precalculus

[small creek]

you'd have to differentiate them if you want to do it algebraically

[novel cargo]

I can differentiate them, but that's not enough

[small creek]

then you equate both derivatives to eachother

so you find the x value where they have the same slope

[novel cargo]

we still need more constraints tho, there are infinitely many solutions

[past meadow]

are there?

.

[novel cargo]

yeah, give me a sec

this is the graph of the equations

there are inifitely many points on the graphs with equal slope

[past meadow]

there are inifitely many points on the graphs with equal slope
@novel cargo

thats not the only condition

you need for them to share a tangent

[novel cargo]

I know

I'm curious how I would set this up algebraically

here's one solution

there is also a second

But, I'm not sure how to set up the equation to come up with the solution

[past meadow]

anyway arz you can set up equations for the tangent lines in terms of their points of tangency (say (a,a^2) and (b,-b^2+6b-5)) and equate coefficients to get a system of equations

[dawn oar]

rip

[past meadow]

which you can solve for a and b

you did intrude on a unanswered question

use #questions channels ig

it was about 20 seconds this time but don't worry about it

[novel cargo]

I see Sneaky, I tried that path but wasn't confident enough and confused about details

[past meadow]

alright, show us where ya got stuck then

[novel cargo]

yeah, this was from a few days ago.

let me do it and come back in a few mins

thanks btw

I'm sorry, I have to go. Will do this later and come back.

[past meadow]

no worries.

[viscid thistle]

how do you find the coordinates of a point on a function when you are given the gradient of the tangent at the point?

[past meadow]

are you given the function?

[viscid thistle]

yep

[past meadow]

since you havent provided the actual question, ill use f(x)=x^2 with the point where the gradient is 3 as an example

[viscid thistle]

alright

[past meadow]

i assume calculus is allowable?

[viscid thistle]

yeah

[past meadow]

so $\frac{dy}{dx}=2x$

[obsidian monolith]

Sneaky:

[viscid thistle]

yep

[past meadow]

so at the point where the gradient is 3

$\frac{dy}{dx}=3$

[obsidian monolith]

Sneaky:

[past meadow]

follow?

[viscid thistle]

so 3=2x?

[past meadow]

yes

and that gives you the x coordinate where you've got that gradient

[viscid thistle]

so x is 3/2 and f(x) is 2.25

[past meadow]

,calc 9/4

[obsidian monolith]

Result:

2.25

[past meadow]

yes

which means the point is (3/2,9/4)

[viscid thistle]

thnx mate

[past meadow]

nw

[viscid thistle]

hi guys @!@

[viscid thistle]

any one @!@

[bleak lance]

May someone please help me find the x-int and y-int for the equation x^2+y^2-2x-8y-19=0?

[viscid thistle]

@bleak lance x-int = 1+2sqrt5 , 1-2sqrt5 y-int= 4+sqrt35 , 4-sqrt35

@bleak lance and also if u need the method just hit me up @!@

[viscid thistle]

!@!

[novel cargo]

the derivative of that is: $\cos{x} - \sin{x} + \sec^2{x} -\csc{x}\cot{x} + \sec{x}\tan{x}-csc^2{x}$

[obsidian monolith]

az:

[novel cargo]

the period is 2pi starting at zero

the mins occur when the derivative crosses zero from negative to positive

this the graph of the derivative

[blissful ridge]

I'm pretty sure, you are not supposed to find the zeroes of the derivative

It's virtually impossible to do

[novel cargo]

I'm exploring. Appreciate if anyone else teaches both of us 🙂

this the graph of the original equation

this also contraticts my previous statement about the mins

the min, not proven, just eye balled, is -inf and it occurs at about pi/2 + 2npi and 2npi

<@&286206848099549185> please correct me and elaborate on this problem, you saints in this dark times

https://media.discordapp.net/attachments/363224154469826562/750760771167977493/Screenshot_13.png

original problem by @viscid thistle

[rigid beacon]

is that supposed to be in absolute values?

cause if it isn't there is no minimum

[blissful ridge]

Yes, it is

[rigid beacon]

you can't say the minimum = -infinity

ok

so then it's not -infinity

cause absolute value makes it so that the range can only potentially be 0 -> infinity

[viscid thistle]

is that supposed to be in absolute values?
@rigid beacon yah

[rigid beacon]

ok so it's not -infinity

after that goddamn that's a hell of a function

[novel cargo]

that's just the teachers way to make you memorize trig derivatives I guess

[rigid beacon]

this is precalc

so no derivatives

[viscid thistle]

its bad idea to use derivitive cuz it six things

[rigid beacon]

have you learned what derivatives are?

and how to find them

[viscid thistle]

theres a intresting method wanna link !@!

[rigid beacon]

?

I mean the only method I can think of involves taking derivatives

but assuming that this is in #precalculus and not #calculus

you don't know what derivatives are

and even then idk for sure if my method works

[viscid thistle]

then use it @!@

[rigid beacon]

what is @!@

[novel cargo]

I'm also curious

[rigid beacon]

but my only guess would be

ignore the absolute values

take derivative of inside

write it all in terms of sin and cos

get common denominators

set numerator equal to zero

see if that gets you anywhere

[viscid thistle]

@rigid beacon u know bprp ?

[blissful ridge]

Setting derivative to zero doesn't work

[viscid thistle]

Setting derivative to zero doesn't work
@blissful ridge yah

[novel cargo]

why?

[rigid beacon]

is this from a bprp video?

