precalculus

[plush trench]

I got 4√3 not 2√3, unlike henry @pliant pecan

[barren hedge]

12/6 is 2 tho

[plush trench]

Sowwy henwy

Check your factorization of √48

[barren hedge]

o

4√3

[plush trench]

Yikes!

[willow bear]

@harsh cipher

Domain: t > 0

[barren hedge]

hey Ann, you know how to do Levi's problem?

[willow bear]

hngh

in bed, can't do that much arithmetic

[barren hedge]

understandable

[twilit shadow]

The answer is supposed to end up as 4/3, -2/3, and 1/2

I got the -2/3 so far, but I messed up on the 1/2

And I can’t figure out what I did wrong

I’ve tried coming back to it

I still got the same thing

[willow bear]

@barren hedge is that your handwriting in your pic

[twilit shadow]

That’s my handwriting

[barren hedge]

that'd be a compliment, trust me

[willow bear]

it's a bit hard to read with your angular and 4-like your eights are @twilit shadow

[twilit shadow]

Yeah I know

I’ll see if I can fix it

[willow bear]

i bet you're one of those people who doesn't put a stroke on their sevens either

[twilit shadow]

That’s how I do it

I have no idea where I learned it

[willow bear]

oh that's ok at least

[twilit shadow]

I hope that’s better

[barren hedge]

4/3 or 3/4?

I got 3/4

[twilit shadow]

Yeah it’s 3/4

My bad

[barren hedge]

oh really?? I've never done this problem in my life and I got it, I'm happy

literally never learned this, I'll send a pic

[twilit shadow]

Nice

[barren hedge]

I'll make a nicer version

[twilit shadow]

On the one you put an X on, I got the same as you there, but where did you get the one with -8 -16 -20/3 | 4/3 from?

Well, I didn’t get the top row, I have no idea where that is from

[barren hedge]

the x is crossed out, for that one what I did was just multiply the lowest row by 4/3 (so I get an 8 in the 1st column)

[twilit shadow]

Okay

[pliant pecan]

@barren hedge @plush trench sorry I got picked up to get food since I hadn’t eaten today

[barren hedge]

oh that's not good

[stuck lark]

can't do math(s) on an empty stomach

[pliant pecan]

It’s not

@stuck lark facts

@plush trench yes, that’s the problem

[twilit shadow]

Wait, did you multiply by 4/3 or -4/3?

[barren hedge]

negative

[twilit shadow]

Okay

[barren hedge]

just noticed I didn't write it out, I didn't think i'd get this far sorry lol.

[twilit shadow]

It’s fine

I was trying to avoid fractions, but if this is how it’s solved then okay

[barren hedge]

well the answer is literally fractions

[pliant pecan]

This is right, right?

[barren hedge]

so that's how I got the idea to multiply by -(4/3)

[twilit shadow]

Yeah, but I was trying to get it as late as possible

[barren hedge]

6ix, no I don't believe that is, always do common denominator

[pliant pecan]

@barren hedge I did? I added 5 to top and bottom of the second fraction to make x plus two into x plus 7

[barren hedge]

gotta do it by multiplication, so a/b + c/d → ad/bd + cb/bd

[pliant pecan]

Ohh... yeah, that’s seems familiar

[barren hedge]

so you'll have to distribute

[plush trench]

Like adding 1/2 + 1/3

Just a lot more things

[pliant pecan]

Let me try it now

[plush trench]

6ix seems to be going through quite a wide range of topics

[barren hedge]

ye lol

[plush trench]

I’ll admit that all his problems seem fairly straight-forward, though, and that’s nice

I really dislike word problems

[barren hedge]

@twilit shadow Idk if you still want it, but here's a somewhat cleaner version.

[pliant pecan]

Sorry, like I said, I’m barely coming back to math and this class is starting off by reviewing previous math courses I’ve apparently taken? Anyways, here’s what I worked out

Good, right?

[twilit shadow]

I have a new problem. I have no idea where to start.

[willow bear]

find how many units of red she uses. that must be less than or equal to 32.

[plush trench]

What did you do at the end @pliant pecan

[willow bear]

then find how many units of blue she uses. that must be less than or equal to 54.

both in terms of a and b, of course. @twilit shadow

[twilit shadow]

Thanks

[barren hedge]

yeah I followed you to the second to last 6ix.

[twilit shadow]

I think that makes a lot more sense now

[plush trench]

@pliant pecan Did you just subtract 1x² from top and bottom? Because you can’t do that

[pliant pecan]

Refresher?

[pliant pecan]

@plush trench I can’t ? I took out the x^2 because it was divided by x^2

[plush trench]

No

[barren hedge]

no, you gotta divide the numerator by the whole denominator

[plush trench]

Rather, try checking if the numerator is factorable in the second to last step

[pliant pecan]

Uh.. factorable meaning..? When you take out (x^2) from the equation?

[barren hedge]

like a coefficient

[plush trench]

For example

[pliant pecan]

I’ll come back to it for sure as I found the answer , since it was the second to last step that I had, but with (x+7)(x+2) as the denominator

[plush trench]

x²-1 -> (x+1)(x-1)

[pliant pecan]

I remember that..

[twilit shadow]

@willow bear like this?. Sorry I got the R and B mixed up

[pliant pecan]

I’ll test it out after I’m done with this practice test, as I think I got it solved correctly here, minus the last step

[barren hedge]

I don't believe the numerator is factorable, Mr. P.

[plush trench]

That’s factoring, when a quadratic can be written as (x-a)(x-b) where a and b are integers

It’s not?

[barren hedge]

You can remove a coefficient

[plush trench]

7,24,35?

[barren hedge]

an integer, but not as (x+a)(x+b)

[willow bear]

@twilit shadow no

[twilit shadow]

Oof

[willow bear]

wait

gimme a sec...

[twilit shadow]

I got my R and B mixed up (I’m using those to represent the dyes)

[pliant pecan]

Uhh... so k = slope, h= amount of turns, and a is..?

[plush trench]

In vertex form?

[willow bear]

R = 4a + b, B = a + 6b

[twilit shadow]

I don’t think that’s right

[pliant pecan]

I faintly remember this, but I think I’m remembering from wavelengths in calculus... not sure

I’m supposed to convert

[plush trench]

@pliant pecan are you talking about vertex form

[pliant pecan]

Standard form...

