help-36

[buoyant holly]

i think vortex has this

sorry T^T

uhhh vortex why was my proposition incorrect

[kind pelican]

nvm its right

[buoyant holly]

oh sweet

[kind pelican]

just that there's a discrepancy between undefined and 0 derivative

but it doesnt mean you're wrong

[buoyant holly]

und is undefined for all of them?

[kind pelican]

yeah which is interesting

[buoyant holly]

ngl i thought it was a german diagram

[kind pelican]

g(t) has a hole

acutally then maybe u are wrong

in general your reasoning is right but if g(t) is undefined at -5 and 5 there can't be a maximum

[buoyant holly]

so are the zeroes the only maximum and minimum?

i dont think i can input DNA in these boxes

thats my only concern

[kind pelican]

it's not a relative minimum or maximum at 0

because the graph decreases, then levels out, then keeps decreasing

[buoyant holly]

i see

so what do i put :<

[kind pelican]

if that makes sense lmfao

[buoyant holly]

yeah

what do i put for maximum and minimum T^T

[kind pelican]

i guess i would just say -5 and 5

[buoyant holly]

fair fair

[kind pelican]

but it isnt really defined

[buoyant holly]

isee

[kind pelican]

so i take issue with the question but

[buoyant holly]

so what is an inflection point

[buoyant holly]

i was like 2 seconds from calling my dean before joining this server

[kind pelican]

lemme repaste the question

[buoyant holly]

thank you

so question g

inflection points

[kind pelican]

mhm

[buoyant holly]

i am still quite confused on what they are

i had a question to identify them and i got it right

its like between maxima and minima

[kind pelican]

concave up --> concave down or vice versa

[buoyant holly]

is that on first deri

[kind pelican]

aka where the second derivative changes sign

[buoyant holly]

i see

[kind pelican]

oh

the graph i pasted is just the graph of any function g(t)

not the first derivative

[buoyant holly]

so its g(t)?

[kind pelican]

yes

[buoyant holly]

so zero

[kind pelican]

an inflection point is when g(t) switches concavity

[buoyant holly]

is the only answr?

[kind pelican]

in ur problem its 0 yes

[buoyant holly]

it says inflection points

worries me

it says my notation is invalid

i think it wants (,)

[kind pelican]

also -5 and 5

altho they aint really defined points

[buoyant holly]

but its neg to neg around -5 and pos to pos at 5

[kind pelican]

wait pause

[buoyant holly]

that is not a change in concavity is it?

:3

[kind pelican]

i mean in response to this question it doesnt matter the sign of g(t)

this whole graph could all be below the y axis

it would still be an inflection point

[buoyant holly]

how would i write that in (,) format :/

[kind pelican]

if you're finding inflection POINTS you cant write it in interval notation

[buoyant holly]

hahaha

says it is invalid

it accepts interval notation tho

[tulip sky]

The inflection point marks the transition from concave up to concave down

Explanation

Identify the inflection point on the curve

The inflection point is where the curve changes concavity

Determine the concavity of the curve before and after the inflection point

Before the inflection point, the curve is concave up

After the inflection point, the curve is concave down

Describe the behavior of the curve at the inflection point

At the inflection point, the curve changes from concave up to concave down. The second derivative of the function is zero or undefined at this point

[kind pelican]

what makes this tricky is that an undefined second derivative doesn't imply a inflection point does it

[tulip sky]

True

[buoyant holly]

sigh

[kind pelican]

so im gonna operate under the assumption that g'(t) is continuous

[buoyant holly]

i has arrows i think

[kind pelican]

and that we don't have a cusp/corner/sharp point/whatever its called in g(t)

[tulip sky]

Thats just my way of remembering how to work it out.

[buoyant holly]

am i supposed to input ordered pairs or smth

like know the y value

sounds impossible

[kind pelican]

it's impossible to know the y value

[buoyant holly]

hahaha

[kind pelican]

are you sure there isnt another part of the problem

[buoyant holly]

it is a 1 part problem and i sent the whole thing

like the questions around it are unrelated

[kind pelican]

ok

ok we know that g(t) has a point on it (0,0)

we know that from 0 to positive infinity it MUST be above the x axis

because it's always positive

and from -oo to 0 its below

that's all u have to do lmao

[buoyant holly]

for the last 2

[kind pelican]

yes

all ur doing is considering the sign of g

[kind pelican]

looks right to me

[buoyant holly]

should i just leave G empty and message my professor

[kind pelican]

you could try (0,0)

actually i think that's it

[buoyant holly]

i shall

ok so

its a little

interesting

[kind pelican]

-5 and 5 shouldnt be inflection points because its undefined there

imo

[kind pelican]

im tripping balls

[buoyant holly]

;/

wut

[kind pelican]

this doesnt make sense

[buoyant holly]

hahahaha

[kind pelican]

how does g(t) go from negative to positive

with a negative derivative

[buoyant holly]

hahahaha

i dont know my friend

[kind pelican]

one sec sorry let me get a pen

[tulip sky]

