help-0

[charred flint]

in the end it doesn't matter at all yeah

choosing a point where the function switches makes it easy to split the integral into 2 parts

[sturdy grail]

it doesn't make sense, we are to get b_n, and the functions intervals is given above, I mean can we choose intervalls that exceeds the boundary?

[charred flint]

the function here goes on forever

you just want an interval that's the length of the period to integrate over

[sturdy grail]

and how is -1 the length of the period?

[charred flint]

T is the period length

d is a starting point you choose

[sturdy grail]

it feels weird i can choose the starting point random

some people uses pi and some not

[charred flint]

so like the function repeats with length 2 right?

[sturdy grail]

yes

[charred flint]

the fourier formula you posted is an integral of length 2, so no matter what d is, you're adding up each point in the function once

[sweet marlin]

Can someone help me with #16

[sturdy grail]

but don't d represent intervall on the x axis, on the bottom it doesn't add with length 2

@sweet marlin not done yet

[sweet marlin]

K

[charred flint]

not sure what you mean

when you plug d=-1 and T=2 in it's an integral from -1 to 1

which the question gives f(t) for

[sturdy grail]

what if we choose

d = 100

[charred flint]

then the integral is 100 to 102, which gives the same a_n's and b_n's

[sturdy grail]

oki I see, but is it good to choose d = 1 ?

[charred flint]

that's fine too

either way you're going to split the integral into f=0 and f=1 parts

[sturdy grail]

normally I'm used to have negative on the bottom of the integral

but it doesn't matter

[hybrid plume]

I know the channels busy plurmorant when you’re done here can u come to channel 5?

[sturdy grail]

@charred flint but let's say we have -1 to 1, which function should I insert, 1 or 0?

what is f(t) in between -1 to 1

[charred flint]

well it's 0 then it's 1 as you go along

to do the calculation you split up the integral from -1 to 0, and 0 to 1

[sturdy grail]

but then we have two integrals

are they to multiply with each other

[charred flint]

nah you just split them with an plus* sign

this sort of thing

[sturdy grail]

but with -1 to 0, the function is 0

and integrate of 0 is 0

so we can skip -1 to 0

and focus on 1 to 0

@charred flint but this would only have worked if you actually chose -1 it would have worked if you used d = 5

[charred flint]

any d will do the same thing yeah

[sturdy grail]

nah, if we chose d = 5 and our period is 2 we will get 7 to 5

right

[charred flint]

sure

and 5 to 6 has f(t)=0

and the integral will really be from 6 to 7 with f(t)=1

[sturdy grail]

what

how

but

[charred flint]

what part don't you believe

[sturdy grail]

so first of I don't think you can split 7 to 5, into 5 to 6 and 6 to 7

[charred flint]

I'm going with 5 to 7

not sure why you're writing it backwards

[sturdy grail]

yeah but how can you split 5 to 7, into 5 to 6 and 6 to 7

[charred flint]

that's how integrals work idk what you mean

[sturdy grail]

oh

yeah

my bad

yeah you can split into functions like that

okay but how is 5 to 6 has f(t) = 0

[charred flint]

so the question says -1 to 0 is f(t)=0

[sturdy grail]

yes

[charred flint]

it also says f(t+2)=f(t)

so we can shift those numbers up and down by multiples of 2 and it still works

so -1 to 0 is 0, 1 to 2, 3 to 4, and 5 to 6...

[sturdy grail]

the reason why I'm so confused is because they are not negative numbers, but I just forget it is just periods that repeat it self. it is just odd that it repeat it self on positive x axis

[charred flint]

right

[sturdy grail]

but it is about the inter vall not the x axis perse

but what if we had three conditions on the picewise what would we have done? then split integral into two pieaces would have done it ?

[charred flint]

for piecewise you split it every time the function changes yeah

[sturdy grail]

@charred flint should d be in t ??

when you subtract

[charred flint]

huh

[sturdy grail]

when you have a integral that has a intervall, you are ought to substract when you put these values in the inte finnish product

nvm yes you should put it in t

so for an example we have the integral -1 to 0 and we are to integrate cos(wnt)

and we get sin() and now we are to plug it in and we get

sin(1)-sin(0) = -sin(wn)

does this mean a_n = sin(wn) ?

[alpine sable]

-1 to 0 is 0

[sturdy grail]

I meant

1 to 0

[alpine sable]

Integral of cos is?

[sturdy grail]

sin

[alpine sable]

sin(1nw)-sin(0nw)

[sturdy grail]

oh

waiiiiit

nvm

[alpine sable]

Got it?

[sturdy grail]

we get sin(nw)

as you typed

but then a_n = sin(nw)

right?

[alpine sable]

Yep

[sturdy grail]

but

wait

[alpine sable]

Waiting

[sturdy grail]

we get

but then we get

wait

what is a_o

is a_o the amplitude?

[alpine sable]

How much is n

[sturdy grail]

infinite

[alpine sable]

What about for a_0

[sturdy grail]

it is 0

so we should plug in 0?

[alpine sable]

Sub in 0 instead of n yeah

[sturdy grail]

but then we get sin(0) = 0?

[alpine sable]

Is it a problem?

[sturdy grail]

no, but then we only have the sum

but how are to deal with the sum I forgot about it

so we have sum( sin(nwt)* cos(nwt))

what are to do with the sum should we leave it there

[spice breach]

can i quickly ask how does multiplication work with roots? (like is 2* sqrt(16) same as sqrt(32)?

[gentle ingot]

Nop

[sturdy grail]

@alpine sable

[spice breach]

then how does it work?

because i got the answer (2-sqrt(32))/2

and it says the final answer is 1+2sqrt(2)

[rancid wave]

Hey, can anyone help with trig functions and triangles?

