precalculus

[viscid thistle]

oh ur right i am illiterate

[gloomy vigil]

wait is wee wee a french word

[viscid thistle]

Bonjour

I believe it is qui qui

[gloomy vigil]

hmm

[viscid thistle]

who who

[fleet yew]

Imo a perfect language would have no conjugation

[viscid thistle]

indonesian?

[gloomy vigil]

a perfect language wouldnt even have the word conjugation in it

[viscid thistle]

Yo y=tanx is pretty nice

[fleet yew]

Conjugation adds nothing of value to language

[gloomy vigil]

there would be no term for conjugation

[viscid thistle]

y=cscx tho

Damn

[fleet yew]

It doesnt add meaning or complexity or subtlety it just makes shit harder

[gloomy vigil]

sounds like a fetish

[viscid thistle]

isnt it for pronounciation

and it does add stuff in tenses

[fleet yew]

English is actually my favorite language because of that

Because in english we dont really conjugate tenses all that much

We just use helping verbs

[gloomy vigil]

what do u think is the most obnoxious language

[fleet yew]

Like the future tense of run is just will run

[viscid thistle]

yeah there arent any like gender conjugations

[gloomy vigil]

you guys are fuckin smart, are any of u over 30

[fleet yew]

What about john stewart mill? @viscid thistle

Utilitarianism?

[viscid thistle]

Read on liberty

[gloomy vigil]

@viscid thistle dont lie i know ur like 45 years old even tho ur taking french

[viscid thistle]

i am conseetantly losing spatial awareness and any kind of awareness and forgetitng what i read and stuff

You might be dying

Jkjk

[fleet yew]

What does that have to do wih anything tho

[viscid thistle]

idk how to expand brane so i can actually think clearly

[gloomy vigil]

expand brane pls

[viscid thistle]

Sleep

[fleet yew]

Like i mean ig i kind of like his philosophy but i was just talking about language itself

[viscid thistle]

And eat healthy

[gloomy vigil]

drink plenty of water

[viscid thistle]

And get cardio

[fleet yew]

Lift wait

[gloomy vigil]

optimal approach is to do everything underwater

[viscid thistle]

aaaaaa

[fleet yew]

Get stronk

[viscid thistle]

I guess But make sure you stay active at least

[fleet yew]

Beat up people who accidentally make eye contact with you

[gloomy vigil]

a banana a day is fine

100 pushups, 100 situps, 100 squats

and a 10km run every single day

[viscid thistle]

No don’t fight

That can cause stress

Stress is bad for your brain

[fleet yew]

Yes fighting is healthy

[viscid thistle]

i went to school and there was pe i shure hope that enough exrsice

[fleet yew]

You need an outlet for physical rage

[gloomy vigil]

Fighting is human nature, as a result because humans are intelligent, human is human thus humanity wins

[viscid thistle]

lol i have stress from mental derangement

Breathing is better

Meditation

[gloomy vigil]

Pent up stress can cause you to malfunction by nutting in the wrong area

As a result, money is lost

[fleet yew]

How do you manage your aggression

Like all that anger you have inside of you

[viscid thistle]

Fighting to get rid of anger isn’t human nature

[gloomy vigil]

I take it out on math

[viscid thistle]

Human nature is socializing and moving a lot

lol i just kill people and then there is a lingering sense of guilt so i dont do it again and i havent ever since

[gloomy vigil]

yeah just leave the bodies in the trunk

[viscid thistle]

yeah

[gloomy vigil]

^

[viscid thistle]

wait voltage r u really in college

[gloomy vigil]

dude i cant believe they thought columbine was the first one

[fleet yew]

The guilt goes away after awhile

[gloomy vigil]

@viscid thistle i havent taken math in 6 years

[fleet yew]

Its all good

[viscid thistle]

oh

[gloomy vigil]

give me a break pls

xd

[viscid thistle]

how?

no i mean

not your math

[gloomy vigil]

man my highschool years...

[viscid thistle]

but your language sounds so gen-z

[gloomy vigil]

it's cuz i talk with a lot of people

[viscid thistle]

like you've spent more time on discord than anywhere else

[fleet yew]

Wait voltage are you like 30

[gloomy vigil]

no

[fleet yew]

You seem gen z lol

[gloomy vigil]

im 19

[viscid thistle]

@fleet yew how old r u

[fleet yew]

13

[gloomy vigil]

bullshit

[viscid thistle]

Lol ur young

Lmao

[gloomy vigil]

ur 13?

[viscid thistle]

oh

13

[gloomy vigil]

if ur 13 forreal, i fucking respect u so fucking much

[viscid thistle]

you're a smart boy

i hope i can be as smart as you one day

[fleet yew]

Im not a boy im a man

[viscid thistle]

Me too I respect u too let’s chat 😃

[gloomy vigil]

i honestly thought everyone here was like 30+

[viscid thistle]

Are you a female or male?

