help-26

[restive inlet]

is the function increasing/decreasing/constant in that interval?
consider what happens with values where 1/x isn't an even integer

[rustic sparrow]

idk 😭

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[neon iron]

how is tg=-root(3) equal to 5pi/3 tg means tanges

[neon iron]

how do i calculate it? complex numbers

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[clear jewel]

A = pi * r^2

A is area

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[gritty vigil]

is the easiest way to find the range of $f(x)=x \cdot \sqrt{2-x^2}$ by graphing it?

[thorny flame]

anantav

[gritty vigil]

if so, what's the second best way? Let's say I already know the domain, and the minimum value the function can take is $-\sqrt{2}$, plugging it in will give me 0 and will arrive at the wrong conclusion that the range starts at 0

[thorny flame]

anantav

[drifting swift]

calculus

find the points at which f'(x) = 0

and look at the values of f at those points and at the endpoints

[gritty vigil]

ah so graphing it is the most reasonable then since I haven't gotten into calculus yet

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[neon iron]

hello

[neon iron]

why are these functions not valid?

is anyone here?

[drifting swift]

1. it's only been 2 minutes be more patient

2. these are not functions, these are just function signatures. and so far there is nothing invalid about them.

show more context.

[neon iron]

yeah they are invalid my professor showed them as examples of invalid functions

[jade thunder]

Those aren’t even functions

[neon iron]

yeah thats what im saying

[drifting swift]

... weh?

[neon iron]

why arent they functions

[jade thunder]

Wow look more context!

[drifting swift]

is your professor claiming that there DON'T EXIST ANY FUNCTIONS from R to N?

like none at all?

[jade thunder]

I wonder what this was for…

[drifting swift]

because i can give you a function from R to N just fine.

$f: \bR \to \bN$ defined by $f(x) = \floor{|x|} + 2$.

[thorny flame]

Ann

[drifting swift]

just to give one example.

or yknow, could also just give a constant function.

OH WIT

wait

okay no

i understand now

[neon iron]

but considering domain and codomain

[drifting swift]

you've fixed the FORMULA of the function as f(x) = x^2.

[neon iron]

so this is the function of x^2

and the things that are ok and not are the domain > codomains

like where x^2 works or not

[drifting swift]

in relation to that formula sure.

[neon iron]

bcs what is f(-2)?

[ancient hearth]

4

[neon iron]

in the second

but can you explain why the not okay domains and codomains arent ok?

[ancient hearth]

4 isn't even in the codomain

[neon iron]

and f(sqrt(sqrt(2))) in the first

for example

they're not well defined

[neon iron]

for every x in domain it must have an image in codomain, and only one

[ancient hearth]

The function is f(x) = x^2 right?

So 2 and -2 have no image

And the function becomes invalid

[neon iron]

isn't a function at all

[neon iron]

okay

my mistake was to not look at the fact that they took the case of x^2

thanks for the help

.close

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[alpine flower]

”Calculate the angles in a right-angled triangle with leg lengths 1 cm and 3 cm, respectively.”

[ancient hearth]

That's easy

Trigonometry

[alpine flower]

Should i be getting diffirent results depending on where i place the 1 or the 3?

[ancient hearth]

It's shown in the diagram

[alpine flower]

There was no diagram

[ancient hearth]

Tan inverse 1/3 is the answer

[ancient hearth]

This

Oh wait u sent it

Nvm

[alpine flower]

No

[ancient hearth]

Ohh

[alpine flower]

The answer is tan inverse 3

[ancient hearth]

3 angles bruh

One will be 90 degree

One will be tan inverse 3

And one tan inverse 1/3

[alpine flower]

6.7

[tawdry raft]

uh...

[vital moth]

,rotate

[tawdry raft]

im confused with trigonometry

[ancient hearth]

Correct me if I'm wrong

But the questions told me to tell the angles right?

[alpine flower]

Yea

[ancient hearth]

So shouldn't I have three answers

Cuz it's a triange

[tawdry raft]

ye fr

[vital moth]

the third is 90

it is right angled

[alpine flower]

^

[ancient hearth]

Which will be 90 tan inverse 3 and tan inverse 1/3

[vital moth]

no need to mention that

[alpine flower]

But there is no tan inverse 1/3 in the answer

19.4 is not tan inverse 3

[ancient hearth]

Hm

So

[alpine flower]

So how am i supposed to know if i should do 3 inverse or 1/3 inverse

[ancient hearth]

The question said angles as in plural

But it also said after legs, respectively

So maybe the first one is base and second perpendicular

[vital moth]

no its correct

i will tell you why

the solution calculated the second angle by using the property that the 2 angles are complementary

if the angles are $\alpha$ and $\beta$ then $\alpha + \beta = 90$

[thorny flame]

calculus is fun

[vital moth]

because the third angle is given to be 90

[ancient hearth]

Yes

[alpine flower]

But why is the arctan of 1/3 incorrect?

[ancient hearth]

Cuz the sides are 1 and 3

But then why isn't tan inverse 3 correct

Cuz they didn't specify the angles

[alpine flower]

I dont get it

[vital moth]

i will tell you

[ancient hearth]

You don't get why it's either tan inverse 1 or 3?

