help-33

[west night]

thanks for the help

[marsh citrus]

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[sage pelican]

Why did they just yeet the 2k?

[sage pelican]

And how does k-6 turn to a positive?

[upper briar]

yeet

well

-(k-6)

[sage pelican]

ohhhhhh

[upper briar]

=-k+6

yeshh

hahhaha

[sage pelican]

What happens with the 2k though?

Nvm

I see

I'm slow

Thank you for your help lmao

.close

[marsh citrus]

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[thick plank]

Pretty sure I got part a.) correct on this, I got lost on part b.) and so forth on parts c.) and d.) I assumed the linear speed of the south and north poles would be 0 as they aren't moving along an arc in this case. Part c.) I assumed was my full linear speed of .26 rad / hr, but I feel like something is off as it gave me a radius of 6400Km and think it would go into an equation somewhere

[thick plank]

sorry my handwriting sucks lol

[ashen blaze]

physics

[thick plank]

trig

[ashen blaze]

hmm

Oh wait you got part a

That was the bit I could help you with

[thick plank]

yeah past that what i did felt too simple lol

[ashen blaze]

Yeah I have no clue

I do physics also, stuff gives me a headache

[thick plank]

the formula for linear speed is v = s/t [expanded???: r(theta) / t = r w ] but idk what values i would be plugging in for these

but yeah idk what values i would plug in

[marsh citrus]

@thick plank Has your question been resolved?

[thick plank]

<@&286206848099549185>

[hollow quest]

not sure if i misunderstand the question but im pretty sure you are supposed to find what the velocity of a person standing on the north and south pole would have. now think about it. if you are standing on the axis of rotation, do you really have any speed?

so it should just be 0 as you thought, unless they are talking about the magnetic poles, in that case they will not be completely along the axis of rotation

[thick plank]

thats what i was thinkin lol

pretty sure its 0 for B

then C would be my full speed @ .26 rad per hour

and D would be .13

but that feels too simple??

[hollow quest]

its a trigonometry question for D

you have that its latitude is 45 degrees

also for C you should also be using linear speed not angular speed

so you have the rad per hour, then you have the radius of the earth, the linear speed can be given by $$v=\omega R_{Earth} \cos (\theta)$$

[elfin berry]

Duh Hello

[hollow quest]

i think at least, this is just off the top of my head, dont quote me on this

so you can see that given it being on the north pole we have $\cos (90)=0$, for the equator we have $\cos (0)=1$. what do we have halfway between the equator and the poles?

[elfin berry]

Duh Hello

[thick plank]

So your saying C would be

[hollow quest]

that does seem to match reality

your units are in km/hr btw

[thick plank]

yeah i saw that

trying to solve d right now

[hollow quest]

also just to comment on what your original thoughts on D was. you said that it would be half, but turns out that at a 45 degree angle we get $\cos (45)=\sqrt{2}/2$

[elfin berry]

Duh Hello

[thick plank]

yeah i realize my original thoughts on d were wrong

i was thinking halfway on a line and not an arc

so V = 1176.63 km roughly

[hollow quest]

looks correct again

1180 km/hr according to google

[thick plank]

ok well it makes sense to me thinking about it

so i guess were all done here lol

woo hooo

thank you

[hollow quest]

but i would try to figure out how to get to that formula tho

it was not something i looked up

i shouldve maybe given you advice on how to get to it instead of just giving it but i wasnt entirely sure it was correct lol

so didnt wanna waste your time getting to a formula that is wrong

[thick plank]

its essentially this one no?

[hollow quest]

the $\cos(\theta)$ is the crucial part of these types of problems tho. you can probably draw the problem and see why it has to be it

[elfin berry]

Duh Hello

[thick plank]

this was the last problem for this chapter so i doubt something like this will be on the exam

[hollow quest]

the trick is to treat the earth as a cylinder. and your latitude will decide what the radius of the cylinder is based on $R_{Earth} \cos(\theta)$

[elfin berry]

Duh Hello

[hollow quest]

alright, well gl with the studies

[thick plank]

thank you! and thank you for your help

.close

[marsh citrus]

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[marsh citrus]

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[winter sapphire]

Hi and thanks for reading, just wanted to preface by saying this IS academically honest. I just need to know what I did wrong, or rather, how to do "it" right.

[winter sapphire]

Questions 12 and 13.. I did an "illegal move." I don't know what's the right way to solve these? I did every problem this way and always got them right so I never even knew I was doing something wrong.. until the test.

I understand that normally you can't distribute a radical like root(9 + 25) does not equal 8, so what makes this work?

[marsh citrus]

@winter sapphire Has your question been resolved?

[winter sapphire]

<@&286206848099549185>

[winter sapphire]

If anyone happens to read this.. After 30 minutes does this mean nobody wants to answer the question and I should just close it or is it worth keeping it open?