[viscid thistle]

yah

https://www.youtube.com/watch?v=wDCToFwOpfQ

lmao lol

[rigid beacon]

oh my god

so

[viscid thistle]

so

[rigid beacon]

you pinged helpers

or someone pinged helpers

[blissful ridge]

Watch the goddamn video

[rigid beacon]

to answer a question

[novel cargo]

I'm the sinner

Press F

[rigid beacon]

that has a solution video

man u good @viscid thistle out here wasting everyone's time

go watch the video @!@

[novel cargo]

tho I didn't know what's going on

sorry y'all

[viscid thistle]

I just wanted the action

[rigid beacon]

I just want you to leave

[viscid thistle]

bruh chill @!@

its justa qs @!@

[novel cargo]

there is a channel for #chill @viscid thistle

you can do this stuff over there

[viscid thistle]

ha ?

i mean Calm down

[limber rain]

@novel cargo Thanks for the help, much appreciated.

[viscid thistle]

Uhh

[autumn marsh]

anyone know what i did wrong 😂

[rigid sun]

understand?

[uncut mulch]

your first two lines

100x^3 dropped a 0 to 10x^3

[autumn marsh]

OH SHOOT

what a DUMB error

[rigid sun]

[autumn marsh]

BRUHHHHHHHHH i was like i ain't seeing it

[uncut mulch]

and you didn't apply prod law ptoperly

you subtracted instead of add

[autumn marsh]

a lil confused on the signs still

haven't done logs since algebra II and this is my summer assignment for ap calc lmao

[uncut mulch]

log(ab) = log(a) + log(b)

[autumn marsh]

is that why the first sign is a +

[rigid sun]

yes

[uncut mulch]

the remaining signs are - due to distribution

[autumn marsh]

gimme one sec to consume this info and make sense of it cuz i think i understand but i'm still a little in the mud

okay so why doesnt the log(ab) = log(a) + log(b) apply to the other ones

[uncut mulch]

it does

[rigid sun]

$-log(ab)= -log(a)-log(b)$

[obsidian monolith]

maleb1964:

[autumn marsh]

OH THE FIRST LOG is positive

[viscid thistle]

\log

[autumn marsh]

the second one is negative

therefore the first sign would be positive

i got it i see it yessss

[rigid sun]

$\log{2}$

[obsidian monolith]

maleb1964:

[rigid sun]

that didn't do shit

[autumn marsh]

lmfao

[rigid sun]

stfu

log() is better

[autumn marsh]

thanks for helping my mental clumsiness homies

[uncut mulch]

also recommend to always put parentheses around your arguments

(spacing is not a substitute)

[viscid thistle]

that didn't do shit
Wdym? it went from ugly to nice, i did not say to use {} that was all your choice mate...

[autumn marsh]

i have returned yet again

i'm unsure where to go from here

[uncut mulch]

its not recommended to write $(y+2)^{1/3}$ on top of the $\cbrt{y+2}$

[obsidian monolith]

ramonov:

[uncut mulch]

it will only result in confusion for the reader

anyway recall the distributive property from earlier.

-log(ab) = -(log(a) + log(b)) = -log(a) - log(b)

[plain root]

h(t) = t2 − 2t
h(x + 5) =

[uncut mulch]

consider also 4 = 2^2

[plain root]

could soeone help me solve this please 🙂

[uncut mulch]

and

also recommend to always put parentheses around your arguments

[plain root]

could someone explain to me how to solve this please functions killing me haha

h(t) = t2 − 2t

h(x + 5) =

[uncut mulch]

$\log_3(y+2)^{1/3}$ is interpreted as $(\log_3(y+2))^{1/3}$. you should instead write $\log_3((y+2)^{1/3})$. Same for the $\log_3((x-2)^2)$

[obsidian monolith]

ramonov:

[autumn marsh]

okay thanks i was a little confused on what you meant

@plain root isnt it just 2(x+5) - 2(x+5) i honestly have no clue, functions are in the deep parts of my brain

i'm also dumber down atm

dumbed

[plain root]

i took pre calc junior year

and for some reason i have to do this stuff in college

[autumn marsh]

same and i'm still stupid

i'm doing ap calc this year (senior) and i cant do basic log shiz

[plain root]

i need to relearn this stuff

i literally just forgot how to do it and got a 20

on my quiz

[uncut mulch]

look up function notation

[autumn marsh]

that's tough i'm sorry man

[plain root]

hahah its fine i can drop the quiz

[uncut mulch]

also feels like you copy and pasted it directly from somewhere,
use ^ to denote exponents

[plain root]

not a big deal but now i just need to waste my time relearning this

[autumn marsh]

@uncut mulch u talking to wham?

[plain root]

i copied it from my homework?

is that not allowed haha

[uncut mulch]

that comments was aimed at wham

[autumn marsh]

i think they mean format

[uncut mulch]

what's not allowed is complete disregard for symbols

[plain root]

disregard for symbols?

