precalculus

[harsh cipher]

I don't know why but after putting in the equation in the red in my calculator and settings the window settings as shown.

I did not get the same graph as the picture.

[clever inlet]

what did you get

[harsh cipher]

There aren't any reflections and amplitude and vertical displacement seem correct.

I got a very weird graph that starts at the middle and does not show the full cycle. (period)

This is what I put in the calculator

4.5 Sin (pi/180(x-4)+4.9. Then window dimension exactly the same.

[pulsar imp]

Hey, I noticed you're missing the closing bracket in the last post

[unkempt burrow]

Hi. Can I ask for help here?

[stuck lark]

if it's precalc

[unkempt burrow]

Yes

It’s very easy for other people but I’m having trouble understanding factoring

I’m taking it online and the instructions are even more confusing

[patent beacon]

Have an example?

[unkempt burrow]

I only understand how they got the -1 and 20 after that im lost

[patent beacon]

I see, synthetic factoring

It's been a while since I've used this method hol up

[unkempt burrow]

I thought the answer would be (y-1) (y+21)

Thank you

[patent beacon]

If that were the answer, then the constant term would have to be (-1)(21)

But it's -7

[unkempt burrow]

Ya the right answer is (3y-1) (y+7)

[patent beacon]

So do you understand that they're looking for two numbers that multiply to (3)(-7) and add to 20?

[unkempt burrow]

Yes

[patent beacon]

Only possibility is 21 and -1

[unkempt burrow]

It’s -1 and 21

Yes

[patent beacon]

They actually write 20 = 21 - 1 into the equation

That is, they take:
3y² + 20y - 7

And write it like
3y² + (21 - 1)y - 7

[unkempt burrow]

I see

[patent beacon]

Finally:
3y² + 21y - y - 7
Can be factored by grouping

[unkempt burrow]

Ok

[patent beacon]

Does it make sense? Feel free to ask if there's something missing

[unkempt burrow]

How can you factor by grouping? Sorry

[patent beacon]

So let's say we have something like:
3y² + 21y - y - 7

I can arrange it like so:
3y(y + 7) - (y + 7)

Now, note that the term in the brackets is the same both times, that's important. Let me do a substitution, let y + 7 = u:
3yu - u

Common factor:
u(3y - 1)

But u = y + 7:
(y + 7)(3y - 1)

[unkempt burrow]

Ohhh okay. I think I understand now. Thank you :)))

[harsh cipher]

@pulsar imp Got it. That bracket cost me 90 minutes or more

@pulsar imp Thanks

[leaden stratus]

Knowing that the angle is 0 < alpha < pi/2, find sin and cos of the angle (we also know the equation in the photo).

How would I do this?

[uncut mulch]

start by expressing it in terms of sin and cos

[leaden stratus]

You mean that I have to replace sec with 1/cos and csc with 1/sin?

[uncut mulch]

yes

makes it much easier to work with

[leaden stratus]

Ok, did that

[uncut mulch]

what do you have now?

[uncut mulch]

simplify

[leaden stratus]

I get 3tana - 4 = 0

[uncut mulch]

continue

[leaden stratus]

So tana is 4/3?

[uncut mulch]

yes

[leaden stratus]

Thanks, I solved it doing a system with

sina = 4/3cosa
sin^2a+cos^2a=1

[uncut mulch]

drawing a triangle would be more efficient

[leaden stratus]

I don't know this method

[uncut mulch]

draw a right triangle where tan(a) = 4/3

[leaden stratus]

Mh

K

Another thing

Pt. 1

Pt. 2

Have I solved it correctly? 🤔

[uncut mulch]

whats the original question?
prove the identity?

you shouldn't write those equations like that since you haven't demonstrated that they're actually equal

instead do
RHS =

= ...

and try to manipulate that 1/( 1 + cos^(x)) while its in the fraction

and eventually reach RHS = LHS

[leaden stratus]

@uncut mulch what?

And yes, it's prove the identity

[kind dust]

is college algebra precal? or is trig college alg

[civic plaza]

College algebra and trig is a part of precal

Trig is usually taught in it's own course separately from a college algebra course

[sturdy haven]

I am taking honors precalc/calc junior year

Any advice

[restive mauve]

do your homework

[sturdy haven]

Damn bro

Thats crazy

[serene heath]

dont fail

[fleet yew]

@sturdy haven think about it in terms of turns

that is, fractions of 2 pi

like 270 degrees is 3/4 of a circle

so it is 3/4 * 2 pi

6pi/4

=3pi/2

also one of the reasons tau is superior to pi

[sturdy haven]

What is a transcendal number

[clever inlet]

transcendental?

[sturdy haven]

Yes

[clever inlet]

not an algebraic number

so not a root of a polynomial equation with integer coefficients

[sturdy haven]

Like e?

[clever inlet]

yes

[sturdy haven]

Sorry e is a root

X-e=0

[clever inlet]

integer coefficients

[sturdy haven]

One is an integer

[clever inlet]

???

e is not an integer

[sturdy haven]

Ohhhhhhhhhh sorry

Thanc for me teach

Also I have a question

[soft night]

😩

[sturdy haven]

How hard is precalculus half year?

