help-0

[hard ether]

oh

so would it be

9 x4?

[novel spruce]

almost, that double counts the corners

it would be 9 + 9 + 7 + 7 = 32 which is none of the above I think

since you count the top and bottom, then count the sides but don't doublecount the corners

[hard ether]

cool thanks

oh wait someone says its 40

[novel spruce]

¯_(ツ)_/¯

[maiden urchin]

now you're not counting the corners at all

[novel spruce]

oh well, it depends if the path is inside or outside the lawn

yeah i'm wrong

so I guess it would be 11 + 11 + 9 + 9 = 40 by the same reasoning, except the path is on the outside

[lone heart]

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[shy loom]

https://cdn.discordapp.com/attachments/565126024736538624/903820308132286474/unknown.png

[shy loom]

how do you simplify this

i have no idea

[hard ether]

maybe factorise it?

[shy loom]

wdym

ohhh

like

difference of two squares?

[hard ether]

uhhhhhh i meant that a^2 + 2ab + b^2 thingy

probably

idk

the names

[glass lichen]

simplify means nothing in this context

what are you defining as being simpler?

[shy loom]

my friend said to

find the domain

[glass lichen]

that's completely different to simplify.........

[shy loom]

idk

[glass lichen]

can you post the question verbatum then?

[shy loom]

ok hang on

[glass lichen]

The actual question should be posted from the getgo as well

[visual bolt]

Function is undefined so no solutions?

[glass lichen]

not true.

[shy loom]

"find the domain of the following functions"

[glass lichen]

Ok so what have you tried?

[shy loom]

uh i dont even know

how to start

[glass lichen]

well.... do you know what the domain of a function is..?

that'd be a good place to start, understanding the question

[shy loom]

uh like the range..?

like where it cuts off?

[glass lichen]

domain and range are different things

and "where it cuts off" is vague

[shy loom]

tbh i have no idea what the domain is but i know what it does

[alpine sable]

yes, domain is similar to range

[shy loom]

yep i've used it

in desmos art before

[glass lichen]

so google it.. or check your notes

[shy loom]

okay

thx for help

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[broken pine]

can someone help me on this problem? I don't know where to start nor do the problem!

[broken pine]

ping me if anyone's gonna help

[lone heart]

@broken pine Has your question been resolved?

[broken pine]

<@&286206848099549185> please help!

[alpine sable]

where can I ask questions?

[broken pine]

in math help

available

like

right above this

[alpine sable]

ty bro

[broken pine]

np

[alpine sable]

i guess you can start there

i havent really learnt this before sorry

[astral dagger]

main thing to note

the distance from any point of a triangle to its circumcenter is constant

https://www.cuemath.com/geometry/circumcenter/ this may help you

[bright swallow]

Help pls

Oh sorry

[charred flint]

@bright swallow use an available help channel above

[broken pine]

uh

anyone please

[broken pine]

ty

[lone heart]

@broken pine Has your question been resolved?

[broken pine]

<@&286206848099549185> pleaaaase hellllppppp

[broken pine]

.

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[jaunty onyx]

hi! would just like to ask help for this question on ideals of gaussian integers

[jaunty onyx]

my thoughts are i can do two things

which is correct? and if lcm, how do i get the lcm of two gaussian integers? tia!

<@&286206848099549185>

[lone heart]

@jaunty onyx Has your question been resolved?

[jaunty onyx]

<@&286206848099549185> please sorry

[lone heart]

@jaunty onyx Has your question been resolved?

[vale wigeon]

@jaunty onyx still here?

[jaunty onyx]

hi yes sorry

still no luck

my thoughts now are

the lcm and the product are associates

so it doesn't really matter which one i choose

is this the right way to think about this problem @vale wigeon ? thank you!

[vale wigeon]

the lcm and the product are not associates

this isn't even true in Z

just find the gcd with the Euclidean algo

then get the lcm by lcm(a,b) = ab/gcd(a,b)

at each step in the division process, do the division as in C, then round to the nearest Gaussian integer

[jaunty onyx]

alright thank you so much @vale wigeon !! :))

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[upper escarp]

how can i get the answer?
my final answer is pi/2 and 3pi/2

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[alpine sable]

i tried to solve this problem, however my answer isn't the same as the one in the textbook

textbook answer

answer i got

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[delicate crescent]

not sure how to do (a)

any help is appreciated

i see

thanks for helping

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[wispy olive]

Is the number of terms in an Arithmetic Sequence = ((First Term + Last Term)/Common Difference) + 1?

[alpine sable]

no it should be ((last term-first term)/common difference)+1

think about the equation un = u1 + (n-1)d

rearrange it for n

[wispy olive]

Shit that's what I meant.

I wrote that in the notebook and asked the wrong thing here 😂 .

Thanks.

[alpine sable]

haha

no worries

[wispy olive]

Just wanted to confirm.

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[wary zodiac]

How do u integrate 1/(x+1)^2

[devout summit]

You know how to perform substitution?

[wary zodiac]

Let u= (x+1)

?

[devout summit]

Yes

[wary zodiac]

Is that how u solve it

[devout summit]

Then rewrite it as u^{-2}

So that you can apply power rule

[wary zodiac]

So -(x+1)^-1?