[sturdy grail]

guys this channel is not done yet

we are done very soon

[rancid wave]

What channel can I go to rn?

[alpine sable]

Dunno, depends on what the problem asks I guess

[sturdy grail]

idk but we are done soon

thats the problem

[alpine sable]

Yeah leave it in that form

[sturdy grail]

and we wouldnt leave in that form what would we do then?

it wants the fourie series

[charred flint]

lhopital's or taylor series to solve that limit

e^x ~~ 1+x+x^2/2+...

[placid zinc]

That's one of the "common limits" too

[alpine sable]

@sturdy grail check how it behaves for a_1, a_2

[sturdy grail]

@alpine sable ah really that ez?

Fourie series got abit easy to understand now. thank you

I don't understand why I would need fourie series in EE

rn we have signals and systems

[alpine sable]

a_3 etc. What you usually get is certain behaviour for odd or even values

You'll see when you get to fourier transform, laplace

[sturdy grail]

I know about laplace transform

what is it you transform in fourier?

@alpine sable derivtate demoniator and numerator

but if you get wishy washy answer, then you should use taylor formula

inotherwords if you get complex dneominator and numerator you should go with taylor formula

[hybrid plume]

Epic while he searches can you check questions 1? Quick question should only take a few seconds

[sturdy grail]

you can perhaps ask ur question

i think

[hybrid plume]

It has 2 small pictures

Don’t want to take up room here

[sturdy grail]

ask if that animu dude is done

no

dont think so

[alpine sable]

@sturdy grail you transform time domain functions to frequency domain

[sturdy grail]

I see

@alpine sable i think you would do taylor formula then

[alpine sable]

Gives you another domain to analyze a signal from

Making some things easier to see

[sturdy grail]

@alpine sable oh frequency domain

ye

[alpine sable]

Sum of many waves. Hard to see which waves specifically in time domain

[sturdy grail]

is the blue frequency

[alpine sable]

Yes

[sturdy grail]

why would you want that

[alpine sable]

For filtering

For example, I only want the low frequency. I make a low pass filter. The freq domain helps me see where the cutoff mark is

[sturdy grail]

what effect does low frequency have on that square wave?

[alpine sable]

Filters out the ripples in the high and low parts of the wave for example

[sturdy grail]

@alpine sable you filter this

[alpine sable]

Yes, just an example

[sturdy grail]

but you make it smoother adding constants tho

so there is no need to filter?

[alpine sable]

Explain

[sturdy grail]

the more constants we have in our fourier series, the more we can replicate the function ie, that wave will smothen out @alpine sable

I don't think I've worked with rienmen sum I think not sure. I'm not so well versed in that sorry.

[hybrid plume]

Np

[sturdy grail]

@alpine sable can I dm you? do you study EE too?

[alpine sable]

I finished some time ago. You can

[sturdy grail]

you graduated?

[alpine sable]

I forgot half

Yes

[sturdy grail]

what do you work as?

[alpine sable]

Technical writer and tutor in my free time

[hybrid plume]

Em could u take a look at my question?

[compact meadow]

Who good at algebra but with graphs

[sleek elbow]

#❓how-to-get-help

[hybrid plume]

@raw shard are you online?

[raw shard]

@hybrid plume yes

@hybrid plume sorry i don’t really remember anything about riemann sums

[hybrid plume]

Np, do you know any helper who would?

[raw shard]

you’d honestly be better off just looking it up lol

no i don’t

i would say just post it and wait for an answer

[sweet veldt]

do i need to make the 2.7 into .27 10^3 or 3.7 in 37 10^4

[raw shard]

@sweet veldt neither, scientific notation is x*10^y, where y is an integer, and x is an number between 1 and 10

[sweet veldt]

so this is my problem right? 2.710^4-3.710^3 correct?

so i have to bring the 2.7 to 27*10^3?

@raw shard

[raw shard]

put \ behind *

edit your message

so it doesn’t do italics

[sweet veldt]

do i leave it that or make it 2.33*10^4

okay sorry im not familiar with the commands

[raw shard]

you should do 2.33*10^4

because 2.33 is between 1 and 10

[sweet veldt]

but also because it was originally 2.7*10^4 correct

[velvet perch]

hi <@&286206848099549185> , is there any way to prove that {NOT, AND, OR} is functionally complete?

it means that you can construct every boolean expression with binary operands using just those three operators

operands meaning the inputs to the operator

well the idea is that you don't need any others

just AND, OR, and NOT

because XOR is just ((P OR Q) AND NOT (P AND Q))

but im trying to figure out how to prove that this is the case

[inner lantern]

busy?

wont take too long

[velvet perch]

no worries

[inner lantern]

Like im just wondering how i go from this to x >= 9

[velvet perch]

i mean

[velvet perch]

isnt it true that this expression will also be > 0

precisely

[inner lantern]

the answer is x >= 9

[velvet perch]

yeah

rewrite the expression as sqrt(x - 9) >= 0

because it is guaranteed that the principle square root of any quantity must be nonnegative

how would i construct the proof tho

would i start with an arbitrary truth table of size n

no no no

im asking how would u start the proof

idk what i can assume

what would that look like

ye

so for an arbitrary expression T(p1, p2, p3, ..., pn)

T is logically equivalent to the DNF of every case

right

[glass lichen]

Yeah... cause sqrt maps to non negative numbers

So it's just the domain

[velvet perch]

every case where T(some input set) = 1

[inner lantern]

not sure what your saying

all i know is if i square both sides it eventually equals x>=10

which is incorrect

[velvet perch]

you can't square both sides

but just ask urself this: can sqrt(anything) be < 0

[inner lantern]

no

[velvet perch]

right

[inner lantern]

so its also sqrt(x-9) >= 0?

