help-0

[near temple]

If the house is $500,000 and they say you need a 20% down payment (you have to pay 20% of the cost of the house to start), what is that down payment?

You can ignore your savings for now, worry about them in a second

[granite iron]

%20x500,000

[near temple]

Which is?

[granite iron]

100,000

then subtract 41,400

[near temple]

Right, so if you have a total savings of 41,400, would you have enough for that down payment?

[near temple]

No need to subtract, it's just asking whether you have enough or not :)

[granite iron]

no its gonna be short 59,000

so no

[near temple]

Exactly :)

[granite iron]

thank you that was my last problem to complete and its currently 4:30 am

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[fair forge]

can someone help me?

[topaz cypress]

ok

?

?

[lone heart]

@fair forge Has your question been resolved?

[fair forge]

i dont know what to do with this

can someone help?

[topaz cypress]

yes

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[topaz cypress]

So, for the first question you move your shape 7 units to the right and 2 up

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[fathom ravine]

I have a question how those formulas are called in English, so I could find some videos about them in YouTube

[fathom ravine]

See, there exceptional trigonometric formulas for trigonometric eqations

[fair forge]

what dot should I move?

[lone heart]

@fathom ravine Has your question been resolved?

[rustic coral]

General solutions of trig equations ig? I don't think there's rlly a name for these

btw, "ig" stands for "I guess" (btw stands for "by the way")

[fathom ravine]

Oh, I got it, thanks!

[rustic coral]

anything else?

[fathom ravine]

How do you understand that sinx=0 has only this answer "pk"? Like people use circle and a triangle inside to explain it, but I just don't understand

Like here

What is opp and hyp? Are they parts of a triangle which has 90° angle?

[rustic coral]

What is opp and hyp?

opposite and hypotenuse, respectively, in a right triangle (with respect to some angle ofc)

[rustic coral]

Here's an easier way: The value of sin is given by the y coordinate of the corresponding pt on the unit circle

so if our sine is zero, what must be the y coordinate be?

[fathom ravine]

If y is zero, then we have a point in x

[fathom ravine]

0 or p, right?

[rustic coral]

y = 0 b/c sin is 0

and the only time when y = 0 is when you have a point on the x axis

which occurs whenever you have an angle that's an integer multiple of pi

[fathom ravine]

Yup

Or, really, we cant have a p/2 or 3p/2 because they lie on y, but because we have sinx=0 so our y has to be zero, so we can only have p period

I started understanding it!

[rustic coral]

I gotta go now tho 👋

[fathom ravine]

Oh, okay, have a good day!

Could you also explain me cosx=-1 later please?

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[fickle star]

How do I find BE?

[trail sage]

any idea what your supposed to use? you can try solving for equation of line and circle but im not sure if that is the best method. Setting D as origin, you have the line DE with equation y=-8/6x and the equation of the circle is (x-3)^2+(y-k)^2=3^2. Do abit of substitution and solve for k where discriminat=0(This means circle and line intersect at one point). Then 8-k will give you EB

[next spade]

let the circle be tangent to that DE line at P

and let BE = x

PE = EB = x by the circle tangents theorem thingy

the hint is to find the full length DE in terms of x and use pythag

[lone heart]

@fickle star Has your question been resolved?

[fickle star]

thanks and I just tried this

but it returns a really long decimal number and it took me a while to get an answer I don't think is right

right now im trying to think of some other way to use length of DE

[fickle star]

Thanks for this also I got 1* from it, which I think is right? Im gonna search up what the circle tangents theorem is now

[hybrid heron]

how about dropping a perpendicular from E to AD

[fickle star]

im not sure how that'll work but i'll think about it, thx

[hybrid heron]

same

@fickle star @fickle star@fickle star

is answer =1

let BE = X

DA = DE-X

DE = 10

DA = 8+X

( dropping a perpendicular from E to AD)

8+x = 10-x

x=1

[fickle star]

I got the same thing, this is a question from my friend so I needa ask her for the answersheet

If I remember I'll dm you if it's correct or not according to the book 🙂

[hybrid heron]

okay

[small tinsel]

could you please help me try to solve this, I spent so much time on trying to figure it out:

[lone heart]

@fickle star Has your question been resolved?

[hybrid heron]

holy hell

[hybrid heron]

what id try first is try to get x1 x2 x3 in terms of lambda

and then plug them in two equations

[small tinsel]

im getting stuck in teh very very last part

its exercise 9.3 on page 3 btw

[hybrid heron]

oh my god

i have never solved anything like this

5 variables

[small tinsel]

its so not cool

[hybrid heron]

😭

[small tinsel]

this is where I am getting stuck:

everything before is correct

<@&286206848099549185>

[small tinsel]

<@&286206848099549185>

[sterile turtle]

Hi, how can I help you?

[small tinsel]

Hi im trying to solve this problem

[small tinsel]

this one

[sterile turtle]

Ok

What methods did you try?

[small tinsel]

this is my work on its EX 9.4

[small tinsel]

my work is above in the pdf

[sterile turtle]

Ok

Try using the 2:X5 method

[small tinsel]

whats that

[lone heart]

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[small tinsel]

?

[small tinsel]

it seems like an acronym, could you use the full name?

[lone heart]

@small tinsel Has your question been resolved?

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[alpine sable]

there exist ε > 0 such that | e^x - 0 | < ε and there is N such that x < N
e^x < ε
log e^x < log ε
x < log ε
N = log_e (ε)
which satisfies the conditions hence
lim x -> -infinity e^x = 0

is this a corrrect proof!

@turbid patio bro are u writing to help 😅 if yes pls react smth a emoji

been typing for a while

lol

[sour verge]

You've got all the pieces right, but it's just worded oddly.
Usually, you do some work to find a suitable N, and then you write the proof, with your work from before explaining why such N is right.

