precalculus

[tropic coyote]

the function is continuous already

so you can just plug 10 directly

[viscid thistle]

why not?

[viscid thistle]

can't one do that with limits already?

[tropic coyote]

yes you can

[viscid thistle]

Not sure what you mean by this

[tropic coyote]

like

lets call D(t) the derivative of the function h(t)

[viscid thistle]

ok

[tropic coyote]

if you do the math you know that D(t) is continuous

so you could calcualte D(10) through limits

but its far easier to just plug in the 10 directly

[viscid thistle]

what do you mean by continous

[tropic coyote]

like its graph doesnt break

it isnt any sudden jump

or gets weird shapes

that make the existence of limit impossible

[viscid thistle]

oh, but that's obvious

this graph i mean

[tropic coyote]

yeah for this one it is continuous

[viscid thistle]

mhm

[tropic coyote]

so you can just calculate D(t) generally

put it as a formula

and put 10 in the formula

[viscid thistle]

lim h(t) = bla bla bla
t --> 10

right?

[tropic coyote]

are you trying to set up the derivative there?

[viscid thistle]

Yes

i'm using the derivative formula

[tropic coyote]

it should be something more like

[viscid thistle]

that's what i did, no?

[tropic coyote]

lim h(10+Δ)-h(10)
Δ->0 ----------------- = D(10)
Δ

[viscid thistle]

so delta t reaches 0?

[tropic coyote]

yes

but t itself shouldnt change

[viscid thistle]

i tried that, but It didn't work

[tropic coyote]

can i see what you tried

it worked for me

[viscid thistle]

alright

i just gave up at the end

lol

also I know i put the fractions as numbers

but whatever

[wooden glen]

hey guys is this question correct?

[tropic coyote]

wait

i think i saw the mistake

you did this right

wait let me send photo

[viscid thistle]

Yes

[wooden glen]

thanks

[viscid thistle]

np

[wooden glen]

this isnt precalculus but can you also check this one please 💀

im thinking its d

not sure

[viscid thistle]

x is linear, x squared is like the on you sent, and x cube is like a zig zag lookin

[wooden glen]

yeah

[viscid thistle]

blud, you taking class in logic?

[wooden glen]

but i thought B was the answer first

[wooden glen]

i got an ACT exam tmrw morning 💀

[viscid thistle]

wait, b and c both sound correct

[opal niche]

👽 hi guys

[viscid thistle]

i just tried 2 x's

[viscid thistle]

sup

[wooden glen]

oh.

[viscid thistle]

you're taking class in philosophy?

[opal niche]

?

[wooden glen]

nah but idk most of the times questions like these come

[tropic coyote]

wait why cant i send photo

[viscid thistle]

you just have to substitute x and try to see if you get the same position

[wooden glen]

im doing ACT international subjects

[viscid thistle]

where did i blunder

[viscid thistle]

what is that

[tropic coyote]

alright let me write it here

[wooden glen]

and im doing M1 for the 3rd time tmrw lmao

[tropic coyote]

-1/30(t+Δt)^3 is part of h(t+Δt) right

[wooden glen]

exams that i need to do so i can get an american high school diploma

[viscid thistle]

d is correct

[viscid thistle]

right

[tropic coyote]

i saw that you wrote it as -1/30 (t^3 + (Δt)^3)

maybe im wrong

but thats what i saw

[viscid thistle]

that's what i wrote it as

[tropic coyote]

yeah thats wrong

[viscid thistle]

hold on, did i?

[tropic coyote]

idk

[viscid thistle]

even I'm confused

[tropic coyote]

imma check again if you wrote it as that

[wooden glen]

thanks

[tropic coyote]

yeah you did

you just put t as 10

(that t=10 step is correct though)

[viscid thistle]

this is what I wrote

[tropic coyote]

yeah but later on

you wrote it as -100/3 + (Δt)^3

[viscid thistle]

yes, that's wrong?

[tropic coyote]

yep

do i explain why

or do you want a quick formula to fix it

[viscid thistle]

10^3 is 1000, times -1/30 is...

wait

where am I mistaken here?

[tropic coyote]

hint: (a+b)^n usually isnt a^n + b^n

[viscid thistle]

bruhhh

ugh

[tropic coyote]

remember (a+b)^n indicates multiplication

[willow skiff]

it doesn't work for n = 2

[tropic coyote]

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

[viscid thistle]

i will NEVER become a mathematician

[tropic coyote]

(a+b)^3 = a^3 +3a^2b + 3ab^2 + b^3

[tropic coyote]

sad

later on math gets cooler

[viscid thistle]

of course, 10 must times delta t

I see

[tropic coyote]

nah more like

10+ Δt must times itself

[viscid thistle]

isn't that the same?

[tropic coyote]

not really

do i explain with a cool visualization

or do you want to just use the formulas

[viscid thistle]

if (a+b) ^n , doesn't that mean that (a+b) (a+b) (a+b)

[tropic coyote]

yes

but its not ab neither (ab)^3

[viscid thistle]

i thought I had factorization in check, how the heck am I still missing

[viscid thistle]

so must times with delta t, no?

and plus

[tropic coyote]

i mean yeah but also gotta sum the 10

yes that

[viscid thistle]

ok so

to clarify

(10 + delta T) ^3 means that 10 and delta t times each other three times and add

agree?

