help-0

[remote heron]

[fossil mason]

This was the only way that worked for me LOL

[remote heron]

oh lol

brute force

hmm

[fossil mason]

But it shouldn’t take more than 3 lines :”)

[remote heron]

yea, i wonder what the issue is with my approach

im sorry im not sure how to get the correct answer

I hope someone comes along though

[fossil mason]

16C5-13C5-10C5+7C5

[lone heart]

@fossil mason Has your question been resolved?

[quasi scarab]

easier than what?

[fossil mason]

Then listing out all possible combinations

[quasi scarab]

that 16c5-.. part is not correct?

@fossil masonoh, i see

i dont know how its called, but u had a similar type of problem not too long ago

its like counting the numbers which are either 2-divisible or 3 divisible

you count each, but then u counted the 6-divisible ones twice so u have to subtract it

the same here:

ALL-THERE IS NO DOCTOR - THERE IS NO DENTIST+ THERE IS NONE OF THEM

sry caps

[lone heart]

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[tame hound]

Does anyone know why we get X divided by two from A to the vertical line, and B to the vertical line?

couldn't one side be longer than the other?

how can we tell if they are equal?

[gray isle]

you have an isosceles trapizium

you can justify that they'd be equal from triangle congruency (HL)

[tame hound]

what's ”triangle congruency (HL)”? we know that the hypotenuse is the same, and they are both 90°, is that the idea then that they're the same?

[lone heart]

@tame hound Has your question been resolved?

[gray isle]

the height will also be the same
HL is the justification that the triangles are congruent
and then you can apply corresponding parts of Cong triangles to justify the bases will have the same length

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[native edge]

It's either a or c

I dont know the steps though

[flat ore]

well its not a or c

wait

[native edge]

Pretty sure it is

Cuz it said diameter

[flat ore]

yeah a and c

nvm

[silver adder]

it is a or c

not both

[native edge]

Now how do I get to the result

[flat ore]

for the center, find the midpoint

of the diameter

[native edge]

Ah

0,10?

[flat ore]

mhm

[native edge]

And then I plug it into the formula

Ah I see

Ty ty

[flat ore]

yeah (x-0)^2 + (y-10)^2

[native edge]

So its A

Alright thank you so much

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[tribal wasp]

Hey I am having trouble figuring out how to approach part eiv?

[chilly merlin]

What topic is this?

[tribal wasp]

intro to linear algebra

[chilly merlin]

I don't know how to do this

You have to ask someone else Sorry

[lone heart]

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[fossil mason]

Could someone help with this ?

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[dawn estuary]

$(22i)^{2.3}$

[bitter vault]

Use curly braces 22i^{2.3}

[dawn estuary]

Why does this not only have a imaginary part, but a real one too?

[ocean seal]

piinfa

[dawn estuary]

I would have guessed the polar angle is 90° but its actually -153°

[worn fox]

Intuitively, because taking powers of complex numbers that are not purely real often involves rotation at some point, so you're going to kick 22i off the imaginary axis by taking a power of it

to calculate you need to write $i = e^{\frac{i\pi}{2}}$

[ocean seal]

iCaird

[dawn estuary]

Thank you! but I am not sure I understand what the equation is for :/

[worn fox]

do you not understand where it comes from or what you would use it for

[dawn estuary]

the second

[worn fox]

if you replace $i$ in your expression with what I gave, then you can calculate powers as usual

[ocean seal]

iCaird

[worn fox]

$(22)^{2.3} \cdot e^{\frac{i\pi*2.3}{2}}$

[ocean seal]

iCaird

[dawn estuary]

Worked out perfectly, appreciate the help

.close

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[hushed inlet]

Can someone help me with this I kinda understand it but im stuck on this

[alpine sable]

probably b

as it has both edges with weight 2

and other 3 dont and this algo adds minimum weight if it doesnt make a cycle

so 2's should go before bigger weighs

[hushed inlet]

Oooh ok

Wait so for this how can I use the shortest route algorithm?

[alpine sable]

dijkstra?

[real glen]

just use greedy method

for each vertex see which has lowest cost edge

[alpine sable]

probably 11

[real glen]

no its 10

ab -> bc -> cg -> gh -> hf -> fe

[hushed inlet]

Hmmm

[alpine sable]

oh right

[hushed inlet]

Do you know how the Nearest Neighbor Algorithm work?

Im kinda confused on that aswell

[topaz elm]

I have something similar to that question as well.

[real glen]

pick a vertex and find its shortest edge connected that vertex with another vertex and repeat this step until all vertices are visited

is the gist of nearest neighbor algo

[real glen]

channel is occupied go to diff channel

[topaz elm]

Oh ok.

[real glen]

also they are two diff graphs lmao

[hushed inlet]

So what vertex would I pick here?

[real glen]

it should be b but let me confirm

[hushed inlet]

Ok thank you

[real glen]

yeah I think i am correct

[hushed inlet]

I also kinda confuse on this as well and this is the last one that I have a question about

[real glen]

is that k5 graph

[hushed inlet]

Yes

[real glen]

looks like it is, then the chromatic number must be 5

do you know why?

[hushed inlet]

ummm not really is there way you can inform me how you got 5?