*1/3

[vital moth]

the first angle is $tan^{-1}{3}$ so the second angle is $90-tan^{-1}{3}$

[thorny flame]

calculus is fun

[alpine flower]

Yes

[ancient hearth]

Yes

[vital moth]

now calculate $90-tan^{-1}{3}$

[thorny flame]

calculus is fun

[vital moth]

and calculate $tan^{-1}{1/3}$ and compare both answers

[thorny flame]

calculus is fun

[ancient hearth]

They will be same obv

But the thing is

How ru supposed to know which one is the answer

Given that nothing is mentioned in the question regarding thus

*this

[alpine flower]

^

[ancient hearth]

Oh wait no there are 3 answers

Nvm

[alpine flower]

Or no

[ancient hearth]

Wdym

[alpine flower]

Ah i dont know how to explain it

Ill drae

Drae

Draw

[ancient hearth]

K

[alpine flower]

,rotate

[alpine flower]

The question gave us a right triangle with the sides of 3 and 1

With that information you can dra the triangle like one of these two

[ancient hearth]

Yes

[alpine flower]

Now how come i only get the right answer when i inverse the tan of (the symbol)

[ancient hearth]

You mean why do you only get the right answer from one of them?

[alpine flower]

When i do it to the first one

Yea

[ancient hearth]

The thing is they are both the same triangle

[alpine flower]

Yes!

[ancient hearth]

From different perspectives

[alpine flower]

Should they share the same 3 angles??

[ancient hearth]

They do

But the thing is

The angle which you are viewing (the one on the left) is now gone to the top in the second triangle

And vice verse

[alpine flower]

Yes

[ancient hearth]

So you will get the 90 degrees minus the answer

[alpine flower]

So i should get angle a, b on the first one

And b, a on the second

[ancient hearth]

Yea

[alpine flower]

But i get completely diffirent angles

[ancient hearth]

How

Wait 1 sec

[alpine flower]

Thats what im askinf

[ancient hearth]

They are the same angles

Lemme send a pic

You will get the same values

[alpine flower]

Oh so the problem is probably

That they round up the number

Pretty rough

[ancient hearth]

Hm

[alpine flower]

They get 71.6, 19.4 and 90

I get 71.56, 18.43 and 90

Yes

Just checked

Their answer was all of the angles added were 181°

Bruh

Thanks for the help!

How do i close this

!close

,close

/close

.close

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[neon iron]

.

hello

[neon iron]

why does lnE cancel itself out and ln40 doesnt?

can anyone help?

[haughty talon]

because ln(x) and e^x are inverse functions. ln(e) = 1 = e^ln(1)

so ln(e^a) = a = e^(ln(a))

[neon iron]

huh

i dont get it

.

[quick gorge]

do you know what ln means?

[neon iron]

yes log

[quick gorge]

and what is its base

[neon iron]

a

which is 40

[quick gorge]

no

[neon iron]

wait

hold

on

is log and ln the same

or not

.

[quick gorge]

ln = log base e

[neon iron]

oh

wth

[quick gorge]

meaning

[jade thunder]

Sometimes log means base e

Sometimes log means base 10

It’s a mess

[neon iron]

what does base e mean?

[jade thunder]

If you read a math book log pretty much always means base e

$\log_e()$

[thorny flame]

Frosst

[neon iron]

huh

what does base e mean

[jade thunder]

e is just a special number

,calc e

[thorny flame]

Result:

2.718281828459

[neon iron]

oh

wth

ln - logbase e

okay so

[quick gorge]

so in this case

b is e

[jade thunder]

But b is a variable

e is a constant

It’s a special constant so we gave it a letter

Also it’s very hard to write the number out so we just named it e

So we can easily refer to it

[neon iron]

@jade thunder @quick gorge do u guys wanna vc and talk abt maths cus i need a bit of help with a few bits and bobs before i start engineering

[jade thunder]

No I’m trying to sleep haha

[neon iron]

ohh

[quick gorge]

I’m at school lol

[neon iron]

whats ur timezoes?

[neon iron]

school has started?

[jade thunder]

e is kinda like pi in a way

we don’t write 3.141….. all the time we just use pi

[neon iron]

oh

ohhhhh

i see

so in what cases do i use ln e instead of normal log?

[jade thunder]

It really depends on the context

Also from the point of mathematics, ln is the normal log

[neon iron]

hmm

alright

thank you

[jade thunder]

If your formula has e in it

Then obviously you want to use ln

If your formula has 3^something

Obviously you want to use log base 3

[neon iron]

okay

i kinda get it

[jade thunder]

(But this will change when you get to calculus, then you’ll see why e is used everywhere)

[neon iron]

ohh ok

ima start to learn calculus tomorrow

@jade thunder whats your timezone?

[jade thunder]

It’s night time here

[neon iron]

oh

wth

its morning here

12:58

.close

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[echo silo]

Hello! My question is this
for a polynomial function with coefficients are rational numbers, if there is an integer X such that its function value is an odd number, can we find infinity numbers of integers with odd values?

[split rover]

$f(x) = 2$

[thorny flame]

tales

[acoustic tangle]

The premise is false for that

"if there is an integer x such that its function value is an odd number"

[split rover]

I don't know how to read

XD

[cursive thorn]

try plugging in X + 2k, where k is an integer, will there be infinitely many values of k that give an odd number for f?

