help-27

[flat marlin]

Because a double negative makes a positive

[crystal temple]

ahh

i get you

[flat marlin]

And that’s why k is so straight forward

because it’s +k

so +-1 is still -1

++1 is 1

[crystal temple]

just one question tho where does this come from

the x-

[flat marlin]

The vertex form

a(x-h)^2+k

The vertex is (h,k)

[crystal temple]

ahh

i get you

thanks alot bro

ur rlly smart

[flat marlin]

No problem! And thanks!

That’s honestly a good question to ask too, I’m pretty sure in my class it didn’t get explained at all, just that the inner portion is the opposite and the outer portion is normal

[crystal temple]

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[deep quartz]

Consider ∞ + ∞ = ∞ in theory.

I have a question about this basic infinity operation. Is it not a fallacy and impossibility to add anything to infinty without rendering it finite? Let's define ∞ as "endless". In order to add one thing to another, both things must be well-defined (having well-established boundaries/parameters). If I attempt to add anything at all to an endless thing, that directly implies that the endless thing must actually end such that that which is being added to it can be properly defined as a distinct entity from the infinite endlessness?

I hope this comes across well, it is difficult to articulate and yet appears to me as clear as a noonday sky.

In order for another thing to "begin" (having an well-established border or boundary) and thereby exist as a definite object, it is necessary that that to which it is being added must also ackowledge this preliminary boundary maintaining the definitity of the addend. So, to add any definite thing to infinity would thereby implicitly state a fallacy in that that infinity cannot be infinite because it is limited by the perimeter where its addend begins and where thereby it must also end.

Therefore, I premise that ∞ + n = error/indefinite because to add a thing to infinite states that it is no longer infinite but that it has become finite such that the addended may be introduced.

Does this make even a lick of sense to anybody else besides me? I know that what I'm trying to explain is valid and correct but there was still a real struggle to properly articulate it.

[hybrid snow]

Infinity is not a real number

It likes to break shit

[uncut crow]

that's just like

philosophy

and doesn't have anything to do the symbol ∞ in math

[restive river]

you cant do operations with infinity

it simply represents increasing without bound

[uncut crow]

there are operations with "infinity" (i'm talking the extended real number system) but people usually misunderstand what that means anyway

[hybrid snow]

Infiniteez nuts

[wooden wraith]

Finally a clear answer

[hybrid snow]

For 16 years I have wandered this earth just to say such things

[uncut crow]

16 years? that explains it

[hybrid snow]

I'm a real philosopher

[devout snow]

@deep quartz Has your question been resolved?

[wooden wraith]

I mean, you're right that inf + n is not well defined, at least in "typical" number systems. But that's simply because inf is not an element in typical number systems, like the reals.

It has nothing to do with infinity having to "end" so that we can add something to it

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[silver sage]

i know its not in english but i can translate if you want, but i guess what really matters is understandable

[devout snow]

@silver sage Has your question been resolved?

[silver sage]

<@&286206848099549185>

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[gritty cloak]

give a Cartesian equation of the plane passing through C and containing D1

help plz

[devout snow]

@gritty cloak Has your question been resolved?

[devout snow]

@gritty cloak Has your question been resolved?

[devout snow]

@gritty cloak Has your question been resolved?

[gritty cloak]

Plz

[devout snow]

@gritty cloak Has your question been resolved?

[gritty cloak]

@restive river

Plz

[restive river]

yes

[last swan]

https://math.stackexchange.com/questions/253635/equation-of-a-plane-given-point-and-line

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[dapper gazelle]

Your friction direction is wrong

Your normal direction is wrong

Only correct directions are rope and gravity

Directions matter.

[rare mantle]

what direction should it be?

[dapper gazelle]

I'm not going to read the working but I'm not sure if fixing the directions will help, but the should

[rare mantle]

why wouldn't the friction be parallel to the ground? I'm confused

same with normal force being perpendicular to the ground

[dapper gazelle]

Hmm

I was assuming the box was at an incline

You make a good point

,w cos(35 degrees) * 60

[woven radish]

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[rare mantle]

yeah sorry for the lack of work lol

Fg was of course 9.8 * 45

[dapper gazelle]

,w 459.81sin(35 degrees)

[woven radish]

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[dapper gazelle]

,w 459.81cos(35 degrees)

[woven radish]

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[dapper gazelle]

,w 60 * sin(35 degrees)

[woven radish]

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[dapper gazelle]

,w 0.12 * (45 * 9.81 - (60 * sin(35 degrees)))

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[dapper gazelle]

,w 0.12 * (45 * 9.8 - (60 * sin(35 degrees)))

[woven radish]

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[dapper gazelle]

@rare mantle It doesn't feel like the problem is set up correctly

[rare mantle]

hmm

how so?