[plush trench]

(h, k) are the (x, y) coordinates of the vertex

[twilit shadow]

For one, they need to be inequalities, and R is the red dye, B is the blue dye, a is the gallons of color a, and b is the gallons of color b

[barren hedge]

Ax²+Bx+C is standard form.

[plush trench]

What henry said

[pliant pecan]

Oh...

[twilit shadow]

So to make color a, a, you need 4B + R

And so on

[barren hedge]

A·(x-h)²+k is Vertex Form.

[pliant pecan]

This practice test says that’s standard form. Ouch. Ok, so h and k are the coordinates of the highest point, correct?

[plush trench]

Not necessarily the highest point

[pliant pecan]

Well highest or lowest, depending on the graph, this is negative so it’d be the lowest

[plush trench]

The extreme point of a quadratic

[twilit shadow]

Whatever. It’s getting really late, I have like 3 tests tomorrow, and I just can’t think correctly. I’ll just ask my teacher to help

[pliant pecan]

With the equation, how would I draw the graph? I could do it by plotting it out 1 by 1 but for a general idea...

[barren hedge]

h and k are* where the function is centered when x = 0

[pliant pecan]

When x=0

So then I just plug it in, right?

[barren hedge]

well the k would be different, my bad.

[plush trench]

The x coordinate of the vertex is -b/2a where y = ax² + bx + c @pliant pecan

[pliant pecan]

Yeah, I don’t think what I did was right

[plush trench]

To get the y coordinate, you plug in the x coordinate into y(x)

[barren hedge]

so h = -b/2a, and k = f(h)

[plush trench]

Yes

[plush trench]

I could explain the -b/2a but I would have to teach you some calculus

10/-10 =

[pliant pecan]

Negative one

My bad

[barren hedge]

didn't you say you took calculus, do you remember the power rule?

if you do, the reasoning for the -b/2a is pretty simple to explain, relatively speaking

[plush trench]

He’d also have to know about maximization/minimization

[pliant pecan]

I took honors calculus in high school but that was what feels like a long time ago.

[plush trench]

What class are all these questions for

[pliant pecan]

Now I can’t even understand college algebra correctly. I mean, give me a formula and it’s as simple as plugging it in, but I haven’t done math in a while and forgot most formulas and rules

[barren hedge]

Pre-Calc does a lot of review.

[pliant pecan]

It’s college pre cal

[barren hedge]

Well, idk if you could follow this, but worth a shot

anything to spare you from memorizing something that seems random

[plush trench]

(Set dy/dx to 0 because you’re looking for an extreme point in y(x))

[barren hedge]

and the x would be the specific x value that y' would be set to 0 to. We'd then call that specific x value 'h' (for the Vertex equation).

[plush trench]

There’s also a formula for the y value of the vertex, but it’s kinda lame

[pliant pecan]

Got it

@barren hedge

[plush trench]

Did you get the process?

[barren hedge]

nice :)

[pliant pecan]

I understood when @barren hedge broke down getting H, and for K you’re saying I need a derivative. I haven’t done those in a while. I thought I figured out K already by plugging h into the function

[barren hedge]

That's what you'd do in Calculus, finding the value for K once you have H is nothing special in Calc. Just gotta plug it back into the original equation.

[pliant pecan]

The answer I had gotten shows up as an answer on here so I’m assuming I had done it correctly?

[plush trench]

Hmm the answer is on the answer key?

[pliant pecan]

Isn’t the derivative like a slope or something ? Can’t remember it too well

It’s not a key, it’s a choice. It’s a multiple choice practice test lol

[barren hedge]

you got (h, k)→(-1, 22)?

[plush trench]

It’s the slope of the line tangent to the graph at a particular point

[plush trench]

Ah

[barren hedge]

and yeah; the derivative is the "instantaneous" slope.

nope

[pliant pecan]

@barren hedge those were the values I had gotten

[barren hedge]

not that, remember the h is negated when it's inside the argument

[plush trench]

Didn’t he negate it

[barren hedge]

oh

[plush trench]

Bruh moment

[pliant pecan]

So then h = -1 would be addition

[barren hedge]

true

[pliant pecan]

That’s what I did lol

[barren hedge]

i told you you were right

[pliant pecan]

Oh

[barren hedge]

totally

[plush trench]

Henry b like

[barren hedge]

good work

[pliant pecan]

20 minutes and 30 problems left lol

FML

[barren hedge]

i need a bucket, all this sweat and I'd drown a desert

[pliant pecan]

I feel like this is easy af and I’m over thinking it

[barren hedge]

i hate timed homework, hmph.

To a mathematician with a PhD, this is very easy.

[barren hedge]

To a person who hasn't taken math for a while, this would be challenging.

[pliant pecan]

I meant this problem but to a PhD I’m sure you understand it all lol

[plush trench]

Bruh do you think they’d remember some of these formulae

[pliant pecan]

That is the correct triangle area formula right?

[stuck lark]

yes

[pliant pecan]

Good lol

[plush trench]

For the area yea

[barren hedge]

6ix, I'd plug in h = 3×L, solve for L, and plug it back in to get h

[stuck lark]

if h is height, L is base...?

[barren hedge]

Yep.

[pliant pecan]

Pft

Easy

[barren hedge]

The question says the height is 3 times the base

[pliant pecan]

I knew it.

[plush trench]

6ix b like

[barren hedge]

lol

[pliant pecan]

Oops

Never mind lol

[barren hedge]

A PhD would probably be too busy creating new theories for Differential Vector Topology or something.

[plush trench]

Wait what

[barren hedge]

derp

[plush trench]

Wdym nvm

[plush trench]

I already drew the sunglasses

[pliant pecan]

Lol

I think I messed up

Oh, I see

Wait, no

[plush trench]

Start again and substitute this time

[pliant pecan]

What would I sub?

Wait, I think Ik

[plush trench]

You usually only want one unknown in an equation

[pliant pecan]

I’m back at dividing by 4 lol

[plush trench]

You already know what b is

[pliant pecan]

Holy fuck I’m dumb as a brick

[plush trench]

Did you figure it out

[pliant pecan]

Then I was doing it right, right? When I divided by 4 to get b, and then was going to multiply by 3?