[gloomy vigil]

that just shows how dumb i am

i forget nowadays

people can get online at like age 5

[viscid thistle]

Never mind as long as you’re 13 we’re good

maybe i will able to spatially ortient myself soon

once i turn 20 i hear the brain gets some kinda boost after potberity

[gloomy vigil]

bro 13 is legal in japan

im jsut saying

[viscid thistle]

Ye

[gloomy vigil]

hit me up AMD teach em some math

bro coronavirus tho

[fleet yew]

Bruh japan would be slick imagine going to nintendo

[viscid thistle]

I stay away from the Chinese people in my school

[gloomy vigil]

LMAO

[viscid thistle]

Lol

[gloomy vigil]

dude it be like thta though

i feel bad for some chinese people

[fleet yew]

You could literally punch sakurai in the face

[gloomy vigil]

lotta them getting bullied cuz of this bs

[viscid thistle]

Funny thing is one of the smartest person in my grade is white haha

[fleet yew]

For not adding waluigi to smash

[gloomy vigil]

Waluigi wouldve been too overpowered

i respect it

[fleet yew]

Sakurai still needs to get his ass beet

[gloomy vigil]

tru

[fleet yew]

Just cuz

[gloomy vigil]

wait so ur not really 13 right

[fleet yew]

He has that sort of look on his face

Like the punch him in the face for no reason sort of look

[gloomy vigil]

yeah a punchworthy face

[fleet yew]

I mean i dont even really hate him but i mean

[gloomy vigil]

lmao

wait are u deleting ur messages

at the speed of light

[fleet yew]

Yeah that kid

[gloomy vigil]

or is my discord actin up

[fleet yew]

Erebus the retard

[viscid thistle]

Woah

[gloomy vigil]

smh erebus

[viscid thistle]

That’s offensive

You’”” offend Voltage

[gloomy vigil]

erebus u cant foo lme

ur not 11th grade

ur 69 years old

[viscid thistle]

I am

[fleet yew]

Sorry i hurt your feelings erebus

[viscid thistle]

Haha how’d you kno

[fleet yew]

Im too honest sometimes

[viscid thistle]

Omg u really r a genius

[gloomy vigil]

bro im a genius of idiots

that makes me have an IQ of like 69

[fleet yew]

Erebus kinda sus

[viscid thistle]

What’s sus?

[gloomy vigil]

erebus rhymes with sus

[fleet yew]

Use urban dictionary

[gloomy vigil]

bus can also be thrown under

[viscid thistle]

Stop bullying me

You’re going to make me cry

[gloomy vigil]

the great 69 is a sex term for the great alexander the great the greatest of greats

therefore he threw alexander the great under the bus when he was a 69 year old

he has sinned and must pay the price

[viscid thistle]

What are you on?

[fleet yew]

Sorry bro but ur deleting messages and that's kinda weird

[viscid thistle]

Stfu bro don’t judge me

[gloomy vigil]

I need some IQ

someone hook me up

every time you delete a message

I lose more IQ

dont do me like dat

[viscid thistle]

Goodnight bro

[fleet yew]

Pay an asian male to do your hw

[viscid thistle]

Friend me

[gloomy vigil]

bro an asian male to do my hw

can i get an asian female

[fleet yew]

No females r dum

[gloomy vigil]

fuck ur right tho

[viscid thistle]

Yo asian females are so sexy

[gloomy vigil]

bro i see

[viscid thistle]

https://www.wikihow.com/Increase-Your-IQ

[gloomy vigil]

so many asian females

sucking asian male dick

for their math skills and other skills

like legit

sometimes i wanna join in the group

lmao

be like, yo asian male, while u smashin that asian female, teach me some math

it aint no cockblock, she's probably learning while u smashin too

it's a win win scenario

[viscid thistle]

Yo I smash while I read out loud

[gloomy vigil]

dude read a soliloquy while 2 hours in session

and then rap eminems rap god

[viscid thistle]

Already did bro

Damn I’m so tired now

[gloomy vigil]

but here's the kicker, do it while u eating out.

[viscid thistle]

Goodnight

[gloomy vigil]

night

whoever made this discord is a fucking legend

[wraith idol]

thank you

[gloomy vigil]

nani ur name is whoever

[wraith idol]

hello

[gloomy vigil]

I have never done drugs or drank alcohol

but if you told me I did today

I might believe you

[wraith idol]

Ok

[gloomy vigil]

Yes

[wraith idol]

Have you learned calc?

[gloomy vigil]

I'm trying

My brain is low on IQ

[wraith idol]

Oof

Buy some fresh IQ

[gloomy vigil]

I need summa dat IQ

loan me some

[wraith idol]

Go to walmart or something

[gloomy vigil]

ill give u some interest

[wraith idol]

Eh just buy them from walmart

[gloomy vigil]

dont worry i can go deep negative IQ

[viscid thistle]

drinc covefefe

[wraith idol]

Oh hi zoph

[pale kettle]

okay can we not be racist jesus

[wraith idol]

?

???

[gloomy vigil]

did we have some racist in there, if so unintended i think

[fleet yew]

No we didnt

[gloomy vigil]

but apologies

[pale kettle]

unintended racism is still bad???

[fleet yew]

I dont think we did lol

[pale kettle]

plenty of sexism too

[wraith idol]

Bruh

Ok wtf

That was pretty sexist and racist

And tbh I am offended

[gloomy vigil]

rip

[wraith idol]

And how can racism be unintended?