[soft night]

Extremely hard

How tf am I supposed to know that

Idk what your curriculum is

[sturdy haven]

You were not part of this conversation

[soft night]

pre calculus is the class before calculus

so

[sturdy haven]

NO WAY

OMG

[soft night]

Yeah

So if ur a god at algebra

Pre calc ez

Quite honestly

[sturdy haven]

I did really well in geometry and above 90s in agelbra 2

[soft night]

Ok

Then you should be fine

most likely

[sturdy haven]

Is it true that

You have to memorize the unit circle

[soft night]

Most students do

[sturdy haven]

Aight bet

[soft night]

it makes life easy

Nobody likes doing that work in their head

If you can just say it without thinking then it’s easy

[viscid thistle]

😩is any1 here😩

[clever inlet]

[viscid thistle]

gr8 okay so

how do i find the full range of a function? pretty sure i need to find the inverse then the domain and that'll be the range, but i tried doing it on f(x)=(x^2)/(1-x^2) and i just keep going wrong somewhere

algebraically not graphically

[clever inlet]

why not just reason about it with limits and testing some stuff

[viscid thistle]

i'm very new to pre calc like the semester just started the other week

it's so simple to find the domain, but i only need help finding the range,,,

[clever inlet]

ok

what did you get when inverting?

[viscid thistle]

1 sec

i did x=(y^2)/(1-y^2) then multiplied both sides by (1-y^2) to get rid of frac and got
x-y^2x=y^2

idk what do now or if i even did that right

[clever inlet]

that looks fine

now try move all y terms to one side

and all non y terms to the other

[trim cargo]

I’m stuck with a question

Need some help

[viscid thistle]

ik i need to do that but idk how

like what do i do with -y^2x

i moved it to right and got

x=y^2+y^2x

[clever inlet]

factor out y^2

[viscid thistle]

like x=(x)y^2

[clever inlet]

almost

[viscid thistle]

😔that's what i get when i factor it😔

[clever inlet]

missing a 1

[viscid thistle]

x=(1x)y^2

[clever inlet]

x = y^2(1 + x)

[viscid thistle]

so x/(1+x)=y^2 then sqrt(x/(1+x))=y then 1+x=0 and 1+x>0

[clever inlet]

x/(1 + x) >= 0

[viscid thistle]

x>=-1 and x>=0 ?

[clever inlet]

= -1?

[viscid thistle]

1+x>=0 sub 1 both sides because frac can't be divided by 0

[clever inlet]

this inequality is satisfied when both the numerators and denominators are positive

or both are negative

[viscid thistle]

😔

[warm crescent]

https://cdn.discordapp.com/attachments/298216246460022784/671248434665226240/638725608947580928.png

I dont get this notation

[heady jewel]

seaech sigma notation

[nova dew]

$\lim_{x\to 0} \frac{3x^3-4x^2}{11x^2-5x^3}$

[obsidian monolith]

CoolShot:

[nova dew]

can i factor out an x² and cancel it out here

or would that be wrong

if I do I get the answer as -4/11 which id apparently wrong

not sure where I'm going wrong here

i think i can cancel it because x≠0 here but only approaches 0?

[plain lake]

you can factor it out because this just means you'll have a hole at 0

it won't effect your limit evaluation

[nova dew]

ic so the answer -4/11 is right?

[plain lake]

yes

[nova dew]

aight thanks

[astral mountain]

How do I see if f'' is 0 or not on this function as example

On a given x value

Without calculating f''

hmm

but there are points of inflection where its not 0 i thought

or is there not?

For this function

Is the inflection at x=3 0

?

or does it not have a f'' value there?

cuz the solution says its not in the domain

of f''

[slow roost]

How do you graph the function 2x-4/x^2-4

Like when I used photomath it said the y intercept was at 1

So how do you find that out

And what is the purpose of the zeros/roots from the graph like I got that the zero was 2

[stuck lark]

graphing the function $x\mapsto\frac{2x-4}{x^2-4}$, do some algebra first

[obsidian monolith]

RokettoJanpu:

[stuck lark]

$\frac{2x-4}{x^2-4}=\frac{2(x-2)}{(x+2)(x-2)}$, note $(x-2)$ on top and bottom

[obsidian monolith]

RokettoJanpu:

[stuck lark]

this means you can really just graph $x\mapsto\frac{2}{x+2}$, except there's a hole at $x=2$

[obsidian monolith]

RokettoJanpu:

[slow roost]

Ohhhh

But how would i approach the graphing

I found the asymptotes

HA: 0

VA: +-2

But it can’t be +2?

[stuck lark]

read my last msg

[slow roost]

Ah I see

[broken minnow]

Can this be re-written as Pvap = e^-Hvap/R*1/T?

[rigid beacon]

@broken minnow

[broken minnow]

Idk what that is LOL

[rigid beacon]

parentheses

do you mean

$P_{vap} = e^{-\frac{\del H_{vap}}{R} \frac{1}{T} + C $

[obsidian monolith]

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

[rigid beacon]

is that what you mean?

(cause you also forgot the add the +C)

[broken minnow]

Yes

[rigid beacon]

then yes

you're correct

that's how you convert from logarithms to exponetials

[broken minnow]

Yes

However

That equation

In this form

Is supposed to be

[rigid beacon]

uh huh

[broken minnow]

A line

[rigid beacon]

?

I mean

A line sure

but which axis is what variable

[rigid beacon]

yes

that is correct

[broken minnow]

Yet

[rigid beacon]

because your y-axis is not y

it's ln[P_vap]

[broken minnow]

K but like

If I transform it to

The exponential form

Shouldn’t it be the same graph ?

