help-27

[vague garden]

i got it

need help with 2a and 2b

what i have tried

[devout snow]

@vague garden Has your question been resolved?

[kindred quest]

<@&286206848099549185>

[devout snow]

@vague garden Has your question been resolved?

[formal hedge]

Give me a sec

Root3/4 is the right answer?

[vague garden]

yes

[formal hedge]

Have u tried lhopital rule

[formal hedge]

Which part do u not get

Wait nvm

Divide by x to numerator and denominator

[vague garden]

Oh i kinda see now, i wasnt dividing numberator fraction by highest power

Thank you

I thought highest power was 4x one

.close

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[pure flower]

So I was trying to figure out the volume of a hemisphere with some calculus.

I took a ring in the hemisphere with some volume $r \left(\cos \theta\right)^2 r d\theta$

If I integrate this from $\theta=0$ to $\theta=\pi/2$, I should get the volume of the hemisphere, right?

That doesn't work. However, it does work if I have another cosine term in there?
What am I doing wrong-?

And why doesn't this work?

Here's a desmos graph:
https://www.desmos.com/calculator/du60jvzamb

[woven radish]

Percy

[pure flower]

If anybody replies here, please ping me while replying

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@pure flower Has your question been resolved?

[pure flower]

<@&286206848099549185>

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@pure flower Has your question been resolved?

[devout snow]

@pure flower Has your question been resolved?

[pure flower]

<@&286206848099549185>

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@pure flower Has your question been resolved?

[pure flower]

lmao i figured it out

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[eager kettle]

sorry if anyone got something similar yesterday and i didnt respond i fell asleep shortly after posting

ive had this explained two ways 1. using transformations and parent functions which gave me a headache and i couldnt follow along at all 2. inserting a number into x such as (-1) (0), etc. and then getting the points... but then what?

assuming we use the insert method and we get some points do i use the constant of 2 to +2 on all the y's of the points we find? e.g i use 0 in x and say it gives me (0, 2) and -1 and it gives me (-1,-3). do i +2 on the y values so that they now become (0,4), (-1,-1)?

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[mellow mountain]

I’m stuck on 2. A after factoring and setting y to zero, what should i do next?

[pseudo basin]

,rccw

[mellow mountain]

Oops

6 should be positive and 2 negative right

[pseudo basin]

well you've got it down to (x-6)(x+2)=0, so what must x be to annul one of the parentheses?

ah oops yes i missed that

[mellow mountain]

I’m uh not sure

Divide?

[pseudo basin]

the thing should be (x+6)(x-2) = 0 yes

that sounds like a random word you just spewed forth in hopes that it sticks

(whether that's what actually happened or not, i have no idea)

[mellow mountain]

What

[pseudo basin]

forget about it

anyway maybe you could have asked me about what the word "annul" means in case you found yourself not knowing

[mellow mountain]

Annul would be to like

Get rid of the parenthesis

[pseudo basin]

no

[mellow mountain]

Oh

[pseudo basin]

the way im using annul here it just means "to turn sth into zero"

i was expecting that you'd say x+6=0; x-2=0 or somesuch

maybe with a different separator between the two

[mellow mountain]

why would that equal 0

[pseudo basin]

do you know the zero product law?

[mellow mountain]

Maybe but I don’t recognize the name

[pseudo basin]

the product of two (or more) numbers equals 0 if and only if there is a zero among the numbers going in

ab=0 <=> (a=0 or b=0)

this is like the entire reason that we bother with factorization yknow

[mellow mountain]

Oh so one of the x’s have to be zero

How do we know which one is zero

[pseudo basin]

not "the x's"

and no we don't

we look at each one

each one gives rise to a solution

(in the simplest cases)

(for more complicated shit you'd consider each (...)=0 an equation in its own right that you need to solve)

[mellow mountain]

So what now

?

[pseudo basin]

i think i made it clear enough what to do

[pseudo basin]

right here

like you break the big equation into two small ones

solve the small ones

[mellow mountain]

So the zeroes would be -6 and -2?

[pseudo basin]

careful w the signs

you messed one up

[mellow mountain]

Oops

Positive 3

2*

[pseudo basin]

-6 and 2 yes

[mellow mountain]

Thanks

What about using the zeroes to find the equation of a quadratic like

3, -5?

Oh I figured that one out

thanks

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[hollow edge]

Can anyone help me get started with this

[hollow edge]

I used Kuratowskis theorem to prove it’s non planar by finding k3,3 as a subgraph but I’m not sure how I would prove part c

[devout snow]

@hollow edge Has your question been resolved?

[hollow edge]

<@&286206848099549185>

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@hollow edge Has your question been resolved?

[hollow edge]

<@&286206848099549185> any ideas?

[devout snow]

@hollow edge Has your question been resolved?

