help-17

[noble whale]

not the right answer

[strong olive]

just send it to tell you whats wrong in it

[noble whale]

ight give one sec

x=-1

thats what i got

[strong olive]

i was talking about how did you got it

[noble whale]

oh

ok

[strong olive]

you should get this:
$$\frac{x^2-3x-2}{x^2-6x+8}$$

[noble whale]

what

?

[twin meteor]

brahim3579

[noble whale]

let me try that

[strong olive]

on the left side

[noble whale]

thats wrong

[strong olive]

?

[noble whale]

i put that answer in and it came out wrong

[strong olive]

iam talking about the left side of the equation

[noble whale]

ye

[strong olive]

no its just a step

[noble whale]

oh

well

i got a new question now

[strong olive]

ok

[noble whale]

thanks

[strong olive]

$\frac{x^2-3x-2}{x^2-6x+8}= \frac{2}{x^{2} - 6x + 8}$

[twin meteor]

brahim3579

[strong olive]

whats your question @noble whale

[noble whale]

\frac{- 4 x + 2}{x - 3} + \frac{3}{x - 1} = - \frac{6}{x^{2} - 4 x + 3}

[strong olive]

$\frac{- 4 x + 2}{x - 3} + \frac{3}{x - 1} = - \frac{6}{x^{2} - 4 x + 3}$

[twin meteor]

brahim3579

[strong olive]

soo?

[strong olive]

did you understand what i did here

[noble whale]

nope

[strong olive]

do you know how to add 2 fractions?

[noble whale]

ye

[strong olive]

thats what i did

try it

[noble whale]

• 4x^2 -9x +11 /(x-1)(x-3)

[strong olive]

why you are distracting yourself here

if you understand the first equation you will understand the second one

[noble whale]

?

[strong olive]

you have a bit mistakes here

[noble whale]

how

i find lcd

[strong olive]

or you have multiplied by -1 on both sides

you should get this:$\frac{-4x^2+9x-11}{(x-1)(x-3)}=-\frac{6}{(x-1)(x-3)}$

[twin meteor]

brahim3579

[strong olive]

@noble whale are you agreeing with me here

and you make an equalization between the upper sides of the fractions

[noble whale]

i did not need to answer that question

i was at 100 percent

i did not relize

[noble whale]

i agree with this tho

[strong olive]

so $4x^2-9x+11=6$

[twin meteor]

brahim3579

[strong olive]

now you can find the value of x

[vocal sleet]

@noble whale Has your question been resolved?

[strong olive]

@noble whale are u gonna help

[vocal sleet]

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[next bay]

In intergral y^4 dx do the d and integral just cancsl out and the answer is xy^4

[sly sierra]

y^4 can be treated as a constant in that case, so yes

[next bay]

Reverse power rule is trippy

I love it

And thanks

[outer warren]

depends if x and y are related

[next bay]

I think it was just a simplfying question so no

[outer warren]

what's the original question

[next bay]

x^4/4+xy^4+7/x+C

[outer warren]

integral of ln(x) isn't 1/x

[next bay]

Welp I've been lied to again

What is it then :3333

[outer warren]

deriviative of ln(x) is 1/x

integrating ln(x) requires integration by parts
or applying a result from integral tables/identites if allowed

[next bay]

Like the D I method?

[outer warren]

well its pretty much only one iteration of by parts
so not much point setting up the DI table

[next bay]

Oki thanks

[outer warren]

what are the other questions in this question set

[next bay]

Just googled reverse power rule practixe lul

[outer warren]

there's a chance that they made a typo with y instead of x

[next bay]

Lul

Anyways thanks for the help

[next bay]

Hey I finished can someone un occupy me

[river kettle]

You type .close when done

[unreal mist]

guys do you know when to use inverse normal or binomial distribtuion in gdc ( model ti-84)

[next bay]

.close

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[slim hill]

I cant get the answer to this question, I'll send my attempts in a seperate message

[slim hill]

I got the 11 part right, but can't get 1

[echo jewel]

uh

[pallid forge]

you have to do this by hand?

[slim hill]

the second attempt is me removing all the zeros and trying the tree

[echo jewel]

is it supposed to be steps like this?

[slim hill]

yes I'm doing prime factorization

[echo jewel]

oh okay

[slim hill]

I cross out the matching numbers at the end of each tree then multiply any remaining numbers

it would become 10:11

[slim hill]

which is none of the answers

[echo jewel]

so I think you got the question wrong

[pallid forge]

should be 36 no?

[outer warren]

you didn't cancel your 0s correctly

[slim hill]

already tried it with 36 and got the wrong answer

[pallid forge]

36 and 3

[echo jewel]

yes

[pallid forge]

not 33 and 30

[echo jewel]

I think he wrote 39

[slim hill]

no its 36

[slim hill]

that leaves me with 11:3, none of the answers

[pallid forge]

it's 36 and 3

3 to 36

no?

[echo jewel]

okay so how about this let's start with the question again

[outer warren]

other costs, not budget

[echo jewel]

yes

[outer warren]

$$33\red{0,000}:3\red{0,000}$$
$$33:3$$

[pallid forge]

ahhhhhhhhh

[twin meteor]

ℝαμΩℕωⅤ

[slim hill]

33 is 11x3

[outer warren]

and then simplify that further

[echo jewel]

spent on office : 36-spent on office

[slim hill]

oh alr I get it now

33 becomes 11x3, and 3 is just 3x1, cancel out the two 3's and it becomes 1:11

[outer warren]

oh and just realised you set up the ratio in the wrong order

[slim hill]

yeah true

mb

meant to be 3 and 33

.close

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[dusky heath]

Can I solve for x by cos(90) = 40 / x?
Basically, can I use the height of the triangle as the adjacent angle, orr?

