect?

[lone heart]

@zinc turret Has your question been resolved?

[lone heart]

@zinc turret Has your question been resolved?

[lone heart]

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[crimson oar]

!status

[lone heart]

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

[crimson oar]

1

[lament wyvern]

what's the formula for the surface area of an open topped cylinder

[crimson oar]

no clue sorry

[vale wigeon]

do you know what a cylinder looks like

[crimson oar]

first time doing this sort of a question

yes

[vale wigeon]

and do you know how to find the surface area of a full cylinder

i.e. closed top

[crimson oar]

yes

[vale wigeon]

ok tell me

how do you find it

[crimson oar]

2pir (r+h)

cause CSA

and area of 2 circles

OH WAIT

[vale wigeon]

yes exactly

[crimson oar]

ITS OPEN TOPPED FROM ONE END

[vale wigeon]

here you just have only 1 circle

the bottom

[crimson oar]

OH

[vale wigeon]

so instead of 2πrh + 2πr^2 you have 2πrh + 1πr^2

[crimson oar]

ohh

and then we find height

and then find volume

[vale wigeon]

yes

[crimson oar]

thank you sm!

.close

[lone heart]

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[weak swift]

If you have an ERROR of 4.13, how do you round it? Do you round it off to 4.1 or 4.2?

[lone heart]

@weak swift Has your question been resolved?

[alpine sable]

4.1 as 4.13 is closer to 4.10

[weak swift]

But then that would make the solution more accurate than it actually is. Note that 4.13 is an ERROR and not a normal value.

@alpine sable

[alpine sable]

The general rule is to round up if the digit after the specified decimal place is 5 or greater, and round down if it is less than 5.

So, rounding an error of 4.13 to one decimal place, you would get 4.1.

[lament forge]

i think probably this depends on who's asking you about this concept of an ERROR

[weak swift]

Wdym

[lament forge]

an ERROR is to my knowledge not a concept with a standard definition (the way that for instance everyone agrees on what "real numbers" are)

so how exactly it's defined and what rules it follows will depend on who defined it, it's not something that we can guess without that information because there isn't one standard that everyone uses

(...to clarify: are the all caps part of the name of the concept, so an "error" would be a distinct thing from an "ERROR", or was that just for emphasis?)

[weak swift]

Error is defined as the difference between the approximate and the exact values. And yes I used all caps for emphasis.

[lament forge]

...ok yeah i guess that's pretty reasonable

although that definition doesn't logically necessitate any particular rule for how to round them, so the question of "who gave you this definition" is still relevant

or more precisely, who's providing the definition of rounding an error

if it's the real world and you're trying to do something that's actually practical with real data, then uh, just don't round it? give as many decimal places as anyone reasonably might want and then explicitly quantify the amount of imprecision of anything that's imprecise

[weak swift]

Let's say there was this problem involving floating numbers and I rounded them off to two decimal places for the sake of simplicity. Then, there's bound to be an error, right? Suppose I'm asked to correct the error to say 1 decimal place then do I round it off up or down?

The question is if I should follow the general rules for rounding off numbers or should I round it off up so that the error interval isn't reduced?

[lone heart]

@weak swift Has your question been resolved?

[lone heart]

@weak swift Has your question been resolved?

[lyric sand]

In the Karush-Kuhn Tucker conditions in nonlinear optimization, I don't understand how a zero gradient Lagrangian would be a necessary condition for global optimality. Or local for that matter. Neither why the Lagrange multipliers need be non-negative.

[lone heart]

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[thin sedge]

how to make f(x) to 1/f(x)

[thin sedge]

,rotate

[thin sedge]

Problem 3

[tight pawn]

just do the opposite when f(x) is big 1/f(x) is small etc ? @thin sedge

[thin sedge]

Wait

Is it where

The asymptotes would be at -2

3

7

-7*

Then u just draw those weird things

Horizontal asymptote -4 right

Or no horizontal asymptote

[tight pawn]

why would it be any horizontal asymptote ?

[thin sedge]

Idk

[tight pawn]

so why do you write it ?

[rose sigil]

there is one though

[thin sedge]

Idk just a maybe thought

was clarifying the problem more but ok

[tight pawn]

you did not write a horizonale one in this case

it's a vertical one

[thin sedge]

ok

[tall topaz]

How did you get this?

[thin sedge]

I just thought maybe the y intercept could be horizontal asymptote bcuz all the x intercepts are vertical asymptotes

[rose sigil]

hi snow

[tall topaz]

Hi

[tall topaz]

This is not true. All the x intercepts are verticals asymptotes because that’s when the function 1/f is undefined since you have division by 0.

Investigate the end behaviour of 1/f.

[thin sedge]

thx

Z#.cl

Z

.close

[lone heart]

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[dapper geyser]

i can not understand equivalent fractions.

[dapper geyser]

@lone heart when will you respond?

[lone heart]

@dapper geyser Has your question been resolved?

[mellow knoll]

please better explain your question

its pretty open-ended atm

[lone heart]

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[drifting gust]

AB ∥ CD and AD + BC = 4√ 10 are given in trapezium ABCD. The area of ​​this trapezoid with height 6 is 72 and it is possible to draw a circle outside. Find the radius of the inscribed circle of this trapezoid

[drifting gust]

<@&286206848099549185>

[true rune]

r=h/2 where h is the height of the trapeze

so r=3

[drifting gust]

i do not think that question is that easy

<@&286206848099549185>

<@&286206848099549185>

[noble frost]

try using cosine rule + the given area

this might be helpful

[lone heart]

@drifting gust Has your question been resolved?

