help-28

[obtuse marten]

this it

[digital shard]

its a right triangle

so <1 and 27 some to 90

sum*

and then the angle next to 70 is 110

soo just use triangle angle sum th to find angle 2

[obtuse marten]

43

45?

63 and 43?

[digital shard]

yep

[obtuse marten]

ok tysm have a good day :))

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[merry topaz]

Can someone assist me with this?

I know that the normal vector is [-2 1 -3]

If we let u = [-4 3 0 ]^T

[green iris]

HI

caps

[merry topaz]

Is the projection of u onto the plane, the perpendicular of the projection of u onto n?

[green iris]

i can help in 3 min

ok

Let's say P is the vector we want to project onto the given plane whose normal is n

Do you agree that P·n gives the magnitude of the component of P that is parallel to n?

[merry topaz]

I already know how projection and perpendicular works.

[green iris]

just follow along

[merry topaz]

ok...

[green iris]

I ask if you agree so u can follow the logic, im not insulting ur intellegence

so I can see if you agree with every step of the logic

[green iris]

so do you agree with this?

[merry topaz]

sure

[green iris]

ok, so do you also agree that the vector component of P that is along n is therefore given by (P·n)n ?

since it literally is just (the parallel component)n

[merry topaz]

yes

[green iris]

ok, do you also agree that P can be written as the sum of the parallel and perpendicular components? so that
P = (perp) + (prll)
we already know what the perpendicular component is, that is just (P·n)n
so we have
P = (P·n)n + (prll)

we also know that the parrallel componnent is just the component of P that is on the surface of the plane

therefore we want to find the parallel component, let's call it P' p prime

so we have
P = (P·n)n + P'

solving for P' we get

P'=P-(P·n)n

which gives the component of P on the surface of the plane

do you agree?

[merry topaz]

yes

[green iris]

nice

did that make sense tho? plz let me know if there was something that didnt make sense

[merry topaz]

yes, it makes sense.

[green iris]

oki doki then, I hope it was helpful :>

plz lmk know if u need help with anything else

[merry topaz]

u basically just explained this then?

[green iris]

ye

well ehh the wording is weird

cause

if u already get the projection of u onto n

it doesnt have any perpendicular component

by like definition

if u do a dot product, ur just asking urself how much of the vector u points towards n

this by definition, doesnt have a perpendicular component

the projection of u onto the plane is just the perpendicular component of u

[merry topaz]

ah okay

[green iris]

if there is still something weird or hazzy plz lmk

[merry topaz]

nope, thank you so much!

[green iris]

nw o7

gl with the rest of ur questions

[merry topaz]

ty!

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[sharp osprey]

Hello

[sharp osprey]

I need help with Gaussian elimination

Say I get to this point with a matrix

[quartz mesa]

i did this recently

show me

[sharp osprey]

2 3 3
0 2 3
0 0 2

the 2s could be anything except 1

[quartz mesa]

ok

[sharp osprey]

tbh

what is the trick to fixing the 2s so that they become 1s

[quartz mesa]

1 1 1
0 1 1
0 0 1

[sharp osprey]

so i want this

Sorry for explaining this so poorly

[quartz mesa]

u just divide the dow?

row

[sharp osprey]

OH

Is that it

oh my god

wait

[quartz mesa]

yea lol

just divide

[sharp osprey]

yeah because 0 divided by anything will be 0

thank you LOL

[quartz mesa]

gotchu man

[sharp osprey]

that answers my question perfectly, again sorry for asking it so poorly

[quartz mesa]

the exam should be ez

[sharp osprey]

you understood what I meant XD

• i didnt show for exam 😭

[quartz mesa]

yea yea ofc i'm going through that rn too

[sharp osprey]

i will have to do it some other time

big L

[quartz mesa]

dang bro that's why ur kinda late

i did that exam like last week

[sharp osprey]

we had it yesterday

truth be told i fucking overslept

i planned on going

felt really shitty

[quartz mesa]

💀💀💀💀

u lost marks?

[sharp osprey]

i am not a good student but i am trying to get better

no no

i can just redo it

some other date

[quartz mesa]

ur in us?

[sharp osprey]

no marks lost

no

sweden

[quartz mesa]

good good

i'm in canada

[sharp osprey]

aight

[quartz mesa]

didn't know sweden has the same shit as us

how old r u?

[sharp osprey]

old bro

im 23

school has never been my thing

now im in uni

bad combo

[quartz mesa]

u do that in uni???

[sharp osprey]

but really interesting program

yes for the first year we only do basic math

some others

did it when they were in highschool

[quartz mesa]

ahhh okok cuz i'm in college

[sharp osprey]

but those were special courses

or whatever

[quartz mesa]

anyways i got econ test tmrw bro

[sharp osprey]

aight thanks for helping again

[quartz mesa]

add me if u ever have another question

[sharp osprey]

ok man thanks

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[hollow moth]

i know e^(pi * i) = -1, but is there a solution for e^(x*i) = -1 in degrees?