[autumn marsh]

@plain root is anything an exponent

[uncut mulch]

$t2 - 2t$ is trivially $0$

[obsidian monolith]

ramonov:

[plain root]

i think i see what i did wrong

[autumn marsh]

that's what i was thinking

[plain root]

some dumbass error

[autumn marsh]

hahahahaha it's okay i misread a 100 for a 10 earlier

[uncut mulch]

and I highly suspected the superscript formatting was lost during copy pasta or something

[autumn marsh]

fair assumption

[plain root]

i forgot a -

[autumn marsh]

oh yikes hahahaha

@uncut mulch what did u mean by recall the distributive property again, i mean i get the property but not sure how it's going to further assist me at the last statement

[plain root]

is a -x^2

= to x

[uncut mulch]

that was intended to address the incorrect signs present in your work

[autumn marsh]

oh damn i got more of those?

i'll take a look again

ah shiiii

is the third sign supposed to be a negative

[uncut mulch]

yes

[autumn marsh]

okay that has been fixed

[plain root]

q(t) = 4t^2 + 5 / t^2

q(−x) =

what would i do w a -x

[autumn marsh]

there's a rule with that

[plain root]

shoot

it wont let me open my book

[autumn marsh]

recollecting thoughts unless ramonov beats me to it 😂

[uncut mulch]

replace t with -x, use parentheses appropriately and simplify as needed

4 = 2^2, so the first log could be simplified further

[plain root]

yes

what happeneds when u get

(-x)^2

[uncut mulch]

that'd just be x^2

[plain root]

ok so the - just goes away?

[uncut mulch]

well (-1)^2 = 1

[plain root]

ya

[autumn marsh]

negative times a negative is a positive

[plain root]

yes

i tried tht

it said i got it wrong

i had 4x^2 + 5

[uncut mulch]

what are you getting?

[plain root]

/ x^2

[uncut mulch]

are you using the appropriate parentheses when entering your answer?

[autumn marsh]

isnt it asking u for a transformation

f(x) -f(x) f(-x) type of thing

[plain root]

ok it worked that time lol

i mustve missed typed omehting

[autumn marsh]

nice

and @uncut mulch why would i do smthn to the 4

like i get it can be broken down to 2*2 but what significance does that have

[uncut mulch]

2^2 an you can apply the power law

[autumn marsh]

oh i can turn it into 2^2 then do the power law

i think i understand maybe

[uncut mulch]

log_3(3) can be simplified to 1

[autumn marsh]

oh crap you're right

just saw that

[uncut mulch]

also a slightly misplaced left parentheses

[autumn marsh]

oh the second line right

[uncut mulch]

yeh

[autumn marsh]

yeah

okay i'm supposed to be getting a 6log base 3 somewhere and i don't see that happening 😂

6log base 3 (x-2)

[plain root]

this one killing me

[uncut mulch]

did you copy down the question properly

[plain root]

ye

idk what the answers tho

does it want 2 values

like

1, 2

[uncut mulch]

that was directed at staepled

[plain root]

my bad

[autumn marsh]

i'm checking

[uncut mulch]

for your question, you have a piecewise function

that behaves differently depending on the value of x

specifically for values less than or equal to 1, f(x) behaves like x^2+4

[autumn marsh]

@uncut mulch yes i did

[plain root]

ohhh so depending o X

its the one u use?

[noble jay]

yes

[plain root]

that makes more sense haha

word got em all right

ty

[uncut mulch]

can you show exactly what the answers are saying for the log question

[autumn marsh]

yeah

it might be wrong tbh

ive been using that to check my answers at least, it's been alright

[uncut mulch]

oh...

they just introduced a factor of 1/3

[autumn marsh]

i figures but the third log on the fraction doesn't change

[uncut mulch]

its equivalent to what you reached

[autumn marsh]

i see that now, why didn't the first log get multiplied

[uncut mulch]

nfi

answers are stupid

[autumn marsh]

lmaooo okay cool so that works

fun, condensing time

that look alright?

[uncut mulch]

nope

[autumn marsh]

rip me

[uncut mulch]

subtraction converts to division

[autumn marsh]

aw crap

[uncut mulch]

also appropriate parentheses

[autumn marsh]

my brain hurts XD

is the second line correct

[uncut mulch]

yes

[autumn marsh]

okay lemme try to fix

[uncut mulch]

looks ok

[autumn marsh]

that's a start

ive been doing math for almost 4 hours this sux

how do i know whether the z goes on top or the bottom

[bleak lance]

How do I evaluate a function that's -f(x)?

[autumn marsh]

@bleak lance i'm looking for ya

[bleak lance]

Thanks!

[autumn marsh]

@bleak lance okay so you just take whatever the whole function itself is and negate it, like f(x)= 3x + 2 and ur looking for -f(x) so u do -(3x + 2) which is -3x-2

[bleak lance]

What if it's a fraction?

[autumn marsh]

its a reflection over the x axis

[bleak lance]

For example 2x+3/9x+1

[autumn marsh]

i don't wanna be wrong so gimme a bit

[bleak lance]

Yup.

[autumn marsh]

i think u might switch variables but honestly don't know i gotta find my better notes

[bleak lance]

I got it. I just needed to distribute -1 to the numerator.

[autumn marsh]

okiiii my bad dude

[bleak lance]

Its ok.

I'm stuck on f(x+h)

Here's my work so far. 7(x+h)+9/9(x+h)-8=7x+7h+16/9x+9h+1.

[autumn marsh]

what're you tryna do

[bleak lance]

Evaluate the function which is 7x+9/9x-8

[glad pasture]

is the answer for this (-infinity,-4] u (-infinity,3)

also is this [-3/2,2)

[bleak lance]

How do I say all real numbers not equal to 5 in interval notation?

[viscid thistle]

(-inf, 5) ∪ (5, inf)

[bleak lance]

I need help finding (f+g)(4)

[viscid thistle]

what is the question?

