help-41

[ionic zodiac]

okay

how do i work out std

for part b how do i use this

[signal furnace]

Meaning [39,57] is the interval of all days within 3 standard deviations of the mean

[ionic zodiac]

so its 3?

[signal furnace]

,calc (57+39)/2

[grizzled pagoda]

Result:

48

[signal furnace]

Yeah

[ionic zodiac]

this is what it says

[signal furnace]

Yeah same thing

[ionic zodiac]

what does it mean 6 std

[signal furnace]

3 standard deviations to the left of the mean + 3 to the right = 6 in all

[ionic zodiac]

oh okay

[ionic zodiac]

and how can i do part C?

[signal furnace]

What’s the z-score formula? Substitute in what you’ll have so far and it becomes obvious.

[ionic zodiac]

Z = x - mu / sigma

so x represents the hours of sleep im looking for?

[signal furnace]

Yeah

[ionic zodiac]

i see

thanks

@weak zinc CHARRRRRRRT

i need help!!

why do we have to convert r to 0.21

or 0.021 i mean

i think

[weak zinc]

That’s 2.1% as a decimal

[ionic zodiac]

OHHH

silly me

[weak zinc]

hehe

[ionic zodiac]

What about this oneee

So I know it can’t be A

B doesn’t sound right

So either C or D

WAITTTT

i got it

That was easy lol

[weak zinc]

awwww

[ionic zodiac]

Does a bigger standard deviation mean he did better or worse?

[signal furnace]

Better (assuming you count sign when determining “bigger”)

[ionic zodiac]

Hm so how would I decide what’s his worst one is it stats

[signal furnace]

That’s the best one

[ionic zodiac]

Why is it his best

Wouldn’t measurement be

[signal furnace]

How do did you get that it’s the worst

[ionic zodiac]

Idk I just looked at the mean and standard deviation and cuz it was lower than the rest I just assumed it was his worst

[signal furnace]

Just find the number of standard deviations above/below the mean

[signal furnace]

That’s what I was referring to here

[ionic zodiac]

I mean we don’t know what 1 standard deviation is here tho cuz it doesn’t tell us right

[ionic zodiac]

Well I mean like

The value of 1 std

Idk if that makes sense

[signal furnace]

Ummm

That’s what I boxed tbh

[ionic zodiac]

73 + 5 is 78 which is his second highest isn’t it

[signal furnace]

…

His score is 88

[ionic zodiac]

So I add the std onto his score

Ok gotcha

[amber wasp]

@ionic zodiac Has your question been resolved?

[amber wasp]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[bronze shuttle]

why is the first = true

[bronze shuttle]

it should just be $=|\emptyset|$

[grizzled pagoda]

Ayanokoji (ALWAYS PING ME)

[fluid wren]

What does the arrow mean?

[honest dagger]

@bronze shuttle what does the arrow mean

[amber wasp]

@bronze shuttle Has your question been resolved?

[amber wasp]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hexed cedar]

is this right?

[outer hull]

is this a test?

[hexed cedar]

its hw

1.3 hw

[hexed cedar]

can a constant graph be linear

[outer hull]

yeah it has a slope of 0

[hexed cedar]

is thos right? the second and first differences are bith not the same byt those are the only iptions

[amber wasp]

@hexed cedar Has your question been resolved?

Channel closed

Closed by @hexed cedar

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[narrow hinge]

can someone help me with this

[narrow hinge]

this is what i did:

oops

wait

checking my work using a online calculator it gave me this

any idea where im messing up?

[quick ridge]

you used lhopital wrong (your derivative was wrong)

[shrewd elm]

derivative of ln(1-x) is what again?

[quick ridge]

it’s derivative of the numerator divided by derivative of the denominator

[narrow hinge]

1/(1-x)?

[shrewd elm]

don't forget the chain rule

you have a - on that x

[narrow hinge]

ohh

thanks

ah forgetting that sign is what messed me

got it thanks guys!