[violet bolt]

pi radians = 180 degrees

[hollow moth]

right, but im entering e^180*i into my calculator (which is in degree mode) and it's giving me a domain error. If i put my calculator into raidan mode and do e^(pi)(i), i get -1

[bright bronze]

e^(i*pi) would give you -1 even in degree mode

[violet bolt]

e^(xi) assumes input is in degree

[hollow moth]

why is my calculator being mean then?

[violet bolt]

changing calculator to degrees just changes the usual trig functions to have the input in degrees ig

[hollow moth]

ok. thx for ur help. i like the celeste pfp

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[wary spindle]

how to calculate these???

P(x=-1) = (-1 + 0 + 1)/ ??

[kindred oxide]

unrelated but is this coderunner?

[wary spindle]

nope

[kindred oxide]

gah. looked similar. mb

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[true lodge]

I need some help

I don't understand how to do this slope

could someone explain it easier to me?

and then give me a question to try and solve

[narrow path]

yes

[placid oak]

Suppose every month I put in £1. Then a = t, where a is the money in my account, and t is the month.

Suppose, instead, I put £200 in every month What do you think the equation would be then?

[true lodge]

1/200

[placid oak]

well, how much money would I have in the account after t months?

I put £200 in every month. So, how much have I put in after 1 month?

[full forum]

@true lodge Has your question been resolved?

[narrow path]

Correct

[true lodge]

oh 200

[narrow path]

Nah flip you mean i am slick

[true lodge]

nah he aint slick

[narrow path]

,tex .alg lesson

lets learn algebra guys

[glossy valve]

Steel

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[dawn owl]

can you please help me with that?

i have tried to prove that q - the root of 2 is irrational with no success

a hint will be much appreciated

[sharp flame]

Contradiction?

[dawn owl]

how to continue?

[sharp flame]

nvm

[dawn owl]

y

[sharp flame]

I was going to do something else

And I realized I was using the property that you're proving

What properties have you established so far

[dawn owl]

i proved (in the same way) that root 2 is irrational...

but doing so for q - root2 is where im stuck rn

[jolly hound]

.reopen

.occupied

occupied.

!occupied

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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).

[jolly hound]

!reopen

!close

.close

close.

i quit

im leaving

[dawn owl]

why spamming my chat

u did this earlier now you doing it again

anyways,

please help me to prove it

i was trying to do it by contradiction with no success so far

a hint will be much appreciated

[rapid rain]

do you know why sqrt 2 is irrational

[lilac flume]

let -2√2q be on the lhs side and transpose everything to rhs

[rapid rain]

Suppose then by absurd 2-sqrt2 is rational, find out what it means about sqrt2

[dawn owl]

did it, i infer that p^2/m^2 - sqrtq - 2 (the rhs) is even

[dawn owl]

wdym absurd, i proved that sqrt2 is irrational but how does it help here?

[languid junco]

from here, just move q to the other side. what does that mean about sqrt(2)?

[dawn owl]

.

[languid junco]

yep, what is a rational number minus another rational number?

[dawn owl]

idk exactly

can be any real number?

[dawn owl]

.

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[sharp swan]

can anyone explain how rk4 (runge-kutta method) works? i get that given a differential equation and initial conditions (x,y), i can get the original function more accurately than euler's method

[sharp swan]

more particularly, what i dont understand is the notion of getting h2 and h3

i get that h2 and h3 are taken from (x+h/2) where h is the step size

so instead of stepping all the way to h from x, i want to go halfway because the gradient has not changed much and is effectively still a "tangent" (sort of) to the original x

but i dont get how numerically h2 and h3 would be different values

becuase from what ive read, the final coordinate is

yn+1 = yn + h(h1 + 2(h2 + h3) + h4)/6

[sharp swan]

i also dont quite underestand how this comes to be

also, as an addendum, could anyone explain symplectic integrators like im 5? i would like to know about what it is and how it works

@terse terrace

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[swift tusk]

how to integerate this ? (left side)
Correction: its 2-v^2

[devout valley]

Is that an a or something else for the denominator's coefficient of v^2?

[lime ether]

4?

maybe

also looks like u

[swift tusk]

its 4

idk if this is better

[leaden ermine]

now there is even a square in the numerator

[spring glacier]

the denominator doesnt seem to have the ability to be factored so i dont think partial fractions will work and 95% of the time thats the only method for integrating stuff like this

[swift tusk]

the professor told us its extremly easy but looks like something is wrong

[spring glacier]

can you show the steps you did to get to this integral? i feel like it might not be correct in the first place

im assuming you were solving a separable differential equation since there were 2 variables right?