[lone heart]

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[real parrot]

can anyone help me generalise the integrals of the type
$\int\frac{1}{ax^2 + bx + c}dx$

[ocean seal]

Wither

[zealous ingot]

Maybe try completing the square and then generalising the result depending on the value/sign of a b and c

[real parrot]

alr

btw @lethal belfry

found the yt solution to the last one as well lmao

[undone ledge]

wild

[real parrot]

I got it

[bright scarab]

substitute x = costheta

[real parrot]

need help witht he 1/quadratic

[quasi vector]

nvm

[bright scarab]

bro simple just sub x = costheta

[quasi vector]

well

for this

[real parrot]

I got it (btw u need to sub x = sinu)

[quasi vector]

just complete the square

[bright scarab]

yeah

[quasi vector]

then based on the sign of the discriminant you can make two cases

[real parrot]

oh so the Sridharacharya method?

[bright scarab]

holy smokes why sin u

[real parrot]

like where you derive the quadratic formula?

[quasi vector]

yep

[bright scarab]

cus in numerator u have cos inverse of x

[real parrot]

check it for urself

[bright scarab]

x = cos theta? seems right

[real parrot]

nope

I tried it

didnt get to a solution

https://brainly.in/question/36386577

[quasi vector]

no??

[real parrot]

this is the solution to the last one

[bright scarab]

yeah but since this is so ambiguos how will we know which one to substitute in exam

half of them will go for sin and other will go for cos

[real parrot]

try for different

[real parrot]

not half, 99%

I also went for cos first

[lethal belfry]

wait, so it wasn't wrong? it was sin(sin(something))? Sorry for digresssing

[real parrot]

no, it was arcsin

they have just copied the ss

[lethal belfry]

complete the square, teh integral depends on teh signs

[undone ledge]

bro that was diff question

[real parrot]

fr

[wind quail]

if $ax^2+bx+c$ can be factorisizes , decomposite it first .

[real parrot]

alr

[undone ledge]

? so how are you comparing with here-

[quasi vector]

substituting u=cos(x) would also work, though it would be much harder

[real parrot]

oh

[ocean seal]

Natural7

[real parrot]

shall use the quadratic formula?

to find the factors?

[undone ledge]

i mean then you can write it in factor method, sure

[real parrot]

$(x + \frac{b + \sqrt{D}}{2a})(x + \frac{b - \sqrt{D}}{2a})$

[ocean seal]

Wither

[real parrot]

these are the factos

[lethal belfry]

you could, but as others have mentioned earlier, the general formula depends on what the "completing the square " yields, it could either be arctan(something) or ln(something)

[bright scarab]

complete the square and use these
1)
1/x^2 + p^2 means tan^-1(x/p))/p

1/x^2-p^2 means ln(x-p/x+p))/2p

1/p^2-x^2 means ln(p+x/p-x))/2p

[real parrot]

hmm

wait cant you do partial fractions?

[bright scarab]

these are the formulas we were made to cram in my country

[undone ledge]

real

[bright scarab]

along with hyperbolic sines and cosines

[real parrot]

aint no way

[bright scarab]

yeah

[undone ledge]

?

[lethal belfry]

where is that? If you don't mind sharing

[bright scarab]

but we have no idea they are hyberbolic sines and cosines

[bright scarab]

india

[undone ledge]

all are indian in this chat btw

[lethal belfry]

no way, I'm from india, don't know anyone who had to do that

[bright scarab]

then why dont they know it

[undone ledge]

(e^x + e^-x)/2 the one defining the hyperbolic sin?

and cos had a -?

[bright scarab]

dont u guys know about ln|x+root(x^2+a^2)

this thing

[undone ledge]

same thing

[bright scarab]

this is wat the derivative of hyperbolic sine

[undone ledge]

derivative?

[bright scarab]

yeah

[undone ledge]

its it just cosh x

[bright scarab]

the thing u put inside integral

[bright scarab]

yeah

[undone ledge]

oh the other way arround

[bright scarab]

ahh yes

[undone ledge]

makes sense

[bright scarab]

lol

[real parrot]

class 12th stuff

[bright scarab]

yeah the last one is sinh i g

im not sure though

[undone ledge]

yeah main integration is taught in 12th , basics and some in 11th

[real parrot]

$\frac{1}{a}\int\frac{dx}{x^2 + \frac{2b}{2a} + \frac{b^2}{4a^2} + (\frac{c}{a} - \frac{b^2}{4a^2})}$

[undone ledge]

sinh ? na that looks arch sinh x

[real parrot]

did it crash?

[undone ledge]

sinch x is just cosh x

[real parrot]

$\frac{1}{a}\int\frac{dx}{x^2 + \frac{2b}{2a} + \frac{b^2}{4a^2} + (\frac{c}{a} - \frac{b^2}{4a^2})}$

[bright scarab]

is it a coincidence these formulas look similar?

[ocean seal]

Wither

Wither

[bright scarab]

is it a coincidence these formulas look similar?

[ocean seal]

Wither

[bright scarab]

is this coincidence the above formulas and this one feels similar

[real parrot]

like this???

[undone ledge]

(arc sinch x)

(I THINK)

checking on net i forgot

[bright scarab]

why the
formula of root (x^2-a^2) is similar to 1/root(x^2-a^2) and so on

like theres is a matchup

[real parrot]

where $k^2 = (\frac{c}{a} - \frac{b^2}{4a^2})$

[ocean seal]

Wither

[lethal belfry]

Yes, same sub while deriving, that should do the trick I think.