Analyze the sign chart for g(t)

g(t) is negative from (-∞, -5), positive from (-5, 0), negative from (0, 5), and positive from (5, ∞)

Analyze the sign chart for g'(t)

g'(t) is positive from (-∞, -5), negative from (-5, 0), negative from (0, 5), and positive from (5, ∞)

Identify critical points

Critical points occur where g'(t) changes sign or is undefined. Based on the diagram, critical points are at t = -5 and t = 5

Determine the nature of critical points

At t = -5, g'(t) changes from positive to negative, indicating a local maximum

At t = 5, g'(t) changes from negative to positive, indicating a local minimum

[kind pelican]

that's what we said but its wrong

[tulip sky]

Oh

[kind pelican]

also g(t) is undefined at those points

so can you really call it a maximum/minimum if they're not defined?

[tulip sky]

Thats odd

Im stuck now

[kind pelican]

i may be tripping

but these signs cant be right either

[tulip sky]

I cant see any other way

[kind pelican]

from -5 to 5

[tulip sky]

Hang on

[kind pelican]

an increasing function with negative derivatives

[tulip sky]

I have no clue any more

[buoyant holly]

so uhhhh

should i jus move on to another question

[kind pelican]

im 90% sure the problem is wrong

so yes

[buoyant holly]

sigh

[kind pelican]

you have all the logic

[kind pelican]

ill think about it more but the number line makes no sense

[buoyant holly]

we did something like this one in a different section

[tulip sky]

Lemme grab a pen

[buoyant holly]

but not quite like it

[kind pelican]

not as in i dont understand but as in it isnt fking possible

excuse the language

[buoyant holly]

yeah

thats what i gathered

[kind pelican]

this on the other hand is possible

ur tryna find the volume for a cone

[buoyant holly]

he doesnt give equation of volume for a cone tho

usually he does

[kind pelican]

ur supposed to know it

ig

[buoyant holly]

bruhhhhhhhhhhhh

do you know it...

[kind pelican]

ye

[buoyant holly]

mm how does one find the height

oh i can just solve

[kind pelican]

wait this problem is also impossible

[buoyant holly]

oh no

[kind pelican]

who is this professor istg

[buoyant holly]

he is a little cooked

[kind pelican]

do you know how big the sector is

[buoyant holly]

i pasted the whole question

aka no

why cant i just solve for h

[kind pelican]

you dont know r

[buoyant holly]

12

[kind pelican]

it's not the radius of the circle

its the radius of the base after you fold it up

which requires knowing how big the part you cut out is

[tulip sky]

My teacher sets wild hw

[buoyant holly]

can i just treat it like the radius of the circle

[kind pelican]

think visually about cutting that circle out, then joining the edges. the radius isn't 12

[buoyant holly]

hahahaha

[kind pelican]

your circumference is smaller

because you've cut out part of it

angle BCA looks like 60 degrees so we can work assuming its 60 degrees if you want

[buoyant holly]

oh boy

i dunno

[tulip sky]

My maths proffeser for my math lesson on monday just set more 💀

[kind pelican]

can i give u an answer to put in

[buoyant holly]

should i move on again

[kind pelican]

then if its right ill explain

[buoyant holly]

fair enough

[tulip sky]

Gimme a min

[kind pelican]

pretty sure the answer is $\frac{8\sqrt{35}}3\pi$

[soft zealot]

Vѳrtєx-

[kind pelican]

if we assume it's 60 degrees

[buoyant holly]

i will attempt

[kind pelican]

if u wanna enter that

[buoyant holly]

ur good if i input it as decimals

[kind pelican]

does the answer allow decimals idk

are u saying the answer's correct?

[buoyant holly]

usually allows decimals and not fractions

[kind pelican]

oh

[buoyant holly]

i havent tried yet

is wrong

[kind pelican]

oh

nvm this is a calc question

ok do you understand how you fold that sector to get a cone?

[buoyant holly]

no

[kind pelican]

hmmm lemme get a diagram

does that make sense

[buoyant holly]

yes

kinda

[kind pelican]

ur folding a piece of paper

so that the arc length is joined to make the circle at the base

[buoyant holly]

so l is 12

[kind pelican]

the slope length is 12 yes

and the radius depends on the sector you cut out

[buoyant holly]

how do i find r with l

[kind pelican]

the arc length BA gives you the circumference of the cone after folding

[buoyant holly]

so 60 deg

[kind pelican]

not quite

[buoyant holly]

m

[kind pelican]

let's say BCA is x degrees

what's the arclength of BA

[buoyant holly]

what is an arclength...