So here, you tried some ε and found that N = ln(ε) works.
Now, you can say that :
for any given ε > 0, let N = ln(ε). Then, for any x < N, we have x < ln(ε) <=> e^x < ε, as required.

[alpine sable]

yeh kinda bad with wording u put it nice way

thanks

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[upper dagger]

can someone please explain this to me (SAT question)

[lone heart]

@upper dagger Has your question been resolved?

[balmy grail]

This is rearranging variables. You have p=1 (from the last 5 words) so m.v=1.q solve for v, and you get your answer

[upper dagger]

i got the right answer doing this but how is p = 1 if it says the price level increases by 1

would it not be p + 1

[balmy grail]

Ah no, it’s asking for change in monetary velocity. We’re solving v= p * (Q/M) and taking the derivative with respect to p I guess,

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[fallow wadi]

Using the multiplicativity of the Legendre symbol and the law of quadratic reciprocity, calculate 155/991

[fallow wadi]

I dont even understand the task

Am I meant to estimate 155/991 or what

[woven plaza]

Yea

[fallow wadi]

Okay and how?

I literally dont understand the task

[lone heart]

@fallow wadi Has your question been resolved?

[mortal trellis]

do you know what "multiplicativity of the legendre symbol" and "law of quadratic reciprocity" mean?

[fallow wadi]

i do not

@mortal trellis can u tell me pls

[mortal trellis]

I suggest looking them up in your course notes

which really is the first thing you should do if you encounter something in an exercise which you dont know

[fallow wadi]

alright

i need to solve it in 1h

is this task simple or hard?

if its hard im gonna go sleep and just get the points somewhere else to pass the course

@mortal trellis

[mortal trellis]

rather simple once you get the idea

[fallow wadi]

okay then i will read it

meanwhile u can give me some tips n tricks

:) @mortal trellis

[mortal trellis]

how about you actually try doing something first?

[fallow wadi]

@mortal trellisis this the solution to the task?

[mortal trellis]

dont wanna check the individual steps

but looks good

[fallow wadi]

wait its

wrong

@mortal trellis

this isnt the correct law right

the (q/p) is meant to be on left, correct?

[mortal trellis]

same thing

[fallow wadi]

no

if u divide my (q/p) that means multiply by (p/q)

[mortal trellis]

are you confusing this notation with fractions?

[fallow wadi]

i guess

[mortal trellis]

(q/p) can only be 1 or -1

so dividing and multiplying by it are the same thing

[fallow wadi]

yea

thanks

i got it

solved

many thanks @mortal trellis

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@fallow wadi Has your question been resolved?

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[fervent patrol]

VOLUME Ana Maria has a rectangular prism with dimensions 20 inches by 35 inches by 40 inches. She would like to replace it with a cube with the same volume. What should the length of a side of the cube be? Express your answer as a radical expression in simplest form.

__ in.

[fervent patrol]

https://tenor.com/view/cat-cat-meme-funnt-cat-black-cat-sleepy-cat-gif-16409614852005252877

[unborn plover]

u good bro

but what's the prism's volume

[fervent patrol]

this question is stumpingme

[craggy forge]

Find volume

lwh

[fervent patrol]

well if the side lengths are 20 x 35 x 40

then its

one sec

28000

[unborn plover]

mhm

[fervent patrol]

do i just cbrt it

[unborn plover]

yeah

[fervent patrol]

i have one more attempt on this question

if its wrong

ill cry

good?

gulp

[unborn plover]

this is right but they want simplest form

[fervent patrol]

kiss me

WTF

I LITERALLY PUT the BOTTOM ONE EARLIER

[unborn plover]

oh i guess it doesn't matter lole

[fervent patrol]

ok well tysm

how do i close

[unborn plover]

!done

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If you are done with this channel, please mark your problem as solved by typing .close

[fervent patrol]

ty

.close

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[summer swallow]

Context: I submitted a quiz(Rational Equations & Inequalities for my Adv Funcs class) and this question gave me a bit of trouble. I ended up guessing it correct.

Question: What's the correct approach, or method to go about it?

Second pic is my approach: I tried to simplify and solve for k while setting x = 0

[devout harness]

how did you get (3) and how did you substitute it into (2)

[summer swallow]

I derived equation (3) from equation (1), which is the left-side of the original equation. Then proceeded to substitute that for x in equation (2)

not sure if that's valid or not tho

[devout harness]

you can't just decide to multiply the numerator and denominator of a random fraction and say it's equal to x

[summer swallow]

oh yeah.. actually that makes a lot of sense now that i look at it

(at the fact that I can't do that)

but is my approach with substituing here the right approach

because I'm still a little confused if that's how I should have went about it

[lone heart]

@summer swallow Has your question been resolved?

[gritty wind]

WHAT IS THE DERIVATION OF PLANCK'S CONSTANT ??

[lone heart]

@summer swallow Has your question been resolved?

[lone heart]

@summer swallow Has your question been resolved?

[lone heart]

@summer swallow Has your question been resolved?

[twin nimbus]

@summer swallow if you multiply both sides by (x-3)(x+2) you'll get (x-1)(x+2) = (k-9x)(x-3)

You can multiply this out to get an equation that looks like ax^2 + b(k) x + c(k) = 0 where a is just a number, but b and c both depend on k.

Now, when a quadratic has only one solution, this is a special case called a double root, and the discriminant is equal to 0. So you have b(k)^2 - 4ac(k) = 0

Then you just solve this equation for k to find out your critical point.

Note that, you then have to double check your answer with the two values of k you get to ensure they result in a valid solution. Because you multiplied through by (x-3)(x+2) if your solution for k implies x has a solution at 3 or -2 it's invalid.