[tropic coyote]

maybe you worded it wrong and thought it right

[viscid thistle]

I said three times, but yeah

[tropic coyote]

but this is how i would say it:

[viscid thistle]

you get the idea

[tropic coyote]

(10 + delta t) multiplied by itself 3 times

[viscid thistle]

that sounds kind ambigious

[tropic coyote]

alright good point

let me edit

[viscid thistle]

yes please

show me

[tropic coyote]

alright wait

so you know how for a number a, a^2 represents the area of a square with each side length being a right?

like

each side length is a

and the area of blue square is a^2

are you getting it?

[viscid thistle]

of course

[tropic coyote]

alright so

[viscid thistle]

yes yes, this I know

[tropic coyote]

wait let me draw 2nd square

this square has side lengths a+b

so its area must be (a+b)^2

right?

[viscid thistle]

Yes

ahh I see

2ab in the corner

i get it

[tropic coyote]

so in total its a^2 +2ab + b^2

[viscid thistle]

(a + b) ^2 is equal to a^2 + 2ab + b^2

yes

[tropic coyote]

yes

you got it right

nice

[viscid thistle]

thanks

had to refresh my memory

[tropic coyote]

you could also do it another way

with distributive

[viscid thistle]

Hmm, I've heard that term but couldn't quite wrap my head around it

[tropic coyote]

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

[viscid thistle]

ohh

[tropic coyote]

with distributive i mean distributive law

[viscid thistle]

just making math more complex than it need to be

lol

[tropic coyote]

sorry if i overcomplicated this

[viscid thistle]

no no, I was reffering to the law you meantioned

[tropic coyote]

but basically your error was that you made (a+b)^n = a^n + b^n

oh alright

[viscid thistle]

MMM

[tropic coyote]

want to try again now?

[viscid thistle]

i always confuse (a+b) ^2 with (a-b) (a+b)

for some reason

[viscid thistle]

yes

[tropic coyote]

alright

tell me if you need help

you can dm

meanwhile imma go back to discussion

[viscid thistle]

will do, thanks!

[warm spoke]

that is a devious lick

[gaunt carbon]

true tbh

quadratic visualizations go so hard

[hot root]

trying to get some help on this question, i need to find b and -b with lines passing through 12,0 and that are tangental to the circle at the origin with a radius of 6

[gaunt carbon]

sure! so this type of problem tests what you know about angles and triangles

now the first step in a problem like this is recognizing that the radius of 6 can be used to make a triangle between the origin, point P, and (12,0)

now since we know that the lines are tangent to the circle, we can establish some right angles

and so by doing that we would be able to recognize a solvable triangle here

so we're able to break this triangle out and solve for x using the pythagorean theorem since we know its a right triangle.

this gives us an $x$ value of $6\sqrt{3}$

[obsidian monolith]

architecture2

[gaunt carbon]

and so from there we can realize that by similar triangles we can find the other angles in this triangle

from there we can use what we know about angles to solve for this triangle here, which gives us the value of b

so by similar triangles we can see this

and then we can use the 60 degree angle to find that the angle between the y-axis and point P is 30 degrees, and we can go forward from there to find b using similar triangles again

ofc keeping in mind that this is the similar triangle we're using

[hot root]

ohhh i didn’t even think of making a triangle, even though i knew CP was perpendicular to (12,0)P lol

i’m assuming this works reguardless of where the point is because a tangental line will always make a right triangle with CP

thank you!

[gaunt carbon]

ofc

[austere flame]

hey is there anyone which is at university level on math?

[tender quest]

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/

[viscid thistle]

@tropic coyote Bro, I need help

I’m STILL!! Stuck at the same problem from yesterday 💀

[tropic coyote]

hi

[viscid thistle]

Hi

[tropic coyote]

what happened

[viscid thistle]

How tf did I even come to this conclusion!!!

[tropic coyote]

alright what happened

[tropic coyote]

send photo of work

[viscid thistle]

I’m seriously contemplating life after the last bit

[tropic coyote]

i think you did an error while calculating (a+b)^3

not sure though

[viscid thistle]

Of course I did

[tropic coyote]

do i give formula for (a+b)^3

sorry

i dont wanna be too mean

[viscid thistle]

It’s okay

just be mean

[tropic coyote]

alright let me send photo

[viscid thistle]

ok

[warped ridge]

$(a+b)^3=a^3+b^3+3a^2b+3ab^2$

[tropic coyote]

yeah that

i forgot the 3's

thanks muhammad

[warped ridge]

You're welcome HSF

[tropic coyote]

anyways so

let me write how it should go

[viscid thistle]

yeah except if it was a and b i was dealing with, I wouldn’t have an issue with visual spatial reasoning

[warped ridge]

I see just replace a with 10 and b with del t

[viscid thistle]

I seriously have no idea where I went wrong

[warped ridge]

Your expansion is wrong

[viscid thistle]

Hmm, how come

[tropic coyote]

let me check again

how you did it

[viscid thistle]

@tropic coyote How quick did you solve this problem?

[tropic coyote]

i used another trick to find derivatives

not limits

so in some minutes

its a lot harder with limits

[warped ridge]

Here's one place I found

[tropic coyote]

oh yeah i found an error

[warped ridge]

I can find others maybe but sorry I'm not doing well

[tropic coyote]

you did 10(Δt)^2 as (10Δt)^2

i think

[viscid thistle]

Ok so How did It was first take (a +b) (a+b) then multiply that with (a+b)

[tropic coyote]

yeah i got that part

[warped ridge]

You're using the first principle arent you?

[viscid thistle]

but thats correct no?

