precalculus

[narrow marsh]

I need to separate the recursion into 2 cases, k>=a, k<a (and the original thing wasn't right anyways)

[blazing parrot]

well good luck

its the middle of the night here and im going to go to sleep

[narrow marsh]

👋

thanks

your table gave me idea for the recursion

[blazing parrot]

my stupidly wrong table heh

[narrow marsh]

$$E_1 = \frac{1}{a}$$
For $k < a$, $$E_k = \left(\frac{1}{a}\right)\left(\sum^{k}{i=1}1+E{i}\right)$$
For $k \geq a$, $$E_k = 1+\left(\frac{1}{a}\right)\left(\sum^{a}{i=1}E{k-i}\right)$$

Ok I think it's this 😂

[obsidian monolith]

Shuri2060:

[viscid thistle]

check a few a's and k's explicitly

[full garden]

hey guys

can someone please tell me where the 12pi/4 came from here

[elder junco]

What is your exact question?

[full garden]

how did they end up getting 12 pi/4

after completing an entire revolution

can someone please help me

[lime bolt]

what is the actual question though

just evaluate csc(13pi/4)?

[full garden]

yes

but she went an entire cycle

and went from 4pi/4 to 12 pi/4

can u pleaaste explain why

[lime bolt]

they have a difference of 2pi, so are equivalent

[full garden]

yes

but how did she end up

with 12 pi/4

[lime bolt]

what do u mean by "end up"

[full garden]

how did she get that number from

when you go an entire cicle

don't you add 2 pi

ohhh

okay

i think i got it

thank you

[lime bolt]

[novel cargo]

$\tan(x - \frac{\pi}{2}) = \frac{\tan{x} - \tan{\frac{\pi}{2}}}{1 + \tan{x} \tan{\frac{\pi}{2}}}$

[obsidian monolith]

az:

[novel cargo]

how would I go about tan pi/2 here?

[echo wagon]

Where did you get this?

tan(π/2) is not defined

[novel cargo]

nr 58

trying to verify

[tardy ridge]

oops

try doing sin(x-pi/2)/cos(x-pi/2)

hmmm...

[novel cargo]

worked like a charme

[tardy ridge]

charm*

[novel cargo]

doubl thanks

[lime bolt]

double*

[low owl]

I'm stuck trying to break down the sqrt of 290000

nvm. had an "aha" moment right after I said that

[fleet yew]

1000 sqrt29

[blissful kayak]

Huh?

1000?

[low owl]

100

[blissful kayak]

1000 squared is 1000000

Not 100000

Oh but I think that's just a simple typo

Did you mean 100\sqrt{29}, AMD?

[spark veldt]

Can someone help me parameterize these

[patent beacon]

@spark veldt
Let's say, random choice, that
x - 20 = cosθ
y + 10 = sinθ

Then what happens to the left side of question c?

[full garden]

hey guys

oh sorry its in use

[spark veldt]

Does this look right

[blissful kayak]

Yes

I'ma steal that problem though because it could be good review for parameterizing conic sections

C:

[proven marten]

better

[stiff oracle]

Desperately need help

Me and friend can't figure it out

[proven marten]

Restrictions are 2pi

do you know what p would do to the sin wave

[stiff oracle]

No

Well I think but don't want to sound dumb

[proven marten]

Well I think but don't want to sound dumb
@stiff oracle Guess

[stiff oracle]

It stretches it right

[proven marten]

yes

so when p becomes bigger

does it stretch wider or narrower

[stiff oracle]

Narrower

[proven marten]

ok so when p is smaller

what happens

[stiff oracle]

Then the curve narrows??

[proven marten]

yes

Are you starting to get an idea of how to solve this

[stiff oracle]

Nope

Because won't it always cross the y=-1

And we need the greatest value for which it doesn't intersect

[proven marten]

Not when theres a restriction of 2pi

if you make it fat enough to not reach -1 at 2pi

you should be g

is the idea im trying to work towards

[stiff oracle]

Ok now I get it

So how do I find the actual value

[proven marten]

Uh

Plug in 2pi at x

[stiff oracle]

2sinp2Pi?

[proven marten]

JC Denton has fainted. Math server chooses @echo wagon !

[echo wagon]

Huh?

[stiff oracle]

..

[echo wagon]

@stiff oracle Like you said, if you make the value of p smaller, the graph stretches.

So you need to stretch it enough so that the first point where the graph touches y = - 1 is outside the interval where you are working

[stiff oracle]

Yeah so you want to stretch it so it doesn't reach the line before the limit but how do I get the value

[echo wagon]

The biggest value of p will be when that points is right outside that interval (i.e. At x= 2π)

So make 2sin(p(2π)) = - 1 and solve for p

[stiff oracle]

Uhh how do I isolate it

Sorry I'm a bit slow

@echo wagon

[proven marten]

this I can help with at least

your goal is to isolate p

so naturally you would divide by 2

[lime bolt]

😼

[lime bolt]

bruh

do u know what sin(0) is

[proven marten]

lol

[stiff oracle]

only thing I know is that value should be close to like .58

[lime bolt]

is p an integer

if it is not, then that could be any value between [-1,1]

but if it is then it is 0

[viscid thistle]

p has to be bigger than 0

[lime bolt]

well is it an integer

[stiff oracle]

Idk does not state I would assume not

[lime bolt]

well then u cant find out the answer

so assuming it is an integer is probably what they want

[stiff oracle]

So it's 0 then

Which makes no sense

Because it says p is bigger than 0

[lime bolt]

yes but, sin(2pi) is 0

and any multiple of 2pi is also 0

[proven marten]