[real parrot]

$\frac{1}{a}\int\frac{dx}{x^2 + \frac{2b}{2a} + \frac{b^2}{4a^2} +k^2}$

[ocean seal]

Wither

[undone ledge]

simmilar , they still different

also ^ yee

anyways back to his question shal we

[undone ledge]

eh you are over complicating it

[bright scarab]

wat is even the question

[real parrot]

generalise integral of 1/quadratic

[bright scarab]

?

[undone ledge]

thinking too much tbh , different casses got different shit dude

[bright scarab]

bro just dont generalise

[undone ledge]

you cant just say " generalising"

sadly

[bright scarab]

like i told u just keep memorise the formulas

[undone ledge]

we litterally gave you so many examples.

[real parrot]

$\frac{1}{a}\int\frac{dx}{(x +\frac{b}{2a})^2 + (\frac{c}{a} - \frac{b^2}{4a^2})}$

[lethal belfry]

You can't

[ocean seal]

Wither

[bright scarab]

this integral makes me wanna puke

[real parrot]

what about 2 conditions for b2 - 4ac

[undone ledge]

?

[lethal belfry]

it depends on Two conditions for the constant

[bright scarab]

x^2 + a^2
x^2 - a^2
a^2 - x^2

remember these 3 alone for gods sake

[real parrot]

let $u = (x + \frac{b}{2a}))$

[ocean seal]

Wither

[real parrot]

yeah ik

[undone ledge]

aight im officially out

[real parrot]

im just doin integrals for fun

[real parrot]

thanks for your contribution

[undone ledge]

here lemme suggest a book

[real parrot]

du = dx

[real parrot]

alr

[lethal belfry]

try a problem book in mathematical analysis , it's only 150 bucks and has many good problems (just a suggestion)

[real parrot]

150

[real parrot]

12k????

[undone ledge]

been there , try to then go through some normal stuff

he meant 150 rupee

[lethal belfry]

150 rupees

[real parrot]

oh lmao

ok

[lethal belfry]

have done that before, don't go too far, you have school too

[real parrot]

yeah 10th boards fr

$\frac{1}{a}\int\frac{dx}{u^2 + k^2}$

[undone ledge]

they are specially spicy when you find a hidden beta/gamma function waiting to be discovered

[ocean seal]

Wither

[undone ledge]

bro eliminated every variable

[real parrot]

aint no way whats that?

[real parrot]

fr lesgo

[undone ledge]

ignore

bro no?

u / k are still a function of x no?

what was u and k again?

[real parrot]

dx = du

[real parrot]

$k^2 = (\frac{c}{a} - \frac{b^2}{4a^2})$

[undone ledge]

what was u?

[ocean seal]

Wither

[real parrot]

let $u = (x + \frac{b}{2a}))$

[ocean seal]

Wither

[real parrot]

this is risky tho

don't wanna enter complex numbers

[undone ledge]

check its domain

yeah

how did you get here again?

[lethal belfry]

are you really in 10th, when I was in 12th, I knew people who knew less than you

[real parrot]

yes, I prepared for nsea thats why I know

[quasi vector]

that is some really bad advice, especially for a math discord server

[undone ledge]

fair

[undone ledge]

hes in 10th and wanted to do some integral , for now if he really want to do it , it would be better without any derivation so yeah why not

[quasi vector]

just write $ax^2+bx+c=a(x+\frac{b}{2a})^2-\frac{\Delta}{4a}$, where $\Delta$ (the discriminant) is given by $\Delta=b^2-4ac$

[ocean seal]

kheerii

[real parrot]

$\frac{1}{a}\int\frac{dx}{u^2 + k^2} = \frac{1}{a}(\frac{1}{k}arctan\frac{1}{k}) + C$

[quasi vector]

every case can be solved in this way, by taking into account the signs of $\Delta$ and a

[ocean seal]

kheerii

[real parrot]

waht

[ocean seal]

Wither

[real parrot]

@quasi vector what about this?

[quasi vector]

you aren't wrong

but

there's no point trying to generalise the integral

because

based on the signs of the discriminant and the leading coefficient the integral changes

I would not recommend you to memorise the formulae either

[real parrot]

oh so what if k^2 < 0

[quasi vector]

derive all of them by yourself using trig substitutions

[real parrot]

yeah ive done em

[quasi vector]

what is k?

[real parrot]

$k^2 = (\frac{c}{a} - \frac{b^2}{4a^2})$

[ocean seal]

Wither

[quasi vector]

ah

[quasi vector]

notice here that k, as you said, is the exact same thing as the $-\frac{\Delta}{4a}$ term here

[ocean seal]

kheerii

[real parrot]

oh yea

so we get only 1 value??

[quasi vector]

let's take some examples here

[real parrot]

ok

[quasi vector]

$\int \frac1{x^2+4x+3} dx$

[ocean seal]

kheerii

[quasi vector]

the first step is to find the signs of $\Delta$ and a

[ocean seal]

kheerii

[real parrot]

both +ive

[quasi vector]

correct

now we complete the square

alternately, you can complete the square in the beginning

$\int \frac1{(x+2)^2-1} dx$

[ocean seal]

kheerii

[quasi vector]

how would you integrate that?

[real parrot]

u sub

[quasi vector]

yeah

[real parrot]

let u = x + 2

[quasi vector]

so tell me what the final answer would be

[real parrot]

alr

[real parrot]

arent we doing partial fraction decomposition here?

[quasi vector]

you can, either method would get you the same answer

[real parrot]

so like can you not do it in the beginning?

[quasi vector]

you can

yes

[quasi vector]

but we are looking for a more general answer

[real parrot]

agreed

[quasi vector]

in terms of inverse trigonometric functions

[real parrot]

tan

wait

[real parrot]

why am getting natural log?