[kind pelican]

what's the length/circumference of the cut out circle

excluding the part that's cut out

[buoyant holly]

also x

right

[kind pelican]

no

[buoyant holly]

according to ur diagr-

oh

[kind pelican]

$\frac{360-x}{360}\times2\pi12$

[buoyant holly]

T^T

[kind pelican]

x/360 is the proportion that's cut out

[buoyant holly]

i see

[soft zealot]

Vѳrtєx-

[kind pelican]

(360-x)/360 multiplied by the original circumference

[buoyant holly]

x is 12?

original circumference

[kind pelican]

we set x as the angle of the sector that's cut out

x is an arbitrary number we're later gonna take the derivative of

[buoyant holly]

(i am like deflating)

[kind pelican]

because we're tryna see what the maximum volume is

[buoyant holly]

my brain is not ready for these words

[kind pelican]

ok i dont think we can solve this problem rn

but i can give a general overview of how

[buoyant holly]

wha

why not

[kind pelican]

o if ur downto do it i can

[buoyant holly]

yes

i gotta do this asap

[kind pelican]

i might also not have time

but we'll see

basically what he's asking you is that given an arbitrary amount that's cut out, how do we maximize the volume given by this cone

the volume varies based on how much you cut out

[buoyant holly]

what do i plug into the equation u gave mne

[kind pelican]

u dont plug in anything

[buoyant holly]

wha

[kind pelican]

we're trying to find a general expression for the volume for an arbitrary angle x

[buoyant holly]

you had sent that before

[kind pelican]

and then we're going to take the derivative of that equation to find the maximum

[buoyant holly]

making equations are not my strongsuit fr

[kind pelican]

yea id prolly ask your prof about this problem

[buoyant holly]

do u know the equation

[kind pelican]

i mean ik how to find it

i have not found it yet

[buoyant holly]

hes gonna give me a zero on the homework:<

i see

holy

wha

[kind pelican]

one sec

given angle $x$ the arc length of $BA$ is $\frac{360-x}{360}\cdot2\pi12$

as a result that is equal to the circumference of our cone, so then to find radius r we do $\frac{c}{2\pi}=r$ to get $r=\frac{\frac{360-x}{360}\cdot2\pi12}{2\pi}$ which simplifies to $\frac{360-x}{30}.$

Then we have the height $h=\sqrt{12^2-r^2}=\sqrt{12^2-(\frac{360-x}{30})^2}$

Our final formula for volume is $V=\pi r^2\frac{h}3=\pi\cdot(\frac{360-x}{30})^2\cdot\frac{\sqrt{12^2-(\frac{360-x}{30})^2}}{3}$

[soft zealot]

Vѳrtєx-

[kind pelican]

lowkey might not be right

but then you maximize V

[buoyant holly]

oh boy

should i skip this one too

next one should be actually easy

[kind pelican]

looks like the maximum is 696.49896

[buoyant holly]

i can try it

[kind pelican]

sure

[buoyant holly]

WHAAAAAAAAAAAAAAAAAAAAAAT

[kind pelican]

actually one sec

[buoyant holly]

IT WAS RIGHt

[kind pelican]

oh cool!

[buoyant holly]

you are actually a legend

[kind pelican]

lmfao

did not expect that

[buoyant holly]

my teacher didnt even come close to explaining how to do that

[kind pelican]

is this college

or HS

[buoyant holly]

yes

[kind pelican]

o

[buoyant holly]

college

i am a sophomore

[kind pelican]

oh fun

[buoyant holly]

so we did something similar to this

with seats and ticket prices at a ball game

[kind pelican]

interesting

so $98+x means 500-x rooms taken

[buoyant holly]

yes

[kind pelican]

so your revenue is (98+x)(500-x) dollars a day

your net losses are 22(500-x) dollars a day

so maximize the equation (98+x)(500-x)-22(500-x)

[buoyant holly]

what is "maximizing" an equation

[kind pelican]

fidn the maximum value

[buoyant holly]

cant just solve for x

[kind pelican]

usually involves taking the derivative and finding where it equals zero

[kind pelican]

that expression isnt equal to anything

[buoyant holly]

oh

[kind pelican]

when u maximize lmk i think i have the answer

[buoyant holly]

212?

[kind pelican]

yessir

[buoyant holly]

is that the answer..

[kind pelican]

no

[buoyant holly]

hahaha

[kind pelican]

look at what the question is asking

[buoyant holly]

what they should charge per day

[kind pelican]

yea

[buoyant holly]

to max profit

[kind pelican]

mhm

so what should they charge per day

[buoyant holly]

is 212 the most money you can charge

[kind pelican]

uhhh i would reread the problem again

our value for x is not the price per day

[buoyant holly]

its the daily room rate

[kind pelican]

no its not

[buoyant holly]

wha

[kind pelican]

read the problem

carefully

[buoyant holly]

sigh

increase of x follars in the dailt room rate

also vacant rooms

[kind pelican]

ye

so whats the answer

[buoyant holly]

whats the difference

[kind pelican]

?

[buoyant holly]

there is no set room rate

i thouhgt

[kind pelican]

we've found that x=212 maximizes the profit

so what's the room rate if x=212

[buoyant holly]

-22?

[kind pelican]

dawg the room rate is 98+x

[buoyant holly]

ohhhhh

[kind pelican]

howd you get -22

[buoyant holly]

ahhahahaha

hoiw did i miss that

im sorry

[kind pelican]

idk

[buoyant holly]

ok so

98+212

310

right?