[quick ridge]

.close

[amber wasp]

Channel closed

Closed by @quick ridge

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[stone mantle]

im having some trouble integrating this to find the arc length

is there an integration technique i can use to make this easier

i tried using a math solver online and it said to use an identity involving sinh but that isnt covered in our course

[limpid sun]

$4+(e^x-e^{-x})^2=4+e^{2x}+e^{-2x}-2e^xe^{-x}=+e^{2x}+e^{-2x}+2=(e^x+e^{-x})^2$

[grizzled pagoda]

everg

[stone mantle]

huh

[limpid sun]

so you can get rid of the qsrt

sqrt*

[stone mantle]

how come your left side doesnt equal the right side

oh i see

i misread sometjing

[limpid sun]

I don t understand the question ... my I made some mistake ...are there some steps that are not clear ?

[stone mantle]

no the font was just kinda small and i misread

that makes sense

[limpid sun]

ooh ok

[stone mantle]

cause it turned from a-b to a+b

thanks! that got me the answer

.close

[amber wasp]

Channel closed

Closed by @stone mantle

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[woven junco]

on step 3 how ddid that happen?

[woven junco]

I've already looked at the proofs for the sum and difference of a cosine and sine

Now I'm looking at the tangent proof

on step 3, I'm a little confused at how it happened really

[uneven saffron]

you mean the third equal sign?

[spare belfry]

You just spilt it into two parts literally

[uneven saffron]

You just divide denominator and numerator with the same value

It’s like 4/6=(4/2)/(6/2)=2/3

[woven junco]

yes

[woven junco]

Oh I think I get it now

Thank you

.close

[amber wasp]

Channel closed

Closed by @woven junco

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[noble musk]

heya

[noble musk]

could someone explain this to me

i really dont understand

isnt (m-2)^2 = m^2 -4

[split sail]

yes

no

[noble musk]

o

[split sail]

it is formula

[noble musk]

wdym

[half rover]

nope

[noble musk]

im so confused

[split sail]

(a-b)² = a² +b² -2ab

[noble musk]

wait is this quadratics

[split sail]

try using this against (m-2)²

[split sail]

yes

[noble musk]

ohhhh okay, welp i dont gotta worry abt that and all then since i thought this wasnt one xd

[noble musk]

yep thanks

[split sail]

no problem

[noble musk]

cya

[split sail]

se eya

[noble musk]

.close

[amber wasp]

Channel closed

Closed by @noble musk

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hard frost]

what does it mean by maximum and minimum values

[strange field]

whats the max output u can get from that expression is the max value

and the same for min, the least value u can get from that expression

[hard frost]

oh kk

how do I do it

[strange field]

think how u can make it one term here

any formula like maybe sinAcosB + cosAsinB = sin(A+B)

[amber wasp]

@hard frost Has your question been resolved?

[amber wasp]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hard frost]

idk

[amber wasp]

@hard frost Has your question been resolved?

[strange field]

construct a right angle triangle with base = 3 and perpendicular = 4, then write the hypotenuse

then try to make this expression

into sinAcosB + cosAsinB

so that it equals to sin(A+B), then u can easily get the max value

[amber wasp]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hardy summit]

can someone tell me if this is correct in finding the general solution of a tan equation

[spark cobalt]

if $\tan(3x+\frac{\pi}{2})=1$, then $3x+\frac{\pi}{2} = \arctan(1)+k\pi$ and you continue from there. the $k\pi$ comes form the periodicity of tan. the other $k\pi$ you added later was not justified.

[grizzled pagoda]

Mohamed Mohsen

[amber wasp]

@hardy summit Has your question been resolved?

Channel closed

Closed by @hardy summit

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[heady valley]

Puzzle involves thinking outside the box and some mathematics.
The goal is to connect all nine circles using exactly 3 straight lines by the shortest route, without lifting the pen. Each straight line must pass through the center of one circle. Start of the path should be on the edge of the circle and path should end on the edge of the circle. Each circle you should pass (use) only once.

Calculate the total path with the pencil, taking that the distance between the centers of two adjacent circle is equal to 6, and the radius of each circle is equal to 2. Divide the number of circles with the total path. Do not round up.

A=3rd decimal digit
B=17th decimal digit
C=12th decimal digit
X=4th decimal digit
Y=16th decimal digit
Z=13th decimal digit

[heady valley]

.close

[amber wasp]

Channel closed

Closed by @heady valley

Use .reopen if this was a mistake.