[hollow edge]

if it’s any help i know it’s from ocr a level further maths decision sample paper 1 but I can’t find a mark scheme anywhere

<@&286206848099549185>

[hollow edge]

.close

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[dark lava]

is that cubed root

or 3 multiplying

if it isn’t cubed root u need some xo such that the stuff under the root sign isn’t negative

i think xo must be 1

can’t be surely

lmk if it is 1?

[livid geyser]

Err so this is a quiz that's being graded?

[dark lava]

they’d should’ve used brackets

[livid geyser]

Can't get help for graded stuff

[dark lava]

ah lads no need to be rude let’s calm it

[livid geyser]

<@&268886789983436800>

[dark lava]

it’s a maths channels lol so jus chill

bro can u close this channel plz

it’s ok

[livid geyser]

No im not

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[opal falcon]

Hi. I wanna learn algebra from basics.
I want free learning site that has lessons and then exercises to learn algebra up to 9th class..

[opal falcon]

What y’all recommend?

[supple knot]

...

Just Google what you typed

Help channels are for math problems

[cold gust]

khan academy is your friend

for me personally: eddie woo and organic chemistry tutor are literal gods in learning math

[opal falcon]

Link it down, please bud.

[cold gust]

google it

[opal falcon]

I

<@&286206848099549185>

[austere ermine]

• https://www.khanacademy.org/: either on this website or you can find Khan Academy videos on youtube.
• https://youtube.com: look up algebra and they will give you videos.
• Books: you can borrow some books on Algebra at the library and find some PDFs online.

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[median bough]

oh idk why that turned into a file

can someone please tell me if this is correct

<@&286206848099549185>

[devout snow]

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

[median bough]

this one too

[median bough]

last one!

[main gull]

They're all good

[median bough]

you promise

[main gull]

Yeah

[median bough]

okay i have all my faith in you 🫶

actually no i dont im letting my brother look it over aswell but thank u

we can close this 😭

[main gull]

Which one are you unsure on?

[median bough]

i am just scared i will get something wrong this is a big test

i need to get a 100% so badly

[main gull]

.close to close

[median bough]

.close

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[fringe root]

Clueless on where to start, any ideas on how to tackle this problem?

[devout snow]

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[fringe root]

.close

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[empty sparrow]

Can someone help me understand piecewise functions

[devout snow]

@empty sparrow Has your question been resolved?

[empty sparrow]

Somebody please save my soul

[devout snow]

No need to ask "Can I ask...?" or "Does anyone know about...?"—it's faster for everyone if you just ask your question! See https://dontasktoask.com/

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[supple knot]

What about them don't you understand

[devout snow]

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[dreamy owl]

I have a question on what I am supposed to do

[dreamy owl]

<@&286206848099549185>

<@&286206848099549185>

[supple knot]

Says to do clustering. Have you learned how to do clustering yet

[dreamy owl]

no lmao my teacher assigned this with no resoucres so i looked it up and i still dont understand

this is also weighed heavy so i came to get help

i understand you are supposed to cluster randomly but i have no clue how im supposed to do that with the data provided

i also dont understand the sample moudle im supposed to be writing down , i dont get the question or what it wants

[manic seal]

21

[dreamy owl]

??

[manic seal]

21

[warm nymph]

ye

paste the sampel space

in to chat gpt

and askf or the pop mean

[dreamy owl]

i want to understand it and you can chatgpt this

[dreamy owl]

???

<@&286206848099549185>

[supple knot]

Yes?

[dreamy owl]

can u help me out?

[supple knot]

Follow the videos you watched then?

[dreamy owl]

they didnt help is what im saying

thats why im asking u

[supple knot]

Very unclear what you're saying

[dreamy owl]

im sorry

[supple knot]

Why didn't the videos help

[dreamy owl]

becuase they dont go into detail or give examples

so can you please help me

[supple knot]

https://www.geeksforgeeks.org/ml-hierarchical-clustering-agglomerative-and-divisive-clustering/amp/

[dreamy owl]

This is code

This doesn’t help at all

im clustering data

<@&286206848099549185>

[desert yew]

Are you trying to cluster data without code?

[dreamy owl]

yea

[desert yew]

Good luck. I would follow an algorithm and work carefully

[dreamy owl]

i only have the data she gave

how would you go abt it

[desert yew]

1.) Choose a clustering algorithm

2.) Cluster the data with a computer

[dreamy owl]

how do you cluster the data with a computer though

[desert yew]

3.) Pretend I did it without a computer

[dreamy owl]

lmao

[dreamy owl]

but i dont even know how to cluster with a computer and formula i dont even know where to get a formula

[desert yew]

You need to look up clustering then

There are some links above

[dreamy owl]

im so confused man but i still appericate you helpinh

[desert yew]

Even if someone was willing to teach you a mini class in it, you would be better off finding a well constructed source

I really don't understand the point of going on discord before checking Google

[dreamy owl]

i did check google thats the thing

and youtube

nothing

she wants me to do it on paper man

start to finish

[desert yew]

https://en.m.wikipedia.org/wiki/Cluster_sampling

This diagram is pretty nice.