[sly sierra]

!status

[vocal sleet]

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

[dusky heath]

Added description to image; just sent the image because by the time I type out an explanation, the channel is already taken.

[dusky heath]

Or wait, sin(27) = 40 / x should work, no?

[sly sierra]

"Can I solve for x by cos(90) = 40 / x?"
this won't work, cos(90 deg) = 0

[sly sierra]

yes this works

[dusky heath]

Ah, right. Also for the right angle, you can't treat the legs as adjacent sides or can you in certain cases?

[sly sierra]

no, the whole sohcahtoa thing only works for the other two angles of a right triangle, it doesn't work for the right angle itself

so you can work with the 27 degree angle or with the y angle (which you can easily compute)

[dusky heath]

Gotcha, thank you!

Does this look right, then?

[lucid bane]

!showwork

[vocal sleet]

Show your work, and if possible, explain where you are stuck.

[lucid bane]

y looks correct

[dusky heath]

I got x wrong the first time; here's what I got for x.

x ≈ 88.1

[lucid bane]

yes

that looks good

now you can either use pythagorean theorem to find z or use tan()

[dusky heath]

I used the Pythagorean Theorem and got 95.5

[vocal sleet]

@dusky heath Has your question been resolved?

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[zealous ledge]

Hello

[zealous ledge]

How to calculate the integral od Arctan(1/x)

[full hatch]

Do you know how to do the normal arctan integral?

[zealous ledge]

Yes

[full hatch]

Have you attempted to do the same trick?

[zealous ledge]

i did this at first

[vocal sleet]

@zealous ledge Has your question been resolved?

[vocal sleet]

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[merry prawn]

is this the same as
-(2 pi sin(pin/2)) / n
right?

[loud cargo]

[
\frac{\pi\sin\left(\frac{3\pi n}{2}\right)}{n} - \frac{\pi\sin\left(\frac{\pi n}{2}\right)}{n}
]

First, we can factor out ( \frac{\pi}{n} ):

[
\frac{\pi}{n} \left( \sin\left(\frac{3\pi n}{2}\right) - \sin\left(\frac{\pi n}{2}\right) \right)
]

Now, we can use the trigonometric identity ( \sin(A) - \sin(B) = 2\cos\left(\frac{A+B}{2}\right)\sin\left(\frac{A-B}{2}\right) ):

[
\frac{\pi}{n} \left(2\cos\left(\frac{3\pi n + \pi n}{4}\right) \sin\left(\frac{3\pi n - \pi n}{4}\right)\right)
]

[
\frac{\pi}{n} \left(2\cos\left(\frac{4\pi n}{4}\right) \sin\left(\frac{2\pi n}{4}\right)\right)
]

[
\frac{\pi}{n} \left(2\cos(\pi n) \sin\left(\frac{\pi n}{2}\right)\right)
]

[
\frac{\pi}{n} \left(2(-1)^n \sin\left(\frac{\pi n}{2}\right)\right)
]

Finally, we can rewrite ( 2(-1)^n ) as ( (-1)^n \times 2 ) for clarity:

[
\frac{\pi}{n} (-1)^n \times 2 \sin\left(\frac{\pi n}{2}\right)
]

So, the simplified expression is:

[
(-1)^n \frac{2\pi\sin\left(\frac{\pi n}{2}\right)}{n}
]

[twin meteor]

squid

[loud cargo]

@merry prawn

[mild flower]

fresh off the gpt press

[merry prawn]

i don't have the alternating sign with my solution, can you tell me where i'm wrong?

this is what i did

sin(n3pi/2) is same as -sin(npi/2)

so i have
pi/n (-sin(npi/2) -sin(npi/2))

so
-2pisin(npi/2)/n

where i'm wrong?

[loud cargo]

cosine of pi is negative one so it factors out

[merry prawn]

i dont have cosine

[loud cargo]

no i meant after i factored it through sin(A)-sin(B)

[merry prawn]

i was asking to look at what i wrote and tell me why this is not matching your solution

[loud cargo]

i know but i need your work to find the error

i can't speculate what you might've done

[merry prawn]

i wrote above 2 messages ago

[loud cargo]

so you did this? (\sin\left(\frac{3\pi n}{2}\right)) has the same value as (-\sin\left(\frac{\pi n}{2}\right)) because both result in -1 when n is an integer.

so, your expression becomes:

[
\frac{\pi\sin\left(\frac{3\pi n}{2}\right)}{n} - \frac{\pi\sin\left(\frac{\pi n}{2}\right)}{n} = \frac{\pi(-\sin\left(\frac{\pi n}{2}\right))}{n} - \frac{\pi\sin\left(\frac{\pi n}{2}\right)}{n}
]

[
\frac{\pi(-\sin\left(\frac{\pi n}{2}\right) - \sin\left(\frac{\pi n}{2}\right))}{n}
]

[
\frac{\pi(-\sin\left(\frac{\pi n}{2}\right) + (-\sin\left(\frac{\pi n}{2}\right)))}{n}
]

[
\frac{\pi(-2\sin\left(\frac{\pi n}{2}\right))}{n}
]

[
-\frac{2\pi\sin\left(\frac{\pi n}{2}\right)}{n}
]

[twin meteor]

squid

[merry prawn]

exactly

[loud cargo]

no i'm dumb

you're right

[loud cargo]

LMAO

[merry prawn]

ok cool

and I'm trying to calc the integral of -tcos(nt)

and basically i get this result

but i don't know how to simplify all of this

it would be this plus the previous solution we just did

cause. I'm really trying to integrate (pi-t)cos(nt)

so i do it in 2 steps .... picos(nt) and tcos(nt)

forget it i'll do tomorrow. it's late

thanks!

