precalculus

[novel dirge]

I started something like that but wasnt sure if it was good so i gave up

[fluid shore]

Yea that was the first mistake you made

giving up

So, how many learn french & english only?

[novel dirge]

70

[fluid shore]

Are you sure?

[novel dirge]

Can I wrote that like this?

[fluid shore]

There are 120 that learn all three, 140 that learn french & english

[novel dirge]

20? But Idk why

Am just guessing cause it cant be negative

[fluid shore]

Well, how did you find out that it was 130 for the other case that we did?

Why did 130 make sense as an answer?

[novel dirge]

If 120 learn all 3

And 2 learn 250

The only difference is in the 3rd

[fluid shore]

In that situation, 250 students learn english and russian. 120 learn all three so they're included in the 250. The only other way you could be included is if you learnt only english and russian. So, there are 130 students that learn only english & russian.

Now, apply the same reasoning to the other portions as well

[novel dirge]

Oh

I get this part now

But did I write it correctly?

[fluid shore]

Nope, what you said didn't really make much sense

[novel dirge]

Nkt said

Written

In the pic I sent

[fluid shore]

Well, what you're doing with (e U r)\f is basically taking the set of students who learn either english or french and don't learn russian. In that way, you're determining the set of students that know only english, only russian and both english & russian (but not french)

So that wouldn't really make sense because that's not 130

That's why you should forget about writing it using intersections & unions for now

Focus on getting an intuition for how to solve it first

[novel dirge]

Ok

F and r only have 60 students

What now?

[fluid shore]

Well, what do you think is the next step?

[novel dirge]

Maybe getting how many students go to each class in total?

[summer monolith]

Are these formulas equivalent or one of the authors is bullshitting me?

[fluid shore]

Well, the next step would be to get the number of students who only learn french, who only learn english and who only learn russian

[novel dirge]

Yep

[fluid shore]

So, how will you determine that?

C'mon, you also have to think. I can't think for you, you have to be leading the discussion. I'm just here to provide hints.

[novel dirge]

I know

I am thinking rn

At least trying to

Would it be better if I write everything I think of?

[fluid shore]

Indeed. But don't just write nonsense. We've gone through a significant portion of the problem.

You should be able to approach it logically from here on out.

[novel dirge]

470 learn e which includes the ones who learn only e and f and the ones who learn e and r

So

If we do the same thing we did in the previous stem

Or no

Wait

[fluid shore]

470 learn english

That includes those who learn english only, those who learn english & french, those who learn english & russian and those who learn all three

[novel dirge]

Yes

Idk how to write what I want to say

Ill take a pic

[fluid shore]

Well, you know how many learn all three

You know how many learn english & french

You know how many learn english and russian

So can you find those who learn only english?

[stuck lark]

ann $\in(E\cap F)\cap R$

[obsidian monolith]

RokettoJanpu:

[novel dirge]

We just remove them all of them from the E?

[fluid shore]

Hush jintarou

Though that's a true proposition

What do you think, Mr Pancake?

[novel dirge]

And - all 3

[fluid shore]

Yes

That's correct

But that's wrong set-theoretic notation btw

[novel dirge]

I know

[fluid shore]

You should say card(E U R) + card(E U F)

[novel dirge]

But I dont know how to write it

What is card?

[fluid shore]

Cardinality

The number of elements in a given set

So card(A) = number of elements in A

[novel dirge]

👍

Ill read more about it

So I just take away everything?

[fluid shore]

Idk, you tell me

Do you take away everything?

Like I said, forget about set theoretic notation

[novel dirge]

I think so bht I am not too sure

[fluid shore]

Why are you not sure?

[novel dirge]

Idk, I feel kinda stupid rn so I doubt everything

And sorry for the typos, I am on phone

[fluid shore]

It's okay

Stop feeling stupid

Do what makes sense logically

[novel dirge]

I have also ben stuck on a really stupid problem with the prpgramI am wprking on for the last 3 days and that is the main reason for my lack of confidence

But for me, taking away all 3 would maje sense cause it is what we did in the forst step

[fluid shore]

Did you understand why we did it in the first step?

[novel dirge]

Yes

[fluid shore]

So continue with what you wanted to do. You're on the right track

But do it properly

Use a proper venn diagram

And forget about set theoretic notation for the moment

[novel dirge]

But idk how to write a correct venn diagram

Now I think it wpuld make more sense do remove only the 2 we re sure about

E U R and E U F

[fluid shore]

?????

[novel dirge]

I guess no

Damn

[fluid shore]

What did i just say that about set theoretic notation

You're not listening to me

[novel dirge]

Idk what that even is so I am definitely not looking at it

[fluid shore]

Arghh fuck it

There you go

That's literally it

Also, when i said set theoretic notation, i meant unions, intersections & complements. I told you not to consider those (for example, writing E U F) because you're not even acquainted with set theory on an intuitive level

You need them acquaintance first before we worry about notation and rigor

[novel dirge]

I drew it like that

But got confused when I saw that the solution in the book is 770

So I thought I did something wrong

[fluid shore]

Add up all the numbers in the diagram

[novel dirge]

But I did do it like that

All all?

[fluid shore]

Yes

-.-

[novel dirge]

Got 770

[fluid shore]

Yes

Like I said, you're not thinking

[novel dirge]

I understand how it is done now

[fluid shore]

You're just doing the problem in a vacuum

So stop doing that. When you're using a venn diagram, for example, think about it logically and proceed to the final solution to the problem.

