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[cunning beacon]

.close

[devout snow]

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[devout snow]

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[lofty monolith]

When finding hessian matrix are f12 and f11 always the same

[stone stump]

no

[lofty monolith]

Ok thanks

.close

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[stone stump]

if you mean f21 and f12, then yes

most of the time anyway

as long as they are continuous for example

this result is called schwarz's theorem (among other names) @lofty monolith

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[restive river]

0 = root of g*sin(theta)*d+v^2

[restive river]

Can can isolate for theta here?

I dont think i am allowed to square both sides sinces 0^2 = 0

[dry oxide]

that not any issue

[stuck field]

But that's also unnecessary, you'd ideally first solve for sin(theta) and eventually theta.

[restive river]

0 = root of gsin(theta)d+v^2
will be the same as
gsin(theta)d+v^2

surely not

[dry oxide]

i mean you can subtract both side by v^2 then take power of 1/2 both side

[stuck field]

Huh?

[restive river]

how can i subtract that

[dry oxide]

is that whole thing under a root?

[restive river]

yes

[dry oxide]

oh ok then

just square both side idk what's the problem here

[frozen aurora]

$\sqrt{x}=0 \iff x=0$

[woven radish]

artemetra

[restive river]

im aware

but it seems weird to me that this would hold true

[frozen aurora]

why not

[dry oxide]

why do u think so

[frozen aurora]

$x=0 \iff x^n = 0$

[woven radish]

artemetra

[frozen aurora]

for any n≠0

[restive river]

i am aware

but still

[frozen aurora]

??

[restive river]

actually nvm im stupid

[frozen aurora]

so what's the issue

[restive river]

-v^2/-2gd

= sin (theta)

i put the wrong equaiton this is the equation after squarring on both sides

right?

[devout snow]

@restive river Has your question been resolved?

[plucky wind]

Whats the equal to sign with arrows on either side mean?

[devout snow]

@restive river Has your question been resolved?

[frozen aurora]

if and only if

[frozen aurora]

looks correct

[devout snow]

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[winter torrent]

this is called ambiguous language

a prime number is odd

i claim this is true because 3 is odd

what do you mean by the statement "a prime number is even"?

and why have you assigned it a truth value of F?

that's true

because like I said, 5 is odd so... a prime number is odf

"it"

what is "it"

your statement: a prime number is odd is true, because there is a prime number (3) that is odd

"the" prime number... so you've picked one?

all you asked so far was whether any prime numbers were odf

which yeah there are many in fact

look into "for all" or "for every" qualifiers

and "for any" or "for some"

no, I mean like saying:

for every prime number p, p is odd or p is even

well, it might be more clear that the breakdown that you wrote out earlier doesn't make sense

this breakdown

[sullen island]

"for all prime p, (p is odd) or (p is even)" is not equivalent to "(for all prime p, p is odd) or (for all prime p, p is even)", that's what hayley is saying

let's even drop the prime assumption to have a clearer example

"for all integer p, (p is odd) or (p is even)" is not equivalent to "(for all integer p, p is odd) or (for all integer p, p is even)"

it's true

all integers are either odd or even

that also works for primes

yes

indeed

why should PvQ be equivalent to "for all prime p, (p is odd) or (p is even)"

you made the for all completely disappear

and the crux of the problem is exactly the for all

[sullen island]

^

[topaz axle]

you're right, you can intepret it as false

like you 've shown

(all primes are odd) or (all primes are even) is false

you can intepret it that way, it's just english words

yeah

you're using words, you expect it to be possibly ambiguous

what's the problem

[sullen island]

what's your point frog ? we're trying to formalize their statement

[topaz axle]

you can't expect anyone to care about that

the convention is that you interpret it the other way

i mean that if you say that you interpreted it wrong because it's english words and you can't exclude this interpretation, it's unlikely to convince anyone

i don't know what you mean

i didn't like read the entire conversation

what's P

it's true

it's true

it's that statement

[sullen island]

yes

[winter torrent]

(all prime numbers are even) is false
(all prime numbers are odd) is false
(all prime numbers are (even or odd)) is true

the third statement is not the logical disjunction ("or") of the first two

"(all prime numbers are even) or (all prime numbers are odd)"

which is false

as expected

"a prime number" is fairly ambiguous -- do you mean some prime number or every prime number?

"a prime number" is fairly ambiguous -- do you mean some prime number or every prime number?

"a number is equal to 17" is that statement true or false?

"a number is equal to 17" is true, by your reckoning?

no

there exists a number that is 17
but not every number is 17

so does "a number is equal to 17" have a truth value or not? and if so, what is it?

[topaz axle]

you said "P : A prime number is odd" at the beginning
you can't say this in the first place, it sounds weird

a numebr is equal to 17 is the same thing

[winter torrent]

i'm asking you because you're the one who is insisting on using this "a" statement

[topaz axle]

it doesn;t have a conventional meaning

[winter torrent]

when i read the original question, it seems to me that it should be read as "every prime number is either odd or even"

but there is a universe in which it means "there exists a prime number that is either odd or even"

[topaz axle]

"A prime number is either odd or even" is a normal thing to say, it has a conventional meaning, when there's "either"

[winter torrent]

no it's not

"everything in the world is either cheese or not cheese"
would you agree with this statement?

[topaz axle]

that's ambiguous tbh

[winter torrent]

ok fair cheese is a bit of a fuzzy boundary

what do you mean by "a prime number is odd" though

it sounds like you mean "every prime number is odd"

programmer, right?

do you know any programming languages?

their logical disjunction would be "every prime number is odd, or every prime number is even"

which is false because it's the disjunction of two false things

"every prime number is either odd or even" means that if you handed me a prime number, I would be able to say, "yes that prime number is either odd or even"

"every prime number is either odd or even" is true
"either every prime number is odd, or every prime number is even" is false
these statements are not the same

oh
well
it's not

if the teachers said that "every prime number is either odd or even" is equivalent to "every prime number is odd, or every prime number is even" then that is incorrect [at least by most reasonable interpretations of those words]

ya

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[last prawn]

is this tending to infinity?