I won't take it personally.. I just don't want to take up a channel if the question is going to be ignored

[hollow quest]

you can divide the top and bottom by $x^2$ to get
$$\lim_{x\rightarrow \infty}\frac{\frac{x^2}{x^2}}{\frac{\sqrt{x^4+1}}{x^2}}=\lim_{x\rightarrow \infty}\frac{1}{\sqrt{\frac{x^4}{x^4}+\frac{1}{x^4}}}

[elfin berry]

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

[hollow quest]

or maybe more cleanly would be to factor out $x^4$ from the square root

[elfin berry]

Duh Hello

[hollow quest]

but would give the same

[winter sapphire]

So the fact that I got the right answer with the wrong math was just a coincidence?

[hollow quest]

yea the answer is right for the wrong reasons. it is very much possible to get the wrong answer with that illegal move

[winter sapphire]

I see 😮‍💨 What a chump (me)

Thanks!

[hollow quest]

no worries

[winter sapphire]

.close

[marsh citrus]

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[still temple]

Is the answer affine subspace?

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

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[glad briar]

Maya has invested $12 000. She invested part of it in bonds paying 8% per annum and the remainder in a GIC which paid 9% per annum. After one year, she earned $1043 in interest from the two investments. How much did she invest in each investment?

[marsh citrus]

@glad briar Has your question been resolved?

[marsh citrus]

@glad briar Has your question been resolved?

[glad briar]

<@&286206848099549185>

Maya has invested $12 000. She invested part of it in bonds paying 8% per annum and the remainder in a GIC which paid 9% per annum. After one year, she earned $1043 in interest from the two investments. How much did she invest in each investment?

[tight furnace]

This'll be a system of equations

You need to solve for 2 things, amount invested in bonds and amount invested in GIC

so you need to find information from the problem that sets up 2 equations

[glad briar]

Uh

So

X can represent the amount invested in bonds

And y for gic

X + Y = 12 000

Then after

[glad briar]

0.8x + 0.9y = 1043

X + Y = 12 000

[tight furnace]

8% is .08

[glad briar]

Yeah

Wait

Ohhh

Im messed up

That was my mistake

🤣

[tight furnace]

dw lol

everything else is good

[glad briar]

I’m good. I was trying to figure out

[glad briar]

Yeah

Thank you

Simple mistake ass

[tight furnace]

np

[marsh citrus]

@glad briar Has your question been resolved?

[marsh citrus]

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[static orchid]

true

every vector of this form is a linear combination

wdym

this is by definition

-2u + 5v is a linear combination of u and v

ye

you need to find a, b s.t. w = au + bv

and you can write it as 2 equations

3 = a * 1 + b * 0
4 = a * 2 + b * 1

yes

[static orchid]

like here

u gets the 3

0 is always a linear combination.

yes

0 = 0u + 0v

when the first zero is the 0 vector of course

and the others are scalars

yes

always

yes

that is a good remark

thx this means alot ❤️ happy 2 help

[marsh citrus]

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[ocean fog]

Ooooi

[ocean fog]

hi one of the hints for this exercise is to build a matrix where the off diagonal index of that matrix is supposed to give the covariance

the matrix I built was
1 0
root(1-e^2) e

is this the right way ?

with this matrix i should get
X' = Matrix * X

[calm anvil]

Bro screw matrixes

[upper briar]

wowwww

[ocean fog]

poor matrix

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[marsh citrus]

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[still temple]

Did I do this right

[marsh citrus]

@still temple Has your question been resolved?

[strong cedar]

yesh

[upper briar]

QUEEEEEEEEEEEEEN

[still temple]

https://media.discordapp.net/attachments/961435932769259614/1021475717512450079/IMG_5061.gif

[sage heath]

[strong cedar]

HI

QUEEN

[marsh citrus]

@still temple Has your question been resolved?

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[sterile flume]

can someone explain how we went from 1/x * sqrt(x^2 - 9 / 9) to 3/x*sqrt(x^2-9)

last 2

how did we take out the /9 in the square root

[sharp vessel]

$\sqrt{\frac{x^2 - 9}{9}} = \frac{\sqrt{x^2 - 9}}{\sqrt{9}}$

[elfin berry]

RedstonePlayz09

[sharp vessel]

After that, multiply both the denominator and numerator by 3

[sterile flume]

ah i see so sqrt(x^2-9) * 1/3 and then u flip it

thx g

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[marsh citrus]

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[sharp vessel]

no problem!