[novel dirge]

I understand

I will try better from now on

And thanks for the help

[fluid shore]

You're welcome.

I may sound very harsh but it's for your own good.

[novel dirge]

Np

I like that

Its better than letting me make the same mistake

Besides

Compared to some of my teachers you are very mild

[fluid shore]

Well, I certainly hope I don't sound too harsh.

I don't like being mean to people.

Except for publius but that's cos he's a memelord

[pale bison]

@fluid shore nou

jk

prank

memes

relax

[fluid shore]

Fuck yes

I'm spreading my virus to everyone

Oooh

[pale bison]

i sen frien req

[fluid shore]

I accept

[pale bison]

i thank

[odd helm]

How would I approach this problem

[pale bison]

what does the rational root theorem states?

and how can you manipulate the problem to use the theorem?

[odd helm]

Isn’t it that the +/- factors of constant/ +/- factors of leading term

[pale bison]

yes, you got the right idea

[odd helm]

Am I supposed to multiply all 3, set them equal to 0

And subtract 81

[pale bison]

so you're looking for some polynomial to work with

yes

exactly

[odd helm]

That’s so much work ...

[pale bison]

[odd helm]

Ok thank you

[pale bison]

np

[uncut mulch]

don't need to expand everything

only need to worry about the coefficients of the leading term and constant when looking for possible solutions

[pale bison]

oh right, good point

fully expand to practice algebra

[dim jungle]

Draw a diagram

30-60-90 triangle property

[clever inlet]

🤔

[odd helm]

How would I approach this I know that intermediate value theorem says that if it is continuous then there is a point where f(c) = 0 but how would I bound that?

The only thing I know for sure is that there is a zero between f(-2) and f(-1)

[viscid thistle]

How would I go about approaching this question

[clever inlet]

Consider the definition of a period

[rigid sun]

counter example

just think of a funciton that has f(c+1)=f(c) for all c

[viscid thistle]

I would think

like f(x) = 5

because regardless of the input, it will always be the same output

[rigid sun]

yup

[viscid thistle]

and it doesn't have a period of 1

there is no period basically

[rigid sun]

it doenst have a period at all

there are no peaks or trophs

and even if you gave it a period, its niot like you could determine what it is

theres nothing to measure

[viscid thistle]

oh ok

As for these two, the answers are false, true respectively right?

[rigid sun]

yes it should be

the final result for 7. is an angle, and there are multiple angles for some ratio

8 is the reverse, with 1 ratio for multiple angles

[odd helm]

Could someone look at my question above?

[median merlin]

someone mind helping me out with this one?

been working on it for a long while and cant seem to figure it out

[uncut mulch]

what have you tried?

[median merlin]

well i tried turning them into factors and then expanding it to get the full polynomial

[uncut mulch]

what were your factors?

[median merlin]

well i had (x-2)^2

but i kind of get lost trying to create the factor for 4-3i as that is what i am having trouble with and need some help

[uncut mulch]

use parentheses to make things easier

(4 - 3i) is a zero
what would the factor be?

[median merlin]

im not really sure

how would I go about doing it

[uncut mulch]

apply factor theorem the same way you did for the 2

[median merlin]

(x-(4-3i)) ?

[uncut mulch]

yes

and what theorem should you apply to get the 4th root/factor

(related to complex roots of a polynomial with real coefficients)

[median merlin]

Complex conjugate root theorem?

[uncut mulch]

yes

[sturdy haven]

Guys

In math courses where you can’t use calculators

How hard do the actual calculations get

[median merlin]

so (x-(4-3i))(x-(4+3i))(x-2)^2?

[uncut mulch]

yeh

applying vietas makes the expansion for the complex factors less tedious

[median merlin]

i never learned that in class

[uncut mulch]

just sum and product or roots

you should've encountered it at least for quadratics, (maybe not by name)

and algebra after that shouldn't be that difficult

assuming they want you to expand everything

[median merlin]

ok i got it right thank you

appreciate the help

[uncut mulch]

np

[sturdy haven]

Hello

How hard do the actual calculations get

In math classes without calculators

Like the arithmetic

[uncut mulch]

they shouldn't be that hard

[empty fulcrum]

Usually you're expected to simplify to a certain point and leave it there

No one is gonna want you to know the square root of 21 or anything like that

[sturdy haven]

What about multiplying/dividing large numbers or decimals

[empty fulcrum]

Oh you'll be doing different kinds of calculations entirely haha

If you've got some nasty decimal you'll definitely have a calculator

[sturdy haven]

Bc im taking precalc next year so idk

[empty fulcrum]

Yeah don't worry about big decimals and such

[cosmic raven]

Higher levels of math become more about understanding the material, not doing long calculations

you almost always have a calculator

[empty fulcrum]

Yeah the calculator won't help if you don't know what you're doing

[viscid thistle]

deg R(x) = 4, zero 4-3i, 2

That’s just

R(x) = (x-(4-3i))(x-(4+3i))(x-2)^2

Not very tedious

Actually yes that is tedious @uncut mulch aya

Aha

The Vieta way is better, you’re right

[odd helm]

How would I approach this problem?

[cosmic raven]

I think we need to see more of the table?

[patent beacon]

@odd helm
Because the function switches sign between -2 and -1, there's a zero in (-2,-1)

That's all I can say with the info given though

[cosmic raven]

^

[odd helm]

Alright thanks

[onyx drift]

i have a test tomorrow and my teacher said that i need to find a polynomial function's equation from a table of values

he didnt even teach us how to do this so is there anyone here that know what to do?