[devout summit]

Yep!

[wary zodiac]

Thanks mate

[devout summit]

+C at the end

[wary zodiac]

Right. Thanks

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[foggy raven]

Hello, may I ask for help. how do I solve the equation for the area of this graph using integrals?

[foggy raven]

Is it safe to assume that both fuctions are sine waves rotated 90 degrees?

[devout summit]

Are exact specifications given?

[foggy raven]

No

[devout summit]

Then how could you even determine the exact area?

[foggy raven]

We don't need to determine the exact area, just find the equation for it

[vale wigeon]

it's the difference of two areas-under-graphs.

in the literal sense

[devout summit]

But you can’t assume this

[foggy raven]

hm... I'll keep exploring

[devout summit]

You can write an expression though\\$\int_c^d(f(y)-g(y)),dy$

[ocean seal]

Euclid31415

[foggy raven]

I see, thanks, I'll watch thishttps://www.youtube.com/watch?v=kgg5Rspf1Js for further explanation

I'll close this now

.close

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[mortal mantle]

im not sure how i should approach this question

[mortal mantle]

what i do understand is taht since we are finding the volume about the y axis, my interval would be [0,1]

but i get stumped from here, would i have to find the integral of y=1/4x^2?

i believe this comes into play but translating it to here is the problem for me

well i think im just supposed to find the integral of 1/4x^2

[mortal mantle]

but ive tried and i got it incorrect

i used an online calculator

but i can snip it

and that gives me 3.9875

which cant be right if you look at the graph

oh yeah i include pi

but taht would make it an even greater number lol

[obsidian crane]

It's the same shape if you rotate it about the y axis

[devout summit]

Third of all, we are rotating about y-axis and not the x-axis

[obsidian crane]

I'm guessing the area will be = integral between (0, 2)

[mortal mantle]

so when we rotate about the y axis, the bound would be like this ?

[obsidian crane]

shouldn't it be this ? (after rotating) I might be wrong

[mortal mantle]

i dont think so?

let me try this once more

[devout summit]

Rotating y=1/4 x^2 about y axis gives a paraboloid

[mortal mantle]

yeah so i would just have to find the integral of pi(1/4x^2)^2

over the bound [0,2]

[devout summit]

It isn’t right

[mortal mantle]

oh wait sqrt(4y)^2

[devout summit]

Yes

[mortal mantle]

oh let me try this

[obsidian crane]

Its important to note you have to rotate the bounded region and also the graph of this parabola is symmetrical about the y axis.

[devout summit]

So basically, it looks like a cylinder with a paraboloid dent on it

[mortal mantle]

i got this but im not sure if it is right

[devout summit]

It would be\\$\int_0^1\pi(2)^2,dy-\int_0^1\pi(\sqrt{4y})^2,dy$

[ocean seal]

Euclid31415

[mortal mantle]

let me try this out hold on

i got it!

but let me understand

so when it says we have to rotate about the y axis, we must make everythin in our equation in terms of y right ?

i think i may have forgotten to pi on the two before i came here ;/

but thank you for the help guys, appreciate it

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[alpine sable]

if i have a right triangle, will every median to the hypotenuse be equal the 2 parts that it created?

[rigid smelt]

yes, because the circumcentre of a right triangle is always at the midpoint of its hypotenuse

[dreamy needle]

Hello 👋, got a question about asymptotes, its been a while for me and I cant seem to work out how to find the vertical asymptote of (x^2+4x)/(x^2)
The Horizontal is 1 and the Vertical is the denominator set to 0 but it doesnt make sense as its just x^2

[alpine sable]

Please make sure to open a new channel instead of taking someone elses

But to answer your question quickly, you do just set it equal to 0 and so the vertical asymptote is x=0 because when you do x^2 = 0 and solve for x, you will get 0

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[gilded ridge]

im cofused on it all pls help there is many questions i need help with

[robust geode]

Say your questions then

[mighty sinew]

Just replace the values in the expression

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[robust geode]

🤔

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[balmy zinc]

hi i dont know how to do this, btw this is transformation of functions

[bold summit]

guys can you help me

what iis

-1038 ( 183 x 092) 99:02 =

[robust geode]

It's not a channel for you @bold summit

Look at the name

[bold summit]

ok sorry

[robust geode]

If you want information on how to get help, feel free to see #❓how-to-get-help

[next chasm]

Im not sure if im right but shouldnt it be something like 1 + 2/(x-2)

[robust geode]

Desmos is for sure a good tool for learning how things change by what you put

For example, you want y=1/x to be shifted to the right by 2 units

Well that means that for example, the forbidden value 0 wouldn't be at 0 anymore, but at ...

2 !

[next chasm]

Yea x cant be 2

Cuz well get 2/0 which gives an error

[robust geode]

That's why Davo wrote "x-2" at the bottom

Because 2-2=0 and that's a no no for your function

[next chasm]

And same goes for left

If you got x

You add +1 to it

For each unit you go left

Think of it this way, if x intercept is at 10 for example

In a graph

If you move it 1 unit to the right

So x-1

The intercept is at 11

Since you need x+1 instead of x to intercept

And before the changes it was at 10

Like here teachers used to explain it that way for students who didnt understand, if you dont get it its fine

But remember when it says left, +1 right, -1

And when it comes to stretching the graph

When it says vertically

It means to the y axis

So for example if before stretching when you have x=1 y=10, and you stretch it by a factor of 2, when x=1 y should be 20, and if you stretch it by a factor of 0.5 y should be 5

Up down basically +-

[lone heart]

@balmy zinc Has your question been resolved?