[acoustic tangle]

I think that's true yeah because every polynomial is periodic mod 2

[icy sky]

you have to be a little careful because they said rational coefficient

[acoustic tangle]

Yeah

[cursive thorn]

||let k be a multiple of the denominators of the coefficients||

[icy sky]

i was about to say that lol

[acoustic tangle]

Yeah or lcm of them right?

[cursive thorn]

also works

[icy sky]

assuming theyre in simplest terms, any one with a denominator that is a multiple of 2 would have an odd numerator, so i think youre covered there as well

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[echo silo]

oh thank you so much

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[rocky jacinth]

Please how do you do root

[rocky jacinth]

for example

i forgot

[flat kindle]

Sqaure root?

[rocky jacinth]

how to change root 10

to another to simpler version

[empty sail]

Can you send a problem you are stuck on?

[rocky jacinth]

like somethinglike

[flat kindle]

you can't

[rocky jacinth]

5 root 2

how do you change

4 root 2

to its orirginal form

[rocky jacinth]

its a concept

[empty sail]

$5\sqrt{2} \neq \sqrt{10}$

[thorny flame]

dldh06

[empty sail]

This?

[rocky jacinth]

yes thanks

.close

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[rocky jacinth]

Good evening

please when i isolve this i got math error

picture of solution

[sweet shard]

, rotate

[restive inlet]

first line is wrong

[rocky jacinth]

How please

[restive inlet]

also you should be using capitals

[rocky jacinth]

Then

What should id o

[restive inlet]

2 is on the wrong side

[rocky jacinth]

how

y

ues

[restive inlet]

p $\redt{is} \ \bluet{twice}\ \gray{\text{as much as}}\ q \
p\ $\red{=} \ \blue{2 \times}$ q

[thorny flame]

ℝam()n()v
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[rocky jacinth]

Ok

Thnaks

.cOSE

.CLSOE

.CLOSE

.close

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[sweet shard]

<@&268886789983436800>

[pastel juniper]

<@&268886789983436800> urgent!

[restive inlet]

<@&268886789983436800> more dings

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[icy sky]

.close

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[icy sky]

<@&268886789983436800>

Ooh im scared

[restive inlet]

i don't understand but it must be bad

[icy sky]

Im curious

[pastel juniper]

how old are you btw?

[icy sky]

Dont be an idiot in this server

[pastel juniper]

9 for sure

[restive inlet]

you should've thought about that BEFORE you posted all this crap

[pastel juniper]

these are hacked accounts

dont bother

[next aspen]

hi

[pastel juniper]

<@&268886789983436800> bro come on

[next aspen]

whats happening ?

racists for what?

for i m black?

im proud of that

[icy sky]

Nah theyre being idiots and think we're discriminating

[next aspen]

ah

fk them

anyway what was that

[icy sky]

Ok finally

Thanks mods

[spare crater]

anything else?

.close

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[vital moth]

hello everyone why is $\varphi$ uniquely determined by $\varphi_0$

[thorny flame]

calculus is fun

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@vital moth Has your question been resolved?

[vital moth]

<@&286206848099549185>

[topaz sinew]

@vital moth Has your question been resolved?

[urban grove]

Can you give more information? i.e. the original theorem statement

We can't tell from this for certain what phi and phi_0 are

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[vital moth]

sorry if i am late i wasnt online

[vital moth]

oh sorry i did pay attention that the pic i sent doesnt contain what they are ill send it

[vernal matrix]

Do you have a definition for S being a system of generators for E? Assumedly any element of E can be written as a linear combination of elements in S?

@vital moth

[vital moth]

yea in other words S is spans E

so from here why is $\varphi$ $\emph{uniquely}$ determined by $\varphi_0$

[thorny flame]

calculus is fun

[vital moth]

if i am right then this means that each $\varphi_0$ points into only one $\varphi$?

[thorny flame]

calculus is fun

[vernal matrix]

The linearity basically means that you can write any element in the image of $\varphi$ in terms of a linear combination of the $\varphi_0 ( x_i )$

[thorny flame]

@vernal matrix

[vital moth]

wait a sec

i am not talking about this

but i may have gotten the answer of my question

i will tell you what i reached and you correct me if you please

first of all $\varphi_0$ maps elements of S into a vector space F so each element $x \in S$ is mapped to a unique element $y \in F$ also $\varphi$ is a map from E to F so each element $k \in E$ is mapped into a unique element $z \in F$ and since S spans E then each element is E can be expressed as one linear combination of vectors of S at least but since each element of S has a unique element in F then each element in E must have a unique element in F

[thorny flame]

calculus is fun

[vital moth]

is what i said right

[vernal matrix]

Hmmm, sounds right though a bit confusingly worded imo

More that if you choose
[
\varphi : E \to F
]
to be a linear extension of $\varphi_{0} : S \to F$ and $S$ spans $E$, then any element
[
x = \sum_{k} \alpha_{k} s_{k}
]
of $E$ (with the $s_{k} \in S$, by the fact they span) will get mapped to
[
\sum_{k} \alpha_{k} \varphi_{0} (s_{k})
]
and the linearity of $\varphi$ gets you that as what you get mapped to regardless

[thorny flame]