[rigid beacon]

No

[broken minnow]

Why

[rigid beacon]

that

[broken minnow]

How do I even graph that tho

[rigid beacon]

ln(P) vs 1/T

well

[broken minnow]

Like is it even a function

[rigid beacon]

yes

let's say Y = ln[p] and x = 1/T

[broken minnow]

Rite

[rigid beacon]

so I get

$ y = -\frac{\del H_{vap}}{R} X + C$

[obsidian monolith]

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

[broken minnow]

Right

[rigid beacon]

that's a linear function of Y vs X

right?

[broken minnow]

I guess

[rigid beacon]

is that not clear to you?

[broken minnow]

Imean yes I see it

[rigid beacon]

ok

[broken minnow]

Y=mx+b

However

[rigid beacon]

exactly

if I sub back in those things

Y = ln[p] and x = 1/T

[broken minnow]

I’m just confused how I’d graph it tbh

[rigid beacon]

I mean

that would be hard to graph by hand yea

[broken minnow]

K but I jus need the logic behind it tbh

For example

If t=1

And let’s say the slope is also 1

It’s essentially

[rigid beacon]

The axis don't increase linearly

[broken minnow]

Lnpvap = 1/1

?

So pvap = 0 ?

[rigid beacon]

what?

[broken minnow]

If I plug in

T= 1

It would essentially be

Ln(pvap)= 1/1

(Assuming those extra letters are zero)

[rigid beacon]

if they're zero

[broken minnow]

Therefore pvap is 0 ?

[rigid beacon]

then ln[p_vap] = 0

well not even

because R can't be zero

can't divide by zero

you're missing the point forget this

your axis aren't increasing straight

[broken minnow]

But r isn’t zero

It’s 1

[rigid beacon]

it's not just T going up linearly

or P_vap going up linearly

[broken minnow]

But it’s apparently a line

[rigid beacon]

the X axis is changing by a factor of 1/T as you move from left to right

not changing by a factor of T

[broken minnow]

Then how is it a line

[rigid beacon]

Y = ln[p] and x = 1/T

if we make these subs

we get a linear function

so instead of an X-axis

we have a 1/T axis

and instead of a Y-axis

we have a ln[P_vap] axis

[broken minnow]

Oh so it’s only a line when you make those substitutions

[rigid beacon]

yes

[broken minnow]

But when you don’t make the substitutions

[rigid beacon]

it's not a T vs P_vap graph

it's a 1/T vs ln[P_vap] graph

[broken minnow]

It’s exponential ?

Decay ?

[analog minnow]

https://gyazo.com/991e9923c6b18f1df7f024668beccb6d

Can anyone help with this? When I do positive infinity I get:

f(inf) = 3-[(-1)/(inf-4)]

and I don't know what that means for my limit..

I have a TI-84 and tried to get a value for x=E99 but it says invalid.. at x=E-99 I get y=2.875

[runic tapir]

The first issue is there's no such value of $f(\infty)$ and an additional one is when you do "plug in" infinity I don't see how you get negative 1 in your numerator and $\infty-4$ in your denominator

[obsidian monolith]

Intel Core i7-8700:

[runic tapir]

Are you familiar with asymptotes?

[analog minnow]

Mildly yes

[runic tapir]

So you know what happens when you divide a constant by a really large number?

[analog minnow]

yes

[valid violet]

Do you know what a limit is?

[valid violet]

that's illegal in 39 states

[uncut mulch]

^

[runic tapir]

Using that intuition is how you can solve that problem. Is there something different about this problem?

[valid violet]

f is implicitly defined only for numbers. infinity is not a number

[runic tapir]

What's tragically funny is that you can get the right answer with the wrong process as written

[valid violet]

it's like evaluating f at x = honeybee

[runic tapir]

$f(\diamondsuit)=?$

[obsidian monolith]

Intel Core i7-8700:

[stuck lark]

plugging in infty into a function is illegal in 1 more state than saying 3(x+2) is equivalent to 3x+2? which state is that?

[valid violet]

well 3(x+2)=3x+2 for x = infinity

[stuck lark]

hhhhhhhhhhhh

[analog minnow]

So I have a horizontal asymptote at x=infinity?

[valid violet]

there is no such thing as "at x = infinity"

are you reading what we're saying

[analog minnow]

assuming x is a very large value like 9999999

[runic tapir]

x can approach infinity

[valid violet]

is that number equal infinity now

that makes calculus easier

do you know what a limit is?

[pliant tree]

you have an asymptote at x=2 and 2=-2 i believe

[valid violet]

limiting behavior?

[analog minnow]

I am not a pro in calculus by any means

Not even close to being good thats why I came here

[valid violet]

why are you avoiding my question. "No" is a perfectly good answer to "do you know ____". I'm not asking to shame you\

[analog minnow]

https://gyazo.com/485f4ac0cc90aa70a2acbd941dba2f6c

[valid violet]

I'm asking because how much you know already changes how I will state my answere

[analog minnow]

This is the example I was given

I understand the limit on this

[valid violet]

I don't think you do, otherwise you wouldn't be trying to evaluate f "at infinity"

[runic tapir]

It's really easy to punch down to precalc students, no need to get anal retentive. If you're going to be a jerk then let other people willing to help do so and you can be on your way.