[quasi vector]

how are you getting tan?

[real parrot]

tan was for that one

the last thing

[real parrot]

dis

[quasi vector]

well yeah

tell me what it would be for this one

[real parrot]

$\frac{1}{2}ln|\frac{x+3}{x+1}| + C$

[ocean seal]

Wither

[real parrot]

this is what I am getting rn

[undone ledge]

yeah same

tanh inverse

[undone ledge]

wait no btoh plus?

what was the integral we talking about here?

[real parrot]

topic change

kinda

we were talkin bout an example

[undone ledge]

this?

[real parrot]

yes

[undone ledge]

coth

inverse

and then x+2/a

blurry memmory sorry

[undone ledge]

what is this?

[real parrot]

wolution

s*

[undone ledge]

x+a/x-a? form ?

1 sec

lemme check

ah yeah

i c

works

arccoth x+2 or that thing

both works

it would depend on mcqs

(carefull if multichoice multi correct)

[real parrot]

frfr

oh

so arctan is not a general solution

cos u cant get ln from arctan

[undone ledge]

ye nothing is general

depends on the coefficient and constant values sadly

if you like to generalise you are going to love coordinate geometry of 11th

(my fav too)

[real parrot]

i love geometry but no geometry in 11th 😭

[undone ledge]

dw its not your regular geometry

[real parrot]

only conic sections

[undone ledge]

yeah thats what im talking about.

[real parrot]

which is more like algebra

[undone ledge]

thats in chordinate geometry.

bro

THATS CHORDINATE GEOMETRY

oops sorry caps

[real parrot]

chordinate frfr

[undone ledge]

real

[lethal belfry]

not if you study it right, it's beautiful when done right

[undone ledge]

^^ real

[real parrot]

GOTTA STUDY IT RN

coffee time

[undone ledge]

desmos for the win

[real parrot]

you still have to study geometry for jee right?

closed and open shapes

[undone ledge]

eh idk

[lethal belfry]

please focus on your boards for now, you'll have a lot of time for all this later

[undone ledge]

im in 11th

[real parrot]

alr

[undone ledge]

just focussing on what is done :)

[quasi vector]

not much, mainly coordinate geometry is asked

[real parrot]

yk just motivation and aspiration to reach hights

[quasi vector]

conic sections and straight lines

[real parrot]

oh

[real parrot]

and 3d aswell ryt

[quasi vector]

from geometry mainly only solution of triangles is asked

[quasi vector]

yeah that too

all of 3d is in 12th only

[real parrot]

yea

[undone ledge]

which is not in mains this year right?

[quasi vector]

these are major chapters they take up like 35% of the questions

[lethal belfry]

neither is most of conics

[quasi vector]

it's not in advanced either

[undone ledge]

ye

[real parrot]

calc be 50% for sure

[undone ledge]

oh?

[quasi vector]

nah

[real parrot]

aint no way

[quasi vector]

more like 35 only

[real parrot]

still 1 topic

I mean you can group many topics in algebra as well

[quasi vector]

how is it one topic...

[undone ledge]

calculus is like

[real parrot]

yea thats what i was sayin

[quasi vector]

calculus is a huge topic even more expansive than all of geometry (coordinate and otherwise)

[undone ledge]

applications , integration , many functions, rules , theory

[real parrot]

sticking to 10th boards for now

[undone ledge]

like thats 75 math syllabus

[real parrot]

but I dont really like Indian education system a lot

they just tell you to accept formulae

[undone ledge]

not a place to talk about here

[real parrot]

fr

[undone ledge]

eh didnt happen in 11th yet

[quasi vector]

not if you have good teachers

[undone ledge]

also you will get to know many proofs in further classes

yeeeeeeee

[real parrot]

still

for example

no teacher tells you how to derive formula for median and mode

[undone ledge]

like bro one chem teacher of mine teaches a 12th topic if small part of it is required in some concept

[real parrot]

unless they're exceptionally interested towards students

[quasi vector]

but if you are interested in these things there is ample time to look them up yourself

the important proofs are usually given by good teachers

[real parrot]

yea

[quasi vector]

but they don't prove everything coz it isn't necessary

[undone ledge]

and sometimes too complex

mostly^

[real parrot]

sometimes students are interested in actually deriving surface areas of shapes

and the teachers just force them to accept it

[undone ledge]

didnt we do that?

[real parrot]

what about curved shapes?

[quasi vector]

what surface area formula is taught that isn't extremely elementary to derive yourself?

[real parrot]

sphere

[quasi vector]

well

[undone ledge]

oh right there was a small fun activity of it in nccert

or some

[real parrot]

4 strings

[undone ledge]

4 circles 1 thread

[real parrot]

oh yea

[quasi vector]

the proof for SA of a sphere is not easy

it can't be taught

[undone ledge]

fair

[quasi vector]

without understanding of topology

[real parrot]

or calc

[undone ledge]

calc for surface area?

[quasi vector]

calculus proofs are pretty "cheaty" imo

[undone ledge]

im not able to imagine that working

[real parrot]

didnt archimedes derive it without topology or calc?

[quasi vector]

plus, the formula for the volume of a sphere comes from the formula for the surface area, so it's a cyclic proof

[real parrot]

hmm

well my doubt is cleared

so ill close this

we'll continue

.close

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[lavish holly]

Any help with the last one?

I've tried induction, but can't get F_{2k+4} to work

[mossy laurel]

I think you can use i

[quasi vector]

I mean, you could write both sequences in terms of powers of the golden ratio, but that seems overkill for this

[lavish holly]

I tried, but can't find the right place to use it...