[barren hedge]

yeah

that'd work

[pliant pecan]

Put the shades back on, I did know it

[barren hedge]

hm

[pliant pecan]

Is it 1089? It should be, right? Let me prove it, hang on

[barren hedge]

should be 66 derp

[pliant pecan]

Holy fuck I’m so dumb. I tried to prove it and the area came out as over 190k

[barren hedge]

I think the problem is that you said the base was 363

[pliant pecan]

Yeah, that can’t be right

[barren hedge]

why'd you divide 1452 by 4

[pliant pecan]

Because I’m dumb. I plugged in 3b as h and did 3b times b

[barren hedge]

o

[pliant pecan]

Oh, that would be squared, not 4b

My bad

[barren hedge]

I think this is a bit easier

Isolate L, plug it into the area formula, isolate for h and done

[pliant pecan]

Yeah because my new solution isn’t working either

[barren hedge]

that's b, we want h

b is 22 in what you gave

[pliant pecan]

I figured I’d get b and multiply by 3 but that didn’t work out fine

[barren hedge]

so multiply that by 3

you'll get the 66

[plush trench]

I’m going to hit the sack guys, or at least try to

I gotta cash in my 3 hours of sleep B)

[barren hedge]

derp, enjoy

[pliant pecan]

Oh yeah, I got it

[barren hedge]

let the boogie man eat your feet

[plush trench]

He She can suck my toes

[pliant pecan]

Night, @plush trench. Thanks for the help

[barren hedge]

oh, he she will

[plush trench]

No homo

gn

[pliant pecan]

Gn

[lethal oracle]

Anyone there that can help?

[willow bear]

[barren hedge]

snez

[pliant pecan]

Yeah, so I failed my practice test due to time. Go into spam random answers into my assignment I have rn to get something better than a 0

Do you guys have some sort of tutoring system?

[lethal oracle]

Radius = 10 inches, velocity= 24ft/sec, RPM=?

[barren hedge]

if you have a question, then people try their best to answer

kinda like a ffa

6ix, didn't you have that exact problem? lol..

[lethal oracle]

I believe I’m doing this right but I keep getting the wrong answer according to my textbook

[willow bear]

uh

[pliant pecan]

Wdym? @barren hedge

[willow bear]

post the question exactly as stated @lethal oracle

[barren hedge]

the radians per second

[pliant pecan]

Oh, no, I had something similar

40 pi rad per sec

[barren hedge]

But in this case, RPM probably means Revolutions per Minute.

[lethal oracle]

It’s 45

I take 24ft/sec and then change it to inches per minute

Then I divide by radius

And 2 pi

Maybe I’m making an arithmetic error

Idk

[barren hedge]

okay, so what value did you get when you changed 24ft/s

I think it is, heh

[lethal oracle]

I got 288in/sec

[barren hedge]

yeah, and convert to min

what'd you get for that

[lethal oracle]

17280in/min

[barren hedge]

hm agreed

[pliant pecan]

Uhhh

I just did a similar one but this feels harder

[barren hedge]

so 275 revolutions per minute was wrong?

[pliant pecan]

Mostly because I end up distributing

[lethal oracle]

Yes

[pliant pecan]

Surely there’s a better way to solve this

[lethal oracle]

The book says the answer is

[barren hedge]

22=½hb is not 11=hb

[lethal oracle]

Ya it is that answer

I was looking at the wrong answer area

[pliant pecan]

It’s not? We did it this way for my last problem though?

[barren hedge]

oh so what did you do wrong lol

oh

[lethal oracle]

For the whole hour I’ve here trying to do this

[barren hedge]

gotta multiply both sides by 2, 6ix

[pliant pecan]

Oh crap

Yeah, my bad

I see that

[lethal oracle]

That you for the help though

If I have more questions I’ll ask

[barren hedge]

ye

[lethal oracle]

I got my first exam tomorrow

[barren hedge]

looks like a quadratic equation to me

[pliant pecan]

Is this literally what I’m expected to solve?

[lethal oracle]

Ya that’s a quadratic

[pliant pecan]

Mine?

[barren hedge]

yep

[lethal oracle]

Ya

It’s favorable

[pliant pecan]

So in a quadratic I’d want to get 44 on the other side, right?

[lethal oracle]

I mean factorable

[barren hedge]

$$\frac{-b±\sqrt{b^{2}-4ac}}{2a}$$

[obsidian monolith]

HenryCastle:

[barren hedge]

yep

[lethal oracle]

Why not just factor it

[pliant pecan]

To get h?

Hm, ok let me try this

[lethal oracle]

Yes

[barren hedge]

how'd you factor that, Alpaka?

[barren hedge]

44 = h·(h+7) isn't too nice to solve.

[pliant pecan]

I don’t think I can do this without a calculator lol

[lethal oracle]

I got h=-11 h=4

[barren hedge]

So remember 6ix, you want to find height. A negative value for height wouldn't make sense.

[pliant pecan]

Hang on

[barren hedge]

lol

[lethal oracle]

What did you Henry

What did you get

[barren hedge]

same

[lethal oracle]

Ya I favored

Factored

I mean

[barren hedge]

oh

[pliant pecan]

I don’t see how I’d solve this without a square root and there’s no answer with one lol

[barren hedge]

how'd you manage to factor it, Alpaca?

[lethal oracle]

Like that

[pliant pecan]

What’s factoring again? Not what is it, but how do you do it? (X-1)(x+1) but what am I putting in for one? A/b/c

[barren hedge]

oh I see

[pliant pecan]

What is that? Looks like an interesting process

[barren hedge]

It's basically an educated guess? Like x²-1 = (x-1)(x+1)

[lethal oracle]

So to factor you set up the diamond

[pliant pecan]

Ok, set up a diamond

And then?

[barren hedge]

diamond? fancy stuff going on

[lethal oracle]

Multiply a and c

[pliant pecan]

Lol

[barren hedge]

don't mind us if we rob it from you.

[lethal oracle]

It’s okay

[pliant pecan]

Lol

[lethal oracle]

So the coefficient of h in this case

[pliant pecan]

So -44

[lethal oracle]

Is one

So it’s just -44

[pliant pecan]

Yup

[lethal oracle]

That goes in the top

[pliant pecan]

I see that

[lethal oracle]

Now you put b(7)

In the bottom

You see that?