[real glen]

so K5 is a complete graph right

meaning every vertex has an edge to another vertex in G

we know from the theorem that we use at most n coloring for graph if G has n vertices

So the max chromatic number for G in our case can be 5. So we are looking to see if we can minimize this number

[hushed inlet]

Oooooh ok

[real glen]

but we notice that if we use 4 colors, then there is a 2 vertex in G that has same colours

but since its a complete graph, they share an edge together

which means we didnt do the graph coloring correctly because if two vertices have an edge, they must have different colouring

so the chromatic number is 5

thats the basic proof of it

[hushed inlet]

Ok I see now thank you cause I was rlly confused on that

Would you happen to be able to help me on this as well? I solved it and I got 92 but I wanna make sure I did it right

[young finch]

Just plug in 7

[hushed inlet]

Where would I plugin 7 exactly

?

[young finch]

The variable

x

You can also figure it out with the pattern of the table

Actually no

The data values aren't safe to make an assumption off of

with just the table

[hushed inlet]

hmm

Im still kinda confused on how to do that

[lone heart]

@hushed inlet Has your question been resolved?

[solemn grove]

y is the score, x is the hours they put in

@hushed inlet

so if they put in 7 hours of work

x = 7

they’re asking you to find y

when x is 7

using the given formula

[hushed inlet]

So it would be 87 correct?

[hushed inlet]

or am I still doing it wrong

[solemn grove]

y= 5.1(7) + 56.3

so 35.7 + 56.3 = 92 right ?

@hushed inlet

[hushed inlet]

yea

[lone heart]

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[hollow pulsar]

Is my answer correct

[real glen]

wait why are you subtracting

[lone heart]

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[trail fern]

is quadratic and 2nd order basically synonymous or always tied together?

[trail fern]

is there a case where quadratic is a different order?

[placid zinc]

"order" is a sus word to use here

Every quadratic is a 2nd degree polynomial, every 2nd degree polynomial is a quadratic

[trail fern]

that part i do understand

but im trying to extend it further and seeing if it's logical

this is the context

i'm trying to see if 9-node and 8-node rectangular elements are both used for 2nd order approximations

and visually they seem to be

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[lost moon]

I have a business, and I am learning how to make projections of future growth, but I feel like I must be doing it wrong because the growth % seems to stay similar. Am I doing projection wrong?

[lost moon]

The column percentages are the change in monthly recurring revenue from month to month, which for the first 4 months, averages 16.29%, is projecting growth like the bottom a correct way of doing this, or is there a more advanced/accurate method for this?

[tacit arch]

,w (17.52 + 16.07 + 15.01 + 16.55)/4

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by riemann#2529

[tacit arch]

there are lots of ways to "project"

this way is fine

https://blog.hubspot.com/sales/regression-analysis-to-forecast-sales

[lost moon]

Just seems like with this way, it must be impossible - either my marketing has to become more efficient (by I don't know what percentage) the whole time

[tacit arch]

there's another one that's arguably better

also 4 datapoints is barely any data

[lost moon]

to maintain 16%, as the MRR number gets bigger, I have to bring many more customers in with the same marketing dollars

gotcha, so more data may show what I am concerned with

like how much it costs to bring a customer in, and how much I am spending on marketing

reading that site now

ah, you were meaning that 4 data points, as in the 4 months, not the lack of data per month

okaym thanks!

.close

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[lone heart]

Please don't occupy multiple help channels.

[tacit arch]

.close

[lone heart]

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[boreal chasm]

Honestly have no idea what to do

Do I have to make an assumption or smth

Are these kind of equations solvable without making an assumption

[limpid spade]

what assumption

[boreal chasm]

for example

assume y is in the form of ae^(-2x)

then 4ae^(-2x) + 6ae^(-2x) + 2ae^(-2x) = 24e^(-2x)

[limpid spade]

first time doing differential equation
's?

[boreal chasm]

first time doing ones with multiple y terms

[tacit arch]

https://tutorial.math.lamar.edu/classes/de/NonhomogeneousDE.aspx

[limpid spade]

that's second order differential nonhomogenous equation

[boreal chasm]

12ae^(-2x) = 24e^(-2x)
a = 2

so ig y = 2e^(-2x) is a solution?

but im assuming there is more solutions

[boreal chasm]

What does it mean

[limpid spade]

look what riemann has sent

[boreal chasm]

English isn’t my mother tongue so it’s hard to understand

[limpid spade]

you do not just plug in values in x²+9x+1=0 to find the zero values

[boreal chasm]

I know

[limpid spade]

translate it and find a source in your mother language

[boreal chasm]

There is a formula for it

Is there a formula for second order differential equations

[limpid spade]

just translate this

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[cyan saffron]

how do i solve this?