[velvet perch]

so we know for a fact that the set of numbers in [-1, 0) is not in the domain

so we can ignore them

[velvet perch]

this expression is equivalent yes

[inner lantern]

Oh oh

[velvet perch]

because of the domain restriction of the sqrt() function

[inner lantern]

i see

[glass lichen]

Which I the same as just the domain

[inner lantern]

a square root can never be a negative

[velvet perch]

ye

[inner lantern]

gotcha

[bold quail]

is this channel free

[bold mantle]

Help

Number 7. Please

[alpine sable]

,graph 5x-2

,w plot 5x-2

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Em#0720

[alpine sable]

Done

[bold mantle]

I need to know how to actually do it on my own so when I have a test I can do the question

pls

[alpine sable]

Make a chart

Like this

[bold mantle]

Is 5x the x value and 2 the y value?

but it doesn't give me the rise over run thing so idk where to plot the other points

[alpine sable]

x | -1 | 0 | 1 |

y | | | |

Sub in -1 into your equation and calculate for y

[bold mantle]

Where did u get-1 from

[alpine sable]

I picked it. You can pick any numbers

[bold mantle]

Why

[nocturne juniper]

the ...x number is the slope

and the number after is the y intercept

[alpine sable]

It's domain is over the whole set of real numbers. It exists for any value. Whatever x i give it, i get a y back

[nocturne juniper]

if you have a line with a slope of 5

then

for each unit of x there are 5 * x units of y

so

if you move 2 x

you move 10 y

good so far?

[alpine sable]

Our methods are different. Choose your path

[bold mantle]

why must math have so many paths

[alpine sable]

Mine is better

[nocturne juniper]

i think mine is simpler

so

[alpine sable]

Choose any 2 numbers elon musk

[nocturne juniper]

tf

[bold mantle]

3,8

[nocturne juniper]

uh

so heres my method

[pseudo quarry]

hELP

[alpine sable]

3 and 8.
5(3)-2=
5(8)-2=

Solve elon musk

[bold mantle]

Oh

[nocturne juniper]

if you have a line with a slope of m, then for each x-position unit you move along the line, you will move m*x y-position units

[bold mantle]

13,38

[pseudo quarry]

can any one help me with this ?

busy ?!!?

[alpine sable]

stop

are u blind

[pseudo quarry]

no

😄

[alpine sable]

you are wasting more time than u need

[nocturne juniper]

the y-intercept just changes the starting y-position

[alpine sable]

it is faster to just LOOK then ask

like wtf

[nocturne juniper]

so if you have y intercept of 3 and slope of 5

then you start at x = 0, y = 3

[alpine sable]

First point is (3,13)
Second point is (8,38)
@bold mantle
Find those coordinates and put dots there

[nocturne juniper]

and for each x-position unit you move 5 y-position units

[bold mantle]

Ok

[alpine sable]

Take ruler and connect them and extend the line in both directions

[bold mantle]

Mhm

[alpine sable]

Now, if you picked 0, 1

It would have been easier to draw and calculate

Makes sense?

[bold mantle]

Ok

[alpine sable]

You pick the numbers that work easier for you to calculate and find on plot

[bold mantle]

Would u mind doing f(x) = 6 for me, step by step, I learn well that way

[alpine sable]

Plot the function f(x) = 6?

[bold mantle]

graph the linear function

[nocturne juniper]

here

[bold mantle]

Ok

[alpine sable]

,rotate

[bold mantle]

oh ok

[nocturne juniper]

another method you can use is just graph two different points of that function

and make a continuous line between them

[alpine sable]

My method yes

[bold mantle]

Could you do f(x) =3/4x - 2 please

[alpine sable]

You tell me

What x should I choose

[bold mantle]

1

[alpine sable]

How much is y

[bold mantle]

2?

[alpine sable]

y = f(x) = f(2) = 3/4(2) -2

y = f(x) = f(1) = 3/4(1) -2

[bold mantle]

,rotate

[ocean seal]

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

Sep 29, 2021, 10:50 PM

[bold mantle]

,graph 5x-2

[nocturne juniper]

ok here

[bold mantle]

,w plot 5x-2

[nocturne juniper]

the other method

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by elon musk#7826

[bold mantle]

Ok

[grizzled sundial]

Thanks but I can't read it lol 😦

[hardy geyser]

this channel is done?

https://gyazo.com/5e8df059cb1a6a6f6954737626822899

why is it not c?

im guessing because it reaches to the 25 and 4 ?

[half skiff]

How to not procastinate

[ancient saddle]

Hello, 25 and 4 are the squares of both semi-major and semi-minor axis, respectively

[quartz osprey]

how do i find the relative minimum?

2 was super specific

everythign around it was positive

so i couldnt pin point it was 2 but after guessing and checking it worked

is there a way to find out that is is 2

[past sundial]

Random question but am I doing this right?
6^5 x 6^-3 = 6^5 / 6^3

[raw shard]

yes

[ivory thicket]

is there a hypothesis in a maths report?

[atomic lodge]

Can anyone help me with this question

Question 13

I tried but I am getting DNE

The correct answer is ||-8||

I googled and found this

But I don’t understand how did they simplify

Anyone?

[alpine nacelle]

They factor x-2 out of the numerator (so it cancels and remove the problem when x->2)

[atomic lodge]

Hmm

[amber depot]

@past sundial Yes

@quartz osprey If you graph the equation you should x = 2 as your relative min then.

In order to locate any relative minimums/maximums you need to graph the equation first.