B in this case is 7

You see that @pliant pecan

[barren hedge]

as in B = 7, not B(x) : x = 7 lol

[lethal oracle]

Ya sorry I made it a bit confusing

[barren hedge]

i notion that we change the function notation from f(x) to f((x))

[lethal oracle]

Nah lol

[barren hedge]

-dies-

[pliant pecan]

Wait

Oh I get it, Henry made me think to plug it in

Ok, now for the factors?

[barren hedge]

||wat ;-;?||

[lethal oracle]

Wait

So did you set up the diamond

You got -44 on the top and 7 on the bottom

Right?

[barren hedge]

The diamond being the X diagram

[pliant pecan]

Just took my first test btw. Spammed my practice test and started answering what Ik on the actual test. Went pretty bad. Had to sub by 00:00 though. It’ll get replaced by my final exam grade though

@lethal oracle yes, I’m there

[lethal oracle]

Now you need to find two numbers that multiply to be -44 but add to be 7

[pliant pecan]

Hm, ok

That seems easy enough

[lethal oracle]

What two numbers do you get?

[pliant pecan]

11 and negative 4

Got you

[lethal oracle]

So now you set these equal to 0

So it’s h+11=0 and h-4=0

[pliant pecan]

But they don’t equal zero

[lethal oracle]

Not yet

[pliant pecan]

Wait, so why’s h coming in?

[lethal oracle]

Yes

[barren hedge]

h is a specific value of X that we're trying to find,

[lethal oracle]

It’s coming in cause we are basically breaking up the orijgnal quadratic into two binomials that are equal to the quadratic that we originally had

[pliant pecan]

Hm, alright

And so h would equal -11 and 4

[lethal oracle]

Yes

[pliant pecan]

And 4 would be the answer

[lethal oracle]

Those are your answers

[pliant pecan]

Got it

[lethal oracle]

No both are

[barren hedge]

(btw these are different h's, not a systems of equations. So something like h₁+ 11 = 0, and h₂ - 4 = 0)

[pliant pecan]

Well it’s impossible for -11 in this case so I’d have to take 4, logically

[barren hedge]

exactly

good thonking

[lethal oracle]

Well it depends if it’s like a question asking about time

Then yes

Negative time is impossible

[pliant pecan]

[barren hedge]

oh but this one is finding height ("length")

[lethal oracle]

Oh

Well if it’s sea levels

Then it could he

You can go below sea level

[pliant pecan]

This will work wonders in the future

[barren hedge]

(the only problem with this technique is that you won't always be able to find factors, in which case you'd have to restart and use the quadratic equation to get the answer)

[pliant pecan]

Lol, it’s nothing but anime emojis in this server

[barren hedge]

ye

[lethal oracle]

Some you can’t find factors

So you have to use the quadratic formula

[barren hedge]

you bullying our emojis??

[lethal oracle]

However factoring has less room for math errors

And is faster

[pliant pecan]

Lol, of course not

[barren hedge]

and easy to check once you get comfortable

[pliant pecan]

Yeah, I’d rather try to factor then use the quad than just go straight to quad

[barren hedge]

we all do

[pliant pecan]

Is there a good practice book for algebra you know of, @barren hedge ?

[barren hedge]

but physics courses will teach you that it's not aboutbwhat you'd rather d-

[pliant pecan]

Lol

[barren hedge]

I don't know any books lol

[pliant pecan]

Ouch

Aren’t you the one with a PhD?

[barren hedge]

I literally just google-

i wish

I google higher level textbook PDFs

[pliant pecan]

You said you had one

[barren hedge]

like Classical Mechanics an-

no I was commenting when you were saying it is "easy" but you found it hard

[pliant pecan]

“To a mathematician with a PhD, this is easy”

[barren hedge]

and saying that to a Math PhD they'd find algebra ez

[pliant pecan]

I kind of thought it implied you had one lol

My bad

[barren hedge]

but to someone who took a break, they'd find it a challenge

oh lol

I'd like a Math and Physics PhD

but I am in college though (like most of us)

[pliant pecan]

Lol

Good

[barren hedge]

no im actually in elementary school, fully qualified to tutor calc 3 and differential equations

ok internet is hard to say things in a joking way, I almost believed myself

[lethal oracle]

Im a high school junior

[barren hedge]

What math are you in?

[pliant pecan]

I wasn’t always this dumb btw. I took honors calculus in high school. I was able to skip algebra and geometry through an exam in high school (geometry one bit me back later as I’d need to apply it in calculus and didn’t actually take the class), and yeah..

[lethal oracle]

Precalc

[barren hedge]

really weird. Honors Calc was a thing but I think they stopped it and went for only AP Calc

[pliant pecan]

This was in 17

2017

[barren hedge]

Oh that was forever ago

it's 2049

[pliant pecan]

What hurt me(fucked me up) was that I left and joined the military, where you don’t use this level of math

And so it left me

[barren hedge]

yeah.. the muscle you don't exercize, atrophies. In your case, math.

At least you got a life (whereas I'm still living with my parents >.>)

[pliant pecan]

Lol, if you call that getting a life

[lethal oracle]

Do you guys play video games

[pliant pecan]

Yes

Very much so

Pokémon, 🍴, and that’s about it atm

[barren hedge]

Used to, but I play a online kid's game (to DEV games, I'm not a creep, sheesh)

[pliant pecan]

Lol

[lethal oracle]

Ah lol

[pliant pecan]

Why?

[lethal oracle]

Idk I always like finding new people to play with

[torn swift]

Rocking USUM still

Though shiny Solgaleo and Lunala event is

[pliant pecan]

USUM was great, I hate that people frowned upon it

They finally had an event to get them shiny??

[torn swift]

My return back since gen 2, I liked it

They will have it in the US soon

[pliant pecan]

Nice, did you legitimately get yours ?

[torn swift]

At GameStop and you need a freaking app or something to get the codes

Still have to pick up shiny zygarde from the mailman lol

[pliant pecan]

I’ve played literally every single game (to the main series- so not including every mystery dungeon)

The zygarde codes still work?