[frozen needle]

given $n+1$ real numbers $y_0,\dots,y_n$ and $n+1$ distinct real numbers $x_0,\dots,x_n$, there exists a unique real polynomial function $P$ which degree is at most $n$ such that $P(x_i)=y_i$ for all $i\in{0,\dots, n}$, and it is given by the formula
$$\forall x\in\bbR,\quad P(x)=\sum_{0\leq i\leq n}\prn{y_i\prod_{\underset{j\neq i}{0\leq j\leq n}}\frac{x-x_j}{x_i-x_j}}$$

[obsidian monolith]

Tuong:

[deep lotus]

that looks so complicated

[keen sigil]

yo i got a question

if Sn = 3^n+1 what is t3?

my thought process is that since S3 is 81 it would be a + ar + ar^3 and subtracting a and ar gives 45 and isolating r gives sq2

and t3 = 9*sq2^2 = 18

but im not sure

ah i think i made a dumb error somewhere there

maybe its sq5

i got no idea lmao

it might be 54

[viscid thistle]

$S_n = 3^{n+1}$

@keen sigil ?

And what is t_3?

[keen sigil]

no, sorry i should've put brackets. its 3^(n+1)

[obsidian monolith]

rudy:

[viscid thistle]

What is T_n???

[keen sigil]

wdym?

[viscid thistle]

if Sn = 3^n+1 what is t3?

[keen sigil]

that's the question lol

[viscid thistle]

What does t3 stand for

[keen sigil]

term 3

of the sequence

[viscid thistle]

...

Uh

[keen sigil]

yea idk

[viscid thistle]

...plug in n=3?

For n=3, we get 3^4 = 81

[keen sigil]

81 is the 3rd term of the series which is the 3 terms of the sequence added together right?

so im pretty sure it's asking what the 3rd term of the sequence is

not the series

[vernal spindle]

I'm confused for this one

[willow bear]

how famliar are you with the concepts of "odd function" and "even function"

and that among the trigonometric functions, sin and tan are in the former class while cos is in the latter

[vernal spindle]

not too familiar we never learned these types

[willow bear]

what

so you don't know that, say, sin(-x) = -sin(x) and cos(-x) = cos(x) for all x?

[vernal spindle]

So I solve for -sect=3.3

[willow bear]

...

no

what you have is sec(-t), not -sec(t)

and those aren't the same

[vernal spindle]

So solve for sec(-t)=3.3?

[willow bear]

that sentence doesn't make any sense

but sec(-t) = sec(t) for all t where both sides make sense

[vernal spindle]

So sec(3.3) = -sec(3.3)

[willow bear]

you're spouting nonsense again

[vernal spindle]

I don't get it really

Or im just over looking it

[willow bear]

sec(-t) = sec(t) for all t where both sides make sense

this alone is already enough. SHOULD be enough. to answer the question you posted.

[vernal spindle]

so sec(t)=3.3

[willow bear]

sec(t) = 3.3, that's given

[vernal spindle]

Ohhh

[willow bear]

how the fuck are you going "ohhh" at me stating that what you just said is literally what the problem's been saying all along

are you asleep or something

[jovial hazel]

So, these 2 methods are used to find the sum of an arithmetic sequence, correct? Is the one to the Right all i need ?

[lucid hearth]

left is sum, right is term

S₅ would be the sum of a series up to 5, a₅ would be the 5th term of a sequence

[novel dirge]

Can someone tell me how the last part is true?

The one I underlined

[willow bear]

you've shown x ∈ A ∪ (A ∩ B) iff x ∈ A

so A ∪ (A ∩ B) = A

[novel dirge]

I still dont get it

How we get that it is equal to only A

[willow bear]

do you follow the chain of equivalences

it really should have one big pair of parentheses around it

[novel dirge]

Even with that I still dont get it😩

Is there a rule for this kr something?

[willow bear]

...

you have two sets

A ∪ (A ∩ B)

and A

and you've shown that being an element of one is the same thing as being an element of the other

[novel dirge]

I think I get it now

Thanks

[jovial hazel]

@lucid hearth Thank you!

[novel dirge]

Yesterady I got help with a probelm where I had to figure out how many students were learning different languages

Now I have a similar one

Thoutgh I understood it yesterday and would be able to solve it the same way

But I am getting a negative number

[willow bear]

can you show the problem then

[novel dirge]

M would be 15-17=-2 which cant be

[willow bear]

,rccw

[willow bear]

can you show the original problem

[novel dirge]

From yesterday or the text of this one?

[willow bear]

this one

[novel dirge]

There are 30 students in a class

19 got a grade in maths

17 in physycs

11 history

12 M and F

[willow bear]

F for physics?

[novel dirge]

7 I and M

Yes

Forgot to translate it

Its called Fizika in my language

[willow bear]

yeah

[novel dirge]

And 5 did P and I

2 did all 3

So I thought I can do it like yesterday

Drew a venn

[willow bear]

what's the question

[novel dirge]

How many did History and not Math

[willow bear]

and why does it say M=15 in your pic when you said there's 19 math students

[novel dirge]

How many did 2 subjects out of the 3

Fuck

Thats the problem

😫

Thanks thouhh

[jovial hazel]

Hey guys, so lets say i have a question that wants me to find the sum of a geometric sequence

(1-x ) + x^2(1- ) + x^3(1- ) .....

So i know it clearly says R can not equal 1

But how can i tell it doesnt if r is x(1-x)?

ahh wait

im stupid

so basically one is finding the sum for infinite number of series and the other is for finite?

or am i still stupid?