[next chasm]

So like if in graph 1/x you got x =1 y =1 right

In the deformed graph

We got 1+ 2/(x-2)

[robust geode]

@balmy zinc Are you still there ? lol

[next chasm]

So it should be equal to -1

[next chasm]

He prolly having a seizure after reading all my texts lmao

[robust geode]

Yeah that's what I'm thinking lol

[balmy zinc]

im a bit confused about vertically dilating and the difference with horizontal dilations on how you write it

[next chasm]

Horizontal means length wise

Vertical - height vise

So if it says horizontal dilitation

If at Y value you have X

Then after dilitation

At Y value you should have 2X

If you dilitate

By 2

[cunning prism]

im new

tf is limits of accuarcy

[next chasm]

And this not your channel

[cunning prism]

im confusion

[next chasm]

You are not confusion

You are confused

[cunning prism]

i have a quiz tmw

no

[next chasm]

We dont help with quizes

Check rules and stop writing in this channel

[cunning prism]

i just need help w limits of accuarcy

ok

[next chasm]

Not here

[cunning prism]

where then

[next chasm]

Open help channel

[cunning prism]

k ty

[balmy zinc]

thanks I understand it now

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[next chasm]

Np

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[frozen tree]

Hey this is a stupid question but

[frozen tree]

??

[quasi briar]

What

[frozen tree]

.close

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[slate kayak]

Hi, what is the greek symbol called in math that looks like a Q

[vale sapphire]

Ω ?

[slate kayak]

No another one

Kind of like an e mix with Q

[vale sapphire]

σ ?

[slate kayak]

No

[quasi briar]

Not your channel btw

[slate kayak]

Its open

It says the other person closed

[quasi briar]

Okay but it isn’t open yet

[vale sapphire]

well technically it's not actually inactivated yet

[slate kayak]

Ohh

Sorry

[vale sapphire]

it's fine just go to another one and i'll be back

[slate kayak]

Okay

[quasi briar]

It’s okay just make sure u read rules because a lot of people seem to not be

[obsidian crane]

φ ?

Just search up "greek symbols"

[echo kelp]

can someone solve this

very ez tbh

[obsidian crane]

-1 ?

[echo kelp]

yes

[quasi briar]

Not your channel

[echo kelp]

ohhh

didnt know

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[mighty sinew]

Let $X=C^0([-a,a])$ be the space of functions continuous on $[-a,a]$ and let $T:X\to \mathbb{R}$ be a linear operator s.t. $Tf=f(0)$. Assuming $X$ has the $L^1$ norm, namely $||f||1 = \int{-a}^a |f(x)|,dx$ show that $T$ is not bounded.

[ocean seal]

Aram

[mighty sinew]

I proved this for the sup norm, but the L1 norm beats me

[vale sapphire]

So you need to show that you can have an arbitrarily large value but still a finite integral, ie a finite area under the curve

i have a solution in mind, but i don't know how to hint at it

Okay, here's a hint : ||Use a triangle||

[mighty sinew]

hm

like a triangle that peaks at 0 and gets sharper and sharper?

[vale sapphire]

And here's a hint that's almost the whole solution : ||k*1/k = 1 yet k isn't bounded||

precisely

[mighty sinew]

I actually thought about that, like a sequence of continuous functions that peaks at x=0 but is 0 everywhere else, but I figured the limit isn't continuous, idk if that's a problem

[vale sapphire]

no

all you need to show is that Tf can get arbitrarily large

You're not trying to show Tf can be infinite

[mighty sinew]

hm I see

[vale sapphire]

peaks at x=0 but is 0 everywhere else
close, but the point of the triangle is to have continuity

[mighty sinew]

yeah sure

so a function like 1-n|x|, |x|<1/n and 0 elsewhere basically

ah makes sense i guess

thx

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[rough salmon]

if i hv N amount of odd nums n M amount of even nums

[rough salmon]

how to know

if the sum of all those nums

is an odd num

[small bear]

Look at the even numbers first, does it matter how many you have? What is the parity of that sum?

[rough salmon]

oh

so i just need to focus on the odd nums right?

ah

[small bear]

Yes, you notice that the even numbers always sum up to an even number

[rough salmon]

so odd amount of odd nums would give ya an odd sum ig

[rough salmon]

ya

thx

tiz server finally has the help channel functions lmao, i hv been for such a long time

ask in an unoccupied channel man

.close

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[south kayak]

Hello how can I know the exact 'definition' of a real life curve ? I need to describe the following chair so that anyone can replicate exactly as it is, and as it has quite a lot of curvy lines, I don't know how to describe them.

[static fern]

sorry buddy

[south kayak]

no problem jaja

[south kayak]

ask in an occupied channel 😂

[oak chasm]

Sorry, this channel is busy. Please ask in one of the channels directly under "Math Help (Available)".