[slender bane]

I am so lost on this trig right now

I will literally pay someone to explain this

[quartz osprey]

this is without graphing iirc

[amber depot]

@quartz osprey If you don't know how to solve the polynomial, here is a video that should help https://www.youtube.com/watch?v=HKDdzBuffoY

what is iirc?

How did your teacher do it? There might be other ways my bad

[slender bane]

if I remember correctly

[amber depot]

oh, thanks

@quartz osprey or this is the other way to do it or that you might be doing https://www.youtube.com/watch?v=WCq3sRzsJfs&t=73s

[alpine sable]

any ideas, must be done without L hopital

[ocean seal]

Andreww

[alpine sable]

Ahh ok

[quartz osprey]

oh no i already solved it lol

it was -2,0,2

the thing was that -2 was- 0 and 2 were both +

i couldt pinpoint the exact location it was a min or a macx

min

cuz as you know it was _ + +

[amber depot]

That's good you solved it

or understood it

[north dune]

Busy?

Please help

How do i figure this out

[stoic elbow]

how can I turn this displacement over time graph into a velocity over time graph

[north dune]

Oh ok thanks can you help me woth this one also

This is it -4

Anyone

[stoic elbow]

one sec

[north dune]

Okay

No

Its credit recovery

[north dune]

Was i correct

[past sundial]

Random question but am I doing this right?
10^-4 x 10^5 = 10^5/10^4

[stoic elbow]

yes

[past sundial]

Okie thanks!

[north dune]

I dont need help anymore by the way

[stoic elbow]

sorry i got lost thinking about something else i think your right

cool

[raven bluff]

guys, I think i'm over thinking this one... how does the 24 become a 4? is it simply because it's being divided by 6?

[remote heron]

yea

[raven bluff]

thanks man

[remote heron]

np

that was easy

too easy

[raven bluff]

just needed to make sure. a beautiful subject but holy crap it makes you overthink to an unnecessary degree at times

[remote heron]

ye

i mean just ignore constants right

dealing with variables

'some constant' times the important part

once you got the variables you can go back and get constants anyways by letting vars be some convenient value

[tawny lion]

how do I find the interval of convergence?

when I ratio test it I just get 0

[raw shard]

@raven bluff nice choice of site to learn calculus

i use that site too

[raven bluff]

it's just algebra at the moment. hoping to get to calc at some point. wait... maybe what i'm learning is used in calc idk yet

[raw shard]

oh lol

yeah i think it might be

simplifying stuff

[quartz osprey]

how do i find the critical points?

i know its 0 and

idk how to find the other number

[remote heron]

other?

[quartz osprey]

theres no way its just 0

[remote heron]

oh, its not 0 i mean

your original function isnt defined at 0

so thats gonna be a problem

critical points will come from g'(x) = 0

[quartz osprey]

yea im finding the critical points or where the derivitive is not defined

[remote heron]

critical points are not where the derivative is undefined

[quartz osprey]

oh

where its disconnected

or i got no clue 😭

[tawny lion]

can u not post your q after mine was unanswered lol

[remote heron]

oh

[tawny lion]

its fine now cuz ur getting help but its just bad ettiquette

[remote heron]

u gotta use the ratio test

[quartz osprey]

https://tenor.com/view/nikocado-avocado-orlin-home-angry-fat-man-angry-cry-gif-22839607

[tawny lion]

yeah I tried that

[remote heron]

[tawny lion]

it didn't yield anything

[remote heron]

hmm

[remote heron]

[quartz osprey]

oh yea its where the derivitive = 0

not where its undefined

lmao

[remote heron]

converges everywhere

[toxic zephyr]

Isn't it also when the function is not differentiable? Which in this case is when the original is undefined?

[tawny lion]

it does?

[quartz osprey]

im not sure

[remote heron]

oh idk

[tawny lion]

bru

[remote heron]

thats the interpretation right

its more a joke than anything

maybe ill try 1s

[quartz osprey]

cant i just set it 4x=-864/x^2

im ngl idk how to solve that now 🤪

[remote heron]

harder than the alternative

[tawny lion]

wait nvm

[remote heron]

turn it into 1 fraction

@tawny lion ?

whatd you find

[quartz osprey]

4x^3-864/x^2

[remote heron]

wheres a fraction 0

what makes it 0? what condition

[tawny lion]

I did, you can see in the third image I sent

[remote heron]

okay

[tawny lion]

r tends to infinity

[remote heron]

yea

oh

factorial trumps polynomial

[tawny lion]

<@&286206848099549185> still stuck

[toxic zephyr]

take it back 1 step

[remote heron]

can you guys go to like

[toxic zephyr]

youre looking for when the function is either not differentiatable (original is undefined) or when the differential equals 0

[remote heron]

8 maybe?

[toxic zephyr]

yeah nws

[remote heron]

im curious about kuramas

[quartz osprey]

[weak heron]

Need help on how they got the unit Run

[fresh wigeon]

if someone could explain this to me i would appreciate it

i know my answer was wrong i chose a random one

i just didnt know how to solve it

[stable pivot]

is anyone here able to help me with a linear algebra problem

[abstract fractal]

Just post the problem. If someone can help, they will

[toxic zephyr]

remember f-1(x) is not 1/f(x)

[sick ledge]

Could someone explain to me how this is (k-1)ak+ak derived from the question?

[toxic zephyr]

its f(x) reflected across the line y=x

or, when f(x) has its y and x flipped

hence, g(x) is equal to f(y) at point x

[tidal thistle]

how do you generate an equation using the bot in here

[sudden gorge]

hi

uniform velocity is instantaneous velocity?