[swift tusk]

its homogenous

i will do my steps really quick

[spring glacier]

ok great thanks

[swift tusk]

i havent changed the order of the denominator so it looks a bit different but it's the same

[swift tusk]

i have shortened alot of steps, but this is like the direct answer

[swift tusk]

v = (y/x) incase its not clear

[spring glacier]

if v = y/x i feel like something went wrong when substituting in v

sorry if its a stupid question but why did the x^2 dissappear?

[swift tusk]

Because that is the method of the homogenous equations

we divide each with the highest power of x

so we can get v = (y/x)

However there are alot of methods, im using this one, if someone could solve it with any way i will really appreciate it

[swift tusk]

Or like someone can integerate this

[spring glacier]

shouldnt it atleast be replaced with a y^2 / v^2 instead od being removed entirely?

(the x^2)

wait

i get it nvm

you divided the numerstor and denominator by x^2 mb

and in line3 whered you get -2v + v^3 from?

[swift tusk]

Ah my answer wasnt in details

but the main question is about the integeral

anyway its an equation

v = (y/x)

y' = xv' + v

i do it directly without substituting since im used to it

[spring glacier]

yes i know its just that the integral seems oddly difficult so im trying to see if its correct

[swift tusk]

Mb try to solve it with another way

[spring glacier]

wait if
v = y/x
then
y = vx
and since y is a function of x
wouldnt y' just be v?

[swift tusk]

its a homogenous equation

[swift tusk]

y = vx
y' = v + xv'

[spring glacier]

wait right v = y/x

i treated it as a constant mb

anyways i dont think the method of integrating factor would work here since we cant isolate a function of purely x, y, and dy/dx each alone

so lets keep going with your method

[swift tusk]

Yeah its 100% a homogenous

integeration factor works only if its linear

[spring glacier]

right

anyways the rest of your steps wre correct so im stumped tbh

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@swift tusk Has your question been resolved?

[swift tusk]

Not yet

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@swift tusk Has your question been resolved?

[leaden ermine]

Are you sure this is the right one?

[swift tusk]

Ye

[leaden ermine]

,w dy/dx = (3x^2+4y^2)/(2x^2-y^2)

[glossy valve]

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[leaden ermine]

uhm yea nice

and this is what you were supposed to solve?

[swift tusk]

This answer is wrong ig

this is not how to solve DEs

[leaden ermine]

How could you verify?

[swift tusk]

because it gave us some values

and its just a homogenous DE without values so its immposible to get numbers like this one without an initial condition/value

i want to solve this with homogenous

i mean technically its homogenous so there is no other way to solve it

[leaden ermine]

,w Integrate[(-u^2+2)/(u^3+4u^2-2u+3),u]

ok the antiderivative doesn't seem impossible

[swift tusk]

Wow

it seems immposible 😂

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[leaden ermine]

yea i wrote a - instead of + at some point

[leaden ermine]

the professor told us its extremly easy
canon event

[swift tusk]

i mean i dont think this is bachelor level solution

it looks like some master degree shit or something

im not even math major

[leaden ermine]

you are just a pro

math is your hobby

[swift tusk]

im an engineer so 😅

[leaden ermine]

so you could use approximations

[swift tusk]

However this looks super complex ngl

[leaden ermine]

😅

engineer: some terms are negligible

[swift tusk]

well this is anti-derivative

there are no values

so kinda it wont work here well

[leaden ermine]

I just feel you either wrote it down wrong or only God knows what your professor thought

[swift tusk]

this is directly from him soo

and i even tried it 30 times

i tried 4 different methods and i kept getting the same ending-integeral

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[eager salmon]

I need help solving this differential equation

so far ive solved the homogenous, but im not really sure how to continue with variation of parameters

[umbral dome]

are you required to use variation of parameters? this seems well-suited for undetermined coefficients

[eager salmon]

yes the problem statement says variation of parameters

[umbral dome]

ok. so do you have the formula for variation of parameters?

[eager salmon]

y particular = u1 y1 + u2 y2?

y1 = exp(2x)
y2 = exp(-x)

iirc i can get one of the equations for u1 u2 by differentiating twice and plugging back in, but im not sure how to get the other equation needed to solve for the two unknowns

[umbral dome]

we also require u1' y1 + u2' y2 = 0

[eager salmon]

is that just supposed to be a boundary condition or some kind of assumption?

can that be assumed for all questions related to variation of parameters

[umbral dome]

that's an assumption we always make for variation of parameters, because it makes the subsequent equation solving simpler

[eager salmon]

i see

is my y particular equation correct?