[mossy laurel]

For n=2k+1

[lavish holly]

I think it was meant to be done via induction, but I might resort to that.

[lavish holly]

F_{2k+1}?

[mossy laurel]

No $L_{2k+1}=F_{2k}-F_{2k+2}$

So $F_{2k+2} = F_{2k}- L_{2k+1} = F_{2k} - F_{2k+1} - 2F_{2k}$

[ocean seal]

black_couscous#1618

[lavish holly]

Still don't get it.

<@&286206848099549185>

.close

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[proud igloo]

As someone who has done differential equations before, and would just need a good book or literally anything structured to recap things, what resources would you recommend for that very purpose?

[proud igloo]

I'm also making the assumption that example problems are easy to find, but if there are any resources that are especially good at providing you example problems, I'd gladly check it out.

[remote heron]

depends on what exactly kind of thing youre looking for. I used pauls math notes to review for PDE.

[proud igloo]

Additionally, I would not say I'm a BEGINNER.

[remote heron]

https://tutorial.math.lamar.edu/classes/de/de.aspx

ODE seems like a big topic but it actually doesnt take that much time to review everything going back through

just focus more on solving/proving/deriving things in general rather than doing specific problems where you can

i feel like the only things that come up having moved way past ODE is VOP and exactness and series TBH

of course the theory

but ymmv

[proud igloo]

I just wanna add that I have no idea what these abbrevations mean.

[remote heron]

sorry

ode ordinary differential equations

i just assumed thats what you mean my differential equations

vop is variation of parameters

is one of the like, 'hammer' methods, the killer methods to solve anything

same thing with series

obviously not solve anything, but they do come up

or are applicable or whatever you wanna say

[proud igloo]

I have no way of grouping stuff within terms. I followed along with the courses, I familiarised myself with differential equations, I got good grates and now I wanna recap. I could just buy the book I was using but I kinda wanna recap it in english which is not the language of the textbook I used.

So some sorta book would be good in my case.

[remote heron]

how long has it been?

[proud igloo]

Not too long, year or so.

But I forget quickly.

[remote heron]

to me it seems crazy to use a book, even if thats true

i mean, it seems crazy to go through a book again like you were retaking the course

just review the major topics

[proud igloo]

I'm pretty good at recapping things, so that's something I can deal with. Like, really are there no good books, if you happen to want to use one?

[remote heron]

see #books

alternatively, #book-recommendations

i would use pauls math notes

again i say all of this as a person who reviewed differential equations and was similarly worried

a class will almost always feel smaller when you go back through it

[proud igloo]

Also, I do not enjoy Blue3Brown2... wait was it.... 3Blue2Brown, there we go. I do struggle with his videos because I feel like he's just showing a bunch of graphics that he wrote in some program, explaining them, but it doens't get me more well-read on the topic. Like it literally works worse than anything else I've ever used.

I dunno if it's just me.

[remote heron]

no its a common complaint

[proud igloo]

Getting him recommended again tends to give me headaches.

[remote heron]

some of the helpers here have brought up specific misconceptions a lot of people have from watching his videos

[proud igloo]

Just curious, do you have any examples?

[remote heron]

ask in #discussion maybe ill probably misremember them lol

[proud igloo]

Alright, thank you jan Niku.

[tardy stag]

his videos are not a substitute for putting in work to understand a topic, no

and especially practice

[proud igloo]

Seems like we've reached the same conclusion then. I've been recommended his videos too much, but it's just never worked for some purposes.

It's not what I did to learn any maths in the first place.

[tacit arch]

Do you have an actual math question

[lone heart]

@proud igloo Has your question been resolved?

[lone heart]

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[fervent ferry]

so i took the derivative of x

x' = -Aae^(-at)cos(wt) - Awe^-(-at)sin(wt)

which becomes
x' = Aae^(-at) ( Bcos(wt-phi))

when this is zero i have maxima and minima

this is zero only when cos(wt-phi) = 0

wt-phi = pi/2

next period is on the next 2pi rotation
wt-phi+2pi = pi/2 + 2pi

left side can be rewritten as
w(t+2pi/w) -phi
so that 2pi/w is the pseudo period. which is the same as the one in the problem.

is this reasoning correct ? because solution seems a bit different and i don't get it

this is the solution, i don't understand what they are doing in the highlighed area

[lone heart]

@fervent ferry Has your question been resolved?

[lone heart]

@fervent ferry Has your question been resolved?

[lone heart]

@fervent ferry Has your question been resolved?

[fervent ferry]

<@&286206848099549185> help

[signal trellis]

I think your derivative is slightly wrong. It should be $x'(t)=-Aae^{-at}cos(\omega t)-A\omega e^{-at}sin(\omega t)$. You then set it equal to 0 and have $-Aae^{-at}cos(\omega t)-A\omega e^{-at}sin(\omega t)=0$. $e^{-at}\neq0$ so it can be divided out along with -A to get $acos(\omega t)+\omega sin(\omega t)=0$. From there, subtract over $acos(\omega t)$ and divide $cos(\omega t)$ to get the result in the answer key.

[ocean seal]

DonDoesMath

[fervent ferry]

i've put a minus too much while transcribing but ok.
why would that be my answer? i don't get it.

what are you trying to do with those operations? i don't get it

[fervent ferry]

but this do answer my question. thanks!

[lone heart]

@fervent ferry Has your question been resolved?

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[unkempt compass]

is there a range restriction on this function or is desmo wrong when graphing it?

[remote heron]

its having numerical issues

[unkempt compass]

range should just be all real numbers right?