[torn swift]

No

[pliant pecan]

Oh, my bad

I got you

[torn swift]

I just haven’t picked it up in game yet

[pliant pecan]

Yeah

Rolling for a certain nature?

[torn swift]

Not competitive at all. Haven’t got the slightest clue. I just play for fun and gather Pokémon for the looks lol.

Shiny Ho-oh was nice to finally get after all the SRs

[pliant pecan]

Which is why you’re a flaaffy / ampharos fan .. lol I’m kidding. I used it in gen 2 as well.

Yeah, I loved the fact that we could get all the legendary Pokémon with usum

Tbh, I wish they’d go back to the way they did it in gen 4 where you got a little extra bit of story line for when mythical Pokémon were released. Unlike how they just give them to you now.

[torn swift]

You want e to the x^2?

[viscid thistle]

yessssss

[torn swift]

$e^{x^2}$

[obsidian monolith]

⚡Amphy⚡:

[viscid thistle]

oh cool ty

how do i write fractions?

[obsidian monolith]

RokettoJanpu:

$\frac{a}{b}$

[torn swift]

\frac{numerator}{denominator}

[viscid thistle]

thank you both

so

So how do i solve the following inequality: $e^{x^2}-e^{x+2} > \ln(\frac{x+3}{x^2+1})$

[torn swift]

Don’t forget )

And use \ln

[obsidian monolith]

tomatoes:

[torn swift]

Looking good now

[pliant pecan]

Wow

Beautiful

[viscid thistle]

um

<@&286206848099549185>

[proud raven]

👋

[viscid thistle]

hey

um i'm really struggling with the inequality above

[willow bear]

you're supposed to post your question first and ping helpers 15 min later

oh

nvm

[proud raven]

he did

[willow bear]

im dumdum

[proud raven]

looks like just properties of logs

but i suck at math

[willow bear]

uhhh

rip

[proud raven]

big oof

[willow bear]

i don't think this has a nice solution at all

[proud raven]

im not sure thats even valid

$e^{x+2}\to e^x e^2$

[obsidian monolith]

jan Niku:

[proud raven]

then uhh

[viscid thistle]

well wolfram can do it and it seems like a simple solution

[proud raven]

$e^x(e^x+e^2)$

then

split up the log

and exponentiate

and isolate for x

🤷

[viscid thistle]

ok wait lemme try that

wait what do i do after i split the e^(x+2)

[proud raven]

idk i was seeing if i could make it cleaner

i fucked up some signs

[viscid thistle]

cool cool

[proud raven]

you dont need to do it

im not sure that method even works

i just dont like exponents in exponents

so e^x(e^x-e^2) feels better

[willow bear]

uh

no

[proud raven]

😦

[willow bear]

e^(x^2) is not (e^x)^2

[proud raven]

isnt e^x(e^x)=(e^(x^2))

oh its not

oh well

[willow bear]

no

it is not

e^x * e^x is e^(2x)

you really really should review your exponent laws

[proud raven]

i dont have time im trying to keep up in class

[viscid thistle]

so um does anyone have any ideas

Here is the inequality once more

$e^{x^2}-e^{x+2} > \ln(\frac{x+3}{x^2+1})$

[obsidian monolith]

tomatoes:

[willow bear]

,w exp(x^2) - exp(x+2) > log((x+3)/(x^2+1))

[obsidian monolith]

Display results online and refine query

Requested by Ann#0413

[willow bear]

[viscid thistle]

wow ok this must be much more difficult than i first thought

which doesn't necessarily mean that it is not simple

although it should be somewhat simple

like high school level

[viscid thistle]

Does anyone have any more ideas? Absolutely anything else

[viscid thistle]

<@&286206848099549185>

Have you actually tried anything

[cyan zodiac]

@viscid thistle I think I got it. The left side stuff is completely irrelevant maybe; take the right side only for now;
rewrite the log of a fraction out as a difference -> log(a) - log(b)

Your only real solutions are when the inside of the log are greater than zero; solve for those inequalities

[viscid thistle]

@viscid thistle yes i have

@cyan zodiac ok i'll do that

well that leaves us with x>-2

Tomatoes

Can you break this into an inequality of functions?

I mean it already is

But more obvious ones

[next willow]

Noticing that $e^t + \ln(t+1) $ is an increasing function is a possible path

[obsidian monolith]

Mat:

[viscid thistle]

^

Actually

oh that was actually asked previously in the exercise

F(x)=e^2+ln(x+1)+1

it asked us to prove that it is an increasing function

then to solve the inequality

e^x^2+ln(x^2+1)>1

Move everything to >0

And use that

oh wait yeah

[next willow]

Mm was it e^2 or e^x ?

[viscid thistle]

$e^{x^2}$

[obsidian monolith]

tomatoes:

[next willow]

In F(x) I mean

[viscid thistle]

oh um e^2

[next willow]

Umm, in that case you would need to prove the function for the inequality is increasing I suppose

But the approach is the same

[cyan zodiac]

Dunno if this is proper enough, but here's what I tried: https://i.imgur.com/VqIC9nX.jpg

[next willow]

Oh nice

How long was that paper btw? Lol

[cyan zodiac]

US letter full height, cropped width

[restive bridge]

https://i.imgur.com/XnAdbI6.png

Can anyone tell me how to solve this?

Giving me major trouble.

[willow bear]

what exactly is giving you trouble here

[restive bridge]

I really just can't comprehend the steps needed to be taken. I've looked at videos of similar problems, and they've given me insight. But even so, I'm not quite clear on how to go about the problem.

The furthest I've gotten is rationalizing the fraction. (and that was only because I realized they did so in one of the videos)

That's the right answer. @blazing monolith

That's why I was confused. I didn't know how to solve it myself.

[obsidian monolith]

JY1853:

[pale kettle]

Feel like giving full solutions isn't great

[restive bridge]

It helps me a lot. One thing I need to ask.
@blazing monolith
Why is the rationalization a positive root(x), when the original numerator is minus?

a^2+b^2

a^2-ab+ab+b^2

(I really need to learn how produce the fancy text

[pale kettle]

Check your work on this expansion

[restive bridge]

I see the issue I made already. The way JY formats it makes it much less confusing. He has the numbers separated via parenthesis, whereas I factored it automatically. (plus I factored it wrong, my rationalization used a minus square root)

[pale kettle]

And that's why you do your work step by step

[restive bridge]

TY guys.