[heady valley]

.reopen

[amber wasp]

✅

[heady valley]

<@&286206848099549185>

ANYONE

😭

[graceful coral]

Nobody is going to be able to make sense of your question, post the original

1. You haven't given any details about how these 9 circles are positioned
2. You haven't even given a single word of explanation as to what the list at the end is about

[heady valley]

List at the end are the specific digits in the answer

So for example A is the 3rd decimal digit so in 3.193, A = 3

I just found this and wanted to know the answer and how to solve it and thought someone here might know

[graceful coral]

Can you post the original question? It seems like there's a lot missing here

[heady valley]

https://www.geocaching.com/geocache/GC5HCFH heres the page

[graceful coral]

I think the question is just nonsense, it's clearly impossible for any 3 segment line with endpoints on the circles to pass through all 9 circles, even disregarding all the rest of it

Oh wait, it just says the endpoints of the path, there are solutions in that case

[amber wasp]

@heady valley Has your question been resolved?

[heady valley]

There is definetly an answer, just on the page you can see over 30 people solved it

[graceful coral]

Finding a solution is easy, proving minimal path length is not

I suspect it's this, but good luck proving that:

[amber wasp]

@heady valley Has your question been resolved?

[heady valley]

Well thats what I need help with

I think its something about triangles and stuff idk

[graceful coral]

I'll leave the proof to someone else, but that's what I think the solution is

[amber wasp]

@heady valley Has your question been resolved?

[heady valley]

Ok Ill see if the answer is correct and get back to you

Can you write that number in decimal with the first 17 decimals digits? @graceful coral

[grim forge]

In the words of my math teacher

Just press calculator

[heady valley]

My calculator cant show that many digits 💀

[grim forge]

Maybe wolframalpha can

How do I invoke wolfram alpha again

[heady valley]

I have no idea

[grim forge]

,w 18+20*sqrt(2)

[grizzled pagoda]

Results provided by WolframAlpha

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

Requested by denzio321

[grim forge]

@heady valley aight here ya go

[heady valley]

ty

[grim forge]

Is this a puzzle for a cache or something

[heady valley]

yup

Sadly the answer is wrong so rip

If you want I can give you the page to the cache and you can try solve it

And when you do slide me the answer 😏

http://www.geocaching.com/geocache/GC5HCFH

[heady valley]

3.5 difficulty is so biased

[versed basin]

HELP

[amber wasp]

@heady valley Has your question been resolved?

Channel closed

Closed by @heady valley

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vital hamlet]

ok, so I think I came up with a solution to thsi

[craggy quest]

ok

[vital hamlet]

can you tell me what are the properties of the tangent line

[craggy quest]

like what do you mean?

say what a tangent line is?

[vital hamlet]

the tangent line is perpendicular to the radius

that is what I meant

idk how to express it differenmtly

[craggy quest]

ok I see that

[vital hamlet]

now u can use that to construct a right triangle

[craggy quest]

ok I saw that idea

just above the C make a new point called Z so Now you have triangle MCZ

but even then since the MZ lenght is the hypotenuse how do you still figure out X and Y

[vital hamlet]

u know the length MZ is not the hypotenuse

MC is the hypotenuse

[craggy quest]

How is not?

Hypotenuse is longest side though

[loud willow]

i am going to spill the beans and say that the way i did it was using coordinates since this is due in 40 minutes

[vital hamlet]

but the right angle is located in Z

not in C

[craggy quest]

oh nvm im dumb

[vital hamlet]

np

[craggy quest]

so we know the hypotenuse length

and the ZC length

[vital hamlet]

yes

now

u will have to use coordinates to finish this

[craggy quest]

so is MZ root 8400

[vital hamlet]

we dont need that

[craggy quest]

ok

how would you use coordinates

[vital hamlet]

let M be the origin (0, 0)

[craggy quest]

ok

[vital hamlet]

now from the triangle you can calculate the slope of the line MZ

[craggy quest]

rise over run right

even then the slope is 20

[vital hamlet]

okay I lied you will need the length of MZ

[craggy quest]

root 8400

wait no thats not right

its root 9600

[vital hamlet]

when simplyfies its 40*root 6

for ease of calculation

[craggy quest]

ok

[vital hamlet]

so you do CZ over MZ

[craggy quest]

the Slopes?

or length

[vital hamlet]

the length of CZ over the length of MZ

[craggy quest]

(20)/40root6

[vital hamlet]

gives you the slope of the line MZ'

now you plug into y=mx+b

I would suggest opening desmos so u can visualize what we are doing

[craggy quest]

ok

so far we have slope

[vital hamlet]

and line

on graph

should look like this

[craggy quest]

whats our b value again

[vital hamlet]