That just means that you're already way too racist

[gloomy vigil]

it's definitely possible

might be too old lol

[wraith idol]

Hope you know that that's a problem

[gloomy vigil]

luckily we as humans can learn

that mistakes are mistakes

and as long as they arent repeated

all gucci

that being said tho

we do need to know what was the bad part

lol

[viscid thistle]

i repeat all my mistakes multiple times before my brain remembers what the fuck it is doing

[gloomy vigil]

im legitimately dumb so please take whatever i say with a grain of salt and warn me if i overstep my boundaries

nothin i say is meant to offend

that being said, i wanted to say somethin just now but i forgot so fuck me.

[fleet yew]

Lol imagine being racist in 2019

[gloomy vigil]

oh right i forgot to say

Culture

Culture is big as fk

i think in brazil or somethin people kiss each other even if they're strangers

if u do that in the united states, u catch a quick 30 year in jail rape charge

i think some dude named vic got something liek that might be wrong though

[fleet yew]

Let y=f(x)

[gloomy vigil]

x = (y-6)/1+8y
x+8xy = y-6
x+6 = y-8xy
x+6 = y(1-8x)
y = (x+6)/(1-8x)?

[fleet yew]

Yea looks good homie

[gloomy vigil]

thanks fam, does that seem like the optimal way ud do it?

i feel like hearing there's an easier way

might be wrong tho

oh damn it's 1 AM, scratch that i gotta wake up at 5 and get to the gym to avoid coronavirus

[fleet yew]

No you did it right

[gloomy vigil]

oh sweet

much love AMD

[fleet yew]

Now go sleep

[gloomy vigil]

i fucking love everyone here at the discord

you're all good people

bless you

[fleet yew]

👍

[scarlet jungle]

Can I get help for question 15?

It's the one where it says "finding the Cartesian equation, sketch the curve whose parametric equations are:
x=1/2...

[fleet yew]

@scarlet jungle solve for t

[scarlet jungle]

But how

I get that you need to use logs but I'm confused as to how to actually do the question

[serene heath]

@scarlet jungle did you figure it out?

you dont really need logs

[hallow flicker]

guys i am gay

[proud sparrow]

we don't care unless it's precalculus

[hallow flicker]

stfu

[pale bison]

[serene heath]

ok meliodas

[fluid shore]

No u

[warm crescent]

The mid points of the sides of a square of side 1 are joined to form a new square . This procedure is repeated indefinitely. Find the sum of i)the areas of all the square ii)the perimeters of all the square.

[languid crane]

geometric sequence

[coarse storm]

@warm crescent Haha, I had almost the exact same question on one of my exams.

What I highly suggest is drawing a diagram

Here is one that I drew

However the patter continues indefinitely

There I have worked out the length of the second square's side.

What do you think would be side lengths of the third and fourth square

and then see if you can determine a pattern

From there, you can use geometric sequences and series

[fleet yew]

This looks fun

And torturous

[viscid thistle]

How would I solve a question like this? "how to solve for k in an exponential continuous growth function"

[hallow flicker]

Can someone find a formula to represent this

Here is an example

Nvm I figured it out

[hallow flicker]

Need help with this

[rigid sun]

just simplify it

tf

what is 10^log(q*n)?

or better yet

combine it all

[hallow flicker]

Yea it’s fucked

Ok look

If you can help me figure out a formula for this

Here is an example for like a formula

I need a formula like this for the other one

[rigid sun]

move the 9 to the outside

[hallow flicker]

How is it gona help?

[rigid sun]

makes it simpler

[hallow flicker]

Not helping

Still really complicated

You there??

[pale bison]

so nothing inside your summation depends on B, correct?

[heady jewel]

n*10^n=10^n+10^n...n times

[hallow flicker]

Wait hold on replace the n with b

[heady jewel]

write it out for n=1,2,3..n

add

[hallow flicker]

No shit

[heady jewel]

all the equations

[hallow flicker]

But I need formula

[heady jewel]

youll get one

dw

its not that straightforward i think

[hallow flicker]

I know for this one but I have been trying the other one for a while still can’t figure it out

Guys

[rigid sun]

divide out a 10

@hallow flicker

did you divide out a 10?

my god

[pale bison]

[rigid sun]

im not quite sure how you're supposed to know how to do this

seems like this is very high level math

for pre cal

@hallow flicker did you divide out10?

not sure if you're expected to know polyalgorithms in pre calculus

because they use calculus to derive more polyalgorithm sums

tf

i guess you'll have to be like newton and literally invent calculus to finish your math homeowrk

[hallow flicker]

Doing it for fun

[rigid sun]

well

i don't think its possible to derive that without

higher levels of math

[hallow flicker]

What do I need to know?

[rigid sun]

clearly its not a simple geometric series or a arithmetic one

you'd need to know calculus at elast

least

beyond that aswell

[hallow flicker]

Ok that’s fine

[rigid sun]

one se

one sec

it should be this

$\sum= 9/10 (\frac{1-(n+1)10^n+n * 10^{n+1}}{81})$

tf

[hallow flicker]

Lol

[pale bison]

$n\sum_{n}^{n}n$?