[slate scroll]

I'm doing an investigation on Bezier curves with a maximum of 4 control points. Does anyone have a suggestion for a problem/topic that I can model using geogebra?

[wary maple]

oops wrong channel

[tidal rain]

Hey if for (x-2)(x+2), the roots are x=2 and x=-2, what are the roots if there was a negative sign in front: -(x-2)(x+2)

[uncut mulch]

when will the value of the expression be 0?

[tidal rain]

oh shit i'm dumb lol i see roots would still be the same

[short sorrel]

right, since the - never creates or changes a 0

in fact, if you prefer, you can actually distribute the - in to one of the factors:

$-(x-2)(x+2) = (-x+2)(x+2) = 0 \ \ -x + 2 = 0 \implies x = 2 \ x + 2 = 0 \implies x = -2$

[obsidian monolith]

Namington:

[short sorrel]

this isnt necessarily to solve it or anything, but it can give one "interpretation" for why it doesnt affect the answer

[rotund spoke]

At my school, I taught myself all of Algebra 2 and all of Pre-cal so I didn't get all of the tips and tricks, loopholes, etc. I never could figure out a way to memorize/remember the unit circle without a note sheet. Can someone hook me up with a good method?

[proud sparrow]

what do you mean by remember the unit circle?

[rotund spoke]

so like drawing it out

more specifically the coordinates

[proud sparrow]

coordinates of a point on the unit circle?

trigonometric functions?

[rotund spoke]

yeah like pi/3 pi/6 pi /4

[proud sparrow]

Well, you can do that by remembering a couple of special triangles

the isosceles right triangle and the equilateral triangle

[rotund spoke]

how would this translate to setting up the coordinates on my unit circle. for example the coords of pi / 3 are (1/2, sqrt of 3/2). Its been a little bit since ive worked with the unit circle so yeah. Sorry if i have the big dumb rn.

[proud sparrow]

well, your coordinates are $(\cos \theta, \sin \theta)$

[obsidian monolith]

Element118:

[proud sparrow]

so, all that needs is calculating/remembering sin and cos for special angles

[rotund spoke]

gotcha

thank you!

[sullen sorrel]

Can someone explain the reasoning behind why the first 3 are even, my brain just isn’t working

[short sorrel]

you know the definition of "even function", yes?

[sullen sorrel]

yeah

[short sorrel]

and you know how multiplication by -1 affects how a function "looks"?

[sullen sorrel]

yes

[short sorrel]

it's a vertical reflection, yes

does being vertically reflected change whether it's symmetrical about the y-axis?

[sullen sorrel]

no

[short sorrel]

hence, (a) is even.

similar logic applies to (b) and (c); the transformation applied doesn't affect whether a function is even

[sullen sorrel]

Yeah I see now

[short sorrel]

we can also do this more algebraically:

[sullen sorrel]

Idk why I couldn’t see that

[short sorrel]

the definition of an even function is f(x) = f(-x)

so if g(x) = -f(x)

g(x) = -f(x) = -f(-x) = g(-x)

i.e. g(x) = g(-x), so g is even

again, a similar thing can be done in parts b and c

if g(x) = f(-x), we have:
g(x) = f(-x) = f(--x) = f(x) = g(-x)
so g(x) = g(-x), again showing g is even

and if g(x) = f(x) - 2:
g(x) = f(x) - 2 = f(-x) - 2 = g(-x)
so, again, g(x) = g(-x)

this algebraic approach should also show why it fails for (d)

[willow bear]

actually, for b, you can just say g = f lmao

[sullen sorrel]

Yeah okay

[willow bear]

since like

[sullen sorrel]

Thank you

[short sorrel]

yeah, true

[willow bear]

f is even so f(-x) = f(x) by defn

[short sorrel]

thats much more direct

[harsh cipher]

Hi

simplifying question. In the last part X= 3/(sqrt 5)

Why can't you leave it as it is. Why multiply sqrt 5/ sqrt 5 to make it X=3 sqrt 5/ 5?

[proud sparrow]

because we really like integers in our denominators

[willow bear]

you CAN leave it as is

it's just that some people insist on rationalizing denominators

at all times

[obsidian monolith]

EvilRobotOverlord:

[viscid thistle]

Does a function being 1 to 1 mean that it is strictly increasing?

[willow bear]

no

[viscid thistle]

sorry

strictly monotonic

[willow bear]

not even that

[viscid thistle]

oh

[willow bear]

take f: [0,2] -> R given by f(x) = x for x in [0,1) and 10-x for x in [1,2]

one to one? yes
monotone? no

[viscid thistle]

wait do you mean these lines

https://www.desmos.com/calculator/enbnd5gtqk

cause i think thosr are monotone

ohh

it's like

one function composed of those two

but like there are 2 values of x that give the same value for y

does that count as 1 to 1

?

[willow bear]

i gave you a PIECEWISE function.

[proud sparrow]

You need to choose which function to use depending on which piece of the domain you are in

[willow bear]

{0 <= x < 1: x, 1 <= x <= 2: 10-x}

this is the desmos syntax

[neat terrace]

I have no idea if this is the right place to ask, but...
https://i.imgur.com/DbL38ME.png
Is it possible to make an equation for this?

I want to be able to get the value of y when x is anywhere between 0 and 1

[proud sparrow]

looks like statistics

where you want to fit some sort of best fit line

how do your points look like?

what model are you fitting?