[valid violet]

I just want to know how to phrase my explanation

[pliant tree]

ok is your question for b) @analog minnow

[valid violet]

there's nothing wrong with not knowing

[runic tapir]

You can gauge that without being patronizing.

[analog minnow]

My feelings aren't hurt, I just don't know how to explain how much pre calculus I know.. I am studying a job position as an engineer technologist and we take a 60hour course on pre calculus online

I know a lot of the other stuff but this one stumped me

[valid violet]

okay

so

to say that a function has a horizontal asymptote

is to say that there's a vertical line y = c such that f(x)-y becomes arbitrarily small as x becomes arbitrarily large

[analog minnow]

If it had a horizontal asymptote at x=0 it would mean it would approach infinity before it reached x=0.. correct?

[valid violet]

err I meant

horizontal line

[pliant tree]

yes jetter correct

[analog minnow]

Okay I understand that much about horizontal and vertical asymptotes

[pliant tree]

or -infinity

[runic tapir]

All an asymptote is is a straight line that is a close approximation to a particular curve as the curve goes off to infinity in one direction. The curve becomes very, very close to the asymptote line, but never touches it.

[pliant tree]

anytime there is a fraction, any x value that makes the denominator=0 is an asymptote

so if it was (1/x) the asymptote would be 0

your best bet is to graph the equations

[runic tapir]

@stuck lark you good buddy?

[stuck lark]

not at all

[analog minnow]

I have it graphed

[runic tapir]

Wanna talk about it?

[analog minnow]

And I understand what it means graphed I just can't get it down on paper

[stuck lark]

$x\mapsto\frac{\sin(x)}{x}$ crosses the horizontal asymptote $y=0$ infinitely many times

[obsidian monolith]

RokettoJanpu:

[pliant tree]

so you should see the line approach infinity or -infinity at 2 and -2

[stuck lark]

that's my first point

[valid violet]

I was about to give that example rokabe

way to be faster

[stuck lark]

second point, i hate it when people dogpile in here

let fauxpas speak only, everyone else please sit down

[valid violet]

I actually have to go, Ill be back in like 10 minutes

so feel free to take over

[stuck lark]

sigh

[runic tapir]

I think I was doing pretty well on my own until other people decided to chime in

[stuck lark]

i don't think so, your definition of an asymptote isn't up to par

[runic tapir]

Do you want to discuss semantics on my definition?

Because I think it's just fine.

[analog minnow]

Your definition makes sense with what I have learned so far

[stuck lark]

my example shatters your definition, you never countered that

anyway that's enough shade for now, good luck helping jetter

[runic tapir]

First off my definition comes from Barron's dictionary of mathematical terms, secondly you're being needlessly picky for the purposes of a precalculus problem.

Anyway back to the problem.

[rigid beacon]

Functions crossing asymptotes is well within the grasp of a precalc class (it was covered in mine) but sure

[runic tapir]

Jetter you want to talk about the original or the one just posted? let's hop over to #help-6

Take it up with Douglas Downing then, Jesus.

[valid violet]

Back. I see Jetter fell to the dark side

[stuck lark]

watch zeta closely just in case an opportunity to save him from palpatine's clutches presents itself

[runic tapir]

How sad of a life do you have to have to talk down to precalc students to feel better about yourselves?

[fleet yew]

How sad of a life do you have to talk down to people who talk down to precalc students to feel better about yourself?

[restive mauve]

how sad of a life do you have to talk down to people who talk down to people who talk down to precalc students to feel better about yourself?

[viscid thistle]

Let A ⊆ R be an interval and c : A → R^2 continuous such that c(A) is unbounded in the sense of the usual metric d on R^2 . We can certainly find a sequence a_n in A such that for each r>0, there exists an N in N, n > N, such that for n > N we have c(a_n) ∉ B_r(0 , 0) . Now let L \subset R^2 be a line, we say L is an asymptote to c if

$\lim\limits_{n\rightarrow\infty} \mathrm{inf}{d(c(a_n),l)\mid l\in L}=0$

[obsidian monolith]

rudy:

[clever inlet]

[viscid thistle]

for a sequence a_n as defined

[fleet yew]

this is the precalc room buddy

[viscid thistle]

Yeah yeah but

This works for @stuck lark’s definition

[runic cradle]

anyone have any idea on this? I think I understand it except for the "what is the steepest roof Calvin can sit on without sliding?" Thank you in advance! (please ping me if you respond)

[patent beacon]

@runic cradle
This is a well known result from physics, the steepest roof is given by tanθ = μ

[runic cradle]

Why is that?

[rigid sun]

in the 1800s people used to sit on their roofs

but nobody likes sititng on flat roofs

so they wanted to know what was the steepest angle they could sit on

and still not fall off

of course now adays we have shingles

so that isn't really a problem

[patent beacon]

You may have found that the parallel component is 160cosθ, and the normal component is 160sinθ

Therefore friction vector is 160μsinθ

[rigid sun]

uhhhhhhhhhhhhhhhhhh

neh guh

[runic cradle]

ohh right

[rigid sun]

neh guh

[runic cradle]

so we want 160μsinθ=160cosθ

[rigid sun]

NEH GUH

那個

😩

[runic cradle]

so 160sinθ=160cosθ(μ) and then dividing by 160cosθ gets us tanθ=μ

thank you

[rigid sun]

yes

kaynex may be on drugs rn

[patent beacon]

Oh yes

I am on several drugs

I see I mixed them up mb

[native sequoia]

I spam 那个 when talking in Chinese irl

[dim ruin]

helps

I get everything that leads up to the red marking (the work on the left), but I cant seem to figure out how I went from what is circled in red to the expression below the red circle..