[marsh citrus]

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[craggy quartz]

idk how to start this

[craggy quartz]

i dont have the total amount of players

idk what to do

[wary kayak]

u dont need the total amount of players

[craggy quartz]

well thats confusing

[wary kayak]

do u know what the table is representing

[craggy quartz]

no

its quite hard to understanding the representation of the table

[wary kayak]

read the

uh

column labels

[craggy quartz]

i did

and i cant visualize it

[craggy quartz]

thats the first thing everyone does so its useless telling me this

[wary kayak]

well u said u didnt understand the table

im just tryna help

jeez

[wary kayak]

wydm u can't visualise it

[craggy quartz]

and im telling you i still dont understand it

[craggy quartz]

well i know what it means but i dont know how to find the probability

[wary kayak]

well u have number of matches

[craggy quartz]

i can see that

[wary kayak]

so u can start by adding all of the matches played

because it says based on this data

[craggy quartz]

and the total amount of injured players / total amount of matches played

[wary kayak]

u want

total amount of matches where zero players were injured / total amount of matches played

bc u want probability of zero injuries

[craggy quartz]

what if i want to find the probability of being injured in the next match

[wary kayak]

u added it wrong

[craggy quartz]

16

[wary kayak]

wydm by next match... so u r assuming zero players were injured the first match?

[wary kayak]

nice

[wary kayak]

BRUH

UR SO.

OK i calm

read the question carefully

especially the first part

"based on this data"

[craggy quartz]

ye

i am referring this table

[wary kayak]

reasonable estimate...

[wary kayak]

so i dont see where the issue is

[wary kayak]

its just what i said here

number of times zero players where injured/ total amount of games

[craggy quartz]

ok

[craggy quartz]

cause theres none

[wary kayak]

what answers do they give as options

[craggy quartz]

lets ignore that

is 4/16 correct?

[wary kayak]

yes

[craggy quartz]

so its 0.25

[wary kayak]

yes

[craggy quartz]

what if i wanted to find the probability of being injured?

[wary kayak]

the u do the opposite

so

[craggy quartz]

other than 1-P(not being injured)

[wary kayak]

mhm

so it would be just 1 - 0.25

[craggy quartz]

how about the other way?

[wary kayak]

wydm other way

[craggy quartz]

like this

[wary kayak]

u would take the favourable outcomes

over the total outcomes

[craggy quartz]

......../total amount of games

[wary kayak]

favourable outcomes is ?

[craggy quartz]

im having trouble finding the favourable outcomes

[wary kayak]

favourable outcomes means when the event occurs

so when someone or more than one person is injured

[craggy quartz]

number of people that was injured/number of matches

im a little confused cause there is more than 1 person

[wary kayak]

ohh

uhh

[craggy quartz]

hmm

[wary kayak]

is this a question

or like u just being curious

[craggy quartz]

im being curious

[wary kayak]

so this

u can

weight the injuries differentely

*differently

iyk what i mean

[craggy quartz]

ratio?

[wary kayak]

so in a game where 4 ppl are injured

[craggy quartz]

like 1:2

[wary kayak]

its weighted as 0.5 games

[wary kayak]

sorta

it would be 4:1

1:4 i mean

[craggy quartz]

hmm

[wary kayak]

yea player to number of matches

wait bruh

im confusing myself

anyways

[craggy quartz]

hmm

[wary kayak]

treat it as one injury per match

[craggy quartz]

why do we do this?

[wary kayak]

so if u had 4 injuries in 2 matches

u would say 1 injury per 0.5 matches

[craggy quartz]

0.5 injury in 1 match

[wary kayak]

yea make sense?

[craggy quartz]

oh wait

[craggy quartz]

my state contradicts this

[wary kayak]

then do that for each numbers

[craggy quartz]

urs correct

ok

[wary kayak]

so for the 3 injuries per 3 matches

what would u get

i just realised an easier way to do this but we can use it to check our answer

[craggy quartz]

1 injury per game

[wary kayak]

mhm

what about 2

again 1 right?

[craggy quartz]

2 matches?

[craggy quartz]

its ok i understand this part

[wary kayak]

mhm

[craggy quartz]

but why do we measure in number of injuries in 1 match

[wary kayak]

we arent doing that

we are saying

[craggy quartz]

and not 5 matches or more

[wary kayak]

how many matches per 1 injury

[wary kayak]

hmm? wdym

[craggy quartz]

i think its how many injuries per match

because we are counting number of injuries in 1 match

[wary kayak]

i dont think we are

look back at what we did

so first

we divided 4 by 2

its basically saying

[craggy quartz]

if we do this. Then the number of injuries will always be 1

[wary kayak]

$/frac{4}{4} /text{injuries} = /frac{2}{4} /text{matches}$

ignore

[craggy quartz]

ok

ok i did it

so do i just add the number of injuries per match / total number of matches

[wary kayak]

yea thats what we want

[wary kayak]

u wrote it wrong tho..

its

0.5 matches per injury

and 1 match per injury

[craggy quartz]

this seems wrong

[wary kayak]

hoq

*how

[craggy quartz]

hmm wait

its correct

[wary kayak]

we divided by the number of injuries

[craggy quartz]

but its the same

[wary kayak]

not rlly

[craggy quartz]

how is mine not the same as yours?

mines wrong

[wary kayak]

because if u referse it

reverse it

does it go back to the original

so look at the last row for eg

[craggy quartz]

how is this wrong?

its like 10meter/60 minutes

we want meter per 1 minute

so we divide numerator and denominator by 60

so it will be 1/6 meter in 1 minute

[wary kayak]

i dont understand what the 2nd and 3rd one represent

[craggy quartz]

ok give me a sec

[wary kayak]

i am confusion but if u feel like its correct i wont question it

[craggy quartz]

u understand this?