[maiden crow]

ok i got it

Focus1: (0,3)
Focus2: (0,-3)

this is the ans

[lone heart]

@south kayak Has your question been resolved?

[polar barn]

well

chair

[south kayak]

eh? xd

[polar barn]

its a chair

not sure how i can describe that

OH

oh

you want to describe a real life curve? @south kayak

[lone heart]

@south kayak Has your question been resolved?

[lone heart]

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[lone heart]

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[thorn kindle]

[lone heart]

@thorn kindle Has your question been resolved?

[lone heart]

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[whole path]

The answer the book gave was 1:50000
What went wrong guys ?

[normal grail]

hello , i want to understand math (algebra ) and using it. i am really good at math but i want to go deeper outside school can you recommend me some books i will really appreciate it and if you know about books to learn about functions (graph)

[whole path]

Kindly go to an available section and ask your question there, thanks

[robust geode]

Refer to your proportionality rule and examples of it

It may help you

[lone heart]

@whole path Has your question been resolved?

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[lone heart]

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• Show your work, and if possible, explain where you are stuck.
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[slate kayak]

The plane V has a parametric description (1st one) & The line L has a parametric description (2nd one)

How do I prove that the line L is parallel to plane V?

[lone heart]

@slate kayak Has your question been resolved?

[devout summit]

Equate both the parametric descriptions and see if there is a solution

[slate kayak]

You mean I should put the line numbers on one side and then put a “=“ and the plane numbers on the other side?

[devout summit]

I assume they have given a,b,c linearly independent

[slate kayak]

Yeah i think so

[devout summit]

Yes

[slate kayak]

Okay will do

[devout summit]

We are basically looking for the position vector of the point of intersection by equating

And since a,b,c are linearly independent, we can equate the coefficients of each of those separately!

[slate kayak]

Ah

[devout summit]

I have to go do some work now sorry

[slate kayak]

Okay bye

[devout summit]

If we show intersection does not exist we have shown both are parallel

[slate kayak]

Thnx for the help

I sitll dont know how to do it

This exercise is different from the others the others dont work with base base they just give the R3 equation instantly

Idk what to do

Ok byeee

.close

[lone heart]

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[rapid nova]

Prove that $y^\frac{3}{5} \arcsin{\sqrt{\abs{x}}}$ is differentiable at $(0, 0)$

[ocean seal]

rept1d

[torpid delta]

$f(x,y)$ ?

[ocean seal]

TC159

[rapid nova]

yes

[torpid delta]

Ah, just to be sure

[rapid nova]

<@&286206848099549185>

[astral dagger]

show that (\underset{(x,~y)\rightarrow(0,~0)}{\lim}~f(x,~y)) exists

[ocean seal]

SubGui

[astral dagger]

since y and arcsin are continuous functions at (0, 0)

you may have no trouble in calculating it

[rapid nova]

yeah, i understand this is what i need to do
though i've trying to do that for a while, unable to succeed
how can I prove that this limit exists?

[astral dagger]

the side limits evaluate to the same value

and this value is the same as f(0, 0)

as f(x, y) is continuous

[rapid nova]

btw are you sure about the limit of $f(x, y)$ itself?
and not $\frac{f(x, y) - f(0, 0)}{\sqrt{x^2 + y^2}}$

[ocean seal]

rept1d

[rapid nova]

i'm not sure if the existence of lim f(x, y) is enough

[astral dagger]

if the function is continuous, then it may be differentiable

[rapid nova]

ah ok

i see

[astral dagger]

but I hope someone else can help you precisely

[rapid nova]

i'll take another look at it, thank you

no, i don't think i can prove it :(

[astral dagger]

you mean in differential equations?

well, boundary conditions are used to find the constant from the general solutions, but it is not its only use

they define how the functions behaves in the neighborhood of the point

[rapid nova]

is it somehow related to my question?

[golden falcon]

not really, it's just that lil.flack0o got bored waiting in his channel and tried to hijack this one

[rapid nova]

i'm not finished

<@&268886789983436800>

[dreamy cedar]

Please do not interrupt question channels. There are several others available right now

[sly mantle]

i think we should start cracking down a bit more on interrupting help channels

they’re in a section literally called occupied

[golden falcon]

while in general this question may be pretty hard, for most well-behaved functions it's enough to prove that all partial derivatives exist in some neighbourhood of the point and are continuous at this point.

One important point, btw. This theorem only proves sufficient conditions, and there are some differentiable functions that don't have continuous partial derivatives. Luckily, I don't think this is your case.

[rapid nova]

How do I do that then?

Prove that all partial derivatives exist in some neighborhood

[golden falcon]

1. Find all partial derivatives analytically. 2. Prove using your favourite definition of continuity that they are indeed continuous at (0, 0)

[rapid nova]

Am i allowed to find partial derivatives before I know they exist?

[golden falcon]

If you can find them, they exist.

You have a nice analytical function, not some horrific specifically-crafted monster, like Weierstrass's function, it should be alright

Although this absolute value does make it slightly harder

You can make your life simpler and just rewrite your function in two branches for x<0 and x>=0, for example

[rapid nova]

Is there a name for these sufficient conditions (a theorem or something) so that I can mention it in the proof?