0

[craggy quest]

is it just 0

because we did not do anything there

[vital hamlet]

becaause we want the line through the origin

yep

now to construct the circles on the graph

[craggy quest]

ok

[vital hamlet]

it's these equations for the circles

now we have succesfully graphed the problem we are trying to solve

[craggy quest]

ok

[vital hamlet]

the numbers that are in brackets with the x are the x coordinate of the center just negative, and with y we dont have any because we want the center on the x axis

[craggy quest]

like i am getting about 42 to 73

[vital hamlet]

now the second circle is the one whos intercepts we are trying to find

[craggy quest]

so 31

[vital hamlet]

well you can look at that or I think if your teacher is going to be grading your work we can do a calculation

[craggy quest]

ok what would be the calculation

[vital hamlet]

so for the second equation of the circle we can substitute for y, we will use the equation of the line so y=20/40sqrt(6) x

[craggy quest]

ooh that tells us the slope

just y or y^2

[vital hamlet]

just y

like this

this gives us a quadratic after simplyfication

and the roots of the quadratic are the x coordinates of the intercepts

[craggy quest]

ok

so just break down the 20 over 40 root6 ^2

[vital hamlet]

well u have to expand out the first bracket than square the second one and add like terms

[craggy quest]

yeah so it would be (400 over 9600)x^2

right

[vital hamlet]

it might be easier if you would first cancel out the 20/40 into 1/2

its a smaller number

[craggy quest]

that would just reduce it down to 1 /24 x^2

[vital hamlet]

yea

[craggy quest]

so whats after that

[vital hamlet]

you calculate the roots of the quadratic you get

[craggy quest]

is the only root 0?

[vital hamlet]

no

[craggy quest]

then what is it?

cause im getting (0/(1/12))

[vital hamlet]

well one root is 41.92 and second is 73.28\

[craggy quest]

ooh you meant the whole thing

[vital hamlet]

yea

sorry

[craggy quest]

no its ok

I should have understood better

so the difference is just 31.36

[vital hamlet]

that is the difference yea

but that is not the answer

31.36 is the length of the base of the right triangle that you can construct between the two intercepts

[craggy quest]

right because the actualy answer is between 40 and 79. something

[vital hamlet]

u need the length of the red line between the intercepts, but u have the length of the blue line between the intercept X and the green line

[craggy quest]

ok

[vital hamlet]

when you calculate the angle ZMC

it is 11.54

[craggy quest]

ok

[vital hamlet]

it is the same angle as between the red and blue line

[craggy quest]

ok

[vital hamlet]

so you do cos(11.54) = 31/x

and solve for x

that is your answer

[craggy quest]

31.6 ....

[vital hamlet]

yea

[craggy quest]

wow never knew desmos could do so much

anyways thanks for the help

[vital hamlet]

no problem

that is why I joined this server

[loud willow]

It should be an integer answer at the end

[craggy quest]

so 32 rounded up

[vital hamlet]

yea

I think so

[loud willow]

I calculated when the line of the slope intercepted the second circle and used the distance between points thing

Anyways they probably won't care it's the last week

[vital hamlet]

well anyways I hope I was of some help, but my brain is not braining anymore its almost midnight so goodbye

[amber wasp]

@craggy quest Has your question been resolved?

[amber wasp]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fathom cape]

Maybe I'm just tired but the n in the text is one more than the n in the lemma, right?

[fathom cape]

Because (c_0, ..., c_nX^n) are the coefficients of n+1 monomials

[amber wasp]

@fathom cape Has your question been resolved?

[amber wasp]

@fathom cape Has your question been resolved?

[amber wasp]

@fathom cape Has your question been resolved?

[eager perch]

yes, you can google the lemma's name and everywhere else it shows up as either deg(g(x))=n-1, or n+1 inside the square root

see for example: https://www.math.auckland.ac.nz/~sgal018/crypto-book/ch19.pdf

[amber wasp]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[burnt cairn]

forgor conditional probability could anyone help

[amber wasp]

@burnt cairn Has your question been resolved?

[split sail]

First of all, do you think the A and B are dependent or independent in this scenario?

Independent is when = P (A|B) = P (A)

If one is causing or interfering with the other it'll be dependent.