[bleak lance]

I figured that one out

Hold on

It’s f(x)=5x+9; g(x)=7x-8

And now I’m stuck on (f/g)(4)

[red tree]

Does that mean f(4)/g(4)

[bleak lance]

Idk

I suppose so

I tried 14 but it said that I was wrong

[red tree]

But f(4)/g(4) isn't 14

[bleak lance]

How do I do that?

Oh I did t see it that way

So I literally just plug 4 in for x?

Sorry guys I mean (f/g)(1)

[glad pasture]

https://cdn.discordapp.com/attachments/641351235215294486/750902036035272774/unknown.png

is 45 [2,infinity) ?

[bleak lance]

Now I'm stuck on a new one

f(x)=4x^2+3x-2

f(-x)

[uncut mulch]

@glad pasture not quite.

[glad pasture]

is it (-infinity,-3]u[2,infinity) ?

[uncut mulch]

capital U for union in plain text

[glad pasture]

ok

[uncut mulch]

but yes

replace x with (-x) and simplify, use parentheses where appropriate

[bleak lance]

f(x+h) = x+h/(x+h)^2+1

[past meadow]

is that a question?

also i assume you mean f(x+h)=(x+h)/(x+h)^2+1

[empty iris]

I think I know the answer but I want someone else’s opinion on it cuz it seems to be too easy and I’m not sure if it’s a trick question or not

[patent beacon]

Not a trick question, haha.

It's pretty direct

You could go further by distributing the square

[ancient acorn]

Hi guys

I want someone who can do VC with me and can clear my doubts related to calculus with kinematics

Anyone?

<@&286206848099549185>

[blissful ridge]

[reef jasper]

i’m not sure if this is even pre calculus but how do u find a slope of 3d coordinates

[blissful kayak]

I think I know the answer but I want someone else’s opinion on it cuz it seems to be too easy and I’m not sure if it’s a trick question or not
@empty iris You can just replace x with a+h

[reef jasper]

i’m given the time and the coordinates at that time is that solvable

actually i figured it out all good

[frigid nexus]

can anyone help me out with this? i've been stuck on it for a few hours now 😅

<@&286206848099549185>

[fossil crown]

From

#❓how-to-get-help

Rule 4

If your question has not been answered for a minimum of 15 minutes, you may use the Helpers tag once. Please do not try to bump your question using this ping unnecessarily. Do not abuse this ping. Do not individually ping users with the Helpers tag without their express permission.

[uncut mulch]

what have you attempted in your hours of work

[tardy ridge]

set up a system of equations using (m/n^2)^a*(m^2n^3)^b=m*n^(-1)

[hexed otter]

How do i do thisss, this is circle btw

[novel cargo]

what do you want to do?

[hexed otter]

How do i do thisss, this is circle btw

[sour plinth]

what about it?

do you want to sketch it?

find the centre and radius?

[novel cargo]

you have 17 more tries to guess their goal

[uncut mulch]

stare at the equation

[sour plinth]

proof by intimidation

[marble jolt]

-2x^3+6x+3=0 How does one find the roots of this? ._.

[viscid thistle]

Quadratic formula or completing the square

[marble jolt]

mmmh have u tried it?

[viscid thistle]

Oh it’s a cubic

My bad

You can try rational root theorem then

[lime sequoia]

yeah just guess and check stuff with synthetic division after using rational roots theorem

after doing that you can use quadratic formula

or maybe factor some more

[jade iris]

write the exponential function f(t)=1238(5^-1/4) in standard form f(t)= ab^t round b to 3 decimal spots

im confused can can someone help

[novel cargo]

f(t)=1238(5^-1/4)

is f(t) a horizontal line?

[red tree]

-2x^3+6x+3 an irreducible cubic btw

[tired zephyr]

Confused on the last two. What is it asking for?

would (c) end up being $c^2(c-4)$

[obsidian monolith]

Ryan - 'Paul Kreinheder':

[tired zephyr]

?

[blissful ridge]

Yeah

[tired zephyr]

so answer is:

$c^3-4c^2$

[obsidian monolith]

Ryan - 'Paul Kreinheder':

[tired zephyr]

?

[blissful ridge]

Yep

[tired zephyr]

thx

[tired zephyr]

Can anyone remind me how to approach this problem? Am I using trig identities to break it down?

[novel cargo]

divide by two, take the square root

[tired zephyr]

thx

so you end up with $sin^2(\theta)=1/2$ ?

[obsidian monolith]

Ryan - 'Paul Kreinheder':

[maiden pelican]

Then take the square root

Then you'll get sin(x)=1/√2

You know what angle gives you 1/√2 right?

[earnest coral]

Guys I’m a bit confused

[tardy ridge]

Relative and absolute extrema. The term extremum (extrema in plural) is used to describe a value that is a minimum or a maximum of all function values. Function achieves relative maximum or relative minimum (relative extrema) at points, at which it changes from increasing to decreasing, or vice versa.

[plain root]

how would i go about getting these

[viscid thistle]

...?

[plain root]

@viscid thistle idk how they got that answer

[viscid thistle]

What are supposed to find with those functions?

[plain root]

Finding Values for Which In Exercises 43, 44, 45, and 46, find the value(s) of for which .

im not quite sure what its asking

[viscid thistle]

Are you trolling?

For which?

[plain root]

bro this is what my text book is asking

idk

[viscid thistle]

...

Are you solving f(x) = g(x)?

[plain root]

bro those r the directions

Finding Values for Which In Exercises 43, 44, 45, and 46, find the value(s) of for which .

the problem is the screen shot above

i have no clue how they got those answers

[viscid thistle]

Finding Values for Which In Exercises 43, 44, 45, and 46, find the value(s) of for which .
This has no meaning

[plain root]

oh lmao

the copy and paste goofed

[viscid thistle]

You are trolling

?