@vernal matrix

[vital moth]

i just wanted to know why it is uniquely determined by $\varphi_0$

[thorny flame]

calculus is fun

[vital moth]

because i slipped on the trivial fact that they are maps so each x in domain of each is mapped to a unique y in the range

[vernal matrix]

Tl;dr the linearity and extension requirements get you a specific output based on $\varphi_0$ and elements of $S$

[thorny flame]

@vernal matrix

[vernal matrix]

If you chose anything else which had the same linearity and extension requirement it ends up being the same as per here

[vital moth]

whats Tl;dr

[vernal matrix]

Difference is that (random bad analogy, best I could think of right now!) you could e.g. like say you want a function $f$ such that $(f(x))^2 = x$, but that requirement doesn’t uniquely determine $f$ (in particular, $f(x) = \sqrt{x}$ and $f(x) = -\sqrt{x}$ both satisfy that)

[thorny flame]

@vernal matrix

[vernal matrix]

Whereas the fact you want both $\varphi$ to be linear and to extend $\varphi_0$ get you a unique map based on $\varphi_0$

[thorny flame]

@vernal matrix

[vital moth]

yes but each x has a unique f here '

[vernal matrix]

too long didn't read

[vernal matrix]

Hmmm, how do you mean? Each input you choose doesn't uniquely determine a function, unless I'm misunderstanding what you mean?

[vital moth]

each x in the domain will be mapped to one f in the range

thats just def of function

[vernal matrix]

True, but there isn't a unique function such that you also have the property stated for the example I gave, which was what I meant and tried to get across

[vernal matrix]

Both of the choices of function here satisfy the condition I put on them

[vernal matrix]

Whereas you won't find another [different] function that satisfies these requirements, there's only one

If that makes it any clearer what I mean?

[vital moth]

why is there only one

i mean thats my question

[vernal matrix]

As per here: given any input, with what they've given you, whatever you get as an output can be reduced to the same thing

[topaz sinew]

@vital moth Has your question been resolved?

[topaz sinew]

@vital moth Has your question been resolved?

[vital moth]

wdym by that

[vernal matrix]

As in you will always get
[
\varphi (x) = \sum_{k} \alpha_{k} \varphi_{0} (s_{k})
]
given
[
x = \sum_{k} \alpha_{k} s_{k} \in E
]
no matter what you do - you can't get anything different from that

[thorny flame]

@vernal matrix

[vital moth]

but $\varphi$ is uniquely determined by $\varphi_0$ which i suppose means that every $\varphi_0$ has one and only one corresponding $\varphi$?

[thorny flame]

calculus is fun

[vernal matrix]

Pretty much - each $\varphi_0$ induces a unique linear extension $\varphi$ (which behaves as per before)

[thorny flame]

@vernal matrix

[vital moth]

why does it do that

what is the proof that it is unique

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[light oyster]

Hello I just got help a second ago

[light oyster]

i get it i just want to make sure im right

so its not just 3 = -1 is incorrect

we would also have 1 = -1

is that right

so the final thing would have look like this

<3, 2, 1 > and <-1, -2, 1>

so all of them are incorrect

except the last 1 does = 1

<@&286206848099549185>

[opal vault]

Whatever value of x you take doesn't work, so there are no solutions

[light oyster]

sure

i thought

1 = 1

works

3 unequal -1 2 unequal -2 1 equals 1

this is so i can just make sure im understanding in correctly

am i right ?

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[placid gull]

hi i’m trying to solve this problem. I’m just getting introduced to this topic so i’m not confident in my answer. hoping for someone to tell me if i did anything wrong

[placid gull]

this is what i did

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[vital finch]

Bruh

yeah

it pinned mine

thanks

[vital finch]

I calculated so far that y=1/2 but I’m not sure what to do next

<@&286206848099549185>

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[vital finch]

oh sorry

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[vital finch]

No

<@&286206848099549185>

[vital finch]

Hello???

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[prisma trellis]

calc 2 disk problem

[prisma trellis]

the answer is incorrect, here is my work

i basically went through the example they gave, which was very similar but had sqrt(x) instead of my sqrt(x/6)

i didnt think this was important since it was used for the calculation of finding the bounds, which I already did using desmos anyways.

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[prisma trellis]

hmm correct answer is 144pi/5 but how

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[signal stream]

I need help with this diff equation, I’m trying to solve like a exact diff equation but is not a exact equation because My ≠ Nx, Is there any other way?

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[analog herald]

Pleas e help

[analog herald]

!status

[topaz sinew]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[analog herald]

1

[drifting swift]

@analog herald would you like a headache-free but very very slightly cheaty way to do this

[analog herald]

yes please

I'll take any way lol

are you still there?

[drifting swift]

yes sorry i was gone for 4 minutes

anyway

imagine a group of 60 people who all applied for the vaccine

10 of them got nothing, 30 got Pfizer, and 20 got Moderna

how many of the people who got Pfizer developed antibodies?

and the same question for Moderna

[analog herald]

24 and 12?

[drifting swift]

asking me or second-guessing yourself?

[analog herald]

It just seemed obvious so I didn't know if there was some trick to it

[drifting swift]

well obvious it is...