[serene heath]

first one is finite no of terms

[jovial hazel]

aha ok and the second one is for infinite, correct?

[lilac pier]

Yes you can tell by the small infinity symbol on S

[jovial hazel]

ye just making sure

[sick seal]

What's the relation between N and M for horizontal asatopes

In rational functions.

[remote veldt]

do you mean asymptotes?

and by N and M, what do you mean? Greatest exponent in numerator and denominator respectively?

[sick seal]

The lines the function dose not cross
If were looking at
Ax^n/Ax^m

As the lead term

[stuck lark]

you can at least preserve capitalization

[remote veldt]

an asymptote isn't a line that the function doesn't cross, it's a line the function approaches in the limit. A horiztonal asymptote exists if m >= n. The horizontal asymptote is at y = 0 if m > n, and at y = the quotient of the leading coefficients if n = m

@sick seal

[sick seal]

Thanks a lot

[remote veldt]

that's not something you should memorize though; remember that a horizontal asymptote is a limiting behaviour, and just take the limit

[sick seal]

Yeah, I just have a test in a few hours and wanna make sure I got my shiz together.

[remote veldt]

ok ok yeah

notice that on this function, in the limit, f(x) approaches y = 0, so y = 0 is a horizontal asymptote, but you cross it at x = 1. The asymptote describes the behaviour in the limit, not the behaviour everywhere

here's a diagram that goes a ways beyond x = 12, and you can see that the function is approaching y = 0

[neon garden]

Can anyone help me with 49?

[cosmic raven]

@neon garden what is the formula for the volume of a cylinder?

[neon garden]

Pi(r^2)(h)

[cosmic raven]

Pi(r^2)(h) = V

It wants height in terms of radius

so what do you think the first step would be?

[neon garden]

Get height alone in the equation?

[cosmic raven]

Yes!

[neon garden]

Oh I was way over thinking it

[polar igloo]

Hey can somone tell me if this looks alright?

[rigid sun]

wrong channel

but yeah looks fine

[pale bison]

I learned power rule in precal check mate

[stuck lark]

i learned precalc in pre-k checkmate

[pale bison]

I bet the first word you ever said was "application"

[stuck lark]

it was "bifurcation"

[pale bison]

differential equation noise intensifies

[stuck lark]

you once said i eat DEs for breakfast. in fact that's what my baby formula was made of

[pale bison]

what type of des exactly?

[stuck lark]

a garden variety for healthy growth. const coefficient, exact, autonomous, cauchy euler, navier stokes, sturm liouville, systems, etc

[pale bison]

and your favorite desert?

[uncut mulch]

2nd dinner

[stuck lark]

multi electron time dependent schrodinger equation for the zirconium atom potential

[pale bison]

i'm very proud of you

[stuck lark]

i think ramonov is a hobbit. also you haven't seen what i snack on in my free time

[pale bison]

ok i take the bait, what do you snack on your free time?

[stuck lark]

perturbation theory & optical transitions

[pale bison]

ok nerd

[stuck lark]

is that an insult

[pale bison]

ofc not i love nerds

~~or do i ~~

[gilded mirage]

how I do this without a graph

[dire maple]

Inequalities?

[gilded mirage]

what about them

[dire maple]

If you do sandwich, i think you would be done.

[gilded mirage]

sandwich?

[dire maple]

Yes

a <= x <= a

Then x = a

[willow bear]

uh

[gilded mirage]

que

[willow bear]

that's

not what the sandwich theorem states

[lucid hearth]

I don't think that applies here..

[native sequoia]

#precalculus
I don't see how sandwich will help here
@gilded mirage if there wasn't a 2 there do you know what it would equal

[gilded mirage]

is this not precalc?

[willow bear]

limits are calculus

[lucid hearth]

as sin(2x) gets so small, sin(2x) = 2x

[gilded mirage]

oh, thats what my new unit is on

[lucid hearth]

so 2x/x = 2

[gilded mirage]

ok so idk if this applies to here, but I think it does

my teacher gave us these theorems list

[lucid hearth]

except don't use that way

[fluid shore]

Use the cheese burger theorem

[lucid hearth]

lol

[gilded mirage]

or like formula

[dire maple]

Cheese burger?

[fluid shore]

Bruh

[gilded mirage]

and its like some weird ass french word

[stuck lark]

$\lhban$

[obsidian monolith]

RokettoJanpu:

[gilded mirage]

like l'hospital theorem or something

its like if a=0

[dire maple]

No lhopital

[gilded mirage]

then f(x)/g(x)=f'(x)/g'(x)

something like that

could I do that

[fluid shore]

$\lim_{x \to 0} \frac{\sin(2x)}{x} = \lim_{x \to 0} \frac{2\sin(x)\cos(x)}{x}$

[obsidian monolith]

Abhijeet Vats:

[fluid shore]

Then separate the limits

[gilded mirage]

why can you do that

[dire maple]

its usual trigonometry

[gilded mirage]

is this like trig identities?

[dire maple]

sin(a+b)

[gilded mirage]

but its sin(a*b)?

[dire maple]

sin(a + a)

[fluid shore]

Anyways, the cheese burger theorem is pretty good for this

[gilded mirage]

is this some type of meme?

[dire maple]

What is the cheese burger

[gilded mirage]

cheeseburger theorem

[fluid shore]

?

No?

It’s a legit theorem

[gilded mirage]

what

[fluid shore]

It’s a corollary of the sandwich/squeeze theorem

[gilded mirage]

why is it called cheeseburger

[dire maple]

I only use sandwich for comp so..