[umbral dome]

seems fine (although for this problem we are using t as the independent variable)

[eager salmon]

oh yeah sorry, i usually just turn everything into x and switch it back at the end because im comfortable that way

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@eager salmon Has your question been resolved?

[eager salmon]

okay i solved one of the u's but it doesnt match wolfram alpha's solution

never mind i think i found the error

i solved my integral wrong

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[torn jolt]

Can someone explain this to me bc I'm confused. The answer is correct however I don't understand it
I know even is f(-x)=f(x)
And odd is f(-x)=-f(x)
Is all I'm doing like making h(x) into h(-x) and making all my x variables a (-)? So like 1/-x+3? But why does that become -1/x+3 i feel kinda slow.

[spice knot]

this comes from "plugging in -x"
if you do h(2) for example, you replace every x with 2
so to do h(-x), you replace every x with -x
this shows that h(-x) is -1/x + 3

the two steps below that are separate, this is just algebra to show what -h(x) would be

comparing h(-x) = -1/x + 3 and -h(x) = -1/x - 3, you can see they dont really match to fit an even or odd function

[torn jolt]

Oh so does the 1/x become -1/x rather than just the denominator x

[spice knot]

first, its 1/(-x)

then that is equal to -1/x

1/(-2) = -1/2 for example

[torn jolt]

OH

OKAYAYAY

THANK UUUU

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[proven dirge]

make an equation for the area of the rectangle then take the derivative and find maximum from stationary points

[queen ocean]

Im stuck on finding the maximum x valur

I already found an equation for the area and the derivative

[woeful pasture]

set the derivative to zero

to find stationary point

then prove max/min using second derivative test

[queen ocean]

For my equation I got cosA-AsinA=0

Where A=x/2, to make the problem easier

[woeful pasture]

is the original equation

${f(x) = 8x\cos(\frac{x}{2})}$

[glossy valve]

k

[queen ocean]

Yea

[woeful pasture]

if this derivative is correcct

then just solve it

[queen ocean]

I forgot how to

A=cot(A)

Idk

[woeful pasture]

hm

,w d/dx(8xcos(x/2))

[glossy valve]

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[woeful pasture]

,w find all real x 8cos(x/2) - 4xsin(x/2) = 0 x is between -pi and pi

[glossy valve]

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[woeful pasture]

what the hell is that solution

[queen ocean]

So during a test with graphing calculator, do I just plug in that equation into the calculator and approximate the zero

[woeful pasture]

yes

thats id do

lol

[queen ocean]

Ok

Thanks

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[summer cypress]

idk where to start

[summer cypress]

its under area of a triangle

the 1/2abSinC

i got an answer of 35.2 but i doubt its correct

[sharp flame]

,w calc 60.5(3.2)^2*sqrt(3)/2

[glossy valve]

Results provided by WolframAlpha

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Requested by neonperseus

[sharp flame]

can we see your working

[summer cypress]

my answer is very wrong

[sharp flame]

the formula works

[summer cypress]

i didnt rlly know hoq to do it

[sharp flame]

well you do know that all the triangles are equilateral

do you know what a b and C represent

[summer cypress]

can u show me pls

[summer cypress]

yea

the 2 sides

[sharp flame]

C is the angle between two sides a and b

yep

[summer cypress]

3

[sharp flame]

and both a and b are 3.2 in this case

[summer cypress]

ohhh yh cz they the same length

[sharp flame]

yep

[summer cypress]

so 1/2x3.2x3.2xSin60

[sharp flame]

yeah that's one triangle

[summer cypress]

is that correct

[summer cypress]

x6

[sharp flame]

your area is formed by 6 suck triangles

yes

that's it

[summer cypress]

got it

tysm

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[slate pendant]

Hi! for this problem, it’s asking me the value for the series at the top of the page

Not only can I not figure out the value, but I got contradictory results trying to figure out its convergence

[full forum]

@slate pendant Has your question been resolved?

[slate pendant]

<@&286206848099549185>

[glacial valley]

Why diverge ?

[slate pendant]

I thought I could separate the sum

in two terms

and the first term diverges because the limit of the argument is not 0

it’s a necessary condition for a convergent infinite sum

[summer fable]

what's the condition for separating a sum?

[slate pendant]

oh it had to be a sum right?

not a difference

lol I see it now

got it

still, how would you go about calculating a value?

was I on the right path turning the numerator to 1?