[summer swallow]

Appreciate you helping out

After multiplying both sides and getting the equation down to ax^2 +b(k)x+c(k)=0, like you mentioned(1st picture). I tried two different approaches.

The first one was the completing the square method to solve the quadratic(2nd picture with black/red text), while trying to consider k in the equation, but I got a stuck near the end of it because in order to find x I'd need to know k. If I could go further, I feel like it'd be somewhat to do with substitution.

The second method(3rd picture with purple/blue text), is my attempt at using b(k)^2-4ac(k) = 0. I did get a value for k at the end, but it was not equal to 14 or 54 like my quiz suggests, so I'm assuming I messed up or went about it wrong somewhere

[summer swallow]

<@&286206848099549185>

Reposting context for any new helpers: I submitted a quiz(Rational Equations & Inequalities for my Adv Funcs class) and this question gave me a bit of trouble. I ended up guessing it correct.

Question: What's the correct approach, or method to go about it?

[wraith stratus]

First picture penultimate line

You combined like terms wrong

-(26+k)x

And -2+3k

You also forgot to write the -2

[summer swallow]

ahh yes, but I think I corrected it in the later steps but let me look at it again

at least the -2 I remember forgetting

[wraith stratus]

You did not as far as I can tell

[summer swallow]

if you look at the second picture you can see I did -6k

[maiden tangle]

you probably want to find a way to cancel x

[wraith stratus]

-2+3k is not -6k

and -(26+k)x is not -26kx

[wraith stratus]

.

[summer swallow]

ahh yeah sorry, I just went back and saw that you’re doing -(26 + k)x

and oo that makes a lot more sense too

and same with -2 + 3k

[wraith stratus]

yes

Then you just need discriminant to be 0

[summer swallow]

okay so if I had my like terms correct, and went with the approach in the third picture

should I get the result I’m looking for?

would that be how to go about it

[wraith stratus]

doesn't matter if you do quadratic formula or complete the square

quadratic formula is literally completing the square

but yes if you do the steps correctly in either approach you'll get the right answer

[summer swallow]

okay thanks a lot

I can finally put this to ease

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[still herald]

What is the factor theorem?

[lone heart]

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[signal wasp]

Can anyone help I got a really hard question

[gaunt elm]

How do i find the circumference in centimeters, of 81pi cm.

[gray isle]

.close

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[gray isle]

@gaunt elmchannel had someone else name on it, to claim a channel, just post the question directly in the channel
don't reply the bot message

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[alpine sable]

how to do research in mathematics?

[alpine sable]

do anyone have maybe some papers that can giveme an idea?

right now I having trouble in setting a research problem

I mean, I know research cant be so different from doing mathematics (the process of thinking) , but I have no idea where to begin

If someone has had a Introduction to research class and has some notes or recorded classes I would appreciate it a lot

[mortal trellis]

I mean, you come up with a problem and try to solve it

read through papers and see what questions they leave open

[small fog]

Basic process is

1. Find open problem
2. Solve it

An introduction to research class is basically a masters degree

[alpine sable]

ok , that seems reasonable at first glance , but the but difficulties appear soon.
how I know what problem to choose?
How I know what problem may be adequate?

[small fog]

What field are you good ar

What problem seems solvable for you

[alpine sable]

mathematical logic / set theory and in general discrete matheamtics

[alpine sable]

I am looking , maybe , for some solved problem in the field , so i can try it by myself

[mortal trellis]

do you have an advisor?

[alpine sable]

Not yet

[mortal trellis]

find one

ask them

[alpine sable]

"An introduction to research class is basically a masters degree"
how can i do a master degree free then (sorry for the stupid question , but no way i could get this by now)

[alpine sable]

what?

[alpine sable]

have you done graduate mathematics / research?

@mortal trellis

[mortal trellis]

did you really just ask where you can get a free masters degree?

I have

[alpine sable]

I am sure that the problem is not doing the research , the problem is setting the sketch for doing research

[alpine sable]

why not?

well , not exactly a "master degree" , but the experience

I am not asking about certification

I am asking about the action of doing research

literally doing it

[mortal trellis]

well I mean you can just start

[alpine sable]

that's where my algorith fails

[mortal trellis]

you'll just have to use a few years to actually understand relevant stuff

[alpine sable]

I dont know

[alpine sable]

can you explain how understanding implies more years?

I know mastery implies more years

But , I mean , the fact of understanding with the purpose of research , isnt that research?

[alpine sable]

bro, you have done it , please , give me an idea how to start
I am not asking you to write me a book , just What would you say to yourself from the past if you had wanted to start doing research at an earlier age?

[mortal trellis]

well first you have to understand what others did

before you can produce new stuff

[alpine sable]

that's the point, research is an action , such as idk , composing music, or walking , right?
producing new knowledge is the social part of research , cause has impact, but if I discover something is new to me, then ¿is that also research?

[mortal trellis]

I would call that learning

[alpine sable]

but how can I do that?

I mean , I am not sure if that is classical learning

but my idea , is not to solve what well trained mathematicians cannot , idk by magic
my purpose is to get training on research , It doesn't matter if it is "artificial" , as long I dont know the answer

so , since I have never done research , I have no idea how to do it.
then i was asking for notes , etc.

(the most I could find was a chapter in book that in summary said , try things by yourself)

[mortal trellis]

well thats a good summary

research is doing random stuff until you find something which helps

[alpine sable]

so , did you did graduate work?
and what you did was to sort of improvise with what you al ready knew , until you got something?

and how did you find a problem?

[mortal trellis]

I had an advisor

who told me: "hey, look at this stuff. this might be doable"

[alpine sable]

basically my problem right now is not having a "problem"

[mortal trellis]

and then I read papers for ages to even understand what the problem is

[alpine sable]

so , what should I do?

