help-10

[trim panther]

Hi

[trim panther]

Is anyone willing ton help rn?

[trim panther]

LMAO

Mb

I thought its kinda late gimme one second my computer is lagghing

Here sorry for the wait my pc is still crashing

I’m on iPad

@unreal musk

[unreal musk]

do you have any ideas?

[trim panther]

cbd = adb

[brazen viper]

That isn't actually true

What kind of quadrilateral is ABCD?

[trim panther]

no?

[trim panther]

trapezoid?

<@&286206848099549185>

i figured it out

using cosine law twice

.close

[obtuse pebble]

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[obtuse pebble]

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[proper canopy]

can someone explain what are parabolas and how to solve parabola related questions?

[proper canopy]

i would appreciate it if someone couild help me within maybe 4 hours

[ember frost]

what do you mean by "parabola related questions"?

[proper canopy]

ill send pic

this type

[ember frost]

to answer your question, parabola is the shape of a quadratic graph

imagine in an idealized environment, no wind no air no friction whatsoever, but there is gravity. throw a ball far away, the trajectory of the ball will be a parabola

[proper canopy]

ty

but how to solve questions like the pics i sent

just need a rough overview

alr

.close

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[trim panther]

hi

[trim panther]

what is the relation bw side length ratios and area ratios

[surreal forge]

consider heights

for example u can say triangle WZP has base WZ and height P to WZ, and u can say triangle UZP has base UZ and height P to UZ

in this case, the heights are equal so the area ratios are equal to the side ratios

[trim panther]

there are so many variables im getting lost

[obtuse pebble]

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[thin owl]

hi

[thin owl]

280 divided by 7

[kind hawk]

28/7 =?

[solemn thorn]

hard question

[mortal mason]

do long division

how many 7's can you fit in 280

keep adding 7 to 7 till you get to 280 exactly or a value close to 280

[mortal mason]

or do this

[dark stirrup]

,calc 280/7

[warm shale]

Result:

40

[thin owl]

tysm

1800divided by three?

[dark stirrup]

Get a calculator

Your phone should have one

[mortal mason]

you should learn long division though

and simplification

[timid silo]

,calc 1800/3

[warm shale]

Result:

600

[mortal mason]

cuh why y'all giving answers

if you remove the 0's from 1800 you end up with 18

and then you have 18/3

which should be simple

and you add the 0's back to the answer

what you do is you divide 1800/100 and then multiply the answer by 100

[obtuse pebble]

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[thin owl]

you are einstein

[obtuse pebble]

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[near grove]

help plsss

[near grove]

i worked out part a

of the question

just not b

the inverse got me lol

[gloomy vector]

do you know that $$f^{-1}(x)=y\implies x=f(y)$$

[warm shale]

Skill_Issue

[near grove]

nope i didnt

[gloomy vector]

!occupied

[obtuse pebble]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[near grove]

ooooo matrixes

[gloomy vector]

do you know how inverse functions work?

[night quiver]

sory

[gloomy vector]

all good

[near grove]

kind of

now i do

[gloomy vector]

alright

[gloomy vector]

do you know how to use this property? (btw, to derive this you just take the function of both sides)

[near grove]

uhm no im really confused right no

so a= g inverse of f inverse (4)

[gloomy vector]

incorrect

gimme a sec

[safe haven]

if you have a function, then you apply its inverse to it, you get the input

likewise, if you have a function's inverse, then apply the function to it, you also get the input

[gloomy vector]

if you let $(g\circ f)$ be a function on its own, using this property you can get $(g \circ f)^{-1}(a)=4 \implies a=(g \circ f)(4)$

[warm shale]

Skill_Issue

[near grove]

oh

so that

cancells out the inverse?

in a sense?

[gloomy vector]

yes exactly

[near grove]

oh

so if we just find

g of f

and then multiply it by 4

then we have the answer?

[gloomy vector]

erm

g of f (4)

[near grove]

nono yeah mv

thats

what i meant

mb*

[gloomy vector]

you already got g of f (x)=2x+11, just plug in x=4

yeah

[near grove]

oh

got it

thx

[gloomy vector]

np

[obtuse pebble]

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[vocal jasper]

How do you round a whole number to the hundredths place?

[midnight breach]

consider the next digit after the hundredths, round down if it is below 5 and round up otherwise

for example 3.251 would be 3.25; while 3.256 would be 3.26

[vocal jasper]

The number I'm looking at isn't a decimal and the ones place has a 1 so how would that work?

[midnight breach]

what is your number?

[vocal jasper]

45961

[midnight breach]

it's the same method, you look at the digit after the hundreds

which will be the tens

there is a 6 in the tens place, which means you round up

ignore all digits after the tens

so 9 -> 10, you'll write 0 in the hundreds place and add 1 to the digit before

any digits from the tens onwards will be replaced with 0s

[vocal jasper]

ohhh ok ty

[obtuse pebble]

@vocal jasper Has your question been resolved?

[vocal jasper]

yes

[obtuse pebble]

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[half notch]

Pls someone help me solve this equality for num 5

[cunning burrow]

You haven't made an attempt

[half notch]

I did

I got like 30

Probably because I made a mistake in the calculations

[cunning burrow]

!show

[obtuse pebble]

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

[half notch]

I'm not strong in fractions especially if there are parentheses

[cunning burrow]

first line there is a mistake

note -a(b+c) = -ab -ac

[half notch]

Wait is it at the 3/4 fraction?