Use Baye's Theorem to calculate the probability.

P ( E ) = P ( E | F ) P ( F ) + P ( E | F c ) P ( F c )

[amber wasp]

@burnt cairn Has your question been resolved?

[burnt cairn]

nvm i got it ty

.close

[amber wasp]

Channel closed

Closed by @burnt cairn

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[stone mantle]

for a tank mixing question like this do i still have dy/dt as rate in - rate out

[split sail]

Your welcome!

[worthy ridge]

I believe so because the net rate of change in salt is the rate it goes in subtracted by the rate it leaves the tank

[stone mantle]

thanks!

i’ll leave this channel open while i solve

[worthy ridge]

Ive done sone problems that are similar to that but only have a rate in

[stone mantle]

that sounds like basically the same thing just a little easier

i think the hardest part is finding the equation for the rate out since volume is not constant

[worthy ridge]

Send solution if you get it 🙏

[amber wasp]

@stone mantle Has your question been resolved?

[stone mantle]

ngl i laid in bed for half an hour ill start now

[amber wasp]

@stone mantle Has your question been resolved?

[stone mantle]

heres what i got

<@&286206848099549185> can someone please check my work?

please my assignment is due in 28 minutes

[stone mantle]

.close

[amber wasp]

Channel closed

Closed by @stone mantle

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[scenic socket]

I need to evaluate the intergral

Here's my current work

[rocky vapor]

Let u = denominator

[scenic socket]

Okayy wait

[scenic socket]

The derivative of (x)^1/2

[rocky vapor]

Ik, why do that tho

U got
du = sqrtx dx

[scenic socket]

Just Du= (x)^1/2?

[rocky vapor]

du /dx = sqrtx

du = sqrtx dx
Just write all steps and go slow

Don't rush

[rocky vapor]

Just substitute now? Did u forget u sub

[scenic socket]

No i just showing the u and du

[rocky vapor]

K

[scenic socket]

Power rule?

[rocky vapor]

Wrong

Try again :)

[scenic socket]

It's hard 😭

[rocky vapor]

Not really

It's hard for me to type on mobile tho xd

[scenic socket]

So , i will say the things i know
So the U is 1+x√x and then the du is √x dx ?

[rocky vapor]

I mean, if u know then why is it a "?"

[scenic socket]

I'm just making things clear to me sir

[scenic socket]

Yes the u has the du and same on the numerator

[rocky vapor]

Yes but du is not in the numerator

[verbal spindle]

just integrate x

what is that?

[violet cobalt]

are you doing u sub?

[verbal spindle]

now u is the same thing

[rocky vapor]

Ur integral should be
$$\int \frac{du}{u}$$

[grizzled pagoda]

JustToPro

[rocky vapor]

Not what u wrote before

[verbal spindle]

which is same as integrating 1/u in terms of u

[rocky vapor]

Yes it seems like that

[verbal spindle]

yea it is 1/u because u is on the bottom of the fraction

justtopro should be able to help well im off

[rocky vapor]

Hmm

[tawny rover]

can u help me ? (help 45) really need

[scenic socket]

Yes

[violet cobalt]

i might be wrong but double check your du

[scenic socket]

(x)^1/2?

[violet cobalt]

hm, it was x * √x, try rewriting it as 1 term of x

you're missing something a little there cuz you got the idea

[scenic socket]

x(x)^1/2

[violet cobalt]

you remember exponent rules?

[scenic socket]

Yup

[violet cobalt]

right, so if you have x * x^1/2 what does that become?

[scenic socket]

(x)^3/2

So (x)^3/2 dx

[violet cobalt]

there you go

[scenic socket]

And now u • du?

Sir?

[violet cobalt]

that became your new du

[violet cobalt]

because you wrote du as x^1/2 as your du in the beginning

[violet cobalt]

i mean your new u value, sorry

[scenic socket]

Its 1/u because u is denominator

[violet cobalt]

mhm

[scenic socket]

I think i'm wrong

[violet cobalt]

give me a few secs hold on

i think im teaching you wrong lol

i js got here so

[scenic socket]

Okay sure sir!

[violet cobalt]

im a girl lol

[abstract canopy]

ok sure sir!

[scenic socket]

My bad 😭

Sure ma'am!