[obsidian monolith]

Publius:

[rigid sun]

fok u

[obsidian monolith]

maleb1964:

[rigid sun]

there it is

test it for yourself

n is the number you end on

lets try 3

[hallow flicker]

How did you figure it out tho?

[rigid sun]

im a god

1+20+300=321

[hallow flicker]

No for real

[rigid sun]

,w calc (1-4000+30000)/81

[obsidian monolith]

Display results online and refine query

Requested by maleb1964#6739

[rigid sun]

gottem

[hallow flicker]

Wtf

Wait let me see

[rigid sun]

this is for just

the 321 is before I multiplied the 9/10

both sums are 321, and obviously when you multiply both by 9/10 you'll still get the same thing

so the real sum should be

,w calc 321*.9

[obsidian monolith]

Display results online and refine query

Requested by maleb1964#6739

[rigid sun]

that

[hallow flicker]

Did you use the Taylor series or something?

[rigid sun]

more than that

[hallow flicker]

Explain

[rigid sun]

that would be long

[hallow flicker]

Just do it

[rigid sun]

no dude

like really long

[hallow flicker]

Or show it on paper

[rigid sun]

read this

[hallow flicker]

Then I don’t believe you

[rigid sun]

https://archive.lib.msu.edu/crcmath/math/math/p/p478.htm

this was before indians started making tik toks btw

[hallow flicker]

Do you actually have a PhD?

[pale bison]

what's the original problem?

[hallow flicker]

Ur mom

[pale bison]

k

[pale kettle]

is this a joke uh

this is just a geometric series

[floral tide]

polylogarithm

precalc

[sturdy haven]

What does the notation f o g(x) and f(x+c)

Mean

[viscid thistle]

f o g(x) means f(g(x))

f(x+c) is just moving a graph left or right, c is some constant I would guess. so f(x+c) = f(x) if c=0

depends on the context

[fleet yew]

f o g

[rigid beacon]

f(x+c) means sub in x+c for x in the function

Which results in a horizontal shift of f(x) yes

[sturdy haven]

Which way

Left or right

[rigid beacon]

depends on the sign of C

if C is > 0, left C

if C <0, right C

[odd helm]

I’m having trouble graphing g(x) could someone explain what I should be doing

[rigid beacon]

try graphing it without expanding it out or send your work of you expanding it out @odd helm

[fleet yew]

$g(x)=\frac{-4x^2}{21}+\frac{40x}{63}$

[obsidian monolith]

AMD:

[sharp marsh]

So how do I set this up?

I don't know what to do with the H

[trail badge]

If $f(x)=5x²-7x$, so probably you have to substitute that in $&f(x+h)$

[obsidian monolith]

Digicat195:
Compile Error! Click the reaction for details. (You may edit your message)

[trail badge]

Like $5(x+h)²-7(x+h) - 5x²-7x$

[obsidian monolith]

Digicat195:

[trail badge]

Idk if is that....

[empty fulcrum]

You've got the right idea

[patent beacon]

@sharp marsh
f(x) = 5x² - 7x
f(u) = 5u² - 7u
f(👌) = 5👌² - 7👌

What's f(x + h)?

[viscid thistle]

if I had to guess 5 ^2 - 7

[empty fulcrum]

You'll plug in (x+h) for every instance of x

[trail badge]

[half aspen]

I need mega help with a problem

Lemme show you what it is

[viscid thistle]

Explain why the sin-1 (-2) and cos-1 (-2) would produce an error message on your calculator, but tan-1 (-2) and sec-1 (-2) would not.

[empty fulcrum]

For that question, thing about the domains and ranges of the sin/cos functions and their inverses

[viscid thistle]

@half aspen use law of sines

since c is the hypotenuse, <c is 90 degrees

and now you know <a

[half aspen]

hold up

[viscid thistle]

and then you can use everything els

e

[half aspen]

what on earth

I'm only in high school pre calc and we haven't learned this

[viscid thistle]

the law of sines?

you learn that in algebra 2

[half aspen]

Not that I know of

[empty fulcrum]

You don't need law of sines for that problem

[viscid thistle]

look it up its easy to use

[half aspen]

Lemme think here

[empty fulcrum]

You can just use the Pythagorean theorem and rearrange for whatever you want to solve for

Then use your final leg to get the other angles

[half aspen]

Ok

But I need someone to show me vecause Ive tried this two times

And I've still got it wrong sadly

Like I drew the triangle

[empty fulcrum]

Well, you already know the other two angles

[half aspen]

How tho

we only know B

And B is 16

[empty fulcrum]

Well, it's a right triangle isn't it

[half aspen]

oh my

[empty fulcrum]

So you know C as well
C is 90 degrees

[half aspen]

im so stuuuupid

[empty fulcrum]

Lol it's ok

[rigid sun]

ik

[empty fulcrum]

Just be sure to read through the problem

[half aspen]

ok thx so much seriously

means a lot

But just one question

[empty fulcrum]

You know how to solve for the other legs, right?

[half aspen]

That's what I was just about to ask

[empty fulcrum]

Do you know how to use an inverse trig function to find a leg?

[half aspen]

sec?

and csc?

and cot?