[real solar]

solving for x or y

[cyan saffron]

im solving for both

i tried getting x in terms of y and the inverse but that leads to nothing

[tacit arch]

show the whole original problem and instructions

[cyan saffron]

(a;b) + [a;b] + 7 = 3a + 3b

this is the original equation

(a;b) is biggest common divisor

[a;b] is smallest common multiple

a,b natural numbers

if (a;b) = d then a = dx, b = dy and (a;b) * [a;b] = a * b

and then i just subtituted

[tacit arch]

where are the instructions?

screenshot the whole thing

[cyan saffron]

the question is if a and b exist

the instructions are in a different language

[rare gale]

well x = 2, y = 2 is a solution to your original equation, dunno if that helps

[cyan saffron]

so is x = 4, y = 4

[rare gale]

(a;b) + [a;b] + 7 = 3a + 3b
but a = b = 2 doesn't work here, so I'm not really sure how you're setting up that equation

[cyan saffron]

i noticed that too

[rare gale]

you're not even using the 7 in any way

[cyan saffron]

the 8 is 7 + 1

[cyan saffron]

(a;b)+[a;b] + 7 = 3a+3b
d+dxy+7=3dx+3xy
dxy-3dx-3dy+d=-7
d(xy-3x-3y+1) = -7
first case d = 1
xy-3x-3y+1=-7
xy-3x-3y=-8
but that leads to x = 4, y = 20, or the other way around, but when i plug that in it's wrong

oh nvm it leads to x = 2, y = 2 or x = 4, y = 4

but it's still wrong

oh wait completely forgot that (x;y) = 1

thanks anyway

.close

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[cyan saffron]

just solve for each and do the division?

[dry tundra]

yeah u divide at the end to find the percentage but i dont know how to find the values of each of the stations

[cyan saffron]

just sum up the terms and substitute and then i think you have something like n * station c + k = 110000

and you know n and k

[dry tundra]

im still lost on what to do

[cyan saffron]

if station a is three times bigger than station c, what does that mean?

@dry tundra

it means station a = station c * 3

station b = station a + 24200 = station c * 3 + 24200

station d = station c + 24200

[dry tundra]

so whats station c?

[cyan saffron]

station c is station c

you know that station a + station b + station c + station d = 110000

[dry tundra]

does it not have any number valuess?

[cyan saffron]

substitute into this equation what i just said

[dry tundra]

so whats the answer

what percentage are each of the sections?

[cyan saffron]

are you here just for answers?

[dry tundra]

both

answer and to figure out how to get the answer so i can do it on my own in the future

[dry tundra]

and now i just add them up and divide each of them by the total to get the percentage right?

[cyan saffron]

sure

[dry tundra]

okay thanks

let me just finish it to see if it is right

okay so i got 21% for section a. Section B = 43%. Section C = 7%

Section D=29%

@cyan saffron can you explain your workings please. I know that to to get section b you add 24200 to section A and Section D is Section C plus 24200 and section A is just Section c *3. but how do i get section C

[lone heart]

@dry tundra Has your question been resolved?

[cyan saffron]

You dont

[cyan saffron]

You have this right here

You substitute and get 8 * station c + 48400 = 110000

[lone heart]

@dry tundra Has your question been resolved?

[dry tundra]

Okay thanks

[lone heart]

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[raven galleon]

Hello! I need help with this geometry exercise
question b)

[raven galleon]

here’s the translation

The figure on the side represents a cube in an o.n. Oxyz. It is known that:

• [ABCD] is a face of the cube and [EFGH] is the face that opposes it (point H is not shown);
point A has coordinates (3, 5, 3);
point D has coordinates (-3, 3, 6);
point E has coordinates (1, 2,-3)

and question b) :

b) Determine the coordinates of point H and comment on the statement: “Point H belongs to one of the coordinate axes”

[alpine sable]

since its a cube

D + vector(AE)

[raven galleon]

it just does not make a lot of sense to me

[raven galleon]

ohh

how didn’t i think of that

would you be able to help me with the last question of this exercise as well?

question e)

it’s to write the reduced equation of the spherical surface with center at D and passing through vertex F

how do i get the radius here

[alpine sable]

radius = |DF|

[raven galleon]

yes but i don’t have the coordinates of F

would i be able to get it if i added vector (DH) to H

[alpine sable]

|DF| = |DH| since its a cube

or any edge really

[raven galleon]

thank you

.close

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[novel lintel]

start from the left

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[cloud zodiac]

Which way is correct? I’m really confused is I change the -/+ that infront of the surd or the one infront of a normal number when rationalising

[cloud zodiac]

Same question but 2 different answers

[alpine sable]

they are same answers?

[cloud zodiac]

No

[south mantle]

They are the same answer, they just took the -1 common from all the terms

[cloud zodiac]

Oh bruh ok thanks

So does that mean that it doesn’t matter which symbol you change. By that I mean it doesn’t matter if I multiply it by -square root of 6 + 3 or by square root of 6 - 3?

[alpine sable]

yes since they are both 1

as long as u dont multiply by 0/0

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[zinc thunder]

Can you help me with problem 10?

[naive valley]

,rotate

[alpine sable]

use circle center

[naive valley]

if you let x be the distance from the center of the circle to U, and let p be the radius of the circle (I'm not using r because you already have an R), then you should be able to find two equations involving x and p

two equations and two unknowns

[zinc thunder]

.close

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[hollow falcon]

I've found the total differentials, but unsure on how to progress, been stuck on this for a few days

[hollow falcon]

Ive gotten to this point (red ink) just fine. But when I progress I think I'm making a mistake or something somewhere.

<@&286206848099549185>

[lone heart]

@hollow falcon Has your question been resolved?

[lone heart]

@hollow falcon Has your question been resolved?