[dapper gazelle]

49.14 - 48.79 is very big

It's not something that can be explained away

Ask your instructor, but most likely the question is wrong

[rare mantle]

hmm okay thank you

[dapper gazelle]

By the way

The friction here is assumed kinetic

yet static friction by usual cases is higher

so a constant force on a constant friction case, when it moves, should actually be accelerating in the usual case

if not the object doesn't move

Finally the setup is weird, no actual rope maintains a fixed angle at 35 degrees when an object is moving horizontally

Everything is weird about this setup

[rare mantle]

yeah..

welp I'll ask my teacher thanks

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[pulsar geode]

Help it’s a simple question

[pulsar geode]

How can I type no absolute in here

The answer for both is no absolute

[quaint citrus]

U sure?

[pulsar geode]

It’s not?

[quaint citrus]

How’d u get that?

Remember, it’s a closed interval

[pulsar geode]

Okay lemme see

Yea I can’t

[quaint citrus]

So what’s f’(x)

[pulsar geode]

-1<0

[quaint citrus]

Right, -1 isn’t equal to 0

So no critical points

Since we have a closed interval , where else can we look?

[pulsar geode]

Absolute extreme

Oh I was hella wrong

It’s

-1,9

4,4

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[tight estuary]

I think I got this wrong, could someone check my work please

[tight estuary]

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[restive river]

I have problem

[restive river]

Jm showing 1min

I have to simplify but jm confuse

( a+b) ( a2 - 2 a b + b2) - 2 a2 b

[devout snow]

@restive river Has your question been resolved?

[restive river]

just expand

the product

[restive river]

thanks but fixed

[restive river]

what?

i mean i did it

.close

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[upper mortar]

quick question, how is (1)/(2*sqrt(x)) given by the power rule for sqrt(x)

how im thinking about it is x^(1/2) -> (1)/(2x^-1/2) which is how i think the power rule is supposed to be done
where i wrong?

[wooden wraith]

$\frac{d}{dx} x^{\frac{1}{2}} = \frac{1}{2}x^{-\frac{1}{2}}$

[woven radish]

tatpoj

[upper mortar]

truth

[wooden wraith]

Then, what does the exponent of -1/2 mean?

[upper mortar]

it means sqrt(x^-1)

or base -2 sqrt(x)

[wooden wraith]

That's true, it also equals (sqrt x)^-1

[wooden wraith]

not sure what you meant by this

[upper mortar]

like the cube root has base 3

negitive square root has base -2

or is it called something else

[wooden wraith]

Oh I see, don't worry about that

Do you know what x^-1 means?

[upper mortar]

1/x

[wooden wraith]

What about x^-2 ?

[upper mortar]

1/sqrt(x)

1/x^2

[wooden wraith]

right

[wooden wraith]

so yeah, x^-1/2 means 1/sqrt(x)

[upper mortar]

and then u multiply it by 1/2

that makes so much sense

[wooden wraith]

mhm

👍

[upper mortar]

dope ty that helps a ton'

have a great day

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[jaunty mantle]

What have you tried

[devout snow]

@jaunty dagger Has your question been resolved?

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[tiny rain]

ok yeah i need help for this lol

@late niche @restive river XD

[restive river]

hi

[tiny rain]

hi

[restive river]

hi hello

XD

[tiny rain]

ive encountered another brain death question

hmm

could we use a binary search tree for this

[restive river]

how would that work?

[tiny rain]

hmm

[main gull]

Fyi don't ping specific people

[tiny rain]

oh ok lol

i just assumed they were okay with it haha

[main gull]

Well you shouldn't assume

[tiny rain]

[restive river]

i was thinking more like

i mean its a graph

lol

[tiny rain]

ah

i dont think

its that graph

[restive river]

just not a graph with points

[tiny rain]

yea XD

[restive river]

but if you could represent that with graph then idk

[tiny rain]

hmm

non-overlapping..