[cunning burrow]

yep

[half notch]

It's like -3/4 right

[cunning burrow]

correct

[half notch]

So that means (-6x - 18) / (4)

Is this correct?

[cunning burrow]

No need bring the constants and variables together

but you are correct

What I would do is write:

8x/5 - 6x/4 -6/5 -18/4

[half notch]

Oh so I can just separate them

[cunning burrow]

correct. It just make simplication easier

[half notch]

So I have this now

The thing is the denominator is different for the like terms

What should I do

[cunning burrow]

you can use equivalent fractions to make the denominator the same

[half notch]

Denominator is now 20

Okay give me a second

I have this now

The problem is

24 - 90

-66

[cunning burrow]

Order of operation

BENDMAS

B: Brackets

E:exponents

N: Negative sign

D:Division M: Multiplication (Notice equal hierarchy)

[half notch]

Addition subtraction

Right?

[cunning burrow]

yep and equal hierarchy for addition and subtraction

[half notch]

Oh wait

Nvm

Can I simplify 24/20 and 90/20

[cunning burrow]

So we have the order of operations and top of that we must work left to right

Note that 1 -2 -2 does not equal 1 - (2-2)

If you want simplify -24/20 -90/20

You won't be able to do so because negative sign in the -24/20

What you can do is take - sign out using factorisation

So we have -(24/20 + 90/20)

Doing that you will get -114/20

[half notch]

Yep

[cunning burrow]

From there it is relatively straightforward

[half notch]

I have this

Omg can I just cross multiply

Wait but why would I

The denominator is literally the same

[cunning burrow]

you can if you want to get rid of denominator. There is multiply ways of making x the subject

[half notch]

Oh wait I forgot to add the equality of 3/10

(2x - 114) / 20 = 6/20

It's still correct right

[cunning burrow]

yep

you could just leave 3/10 as it is on the right hand side

[half notch]

Omg I'm literally stuck

[cunning burrow]

(2x - 114) / 20 = 3/10

So what do we now?

If a divide by b = c. Then a= ??

[half notch]

bc

I think

[cunning burrow]

correct because multiplication is defined as the inverse of division

[half notch]

So can I just multiply by 20 on both sides?

[cunning burrow]

correct

[half notch]

2x - 114 = 6

[cunning burrow]

yep

[half notch]

x = 60

Omg finally

Tysm

[cunning burrow]

!done

[obtuse pebble]

If you are done with this channel, please mark your problem as solved by typing .close

[half notch]

.close

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[spark horizon]

can anyone explain why all values of p must be considered in combination with duplicates

[obtuse pebble]

@spark horizon Has your question been resolved?

[spark horizon]

<@&286206848099549185> 🙏

[obtuse pebble]

@spark horizon Has your question been resolved?

[obtuse pebble]

@spark horizon Has your question been resolved?

[obtuse pebble]

@spark horizon Has your question been resolved?

[plain charm]

Can you state the question clearly?

[rigid skiff]

Yes please

what do mean

[obtuse pebble]

@spark horizon Has your question been resolved?

[obtuse pebble]

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[static pebble]

I don't understand how to do part c & d

[dark stirrup]

where is part d?

[static pebble]

Oops my bad I meant b&c

[dark stirrup]

Well did you expand $(z\pm z^{-1})^2$ yet?

[warm shale]

SWR

[static pebble]

Yeah I got 4cos^2theta and -4sin^2 theta

[dark stirrup]

You should use what you got in part a also

[static pebble]

Yeah I used that to expand

[dark stirrup]

Can you show? Because that's not making sense then.

[static pebble]

It's in the picture i sent

Or am I doing it wrong 😔

[dark stirrup]

oh

[dark stirrup]

What's going on here?

[static pebble]

I'm looking at what's inside the brackets and using the formula from part a to expand it into 2cos theta

And then in the next line I square it

[dark stirrup]

inside which brackets?

[static pebble]

Z + z^-1

[dark stirrup]

How are you getting this? Are you saying n=1?

[static pebble]

Yeah

[dark stirrup]

where did d come from here?

[static pebble]

From part a substitute n as 1

[dark stirrup]

and how does that give you d?

[static pebble]

It says 2 cos theta

😭

[dark stirrup]

That's a rough 2

No matter how hard I look, I do not see a 2

but okay sure

$z+z^{_1}=2\cos\theta$, so $(z+z^{-1})^2=(2\cos\theta)^2=4\cos^2\theta$. No complaints there.

[warm shale]

SWR

[dark stirrup]

But I would next evaluate $(z+z^{-1})^2=(z+z^{-1})(z+z^{-1})$ and multiply it out.

[warm shale]

SWR

[static pebble]

So like 2cos theta * 2 cos theta?

[obtuse pebble]

@static pebble Has your question been resolved?

[obtuse pebble]

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[versed eagle]

I’m presented with this problem but the answer key says non existent when I was able to get an answer

[versed eagle]

i believe i understand that its 12/0

[tribal bluff]

is it number three?