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[weary solar]

Evaluate $\sum_{n=0}^{\infty}\frac{(-1)^n\left(\frac{\pi}{2}\right)^{2n}}{(2n+1)!}$ without the use of a calculater.

[twin meteor]

mXd

[hybrid flicker]

!status

[vocal sleet]

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

@weary solar Has your question been resolved?

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[pallid flower]

Just want to verify my answer

[vocal sleet]

@pallid flower Has your question been resolved?

[pallid flower]

<@&286206848099549185>

[true cliff]

what language is that

[pallid flower]

Khmer

[true cliff]

oh

[viral shell]

Seems right, all the steps are correct

[pallid flower]

Ty

.close

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[thin vale]

What is the contradiction here?

[vocal sleet]

@thin vale Has your question been resolved?

[thin vale]

<@&286206848099549185>

[regal bane]

Because 4 does not divide 6

So H can't exist as described

@thin vale

[thin vale]

yes, I just realized that myself also. Thank you

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[potent delta]

Can someone explain the intuiotion

behind this

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[dusty timber]

In a right triangle, the height lowered to the hypotenuse divides the hypotenuse into two parts whose difference is equal to the length of one leg. Determine the angles of the triangle.

[misty night]

do you have a diagram, i dont know what you mean by "the height lowered to the hypotenuse"?

[dusty timber]

it is translate,wait

[misty night]

so is the question saying, assuming x > y, x - y = either a or b?

[dusty timber]

yes

[subtle shell]

.

[misty night]

im not sure how you would find the angles

[dusty timber]

well i think since u have 1 angle(90 degrees) it has to be a special triangle,no?

[misty night]

well because it's a right triangle and pythag is $a^2 + b^2 = c^2$

[twin meteor]

AnimalWave

[misty night]

c = x + y

if we let x - y = b then we solve for a in terms of x and y

[dusty timber]

with it u get b or a=2*sqrt(xy)

[misty night]

you need the side length of the line splitting the triangle in two

then you can use the sin or cosine rules to start finding angles

[dusty timber]

i dont have the lenght of the line,i tried sine law and gor:

1/x+y=(x-y)sina=asinb

a is alpha,b is beta

but idk what to do now

[misty night]

idk

[dusty timber]

<@&286206848099549185> can yall help me?

[dusty timber]

.

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[dusty timber]

does no one know the answer??!

[vocal sleet]

@shadow jewel Has your question been resolved?

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[icy fern]

guys did i write this correctly

[icy fern]

in context of geometric series

ping me on reply pls

[potent anchor]

the sum is just a_1 / (1 - r)

oh that is S_n

[icy fern]

wdym

i have written it for a=1

first value of a is 1

why should it be 0

if i wrote these correct, then is this correct too

if i consider a_n as the general term or any term of the series

then what is the formula for writing the sum of all the terms that follow a_n

[icy fern]

THIS is the formula?

[vocal sleet]

@icy fern Has your question been resolved?

[icy fern]

find an infinite geometric seriees whose sum is 6 and each term is four times the sum of all the terms that follow it

<@&286206848099549185>

i found r equal to 1/5 but now how do i find the first term, and the second term....

.close

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[mint remnant]

also, what is the difference between "is true" and "is necessarily true"

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[mint remnant]

<@&286206848099549185>

[hushed pewter]

Necessarily true means it must always be true in every case

[mint remnant]

so which is the answer?

[knotty sun]

What have you try, maybe try some conter exemples for necessarily true

Try it with (a) u will have some results

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@mint remnant Has your question been resolved?

[mint remnant]

a, b and c are all correct arent they?

[knotty sun]

No

[mint remnant]

how come?

[knotty sun]

A IS not necessarily true

[mint remnant]

how could you have an injective function that isnt monotone increasing/decreasing?

i tried sketching a bunch of graphs

[knotty sun]

WE need something else to be true

Another condition

[mint remnant]

im lost

[knotty sun]

There exists some injective functions which IS not monotone increaqing or decreasing

Try to sketch one

[mint remnant]

thats what ive done

i couldnt get one

[knotty sun]

Sry I need to go I'll give u some hints : a is false check continuity , B IS false easy to show, with a and B you Can deduce c

[mint remnant]

all good

thanks

[knotty sun]

If on B WE had strictly monotone then it's true try to see the différence and maybe even prove it by good luck

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[vapid bobcat]

this question is really weird can someone help please

so for part b you get 8 different values for a and b but how are you supposed to know which one to use

[iron parrot]

what is $z^{\cdot}$?

[twin meteor]

Dork9399

[iron parrot]

is it the conjugate?

[vapid bobcat]

z conjugate

yes

[iron parrot]

ohk

[vapid bobcat]

any progress?

[vast shale]

they already gave it in the question ?

z z* = 18

?

[vapid bobcat]

yes

[vast shale]

then why do we have to prove that it is a real number ?

[vapid bobcat]

so (a+bi)(a-bi) = a^2 + b^2

ok but part b

[vast shale]

in the second clue

multiply and divide z/z* with z

now you have z^2/(zz*)

expand z^2

and equate the real annd imaginary parts on both sides

[vapid bobcat]

thats what i did

[vast shale]

you didn't get it ?

[vapid bobcat]

i got the values for a and b

[vast shale]

that is your answer?

[vapid bobcat]

no i dont know which values to use

[vast shale]

i don't get you

[vapid bobcat]

is a sqrt2 or 4

[vast shale]

what is the value of a and b ?

which you had obtained?