[restive river]

this is a really dumb way

but you could draw a number line with every single start/end time

then

whenver theres a job, you choose a new color and draw a line between the two points

but on the way you include every other point you pass through

idunno

[tiny rain]

tbh

[tiny rain]

thats exactly this

but in a more graph -theory manner

[restive river]

yeah

idk how

other than what i said

[tiny rain]

hmm

i still have the feeling that we need to us etrees

[restive river]

i dont really see how trees can be involved...

cuz its not like ur going downwards

[tiny rain]

lemme draw an example

[tiny rain]

ok yeah i dont see it anymore

LOl

LOL

@restive river

would this make sense?

like, to find "groups" that dont overlap

ill go down the tree on the left and at the same time, on the right

till right.min > left.max

[restive river]

hmm

sorry i had to brb

i dont really get it lol

[tiny rain]

hmm

because like, the at every node it contains the min and max of both left and right subtrees

a better example

[restive river]

oh

[tiny rain]

so here a clear nonoverlapping set is all the elemnts under two nodes that dont overlap

i guess

idk

like (1,7) isnt in (13,15)

i mean

(1,7) isnt in (11,30)

[restive river]

i mean this only works for a speific case

[tiny rain]

so every node under (11,30) and (1,7) are non overlapping sets

oh wut

[restive river]

what if the jobs are like (1, 2) (3, 4) (6, 23)

like if theyre all seperate this doesnt really work

[tiny rain]

erm

but if they are all separate, their x and y wont overlap

so i could just return all of them

oh wait

[restive river]

this isnt a computer program

XD

"return"

[tiny rain]

XD

right.. this wont work

[restive river]

lol

[tiny rain]

ok lemme just wait for the official answer

ive been stuck at this for too long

[restive river]

alr

[tiny rain]

ah

my brain

adjsa9idajsd

ded

wtf

[restive river]

LOL

[tiny rain]

brehhhhhhh

BREH

[restive river]

OMG its send + more = money!!!!

[tiny rain]

BREEEEEEEEEEEEEEEEEEEEEEEH

[tiny rain]

THIS IS THE VIRUS ONE CONTINUED

ded

brhehehehe

[restive river]

this is so sad

[tiny rain]

i hate my life

[restive river]

oh this looks interesting

[tiny rain]

wiw

[restive river]

that was all problem 1

[tiny rain]

wow

[restive river]

💀

i need to sleep now

byee

[tiny rain]

ded

byeye

thanks

.close

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[sleek estuary]

if not then why is the bound of floor(x) x-1 and x

😦

[wooden wraith]

No, it's not like some kind of definition for the floor function, just a statement about it.

Take each side one at a time

floor(x) <= x

Do you agree with that?

[sleek estuary]

yes

[wooden wraith]

That's the right half of the inequality

The left half then

x-1 <= floor(x)

I think it's not too hard to convince yourself of this either

the floor is never more than one unit less than x

[sleek estuary]

hmm

okay what if let's say we got x^2

then it would be

x^2 - 1 <= floor(x^2) <= x^2

right?

[wooden wraith]

Yes, that's true

[wooden wraith]

Do you see why this is true?

[sleek estuary]

on this one

[wooden wraith]

What's floor(3.99999)?

[sleek estuary]

3

how is 3.9999999 - 1 = 3

[wooden wraith]

It's not

We said x-1 <= floor(x)

not x-1 = floor(x)

[sleek estuary]

ohhh

yea

[wooden wraith]

In other words, x-floor(x) <= 1

The floor function never reduces the number by more than 1

If it did, it would go past another integer

[sleek estuary]

yeaa

okay wait

I will do this

wait wait

is floor(x) * floor(x) = floor(x^2)?

[wooden wraith]

No,

for example 2.5^2 = 6.25

[sleek estuary]

hmm if I can't just multiply by floor(x)

does that mean I can just do this:

4x^2 - 5x + 1 -1 <= [4x^2 - 5x + 1] <= 4x^2 - 5x + 1

actually this ^

[sleek estuary]

because you said this

[wooden wraith]

Yes this is true

[sleek estuary]

LETS GOOO

wait I got 1 more question lemme just find the example in the ppt

[wooden wraith]

Ahh, now this is a piecewise definition of the floor function

The ... is just showing that the pattern continues in both directions

[sleek estuary]

oh ok

[wooden wraith]

It's true, don't you agree? For example, [x] = -2 if -2 <= x < -1 ?

[sleek estuary]

ohh yeah

because if we had -2 <= x <= -1 and x was -1 then it would be wrong

[wooden wraith]

Right, [-1] = -1

[sleek estuary]

WWWWWWWWWWWWWWW

[devout snow]

@sleek estuary Has your question been resolved?

[devout snow]

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[serene quarry]

howcome thats the domain and range?

and also for this one

[polar bolt]

Because thats the input you can plug in?