[plain root]

f(x) = g(x)

[viscid thistle]

Like tf

[plain root]

i forget how to solve these its prob stupid easy

[viscid thistle]

Yeah solving f(x)=g(x) gives the solutions

But wtf

[plain root]

how do i go about that again

just literally set them equal to eachother

?

[viscid thistle]

What do you think

f(x) = g(x)

[plain root]

yep

i havent dont math in like 8 months

this is my calc class bro

not even pre calc

[viscid thistle]

...

Ouch

[plain root]

im literally in college doing this stupid stuff

[viscid thistle]

#calculus then?

[plain root]

this aint considered calc lmao

[viscid thistle]

Not even #precalculus probably

Anyway good luck with the exam

[plain root]

cs major is a joke

this isnt an exam

[viscid thistle]

Idfk the us weird ass names for contents, but i still think you are trolling unless you give us a pic.

Are you American?

...

[plain root]

i am

[viscid thistle]

Not you lol

I swear American colleges are weird

[plain root]

im literally in like a top 40 cs program and we do this stupid math

[viscid thistle]

It's not "stupid"

Solve f(x)=g(x).

@plain root

[plain root]

yep ty

[jaunty spruce]

Can anyone help me with this?

[fiery creek]

@jaunty spruce write out the definition of (h o g)(x)

it's h(g(x)) correct?

now what do you do here

[past meadow]

hog

[bleak lance]

Is there anything I can do to gain a more intuitive understanding of precalculus?

Like how does it relate to real life like min, max, domain, range, etc?

[viscid thistle]

3blue1brown has a youtube series on it that aims to do exactly that

how do you write f'(8) in dx/dy notation?

you mean dy/dx ?

$$\frac{df}{dx}(8), \left. \frac{df}{dx} \right|{x = 8}, \left. \frac{d}{dx} \right|{x = 8} f$$

[obsidian monolith]

TTerra:

[viscid thistle]

are a few of the ones i've seen

last one is probably uncommon

oh right okay

thnx

first two are most common i'd say. that's all i can come up with off the top of my head

[bleak lance]

I think my precalcus course may have turned into calculus because it wants me to do something with a secant line.

Correct me if I'm wrong?

Different quotient

I gotta learn so much.

[viscid thistle]

this is the beginnings of calculus, yes

isnt secant just the tangent at a point

but it's not necessarily "calculus"

[bleak lance]

Huh. What is it? Just advanced algebra?

[viscid thistle]

precalculus is the best word I can think of

looking at secant lines formed by points getting closer and closer is like

how calculus is usually introduced it seems

well, how the derivative is introduced

because that's what it is

so i guess it's precalc

because it precedes calculus

[bleak lance]

Yeah.

It is.

I need to learn so much.

[viscid thistle]

we all do 😔

[bleak lance]

Almost everything is hard

XD

[viscid thistle]

That's what the discord and the internet and youtube are for lmao

[bleak lance]

True.

I wished I could just watch one video that would make everything click for me.

[ornate wolf]

any hints on how i can find eachh unit vector?

[willow bear]

you can't and you don't need to. what are you asked to evaluate?

@ornate wolf

[ornate wolf]

I'm asked to find 2a⋅5b

you can't and you don't need to. what are you asked to evaluate?
@willow bear oh..

[willow bear]

yeah, you can find 2a · 5b without calculating a and b individually, since you know the value of a · b

unless you're allergic to multiplying single-digit numbers together

[willow bear]

whom pung

[novel cargo]

precalc abondoned today

we doomed

[willow bear]

yes

[agile owl]

yes

[viscid thistle]

yes

[hallow thunder]

yes

[novel cargo]

yes

[tardy ridge]

yes

[lime bolt]

no

[raven flare]

no

[blissful kayak]

Yes

[stuck lark]

对

[fiery creek]

If x + 1/x = 5 then find the value of x^3 + 1/x^3

cab sineibe help me with this?

can someone*

what i did was just solved the quadratic

can i just sub in the two values?

[slender river]

i mean ... sure?

i don't see why not

[fiery creek]

i feel like it's a little bit strange

so i'm just double checking

[slender river]

is cool

[vale pewter]

Hint: expand (x+1/x)^3 and see what you get

@fiery creek

[thorny bluff]

What does no term in x² mean

Is it (1)x²

Or (0)x²

[sour plinth]

zero

[whole vessel]

Hey, i have a quick question on my precalc hw, im doing number 59. I’ve discovered the pattern on how to get the imaginary part, but not the real part.

If anyone knows the pattern here, I would appreciate the help.

[uncut mulch]

Re((1+i)^(n+1)) = Re((1+i)^n - Im((1+i)^n

its very similar to the imaginary part

[whole vessel]

ah I see, so the imaginary part subtracted from the real part becomes the next term in the imaginary part?

[viscid thistle]

i can't believe you are learning imaginary numbers in precalc

what grade is this?

[uncut mulch]

becomes the next real part

their sum would be the imaginary part

[viscid thistle]

Jesus is this US?

[whole vessel]

yes

[viscid thistle]

US curriculum is def tougher than Canada's

[strong ermine]

yes

for sure

tb bro help me out

[whole vessel]

I mean I am 2 years ahead of standard, but I don't know much about the candadian system

[strong ermine]

me too!

[whole vessel]

we got to the same school m8

[strong ermine]

oh...