[maiden dagger]

I am so lost

is this supposed to be a derivative?

[weak heron]

nvm i solved my own question

[rigid smelt]

suppose that g^(5005) is just an exponentiation

just find g(-3pi/4) and raise it to the power of 5005

[stable pivot]

hey waler would you be willing to help me with some lin alg work

[rigid smelt]

just post it in an unoccupied channel

[maiden dagger]

Is that how this works?

[rigid smelt]

yes

supposing that we are talking about exponentiation

[maiden dagger]

https://math.stackexchange.com/questions/3536876/what-does-fnx-mean

[rigid smelt]

but sometimes f^n(x) can also be used to notate f(x) is compound in itself n times

[maiden dagger]

hmm

okay

[rigid smelt]

tho if it really does mean f(x) is compounded in itself n times, then theres probably some kind of theorem here

or maybe some cancelation in g(x) that can make the composition really easy to solve, but i cant see that for now

[maiden dagger]

yeah.. we're in the derivative unit

[rigid smelt]

eh no, this has nothign to do with derivative

[maiden dagger]

okay

ty

[alpine sable]

can anyone help me with question 21?

also draw the triangle for me

[stable pivot]

sohcahtoa :)

can someone help me with this

[placid zinc]

So A = LU and we want to solve LUx = b

What's the solution to Ly = b?

Once you have that, realize that Ux = y, and solve that

[ember stream]

can I know whether |AB x AC| = |AB| x |AC|
and if so, why?

cross products and vectors I am talking about

[south arch]

hiiii can someone pls explain why the 6xyz turned into 6yz & 6xy(dz/dx)?

[tidal thistle]

may I ask

[rigid wind]

chain rule when differentiating w.r.t. x

[haughty falcon]

One message removed from a suspended account.

[jagged imp]

I heard google.com knows

[haughty falcon]

One message removed from a suspended account.

[chilly veldt]

Or Wikipedia

[haughty falcon]

One message removed from a suspended account.

[raw shard]

bruh

[haughty falcon]

One message removed from a suspended account.

[raw shard]

you’re trolling

[rigid wind]

273/1 ?

lol

[haughty falcon]

One message removed from a suspended account.

[haughty falcon]

One message removed from a suspended account.

[rigid wind]

2730/10 if you wanna be sophisticated

[haughty falcon]

One message removed from a suspended account.

[rigid wind]

ah just random troll

[haughty falcon]

One message removed from a suspended account.

[raw shard]

now i know for sure you’re a troll

[haughty falcon]

One message removed from a suspended account.

[raw shard]

thanks

now stop

[haughty falcon]

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

[raw shard]

keep doing it i don’t care

i’ll just get a mod or something

[haughty falcon]

One message removed from a suspended account.

One message removed from a suspended account.

[raw shard]

no

[haughty falcon]

One message removed from a suspended account.

[raw shard]

yes

[haughty falcon]

One message removed from a suspended account.

[raw shard]

both of those are integers

[haughty falcon]

One message removed from a suspended account.

One message removed from a suspended account.

[raw shard]

the numerator and denominator must be integers

[haughty falcon]

One message removed from a suspended account.

[raw shard]

idk why i’m replying to you, you’re a troll

[haughty falcon]

One message removed from a suspended account.

One message removed from a suspended account.

One message removed from a suspended account.

[hardy gulch]

, the set of rational numbers (\Q) is defined by
[ \Q = \left{ \frac{p}{q} : p, q \in \Z, q \neq 0 \right}. ]

[ocean seal]

ricey

[haughty falcon]

One message removed from a suspended account.

One message removed from a suspended account.

[hardy gulch]

yuh

[raw shard]

if they don’t know what a rational number is they won’t know what that means @hardy gulch

[haughty falcon]

One message removed from a suspended account.

[late kernel]

im struggling with this question , can someone help please, thx

[velvet perch]

i presume direct proportion means that x^2 = ky for some constant k

[covert juniper]

@late kernel So x^2 is proportional to y. So if x is doubled, (2x)^2 =4x^2 so y is multipled by 4

How would I do an epsilon n proof for $\frac{3x+3}{\sqrt{x^2+1}}$

[ocean seal]

ALBERTO BALSAM

[late kernel]

ohhhh

ok i understand now thanks alot dud

[covert juniper]

np

[ember stream]

what are you trying to prove?

that it approaches a specific value?

[covert juniper]

Yeah, sorry meant to put n instead of x, I want to prove it converges to 3

[ocean seal]

Ryuzaki
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[covert juniper]

Ill rewrite it

[tender belfry]

Can i define a mathematical point as a hypothetical geometrical figure having no width, thickness or length i.e x=0,y=0,z=0?

[covert juniper]

hey im already in this channel boss

find another

[tender belfry]

Ok

[ocean seal]

ALBERTO BALSAM

[white kiln]

How do i solve this Im helping a friend

[amber depot]

@white kiln See what both numbers are divisible by. 18 and 24 both are divisible by 6 and 3. Use the highest one so you don't need to reduce it more.

[silk pivot]

https://gyazo.com/2aebf5111bbad04445523cece42cd375

can someone tell me where f and f' is continuos

please

please someone help me

[alpine sable]

u got your solution in other chats so ill assume i can ask here

can sb pls help me w this

https://artofproblemsolving.com/wiki/index.php/2011_AMC_10A_Problems/Problem_22

i got 2880 lol

i drew the pentagon and counted the number of possible cases each vertex so 6x6x5x4x4=2280

can sb pls help me ;-;

[kindred warren]

shouldnt it be 6!