[wary kayak]

yw

YEA

no caps

[craggy quartz]

yee

just like this

i want to find km/minute

if it moves 30km/3minute

[wary kayak]

ik

[craggy quartz]

we do ........

[wary kayak]

but u did the last row

wrong

[craggy quartz]

ye ur right

[wary kayak]

which threw me off

bc u used my way

i put everything in per injury

[craggy quartz]

oo

what now?

after finding number of injuries/match or number of matches/injury

[wary kayak]

ohhh

[wary kayak]

so u want to find probability of being injured

so

[craggy quartz]

yes

[wary kayak]

u take favourable outcomes

which is just

injury per match

right

[craggy quartz]

ye

[wary kayak]

over number of matches

which is 4

[craggy quartz]

4.2?

[wary kayak]

no

4.2/4

[craggy quartz]

4.2/4=1.05

it should be 0.75

[wary kayak]

no

the chance of getting injured per match is 1.05

so basically

each match u expect

1 person and 5/100 of a person to get injured

make sense?

[craggy quartz]

why over 4?

4.2 injuries in 4 matches?

[wary kayak]

yea

because u put everything over 1 match right?

[craggy quartz]

chance of being injured per match is over 100%

[wary kayak]

well i made error

it should be 4.2/5

[craggy quartz]

well why?

[wary kayak]

5 rows

u put all the rows

into

1 match

yea?

[craggy quartz]

ok

then its 0.84

[wary kayak]

it can be over because ur saying one person and a bit is injured

notice 4 injured person per 2 matches

thats a 200% chance of someone getting injured

[craggy quartz]

thats why not having the total number of players in the team is confusing

[craggy quartz]

theres only 1 person playing per game?

[wary kayak]

no

[craggy quartz]

well thats what ur saying

[wary kayak]

that is not what im saying

im saying probability of 1 person getting injured

is 200%

[craggy quartz]

ok

what now?

so how do we calculate?

<@&286206848099549185>

[wary kayak]

calculate what

[craggy quartz]

how do i find the probability of being injured other than 1-P(Not being injured)

[wary kayak]

just do

matches where at least one person is injured

it doesnt matter if there is more than one injury

what u want is

[craggy quartz]

same proportion

[wary kayak]

probability of at least one injury

so it doesnt matter if there are 4 injuries

u just say

so u would do

5+2+3+2/16

[craggy quartz]

ok

thanks

im satisfied now

thank you

.close

[marsh citrus]

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[craggy quartz]

.reopen

[marsh citrus]

✅

[craggy quartz]

the number of injuries per game does not matter

is the a matter of there is injuries and there is no injuries

thanks btw, have a nice day

.close

[marsh citrus]

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[wary kayak]

yes

well u r the one asking the question

[marsh citrus]

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[raw island]

how did this line occur

[late geode]

can you change the image format to jpeg

[sharp vessel]

Or just take a screenshot

[marsh citrus]

@raw island Has your question been resolved?

[marsh citrus]

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[kindred ore]

hello i have a question

[kindred ore]

i graphed the solids in geogebra3d and also the plane for w=0

i dont really understand the relationship at all

[rich mulch]

What do they mean with solid

[kindred ore]

it just means the 3d volume in between the two spheres

[craggy bolt]

You mean 4d?

[kindred ore]

S is in 3d i believe

the triple integral is in 4D

[full tree]

Maybe make reference to the triple integrals with the integrand x, y and z give the x, y and z values of the center of gravity. And due to symmetry this is the origin.

[kindred ore]

thanks

.close

[marsh citrus]

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[leaden wedge]

how can this be true. if it is not not regular, then it is regular right? what else can it be

[still creek]

I don't know language theory or whatever but just because something can prove something else doesn't mean that it always will

[abstract oyster]

This is saying: if you're trying to prove some language L is not regular, the pumping lemma may help

[leaden wedge]

so it is possible that it is not regular that the pumping lemma can't prove

[abstract oyster]

If you're trying to prove some other language M is regular, forget you know about the pumping lemma

[leaden wedge]

so if X is a language that is irregular, then it is possible that the pumping lemma doesn't prove that it is irregular.

[marsh citrus]

@leaden wedge Has your question been resolved?

[marsh citrus]

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[abstract oyster]

That's not what this slide is trying to say

.reopen

Though it is true

[marsh citrus]

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[hallow minnow]

Is this valid? Or how should I simplify

[marsh peak]

No that's not how you take square roots

[hallow minnow]

How do u take square roots

I forgot

💀

[marsh peak]

In this case just make common denominators and expand the brackets

And hope that the expression is smth^2

[hallow minnow]

wait im confused how did they expand this

ohhh nvm i get it

How would u integrate this?