[alpine sable]

did you understand it finally?

[mortal trellis]

more or less

[mortal trellis]

well you dont seem to want to do the actual usual things. like going to university and getting an advisor

[alpine sable]

but what do you mean by usual?
like doing it , or waiting to the moment until the corresponding moment

?

[alpine sable]

I mean , by usual you refer to going to a graduate program , or by asking for help with a professor

?

[mortal trellis]

ask any researcher and they will have done those things

both

[alpine sable]

so you are suggesting me , that i should go to the mathematics faculty at my university and ask for advice there?

[mortal trellis]

yes

[alpine sable]

ok
there's the possibility they will said me "no , you shouldn't do research at your age, you should focus on other things"
or maybe they are not going to pay attention
have you experienced that?

I mean , that has happened to me before, in different situations, I am not sure how to avoid that from happening

not exactly tha example before

[mortal trellis]

how old are you

if you bring up your age

[alpine sable]

18

not exactly with research , just 2 times

other were with linear algebra , when i was in 7th grade , etc

[mortal trellis]

what even is your background in math

[alpine sable]

engineering math (computations)
Olympiad mathematics (not gold level)
and discrete mathematics

so

[mortal trellis]

how about you actually just go to university and get a degree?

if you wanna do math anyway

[alpine sable]

well , I cant tell you my whole life in chat , but to give context

next year i will study mathematics

right now , I am in a special situation , where I am studying other thing and have free time

so , any ways

what's the problem with doing research

?

I mean , why not

[mortal trellis]

well you dont seem to want to do the things that people suggest

of either going to university or like the book you said you read, just trying things

[alpine sable]

but , you think asking a professor would be useful?

[mortal trellis]

pick up a random textbook or paper and try understanding it for example

[alpine sable]

I am already studying mathematical logic

[mortal trellis]

well depends on the prof obviously

[alpine sable]

this idea , aobut doing research ,relies, in according to what I have seen , is that research is fun

[mortal trellis]

depends on who you ask, but sure

[alpine sable]

and I would like to do it
but simply trying things (which i have done, but not as research)
is creative , but I feel sometimes doning that puts me far from the topic I am studying,
so for example , the other day i was thinking in some theorem of abstract algebra, and then I begin thinking and trying things by myself

but

I would like to find a research problem in mathematical logic , so I could keep myself in the topic

[mortal trellis]

yes you will go on completely random tangents sometimes

thats normal

[alpine sable]

and that's what i have no idea how find one

ok , thanks any ways

I think i would go to the mathematics departament and ask for advice there, since I know a professor there

but , idk , i feel that they will say me , "just try things by yourself"
and i will get stuck

[mortal trellis]

welcome to research.

you will get stuck

all the time

[alpine sable]

yeah , but , I am stuck in finding a problem, so I have not even begin and I am already stuck , I've been trying for at least a month to find a problem that suits

I will keep trying then , i guess

thanks

🫡

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[empty grotto]

Options are, 1: free-throw percentage or, field-goal percentage.

2; intercept, correlation coeficcient, or coeffiecent of determination or slope

3: 0, or (1.or -1)

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<@&286206848099549185>

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[broken jetty]

Looking for an explanation on how this becomes this

[north hearth]

The inverse sin

[fleet crown]

are you familiar with inverse functions?

[shy dove]

Or you could reference the unit circle

[fleet crown]

ye, just look at the unit circle and see for which angle the sine is sqrt(3)/2

technically this solution (pi/3) is incomplete though...

[broken jetty]

what exactly is a unit circle?

[hushed locust]

the unit circle is how we extend trigonometric functions (which we defined for angles less than 90 degrees aka pi/2 with right triangles), to all angles

[broken jetty]

Yeah, this hasnt been taught in my lessons (much like quite a lot of things)

There are gaps in the teaching material and I have no teachers to ask questions about so I'm just trying my best to understand how to turn that first equation into the second

[hushed locust]

so for acute angles, every output of the sin function must have a unique input

there are special triangles you are expected to remember which give known results for the value of trig functions at certain angles (30, 45, 60 degrees)

[broken jetty]

alright

[hushed locust]

the first one comes out of cutting a square in half, the second one comes out of cutting an equilateral triangle in half

[broken jetty]

okay, makes sense

wait

Am I just converting the angle to radians?

aha I am!

[hushed locust]

either way the output is the same, but if they expect the answer in radians then you do have to convert to radians

[broken jetty]

that is where that fraction came from

I got it now I think, thank you so much!!!!!\

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[warm shale]

how to solve this?

[wraith stratus]

!status

[lone heart]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[warm shale]

1

😭

[wraith stratus]

ok so we want the integral of something to find the area right

[warm shale]

yes

[wraith stratus]

well do you have any ideas what/how we shouldintegrate

[warm shale]

since definite integral is equal to area under the curve

can i do integral of cosx from 0 to pi/4?

for the first part

or does sinx also contribute to it

[wraith stratus]

draw a picture of cos(x) from 0 to pi/4

and then sketch the region of area you would get if you integrated

[warm shale]

purple would be cosx and red would be its integral?

@wraith stratus

[wraith stratus]

it should be everything underneath

so it actually looks like this

[warm shale]

oh i see

can i find definite integral of cosx then minus definite integral of sinx? For the first part

[wraith stratus]

yep

then what would happen from pi/4 to pi/2

[warm shale]

integral of sinx minus integral of cosx?

[wraith stratus]

yep

alternatively

you can notice that the two integrals are symmetric

the area from 0 to pi/4 is the same as the area from pi/4 to pi/2

so a nice way to save some time would be to just compute 2 * the first integral

[warm shale]

ohh i understand

thank u so much!