[versed eagle]

buttt what i did is i put the denominator in standard form then plugged in 0 and got 1/12

[versed eagle]

yes

and also isnt 12/0 undefined rather than non existent. i just dont get it

[tribal bluff]

what is the answer?

[versed eagle]

ill also mention the answer key is slightly broken but i just want to check if i did the problem wrong or im missing something

[tribal bluff]

according to the texbook

[versed eagle]

this is a review paper and it says the answer is non existent

but the answer key is a little broken because for #3 there are 3 problems to solve. whereas the key just tells me an answer for 1 problem.

[tribal bluff]

ye it is unbounded

[versed eagle]

it appears like on #2 its asking for first question so im assuming its the same

[tribal bluff]

its probobly meaning that it is unbounded

because both sides of the function approach infinity

[versed eagle]

its saying limit is non existent

dne

[limpid eagle]

yeah technically limits to infinity don't exist

cause they don't approach a singular number

but we still notate them as to infinity just for the kicks yk

[versed eagle]

oh okay...but how do i figure that it goes to infinity?

sorry im like really bad at reading how graphs work

but why do we know it goes to infinity

[limpid eagle]

idk if invinoveritas wants to explain that I'm kinda intruding here

[tribal bluff]

do you have a graphing calc?

[versed eagle]

mhm

but i mean just based on looking at the problem

[tribal bluff]

nono go ahead@awsome rat

[versed eagle]

we are not allowed to graph with calculator

[tribal bluff]

oh then theres another way

[limpid eagle]

nah you got it

I gotta do my hw anyway lmao

[versed eagle]

oh i do see we have asymptote at x=6

[tribal bluff]

wait btw

are you in algebra or in calc

[versed eagle]

calc

[tribal bluff]

in calc we just use lhopitals rule

[versed eagle]

ik but we havent learned derivatives yet

we have to do it algebraically

[deft monolith]

Is prolly calc 1 so to recognize it as a c/0 form is prolly easiest

[limpid eagle]

you wanna look at its behavior around 6

[tribal bluff]

^^^^

[limpid eagle]

on the left and right

so plug in a point SUPER close to 6 from the right

and another from the left

so e.g. 6.1

and 5.9

[versed eagle]

ah right

[limpid eagle]

so take 6.1, you got a limit of a number divided a SUPER small number

an infinitely small number in fact

so it's infinity on the right

same principle on the left

[versed eagle]

so i get the super small and super big thing

and we're plugging in 6.1?

[limpid eagle]

just a number that's super close to 6 on the right

just to simulate the behavior

[versed eagle]

mhm

[limpid eagle]

you could pick 6.01, 6.001, etc.

[versed eagle]

yeah

idk how that like

results to small number

[limpid eagle]

wdym

[versed eagle]

wait...

oh

[tribal bluff]

for this problem you just have to know the asymptotes in the function

[versed eagle]

since on the denominator using a number x>6 but very close to it, its going to end up being a number super small

[tribal bluff]

there is a vertical asymptote at x=6

[versed eagle]

like 6.0000001-6 is just .0000001 or yk infinitely close to 6 but greater

ye i get you guys

no i like to understand both the visual aspect of it in simple terms and then how to see it algebraically

i often get confused

[tribal bluff]

for this problem it is a little hard to solve algibreically at least for me

[limpid eagle]

no I feel you

same here

[tribal bluff]

i just visualize the graph in my head

[versed eagle]

yeah i try to visualize it my my head as well but like i dont realize what it should look like

[tribal bluff]

for these kinds of rational functions its best to identify the asymptoe first

asymptote*

[versed eagle]

true

id like to get better at understanding the numbers so i can graph it in my head

[tribal bluff]

gimme 2 secs ill show u the steps algibraically

[versed eagle]

ty

idk i feel like in math class we really just sped through learning how to graph stuff apart from basics like translation and dilations

like the x># n shit we just skimmed through

[tribal bluff]

my favoraite limit calc 🙂

the thing with this limit is just recognizing the bounds

[versed eagle]

wdym "this limit" ?

[tribal bluff]

there are special limits

[versed eagle]

btw what program is this

[tribal bluff]

and this is one of them 🙂

[versed eagle]

based on what?

[tribal bluff]

https://www.emathhelp.net/en/

[versed eagle]

the sum/difference thing?

[tribal bluff]

based on the asymptotes

[versed eagle]

wow, ty

[tribal bluff]

np 🙂

if you need steps but dont know how to get the answer just use this 🙂

[versed eagle]

tyvm

i think the key to be understanding many math concepts is simply studying graphs as much as possible

[tribal bluff]

its kinda both

[versed eagle]

and immediately recognizing what something means

at least for me i mean

[tribal bluff]

its both the algebra and the graphs for me

[versed eagle]

because for in my current state, graphs seem to be everything, end all be all

[tribal bluff]

its kinda like a toolbox

u pick the tools, and use the tool that fits best

[versed eagle]

mhm

[tribal bluff]

on tests, its the tool thats the fastest

[versed eagle]

i think id just be less confused if i just like, knew how to solve everything algebraically or could recognize things in my head fast

[deft monolith]

Assuming you have to move through the calculus'es this might come back to bite ya

[versed eagle]

idk, might need to do that over fall break or something lol

[versed eagle]

wdym?