[marsh citrus]

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[marsh citrus]

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[stoic quail]

,,|x|\left(\frac{x-1}{x^2+2}\right)\sim\frac{|x|}{x}

[elfin berry]

Umma.Gumma

[stoic quail]

can someone explain me why is the first side asymptotic to the second one

[upper briar]

as x goes to inf?

[stoic quail]

yep

[upper briar]

hv u tried taking limits

[stoic quail]

yes this is actually where I got from a more complex limit

[upper briar]

of 1 over the other

btw when u mean explain

u mean explain how to show

or intuitively y they r ~

[stoic quail]

yes I would be glad if you could show how

[upper briar]

anw if u take lim to inf

the |x| shld cancel

(x-1)/(x^2+2)

[stoic quail]

please write actual words, reading becomes painful otherwise

[upper briar]

[stoic quail]

ty :)

[upper briar]

anw

just

$\lim_{x \to \infty} \frac{|x|\left(\frac{x-1}{x^2+2}\right)}{\frac{|x|}{x}}$

[upper briar]

anw

u can kinda c the const terms will cancel

x will also cancel

[stoic quail]

I don't understand what you write

[upper briar]

which

the shortform?

[stoic quail]

got it ty

.close

[marsh citrus]

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[upper briar]

um

thats good

[marsh citrus]

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[night arch]

For f(x) = √(x^2 − 1) and g(x) = √(x − 3), determine the subset of the domain of g on which
the composition f ◦ g is well-defined. What is the domain of g ◦ f? Find formulas for (f ◦ g)(x) and (g ◦ f)(x).

[marsh citrus]

Please don't occupy multiple help channels.

[night arch]

Anyone able to help out with this?

[marsh citrus]

@night arch Has your question been resolved?

[marsh citrus]

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[languid notch]

i need help with qs b and c

[marsh citrus]

@languid notch Has your question been resolved?

[marsh citrus]

@languid notch Has your question been resolved?

[marsh citrus]

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[modest fractal]

I just started learning domain and range today

Could someone explain to me how I can approach b)

Yes, I pay attention in class, and yes, my teacher has been absent for two weeks

[shell vigil]

So domain is all the possible x values

And range is all the possible y values

[modest fractal]

Ok!

What would be the first step I take?

Oh wait that is like a circle

[shell vigil]

Yes

Therefore for c it’d also be no

[modest fractal]

No, it is a function

[bright jay]

Don't give out answers

[shell vigil]

Sorry sorry

[modest fractal]

It is practice nothing evaluated

[bright jay]

Does that graph pass the vertical line test?

[modest fractal]

What test?

I haven't done that test in school yet

[bright jay]

Still, it's a learning experience, hence you should try it on your own

[shell vigil]

Yep yep

[modest fractal]

Ok

[bright jay]

The vertical line test is a method to test if the relation/equation is a function

[modest fractal]

So if there is a vertical line, then it is a function?

That means only x = # would be a function?

[bright jay]

You draw a vertical line, and if it passes through many parts, then it it not a function

[modest fractal]

Oh wait

If there is two points on one line

Then that means two outputs though?

[shell vigil]

In a function each input should only have one output

[modest fractal]

But then how is that a function?

[bright jay]

https://youtube.com/watch?v=Mxe2lX1htNk
Here's a short video

[modest fractal]

If it has two outputs?

Ok

[bright jay]

It's not

One input has to have one output for it to be a function

[modest fractal]

Can there be two inputs to an output?

Oh yeah there can

A horizontal line

[shell vigil]

A horizontal line would not be a function I believe

Or well they might be

Not sure on that one

[bright jay]

Horizontal line test would be used to test if the inverse is a function

[marsh citrus]

@modest fractal Has your question been resolved?

[modest fractal]

Yes, thank you for your assistance @shell vigil and @bright jay

.close

[marsh citrus]

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[sonic pier]

Hey. I need to give a function R->R that is defined in 1 but not steady in 1.
Can anyone help me with that?

[sonic pier]

Would f(x)=|x-1| suffice?

[glacial hedge]

Steady isn't a math word for this. Do you mean continuous or differentiable

Differentiable is whether or not f'(1) exists

[glacial hedge]

If the answer is differentiable, then this is indeed a function that's continuous but not differentiable at 1

[sonic pier]

It seems what I thought meant "steady" would describe "continuoues"

So my function is wrong :/

[glacial hedge]

Differentiable ist über "das funktion hat ein derivativ oder nicht ?"

[sonic pier]

I think "Ist differenzierbar" would be the german translation.

But in german it asks of a function that is "stetig"

[glacial hedge]

As you can see from similarity, these are all about having a derivative/derivat

Not sure about the german word lol

[sonic pier]

hm yes. If it would be about differentiable I could make a function where f'(x) = 1/(x-1)

But I think continuous is asked here.