I think the rest is just your judgement

Most of the questions is justifying your choices anyway

[devout snow]

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[brave hollow]

can someone explain how to do numbers 2 and 3?

[brave hollow]

ignore the writing that wasn’t me

[eager lodge]

,rotate

[brave hollow]

thanks

i have my test tomorrow

i understand most things

but not this

[eager lodge]

first what's p'(x) in terms of f(x),g(x),f'(x) and g'(x)

[brave hollow]

wdym

[eager lodge]

try to differentiate p(x)

i.e. differentiate f(x)g(x)

[brave hollow]

f'(x)g'(x)?

[eager lodge]

no

you should memorize the differentiation rules

it's f'(x)g(x)+f(x)g'(x)

now plug in -2

[brave hollow]

oh yeah

wait whats that rule called

i remember learning it in class

[eager lodge]

product rule

[brave hollow]

oh yeah

so if i plug in -2

would it be (0)(-2)+(-2)(0)?

[eager lodge]

no

we don't know f'(x) and g'

we can only determine the sign

[brave hollow]

oh

so now what

[eager lodge]

f(-2)=0

so p'(x)=f'(x)g(x)

we know g(x)

we just need the sign of f'(x)

[brave hollow]

g(x) is -2 right

[eager lodge]

no

[brave hollow]

im so confused

[eager lodge]

oh the graph doesn't give y value

what's the sign of g(-2) and f'(-2)

[brave hollow]

sign?

[eager lodge]

positive or negative

[brave hollow]

oh

negative

right

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@brave hollow Has your question been resolved?

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[night cave]

Quadratic question

[restive river]

hi

what are you taking

[night cave]

I was asked to solve
-x^2+3x+7 = 0

I usually make the "a" positive so it's not annoying and then solve, and it usually is fine, vut for some reason I turned it into a positive (I am aware that i have to change the others coefficients ) and i turned out with a different answer than the original question

[pseudo basin]

I was asked to solve
-x^2+3x+7

did you miss a "=0" there

[night cave]

fixed

[pseudo basin]

so

you were given the problem -x^2 + 3x + 7 = 0, you multiplied both sides by -1 to get x^2 - 3x - 7 = 0, but now that you've solved it, your answers don't match the book.

is that what's happening?

[night cave]

After thinking about it, my answer should be the opposite as I changed all the signs to their opposite, what i'm asking is, is it correct still though? my graph is the literal opposite of the answer in the book

[night cave]

yeah exactly

[pseudo basin]

ok

show your work, your answer and the book's answer.

my answer should be the opposite as I changed all the signs to their opposite,
no

[night cave]

Why not?

[pseudo basin]

the x-intercepts stay the same after a vertical flip

anyway right so

the instructions say to solve the thing by graphing

this means you're expected to graph y = -x^2 + 3x + 7 and not y = x^2 - 3x - 7

[night cave]

No no, sorry i must've been not clear

I got the same x intercepts

I got the same solution, it's just that my graph is flipped

I was wondering if that's okay

or if that's not going to acceptable

[pseudo basin]

that's sth to ask your teacher

[night cave]

Alright

.close

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@half cape Has your question been resolved?

[half cape]

<@&286206848099549185>

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[lapis stream]

hello im not sure how question b works

can someone explain to me what it means by sheets per n mm

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[nova basin]

can i remember the quotient rule as

[nova basin]

(f'(x)g(x) - f(x)g'(x))/(g(x))^2

[proud perch]

Sure

[nova basin]

if i rearrange it itll be easier to memorize bc its part of product rule

[winter patrol]

missing ()

[nova basin]

where

[supple knot]

numerator

[nova basin]

also why is (g(x))^2 on the denominator

[unreal eagle]

rearrange it how?

[nova basin]

the way i typed

[unreal eagle]

oh

yes

just remember: multiplication is commutative but subtraction is not commutative

[nova basin]

ok

[winter patrol]

also why is (g(x))^2 on the denominator
the way i typed
not sure what you mean

[nova basin]

like

in quotient rule theres a (g(x))^2 on the denominator

also is this a typo

it looks backwards

[winter patrol]

yeh that's a typo

what's your issue with (g(x))^2

[nova basin]

like what differentiates product and quotient rule is the sign difference in the numerator

and the (g(x))^2 in the denominator

what does the (g(x))^2 represent? like why is it not g(x) or f(x)g'(x)

or something

[winter patrol]

(g(x))^2 is the square of g(x)

this is the end result after simplification with exponent laws

look up proof of quotient law should give more insight

[nova basin]

oop ok thx

.close

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[plucky wind]

How do I do question 2?

