help-10

[restive gorge]

you just got f'(a) with f(a) mixed

[half carbon]

poo

that looks a whole lot better

[restive gorge]

may i know what cs problem 😅

[restive gorge]

this reminds me of something

[half carbon]

so basically the problem is converting 300k+ something csv file into nice formatted data in under 10 seconds

[restive gorge]

like someone is getting pulled and torn into a black hole

[half carbon]

just like my brain :D:D:D:D:D

[half carbon]

OKAY SOOOO that's everything?

[restive gorge]

yea

see how they are parallel

x-intecepts are parralel to each other

and y-intercepts to each other

[half carbon]

yeah, that's actually very cool

[restive gorge]

just wanted to ppint out why the slopes were the same

but thats it

take a screeno and sendoo to teachooor

5. is trivial

[warm shale]

adonhs

[half carbon]

YAY last problem

that looks scary

[restive gorge]

just use log diff.

and derive a formula

so what do you do first

since it says log. diff.

[half carbon]

well we can take the natural log of both sides

[restive gorge]

ok

now

natural log btw is ln but continue 😄

[half carbon]

oops yeah that's my bad

[warm shale]

Someone

[restive gorge]

Now

[half carbon]

the lovely product rule?

[warm shale]

adonhs

[restive gorge]

yes

[half carbon]

oh goodlord okay

[restive gorge]

12 hours shift

[half carbon]

what's the derivative of g(x)

the hecc

[restive gorge]

trivial

dg/dx

or g'

[half carbon]

so just g?

lol

[restive gorge]

g'

'

[half carbon]

wot

[restive gorge]

wot

g' = g'(x) = dg/dx

[half carbon]

right

[restive gorge]

never encountered that notation?

[half carbon]

so that's just it?

[restive gorge]

uhm ye why not

[half carbon]

sorry i've never worked with variables like this i think

oh

[restive gorge]

but you destroyed 1) with implicit differentiation X)

[half carbon]

aha that's less scary with only x and y

okay now the derivative of ln(f(x))

[restive gorge]

yea

ln(f(x))?

differentiated

[half carbon]

chain rule it?

[restive gorge]

yea

[half carbon]

you know you're tried when you forget the chain rule, wow

so it's $\frac{1}{f(x)} * g'(x)$

[restive gorge]

i don't know when i am tried

[warm shale]

Someone

[half carbon]

that's fair

[restive gorge]

where did g' come from

it's f(x) so the inner derivative is...=

[half carbon]

yeah, my bad, just assign stuff to weird variables in my head

f'(x)

[restive gorge]

yeaaa

[half carbon]

which is just d/dx

[restive gorge]

df/dx

[half carbon]

ah

[restive gorge]

X)

[half carbon]

so now we have all 4 variables for the product rule

[restive gorge]

yea (i guess)

since you did ln(f(x))

[half carbon]

$f=g(x)$
$\$
$\$
$f'=\frac{dg}{dx}$
$\$
$\$
$g=ln(f(x))$
$\$
$\$
$g'=\frac{1}{f(x)}\cdot\frac{df}{dx}$

[restive gorge]

what is ln(y) differentited

[warm shale]

Someone

[restive gorge]

my nightmare manifested

😂 😭

[half carbon]

[restive gorge]

i know it's your thing for structure and stuff

but cmon

[half carbon]

lmao my variables are pretty bad

[restive gorge]

f = g

[half carbon]

shush 😂

[restive gorge]

and g = ln(f(x))

lmaooooooooooooooooooooo

so f = ln(f)?

g = ln(g)

[restive gorge]

but yea that's essentially it

bravo

[half carbon]

sheeeesh okay now

[restive gorge]

you're funny actually

[warm shale]

Someone

[half carbon]

that's so messy

[restive gorge]

wanna se an alternative?

[half carbon]

yes pls

(i don't want to do it my way)

[warm shale]

adonhs

[half carbon]

uhhhh

[restive gorge]

up to you

[half carbon]

so either of those would be the answer technically?

[restive gorge]

it's just a notation thing yea

[half carbon]

oh dang, okay so it wasn't that bad

[restive gorge]

the same way people write instead of y(x) they write only y

but ok the left side's missing

ln(y)

[half carbon]

right

$ln(y)=g'ln(f)+\frac{f'}{f}g$

[warm shale]

Someone

[restive gorge]

noo

[half carbon]

fgwahjfhai

[restive gorge]

ln(y) must be differentiated too

[half carbon]

ah

1/y

[restive gorge]

almost

y is a function of x

D:

[half carbon]

1/y dy/dx

lol

[restive gorge]

yea

lol

[warm shale]

adonhs

[restive gorge]

Now you can solve for y'

[half carbon]

aha no clue

[restive gorge]

yea you are done

[warm shale]

adonhs

[half carbon]

oh my lord lol

[restive gorge]

here lol

https://www.youtube.com/watch?app=desktop&v=SUxcFxM65Ho

we got it almost 1:1

4:00

[half carbon]

that's actually so funny

[restive gorge]