[empty fulcrum]

Sorry, mathematical inverse, not reciprocal

[half aspen]

ohhhhh yeaaaaaa

[empty fulcrum]

Like sin^-1

[half aspen]

Yeaaaaaaaa

yessss

[empty fulcrum]

Try that

[half aspen]

ok lemme try dat here

[empty fulcrum]

Just a little bit of algebra should get those legs for ye

[half aspen]

ok

ill keep you updated

ok i'm still lost for some reason, im really sorry

[empty fulcrum]

Don't apologise, that's what we're here for

What's got you stuck?

[half aspen]

lets see

im stuck on the idea of how to use the invereses to find the legs. Like I've dealt with using them to find angles

I'll show the problem again for reference here

[empty fulcrum]

Let's go ahead and set up one of the problems
I'll show you the steps for one, snd leave it to you to find the other

[half aspen]

Ok

So first off we've got b being 12. And then Angle B being 16 degrees

[empty fulcrum]

Can you see what I've done here?

[half aspen]

Yep I can

Lemme just analyze this

[empty fulcrum]

Oops one sec

[half aspen]

It's ok I have the original on another tab

[empty fulcrum]

I had the inverse backwards, make sure you account for that

You should get 43.5355

[half aspen]

ok

[empty fulcrum]

Looks like you rounded wrong in your answer

[half aspen]

ohhhhhhhhh noooooooo

Oh my god

[empty fulcrum]

Hehe it's ok

[half aspen]

im literally dying in laughter rn

[empty fulcrum]

But now we know

[half aspen]

ye

and then we can just do pythagorean theorem

[empty fulcrum]

Yeye

[half aspen]

ye boiii

[empty fulcrum]

Anyways, you know in the future that Sin(B) or whatever is equal to that ratio 12/c

[half aspen]

ok

[empty fulcrum]

And you can take advantage of that in the future

[half aspen]

ye i will

thanks so much

ill come on here again if i have any more questions

[empty fulcrum]

Good luck!

[half aspen]

thanks!

[sharp marsh]

@patent beacon f(x+h) = ((5x² - 7x) + h)?

[patent beacon]

Nop. That's taking an h and adding it to the end

f(x) = 5x² - 7x
f(u) = 5u² - 7u
f(👌) = 5👌² - 7👌

You are taking every x in the equation, and replacing it with an x + h

[viscid thistle]

how would you do this
A circle has a radius of 10 and a chord of 16. determine the distance from the midpoint of the circle to the midpoint of the chord
it says 6
but how do you get that?

[sharp marsh]

@patent beacon Wait I'm confused

how does that work?

Cause x doesn't = x+h

[patent beacon]

f(x + h) is the same as f(x), except there's an x + h everywhere that x was

@sharp marsh

[sharp marsh]

But isn't there a + h?

I don't understand how f(x) is equivalant to f(x+h)

[rigid beacon]

Say f(x) = e^x

f(2) = e^2

f(u) = e^u

f(x+h) = e^(x+h)

@sharp marsh

x =/= x+h

but when we say f(x+h)

we mean REPLACE all the inputs in the function with x + h

[sharp marsh]

got it

😄

[vernal spindle]

Am I doing this question right

[stuck lark]

@vernal spindle gj

[vernal spindle]

Am I suppose to connect the points or anything else

[stuck lark]

why

[vernal spindle]

Just curious

[stuck lark]

for what reason

[vernal spindle]

Since I haven't drawn one of these before but it shouldn matter it would be correct either way right?

[stuck lark]

connect which points?

[vernal spindle]

like the line with one of the points

[empty fulcrum]

Nope

It's discontinuous

Are you familiar with discontinuous graphs?

[stuck lark]

like the line with one of the points
wdym

[vernal spindle]

like this or something

[stuck lark]

that doesn't make f a function anymore

[vernal spindle]

ahh I see, makes sense didnt think of that

[sterile kernel]

Hi, i have a question: after we apply binomial expression to (1+dx/x) where did this x^40 go?

[stuck lark]

factor: $x^{40}\sbr{1+\frac{\delta x}x}^{40}-x^{40}=x^{40}\br{\sbr{1+\frac{\delta x}x}^{40}-1}$

[obsidian monolith]

RokettoJanpu:

[sterile kernel]

I get it now! Thanks! :)

[stuck lark]

you're welcome

[viscid thistle]

that doesn't look like precalculus

that might be postcalculus

[hallow flicker]

Figured it out @rigid sun

[viscid thistle]

A little bit later can someone help me with graphing tangent functions?

[gloomy vigil]

x^2 - 2x = 5

x^2 -2x -5 = 0? Quadratic formula?
-b+- sqrt b^2 - 4ac

all over 2a

=
2+-sqrt24
all over 2

make them each diff fractions 2/2 = 1 +- sqrt 24 which is sqrt4 * sqrt 6 = 2sqrt 6/2 = 1+- sqrt 6?

yo can someone jog my memory on this stuff real quick

i think log2 6sqrt64 wouldve worked but

[uncut mulch]

bad text, don't write 6th-root() as 6sqrt()
try writing the radical as an exponent with a base of 2

[gloomy vigil]

hmm

[waxen yoke]

looks like 6(sqrt(64))

[gloomy vigil]

im totally stumped

oh wait

no im not

log2 7sqrt 8^2

shit i did the

bad text again

log2 6th-root(64)

log2 7th-root(8^2)

this is then log2 of 8 and that's 3

[uncut mulch]

this is then log2 of 8 and that's 3
what about the rest of it? that isn't what you currently have

[gloomy vigil]

uh

log base 2 64 ^1/7

yep im having a stroke

[uncut mulch]

and 64 = 2^?