[plucky wind]

Heres the memo

How tf this make any sense

[devout snow]

@plucky wind Has your question been resolved?

[topaz axle]

the layover time is weird, like we don't know if it's supposed to be already included into 13.4 or not

they assume not included, which makes sense, why mention it at all otherwise

and it has nothing to do with the question, it's just a random thing you could get wrong

[devout snow]

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[devout snow]

Please don't occupy multiple help channels.

[royal kestrel]

how do you rewrite/simplify this

[unreal eagle]

you could take out the common factor which is 6xe^-x

[royal kestrel]

so it would beeee

6xe^-x(2-x)

@unreal eagle

[unreal eagle]

yes

[royal kestrel]

thanks

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[thorn lagoon]

Mike is building a new swimming pool in his backyard. The pool is rectangular and has dimensions of 14 feet by 10 feet. Mike also wants to build a walkway (3 feet wide) all around the pool with tiles. What will be the area of the tile walkway around the pool?

[thorn lagoon]

The part I was stuck on was how the walkway that was 3 feet wide would be around the rectangle that is 10 feet wide. I don't really have any work because of that.

[hybrid snow]

Try drawing it out

Scyuslly

Actually

Have you played Minecraft @thorn lagoon

[thorn lagoon]

I have yeah

[hybrid snow]

Okay so

Imagine you build a pool with a surface area of 14 x 10 blocks

And then you're gonna build some path that extends 3 blocks from each side around that pool

So if you imagine what that looks like

You can find the area of the path

[thorn lagoon]

like this?

[hybrid snow]

Well

Extends 3 vlocks from

So like

[thorn lagoon]

ohhh

okk thank

thanks

lemme try and find the area then

i got 182 but thats one of the answers

i did 13 times 17

wait nevermind

I got it right ok thanks a lot for the help i really needed it

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[restive river]

Why would the sqrt function be included whilst the absolute value is non-included?

[patent marsh]

sorry can you elaborate on what you mean by "included" and "non included"?

[restive river]

sure

so for sqrt x, it contains an equal or greater than symbol indicating that 1 is included within the set of possible numbers

[patent marsh]

<@&268886789983436800>

ok now that's out of the way lmao

[restive river]

while for absolute value x, it has a less than 1 symbol meaning that 1 is not a part of the possible numbers

[restive river]

😂

[patent marsh]

I wouldn't think too much into that. That's just how it's defined. We could've easily included the x = 1 into the absolute value and not hte sqrt

it just happens to be that they both equal the same value at 1

for example, say instead we had sqrt(x) + 1

then it would look like this

[restive river]

so essentially what your saying is absolute value is in fact included but for graphical reasons it must not be included?

[patent marsh]

it just means that up to but not including 1, we use |x| to define our value.

With a piecewise function like that, we typically have the "included value" with one of the functions

|x| is included for x less than but not including 1
sqrt(x) is included for x greater than or equal to one

does that make sense?

it just happens to be that at x = 1, the function values are the same so it's continuous there

[restive river]

hm, because if I were to try to sub in 1 for the parent function |x| I would get 1 back, giving me the same point meaning it is included

[restive river]

so it wouldn't work out for us if we had both included and equal to for all of the equations?

[patent marsh]

yeah at that point it wouldn't be a function

recall the vertical line teset

*test

do you remember that?

[restive river]

right right, so if both of them were the same thing then it would technically be connected making them both one thing and therefore not making it piecewise

[vocal tartan]

As an aside, Desmos supports proper piecewise functions

[patent marsh]

Not quite. 1 is not in the domain for |x| in this case. It just happens to be a coincidence that if that was included, then the value would be 1

[restive river]

or am I getting the wrong idea

[patent marsh]

oh sweet, I had no idea! Thanks 🙂

[restive river]

yeah I do

[patent marsh]

no what makes it piecewise is the fact that we have multiple functions that behave differently based on the domain

what would make it not a function is if we included 2 points (also applies if it's the same point) that fall within a vertical line

so one of the functions needs to be inclusive and one needs to be exclusive

sometimes it just works out like your problem though, lol

[restive river]

ohh right

so what your saying is the verticle line would not technically pass through the non-included dot

making it a function

[patent marsh]

yep you're on the right track 🙂

yep you nailed on the head with that edit

nice work!

[restive river]

thanks

so does this work vice versa?

just as long as one is included and one isn't

[patent marsh]

yeah that's the key here

So like this is a function:

[restive river]

oh okay, thought there was some concept I wasn't getting lol

[patent marsh]

This would not be a funciton

[patent marsh]

nah you just have to think it out loud sometimes, you're doing fine 🙂

[restive river]

yeah makes sense, so I guess it would be breaking math laws in order to not break them

[patent marsh]

did you need any more help?