[kind pelican]

try it

[buoyant holly]

yay

how much time u still have

i technically have 2 question left

[kind pelican]

uhhhh

im prolly headed out soon so not a lot

[buoyant holly]

awwww

[kind pelican]

find the second derivative

[buoyant holly]

ohhhh

i had graphed it and just yoloed

this is

problematic

[kind pelican]

should be between 6 and 12

[buoyant holly]

what should be

oh concave up

sry

[kind pelican]

concave down...

negative second derivative is concave down

[buoyant holly]

whatr

oh the red one is

my b

so -oo,6)U(2,oo) are concave up?

because second der is positive

[kind pelican]

try it ig

i cant give you everything 😭

[kind pelican]

also idk how you got 2

[buoyant holly]

my b my b

12

i meant

what do i do for minima

itwas correct

[kind pelican]

there isnt one

[buoyant holly]

but i gotta put something there...

[kind pelican]

idk how the relative maxima is 9 either that seems wrong

[kind pelican]

oh t=9

i see

a relative minima doesnt exist idk what to tell you

n/a

none

[buoyant holly]

none of those are allowed options...

[kind pelican]

welp then idk

sorry

[buoyant holly]

u have time for 1 more?...

[kind pelican]

send

probably not but

[kind pelican]

alr i feel like the first problem we did prepares u for this

i dont have time sorry

[buoyant holly]

thats fine

thank you so much

[kind pelican]

yeah np

[final saddle]

@buoyant holly Has your question been resolved?

[buoyant holly]

not entirely

one left

i tried solving it alone

but i failed

[buoyant holly]

<@&286206848099549185>

T^T

i dont understand why the concavity questions is wrong

i followed what me and vortex did for the prev question

2nd deri for concavity questions

i think it was 1st deri for intervals but i mighta messed that one up

[buoyant holly]

.close

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[frosty ibex]

Can someone please explain why it is so important for a and m to be coprime to find

ax = 1 (mod m)?

Basically why coprime is needed to find a modular inverse

[pastel cosmos]

Because if they are not coprime then ax cant be 1 mod m

Suppose a and m are not coprime, then gcd(a, m) = d > 1

ax = 1 (mod m) means there exists an integer k such that

ax = mk + 1

But d | ax and d cant divide mk+1, this is a contradiction

[frosty ibex]

Thank you for all of this so far, so d | mk but d does not | 1. Why is it an issue that d can't divide 1? Would the beginning of the proof say that like all numbers in this proof are integers?

[pastel cosmos]

If d cant divide 1, then d cant divide mk+1

This means d cant divide ax

But d can divide a, so d can divide ax

which becomes a contradiction

[frosty ibex]

ohh i see, so since ax = mk + 1 (mod m), if d divides one side but not the other then that is a contradiction

[pastel cosmos]

Yes

[frosty ibex]

ahh thank you so much i really appreciate it. i saw with numbers how you would never get an x value but couldnt figure out how to prove it

.close

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[slender sky]

I need help with this equation so I'm assuming I have to rewrite both of the expressions to Y

[slender sky]

this is my work so far am I on the right track?

[frosty ibex]

Hi @slender sky, can you walk me through what you are trying to do with your work?

[slender sky]

I orioginally thought that I cant integrate this in respect to x and only y

so i tried changing both expressions to y

but now im lost thinking i did somethign wrong

[frosty ibex]

I finished calc last spring, but if my memory suits me right then I would solve this with the following

Find the integral of y^2 - 6y - (4y - y^2)

do that on the interval from y = 0 to y = 5

[slender sky]

Ohhhh

so theres realy no need to

rewrite anything?

just integrate

and plug?

[frosty ibex]

Yeah from what i remember that is what you want to do, just do right - left, integrate and plug

[slender sky]

oh dang

okay

thakn you so much

LMFAOAO

i was panicking

[frosty ibex]

Yeah no you are good, sometimes they want top - bottom but sometimes they want right - left, so you just want to have your equations with respect to x or y based on what makes sense

[slender sky]

wait just want to clear it up shouldnt it be (4y-y^2)-(y^2-6y)?

since 4y-y^2 is the red

[frosty ibex]

Ohh yeah that is right

[slender sky]

okok perfect tysm

[frosty ibex]

I do not blame you for being confused on this one haha

[slender sky]

haha thank you so much for your help

my biuggest problem is i dont know when to change my equations in respect to x or y and thast what messed me up with this one

[frosty ibex]

Yeah of course! I think your equation is something like 10y - 2y^2

Integral would be 5y^2 - 2/3y^3 + C

Plug in our values

5(5)^2 - 2/3 (5)^3 - [5(0)^2 - 2/3 (0)^3]

[slender sky]

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[slender sky]

Sorry another question! I need help with this problem.

[slender sky]

I struggle with graphing and I don't really know hwo to graph 2x+y^2=8 without using desmos but the integration part isn't hard for me

I really just need help with finding the bounds and whether to integrate in respect to x or y

and I can do the rest

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@slender sky Has your question been resolved?