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[solemn sierra]

give channel pls

[vale crag]

you have it now

[solemn sierra]

ok

im starting to fail

any math tips

algebra

(ping me when responding)

[fleet crown]

git gud

what kind of tips are you looking for?

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[vagrant ravine]

Hi

[vagrant ravine]

Is summation notation differentiable?

[rose sigil]

example?

like... functions can be differentiable

[vapid drift]

you cannot differentiate notations im sorry

[rose sigil]

and you can write a sum of finitely many functions in summation notation

[vagrant ravine]

Idk
Something like that (i just made it up)

[rose sigil]

is that what you mean

upper index is x?

[vagrant ravine]

This is called taylor series, right?

[vapid drift]

x would need to be an integer

[rose sigil]

this function is either nonsense or not continuous

[vapid drift]

so no

[vagrant ravine]

Oh

Can you give an example where a summation can be differentiable?

[vapid drift]

im kinda getting what you mean and i think answer is yes

[long axle]

if youd made the E a little less spiky and a little more curvy it'd work very nice

[rose sigil]

$\sum_{n=1}^{3} e^{nx}$

[ocean seal]

slayla

[rose sigil]

this is just e^x + e^(2x) + e^(3x)

which is differentiable

[vagrant ravine]

The onew i make up has an interesting "curve"

[rose sigil]

this is not continuous

[vagrant ravine]

Wait so the summation has to be defined

[vapid drift]

it obv needs to be defined

[rose sigil]

what would it mean for a summation to be "undefined"

[vagrant ravine]

By defined i mean having a number on the sigma

[vapid drift]

above it?

its always defined even without the number above

[vagrant ravine]

Hmm

I see

Ty

[rose sigil]

i don't wanna say 'need' but let's go with yes anyway

[rose sigil]

to this question

[vapid drift]

since sometimes summation can be along a set

[vagrant ravine]

I guess it can be infinity?

[vapid drift]

it can

[rose sigil]

yes but that's a different story

[vagrant ravine]

Maybe it can be broken down to geometric series with | r | < 1

[vapid drift]

you mean a series?

[vagrant ravine]

Isn't any symmation called a series

[vapid drift]

if its infinite its called a series

but im not completely sure

[vagrant ravine]

Really?

[vapid drift]

thats how i remembered it

[long axle]

who wants to see evolution

[rose sigil]

series usually means infinite series

[vagrant ravine]

Oh

[vapid drift]

https://en.wikipedia.org/wiki/Series_(mathematics)

[long axle]

anyone wanna see evolution? for math

[vagrant ravine]

Sure?

[long axle]

see you have to make it a little less spiky

and a little more round

[vapid drift]

bruh

[long axle]

and voila, its evolution

[vagrant ravine]

Ok

I guess

What you mean by Z and R

[vapid drift]

you 'continued' it

[long axle]

Z is integers, R is real numbers

[vapid drift]

not sure if its helpful here really lol

[long axle]

i just wanted to showcase evolution

[vapid drift]

👍

[rose sigil]

what are these even doing here

[vapid drift]

its just a visual joke

[long axle]

thats just showing the evolution, how it becomes less spiky and more curvy

and evolves into integral symbol

[vagrant ravine]

I usually write sigma like that lol

[rose sigil]

worst joke i ever heard in my entire life

[long axle]

🦦

[vagrant ravine]

It is not that bad

[wraith stratus]

the middle one looks like the squiggly thing in my eye

[rose sigil]

$\xi$

[ocean seal]

slayla

[rose sigil]

that one?

[wraith stratus]

no

this one

https://www.youtube.com/shorts/IOhjyLyANRc

[rose sigil]

oh i never watch that show

by "in my eye" i thought you meant

like

from your perspective

it looks a squiggly thing

[wraith stratus]

that's because it is a squiggly thing

[rose sigil]

you're so right

[lone heart]

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[vagrant ravine]

.close

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[strong viper]

what steps are taken to simplify 45-(210-4X45) to 5X45-210

[vapid drift]

first of all 45-(210-4x45) = 45-210+4x45

2nd, 1x45+4x45=5x45

so 45-210+4x45 = 5x45-210

[strong viper]

how did you get from 45-210+4x45 to 5x45-210

[vapid drift]

do you understand this?

[strong viper]

ah ok i figured it out. was confused where the 1x45 came from but I see it can be rewritten as -210+45+4*45 which is the same as -210+1x45+4x45. ty

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[ocean seal]

Jacob L

[livid tundra]

yeah

1.5 is a real number

[hot plover]

Hi

Wait

[gray isle]

you course taught you incorrectly

did you mean Q instead of R for the set of rationals

[ocean seal]

Jacob L

[clever folio]

It's always just going to be a countably infinite number or a finite number. You aren't counting the number of numbers in R or [0,1]. You're counting the number of digits of a real number.

[tacit needle]

R is real numbers not rational

[clever folio]

How many digits does the number 1.11111.... have?

[tacit needle]

but to answer your question, the root of any number that is not itself the square of a rational number, is irrational

[clever folio]

There are infinitely many digits, but it's a countably infinite number of digits.

[clever folio]

I'm sure there is a function for it. I just don't know off the top of my head a nice arithmetic way to express it.

This is irrelevant.

If a number r has finitely many digits it has a unique representation in base 10 when you exclude repeating digit representations.

You can count powers in that representation to get the number you want.

That gives you the existence of the function I think.

I just don't know a nice formula for it.

Take something like 0.123

That is 1(1/10)+2(1/100)+3(1/1000) right?

Notice how there are 3 digits and 1000 is 10^3?

We can always do tricks like this to count digits when we are talking about numbers with only finitely many digits when we ignore repeating decimals.

So like we have to disallow stuff like 0.99999... for 1

Now look at this 12.345

That is 1(10^1)+2(10^0)+3(10^-1)+4(10^-2)+5(10^-3)

So we can't just count read the last power of 10 off or anythinf.