[viscid thistle]

If thats what its called, then sure

[tropic coyote]

let me send photo of my own work

[warped ridge]

$10(\Delta t)^2 \neq (10\Delta t))^2$

[tropic coyote]

yeah what muhammad said

one is 10ΔtΔt

the other one is 100ΔtΔt

[viscid thistle]

I don’t know any other ways then using limits

well other than using tangent lines

[tropic coyote]

the other tricks basically depend on limits

[viscid thistle]

but screw that

[warped ridge]

You're basically in the process of learning it dw

It's not about speed it's about understanding

[tropic coyote]

i dont know why it keeps getting rotated

im trying to do it like you did

so you can find error

[warped ridge]

,rccw

[warped ridge]

There

[viscid thistle]

This is hard to read ngl

[warped ridge]

Wait

[tropic coyote]

sorry if its blurry

[warped ridge]

I can't write cause I'm literally in bed but

[tropic coyote]

ill send photo of next step

[viscid thistle]

😂

[viscid thistle]

I’m unaware, are there any other tricks than limits?

[warped ridge]

$$h(10+\Delta t)=-\frac1{30}(10+\Delta t)^3+\frac52(10+\Delta t)^2$$

[viscid thistle]

Using limits is a tedious process

[tropic coyote]

i mean there's some patterns in derivatives

like the power rule, chain rule, the fact that derivative is linear

etc

[viscid thistle]

speaking of, that’s exactly what I’ll learn next

[warped ridge]

Lemme actually write wait

Bruh

[tropic coyote]

trickster

are you noticing any error in your work yet

[viscid thistle]

Hmm?

ugh, I have to think know

Ok lemme see rq

[tropic coyote]

i did a mistake in a line

i wrote 20Δt as 20Δt^2

[viscid thistle]

oh

[tropic coyote]

its not in the cubic part though

that part's fine

[viscid thistle]

I got the exact same result

[tropic coyote]

,rccw

[viscid thistle]

but i wrote 10 (delta T)^2 as (10 delta T) ^ 2

[tropic coyote]

yeah thats the error i found

theyre different things

10Δt*10Δt = 100ΔtΔt

10Δt*Δt=10ΔtΔt

[viscid thistle]

Did I do that?

[tropic coyote]

you did the wrong version

[viscid thistle]

Ugh, I probably have to redo this entire thing

[warped ridge]

Uh I'm tired again

[viscid thistle]

it’s so easy to lose control over things

[tropic coyote]

alright it should look like the last one

do i simplify to almost last step so you can revise your own work

or do you wanna do it yourself

[viscid thistle]

I wanna do it myself

[tropic coyote]

alright

ill still have paper just in case

[viscid thistle]

okay

so to clarify, I can do (a+b) (a+b) then multiply that with (a+b)

correct?

@tropic coyote

[tropic coyote]

yes

[viscid thistle]

Okay

I tried learning the binomial theorem but it gave me a brain tumor

[tropic coyote]

binomial coefficients are easy to learn if you think of it as pascal's triangle

[viscid thistle]

so I’m just doing it the old way

[tropic coyote]

alright

[viscid thistle]

Yes its easy to understand

but Goddamn is it tedious

and looooooong

[tropic coyote]

nah its also easy to calculate up to ( 10 k )

calculate all of them i mean

[warped ridge]

Don't actually learn binomial expansions and do hard questions

[tropic coyote]

wanna see a cool math trick?

[viscid thistle]

actually no, it’s not so easy. Until you get to nCr ! etc then it gets complicated

[warped ridge]

They're easy the combinatorics way

nCr is the easiest thing tbh

[viscid thistle]

Sure

[tropic coyote]

alright let me use pc drawing for this

[warped ridge]

Wait why do I have med lol

[viscid thistle]

it sounds like a riddle if you don’t even know what it means

[warped ridge]

Kinda... I always thought differently about it since my first combinations class in 2021

[warped ridge]

Idk before that I didn't care

[tropic coyote]

there i ordered the first few binomial coefficients in a triangle

[viscid thistle]

Yeah, pascals triangle

[tropic coyote]

see any pattern there?

[viscid thistle]

Yes

[tropic coyote]

what is it

[viscid thistle]

1’s are always outside and the middle ones add up

[tropic coyote]

yeah

turns out the middle ones always add up

[viscid thistle]

yes

[tropic coyote]

look at it with more numbers

[viscid thistle]

ive seen it, but thats not the issue

the problem is the nCr or whatever it means

nCr/ ncr !

or sum like that

[viscid thistle]

are you a programmer by any means?

[warped ridge]

Ummh... No?

I do code tho

[viscid thistle]

You doo?!

[warped ridge]

Yeah?

[tropic coyote]

yeah he did some cool things on desmos

mandelbrot fractal

[warped ridge]

Ah shhhh

[viscid thistle]

but do you code on python?

[warped ridge]

Yeah I code in manim

[viscid thistle]

I’m kinda in need for some lectures in python with physics

[warped ridge]

Why does it sound tempting for me

'Physics'

[viscid thistle]

cool word I guess

[warped ridge]

I gotta stop gobbling libretexts on my morning walks tbh

[tropic coyote]

i should do it more

[viscid thistle]

but yeah, physics + python

[warped ridge]

I don't do physics in python

But as HSF revealed... I do physics in Desmos

[viscid thistle]

I have no idea how python works, even though i had some python lectures in my physics class

What’s desmos?