[gaunt matrix]

looks like it

[radiant dune]

divide by 6^x in numerator and denominator, and it seems like it is tending to infinity

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[neon folio]

On the graph of x^2 is x=0 an inflexion point?

[neon folio]

Or just an extreme point

[scarlet sequoia]

just an extreme

global

since f''(x) = 2

[neon folio]

So inflexion points are found when the second derivative at that point is 0?

And extreme points when the first derivative is 0

[scarlet sequoia]

f''(x) = 0 and it changes sign at a point

(concave up and down)

[neon folio]

Si this isnt enough?

[scarlet sequoia]

yep that's not enough

e.g. f(x) = x^4

f'(x) = 4x^3
f''(x) = 12x^2

f''(x) = 0 if x = 0 but that's not the inflection point

[neon folio]

So what do in need more

[scarlet sequoia]

f'' has to change its sign at the point

[neon folio]

Ok

[scarlet sequoia]

and hence here

12x^2 is nonnegative

it means f(x) is concave up on the entire domain

and no inflection points exist

[devout snow]

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[restive river]

because its exponential not polynomial

when the x is in the exponent the formula is $\frac{d}{dx}a^x=\ln{a}\cdot{a^x}$

[woven radish]

HadarS

[prime egret]

The power rule only applies when you have x^some power

Not (some number)^x

[devout snow]

@restive river Has your question been resolved?

[prime egret]

No power rule means derivative of x^n is nx^(n-1)

Right

Correct

Why should it?

2 is just a constant scalar

It’s multiplying the expression you can just take it out of the derivative

Are you asking why the 5 disappears but not the 2 in this question

Then it’s because we’re adding the 5

If it was 5•x^2 you’d get 10x

Np

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[cobalt torrent]

help how do I find the coordinates? my teachers didnt teach us how to

[cobalt torrent]

or answer the drawing room coordinates

[devout snow]

@cobalt torrent Has your question been resolved?

[cobalt torrent]

<@&286206848099549185>

[hollow pivot]

Use the coordinate graph?

[cobalt torrent]

im confused on the drawing room part

help

🙂

[cobalt torrent]

helpppp

[devout snow]

@cobalt torrent Has your question been resolved?

[cobalt torrent]

hello

[sleek panther]

the center of cordinate is 0,0

if you go down the right part goes down too

so you must count the squares until each point, and then decide if its positive or negative. You can decide wheter its positive or negative before or after which ever one you prefer

[cobalt torrent]

so is the drawing room 2 and 8?

[sleek panther]

wait the question isn't asking to get position of the points

its asking why this would be useful

[cobalt torrent]

oh

[sleek panther]

image is that of a floor of your house ig

useful because you dont need to guess how much carpet you would need to cover the floor

you can use math

[cobalt torrent]

our teacher told us to find the coordinates on the pic

like the dots

[sleek panther]

oh

then starting from origin, you count the squares

you must move with l's

you cannot make a straight line because you want to count x and y

[cobalt torrent]

oh ok thanks

[sleek panther]

here u move right 2 times, than move up 3

the notation for this is (2,3)

[cobalt torrent]

ok

I now get it

[sleek panther]

type .close to close this help channel, and its great u understanding now ! very god

[cobalt torrent]

.close

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[floral cradle]

What is the force body diagram for a bike going in a straight like that's accelerating?

[tender lotus]

#old-network

[devout snow]

@floral cradle Has your question been resolved?

[topaz axle]

the road is pushing the bike?

kinda interesting question

[devout snow]

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[velvet goblet]

<@&286206848099549185> I dont know how to calculate the area with all these nuimbers! help

[severe nymph]

Try to split the shape up

What shapes would be easier to calculate the area with?

[velvet goblet]

2 rectangle

[novel swan]

Ain’t no way 💀

[devout snow]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[velvet goblet]

what

help me zaageta

[smoky nimbus]

Break that shape into easier shapes that you can find the area of

Like the two rectangles

[velvet goblet]

yeah

so I would do 5x3 and 7x1 and add them together?

[honest thorn]

how old are yoou

[velvet goblet]

13

so its 22 less goo

ty

[smoky nimbus]

It's not

[velvet goblet]

sorry, the school system where I come from doesnt teach anything

its not?

length times width

[smoky nimbus]

How did you spilt the shape?

[velvet goblet]

2 recs

[smoky nimbus]

Where did you split it at

[velvet goblet]

top and bottem

the place where it sticks out and the big rectangle

wait I think I know 5-1 because the 5 is not the width or length anymore

[sleek panther]

did u subtract 7 by 3?

[velvet goblet]

oh

sorry one sec

[smoky nimbus]

Yes

Exactly that

[smoky nimbus]

I think they split it this way

Not vertically

[sleek panther]

oh

[velvet goblet]

19?

[sleek panther]

yes

[velvet goblet]

tysm

im sorry canadian schooling is terrible

they dont teach but assign it thinking we know it

[sleek panther]

its not bad, i think u did good

its great that u r using free time to learn more

[velvet goblet]

ty

[sleek panther]

also make sure to type .close

[velvet goblet]

.close PS ty again

[devout snow]

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[hearty heron]

not sure what i'm doing wrong here

[hearty heron]

i shouldn't need to simplify for my answer btw

This is my work

[supple knot]

just plug in 12 and 3 here and don't do the rest

[hearty heron]

oh do i not need to sub in the u value

[supple knot]

if you do this, then there's no need to change the integral bounds

[hearty heron]

oh i see

ty

.close

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[jolly swan]

Can someone show me that the definite integral is f(b) - f(a)

[jolly swan]

using a graphical method

[supple knot]

!original

[devout snow]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[jolly swan]

I want to visualize why it is f(b) -f(a)

[jolly swan]

I mean, why isn't it f(b) + f(a)?