I think youre forgetting it has an amplitude of 2 kane

[lime bolt]

2times 0 is 0

also the denomintor cancles out anyway

[stiff oracle]

So jc how do I isolate p could you show me

[proven marten]

2sin(p(2π)) = - 1

Do you know how to solve equations

[viscid thistle]

You will get negative result then

[stiff oracle]

That's what I did

[lime bolt]

bruh u do know that sin(2pi) is 0 right

[viscid thistle]

Bud, its has amplitude of 2

[lime bolt]

no it doesnt

it is divided by 2

[viscid thistle]

Just check the exercise

[lime bolt]

also it doesnt matter even if the amplitite is 100000000000000000000

because it is being times by 0

[viscid thistle]

I dont get it

[proven marten]

kane is right

[stiff oracle]

@proven marten I get a negative value

[viscid thistle]

Yes its negative 4.5 smth

[proven marten]

if it can be negative, then it can be positive

[lime bolt]

how are u getting negative

[viscid thistle]

By puting negative 1 as y value

[lime bolt]

?

[viscid thistle]

-1/2sin(2pi)

[stiff oracle]

@proven marten

[lime bolt]

bruh

are in degrees mode.......

[proven marten]

lmfao

[viscid thistle]

Omg

[lime bolt]

what u are doing is lirerally dividing by 0

also that is not even what the question is at all

[proven marten]

Is TKO the friend of M&M

[viscid thistle]

Yes

[lime bolt]

even if u had it in the right mode, that is not how u solve this question

[stiff oracle]

wym

[viscid thistle]

Yes, it gives error, but thats what I understood from Denton

[stiff oracle]

Jc said to isolate p

To get value

[lime bolt]

how can u isloate p....

that isnt even what the quetsion is asking

[stiff oracle]

It's asking for a value of p

[lime bolt]

no it isnt

it just says evaluate the expression

[proven marten]

uhm kane

it says to find the greates t value of p

[stiff oracle]

"find the greatest value of p such that the graph of g does not intersect the line y=-1

[lime bolt]

this is what i am looking at

well if that is the case, then i have been looking at a different quetsion for the past 5 minutes

wait lol is that not the question @proven marten

[viscid thistle]

Ahhh

[lime bolt]

lol i thought this was the question

[stiff oracle]

Nope

So how do I isolate p

[proven marten]

okd

do you guys know trig stuff

[stiff oracle]

Let's just say no

[lime bolt]

so it reaches -0.5 at -pi/6

so when u times by 2 it intersects, if p=1

so we need the input to never be greater than pi/6

[stiff oracle]

So p is pi/6

Well smaller than

[lime bolt]

but then u can make x arbitrarily large

so therefore as long as |p|>0, it always interesects

which means the only value is p=0

[stiff oracle]

Yeah but it can't be 0

[lime bolt]

why not

[viscid thistle]

And we have to find the greatest value

It says that in exercise

[lime bolt]

yea the greatest is 0

[stiff oracle]

It says p>0

[proven marten]

kane theyre right

[lime bolt]

yea but i can find a contradiction though

[viscid thistle]

Its 3 mark question btw

[stiff oracle]

Supposed to take 6min to do

[lime bolt]

say we have a value p which works, make x=(pi/6)/p

this this input equals -1 for whatever p

[proven marten]

kane uh so

I did some desmosing

and

the value does go greater than 0

[stiff oracle]

@proven marten can u tell me how to isolate p and get the greatest value

[lime bolt]

are u guys following my argument, i just proved that there isnt a p

[stiff oracle]

This isn't TOK

[viscid thistle]

Ahhhhh

[lime bolt]

oh guys!!!

the question says 0<x<2pi

i didnt see that

[proven marten]

lmfao

[lime bolt]

if that constrait wasnt there than i was right

[proven marten]

This isn't TOK
@stiff oracle Are you an IB student?

[lime bolt]

and no such p works

[stiff oracle]

Ffs

Yes jc

[proven marten]

lmfao

lets go

ib

[viscid thistle]

Thats what denton tried to show us

[stiff oracle]

Please man

1 hour just trying to find a p value

[lime bolt]

oh ok now it is trivial

[proven marten]

Why arent you guys in the IB server though

[viscid thistle]

Whats the difference?

[stiff oracle]

Because we just want math help

[lime bolt]

so the highest value is just 2pi/(pi/6)

[stiff oracle]

And just want p value

[proven marten]

Whats the difference?
@viscid thistle They would be more familiar with the curriculum ?

[lime bolt]

that is the answer guys

[viscid thistle]

We dont know the answer

[proven marten]

go to ib resources

its probably a past paper question

[lime bolt]

wait actually that only works for negative x

i need to do 2p-pi/6

ok that works i found p

[viscid thistle]

IT'S 3 MARK QUESTION! It shouldnt be this extrime

[lime bolt]

yea it is absolutely trivial

[stiff oracle]

This is giving me depression

[proven marten]

What math are you guys taking

[stiff oracle]

AA SL

[lime bolt]

the answer is : 2pi/(15pi/6)

and just rearrange a bit

[viscid thistle]

Could u please give step by step?

[stiff oracle]

^^

[lime bolt]

but like striclty less than that which is kinda weird

[stiff oracle]

Our small brains can't habdle

Handle

[lime bolt]

well u need the input to be less than 15pi/6

[viscid thistle]

How did u come up with 15pi and 6?