[rigid sun]

youre telling me you forgot what you did?

[viscid thistle]

Mate are you an 84 year old granny with dementia

[steel veldt]

isn't that orange xd

[verbal leaf]

My teacher wrote on my test that “this is a rest, not a VA” and I’m not sure what rest means?

(The question at hand was to discover every asymptote possible of a rational function)

[clever inlet]

🤔

the only thing i can think of is a removable discontinuities

cause those get confused with VAs sometimes

but i dn't know what a rest is

do you have the full context?

[median sandal]

A rest possible a stationary point? Not sure lol

[mossy kestrel]

hello

anyone good with composition of functions

[rigid beacon]

Just send your question

[median sandal]

Ask your question, I am sure someone will be able to help 🙂

[mossy kestrel]

og

oh

sorry hold on

suppose f and g are the functions defined by f(y)= √y and g(z)= z+1/2-z

a) evaluate (f+g)(4)

[rigid beacon]

So that means add together f and g

And then plug in 4

[mossy kestrel]

what does the 4 mean

oh

so like√4 + 4+1/2-4

[rigid beacon]

Use parentheses but yes

[mossy kestrel]

oh wow

okay that was easier than i thought

i was really sick last week so i missed a ton of my classes so now im super behind

and my midterm is on thursday lol

so the answer is -.5?

[rigid beacon]

Yes

[mossy kestrel]

so what happens when its (f+g)(-1)

cause √-1 is i

[stuck lark]

identify the domains of f & g in order to identify the domain of f+g

doesn’t seem specified so ig assume the largest set of real numbers that “works” with the definitions of f & g

[mossy kestrel]

how do i do that

find the domain

[patent whale]

I've got this function, how do I know if it's continuous? How to calculate it? I don't understand tbh. I think it is continuous but I need to write it formally

[fading token]

[uncut mulch]

limits / definitions of continuity

[wet steeple]

It would have to approach 0.

from both sides to be continuous

[patent whale]

well yep but 0 is out of the domain

[fading token]

What is the definition of continuous you have to work with?

The formal epsilon-delta definition?

[wet steeple]

It’s piecewise; 0 is explicitly within the domain

And yeah that looks continuous

[patent whale]

they didnt tell us what definition of continuous we have to work with

something like this id guess

yep

[fading token]

That's the formal epsilon-delta definition

This particular function is usually done as follows (the lazy way):
when x is not 0, the function is continuous (because it's a product/composition of continuous functions)
when x approaches 0, you can show (with e.g. the squeeze theorem) that the function approaches 0 to any arbitrary amount

So the function is continuous everywhere (because the value of the function at 0 is defined to be 0)

this does require some preliminary knowledge, so I find it strange that you have to go through the extra hoops by proving this from the bare basics of the definition of continuity

[patent whale]

well yeah i dont understand it either

but i just have to

anyway, thanks

[fading token]

So, to rephrase, you do have to employ the definition of continuity, but only in the case of x = 0 (I think, or otherwise use the squeeze theorem)

When x is non-zero, you can rely on the well-behavedness of x*sin(pi/x)

[obsidian monolith]

WhipStreak23:

[fading token]

[stuck lark]

$x\mapsto x\sin\br{\frac\pi x}$

[obsidian monolith]

RokettoJanpu:

[fading token]

[obsidian monolith]

WhipStreak23:

[stuck lark]

nani

[harsh cipher]

Question

From the unit circle in trigonometric functions

How do I know at pi/4 the coordinates are root 2/2 , root2/2?

[sharp marsh]

(-1 - 3)^2 + (-1+4)^2 = r^2

-4 ^2 = 16

3 ^ 2 = 9

25 = r^2

R = 5

no?

[valid violet]

What's the standard form of a circle @sharp marsh?

Your conclusion that r=5 is correct

But the rhs of the standard form of a circle isn't r

[sharp marsh]

r^2

Oh

[runic tapir]

did you lose your ℌonorable role @valid violet ?

[valid violet]

I never had a role

I can't be trusted with such power

[serene heath]

you're honourable in my eyes 😽

[obsidian monolith]

Pingu:

Pingu:

[sharp marsh]

Slightly confused

[reef rune]

use desmos

graph all the equations and see which ones intercept the x axis 3 times

which means its not a quadratic

[sharp marsh]

oh

Would it just be the first one then?

[runic tapir]

Yes

[sleek pawn]

hi

really simple thing but how would I solve this?

$\lim_{x\to3}\frac{x^2-4}{x^2-5x+6}$

[obsidian monolith]

A regular kugelblitz:

[fleet yew]

Factor top and bottom

[sleek pawn]

that gives me ((x-2)(x+2))/((x-3)(x-2))

3-3 at the denominator

[fleet yew]

Cancel the x-2

[sleek pawn]

mhm that gives me x+2/x-3

5/0

[fleet yew]

Long division

[sleek pawn]

lol what?

[fleet yew]

Polynomial division

[sleek pawn]

what do I divide by?

[fleet yew]

Do you know how division works lol

[sleek pawn]

I mean yeah, haha

but like, what do I divide? 5/0?

[fleet yew]

No divide the polynomials

You can do division with polynomials lol

[sleek pawn]

hmm I'm not sure I've tried that before

how would I do it?