[native sequoia]

if you don't know $\sin(2x)$ identity then you can instead do $\lim_{x \to 0} \frac{\sin(2x)}{x} = 2\lim_{x \to 0} \frac{\sin(2x)}{2x}$

[fluid shore]

Oh, cos the guy who proved it won a fields medal

[lucid hearth]

yeah

[obsidian monolith]

EpicGuy4227:

[fluid shore]

and he worked at macdonalds apparently

[lucid hearth]

or u can sub 2x = u

[gilded mirage]

i got this

[dire maple]

Link it with math

[gilded mirage]

ohhh thats smart

i didn't know you could do that with limits

[fluid shore]

Yea just apply the cheese burger theorem next time

Prank

[gilded mirage]

i still don't know if you're joking

[native sequoia]

are you talking about this?

[gilded mirage]

that looks too much for my ability

if thats what this so called cheeseburger theorem is

[fluid shore]

No epic, that’s the wrong one

Dude i’m just memeing lol

[native sequoia]

XD it would still be a meme

[fluid shore]

I gave a serious answer at first, I have to meme around after that

[gilded mirage]

ok but like how do i find limits without a graph

idk what splitting them into sin(x)cos(x) does

[dire maple]

Theres that u sub

lim sin(u)/u/2

[fluid shore]

You can just split them after:

$2 \cdot \lim_{x \to 0} \frac{\sin(x)}{x} \cdot \lim_{x \to 0} \cos(x)$

[obsidian monolith]

Abhijeet Vats:

[gilded mirage]

so you try to split them into like, interpretable limits

[fluid shore]

All three are standard limits so you should be able to get them easily

[gilded mirage]

so its just manipulation

[native sequoia]

it's voodoo magic from analysis

[gilded mirage]

but does that hospital rule apply here

or is it useless

[dire maple]

hopital? Thats calc

[gilded mirage]

we learned it today with a sub

thats why im confused

[dire maple]

Sub?

[gilded mirage]

substitute

[native sequoia]

teacher

[dire maple]

eh..

What does the sandwich state again?

I always used it in comps so i never got to the formalities

[gilded mirage]

sandwich is the samething as squeeze theorem right?

[fluid shore]

Yes they’re the same thing

[dire maple]

Can you state it?

Ah, let me google it

[gilded mirage]

ohhhhh

so you used this

[willow bear]

you could also multiply and divide by 2 instead

and get 2 * sin(2x)/(2x)

sin(2x)/(2x) -> 1

[dire maple]

By the way, i never said sandwich theorem

[willow bear]

If you do sandwich, i think you would be done.

[gilded mirage]

so sinx/x=1 ?

[willow bear]

sin(x)/x doesn't EQUAL 1 ever

it APPROACHES 1 when x goes to zero

[dire maple]

I did not say it was a theorem

[gilded mirage]

oh so ->1

[willow bear]

then what is it, einstein

[fluid shore]

Ann, epic suggested that approach already

[dire maple]

Nothing

[gilded mirage]

so in this case, I can simplify to 1

so that (2sinx*cosx)/x -> 2cosx

[willow bear]

no

cos(0)=1

[gilded mirage]

wait so its right?

i just need to simplify

2cosx -> 2(1) -> 2

omg its right

omg i get math for once

[dire maple]

Me noticing that i got sandwich wrong

[gilded mirage]

so I just to memorize these trig identities and it'll be fine

atleast for trig limits

[native sequoia]

there's a ham sandwich theorem

[fluid shore]

Don’t memorize

Oh shit nice

[gilded mirage]

i am not going to derive them, that sounds like too much work

[dire maple]

Oh, i met that theorem before

[fluid shore]

Don’t memorize trig identities, you can find proofs for them and learn those instead

[native sequoia]

i first saw it on numberphile way back

[gilded mirage]

we did one proof on it today

[dire maple]

numberphile is a bad source

[fluid shore]

<Wants to learn math
<Doesn’t want to work to learn math

[gilded mirage]

it was a simple one though

tan(x)=sin(x)/cos(x)

[dire maple]

that is not a formula

[gilded mirage]

no but like I find it easier to memorize them

[fluid shore]

Unfortunately, math doesn’t reward those who blindly memorize

At some point, you’ll end up getting punished for it.

[dire maple]

Can you use complex for trig identities?

[gilded mirage]

i mean like for now, I have to memorize them, my teacher is making us do proofs throughout the unit on identities

maybe after I'll find them more useful

[fluid shore]

Sure

[dire maple]

Can i use sandwich for:
1 <= sin(x)/x <= cos(x)

[stuck lark]

in a reasonably tight deleted neighborhood of x=0, sin(x)/x is actually less than 1 and greater than cos(x), so you instead have cos(x) < sin(x)/x < 1 which is fine for applying squeeze theorem to

[dire maple]

Ah, i got the signals wrong

[odd dagger]

$\prod_{k=1}^{n-1}\tan\left(\frac{\pi k}{n}\right)$

[obsidian monolith]

tadders:

[odd dagger]

how do i simplify this

[uncut mulch]

what specifically is the question asking for?

[odd dagger]

simplify it so it isn't represented as a product but an expression in elementary functions

should i try n=2, 3, 4 and make a guess

[willow bear]

are you sure you aren't gonna run into any issues for n even

what with multiplying by an undefined value and all

[odd dagger]

@willow bear yea i have to consider special cases

[dire maple]

Is $ \tan\left(\frac{\pi}{2} + x\right) \tan\left(x\right) $ be of any help?