[lone heart]

@hollow falcon Has your question been resolved?

[tacit arch]

You look like you're on the right track
https://math.stackexchange.com/questions/2362700/formula-for-total-differential-with-respect-to-polar-coordinates

[bright terrace]

lol

[lone heart]

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[exotic kestrel]

.opem

.open

[near sluice]

Hi! Can anyone please help me with this question. I am confused about type II error and dont know how to calculate beta for the test.

[remote heron]

power?

im not sure what the greeks mean in this context though

what is beta?

[lone heart]

@near sluice Has your question been resolved?

[near sluice]

Beta is the type II error

[near sluice]

What do you mean with the greek letter?

[remote heron]

okay so they want the probability of making a type ii error to be 0.1

and type ii error is like uhh

,w type ii error

[ocean seal]

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Requested by jan Niku#2119

[near sluice]

so the type ii error is accept H0 when H1 is true

[remote heron]

this says the opposite

hmm i might be too tired to remember how to do these

[near sluice]

Please help me

[remote heron]

well youd usually have 2 means floating around

[near sluice]

I think question a may help we ans for question b

[remote heron]

thered be a mean from the null hypothesis

and then a null from some data

[near sluice]

Yes, I just state H0: miu = 85 and H1: miu = 100

then I dont know how to do next

[remote heron]

okay lets start with a

you havent done a yet?

[near sluice]

not yet. I just realized I did it wrong

[remote heron]

okay

hows this look for starts

this is just the rejection region on the proposed distribution

[near sluice]

what is the 2/3

[remote heron]

the proposed proportion in the report

oh

its not a proportion

i will change

sorry i am very tired lol

[near sluice]

No you're fine

[remote heron]

okay

[near sluice]

Okay so the red zone is the rejection region, right?

[remote heron]

correct

which im thinking is here and one sided because the professor believes that the true proportion is less right

so he wants a really, really low number

then he can say for sure that 100 is too high

[near sluice]

Okay! Got it

I understand what you are saying

[remote heron]

i just did this but

i think -1.96 is the wrong number

okay

does this calculation make sense?

im trying to find the high value in the rejection region

we know the area to the left of this value we want to find will be 0.05

values at least as extreme as the highest value which will cause rejection

[near sluice]

yes it makes sense to me

[remote heron]

so we can fill out a little more

excuse my drawing

the blue distribution is the true distribution

the green is the one proposed by the report

and the red value 85.12 is the least extreme value on the green/proposed distribution which will cause rejection at the 5% level

good to there

?

[near sluice]

yes

sound good to me

[remote heron]

okay so we now need to find out where a type ii error occurs

,w type ii error

[ocean seal]

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[remote heron]

i personally find these things impossible to track lol

i have to think very very hard

[remote heron]

right

[near sluice]

yes so this is the type II error

[remote heron]

so we would fail to reject

meaning that we would be to the right of the red line

but on the blue/true distribution

does that make sense?

this is the probability that we make a type II error

the further away the mean of the true distribution is from the mean of the proposed one, the lower this probability

as the means get closer, it becomes much more likely, since evidence must be a lot stronger

this is maybe the weird conceptual jump

but can you identify the region which makes up P(type II error)?

starting where, integrating in which direction, and on which distribution?

[near sluice]

So we need to use integrating to find type II error?

[remote heron]

well, in reality you will use a t-table or a z-table

most likely

but by integration i mean area under a curve

its maybe a bad word to use here

can you identify the region where a type ii error occurs?

forget about integration

[near sluice]

so you mean we find the P( X <85.12)

[remote heron]

you can jump straight to calculation

but theres so much like

1 minus and complement and weirdness

its nice to have a picture you can point to

here uhh

im using this to review for myself too

here is where we make a type two error

the vertical red bars

in this region, we get a number which is not extreme enough to reject

the least extreme value that causes us to reject is 85.12

so we get maybe like 87

fail to reject

but its false (we know the true mean now)

anything further to the left from 100 we correctly reject

the jump is to this probability

areas under these curves (normalized) are probabilities

so if we normalize the true distribution, and integrate to the right of this value, we will get the probability of making a type ii error

thats a pretty big conceptual jump maybe, does it make sense?

wow i typed a lot feel free to just read for a sec

[near sluice]

okay maybe I have the idea to solve problem a

[near sluice]

it helps me alot

[remote heron]

here i can get the answer

if you want to compare

[near sluice]

Yes, please. I really appreciate it

[remote heron]

wait we never used n

well what number did you get

lemme grab my notebook haha

[near sluice]

okay i got 75.81

[remote heron]

conceptually okay but i think I dropped an n

yea i need to correct

[near sluice]

9/sqrt(150)

[remote heron]

hmm you should be using a normal table

[near sluice]

so I got x = 75.81

[remote heron]

rejection region boundary?

[near sluice]

yes

[remote heron]

hmm i get slightly different

oops

1s

gosh i dont understand

$-1.645 = \frac{ \sqrt{150} ( x - 100 ) }{ 9 }$

yea?

[ocean seal]

jan Niku (@pomodoro role)

[near sluice]

oops

my bad

[remote heron]

but this seems so high

it gives a rejection region of up to 98.79

that seems unreasonable

but maybe with 150 people its enough?