[glass lichen]

proof of differntiability in multivar typically follows the following process iirc:
Find the partials
Compute the tangent plane
show that the tangent is a good approximation

[golden falcon]

Then find the derivatives for each branch and prove that they are continuous using limits, for example

[golden falcon]

I don't think there's an epic name for it

[rapid nova]

not an epic name but just something so that i can google more if i need

[golden falcon]

You can call it something like A sufficient condition for the differentiability of the function
in terms of partial derivatives

[rapid nova]

ok thank you

[golden falcon]

Or at least that's what it's called in almost every textbook I've seen

The main problem you will encounter is trying to prove that multivariable limits exist, but it shouldn't be too hard either.

[lone heart]

@rapid nova Has your question been resolved?

[rapid nova]

ok, so for example
[
\pdv{y} \qty(y^{3/5} \arcsin{\sqrt{\abs{x}}}) = \frac{3 y^{-2/5} \arcsin{\sqrt{\abs{x}}}}{5}
]
but according to WolframAlpha
[
\lim_{(x, y) \to (0, 0)} \frac{3 y^{-2/5} \arcsin{\sqrt{\abs{x}}}}{5}
]
does not exist

[ocean seal]

rept1d

[rapid nova]

i know WA can be wrong sometimes but i'm not sure

[golden falcon]

well, it looks right to me. Lemme look into it quickly

[golden falcon]

Are you sure that you need to prove that the function is differentiable and not to check if it's differentiable or not?

[rapid nova]

yes

[golden falcon]

Welp

too bad

[rapid nova]

i only need to prove it for (0, 0)

[golden falcon]

too bad

Although wolfram happily tells that there are some points where it is differentiable

It's just that this amazing domain doesn't contain (0, 0) unfortunately

[rapid nova]

can it be that WA is wrong?

[golden falcon]

Extremely unlikely

But everything is possible. Your best bet will probably be (dis)proving the differentiability using the general definition

[rapid nova]

so it's either wolfram is wrong or my teacher is a troll

or both

[golden falcon]

Which is something like this: 1. $$ f(x, y) - f(0, 0) = f'_x(0, 0)x + f'_y(0, 0)y + \alpha(x, y) \sqrt{x^2+y^2}$$ 2. Find $$\alpha(x, y)$$ analitically and show that $$\alpha(x, y) \sqrt{x^2+y^2} \neq o(\sqrt(x^2+y^2))$$ at $(x, y) \rightarrow (0, 0)$ or something like this

[ocean seal]

Dmytr

[golden falcon]

If your teacher is a troll, proving that the function is non-differentiable will be a sufficient counter

[rapid nova]

that helps

thank you

.close

[lone heart]

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

need some help on a standard deviation question

[alpine sable]

ima send a pic of the question

anyone?

?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

anyone

?

[torpid delta]

https://www.youtube.com/watch?v=IaTFpp-uzp0

try watching this

[alpine sable]

I did

but the question is confusing

[torpid delta]

alright

$\sum_{i=1}^{N}(x- \bar{x})^2$

[ocean seal]

TC159

[torpid delta]

$= \sum_{i=1}^{N} x_i^2 - 2\bar{x}\cdot\sum_{i=1}^{N}(x_i) - N* \bar{x}^2$

[dense tangle]

Could I have some help soon as you are done helping the other person?

[ocean seal]

TC159

[torpid delta]

yeah sure

@alpine sable

[alpine sable]

yes

[torpid delta]

.

do you understand why?

[alpine sable]

this is a little complicated

[torpid delta]

uhhh

[alpine sable]

all I know is the normal formula

[torpid delta]

this is an intermediate step

let u be the mean alright?

[alpine sable]

yup

[torpid delta]

$(x-u)^2 =x^2 -2xu + u^2$

[ocean seal]

TC159

[torpid delta]

for every x, right?

[alpine sable]

yup

[torpid delta]

therefore $\sum_{i=1}^{N}(x- u)^2$

[ocean seal]

TC159

[torpid delta]

$= \sum_{i=1}^{N} x_i^2 - 2u\cdot\sum_{i=1}^{N}(x_i) + N\cdot u^2$

because we sum the square of every x_i

because 2xu factors as 2u(x)

so the sum of 2ux_1 + 2ux_2 .... = 2u(sum of all)

[alpine sable]

yup

[torpid delta]

wait

there's a - supposed to be a +

[ocean seal]

TC159

[alpine sable]

oh ok

[torpid delta]

you have N which is the number of archers right?

[alpine sable]

sorry

[torpid delta]

lmao

[alpine sable]

it just randomly came up

[torpid delta]

N is 20. you calculated u and have the sum of the squares

you can substitute everything to get

$\sum_{i=1}^{N}(x- u)^2$

[ocean seal]

TC159

[torpid delta]

but if you have this

then you can easily calculate

[alpine sable]

yes..

[torpid delta]

$\sqrt{\frac{\sum_{i=1}^{N}(x- u)^2}{N}}$

[ocean seal]

TC159

[torpid delta]

et voila

standard deviation

[alpine sable]

oh

nice

can u help me apply all this in the question

[torpid delta]

yeah

[torpid delta]

sum of squares is the left side

which is 3452360

[alpine sable]

yes..