[summer fable]

no, not that

[slate pendant]

oh…

[summer fable]

both the splitted sums must converge
here, since both diverges to infinity, you can't really make any claims about its convergence

take for example $\sum_{n=0}^\infty (n-n)$

[glossy valve]

Sepdron

[slate pendant]

I see

[summer fable]

it obviously is 0, but if you split it into the sum of n, then yea you get my point

[slate pendant]

ohhh

I thought that for a series to converge its split sums had to converge as well

[summer fable]

yea because both diverges here, it's not true
if only one of them diverges though, (I think) you would be able to conclude that the original series diverges

[slate pendant]

so it diverges

weird

it was an exam question for a previous year

[summer fable]

in your case, both of the split sums diverges

[slate pendant]

and what about your example (n-n)

you could say both diverge there too

but the sum converges

[summer fable]

yea, it'd be $\sum_{n=0}^\infty n - \sum_{n=0}^\infty n$

[glossy valve]

Sepdron

[slate pendant]

oh

yeah

[summer fable]

if both diverges, we can't say anything about the original sum

[slate pendant]

yup

awesome

such a weird question to put on a test

thank you so much you really helped me out tonight

[summer fable]

np, your original sum probably converges btw

[slate pendant]

whaat

lmao what do you mean

[summer fable]

by the first test, it shows that it converges

[slate pendant]

ohh

right

hm

do you have any idea for how I should calculate its value 😅😅😅

[summer fable]

I don't, I don't really know how to evaluate sums like that

I'll try it though

[slate pendant]

thanks so much

anyways don’t feel pressured

it’s way to late to be asking haha

[summer fable]

yea I'm pretty sure I have no idea on how to approach this lol

[slate pendant]

thanks for trying anyways

bye

.solved

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[red iron]

can anybody explain to me how it got the the final answer?

[willow geode]

do you know what is quotient rule?

[red iron]

yep

[willow geode]

tell me its basic outline?

[red iron]

lo d hi hi d lo?

over lo^2

[sudden condor]

Ngl love it being defined like that imma use it

[sudden condor]

You are forgetting a sign here tho

[red iron]

oh yeah -

[sudden condor]

so (h high l low)
h'l-l'h/l^2

[red iron]

yes

i got that part

[sudden condor]

ok what about the answer that bothers you ?

[red iron]

how this

turned into this

[sudden condor]

Some algebra simplification

(3+4w^3)(2w^2+1)=
8w^5+4w^3+6w^2+3
(3w+w^4)(4w)
12w^2+4w^5 (all negative)
And then you can simplify it

If a step doesn’t look obvious I can explain it

[opaque elk]

Open the brackets and many stuff get cancelled out

I'll give step by step in like 2 hours if u want

Cuz I'm out rn

[red iron]

ok so you multiply the parantheses ang get those

but is still have no cue on how you get to

sorry if i took too long to reply i tried answering it in my scratch

[sudden condor]

ok so for the first 2 brackets
you can write it as
3(2w^+1)+4w^3(2w^2+1) you know how simplify this algebraically ?

[red iron]

nope

[sudden condor]

Well it’s ok

[sudden condor]

you ever took exponent rules ?

[red iron]

yes?

[sudden condor]

Like the algebra one not the one for the derivatives

[red iron]

then no

[sudden condor]

Like for example
4w^3*2w^2 using the rules above it equals (4)(2)(w^3)(w^2)=8(w^(3+2))=8w^5

[red iron]

ok

got it

[sudden condor]

So can you use those rule to simplify this expression

[full forum]

@red iron Has your question been resolved?

[full forum]

@red iron Has your question been resolved?

[red iron]

got it

[sudden condor]

Should be -6w^2

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[neat terrace]

can someone help me out on b

i am extremely lost

[hallow vault]

hm

use the log base change property

[rapid rain]

you now know from a (ii) that y = ln(x)/ln(a)

should be pretty easy knowing the derivative of ln

(beware: ln(a) is constant)

[full forum]

@neat terrace Has your question been resolved?

[neat terrace]

Is it just quotient rule?

Ohhhh

Lna goes to 0 innit

Ahhhh

No

Wait

Why is it when I use quotient

Idk if I can read my writing

It’s just that

I have lnx/lna^2

In addition to the term I wanted

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[silent plover]

what is the logic behind this

[silent plover]

I have a guess but I do not know if I am right

my guess is that we're using this formula, to reach that other formula

[full forum]

@silent plover Has your question been resolved?

[rapid rain]

yes that fomula is used

basically cos(x-y) = cos(x)cos(y) + sin(x)sin(y)

and we use this formula a bunch of times for different angles phi

when we reach this

we just take x = pi/2 - alpha, y = beta

then it's cos(x-y)

[rapid rain]

formula applies

[silent plover]

yeah.

[rapid rain]

and we use that cos(pi/2 - x) = sin(x) and sin(pi/2 - x) = cos(x)

to revert back

[silent plover]

Yeah, thank yah

so, my guesses were right

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[neat terrace]

for b

I got it wrong

cause I did 180 - theta

instead of 360 plus theta

why is what I did incorrect

they are both sin intervals

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[torn jolt]

HOW IS THIS WRONG?!