[near sluice]

do we need to sqare root the population variance

[remote heron]

the normal thing is $z=\frac{\sqrt n ( x- \mu ) }{ \sigma}$

for known $\sigma$

[ocean seal]

jan Niku (@pomodoro role)

jan Niku (@pomodoro role)

[remote heron]

so you need to uhh

oh yea

you need to sqrt 81

to get std dev

[near sluice]

yah you true

wait I thought X- 85?

I got x = 83.79

[remote heron]

are you sure?

[near sluice]

I am confused between square root variance or not

because it is already variance

[remote heron]

sigma squared is variance

sigma is std dev

oops

there we go

[near sluice]

Hmmm

[remote heron]

it seems so high but playing around i think its just

[near sluice]

miu = 85

[remote heron]

asking 150 people drives your variance down so low

[near sluice]

i guess

[remote heron]

huh?

[near sluice]

x-85 / sqrt(81/150)

that's my equation

[remote heron]

no, you are using the null mean

from the report

you want to find the least extreme value that will let reject that hypothesis

either way, with how tight these are

i dont think the probability of making a type 2 error is very high

[near sluice]

Okay got it

[remote heron]

dont suppose you have the actual answer

because it seems like beta should be essentially 0 here

[near sluice]

why you got beta = 0? can you please explain for me?

[remote heron]

well like

okay so the null

the variance is super low

like less than 1

maybe 0.8? something ilke that

you know about normal distributions, how like

by 3 standard deviations away from the mean

you have nothing

so if we move from 100 to 85

along a distribution with variance of 0.8

there just isnt anything there anymore

as far as probability

[near sluice]

yes I know that

[remote heron]

i could be wrong but thats what im seeing calculating

that we are asking so many people that we are very, very unlikely to not be able to reject the null

i mean if its really not true, and you ask 150 people, you should almost certainly see that

5 or 10 maybe not but after 150 we'd have to see something

so id say like

there is negligible overlap between these distributions

then its extraordinarily unlikely we fail to reject the null hypothesis, as we know it is false

[near sluice]

okay i undestood

[remote heron]

and really, this should say xbar

not x

does that help with part b lol

[near sluice]

yeah i know

[remote heron]

i really have to go to bed

[near sluice]

it helps a lot

lol thank you

[remote heron]

n is a weirder one to solve for

[near sluice]

have a good night

LOL

[remote heron]

you usually need to use like

okay here i can give a short thing

if you want

[near sluice]

YES

[remote heron]

so they say beta is 0.1

this comes from your true distribution

[near sluice]

ok! note it

[remote heron]

then, rejection region is on null distribution

[near sluice]

Cool!

Thank you so much for your help

[remote heron]

lemme draw it this way

[near sluice]

OMG you are so supportive.

[remote heron]

should i stop

[near sluice]

[remote heron]

i have to do this on my final in

uhh

36 hours

so i wanna know

[near sluice]

Yes you can stop, I think I can figure out

Thank you so much again!

[remote heron]

hahah

have a good one 👋

[near sluice]

You too buddy

[remote heron]

i got ||n=4|| 😌

now i can sleep

[near sluice]

LOL

okay! have a good night

[lone heart]

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[trail hare]

what is 2+2

[alpine sable]

I have been waiting for this

Yet again

[worn fox]

Have they tried logs?

[alpine sable]

Hope that helps

in the first term x=π/2

In other teem

x=0

[trail hare]

so we need to solve this with the help of the photosynthesis of a forehead right?

[alpine sable]

2+2=2 * 2
e^ln(2+2)=e^(ln(2 *2)) = e^(ln(2) + ln(2))

[trail hare]

mmm ok

i understand

thank

[alpine sable]

It's .close

[trail hare]

.close

[lone heart]

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[trail hare]

yez

[lone heart]

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[delicate geyser]

How do i prove 53 * 83 * 109 + 40 * 66 * 96 is composite

[lone heart]

@delicate geyser Has your question been resolved?

[delicate geyser]

<@&286206848099549185>

[hard patio]

wow, i really wanna learn ways of proving this too

[rare gale]

,w factor(53 * 83 * 109 + 40 * 66 * 96)

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[rare gale]

I guess explicitly writing out the result as the product of two integers proves that it's composite 🙂

[hard patio]

yeah it does, but maybe theres some creative way to do the same?

[rare gale]

I'd be curious...can't think of a simpler way to try to factor a number n than to try dividing it by every prime up to sqrt(n). easy enough in a few lines of code using a computer, but it would certainly be a pain by hand. if there's anything more clever than that i'd be curious too. in the case of this expression you'd have to try every prime < 856

[hard patio]

there is something cheeky going on in this question lol

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[amber iron]

how do i express this in condensed form

[amber iron]

i might be able to get some combination of factorials and exponentials to express this, but not sure how...

[silver adder]

u could use product notation

[amber iron]

nah, thats cheating 🙂

plus this will go inside another sum, so its gonna look very clunky with product notation

ok yeah i got it

but its a pretty large expression

[prime badge]

https://oeis.org/A008545

(but upside down)

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[zinc urchin]

in a circle that outwards a right triangle, is the hypotenuse of that triangle the diameter of the circle?

[serene sigil]

like this?