[torpid delta]

sum of their scores is 8280

mean is 414

so

[alpine sable]

yup

wait

how did u get 434

oh ok

[torpid delta]

I didn't zoom in, looked like a 3

3452360 - 2*434*8280 + 20* 434^2

[alpine sable]

but am I correct about the mean

[torpid delta]

yes, you are

8280/20 = 828 /2 = 414

[alpine sable]

oh ok

[torpid delta]

google says this is 32440

[alpine sable]

yup

[torpid delta]

so you calculate sqrt(32440/20)

40.2740611312

nearest whole number would be 40

[alpine sable]

wait

[torpid delta]

Am waiting

[alpine sable]

all I do is 32440 divided by 20

[torpid delta]

then take the square root

of that

[alpine sable]

lamme try

[torpid delta]

I already did

[alpine sable]

oh nevermind

[alpine sable]

so 40 is the answer

[torpid delta]

yes

[alpine sable]

what about the squares of their score

[torpid delta]

what?

I substituted them here

[alpine sable]

ohh ye

[torpid delta]

it's the $\sum_{i=1}^{N} x_i^2$

[ocean seal]

TC159

[alpine sable]

do u know how to do the second part

[torpid delta]

what second part

I've already done everything xD

Let's go over again, alright?

you want to calculate this

but to calculate this you need to calculate this

You know that $(x-u)^2 = x^2 - 2xu + u^2$

[ocean seal]

TC159

[alpine sable]

one archers score is incorrectly

u know the pic I put up

[torpid delta]

you do that after

putting the first value

that's the second exercise

[alpine sable]

ye but how I lost myself trying to

[torpid delta]

xd

I'm the hyperactive guy here not you xdd

anyway

[alpine sable]

so do I take away that value from the 8280

[torpid delta]

anyway you know

so you substitute to get

[alpine sable]

yup

[torpid delta]

$\sum_{i=1}^{N}\left[ x_i^2 - 2x_iu + u^2\right]$

I can distribute the sum to have

[ocean seal]

TC159

[torpid delta]

$\sum_{i=1}^{N} x_i^2 - 2u \cdot \sum_{i= 1}^{N} x_i + \sum_{i=1}^{N} u^2$

[ocean seal]

TC159

[torpid delta]

first sum is the sum of the squares

second sum is the sum of all scores

third is a constant sum so it is equal to the itself times the number of times it repeats, in this case N

therefore giving you

$\text{Sum}{\text{squares}} - 2u \cdot \text{Sum}{\text{Scores}} + N \cdot u^2$

[ocean seal]

TC159

[torpid delta]

You know all of these values so you can just substitute

[alpine sable]

after all this it says: "One archers score is incorrectly recorded as 349. They actually scored 369"

[torpid delta]

alright, but first do this exercise ok?

that's the next one

or have you done this one?

[alpine sable]

alright

I havent

it's the point I lost out everything

[torpid delta]

anyway substitute to get $\sum_{i=1}^{N}(x_i- u)^2$

[ocean seal]

TC159

[torpid delta]

and then substitute in the formula to get the standard deviation

[torpid delta]

wdym?

[alpine sable]

then how do I calculate the new mean

[torpid delta]

oh that's easy

[alpine sable]

yup

[alpine sable]

yes...

[torpid delta]

what this is saying is that basically the archer scored 20 more points

so the total number of points is the original + 20

that is 8300

8300/20 to get the mean

[alpine sable]

415

[torpid delta]

so the mean is 415 and the sum of scores is 8300. HOWEVER

you do not know the sum of the squares

[alpine sable]

correct

[torpid delta]

How do you calculate the new sum of the squares? simple, since he had 349
you simply add (349 + 20)^2 - 349^2

which is 40*349 + 400

[alpine sable]

14360

[torpid delta]

3452360 [old number] + 14360 [difference] = [new number]

[alpine sable]

3466720

[torpid delta]

okay so now you have

the mean, the sum of squares, the sum of the scores, and the number of archers

considering u is the mean and N is the number of archers, are you missing anything in this formula?

[alpine sable]

so we do square of the new number divided by the n of archers?

[torpid delta]

what?

[alpine sable]

I meant square root

[torpid delta]

No, first we substitute here...

[alpine sable]

oh

[torpid delta]

do you not remember?

[alpine sable]

I got confused

[torpid delta]

we have this

[alpine sable]

let me try

to get the new answer

[torpid delta]

and since we can't calculate this directly, we tried to change this part:

and got this:

[alpine sable]

u is?

[torpid delta]

dude

do you have 1 second memory?

[alpine sable]

oh ok

[torpid delta]

Anyway, are we missing anything?

No, so lets substitute

3466720 - 2*415*8300 + 20* 415^2

which is 1374377720

so now we have:

$\sqrt{\frac{1374377720}{20}}$

[alpine sable]

how did u do it so quick

I'm still typing

nvm

[torpid delta]

I copypasted into google

[alpine sable]

oh

I'm using a calc lol

[torpid delta]

yo wtf I made a mistake somewhere

[alpine sable]

wdym

[torpid delta]

substituting we have**

3466720 - 2*415*8300 + 20* 415^2

which is 22220

[alpine sable]

k

[torpid delta]

$\sqrt{\frac{22220}{20}} =33.331666625$

[ocean seal]

TC159

[torpid delta]

rounding to nearest whole is 33

[alpine sable]

alright

lamme mark it

shall I mark it

[torpid delta]

If you feel confident I got everything right.