[vapid bobcat]

a= +-sqrt 2 or +- 4

b= +- sqrt 2 or +-4

[vast shale]

when a is +-sqrt 2 b would be +-4

and vice versa

[vapid bobcat]

but i looked at the anwer and it said

only +-(4 + sqrt 2) is correct

not any other combination

[vast shale]

they did not give any other conditions in the question

did they?

[vapid bobcat]

nope

[vast shale]

well maybe the answer was not complete

[vapid bobcat]

who knows

i guess u just have to get lucky

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[ebon rampart]

Stuck at lecture 4 , only that , i solved everything else so i need help , grade 8 geometry math

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[rough pine]

need some help please

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[rancid kestrel]

How would I do x times 11 times 13

[rancid kestrel]

Oh

Ok nvm lol

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[snow kindle]

helpies

[hallow plover]

welpies?

[snow kindle]

ok so anywat

way

why are oranges called oranges

but apples arent called red

wait

one more question

[hallow plover]

cause apples can be many colors

[snow kindle]

also

are you a jittleyang or fulinitogin

[hallow plover]

I'm a wigglywot

[snow kindle]

same

thank u

[pale perch]

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[restive gazelle]

good evening everyone
iam a software developer and i would like if someone could "proof read" if this makes sense?
iam not very familiar with math but very good with code on its own

this sheet is used to explain a isPrime checker i implemented. would this make sense for a math person as well?

[restive gazelle]

forgot to mention the number we have as input is always between -9223372036854775808 and 9223372036854775807

[trail shoal]

It is a common proof, coded it myself as well.

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[restive gazelle]

thanks

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[rough zenith]

Find both turning points of the curve y=2x^3 + 9x^2 - 24x + 5

[rough zenith]

so f'(x) = 6x^2 + 18x - 24

x^2 + 3x -4 = 0

x=-4 or x=1

then i substituted th two values

so i got both y=0

so i got (4,0) and (1,0)

but the correct answer was (-4,117) and (1,-8)

[open sun]

did u plug it back into the original function

or the deriv

[rough zenith]

OHHH

[open sun]

ye

[rough zenith]

yeah i plugged it in the derivitive

oops

thanks

[open sun]

allg

[rough zenith]

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[vast shale]

Need help with a little something

A coin is tossed 400 times, with 200 consecutive heads and 200 consecutive tails as the result.
What is the probability that the probability of an individual toss being heads is 50%? In other words, what's the probability that this is a fair coin?

[vast shale]

Tried binomial distribution, and I’m thinking rule of succession ? Not sure, need help

[potent anchor]

[pale perch]

who was tossing this coin, they have probablility manipulation powers or something

[vast shale]

Just a hypothetical

What is the chances of heads being 50% on the next toss, in other words - whats the chances of a fair coin?

Rule of succession states 100%, but then again 200 consecutive is unlikely regardless

[thin vale]

What coins are we sampling from?

[vast shale]

Just any random coin

[vocal sleet]

@vast shale Has your question been resolved?

[fading plume]

no clue, but intutively not knowing the sample space is an undefined variable

= doesn't give us enough information to solve?

[vast shale]

Sample space is heads or tails

S={H, T}

[fading plume]

sorry not sample space

the space of coins

[vast shale]

Ohh that’s what you mean

Hmm I’ll think of a way to define it

I can’t really define it for 400 tosses

[fading plume]

it's been a while since i've done this kind of stats but i was thinking like
the "true" probability is on a bell curve around 50%

[vast shale]

It was pretty much just a random spur of the moment question because I was prancing around my room, I’m not sure how I could work it out so it annoyed me

I can work out the probability of getting 201/401 heads

I’ll have to just stick to 100% due to rule of succession

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[dark kiln]

this has no answer

this is exactly like, "today I lost my wallet, what is the probability that my name is Lim"

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[velvet cove]

there are two bag, bag 1 contains 7 blue balls and 8 red ball, bag 2 contains 14 blue balls and 3 red balls. Respectively take one ball from two bags, calculate the probability of getting at least 1 red ball

[velvet cove]

do i just do 7/15+14/17

[muted ivy]

How to derivitive x²/ 4x+1

[velvet cove]

!help

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To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[ebon granite]

Calculate the probability of getting no red ball first.

1-P(no red ball)=P(at least 1 red ball)

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[quartz beacon]

A group of friends consists of seven men and five women. Louis and Louise are the only married couple.
From this, in how many ways can three men and three women be chosen in which the married couple is not together?

[quartz beacon]

if i do the total possibilities - the possibility where they are together wouldnt that just be 350 - 1 or am i missing another possibility

[dark kiln]

it means you have options of choosing neither of the two, or only Louis or only Louise

you solve it three times and add

that makes sense, subtract having both

[quartz beacon]

is that only one possibility then

[dark kiln]

i count 90 ways to have both

[quartz beacon]

how do you get 90

[dark kiln]

(6c2)(4c2)

[quartz beacon]

do you have advice for understanding these exercises btter

[dark kiln]

no

[quartz beacon]

because i keep missing something

😭

what do i do then

[dark kiln]

the standard advice is "just practice lmao"

i generally agree, over time your brain will give up and be like "ok I get it just stop"

[quartz beacon]

ive done all the exercises in the book

and i still cant do some whenever i see a new problem

because ill have done so many exercises that it just doesnt start to feel the same anymore and i would have done the exact same problem but i wont notice it

[dark kiln]

over time can mean 50−100 weeks

[quartz beacon]

well i have a test this friday

so thats lovely

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[plush garnet]

hi I've been thinking about something and I don't know how to calculate a formula for it

[plush garnet]

let's say there's a button

each time you press the button your score goes up by 1

but the chance of your score resetting to 0 goes up by 1% each time you press it as well

what would the formula be to calculate the chance of getting x ( a random score )

oooooh shit I got it

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[potent flame]

hello. can anyone help me with this question

[potent flame]

i have this formula

how can i calculate the risk premium given these values

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[bitter sequoia]

hi! could someone please help me with this question?

im not sure whether the angles i have written are correct

and I don't know how to find x

[orchid wren]

Hii

[bitter sequoia]

hello :)

[orchid wren]

Can you send the fresh question ?