[lime bolt]

and the highest value it can attain is <2pi, so divied 2pi by that

because (sin(15pi/6)=-0.5

[stiff oracle]

Where does the 15pi/6 come from

[lime bolt]

oh wait it doesnt

just find the value for which it does

and then do the same thing

[viscid thistle]

Kane, i think we should just call it a night

[stiff oracle]

Are we getting trolled

[proven marten]

not sure

usually he helps

[lime bolt]

no this is literally the answer

[stiff oracle]

JC please

Ik you know how to explain it

[proven marten]

kane is meant to be better than me in math though

[lime bolt]

oh guys the issue i made is that i misread my 12 as a 16

yea that answer is: 2pi/(11pi/6)

[proven marten]

lol

idk if he s trolling

[stiff oracle]

JC it would mean a lot of you could explain it to me

[lime bolt]

look there have been a couple of issues today: first i didnt know the question, second i didnt know x<2pi, now i misread my handwiritng

but now everything is good

[viscid thistle]

Alright

Can we get step by step?

Bc what is 11pi and 6?

Like how did u come up with that

[proven marten]

JC it would mean a lot of you could explain it to me
@stiff oracle bruh Im as clueless as you are rn

[lime bolt]

sin^-1(-0.5)=11pi/6

[proven marten]

Im guessing you guys are M21s though

Im trying to find a past question like this so please bare with kane for now

[lime bolt]

so cant have the input to be more than 11pi/6

[stiff oracle]

Im trying to find a past question like this so please bare with kane for now
@proven marten ok thanks

The numbers are coming from nowhere

Kane

Where do u get them

[proven marten]

<@&286206848099549185>

[lime bolt]

oh guys

i realized why it didnt work

i have the correct answer

i can explain it all, my idea was completely correct earlier but i accidenly made one mistake

the issue is that sin equals -0.5 at two points 0<x<2pi

and i accidently accounted for the later one, not the earlier one when i meant to do the earlier one

so the first time that sin(m) equals -0.5 is at 7/6pi

now we cant have the input 0<m<2pi to ever equal this, as 2 sin(m) would therefore equal -1

so the highest value we can obtain is 2pi, therefore p needs to be 2pi/(7pi/6)

[stiff oracle]

Where do the numbers come from

And we are supposed to do this without a calculator

[lime bolt]

which gives the final answe of 7/12

you dont need a caclulator if u know what sin(pi/6) is

but it is easier with a calculator

[viscid thistle]

Its paper 1 question, so we cannot use calculators as well

[lime bolt]

ok it isnt needed

but do u guys understand this now

@proven marten

[stiff oracle]

Not really where do the numbers come from

[lime bolt]

for now, dont think about the numbers ill explain after

but do u understand what im saying

[viscid thistle]

We got the answer, we understand, now what

[lime bolt]

are sure u understand

idk if u do

[stiff oracle]

I don't at least

[lime bolt]

so i guess im gonna repeat myself then

[viscid thistle]

No no no, we just understood that u gor the answer

[lime bolt]

ok ill explain to M&M first then

[stiff oracle]

7/12 is the answer but without knowing where the numbers come from or what to do with them it's confusing

[viscid thistle]

So first, why do we need to equal sin to -0. 5

[lime bolt]

becasue if it does then 2 times it equals -1

and we cant have it to equal -1

[viscid thistle]

Why negative?

[lime bolt]

do u not know that 2*-1/2=-1?

[stiff oracle]

Can u explain the numbers please and what to do to get 7/12

[lime bolt]

yea im doing that

[viscid thistle]

Okey, sorry

[lime bolt]

so u guys understand why sin(m) can not equal -0.5 now?

[stiff oracle]

No

[viscid thistle]

No

[lime bolt]

well as i already said, if it does then 2sin(m)=-1

and the question says this cant happen

[stiff oracle]

Oh you mean the y

[lime bolt]

u understand?

[stiff oracle]

Like the line

[viscid thistle]

Yes i got it as well

[lime bolt]

ok lets move to the next bit

the highets value of x we can have is 2pi

[viscid thistle]

Yes

[lime bolt]

also the lowest value of m such that sin(m)=-0.5 is 7pi/6

ok?

[stiff oracle]

But how do u get 7pi/6

[viscid thistle]

Yea this is where it gets confusing

[lime bolt]

so u know that sin(pi/6)=0.5 right?

[stiff oracle]

Yea

[lime bolt]

and sin(x+pi)=-sin(x)

so pi/6 +pi=7pi/6

[stiff oracle]

Ok but why do you divide by 6 and how do you know to

Ik that it equals .5

[lime bolt]

so u guys understand everything so far?

[viscid thistle]

No

[stiff oracle]

No

[viscid thistle]

Where is th 6 coming from?

[lime bolt]

it is coming from sin(pi/6)=1/2

[stiff oracle]

Ok but why do you divide by 6 and how do you know to
@stiff oracle

[lime bolt]

this is just a fact that u know

[viscid thistle]

Hmm

Shit

You are right

[stiff oracle]

Are u talking about the unit circle

[lime bolt]

ok and as i said again sin(x+pi)=-sin(x)

and pi/6 +pi=7pi/6

[stiff oracle]

Wouldn't that be 2pi/6 if you add them

[lime bolt]

no

[stiff oracle]

Can u explain that then

[lime bolt]

pi=6pi/6

[stiff oracle]

Ohhg

[lime bolt]

ok so everything makes sense now?

so far

[stiff oracle]

Yes

[viscid thistle]

Yes

[lime bolt]

ok so the highest value of m we can get is 2pi

and we need to makes sure m is always less than 7pi/6

[stiff oracle]

M is just x btw right

[lime bolt]

m=px

[stiff oracle]

Ok

[lime bolt]

and when we have x as 2pi, we need p to make it less than 7pi/6

and the highest value(which is the quetsion wants) is ...

i mean (7pi/6)/2pi

which equals 7pi/12pi

=7/12

you guys understand?