[obsidian monolith]

Ebisun:

[dire maple]

Sorry for the ping

[obsidian monolith]

Kelfran:

[lucid hearth]

because with first term and last term, tan(α+β) = tan(1+n-1) = tan(n)

second term and second last term tan(α+β) = tan(2+n-2) = tan(n)

Not sure about the numerator tho

[stuck lark]

\tan

[jovial hazel]

Find the sum of the infinite geometric series with first term 1 and common ratio 2/3

im using this formula

but im guetting the wrong answer

[dire maple]

Work?

[jovial hazel]

yes 1 sec

[dire maple]

Rationalize

[jovial hazel]

@dire maple wdym?

[dire maple]

The denominator is 1/3

[jovial hazel]

yes

[dire maple]

You can multiply both numerator and denominator by e

3*

[jovial hazel]

hmm i gotta look that up

[sturdy haven]

Helllp

[jovial hazel]

but was my use of the formula correct? @dire maple

[dire maple]

Yes

[jovial hazel]

ok thats great

[lament garden]

Hi, i need help with 2 questions

[dire maple]

Is this pre-calc?

[jovial hazel]

@dire maple tell me if you get annoyed by me pinging you, but so basically since 1/3 is the same as cube sqrt we can rationalise it?

[dire maple]

cube sqrt?

wdym

[lament garden]

Yes it’s pre-cal

[dire maple]

x⅓?

[jovial hazel]

i mean 1/3 3sqrt thing

[dire maple]

I still do not get it

[jovial hazel]

when there is a small number where the sqrt is

[dire maple]

Ah

Index?

[jovial hazel]

i think so?

[dire maple]

If you are taking the 1/3'th root of it, it should be the cube yes

[jovial hazel]

the 3

Yes but thats why we can rationalize it ?

[obsidian monolith]

Ebisun:

[jovial hazel]

ok

thank you 🙂

[dire maple]

@lament garden Use lenght of the circumference

[lament garden]

My pre cal teacher didn’t teach anything about that that’s why I’m asking help he barely teaches stuff

[dire maple]

You know the formula 2r Pi, right?

[lament garden]

Yeah

[dire maple]

Then, you know how to calculate the distance of two points in the circumference

[flat grove]

Can some explain me something more about vectors?

[cosmic raven]

@flat grove sure

[flat grove]

I mean, like everything that is basic about that

😅

[cosmic raven]

What do you know about vectors?

[flat grove]

What is it, why do we use that and how

how we write it down

I have exam about vectors in thursday and I do know nothing about it

[dire maple]

Like this one: [ a1 a2 ... an ] ?

[flat grove]

It's more like an arrow @dire maple and it has something to do with moving or sth like this

[dire maple]

Ah

You can define a vector by it's origin and it's end

Maybe stuff like sum of vectors and unit vectors?

[flat grove]

Yup

[cosmic raven]

So a 2-d vector is represented by two numbers

[flat grove]

You can tell everything about that and I'll say what I had not in the class. Book has something about this topic but i doesn't really understand that

[cosmic raven]

these two numbers are its x component and its y component

sorry 1 min

trying to find out how to write them in latex

[dire maple]

Isnt that for vectors in origin?

[cosmic raven]

usually written as:

I'm getting there @dire maple

$\langle x, y \rangle$

[obsidian monolith]

Espo:

[cosmic raven]

but it can also be written as:

$\begin{bmatrix} x \ y \end{bmatrix}$

[obsidian monolith]

Espo:

[cosmic raven]

Vectors can also be written as a magnitude and an angle, though

The magnitude is just the hypotenuse of the triangle formed by the x and y components

a is the magnitude

x and y are the components

$a = \sqrt{x^2 + y^2}$

[obsidian monolith]

Espo:

[cosmic raven]

just pythag theorem

@flat grove you still here?

[flat grove]

Yup

[cosmic raven]

any questions?

You can add vectors, subtract them, multiply them by constants, and multiply them by other vectors in a few different ways

[flat grove]

what are they used for?

[cosmic raven]

They are used for tons of things. First of all, in physics, variables are either scalers (normal numbers) or vectors. Vectors are numbers with a direction

If you add two vectors that face opposite directions, you're going to get a smaller vector

Acceleration, for example, is a vector

They're also used in multivar calc a lot

You can represent lots of things as vectors

In linear algebra, you learn about vector fields

vector fields are a way to represent some situation using vectors

it's kind of hard to explain without getting too complicated

If you go into higher level math, you'll use them a lot

or physics

[flat grove]

My topic in book is called vector on plane (without coordinate system). Translation can be not perfect

[cosmic raven]

https://www.youtube.com/watch?v=fNk_zzaMoSs this video will explain vectors better than I ever will be able to

[flat grove]

Okay, I'll look into that

[harsh cipher]

Hello

Question

[torpid pond]

what're you stuck on

[viscid thistle]

Can anyone help me find the sequence of the n term

The sequence is: 2/3, 3/4, 4/5, 5/6, 6/7

i cant find a geometric or an arithmetic sequence...