[supple knot]

it's in the proof

if you haven't taken differential or integral calculus, it isn't gonna make much sense

[jolly swan]

give an example to find M. A + M = N, so A = N - M. I can't see this in the context of integrals with Barrow's Rule. Can you explain this in a visual way?"

[supple knot]

what are you talking about

What are A, M, and N?

[supple knot]

read the proofs here
https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus

[devout snow]

@jolly swan Has your question been resolved?

[jolly swan]

thx

[devout snow]

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[rough hatch]

How do i simplify

[dense jay]

,rccw

[dense jay]

what have you tried thus far

[dense jay]

anything more?

hmmm

how did you get that actually

[rough hatch]

Is it right

[dense jay]

cscx isnt the same as cos x no

[rough hatch]

Oh
I didnt notice it was csc

[dense jay]

[rough hatch]

So is it csc instead

[dense jay]

yeah

[rough hatch]

Is that simplist form

[dense jay]

nope

[rough hatch]

Is it this

[dense jay]

upside down is impressive

,rccw

[dense jay]

seems okay so far

there is more you can do ig

were you asked to make it into something specific?

[rough hatch]

Just sats simplify

[dense jay]

just debating whether splitting the fraction would really be considered 'simpler'

we can do it if you want, even if for nothing but a fun exercise

[devout snow]

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[flat marlin]

So for the question here

It wants 6 subintervals over the interval [3,7]?

I just want to make sure I'm interpreting this right

or the other option is that it wants 5 subintervals

Ah I got it it is 6

.close

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[solar stream]

The value of a car depreciates at a rate of 12.5% every year. Determine how long it will take the car to be worth its original value.

[solar stream]

the formula my teacher gave me was a=p(1+-r/n)^nt

ik you would plug in 0.125 for r

but idk what to do after that

a=amount after a certain amount of time

p=principal amount

r=rate

n=number of compounds and t= time in years

[topaz axle]

the question doesn't make sense, it should say 60% its orginal value or something

[solar stream]

sorry thats my fault

it should say be worth half its original value

[topaz axle]

okay

[devout snow]

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[devout snow]

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[slate raptor]

I am trying to solve this ODE using laplace and im lost on how to proceed

[random temple]

split Y into a sum of two fractions

[slate raptor]

partial fraction decomposition?

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[vivid estuary]

I got the derivative and second derivative right by how can I find where the function is increasing and decreasing

[solar goblet]

solve P'(x) = 0 and create a variation table

[vivid estuary]

Thanks and the last question I couldnt' complete was this one, for the function 2sin(x) + x, how can I find the transition points

I looked at the graph, tried the inflection and critical points

used chegg, gpt, and a bunch of other things but none of them were right

ignore the -1/2 was just a random try

here is the graph

the min is lower than the -2 out of the interval

[solar goblet]

There are three kinds of transition points, they are point of local maxima, point of local minima and inflection point.

in short you are basically finding extrema of the function within certain range

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[devout snow]

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[jolly light]

Hi, I'm stuck with the scenarios where $x_1<x_2$ in the proof above, I'm not sure where exactly to go from there

[woven radish]

GratedRacer08

[thin fern]

I'd let $a = x_1+x_2$ and $b=x_3+x_4+x_5$, so $a+b=50$. Then you can show that $3a \leq 2b$ and go from there.

[woven radish]

Ari

[jolly light]

It has to be a proof by exhaustion, for this assignment

[thin fern]

oh

[devout snow]

@jolly light Has your question been resolved?

[jolly light]

<@&286206848099549185>

[jolly light]

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[spring bison]

how do you solve the derivative of absolute values? like

[unique kelp]

solve it both for x > 0 and for x < 0

[random temple]

remember that d/dx 1/x is ln|x| so you don't have to worry about absolute values

[devout snow]

@spring bison Has your question been resolved?

[spring bison]

wait so whats the derivative of ln(|x|)

and why wont i have the worry about the absolute value

ik d/dx ln(x) = 1/x, would it be the same regardless of absolute value symbols?

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[vast violet]

so

\this is on the top of numerator

i am graphing asymptotes stuff like that

And i need x intercept

so i set the numerator which is 4x^2-36=0

and i got 4(x-3)(x+3)

so is it only -3,0 and 3,0

or 4,0 3,0 and -3,0

[dark sable]

depends on the denominator

[vast violet]

o

Ok i send pic

[dark sable]

no that can't be right

[vast violet]

oh

[dark sable]

if the denominator is also equal to 0 when the numerator is 0, then it's not an asymptote, it has no value

[dark sable]

yeah this is correct

[vast violet]

Ohk

Perfect

thnx

uh

Is it best i factor out this problem

[devout snow]

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[mint cove]

is the answer given here wrong? in the expansion of (7-4i)(2-i) i get -4i^2 which i thought was +4, but it's written as -4

[mint cove]

fuck nevermind, i just realised i missed the negative hahah

though i was wondering if it was appropriate to treat -i^x as (-1)^x * i^x generally

-i^x questions were a bit confusing to me

[rigid shadow]

just leave it as -i^x

[mint cove]

alright yea, that makes sense, i think i was just overcomplicating things in my head. sorry ive been studying all day hahah

thank you though

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[bitter patrol]

Why is the hole only x=0 and not x=0 and 1

Don’t x-1 and x cancel out

Please @ me when someone gets here

[toxic cargo]

Howd u get this

[devout snow]

@bitter patrol Has your question been resolved?

[bitter patrol]

@toxic cargo

I Dk

That’s useless work

[toxic cargo]

Me too bro idk hole in a graph thing

Sryy

<@&286206848099549185>

Help

[woven radish]

Couldn't find an attached image in the last 10 messages.