[gloomy vigil]

64 = 2^6

[uncut mulch]

yes

[gloomy vigil]

oh

im back in action

log base2 2^6

2^6/7*

[uncut mulch]

don't forget about the ^(1/7)

[gloomy vigil]

right

[uncut mulch]

and parentheses

[gloomy vigil]

so it's like

log base 2 2^6(1/7)

which is log base 2 2^(6/7)

logbase 2 cancels the 2 and the result is 6/7

[uncut mulch]

bad placement of paranetheses in the second line

[gloomy vigil]

uh

[uncut mulch]

log base 2 (2^6)^(1/7)

[gloomy vigil]

right i forgot that it's another exponent

wait so it's 6^ 1/7

[uncut mulch]

or log base 2 2^(6(1/7))

[gloomy vigil]

oh right

law of log lets me move the 1/7 to outside

so it'd end up being 1/7 * 6 = 6/7

hm dam my brain

\

ok i think i understand fully now

another problem is

log base 3 7throot of 81

this results in

log base 3 (3^4)^(1/7)

1/7 moves out in front and the log base 3 cancel, 4 * (1/7) = 4/7

[viscid thistle]

loga a^1/7 = 1/7

[uncut mulch]

that works

[gloomy vigil]

😓

phew

thanks for the help

i think im back on track now

i need to like learn how to write things online properly tho, keep using wrong terminology and bad parentheses placements

much love thx again

[pale bison]

no problem

[gloomy vigil]

applying some mastery

2^(2x+1) = 8^(3x)

logbase 2 2(2x+1) = logbase 2 8 ^(3x)

2x + 1 = 3x(3)

2x+1 = 9x -> 1=7x x = 1/7

[pale bison]

yeah that works

[gloomy vigil]

thx boss

[gloomy vigil]

3^x = 8

what's 3^x+2

is this some log shenanigans

logbase 3 3^x cancels out leaves only x = logbase 3 8

3^(logbase3 8)+2 =

im guessing the 3's cancel out and then it's 8 + 2 for = 10?, although.. i dont think so

[clever inlet]

I mean

There's a simpler way to do it

[gloomy vigil]

teach me the way pls 😮

[clever inlet]

What happens if you multiply both sides by 3^2?

[gloomy vigil]

hm

3^x = 8

(3^x)(9) = 72

[clever inlet]

Yes

Now what can we rewrite 3^x * 3^2 as?

[gloomy vigil]

hm

that's gg but how did you come up with the 3^2

is it just something to see

and notice etc

[clever inlet]

3^(x + 2) = 3^x * 3^2

[gloomy vigil]

gotcha

wow that's neat

thanks fam

[neon garden]

Can anyone help me with question 5? I understand the basics of the theorem but what I’m confused on is how you show that f has a zero between a and b

[uncut mulch]

describe the theorem

[neon garden]

In the orange

[uncut mulch]

and do you understand it completely?

[neon garden]

I think I get the basics

So if you pick a point of the y axis, and draw a line to the graph, the corresponding x point will be between a and b

If that makes any sense xD

[gloomy vigil]

i read it about 6 times and still don't understand

[uncut mulch]

no

[neon garden]

It made more sense once I watched a khan academy video on it

No?

[uncut mulch]

takes on every value between f(a) and f(b) in the interval [a,b]

[gloomy vigil]

🤔 hm

[uncut mulch]

eg for a polynomial f, if
f(a) was 0 and
f(b) was 1
then f takes on all the values from 0 to 1 in the interval [a,b]

[clever inlet]

I mean

I just picture it as imagine drawing the curve

[uncut mulch]

^

[neon garden]

Am I understanding this right?

[gloomy vigil]

so it's all the stuff between a and b

[neon garden]

Ok I think I get what you are saying

so going back to question 5

[uncut mulch]

that graph isn't labelled properly

[neon garden]

how so?

Should the endpoints just be a and b, not f(a)?

[uncut mulch]

points aren't a single value

[neon garden]

oh yeah

[uncut mulch]

you also don't label coordinates as x or y

x and y are the axes

[neon garden]

yeah ik it was just a quick example

shouldn’t have used those variables

but is the basic principle right?

[uncut mulch]

x-coordinates at those lines are a and b

well, that's just a graph

but do try and apply what you think, to Q5

[neon garden]

Ok so for number 5 I got f(3) equals -2 and f(4) equals 10.

Now this is where I’m confused

how would you use the theorem to prove it?

[clever inlet]

Well

0 is basically

Not positive or negative right?

[neon garden]

Yeah

[clever inlet]

So if f(a) and f(b) are different signs

What does that tell you about the interval [a, b]?

[neon garden]

it includes 0?

[clever inlet]

Yes

[neon garden]

Oh now I get it

[gloomy vigil]

O_O

[clever inlet]

Note

It tells you that it includes at least one zero

It may contain more

We don't know

And for the context of this question

We don't care

[neon garden]

So if f(a) and f(b) are the same signs can you still use the theorem and prove it?