[stone pilot]

yes

[zinc urchin]

thanks

.close

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[zinc urchin]

.reopen

[lone heart]

✅

[zinc urchin]

Since, I'm already here:
A circle is tg with 2 coordinate axes and passes through the point M (2,1). Write the equation of the circle

My solution so far.

I think there is a better explanation of the problem than the one I did in the picture

https://www.youtube.com/watch?v=udtoCSCRW8Y this is probably the solution

.close

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[opaque hinge]

Ok so

Why is du=2xdx

Where did the dx come from

[vale wigeon]

du/dx = 2x

[opaque hinge]

But where did the dx come from

Like he derived x^2 + 5 to 2x dx?

[flat ore]

if u is x^2 + 5 then du/dx = 2x => du = 2x dx

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@opaque hinge Has your question been resolved?

[alpine sable]

du/dx=derivative of x^2+5=2x
=>du=2x*dx

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[alpine sable]

any help on how to solve it

[prime badge]

confusing tbh

[stone pilot]

this reminds me of something

[alpine sable]

I was thinking of Bayes' theorem

[prime badge]

apparently it doesn't fail all the time, when the fault is present

it's a three storey story

oh

everything they say is for faulty device, that's not part of the equation

it's a trap

[alpine sable]

wdym

[prime badge]

i mean it's confusing on purpose

[stone pilot]

oh

[prime badge]

doesn't matter

that's what i think it says

clearly x is 0.1, so the answer is 0.01

[stone pilot]

rephrasing: a test will detect a fault when the device is faulty 90% of the time
the device will fail when the device is faulty but not detected by the test 10% of the time
whats the probability that a faulty device will not get detected by the test and will fail

[alpine sable]

oh 0.10*0.10 = 0.01

[prime badge]

correct

[alpine sable]

thank you both my brain exploded haha u too smart

thanks @prime badge

thanks @stone pilot

.close

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[fresh fjord]

yo

[fresh fjord]

ping plz

<@&286206848099549185>

nvm its adf

.close

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[tough tangle]

Im pretty sure the book's answer is wrong, can someone confirm?

at k = 1/3, x = ln(2t-1) is invalid

therefore i gave the minimum value of k to be 1/2

[bitter vault]

you're right

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[tough tangle]

thanks

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[fervent aurora]

\

[fervent aurora]

How do I solve this?

[lone heart]

@fervent aurora Has your question been resolved?

[round forge]

try drawing a graph to visualize the right riemann rectangles

[fervent aurora]

I mean

technically

[ocean seal]

$₭¥𝔪𝔞𝔯𝔦𝔬

I just have to do $(15-4)/3 * (6.5 + 6.2 + 5.9 + 5.6)$

$₭¥𝔪𝔞𝔯𝔦𝔬

[fervent aurora]

I followed the right reimann sum

but Im not getting the right answers

What am I doing wrong?

[proper tangle]

the width is not fixed

width of the subintervals varies

[fervent aurora]

wdym

So wut do I do

[round forge]

you can't use the equation here because the equation implies the width (b-a/n) is the same for each interval (4-->7, 7-->12, 12-->15 are not separated equally)

so you have to calculate the riemann sums manually, by hand

draw a graph of the rate

and how it changes over time

to see this visually

[fervent aurora]

Uhhh

are you sure?

This problem should be solved fairly quickly

is there really no faster way to solve this?

[round forge]

yeah

[fervent aurora]

well

aight thx man

[round forge]

np

[fervent aurora]

.close

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[fiery spire]

Hey, can I have help with this?
I have a R3 matrix, the lines of the matrix are shifted by different values (each row is shifted by a value). I need to derivate the resulted matrix by the column vector of the shifting values.
In other words, what is the derivation of a shifting operator L(Matrix, Row) with respect to row?
Thanks you !

[fiery spire]

<@&286206848099549185>

[devout wraith]

French?

[fiery spire]

Pourquoi pas!

[devout wraith]

if so i can help you i don't speak english well

yes french? lol

[fiery spire]

Yes I don't mind if it is in french

[devout wraith]

d'accord, alors tu fais la matricielle du droit en souhaitant la dérivée et en l'a considérant comme nul, soit l'équivalent de 0. Sinon la vectorielle me paraît simple et donc tu fais comme dit avant : tu considères nul la valeur et tu as de quoi faire ton exercice. Et essaye de le résoudre en 2éme degré (= quadratique)

[fiery spire]

Merci pour ta réponse, mais je n'ai pas vraiment bien compris, est ce que c'est possible d'avoir un exemple

[devout wraith]

Ah désolé, sinon tu peux attendre d'autres helpers je suis désolé, je suis pas très bien doué en démonstration d'exemples, lol

sorry, have a good day

[fiery spire]

Alright, thank you in all cases

<@&286206848099549185>

[lone heart]

@fiery spire Has your question been resolved?

[lone heart]

@fiery spire Has your question been resolved?

[fiery spire]

<@&286206848099549185>

[alpine sable]

Hi, are you trying to implement this in a programming language, or just looking for a formula ?