[remote heron]

hmm

yea i guess so

[limpid turret]

Recall that log grows VERY SLOWLY

[unkempt compass]

so its just not drawing it quickly or something with our transformation?

although that really shouldnt be the case with -log...that part that goes up the y axis should be going fast

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[steep jackal]

when does the comparison test fail

[steep jackal]

the one without limit

[tacit arch]

Show the test

[steep jackal]

the ak>bk or < one

where u check for bigger series and smaller series

[steep jackal]

if bigger converges smaller convs...this one

and if smaller divs..bigger also divs

[tacit arch]

Show the exact test and all the details

Screenshot or picture is best

[steep jackal]

done

<@&286206848099549185>

[tacit arch]

Whenever the assumption isn't true

In the first bullet point

[lone heart]

@steep jackal Has your question been resolved?

[steep jackal]

no like...the degree part

theres something there right

[tacit arch]

Where does it say degree here

[steep jackal]

the note part

[tacit arch]

That's not part of the comparison test

It's an application to specific types of sequences just to make things easier

[steep jackal]

it is

like a trick

but like it fails right

when does it fail

thats my question actually

[tacit arch]

It isn't

[steep jackal]

yea its a trick

[steep jackal]

like just help me understand wehn that fails

when does that fail*

[tacit arch]

It's a shortcut for specific types of sequences

[steep jackal]

yea what types

like when does it fail

[tacit arch]

Polynomials

[steep jackal]

when degree of numerator is greater?

[tacit arch]

Like it says in the hint

[steep jackal]

it works for some cases of p1/p2

where p is a polynomial in k

ig thats the only case wehre it works

[steep jackal]

or like both equal?

[tacit arch]

Try a couple examples

[steep jackal]

ok

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[tranquil cipher]

hii! what is 1/cosx equal to again

[tranquil cipher]

like another identity to replace it with

[fervent kestrel]

Secant(x)

[tranquil cipher]

thank you!!

[vale wigeon]

it's equal to sec(x), but that's not really much of an identity

[tranquil cipher]

ohh i see i see

[vale wigeon]

just a somewhat-dated named function

[tranquil cipher]

thank you!!!

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[tranquil cipher]

hii i just wanted to ask how 1/u^2 became -1/u after it was integrated, thanks a lot!!

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[tranquil cipher]

oopss

[tranquil cipher]

ahh wait i think i remember it now, thanks!!

.close

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[fervent kestrel]

[tranquil cipher]

.reopen

[lone heart]

✅

[tranquil cipher]

helpp im actually confused

1/u^2 you reciprocate it right so it becomes -u^2 then u apply integration power rule

[fervent kestrel]

yes

wait no

it's

$u^{-2}$

[ocean seal]

dragonbreath

[fervent kestrel]

not -u^2

[tranquil cipher]

OHHH rightt i see it now

THANK YOU!!!

and it comes u^-2+1 so just u then reciprocated again thats why its negative 1/u

oh NO

it beocomes u^-1

[fervent kestrel]

using just "u^-2 + 1" you would only get 1/u, you need to divide by the new power. which is -1

[tranquil cipher]

Yes yes i see it now thank you so much

[split mantle]

$(u^{-1})' = - u^{-2}$

[ocean seal]

Good

[tranquil cipher]

thanks a lot guys!!

.closed

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[tranquil cipher]

hii! im solving something rn and this is just part of the solution but it wasnt really explained further so i just wanna verify if this process is correct based on how i understood it? thanks!!

[quasi vector]

the last expression should be under an integration sign.

[tranquil cipher]

ohh yes yes sorry i forgot

thank you!!

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[brave belfry]

yo

[brave belfry]

who can help wit pre algebra

i have to turn it in asap

!15m

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[fervent kestrel]

What do you have to do?

[alpine sable]

what are you tasked to find

can i see the full question above

[brave belfry]

i js need help wit the first question

it says

find each missing length to the nearest tenth

[alpine sable]

the part that you cut out

[brave belfry]

the teacher put my full name

let me crop it out rq

[fervent kestrel]

missing lengths? there aren't missing lengths?

[alpine sable]

[tall topaz]

All lengths are given

[brave belfry]

idk

[alpine sable]

did ur teacher give u answer sheet instead

[brave belfry]

nah he didnt

this is a quiz

[tall topaz]

[tardy stag]

well 1) we can't help you on quiz / test / etc
but 2) yea this doesn't make sense lol

[brave belfry]

i didnt make the paper

here

the answer is sum like this

my hand writing is ass bru

[alpine sable]

thats a different sheet tho

the first one you posted had all the lengths listed

[brave belfry]

ik its a diff one

the answers are sum like that

[alpine sable]

your original paper has ALL the answers listed

there are no missing lengths

so what are you even asking for

[brave belfry]

if i could show u a video of how he did it i would but i cant

[alpine sable]

[alpine sable]

Am i speaking to a wall? Again, there is nothing to solve in what you have sent

[brave belfry]

yea u are

my brain is the size of an atom thats why i called help

[tardy stag]

considering both of the things i said here, i'm going to close this thread. you should check with your teacher to make sure that you didn't get an answer sheet instead of a sheet of questions

.close

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[brave belfry]

i cant

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[orchid perch]

this is from wikipedia

does the existence of the result imply the existence of the operands?

i.e., if we know x*y is in the set closed under *, are x and y necessarily in the set?

[wide tartan]

no, for example if you take your operation to be addition and the set to be the integers

[orchid perch]

The closure property of a binary operation expresses the existence of a result for the operation given any pair of operands.[4]

[wide tartan]

then 1/2+1/2=1

[orchid perch]

ah

hmmmm

[wide tartan]

but i could also do this for any operation i want

i can make a superset with two new elements x and y, and extend the operation to make x*y in the set

[orchid perch]

this is kind of unrelated, but this is the original problem:

i cant just assume L_x and L_z exist that recognize x and z

even though regular languages are closed under concatenation

[wide tartan]

sorry, i don’t know much about regular languages, so i’m sorry if this is not helpful, but it seems as though you will have a language that recognizes x because x is in Sigma* right?

and same with z?