[violet cobalt]

ohh, okay so remmeber when you simplified the x * x^1/2 as x^3/2?

[scenic socket]

Yeah

[violet cobalt]

so u = 1 + x^3/2

do you agree?

[scenic socket]

Yea

[violet cobalt]

take the derivative of that

of the u value

[scenic socket]

Hang on

3/2 (x) ^1/2

[violet cobalt]

you're missing something with that

[scenic socket]

Dx

[violet cobalt]

yup

so then du = ?

[scenic socket]

...

[violet cobalt]

my bad

im slow

[scenic socket]

It's okay

Now u • du?

Wait in this problem do we need the power rule of integral?

[violet cobalt]

du = 3/2 (x)^1/2dx but you want to replace the numerator part right?

[violet cobalt]

not really, it is u-sub but because your derivative has a integer multiplied to it

[scenic socket]

Yes we wanna get rid of that.

[violet cobalt]

yeahh but you can't replace, or as you say get rid of it unless you set du as the same as the numerator

the du = 3/2 (x)^1/2 dx is almost the same but we don't want the 3/2 there

what should we do?

[scenic socket]

Move? Infront of integral?

[violet cobalt]

allllmost got the idea

[scenic socket]

Not right?

[violet cobalt]

no it is right

buuuut

say if you wanted to solve for 2/3x = 1 how would you solve for x?

[scenic socket]

Omg another math question.

[violet cobalt]

yeah, thats how i teach people lol

[scenic socket]

Wait hahahha

[violet cobalt]

it keeps their brains moving

i promise you can do it i think you're just overcomplicating it is all

[scenic socket]

Is it multiply?

[violet cobalt]

yesss

x = 3/2 right?

[scenic socket]

Yes

[violet cobalt]

soo if we apply the same idea to du = 3/2 (x)^1/2 dx , we get 2/3 * du = (x)^1/2 *dx

dooo ya agree?

[scenic socket]

2/3?

[violet cobalt]

mhm, because 3/2 * 2/3 = 1

[scenic socket]

Leme write

[violet cobalt]

yeah ofc go for it

its hard to visualize

[scenic socket]

So i need to multiply 3/2 on Du?

[violet cobalt]

2/3 to du

because you multiplied 2/3 to the 3/2 (x)^1/2 dx part

for it to become (x)^1/2 * dx to be replaced or get rid of

the whole point of U-sub is to make U or du match the part of the equation for it to be replaced

here let me write it on a piece of paper its better than explaining it

[scenic socket]

it's a pleasure.

[violet cobalt]

sorry for it being sideways

[tropic wadi]

,rotate acw

[scenic socket]

i'm using laptop rip

[violet cobalt]

thank you lol

the boxed part matches the numerator, thats why we want to get rid fo the 3/2 for it ot fully match

and for that we multiply the entire thing by 2/3

[scenic socket]

i get it now, so the 2/3 help us to make our du and match the numerator.

[violet cobalt]

yess!!

im gonna start using the paper hold on

alright so now you can put the 2/3 in front of the integral

i split the original top equation into 2 parts for easier replacement

now all the stuff becomes u's

lmk once you absorb all of that

[scenic socket]

okay let me process first

[violet cobalt]

yup yup

[scenic socket]

do the sqrt x dx will be cancelled cauz of the numerator?

[violet cobalt]

sooo this is where u * du gets applied

it doesnt get cancelled it actually gets replaced

with u's and du's

[scenic socket]

ohhh i see

wait

[scenic socket]

yea because they are equal?

[violet cobalt]

YESS!!

jeez you learn quick

[scenic socket]

and now, 2/3 will move infront?

[violet cobalt]

yup yupppp

[scenic socket]

thank you.

[violet cobalt]

and thats how you get du / u

or in this case 1/u * du

because the u part replaces the denominator

[scenic socket]

okay now i'll try to solve

[violet cobalt]

yupp js integrate like normal

dont forget the + C!

and turn the u's and du's back to whatever you made them equal from when they were x's

[scenic socket]

I'm done wait

[violet cobalt]

i aint going anywhere lol

[scenic socket]

https://tenor.com/view/sideeye-gif-3470529490399229032

[violet cobalt]

fully done?

what did you get then

[scenic socket]

sorry it's a mess huhu

[violet cobalt]

YEEESSS YOU GOT ITTTTTTTTTTTTT

IM SO PROUD OF YOU

https://tenor.com/view/bocchi-bocchi-the-rock-bocchi-the-rock-gif-clap-clapping-gif-27209950

[scenic socket]

Im crying lol

[violet cobalt]

why?