X)

pleasure doing businesss

[half carbon]

thank you so so much!

i can finally sleep 🙏

❤️

[restive gorge]

😂

have a got recovery

[half carbon]

xD

<3

.solved

[obtuse pebble]

Channel closed

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[obtuse pebble]

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[marble vigil]

ok i need some help

[marble vigil]

how do i do question d

[gilded needle]

first find $P(B \cap \overline A)$ from the given info

[warm shale]

Bungo

[gilded needle]

from that you can find $P(B \cap A)$

[warm shale]

Bungo

[gilded needle]

and then it's smooth sailing

[marble vigil]

how do i find P(B intersection not A)

@gilded needle

[gilded needle]

you have $P(B | \overline A)$ and $P(A)$, do what comes naturally with that info

[warm shale]

Bungo

[marble vigil]

what comes naturally with that info

i do not understand this at all

[gilded needle]

what's the definition of $P(B | \overline A)$

[warm shale]

Bungo

[gilded needle]

in terms of other probabilities

[marble vigil]

i don’t know

[gilded needle]

well you'll need to know that for sure

look up conditional probability

[marble vigil]

it makes sense on a venn diagram

it’s everything highlighted

[marble vigil]

oh i know now

@gilded needle

[gilded needle]

yes

[marble vigil]

so how do i find that

[gilded needle]

you know the thing on the left hand side and the thing in the denom of the right hand side

so you can solve for the numerator of the right hand side

[marble vigil]

i multiply both sides by A’?

i asked chat gpt and it all makes sense until it says to substitute into the formula to find a union b

@gilded needle

<@&286206848099549185>

<@&286206848099549185>

,close

.close

[obtuse pebble]

Channel closed

Closed by @marble vigil

Use .reopen if this was a mistake.

[fathom flicker]

.reopen

@marble vigil

[obtuse pebble]

✅

[marble vigil]

bruh

[fathom flicker]

!15mins

[obtuse pebble]

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

[marble vigil]

my question hasn’t been answered for way longer than 15 minutes

[fathom flicker]

!nogpt

[obtuse pebble]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[fathom flicker]

It says once, and you tagged them multiple times

before closing and opening a new channel, and tagging Bungo

Please be patient

[marble vigil]

ok sorry

it has been 40 minutes tho

[vital holly]

gpt is all we have in this world full of posers 🥀

[fathom flicker]

It is meant to just be 1 ping in total

[frank tide]

I wish gpt could be my valentine

[marble vigil]

i wish gpt could answer my math question

[fathom flicker]

Okay but this channel is getting a bit full and off topic now

Isaac if you wish to restart with a new one, with the rules in mind, go ahead

we can close this

[marble vigil]

ok

works for me

[fathom flicker]

.close

[obtuse pebble]

Channel closed

Closed by @fathom flicker

Use .reopen if this was a mistake.

[marble vigil]

wait can i post the same question?

[fathom flicker]

Yes go ahead

[marble vigil]

alright

[fathom flicker]

This channel got a bit spammed

wasn't my intention

[marble vigil]

alg

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
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[next crescent]

just wanted to kinda check my answers since i dont fully understand proving vec spaces

[gritty vessel]

what did you get for each answer?

[next crescent]

a. no, not closed under addition (let a = x^3 + x^2 - x and b = -x^3 + x^2 + x )
b. no, not closed under multi (take k = -1)
c. no , does not contain 0 vector (i think)
d. yes
e. no, not closed under addition
f. yes

[radiant osprey]

(b) you are incorrect

[gritty vessel]

for (b) I'd take a closer look. if f has 2024 as a root then (-f)(2024) = -f(2024) = 0

[radiant osprey]

(e) is confusing lol

i assume this is for fixed x

[next crescent]

oh i see

i went too fast and distributed wrong, oops

[gritty vessel]

also for (e) not only is it not contained under addition, it just doesn't contain 0

you are correct, I'm just pointing out a slightly easier way to do that one

[next crescent]

thats one of the things im kind of confused on

how can you tell if it contains 0 or not

for c i was able to tell b/c if you take x = (0,0,0) it was fairly clear that it wouldnt equal 365, but for other problems i cant tell if it contains 0 or not

[radiant osprey]

well take (c) as an example

this is a set of vectors so we know that to add them you just add the vectors elementwise

a zero element is something such that v + 0 = v for any v

so it's pretty clear that the zero is (0,0,0)

a similar logic applies to the rest

(e) is a set of matrices so we know that to add them you just add the matrices elementwise

very similarly to the case of vectors

[next crescent]

im still kind of confused on how that wouldn't contain 0

[obtuse pebble]

@next crescent Has your question been resolved?

Channel closed

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[timid silo]

integration can be used to find the area under the graph f'(x), but what can f''(x) be used for, and also differentiation

[timid silo]

what are their purposes

[timid silo]

is it to find min and max values

[ember frost]

to determine what the critical points are

[timid silo]

wym

[ember frost]

aka this

[timid silo]

questions like this hurt so much

[timid silo]

oh

.close

[obtuse pebble]

Channel closed

Closed by @tender cairn

Use .reopen if this was a mistake.