Nov 14, 2023, 12:51 PM

[random gust]

@toxic cargo because at x=1 function tends to infinity, at x=0 function tends to 0 which is exist but not equal to 0 so there is hole for the value x=0 learn some basics of limit , or draw the graph of (x-1)/(x-1)^2 you got your answer further more the question is about holes not discontinuity if it was then both be the answer

are you clear?

[devout snow]

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[young wing]

How to solve 59049=3^n-1

[young wing]

Solving for n

Can u solve it without logs?

[drifting sierra]

Repeatedly divide by 3?

[young wing]

ok so using logs is the easier way

[drifting sierra]

Well yeah if you have a calculator

[young wing]

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[abstract prism]

<@&286206848099549185>

[mint stirrup]

Just take limit as $x\rightarrow\infty$

[woven radish]

Marin Kitagawa

[abstract prism]

root(4x-2/x)/1+1/x

which goes to root(4x)/1

but how do I take the square root of 4x? Is it just 2?

[mint stirrup]

You're so close. But The terms inside the square root is wrong. Clue: $x = \sqrt{x^2}$. So, will it still be $4x$ inside the root?

[woven radish]

Marin Kitagawa

[abstract prism]

hm. When finding the limit wouldn't it be sqrt(4x^2/x-2/x) for the numerator

[mint stirrup]

You have to divide by $x^2$ inside the root even though you're dividing numerator and denominator by $x$. Because, as said, $x$ becomes $x^2$ inside the root

[woven radish]

Marin Kitagawa

[abstract prism]

i see

so the final answer would be 2 because it simplifies to 2x/x

or is that wrong?

[mint stirrup]

Yes. You're right. It'd simpilify to $2$. So, the horizontal asymptote will be $y=2$

[woven radish]

Marin Kitagawa

[abstract prism]

alright, thanks for your help. 🙂

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[last prawn]

Is it divergence or convergence

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[snow sentinel]

find a number where:
number < 10.000.000 and number > 1.000.000
Number = (sum of digits of number)^2 = rootOfNumber^2
Do not end in 0,
root is an integer

[snow sentinel]

Can someone help me find such number I have been struggling 😭

[frozen aurora]

roof of number? wdym?

sqrt()?

[snow sentinel]

yeah the root

[frozen aurora]

huh

but..

[snow sentinel]

for instance:

[frozen aurora]

$\sqrt{x}^2 = x$

[woven radish]

artemetra

[snow sentinel]

1296 = (1 + 29 +6)^2 = 36^2

[frozen aurora]

so what's the point of writing Number = rootOfNumber^2

[snow sentinel]

^

[frozen aurora]

oh

[snow sentinel]

find a number than verifies this

[frozen aurora]

i see

[snow sentinel]

cuz 1 + 29 + 6 = 36

[frozen aurora]

wait why 29

[snow sentinel]

1296 , 1 29 6

[frozen aurora]

1+2+9+6

[snow sentinel]

yeah it could also be 1+29+6

[frozen aurora]

oh so it could be any one of them?

[snow sentinel]

yep

any combination of the digits in order

[frozen aurora]

interesting

well there are 8 possible combinations of these

one of them is trivial

[snow sentinel]

yep

but the numbers in 1m - 10m have much bigger combinations

[frozen aurora]

$2^{\log_{10}(n)}$

[woven radish]

artemetra

[frozen aurora]

combinations

[snow sentinel]

yes

if it's not very easy to find I don't really mind it, I am doing an assignment and I need to find such numbers, However I have a problem in my program and I need an example number in that range to calculate it

I just came and asked just in case there is any trick other just bruteforcing

[frozen aurora]

well the first filter is that number must be a perfect square

that's already much less numbers to consider

but tbh idk a rigorous way to find this

[snow sentinel]

Alright, thanks for help anyways

[frozen aurora]

the different combinations of digits is what trips me up

[snow sentinel]

Yeah it's very confusing

Can I show you my output of my program? I tested for a number to see if it checks all of the combinations, it seems though it doesn't?

[frozen aurora]

yes

you can show the code too

[snow sentinel]

well let me change the output to make it more clear

Code is pretty chaotic

Debug: N=9991921, root=3161, sum=0, d=991921, b=9, i=6, j=6
Debug: N=9991921, root=3161, sum=0, d=91921, b=99, i=6, j=5
Debug: N=9991921, root=3161, sum=0, d=1921, b=999, i=6, j=4
Debug: N=9991921, root=3161, sum=0, d=921, b=9991, i=6, j=3
Debug: N=9991921, root=3161, sum=0, d=21, b=99919, i=6, j=2
Debug: N=9991921, root=3161, sum=0, d=1, b=999192, i=6, j=1
Debug: N=9991921, root=3161, sum=9, d=91921, b=9, i=5, j=5
Debug: N=9991921, root=3161, sum=9, d=1921, b=99, i=5, j=4
Debug: N=9991921, root=3161, sum=9, d=921, b=991, i=5, j=3
Debug: N=9991921, root=3161, sum=9, d=21, b=9919, i=5, j=2
Debug: N=9991921, root=3161, sum=9, d=1, b=99192, i=5, j=1
Debug: N=9991921, root=3161, sum=18, d=1921, b=9, i=4, j=4
Debug: N=9991921, root=3161, sum=18, d=921, b=91, i=4, j=3
Debug: N=9991921, root=3161, sum=18, d=21, b=919, i=4, j=2
Debug: N=9991921, root=3161, sum=18, d=1, b=9192, i=4, j=1
Debug: N=9991921, root=3161, sum=27, d=921, b=1, i=3, j=3
Debug: N=9991921, root=3161, sum=27, d=21, b=19, i=3, j=2
Debug: N=9991921, root=3161, sum=27, d=1, b=192, i=3, j=1
Debug: N=9991921, root=3161, sum=28, d=21, b=9, i=2, j=2
Debug: N=9991921, root=3161, sum=28, d=1, b=92, i=2, j=1
Debug: N=9991921, root=3161, sum=37, d=1, b=2, i=1, j=1```

This is for 9991921

Let me rearrange the print so it's like digit1+digit2+...