[left bone]

,w .99x+.96 = 12

[glossy valve]

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Requested by tuzis

[left bone]

ur correct, answer is a typo

@torn jolt

[torn jolt]

Tysm

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[indigo elk]

.

[proper crypt]

anyone who can help me with my questions about algebra and geometry? im in 10th grade (almost 16) and i really dont know how to do algebra and im bad with geometry.

[silk vine]

Just ask your questions (one at a time, preferably)

[proper crypt]

i dont know how to do stuff like a(x + 7) = 2x = 22

stuff like that

or similarly

basically anything in algebra and geometry im unable to do.

[bitter beacon]

if you need math teacher i am here

[faint karma]

you know what

if you are crap at algebra

you can buy this book

it is really good

https://www.simonandschuster.com/books/Painless-Algebra/Lynette-Long/Barrons-Painless/9781506268064

but you can ask me questions too

[proper crypt]

is like

algebra and geometry very important for coding

[slate violet]

no actually, it's useful for other things though

[bitter beacon]

not at all

[proper crypt]

you serious?

[faint karma]

they are tho bruh

[proper crypt]

but i thought variables ARE algebra though, well

i guess variables are

kinda easy

[faint karma]

having good math capacities are very important for programming

[proper crypt]

but what else would be used in coding

[faint karma]

it is mostly logic

but some math principles can be important

[proper crypt]

what if one were to use chat gpt, i personally dont want to use an AI for math, i wanna have intellegence.

[faint karma]

then learn your algebra ?

i dont understand what your question is

[proper crypt]

thats my main problem tho

i dont know where to learn algebra other than youtube and books, and books cost money which i do not have. 🤷‍♂️
and youtube is also kinda dumb most of the time.

[slate violet]

https://www.youtube.com/watch?v=fehAgOqTR44

[faint karma]

can your parents afford you a book ?

[slate violet]

found the video I was looking for!

[faint karma]

are you even at school ?

[proper crypt]

i am

im just not very smart

[faint karma]

then focus on your studies at school bruv

[proper crypt]

thats what i try to do

[faint karma]

watching youtube aint gon help

[slate violet]

it might if YT teaches better than school

[proper crypt]

well i mean

[faint karma]

nah it doesnt

[proper crypt]

i think i just learned some algebra

off of a yt video just now

[slate violet]

you can't say that for 100% of students

[faint karma]

no$

[slate violet]

there are genuinely some shit education systems

I don't know if that's true for them but just raising the possibility

[faint karma]

what country are you from ?

[proper crypt]

usa

[slate violet]

have you tried Khan Academy?

[proper crypt]

the algebra i made for myself was: 4x + 2 = 14.

but i solved it to be 3

is that correct?

[proper crypt]

no

[slate violet]

then try it

[slate violet]

yep, subtract 2 from both sides, 4x = 12
divide both sides by 4, x = 3

[proper crypt]

omg i think i just learned that

thats like

awesome

[faint karma]

yh youre gonna get good classes then

[slate violet]

https://www.khanacademy.org/math/ncert-class-8/x4eb5a6db275bcce1:linear-equations-in-one-variable-ncert-new

[proper crypt]

the usa doesn't have a good education system

[faint karma]

IT DOES STFU

[slate violet]

you can practice this concept in the link I sent

[faint karma]

stop looking for excuses

[slate violet]

well I mean education varies so much in the 50 states

[proper crypt]

it really doesn't

[faint karma]

if you aint getting good results you just aint working enough

[slate violet]

you're not helping by constantly denying what they say

[proper crypt]

i've learned more off the yt video i watched in 2 minutes then i had in an entire class of algebra

[slate violet]

great! basically you just needed some direction right

[proper crypt]

yeah

[faint karma]

that is impossible.

[slate violet]

keep sticking with Khan Academy, for the quizzes

[faint karma]

you just dont listen in class

what do you think

[slate violet]

the material is everywhere, from YT to textbooks ofc

never underestimate a good textbook like Axler's precalculus

[proper crypt]

my hearing is bad, they are slow in teaching, and i have adhd so im getting distracted.

[slate violet]

maybe that's a bit advanced for you rn but just saying

[faint karma]

https://www.simonandschuster.com/books/Painless-Algebra/Lynette-Long/Barrons-Painless/9781506268064

[slate violet]

you can always flip through old versions

for free

[faint karma]

there it goes

if your hearing's bad go to the front row

[proper crypt]

these are genuine things im diagnosed with (the slow teaching is a school problem)

[faint karma]

if your teacher is slow he prob isnt

[proper crypt]

if you wanna be rude and not really help me you can leave, south is being kind enough to help me out without being rude.

[faint karma]

look

[proper crypt]

im a slow learner and not very smart in school and i dont do good under pressure.