@neat terrace

[neat terrace]

https://i.imgur.com/r2G3rUU.png

[proud sparrow]

yeah, just get the equation of that best fit line, and then substitute in the values for x

that's one way about it

[neat terrace]

I need an exact result though

[proud sparrow]

yeah, you can substitute in the value for x and get an exact result

or are you going to linearly interpolate between two points?

that's another way to get values

[vernal rapids]

fourier series

You can approximate by sin functions or polinomials
But the simplest way is just to make it a piecewise function

[proud sparrow]

haha we only have it at a couple of points though

[vernal rapids]

$f\left(x\right)=\left{0\le x\le.15:\frac{72}{0.15}x,.15\le x\le.19:\frac{6}{0.04}\left(x-.15\right)+72,0.19\le x\le0.23:\frac{6}{0.04}\left(x-0.19\right)+78,0.23\le x\le0.26:\frac{6}{0.03}\left(x-0.23\right)+84,0.26\le x\le0.84:\frac{90}{0.55-0.26}\left(x-0.26\right)+90,0.84\le x\le.87:\frac{6}{0.03}\left(x-.84\right)+270,.87\le x\le.91:\frac{6}{0.04}\left(x-.87\right)+276,.91\le x\le.95:\frac{6}{0.04}\left(x-.91\right)+282,0.95\le x\le1:\frac{72}{0.05}\left(x-.95\right)+288\right}$

desmos format

[obsidian monolith]

DarK:

[vernal rapids]

and it doesnt fit in the picture-

yay

[lunar mountain]

can anyone explain why theres a difference in counting combinations in these 2 situations:

when deciding the probability of throwing a dice roll with a SUM IS 9 OR HIGHER: 6-3 and 3-6 are counted as two different combinations

when deciding the probability of WALK AT LEAST ONCE in terms of transportation with two trips: WALK - WALK are not counted as two combinations

It doesn't make sense to me why it'd be counted in one situation or not the other. For the total sum, it doesn't matter if the first or the second throw is a specific number. Neither should it matter when we try to determine if a person has walked at least once

[willow bear]

WALK-WALK is the same as WALK-WALK

[lunar mountain]

Is DICE A: 3 and DICE B: 6 not the same as DICE A: 6 and DICE B: 3 with that logic?

Because the outcome is the same

[willow bear]

it's not

swapping two equal things doesn't produce a different outcome

[lunar mountain]

I don't understand the logic behind why 6+3 = 9 is not the same as 3+6=9

And if those are counted as two different combinations, then WALK morning and WALK evening is not the same as WALK evening and WALK morning

[willow bear]

...

[short sorrel]

@lunar mountain how many ways are there to roll 6-6 on a die?

On two dice*

[lunar mountain]

2 times

[short sorrel]

How so?

There's only one possibility:

The first roll is a 6

And the second roll is a 6

[lunar mountain]

hm

[short sorrel]

But if we want to count the probability of rolling a 6 and a 3, in no particular order

There's two possibilities:

First roll 6, second 3

Or first roll 3, second 6

[lunar mountain]

think u made it click bro

thank you

[tawny comet]

Guys, I am so confused on what I'm being asked to do for number 47

[willow bear]

do you know what $f \circ g$ is?

[obsidian monolith]

Ann:

[tawny comet]

No, I don't... That's what made it even more confusing

[willow bear]

Function Composition

[tawny comet]

Oh, is that what it means?

[willow bear]

well

idk i just read off the topic for you since your worksheet lists it

idk

[tawny comet]

Right...

[willow bear]

i mean idk

[tawny comet]

Any idea on how I would go about doing this?

[willow bear]

http://lmgtfy.com/?q=function+composition

[zinc citrus]

Function composition is basically where you plug in a function to another function

f o g = f(g(x)) if that form seems more familiar to you, it’s just a different way of writing the same thing

[tawny comet]

Oh, alright!
I got it!

Thanks!

[shrewd urchin]

,w tan^{-1}(2)

[obsidian monolith]

Display results online and refine query

Requested by Krishna#4971

[willow bear]

lul

take the {} off

,w tan^-1(2)

[obsidian monolith]

Display results online and refine query

Requested by Ann#0413

[shrewd urchin]

How can i do that problem @willow bear

[willow bear]

compute the angle between your vector and i

[pliant gorge]

how do i factor when a is not 1

[shrewd urchin]

,w tan^-1{3/1}

[obsidian monolith]

Display results online and refine query

Requested by Krishna#4971

[pliant gorge]

like for 2x^3-5x-3

[shrewd urchin]

,w 1.249rad.to degrees

[obsidian monolith]

Display results online and refine query

Requested by Krishna#4971

[tawny comet]

Quick questioon y'all

So like, I understand what they mean by (f^-1og^-1)(x)

But what happens when they say

(f^-1og^-1)(2)

Instead of the x at the end

They replaced it with the number 2.

What do I do with that?

[pale kettle]

What's the difference between f(x) and f(2)?

[tawny comet]

You substitute 2 for x

Is that all I do at the end?

[pale kettle]

Yes

[tawny comet]

Oh, great!

Thanks 😄

Oh, yup, got the right answer now! 🙂

[wraith idol]

Bruh

[viscid thistle]

[river coral]

@viscid thistle hey friend 🤡

[viscid thistle]

@river coral hi friend

[tidal rain]

can someone explain the steps my professor did here

[short sorrel]

3^15 = 3^10 * 3^5, and 27 = 3^3

2^10 * 3^10 = 6^10

6^10 / 6^12 = 6^-2, and 3^5 / 3^3 = 3^2

then simplify from there

alternatively, break down 6^12 into (2*3)^12

which becomes 2^12 * 3^12

and then you can, again, simplify from there

[tidal rain]

im confused about where the 3^25/81^12 came from

[short sorrel]

i think thats there as a "here's some common mistakes which you shouldnt do"

since theres no justification for that

[tidal rain]

so is the only part that really matters

i'm just really confused because it seems like my professor's work is so messy

[viscid thistle]

for 6^12 use the formula: (a * b)^n = a^n * b^n

[barren hedge]

yeah, the circled is the only part that matters, the rest is random and unnecessary (probably to show another case).

[viscid thistle]

anyone know how to solve this problem?

[short sorrel]

your answer for volume doesn't seem simplified

seems correct after simplification, though

[viscid thistle]

@short sorrel o

what was the answer?

gotta be more simplication

?

[short sorrel]

you should get a simple trinomial

$(8x^3 + 16x^2 + 6x) - (6x^2 + 24x) \ \ 8x^3 + 16x^2 + 6x - 6x^2 - 24x$

[obsidian monolith]

Namington:

[short sorrel]

and just subtract

[note also that you forgot an x in your answer input]

[viscid thistle]

hmm

[hushed ember]

A square hut with side lengths of 5 m is to be surrounded by a veranda of width x metres.
Find the width of the veranda if its area is to be 24 m2.

can anyone help me on this one?