[viscid thistle]

I feel extremely behind and im about to go to college in like few days

lol

[strong ermine]

ur all good

[whole vessel]

you'll probably cover the advanced stuff in college though, so no worries

[strong ermine]

yup

[viscid thistle]

i got 3 math classes coming up in first year

linear algebra, derivative calculus (which i have ap credits for), and integral calculus

im kinda scared

[past meadow]

linear algebra poggers

[viscid thistle]

how hard is linear algebra

i just know the basics

like adding and multiplying matrices

[novel cargo]

maybe start reading, self learning in advance

[strong ermine]

yeah im doing BC next year

[novel cargo]

I mean, do Khan + a textbook or stuff.

[viscid thistle]

take as many ap exams as possible. I regret not taking enough ap tests

[novel cargo]

don't rely solely on school curriculum if it sucks

[strong ermine]

ok

[viscid thistle]

Im stuck with 7 courses per term in first ytear

[strong ermine]

should i be taking the ap quiz for ab and bc?

cause its the same class basically

[whole vessel]

yes

[viscid thistle]

i just did ab

[strong ermine]

personally, i think BC is better fit for me

[viscid thistle]

and ap chem which i totally bombed on cuz of this stupid corona online exam

[strong ermine]

ah yeah

that is tough

[whole vessel]

I see, I am skipping ab and deciding to go to bc next year

[viscid thistle]

Lmao i retook ap chem test 4 times

[strong ermine]

ye

[whole vessel]

oof

[strong ermine]

oh god that sucks

f in the chat

f

[viscid thistle]

but still counldn't submit cuz server kept on crashing fr

[strong ermine]

yeah that was common occurence from what i've heard

[whole vessel]

yeah

[strong ermine]

i am taking apwh and apcsp this year

[whole vessel]

same

[viscid thistle]

wait yall americans are kinda obliged to take a lot of ap exams to get into college right?

[whole vessel]

lol yeah

[strong ermine]

next year, apcsa, ap calc bc, ap physics, apush, and ap english (:

[whole vessel]

but the SAT score is what counts more

[viscid thistle]

damn

[strong ermine]

it sucks

[viscid thistle]

SAT, aps that's rough af

[whole vessel]

yeah def

[strong ermine]

yes it really is

but university of california is removing sat requirement

so thats fun

[viscid thistle]

OH

[strong ermine]

by 2024 i think

[viscid thistle]

i didn't know university of california is aka berkley lmao

[strong ermine]

yeah

my cousin is applying to university of waterloo

[viscid thistle]

oh shoot

i got rejected from that school

lol

[strong ermine]

lol

[viscid thistle]

that school's tough to get into

[strong ermine]

he is from singapore

[viscid thistle]

and rlly hard to sruvive

[strong ermine]

yeah

he's a smart kid

[viscid thistle]

oh

[strong ermine]

but idk either

[viscid thistle]

only 1 kid at my school got into waterloo

[strong ermine]

ah

thats tough

[whole vessel]

I mean Arjun has a cousin in every ivy league lol

[strong ermine]

lol

(he's not wrong)

[viscid thistle]

i also applied to University of Toronto but they lost my application so they couldn't make a decision

[strong ermine]

oof

that sucks

[whole vessel]

aw

[strong ermine]

sorry mate

[viscid thistle]

yeah

[strong ermine]

so where are you going?

[viscid thistle]

UBC

University of British Columbia Vancouver

[strong ermine]

nice

[whole vessel]

oh nice

[viscid thistle]

is that school known in the US
?

[strong ermine]

no

[whole vessel]

yes

[strong ermine]

i dont think so

ok toby...

[whole vessel]

I've heard of it, but maybe that's just cause I have relatives near by

[viscid thistle]

cuz i know 100% Americans know about waterloo really well

[strong ermine]

main international schools i know are in singapore, uk, india

not canada

[viscid thistle]

A lot of incoming first years at UBC are from India

[strong ermine]

yeah

most of my family went to IIT

[viscid thistle]

they are all part of this Indian version of IB

i forgot what it was called

[strong ermine]

yeah

idk either

most indians i know came internationally for masters

not undergrad

so idk the whole system for that

[whole vessel]

what are you majoring in?

[strong ermine]

is ur uni virtual?

[viscid thistle]

Im going into first year engineering so we just compete in first year and then choose our 2nd year specialization based on our gpa and interests

yes

[strong ermine]

qh

ah

[viscid thistle]

the entire first year is virtual

[strong ermine]

what disciplinary are you most interested in

[viscid thistle]

Comp Eng/Elec Eng

[strong ermine]

nice

i like mechanical

and elec

[viscid thistle]

oh i initially applied to ubc thinking i wanna major in mechanical

[strong ermine]

ah

what made u change ur mind?

[viscid thistle]

and then i looked at the competitiveness for 2nd year mechanical

[strong ermine]

oh i see

[viscid thistle]

it's like insane

and mechanical is pretty much dead in Canada

[strong ermine]

huh

why is that?