[stiff oracle]

Don't get the last bit

And TKO doesn't get that 6/pi + pi = 7pi/6

[lime bolt]

no it is pi/6

not 6/pi

[stiff oracle]

I meant thst

[lime bolt]

pi/6+pi=pi/6 +6pi/6=7pi/6

m&m what bit dont u understand

[stiff oracle]

(7pi/6)/2pi

Why the 2pi

[lime bolt]

ill write it down wait a minute

[stiff oracle]

Isolating p

Got it

[lime bolt]

so that is the answer

everything good?

[stiff oracle]

Now can you write on paper as full equation from start to 7/12

Ik it's a lot to ask

[lime bolt]

write down the final equation?

it is just 2sin(7x/12)

[stiff oracle]

No like from 2sinpx

[lime bolt]

idk there isnt a point

if u want to refresh u can just reread what i said

[stiff oracle]

Ok and also why is it not negative 7pi/6

Since y is -1 not 1

[lime bolt]

u can reread if u forget

[stiff oracle]

Now I get it

Ok thanks

[lime bolt]

👍

[viscid thistle]

Thanks a lot man

[stiff oracle]

@lime bolt

Is this reasonable to do in 6min

[lime bolt]

Yea I pretty much had the idea instantly

The reason this took longer than it should have is that first I didn’t read the correct question, and then when I did I skimmed it and missed an important part about x, but was still correct

[stiff oracle]

Yeah but even so this feels like HL and still 6mins is a bit harsh

[lime bolt]

I guess so

[stiff oracle]

So is it reasonable or not

I'm just curious

[lime bolt]

Yea I think so

Although I have no idea what exam this is

[regal kernel]

Is it possible to know how to do problems like arcsin(9) by just using memorized trigonometry exact values from 0 to 90 degrees (meaning no unit circle)?

@lime bolt

[late inlet]

@regal kernel Why would you ever need to know them? lol

And not to my knowledge, no.

[regal kernel]

@late inlet I just had a homework problem that had that, but I believe I can get by just by knowing how to get all the exact values

[echo wagon]

@stiff oracle wow, sorry for going to sleep. That took longer than it needed to, lmao

[shrewd tendon]

can someone help with this one?

[echo wagon]

Divide the numerator and denominator through by x

@shrewd tendon

[shrewd tendon]

what about the signs though

[echo wagon]

@shrewd tendon sorry for disappearing

What signs? Do what I said and show me what you get?

And @ me

[shrewd tendon]

@echo wagon

[echo wagon]

How did you get that?

Just divide through by x

Do not evaluate the limit

[shrewd tendon]

idk what you mean then

[echo wagon]

$\sqrt[3]{\frac{x-3} {5-x}} = \sqrt[3]{\frac{1-\frac{3}{x}}{\frac{5}{x} - 1}} $

[obsidian monolith]

Lunasong:

[echo wagon]

Divide the numerator and denominator by x, don't know how I could have been more clear

[willow bear]

this is too small to read

[dawn oar]

there ya go

[willow bear]

ok, what have you tried so far

[dawn oar]

I see q,x and c

3 variables for a factoring equation doesn't make sense to me

[willow bear]

q isn't a variable, it's the name of a polynomial

you can read p(x) = (x-c) * q(x) as "p(x) = (x-c) * (some other polynomial)"

but more pertinent to the problem have you found p(-8) yet?

have you done the long division of p(x) by (x+8)?

[dawn oar]

long division?

nope

[willow bear]

then do it

[dawn oar]

will do

but why x+8?

[uncut mulch]

when c = -8
x - c = x - (-8) = (x + 8)

[dawn oar]

Also sorry for the delays in response

but what do I do after that?

[uncut mulch]

well p(x) is a quadratic,
finding the other factor should be quite simple if you already know one of them

[willow bear]

have you done the long division?

if yes, then can you show what you've ended up with?

[dawn oar]

3(2x+1)

[willow bear]

6x+3 is your quotient

you divided 6x^2 + 51x + 24 by x+8 and got 6x+3

therefore

6x^2 + 51x + 24 = (x+8)(6x+3)

[dawn oar]

Thanks!

I understand a little bit better

What do I make of q(x) though?

[willow bear]

q isn't a variable, it's the name of a polynomial
you can read p(x) = (x-c) * q(x) as "p(x) = (x-c) * (some other polynomial)"

[dawn oar]

but for solving I mean

That's what threw me off

Do I ignore it?

[willow bear]

do i need to repeat myself again?

[tardy ridge]

Just plug in the value of -8 into the polynomial and see what you get

if you get 0 then x+8 is a factor

[bleak lance]

Find the equation of a line that is perpendicular to the line x = - 7 and contains the point (3, -6).

[viscid thistle]

@bleak lance what have you tried so far

[lime bolt]

Just do perpendicular gradient thing and equation of line thing

[autumn marsh]

hey is anyone available to explain something to me

i'm having a brain fart

easy precalc

[lime bolt]

[mighty onyx]

If 275 mg of a radioactive element decays to 200 mg in 36 hours, what is its half-life? Round to four decimal places for intermediate steps. Round to the nearest whole number for Answer.