I don't know how to get to it

[woeful sierra]

it's not a geometric or an arithmetic sequence b/c it doesn't have a common ratio nor a common difference

[lusty gorge]

Can anyone help me with 2

[woeful sierra]

in this case x sub n is just n/(n+1)

[torpid pond]

,rotate

[torpid pond]

@lusty gorge what've you gotten so far

[lusty gorge]

I don’t really get the question

[viscid thistle]

@torpid pond wait so what would it be?

https://media.discordapp.net/attachments/481626699700764679/682059690586276065/IMG_20200225_210129428.jpg?width=754&height=565

here's the pic in case it helps

it's example 6

the bottom one

[torpid pond]

$a_n = \frac{n+1}{n+2}$

[obsidian monolith]

Sam:

[torpid pond]

@lusty gorge so the problem tells you that pressure is changing with depth

let's call pressure P and depth x

[viscid thistle]

so what type is it if its not geometric or arithmetic

[torpid pond]

i don't know what you'd call it

anyway, it says that pressure "varies directly" with depth

meaning that pressure is equal to depth times some number k

$P = kx$

[obsidian monolith]

Sam:

[torpid pond]

when depth is 10 feet, pressure is 4.3 psi, so let's substitute those in

$4.3 = k(10)$
$k = 0.43$

[obsidian monolith]

Sam:

[torpid pond]

so we get an equation for pressure in terms of depth, P = 0.43x

that help?

[viscid thistle]

But if it's n+1/n+2, if we use it on the term 2/3, it would make it 3/5, instead of 3/4 (which is the next term after 2/3).

@torpid pond

I don't think that would be correct

Right..?

[torpid pond]

i think you're just getting a tad confused

n is the "index" of the term

so for the first term in the sequence, n = 1, which gives us 2/3

for the second term, n = 2, giving 3/4

etc etc

[viscid thistle]

ah... so the end result ends up being n+1/n+2 = an

right?

[torpid pond]

yes

this is result

[viscid thistle]

ah... thank you very much

i understand now

[torpid pond]

any time

[viscid thistle]

🙂

[harsh cipher]

didn't get why a/b was assigned between 1 and -1

[uncut mulch]

without the restriction, you won't know for certain how many solutions there are

[harsh cipher]

hmm okay!

yea, where it said this it must be the case

then it must be the case confused me...

I usually write down list of questions to ask the teacher when I'm at school

yea it's an online course I'm taking to upgrade my courses to get into uni

[uncut mulch]

the given interval 1<a<b
ensures that
0 < a/b < 1

[harsh cipher]

to upgrade my grade

[uncut mulch]

actually nvm i derped, what they had was fine

[vague zephyr]

dont know how to solve the last one

[rigid sun]

@vague zephyr

are the green boxes correct? or are the just green because you typed something in

[vague zephyr]

they are correct

i solved them earlier but dont recall how to solve the last one

[rigid sun]

well just do what is inside the parenthesis

literally do what it says no?

what is h(-3)?

[vague zephyr]

7

[rigid sun]

ok

now substitute

[vague zephyr]

1/7

[rigid sun]

ok

[vague zephyr]

so would that be the answer?

[rigid sun]

yeah

[vague zephyr]

thanks man

[viscid thistle]

Could anyone help out with this

<@&286206848099549185>

[thin pewter]

ok

so we know a1 is -2 right

and a2=-3 times a1

[viscid thistle]

Yes

[thin pewter]

substitute a1

[viscid thistle]

so a2 = 6?

[thin pewter]

yeah

and repeat the steps

all the way to a4

[viscid thistle]

wait

how did u get a2=-3

[thin pewter]

a2 isn't -3

[viscid thistle]

oh sorry wait i misread

[thin pewter]

a2 is -3 times a1

[viscid thistle]

so what would a4 equal

it would be

[thin pewter]

well a2 is 6

so a3 would be 6 times -3

[viscid thistle]

so 6 times -3

ohhhhh

[thin pewter]

yup

[viscid thistle]

then for a5 id do -18 times -3

right?

[thin pewter]

a4

not a5

[viscid thistle]

a4*

yes

[thin pewter]

but yeah

[viscid thistle]

so the concept is that i keep taking the number

that i got

and use it for the next one

right?

[thin pewter]

yes

[viscid thistle]

ah

thank you mate

🙂

[thin pewter]

yup no problem

[viscid thistle]

so for a2 on example 8, it would be 4 times 3

but id subtract 12 by 1?

for a2

@thin pewter

[thin pewter]

nah

it would be 3(a1-1)

the a1-1 is in parenthesis, meaning that it you have to solve that part first

a1=4

so 4-1=3

and 3 x 3 is 9

so a2 would be 9

[viscid thistle]

ohhh

so a3 would be 9-1 = 8

8 times 3

[thin pewter]

yeah

[viscid thistle]

24 would be a3

ahh

thank you again haha

[thin pewter]

np

[high light]

I have a math test to@tomorrow and me and my friend don’t get this

number 26

[fleet yew]

@high light bro

This is simple

[high light]

howww

[fleet yew]

Split the triangle in half

[high light]

omg

trhank you

[fleet yew]

👍

[high light]

:)))))

[winter isle]

i’m confused on number 51

how do you come up with equations

[willow bear]

well what's your unknown

it's the amount to be put in the 3.5% bond

call it x

then write out an expression for how much goes into the 5% bond, in terms of x, keeping in mind that you have a total of $24000 to invest

then write out how much interest you'll get, in terms of x

then equate that to 930

and that'll be your equation

does everything i've said make sense to you? @winter isle

[forest kiln]

how would i even start problem 8

[fading token]

any domain with at least two points should do

of course, with a suitable co-domain which needs to be defined

[still yew]

Funny thing that happened two days ago: We just learned the difference quotient with the function f(x) = x^2.

When we did everything, I yelled, "LOOK, WE ALMOST DID THE DERIVATIVE"

[fleet yew]

@still yew k

[neon garden]

I don’t understand how to do 3, can anyone explain it?