[analog herald]

second guessing lol

[drifting swift]

there is no trickery here

there is nothing to second-guess yourself about i am just having you compute some percentages

anyway

• Unvaxed: 10
• Pfizer, antibodies: 24
• Pfizer, no antibodies: 6
• Moderna, antibodies: 12
• Moderna, no antibodies: 8

total = 60

now you are asked to find the probability that a person got either vax given that they have no antibodies

[analog herald]

would it be (6+8)/(6+8+10)?

num of no antibodies with vaccine/num with no antibodies total?

damn I have no clue

@drifting swift you still here?

[drifting swift]

yes this is correct

[analog herald]

oh okay

how would you do it for one person though?

[drifting swift]

wym one person

you could work it all out the honest way with fractions and shit

but we encapsulate the concept of "one randomly selected person (from our group of 60)" in the fact that we divide favorable by total

[analog herald]

yeah

here's what I have so far:

if 1 person applies for a vaccine, then he has a 1/6 chance of nothing a 1/3 of Pfizer and 1/2 of of Moderna. Which means a chance of:

1/6 being unvaxxed
1/3*

I'm just following the same logic as for 60 people

[drifting swift]

yeah so what is the chance that the person has no antibodies and got pfizer

[analog herald]

if 1 person applies for a vaccine, then he has a 1/6 chance of nothing a 1/3 of Pfizer and 1/2 of of Moderna. Which means a chance of:

1/6 being unvaxxed
1/3 * .8 Pfizer + antibody
1-(1/3 *.8) Pfizer + no antibody
1/2 * .6 Moderna + antibody
1 - (1/2 *.6) Moderna + no antibody

P(...) = (Pfizer + antibody + Moderna + no antibody)/(Pfizer + antibody + Moderna + no antibody + being unvaxxed)

[analog herald]

@drifting swift does this look right?

[drifting swift]

ouch italics

[analog herald]

oops

[drifting swift]

also misuse of + sign

better to have & there ..

1-(1/3 * .8) Pfizer + no antibody
this should be 1/3 * (1 - 0.8)

[analog herald]

oh yeah

but the overall setup looks good other than the details?

[drifting swift]

i mean

i guess?

[topaz sinew]

@analog herald Has your question been resolved?

[analog herald]

I got 8/13 probability do you know if this right?

[drifting swift]

looks sus

no, definitely not right, it should be 7/12.

[analog herald]

oh I did:

$\frac{(\frac{1}{3})(.2) + (\frac{1}{2})(.4)}{(\frac{1}{3})(.2) + (\frac{1}{2})(.4) + \frac{1}{6}}$

[thorny flame]

sadkid

[analog herald]

do you know where I made a mistake?

it looks pretty close

[drifting swift]

ah fuck

maybe i screwed up

yeah i did

fuck

it was 20 people for pfizer and 30 for moderna. oops.

[analog herald]

oh okay

bing chilling then

I've got no more questions for now

thanks for all your help @drifting swift

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[neon iron]

For this ---

[odd pagoda]

no

min a + min b <= min(a+b)

[neon iron]

I see. Thank you 🙂

[odd pagoda]

because on the left the minimums can be at two different places

[neon iron]

Indeed!

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[neon iron]

.reopen

[topaz sinew]

✅

[odd pagoda]

you don't have to delete your question

[neon iron]

I see.

Will keep that in mind.

Thank you for your help today 🙂

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[odd pagoda]

youre welcome

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[slate current]

the answer is 3

[slate current]

but like if it was (-2,3)

would the answer be 7/2

since its not inclusive???

[fierce ember]

show your work

[drifting swift]

why would the answer be 7/2?

also rates of change are really only spoken of on closed intervals

bc really they are defined not by an interval but by two points lol

[slate current]

because dosent () mean not inclusive

so like

wait

idk

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[wide bane]

Hii

[wide bane]

Solve the following 4 equations by first introducing a tautology

[drifting swift]

... do you have any solved examples of "introducing a tautology"

[wide bane]

trying the first one now

give me a moment

i think i found something that might work

[drifting swift]

im more curious about what method hides behind that name

which i've never heard before in my life

so it is probably a language difference that i don't speak enough danish to overcome

[wide bane]

@drifting swift do you understand it?:)

[drifting swift]

yes but i think that's a little bit clunky with how it is written

and even more clunky with how it is named

i would call this "case analysis"

since we consider separately two cases, one where x < 0 and the other when x ≥ 0, and resolve the equation to a linear one in eacah

i mean this does have the advantage of clearly displaying the underlying logic so there's that

[wide bane]

oh okay

im struggling with number 3

@drifting swift the absolute value of -1 is 1

so it would be -6x+1=-4x+3 in one case and 6x+1=-4x+3 in the other right?

[topaz sinew]

@wide bane Has your question been resolved?

[drifting swift]

no

you don't have |-1| you have |2x-1|

[wide bane]

not -6x+3=-4x+3 either

oh

[drifting swift]

you have two cases:

x ≥ 1/2 & 3(2x-1) = -4x+3
x < 1/2 & 3(-2x+1) = -4x+3

[wide bane]

why those 2

in my previous ones i just used x < 0 and x ≥ 0 and that was good enough

[drifting swift]

now it's 2x-1 < 0 and 2x-1 ≥ 0 respectively.

because 2x-1 is what's inside the absolute-value bars. and not just x.

[wide bane]

Ohh

[wide bane]

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[neon iron]

Solve a quadratic equation that represents the path of an object in motion.