[restive river]

nope, I appreciate you greatly!

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[devout snow]

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[torn lagoon]

start by squaring both sides

[scarlet sequoia]

assumptions (domain), then square both sides

[lean yew]

Mhm

Now

[silver nest]

solve for x?

[lean yew]

X is equal 3

[scarlet sequoia]

so then what's the issue

except that x = 3 is wrong

[pastel pasture]

I don't think that's right

[safe knoll]

isnt x=3 wrong tho?

[lean yew]

😑😑

[silver nest]

bro took a wild guess

[lean yew]

Yea it's wrong

[safe knoll]

also pretty sure u get 2 solutions for it

[silver nest]

make sure when solving for x, put x on one side of the equation

[silver nest]

yes, because of the square i think

[lean yew]

Yep

There r 2 sl

[pastel pasture]

one of the might be outside the domain constraint so check for that

[lean yew]

Ight

[silver nest]

what would be the domain constraint? isnt he getting rid of the square root? (Im learning precal, sorry idk)

[pastel pasture]

well squaring would create extra solutions since it gets rid of the root

[scarlet sequoia]

you can't take square root of negatives, furthermore LHS should be non-negative

[pastel pasture]

Both quantities on either side of the equality can only be positive

[lean yew]

After taking square

Next step?

[pastel pasture]

solve

[scarlet sequoia]

solve quadratic

[pastel pasture]

[lean yew]

👽

Ok thanks

.close

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[pseudo basin]

well why is it that if x ∈ A then x ∈ B?

[lean yew]

Who knows

[pseudo basin]

i was asking OP, not you.

[lean yew]

OP is Busy at this moment plz wait😂😂🤣

[fluid root]

i am sorry

[pseudo basin]

this is not even remotely funny or helpful.

@fluid root what are you confused at, exactly?

[fluid root]

what is intersection?

is that one the answer?

is that a belong to b?

[pseudo basin]

no, intersection is denoted with ∩ and is not even involved in your problem

A ∩ B is the set of all points that belong to both A and B simultaneously

also don't confuse ∈ (belongs to) and ⊆ (is a subset of)! these are two very different relations.

[fluid root]

a is a subset of b

by definition of subset?

[pseudo basin]

uppercase A and uppercase B

yes the correct option in the dropdown is "by definition of subset"

[fluid root]

thanks

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[scenic surge]

Can someone explain how they got P(A) and P(B)

[grim burrow]

how does an ordinary deck of 52 cards have five spades

oh nvm, there are 13 cards in a suit, brainfart

[pseudo basin]

you draw 5 cards from the deck

there are 52C5 ways to do that

and there are 13C5 ways to draw a spade flush

[scenic surge]

but it says

all spade hand

[pseudo basin]

do you understand this Y/N

[scenic surge]

for B

[pseudo basin]

yes so that's for B

the numerator

im explaining what happens on the numerator

do you understand my explanation yes/no

[scenic surge]

right i dont get it still

no

[pseudo basin]

you draw 5 cards from the deck
there are 52C5 ways to do that

understand? Y/N

[scenic surge]

yeds

yes

[pseudo basin]

and there are 13C5 ways to draw a spade flush

a.k.a. a hand of 5 spade cards

[scenic surge]

but we have 4 spades no?

[pseudo basin]

what?

[scenic surge]

how is that even possible

[pseudo basin]

do you know how a deck of cards works

[scenic surge]

no

[pseudo basin]

bruh what

never played any card games?

[scenic surge]

never

[pseudo basin]

no poker, no go fish, nothing like that?

missing out

ok so alright

[scenic surge]

wasnt allowed so never bothered

[pseudo basin]

then let me be the one to explain to you the structure of a deck of cards

there are four suits: spades ♤, hearts ♡, diamonds ♢ and clubs ♧

in each suit, there are 13 cards of the following ranks: Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2

[scenic surge]

if thats the case

then wont that imply

that we have 4 aces in total

[pseudo basin]

yes we do

[scenic surge]

so how does one draw a hand with 5 ace

[pseudo basin]

we're not going for 5 aces

we're doing for 5 SPADES

[scenic surge]

wait whats a spade

[pseudo basin]