[uncut mulch]

which part don't you understand?

[neon garden]

Here’s a better picture

Well

I don’t know how to start

[uncut mulch]

did you know how to do the other questions?

[neon garden]

I don’t get what it means by “r varies directly as s and inversely as t”

I understand #1

[uncut mulch]

$r = k \cdot \frac st$

[obsidian monolith]

ramonov:

[neon garden]

Alright

[uncut mulch]

if you don't quite understand the term, look up inversely proportional

[neon garden]

So proportional is y = kx and inversely is y = k/x

I get that part

So for number 3 if it’s directly proportional you just put it in the numerator?

[uncut mulch]

yeh

[neon garden]

Oh ok

[gilded mirage]

is this just like algebraic manipulation?

[clever inlet]

Probably

[gilded mirage]

ok good

tbh idk what to do, i factored the denominator into (x-5)(x+3) and now im stuck

i tried getting x+3 in the numerator but idk how I could

[empty fulcrum]

Recall that x^2-9 is a difference of squares and can be factored as such

[gilded mirage]

oh so like perfect square

(x+3)(x-3)?

[empty fulcrum]

Ye

[gilded mirage]

and now i have x-3/x-5

do I just plug in -3?

orrrr

[empty fulcrum]

Yep

[gilded mirage]

idk

[empty fulcrum]

No that's correct

[gilded mirage]

why couldn't I do that initially?

[empty fulcrum]

Because you would have a denominator of 0

[gilded mirage]

oh

[empty fulcrum]

As long as x isn't negative 3, you can reduce this fraction, and the reduced polynomial will reach the same point that the OG would have as its limit

[gilded mirage]

omg 3/4

[empty fulcrum]

Ye

Very good ♥️🦈

[gilded mirage]

Does this look right

[willow bear]

yes\

[gilded mirage]

[gilded mirage]

What would it be?

Is there a possible exponential equation for this

[gilded mirage]

Nvm solved

[vapid torrent]

is the average represenatitive of the distrubtion here? how can i tell when it is/ is not

<@&286206848099549185>

i would say no, right? since its skewed pretty heavily on the left?

anyonr

[valid violet]

Im not sure what "avg representative" means

[vapid torrent]

@valid violet im not either, but i think it asking of the average here represents the distribution well

[valid violet]

Ah

That's not a very mathy question

It's subjective

And it's really not right that they say "average" here without saying what type of average

It usually means arithmetic mean but it's sloppy to just say "average"

i would say no, right? since its skewed pretty heavily on the left?
@vapid torrent

Why does 4that mean the avg isn't representative?

[vapid torrent]

when would it not be then? @valid violet

[valid violet]

I didn't say it was or wasnt

Im asking you to justify your statement

[vapid torrent]

@valid violet because it kind of skewes it to one side

[valid violet]

Does it skew towards or away from the mean

[vapid torrent]

the mean doesnt skew away from the mean?

[valid violet]

Youre saying the data are skewed

If the data are skewed to be close to the mean

Then does that mean the mean is a good representative or a bad one?

[vapid torrent]

bad @valid violet

[valid violet]

I would say good actually

it means most of the data is near the mean

if most of the data is near the mean, the mean is near most of the data

why do you think bad?

[vapid torrent]

that makes sense actually

i have one more q

Based on this line, estimate the ratio of frequencies (n) between x and x + 1, where x is magnitude.

what does that mean @valid violet

[valid violet]

they're asking about something similar to slope, except the data aren't continuous here so it's not exactly slope

you're familiar with slope being rise over run, yes?

[vapid torrent]

yes

@valid violet

[valid violet]

so here the "run" is just 1, the difference between x and x +1

because x - (x+1) = 1

they're asking you to estimate the "slope" of this "curve"

I'm using quotation marks because it's a histogram, not a curve

[vapid torrent]

ok but at whatr points @valid violet

[valid violet]

they say "estimate" so you want to find one that approximately works for the whole histogram

[vapid torrent]

how would i do that

[valid violet]

I dunno, how do you find the slope of a line?

[vapid torrent]

rise over run

first and last point

log10(4.4)-log(10)(0) / (4.5-8.75)

@valid violet

[valid violet]

uh I dont know where those numbers are from

[vapid torrent]

estimates

[valid violet]

why log_10(4.4)

[vapid torrent]

from the graph

its where it maxes it out roughly

[valid violet]

the one you sent me has no axes labelled

[vapid torrent]

it does its in grey over black :/

[valid violet]

lol

[vapid torrent]

hard to see ahah

[valid violet]

okay, so, is it justifiable to use one slope for the whole histogram?

is that a reasonable thing to ask for?

in general for sure not

[vapid torrent]

yes since its linear

seems to make sense

[valid violet]

like in your first question it doesnt make sense

aah, so you're saying

[vapid torrent]

this is what i think i am not sure

[valid violet]

the tops of the bars look like they're approximately in a straight line?

[vapid torrent]

well the line is literally linear and its the line of best fit

[valid violet]

yes but you can find the best fit line for data of any shape

[vapid torrent]

oh

so should we use the boxes

we can use the top left box and the top right one

[valid violet]

are these data appropriate to fit with a straight line?

let me find a picture one sec

https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0180701.g007&type=large

here the person found the best fit line

but it's not at all obvious to me that finding the best fit line was a good idea

clicking on the page it comes from

they justify their line with a value called the p-value

[vapid torrent]

ok

so we can use the boxes then

[valid violet]

so it is indeed justified probably

maybe

complicated