6 factorial

oh wait there are 5 corners nvm

wait it should still be 6 factorial

[alpine sable]

There are $6$ colors to choose from, and the ends of each diagonal must have different colors

[ocean seal]

kk9

[alpine sable]

thats the problem ;-;

[kindred warren]

by ends of the diagonal you mean the corners right

[alpine sable]

yeah

like AC cant have the same colour

[kindred warren]

ok

so for one corner

you have 6 options

second corner you have 5

third corner you have 4

and so on

that just becomes 6x5x4x3x2

hmm

but that becomes 720

and that isnt an answer

[alpine sable]

yeah :'(

[kindred warren]

interesting

[alpine sable]

i dont understand the explanations

There are $6$ ways to assign a color to $A$. WLOG, give vertex $A$ a color; we can multiply by $6$ at the end. Since vertices $A$ and $C$ cannot have the same color, there are $5$ ways to assign colors to vertex $C$. Using this same logic, there are $5$ ways to assign a color to vertices $E$, $B$, and $D$, giving a total of $5^4=625$ ways. However, vertex $D$ cannot be the same color as vertex $A$. To use complementary counting, we need to find the amount of ways for $D$ and $A$ to have the same color. Notice that this is equivalent to the amount of ways to arrange colors among the vertices of a square. Using the same logic as above, there are $5^3=125$ ways, except we must subtract the number of ways for a triangle. Each time, there is $1$ less vertex, so $5$ times less ways to color. This process stops when there are only $2$ vertices left; in this case there are simply $5$ ways to color this figure. So in conclusion, there are $6(5^4-(5^3-(5^2-(5))))=6(5^4-5^3+5^2-5)=\boxed{3120 \ \mathbf{(C)}}$ ways.

[ocean seal]

kk9

[kindred warren]

OHHHH, i thought every corner must have a different colour

[alpine sable]

so how can we solve it? :p

[kindred warren]

but its just that the ones next to it cant have different colours

[alpine sable]

so how can we do this ;-;

[kindred warren]

hm

[alpine sable]

😭

[kindred warren]

why cant A and C have the same colours?

they're not next to each other

[alpine sable]

idk

dkfhaksdjfh

ded

could i ping a helper later ;-;

[kindred warren]

sure

[alpine sable]

Each vertex of convex pentagon $ABCDE$ is to be assigned a color. There are $6$ colors to choose from, and the ends of each diagonal must have different colors. How many different colorings are possible?

can sb pls explain this ;-;

[kindred warren]

oh i know

so A cant have the same colour as D and C

[ocean seal]

kk9

[alpine sable]

yeah

[kindred warren]

B cant have the same as E and D

[alpine sable]

yep

thats true

[kindred warren]

yeah but im stuck on how to find the total possible combinations

[alpine sable]

same 😭

i suck at math

https://artofproblemsolving.com/wiki/index.php/2011_AMC_10A_Problems/Problem_22

i always get stuff wrong at casework so i rather not do it

can sb pls explain solution 3 ;-;

[edgy orbit]

hi

[alpine sable]

hi

;-; can sb pls help

;-;

ok ig u can take this channel ill move

[violet glacier]

anyone?

[slate patio]

solve for tan A using quaddratic formula, then use trig ratios?

[alpine sable]

Can you calculate definite integrals using only arithmetic?

[violet glacier]

pls

show

the steps

[crisp grove]

u can approximate it with numerical methods

[placid zinc]

Some, yes. See Guassian quadrature

[velvet perch]

when u add an edge, u add a pair of vertices right

thered be a connected component when neither of those vertices are contained in the subgraph i think

does it say G is connected

why would u construct A that way

whats the context

Oh

well even if A is connected, adding vertices that arent in A but are in G would create a connected component right

yeah

but if A is connected, that doesnt imply that G is connected right

you could add an edge that isnt connected to A

wdym

well udk if G \ A is connected either

[olive inlet]

Is this channel free?

[alpine sable]

help anyone?

[unkempt remnant]

Can someone help explain this question to me? I solved everything correctly besides the part about additional material wasted on support structure being 14% i’m not sure whether to add 14% of the weight or take it off. And if i add it, from where do i find the 14%?
X=0 Y=0 Z=4

[alpine sable]

ok

[charred flint]

you'll have to explain to me every part of that question

[unkempt remnant]

Which one of us? >.<

[charred flint]

@unkempt remnant add the weight

since it's extra cost

[olive inlet]

Sorry I didn't saw his question D:

[unkempt remnant]

Yeah so the weight i got of the finished product is 2.897kg, then i added 0.33kg to it from the CNC machning bit which adds up to 3.227kg. What’s left is the 14% additional material wasted, how do i find out what value do i get 14% off to add

[charred flint]

it's fine, I just don't know what m or Decoder are

idk what the CNC bit is because I can't see question 5, but the answer is just adding the normal cost plus 14% of the material cost extra

[unkempt remnant]

Oh so like if the final cost is $4500 i multiply it by 14% and then add 4500 to whatever that value is?

[charred flint]

yup that works

if that final cost is the material cost, idk the full situation

[unkempt remnant]

Final cost is for the raw material before any machining

[charred flint]

sounds good

[unkempt remnant]

But we don’t know what the weight of the raw is

[soft zodiac]

Can someone help me to solve: arcsin(sin(10pi/9))? It has to be an exact value and we can't use a calculator.

[wary stream]

Use the unit circle

[soft zodiac]

10pi/9 isn't on the unit circle though...