I got 66 hours but I tried that and 67 and 65 but It said I was wrong

[uncut mulch]

show work

[uncut mulch]

decay isn't linear

it's exponential

look up exponential (growth)/decay
and there's also a specific formula for the case of half life

[mighty onyx]

Oh I got it, it is 78 hrs

[vivid glacier]

guys someone pls help me here, how should I know the distance she traveled in day 2 if the distance vector of day 2 is not given? (I don't want to know the answer, I want to know how do I get the distance vector of day 2)

hmm probably \vec{d}_2 is = -5î-7(^j)

but idk

oh ok I got it right

the only think I needed to know was that \vec{d}_1+\vec{d}_2+\vec{d}_3 = 0

[blissful kayak]

Maybe try to see what vector cancels both d_1 and d_2 out?

I dunno

[strong ermine]

Brain fart... pls help

[shrewd tendon]

can someone help me with this question

please

[strong ermine]

Um... is that the entire question?

I havent reaxhed that far in pre cal but that doesnt seem like a lot to go off of

[patent beacon]

Worth looking at first, is the limit
(x - 3) / (x - 5)

First off, if your limit is to -inf, do yourself a favor and sub u = -x to make it +inf

It won't really matter here but it matters sometimes

You can find that limit by dividing top and bottom by x:
(1 - 3/x) / (1 - 5/x)
Which approaches
(1 + 0) / (1 + 0) = 1

@shrewd tendon
Your question is very similar.

[shrewd tendon]

but thats not the answer right?

the answer is

[vagrant vortex]

@strong ermine P(x) = R(x) - C(x)

you can find P(x) like that

[vagrant vortex]

for question a: for there to be a profit, P(x) > 0

that will tell you what's the x (how many customers) needed for the business to turn a profit

same thing with b

[strong ermine]

Ok

[vagrant vortex]

just solve when P(x) = 60000

and you're there :D

[strong ermine]

Thanks

[vagrant vortex]

happy to help :)

[viscid thistle]

im confused how is this wrong

[blissful ridge]

ln(0) is undefined

You end points shouldn't be included

[viscid thistle]

wdym by they shouldn't be included?

()

[]

[blissful ridge]

Do you know there difference between [] and ()

[viscid thistle]

oh that yea closed and open i tried that before

ln(0) undefined

Not included in domain

(-x,x) where x>0 asserts that 0 is included in the domain

[willow bear]

what's the original f

[rigid sun]

nice

[viscid thistle]

Need help with this

Why must these exist

Hahaha

Anyway what’s confusing you

Nah it’s a joke

The answer is C

[gloomy path]

uhh

[viscid thistle]

Great

[gloomy path]

the answer is E

none of the above

[viscid thistle]

What is the answer then

[remote raptor]

can someone tell me how 8x^1/3 - x^-2/3 can be simplified to x^-2/3 * (8x - 1)?

basically how does it work that you can pull a ^-2/3 out of 8x^1/3 and have it become just 8x

plz @ when answering thx

[rigid sun]

? what

,w graph 8x/3 - 1/3x^2

[obsidian monolith]

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[remote raptor]

No

8x^1/3 - x^-2/3

1/3 and -2/3 are exponents

[rigid sun]

[remote raptor]

right...

anyway

[rigid sun]

factor

[remote raptor]

how does pulling a ^(-2/3) out of 8x^(1/3) make it just 8x

i dont get it

[rigid sun]

1/3 - (-2/3)=1

$\frac{x^a}{x^b}= x^{a-b}$

[obsidian monolith]

maleb1964:

[rigid sun]

$1/3 - (-2/3)=1$

[obsidian monolith]

maleb1964:

[rigid sun]

got it?

it wouldn't be so hard to see if you wrote it as $ 1/x^{\frac{2}{3}$

[obsidian monolith]

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

[rigid sun]

negatives are eyerape

[peak token]

The minimum/ maximum values of a function are also its vertex, right?

[sour plinth]

vertex refers to parabolas only

[peak token]

Yes

[willow bear]

one typically only speaks of vertices for parabolas yeah

[sour plinth]

otherwise, they're called stationary points

[peak token]

Its a quadratic

[willow bear]

do not say function to mean quadratic function

not all functions are quadratic

[peak token]

Oh

Yeah sorry should have been more specific

[willow bear]

anyway, the vertex of a parabola is its sole extreme point - minimum or maximum depending on the sign of the leading coefficient

[peak token]

Ok cool. I know how to get it from the aos and whatnot just wanted to make sure they're the same thing

[willow bear]

they aren't the same thing, extreme points are a more general concept

because as i said earlier,

not all functions are quadratic

[peak token]

I'm not sure I understand, but I think for what I'm working on they can be treated as the same thing but minimum/maximum is an umbrella term that will be used for other things later.

Thanks

[uncut mulch]

yes it is calculus. search it up.

[wanton dust]

How do we call the conditions in a by parts fonction?

Conditions?

“by parts conditions”?

[tardy ridge]

piecewise?

[wanton dust]

Yes!

It his better to call it piecewise fonction then fonction by parts?

[willow bear]

piecewise is the english word yes

and in english it's function

[wanton dust]

Oups

Thanks for correcting me.

So how do we call the conditions of the piecewise function?

“conditions”?

[willow bear]

the conditions maybe

there is no special word

[wanton dust]

Thank you!

So if I wrote this

The description of the nonperiodic function $\text{e}^{i \nu\phi'}$ over the domain $\phi'\in\left[\phi_{\text{G},0},\phi_{\text{G},0}+2\pi\right[$ is equivalent to describing this nonperiodic function as a piecewise function in terms of $\phi_\text{G}\in\left[0,2\pi\right[$ where conditions depend on $\phi_{\text{G},0}$.