[bitter sequoia]

sure! gimme a sec

[orchid wren]

Okk

[bitter sequoia]

there you go

[orchid wren]

Ok thanks

Hey i will be referencing to this picture ok

@bitter sequoia there ?

[bitter sequoia]

yep okay

[orchid wren]

Ok so ypu see60degree angle?

[bitter sequoia]

yes

[orchid wren]

Using that you can find length of EB

Tan 60° formula ok

So you have full length of AB now

[bitter sequoia]

One sec ill just write it

[orchid wren]

Ok

[bitter sequoia]

So EB is 2sqrt 3

[orchid wren]

Yeah

Now

We see EC parallel to AD

Right ?

[bitter sequoia]

Yes

[orchid wren]

So. BE/BA = EC / AD = BC /BD

Remeber this ?

Now you can calculate EC too

And AD too from the first two ratios

[bitter sequoia]

What is this rule called?

[orchid wren]

Bro i really forgot the name of the theorem

its extended midpoint theorem

I guess

[bitter sequoia]

ahhh ok

I don't think I've learnt it before but okay

[bitter sequoia]

We know EC is 2 tho

[orchid wren]

Hey

Triangle proportionality theorem

[orchid wren]

Yeah more easy

Then yoh know length of AB and AD now use pythagoras

[bitter sequoia]

Okay so it would be 2/2+2sqrt 3 = 2/AD ?

[orchid wren]

Yeah

Hey there

[bitter sequoia]

yeah just trying to solve for AD

[orchid wren]

Sorry bro

[bitter sequoia]

it's fine

[orchid wren]

Just forget the theorem i said

[bitter sequoia]

Okay

[orchid wren]

math aint mathing then i forgot the statement heres another approach

We have AB right ?

Angle ADB = 60

So apply trogonometric functions again to find x

sin 60 ° = AB /BD

Got it ?

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[serene lantern]

I have made a 3d physics engine but I need to add rotation to the collision response. If I have the contact points of the cubes how can I find the right amount of rotation to add to the rotational velocity? I use quaternions for the cubes but idk what I should use for the velocity itself. This physics engine is for a game.

[serene lantern]

@spiral turtle you previously replied to my message about "faking" the rotations. how could I do this?

[spiral turtle]

Just choose a random rotation vector upon impact

[serene lantern]

there has to be a way to make it react based off the collision and not just be random.

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@serene lantern Has your question been resolved?

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@serene lantern Has your question been resolved?

[serene lantern]

<@&286206848099549185>

[upbeat hollow]

It's for velocity right? Can u use the velocity formula/ like distance over time on where the cubes or move/rotate? I'm kinda guessing but hope it helped a little..lol💀

[serene lantern]

thats not what I need

I need to find the right ammount of rotational velocity to add to objects

based on a collision

[upbeat hollow]

Oh

Idt I know about that sorry

You making a game though? That's pretty cool

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[serene lantern]

<@&286206848099549185> ?

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@serene lantern Has your question been resolved?

[serene lantern]

<@&286206848099549185> anyone?

[minor rover]

this is really cool, sadly i dont know your answer

have you tried asking an Ai service sometimes even if not fully correct they can give you a great hint in the right direction

[final otter]

Could be that on the physics server (see #old-network ) it'll be easier to find someone to help for this one @serene lantern

In principle, I think you should get a lot out of conservation of angular momentum of the system. Just like you can deduce the velocities of two particles after collision from momentum conservation, you can probably deduce the angular velocities like that

Yea, only additional input is that to describe the angular momentum in terms of angular velocity, you need to get the inertia tensor of a cube. that's not too hard, it's a diagonal matrix $M$, and then you get that the angular momentum equals $L = M \cdot \omega$ where $\omega$ is the angular velocity

[twin meteor]

Lartomato

[final otter]

So yeah, high-over answer is that the system of equations given by energy conservation & angular momentum conservatino should allow you to deduce the angular momentums and hence the angular velocities of the cubes after collision @serene lantern

Don't have the time to fill in the blanks right now though, gotta go to the dentist 😄 perhaps you can do the rest yourself or alternatively go to the physics server in #old-network

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@serene lantern Has your question been resolved?

[serene lantern]

ok, I will resolve this thread but pls inform me when you get back

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[echo jewel]

good morning

[echo jewel]

this using the integral

is that like a common knowledge or what

what is this identity

[upper pebble]

you're in preuni or undergrad?

[echo jewel]

preuni

after high school before uni

idk the general education

system

[upper pebble]

Okie just realised the A and B are constant terms so Yes this is kind of something like you should know not an actual identity but helps a lot

[echo jewel]

sorry didn't point that out first

[echo jewel]

okay

[upper pebble]

not an actual identity its just derived to make it easier to solve other questions of same pattern

[echo jewel]

should I recite it

[upper pebble]

not necessary if you know how to solve integrals by substituting or commonly known as u-substituition

[echo jewel]

oky

also

the question is 4a, why does different constant come out, which one is the right one or is it both

[dull bear]

it's both: they're equivalent, if you notice that multiplying your constant by 2 gets you theirs

You have $\frac12 y^2 = \frac18 \ln\abs{4x^2 + 1} + \frac12$ when taking into account your constant, they have $y^2 = \frac14 \ln\abs{4x^2 + 1} + 1$ which is exactly the same as yours when you multiply by 2

[twin meteor]

@dull bear

[echo jewel]

ohhhhhhh

I got what you mean

thanks

[dull bear]

They really shouldn't have used the same +C though between the lines, as the constants are slightly different, though of course you can relabel them and all, call the new one D where D = 2C or something

[echo jewel]

I see

understood

cya

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[tulip cedar]

I know we get $\phi^3 -\phi^2 - 4\phi + 4Id$

But i don’t know what to do with that

[twin meteor]

Bean Man

[tulip cedar]

I see that it’s over R, do I get 8v -4v - 4v + 4 = 4??