[fleet yew]

Like straight up do (x+2)÷(x-3)

[sleek pawn]

oh

I thought the original polynomials

[fleet yew]

How are you learning limits and not know polynomial division lol

[sleek pawn]

idk I have many learning gaps

I think I've done it before but I might not remember

[fleet yew]

Anyway you should just know that if you have a function in the form A/0

Where A is not 0

And is a constant when you plug in x

You can just say the limit is at +-inf

No two sided limit exists for a hyperbola

[sleek pawn]

is that always the case or does it only apply to hyperbolas?

[fleet yew]

Not always

But usually yeah

[sleek pawn]

and how would I solve it with long division?

[fleet yew]

Look up polynomial divison on khan or something

[sleek pawn]

oh ok

thanks

[scarlet beacon]

anyone care to help? The other channels are being used.

[clever inlet]

What have you tried

[scarlet beacon]

I am lost

i don't know how to tackle it.

this is new material

[valid violet]

What's "your formula"

[scarlet beacon]

x=-6

[valid violet]

In the question it says to use "your formula "

[scarlet beacon]

I know. I am confused. I don't see a formula.

[uncut mulch]

probably the formula to get the equation of the appropriate line

[scarlet beacon]

Really not trying to play dumb but super lost.

[uncut mulch]

can you determine the equation of the line given 2 points (on the line)?

or given the slope and a point

[scarlet beacon]

I can find slope. Rise/run

[sharp marsh]

How do I do this?

I know it involves (0,0)

[rigid sun]

wow

thats crazy

[sharp marsh]

?

[rigid sun]

wouldn't it be cool if a function gave you a y value with a given x value

it would be cool because then you could see what y value goes with each x value

[sharp marsh]

Don't you have to get the origin?

[rigid sun]

it would also be cool if there was a coordinate system

where coordinates are represented in the form

(x,y)

[sharp marsh]

.

[rigid sun]

where x gives the x value location of the point you want, and the y value is how high or low it is

that would be insane though because then everyone would be able to test if points passed thorugh the origin

they could put 0 in for x and see if y=0

they could put 0 in for x and see if y=0$$

[obsidian monolith]

maleb1964:
Compile Error! Click the reaction for details. (You may edit your message)

[rigid sun]

[sharp marsh]

[rigid sun]

they could put 0 in for x and see if y=0$$

[obsidian monolith]

maleb1964:
Compile Error! Click the reaction for details. (You may edit your message)

[rigid sun]

https://cdn.discordapp.com/attachments/363224154469826562/671941462795223060/Screen_Shot_2020-01-28_at_11.54.56_PM.png

[sharp marsh]

i got it

o

[fleet yew]

If it's implicit it's not a function

Implicit function is an oxymoron

[sharp marsh]

y = -8/6 = -4/3?

[clever inlet]

You don't need the extra parentheses

[sharp marsh]

ohhh

thx

Much appreciated

[viscid thistle]

How do you find the cotangent of an angle without a calculator

[fleet yew]

@lilac relic my bad lol i guess that is correct

I just had learned in school that if it was implicit then it wasnt really a function

No wait wikipedia itself says I'm right

If tou look under the definition of function

[viscid thistle]

"Wikipedia"

[fleet yew]

"In mathematics, a function is a relation between sets that associates to every element of a first set exactly one element of the second set. "

See you cant have multiple y values for one x value

so x^2+y^2 =1 is not a function because there are multiple y values for the same x

[viscid thistle]

Can someone help me with my question

I am really stuck

[clever inlet]

Learn your special angles

Beyond that

Yeah

Kind of difficult

[fleet yew]

Cot generally equals reciprocal tangent

Technically not always but usually

[viscid thistle]

My only lead is that cotangent theta is equal to cos theta divided by sine theta this barely helps me as how do I find cosine and sine without a calculator as well

[clever inlet]

For any arbitrary angle?

Or just specific angles?

[fleet yew]

Ok that image scrambled

http://mathworld.wolfram.com/MaclaurinSeries.html

Here

Scroll down to where it says tan x

[clever inlet]

That kind of just pushes the issue along though doesn't it

[fleet yew]

What i was saying before is that cot is defined at points where tan is not

Like points where cosx=0

[elfin birch]

https://gyazo.com/5460f3621c9e176355269f1d7f085db9
how tf did i get this wrong

csc600 is -2root3/3

[clever inlet]

Lul

[elfin birch]

bruh

[clever inlet]

[elfin birch]

thats right tho, right ?

like im doing it right ?

[clever inlet]

It is

[elfin birch]

ok thats all that matters

ty

[viscid thistle]

@clever inlet for this specific problem I want to find the cotangent of 30 degrees

[clever inlet]

Special angle

These you should know

[viscid thistle]

So how do I do it

[slow roost]

How would I figure 12c our from my graphing calculator

I tried doing the label but it wouldn’t work

Value only works for x

[elfin birch]

if the sin = 7 does that mean that sin = 7/1 ?

so r = 1 ?

https://gyazo.com/837ea8e4a55ef53694efaf2fb8f1815d

or no

<@&286206848099549185>

[viscid thistle]

@lilac relic why root 3

Okay I understand

That

It's that due to reciprocal functions right

I have no idea what tan 39 is

I get to 1 / tan 30

Then pass that I don't know how to get to the route 3

Root*

What principle says that

Is there a conversion

Yes true

[elfin birch]

yo phil

[viscid thistle]

I know that 10 x equals sinx / cos x but how does that make tan 30 root 3

Tan*

Not 10

But how

Still confused by how

Yes

Yeah

Now hold on how do we know any of the lengths of the triangle

Wait what all I know is that I have all the angles but no lengths how do you figure out any of the lengths with just all the angles

Sorry if u just explained it dont understand

And I know it's a right triangle

Oh so we free assign as a ratio type thing

would the answer always be the same as the answer you would put in a calculator

And how

Hmm I guess that makes sense so let me work it out

Thank you so much man

How do I rationalize the numerator √2x + √2y/y

just need a quick refresher

I do conjugate first?