[deft monolith]

Idk, I had a flashback to calc2 and the wacky functions you have to integrate

[versed eagle]

rip

yeah i just have to study functions very extensively

my teacher just moves too fast 😭

the super smart kids in my class seem to get everything pretty fast and also think more in depth than i do, maybe even over think

i think im just a step behind unfortunately

anyway, i doubt im done using this server tn for this review, but ty for the help ya'll

[brisk arrow]

Those smart kid probably already done similar things a thousand times

[versed eagle]

idk, we're just juniors in high school, they just seem to get things

[wooden cipher]

practice makes progress

[brisk arrow]

That’s why you can’t keep up with them, as you do less exercise

[versed eagle]

well, i dont think they actively apply it in their lives

but they probably are more studious than me

i still study myself, but not extensively or anything

a good study sesh for me is like an hour to an hour and a half, which i guess is nothing in comparison

i wish i had the time and motivation to take hours upon hours to master a subject

[brisk arrow]

You have the time

[versed eagle]

i do sure, but school exhausts me

[limpid eagle]

you can always get motivation from studying or at least being on a similar study plan as a friend

studying with friends always makes things easier

[versed eagle]

yes id like to join or find a study group, but i dont really have friends like that at school or people who do that nor can i drive anywhere as idk how to drive yet without being deathly afraid

i think that would be fun and motivational

i just am not in that position

[limpid eagle]

well other than that it's just discipline, try to get into the mindset to obsess over a concept until you quite literally got it nailed down

[versed eagle]

id have to find some online study group

yeah

[limpid eagle]

that's what motivates me at least

if I don't understand a concept

[versed eagle]

im trying to also romanticize school

[limpid eagle]

I LITERALLY don't get up

until I understand it fully

[versed eagle]

math is just burning my brain tho

[versed eagle]

thats exactly what i want to do

but im just too exhausted all the time

and not understanding my teacher during math class is so depressing and bothersome and burns my brain trying to understand everything

also my calc class is a block class, so ab/bc

[limpid eagle]

lmao same I get the creeps driving places

just got my permit so I'm kinda on the edge still

[versed eagle]

yeah i just got my permit too

but like even driving in my neighborhood is nerve racking

[limpid eagle]

real

[versed eagle]

anyway i totally want to get into that mindset of obsessing a math topic till i fully understand it

[limpid eagle]

especially with all that talk from the people around you growing up saying a car is a weapon, you know that right?

[deft monolith]

Watch math YouTube like a mf if you want to get good at it btw

[versed eagle]

i just have no motivation yet

[versed eagle]

lol

[versed eagle]

yeah fr

Brian McLogan and the Chemistry Tutor kid coming in clutch every single time i swear

[limpid eagle]

the organic chemistry tutor 😍

[versed eagle]

i love Brian McLogan tho because he makes things soooo simplified

and then organic chemistry tutor gives me step by step problems to practice

[deft monolith]

Blackpenredpen and 3blue1brown on top as well

[brisk arrow]

^

[wooden cipher]

sit down and do it

[versed eagle]

ill be sure to check them out

[wooden cipher]

itll be like medicine

[versed eagle]

maybe bookmark

[wooden cipher]

or exercise

but eventually its second nature

[limpid eagle]

crazy advice

but true nonetheless

[versed eagle]

well thanks for the advice lol

probably will be seeing me again since im still working on this review i just started lmao

i may not know limits well, but im at mine.

[wooden cipher]

just keep at it

and youll be a master

[limpid eagle]

not the dad joke 😭

[versed eagle]

its very fitting for my position rn

[versed eagle]

i literally dont even want a job that has much to do with math, i just want to master it so im less stressed and so its a breeze to get a good grade 💀

and also to build a better study ethic and mindset

[wooden cipher]

keep taking the medicine

that sounds like an indoctrination 💀

[versed eagle]

lmao idfk

.close

[obtuse pebble]

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[whole warren]

what went wrong here

[whole warren]

Thats the question

[wooden cipher]

you forgot if x^2 = c, then x = +-c

i.e. you forgot to consider -sqrt(3)/2

[whole warren]

So it would also be 5pi/6 and 7pi/6

okay thanks bro

[wooden cipher]

youre welcome

[whole warren]

.close

[obtuse pebble]

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[whole warren]

the question

[obtuse pebble]

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[real coyote]

I need help with this topic "operation of functions" like addition of functions. I really need help with this because ive been sick for 3 days and didnt know this topic. Really appreciated if helps

[tepid yoke]

Are you allowed to ask for help on this? Is it an assessment?

[real coyote]

Yes my prof says it is fine when i get struggled with this topic since i didnt know anything about this

[tepid yoke]

Do you know how to add 5x + 2x

[real coyote]

Is it 7x?

[tepid yoke]

Yeah

You just add all the terms together from both functions for addition

[real coyote]

So how do i deal with the b part "f(x)-g(x)"? Do i do the same thing?

[tepid yoke]

Yes you just subtract the terms of the second function from the first

[real coyote]

How about the multiplication part? g(x) ° f(x)?

ive been stuck there because it is in reverse and ive been tricky on that part

[tepid yoke]

Well in multiplication order doesn’t matter

fg = gf

[real coyote]

Oh how last one how about the g(x)/f(x)?