[serene quarry]

what does the xetr mean

or yetr

[polar bolt]

What?

[ancient furnace]

Pretty sure it’s just an R

Like x belongs to real numbers

[serene quarry]

hmm

by xetr i mean this

i think i might be reading it wrong

[polar bolt]

${x \in \bR}$

[serene quarry]

and it might be XER but weirdly formated

[woven radish]

ScapeProf

[serene quarry]

yeah

[polar bolt]

That is what that is

[serene quarry]

what does it mean?

[polar bolt]

The set of real numbers

[serene quarry]

ah ok

so if x were to be 2 would it be something like

${2 \in \bR}$

[woven radish]

Friznap

[polar bolt]

What?

${x \in \bR}$ means $(-\infty,\infty)$

[woven radish]

ScapeProf

[polar bolt]

If you prefer that notation

[serene quarry]

ohhh

so it means it can be any set of points? sorry im a little slow

[polar bolt]

It can be any number (in the real numbers) yes

[serene quarry]

okay thank you

[serene quarry]

wait, so then what would the domain for this mean?

[polar bolt]

$[-3,-1]$

[woven radish]

ScapeProf

[serene quarry]

but what does this mean?

howcome theres a line in the middle

[polar bolt]

Means what I wrote above?

[serene quarry]

ohh so thats just the point

[polar bolt]

What?

No

[-3,-1] is all values between -3 and -1 (inclusive)

So say -2, -1.4, -1.2782828171661818171617817161,…

[polar bolt]

That line means “given”

[serene quarry]

so what its saying is the the function is the set of real numbers given [-3, -1]

[polar bolt]

What?

1. Don’t mix notation

Either say the x in R given -3<=x<=-1 or [-3,-1]

2. a function is just a function, what is “the function is the set of …” supposed to mean?

[serene quarry]

im not sure its all new to me

but i get what youre saying

ohhh.. i think i caught on

so i dont need to write the whole equation of this out

instead i can just write [-3, -1]

unless im wrong

[polar bolt]

They mean the same, yes

[serene quarry]

okay thank you i appreciate it

[devout snow]

@serene quarry Has your question been resolved?

[devout snow]

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[restive river]

want to know the final answer of this question

[bright burrow]

Im guessing partial fractions?

[restive river]

which app?

[bright burrow]

Maple calculator

But usually it's recommended to use wolfram

[restive river]

not getting the same answer 😦

[bright burrow]

There could be multiple answers

As in you can check on desmos

f(x)= your answer

f'(x)

[restive river]

i don't know how to use desmos

[bright burrow]

If f'(x) graph matches with the graph of the integrand

Then your answer would be correct

[restive river]

could you please check it for me?

[bright burrow]

It would be better if you learn it by yourself imo🤔

[restive river]

ok i'll try

how to type my answer there?

[bright burrow]

^

[restive river]

i am getting this :c

[bright burrow]

Doesnt open for me, can you send a screenshot

https://www.integral-calculator.com/

This is also another website i use

[bright burrow]

Which colour is what

[restive river]

red-the answer which i got

and blue is for the derivative of the function

[bright burrow]

Hide the red colour

[restive river]

how?

[bright burrow]

And in another line write out the integrand, and check if it overlaps the blue

[bright burrow]

Click on the red colour

[restive river]

its not

i lost my graph 😱

[bright burrow]

What is your answer😞

[devout snow]

@restive river Has your question been resolved?

[supple knot]

👻 'd

[devout snow]

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[tiny rain]

@uncut crow hi 🙂

[uncut crow]

[tiny rain]

its like the typical olympiad question but steriods

[uncut crow]

i’m thinking about it but it might be too hard for me T_T

[tiny rain]

[manic sedge]

FORTY + TEN + TEN = SEXY

[tiny rain]

[manic sedge]

Yaameto qudasai

[tiny rain]

@uncut crow hmm, im thinking that we could separate the letters above the ---- and under, into bipartite graphs

nvm wat am i saying

we cant

[uncut crow]

what i’m struggling with is how to implement the digit position

like 1s or 10s or 100s or 1000s

[tiny rain]

what have u come up with

[uncut crow]

nothing really lol

[tiny rain]

O.o

hmm

for this we def gotta use directed graphs right

[uncut crow]

yea i’d say so

[tiny rain]

hm

we dont usually contain duplicated vertices

in a graph right

[uncut crow]

no

[tiny rain]

um

so we dont orr

[uncut crow]

oh sorry, no we don’t loll

[tiny rain]

this is so hard

[uncut crow]

[tiny rain]

AAAA

[uncut crow]

it might have to be a really big graph

[tiny rain]

i literally have nothing

[tiny rain]

yes

the foolproof way would be like

every permutation

LOL

just label all the nodes as such and find all possible permutations

mmm yes exponential time complexity

[uncut crow]

.-.