[orchid perch]

no it can be irregular even if its in sigma*, its all g haha you helped alot fwiw

.close

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[vagrant agate]

A man walks at a steady course bearing 122 degrees from A to B . If A is 86 m further west than B find to the nearest metre how far the man has walked

[vagrant agate]

Im not sure how to draw the diagram for this questions

?

[sour verge]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[devout dirge]

oh sry

[vagrant agate]

<@&286206848099549185>

[sour shore]

first draw a line with bearing 122 deg and fix A as the origin, representing the man walking from A to B

Now draw a line that represents this information: "If A is 86 m further west than B" that is, what does it mean to go 86m west starting from B

can you show your diagram here when you are done?

[vagrant agate]

Would it look like this?

Ohhh i think ive got it thanks

like sin90/AB = sin58/86

then AB = 86 sin90/sin58

[sour shore]

aight that's goood

[vagrant agate]

ok thank you very much

[sour shore]

wait

yep looks good

[vagrant agate]

ok thanks

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[alpine sable]

Do you agree with chatgpt that these what I need to learn to be a Mathematician who specialized in Logic and foundations?

• Only answer if you are sure about your answer

• In case if you don't agree with chatgpt and you are sure about that, Please tell me in the right arrangement what I should learn to be a Mathematician who is specialised in Logic and Foundations

For example
1-
2-
3-

[west cipher]

i agree

just go to school

[vale wigeon]

sounds approximately right. probably generic enough that gpt doesn't have a lot of room to fuck up there.

how old are you tho

and/or what level of education

[sour shore]

Do you want to be a professional mathematician? Or just study that topic? Note that many topics in logic and foundations are pursued under computer science instead as well. This is also not really the right channel for this qn.

[fallen verge]

why do you want to specialize in logic and foundations?

[marsh rapids]

This isn't specialization
All math majors I know take those

[fallen verge]

yeah its par for the course, i was thinking perhaps its to become a prof, but you would still need to be researching something else for your doctors thesis

[mortal trellis]

well most people just do naive set theory and no zfc stuff

[marsh rapids]

Most people aren't math majors

[mortal trellis]

most math majors then

still the same point

[marsh rapids]

It's literally a mandatory course in our first year in this uni
3rd undergrad logic and foundations

Technically just logic

First order, 2nd order, monadic stuff, axiomatics, etc

[sour shore]

As in, the working mathetmatician uses naive set theory, unless they specialize in it

[marsh rapids]

But I'm not taking it so I don't know the details

[mortal trellis]

well of course it differs from university to university. I for example never needed to take such a course

[sour shore]

Pretty much if you want to do logic and foundations at the research level you'd probably be better served looking at computer science depts

[marsh rapids]

CS logic be like: so for each first order statement there's a finite automata that recognizes the same language

And vice versa

[sour shore]

Well many CS subfields explore different models of logic

[alpine sable]

you agree with all what it said, right?

[alpine sable]

I see, thanks. I am 22 years old

[alpine sable]

professional mathematician

[alpine sable]

logic and foundations is a field in Pure mathematics and that's what I want to specialise in

[alpine sable]

it is, like topology and ..etc

[marsh rapids]

It is a specialization

[marsh rapids]

This alone is not

[fallen verge]

it is, but why do you want to specialize in it

[alpine sable]

gotcha

[sour shore]

ummm

[alpine sable]

what do you mean?

[alpine sable]

I like it

[sour shore]

Well you need a degree but you shouldn't be taking answers from discord or chatgpt

[alpine sable]

I see

[sour shore]

what do you know so far about mathematical logic?

[fallen verge]

have you asked an advisor about this yet?

[alpine sable]

I am a complete beginner in mathematics

I just wanna know guys if you agree with chatgpt or not

[sour shore]

https://www.coursera.org/learn/logic-introduction
perhaps give this a go first and see if you like it

[fallen verge]

just because chatgpt said something that sounds vaguely right, please dont trust it in the future

[alpine sable]

ok

just lemme know do you agree with what it said?

[sour shore]

No

[alpine sable]

so if you don't agree with what it said, **Please tell me in the right arrangement what I should learn to be a Mathematician who is specialised in Logic and Foundations

For example
1-
2-
3-
**

[sour shore]

I cannot.

[alpine sable]

so why do you disagree at least?

[alpine sable]

do you mean that you agree with what it said this time but I shouldn't trust it in the future always?

[marsh rapids]

Talk with your advisor about it

Don't trust random people on the internet about how to structure your studies

[alpine sable]

I don't have an advisor

so I am trying to gather much knowledge as possible

[sour shore]

In the first place, step 2. is what happens in most math undergrad curricula, so ChatGPT has got the arrangement wrong.

Well are you in a position to study math as an undergrad?

[marsh rapids]

Step 2 is really the first thing you should do

[alpine sable]

do you mean that you agree with what it said this time

?

chatgpt I mean

[marsh rapids]

No

I've already made that clear

[alpine sable]

okay thanks everyone

[marsh rapids]

If you're looking for a clear yes/no or a clear path towards post-graduate studies, then don't

[alpine sable]

.close

[lone heart]

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[lone heart]

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[wheat isle]

How can I approach part B?

what even is the formula for the law of conservation of energy?