So i solve the a part is this right? I add 5x+2x it will be 7x and i add 11 and 10 so it will be 21 so the a part is 7x and 21 is that right?

And in b part i did 5x - 2x = 3x and 11 + 10 = 21

You there?

[obtuse pebble]

@real coyote Has your question been resolved?

[void quartz]

correct

[void quartz]

yes, 7x, but watch out

you added 11 and 10, instead of -10

[void quartz]

this is not multiplication, multiplication is in 2.e

its called the composition of g and f

[real coyote]

Oh

[void quartz]

g(x) o f(x) = g(f(x))

[versed eagle]

Isn’t that composition?

Usually the o thing means composing, a dot meaning multiplication

[real coyote]

Sorry ive been new to this topic

[versed eagle]

This here

[versed eagle]

It’s ok

Composition is real easy, unfortunately I can’t explain rn cuz I gotta sleep

[real coyote]

No worries

[versed eagle]

But in this case Im not sure what the question is asking for myself

Unfortunately I’m not a helper or anything

[real coyote]

Its ok

[versed eagle]

But definitely look up composition in math 👍

[real coyote]

Okay thanks

[obtuse pebble]

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[echo cosmos]

Hello! I am learning real analysis and am trying to prove that the set of all subsets of the natural numbers has cardinality equal to $\mathbb{R}$. Or, more formally, $$|2^{\mathbb{N}}|=c=|\mathbb{R}|$$

[warm shale]

Eater of Bees

[echo cosmos]

My proof so far goes as follows: we know that the power set of any set is strictly greater than its base, so $|2^\mathbb{N}|>|\mathbb{N}|$, and $|\mathbb{R}|$ is to our knowledge (the continuum hypothesis) the smallest cardinality bigger than |\mathbb{N}|, so to demonstrate equivalence we need only find an injective function from $2^{\mathbb{N}}.

[warm shale]

Eater of Bees
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[zenith raft]

this approach feels a little bit immoral to me

[echo cosmos]

I have a proposal for such a function, but its pretty janky and informal. It goes as follows: given a set $A\in 2^\mathbb{N}$, pick the representative such that the numbers are listed in increasing order. Then, if it is finite, treat the elements of A as a string and append them together

[warm shale]

Eater of Bees

[echo cosmos]

assign the first digit as the cardinality of A and the digit run as the appended elements of the set

if it's infinite, then assign the first digit to negative one and the digit run as the appended sequence

ok yeah so its very immoral

its a hard problem, I wasn't sure how to approach. Are we supposed to just come up with a bijection raw? I could not think of one for the life of me

I guess, now that I think about it, there must be only countably infinite subsets with cardinality $|\mathbb{N}|$, so I can assign these to the negative numbers and skip the weirdness of strings for infinite subsets

[warm shale]

Eater of Bees

[zenith raft]

making an injection from 2^N to R and vice versa is more moral

[echo cosmos]

oh, that makes a lot more sense, yeah

So then, two injections in opposite orientation

hmm. From a real number, how would I assign a subset to ensure no two real numbers map to the same subset? again, very difficult. Maybe I should come back to this once I have a more real proposal

[zenith raft]

you could look for an injection from R to 2^Q instead if you know |2^Q| = |2^N|

i think that's much easier. at least i can think of a bunch easily and i don't have any in mind for R to 2^N

e.g. ||map x to (x-1,x+1) intersect Q||

[echo cosmos]

this is a subset, because every rational number has infinite representatives?

[zenith raft]

what?

[echo cosmos]

And its unique because every x is unique?

A subset of Q.

[zenith raft]

wdym representative

[echo cosmos]

like, aren't we mapping into the set of subsets of Q?

[zenith raft]

yes

[echo cosmos]

oh, you mean, just the set containing the one element

[zenith raft]

no

[echo cosmos]

$f(\sqrt{2})=\frac{sqrt{2}-1}{sqrt{2}+1}$

[warm shale]

Eater of Bees

[echo cosmos]

$f(\sqrt{2})=\frac{\sqrt{2}-1}{\sqrt{2}+1}$

[warm shale]

Eater of Bees

[zenith raft]

no - the map $f:\bR\to 2^\bQ$ defined by $$f(x) = (x-1,x+1)\cap \bQ$$

[echo cosmos]

Is this a subset of Q?

[warm shale]

:bending_skull:

[zenith raft]

so e.g. f(0) is the set of rational numbers in the interval (-1,1)

[echo cosmos]

Ohhhhh. I thought the first parameter was the numerator and the second parameter was the denominator

yeah, an open interval makes a lot more sense

ok, I'll come back to this tomorrow. Thank you for now.

.close

[obtuse pebble]

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[zenith raft]

[obtuse pebble]

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[shrewd trench]

why is it multiplied with 10^-3 ?

what is it converting it from and to

[unkempt vault]

a liter is 10^-3 cubic meters

and all the other units (like Joules) are defined in terms of meters

so cubic meters are the "natural" unit for volume

[frigid prawn]

meters are cool

[shrewd trench]

aha

okay

thank you

[obtuse pebble]

@shrewd trench Has your question been resolved?