[slender sky]

.close

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[faint kestrel]

i don't understand it, and idk what to do

[long fable]

not to sound passive aggressive but like

did u even read the project

directions

[faint kestrel]

i did

[long fable]

whats there not to understand

[radiant cradle]

Where u didn't understand

[faint kestrel]

im just stresed about it

[faint kestrel]

the algebra part, where you convert it

Im just confused on what to do

[long fable]

that is a very shitty worded question i cant lie

[faint kestrel]

i know

[long fable]

very open ended

[faint kestrel]

i think he uses chat gpt

[long fable]

but i assume they described it in like more detail in class or something

[faint kestrel]

nope

he just gave it

and ran off

i asked him what to do

he said use your notes

bruh....

[long fable]

well

the algebra it wants is gonna be something like

[faint kestrel]

Do you want to see the notes, he didnt even write the title

[long fable]

i get it

for example

if the number of flowers in each row

increase by a multiple of 3

each time

your algebra would be

3n

cause for every value of n there is 3 flowers

or like

if it involves rows of flowers increasing by 3 in each row

u could do something like

[faint kestrel]

okay

[long fable]

a1 + (n-1) times d

where a1 = 5

and d is 3

[faint kestrel]

Im so confused

[long fable]

do u know what a sequence is

[faint kestrel]

yes

its like a pattern

[long fable]

so like

picture your garden

there are rows

horizontal

[faint kestrel]

yeah

[long fable]

first row 3 flowers

2nd 6

3rd 9

and so on

[faint kestrel]

yes

[long fable]

the first term in the sequence

ok so

basicallt

just make a sequence

or look one up

and design the garden

based on

how the sequence increases

[faint kestrel]

okay

how do you write the answer?

In what format

[long fable]

well

it says you need to make a poster

[faint kestrel]

yeah

[long fable]

and draw a garden on this poster

or something

so

just that

[faint kestrel]

thats it

?

[long fable]

looks like it unless i missed something

but u also need to right out the sequence

[faint kestrel]

okay

it seems that i got it

ill dm you if i need any help

[long fable]

also it looks like they want a slightly complicated sequence

since it wants 3 different patterns

[faint kestrel]

yeah

i kinda got it

Thx

[long fable]

np

[faint kestrel]

@long fable can you close this then?

[long fable]

im not a helper

[faint kestrel]

oh

[long fable]

i literally joined here 15min ago

[faint kestrel]

okay

ima try to close it

.close

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[faint kestrel]

it worked

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[tranquil pine]

So its possible right to determine the surface area using the surface area of revolution

[tranquil pine]

As in im modeling a bottle

And i want to find the total surface area

Uding the equations i have gathered that make up the bottle

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@tranquil pine Has your question been resolved?

[final saddle]

@tranquil pine Has your question been resolved?

[final saddle]

@tranquil pine Has your question been resolved?

[tranquil pine]

<@&286206848099549185>

So this is the eclipse im trying to model

Somebody already got the equation for me (x-20)^2 /7.5 -y^2/5 =1

But im so confused how they got the 20

Like i tried substituting values but i keep getting 17

@lapis sonnet

[lapis sonnet]

hmm

can we back up a bit what do you mean by model here

lyou want to make something like this?

[tranquil pine]

No i want to make something like this

[lapis sonnet]

here's an example of how I'd do it in desmos, I use the regression stuff as a separate thing, not the one built in to the list since it's kind of broken
https://www.desmos.com/calculator/yodidh0ioj

if you move a dot and it freezes, pressing Ctrl+Z fixes it for me

[final saddle]

@tranquil pine Has your question been resolved?

[lament vale]

Yes, but for that purpose you'd need to take a photo of the bottle from a different angle

This angle is good:

This angle is bad:

Mainly because the cap is a cylinder

However, if you consider the surface of revolution of the red curve here you'd get something that looks like a bullet

So not a cylinder

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[tranquil pine]

why are we doing a dot product with T ?

tangent vecotr

tangent unit vector?

even for work done its just F.ds right

brb

ah

[broken slate]

Yo

[drowsy epoch]

Maybe this helps
https://www.hsc.edu.kw/student/materials/Physics/website/hyperphysics modified/hbase/wint.html

[tranquil pine]

DANG

[broken slate]

Gold

[tranquil pine]

i was watching this video

https://www.youtube.com/watch?v=059LjQ2oLBM

DANG

[broken slate]

He gave you the direct resource

[tranquil pine]

this is way more intresting that triple

[tranquil pine]

yo

[tranquil pine]

i got it

thanks

[broken slate]

Goo

D

[tranquil pine]

lol

.close

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[drowsy epoch]

explain it.

[tranquil pine]

.reopen

[final saddle]

✅

[drowsy epoch]

🫵🏻

[tranquil pine]

.

[drowsy epoch]

[tranquil pine]

bacc what the heck

so we have this

we are taking a small part of the curve ds

now we know that work done is F.ds

[vital surge]

[drowsy epoch]

yours is slower but coutnerclockwise 😦

[tranquil pine]

which we can rewrite as component of F along the curve direction times ds

[drowsy epoch]

coutner 😦

[tranquil pine]

curve direction is just the unit tangent vector

so what are doing is finding F along the curve direction i.e Force along the tanegent vector

F along tangent vector is F.T

we are just rewriting F.ds as F.T ds

ds is magnitude and T is the direction

i got it right?