[obtuse pebble]

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• 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.

[final sage]

wrong channel

nvm

.close

[obtuse pebble]

Channel closed

Closed by @final sage

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[shut crater]

I need help with this word problem.

Find an equation for the line tangent to the graph of f at (3,92), where f is given by

f(x)= 5x^3-5x^2+2

y= ?

[tepid yoke]

Do you know how to take the derivative of f(x)

[shut crater]

yeah i got the derivative to be

f'(x) = 15x^2-10x

[tepid yoke]

Ok so we know that’s the slope of the function, so you need to find the slope at the given point

[shut crater]

i thought to do that i'd substitute the x value into the derivative and by putting in f'(3)=105 but that was wrong

[tepid yoke]

Did you sub that into the equation of a line?

We know y=mx+c and m at the point x=3 is 105

[shut crater]

oh mah gosh

no i didn't do that

gimme a min 😭

[tepid yoke]

Yeah your looking for the equation of the line not just the slope

[shut crater]

wait so...

y = mx+c

m= 105, x=3, and c=92? i put it all together to get y = 407 but that wasn't correct

[tepid yoke]

Not quite, we don’t know c yet

[shut crater]

ohhh

OH

okay wait wait i think i got it

okay i tried a couple things and it didn't work... i feel like i'm on the brink of understanding.

i input the values I know

92=105*3+c

and with simple algebra got

-223=c

but that's not right

I also input y=105*3-223

and that doesn't work either. it makes sense thought because it equals 92 which we know is the y coord at x=3 but ahhhhh

[sage dagger]

r u still stuck

[shut crater]

yes

[sage dagger]

okay

do u wanna restart just so like its easier for me to explain

[shut crater]

yeah that would be great

[sage dagger]

so you took the derivative to be f' = 15x^2 - 10x right

[shut crater]

yes

[sage dagger]

but you want the derivative at the point x = 3

to find the tangent

[shut crater]

yes to get what y=

[sage dagger]

so what you really need is f'(3)

[sage dagger]

we need the gradient

[shut crater]

when i put 3 into the derivative of f(x) i got 105

but when i put it into my math homework thingy it's wrong

[sage dagger]

we arent done

[shut crater]

ohhhhhhhhh

[sage dagger]

so now we know that the derivative or gradient at the point x=3 is 105 yes?

[shut crater]

yes

[sage dagger]

we will call this "m"

[shut crater]

okay

[sage dagger]

We will use the form $y-y_{1}=m\left(x-x_{1}\right)$ and rearrange it to solve for y later

[warm shale]

water beam

[sage dagger]

we actually have everything we need, we know y1, m and x1

[shut crater]

oh WAIT THIS LOOKS FAMILIAR

[sage dagger]

can you fill in the blanks

[shut crater]

yes give me a sec

[sage dagger]

you should, its the form y = mx+b

just written differently

[shut crater]

y-92 =105(3-
what would x1 be?

[sage dagger]

something is wrong

[shut crater]

oh boy

[sage dagger]

why did the x go away

you keep x but you change x1 for what you know

[shut crater]

OH

silly me

okay so
y-92=105(x-3)

[sage dagger]

yes

now simplify

[shut crater]

aight

y=105x-223

[sage dagger]

yeah

and ur done

[shut crater]

OMGOSH BLESS UR SOUL

[sage dagger]

[shut crater]

you are literally an angel i hope you have a great day/night thank you so much

[sage dagger]

np

[shut crater]

.close

[obtuse pebble]

Channel closed

Closed by @shut crater

Use .reopen if this was a mistake.

[obtuse pebble]

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

[crude nacelle]

12X^2 - 28X - 5

[crude nacelle]

Now ik how to solve the second degree equatins

[crude nacelle]

but i'm stuck at this one

also ik how to solve it with the calculator and i did it, but i want to know how to solve this type

[grim ocean]

u can solve it with quadratic formula, cross multiplying or completing the square

[crude nacelle]

wdym?

[grim ocean]

also when u said u solved it with a calculator, is that quadratics formula

[grim ocean]

hm ok how do i explain this

[crude nacelle]

fr? ;-;

[grim ocean]

ok so this is the quadratics formula

and u cna use that to find the roots

but its the harder way

the easier way is cross multiplying

[crude nacelle]

wdym by cross the multiplying?

[grim ocean]

like an example is this

[crude nacelle]

my main language isn't ENglish so excuse me

[grim ocean]

oh alg

[grim ocean]

wait

that example is wrong

sorry i just pulled a random one off the internet

[crude nacelle]

yeah i'm staring at it to understand 😂

[grim ocean]

lmaoo

[grim ocean]

ok so for this, what are the factors you know that can multiply to 12

(12 being the coefficient of x^2)

@crude nacelle

[crude nacelle]

srry wait a sec

1 and 12

2 n 6

3 n 4

[grim ocean]

yep

ok so with the cross multiplying method, its more of a guess and check situation

ok this is a better example

do u see how with this, they found two factors of 3x^2

which in that case is 3x and x

cus 3x * x = 3x^2

[crude nacelle]

okok

[grim ocean]

and then for the constant (which is 3), they found two factors which multiply to 3

which r 1 and 3

[crude nacelle]

ig i understand

can u give an example for me to solve?