But we can just add the magnitudes of the biggest and smallest powers I think.

Sorry mixed it up

The biggest power in front of the decimal point is 1, the smallest power is -3

Oh magnitude as in absolute value

But I was also off by 1

You see how if we add 3 and 1 we'd get 4 but our original number had 5 digits?

We just need to add 1.

[clever folio]

We're just counting the number of powers of 10 here is all

Which is the same as counting digits.

The point is that we can write out any number with finitely many digits this way, which tells us those "biggest" and "smallest" powers exist (and are unique).

So, we have a mapping that takes numbers with finitely many digits and spits out the number of digits based on the process we just did.

That is a function.

This tells us the function exists.

But calculating it is a different story.

I want to say you can just scale by some power of 10 and count digits but that doesn't work.

Like say you have .123, then 1000(0.123)=123 and you just apply the log formula.

But this doesn't work well

Picking the power of 10 is annoying and you basically need to already know the digits

And 0.001 won't work for this.

What is W?

I think I get the idea you are going for, but I think this doesn't work.

The log(x) formula needs a +1

The f(10x) thing you are trying to do will fail because of the 0.0001 issue I mentioned earlier.

If you're willing to accept floors and ceilings though, then you can use that to define the integer and fractional parts of a number.

We already know how to calculate the integer part from the log formula here

So all we really need to worry about is counting the number of digits for fractional parts.

The f(x), f(10x) thing is kind of hiding something recursive in the background.

If you didn't notice that.

Like, if you took a number 0.123 and multiplied it by powers of ten until it were an integer you'd end up multiplying it by 10 3 times.

The NUMBER of times you do this multiplication is the thing you want.

Probably something like this works better

Define g(x) = 0 if x is an integer

Define g(x)=1+g(10x) if x is not an integer.

Now take x to be a number with a terminating decimal representation like we mentioned before.

Define our digit counting function f as follows

f(x)=[floor(log(int(x)))+1]+g(frac(x))

int denotes integer part, frac denotes fractional part.

These are definable from the floor function.

We already know the integer digit counting function works.

The g function just adds one and scales its input by ten.

So, something like this happens

g(0.123)=1+g(1.23)=2+g(12.3)=3+g(123)=3+0=3

You can verify yourself this works for the weird edge case of stuff like g(0.0001) as well.

Okay, for time complexity notice floors, mods and basic arithmetic like this is fast. It should be linear time I think.

This is absolutely not worth a paper lmao.

This is like an intro programming course exercise in the form of basic arithmetic.

Like, I've absolutely written programs to do this in my cs classes.

Well I guess it depends on what you mean by a paper?

Paper for what?

Mathematics research paper for what?

Is this like a hw thing?

So, actual mathematics research is super specialized. I wouldn't expect anything you do to be publishable. But for fun you can write papers for yourself on whatever you like.

It doesn't matter if it's simple arithmetic or anything else.

What I would say is like, focus on learning the basics rather than trying to publish this kind of stuff though.

Writing is good for learning.

But putting out a bunch of stuff into the public eye you make for practice could be awkward as you get more skilled.

[clever folio]

For the actual problem you should work out to yourself why this works as well as filling in the edge cases. I ignored negatives, irrationals and the number 0 for this formula.

I may also have a silly arithmetic mistake in there I didn't notice lmao.

Or maybe not.

[lone heart]

@alpine sable Has your question been resolved?

[clever folio]

What do you do for irrationals vs rationals?

Also what about 0?

Sounds fine to me.

It's mostly to avoid gaining a reputation as a crank

You know those people who spend a bunch of time spouting nonsense about math that doesn't make any sense?

Well there's a difference between a little bit of error making because you are still learning vs just spouting nonsense because you decided you were right and don't care to learn ya know?

My number theory prof used to tell us to study by lecturing to our teddy bears lol.

You can always correct things later if you go that route I suppose.

Do you know anything about integration?

Defining the riemann integral from first principles and proving the fundamental theorem of calculus would be kinda nifty for somebody in calculus.

It's accessible in that every calc textbook does it, but very few calc students would carefully work through that on their own.

There are also vaguely related topics like line integrals and riemann-stieltjes integrals that are sort of approachable conceptually that could be fun to write about.

For either I wouldn't expect or look for anything super rigorous to say. Mostly something expository to do with what they are, what they do intuitively, what applications they have etc.

Also ode stuff might be nifty.

There are also nifty counterexamples worth thinking about in analysis.

Continuous everywhere differentiable nowhere functions.

A bunch of other weird ones.

Oh yes I forgot.

You know some modular arithmetic?

Roughly yeah.

If you have say {0,1,2,3,4}

You can define a new + operation on this set by using the normal addition and taking the remainder after.

Remainder mod 5

You can define multiplication similarly.

{0,1,2,3,4} means "the set containing 0,1,2,3,4"

An operation on a set is a function that takes in two numbers from a set and spits out a number from that set.

Just like how the usual arithmetic ops (ignoring division) are functions on the reals.

Well + for the real numbers takes in two real numbers and spits out a real number.

So if we define + and * on 0,1,2,3,4 like I mentioned earlier now we have a system of arithmetic where 4+1=0

Because the remainder of 4+1 (which is 5) after division by 5 is 0.

You remember how if ab=0 with normal arithmetic then either a or b is 0?

In our 0 thru 4 arithmetic this holds (you can brute force check every case).

We can define similar systems of arithmetic for 0,1,...,p-1 for any prime p

[clever folio]

And they will all have this property

What I mean is that with our new 0 thru 4 arithmetic, we also have the property that ab=0 implies a is zero or b is zero.