[dull bear]

Wait what does the $E_{\phi}(2)$ mean?

[twin meteor]

@dull bear

[dull bear]

But sounds about right if it's what I'm thinking

[tulip cedar]

Eigenspace of the eigen value 2

wrt phi

[dull bear]

In that case yep

[tulip cedar]

alright thank you

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[tulip cedar]

.reopen

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✅

[tulip cedar]

wait I missed a term

8-4-8+4 = 0

[dull bear]

Yep minimal poly has no repeated roots

[tulip cedar]

oh wait X^2-1 can be factored into (X+1)(X-1) right?

alright all good thank you

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[wicked tusk]

Good morning! I have an exercise that I can't understand.

Let A be a square xnx matrix. Calculate as a function of n and the determinant of A, the determinant of 2A.

There is a property that says that if I multiply a matrix A by a scalar K, then the determinant of the new matrix is ​​k^n.det(A).

What I tried to do is apply Laplace's theorem, I considered the sum and product of the elements of a first row, that is the det(A).

Now, if I have 2A, then all the elements of A are multiplied by 2, therefore the elements of the first row as well, so the new determinant will be 2det(A), but of course, I am not considering the cofactors, it seems to me, It confuses me.

I know that, if I have a 40x40 matrix and I know the determinant of A, then the determinant of 2A will be 2^40.det(A), but I don't understand why that 2^40 (2^n)...

[brisk cloak]

if you multiple a matrix by a number k, lets say the k is 2, you multiply all elements as you said. so when doing the calculation for the determinant u can see that a multiplication by 2 appears for every element, and u do it n times since the matrix is nxn. so you have a 2x for the first element, a 2x for the second, a 2x for the third.....all the way to 2x for the nth element

so how many times 2's do u have? n. so 2^n

[wicked tusk]

ohh, i think i get it now

Thanks you 😄

[brisk cloak]

nw

[wicked tusk]

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[summer lotus]

not sure how to go about this

[outer warren]

start with getting an expressioon for a_4

[summer lotus]

a_4?

[outer warren]

the fourth term

[summer lotus]

not sure how to do that

[outer warren]

using what's given
$$a_4$$
= ?

[twin meteor]

ℝαμΩℕωⅤ

[wicked shard]

Just plug it in

[summer lotus]

-2?

[outer warren]

how are you getting -2

for a_4

[summer lotus]

a4= 3 a4-1 +2

[outer warren]

use _ to denote subscript

and also ()

[alpine barn]

To find the nth term of this sequence ur gonna need the value of the ones before n

[outer warren]

a_4 = 3a_(4-1) + 2

the bolded part simplfies to 3

you'll have
$$a_4 = 3\blue{a_3} + 2$$

[twin meteor]

ℝαμΩℕωⅤ

[outer warren]

and then apply it again until you get a_1 which you have the numerical value for

[summer lotus]

which is -2

[outer warren]

a_1 is -2

if that's what you mean

[summer lotus]

yes

so

3(-2) + 2

• _ -

[outer warren]

actually you could go the other way. might be easier

get a_2
then from that get a_3
then a_4

[summer lotus]

im still

lost here

[outer warren]

from what's given what's
a_2

[summer lotus]

a b c d e f g ... h i j k lmnop ... q r s... t u v... w x.... y and z 🎶

[outer warren]

if you're not going to be serious about this i am not going to indulge you

[summer lotus]

no im serious im just lost

i just started this unit

• 28?

-28

?

[outer warren]

how are you getting that value
what's that value supposed to be for?

[summer lotus]

a4

[summer lotus]

mathway

[outer warren]

that seems right

[summer lotus]

so its right?

im not even on this unit im trying to get ahead

and learn it

before we do it in class

[outer warren]

have you done any form of substitution before?

[summer lotus]

no

this is alg 2 i think

im in alg 1

[outer warren]

sub is part of algebra 1

e.g. what is
x + 5 when x=3

[summer lotus]

oh yeah i can do that

[outer warren]

if you can do that, you know substutiion

you have the general term:
$$a_n = 3a_n-1 + 2$$
(for integers $n\ge 2$) \
to get equation for your desired term, just subtitute your desired integer $n$ value for all $n$ in that equation

[twin meteor]

ℝαμΩℕωⅤ

[summer lotus]

right so like

a (4) = 3a(4 - 1 )+2

[outer warren]

misplaced parenthses

that whole 4-1 should be in ()

[summer lotus]

4-1 =3

[outer warren]

as that's the index (written in subscript)

[summer lotus]

3a_(4) = 3 a_3+2

[outer warren]

no

why do you have two a_3 there

[summer lotus]

because the parenthses

4-1

[outer warren]

how does that result in two a_3

[summer lotus]

^

[outer warren]

doesn't answer my question

[summer lotus]

i thought we were solving it

[outer warren]

of why you have two a_3

[summer lotus]

here

it was a typo

[outer warren]

ok

please try to read my questions carefully in the future

anyway

so
$$a_4 = 3a_3 + 2$$

[twin meteor]

ℝαμΩℕωⅤ

[outer warren]

and you can apply what you just did to the a_3

[summer lotus]

3a_(4+2)

?