[viscid thistle]

<@&286206848099549185>

i have been summoned

i shall help you good S I R

so basically you want to make different of squares on the numerator right @viscid thistle

[uncut mulch]

is that sqrt(2)*x or sqrt(2x)

[viscid thistle]

also i assume you mean $\frac{\sqrt{2x} + \sqrt{2y}}{y}}$

[obsidian monolith]

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

[uncut mulch]

extra} on the end

[viscid thistle]

Yes

exactly this question

what have you tried so far btw

conjugate so it would be multiplying the conjugate of 2x+2y with 2x-2y on both numerator and denominator

not sure what you mean by "conjugate"

but basically

[vernal moon]

...

[viscid thistle]

multiply the top by (sqrt(2x) - sqrt(2y))

that's all

[vernal moon]

yes

thats what he means

[viscid thistle]

and then figure out the rest

@vernal moon oh

[vernal moon]

hes putting the numerator

in form a+b

[uncut mulch]

did you mean conjugate of
sqrt(2x) + sqrt(2y)

[vernal moon]

and multiplying it by

a-b

[viscid thistle]

yea

so then what's you're problem?

seems like you know what you're doing

[uncut mulch]

^

[viscid thistle]

well I'm not sure what the next step would be after that

2x-2y/y(sqrt(2x) - sqrt(2y)?

[uncut mulch]

parentheses

assuming they've been correctly placed
you've achieved your goal of rationalising the numerator

[viscid thistle]

parentheses on bottom right

sorry I'm just making sure I literally forgot stuff after not studying math for a month

[mossy kestrel]

when showing a rational number how do you know how much to multiply it by when subtracting x from it?

is by how many numbers its repeated by?

so if the number is 1.2345 and 345 is repeating

would i multiply it by 100

oh wait no 10000

[uncut mulch]

let $x = 1.2\overline{345} \
10x = 12. \overline{345} \
10000x = 12345.\overline{345}$

[obsidian monolith]

ramonov:

[mossy kestrel]

how do i know when to multiply by 10, 100, 1000, 10000

[vernal moon]

do the position of the start of the repeating sequence

[uncut mulch]

multiplying by 10 and 10000 here
gets you the 345 repeating after the dp

[vernal moon]

plus the length of the sequence

[hallow flicker]

Someone help me find the function

[rigid sun]

IF YOU LIKE TO TALK TO e

one sec

stop

move

no

[slow roost]

Lol whenever someone talks over me they don’t get scolded at 🤷🏻‍♀️

[rigid sun]

you know what

@weak storm

does this make sense to you

vectors don't have to move tip to tail

i could easily just

move all the vectors apart like 5 feet and they would not be tip to tail

vectors are just a magnitude and a direction

look at vector A+ (-B)

your start at the bottom of A

and then go all the way to the end of B

remember A+ -B= A-B

its actually a nice tool to use parallelo gram method

no

those are two separate vectors

one shows vector A and the other shows vector B

one meta strat to subtract vectors is to use tip to tip

you see, in the diagram you have A-B

so think of it as

the tip of B to tip of A, where the end of A is the tip of the resultant vector

so yeah

you can think of vectors as like

reading

like everyone reads english left to right

ye

[mossy kestrel]

http://prntscr.com/quvuzy

can someone explain c)

it doesnt really make sense

[mossy kestrel]

halp

[hallow flicker]

Can someone help figure out a function for this graph

[rigid sun]

what does it look like to you?

bruh

do you know what functions look like that?

[hallow flicker]

No

I’m brain dead

[rigid sun]

oh

then ur fucked

[hallow flicker]

What

Just give me a function that can give me the same thing

[rigid sun]

here

look at this chart

[hallow flicker]

Ok so I could try like tan of positive x

But like it won’t have the gap in between

[rigid sun]

from these two graphs

[hallow flicker]

Cosec

[rigid sun]

ok

[hallow flicker]

But how do I get the gap on the middle

[rigid sun]

what do you think

[hallow flicker]

Just tell me

[rigid sun]

do you know a way to make a function always negative?

[hallow flicker]

No

|x| makes it always positive right

[rigid sun]

yes

so...

[hallow flicker]

So -|x|

[rigid sun]

ok

[hallow flicker]

But look there still won’t be a gap tho

They will simply alighn themself

[rigid sun]

you can change the period

[hallow flicker]

What does that mean

[rigid sun]

well

you want them to be spaced further apart no?

sheet

one sec

[hallow flicker]

Yea

[rigid sun]

you may have to restrict the domain

or

[hallow flicker]

So what do I do to restrict the domain

Dude

[rigid sun]

you'll need

some

[hallow flicker]

Can you explain

[rigid sun]

function clipping tools

one sec

let me do this myself

[hallow flicker]

Ok

[rigid sun]

that was a huge pain in the ass

@hallow flicker

let me ask you this question first

can you name functions that are undefined when the input is negative?