[grim ocean]

hm

3x^2+10x-8

just a hint: for the constant, two factors have to multiply to -8

[crude nacelle]

hm

[grim ocean]

ping me when ur done

[crude nacelle]

(3x+2)

is the first

(x-4)

is the second

@grim ocean

[grim ocean]

r u sure 🙂

[crude nacelle]

tbh

[grim ocean]

u got the factors right

[crude nacelle]

no

[grim ocean]

i think u shud check ur signs

[crude nacelle]

hmm

[grim ocean]

also an easy way to check if ur right or not is to expand ur answer

[crude nacelle]

i reversed them?

[grim ocean]

it shud match the original trinomial

[grim ocean]

correct

[crude nacelle]

then the signs are right?

[grim ocean]

yes it shud be (3x-2)(x+4)

now try it with ur example

[crude nacelle]

12X^2 - 28X - 5

[grim ocean]

yes it has more factors, but its still doable

[crude nacelle]

should i make the 12x^2 like 11x and x?

[grim ocean]

ah no cus 11x * x =11x^2

what two factors can multiply to 12x^2

[crude nacelle]

it's

12x^2 and x

no

12x and x

[grim ocean]

yes

theres more

[crude nacelle]

yeah

what should i pick?

any?

[grim ocean]

yea u hv to guess and check

[crude nacelle]

.

[grim ocean]

it seems like theres a lot

but there actually isnt

[crude nacelle]

what

explain pls 🙂

[grim ocean]

wait wat do u want me to explain

the possibilities?

[crude nacelle]

yeah

[grim ocean]

ok so

[crude nacelle]

so

[grim ocean]

12x^2 can be split into 3 ways right

[crude nacelle]

ye

[grim ocean]

12x*x

3x*4x

and 2x*6x

now

u also have to find the factors for -5

and there's only one way

which is 1 and -5

[crude nacelle]

why not -1 and 5?

[grim ocean]

oh yea that too sorry

[crude nacelle]

ok

[grim ocean]

so now u just cross multiply the factors

and add up the result of the cross multplication

and when u add it up

it shud add to -28

[crude nacelle]

wai what

(2x+1) and (6x-5)

it has to be this

right?

i solve it by myself so excuse me if the signs are also wrong

[grim ocean]

ok u nearly got it right

u just swapped the -5 and 1 around

[crude nacelle]

wait is there a right place to put them on? ;-;

[grim ocean]

yes cus if u swap them, then they dont add up to 28

[grim ocean]

also sorry i realised this eaxmple is wrong too💀

[crude nacelle]

well how can i know

[grim ocean]

how can u know if there's a right place to put them?

[crude nacelle]

idk

i'm asking 🙂

[crude nacelle]

no no this one is good

[crude nacelle]

the larger number comes first right?

i'm feeling stupid

[grim ocean]

ok sorry for the messiness, had to do this with a touchpad

[grim ocean]

anyways do u get wats going on here

[crude nacelle]

wait a sec

[crude nacelle]

is that your hand font? 💀

i can't read!

[grim ocean]

^^

[grim ocean]

💀 o man

[crude nacelle]

ok ;-;

nono i can read now 😂

[grim ocean]

its usually prettier than that dw💀💀

i just cant write with a touchpad

[grim ocean]

okok good

[crude nacelle]

ok 😂

[grim ocean]

wait i hv to go for like 15mins is that ok

[crude nacelle]

i beleive cuz it's the same w me

[grim ocean]

lmaoo

[crude nacelle]

ok you helped alot fr

i can close the channel now

[grim ocean]

all good 🙂

[crude nacelle]

how can i close it again?

[grim ocean]

.close

[crude nacelle]

.close

[obtuse pebble]

Channel closed

Closed by @crude nacelle

Use .reopen if this was a mistake.

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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[tiny lake]

Which value of

makes

a true statement?

[tiny lake]

.close

[obtuse pebble]

Channel closed

Closed by @tiny lake

Use .reopen if this was a mistake.

[obtuse pebble]

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Remember:
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• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[dark hedge]

Hi

[sturdy jasper]

I'm solving this problem

[dark hedge]

Ohh u opened it

Nvm

[sturdy jasper]

sorry

[dark hedge]

It's okay

[sturdy jasper]

I know you can do u-sub with
u = cos(x)
but why can't you rearrange it as
(1-sin(x)^2)^2 * sinx * cosx * dx
and set u = sin(x)?

so the new equation is
[u^5 - 2u^3 + u] du

then you can easily integrate

I tried that method and I got a different answer from the accepted answer

can anybody help me on that

[obtuse pebble]

@sturdy jasper Has your question been resolved?