[fiery spire]

Trying to inplement this in pytorch (python)

[alpine sable]

I see, I think there is a shift function in python for arrays. you can write a loop on the rows of the matrix, and in each iteration i , the row i will be shifted by the ith element of the vector of shifting values

[fiery spire]

The shifting is implemented for the forward pass

but the backward pass require the derivation of the shifting with respect to the input which is the latencies (thee column vector)

I am stuck in the backward pass

If there is a formula, it may help

[alpine sable]

I am not familiar with these terms (never worked with pytorch), but if you already have the vector of shifting values, what's preventing from writing the loop inside your code.

[alpine sable]

I don't think there is an easy formula for shifting each row with different values, we can permutate rows and multiply them by constants (elemntary row operations) and even shift the entire matrix, but individual rows, not to my knowledge

[fiery spire]

I don't know how to derivate an operator, shifting is not an function is an operator in math

I don't know how to derivate it

[alpine sable]

what do you mean by derivating ?

[fiery spire]

derivation

sorry for my english x)

[alpine sable]

haha english isn't my native language either.. so you want the derivative of an operator ? why doing this

[alpine sable]

well shifting is a multiplication by a specific matrix

not sure it's an operator

or maybe could be defined as such

but how is the derivative relevant here

[fiery spire]

Shifitng is like a trnaslation in math

f(x-a) where a is the translation, equivalent to a shifitng value

If we can derivate of a row vector with respect to a single shifting value. It would help

[alpine sable]

well if you have a matrix instead of a function f, shifting a matrix a row down for example is equivalent to multiplying it by a well known matrix (all of its coefficients are zeros except one coefficient in the desired row, or something like that)

[alpine sable]

I don't understand here

we usually calculate a derivative with respect to a variable

[fiery spire]

How to find this matrix, a genearl formula

[alpine sable]

not a fixed value

[alpine sable]

as far as i know don't think there is a formula, look at this example

notice the matrix A was shifted down when we multiplied it by S

in the left

but this is shifting an entire matrix

not one row individually

[fiery spire]

I have tried already to shift with a matrix didn't work, on python I used broadcasting indexes to shift each row indivudualy, and it worked without a need to a loop

[fiery spire]

Assuming that we have a vector and we shift its elements with a x pixel.

How to derivate the new vector produced with this shifting, with respect to x.

Assuming x = 1

[alpine sable]

I guess you just need to multiply this vector by the column vector $(0, 1, ....,0)^T$

[ocean seal]

AimaneSN

[alpine sable]

I think a general formula (for shifting vectors) would involve the delta kronecker symbol, but not sure how to write it

[fiery spire]

It would produce a scalar

[fiery spire]

Can you give more details please, not familiar with knonecker symbol

[worn fox]

take the identity matrix and move all the columns to the right, that'll shift your vector down by one

[alpine sable]

Sorry you're rightt, we should multiply it by a matrix where the first column vector is $(0, 1, ....,0)^T$ and all the remaining column vectors are zeros, but not sure, I need to write this down

[ocean seal]

AimaneSN

[alpine sable]

it's simply $\delta_{i,j}=1$ if i=j, and 0 if not

[ocean seal]

AimaneSN

[alpine sable]

it should be useful here because we only deal with 1's and 0 's

[fiery spire]

Still can't figure out a derivation of the row with this symbol

[alpine sable]

multiplication in the right? in the left?

[worn fox]

uh on the left

[alpine sable]

Ah I see

[fiery spire]

No he mean that the identity matrix is shifted right to get the targeted shifting with the row

[alpine sable]

Oh

you mean the matrix S

[fiery spire]

yes

[worn fox]

i was specifically referring how to go from the first vector here to the second

i gather your problem is more complicated than just that

[fiery spire]

As it seems yes

[alpine sable]

I really think it's better to work on the problem using shift functions in python, even if there is a math formula it would be complicated to implement it in python

[alpine sable]

why can't you shift the vector simply using a shift function, or is it not possible

[fiery spire]

I have implemented the shifting, it is not the problem, the problem that pytorch is not able to derivate it alone, I have to do it manualy

[fiery spire]

The derivation problem is not easy not the shifting

[alpine sable]

again not sure what you mean by derivation here

do you mean this

https://mathinsight.org/derivative_matrix

[fiery spire]

This

[alpine sable]

well this is shifting, no ?

you said it's not a problem

[fiery spire]

Yes the shifting part is done but the derivation not

derivation of the shifting output with respect to the latency

[alpine sable]

still don't understand here

can you give an example

[fiery spire]

Not sure if you would accept it, but would you like to organize a meet (goole meet)

It would be easier to explain

[alpine sable]

would like to but on my phone here haha

yeah it's difficult to explain this by writing

[alpine sable]

so the output is a matrix right ?

[fiery spire]

Yes

For a second

forgot everything that I have already said

[alpine sable]

and you want the derivative of this matrix wrt to something?

[alpine sable]

okay nvm

[fiery spire]

I will explain with the simplest example possible

[alpine sable]

okay

[fiery spire]

Assuming that we have a vector, using a shifting function (already existing and working perfectly), it is shifted by x pixel.