Emily threw a ball up in the air from her tree house. It followed the path given by the parabola y = - 2x^2 + 14 x +60, where x is the distance from the tree house (in feet), and y is the height of the ball (in feet).

At what distance from the tree house did the ball strike the ground?

[neon iron]

$y = \frac{-b\pm\sqrt{-b^{2}}{-4ac}}{2a}\
y = \frac{-14 \pm \sqrt{-14^{2}}{-4(-2)(60)}}{2(-2)}\
y = \frac{-14 \pm \sqrt{196+480}}{-4}\
y = \frac{-14 \pm 676}{-4}\
y = 172.5\
y = -165.5$

[thorny flame]

Chocolate

[neon iron]

how can I solve the question above

$y = - 2x^{2} + 14 x +60$

[thorny flame]

Chocolate

[flat kindle]

isn't this the solution?

[neon iron]

I just noticed I forget the root in 676

[craggy haven]

those should all be x = not y =

[neon iron]

I need to fix it

thank you

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[half edge]

doing some financial mathematics, had a bit of trouble with this problem then i saw the solution and it made sense. when i first attempted it, i did it as so: $i_t = \frac {A(t)}{A(t-1)} - 1$ then i defined a period as two years and so $i_1 = \frac {A(1)}{A(0)} -1 = \frac {561.80}{500} - 1 = 0.1236$ is this wrong because it asks for the annual effective interest rate? and i calculated the biennial effective interest rate im guessing?

[thorny flame]

Stephen

[half edge]

i_t -> effective interest rate, and A(t) is the amount function representing the amount of money in the fund at any time t

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@half edge Has your question been resolved?

[halcyon marsh]

why make the period as 2 years if you want the annual rate?

[half edge]

is that not allowed?

well its wrong ig

but does that mean i calculated the 2-year effective interest rate?

[halcyon marsh]

yeah ig

[half edge]

ah i see, thank you

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[candid kindle]

how lol

[sweet shard]

Did you do a

[candid kindle]

Yeah just did point slope

Just tried convertix that to standard and using substitution but that didn't work out

i got it

i just solved wrong

but can anyone tell me the easiest way to do this for the future

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[restive heath]

hi, uhm, I got this set of patterns, binary numbers,
is there by any chance a way to perform accurate predictions to make an extended set?

[ivory leaf]

what do those numbers mean

???

[restive heath]

I noticed some things repeating, that's why I highlighted them

[shrewd horizon]

,rccw

[shrewd horizon]

where did you get these numbers?

[restive heath]

some patterns, made using some calculus

[restive heath]

will it bother if I keep it private? 🥲

[ivory leaf]

all i can tell you is the first one is 5

[restive heath]

5?

[restive heath]

I will give a similar example of my case

let's say you got something, it can either be blue or not blue
if it's blue, then write "1", otherwise "0"
and return to a new line whenever the current line ends with at least 3 to 5 zeros (optional, just for more readability)

[shrewd horizon]

...hmm
ok yeah i have no idea what's going on here then

[shrewd horizon]

the issue is that without seeing the context i don't have any intuition for what kind of pattern to expect

[restive heath]

chances with some tries per each 10 in chronological order:

• 40%
• 40%
• 20%
• 20%
• 30%
• 20%
• 20%
• 30%
• 20%
• 10%

[shrewd horizon]

and also if i do happen to have an idea i can't compute more values to check if it works

[restive heath]

same lol, that's why I asked if there's a possibility to make a prediction of the next digit

oh wait, I'm dumb

I'll just code a small ai model based on these numbers, hopefully it can recognise the pattern faster than us

[shrewd horizon]

i really doubt it
this is nowhere near enough data for an AI to get anywhere afaik

hang on a second

[restive heath]

I mean, 101 digits must be almost enough

[shrewd horizon]

i think the numbers on the left are just the prime numbers

[restive heath]

kinda

I noticed that too

but I tried locating prime numbers, I found some that aren't prime unfortunately

[shrewd horizon]

...what are they? it looks fine to me

[restive heath]

the digit number 52 (starting the count from 0) isn't prime, but that index represents 1

[shrewd horizon]

wait where's 51? there are only 47 numbers

[restive heath]

yeah, I noticed it 😂

[restive heath]

continue to the right

because I didn't have enough space to continue

[shrewd horizon]

oh
i assumed that was just something separate

yeah in that case the first issue is actually 49

[restive heath]

yeah

I'll just try to identify the pattern this night, 'cause I really need it on a neurology project

imagine if I accidentally write the most accurate expression for prime numbers 😭🤣

[shrewd horizon]

...given that it's basically perfect other than that, are you sure you didn't just miscalculate 49, 51, and 57?

or possibly some measurement artefact if this is supposed to be something with relevance to the real world

[restive heath]

it's not me who calculated that, those are given data, precisely written

[shrewd horizon]

maybe the person who gave you the data was wrong...?

either that or the rule is actually "prime numbers, 49, 51, and 57", which, i'm not really sure how to continue that other than guessing it's probably mostly primes

[restive heath]

it's actually related to our neurones, to predict the next nervous flow (i apologise, idk the exact name in English )

[shrewd horizon]

...in that case i am very surprised that prime numbers would come up at all

[restive heath]

it can be the case too, but I still need to identify those who aren't prime in the rest of the set
given these small data with only 3 that are not prime numbers but written as "1", i can't really work with that