Combination trying: sum=0 + (991921 + 9)
Combination trying: sum=0 + (91921 + 99)
Combination trying: sum=0 + (1921 + 999)
Combination trying: sum=0 + (921 + 9991)
Combination trying: sum=0 + (21 + 99919)
Combination trying: sum=0 + (1 + 999192)
Combination trying: sum=9 + (91921 + 9)
Combination trying: sum=9 + (1921 + 99)
Combination trying: sum=9 + (921 + 991)
Combination trying: sum=9 + (21 + 9919)
Combination trying: sum=9 + (1 + 99192)
Combination trying: sum=18 + (1921 + 9)
Combination trying: sum=18 + (921 + 91)
Combination trying: sum=18 + (21 + 919)
Combination trying: sum=18 + (1 + 9192)
Combination trying: sum=27 + (921 + 1)
Combination trying: sum=27 + (21 + 19)
Combination trying: sum=27 + (1 + 192)
Combination trying: sum=28 + (21 + 9)
Combination trying: sum=28 + (1 + 92)
Combination trying: sum=37 + (1 + 2)```

Here

does it try all combinations?

[frozen aurora]

i.. have no clue

how are you generating them

[snow sentinel]

yeah I mean

whats the math trick to find how many combinations there are

for the number 9991921

[frozen aurora]

.

basically 2^{number of digits - 1}

do you see why that's the case?

[snow sentinel]

32 combinations?

yeah I see

[frozen aurora]

should be 32

let me try writing my own thing

[snow sentinel]

well I don't have 32 combinations here....

I don't know which ones im missing

Do you want my code?

[frozen aurora]

what language

[snow sentinel]

C

[frozen aurora]

wow

yes, go for it

[snow sentinel]

It's an algorithm so there's no tricky part in it

uint64_t checkFlawless(uint32_t root) {
    uint64_t N = root * root;

    uint64_t sum = 0;
    uint64_t Stmp = 0;
    int intLength = lenHelper(N);
    uint64_t d, b;
    uint32_t c = 1;
    uint64_t tmp = N;

    for (int i = intLength - 1; i >= 1; i--) {
        for (int j = i; j >= 1; j--) {
            uint64_t ten = powOf10(j);
            d = tmp % ten;
            b = tmp / ten;
            Stmp = sum + d + b;

            if (Stmp == root) {
                return N;
            } else if (N==9991921) {
                printf("Combination trying: sum=%d + (%d + %d)\n", sum, d, b);
            }
        }

        sum += tmp / powOf10(i);
        tmp = tmp % powOf10(i);
    }

    return 0;
}```

[frozen aurora]

although makes sense considering the need for speed

[snow sentinel]

I mean, yeah but with python its much easier

basically let me explain my algo:

[frozen aurora]

also what shouldn't end in 0

[snow sentinel]

I just asked this in the specific question because my program can very easily find such number like a human can

[frozen aurora]

ah okay

[snow sentinel]

my program has errors for some reason finding more complex combinations and I don't know which combinations I'm missing

[small aspen]

Does anyone here speak spanish?

[snow sentinel]

??????????

[small aspen]

Do u?

[snow sentinel]

for the first loop:
we get the number 1296 and we start splitting it 4 times
1,296
12,96
129,6

[small aspen]

I need help and my class is in spanish

[frozen aurora]

#❓how-to-get-help

[frozen aurora]

mhm

[snow sentinel]

for the second loop is where it gets tricky:
it saves the first digit in the sum
so sum = 1 (from 1296 -> 296)

and we apply the same algo

sum + 2 + 96

sum + 29 + 6

[frozen aurora]

my idea was that if i make a loop from 0 to 2^{number of digits - 1}, the binary representation of each number within a loop will act as an on/off switch for the presence of a split or not

like

[snow sentinel]

I thought of it

but

look in this situation:

1296 (we move the split)
1,296
12,96
129,6

until now good

when we go to 2 splits

1,2,96

12,9,6

and then

1,29,6

u need to split the commas and not move them together

[frozen aurora]

this works with any splits

*any number of splits

[snow sentinel]

hm

I don't really get how we are going to do that

1296 -> 000
1,296 -> 100?

[frozen aurora]

1296 -> 4 digits -> loop from 0 to 2^3 -1

000 -- 1 2 9 6
001 -- 1 2 9,6
010 -- 1 2,9 6
011 -- 1 2,9,6
100 -- 1,2 9 6
101 -- 1,2 9,6
110 -- 1,2,9 6
111 -- 1,2,9,6

[frozen aurora]

kinda

[snow sentinel]

oooh

aha

so we can just use

[frozen aurora]

this will always yield all combinations

[snow sentinel]

binary loop

and the number the binary loop gives us

is where to place the commas

[frozen aurora]

yes

precisely

[snow sentinel]

that's insane

I would have never thought of that

[frozen aurora]

thank you thank you

[snow sentinel]

Alright I guess I can handle the implementation except if you want me to keep you updated hahaha

[frozen aurora]

not sure tho how to effciently realize this in C

[snow sentinel]

give me a second to think

[frozen aurora]

ig you can make an array [1,2,9,6] into [1, 10, 2, 10, 9, 10, 6] where 10 is like a flag and then replace 10 with 11 where you need a comma and then parse the list

[snow sentinel]

I don't think an array is needed wait

[frozen aurora]

but the extra allocations feel unnecessary

oooOoOOOOooOOOOh i've got it (but i'll wait for you)

[snow sentinel]

sum = 0;
num: 1296
010 -> ```

we can do a math trick to get the 12 add it to sum and then get the 96 and add it