[wary stream]

Make it appear on the unit circle

[strong furnace]

use the definition of arcsin() and property of sin() i.e. sin(n*pi+(-1)^n*x)=sin(x)

[wary stream]

Oh, wait, it's divided by 9

[broken valve]

Guys what is 4+3

[wary stream]

No

Don't ask troll questions

[broken valve]

I'm serious

[strong furnace]

definition of arcsin() is inverse function of sin(x) for x in [-pi/2,pi/2] btw

[wary stream]

Then use a calculator

[broken valve]

Okay so what's the square root of 980

[wary stream]

Use a calculator

[strong furnace]

Baguette I hope you find something better in life I wish you nothing less

[broken valve]

Ok

[broken valve]

shit i'm not mentally okay

[soft zodiac]

What would n be in my case?

[strong furnace]

you're gonna have to decide that based on the restriction of domain of sin(x)
(restriction is [-pi/2,pi/2] so you would want your input to be something like arcsin(sin(a)) with a in [-pi/2,pi/2])

[mental peak]

Guys need help with my pre calc

Can someone hep me with this

everything.

lmfao

[soft zodiac]

i figured it out after a bit, thanks

[covert juniper]

Does there exist a 3x3 invertible matrix A such that $BA^T=A^{-1}C$ where B and C are are arbitrary 3x3 matrices?

[ocean seal]

ALBERTO BALSAM

[mental peak]

lmao

just giev me the damn answer my parents are not gonna pay for my tuition if i dont pass the test

4

[strong furnace]

is there context to this because ABA^T=C just gives you a matrix C for any matrix B of you choice

[mental peak]

common

no

its 3 in the damn morning

i have a test in 5 hours

i havent took notes and studied at all

frick my parents are gonna kill me

ffs

i told them i got a perfect score on my last pre calc longtest

the truth is i failed

i got 47%

ffs

[rigid wind]

lmao

[strong furnace]

I know you're trolling but if you lied about your results and actually feel guilty you can use that energy to redeem yourself, I have done it more than once

[mental peak]

yes exactly

i learned my lesson

not to get caught

[strong furnace]

your plan depends on others helping you out so I wouldn't say you learned your lesson even if it was academic dishonesty but sigh 😕 you are not going to get help here when you phrase it like that

[mental peak]

its my parents fault

i want to be a damn lawyer not an engineer

what a waste of tuition money man

[strong furnace]

if they are more blatant about cheating on a test even if it as a joke I would ping mods but I am 99% they are trolling cuz last time they asked a fractions problem and now they're on some basic calculus within 2 days

[mental peak]

oh

ig iam too dumb to be true

[mental peak]

XDDDA

sigh.. im just gonna drink hotdog juice after the test bye

.

iam not trolling wtf ...... i only troll on valorant

XDD\

iam kinda wasting my time when i waste ppls time

[sly mantle]

they left

[sly mantle]

i'd rather you let us know of your suspicions (can be by modmail if you prefer to keep it private) instead of sitting on em

[covert juniper]

I mean to ask given any two symmetric matrices, is there some choice of B such that it always holds?

[river remnant]

Is this question a typo?

How do you get cos(2x)=1? The triangle wouldn't exist, right? You would just end up with a straight line

[compact lynx]

@river remnant I'm lost on what you're asking

[river remnant]

the question is giving me cos(2x)=1

[compact lynx]

yeah, I'm lost on why you're asking about a triangle being a straight line

[river remnant]

but cos(any angle) shouldn't be 1, because the triangle wouldn't exist, right?

[compact lynx]

hmm

it won't be a traditional triangle

you've done the unit circle yes?

[river remnant]

yeah the answer would just be x=0 right

probably typo

[compact lynx]

x=0, x=pi, x=2pi

[river remnant]

when x=pi wouldn't it be -1 not 1

[compact lynx]

no, because it's cos(2x) not cos(x)

which means the period is 2pi/2

anyway yeah cos(x) = 1 means it's not a traditional triangle but cos can still equal 1

remember cos is just the measure of the ratio between the adjacent and hypotenuse

or x/r

and that occurs on the horizontal line portions of the unit circle

[river remnant]

yeah thanks

[ocean seal]

ALBERTO BALSAM

[remote silo]

x^2 divided by 7x^2

anyone?

[compact lynx]

how would you solve

5x

x

@remote silo

also yea sry i dont remember enough lin alg to help :(

[remote silo]

x is counted as 1 right?

nvm

[compact lynx]

yeah i mean, how would u simplify that

i'm also asking that as an example for him, not a question

@remote silo But yeah,

[compact lynx]

^

how would u simplify 5x/x

[remote silo]

5x^2?

[compact lynx]

hmmm

how would you solve say

10/2

[remote silo]

yes i know

[remote silo]

5

[compact lynx]

how about 5*2 / 2

you can either evaluate that as 10/2

OR you can cancel out the 2s on the numerator and denominator

and get the answer, 5 right

[remote silo]

yeah

[compact lynx]

so how about 5*x / x

[remote silo]

still 5x?

[compact lynx]

why x?

look at the 5*2 / 2 example we did above

just think of x as a number

because that's what it is

it's just some arbitrary number, it's not anything too complex or different

[remote silo]

so its 5?

[compact lynx]

yes, you just cancel the 5 term from the numerator and denominator

so how about x / 7x

[remote silo]

7

[compact lynx]

no

think about the placement of the division sign

[remote silo]

-7?

[compact lynx]

no

how would u simplify 14/21

[remote silo]

14/21 or 21/14?

[compact lynx]

what..

[kindred warren]

14/21

if you scale the numerator of a fraction, and scale the denominator by the same number, then the fraction has the same value

so what is the highest common factor is 14 and 21

[compact lynx]

i think you gotta really brush up on basic arithmetic skills before moving onto / continuing in algebra

[remote silo]

can you help on multiplying and dividing rational expression though?