[shrewd horizon]

yeah i think this just isn't enough data to exactly predict the rest of it

[restive heath]

same lol

[shrewd horizon]

i tried the OEIS and this sequence is not in there which suggests there probably isn't some really simple explanation for why those three specific numbers

[restive heath]

I will try to go back next month to M6 medicine university to gather some data if I'm allowed to do so again 🥲
because collecting such data isn't permitted, luckily I knew some friends there who let me get them lol

[restive heath]

actually there mustn't, otherwise we could predict how a human brain will work in an isolated environment (no sense stimulations)
but I do still wanna try to find a pattern, 'cause in science there's nothing such as randomness

well, @shrewd horizon thanks for the help, I do really appreciate it, even more after noticing the prime numbers thing too (I'm more certain I'm not hallucinating 🤣)
and good night! <3 (it's 2:24am here lol)

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[frozen edge]

Can someone explain to me the last part?

[frozen edge]

I thought AB=OD

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@frozen edge Has your question been resolved?

[frozen edge]

<@&286206848099549185>

[sonic escarp]

can you explain why you thougt this (and do not argue with the sketch, sketches are often misleading)

[frozen edge]

Well nvm then

But how are the triangles similar?

[sonic escarp]

both have a right angle (ABC at B, OCD at C) and the angles at A and O are also the same as ABand OD are parallel. two same angles (and therefore three same angles) are enough for similarity.

[frozen edge]

Ah alright

Makes sense, had no idea what that notation was

Thanks

[sonic escarp]

AB would be equal to OD if B would be direct "above" O, this would mean the lenght of AB = BC which is not the case here.

[frozen edge]

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[fierce lake]

Hi!
So i have a question im stuck on for an assignment.
So i have two vectors. Vector C = [2, 5] and Vector D = [t, 3]. Where t is a given number.

Find the two values of t, so the angle between vector c and d is 45 degrees.
Anyone got any idea how to do this? I can use CAS for it.

[ionic oar]

Just dot product?

[thorny flame]

NEON

[fierce lake]

1 sec

Like this?

[sonic escarp]

there should be a t in the numerator.

[fierce lake]

Yeah think i fixed it, like this right?

[sonic escarp]

yes

[fierce lake]

Is this right? Im using degrees to calculate

But i cant remember if i need to use radians

[sonic escarp]

degrees are given.

[fierce lake]

Ye ofc, that seems obvious now aha. Thanks a lot for the help, very kind of you! 🙂

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[eternal wyvern]

<@&286206848099549185>

I need checking my Ans

Real quick

(17 C 3) - 2 * (9 C 3)?

Is this right?

Pls

[calm jackal]

Applying Combination or Permutation?

[eternal wyvern]

Yea

[calm jackal]

It didnt say it has any placement so combination hmmm

[white topaz]

(17 C 3) - 2 x (9 C 3)
= 680 - 2 x 84

[eternal wyvern]

Choose 3 points from the total 17 points and the trianglea are degenerate iff all lie in a line

I've 2* 9 C3

[eternal wyvern]

So correct?

[vale jacinth]

Looks correct

[calm jackal]

Ill let him handle this

[eternal wyvern]

Ok nice

Tyty

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[sonic ibex]

where would where would 2x^4 appear in real life its such a weird graph that i can't imagine seeing it in any sense

[glossy acorn]

Like y = 2x^4 ?

[sonic ibex]

yeah

[glossy acorn]

Well if you want to graph, first you would do x = 0 to find the y intercept which will be zero.

[sonic ibex]

no but waht's the real world use? i can graph it

[glossy acorn]

oh

[sonic ibex]

actually nvm homie i got an answer by ai dw abt it

have a good rest of ur day!

[glossy acorn]

ok you too!

[sonic ibex]

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[icy pilot]

-y^3 = x - 10

[icy pilot]

Solving for y

Is the only way to solve this to cube root before dividing by -1?

Is it at all possible to work it after dividing by -1

[distant nymph]

Sure is.

Either way is fine.

[icy pilot]

You get y^3 = -x + 10

Where do you go from there

Oh wait thats cube not square

Lowkey making me hate math

@vernal vale post that again

[vernal vale]

im just showing it doesnt matter the order

[icy pilot]

Why does dividing -1 put it out in front

[vernal vale]

you can get to one from the other

[thorny flame]

jan Niku

consider that 
\begin{align*}
-y &= \sqrt[3]{x-10} \\
y & = -\sqrt[3]{x-10} \\
y &= (-1)^{\sfrac13} \sqrt[3]{x-10} \\
y &= \sqrt[3]{(-1)(x-10)}
\end{align*}

[vernal vale]

yea more clear ig

[vernal vale]

consider it multiplying both sides by -1

does that answer your question?