[shrewd trench]

another question

from where did this R come from

nvm apparently it's a constant

[obtuse pebble]

@shrewd trench Has your question been resolved?

[obtuse pebble]

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[grizzled shore]

i might be being really dumb but

[safe ravine]

Hello

Im here

[safe ravine]

Ok

[grizzled shore]

where are these things from the span coming from

😭

[safe ravine]

I myself don't know

😭

[wild swallow]

which span specifically

[grizzled shore]

both of them

[wild swallow]

idk they just did some magic for the first one

[grizzled shore]

idk what im doing and waht im doing wrong but why is it those 2

[wild swallow]

second one you just stare at the matrix

[grizzled shore]

shouldnt the first one be you pick the first and 4th column of the original matrix A-I

[wild swallow]

you'd have to rref A - 1 to compute the kernel

[grizzled shore]

he did

on the top right it says gauss elim

[wild swallow]

too far in the corner

[grizzled shore]

oh but then (1, 0, 0, 0, 0) is col 1

[wild swallow]

is there a better view

[grizzled shore]

and (-1, 0, 1, 1, 0) is col 4

and he just did col 4 -> col 4 + col 1

[wild swallow]

you have to stare at the rref and figure out the linear combos

like you know the rank is 3

so you need two lin indep things to span the kernel

[grizzled shore]

i thought u just pick the non-pivot columns

[wild swallow]

first column of the rref is all 0

[grizzled shore]

of the original matrix

[wild swallow]

no

that's not how it works

[grizzled shore]

wtf it's always worked

[wild swallow]

that's how you get free variables

[grizzled shore]

doesnt the pivot columns in the ref tell you which columns of A form a basis of col(A)

[wild swallow]

yes

[grizzled shore]

so then the columns of A that don't correspond to a pivot column in the REF will be redundant

if you take the span of the columns of A vs take the span of only the columns of A that correspond to pivots

they'll be the same

ok but those columns dont form a basis for ker(A)

and we want a basis of ker(A)

[wild swallow]

yeah those columns aren't necessarily elements of ker(A)

the rref of A - 1 tells you the linear dependencies between the columns

you can just stare at it to extract the kernel

like the first column is all 0s

so you just take (1, 0, ...)

that'll get killed for sure

then you see that the 3rd and 4th columns are negatives of each other

so (0, 0, 1, 1, 0) works

that's your 2 vectors spanning the kernel

[grizzled shore]

so i just have to

look

with my eyes

and inspect it

that's so cringe

[wild swallow]

well

you can do it more systematically

but that will require you to write more

and i don't like writing more

you can write out the free variables and solve for the basis

[grizzled shore]

kinda cringe

ok

thank you

.close

[obtuse pebble]

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[vernal lance]

A(-5, -4) ,B(−1, 3) , C(11,4), D(3, − 5)
Find the area of a kite without using a calculator

[safe ravine]

,w define Pick's Theorem

[warm shale]

Results provided by WolframAlpha

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

Requested by oppailol.

[safe ravine]

See this is goated

For finding area of simple closed figures/polygons

If u have plotted the figure

@vernal lance

[wild swallow]

at that point you may as well just use shoelace

[vernal lance]

Without using a calculator I may as well use a shoelace?

[safe ravine]

Use this

[vernal lance]

lol

[wild swallow]

yes

[safe ravine]

Use pick's

[vernal lance]

thats what my teacher said too

[wild swallow]

shoelace is so much simpler to apply

[safe ravine]

Or else u can use simple

Geometry

Break into triangles

[wild swallow]

,w shoelace formula

[warm shale]

Results provided by WolframAlpha

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

Requested by tearfox

[safe ravine]

Is it not more calculative?

Without a calculator?

[wild swallow]

you're saying you can't multiply and add a couple 1 digit numbers

[safe ravine]

Okok

Okok

[vernal lance]

whats x3 and y3?

xn and yn

[safe ravine]

3rd vertice

Of the polygon

Aka in this case kite

[wild swallow]

list your coordinates in order

[vernal lance]

hold on lemme grab a book

[wild swallow]

(-5, -4)
(−1,  3)
(11,  4)
( 3, -5)
(-5, -4)

sum the products along the \ slanting diagonals, subtract the products along the / slanting diagonals

(-5)(3) + (-1)(4) + (11)(-5) + (3)(-4)
- (-4)(-1) - (3)(11) - (4)(3) - (-5)(-5)

that's twice the area of the polygon

https://upload.wikimedia.org/wikipedia/commons/a/a9/Shoelace3.png

this is the wikipedia image for how you do it

[vernal lance]

Alright

seems doable

@wild swallow do you add all of the sums together from top-left to bottom right and top-right to bottom left, them subtract them?

[wild swallow]

add the red pairs, subtract the blue pairs

[wild swallow]

i've written it out here for you to check against

[vernal lance]

alright

this was the math when I asked AI thats why I was asking

because im pretty sure 80 is right anyway?

[wild swallow]

well your first mistake was asking AI

[vernal lance]

lmao

true

[wild swallow]

,calc (-5)(3) + (-1)(4) + (11)(-5) + (3)(-4) - (-4)(-1) - (3)(11) - (4)(3) - (-5)(-5)

[warm shale]

Result:

-160

[vernal lance]

same answer regardless?