@hallow flicker

bruh

this dude

anime

[hallow flicker]

Yo

Can you just give me the function

[rigid sun]

no tf

[hallow flicker]

Why

Wtf

[rigid sun]

that would be like

[hallow flicker]

And no I can’t

[rigid sun]

how about

log(x)

or sqrt(x)

[hallow flicker]

What about squat root of x

[rigid sun]

those are two functions that make numbers undefined

[hallow flicker]

Ok

Wait let me try it

[rigid sun]

but what we also need to consider

is that those function

1. make negative numbers into undefined outputs

2. are not periodic

aka, they make the entire -x axis negative and the rest is defined

hmm...

if only there was a way we could make certain imputs PERIODICALLY negative

[hallow flicker]

Ok I couldn’t do it

[rigid sun]

look at this

[hallow flicker]

Ok

[rigid sun]

so we already went over the abs value and the negative

[hallow flicker]

Why is it so complex looking

[rigid sun]

we already went over csc or 1/sin

the real magic is on this inside

of sin

[hallow flicker]

Why do you need sin of arcsin?

[rigid sun]

first

lets simplify this down

what is e^ln(n)?

[hallow flicker]

N

[rigid sun]

good

now what is the arcsin of sinx?

[hallow flicker]

X

[rigid sun]

yes

now all of that on the inside of the sin simplifies down to x

which is

sin(x)

the reason i have the arcsin in there is to make sure that the function retains its original shape

ok

so lets look at your picture

[hallow flicker]

Wait let me try this

[rigid sun]

from this picture, it appears that only values from pi to 2pi are undefined

hmmm, so we want to use negative values to make the gaps undefined

if only there was a function that made values from pi to 2pi, periodically negative

[hallow flicker]

I thanks dude

[rigid sun]

hmmmmm

[hallow flicker]

But you don’t need the other parts

[rigid sun]

tf you mean

[hallow flicker]

Like wouldn’t that work?

[rigid sun]

yes

[hallow flicker]

Ok well thanks a lot for that idea using e and ln

Ur actually the best

[rigid sun]

but i kept with the form we were using earlier

that should work also

[hallow flicker]

Yea

Thanks man

[fading token]

@hallow flicker nice nickname

[lilac tide]

kill me now

we’re doing vectors in precalc

but it’s just scalar multiplication and addition

[fading token]

not unimportant

[lilac tide]

but so boring and easy

[fading token]

I'm sure you'll get to do some challenging stuff soon

[languid crane]

It’s easy yes

But there will be challenging stuff later

[soft night]

Isn’t like

Almost all of math multiplication and addition

Besides number theory

That can suck my pp

[viscid thistle]

lol

almost none math is multiplication and addition

[pale kettle]

Fuck you

Number theory is cool

[viscid thistle]

Need help on this

Can't visualize this for some reason

<@&286206848099549185> not sure if I am supposed to @ u guys. Sorry if your not supposed to

[narrow hawk]

not really the place for precalc is it

[uncut mulch]

not sure yet you did it anyway 😦

[viscid thistle]

So I am not supposed to?

[uncut mulch]

#❓how-to-get-help

[viscid thistle]

I am sorry

[uncut mulch]

15 minute rule

[viscid thistle]

What does that mean

[viscid thistle]

But seriously can someone help me with my problem

[valid violet]

At first glance, I'm not seeing how the width of the pool is relevant

Is this from a book that sometimes puts extraneous info in problems

[viscid thistle]

It's just a page I got from my teacher. All I did was pull up the online version of it to screenshot for you guys

[valid violet]

You want to look at it from the side

Like underground next to the pool looking at it sideways

Not from above

[mossy kestrel]

http://prntscr.com/qvas0j

can someone explain this step by step

[valid violet]

it's asking for the solution to -3=7x-5

[mossy kestrel]

oh really

oh

[valid violet]

yes. when you evaluate f(x), you put in x = whatever

[mossy kestrel]

fuck

[valid violet]

whne you evaluate f inverse, you put in f(x) = whatevere

[mossy kestrel]

look at how my professor wrote it

2/7 = x

[valid violet]

in general finding the inverse is more difficult than the regular function, and there might be no solution or multiple solutions

[mossy kestrel]

http://prntscr.com/qvasnq

the arrows were confusing

[valid violet]

well it's not wrong

it means "if and only if"

[mossy kestrel]

oh

[valid violet]

functions of the form y = mx+b always have inverses and it will always be possible to solve for the inverses

in general a function might have no inverse

or the inverse might not be a function

[mossy kestrel]

how do i know if it doesnt

[valid violet]

actually I need to correct myself

constant functions like y = 5 are not invertible

so I mean non-constant functions

uh that's actually a really difficult question in general

[mossy kestrel]

i havent learned it so should i just assume these all have inverses

[valid violet]

no

you should put in f(x) = whatever

and see if it's possible to solve for x

later on you'll learn more about when to tell if a function has an inverse

without actually finding the inverse

well

if they use the notation

$f^{-1}$

[obsidian monolith]

gfauxpas:

[mossy kestrel]

so to check that

would i plug 7/2 into the function

[valid violet]

they probably are telling you there is an inverse and the inverse is a function

that's the implication of the notation