[tranquil pine]

conclusion

[drowsy epoch]

I thought F.Tds = F.dr

[tranquil pine]

yes

oh

i meant

F.ds is the formula we use in physics

bruh

F.ds = Work Done

F.T ds is work done

[tranquil pine]

use this while finding the work done through line integrals

wait no

yes

nnvm

[tranquil pine]

@drowsy epoch am i right ?

its hard to visualize the integral though 😔

[drowsy epoch]

i think so? lol

[drowsy epoch]

true

[tranquil pine]

oh wait

[tranquil pine]

that represents a vector field?

but 3b1b said that vector fields need 4D

[drowsy epoch]

no it's a scalar field

[tranquil pine]

💀

[drowsy epoch]

geometrically you are integrating a scalar field over a curve and the result the surface area

they way I understood also is F.T is just work done comes from physics and then we have ds, so we get the work done along an infinitesimal small distance and summing these up to get the total work along a curve

[tranquil pine]

👍

[drowsy epoch]

I guess you liked my comment

[tranquil pine]

i couldn't undertand it
so a neutral reply 👍

[tranquil pine]

also i forgor how this is the case

so watching a video

[soft zealot]

𝔸dωn𝓲²s

[drowsy epoch]

ds is a small piece of arclength

multiply that by a height f

you get that yellow surface summing these up

[tranquil pine]

ohh yes

i overcomplivated it again

[drowsy epoch]

you are an intelligent person

[tranquil pine]

i know

[drowsy epoch]

just a chill guy too

[tranquil pine]

i have to google what "chill guy" means

[drowsy epoch]

https://tenor.com/view/chill-guy-my-new-character-gif-2777893510283028272

[tranquil pine]

"The Chill Guy represents the idea of acting cool in uncomfortable situations."

😂

[drowsy epoch]

in all situations*

[tranquil pine]

XD

.solved

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[spring plank]

So basically i am triyng to find the function of the parabola, but so that it fits over the shape im trying to model, i used matrices and the quadratic formula to do it but it isnt fitting correctly do you guys know any other way of doing it. the points are C (6.7497, 0.2181), D (6.6690, 0.3206) E (6.7189, 0.4038)

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[rigid haven]

wondering if i did this problem correctly?

[shut gazelle]

Your y < 2x + 9 graph looks wrong

[rigid haven]

k ty

[final saddle]

@rigid haven Has your question been resolved?

[rigid haven]

does this look correct?

[runic tulip]

a fellow chill guy i see

[rigid haven]

.close

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[onyx peak]

you can use the cos(a + b) identity

to simplify cos(theta + 90)

or just think about how the graph shifts

[rustic mantle]

Cos(theta)cos90

[onyx peak]

okay and cos90 is?

wait what

[rustic mantle]

0

[onyx peak]

okay

but you're missing -sin(theta)sin(90)

the formula is cos(a)cos(b) - sin(a)sin(b)

[rustic mantle]

Ok

Cos(theta) * cos90 - sin(theta) * sin90

0-1

[onyx peak]

0 - sin(theta)*1

[rustic mantle]

-sin○+6sin○

5sin(theta)

[onyx peak]

yep

now you can do part b)

[rustic mantle]

Sin^-1 =1/5

[onyx peak]

you sure?

check again

[rustic mantle]

2/5

[onyx peak]

Yeah

x = sin^-1(2/5)

[rustic mantle]

I can do the rest

Thx

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[runic tulip]

bro tryna open em all

lmao

[zealous sigil]

lol

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[fervent aspen]

Ok so let n = 2^(k-1) . j, k > 1, j odd
σ(n) = σ(2^[k-1]) . σ(j) = 2 . 2^(k-1) . j (since n is a perfect number)

σ(2^[k-1]) = 2^k - 1

So (2^k - 1) . σ(j) = 2^k . j

Since 2^k has only factors 2 and 2^k - 1 has no factors 2, σ(j) = 2^k . m, where m is odd (since j has no factors 2)

Now, (2^k - 1)m = j
If j is prime, j = 2^k - 1 (since k > 1 so 2^k - 1 has an odd factor that is not 1, sp ot must be equal to j on the rhs which has only 1 odd factor as j is prime)

But i just cannot prove that j is prime

Can anyone help?

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@fervent aspen Has your question been resolved?

[fervent aspen]

<@&286206848099549185>

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@fervent aspen Has your question been resolved?

[fervent aspen]

Dawg i found it on wikipedia, whats there is exactly what i did but i could not do the last part 😭

.close

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[ruby quarry]

pls can I have some help with this question

[ruby quarry]

I think I only tick a since you can express that as a finite automaton

wheras Im not so sure about the others

[final saddle]

@ruby quarry Has your question been resolved?

[ruby quarry]

<@&286206848099549185>

[candid hull]

alright, what automaton do you have in mind for a) ?