[wild swallow]

so it's 80

[vernal lance]

I got another question

That I thought I answered right but was apprarently wrong

A trapezium is enclosed by the straight lines y = 0 , y = 3 , y = 7 − x , and x = k , where k is a constant.
Find the possible values of k given the trapezium has an area of 24 units2.

[wild swallow]

this looks pain i'll let someone else handle it

[vernal lance]

lmao

[obtuse pebble]

@vernal lance Has your question been resolved?

[vernal lance]

,calc (-4)(-1) - (3)(11) - (4)(3) - (-5)(-5)

[warm shale]

Result:

-66

[vernal lance]

,calc (-5)(3) + (-1)(4) + (11)(-5) + (3)(-4) - (-4)(-1) - (3)(11) - (4)(3) - (-5)(-5)

[warm shale]

Result:

-160

[vernal lance]

.close

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

i forgot how you simplify 2/3 x, when x value is 3

[timid silo]

well

like the denomintator get divided by X which is 3 right

so

2/1

and then

what.

yes

[solemn thorn]

its 2

[timid silo]

then thats it

the answer is 2

no bc

[solemn thorn]

yea

[timid silo]

what is

wjatt]

?

oleikwdj

jodifskp

DONT

WE

USE

numratators

sometimes

no

like

no

[solemn thorn]

2/3 × 3 = 2 thats it

[timid silo]

(2/3)*3 = 6/3 = 2.

no u do

what

[solemn thorn]

bro

[timid silo]

WAIT I sent my msgs its not sending

nvm'

ugh its happening again

go to 1:24
https://www.youtube.com/watch?v=QYdjQCPFdlI
like what did he do

sorry late reply my wifi - the country is sileincing freedom of speech and slowing down wifi

gonna ping bc like i need to finish this under an hour - sorry ! 🦖

@timid silo 💗

istgg

.reopen

.close

[obtuse pebble]

Channel closed

Closed by @keen trellis

Use .reopen if this was a mistake.

[timid silo]

.reopen

[obtuse pebble]

✅

[timid silo]

yes

I NEED THIS PLEASE

like dont watch the whole thing

hello

just the

1:24

idk

i cant watch

OH WAIT

ok this wont work

ill jsut ask

verbally

ok so

im graphinh grade 10 linear equations

on a coordiniate plane

[timid silo]

and in this video i have a similar equation to that

which is y = 2/3x - 4

so hes using the table chart format

so like

i think yk how to do that

Ok so my question is

how do u simply 2/3 when x = 3

bc

step by step

ur doing this right

2/3 divided by 1/3

??????/

so like

we get

2/1

[timid silo]

so then do we subtract 2/1 with 4/1??

if x = 3 and y = (2/3)x-4 then you will have (2/3)*3-4 = 6/3 - 4 = 2-4 = -2

whats *

multiplication

2*3=6

2*3 = 2+2+2=6

[obtuse pebble]

@timid silo Has your question been resolved?

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[hoary kindle]

for part e, why isn’t this correct?

[hoary kindle]

and how do i know how the curve is supposed to look like for these types of questions?

[timid silo]

you’ve drawn something that isn’t a function

[hoary kindle]

oh yea

so how do i know how to draw it

like i could draw something that passes the vertical line test but how do i know its correct

[obtuse pebble]

@hoary kindle Has your question been resolved?

[earnest ermine]

First of all the funstion doesnt exist for y=2

or anythign above y=1 for a matter of fact

and plus no equation describes two curves that intersect in the fasthion you have drawn

[hoary kindle]

sooo?

why doesnt a function exist above y=1

[earnest ermine]

sub in 1

what do you get

[hoary kindle]

3/5

wait do u mean sub x = 1

or y =1

[earnest ermine]

no i mean y=1

[hoary kindle]

oh whoops

x = 0?

[earnest ermine]

you will end up with a negative square root

which is complex and not something related to what you are doing right now

no

1=8/4+x^2

[hoary kindle]

ohh that equation

[earnest ermine]

i mean sub in y = 2

mb

2=8/4+x^2 -1

which then goes to

[hoary kindle]

but then finding the range would be easier in this case then

[earnest ermine]

yes if you found ur range you would see that the funtions range is (-1,1]

and what you have drawn goes beyond y=1

ur graph should join

[hoary kindle]

wait so how do u find the range

[earnest ermine]

no real methods besides observe for example

u can test values

and what would help you is learning graph shapes

[hoary kindle]

thats tiring

[earnest ermine]

and what shapes do and dont exist

for a function which is not a peicewise funstion it will never look like what you drew

its just learning and do large amounts of graphing to get comfortabke with graph shapes

if you want to check use a graphing calculator online

[hoary kindle]

yea i tried it

so if i want to find the range

i would have to sub in multiple values

to find it

[obtuse pebble]

@hoary kindle Has your question been resolved?