[scenic socket]

Ur the first person to say that to me

[violet cobalt]

oh

[scenic socket]

Btw nice i like this anime

[violet cobalt]

im planning to watch it sometime

[scenic socket]

BTW Thank you!.

A big help

[violet cobalt]

yuuup

[scenic socket]

I'm Collage so this might help.

[violet cobalt]

if it makes you feel better, the toughest part that everybody makes a huge mistake on is the algebra in calculus

[scenic socket]

i Agreed 👍

ohh btw can i add you?. i need to ask ur permission, its okay if it's not possible or your friends list are full i totally understand it.

[violet cobalt]

yeah, sure i dont see why not

[scenic socket]

Ohh okay, Cyaaa.

.close

[amber wasp]

Channel closed

Closed by @scenic socket

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tacit pelican]

hi uhm

[tacit pelican]

so when i do

like

evaluating

nc0 + nc2 + nc4 + nc6 +...

im getting

2^n-1

why is it that

when i do nc1 + nc3 + nc5 + nc7 + ...

its also 2^n-1

is that correct ?

[solar gust]

You mean $2^{n-1}$ or $2^n - 1$

[grizzled pagoda]

YakuBros

[tacit pelican]

i mean

to the power

the first one

why is it that they are both the same

?

[solar gust]

$2^n = (1+1)^n = \displaystyle\sum_{k = 0}^{n}\dbinom{n}{k} = \sum_{\substack{k = 0 \ k \ \text{is even}}}^{n}\dbinom{n}{k} + \sum_{\substack{k = 0 \ k \ \text{is odd}}}^{n}\dbinom{n}{k}$

[grizzled pagoda]

YakuBros

[solar gust]

You can split into two cases according to whether a fixed element is in the combination or not, and thus reduce even/odd counting formulas for even n

Unfortunately, i dont have time to explain more, i really think that you will achieve to find out anyway

[vernal surge]

right, you could also do $0 = (1-1)^n = \sum_{k=0}^n \dbinom{n}{k} (-1)^k$ and derive that they are indeed equal from there, by extracting all the positive and all the negative summands

[grizzled pagoda]

rbit

[amber wasp]

@tacit pelican Has your question been resolved?

[amber wasp]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[stoic locust]

Hi

[stoic locust]

Ismy proof that the centoid divides the median in the ratio 2:1 correct?

[GBD] = [GDC] = X (median divides into two equal areas)
Similarly, other triangles have equal areas.
Let the other two pairs have areas X and Z
In triangle ABC, [ABD] = [ADC]
X+2Y = X+2Z
Y = Z
Similarly, Y = Z = X
[ABG] = 2*[GBD]
Ratio of areas = ratio of bases (heights to be the same)
2:1
Proved.

[amber wasp]

@stoic locust Has your question been resolved?

[stoic locust]

<@&286206848099549185>

t

hiiiiiiiiiiiiiiiiiii

jo

e

done

.close

[amber wasp]

Channel closed

Closed by @stoic locust

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tribal stump]

having trouble with both, not sure where I should start

1.1 $$ A \cdot B = AB cos (\theta) $$
1.4 $$ A \wedge B = AB sin (\theta) \hat{n} $$

[grizzled pagoda]

dindu

[tribal stump]

<@&286206848099549185>

[tepid verge]

be careful with your notation

I assume A and B are vectors -- or are they scalars? it's ambiguous by what you've written

[tribal stump]

it's in the description of the problem

[knotty reef]

Problem 1.2 right?