[outer warren]

no

how are you getting that

[summer lotus]

you said apply i did what i did before

[outer warren]

why do you suddenly have a_6 popping up

using what's given
a_3 = ?

apply the exact same thing you did to get an expression for a_4

[summer lotus]

a _ 3+ 2

[outer warren]

no

it really feels a lot of these are major typos

one mistyped character screws everything up

[summer lotus]

a _ 5

[outer warren]

can you try to be more careful before you send and/or write your attempted work on paper or paint

no

you shouldn't be getting a_5

[summer lotus]

paint?

[outer warren]

drawing program on windows pc

[summer lotus]

what would you like me to do

instead of saying "just do this again" like idek what i did

[outer warren]

describe what you did to get
a (4) = 3a(4 - 1 )+2

[summer lotus]

4-1 = 3

[outer warren]

no before that

what was the exact step / thought you had before writing that equation i just copied

[summer lotus]

i made n into 4

[outer warren]

yes

[summer lotus]

but theres no n in ^

[outer warren]

there isn't an n in a _(4) = 3a_(4 - 1 )+2 either

i made n into 4
you used an equation that had n in it
replaced that with 4
and that got you an equation telling you an expression for a_4

[summer lotus]

there was an n and you made me replace it with 4

[outer warren]

yes

and that got you an equation telling you an expression for a_4

[summer lotus]

okay so who am i replacing now

[outer warren]

same idea

to get a_3

to get a_4 you replace n with 4
to get a_3 what do you replace?

[summer lotus]

a?

4_3

[outer warren]

no

[summer lotus]

then whatttttt

[outer warren]

don't overthink this

if you have
$$a_n$$
what can you replace to get $a_3$

[twin meteor]

ℝαμΩℕωⅤ

[summer lotus]

3

[outer warren]

what with 3

[summer lotus]

a n make it a 4

or a 3

[outer warren]

and what exactly did you replace plant to replace to make that happen

[summer lotus]

replace n

[outer warren]

yes

exactly

to get a_4 you replaced n with 4
to get a_3
the same idea applies
replace n with 3

and the same will apply for a_(any other valid number)

[summer lotus]

$$a_4 = 3a_4-1 + 2$$

[twin meteor]

bunny h.

[outer warren]

{} around the 4-1 to keep it all in subscript
if you're trying to use the bot

[summer lotus]

$$a_3 = 3a_3-1 + 2$$

[twin meteor]

bunny h.

[summer lotus]

thats what you want me to solve?

[outer warren]

not solve, just apply

[summer lotus]

okay where should i apply to get the answer

[outer warren]

you had
$$a_4 = 3\blue{a_3} + 2$$
and knowing $\blue{a_3 = 3a_2 + 2}$
$$a_4 = 3\blue{(3a_2 + 2)}+2$$

[twin meteor]

ℝαμΩℕωⅤ

[outer warren]

and then repeat for the a_2

[summer lotus]

but i just need to know the 4th term no?

[outer warren]

yes

and to get that you'll need to at some point use the numerical value given for a_1

[summer lotus]

okay so here we have

[outer warren]

also note that i at one point mentioned that it would be easier and less tedious to first find the numerical value for
a_2 then from that a_3 and then from that a_4

[summer lotus]

$$a_4 = (3a4)+2$$

[outer warren]

no

[summer lotus]

okay can you solve it on paper or paint with all the steps

and then i can try to dissect what you did

[outer warren]

you're perfectaly capable of doing the steps

you've done it twice already

once for a_4, another for a_3
do it again for a_2

[summer lotus]

the issue is i dont know what i did in the middle of you explaining it. if you write all of it down i can physically see it with all the steps in order

[outer warren]

the step is just basic substitution

that is all

there isn't much more to it

if you understand substitution/replacement, you shouldn't have any issue

[summer lotus]

no i get what youre saying

im not seeing the order

[outer warren]

what order

[summer lotus]

the steps of you solving it

if someone showed me this i can figure out what they did and replicate it

[outer warren]

pretty much only two steps have been done so far

i don't count the trivial simplification of 4-1=3 and 3-1=2

[summer lotus]

so im asking you to type all of it out or write it down somewhere from top to bottom so i can explain it to myself

[outer warren]

applying the definition given you had
$$a_4 = 3\blue{a_3} + 2$$
and applying the definition again
$$\blue{a_3 = 3a_2 + 2}$$
combining those (substituting the blue)
$$a_4 = 3\blue{(3a_2 + 2)}+2$$

[twin meteor]

ℝαμΩℕωⅤ

[summer lotus]

cus ive spent almost an hour trying to just figure out what youre saying

[outer warren]

do you have any issues with anything there

[summer lotus]

so

$$a_2 = 3a_1 +2$$

[outer warren]

a_2, but yes

[twin meteor]

bunny h.

[summer lotus]

$$a_3 = 3(3a_1+2)+2$$

am i on the right track here?

[twin meteor]

bunny h.

[summer lotus]

right i second guessed myself

[outer warren]

steps are going back and forth,
but its valid

[summer lotus]

so

now what

[outer warren]

you have a_1 given to you

which allows you to determine the numerical value of a_2

[summer lotus]

a_1 = -2

$$a_3 = 3(3 __-2 +2)+2$

[twin meteor]

bunny h.
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[summer lotus]

yeah idk

[outer warren]

please just write it up on paint or online drawing program like sketch.io

[summer lotus]

i have a macbook not windows

[outer warren]

does your macbook have a drawing program

if not use sketch.io

[summer lotus]

okay i substituted a1 for -2

[outer warren]

$\red{a_1} = -2$\
use the equation above / substitute the $\red{a_1} = -2$ to get the numerical value of $\blue{a_2}$ \
$\blue{a_2} = 3\red{a_1}+2$ \
repeat \
$\violet{a_3} = 3\blue{a_2} + 2 \
a_4 = 3\violet{a_3} + 2$

[twin meteor]

ℝαμΩℕωⅤ

[summer lotus]

so for a_2

=3

[outer warren]

no, how are you getting 3 for a_2

show how you're substituting
a_1 = -2
into
3a_1 + 2

[summer lotus]

$$a_2 = 3-2 +2$$

[twin meteor]

bunny h.