[warped ridge]

😫

[tropic coyote]

https://www.desmos.com/calculator?lang=en

[viscid thistle]

I almost went insane💀

[tropic coyote]

what

[viscid thistle]

can’t lose my sanity over calculus

[viscid thistle]

nothing, it’s just that calculus graphs give me ptsd

[tropic coyote]

oh

sad

[viscid thistle]

remind me of the hell I’m about to endure in the future

[tropic coyote]

calculus gets easier as you go

there are some cool new tricks

[viscid thistle]

Duh

I remember looking at limits when I was first a math newbie

like when I was learning basic algebra

[warped ridge]

Well applied calculus is fun

[viscid thistle]

and now I’m here doing them

[warped ridge]

That's the only thing I like in physics

[viscid thistle]

Yeah but not so fun doing the math itself and losing your mind in the process 😭

[tropic coyote]

anyways if you want to i can give you photo of next steps i did

[viscid thistle]

there are more steps?

[warped ridge]

Uh what'd you do

[tropic coyote]

yeah like 3 steps

[viscid thistle]

i thought h’(t) was it

[tropic coyote]

yeah thats it

just h'(t)

[warped ridge]

Did you put the limits?

[viscid thistle]

yes

[viscid thistle]

yeah the next step is factoring no?

then substituting t with 0 and using the remainders

[tropic coyote]

yes

next step you divide delta t

[viscid thistle]

You didn’t even factor first?

[tropic coyote]

i mean you could

[viscid thistle]

so when you divide you divide all the terms right?

[tropic coyote]

yes

[viscid thistle]

since it ain’t factored

[tropic coyote]

yep

sorry my delta looks like a 0

[viscid thistle]

ok

[tropic coyote]

so it may be kind of confusing

[viscid thistle]

looks normal

lol

[tropic coyote]

oh alright

so you get left with the terms that were next to a single delta t

and those terms are

-(300)/30

• 5*(20)/2

[viscid thistle]

hold on, you haven’t multiplied with -1/30, that’s what bugs me the most

[tropic coyote]

i did though

[viscid thistle]

Why is -1/30 standing outside the parentheses?

[tropic coyote]

thats multiplying

sorry i left the distribution for later

[viscid thistle]

yes so… don’t u remove the term after multiplying

well i don’t know how you americans do it, but seems like we have our own methodology

[tropic coyote]

im not american

i mean yes im in south america

argentina

[viscid thistle]

Oh

Ohh

Hmm alright

well south america is still america

[tropic coyote]

its still another country

[viscid thistle]

[viscid thistle]

I know I was just joking

[tropic coyote]

oh good

i was almost horrified

[viscid thistle]

You couldn’t tell?

[tropic coyote]

nah sorry

sometimes im bad with sarcasm

[viscid thistle]

bruh

no problems

[tropic coyote]

anyways do you want to do the factoring yourself now?

[viscid thistle]

at last, I’ll try this dumb problem one last time

[tropic coyote]

because it seems we have different ways of doing it

[viscid thistle]

Yes

[tropic coyote]

small details though

[viscid thistle]

But wait, do you get -delta T/30 after multiplying delta T with -1/30?

[tropic coyote]

yes

[viscid thistle]

just to make sure

Okkk

[tropic coyote]

that actually does distribute

because its just multiplication

no exponentiation

[viscid thistle]

yeah

[tropic coyote]

anyways tell me if you need help

imma go to discussion

[viscid thistle]

so far this is what I have, any mistakes? @tropic coyote

this is the (10 + t)^3

h(10) i got 650/3 or 216.66

if it’s wrong then just say it

[tropic coyote]

nah thats right

at least first part

let me check 2nd one

yeah its right

[viscid thistle]

Ok… moving on

@tropic coyote agree?

the sum of h(10) is 650/3

of what I got

hello?

@tropic coyote Are you alive?

Sorry If I’m bothering you

[tropic coyote]

back

sorry i was afk went to bathroom

[tropic coyote]

yeah i think thats right

[viscid thistle]

Alright

[viscid thistle]

No problem

and now we subtract

[tropic coyote]

yeah you substract h(10+Δt)-h(10)

and then divide by Δt

[viscid thistle]

leaving only h(10 + T) cuz 650/3 - 650/3 equals 0

okay

[tropic coyote]

theres a slight error there

you also substracted part of h(10+Δt)

because the 2nd 650/3

comes from the expansion of h(10+Δt)

[viscid thistle]

What?

[tropic coyote]

oh sorry

just continue like you were doing before

and ill tell you if theres an error

[viscid thistle]

Alright

kinda made my heart jump

[tropic coyote]

every step up to what you showed me is right though

[viscid thistle]

Alright

[tropic coyote]

so even if you get a step wrong now you wont have to start from scratch

[viscid thistle]

now, i still have the multiplier-1/30

I’ll multiply it with all the terms

And this is what I’m left with

I feel like I’m doing a mistake here

[viscid thistle]

@tropic coyote

[tropic coyote]

back

let me check if the math works out

nah that parts wrong

sorry

[viscid thistle]

Bruhhh😭🔫

[tropic coyote]

I MEAN

HE

HEY

[viscid thistle]

ok where did I blunder?