When I look it up I’m getting different results so

[alpine sable]

#old-network there is an physics server for this questions.

[wheat isle]

I’m aware.

[tardy stag]

initial energy = final energy

there's kinetic energy and gravitational potential energy to consider here

[wheat isle]

this is my data sheet that I have but I’m not entirely sure what to use

like this is a sample answer

but where did they get that from??

[tardy stag]

that's your GMm/R formula you were using earlier

[wheat isle]

theres no 1/r1 - 1/r2 thing there tho

[tardy stag]

distribute the GMm

[wheat isle]

(GMm)/r1 - (GMm)/r2 theres two GMm's but on my formula I only have one

where does the second one come from

[tardy stag]

what is that formula?

it says U

what is U

[wheat isle]

its GPE

gravitational potential energy

[tardy stag]

okay great

now looking at your answer sheet

what does the line directly above that 1/R1 - 1/R2 thing say?

[wheat isle]

change in kinetic energy = change in potential

[tardy stag]

correct, so change in potential energy is the final potential energy minus the initial potential energy

[wheat isle]

yeah

[tardy stag]

yes

[wheat isle]

I have the formula as delta U = mg*delta h

for change in potential

[tardy stag]

that is valid if g is constant or nearly constant

[wheat isle]

wait

theres multiple i think

[tardy stag]

in this case it is not

[wheat isle]

oh okay

[tardy stag]

gravity near the earths surface is effectively constant, but this problem involves rockets

[wheat isle]

and its constantly going in higher altitude right so it changes

[bright scarab]

yo wat is GMM?

geomtric mean?

[tardy stag]

that's correct, which is why we use the other form

[bright scarab]

oh wait im stupid seems like physics to me

https://discord.gg/2tHX9gkW

[wheat isle]

Wait which formula? the -GMm/r one?

[tardy stag]

yes

that is the gravitational potential energy of an object even at high altitudes

[wheat isle]

oh is this where that "extra" GMm/r comes from

[tardy stag]

negative for some reason, not quite sure why

yes

[wheat isle]

i see

[bright scarab]

see bro its just basic subtraction
GMm/R is potential energy for a particular point and gravity is a conservative force
and speaking of conservative force we only need the change in the energy rather than the actual one
1/r1 - 1/r2 signifies a potential difference

[wheat isle]

are you talking about the negative sign for -GMm/r?

[tardy stag]

yeah

[wheat isle]

our teacher told us awhile ago that the negative is supposed to be there but I cant remember why

[tardy stag]

oh ok I see why

[bright scarab]

negative tells the direction of work done

[tardy stag]

you need it to increase as r increases so that makes sense

[bright scarab]

keep in mind that potential energy of a conservative force is always opposite to that of work done

[wheat isle]

so it becomes

hpld on

$-\frac{GMm}{r_{1}}+\frac{GMm}{r_{2}}$

[ocean seal]

water beam

[tardy stag]

yeah

[wheat isle]

alright

[tardy stag]

they might have 1 and 2 flipped from yours it's fine

[wheat isle]

o right

and the r1 r2, are they from points 1 and 2 or are they from the same point

[tardy stag]

they're from points 1 and 2

[bright scarab]

u keep a reference point as ground zero and start measuring from it

similar to origin

[wheat isle]

hm

does it matter the order in which i plug in the points like

would point 1 be my r1

4.3x10^6 as r1

[tardy stag]

in this case if you flip them you'll just get negative mass

but yes you should be consistent where possible

[wheat isle]

wait so how do I know which is the correct order?

[bright scarab]

bro just plug and chug the results

its not like electrostats where results differ

higher the object higher is the potential energy

and objects tend to higher potential to lower potential

[wheat isle]

ok i got the answer -8.5x10^23

but im guessing i can just disregard the negative because you cant negative mass

nice

.close

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

am i supposed to use the product rule in this case:

[deep raft]

when i partiel derive for x

[zealous ingot]

Just expand and differentiate term by term

[deep raft]

so expand to 16x^3+8xy-6x?

[zealous ingot]

Yes

And then differentiate wrt x like normal

[deep raft]

ite

.close

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[ruby current]

Can also use product rule

[deep raft]

yea but i seems to get to different thing

[ruby current]

Show work?

[rancid jay]

love the english

[lone heart]

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[uneven canyon]

This is the solution to an exercise in relational algebra where we need to get the count of something

[uneven canyon]

But why are we doing a projection operation on count(*)

The exercise definition, for context

There is no attribute called count(*) to project, so this doesnt make sense to us

Should it not just be
count(σsid=3∧achievedpoints>=0.5∗maxpoints(student ◃▹ handsin ◃▹ exercisesheet))

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@uneven canyon Has your question been resolved?

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@uneven canyon Has your question been resolved?

[lone heart]

@uneven canyon Has your question been resolved?

[wispy ether]

wow your patience is admirable you do know you can ping helpers after 15 minutes of no response

[lone heart]

@uneven canyon Has your question been resolved?

[uneven canyon]

<@&286206848099549185>

[twin nimbus]

@uneven canyon I'm not an expert in relational algebra, but I've done a thing or two in databases. In SQL dialects SELECT count(*) FROM some_relation; gives you the count of rows. Given that the projection operator seems to work like the argument to SELECT from what I've read, this would indicate that count(*) is acting similarly here to what you would expect from SQL. I'm not sure about the finer points of why count(*) is written the way it is though, and what, technically, is going on behind the scenes here. I hope this helps.

[twin nimbus]

<@&268886789983436800> can someone please explain to Dagobert how to get help?

[worn fox]

@fringe mantle please read #❓how-to-get-help , open your own channel and don't type in this one again

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