[tiny rain]

how would we even represent something like

x + y = z

yeah i have no idea..

[tiny rain]

actually i think the next part provides a hint (sort of)

it says should u use BFS or DFS

[uncut crow]

that’s not much of a hint to me .-.

[tiny rain]

hmm

maybe the end of arrowss represents "add"

then if the node is a leaf, its the result?

so A add B = C add A

dammit

this is so hard

[devout snow]

@tiny rain Has your question been resolved?

[uncut crow]

@tiny rain do you know about weighted graphs?

[tiny rain]

yes

[uncut crow]

that’s probably needed here

i think in however you set it up, edges could be weighted for how much the vertices are valued

[tiny rain]

hmm lemme try again with this new clue

[devout snow]

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[rough shard]

Can anyone help me with this question: John wanted to buy a coat that was $5500. He invested $700 at a rate of 3.6% for 4 years. How much does he have to pay monthly?

[restive river]

John is an idiot

[uncut crow]

hey it’s gotta be an amazing coat

[azure sun]

well is it compounded or simple

[rough shard]

Simple

[azure sun]

is the rate monthly or yearly

[rough shard]

Yearly

[azure sun]

is it compound interrst or simple interest

[rough shard]

Simple

[restive river]

So it is growing linearly?

[rough shard]

It was a question that popped up in my friend’s 8th grade maths test

[azure sun]

yes

[restive river]

Yeah just find 3.6% of 700 and add that for 4 years

[azure sun]

yes

[restive river]

Don't know why my guy is waiting for 4 years to get a coat

But you know what

Not judging

[rough shard]

What’s the answer

[restive river]

.

700 + 4(x) and x being whatever number u got from that

[rough shard]

ok

[azure sun]

well he cant buy with that rate

after 4 years the value he get back will be 800.8

dollars

[restive river]

Oh the question is how much he needs to pay monthly

With the investment he made? Well that's kinda going to be insufficient

[rough shard]

what do you mean by insufficient

[restive river]

800 dollars is not getting you a 5500 dollars coat

[rough shard]

ok

that makes snse

sense

does John have to pay 4800 or 5500? Does the investment of 700 count as he paid

[restive river]

the question does not make sense or specify anything

[rough shard]

oh ok

[restive river]

did he buy it with installments?

if it is monthly then he has to pay like 114 dollars a month

but most companies would give u like an interest on that

[rough shard]

114 for 48 months?

[restive river]

and even then, did he buy it when he deposited his investment into the bank or four years later?

it is vague lmao

[restive river]

yes

about that

u can round to 115 ig

[rough shard]

so the investment of 700 doesn't count as paid

[restive river]

i mean if he paid with it then he is not really investing anything

[rough shard]

oh ok

[restive river]

idk it seems like they mashed up two completely different questions together lmao

the question is nonsensical

[rough shard]

true

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[devout snow]

@muted sierra Has your question been resolved?

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@muted sierra Has your question been resolved?

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[frank sun]

https://i.imgur.com/xe9zvYz.png

[frank sun]

why is a1 and a2 equal to zero

[magic pine]

you began with the assumption that y is a polynomial, so if you multiply it by x^2, the smallest power of x will be at least 2

so the coefficients for x^0 and x^1 must be 0

[frank sun]

oh oke

one more thing i dont understand is how they get a3=162/3 (basically how they got the an+1= 1/(n+1) part)

nvm got it

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[serene leaf]

Would anyone know how to do this?

[serene leaf]

I've just started my math course and it's legit killing me

and I have barely any clue on how to tackle this question

[wooden veldt]

Just treat the i j k as variables and distribute like normal

If you can expand things like 5(x+2y) you can do this question

[serene leaf]

so it's legit just treating those as the same way you'd treat a normal variable?

so the answer would just be

-37i-9j+47k?

[wooden veldt]

Yes

[serene leaf]

perfect

and then representing the vector in form xyz...?

would it just be throwing it onto a graph?

[wooden veldt]

i=(1,0,0), j=(0,1,0), k=(0,0,1)

[serene leaf]

okay...

thanks for the help

!

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[restive river]

If Z is defined as this and there is ¬Z in my task is it all natural numbers excluding natural cubic numbers or all real numbers excluding natural cubic numbers?