[tropic coyote]

idk can i see how you did h(10+Δt)-h(10)

[tropic coyote]

why do a +650/3

[viscid thistle]

h(10) was 650/3

[tropic coyote]

yes

also you forgot the (5(10+Δt)^2)/2 part

[viscid thistle]

💀

[tropic coyote]

alright can i tell you how i would do it

like

an overview

[viscid thistle]

I always forget

[tropic coyote]

summary

[viscid thistle]

Ok tell me

[tropic coyote]

ok so

i got (h(10+Δt)-h(10))/Δt right

[viscid thistle]

yuh

[tropic coyote]

so you got ((10+Δt)^3)/-30 + (5(10+Δt)^2)/2 - 650/3 right

[viscid thistle]

yes

[tropic coyote]

now you can pick the same terms in the expansions of both of the parts of h(10+Δt)

to get 650/3

so you get 650/3 -650/3

and youre left with only numbers that are multiples of Δt

[viscid thistle]

only numbers that are multiples of T you say

[tropic coyote]

nah Δt

[viscid thistle]

Yeah

[tropic coyote]

remember we already set t=10

[viscid thistle]

Ohh

huh

[tropic coyote]

so t can't appear again

just Δt

[viscid thistle]

you’re not using limits?

[tropic coyote]

yeah im using limits

but im using Δt->0

sorry if we're using different variable names

[viscid thistle]

when i say t im reffering to delta t

[tropic coyote]

oh alright

yeah then

what you said

[viscid thistle]

i just don’t know how you get the triangle

but wait

[tropic coyote]

i got big keyboard

real

[viscid thistle]

if t approaches 0, then how do you set T equal 10?

[tropic coyote]

i really dont get how it's an issue sorry can you like

explain more

[viscid thistle]

because with deltas, we’re expressing a change from t1 to t2

[tropic coyote]

yeah

[viscid thistle]

so in essence it would be like saying delta t approaches 0, because the number is, well 0

with comma

if im not mistaken

and making a fool out of myself

[tropic coyote]

yeah basically

you can treat Δt as like

an "infinitesimally" small number

[viscid thistle]

Yes

so where does 10 come from?

[tropic coyote]

from the problem

the original wording of the problem

"find the growth rate at t=10"

[viscid thistle]

t is x in this scenario

[tropic coyote]

yeah you could think of it as that

[viscid thistle]

up until this point the book im studying always sets “lim delta x approaches 0”

[tropic coyote]

just notation difference

small detail

[viscid thistle]

So either Im genuinely missing something or plain stupid

i’d bet on the latter

[tropic coyote]

the problem is

you cant set Δt=0 directly 0

until you finish solving the problem

because of an issue

[viscid thistle]

what issue?

[tropic coyote]

we're also dividing by 0

Δt

so you have to wait until it's in an acceptable form to set equal to 0

[viscid thistle]

yes naturally

but I’m presupposing we have the denominator cancelled

[tropic coyote]

yeah but that happens later

meanwhile you have to treat Δt as if it werent 0

[viscid thistle]

ok, so continue where you left off

[viscid thistle]

.

[tropic coyote]

ok so from this part right?

oh

[viscid thistle]

mhm

[tropic coyote]

well once youre left with only numbers that are multiples of Δt in the numerator

you can cancel them out with the Δt in the denominator

[viscid thistle]

yes

[tropic coyote]

and you get some terms that do still have Δt

and some constant terms

the terms that still have Δt go to 0

so you can just erase them

cancel them

whatever

but the constant terms

turn out to be

-(300/30) + 5(20)/2

which adds up to 40

[viscid thistle]

Mhmm

[tropic coyote]

and the limit

[viscid thistle]

alright

[tropic coyote]

lim 40
Δt->0

is 40

[viscid thistle]

Yes

[tropic coyote]

because Δt doesnt do anything

so we solved the problem

Q.E.D

[viscid thistle]

whatever the last part means

but ok I’ll try it this time

[tropic coyote]

fancy math way of saying "LETS GO PROOF SOLVED HAHA YOUR MOTHER"

[viscid thistle]

@tropic coyote

ok… now it should be correct

did I make a mistake here?

is my 3T^2/2 correct?

3 times delta t that is???

[viscid thistle]

Wha?! 😭🔫

https://tenor.com/view/discord-mod-moderator-discord-moderator-delete-moderator-snitch-gif-27063075

[tropic coyote]

back

you got 40 so i assume its right

congrats

[viscid thistle]

No wait, check my calculations

please

is 5 multiplied with delta t^2 + (- delta T) ^ 2 = 3delta t ^ 2 / 2?

[tropic coyote]

alright let me check

[viscid thistle]

this plus this

[tropic coyote]

yeah i think its right

checked more critically now

5Δt^2/2-Δt^2 = 3Δt^2/2

its right

[viscid thistle]

Finally I can sleep in peace

[tropic coyote]

congrats

yay

[viscid thistle]

😭

Such a pathetic fool I am

[tropic coyote]

do you want any resources to keep learning math

or do you wanna take a rest

[tropic coyote]

nah its ok at least you got to solve it correctly

[viscid thistle]

It’s actually night now, and my time has come to sleep

[tropic coyote]

oh

its 6:47 for me

pm

[viscid thistle]

but I’m seriously considering staying up all night to read some crime & punishment and study

[tropic coyote]

i slept at 3 am today

but im on summer vacation so oh well

[viscid thistle]

Well it’s not exactly something a neurobiologist would recommend😅

[tropic coyote]

well lucky for you im not a neurobiologist

[viscid thistle]

I want to have a good sleep rhythm

[tropic coyote]

yeah i used to have a good sleep rhythm

like a week ago

idk why im staying up so late now

[viscid thistle]

I wanna sleep consistently at 11 and wake up at 8, but I have so low energy when I do that

For some reason I’m super active at nights

[tropic coyote]

same

[viscid thistle]

also I have an addiction to discord cuz i live in a dorm

[tropic coyote]

anyways

this isnt discussion

[viscid thistle]

so I’m pretty isolated from everyone

[tropic coyote]

so we should probably talk there

oh sad

[viscid thistle]

https://tenor.com/view/byuntear-american-psycho-staring-thinking-gif-26991038

you’re right

[tropic coyote]

cya there

[viscid thistle]

Well, thanks for the help, whoever you is

[tropic coyote]

im hsf, pro math sis B)

(explosion behind my back)

[viscid thistle]

😂

lol

funne

[uneven solstice]

im play a LOL

https://tenor.com/view/yalcinhero-gif-22726491

[willow dagger]

@quasi glade you are familiar with the idea of factoring a polynomial into linear polynomials right?