[elder glacier]

@remote silo what is 2 /( 2 * 7)

[compact lynx]

especially if whatever you want to do in the future requires further mathematics you'll struggle a lot at this rate, it'd be in your best interest to go through various lessons from sites / youtube channels

[remote silo]

7?

[compact lynx]

@remote silo if you are unable to simplify 14/21 or 5*x / x giving you the answer to your question wouldn't help you at all

[elder glacier]

no man

just cancel the 2's

and your left with 2/2 on the numerator

which is 1

and (7*2)/2 on the denominator which is 7

so you get 1/7

i really can't see why my solution of y=4x/3 + 5/3 is incorrect, ive been stuck on it since last night, could someone share some wisdom

[north blade]

What is the chance of a 1.4% thing happen twice in a row

[elder glacier]

@north blade (1.4%)^2

[compact lynx]

(0.014)(0.014)

[north blade]

0.000196%?

[compact lynx]

no, this is the raw probability between 0 and 1

if u want it back into probability u need to multiply by 100

[north blade]

oh yeah

[compact lynx]

it's like how P(A) = 1 means there is a 100% chance of event A occurring

[elder glacier]

<@&286206848099549185> can someone explain why my answer is incorrect im so lost.

i even changed the syntax of the equation to 4x/3 + 5/3 since it was incorrectly written in my answer

[harsh belfry]

Was wondering if someone could help me figure out where I was a big stupid dumb idiot.

I first differentiated the function between f(x) and g(x)
and their primes, one using power rule the other using chain rule

then I utilized product rule to put it into this equation

(second writing out their derivatives)

[placid zinc]

No need to consider -2 as its own function

Constant multiple rule: Take the derivative as if the -2 isn't there, and throw it back on after

d/dx[-2f(x)] = -2f'(x)

[harsh belfry]

o

interesting

[placid zinc]

The product rule will work and get you the same thing

[harsh belfry]

yeah so my issue was actually that I didnt use chain rule on g(x)

instead I used power rule and completely forgot about the 1/2

so I ended up with an extremely similar answer

[elder glacier]

<@&286206848099549185>

[harsh belfry]

vs the real answer

[harsh belfry]

I see what I did wrong while explaining what I did, and thanks for the advice

I keep neglecting that constant multiple rule exists

thanks!

[ancient shale]

Could someone give me a hint? I know how to simplify this sums without the 5 * in front but not with it.

[placid zinc]

Simplify? Just get the sums

5[(1 + 3/5) + (1 + 6/5) + (1 + 9/5)] - [...

[ancient shale]

yeah sure i could but is it possible to simplify two sums when i have a factor in front`?

[harsh girder]

You can combine the two summations into one

[placid zinc]

It just means "compute the sum, then multiply it by 5"

Notice I gave that part explicitly

[ancient shale]

nah not with the 5 in front

[ancient shale]

then my thought was wrong, thank you

will try it now

it was correct

[harsh girder]

$5 \cdot \sum_{k=1}^{3}\left(1+\frac{3}{5} k\right)-\sum_{k=1}^{3}(4+4 k)=
\sum_{k=1}^{3}\left(5+3 k\right)-\sum_{k=1}^{3}(4+4 k)=
\sum_{k=1}^3 (1-k)=-3$

[ocean seal]

秋水

[elder glacier]

can someone explain why my first answer was incorrect, ps i changed the notation so now its 4x/3

[harsh girder]

maybe should be written as 4*x/3

[elder glacier]

yea i had changed it

to 4x/3

still incorrect

ive been stuck on all last night and all this morning

[harsh girder]

do you have *

[elder glacier]

yep

tried all notation

syntax*

[ancient shale]

wow so i can really just multiply the frontfactor with the sum?

[harsh girder]

yes, like k*(a1+a2+...)=ka1+ka2+...

[ancient shale]

thx man

[spare vale]

Can someone help when youre done

[ancient shale]

im done

[spare vale]

Okay let me send it

Q6

[harsh girder]

You just need to calculate the distance from the origin to the line

[spare vale]

So route 10

I dont know what that means

[harsh girder]

Or you combine the two equations and then the two real roots of the quadratic equation are equal

[spare vale]

Eh

[harsh girder]

$x^2 + (-3 x + 10)^2 = 10$

[ocean seal]

秋水

[spare vale]

What do i do from there

Expand?

Is that what im meant to do

But if i find x what do i do eith it

[harsh girder]

$(-3x+10)^2=9x^2-60x+100$

[ocean seal]

秋水

[harsh girder]

not 9x^2+100

[spare vale]

Huhhhh howd u get that

[prime fjord]

$(a+b)^2 = (a+b)(a+b) = a^2 + 2ab + b^2$

[ocean seal]

egg bird

[spare vale]

Okay now what

[prime fjord]

Find x, find y

Then since one point from the line touches the circle, it must be a tangent

[spare vale]

Is x 3 and y 1

[prime fjord]

Yes

[spare vale]

How do i say that shiws its a tangent

Shows*

[prime fjord]

Say that since the line and circle intercept at just one point, it must be a tangent

[spare vale]

Okay thankksss

[harsh belfry]

Found it!!!!!

[gentle ingot]

!!!

Great job

[harsh belfry]

Haha thanks

Careless mistakes are my downfall.

[gentle ingot]

Same though

[harsh belfry]

Hey asher...

Never mind

how is that not my answer?

[harsh belfry]

I thought I did this correctly

is there any chance I screwed up somewhere else I didnt notice?

[harsh girder]

yes, you are correct

[harsh belfry]

huh wow

but it got marked wrong

will email my professor

[harsh girder]

may be write as

$\frac{6 x}{\sqrt{6 x^2+1}}$

[ocean seal]

秋水