[alpine sable]

yes I get that

Okay it''s shifted

[fiery spire]

Example if x=1

[alpine sable]

okay

[fiery spire]

thius only an example, x is a variabl

variable*

[alpine sable]

okay and then

[fiery spire]

so : output_vector = Shifting(input_vector, x)

All I need is derivation of output_vector with respect to x

[alpine sable]

yes that's what I meant

[fiery spire]

d(output_vector)/dx

And so do I x)

[alpine sable]

haha I think I understand now

but one question

why do you need it

[fiery spire]

I am working on ML project that include this idea

[alpine sable]

Oh I see

but I mean

let's say you have this derivation

what's the next step

[fiery spire]

When we are training neural network model, we have to retro propagate the error

using backpropagation

[alpine sable]

one remark here, I think you already know that the derivative doesn't always exist. Not everything is differentiable. I suspect "derivative of a vector" simply doesn't make sense.

[alpine sable]

Oh.. looks interesting

[fiery spire]

This is what I am afraid of

[alpine sable]

we know that some functions in math don't have a derivative

also when you write something like d(output)/dx

this means x can have infinitesimal change

but x in your example only takes the values 0, 1 , 2

this is obviously not infinitesimal

x can't be for example 0.0001

[fiery spire]

I wouldn't mind if there is an approximation, it is allowed in ML

yeah I see

[alpine sable]

I see. so let's say that instead of d(output)/dx we just say we're looking for the rate of change $\frac{\Delta(output)}{\Delta x}$

[ocean seal]

AimaneSN

[fiery spire]

Yes possible

[alpine sable]

I am not sure $\Delta(output)$ means anything here either, we're simply calculating a difference between a vector and its shift

[ocean seal]

AimaneSN

[alpine sable]

doesn't seem to make any sense

[fiery spire]

It make sens in ML, beleive me x)

[alpine sable]

haha

[obsidian cave]

If you're training the model by gradient descent, I'm not sure how it would work with a non-continous operation like shifting

[fiery spire]

If we can find a way to make a continuous approximation possible, seems possible

[obsidian cave]

For a particular row, the value of the shift will be an integer. Say the loss is high when the value is 2, I couldn't imagine a way for the model to predict what the loss to be when increasing or decreasing the shift because it could change drastically, the next minima could be at 12 with no gradient leading towards it

Then again not saying it's impossible, just saying it's difficult for me to imagine how it could be done

[alpine sable]

yep i had similar ideas.. the number of shifts can be anything so $\Delta(output)$ doesn't seem to have a formula at all, and it's certainly not a continuous variable

[ocean seal]

AimaneSN

[fiery spire]

Even if it is not a continous, I suppose that the output of this derivation is a vector of 1 and 0,

[alpine sable]

usually approximation goes from continuous variables to discrete variables, I am not familiar with the inverse, or if it's possible in this case

[alpine sable]

it can also be -1 I think

[fiery spire]

I can just multiply this vector by continous function like this one

The result will be continious

[alpine sable]

if you do this you no longer have values that make sense I think

[fiery spire]

Nono

I am confusing with an other thing

[fiery spire]

Yeah I am comfusing with another thing

doesn't make sens

seems that it is not possible to create

[alpine sable]

yeah that's what I suspect

the values this vector takes aren't continuous

there has to be some other way to approach your problem

[fiery spire]

can't see how

[alpine sable]

it depends on what you want to do with the shifted vector

that's what I don't understand

[fiery spire]

Are you familiar with ML loss backprobagation

[alpine sable]

nope not at all

[fiery spire]

If not, in order to reduce the loss (difference between targeted output and the current output)

For each parameter of the model, we derivate the loss by this parameter

the new parameter w = w - alpha * (d(loss)/dw)

alpha is the learning rate, somehow how quick with your model converge to the ideal parameter

loss is the produced by differente layers which means for example loss = f(g(t(y(input)))

[alpine sable]

Ah I see

[fiery spire]

so the derivation d(loss)/dw = df/dg * dg/dt * dt/dy * dy/w

chain derivation

[alpine sable]

I suppose the loss function must be differentiable

[fiery spire]

those internediate function have to be differentiable

so the d(loss)/dw wouldn't be 0

[alpine sable]

okay, but as I said you don't have the right to write d(loss)/dw unless loss(w) is differentiable

[fiery spire]

if so our parameter can not learn, to be stuck, so the loss never tend to 0

[fiery spire]

yes which means that all f g t y function have to be differentiable

in my case one of them which is the shift function, is not differentiable

[alpine sable]

Yep that was the problem

I think the shift should be replaced by something else

[fiery spire]

I have to find out n approximation or a trick to make it differentiable

[fiery spire]

I can't in my model

[obsidian cave]

Which matrix exactly are you shifting?

[fiery spire]

the input, typical all images of a dataset

[obsidian cave]

and the dataset is labeled?

[fiery spire]

yes

In my case it is a supervised classification

[obsidian cave]

which loss function are you using?

[fiery spire]

CrossEntropy

[obsidian cave]

classification? so where does the row shifting come in?

[fiery spire]

row shifting are parameters to train

this why I have to derivate with repect to them

[obsidian cave]

the parameters themselves are being shifted?

why not backpropagate normally?

[fiery spire]

No

inputs are being shifted

and shifting parameters have to be trained by backprop

[obsidian cave]

Ah I see

And just to be sure is the amount that each row should be shifted in the labels?

[fiery spire]

No

the amount that each input should be shifted is a parameter, like weight and bias

[obsidian cave]

Im sorry Im confused