Just the concept, not the computations

[quasi glade]

yea turning some qx^3 + nx^2 + nx + p

into x+n or somethin

i got that

got that all day

theres this one specific thing i been lookin at

[willow dagger]

yeah so basically, what this relies on is the fact that you can write whatever polynomial this is in the form $f(x) = (x-a_1)(x-a_2)\cdots(x-a_n)$

[obsidian monolith]

nHail

[willow dagger]

The product of a bunch of linear factors

When you multiply this out you will get $f(x) = x^n + \text{( a bunch of stuff in the middle)} + a_1\times a_2\times\cdots\times a_n$

[obsidian monolith]

nHail

[willow dagger]

so the last factor is a product of all the roots

So from here you can see a restricted version of the rational root theorem:

if you have integer roots, they must divide the constant term.

Does this make sense so far?

[quasi glade]

i think this is stuff i know

but

Ill show what i got

Synthetic division i think is the part of this is confusing me

[willow dagger]

Okay, the second half is a bit weirder, but it explains the part about the denominator dividing the leading coefficient

[quasi glade]

this is an exmple problem i got coming from some video i look up

this whole process

trying to find roots of that polynomial

that process at the bottom i dont get at all

[willow dagger]

I'll admit I'm rusty on synthetic division, I don't think I was ever taught that

but I can explain the rest of the rational roots theorem if you want

[quasi glade]

idk

do you think i should check the help channels

talk in there maybe someone will know whats up

[willow dagger]

Yeah you can try, if you have a specific problem

[quasi glade]

idk this could be a specific problem but it could also be a broad concept

[willow dagger]

You won't get much success there with "can someone explain this entire broad concept" though

[quasi glade]

yea

i must reiterate my reading comprehension SUCKS so #❓how-to-get-help didnt really do much for me

maybe perhaps youtube

my beloved

[uncut mulch]

if you're struggling with synthetic division
start with polynomial long division

[quasi glade]

i know polynomial long division

[uncut mulch]

synthetic division is pretty much a condensed version of that

[quasi glade]

how so

[uncut mulch]

can you do polynomial long division for
(2x^3 -12x^2 + 22x - 12)/(x-1)

[quasi glade]

i can run that through rn

[uncut mulch]

and there's also a mistake in that image you posted

[quasi glade]

Idk I just copied half of what I seen

[uncut mulch]

either what you read was wrong, or you didn't copy it down correctly

[quasi glade]

boom get long divided

[quasi glade]

could be either, I just wrote that to convey my point

like what process I was yapping about

[quasi glade]

how do I get those numbers without doing the whole process

[uncut mulch]

multiply the sum to the root, in this case 2 * 1 = 2

then add

and repeat

[quasi glade]

so the term being multiplied is just z from (x-z)

okay

its clicking

it is beginning the long and strenuous process of clicking

if it would be x-6 then the thing we multiply by would be 6 leading to
2 0 22 120 at the bottom

which would make a polynomial 2x^2 + 0x + 22 + (120/(x-6))

so that wouldnt be a zero would it

or a root

or whatever

cuz that last addition needs to be 0 if i recall right

[uncut mulch]

correct

[quasi glade]

and x-1 would be a factor of the polynomial right

[uncut mulch]

yes

[quasi glade]

(2x^2 - 10x + 12) * (x-1) in the end

right

finally makes sense

i completely missed that unit last year I appreciate it

[viscid thistle]

can someone help me understand a problem that I’m facing?

[hushed sphinx]

If you'd describe your problem, the odds of someone being able to help would be much higher.

[viscid thistle]

Right

So here is my problem

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

find the tangent line at (2,0)

[hushed sphinx]

That looks more like #calculus.

[viscid thistle]

oh my bad

[narrow rain]

Does anyone know how to do this?😭

[viscid thistle]

trigonometry?

i dunno, all I know is SOH CAH TOA

lol

[shadow summit]

!da2a

[tender quest]

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/

[hushed sphinx]

They were already told that and posted their problem and moved to #calculus and got help there.

[shadow summit]

Take the derivative of f(x), and then plug in your point to fine the gradient. Then solve y=mx+c.

[viscid thistle]

aight bruh, habit

[shadow summit]

idk man, i learnt this stuff in precalc

[shadow summit]

did you end up finding it?

[viscid thistle]

Yes, appreciate the help though

[grim nimbus]

I have a question will anybody be able gto help me

A can do a piece of work in 10 days and B can do the same work in 15 days. If they start working toga=ether then in hiw many days can A and B can complete the work?

[narrow rain]

no. S= rθ (Help meee)

[viscid thistle]

bruv, I have no clue

I have my own shi to solve

[keen wharf]

yall help

i cant answer this BYEEE

[willow bear]

do you need/want help with this or not...?