I can tell you for a fact that the mean is correct

[alpine sable]

alright

damn ur a geniua

genius

but

the first standard deviation is 35

still ur intelligent af

[keen wasp]

why is this muyltiplication allowed

this is some context

pls ping me if u figure it out

[wary stream]

#❓how-to-get-help

Don't ask in an occupied channel

[alpine sable]

ima close the room so u can have it

[keen wasp]

oh wait

[alpine sable]

no worries we r done

[keen wasp]

oh sorry i didnt reralize u guys changed these

[alpine sable]

dont worry lol

[keen wasp]

sorry

[alpine sable]

let me close this

u have to post ur attachments again tho

.close

[lone heart]

Channel closed

Closed by @waxen axle

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[harsh belfry]

Needed some help with this question

[harsh belfry]

I've been stuck on this for awhile.

I know that the car 70 feet away (y)

and the distance the light travels is the variable I'm searching for

[wary stream]

Do you know the speed of light?

[harsh belfry]

I do

[torpid delta]

isn't this a physics question?

[harsh belfry]

Calculus

[torpid delta]

huh

that's cool / weird

[harsh belfry]

Its very similar to some physics questions ive seen though.

[wary stream]

Do you have the full question?

[torpid delta]

c

[wary stream]

Never mind

[torpid delta]

oh wait

[harsh belfry]

I made it a bit bigger

[torpid delta]

[harsh belfry]

I'm guessing I would use sine here right?

O/H

70/x

[torpid delta]

i am horrible at interpreting questions

[harsh belfry]

sin(70/x)

[torpid delta]

what does it mean for the light to move across the wall

[wary stream]

Derivative

[harsh belfry]

So tc159 it doesnt mean the speed of the light itself it means the speed at which the police light rotates

ie the wall

[torpid delta]

are you calculating the limit of the variation of the position right part of the light beam in respect to delta t or the left

[harsh belfry]

Should I find the derivative of sin(70/x)

[harsh belfry]

Not sure how to answer that question.

[torpid delta]

Are we calculating the speed that the right part of the beam or the left..

that's my main question

[wary stream]

The x is the distance

[torpid delta]

so the left?

[wary stream]

Yes

[torpid delta]

number of feet are usually constant (2)

[harsh belfry]

I'm not sure where to start here.

[torpid delta]

y = tan(theta) * x

[harsh belfry]

Should I find the derivative of that

[torpid delta]

v_theta = 28rev/m

1 rev = 2pi

v_theta = 56pi/m

v_theta = dtheta/dt

@wary stream how do you suggest solving this, partial x, partial theta?

[harsh belfry]

https://tenor.com/view/confused-the-office-michael-scott-steve-carell-explain-this-to-me-like-im-five-gif-4527435

I'm very confused.

[raw shard]

why would it be partial derivatives

[torpid delta]

that's my first guess

oh wait y is fixed...

nevermind

I'm pretty stupid

[wary stream]

You keep trying to overcomplicate things

[raw shard]

you realize this is probably a calculus 1 problem right

[torpid delta]

I have no idea, at what level of education people are

anwayy

[harsh belfry]

I am in calculus 1

I have no clue what a partial derivative is

[raw shard]

post the question again and i can attempt to help

[raw shard]

i suck at these problems though

[harsh belfry]

@30 deg f/sec @raw shard

[torpid delta]

(what is calculus 1 by the way, I never used that naming )

[raw shard]

there are different calculus classes, it’s 1, 2, then 3, partial derivatives are 3

[wary stream]

Differential calculus

[torpid delta]

so calc 1 is like limits, derivatives early calculus?

[raw shard]

basic integrals too

but back to the problem

[torpid delta]

I see

[raw shard]

yeah i can’t help with this, i’m terrible at setting these up sorry

[harsh belfry]

No problem

[torpid delta]

The way I'd solve it is probably too complicated sorry...

[harsh belfry]

ah.. I guess I'm just screwed then

https://tenor.com/view/hide-the-pain-harold-gif-10576512

[raw shard]

these kinds of problems are called related rates if you wanna look into them

[harsh belfry]

Will watch some youtube videos on it in the mean time. Do you think I should be able to ping helpers?

[torpid delta]

I would probably solve it like this $\theta(t) = 8* 2pi/60*t, x(t) = 70 \frac{\cos(\theta)}{\sin(\theta)}$

[raw shard]

yes

[torpid delta]

oh wait

you have a purely time dependent formula for theta

[raw shard]

you can definitely ping helpers

[torpid delta]

so you can get a purely time dependent formula for x

[raw shard]

just post the problem again if you do

[torpid delta]

@harsh belfry
$\tan(\theta) = \frac{x}{y} = \frac{x}{70}$

[ocean seal]

TC159

[torpid delta]

yes?

[harsh belfry]

uhh

[torpid delta]

$x = 70 \cdot \tan(\theta)$

[ocean seal]

TC159

[harsh belfry]

70*tan(30 degrees)

right?