I'm just abbreviating 0,1,2,3,4

Yeah these are finite sets of naturals.

[clever folio]

This

Do the usual ops you already know and take the remainder at the end.

Gotcha

Try it on 0,1,2,3,4,5 and see if the ab=0 thing works for that.

(This will be ops mod 6 now fwiw)

[novel idol]

hi

a+b+c=32 what is value of a

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[manic sundial]

does anyone know how he did number 4

i have no clue as to how I can solve the IVP

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[steady aurora]

Can someone help me with the second exercise?

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[winged sinew]

Hey math heads I got a question

[winged sinew]

I’m trying to bake a cake that takes 3 different ingredients but if I mix a certain combination of these ingredients it will make a chocolate cake all the other combinations will be a basic cake the catch is that I can only use 6 of each ingredient but I have to use at least 1 of each using trial and error how many different combinations is possible using this my desired outcome is to make the chocolate cake

[jagged cobalt]

so if somehow you add too much cocoa powder, it will become vanilla, blimey

[winged sinew]

Exactly

[jagged cobalt]

so you need to keep the ratios correct or what?

[winged sinew]

I need to find the right ratio

But the end goal is to really figure out how many trial and errors of making the cake it would take

How many possible different combination

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[warm fractal]

I already asked this but now I am asking if my calculations are right

[warm fractal]

Option A

24000* 1.04=24960
24960* 1.04=25958,4
25958,4* 1.04=26996,736
26996,736* 1.04=28076,61
28076,61* 1.04=29199,67

Sum of all the equaitons: ca. 135189

Option B

25000+26000+27000+28000+29000=135000
So option A is more

[jagged cobalt]

,w 24000+sum from n=1 to 5 (24000*(1.04)^5

[ocean seal]

Results provided by WolframAlpha

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Requested by aldrnari_

[warm fractal]

so can you explain that bit in detail 😅

[jagged cobalt]

,w 24000+sum from n=1 to 5 (24000+1000n)

[ocean seal]

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[jagged cobalt]

the first one is just the starting salary is 24000
then + 24000*1.04

then + 24000*(1.04)^2

...

• 24000*(1.04)^5

[warm fractal]

this is what I did except you did one more

[jagged cobalt]

the way you wrote it excludes the salary of the first year

24000

you only included the raises

[warm fractal]

So the question really asks how much you earned in 6 years?

[jagged cobalt]

yeah

[warm fractal]

in that sense you don't get a raise in your first year

[jagged cobalt]

first year + 5 years of raising salary

[warm fractal]

hmmm

Damn why tf do I get so many different opinions on a question like this

I am not sure what to believe and this will be on my exam

[jagged cobalt]

thats just how i read it in any case, it would only make sense to me that the raises apply to subsequent years after the first

otherwise it would just be your starting salary, not really a raise

it wouldnt change the result of which is better any way since theyd both have that

[warm fractal]

In my opinion we are calculating directly from the raise and not including the starting salary

[warm fractal]

yeah

I am closing this topic again thank you!

.close

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[warm fractal]

.reopen

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✅

[warm fractal]

.close

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[autumn dock]

$\lim_{x\to \infty} {x^{\frac{3}{2}}\left(\sqrt{x+1}+\sqrt{x-1}-2x\right)}$

[ocean seal]

Arian

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[autumn dock]

$\lim_{x\to \infty} {x^{\frac{3}{2}}\left(\sqrt{x+1}+\sqrt{x-1}-2x\right)}$

[ocean seal]

Arian

[autumn dock]

How to solve this?

[eager sonnet]

Open a new channel

[autumn dock]

Ok

[eager sonnet]

Pls read the bots instruction

Thanks

Close this

.

Not!

.close

[autumn dock]

OK, will read instructions

[eager sonnet]

Wait nvm

Just go another channel

[autumn dock]

OK, thanks

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[random hull]

How can I prove the difference of surfaces between the equilateral triangle and the circular sector is minimal if the radius of the sector is equal to the height of the triangle?

[sharp sail]

i can prove that with my common sense, idk with math though

well, you can do something, since the area of triagle is fixed, you can prove that area of circular sector is maximum when r = h, hence keeping difference minimal

[random hull]

That what I asked

[jagged cobalt]

write an expression for the area, then use derivatives to minimise it

[sharp sail]

area of sector = (angle / 2pi) * r^2
for eq. triangle angle is always 60, hence area is max when r is max

[sharp sail]

wouldn't that be overkill

[random hull]

nah i'd like multiple methods

[random hull]

how to?

[random hull]

that's not a proof

you just gave info on the ex

[sharp sail]

well it is, but since youre asking precisely about the derivative proof, id help you with that tii

too*

[random hull]

what's the function of a sector?

[sharp sail]

ar(triangle) = A (constant)
ar(circle) = (pi/6) * r^2
difference = A - pi/6 r^2

d(difference)/dr = -2r
thus difference is a decreasing function and decreases with r
hence for diff to be min, r is max, which is height of triangle

[random hull]

uh

[sharp sail]

is that good enough

[random hull]

I see

I was gonna integrate lol

[sharp sail]

bruh why

[random hull]

i want many methods

[sharp sail]

remember, to find the points of maxima/ minima we always differentiate

[sharp sail]

bro cmon

[random hull]

what is wrong with that?

[sharp sail]

nothing, but howd you do that with integral?

[random hull]

idk i'll figure it out

you just gave me the idea

[sharp sail]

lmao no i didnt

anyways goodluck lol

[random hull]

when i hear differentiation i hear analysis

[sharp sail]

its good you like figuring out stuff

[random hull]

so

what's the function of a sector?