[glacial hedge]

The simplest example of a discontinuous function is to be 0 everywhere and 1 at the point of discontinuity

That's one of the simplest things you can do

[sonic pier]

Ah yeah. That's true.

Alright. Thanks a lot 😅
I was trying to find something with a "numerical" function but I could have just defined it like this.

[glacial hedge]

Btw if you're trying to translate math terms: go to the german wikipedia page by searching the german name, then switch to english on Wikipedia to get the page's english name. Usually that's the translation, or something similar, in which case you usually get the word you're looking for by just reading the start of the intro block

[sonic pier]

Ahh. Very handy :D

[glacial hedge]

If you study some more math, you'll find that numerical functions defined by formulas are actually very limiting, and that we can think of a great number of functions that don't look like that at all (be they numerical or not)

[sonic pier]

Interesting :D

Your wikipedia tip already helped me with the next question I was preparing (mostly translating) where I used the term "quantity" instead of "set".

[glacial hedge]

A function is just an input -> output mapping, which is much more general

[sonic pier]

True. I probably was used to it being "numerical" so my horizon didn't think of that.

.close

[marsh citrus]

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[glacial hedge]

For instance you can have the mod n function : k -> remainder of the euclidian division of k by n

Or a function that to a line in R^2 gives the line with double the slope and same y-intercept

[marsh citrus]

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[marsh citrus]

Please don't occupy multiple help channels.

[late raft]

i need help with part c

someone pls

[upper briar]

that looks

so cursed

[late raft]

lol

[true flicker]

Brush yo teeth

[late raft]

help me do c

[still temple]

Ew

[late raft]

part c anyone

[still temple]

I like that emoji

[quasi osprey]

Same

[still temple]

Also you ping helper I think when you don't get help

[late raft]

<@&286206848099549185>

[amber terrace]

which part do u need help with

[late raft]

part c

[amber terrace]

welp ive never heard of this intermediate value theorem

rip

[late raft]

<@&286206848099549185>

.close

[marsh citrus]

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[vital tartan]

I'm confused, how can any of the following options make the overall statement an empty set?

[marsh citrus]

Please don't occupy multiple help channels.

[proven timber]

What have you tried?

[vital tartan]

This quiz randomly generated what the whole statement equals to. The last two attempts were {1, pi, clover} union symbol A = pi

and {1, pi, clover} union symbol A = 1

[proven timber]

That's not a union symbol

[vital tartan]

intersect symbol?

is that what you call it

[proven timber]

Union symbol is a U

That's an intersection, yes

[vital tartan]

but yeah, now it's equal to empty set

[proven timber]

Let's try each option in order

Let's say A = {♡}

What's {1, π, ♧} n {♡}?

[vital tartan]

Well that wouldn't work because heart is not in the first set, right?

[proven timber]

What is the definition of an intersection of two sets? What does it give you?

[vital tartan]

set of all elements which are common to set A and B

[proven timber]

And what if sets A and B have no elements in common?

[vital tartan]

oh, it produces an empty (disjoint) set?

[proven timber]

Yes

If the sets have no elements in common, the set containing the elements in common is quite empty

[vital tartan]

thank you so much! I understand now! :D

.close

[marsh citrus]

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[marsh citrus]

Please don't occupy multiple help channels.

[vital tartan]

is this asking if it's possible for a ordered pair to exist in natural numbers?

just need help interpreting the question is all

not the actual answer

[proven timber]

You need to close your other channels when you're done

[vital tartan]

i did, with .close

or is there some emoji check

i didn't click

oops

[still temple]

(1,3) is in N² but i don't have an explanation

[proven timber]

I'm pretty sure that's what it's asking, yes

[vital tartan]

it just is?

oh

okay since it exists in N^2 but not N

I guess I have my answer

.close

[marsh citrus]

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[vital tartan]

thank you!

[still temple]

You take 1 in N and 3 in N so (1,3) is in N x N

[marsh citrus]

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[sharp sigil]

Is my work here correct? Is the answer 63N

[marsh citrus]

@sharp sigil Has your question been resolved?

[upper briar]

#❓how-to-get-help

@harsh onyx

[marsh citrus]

@sharp sigil Has your question been resolved?

[marsh citrus]

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[scarlet oracle]

Find the limit L of lim x^2 as x->0 and prove using epsilon delta proof

[marsh citrus]

Please don't occupy multiple help channels.

[scarlet oracle]

any help

[main idol]

close your other channel

and read this like i said
#help-39 message

[true flicker]

Let £ > 0 be arbitrary
Let epsilon = min {£,1}

[marsh citrus]

@scarlet oracle Has your question been resolved?

[marsh citrus]

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[livid shale]

what the red circle indicate

[livid shale]

hello

[mystic minnow]

Symmetric difference

[livid shale]

ok

.close

[marsh citrus]

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[brave pumice]

<@&286206848099549185> @marsh citrus

[brave pumice]

<@&286206848099549185>

[upper briar]

das

a lot of pings

no1 even came

i feel bad for u

#❓how-to-get-help

here

oh and

!15min

[marsh citrus]

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.