[frozen aurora]

oooooooh right

[snow sentinel]

also

[frozen aurora]

you can use them to determine when is the next number

[snow sentinel]

010 -> is 1296 % 10^2 and 1926 /10^2

[frozen aurora]

'hyperdigit' lol

[frozen aurora]

yes

[snow sentinel]

where 10^(location of comma)

[frozen aurora]

niiice

wanna start a software consulting company

[snow sentinel]

No idea what that is but it sounds interesting

hahaha

oh, problem solving basically

[frozen aurora]

yes lol

[snow sentinel]

haha well I don't know if you are being serious or not, it sounds good but I have many studies now and I don't think I could really do that haha

[frozen aurora]

nah i was joking

[snow sentinel]

hahaha alright

[snow sentinel]

thing is:

sounds good, how do I apply it in a loop for any number

what we have available:

powOf10(n) //returns power of 10 raised to n
lenHelper(n) //returns length of the number

basically:

length = len(str(1296))
for i in range(0, 2**(length-1)):

[frozen aurora]

i see i see

[snow sentinel]

we got the numbers, now

how can I think of them in binary...

[frozen aurora]

to get every digit of a binary you do >> and % 2 in a loop

[snow sentinel]

I get the digits going right or left?

for example

I have the binary number:

100

I'll get the digits as 100

or as 001

[frozen aurora]

up to you

*up to how you implement the loop

[snow sentinel]

so

ah you are bitshifting towards right

so I'll get the last digit

[frozen aurora]

for i in range(0, math.floor(math.log2(n)+1)):
    print(f"digit {i}:", (n>>i) & 1)

"& 1" is the same as "% 2" in this context

[snow sentinel]

so

n = 1296
length = len(str(n))
for i in range(0, 2**(length-1)):
  for y in range(0, math.floor(math.log2(n)+1)):
      print(f"digit {i}:", (n>>i) & 1)```

well, something wrong

[frozen aurora]

y is the digit

[snow sentinel]

digit 0:

digit 0: 0
digit 0: 0
digit 0: 0
digit 0: 0
digit 0: 0
digit 0: 0
digit 0: 0
digit 0: 0
digit 0: 0
digit 0: 0
digit 0: 0```

That seems good

[frozen aurora]

not i

[snow sentinel]

ah

true

I didn't see that mb

n = 1296
length = len(str(n))
for i in range(0, 2**(length-1)):
  for y in range(0, math.floor(math.log2(n)+1)):
      print(f"digit {y}:", (n>>y) & 1)```

You're typing for so long it's scary hahaha

[frozen aurora]

this will be my magnum opus

you'll have to wait for a sec

[snow sentinel]

haha alright

[frozen aurora]

i have an idea
loop over digits of n and digits of commas (at the same time) and have another counter of power. not sure how to explain it but i'll just show an example and i think you'll get it

initially:
n = 1296
suppose the commas are at 100 (so we should get 1,296)
sum = 0
power = 0

now, iterate from the back:
n%10 = 6
therefore increase sum by 6*10*power = 6*10*0 = 6 -> sum becomes 6
n = n//10
comma = 0
power++ (power became 1)

next step:
n%10 = 9
therefore increase sum by 9*10**power = 9*10*1 = 90 -> sum becomes 96
n = n//10
comma = 0
power++ (power became 2)

next step:
n%10 = 2
therefore increase sum by 2*10**2 = 2*10*2 = 200 -> sum becomes 296
n = n//10
comma = 1
oh shit, comma is 1
reset power = 0

next step:
n%10 = 1
therefore increase sum by 1*10**power = 1*10* 0 = 1 -> sum becomes 297
n = n//10
comma = 0 (assume there's another 0 at the front of every comma mapping)
power++ (power became 1)

this completes the loop

[frozen aurora]

@snow sentinel

[snow sentinel]

Alright I got it

comma = reset counter for power

[frozen aurora]

yep

[snow sentinel]

sounds like a perfect solution

and a bigbrain one

[frozen aurora]

thank you thank you

[snow sentinel]

Let me try to make it in Python (First) xd

#1296
n = 1296
root = 36

def func(n, root):
  length = len(str(n))
  for i in range(0, 2**(length-1)):
    n = 1296
    c = 0
    s = 0
    for y in range(0, math.floor(math.log2(n)+1)):
        last_digit = (n>>y) & 1
        if last_digit == 1: c = 0
        s += last_digit*(10**c)
        n //= 10
        c+=1
    if s == root: return n
  return 0

[frozen aurora]

wait why s += 2*(10**c)

maybe s += last_digit*(10**c)?

[snow sentinel]

ah yeah

mb

func(1296, 36)
0

:0

#1296
n = 1296
root = 36

def func(n, root):
  length = len(str(n))
  for i in range(0, 2**(length-1)):
    n = 1296
    c = 0
    s = 0
    for y in range(0, math.floor(math.log2(n)+1)):
        last_digit = (n>>y) & 1
        if last_digit == 1: c = 0
        s += last_digit*(10**c)
        n //= 10
        c+=1
    if s == root: return n
    else: print(s)
  return 0

uhh

s is always 1 for some reason

what does this give?

math.floor(math.log2(n)+1)

can't we just last_digit = (n>>1) & 1

wait I think I did something wrong oops xD

#1296
n = 1296
root = 36

def func(n, root):
  length = len(str(n))
  binary_len = length-1
  max_comb = 2**(binary_len)
  
  for i in range(0, max_comb):
    n = 1296
    c = 0
    s = 0
    for y in range(0, binary_len):
        last_digit = (n>>1) & 1
        if last_digit == 1: c = 0
        s += (n%10)*(10**c)
        n //= 10
        c+=1
    if s == root: return n
    else: print(s)
  return 0```

everything is 0 💀

[frozen aurora]

number of digits in a binary number

[frozen aurora]

but tbh it's unneeded

[snow sentinel]

that's binary_len

oh no its not

wait

oh wait

yeah it is

lol

1296 -> 3 slots -> 3 binary, 2^8 different combs

where is my code wrong tho lol

ah

last digit is is not n >> 1

[frozen aurora]

def sum_by_partition(n, commas):
    sum_ = 0
    power = 0
    while True:
        if n == 0:
            return sum_
        sum_ += (n%10)*10**power
        n //= 10
        if (commas & 1) == 1:
            power = 0
        else:
            power += 1
        commas >>= 1

ta-da

this works

[snow sentinel]

sum_by_partition(1296, 3)
27

shouldn't it be 36 lol

[frozen aurora]

why?