[willow bear]

what have you tried and where are you stuck

[tidal rain]

how does 5^1/3 times 6^2/3 become 180^1/3?

[native timber]

$\sqrt[n]{a}\cdot\sqrt[n]{b} = \sqrt[n]{ab}$

[obsidian monolith]

Jiramide:

[tidal rain]

ohhh i feel dumb 6^2=36 and 36*5=180

how do i do this problem?

[native timber]

Multiply the both sides of the fraction by the denominator's conjugate

[tidal rain]

a^1/3-b^1/3 wouldn't work right

[native timber]

Ah it's cube root mb

[tidal rain]

oh conjugate is only for square roots?

[native timber]

Yeah since only difference of squares factor into term * conjugate form

Have you learned about the sum or difference of cubes?

[tidal rain]

these are the only notes my professor has given

[glossy grail]

((a^(8/3) / b^(1/2))^2 ) (b^(3/2) / a^(1/2))

😅

[tidal rain]

i hope this is right?

[native timber]

Hmm I'm not really sure how you'd do this (you could probably arrive at sum of cubes if you really stare at the notes) but I'm on phone and it's rlly hard to type

[upper flint]

I need help with sequences

[pale kettle]

[grave furnace]

Iirc you just have to find how much the sequence changes each term to get from 22 to 64 in 6 terms, and if you know how to write a recursive and explicit formula you should be good

[upper flint]

19^

What term do i stop at

Like what do i write at the top of the sum symbol

[lucid crow]

infinity

$\sum_1^{\infty}(2n-1)$

[obsidian monolith]

Mechanist FD:

[proud sparrow]

@upper flint First term is (2*1-1), second (2*2-1) and so on

[upper flint]

@proud sparrow Ik

[proud sparrow]

so you start at 1 and end at n

[lucid crow]

yes

if you used 0 you would get -1 for the first term

[short sorrel]

um

why the fuck would you write infinity there

[uncut mulch]

$\sum_{k=1}^{n} (2k-1)$

[obsidian monolith]

ramonov:

[lucid crow]

o sorry

[short sorrel]

^

[lucid crow]

n

[uncut mulch]

the answer is quite nice

[short sorrel]

yeah, this is a fairly well-known sum, it turns out.

in fact, you might be able to guess the pattern just by testing

1 + 3

1 + 3 + 5

1 + 3 + 5 + 7

[viscid thistle]

Hello, someone can help me?

[stuck lark]

[viscid thistle]

I want to know if this is the correct way to do this

[uncut mulch]

why did you write
x^2 for k=0

those caluculations would be for the first term
what is the question asking you to do?

[viscid thistle]

o_o just replace k by 0 Everytime I saw a K

Oh I see

I did a mistake

What about that? Is that correct?

[patent beacon]

Σ means "sum"

[uncut mulch]

=2
and then you'd have to write out the next few terms

[patent beacon]

k = 0 below, and n above, means to sum the terms from 0 to n

So you've got the first term, but there's more

[uncut mulch]

followed by ... and the final one or two terms

[viscid thistle]

I did this for the third one

[uncut mulch]

for the top one leave them as fractions

4/3 != 1.3

[viscid thistle]

Really? Why?

[uncut mulch]

these sums and sequences are better left as fractions so see their patterns

[viscid thistle]

Oooh okay

[patent beacon]

You generally don't want to use decimals in a math class. They imply you're approximating the answer

[uncut mulch]

how many terms did you write for the second one?

[viscid thistle]

5

[uncut mulch]

that sum doesn't end at i=6

you'd need indicate that it keeps going until i=n

i meant for your SUM of (2i -1)

[viscid thistle]

How do I do that??

Like, indicates it goes on?

With ...?

[uncut mulch]

followed by the term where it ends
the last 2 terms is usually better but one is enough

[viscid thistle]

But it says n, there isn't an actual end

[uncut mulch]

your last term would be when i=n

which would be (2n - 1)

[viscid thistle]

Big brain...

So... Like that?

[uncut mulch]

yeh

[viscid thistle]

Cool

[uncut mulch]

for the first one, you could leave them in the form ^4
and for the current question, leave them as powers of 2

[viscid thistle]

I don't want to risk it, this teacher I have it's kinda scary to me

Is this okay :/

[uncut mulch]

the denominator is
2k + 1
not 2^k + 1

[viscid thistle]

Right...

I didn't changed much though, still send prove that I listen to you :)

Thank you very much

[uncut mulch]

don't write -1x or 1x^2
just -x and x^2

remember the ... and nth term and you should be good

[viscid thistle]

Thanks again Ramonov, have a great night

[candid onyx]

Not sure what I replace here.

[stuck lark]

what've you tried so far?

[candid onyx]

x^2 + 1 + h - (x^2 +1) / h

is that correct?

[tired zephyr]

G-father, you’re missing the -f(x) part

[candid onyx]

that is what i did but it doesn't feel right

[tired zephyr]

(((x^2 +1) + h) - (x^2 +1))/ h

[pine galleon]

result is 1

[tired zephyr]

Yes

[candid onyx]

i did it right ?

h/h reduces to 1

[tired zephyr]

X-x. Cxl each other out leaving you with h/h which is 1

[candid onyx]

thank you!

[tired zephyr]

Struggling with domain of this

How is this plotted?

[proud wraith]

When do you know to use "{}" or "()" for answers

Ex) Why does this one use "{}" for it's answers which are {-4,-4/3}

when this one uses "()" for it's answers which are (7,11)

Sorry if I cut anyone.

[short sorrel]

curly brackets {} denote a set

round/square brackets (), [], (], or [) denote an interval

the first question uses {} because there's a finite set of solutions

[silk cedar]

I’m about to start an astrophysics corse it’s I’ll@probably be taking calc and physics

[short sorrel]

which can be listed individually

the second one uses () because you can't list the solutions

its an inequality, so the solutions will be an interval

{-4,-4/3} indicates that the solutions are -4 and -4/3, and ONLY those

(7,11) indicates that the solutions are all numbers BETWEEN 7 and 11

(excluding 7 and 11 themselves)

for more, look up "set notation" and "interval notation"