[marsh citrus]

@brave pumice Has your question been resolved?

[brave pumice]

.close

[marsh citrus]

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[marsh citrus]

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[still temple]

is it a closed system?

so E = K + U

[marsh citrus]

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[marsh citrus]

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[lucid hill]

Im stuck on b (i), can someone help me?

[glass viper]

do you know what's the connection between a function and its second derivative ?

[lucid hill]

yeah i got it :P

.close

[marsh citrus]

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[marsh citrus]

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[flint briar]

Why did we multiply x³-4x+3 by 2?

[stoic saddle]

to make the long division work out nicer, by the looks of it

[marsh citrus]

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[marsh citrus]

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[plucky badge]

.close

[marsh citrus]

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[still temple]

Viena lygiagretainio kraštinė 5 kartus ilgesnė už kitą. Koks gali būti to lygiagretainio perimetras, jeigu lygiagretainio krašto ilgiai išreiškiami sveikaisiais skaičiais?

[marsh citrus]

Please don't occupy multiple help channels.

[swift cypress]

english?

[still temple]

owh ye

i forgot

One side of a parallelogram is 5 times longer than the other. What can be the perimeter of that parallelogram if the side lengths of the parallelogram are expressed in whole numbers?

could you help?

plz

[leaden monolith]

We don’t help on timed tests…and don’t occupy multiple help channels, type .close in the ones you are no longer using

[marsh citrus]

@still temple Has your question been resolved?

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[thorny jungle]

is this correct?

The answer is the same at the back, except, it had $\dfrac{1}{x^2+C}$

[elfin berry]

KN

[still temple]

because C is arbitrary

your answer is correct

just leave it as +C, we usually don't care about signs when it comes to integration constants in ODEs

(unless we have initial or some kinds of conditions)

[thorny jungle]

ah i see

thanks

.close

[marsh citrus]

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[marsh peak]

So, what's the question?

[novel elbow]

so

ahm

find the derivative using the four-step rule

I know how it's done but I'm having troubles solving this one

[marsh peak]

What's four-step rule?

[novel elbow]

I'm not sure how to explain it

[marsh peak]

Alright, but you are familiar with power rule and chain rule, right?

[novel elbow]

I know that... but it should be solved through four-step rule of derivative...

[late geode]

limit definition?

[novel elbow]

yes

can you help me?

[late geode]

show what you've managed to do so far

[novel elbow]

wait

I don't know if this is right

I'm stuck here...

is my substitution correct?

[marsh peak]

Yeah you were on the right path

Despite the non-standard notation

[late geode]

its one of the less common ways to it

continue

[marsh peak]

(hint: difference of squares)

[novel elbow]

I did... hahahaha but it's too long and I think it's wrong

but I'll show you

I don't really know if doing it correctly

[late geode]

pic quality is so low

[novel elbow]

oh sorry...

[late geode]

but it looks like you crossed that out for no reason

the $ab\Delta x$ doesn't cancel with anything and you should have a total of $2ab\Delta x$ later in your work

[elfin berry]

ℝamonov

[novel elbow]

okay I'm done with it now

so

here's what I have now

2a^2xdeltax + a^2deltax^2 + 2a2bdeltax

oh so it's just 2abdeltax? instead of 2a2bdeltax

[late geode]

for that last term yeh

[novel elbow]

so what's next now?

[late geode]

this was just the numerator

remember that you had a Delta x in the denom

simplify the fraction

[novel elbow]

okay I think that's the hard part

[late geode]

try not to overthink

you can even first split your fraction as a sum of 3 fractions if you want

[novel elbow]

I'm stuck

[late geode]

would you be able to simplify something like
$$\frac{2a + 6b + 8c}{2}$$

[elfin berry]

ℝamonov

[novel elbow]

hmmm... through lcd?

oh

lemme try...

is this correct?

[late geode]

no

taking the limit as Delta x → 0
is not the same as rubbing Delta x out

specifically
as Del x → 0, a^2 Del x isn't a^2

[novel elbow]

OH!!!!

I seee...

so it's just 2a^2x + 2ab?

[late geode]

yes

[novel elbow]

thanks ramonov...

🙂

I'm too slow...

@_@

[late geode]

the simplification is a lot less tedious if you factor the numerator as

(hint: difference of squares)

[marsh citrus]

@novel elbow Has your question been resolved?