[stone stump]

can you give the whole problem completely as stated?

[restive river]

If you need any part translated

[stone stump]

well it says universe N

so everything is with respect to that

[restive river]

oh I see

thank you

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[strong pike]

Could someone please tell me where the -5 comes from and why it's like that? It's the only equation i don't fully understand.

[sonic smelt]

They moved 6 * 2^x to the other side

Making it 2^x - 6 * 2^x = -10

[strong pike]

I get it now, thank you, very confusing at first.

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[candid forge]

Hey hi, I have a question about using scipy to estimate a parameter of a pdf.

[candid forge]

We've been given a dataset and a pdf of a distribution, and we're asked to use 2 different methods to find the parameter of this pdf.

this right here is my pdf, so it's something... weibull? ish?

and we're asked to find the parameter Theta such that this pdf is the best fit for our dataset. So i did some googling, and now i want to us the rv_continuous class from scipy to be able to do stuff with this

and i cannot for the life of my figure out how to use it correctly

so i have no clue what i am and what i am not inheriting - and i have no idea how to then write the function correctly

if i do this:

and if i don't define it, i have no clue how to get that scale parameter into my function

[devout snow]

@candid forge Has your question been resolved?

[devout snow]

@candid forge Has your question been resolved?

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@candid forge Has your question been resolved?

[candid forge]

.close

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[maiden zinc]

how can i calculate cos(arccos(1/4) + arccos(1/5))

[scarlet sequoia]

use cos(A+B)

[maiden zinc]

good idea

[scarlet sequoia]

then cos(arccos(x)) = x (for |x| <= 1)

and for sin(arccos(.)) u can use right triangle

[maiden zinc]

it's sqrt(x - 1) right?

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[restive river]

Can someone help me decipher this task?

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[restive river]

Define X := {3, 5, 7}, Y := {2, 4, 6, 8}, Z := {n³ : n ∈ N}
How do I solve v) ?

[restive river]

the unions/intersections are finite, so you could write out all twelve sets

Sorry, what do you mean with all twelve sets? Which twelve sets?

the twelve sets {x+y} for every x∈X and y∈Y

Can you please help me out here? I dont know how you got 12

there are 3 elements in X and four elements in Y, so there are 12 combinations of x and y

(note that they may not be distinct)

try working out the thing inside the brackets first, before working out the intersection

Combinations as in {3,4},{3,2},{3,6}, {3,8}, {5,2}, {5,4}, {5,6}, {5,8}, {7,2}, {7,4}, {7,6}, {7, 8}

And now what? Sorry its late and my focus is gone

yeah

fix x first, then find the union over all y's

then intersect those three sets

So the intersection of {3,5,7} with {{3,4},{3,2},{3,6}, {3,8}, {5,2}, {5,4}, {5,6}, {5,8}, {7,2}, {7,4}, {7,6}, {7, 8}}?

Its zero

no

write out the set U_y{3+y} first

then instead of 3, also put 5 and 7

What would the set of U_y{3+y} look like? Sorry, I'm not too familiar with the notations yet

[devout snow]

@restive river Has your question been resolved?

[restive river]

the union of sets {3+y} for all y∈Y

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@restive river Has your question been resolved?

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[fossil moth]

If the radius of a sphere is increasing at a rate of 3 cm per second, how fast is the volume increasing when the radius is 4 cm?

[fossil moth]

my answer is 804.25 but that doesnt seem to be right

[vivid cliff]

do i#u know

do u know

the chain rule

for this qn

$\frac{dV}{dt}=\frac{dV}{dr} \cdot{\frac{dr}{dt}}$

[woven radish]

Springsskateboard

[fossil moth]

yea

[vivid cliff]

yeah so wats the expression for dV/dr?

[fossil moth]

(dV/dt)/(dr/dt)=dV/dr

[vivid cliff]

no I mean

u know V=$\frac{4}{3}πr^3$

[woven radish]

Springsskateboard

[vivid cliff]

so what’s dV/dr

[fossil moth]

shiiit, wait so V is dV/dT and the right is dr/dt

[vivid cliff]

wdym V is dV/dt?

[fossil moth]

deriving v is equal to dv/dt

[vivid cliff]

no

it’s equal to dV/dr when u find derivative for V

$V=\frac{4}{4}πr^3$

[woven radish]

Springsskateboard

[vivid cliff]

do u see any t here

there’s r

[fossil moth]

no sir!