[icy pilot]

And whats up with the 1/3 exponent

How does it go inside the cube root

[vernal vale]

maybe this makes it even more clear

1s

[icy pilot]

[thorny flame]

jan Niku

\begin{align*}
-y &= \sqrt[3]{x-10} \\
y & = (-1)\sqrt[3]{x-10} \\
y &= \sqrt[3]{(-1)} \sqrt[3]{x-10} \\
y &= \sqrt[3]{(-1)(x-10)}
\end{align*}

[vernal vale]

hows that

from line 3 to 4 is just standard exponent rule

[thorny flame]

jan Niku

[icy pilot]

How are you able to cube -1 without effecting y

Or is it effected

[vernal vale]

well (-1) is equal to the cube root of (-1)

so it has no impact

[icy pilot]

I see

[vernal vale]

this is where i felt the other way was more clear with the cube exponent

but it doesnt matter this is all ultimately trivia wrt your original problem

thought it might be nice to show that you can do it either way, though

odd roots have nicer properties in that way

[icy pilot]

Always nice to learn more about math

[vernal vale]

yea

[icy pilot]

I was gonna ask how cubes are exponents

But I just thought its cuz 1/3 right

[vernal vale]

how cubes are exponents? how do you mean?

[icy pilot]

Since this rule only applies to exponents how it applies to cube roots

[vernal vale]

im not sure i understand, this rule is just good in general

it works by more fundamental associate and commutative properties of multiplication

it doesnt have anything to do specifically with cube roots

[icy pilot]

Why does x^2 + 8 have the domain of [0, inf) btw?

[vernal vale]

were using that $(-1)\cdot (-1) \cdot (-1) = (-1)$

[icy pilot]

Shouldnt the range be that

[thorny flame]

jan Niku

[vernal vale]

so $(-1)^3 = -1$ giving $(-1) = \sqrt[3]{-1}$

[thorny flame]

jan Niku

[icy pilot]

Gotcha

[vernal vale]

neither of these sound right

its not the domain or the range

[icy pilot]

What is it?

f(x) = btw

[vernal vale]

[0, inf) is maybe the domain of a square root?

[icy pilot]

Mb

[vernal vale]

so you might be only sharing part of some expression or something youre looking at

[icy pilot]

?

[vernal vale]

huh? idk what that means

[icy pilot]

Its a function

[vernal vale]

maybe im missing some context or something

what are you asking?

[icy pilot]

The function f(x) = x^2 + 8 has the domain of [0, inf) right

[vernal vale]

no

[vernal vale]

the domain is the collection of numbers that x can be, right?

what restrictions do we need to put on x here?

[icy pilot]

What is it?

[vernal vale]

I'm asking you lol

what are the problem values of x

[icy pilot]

Nothing

[vernal vale]

right

so why are you excluding half the reals

[icy pilot]

So what do I do answer rofl

(Its not graded)

[vernal vale]

its different when its an inverse function, i think

probably easier to just solve it with a graph

,w graph sqrt(x+3)-

2

damnit

[thorny flame]

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[vernal vale]

,w graph sqrt(x+3)-2

[thorny flame]

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[icy pilot]

[-3, inf)

[vernal vale]

the domain of your inverse function is (at best) the range of the original

this is an at-best situation

(the function is one-to-one)

[icy pilot]

What does at best mean

[vernal vale]

you can consider something like f(x) = x^2

[icy pilot]

Ok

[vernal vale]

the inverse here has to be split, right

otherwise its not a function

[icy pilot]

whats that meannn

[vernal vale]

okay so you have f(x)=y=x^2

,w graph y=x^2

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[vernal vale]

the naive inverse would be f(y) = x = y^2

,w graph y^2=x

[thorny flame]

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[vernal vale]

you cant write this as a function of x

its required that a function of a variable map an input to a single output

but here, for each input, you have 2 outputs

[icy pilot]

So.. you mean the domain of the inverse is only the range of the original function.. if that inverse is a function?

[vernal vale]

yea i guess

i guess here you could just say theres no inverse

idk again were on a stupid tangent

its not really related to your original problem

[icy pilot]

Lol

[vernal vale]

which is just

[icy pilot]

But every inverse will be one-to-one?

[vernal vale]

the domain of the inverse is the range of the original

[vernal vale]

i think in the strict sense yea

,w inverse function

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[vernal vale]

that "for any x" part i think is the issue

so you'd say by the definition x^2 has no inverse

(its not one-to-one)

its not really relevant in your problem

[icy pilot]

God help everybody who studies math 🙏

[vernal vale]

idk i think were doin alright

me with what i barely remember and you with what you are still learning

[icy pilot]

Its great once you finally get it.. but there is too much ahead

.w graph sqrt(2-x) + 8

[vernal vale]

,w graph sqrt(2-x) + 8

its a comma

[thorny flame]

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[icy pilot]

Thanks

Appreciate you taking the time to aid me 🙏 Good luck

[vernal vale]

no problem hope it was helpful

[icy pilot]

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[neon iron]

Hi Everyone

[neon iron]

can someone help me start off on this problem

[craggy haven]

drawing a graph (even a low-quality sketch) is always a good start

[neon iron]

what ab desmos is that fine?

this is what i got on desmos before and I tried eyeing the slope but it didnt work lol

[craggy haven]

yeah eyeballing isn't going to help you here

okay so you know where the region is right

[neon iron]

yeeepp

[craggy haven]

that's really the only part of the graph that we care about

and it mentions a line passing through the origin

[neon iron]

oooooo

😭

thats it?

[craggy haven]

so like this is what my sketch would look like

maybe label where the parabola intersects the x axis

so then just figure out - using calculus probably - the x value of P such that those two areas are equal

[neon iron]

it intersects (0,0) and (1.167, 0)