"a spade" means a card in the spade suit

[scenic surge]

ohhhhhhhhhhhhhhhhhhhhh

ok

I see

I get the numerator part

in the denom why did they add 13, 5

[pseudo basin]

let me take a photo

[scenic surge]

if we r lookin for atleast 4 spades

then wont it be

(13, 4) (39, 1) / (52, 5)

oh alr

[pseudo basin]

no, 13C4 * 39C1 is exactly 4 spades, not at least 4 spades

[scenic surge]

oh true

oh so thats why they added

(13, 5)

where it could be 5 aces too

spades

[pseudo basin]

they counted all hands of these two types

[scenic surge]

ahhhh

[pseudo basin]

on the left are the 5-spade cards, of which there are 13C5

[scenic surge]

i understand the whole thing now

tysm

[pseudo basin]

shame on your family for banning you from card games btw

it's actually quite shitty of them imo

[scenic surge]

😭

none of my friends played it either

so never rlly bothered

[pseudo basin]

i mean you say you weren't allowed

rather than you didn't have the opportunity

it's whatever

[scenic surge]

yuh that too but shit if one of my friends put me on

maybe i would have fucked with it

but thanks

doe

[pseudo basin]

yw

[scenic surge]

.close

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[devout snow]

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[urban hornet]

A large number of particles are moving with same magnitude of velocity v but in random direction. What is the average relative between any two particles averaged over all the pair (2d motion)

[devout snow]

@urban hornet Has your question been resolved?

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[restive river]

hello is any1 good w matrices

[unreal gorge]

just drop your q

[devout snow]

@cinder elm Has your question been resolved?

[gloomy seal]

Maybe that was the question

[devout snow]

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[umbral roost]

Assuming I did the exercise correct so far, how to I do the second part of the question asking me to sketch the solution curves and if the origin is a sink, source, saddle, center or (un)stable
spiral.

[umbral roost]

this is the question

this is my process so far

[devout snow]

@umbral roost Has your question been resolved?

[devout snow]

@umbral roost Has your question been resolved?

[devout snow]

@umbral roost Has your question been resolved?

[devout snow]

@umbral roost Has your question been resolved?

[timber pebble]

@umbral roost still around?

i think i can help ya

please dont be gone

[umbral roost]

I’m around @timber pebble

[timber pebble]

oh, hey, whats up @umbral roost

i wanted to tell you about the poincare diagram

its something you can derive yourself

the diagram classifies all 2d linear systems

heres maybe a better image

[timber pebble]

guess i should specify: with constant coefficient

for example, here you trace is -4

and your determinant is -10

this describes a saddle

feel free to ping

iyw

[devout snow]

@umbral roost Has your question been resolved?

[timber pebble]

@umbral roost dont take my word for it

https://faculty.sfasu.edu/judsontw/ode/html-snapshot/linear07.html

[umbral roost]

alright thank you @timber pebble, I checked out the images you sent me. I also watched this youtube video: https://www.youtube.com/watch?v=dpbRUQ-5YWc and now my answer looks like this:

does it seem correct to you, and is the phase portrait the same as sketching solution curves in the x_1,x_2 plane?

[umbral roost]

.close

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[wintry jasper]

i saw this question online

[wintry jasper]

isn't it just invalid?

if the distance b/w a and b is 45, and the distance b/w b and c is 50
then the distance b/w a and c should be 95?

but they specify it as being 90

is there something i am missing here

[wintry jasper]

the reason i ask is because the website also has a solution for the question

[sweet tide]

It means the cars are not all moving at the same speed

[wintry jasper]

what would the end state be like then

like i dont understand how the distance between A and C comes out to be 90

a diagram or something would help

basically this is what i am confused about

how can that distance be 90 and 95 at the same time

[sweet tide]

When car a ends the race b is 45km behind, and when car b ends the race car c is 50km behind. But some time passed between when car a finishes and when car b finishes and the 3 cars are moving at different speeds

[wintry jasper]

ohhhh thats what the question means

shit i misinterpreted it

thanks

[sweet tide]

Np

[wintry jasper]

!close

.close

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[arctic quest]

this question

[arctic quest]

can it be solved by (dy/dx)*(dx/dt)

to get dy/dt

This is what i tried

[finite briar]

u could but u could also substitute for x(t), in y(t) (i dont see any simplification tho)

[arctic quest]

yea thats the reason i didnt bother substituting, thats ussualy how id go about, but didnt see any potential

alright thx :D

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[zealous umbra]

abahaha i haven't a clue what I must do

[twin wedge]

3log3 x + 6 = log3 9x

[zealous umbra]

wait what

going too fast

[sand dove]

what he meant is substitute y with what it's equal to

[zealous umbra]

oh okay

so

log 9x = 3log x + 6

?

[sand dove]

yes

[zealous umbra]

whaatt then

[sand dove]

log(ab) = ...

[zealous umbra]

log 9x = log x^3 + 6?

[sand dove]

Nonono

not that way

[zealous umbra]

log 9x = 3log x + 6

what then

[sand dove]

3logx is fine

where else can you use log(ab) = ...

[zealous umbra]

with 6? but then 6 would need a log no?