[vivid cliff]

yeye

so when u differentiate its with respect to r

[fossil moth]

ok that makes sense

[vivid cliff]

pretend that said 4/3

ye so

differentiate V

[fossil moth]

v'=4/3pi3r^2?

or v'=4pi r^2

[vivid cliff]

yep

so dV/dr=$4πr^2

so rmb the chain rule

$\frac{dV}{dt}=\frac{dV}{dr} \cdot{\frac{dr}{dt}}$

[woven radish]

Springsskateboard

[vivid cliff]

what u want to find

is how fast the volume is increasing

that means dV/dt is what Ure finding

they gave u info that radius is increasing 3cm/S

that’s dr/dt

$\frac{dV}{dt}=\frac{dV}{dr} \cdot{3}$

[woven radish]

Springsskateboard

[vivid cliff]

we just found dV/dr

[fossil moth]

so is it just (4pi r^2)3

[vivid cliff]

so

[vivid cliff]

yes

they said when radius is 4

so plug r =4

[fossil moth]

192pi

[vivid cliff]

yep

[fossil moth]

603.19

[vivid cliff]

if ur allowed to leave in terms of pi

[fossil moth]

alright that makes plenty sense

[vivid cliff]

but if not then ye 603.19 works

[vivid cliff]

aye nice

[fossil moth]

thanks a bunch .close

[vivid cliff]

npnp

[fossil moth]

.close

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[mortal dagger]

I am not understanding how to get B in this part:
Imagen

[devout snow]

@mortal dagger Has your question been resolved?

[mortal dagger]

<@&286206848099549185>

Anyone.... please?

<@&286206848099549185>

Damn

Thanks for the help

.close

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[tender pond]

Hi so im just re entering trig for grade 11 and need to jog my memory. This problem is pretty basic but I cant seem to use sin to turn one of my variables into fraction? Im a little lost and need help.

[timid echo]

Use sin rule

U know ABC = 99

[tender pond]

yeah

[timid echo]

So 16/sin(99) = X/sin(42)

[tender pond]

so I did sin99 over 16 and got a decimal that weirdly converts to a fraction

Bu tht efraction is goofy

[timid echo]

And just rearange

[topaz beacon]

Make sure your calculator is in degrees

[tender pond]

alright one sec

so I do sin(99) over 16?

Or is it the other way?

I got 0.0617305 and it doesnt convert to a fraction

Well it does but its very awkward

[timid echo]

Just do 16/sin99 *sin42

[tender pond]

isnt it sin99 over 16

Not 16 over sin99?

[timid echo]

U can use it either way round

[tender pond]

ok

[timid echo]

In this case its better to have 16/ because ur X variable is on top

So answer should be smthn like 10.8?

[tender pond]

Here could you solve it and send me your process

Because im very confused

[timid echo]

Sin rule is

A/sin(A)=B/sinB

The side is a

Angle is A

[tender pond]

So I did it like you said and got 10.839

[timid echo]

Yep that should be right

[tender pond]

But like if you put sin over x vice versa you get different answers

How do I know when to put sin over and x under etc?

[timid echo]

BC then u get sin 99/16= sin42/x

Which is harder to rearange

[tender pond]

And also how did you make it so that you multiply your result by sin42?

[timid echo]

BC I just rearranged 16/sin99=X/sin 42

U just times both sides by sin42

[tender pond]

I see now

Thats kinda weird

[timid echo]

How come

[tender pond]

Well like I didnt even learn this beforehand and my teacher assigned me this

She didnt even explain this technique

[timid echo]

Mm well can't help u with that mate sorry lol

[tender pond]

I know

But thanks still

[timid echo]

Nw

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[patent marsh]

find the slope with $m = \frac{y_2 - y_1}{x_2 - x_1}$ and then find the line with the point slope form: $y - y_1 = m(x - x_1)$

[woven radish]

MellowDramaLlama

[lone mantle]

so the slope is 6

then i got

6--6 =6(1--1)

is that the final answer?

[vivid cliff]

no

[lone mantle]

oh

[vivid cliff]

that’s not how u use the formula

[lone mantle]

then

?

[vivid cliff]

y-y1=m(x-x1)

u know m

which is 6

[lone mantle]

yes

[vivid cliff]

which coordinate do u wanna use

[lone mantle]

1,6

[vivid cliff]

okay

so 1 is x1 and 6 is y1

plug that in

and then simplify

and that’s it

[lone mantle]

y-6=6(x-1)

?

[vivid cliff]

yep

simplify

and u only want y on the right side

[lone mantle]

so my page decided to refresh and give me a new problem

[vivid cliff]

same thing

[lone mantle]

slope is -1

so i just plug in one of the coordinates?