[obtuse pebble]

@sturdy jasper Has your question been resolved?

[strange zodiac]

(x+2) (x-4) -x = 2(x-3)² -12

Can someone help me

Im kinda stupid

[rough marten]

@sturdy jasper

Juz change cos⁵x to (1-sin⁵x)

And u will get integrate( sinx - sin⁶x) dx

[sturdy jasper]

sir you are imperializing my channel

[rough marten]

!occupied

[obtuse pebble]

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

[sturdy jasper]

i'm not really having an issue solving it, i'm just curious how the two answers are different

im pretty sure this answer (what i got)

is equivalent to this

[rough marten]

U let u =sinx and u= cosx ?

[sturdy jasper]

i used the trig identity (1-sin(x)^2)^2 for (cos(x))^4

set u = sin(x)

du = cos(x) dx

[rough marten]

(1-u²)²u x u

Right?

Wait no

Another cos

[sturdy jasper]

(1-u²)²u du

[rough marten]

Ye

[sturdy jasper]

then u^5 - 2u^3 + u du

then i found the antiderivative, plugged in sin(x)

i think that answer should be correct, but when i plug in a sample value for 'x' in both answers, i get a different number

just wondering why that is

[rough marten]

Uh hold on I'm walking back home lmao

[sturdy jasper]

ur good lol

dont get your chain snatched over a math problem

[rough marten]

@sturdy jasper

What val did u sub in

U get different values cuz of +C

The constant for each equation is different iirc that's what my tcher said

[sturdy jasper]

yeah thats my area of confusion i guess

how that works

i plugged in a few values, 1, 3, 8...

the answers disagreed each time

so how do you find the +C values, if at all?

[rough marten]

U will have to be given more info ig

Like coords

[sturdy jasper]

coords?

like points?

[rough marten]

Coordinates

Yea

If it's juz pure integration simple as this, don't use substitution lul

If u know the +C for both, den u sub in u shud get the same ans

[sturdy jasper]

then how can you know for certain that the two answers are equivalent without knowing the constant

[rough marten]

Hmmm ,not sure for that

But if u were given limits u can compare

Juz do more practice and don't get wrong

[sturdy jasper]

i havent been taught how to calculate the constant yet

so that might be the problem

thank you for your help though

[rough marten]

Ahhh ok

That's weird , usually we learn to find +C only learn substitution

Ig different teaching style then

[sturdy jasper]

im guessing you're in AP calculus BC?

[rough marten]

What's that

[sturdy jasper]

its a college-level class they usually take in highschool

its like calculus 1 and 2 combined

[rough marten]

Hmm I'm in college taking A level Cambridge sooo idk bout that

[sturdy jasper]

oh i think its an american thing

AP classes

i think A-level Cambridge should be similar

well thank you anyways

.close

[obtuse pebble]

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[obtuse pebble]

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[proud yacht]

idk what happened the channel was out of my channel list and I couldnt reply back @hexed gull

so I get that until I have even number of friends, the friends at last posn would always be eliminated

idk how this helps but just trying to find a pattern

im getting nowhere tho

[golden night]

did you start from 1

you need to start from the most basic thing

and then go up

[proud yacht]

I did observe that

for even number of friends

n-1 th (I observed this only for n = 4 and n = 6) was the winner

so is it like for any even number of friends, the friend at the last second place wins

[obtuse pebble]

@proud yacht Has your question been resolved?

[obtuse pebble]

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[graceful marten]

nvm

.close

[obtuse pebble]

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[last pilot]

lmao

quickest channel open and close ever

[obtuse pebble]

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[still cloak]

Help

[obtuse pebble]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[last pilot]

@still cloak what do you need help with

??

waits

[still cloak]

well i need a better understanding in algebra linear equation in one variable and addition to division of polynomials

i kinda suck at math

[last pilot]

in what, exactly?

is there a specific question

or just the entire topic

if the latter, go to #prealg-and-algebra

[still cloak]

latter..?

[last pilot]

the second one

(in this case)

@still cloak what i meant

is that if you have a specific question

ask here

if not, go to #prealg-and-algebra

[still cloak]

ohh ok

[last pilot]

and before going

[still cloak]

ask math questions here?

[last pilot]

specific questions yes

if you don't have one, do .close

[still cloak]

ohh my bad sorry

[last pilot]

np

[still cloak]

.close

[obtuse pebble]

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[obtuse pebble]

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[graceful wind]

this is more physics

[graceful wind]

can distance from axis of rotation be negative

im guessing it can

[last pilot]

discord.gg/physics

[viscid gull]

no distance is always nonnegative

[graceful wind]

ty

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[hoary kindle]

could someone tell me if i’ve done question 3 correct so far?

[stuck isle]

there is a simpler way of eliminating theta

[hoary kindle]

how

[stuck isle]

you can square both the equations

and add them

[hoary kindle]

i tried that

but i got some weird result

hold up ill show u

[stuck isle]

what did you get

[stuck isle]

i think you've made a mistake here

first try squaring the equations individually

and then adding them

(x + y)^2 = x^2 + 2xy + y^2

(x - y)^2 = x^2 - 2xy + y^2

[hoary kindle]

so x^2 sin^2 theta + y^2 cos^2 theta i do first?