[clever inlet]

If it contains the same signs

It may have a zero

It might not

It's not conclusive

[neon garden]

Ah

So all your looking for is the opposite signs?

[clever inlet]

Sometimes you can subdivide the interval further and check that

Yeah

[neon garden]

Alright I get it now, thanks a lot

[gloomy vigil]

how would you explain the definition of continuous?

in regards to functions i guess

[clever inlet]

A very handwavy description would be again

Imagine drawing the curve

Otherwise just consider limits

[gloomy vigil]

i c

[neon garden]

For 31 b the answer key tells me the answer is -abc can anyone explain why that is?

[uncut mulch]

what's the x-coordinate of the y-intercept?

[neon garden]

0

oh

I’m so dumb

thanks

[gloomy vigil]

oh shit that makes sense

lol i was looking at A instead of B

[full garden]

hey guys can I ask a question please

[clever inlet]

🤔

[full garden]

right here the book says the transformation has a K value of 1/3

[clever inlet]

🤔

[full garden]

but here it says that the a value is doing the transfomration by 4

[gloomy vigil]

[full garden]

why does the first one get affected with the K and not a

and likewise for the other one

[clever inlet]

What is a

What is K

[uncut mulch]

can we get more context?

^

[full garden]

I can't tell becasue like the problems that I see the K is inside of the bracket

[uncut mulch]

transformation of what?

[full garden]

it's for transfomrations

horizontal and vertical

why does the first one have a horizontal and not vertical

horizontal stretch

sorry I am very bad at explaining

[sleek pawn]

what is K equal to?

[full garden]

for horizontal stretch / compress

[valid violet]

I think i see what he's asking

If you have a scalar multiple in a function

Is it dilating the x or the f(x)?

I think that's the q

[full garden]

this one guys sorry for not explaining well

[valid violet]

Yeah so there's nothing special about the letters k and a, your question is

[full garden]

sorry

[valid violet]

When something is multiplied by a number

[full garden]

yeah

[valid violet]

Its okay

[full garden]

thank you

[valid violet]

Is it scaling the argument x of the function, or the f(x)?

I have to go but that's your q

[sleek pawn]

that looks weirdly like a sine or cosine

[hexed scaffold]

pls rich

[full garden]

noo bro I haven't gotten to that yet

it's says g(x) is parent function of the square root function

[valid violet]

For the first q

[full garden]

what is the tranformation of this

yeah

[sleek pawn]

well just solve for k ig?

[valid violet]

x is being scaled by 1/3

f(x) is being scaled by 1/sqrt(3)

It's both

[full garden]

I thought it would be three

bro why is it 1/3 and not just 3

[valid violet]

And i really have to go now gl

[full garden]

thank you bro

guys can someone please tell me why x is being scaled by 1/3 and not 3

[sleek pawn]

I'm going to try...

[full garden]

please bro

[sleek pawn]

ok so... g(x) is being inserted into that function you showed earlier?

[full garden]

yes bro

[sleek pawn]

oh

yeah then it's simple

[full garden]

4 u

[sleek pawn]

so basically, you can break it up like this

[full garden]

yes bro

thank you btw for helping me

[sleek pawn]

$\sqrt{\frac{1}{3}x}$

right, np

[obsidian monolith]

A regular kugelblitz:

[sleek pawn]

do you see it now?

[full garden]

oh yeah

bro and this is the same thing it's on top so it's being multiplied by 4?

[sleek pawn]

well yeah

1/x times 4

so you get 4 on top

[full garden]

thank you so much bro thank you idkh I wasn't able to see that

thank you so much for your help

thank you

[sleek pawn]

no worries

it's really just about practice

[full garden]

bro do you like do all the questions from the school's book + an outside of school book to get this good

do you get 100 in every test 😆

[sleek pawn]

I actually do really bad at tests, lmao

[full garden]

oh

[sleek pawn]

yeah but it's about trying ig

[full garden]

you're very smart tho

[sleek pawn]

nah not really, it's fairly simple once you get it

[full garden]

bro but how do you keep up with like math along with other heavy subjects like chem and physics

[clever inlet]

🤔

[sleek pawn]

well they're not that math heavy

[full garden]

I am kinda stupid so I don't really have patients for all of them

[sleek pawn]

but I also suck at physics and chem

so

lmao

[full garden]

I mean yeah but like their own principals and stuff

bro if you come to my school, my teacher would like litearly fall in love with you

she likes smart kids

at math

[sleek pawn]

eh

I think everyone is quite bad at it in the beginning

so you shouldn't give up even if you don't get it at first

and then it'll get easier

you don't really need to be smart or anything

[full garden]

really

bro

[sleek pawn]

yup

[full garden]

but what if like the teacher you know never brings any questions from the book

and they are extreemly different to what she tought

[sleek pawn]

ask as many questions as you can

[full garden]

like last week we were taught the domain and range for like the basic parent fucntions

and I thought I was the sh!t 😆

but then I got many of them wrong

so I feel like you know, intelligence is required bro

[neon garden]