[viscid thistle]

Canada doesn't like to produce hardware stuffs

[whole vessel]

ah

[strong ermine]

makes sense

[viscid thistle]

it's mostly natural resources/software based

[strong ermine]

we are from bay area

so lots of options

[viscid thistle]

oh damn

[strong ermine]

i could go into software side of things

[viscid thistle]

heard that it's extremely expenisve there

[strong ermine]

yes

[whole vessel]

yes

Cost of living or college?

both

[strong ermine]

many leave

[viscid thistle]

cost of living

[whole vessel]

yes

[strong ermine]

but its still getting lots of people

in

[viscid thistle]

it's kinda shocking that you could barely survive with 100k in the bay area

[strong ermine]

yeah

[whole vessel]

I mean its not that bad

[strong ermine]

i think there's a lot of systems in place tho

to make life a lil' easier

[viscid thistle]

Vancouver is pretty expensive too. That's why most ppl move to Alberta cuz cost of living is 2-4 times cheaper and wage is nearly 2x higher in Alberta

oh

[strong ermine]

ah

alberta is pretty

[viscid thistle]

oh what

[strong ermine]

but i have heard they are crappy drivers

[viscid thistle]

whenever we go to alberta we always say alberta is ugly

yes true

[strong ermine]

oh

[viscid thistle]

albertan drivers are big memes in BC

[strong ermine]

they have nice lakes tho

yeah cause roads are st8 right

[viscid thistle]

oh yeah and it's pretty flat

yes

[strong ermine]

whereas BC has turns

bruh this is so pretty

[viscid thistle]

Vancouver side a lot of turns

rural side of BC is like straight

and deserts

this is basically east side of BC

[strong ermine]

bruh thats low res image

[viscid thistle]

west side of BC

[strong ermine]

u did em dirty

[viscid thistle]

lmao

yes we call them redneck area

cuz it looks like texas

[whole vessel]

yeah

[strong ermine]

bruh tx?

nah fam

[viscid thistle]

lol ppl in vancouver don't travel

[strong ermine]

also rednecks arent tx

they are farther east

[whole vessel]

tx is turning blue

Agreed

[strong ermine]

69% of those who vote are in urban areas

which are alll democrat

[viscid thistle]

how about georgia

[strong ermine]

so soon boys

[viscid thistle]

i heard georgia is full of good minded christians

[strong ermine]

yeah

[viscid thistle]

not like those white power ppl in mississippi

[strong ermine]

its like australia lmao

cuz we sent prisoners there

[viscid thistle]

georgia?

[strong ermine]

ye

[viscid thistle]

woah

[whole vessel]

haha, I mean most of California by land mass is red necks lol

[strong ermine]

that was most of revenue i think

back in the day

[viscid thistle]

i thought georgia was like the safest state

[strong ermine]

georgia is good

[whole vessel]

it is now

[viscid thistle]

i went to california LA before

[whole vessel]

oh god

[strong ermine]

we are talking 200 years ago

[viscid thistle]

it was quite scary

[strong ermine]

oh yeah

[whole vessel]

yeah I hate LA

[strong ermine]

lots of crackheads

[viscid thistle]

lmao yes

[strong ermine]

LA isnt great imo

[whole vessel]

there is a huge problem with managing the city

[strong ermine]

yeah

rednecks are uneducated folks in the south

[viscid thistle]

some guy was beating the hell out of our hotel door and was begging to be in

[strong ermine]

georgia and florida

mostly

oh god

[viscid thistle]

florida is redneck state?

i thought florida was like california #2

[strong ermine]

hm

not really...

it is swing state

[whole vessel]

the thing is, in metropolitan areas yes

[strong ermine]

both republicans and democrats

[viscid thistle]

oh

[strong ermine]

but it is like big retirement community

[viscid thistle]

i hear some wild stuff from florida

[whole vessel]

but rural in California and florida is redneck

[strong ermine]

so lots of republicans

[viscid thistle]

oh

[whole vessel]

oh yeah, Florida is crazy man

[strong ermine]

yes

[whole vessel]

Would not want to live there

[viscid thistle]

seems like US is like either democrat or republican

[strong ermine]

its ok tb

lets not generalize

yeah, people chose party over people

political parties are personality traits now lol

[whole vessel]

yes, the two party system is quite strong

[viscid thistle]

in canada, even the most right wing person supports gay marriage

[strong ermine]

ye

here there is lots of bs media

which is an issue

[whole vessel]

yeah, on the global political axis our democrats are even right wing

[strong ermine]

they care too much about ratings

[viscid thistle]

lmao

[strong ermine]

guys

perhaps we should migrate our discussion

to another chat

[viscid thistle]

im ready for the migration

[strong ermine]

oki

where too?

to

[obsidian monolith]

Manan:

Manan:

[somber yew]

This method is rather tedious to compute the sum of 10 terms, so I'd appreciate some help in figuring out a better method.

[obsidian monolith]

Manan:

[blissful ridge]

General term is
$tan^{-1} \left(\frac{1}{n^2 + n +1}\right)$

[somber yew]

Yeppp

[obsidian monolith]

The Godfather:

[blissful ridge]

$n^2 + n +1=(n+1)^2-n$

[obsidian monolith]

The Godfather:

[somber yew]

Makes sense.

[blissful ridge]

We need to make it telescopic

[somber yew]

Ooofff telescopic sums; I so hate them.

Aight I'll give it a try now, thanks for helping out again!

[distant grotto]

hey can someone explain how subbing in 2 in the second integration leads to 16 and -18

[willow bear]

line 3 is continued on line 4

[willow bear]

yes

[distant grotto]

so basically

[willow bear]

line 3 is the first square bracket, line 4 the second

[distant grotto]

u sub in 5 and 2

i was just really confused how 3(2)^2 leads to 16

and 11(2) is 18

am i missing something here? xd

[willow bear]

line 3 is the first square bracket, line 4 the second

the second square bracket's evaluation is on line 4

[distant grotto]

oh wait so

oh god im so stupid 🤦‍♂️

thanks lmao

[marble locust]

I have a question.