[stuck isle]

yes

tell me what you get

[hoary kindle]

wait so do i start from the very beginning, like from the original euqations or just from a^2 + b^2 = blah blah

[stuck isle]

no no

what i mean is

[stuck isle]

you have made a mistake in squaring the equation

[hoary kindle]

ohhh

[stuck isle]

so im telling you to do this: (xsin0 + ycos0)^2 correctly

you get me?

[hoary kindle]

yea i got u

[stuck isle]

yes

now add them

[hoary kindle]

like the whole thign?

[stuck isle]

yes

[hoary kindle]

ok

[stuck isle]

the middle terms in both the equation will get cancelled

[hoary kindle]

do ui then just factor out sin and cos

[stuck isle]

yes

you can take x^2 + y^2 common

[stuck isle]

yes

[hoary kindle]

would that be (x^2+y^2) x (y^2 + x^2)?

since sin and cos = 1

[stuck isle]

so now you can take (x^2+y^2) common

[hoary kindle]

so it's (x^2+y^2) sin^2 theta + cos^2 theta?

[stuck isle]

yes

which is equal to 1

[hoary kindle]

ohhhhhhhhhhhhhhhhhhhhhhhh

[stuck isle]

got it?

[hoary kindle]

that makes so much more snese

yep

thanks

[stuck isle]

anytime

[hoary kindle]

.close

[obtuse pebble]

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[obtuse pebble]

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[junior stirrup]

how do i do the question when the nth is 3

[junior stirrup]

help

[rotund bloom]

find the differences of subsequent terms until the difference becomes constant

then divide that by 2 to get the coefficient of a in ur quadratic equation

[junior stirrup]

and how do i do that 💀

[rotund bloom]

like
4, 7, 13, 22
3, 6, 9
3, 3

[junior stirrup]

yes

[rotund bloom]

u take the difference of (n+1)th-nth term

now ur a coefficient will be 3/2

[junior stirrup]

okay

[rotund bloom]

basically ur constant row, take that number and divide by 2

then jus use quadratic equation to solve

[junior stirrup]

okay!

thanks!

[obtuse pebble]

@junior stirrup Has your question been resolved?

[obtuse pebble]

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[versed wyvern]

Can some one help me in this question

I know that the domain = x belongs to domain f and f belongs to domain g

But I could not solve it

[rotund bloom]

did u find an expression for g(f(x))

[versed wyvern]

Oh yes I forget that I find it and it was undefined

It was (-x^2)^1/2

That's mean the domain is also undefined right?

[torpid cave]

No

Whats the domain of $\sqrt{x}$

[warm shale]

casework

[rotund bloom]

g(f(x)) is yielding a complex valued function

[versed wyvern]

Yeah

But it's calc 1, we dont use complex value now

[rotund bloom]

so domain is undefined

[versed wyvern]

OK thanks

[rotund bloom]

np

[versed wyvern]

.close

[obtuse pebble]

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[torpid cave]

0 be like 😦

[rotund bloom]

fair point

[torpid cave]

The domain is {0}

[rotund bloom]

@versed wyvern ^

[versed wyvern]

Oh I got it thanks

[obtuse pebble]

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[main bay]

hi i think i royally fucked up my midterm but wanted some help just walking through one of the problems:

worker has utility U(I,L) = 2ln(I) + 5ln(L)
wage is 25 $ and they have 40 hours per week to work. any hours used not working go towards leisure.

what is the budget constraint?
what is the optimal hours?

what are the optimal hours if wage increases to 30 and the worker has a max hours of 20; if wage decreases to 20 and worker has max of 20 hours?

[obtuse pebble]

@main bay Has your question been resolved?

[obtuse pebble]

@main bay Has your question been resolved?

[obtuse pebble]

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[haughty shore]

can someone explain why that w is the only solution to least squares

well it makes sense why it is the only solution but how can you have more than one solution

shouldnt it always be possible to draw a vector from the span of V to v such that it is perpendicular

[kind hawk]

well you cant have more than one solution. you have a unique solution. thats the point

[haughty shore]

oh so for least squares solution to an overdetermined systems

its not possible to have more than one solution right

.close

[obtuse pebble]

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[formal violet]

can someone please verify my answers and tell me if they are correct?

<@&286206848099549185>

[obtuse pebble]

@formal violet Has your question been resolved?

[formal violet]

<@&286206848099549185>

[obtuse pebble]

@formal violet Has your question been resolved?

[obtuse pebble]

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[cosmic portal]

i do need some help with my math, im doing what my notes are telling me to do but its not the Right answers

[brisk grove]

(4) is incorrect

The limit of g(x) as x approaches -1

[cosmic portal]

how so?