[sharp sail]

you mean area of a sector
its (angle of sector)/360(degress) * radius^2

[random hull]

function

half a circle is f(x)=sqrt(1-x²)

[sharp sail]

ayo whats the use of that here

idk or i cant remember it anyways

[random hull]

i'll integrate the difference of functions

one for the sector

one for the triangle

integrate from 0 to x and just half of the shape

because it's easier

[subtle sentinel]

Do you guys know what Geometry is?

[random hull]

ye

[random hull]

uh ok

[subtle sentinel]

Why is statement 5 "Theorem 1"?

[random hull]

if you want help find another channel

[subtle sentinel]

wdym

[random hull]

and delete ur msgs

[subtle sentinel]

lol

[random hull]

#help-0

it's my channel!!

[lone heart]

@random hull Has your question been resolved?

[random hull]

@sharp sail i found the difference of surfaces

using integration

it's an expression related to x

[lone heart]

@random hull Has your question been resolved?

[willow seal]

7×60

[lone heart]

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[alpine sable]

Can someone explain this to me (14)

A linear regression shouldn’t be a residual plot

Because it’s not a residual regression

[subtle light]

well its the residual for the linear regression

you can analyze and make conclusions on the regression line using the residual

[alpine sable]

Ok

So then the answer would be a

[subtle light]

yeah id say so

[alpine sable]

.close

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[alpine sable]

Thank

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[lusty wraith]

I was wondering if somebody can help me point out my mistake when i was adding multiple compound fractions. My answer and the textbook's answer differ slightly, so I was wondering if it's possible to have different answers based on the way i factored out my polynomial? If my answer is wrong, I was hoping somebody can point out any mistakes i made. Thank you.

[charred flint]

yup they're the same https://www.wolframalpha.com/input?i=(-17c%2B16)%2F15%2F(c-1)-(c%2B2)%2F(5c-5)%2B(c-2)%2F(3c-3)-c%2F(1-c)

[lusty wraith]

Thank you for the confirmation @charred flint. I had a quick question as well. Is there rule which states constraints in which way i am allowed to factor out a negative? Or is it up to my discretion?

for example: (-17c^2+17c). Do i have to factor out the negative? Or can i just factor out just 17?

[charred flint]

there's no rule for that

sometimes it definitely makes it look nicer but sometimes it's 50/50

[lusty wraith]

Ok makes sense

Awesome thanks for the help!

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@lusty wraith Has your question been resolved?

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[wary salmon]

is harmonic series just 1/AP series

[coral flower]

yea

[wary salmon]

so then 1,1/5,1/9,1/13.... is hp right?

[coral flower]

ye

[wary salmon]

ok thanks

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[gray isle]

!status

[lone heart]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[vapid tide]

2

[gray isle]

show work

[rancid marten]

where

[vapid tide]

well idk if its right

i put a+b into two functions

it got the first and last answers in the multiple choice

[gray isle]

why two?

[vapid tide]

idk which one to do

[gray isle]

consider the given restriction
a>=1 and b>=3

[vapid tide]

cause a and b follow different rules for the function

[vapid tide]

mhm

[gray isle]

what are the range of values the whole
a + b
can attain

[rancid marten]

did you do g(a+b)=g(a)+g(b)

[vapid tide]

lemme try

[rancid marten]

no

it's wrong

[vapid tide]

oh ok

[gray isle]

it was a question of whether you did
not telling you to do that

what are the range of values the whole
a + b
can attain

[rancid marten]

i thought you did g(a+b)=g(a)+g(b)

[vapid tide]

nah

[rancid marten]

hint:add the inequalities

[rancid marten]

good

[vapid tide]

idk

[gray isle]

hint:add the inequalities

[vapid tide]

how so

im a visual learner

[gray isle]

$a \ge 1 \
b \ge 3$ \
add each side

[rancid marten]

bruh

[vapid tide]

like in the bracket?

[ocean seal]

ℝαμΩℕωⅤ

[vapid tide]

what

u just reworded it

show me

[gray isle]

do you know what add means

[vapid tide]

yes ofc bro

[gray isle]

do you know what side means

add the stuff on the left side
add the stuff on the right side

don't overthink

[vapid tide]

a+b> _ 4?

[gray isle]

yes

[vapid tide]

idk how to get the sign

[vapid tide]

OHH

[gray isle]

= to represent that in text

[vapid tide]

ah ok

[gray isle]

now that you know that the input
a + b > = 4
do you now know which piece you should be using?

[vapid tide]

x^2 ???

[gray isle]

yes

[vapid tide]

okok

so its c

[gray isle]

yes

[vapid tide]

ok i get it

thx

i was overthinking it lol

ok byee

.close

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[outer cliff]

for part di are we assuming q1 = 3?

and how did they get part dii?

heres the answer:

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@outer cliff Has your question been resolved?

[vestal flume]

q1 is 3 yes, you can see where the box begins.

[outer cliff]

ohhh didnt notice the graph behind it

[vestal flume]

Then if half spend less than a, then a reasonable estimate is the mean. Since it splits the data

[outer cliff]

yeah 7

I was confused why it was 7

didnt notice the graph lol

ok tysm for the help

.close

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[rapid gate]

no clue where to begin

[exotic canopy]

recognize that the sum in the parentheses is a geometric progression

over (-z)

[rapid gate]

what u mean?

[exotic canopy]

in this case a=1, and r=(-z)

[rapid gate]

o

[empty mason]

you could notice that in the second bracket, you can factorise the z^2-z as z(z-1), z^4-z^3=z^3(z-1) and so on until z^14-z^13 factorises to z^13(z-1) from which you have (z-1)(z^1+z^3+z^5+...+z^13) which the second paranthesis in here can be further factored

[rapid gate]

are you sure this is ideal during an exam?

[empty mason]

yes, it is actually a fast way of factorising the second bracket rather than using synthetic division

[rapid gate]

oo

why not just expand it?