[summer lotus]

3-2 = 1

1+2 =3

a_2 = 3

[outer warren]

3a_1 is the product of 3 and a_1

not the concatenation of 3 and whatever a_1 happens to be with disregard for parentheses or order of operations

$3a_1 = 3 \times a_1$

[twin meteor]

ℝαμΩℕωⅤ

[summer lotus]

-6

[outer warren]

and what do you get when you add 2

[summer lotus]

-4

[outer warren]

yes

that'll be your a_2
then repeat to get a_3 and then from that a_4

[summer lotus]

-10

for a_3

-28

a_4

[outer warren]

yes

[summer lotus]

thank you

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• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
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[royal obsidian]

I have gotten access to an excel spreadsheet showing the electricity production in a certain country each month from 2010 and to the day today. I would like to shorten the spreadsheet so that it only shows production values every year, by adding up cells, but I was wondering if there's a way for Excel to do the job automatically

[royal obsidian]

Here, I've coloured the cells myself to make it easier for you to follow along. However, the cells extend all the way down and aren't coloured.

I've tried using the sum function (which in the video is shown as SUMMER due to my device language) to finish the first two years, with the hope that excel would autodo the rest. That does not seem to be the case.

Any help would be greatly appreciated.

[vocal sleet]

@royal obsidian Has your question been resolved?

[royal obsidian]

<@&286206848099549185>

[minor rover]

you should be able to copy paste

it down

in the cells below

and the formulas will autoadjust

C4:C15 becoming C16 to C27

[vocal sleet]

@royal obsidian Has your question been resolved?

[royal obsidian]

I don't believe that this works on Excel, though. You're using Google Docs.

Thanks for the input, though, it might actually be more convenient for me to simply import the date into Google Docs then export it to excel in order to create the desired diagram.

[minor rover]

you're probably right

[vocal sleet]

@royal obsidian Has your question been resolved?

[vocal sleet]

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[distant cradle]

Hello everyone! I am struggling with homework about limits (photos) it is about knowing and explaining what kind of limit is it: divergent, convergent or oscillate(?) it is in spanish. :// I dont know how to get the answers right nor how to know which is what, I would be glad for help! thanks a lot beforehand

[hallow plover]

Can't read spanish, are these limits tending to infinity?

[distant cradle]

yes! I can send the translation of the exercise

it would be broken english but it is the best I could do: Study the limit at infinity of each of the following sequences justifying your answer. Then, classify them according to their convergence in convergent, divergent or oscillating.

[hallow plover]

Alright so let's look at the first one

First, how would you write it down in limit notation?

[distant cradle]

I would write it: lim a(n) = 2n - 1 (not sure how to write fractions or anything mathematical on discord)

[hallow plover]

Usually a notation like this is used

That L being the value in this case

[distant cradle]

okay okay got it

[hallow plover]

So how would you go about evaluating the limit of 2n-1

[distant cradle]

that is what I dont know :/

[hallow plover]

The first thing to do is plug in infinity

and see what happens

[distant cradle]

uhh, and how do you do that then? I am sorry for those questions, I am lost in this

[hallow plover]

well if we plug in infinity instead of n we get 2 * inf - 1

2 * inf is still inf

and inf - 1 is still inf

right?

[distant cradle]

right

[hallow plover]

So the limit of the first sequence is inf

[distant cradle]

right, okay. but how would you write it down?

[hallow plover]

lim an = 2 * inf - 1 = inf - 1 = inf

of course you use the infinity symbol and not the word inf

since we got infinity as the result this is a clear case answer

[distant cradle]

and how to know if it is covergent, divergent, etc?

[hallow plover]

A limit is convergent if it tends to one specific value

it's divergent if it tends to -inf or +inf

and it is periodic if it neither tends to one value nor to -inf or +inf

so which is this one?

[distant cradle]

divergent?

[hallow plover]

Pardon I said periodic, I meant oscilating

yeah it's divergent

correct

[dull bear]

Divergent is just "not convergent" going to an infinity is only one type of divergence

[some places even include going to infinities as "convergence", but another matter ]

[hallow plover]

yeah but I'm simplifying for the scope of this exercise

Since it asks convergent, divergent or oscillating, so it implies you have to use only one

[distant cradle]

so it is divergente, right?

[hallow plover]

yeah

you could argue that oscillating are also divergent then, but since it says "or" in the problem sheet I assume they're meant to differentiate that way for the sake of the exercise

[distant cradle]

we have to use only one from it

I will be back in few minutes

I am back

[hallow plover]

Let's move on to the next one

[distant cradle]

B) has to be divergent as well no?

[hallow plover]

Right, how did you arrive at that?

[distant cradle]

Infinite ^ 3 is still infin; 10 - infin is still infin

No?

[hallow plover]

technically -inf (inbefore I get bonked again, ik this is iffy but for the sake of the exercise I let it slideee)

so yeah it's divergent

[distant cradle]

And the a is + or - ?

I will write it down just to be sure

[hallow plover]

a?

[distant cradle]

Yes

[hallow plover]

you mean exercise a?

[distant cradle]

yes - a) - divergent