[brisk grove]

You did the other questions correctly, I think you'll get it without my help

[cosmic portal]

thank you

.close

[obtuse pebble]

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[cosmic portal]

.reopen

[obtuse pebble]

✅

[cosmic portal]

this question does not really have anything similar on my notes, and im kinda confused by it

im not 100% sure what to do

<@&286206848099549185>

[rapid tusk]

Ok so as x increasing towards infinity

What does f(x) approach?

[cosmic portal]

2?

[rapid tusk]

Yes

So what about as x decreases towards negative infinity

[cosmic portal]

i wanna say -2

[rapid tusk]

Not quite

[cosmic portal]

if not then 2

[rapid tusk]

It is 2 but do u know why?

Looking at the graph

We can see it is becoming closer and closer to 2 as x decreases

[cosmic portal]

oooooooooooh

[rapid tusk]

Now as x approaches 2 from the right (2^+)

From the graph what can we say about f(x)

[raw pike]

hello

[cosmic portal]

its infinite?

[rapid tusk]

Correct it is shooting upwards towards infinity

As x approached 2 from the right

[raw pike]

2
2

• infini

• (- infini)

[rapid tusk]

But how about from the left? (2^-)

[cosmic portal]

that would be -inf right

[rapid tusk]

Yup exactly

[cosmic portal]

omg thank you

[rapid tusk]

Np

[cosmic portal]

i think i understand it a bit more now

.close

[obtuse pebble]

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[rapid tusk]

Didnt want to just say the answer incase they didnt know why

[raw pike]

ah okey
i am bored so just checking channels and answering
you right

[rapid tusk]

All good

[cosmic portal]

.reopen

[obtuse pebble]

✅

[cosmic portal]

id assume it is similar to the first question

(f) and (e) would be -4

im just not fully sure what (c) and (d) would be

sorry for reopening so much

<@&286206848099549185>

[cobalt dune]

is c lim x-> 4 or x-> -4

[cosmic portal]

x->-4

[cobalt dune]

shouldnt have a limit

cant really approach it from the right side

since it goes to eternity

[cosmic portal]

so it would be DNE?

[cobalt dune]

yep

if im not wrong you cant approach it from left either

oh wait yeah

even if you can approach it

left and right side goes to different results

its DNE

[cosmic portal]

for (c) right?

[cobalt dune]

yyep

remember lim x-> a = lim x-> a- and lim x-> a+

[cosmic portal]

ah ok

[cobalt dune]

f(-4)
hmm

[cosmic portal]

those always confuse me lol

[cobalt dune]

i mean it's either 2 or also DNE

in limits, lim x->a = f(a) is only possible if said function is continous in that point

it's likely f(-4) is 2 but i'm not %100 sure

[cosmic portal]

i did try both but may be because anothe question is wrong

[cobalt dune]

another question is wrong?

which one

[cosmic portal]

it does not say which it just says that one of the above questions is wrong

[cobalt dune]

btw is a x->4-

if so answer to be must be +inf

[cosmic portal]

ooooooh

i changed it and it still syas what is wrong

im not fully sure where im wrong

[obtuse pebble]

@cosmic portal Has your question been resolved?

[cosmic portal]

.close

[obtuse pebble]

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[bleak skiff]

how do i show that f(x+iy) = sqrt(|xy|) is neither holomorphic nor complex differentiable at 0

[brave bramble]

Holomorphic in region R = complex differentiable everywhere

So really we just need to show it's not complex differentiable at 0, which the CR equations are used for

[obtuse pebble]

@bleak skiff Has your question been resolved?

[bleak skiff]

and if the equations are verified at 0?

because the partial derivatives at 0 are both 0

$\frac{\partial f}{\partial x}(0,0) = 0$

[warm shale]

lilisworld.

[bleak skiff]

$\frac{\partial f}{\partial y}(0,0)=0$

[warm shale]

lilisworld.

[bleak skiff]

wait

uhm actually no

.close

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[cedar ravine]

i need someone to help me and explain who to solve this problem , thanks

[surreal solar]

Part = number of athletes who took more than 24s
Whole = total number of athletes

[cedar ravine]

8+9+5 = 22 / 25 * 100 = right?

[surreal solar]

Not quite

Your whole is correct, but not your part. Can you see why?

[cedar ravine]

so 8 is not included?

[surreal solar]

That's right!

[cedar ravine]

so
9+5 = 14
---- x 100 =56
3+8+9+5 =25

[surreal solar]

Yep, 56%

[cedar ravine]

thank you very much

[obtuse pebble]

@cedar ravine Has your question been resolved?

[obtuse pebble]

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[weary depot]

I tried to use a contradiction, but I don’t think I did it correctly

[gritty vessel]

contradiction is probably the right approach, but the issue is that you set a and b to be the same thing. you should let a = 2k + 1 and b = 2m + 1

[weary depot]

Ohh right ok got it will try now

😭

Do I need to use another method ?