[obsidian monolith]

Ozzy:

[wanton dust]

Is it clear?

[novel cargo]

if I wanted to solve this analytically, how would I proceed?

As I understand, these tangent lines have the same slope

[viscid thistle]

Do you know derivatives?

[novel cargo]

yes

[viscid thistle]

Say no more

[novel cargo]

I could set up a general equation for each line and the set them equal each other

[viscid thistle]

Uhm first find slope

Using derivatives

[novel cargo]

finding slope without considering other constraints doesn't work

there are infinitely many slopes that are equal between the tangent lines of both graphs

these are the graphs

[viscid thistle]

finding slope without considering other constraints doesn't work
Exactly

Functions need to be tangent

So f(a) = g(a)

Where x=a is the coordinate of tangency

[novel cargo]

are f and g derivatives of the functions?

[viscid thistle]

No

f and g are the 2 parabolae

[novel cargo]

we looking for a line like this

f(a) = g(a) doesn't work beause the tangency of the line with the parabolas isn't necessarily at the same x coord

[viscid thistle]

Wait

Oops

[novel cargo]

f'(a) = g'(b)

maybe for the slope and a and b the x coords

[viscid thistle]

Setting up line equation would be good

[novel cargo]

I have to go

come back later

[viscid thistle]

Limit as x approaches infinity

That wouldn't exist right?

Or would it be 0

Nice drawing

[lime bolt]

it depends if f(x) is 0 for x in its domain

[viscid thistle]

Well lets say it wasnt

That would be nonexistent aint it?

[lime bolt]

yea

well it depends on what u mean by nonexistent, it still exists, just isnt on a point on the graph

[viscid thistle]

Wait holdon

Heres a full picture

so limit as x-> infinity

that would not exist or be 0?

[lime bolt]

the limit still exists

it doesnt matter if it is on the graph ever or not

[viscid thistle]

ok

So i see

It will approach 0 basically, correct ?

[lime bolt]

it depends on what the function actually is, but if it stays similar to that then yea

[viscid thistle]

Alright thanks 👍

[grave kiln]

How to i calculate the intergration of 1/(x+1)²

please give me some tips

[viscid thistle]

u = x + 1

[grave kiln]

what is u though ? 😦

[lime bolt]

it is just a substitioun

[viscid thistle]

A random variable

[lime bolt]

also du=dx

[viscid thistle]

t = x + 1

y = x + 1

All the same

[grave kiln]

ok i see but where do i put it in :v

i can't see how it can help me

[viscid thistle]

In the integral

Do you know how substitution works?

[lime bolt]

do u know the integral of 1/u^2 du

[grave kiln]

substitution i think so

1/u² not sure

but i can try

[lime bolt]

hint: write it exponentially

[grave kiln]

Somehow i got to the Basel problem 😦

[viscid thistle]

Are you integrating or is it a sum?

[hallow hazel]

For arithmetic sequence, since the sequence goes in a negative motion; wouldn’t it be f(n)=f(n-1)+(-13) or would it just be f(n)=f(n-1)+13

[tardy ridge]

f(n)=f(n-1)-13

[hallow hazel]

thanks

[grave kiln]

I'm trying to prove that the intergration of 1/(x+1)² = -1/(x+1)

i think we misunderstood each other

sorry was afk to ask my neighbor about this :v good friend

[bleak lance]

May someone here please help me out?

I need help with putting this in general form

[viscid thistle]

Do you know how to general form looks like?

[mighty onyx]

At the beginning of an experiment, a scientist has 396 grams of radioactive goo. After 120 minutes, her sample has decayed to 24.75 grams. Round to four decimal places in every intermediate step.
What is the half-life of the goo in minutes? Round to the nearest whole number. Answer is 30
Find a formula for G(t), the amount of goo remaining at time t. G(t)=_______

Wouldn't the formula be $G(t)=396*0.5(t/30)$

[obsidian monolith]

Albot1288:

[mighty onyx]

anyone?

[rigid sun]

bruh

it just gave you the answer?

or did you figure that out?

@mighty onyx anyway since you somehow got the answer

if you just cheated the question or not

you can easily check if your formula works by checking it analytically

and then checking it numerically

that's the best approach for all practice problems, so then you get better number sense and can quickly formulate equations without thinking very hard

what is the type of function that is used to calculate half life?

@mighty onyx

[mighty onyx]

exponential

[rigid sun]

ok

is this $G(t)=396*0.5(t/30)$ exponential?

[obsidian monolith]

maleb1964:

[mighty onyx]

I believe so

[rigid sun]

where is the exponent?

[mighty onyx]

I feel dumb now

[rigid sun]

remember, exponents are indicated by either using the ^ symbol, or as a smaller number above the base

$x^y$ is x to the power of y

[obsidian monolith]

maleb1964:

[mighty onyx]

yeah

[rigid sun]

x^y is also x to the power of y

[mighty onyx]

would it need to be $396^{-0.5(t/30)}$

[rigid sun]

hmm

think about this

how do we take 1/2 of something?

[obsidian monolith]

Albot1288:

[rigid sun]

don't we just multiply it by 1/2?

so let's start with this

$396 * .5$

[obsidian monolith]

maleb1964:

[mighty onyx]

it's the same as dividing by 2

[rigid sun]

yes

but dividing looks nasty

lets say we want, ANOTHER half

what would we do?

$396*.5*.5$ no?