@ruby quarry

[ruby quarry]

ok I just tried creating one, I think it might be impossible actually

because you would need to count the number you go above or below 0 each time and an automaton can't do that

[candid hull]

well a finite automaton certainly can't if you have infinite floors yeah

[ruby quarry]

yeah, therefore that language cannot be regular

with b, I would assume the same logic applies there, you would need a method of counting

with c

hmm

we can set floors below zero or above 10 as accept states with 10 states in the middle so I believe this is regular

not sure about d tbh

[candid hull]

yup, very similar to a, you still need to take into account all the Ups & Downs you got

[candid hull]

it's the reverse

you wanna accept words that stay between 0 and 10

but yeah once you go out of bounds, you can just stop counting

[ruby quarry]

ah yes

[candid hull]

so like 11 accepting states for 0 to 10 inclusive

• 1 reject

[ruby quarry]

yeah

with d), I am looking for a language of all instructions that never visit a floor below 0 or above 10, and that returns to floor 0

[candid hull]

yeah

[ruby quarry]

can we say that this is regular because you can have a similar finite automaton to c), but with only 1 accept state

[candid hull]

exactly

just accept 0

[ruby quarry]

ah

thank you

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[marsh temple]

[rocky talon]

?

You were taking so long to write allat just to delete your message

[tranquil pine]

:P

it was from a game

Sigma sigma boy sigma boy sigma boy

How to get green role!!’

play roblox for 5 hours everyday and you will get it

Real..

stay active in help channels

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[umbral shuttle]

am i right with B here

[dry talon]

I'm not directly going to give you the answer, however you can check your textbook on conic sections for the definition of a hyperbola.

This is also a great resource: https://sourcely.co/0KDJzp0

Here's an open source textbook if you're in the mood for a bit of reading: https://sourcely.co/GpXDMX5

[umbral shuttle]

I looked up conic sections, and looked at the image results.

A hyberbola is a plane that is perpendicular to the base of a double cone.

it has to be B no?

[radiant dragon]

hi

[umbral shuttle]

am i right here

[umbral shuttle]

<@&286206848099549185>

.close

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[ruby quarry]

pls can I have some help with this

[final saddle]

@ruby quarry Has your question been resolved?

[ruby quarry]

<@&286206848099549185>

I think a is eliminated because of the kleene star after the (aa**bb*)

because once you are at 3, there is no option for a

b eliminated for the same reason

<@&286206848099549185>

[rustic sinew]

Disclaimer, not my field.
Your argument for a. And b. Looks good.
I want to say. c. Looks the best.
d. A is not an accept state, and same argument as a and b
e. Is tempting, but Abe is not an accept state

[ruby quarry]

thx for ur help, just wanted to clarify. Does (b U a)* mean any combination of a's and b's 0 or multiple times, or rather either a or b 0 or multiple times

wait but for C, aac isn't an accept state? is aac valid?

<@&286206848099549185>

[ruby quarry]

I looked this up btw, I this it means either a or b

<@&286206848099549185>

[brisk charm]

@ruby quarry Wait so how far did you get and what are you still confused about? I can help

[ruby quarry]

perf thank u

[ruby quarry]

firstly, is my logic here correct?

[brisk charm]

Yeah, it doesn't seem like there's any way to get an a immediately after a b

[ruby quarry]

cool

in my mind the answer is none of them but I'm pretty sure that's wrong

B would be eliminated via the same logic

for C aac isn't an accept state

for D, a isn't an accept state

for E, abe isn't an accept state

[brisk charm]

Yeah your logic seems right, I'll look closer

wait

just to clarify, is e a letter of the alphabet here, or does it stand for empty string?

[ruby quarry]

empty string

[brisk charm]

Oh

Then you can get a after b

if you do 1 -> 2 -> 3 -> 1 -> 2

that would be a b e a, so just aba

[ruby quarry]

oh wow

didn't know that

[brisk charm]

And "abe" doesn't make sense here, it would just be "ab"

Since e isn't part of the alphabet

It just represents an empty string

[ruby quarry]

ah ok

[brisk charm]

That tripped me up, this is terrible notation lol

[ruby quarry]

yeah lmao

[brisk charm]

I usually see ε for empty string

Okay but anyway yeah you'll want to revisit some of your earlier logic

Let's start with A

[ruby quarry]

yeah, gotta revisit all of them

[ruby quarry]

cool

[brisk charm]

Take a look at it, think about it, and tell me what you're thinking

[ruby quarry]

sure, the first (𝑎𝑎∗𝑏𝑏∗)∗ seems valid now

now onto the next part

aa* is valid and would take you to 2

[brisk charm]

yup

[ruby quarry]

𝑎𝑎∗𝑏𝑏∗(𝑎𝑎∗∪𝑐))𝑐∗ this term

hmm

𝑎𝑎∗𝑏𝑏∗ is valid and brings you to either 2 or 3

from either 2 or 3

𝑎𝑎∗ is valid

however C isn't from 2

therefore not valid?