[marsh citrus]

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[cloud iron]

Chain rule yields 3x^2 from the x^3 exponent

[upper briar]

,w derivative of e^(f(x))

[elfin berry]

Results provided by WolframAlpha

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Requested by Circle#0025

[upper briar]

the f' in this case is 3x^2

[forest bone]

$$e^{x^3}$$
You can already apply the chain rule here, you don't need to split x³ into x•x². The inner function is x³, the outer function is e^x

[elfin berry]

Andrea276
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[bitter warren]

Oh I was working with the n(f(x))^(n-1)*f'(x) rule

Ill rework it with the eulers number rule

Okay thank you so much thats a really handy rule to remember

.close

[marsh citrus]

Channel closed

Closed by @bitter warren

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[forest bone]

You can't use that since the power is not a constant, but another function

[upper briar]

yesh

[marsh citrus]

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[slow dock]

Four large containers are filled with coins. The first contains only 10kr, the second 5kr, the third 2kr and the fourth 1kr. In how many ways can you select coins to add up to 20kr?

how do i solve this?
I thought i should put it as an equation: 10x + 5y + 2z + 1w = 20
but idk what to do with it

[eternal tundra]

i would just bruteforce hehe

but that is not efficient

[slow dock]

is there another way?

[eternal tundra]

probably yeag

[slow dock]

do you have any place i can search it up?

[eternal tundra]

sadly no but others here have hopefully more info

[slow dock]

thx anyways

<@&286206848099549185>

<@&286206848099549185>

[marsh citrus]

@slow dock Has your question been resolved?

[slow dock]

@tight lance

<@&286206848099549185>

[sage heath]

@slow dock isn’t it just C(n+r-1, r-1)

ig its formula

no?

wait no

lemme think

[slow dock]

Ight.. take ur time

[sage heath]

i think it has something to do with it

[slow dock]

I have no idea tbh is Why I need help.. I have asked 3 otjer People and all they say it should be possible to do something but they want to brute force it

[sage heath]

what do you get by brute force anyway?

or do you have an answer?

[slow dock]

I dont

[sage heath]

oh okay

i’m sorry 😞 i’m totally blank rn

[slow dock]

no problem, I thank you for your time that you took to try to help me

[sage heath]

you should look up stars and bars theorem, i’m sure it has something to do with it

it is something like this

idk if it’s readable

okay well

[slow dock]

thanks a lot

[steady carbon]

its certainly a combinatorics question

just not sure where it falls

[sage heath]

the part 10x + 5y+2z+w =20 just makes me think it’s related some how

[slow dock]

I see where you are coming from yes

[steady carbon]

if x = 2, y, z, w = 0
if y= 4 x,z,w = 0
likewise for z=10 and w=20

so these are our bounds

[slow dock]

I found a summrizing slide from my teachers lecture, these are the things we apperntly went over:

[steady carbon]

thats just the permutation and combination formulas

unless im missing something here

[slow dock]

yea that is why it is so confusing cause it has to relate to the question

here is my question if we simplify it , let us say that we have we have two jars, one filled with 2kr and one filled with 1kr, how many ways can we add up to 4kr

I would assume 3

now let us say three jars, one filled with 5kr, one filled with 2kr and one with 1kr and we want to add up to 10kr, how many ways now

i count 8 ways

how does one get a formula out of this?

unless what i am doing is just stupid

[steady carbon]

no, thinking about the question is never stupid

[slow dock]

true

could it just be 2+1, and 5+2+1 ??

doesnt seem likely

[steady carbon]

from this i can deduce by reduction but not sure where the formulas relate

case 1: x=2
case 2: x=1, y=2
case 3: x=1, y=1, z=2, w= 1
case 4: x=1, y=1, z=1, w=3
case 5: x=1, y=1, w=5

etc.

[slow dock]

i guess bruteforce is the only way

[steady carbon]

when we think like this though, we can see that some instances repeat

so we need to get rid of those

so its not a permutation then

[slow dock]

Choose 2 ten kroner
Choose 1 ten kroner
-Choose two five kroner
-Choose a five kroner
--Choose 2 two kroner and 1 one kroner
--5 1kroner
-Choose zero five kroner
--Choose 5 two kroner 0 one kroner
--Choose 4 two crowns 2 one crowns
--Choose 3 two crowns 4 one crowns
--Choose 2 two crowns 6 one crowns
--Choose 1 two kroner 8 one kroner
--Choose 0 two kroner 10 one kroner
Select 0 ten kroner
....

we know that there is 8 ways to calculate 10kr in 5's,2's,1's so 20kr should just be 16 ways

so 26 ways?

[steady carbon]

i believe there are more

since 10kr jar is going to be able to swap in for more

[dim gull]

Um dos eletrodomésticos que podemos presenciar o movimento circular é na máquina de lavar roupas. Neste eletrodoméstico existe uma etapa chamada centrifugação que evidencia este tipo de movimento. Considerando um cesto que gira com uma frequência de 50 Hz e possui um raio de 20 cm, qual é a velocidade linear em m/s, tendo como referência um ponto na parede deste cesto.
Dados: π = 3 Peso: 0,5.
30
40
50
60
70

[slow dock]

I brute forced it and if I did it correctly it should be 38

thanks a lot for your time, i really appreciate the time you took to help me

.close

[marsh citrus]

Channel closed

Closed by @slow dock

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[still temple]

I need help simplifying this,