[obsidian monolith]

maleb1964:

[rigid sun]

but isn't that also $.5^2?$

[obsidian monolith]

maleb1964:

[mighty onyx]

or $x^{-2}$

[obsidian monolith]

Albot1288:

[rigid sun]

so as you can see, the amount of halves that occurred in a process, or the amount of halves we wanted to do, is has a 1 to 1 ratio to the exponent

no

so, if we working only with HALVES

should the exponent be on 396 or .5?

[mighty onyx]

.5

[rigid sun]

ok

so now we have $396*.5^{something}$

[obsidian monolith]

maleb1964:

[rigid sun]

now as i mentioned earlier

the amount of halves we need or the amount of halves that occured needs to equal the exponent on .5

how do you figure out how many halves (or half lives) occured?

[mighty onyx]

count them?

[rigid sun]

ummm

sure

that works

so lets do that

,w 396/2

[obsidian monolith]

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[rigid sun]

,w 198/2

[obsidian monolith]

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[rigid sun]

,w 99/2

[obsidian monolith]

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[rigid sun]

,w 49.5/2

[obsidian monolith]

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Requested by maleb1964#6739

[rigid sun]

wow

so 396 was reduced to 24.75

how many halves did it take to get there?

[mighty onyx]

4 times

[rigid sun]

ok

so that means in order for the process of getting 24.75 to occur, we needed 4 half lives

and from earlier, we also know that the number of halves (or half lives)= the exponent

so now we have $ 396*.5^4$

[obsidian monolith]

maleb1964:

[mighty onyx]

$396*.5^{(120/30)}$ so I just needed to simplfy my original equation

[rigid sun]

now we have the information that 4 half lives took place in 120 minutes

[obsidian monolith]

Albot1288:

[rigid sun]

that's not an equation

[mighty onyx]

G(t)=_____ is given

[rigid sun]

it's also not a the right one

you have a quantity

$396*.5^{(120/30)}=24.75$

[obsidian monolith]

maleb1964:

[rigid sun]

do you know what needs to be fixed

(we need a variable in there)

[mighty onyx]

I need to find it for amount of time at time t

[rigid sun]

yes

wait woah tf

[mighty onyx]

what

[rigid sun]

the amount of goo at time t you mean

bruh

[mighty onyx]

yeah

[rigid sun]

ok

so you already know that half lives come every 30 minutes

what if we had t amount of time

how many 30 minute blocks are in t?

can you make an expression for that?

bruh

[mighty onyx]

$G(t)=396*.5^{(t/30)}$

[rigid sun]

not quite

[mighty onyx]

wait

[obsidian monolith]

Albot1288:

[rigid sun]

there you go

now technically on like exams and stuff you wouldn't have this much time

but what i recommond you do is watch some videos after ur done with ur work

to get more familiar with it

[mighty onyx]

but when I put it in it says it's wrong

[rigid sun]

check your notation

[mighty onyx]

I put it in 396*.5^(t/30) because he doesn't use syntax

[obsidian monolith]

Albot1288:
Compile Error! Click the reaction for details. (You may edit your message)

[rigid sun]

well it's obviously right

120/30=4

.5^4=1/16

,w 396/16

[obsidian monolith]

Results provided by WolframAlpha

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Requested by maleb1964#6739

[rigid sun]

ffs

[mighty onyx]

yeah

[rigid sun]

idk

perhaps he wants it in fraction form

check if there are special instructions

[mighty onyx]

my teacher has a weird way of doing this sometimes

just says don't use spaces

[rigid sun]

396* (1/2)^(t/30) is the same thing

[mighty onyx]

let me check

[rigid sun]

well i gtg

[mighty onyx]

nope

[rigid sun]

but if it keeps doing it

just email ur prof

cus obv that's retarded

that's not a valid way to get something wrong

that's not testing your knowledge of content

[mighty onyx]

he said last week when we complained that he's gonna go through and see if our thing works and give us credit

[rigid sun]

that's just cancer

good

[mighty onyx]

but still cancer

[rigid sun]

lol

[mighty onyx]

see ya

[bleak lance]

How can I get my PhD in Quick Maff?

[viscid thistle]

Can anyone solve this

[hallow hazel]

doesn’t look bad

[patent beacon]

Sure. Multiply both sides by the common denominator

That is, multiply both sides by
x(x + 1)√x
To get rid of fractions

Getting a pretty large polynomial though. Wonder if there's a better way?

[hushed sorrel]

surely 'not difficult but a tricky one' is a bit contradictory lol

[viscid thistle]

I’ll try multiplying but I think the answer is an integer

[hushed sorrel]

the problem is that square root u get on the RHS

makes the polynomial degree basically twice as big :(

[viscid thistle]

What answers do you guys get

[hushed sorrel]

u have an answer?

[viscid thistle]

An X=

I just get a formula and no integer

[hushed sorrel]

wdym

it doesnt have to be an integer

[viscid thistle]

Here’s my work

[hushed sorrel]

oh I dont think thats too useful

[viscid thistle]

The boxed formula is the answer I got

Can I go further in this or is this basically as far as the answer goes

[hushed sorrel]

well the answer is a number

not sure how to progress from there

Ive tried something unusual- x=tany

which gets me to the trig equation -2cot(2y)+1/2 sin(2y) = cot^2(y)

but dont think it progresses past there

very epic how double angle comes in and seemed promising tho

[viscid thistle]

How do you know the answer is a number

I just assumed it was

[hushed sorrel]

when it says solve the equation

it means

find the number (or numbers) which x can be

[viscid thistle]

Yeah that’s what I was thinking

[hushed sorrel]

so the following is true

[viscid thistle]

I just am stuck on this one

[hushed sorrel]

its quite hard and its annoying because it doesnt look hard

[viscid thistle]