[jagged pecan]

Do you know the answer for x I am getting the answer

[shadow summit]

Anything to the power of 0=1, so the inside of the log is equal to 0. Then solve for x.

[summer ruin]

log is undefined when the input is zero

[jagged pecan]

Ain't it sqrt(3) to what equal that term is 1 so we have to equate that term to sqrt(3)

[shadow summit]

No, x^0=1

[jagged pecan]

But as transparent elemental said log with input 0 is undefined

[shadow summit]

What?

[jagged pecan]

Like log base a input b means what to the base a equals b

So nothing to the base is equal zero

[shadow summit]

Wait nvm

I’m tired

[jagged pecan]

Which real number with how much power is equal zero

Isn't it undefined

[shadow summit]

You can just do sqrt(3)=(inside log)^1.

[shadow summit]

Yes, I wrote that at 2am, so I apologise.

[jagged pecan]

So my solution is right

Or not

[shadow summit]

Bro I wasnt even responding to your question.

[jagged pecan]

I am saying did you got the same solutions after solving it again

[shadow summit]

Idk bro I’m in my bed at 3am listening to MF DOOM and reading manga. I do not have it in me to do mental math.

[jagged pecan]

Kk

,ti

[obsidian monolith]

The current time for blunder69 is 10:31 PM (IST) on Mon, 11/12/2023.

[jagged pecan]

It's time for me to sleep btw

[shadow summit]

,ti

[obsidian monolith]

You haven't set your timezone! Set it using the interactive timezone picker with ,ti --set.

[shadow summit]

,ti —set GMT+10

[obsidian monolith]

Your timezone has been set to Etc/GMT+10!
Your current time is 07:03 AM (-10) on Mon, 11/12/2023.
Note that due to the POSIX standard, the timezone Etc/GMT+10 represents the time in GMT+10.
If your time is incorrect, consider setting your timezone to Etc/GMT+10, where the time is currently 07:03 AM (-10) on Mon, 11/12/2023.
You can read more about the standard at https://en.wikipedia.org/wiki/Tz_database#Area.

[shadow summit]

Eh that’s wrong

I’m going to bot channel

[jagged pecan]

Kk

[woeful cedar]

Bro someone help plz

[jagged pecan]

Whats difficulty is coming in solving 24sin^2x=24-12cosx

[shadow summit]

you can divide by 12 at the start, should make things a bit easier.

[willow bear]

try omitting the + 2πn in each one

you only want the solutions in [0, 2pi) not the general solution

can't tell if this is the only mistake but it is at least one

[jagged pecan]

After dividing by 12 both sides just put sin^2(x)=1-cos^2(x)

[jagged pecan]

It will be a quadratic in cosx

[shadow summit]

Not cos^2

[jagged pecan]

What it's an identity sin^2(x)+cos^2(x)=1

[jagged pecan]

I am saying to use that identity

[shadow summit]

That just feels like over complicating.

[viscid thistle]

hi guys

does x^(1/2) has lim at zero?

[limber patrol]

does not exist

because the left side limit does not exist

[viscid thistle]

x^(1/2) is square root of x. Square root of 0 is ...

[rocky wind]

Formulas of log: Let a, b > 0 and s be any real number.
definition of log: aˢ = b ⟺ s = logₐ(b). in particular, logₐ(a) = 1 and
common log: log(a) = log₁₀(a). in particular, log(10) = log₁₀(10) = 1
change of base formula: logₐ(b) = log (b)/log(a)
product → sum: log(ab) = log(a) + log(b)
power → multiple: log(aˢ) = s log (a)

[summer ruin]

limit of a sum is not equal to sum of limits in this case

(not that limits have anything to do with infinity arithmetic in the first place)

[rocky wind]

think: $\bZ \setminus 2\bZ = ?$, $\bZ \setminus (\bZ \setminus {1}) = ?$

[obsidian monolith]

vin100

vin100

[hushed sphinx]

On the other hand, the limit of -a + (a+1) is 1, and the limit of (100-a) + (a-58) is 42.
Knowing that two seqences diverge to -infty and infty is not enough to know how their termwise sum behaves.
So such limits would not be a good argument for defining a meaning for (-infty)+infty.

[silk needle]

is there any way to find the vertex here? how can I use the points?}

[mental sonnet]

hey every one i am a little confused what is considered precalculus

[hushed sphinx]

It's a chiefly American term for a loose collection of high-school topics about (single-variable) real functions that can be taught without using the concepts of derivatives.
The basic concept of function; graphing functions; asymptotes; domains and ranges; maxima and minima, monotonicity; sometimes linear functions; particular functions of mathematical importance (trig functions in radians, and their inverses, exponential functions and logarithms, rules for manipulating those). Sometimes a basic non-rigorous introduction to limits is given, at other times that seems to be postponed to actual calculus.
The name seems to indicate it is usually taught from a perspective of "don't even think this will be interesting or useful in itself, it's just a bunch of stuff you need to ~~know ~~ be able to do before you get to calculus".

[astral wyvern]

it seems that you’ve already determined that this can be modeled by a quadratic function, whose graph has reflection symmetry along a vertical axis. knowing this, do you see any 2 profits that are equal? and what does that help you conclude?

[midnight root]

help

[shadow summit]

Hey, would you mind giving a translation for each question? Without knowing the question I don’t have a way to help you.