[snow sentinel]

36*36 = 1296

[frozen aurora]

no this is just for the sum

like

297```

[snow sentinel]

ah

aah

wait let me combine them

ah mb

wait

def sum_by_partition(n, commas):
    sum_ = 0
    power = 0
    while True:
        if n == 0:
            return sum_
        sum_ += (n%10)*10**power
        n //= 10
        if (commas & 1) == 1:
            power = 0
        else:
            power += 1
        commas >>= 1

def checkNumber(N, root):
    total_commas = len(str(N)) - 1
    for comma in range(2**total_commas):
        sum = sum_by_partition(N, comma)
        if sum == root: return N
    return 0

print(checkNumber(1296, 36))```

Seems to be working like a charm :))

Let me convert it to C

[frozen aurora]

wowie

[frozen aurora]

this ran really quickly in python actually

[snow sentinel]

Yeah

The assignment is in C tho

haha

[frozen aurora]

ah lol

good luck

[snow sentinel]

Thanks!

[frozen aurora]

no problem, this was fun

[snow sentinel]

#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>

uint64_t int_pow(uint64_t x, uint8_t y) {
    uint64_t temp_x = x;
    while (y > 1) {
        x*=temp_x;
        y--;
    }
    return x;
}

uint64_t sum_by_partition(uint64_t N, uint8_t commas) {
    uint64_t sum = 0;
    uint8_t power = 0;
    while (N != 0) {
        sum += int_pow((n%10)*10, power);
        n /= 10;
        if ((commas & 1) == 1) {
            power = 0;
        } else {
            power++;
        }
        commas >>= 1;
    }
    return sum;
}

uint64_t checkNumber(uint32_t root) {
    uint64_t N = (uint64_t) root*root;
    uint8_t total_commas = lenHelper(N) - 1
    uint64_t sum;
    for (uint8_t comma = 0; comma < int_pow(2, total_commas); comma++) {
        sum = sum_by_partition(N, comma);
        if (sum == root) {
            return N;
        }
    }
    return 0;
}```

Looking good haha

ah shit I have done something wrong idk

I don't have anything different wtf any ideas? @frozen aurora

[frozen aurora]

uh

[snow sentinel]

ah

lenHelper(N) - 1

for some reason lenHelper returns 7

wtf how

ah wait

I give the N not the root

wait mb

uhh

comma=0
1550

there's something wrong in sum_by_partition

I think

we can't really use >>

while(true)

causes buffer overflow and probably reads other numbers :>

no wait wat

@frozen aurora

Help

trilon@AK-47:~/flawless$ pypy flawless.py
('hello:', 6)
('hello:', 90)
('hello:', 200)
('hello:', 1000)
('hello:', 6)
('hello:', 9)
('hello:', 20)
('hello:', 100)
('hello:', 6)
('hello:', 90)
('hello:', 2)
('hello:', 10)
('hello:', 6)
('hello:', 9)
('hello:', 2)
('hello:', 10)
('hello:', 6)
('hello:', 90)
('hello:', 200)
('hello:', 1)
('hello:', 6)
('hello:', 9)
('hello:', 20)
('hello:', 1)```

added this print: py awaw = (n%10)*10**power print('hello:', awaw)

[frozen aurora]

bruh

okay let's see

[snow sentinel]

okay

focus on these 4

('hello:', 6)
('hello:', 90)
('hello:', 200)
('hello:', 1000)```

these first four are iteration for 000,

alright?

sum = 1296

for C now...

calc=60
calc=90
calc=400
calc=1000

third iteration is 400 ???? (instead of 200)

first is 60 (instead of 6)????????

I found the shitty little ass hole

@frozen aurora

python: py (n%10)*10**power

it does first the raise to power, then the multiplication

god dammit

I was like: why does he multiply by 10 and then I realized...

[frozen aurora]

huh?

um

yea

oooooh i see now what's wrong with the C code

yes

[snow sentinel]

Alright it works

i think

haha

o oh

it doesn't

almost there!

I get the number: 489984803178

for 1 10000000000

My teacher gets: 499984803178

How is that even possible

the difference is : 1000000000

which doesn't have a root

[devout snow]

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[dire python]

How would it be possible that x=0 is a c.p,if f is increasing through it?

[wooden veldt]

Think about f(x) = x³

[dire python]

Something like this?

[devout snow]

@dire python Has your question been resolved?

[frozen pier]

Can someone help me with this task pls:
Determine all integers n for which real numbers x,y exist in such a way that the following equations are satisfied:
x+y=n
x³+y³=n²

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[versed bronze]

can someone help me with this
The graph of the function f(x)=2∣x−1∣−1 with Df =⟨−3;3⟩ was translated in parallel by a vector, resulting in the graph of the function g with the domain Dg=⟨−5;1⟩ and the range g(Dg)=⟨2;10⟩. Provide the translation vector and the formula for function g.

[devout snow]

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

[versed bronze]

1. I don't know where to begin.

[lunar harbor]

Start by finding the range and domain of f

Then consider how ||they were shifted to get g||

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[devout snow]

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[royal marsh]

how to solve the quadratics formula give a hard example

[jaunty mantle]

What do you mean solve the quadratic formula

[lusty sapphire]

Ax^2+Bx+C=0

[supple knot]

don't use help channels to ask for questions for you to do

.close

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[indigo stag]

Does anyone have an idea on how to solve this?