[faint karma]

saying your teacher is bad aint a solution

[proper crypt]

my teacher isn't bad

its just that they dont teach fast enough to keep my adhd on track

[faint karma]

and saying you aint smart either

[faint karma]

all i can say is if you wanna learn with something else at least do it with a book

not with the internet

[slate violet]

I agree intelligence isn't fixed but like they're just being honest with their situation right now

[proper crypt]

i do wanna get programs

that block certain apps at certain times

so i can jUST focus on school

[faint karma]

oh

[proper crypt]

i really just want to better myself

[faint karma]

i can give you some

[proper crypt]

what're some

[faint karma]

a sec

[proper crypt]

alr

[faint karma]

https://blocksite.co/

here

also

you can ask your parents to set a parental control

i did that on my phone last year and gyat damn my results are high

[proper crypt]

i dont like trusting my parents sometimes tho, sometimes they set it WAAAY too long, like 12-14 hours of studying lmao

[faint karma]

uh

no i mean like having 1-2 hours of screen time is more than enough

[proper crypt]

exactly

[faint karma]

i even got half an hour on my phone lol

[proper crypt]

its just 12-14 hours prevents breaks mostly

[faint karma]

they give you 12 hours screen time ?

[proper crypt]

12 hours of studying

not anymore but

thats what would happen

trust me lol

[faint karma]

but how much screen time for ytb discord and shi do they give you

[proper crypt]

probably like 3-4 (after school and studying)

if im available ofc

[faint karma]

oh thats a bit too much

[proper crypt]

honestly i agree atp

[faint karma]

tell them to put it to 1

so the rest you can fully study

[proper crypt]

i play too many games and i just want to be able to improve my life

[proper crypt]

i really agree with that

[faint karma]

oh i fully understand

also

from experience if you have a full weekend of free time dont study for a day straight

especially if you have adhd

take like between 2 and 4 hours of time where you do smth else (but no screens)

[proper crypt]

so like, study for 2 hours, take a break, and repeat?

[faint karma]

for example my typical study day is 10 - 12h30 study then lunch then at 15 i go skating till 17

[faint karma]

nah

do breaks every 45 minutes

[proper crypt]

alr

[faint karma]

but for the breaks dont only stay at home

you can do outside activities

if you take an hour break

like skating

or idk if you play an instrument do some for 1 hour

[proper crypt]

alr bet

what if i wanna like

take walks and stuff outside

is that good?

like nice fresh air for a break.

[faint karma]

yess thats perfect

you can take 1 hour to go outside when you're feeling overwhelmed

[proper crypt]

bet

this is alot help, thank you @faint karma @slate violet
its really nice to know people out there can help you advance yourself.

[faint karma]

yep

honestly i was in the same situation as you last year

i really wanted to get good at school

[proper crypt]

fr?

[faint karma]

so yh i started taking the good habits for studying and stuff

[proper crypt]

are you like a pro at it now?

[faint karma]

well i got pretty efficient

[proper crypt]

thats really cool, do you think i'll advance to that level?

since im in 10th grade and im still pretty slow on algebra and bad with geometry

[faint karma]

you gotta really set your objectives

if you have clear objectives you can accomplish them

[proper crypt]

alr bet

[faint karma]

but you'll really have to do everything to reach them

so if it means for example lowering your screen time and stuff you gto

[proper crypt]

alr, well before i continue studying my math

maybe i should go outside

and just get some air

thank you guys so so so much for the help

[faint karma]

yep go on

no problem 🙂

[proper crypt]

also how do i close the help thing, i dont wanna occupy it forever lol

[faint karma]

you can add me so i can help you if you need anything

.close

[proper crypt]

alr bet

.close

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[vast surge]

Hello, I have issues with this exercise: Proof that $x_n >= sqrt(2)$
I tried induction for hours, but with no success. (Will post my attempts in a minute). Where do I even start?

[glossy valve]

David

[vast surge]

n is only positive natural numbers

[silk vine]

Are you allowed to use derivatives?

[vast surge]

no

[fast peak]

am gm

[vast surge]

what dies this mean?

[fast peak]

(x+y)/2 >= sqrt(xy)

arithmetic mean geometric mean inequality

[silk vine]

I got a solution as well now

You can show that 1/2 + 1/x^2 >= sqrt(2)/x

[full forum]

@vast surge Has your question been resolved?

[vast surge]

Yes

.close

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[vast surge]

Thanks

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[real harbor]

Does anyone have a trick for understanding discrete mathematics?

[real harbor]

I read this as:

'For every x, if D(x) OR B(x) is TRUE THEN C(x)'

I saw Ann has neither B(x) nor D(x) as true, and therefore selected she's a proof why it's false

Or does anyone know a good course for studying discrete mathematics?