I could try it

[torpid delta]

yeye but there are several

angles

now notice this

[harsh belfry]

mind telling me how you got there?

[torpid delta]

this triangle

tan = O/A = x/y

[harsh belfry]

Yes

x/y

[torpid delta]

anyway

it's doing 28 revolutions per minute

correct?

[harsh belfry]

38

[torpid delta]

have you learnt radians, by the way?

[harsh belfry]

I have not

I briefly saw them in class is all

[torpid delta]

what the fuck, this involves the derivatives of trig functions

how could you not have learnt radians xddd

[harsh belfry]

I mean I personally am not at all experienced with them

[torpid delta]

anyway basically a revolution is a single turn which corresponds to the perimeter of a circle of radius 1, aka 2pi

[harsh belfry]

I just know they have to do with angles

[torpid delta]

basically radians are a unitless way to describe angles

If an angle has x radians, then the angle of the arc of radius 1 and length x is x radians

basically radians relate to the arclength of a circle of radius 1

anyway

since it spins at 38 rpm

it does 38 revolutions, aka 38 * 2pi

per minute

38*2pi/60 per second

$\theta = \frac{76\cdot \pi}{60}t$

[ocean seal]

TC159

[harsh belfry]

38*2pi got it

[torpid delta]

anyway

substitute in the equation for x to get

$x = 70 \cdot \tan(\frac{76\cdot \pi}{60}t)$

[ocean seal]

TC159

[torpid delta]

derivative on both sides

[harsh belfry]

product rule right

well 70's deriv is 0

[torpid delta]

$v_x = \frac{70 \cdot 76 \cdot pi}{60} \cdot \sec^2 \left(\frac{76\cdot \pi}{60}t\right)$

[ocean seal]

TC159

[torpid delta]

now all we gotta do is get the corresponding time for the corresponding time

which isn't hard since that is exactly theta we have that inside secant squared

$v_x = \frac{70 \cdot 76 \cdot \pi}{60} \cdot \sec^2 \left(\theta \right)$

[ocean seal]

TC159

[harsh belfry]

right?

[harsh belfry]

I need to re-read this a couple of times give me a moment

[torpid delta]

I might've messed upif you have an r

[harsh belfry]

oops sorry it was a typo

[coral pagoda]

Based on previous discussions, they struggled a bit in trig. So they learned, but probably forgot about it.

[torpid delta]

I see

[alpine sable]

TC r u currently busy

[torpid delta]

y

[alpine sable]

ok nvm

[torpid delta]

why?

Go to an open help channel

this one is taken

[alpine sable]

ok

[harsh belfry]

Currently watching a video on related rates to hopefully get better at this.

If you wonder why I've gone radio silent

Will be closing.

.close

[lone heart]

Channel closed

Closed by @harsh belfry

Use .reopen if this was a mistake.

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[alpine sable]

hi

[wary stream]

What's your question?

[alpine sable]

how do i do it'

[wary stream]

Do what exactly?

[alpine sable]

everything.

[wary stream]

There's no question

What are you trying to do?

[alpine sable]

I think u prove it

differentiate

[wary stream]

That's more helpful then saying " how to do it "

[cunning obsidian]

With respect to x or y?

[wary stream]

Probably y

[alpine sable]

idk it just says differientiate

[cunning obsidian]

Probably gonna find dy/dx xd

[wary stream]

Implicit differentiation

[alpine sable]

lol fm

put the full question up if u can

[cunning obsidian]

Start by differentiating both sides

[alpine sable]

is this better? tf

[cunning obsidian]

It is

[alpine sable]

What do I do

[cunning obsidian]

Left side is correct but you also have to differentiate right side, which can get annoying expanded

I suggest using chain rule

[wary stream]

You didn't differentiate the right side

[alpine sable]

bc idk how

so lmk how i do it

[wary stream]

Product rule

And chain rule

[alpine sable]

so i do product rule 2 times?

[wary stream]

Yes

[alpine sable]

for the right side

oh

[cunning obsidian]

Product rule works too

[alpine sable]

ok

[cunning obsidian]

It’s just less ideal

[glass lichen]

implicit on sin(x+y) is going to be much easier and more efficient btw

[cunning obsidian]

^

[wary stream]

That too

[cunning obsidian]

$\frac{d(\sin (x+y))}{dx}=\frac{d(\sin (x+y))}{d(x+y)}\cdot \frac{d(x+y)}{dx}$

[ocean seal]

3_n

[alpine sable]

Is this right

[cunning obsidian]

Not quite.. you missed the dy/dx’s

[alpine sable]

Where do I put them

[glass lichen]

anywhere you differentiated y

[alpine sable]

So wherever I see y

[glass lichen]

no

$\dv{x}\cos(y)=-\sin(y)\dv{y}{x}$ for example

[ocean seal]

Mosh

[glass lichen]

⛓️ 📏

[cunning obsidian]

XD

[alpine sable]

Idk what that is supposed to mean

[glass lichen]

chain rule

[alpine sable]

where tf do I use chain rule

And I was talking ab the example

[glass lichen]

...

if you have cos(y) you have cos(y(x))