[devout snow]

@indigo stag Has your question been resolved?

[indigo stag]

<@&286206848099549185>

[frozen aurora]

substitute x=-10pi/3

[indigo stag]

I did that and I got 8.675, is there anything else i have to do? because the question is worth 4 marks?

[frozen aurora]

no, you have to express it in an exact form

show your work (aka don't just substitute into calculator)

[indigo stag]

sorry im still kind of confused my teacher kind of just gave us this assignment but never went over this in a lesson. alright so after put x=-10pi/3 into the equation do I just simplify it?

[frozen aurora]

yes

[indigo stag]

This is what I have right now, I feel like it’s wrong

and the result of that is 0

[devout snow]

@indigo stag Has your question been resolved?

[indigo stag]

<@&286206848099549185>

[devout snow]

@indigo stag Has your question been resolved?

[devout snow]

@indigo stag Has your question been resolved?

[devout snow]

@indigo stag Has your question been resolved?

[fickle acorn]

impossibile

i tried doing the graph

and there's no matching point

[devout snow]

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[ember cargo]

this is what i have so far

how do i put these in interval notation

and how do i start on the 3rd question?

[tulip oak]

According to this website's graph

[ember cargo]

is this right?

[ember cargo]

thank you

[tulip oak]

Sorry my photo is stuck on sending

Oh notice that (2x-7)<0 could be a case

[ember cargo]

i believe a bar symbolizes absolute value?

[tulip oak]

Yes

[deep vortex]

Why 0 < ?

It should be a -9

[ember cargo]

oh okay

would my method of solving be good otherwise?

[deep vortex]

Yes

[ember cargo]

okay ty

[deep vortex]

Though it won't always work

Imagine if there was an x on the RHS but not on the LHS

If you subtracted that, then you'd have it on the LHS

So the better technique in that case would be to break it up

In this case, your method is faster

[deep vortex]

E.g. $|2x - 7| < 9 + x$

What would you do now?

Subtract x?

But then you'd still have -2x on the LHS

[deep vortex]

Also, why do you need the number line?

The inequality tells you x must be between 3.5 < x < 8

Why say x < 3.5 is false? Of course it is false

[ember cargo]

oh the number line is required

[deep vortex]

Ah, so the exercise asks you to draw one

[ember cargo]

yes

[deep vortex]

Well, then I'd still leave out the table

[ember cargo]

thats also required 😭

[deep vortex]

You have that x must be between 3.5 and 8 already

Ah

[deep vortex]

Correct the 0 to -9 though and you'll have a different result

[ember cargo]

i see

[ember cargo]

i’ll keep these in mind

[deep vortex]

I prefer the method where you have the inequalities right away though

[ember cargo]

yeah we were asked to look at it that way

cuz im actually just in 9th grade

[deep vortex]

Well, it's not like the inequality version is too hard for 9th grade, lol

[ember cargo]

i know.. i do agree that some of these are redundant tho 😭

anw i’ll try solving with -9 now

[devout snow]

@ember cargo Has your question been resolved?

[ember cargo]

can i get help with the 4th one now?

[deep vortex]

Do the two cases like above

[deep vortex]

Is this a test, btw? (1 point each)

[ember cargo]

like this then?

[ember cargo]

extra credit

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[devout snow]

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[ember cargo]

.reopen

[devout snow]

✅

[ember cargo]

<@&286206848099549185>

[devout snow]

@ember cargo Has your question been resolved?

[ember cargo]

<@&286206848099549185> i just need to know if the sign is right 😭

is it actually supposed to be greater than or equal to

[empty girder]

the sign is correct.

[ember cargo]

no solutions then?

[empty girder]

first equation | 2x - 5 | ≥ 3 that means: 2x - 5 is greater than or equal to 3, 2nd -3 ≥ 2x - 5 ≥ 3 This means that 2x - 5 is between -3 and 3

These two equations are equivalent

[ember cargo]

but as per the signs, it must be less than -3 and greater than +3?

[ember cargo]

how tho

[empty girder]

the signs are reversed when you multiply or divide by a negative number

f example if you have a > b then -a < b bcuz multiplying both sides -1 changes the direction of inequality

[empty girder]

to solve for x you need to add 5 to all sides then divide by 2

[ember cargo]

4 ≤ x ≤ 1?

no solution then?

[ember cargo]

.close

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[frozen pier]

For a natural number n, P(n) is the product of its different digits of 0.
For example, P(2023) = 2 · 2 · 3 = 12.
Determine how many four-digit numbers n with the property P(n) = 12 exist.

[frozen pier]

Can omeone help me with this question

someone

pls

[frozen aurora]

find factorisation of 12

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[mental edge]

Whats the formula to calculate derivative of si x^cosx

[mental edge]

Fx^gx

.close

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[vague perch]

please ignore the horrific hand writing 😓 just provign the limit of a sequence here and I was wondergin why my prof stopped at this step

[vague perch]

(highlighted)

couldnt they have just continue and said 4/sqrt(n) then 4 since n>1?

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[vague perch]

.close

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[spice linden]

Guys, how do I solve this question?

[spice linden]

How do you even begin to analyze a recursively defined sequence?

[wooden veldt]

You might try and see if its increasing/decreasing and bounded above/below

[spice linden]

I checked

[rich summit]

Have you done linear algebra?

[spice linden]

it is decreasing except in the first 3 terms

[spice linden]

I'm doing it in uni rn

but this question is from analysis class

[rich summit]

It might be overkill but you can represent this as a matrix, where you multiply the vector (a0, a1) with different powers of the matrix to get the nth term

[rich summit]

this works better probably

[spice linden]

that is probably overkill

can i just say that it's decreasing but since it can never be negative, it has to be converging towards zero?