[vivid cliff]

yep

[lone mantle]

y--7 = -1 (x--1) ?

[vivid cliff]

yep

nice

simplify

[lone mantle]

thank you!

[vivid cliff]

npnp

[lone mantle]

.close

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[somber minnow]

what do i choose delta as?

so i have |x-0| < delta

then |f(x) - f(0)| = x^3 + 2sqrt x < delta^3 + 2 sqrt delta

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[short stag]

help huhu

[devout snow]

@short stag Has your question been resolved?

[short stag]

<@&286206848099549185>

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@short stag Has your question been resolved?

[devout snow]

@short stag Has your question been resolved?

[devout snow]

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[wide ember]

i dont understand how the answer can be 39

<@&286206848099549185>

[rotund heron]

Looks like an Indian batsman

Mind showing your work?

[wide ember]

i dont have an idea about how to start

[devout snow]

@wide ember Has your question been resolved?

[wide ember]

<@&286206848099549185>

[rotund heron]

Start out by letting the innings for which his average was 15 as x

[wide ember]

you mean like total runs as x

[rotund heron]

So, his total runs= 15x

[wide ember]

ok

[devout snow]

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[wide ember]

.reopen

[devout snow]

✅

[rotund heron]

Now manipulate the first part of the question algebraically

[wide ember]

ok so thatd be 15x+23/x+1=16?

[rotund heron]

Yes

[wide ember]

x=7?

[rotund heron]

Ye

So his score is? 15x

That would be?

Lmao I keep forgetting the channel

[wide ember]

105

[rotund heron]

So, basically in his next inning he has to make his average 18.

So again assume the runs he has to make in this to be y

[devout snow]

@wide ember Has your question been resolved?

[wide ember]

so 15x+y/x+1=18

[rotund heron]

You already found what x is

So why not plug that in

[wide ember]

105+y=18x8

so y=39?

[rotund heron]

Yay

[wide ember]

whoooo

done

thnks

[rotund heron]

WOOHOO

Have a good day

[wide ember]

you too

.close

[devout snow]

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[devout snow]

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[spring bear]

I am trying to model the inside layer of the bowl knowing the equation for the outside layer and the thickness of the walls

[spring bear]

here is an over- version of the problem

what i have tried is horizontally translating the function righwards which clearly doesnt work since the thickness of the bowl decreases

i am not sure how to find the equation for the inside layer

i though it might have something to do with tangents or sum of horizontal and vertical translation but i am not sure

what math topic could even help me find the equation of the outer layer?

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@spring bear Has your question been resolved?

[spring bear]

<@&286206848099549185>

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@spring bear Has your question been resolved?

[spring bear]

.close

[devout snow]

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[hybrid snow]

Exponent rules

$$a^bc^b = (ac)^b$$

[woven radish]

Umbraleviathan

[hybrid snow]

Exponent product rule

[meager basin]

an index

[woven radish]

Yousuf

Yousuf

[hybrid snow]

It just is

I haven't done a proof on it

Something that proves a theorem or phenomenon

You can probably google it online

Yes that's the binomial theorem

What about it

[devout snow]

@restive river Has your question been resolved?

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[spark magnet]

https://media.discordapp.net/attachments/423244559682764800/1039596345750728824/rn_image_picker_lib_temp_adaa77d1-65d2-43f1-b807-b490937bb1d7.jpg

[pseudo basin]

your first image is not showing up

[spark magnet]

I got smthg liek f(-1/y) =0

[spark magnet]

The second image wud di

Do

[pseudo basin]

k

[pseudo basin]

show work

[spark magnet]

I don't know how to..

[pseudo basin]

i find this hard to read

[spark magnet]

Can u just tell me how to get started or smthg

[grave lance]

u cant put x=0 as that isnt in the domain, instead try getting z=0

[spark magnet]

It is in the domain

Ryt

[grave lance]

it says R-{0} in the question

[spark magnet]

Ohh yea sryy

What can u do then

[grave lance]

can u make z(=1/y) equal to 0 somehow?

[devout snow]

@spark magnet Has your question been resolved?

[spark magnet]

Tanks

[devout snow]

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[devout snow]

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[past wyvern]

Can someone help me with this?

[dark lava]

Try and think about what p does

When something is to the power of 1, x^1 is just x

[past wyvern]

Would b = 4 then?

[dark lava]

Not quite

When the power is less than 0, you put x under 1

So 1/x when p is -1