I’ve been just rearranging the equation

I’ll try doing some other things that may get the equation smaller

Less variables in the equation would be nice

[lunar wind]

https://gyazo.com/68050a1f5cac00107b56c5a6825bdba8

Anyone know which one it would be

I am guessing C but I have no idea tbh

[viscid thistle]

It’s not B or E for sure

So now you have a 33% chance of being correct lol

Instead of 20%

[lunar wind]

It ended up being D

Which I ended up going with

however

I looked it up and on the interwebs it said it could be negative

but maybe I read it incorrectly

[viscid thistle]

At least I helped narrow down the choices

[vast veldt]

https://media.discordapp.net/attachments/747848215050846239/750183721004695572/unknown.png?width=730&height=272

could someone help me With E? i do not understand the question and i am stuck

[dawn oar]

I feel bad because I just did this yesterday but after dividing I'm a little bit stuck

what do I do after division?

[dim jungle]

what did u get after dividing

[dawn oar]

The first image

[strong ermine]

Show full question for 1st one

[karmic sundial]

Hey guys just making sure I'm studying the right things since I'm an autodidact, precalc is trig+alg right?

I'm trying to learn this because I need it for chem

[willow bear]

trig, exponentials and logs

and a hearty helping of algebra

[viscid thistle]

also, i see you are new to discord, you can check out the channel #old-network , if you scroll up a bit, you can find a chemistry server.

@karmic sundial

[tardy ridge]

@dawn oar why did you multiply everything by 5/2

[tired zephyr]

Having a minor memory lapse with the shift function of:

If h is negative, does it shift left or right?

[tardy ridge]

->

[novel cargo]

discord giving you hard time too?

[tired zephyr]

Images seem to take forever to load.

So with this function, the -root mirrors the graph about the X axis. So I would assume:
Domain: (-infty ,8]
Range: (-infty,0]

[novel cargo]

domain: [-8, inf)

@tired zephyr

[tired zephyr]

thx

[remote raptor]

6/(i+1) how can this be written in standard form?

[willow bear]

is i the imaginary unit?

if it is, then multiply the num and denom of $\frac{6}{1+i}$ by $(1-i)$ to make the denominator real. it should be clear from there.

[obsidian monolith]

Ann:

[bleak lance]

May someone please help me graph a circle?

[willow bear]

in what context?

what graphing tool, if any, are you using?

what do you know about the circle? do you know its center and radius? or perhaps three points said to lie on it?

[bleak lance]

MyMath Lab

I'll upload an image of what I have so far. Hold on.

There.

May someone please help me?

[viscid thistle]

Are you gonna ghost me like the 2 last times?

[bleak lance]

No. I’m sorry about that.

You there?

I may just do another problem. I don't wanna spend too much time trying to figure out what's going on. I'm gonna contact my instructor about it.

[bleak lance]

I'm on a new problem now.

Find the standard form of the equation of the circle having the following​ properties:
Center at the origin

Containing the point (3,-6)

[novel cargo]

you solved that @bleak lance ?

236

[bleak lance]

I got it.

I got help from someone else

[hexed bolt]

Someone help rq on this

[tired zephyr]

@hexed bolt (4(x+Δx)^2-2(x+Δx))-(4x^2-2x))/(Δx)

That should get you started

[hexed bolt]

Thank you so much

[hushed sorrel]

can u cheat and just differentiate it :p

as in not from first principles

[viscid thistle]

Bruh

[hushed sorrel]

soz please dont hit me

i am innocent

[lime bolt]

[viscid thistle]

[mighty onyx]

In the year 2005, a picture supposedly painted by a famous artist some time after 1655 but before 1705 contains 99.5 percent of its carbon-14 (half-life 5730 years).

Wouldn't I use the Half-life Formula of $0.995=(1/2)^{(t/5730)}$

[obsidian monolith]

Albot1288:

[mighty onyx]

If I'm right I just need to put in 1705 for t, right?

nvm just leave it as t and get the alternate form

[limber rain]

Can anyone walk me through the first one?

In other words, how would I input that function into the quadratic formula?

[low owl]

is that precal? that looks like something I had to do in "college algebra" last semester -- can't remember how for the life of me though lol

[limber rain]

Yeah, the focus is on the domain, range, zeroes ect. The quadratic formula is from Algebra 2, but we have to use it for this section for some reason.

We need the function to find the discontinuity, but I really don’t know how.

Really what I’m asking is, what parts of the fraction are a,b, and c.

[novel cargo]

AFAIK, you can't use the quadratic formula to find zeros of the denominator because the denominator is a first degree equation. It's "a" is zero, so the denominator of the quadratic formula (2 * a) would become zero, which is undefined.

It would make sense to use the quadratic formula on the denominator of #8 which is a second degree polynomial tho

[tepid hull]

actually

You can use polynomial

division if im not mistaken

you get a remainder

[novel cargo]

just put 4x - 2 = 0 and solve for x and you will have your discontinuities and domain

[tepid hull]

@novel cargo

That Function is continious though at x=1/2

[novel cargo]

how so?

[tepid hull]

I ment the function is still continus

except at 1/2

[novel cargo]

well then it isn't continuous

definition of continuity is fhat f(x) is defined, lim f(x) as x approaches c exists and that lim is equal to f(c)

at x = 1/2, f(x) is not defined

[tepid hull]

yes

its is continus where its defined

that what i said

[novel cargo]

true

it's continues except at 1/2

[tepid hull]

Yea

we both on the same page

[novel cargo]

how would I solve this algebraically?