[gritty vessel]

you squared your binomials wrong. it should be $4k^2 + 4k + 1 + 4m^2 + 4m + 1$

[warm shale]

Awesam

[gritty vessel]

and then basically what you can do is write it as a multiple of 4 plus 2

so it's a multiple of 2 but not a multiple of 4 but a square can only be odd or a multiple of 4

and therein lies the contradiction

[weary depot]

Thank you so much

Does this look alright

[gritty vessel]

yeah that's good

[weary depot]

Thank you !!

.close

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[dim terrace]

im just a bit confused because i thought AFTER we use the product rule for the left and right side of the minus sign, we then have to use the rule for adding/subtracting functions. can i get more info on why this isn't the case?

[obtuse pebble]

@dim terrace Has your question been resolved?

[kindred valley]

d/dx (f(x) - g(x)) is f'(x) - g'(x)

[dim terrace]

Yes. I know I'm a bit confused, I just need some clarification on the "rules" per say.

I get the impression that I'm not "done" when I use the product rule on the left and right side of the minus sign. It's like I want to find the derivatives again because I want to do derivatives everytime there is another operand

So essentially, since we've already found the derivatives of the left hand side and the right hand side of the subtraction

we've already performed the subtraction rule

simply by using the product rule twice

[obtuse pebble]

@dim terrace Has your question been resolved?

[obtuse pebble]

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[spark jungle]

Hello I am confused how the P and Q works

[spark jungle]

I know the P is the last number (36) and Q is (2) but what does P/q do

Like they got -3 but did they just guess until it worked

Is there a faster way or did they guess -1, 1, -2, 2, -3 and got it

[latent walrus]

-36

but yeah you have to just test them all

sometimes none of them will be zeros

[spark jungle]

That takes so long

No faster way?

[latent walrus]

not really

[obtuse pebble]

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[gilded drift]

I'm back with a weird question
Ysaac and his problems are in a Cartesian plane. Ysaac cannot escape his problems. Every time Ysaac moves, his problems always follow such that the distance between Ysaac and his problems is always 5 units. His problems always stay on the y-axis. At what rate are his problems following him downwards the y-axis when Ysaac is on (4, 0)? Assume Ysaac is running at a speed of 1 unit per second in the direction of the positive x-axis.

Is the answer
4/3 units per second

[latent walrus]

his problems? what kind of life is ysaac living

[gilded drift]

damn I guess I can't be depressed

[gilded drift]

so is it 4/3 '<'

x^2+y^2=25
2x dx/dt + 2y dy/dt = 0
dy/dt=-x/y dx/dt
=-4/3 * 1
since it indicates downwards, 4/3?

[obtuse pebble]

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@gilded drift Has your question been resolved?

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[tribal crescent]

Im not sure where the 255.52 came from

I get the 104.48 but the 255.52 doesnt make sense

<@&286206848099549185>

[outer needle]

do you know about the unit circle?

for sin and cos

and do you understand what your teacher wants when he asks for all solutions 0<=x<2pi

[outer needle]

?

[tribal crescent]

I know the unit circle

[tribal crescent]

Doesnt that mean any quadrant?

[small lance]

dont you have to put the -1 like in the radian value? or so

[outer needle]

you know there are infinite solutions for sin(x) right?

this is limited to 0-360°

which is 2 solutions

[tribal crescent]

ohh yea i get that part

but how do you get the second solution of 255.52

[outer needle]

sec I got you

sinx=k then x1=v+360n and x2=180-v+360n

[tribal crescent]

what does v and n stand for

[outer needle]

angle and n is just an addon for if you have to find all infinite solutions

I gave you the equation for sin

sorry bro

hold up

cosx=k then x=+-v+360n

if you were solving for 0<=x=4pi then you could put 2 for n

idk if that comes up a lot tho

[tribal crescent]

ohh

so -104.48 + 360

[outer needle]

yeah

[tribal crescent]

okay tysm bro

[outer needle]

np

[tribal crescent]

.close

[obtuse pebble]

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[pearl nexus]

how do i find the vertex of these two

[cunning burrow]

The vertex is midpoint of the x-intercepts

[pearl nexus]

yes i know

how do i find it

though

[teal turret]

nah just do (-b/2a, h(-b/2a))

[pearl nexus]

does that work?

[teal turret]

yea

[pearl nexus]

okay thanks

[teal turret]

np

-a/4 is correct, a^2/8 isnt

wait did u get what i meant by a & b in: (-b/2a, h(-b/2a))

a is the coefficient of x^2 term, b is coefficient of x-term

in p(x) = ax^2 + bx + c

[obtuse pebble]

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[leaden jetty]

Two cars are moving towards each other, one at 120 km/hr and the other at 80 km/hr, with a distance of 1000 km between them. There's a fly starting from the same point as the first car, flying at 360 km/hr, and it goes back and forth between the cars. The question is asking for the number of times the fly will touch the cars before they meet.

[leaden jetty]

We had a hyptotectical question in my maths class

Teacher couldnt solve it

[lapis charm]

its infinity

[leaden jetty]

Is it limit?

Or actual infinity

[lapis charm]

i mean

interesting question

[leaden jetty]

All we had is the 2 cars will mert in 5 hour so the fpy will travel 1800 km