So I was asking my counsleor if I can be bumped up to Algebra 2 since I was taking Geo at home. I emailed her and she said that Pre calc will be a struggle and if you dont take geo at school you aint gonna be ready.

What is Pre-calculus about?

[patent beacon]

Usually the final functions necessary to do calc. The course will finalize:

• Higher degree polynomials
• Trigonometry
• Exponentials and logarithms

I personally am of the opinion that much of hs math is skippable with enough effort, the right mindset, and the right reading material.

But if your end goal is good grades, why bother skipping?

@marble locust

[marble locust]

You could probably learn this in Algebra 2 right?

[tardy ridge]

Take the pre Calc course on cemc open courseware and see how you feel

If you can do the extension problems you are fine

[marble locust]

Cemc

[rain mulch]

I don’t understand how it is wrong tho

I checked both the limit on both function and they don’t match? Am I missing something important

[novel cargo]

you mean both equations

there is only one function

[rain mulch]

Oh my bad

Yes

[willow bear]

pay attention to where the limit is being taken.

[novel cargo]

so, 4 is only part of the domain of one of the equations

[willow bear]

it's not $\lim_{x \to 1} g(x)$, it's $\lim_{x \to 4} g(x)$

[obsidian monolith]

Ann:

[rain mulch]

Ok

I know the answer is 2

[willow bear]

it's not at the meeting point of the two conditions.

it's entirely within the "x>=1" condition

[rain mulch]

But

In similar problem like this

[willow bear]

i'm pointing out the dissimilarity

[rain mulch]

Sometime they told me to check both, and sometime only 1 condition

[novel cargo]

is 4 >= 1 or is it between -8 and 1?

[rain mulch]

Obviously the first one

[novel cargo]

then act on it

[willow bear]

^

[rain mulch]

Then how come this is wrong???

[novel cargo]

how did you get 2, I' curious?

[rain mulch]

So x is approaching -3

Which is in the first condition

Then I just sub -3 in

[novel cargo]

what's the definition of the existence of the limit?

[rain mulch]

Something that is distinticely known as a border

[novel cargo]

the function isn't continuous at -3

in other words, approaching -3 from the left does not equal approaching -3 from the right

[rain mulch]

How do you know

[novel cargo]

-7 <= x <= -3 is the domain of sqrt(7+x)

x > -3 the domain of x^2-5

-3 lies on the boundary of the first equation

sqrt(7-3) = 2

(-3)^2 - 5 = 4

so, at -3, f(x) changes abruptly from 2 to 4 with no values inbetween

[rain mulch]

O

I see

Thanks

[whole vessel]

I’m not sure what they mean on letter b for this one. I’ve separated the real and imaginary parts by placing them on opposite sides of the equation, but I’m unsure how they want me to create 2 separate equations.

[blissful ridge]

Compare the real and imaginery parts

[whole vessel]

This is what I have: a^2 - b^2 = i - 2abi
What do you mean by compare them?

[blissful ridge]

No, what you are doing is not the way to go about it

if a+ib=c+id
Then it means
a=c and b=d

Comparing the real and imaginery parts

[whole vessel]

Oh I see what you mean

thanks

[swift glacier]

I don't know why -4pi/10 is wrong, it's not simplification either

[rigid sun]

does it specify a domain?

idk man

looks like you're fucked

[uncut mulch]

the angle is obtuse and doesn't have a complement

[swift glacier]

hmm no specified domain

it doesn't have a complement?

[rigid sun]

lol bruh

what a prank

[slate scroll]

how does this even work?

i understand that as angles, these values are equivalent

but idk it just feels wrong when they are written as values like that

[tardy ridge]

this is screenshotted from quora.

[blazing raven]

Hmm 0 = 2pi. That's it.

(The radian measures represent the same angle.)

[low owl]

I'm having a rough time. It says to use a coterminal angle to determine the exact value....but it doesn't show how to find a coterminal angle...

do I just keep subtracting 2*pi from the angle until I get the lowest possible ?

[ornate wolf]

I found the vector of <4,7,6> - <1,2,3> = <3,5,3>

and cross product with (1,1,1) to get (-2,0,2)

not sure if i'm right, and what's next?

[novel cargo]

I haven't learned this topic yet but one equation that you could set up is as follows:

1 + 2a + 3b = c

now you need two more equations

from the line equation you can get other points on the plane to set up the other two equations

take t = 1

[slate scroll]

if the cross product equals (-2,0,2)

[novel cargo]

then the point (5, 8, 7) lies on the plane

set this up for another equation

continue Kanga

[slate scroll]

hang on I need to calculate some stuff

[novel cargo]

since you can define a plane with one point and a line (provided the point isn't on the line), you can use the three point (two from the line, one that was originally provided), to set up three equations and solve a, b , and c

[slate scroll]

ok your cross product is correct

now the coefficents of x,y,z should be the same direction vector that you found when using cross product

and you know that the coefficient of x is 1

therefor you multiply that direction vector by -1/2 to make the x-component 1 as follows:

-1/2*<-2,0,2>=<1,0,-1>

therefore a=0 and b=-1

now you can use az's equation to find c: 1+2a+3b=c

1+2(0)+3(-1)=-2

therefore c=-2 @ornate wolf

[novel cargo]

if you finished, look at my primitive solution without cross product and stuff, and tell me if it works

with three equations, three unknowns

one point is given, two are taken from line equation