[solemn thorn]

just find the values that makes it 0 and make a inequality? table (didnt learn math in english so might be using the wrong terms)

[hoary kindle]

in that case x = plus minus 2

[solemn thorn]

yeah and from that you can find y is negative between (-∞,-2)u(2,∞)

[hoary kindle]

wait what

[hoary kindle]

i sort of get it

[solemn thorn]

if the value of x is anything smaller than -2 f(x) will be a negative always

f(-2)=0 and anything inbetween -2,2 is positive

so you draw the function based on that

[hoary kindle]

oh yea i get u now

[solemn thorn]

and you've already drawn y=-1 never happens it just keeps getting closer from both sides

and you can find the max value by taking its derivative

[hoary kindle]

idk derivatives

[solemn thorn]

well you can kinda guess then, you did draw the maximum point on X=0 line anyway which is correct

you just have to find the value of y

[hoary kindle]

.close

[obtuse pebble]

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[earnest ermine]

first question

[obtuse pebble]

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

[earnest ermine]

2

[obtuse pebble]

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

[earnest ermine]

dont know where to go after the second line

[earnest ermine]

yh

[hardy widget]

Note that $\cos^2 x=1-\sin^2 x$

[warm shale]

Civil Service Pigeon

[earnest ermine]

uhuh

[hardy widget]

So $\int \sin^5 x \cos^2 x \dd{x}=\int \sin^5 x \dd{x}-\int \sin^7 x \dd{x}$

[warm shale]

Civil Service Pigeon

[hardy widget]

The rest is basic algebra

[earnest ermine]

ok let me have a try

oh got it thx

[hardy widget]

!done

[obtuse pebble]

If you are done with this channel, please mark your problem as solved by typing .close

@earnest ermine Has your question been resolved?

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[earnest ermine]

when added to a quantitiy of water, 6 grams of a chemical dissolves at a rate equal to 20% of the undissolved chemical per hour. If m grams is the ammount of chemicla dissolved at time t hours, then what differentail equations does m satisfy

[earnest ermine]

the answer if dm/dt=(6-m)/5

need explanation on how

[obtuse pebble]

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[obtuse pebble]

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[graceful marten]

Whats another way of doing B ii

Its just I dont fully understand the values im taking P(Dog), P(Wet)

[rose scroll]

P(dog) is sum of the entire row

Similarly P(Wet) is the sum of whole column

Coz for all the elements in row, eg if its Dog and Dry = 11, it is still dog.
So you count all such under the dog category(which is the whole row)

So, P(Dog) = 11+28+8 / 80

Thats 47/80

[graceful marten]

yeah

Question

What would just Dog U Wet' be

[rose scroll]

im not sure i understand what you mean

Ohh okok

[graceful marten]

Whats the pobability of it being a dog and not being wet

[rose scroll]

I just saw the edit

[graceful marten]

my bad^

11+8 /80 ?

What about Dog or wet'

[rose scroll]

Dog and Wet' would be sum of the rest of the elements (the 6 leftover ones in the table)

Coz its union

[graceful marten]

right

how could i figure out the union bit of it

47/80 + (11+8) /80 - overlapping

[graceful marten]

wait all 6?

[rose scroll]

Yes

Coz dry is included in wet'

and so is raw

[graceful marten]

so Dry 11+10 and raw 8+4

-33/80

?

[rose scroll]

Not 6, 4 my bad

[graceful marten]

okok

[rose scroll]

I took it as 3x3 table mb

[graceful marten]

hehe

[rose scroll]

But yea, it would be 33/80

[graceful marten]

ohhhhhh

I cant beleive im getting it

[rose scroll]

Congrats 🙂

[graceful marten]

thank you

is it normal to not understand it first hour, and then once you come back to it you just get it

[rose scroll]

Totally

[graceful marten]

hmmm

[rose scroll]

You need a stroke of inspiration, and it can come from anywhere anyplace

[graceful marten]

ER

alright

Well thank you

: >

[rose scroll]

np

[graceful marten]

appreciate it

bdusdubsu

[rose scroll]

you can .close it if you want to 🙂

[graceful marten]

right

.close

[obtuse pebble]

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[graceful marten]

tyty

[obtuse pebble]

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[crude cape]

I think I solved it wrong, I don't know if there is an easy way to find the distance that is furthest from the line

[stone holly]

,rotate

[stone holly]

is that the original ques?

[crude cape]

Just the above, the drawing and f(x) and g(x)

I did the rest myself

The area of the triangle is 1/2 base times height

So I thought if I could rotate the graph the same slope as the line I could see where it has the greatest height

I don't know if there is any way to do it

[stone holly]

it's correct i guess

[crude cape]

But subtracting the parabola from the straight line gives me the vertical distance and it is possible that the most optimal distance is diagonally.

So I'm doubting if how I did it in the image is correct

[stone holly]

but if you geometrically if it goes diagonally the base length would also dec

which would result in dec. of area

[obtuse pebble]

@crude cape Has your question been resolved?

[obtuse pebble]

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[wheat sonnet]

Is there a software or website for graphing modular surfaces in 3D? Im interested in complex analysis

[wheat sonnet]

<@&286206848099549185>

[stone holly]

blender

https://youtu.be/nT3WYFxvPLk

[wheat sonnet]

sure thanks, is that what most people use?

[civic socket]

some ppl use tikz

[stone holly]

it's famous

[wheat sonnet]

is it possible to create a website where visitors can graph functions without coding?

if it is then it mustve been made already

[stone holly]

google it

someone on reddit would've asked it

[wheat sonnet]

dont think so