[sand dove]

no

not with 6

what's left?

[zealous umbra]

the log 9x

[sand dove]

yes

[zealous umbra]

3log x - log 9x + 6?

[sand dove]

?

[zealous umbra]

UM

-3log x + log 9x = 6?

[sand dove]

ok but you still didn't use log(ab) =...

[zealous umbra]

log (x^-3/9x) = 6

i dont think that's rught

[sand dove]

No... not yet

log(9x) = ???

[zealous umbra]

oh

OH

log 9/logx?

[sand dove]

no

[zealous umbra]

oh

[sand dove]

log(ab) = ?

[zealous umbra]

HELP ME OUT PLEASE

IDK

[sand dove]

ok, what's the formula for log(ab)?

[zealous umbra]

log a + log b

[sand dove]

YES

so log(9 x) = ?

[zealous umbra]

log 9 + log x

omfg

[sand dove]

thanks

[zealous umbra]

shoot me

in

the

head

okay so

[pastel pasture]

pew

[zealous umbra]

ty

log 9 + log x = 3logx + 6

[sand dove]

yes

so that means log x = ...

[zealous umbra]

log x = 3 log x - log 9 + 6?

[sand dove]

bring every log x on one side

[zealous umbra]

log x - 3 log x = log 9 + 6?

[sand dove]

yes

simplify $log_3(9)$

[woven radish]

rafilou2003

[zealous umbra]

log x - 3 log x = 8?

[sand dove]

yep

meaning log(x) = ?

[zealous umbra]

HUH

[sand dove]

simplify the left hand side

[zealous umbra]

o

log (x/x^3) = 8?

[sand dove]

no

I mean technically correct but stop thinking about logs

[zealous umbra]

log x - 3 log x = 8

[sand dove]

If I let X = log x

[zealous umbra]

oh is it just 2 log x

[sand dove]

that means that X - 3X = 8

[sand dove]

small error

1 - 3 = ...

[zealous umbra]

OH

-2 log x

[sand dove]

yes

[zealous umbra]

-2 log x = 8

[sand dove]

-2 log(x) = 8

so log(x) = ?

[zealous umbra]

how do i figure that out

[sand dove]

what number, multiplied by -2, gives 8?

[zealous umbra]

-4

[sand dove]

yes

so log(x) = ?

[zealous umbra]

o damn

-4?

[sand dove]

yes

so x = ?

[zealous umbra]

hm

is it still -4

[sand dove]

x and log3(x) is not the same

what is the link between them?

[zealous umbra]

both x

[sand dove]

???

[zealous umbra]

I DONT GET IT

CAN U JUST

TELL ANS

and ill reverse reverse

[sand dove]

what's the definition of log

[zealous umbra]

I

log base (b^x) = x

[sand dove]

yes exactly

so if log(x) = -4

then x = ?

what's the operation that cancels log?

[zealous umbra]

3^-4

[zealous umbra]

what

[sand dove]

yes!!

[zealous umbra]

Omg

ily im so sorruy

[sand dove]

so now I think you just have to give the value of y

[zealous umbra]

wait lemme note down

OKAY DONE

[devout snow]

@zealous umbra Has your question been resolved?

[devout snow]

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[devout snow]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

@zealous umbra Has your question been resolved?

[zealous umbra]

.close

[devout snow]

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[devout snow]

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[woven radish]

gkeocog

[devout snow]

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[void iris]

Are you trying to figure out the function R(x)?

[long horizon]

Yeah

[void iris]

Ok, revenue is the amount of purses x price per purse

both are affected by the number of price reductions

the number of purses sold in a month goes up and at the same the price of a purse decreases

did you get it?

[devout snow]

@long horizon Has your question been resolved?

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[frank sun]

https://i.imgur.com/XD6rFrR.png

[frank sun]

https://i.imgur.com/EqoJ9a0.png

i have no clue what the next step is

[hybrid snow]

It looks like it wants you to evaluate every integral wrt a from 0 to t

[frank sun]

wrt?

[devout snow]

@frank sun Has your question been resolved?

[devout snow]

@frank sun Has your question been resolved?

[frank sun]

<@&286206848099549185>

[turbid parrot]

with respect to

[turbid parrot]

So basically youre stuck on solving for a, right?