The easiest answer is to just see the pattern in what is correct and replicate it 'If C(x) is wrong it's a counter-example' like in this new one

but it seems kinda hard to properly understand if I'm wrong?

I guess I'm wondering if my interpretation is correct, or if anyone has good resources for learning this stuff.. Khan academy doesnt have a discrete math course, neither does brilliant

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@real harbor Has your question been resolved?

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@real harbor Has your question been resolved?

[real harbor]

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[zinc gull]

Hi how do I solve this?

[safe trench]

Draw this shit

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[dire grove]

Anyone have any ideas how to solve this ??

[lament badge]

take the derivative

[torn jolt]

L'opital

[light cairn]

we can use small angle approximation

[dire grove]

but you have to use quotient rule right and that just further complicates everything

[torn jolt]

They meant l'opital

[light cairn]

the value will be equal to the limit of sin(pi(1-x^2))/x^2 = lim sin(pix^2)/x^2 = pi

[dire grove]

but you are taking derivitive with lopital and since the division is there you have to use quotient rule

[torn jolt]

Are you aware of how to use l'opital

[dire grove]

if there is indetermined form you take derivitive of the limit???

[torn jolt]

No,only when it's a 0/0 form

[dire grove]

or infinity over infinity

that undetermined

thats

[dire grove]

from where?

[light cairn]

this

i think i did wrong

nvm

1-sin^2x

sin x = x for x tending to zero

@dire grove

[dire grove]

but is there any proof for that?

[foggy trout]

I think you can also use the squeeze theorem

[dire grove]

never heard of it

[light cairn]

ya from taylor series

sin x = x - (x^3)/3! + (x^5)/5! and so on
so limit of (sinx)/x at x->0 is 1

[foggy trout]

Sorry I thought it was lim x->inf u can't use it here

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[lavish elm]

I need help with each question i feel like i havent been taught and dont know where to start

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Please don't occupy multiple help channels.

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[lavish elm]

<@&286206848099549185>

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[brittle thorn]

Hi , i'm struggling woth 9b) , sorry it's in french 😭

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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.

[robust slate]

What’s f

[hidden harbor]

what's the result of II

[brittle thorn]

oh ofc sorry

[robust slate]

$\hat{f}(k)=\frac{1}{n} \sum^{n-1}{p=0} \left(\frac{p}{n}-\frac{1}{2} \right) \omega^{-kp}=(\cdots)+\frac{1}{n} \sum^{n-1}{p=0} \frac{p}{n} \omega^{-kp}$

[glossy valve]

Civil Service Pigeon

[robust slate]

The first sum is just using the formula

For the second sum, consider what happens if you multiply it by $\omega^{-k}$

[glossy valve]

Civil Service Pigeon

[robust slate]

Further hint: ||subtract the two||

Alternatively, differentiate an appropriate power series

Pick your poison

[brittle thorn]

Thank you

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[wheat garden]

A skier is traveling along the top of a circular hill. Assuming the skier just barely stays in contact with the hill at the top, find the angle that the skier leaves the hill.

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[cobalt rune]

How do i start on #3?

[cobalt rune]

I tried using substituion but got no where at all

Not sure where to start

[tidal rain]

divide

u can find the other factor after dividing

and hten multiply the two factors together

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[cobalt rune]

.reopen

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✅

[cobalt rune]

How do i divide out c and d?

[tidal rain]

U don’t

you're supposed to work out c and d

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[next otter]

yo

[next otter]

5. From the new point, what is the(unit) direction vector and how many degrees do you need to
   turn the ship to face asteroid 1, then asteroid 3, then asteroid 2? How long does it take to make
   each turn

So I made my new point (5,27) however with that new point my arctangent comes up as undefined making it impossible to make a new vector

5-5 = 0. 9-27 = x/y = 0/-18. arctan(-18/0) = undefined

[spiral vigil]

forget arctan

and think with your brain

[next otter]

would it be 0

because anything divided by 0 is undefined which wouldn't be 0

would it be 270

.close

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[next otter]

nvm still not getting it

.reopen

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[next otter]

if the arctan is undefined then how do you make a vector with it

-90 degrees

because its 90 degrees straight down

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[astral ibex]

I need help

[astral ibex]

their the same btw

<@&286206848099549185>

<@&286206848099549185>

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[torn jolt]

i can help!

just charging my ipad real quick

si

@astral ibex I recommend

using the arc length formula

2pi(radius) times rhe degrees over 360

since tje problem is in degrees

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[rugged raft]

stat1

[rapid rain]

which ones do you think are false/true?

[rugged raft]

stat1 dunno how to begin

[nova basin]

try to prove it or try to build a counter-exemple
If you fail ask yourself why and use it to do the opposite

[rugged raft]

a is false, if xn=npi

C is false

[nova basin]

assume xn converges

they say