Nah it’s just work

[sleek pawn]

nah, just practice

mhm

[full garden]

lmao you guys are actually motivating me to work harder rn fr

[sleek pawn]

ofc! haha

yeah it's all about that

[full garden]

bro I think I should be appreciative that us 16 year olds are doing this stuff, while in other countries are doing calclus by that age

right bro

like some kid told me that in his country in Albania kids our age are doing calc 2 intro

[sleek pawn]

oof

[full garden]

yeah bro I feel really dumb and I should be 😆

they are doing like Canadian uni math in hs

[neon garden]

I’m taking pre-calc next year but I’m working on it rn, just so next year feels like a breeze

Makes it a lot less stressful

[sleek pawn]

I'm actually taking calc rn, lol

but yeah

just like, use that as an incentive

[full garden]

nice bro

did you do advanced functions at school yet

[sleek pawn]

advanced functions?

[full garden]

yeah I think it's like a prerequisite for taking calculus in grade 12

wait are you in Canada or the US

[clever inlet]

[sleek pawn]

none, lol

what are advanced functions about?

[sleek pawn]

are they like... transcendental functions?

exp, log, trig, etc.

[clever inlet]

[full garden]

they are all thinngs you can do at sleep

[sleek pawn]

@clever inlet I swear that's what they're called in my curriculum

right, yeah they aren't that complicated

[full garden]

4 u

[sleek pawn]

no it's not about intelligence really

just practice

it might look hard but hs math isn't hard

it just takes patience

[full garden]

thank you bro

[sleek pawn]

no worries

[full garden]

but do you like physics class more or math

[sturdy haven]

I have a question

[sleek pawn]

idk, I haven't taken physics in a while, lol

[full garden]

like this is gonna make me sound extremely ignorant but I feel like phsics is more practical bro imo

[sleek pawn]

yeah no ofc

[full garden]

it's not all about finding domain and range and intercepts

I feel like it actually you know solves real life problems

sorry @sturdy haven

[sturdy haven]

Im taking an exponential functions test tomorrow and I pretty much understand it, but one part is confusing

how do I change the units of time for an exponential function

[clever inlet]

[sleek pawn]

right

[sturdy haven]

Like if it is in every hour how would I change it to minutes or days

[clever inlet]

Multiply

Or divide

I mean

[sleek pawn]

yeah, you still have to express the quantity in hours

so for example if you have a day, that's 24 hours

[sturdy haven]

So how would I do that

[sleek pawn]

multiplying or dividing

let's say you have 4 days

if each day has 24 hours you multiply by 24

so you get 96 hours

[sturdy haven]

So t/94

[sleek pawn]

no no

the coefficient of t is another thing

what does your problem look like?

[sturdy haven]

If a population starts with 3000 bacteria and it increases at a rate of 32 percent over an hour

How much is its daily rate of increase

[sleek pawn]

ok I'm surprisingly rusty on this, lol

but looking at my notes I think this is what you have to do

well first of all set up your function

3000e^0.32t

right?

oh wait

no I'm wrong, sorry

so 3000 is your initial population

P_0

hmmmmmm

brb

[viscid thistle]

mind if I ask a question from my hw?

[sleek pawn]

I suppose not

hold on though

@sturdy haven I'm back. ok so you do that thing I sent, the function

[sturdy haven]

?

[sleek pawn]

yeah 3000e^0.32t

and then plug in the 24 hours

[sturdy haven]

I think thats wrongf

[sleek pawn]

right

no yeah I see it

lol

there's something I'm missing

[sturdy haven]

It should be 3000(1.32)^t24 I think

Because the twenty four t is still in hours

It is just always being multiplied to make a day

[sleek pawn]

ok so your base would be the 32 percent?

I don't remember exp functions before e

my notes say it's like P_0a^rt

you plug in t and find r

but is a=0.32?

[sturdy haven]

Thats continuosly compounded interest formula

[sleek pawn]

no continuously compounded would have e in the place of a

[sturdy haven]

Ohh

No the rate would be 1.32

[sleek pawn]

yeah I think I get it now

hmm?

oh right

mhm it's increasing

[sturdy haven]

Because if it is just .32 that is saying that only 32% remains

[sleek pawn]

yeah yeah, you're right

so just solve for r now

[sturdy haven]

So if it is increasing the units from smaller to larger, I multiply, I and if it is decreasing them, I divide?

[sleek pawn]

yeah

but I mean you want to find the rate

[sturdy haven]

Thanks

[sleek pawn]

the rate isn't 24

like, you have this: 3000(1.32)^r(24)

[sturdy haven]

Rate is 1.32

[sleek pawn]

no that's the base

[sturdy haven]

No its time

[sleek pawn]

iunhjeiuahyefyuhaf

[sturdy haven]

Time x 24

Loll

[sleek pawn]

is it?

if you plug that then what's there to find?

[sturdy haven]

Nothing

[sleek pawn]

hmmm

I'm not sure that's completely right

no yeah it is

sorry if I made it confusing

there you go

[viscid thistle]

whats the question

[fresh sparrow]

I got A. Although my book says B?? How did they get B???

Please @ me

[harsh cipher]

question

Why divide (pi/2) / 4?

is it because the first grid has only 4 squares?