[brisk charm]

So what you're saying is that there's a string accepted by the regex but not the NFA?

What's the string?

[ruby quarry]

so it would be aabbaabbaac

that might be complicated to read soz

the middle term in the second set of brackets: 𝑎𝑎∗𝑏𝑏∗(𝑎𝑎∗∪𝑐))𝑐∗ is what makes it invalid imo

the ending c

wait I might've made a mistake

you can get to c from a using e

[brisk charm]

Yeah that's true

[ruby quarry]

is it possible to say that since nearly all the terms have a kleene star, if we end up back at state 1 the expression is invalid because we haven't ended up at an accepting state

can you say simply an empty string from state 1 invalidates everything?

[brisk charm]

I'm not sure what you mean by that

But certainly the empty string is not accepted by this NFA because state 1 is not accepting, and there's no e paths going out from state 1

[ruby quarry]

yeah that's what I mean

therefore the expression is invalid

because of the kleene star in the first term (𝑎𝑎∗𝑏𝑏∗)∗ that means that you can begin your string with an empty string

and that is invalid like you said

[brisk charm]

That doesn't make sense

The empty string is not a member of the alphabet

It just means "don't insert anything into the string here"

The empty string is not actually present in a word as a symbol

[ruby quarry]

but as an example, (𝑎)∗ means either a, aa, aaa, ... or empty string

right

[brisk charm]

yes

[ruby quarry]

ok

do you agree that the expression is invalid?

as an example, aabbaabb empty string

[brisk charm]

again that doesn't make sense, "empty string" isn't part of a string

you're really just saying aabbaabb

any example of a string you come up with to test should not have the words "empty string" in it

[ruby quarry]

ok

just simply aabbaa?

end up in state 2 which is not an accepting state

[brisk charm]

ah but the NFA does accept that string

it can end up in state 4

[ruby quarry]

because of the empty string?

[brisk charm]

yup

the e arrow pointing from 2 to 4

[ruby quarry]

in that case I don't see an issue with any string then

so the expression is valid

[brisk charm]

alright

so we're saying part a is valid?

what about part b

[ruby quarry]

yh

[ruby quarry]

starts off with (𝑎𝑎∗𝑏𝑏∗)∗ like a

but we end up in state 2 after aa*

then theres 2 routes to go down

c* which is valid

or 𝑏𝑏∗(𝑒∪𝑐𝑐∗)

this empty string is throwing me off

the empty string would take you back to state 1

[brisk charm]

it can be tricky to think about, you got this

[ruby quarry]

cc* is valid

I'm gonna go with valid because the empty string after is the same as just staying in state 3?

[brisk charm]

okay and then what about c

[ruby quarry]

like the answer c?

𝑎(𝑏∪𝑎)∗𝑐𝑐∗

I see no issues tbh

I think its valid

[brisk charm]

there's two ways that it could fail right

either the regex accepts strings which are not accepted by the NFA

or the NFA accepts strings which are not accepted by the regex

did you check both of these scenarios

[ruby quarry]

only checked this ig

[brisk charm]

alright you gotta also check the other scenario to see if it's possible

[ruby quarry]

aabc is accepted by the NFA but not by the regex

[brisk charm]

aabc is accepted by the regex

(b ∪ a)* gives ab and c* gives the empty string

so you get aabc

[ruby quarry]

I thought (b ∪ a)* means only a, aa, ... or b, bb...

not both

[brisk charm]

No that would be (b* ∪ a*) I think

[ruby quarry]

interesting

ah

ab

[brisk charm]

what about ab?

[ruby quarry]

yeah its not valid

[brisk charm]

as in, ab is accepted by the NFA but not by the regex right

[ruby quarry]

yh

[brisk charm]

yup, awesome

I gotta run for the night but hopefully this gives some insight for how to approach the problem

[ruby quarry]

nws, thanks for all ur help

[brisk charm]

you're welcome!

[ruby quarry]

uhh idk if ur still there or not, but at the top of the question it says which of the following regex are regular languages that are accepted by the NFA

[ruby quarry]

does that mean it still has to go both ways

[brisk charm]

yes, language accepted by regex = language accepted by NFA

[ruby quarry]

cool thx, btw my final answers are a and b if u ended up answering the question

[final saddle]

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[grand forum]

How would i do part b?

[final saddle]

@grand forum Has your question been resolved?

[grand forum]

Yes

Apparently this is what im doing

But lowkey im very lost and i dont have an equation to start with 🤨

[grand forum]

I just use y= -2x + 4?

im lost

but what equation am i working with 🧍‍♀️

AM I SLOW HELP

no cause i did that and the answers were wrong

🧍‍♀️

I erased it 💀

This is where im at 💀💀💀💀

[grand forum]

no because in this unit we must find perpendicular slopes to determine the poi and thennnn calculate the length of the line (distance)

But im not sure what formula im support to use to begin finding the other perpendicular slopes

im like 🧍‍♀️ really lost

Yeah but i need to slove using those steps

Otherwise she will legit fail me

I just dont understand what my equation is 🧍‍♀️