[frank sun]

no clue how they inserted a(0) and a(t)

[turbid parrot]

Oh

Well a is just a(t)

wait no

Can you show tje entire context

[frank sun]

https://i.imgur.com/DMYaN4b.png

im at t2 rn

[turbid parrot]

Ah

Ok so the first thing to note

[frank sun]

its like they just do a(t)-a(0) lol

[turbid parrot]

Multiply the whole thinh through by -1

Then your left with $-\frac12ln(a)+\frac{1}{4a^2}+C=t$

Notice that you can bring that -1 into the ln

[frank sun]

$-\frac12ln(a)+\frac{1}{4a^2}+C=t$

[woven radish]

randomokay

MTBO

[turbid parrot]

Zeav

Yeah

$\frac12ln(a^{-1})+\frac{1}{4a^2}+C=t$

[woven radish]

MTBO

[frank sun]

dont think u have to do the a^-1 in the ln

right

[turbid parrot]

I mean, thats what they did

[frank sun]

mhm ye ig

[turbid parrot]

Ok whatever, lets just insert 0 into the whole thing, that will probably give us the constant I suppose

[frank sun]

a=0?

[turbid parrot]

$0=\frac12ln(\frac1{a(0)}) + \frac1{4a(0)^2} + C$

[woven radish]

MTBO

[turbid parrot]

So $C=\frac12ln(a(0)) - \frac1{4a(0)^2}$

fucker

[frank sun]

lol

ye c=0 basically

[turbid parrot]

No

[woven radish]

MTBO

[turbid parrot]

This is what C is

[turbid parrot]

Insert this C into the last thing here, combine terms

and done

I think

[frank sun]

what about the - sign before the ln

[turbid parrot]

It does look correct at the very least

[frank sun]

oh nvm

[turbid parrot]

Its been eaten up again

Yeah

[frank sun]

u swapped it

[turbid parrot]

I shouldve clarified

Yep

[frank sun]

so basically u just solved it for c

and then u get an implicit solution

[turbid parrot]

Yeah

[frank sun]

alright thanks

[turbid parrot]

No problem

[frank sun]

oh 1 more thing

[turbid parrot]

Sure

[frank sun]

when should you change positive/negative sign for the C constant

in that example u kept it as a positive

[turbid parrot]

Uhhh

Before you insert any specific values, just do what is easiest to write

Once you do insert some specific numbers, you cannot treat C as independent any more (I think) so you shouldnt change the signs any longer

Beforehand you can do with C whatever you want

[frank sun]

mhm oke

thanks again

[turbid parrot]

Since its just a constant, you can say that c=-C, then “delete” C, and say C=c

Pretty much the constant eats up any constant thrown at it

[frank sun]

ye its a bit confusing sometimes

[turbid parrot]

Yeah, I guess so

You gotta be really careful too not to “eat up” too much

If your not comfortable, treat C as a normal variable

[devout snow]

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[heady coral]

Hello, I am studying transformations of a bivariate vector but I do not understand what is in blue

[wicked turtle]

that's just the binomial theorem

with some of the worst choices for variable names that i've seen in a while

[heady coral]

I don't understand what it is being used for.

I'm clear until before the blue part, then I get lost

[wicked turtle]

the blue expression on line 3 is simplified to the blue expression on line 4

i.e. it's being used to simplify

[heady coral]

Ok thanks a lot for your help

.close

[devout snow]

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[primal gale]

Six problems (numbered 1 to 6) are set for a math test. A student can score 0, 1, 2 or 3 points for each problem. Find the number of ways to score a total of 15 points for the six problems.

[primal gale]

<@&286206848099549185> Six problems (numbered 1 to 6) are set for a math test. A student can score 0, 1, 2 or 3 points for each problem. Find the number of ways to score a total of 15 points for the six problems.

[devout snow]

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

[cloud shoal]

Is this available?

[primal gale]

This is an occupied channel.

[cloud shoal]

How do i go

Somewhere

Not occupied

[primal gale]

Go to an empty channel, such as #help-4

and post your question

Your question will be posted as your own occupied channel once you do that.

[finite cliff]

Listing sounds efficient

Because 222222 < 15

333330
333321
333222

That's all your choices already

@primal gale

if you count permutations then it's harder

Like whether
333330 = 033333

[devout snow]

@primal gale Has your question been resolved?

[devout snow]

@primal gale Has your question been resolved?

[devout snow]

@primal gale Has your question been resolved?

[primal gale]

IM DONE

[restive river]

.close

[devout snow]

@primal gale Has your question been resolved?

[devout snow]

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[devout snow]

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[harsh narwhal]

Hi, I am looking into motion parallax and how it affects object motion at different distance. I am curious about the math which goes behind it analyze the movement. For example, if I know that the speed of the object is 6 m/s and it is 20 m from the observer. Observer is stationary. Can we can calculate how the object will perceive to move if it closer to the object like 10m and away like 30 m?

[devout snow]

Please don't occupy multiple help channels.

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[sacred whale]

does anyone know how i could find the cross sectional area of this wrench?

[desert yew]

Yeah, with a lot of effort

or load it up into some cad software. You seem to have the dimensions

The CA will vary, obviously, depending on where you slice

[sacred whale]

how could i find it using a cad software?

@astral elk !?