[quaint heath]

how those are equal

<@&286206848099549185>

[viscid thistle]

2CC = C+C

[viscid thistle]

I.e, 2CosxCosy=Cos(x+y) + Cos(x-y)

[whole spruce]

Can someone show me how to do this question without graphing it.
A sinusoidal function crosses its minimum at ( 20 π , − 10 ) and then the next key point, its center at ( 24 π , − 8 ) .
a) Create a sine function that models this graph
b)Create a cosine function that models this graph
i know my amplitude is 2 and vertical displacement is -8, how do i find period and phrase shift?

[pearl tree]

i definitely just failed my precalc final

[empty salmon]

[shadow summit]

Skill issue

[warped cipher]

Sorry to hear that :(

[burnt hemlock]

i think i also failed my precalc test

[pearl tree]

I mean I won’t know until it’s graded but for sure did not study enough for the test I have an 95 currently in the class I’m just really wanting a 4.0 this semester

[pearl tree]

LET'SSSS GOOOOO i PASSED AND KEPT MY A

[smoky pendant]

can someone help me with this^

[proud raven]

where is sine maximized?

A and B will be the same distance from this argument

[smoky pendant]

at pi/2?

thats when sin is 1

[proud raven]

sure

so sin(C) = max -> C=pi/2

how far is A from C?

how do we know that B and A are the same distance from C?

[smoky pendant]

pi/4?

[smoky pendant]

since they're equal to each other

[proud raven]

,calc pi/2-pi/5

[obsidian monolith]

Result:

0.94247779607694

[proud raven]

noo

[proud raven]

this is wrong tho

[smoky pendant]

wait so its 3pi/10

so i add that to pi/2 to get b?

since its the same distance

so it would be 4pi/5

[burnt hemlock]

[lone palm]

I'm kinda lost

[shadow summit]

On the right side you have to simplify. Then use log(a)=log(b) therefor a=b rule.

[gaunt carbon]

yeah

dont forget subtraction becomes division when working with logs

[opal tree]

Make sure the coefficients of the logs are the same

[loud swift]

I need help with this problem

[obtuse mulch]

Think about what you need to have a vertical and horizontal asymptote

[loud swift]

Well how would you go about solving it

[elfin loom]

the question mentions k but it is not given in the function

are you sure that there is no printing error

[loud swift]

Oh the values ?

Its in the function at the numerator though

[elfin loom]

oh my bad

[loud swift]

This is the full problem by the way

[elfin loom]

for fx to have horizontal asymptote at y=0, the function fx must approach 0 as x approaches infinity

[loud swift]

Right

So plug in a big number?

[elfin loom]

no

[loud swift]

Oh

Well now I'm confused how would we do this

[elfin loom]

just compare the degree of numerator and denominator

we need y =0 for x approaching infinity

which means we need an x in denominator

degree of numerator<= degree of denominator

therefore k+2<5

k<3

[loud swift]

Wait but I thought 3 was wrong

[elfin loom]

answer can be 2 also

3 is indeed wrong

[loud swift]

But how would we get that answer

[elfin loom]

my mistake

[loud swift]

I did what you did

[elfin loom]

there would be no = sign in k+2<5

[loud swift]

Oh

Because it couldn't be equal

[elfin loom]

if there were an = sign then we would get k=3 and asymptote at y=1

we want asymptote at y=0

hence k+2<5 and not k+2<=5

[loud swift]

I see now I see now

Thank you so much

[quasi glade]

@woven compass you were typing

[blazing cobalt]

how do i learn limits

[shadow summit]

There’s a few ways, you can learn formally in your class, you can read a textbook, or you can watch videos on YouTube (Organic Chemistry Teacher and Khan Academy).

[blazing cobalt]

well

my teacher is pretty bad

the organic chemistry tutor is good

and khan academy i use too

but its confusing at times

textbooks dont really help

thing is

the school syllabus is pretty rushed

and it has the randomest stuff

and i have a test this week is why im concerned

[shadow summit]

How is the teacher bad?

[blazing cobalt]

rushed

gives us too much and unnecessary infromation

hard to process

and doesnt really care about every student

[shadow summit]

Dam that sucks

[blazing cobalt]

yeah

[shadow summit]

Limits are pretty easy though

If you are new to calculus the tldr of limits is just plugging numbers into the equation as they get closer to the number you want to actually plug in.

Take $\lim_{x\to0}f(x)=\frac{1}{x}$

[obsidian monolith]

TheLord26

[shadow summit]

Just plug in small numbers

You might start with f(1)

Then f(0.1)

Then f(0.00000001)

And you will see a pattern

As x gets smaller f(x) gets bigger

[blazing cobalt]

😭

[shadow summit]

So you then say the limit approaches infinity

There’s more advanced ways but for that I would highly recommend watching lectures on YouTube and working through text book questions.

[shadow summit]

?

[blazing cobalt]

i dont like limits

or calculus

[shadow summit]

Calculus is easy

Just gotta put in the time

It’s algebra with extra steps.

[grand sedge]

Yo bro

I need help

[blazing cobalt]

dont we all

😭

[grand sedge]

I don't really need help but like a tip

I have a ACT coming up

[blazing cobalt]

february ?

[grand sedge]

and I heard 12% of time pre calculus question is asked on it

I have no clue how to solve them

just want some tips to solve without even looking at it

[grand sedge]

yeah

[blazing cobalt]

good luck

[grand sedge]

thanks

last time I got 26 on ACT math

hoping for 30 or 31 this time

[blazing cobalt]

for realsies

[hushed sphinx]

In February should give you some time to start studying, but if you want to "solve without even looking at it", you're out of luck from the beginning.

[grand sedge]

i know but any tips