[tribal stump]

they're vectors

yeah

i don't want the solution yet

just a nudge towards solving it

[tepid verge]

but seriously I think you mean $u\cdot v=||u||\times||v||\cos(\theta)$ and $u\land v=||u||\times||v||\sin(\theta)\hat{n}$

[knotty reef]

Take examples
Take the unit vectors ican j cap and k cap

[grizzled pagoda]

Flip

[tribal stump]

i have bad eyesight so thats why i don't use the norm markings haha

[tepid verge]

not to make an eyesight joke but I see you lol

[tribal stump]

i mark vectors with lowercase letters and their magnitude with uppercase letters

[tribal stump]

hmmm but those are not coplanar

[tepid verge]

I dislike the vertical bars because astigmatism. it makes it hard to count sometimes

[tribal stump]

i need to show it for the coplanar case first probably because there's some pedagogical benefit in it

[knotty reef]

Ok take vector a and vector b and apply your condition
Hint - || is (a×a)×b same as (b×a) ×a ||

[tribal stump]

well yeah that's what they're asking me to prove haha

these are actually the same because cross products are associative but i'm trying to prove that it is

cuz a x a = 0

[knotty reef]

So (a×b) ×a = 0

[tribal stump]

no?

[knotty reef]

ul be disheartened to learn that it is not the truth

[knotty reef]

Yea so it forms a counter example

[tribal stump]

how? they're not asking me about commutativity

but associativity

as stated a x (b x c) = (a x b) x c

which should be true

oh wait

ig order should matter

[knotty reef]

(a×a) ×b = 0
(a×b) × a !=0

[knotty reef]

why so

[tribal stump]

yeah no i see it now

[knotty reef]

I tried to give you a hint but it slipped from your eyes ig

[tribal stump]

because (a x a) x b != a x (a x b)

due to the fact that a x b is perpendicular to a and not is not the zero vector

@knotty reef any ideas for problem 1

that would be the harder one

[tribal stump]

need to show that $$ a \cdot (b+c) = (a \cdot b) + (a \cdot c) $$

[grizzled pagoda]

dindu

[tribal stump]

the same for the cross product

without using any components

[knotty reef]

Let me think

[knotty reef]

Take three vectors a b c
Take angle between b and c to be theta and angle between a and b to be phi so the angle between a and c will be theta + phi
(I think a graphical proof would be still much better in such cases)

[tribal stump]

yeah thats what i figured

[amber wasp]

@tribal stump Has your question been resolved?

[tribal stump]

.close

[amber wasp]

Channel closed

Closed by @tribal stump

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[south ledge]

A man is dealt a poker hand (5 cards) from an ordinary playing deck. In how many ways can be dealt a straight ?

I searched this question on Google and I got confused if there is 9 or 10 sets of straight I can make

[south ledge]

like here. why did they not consider A2345?

[dull pike]

Because A can be 1 or 14

[sinful sapphire]

it's just whatever the author thinks is true

no way to be ceratin

[dull pike]

But not both at the same time

Well, he said he is playing poker with 5 cards so

10 sets

[sinful sapphire]

i would say 10

[south ledge]

Okay thanks. I got 10240

.close

[amber wasp]

Channel closed

Closed by @south ledge

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pine fjord]

Hi

[pine fjord]

Can somebody help me wiith this derivation pls

[amber wasp]

@pine fjord Has your question been resolved?

[pine fjord]

End.

Yes

?

.close

[amber wasp]

Channel closed

Closed by @pine fjord

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sleek zenith]

$x - 6^x = -3$

[grizzled pagoda]

Alex

[sleek zenith]

i had to get 5 decimals precision

i used this

$f(x_{n+1}) = x_n - \frac{f(x_n)}{f'(x_n)}$

[grizzled pagoda]

Alex

[sleek zenith]

$f(x) = -6^x + x + 3$

[knotty reef]

Newton Ramphson method right?

[grizzled pagoda]

Alex

[sleek zenith]

Yes

$f'(x) = -6^x \cdot \ln{6} + 1$

[grizzled pagoda]

Alex

[sleek zenith]

here i chose 1 because by inspection it is the closest number i can think of

$f(x_0) = -6^1 + 1 + 3 = -6 + 1 + 3$

[grizzled pagoda]

Alex

[sleek zenith]

$f(x_0) = -2$

[grizzled pagoda]

Alex

[sleek zenith]

$f'(x_0) = -6^1 \cdot \ln{6} + 1 = -6 \cdot \ln{6} + 1$

$f'(x_0) = -9.75056$

[grizzled pagoda]

Alex

[sleek zenith]

$f(x_1) = 1 - \frac{-2}{-9.75056}$
$f(x_1) = 0.79488$

this is correct like this, right?

[knotty reef]

Shoudnt it be xn+1 rather than f(xn+1)

[sleek zenith]

where exactly

[knotty reef]

Yea the rest seems to be good
But this doesn't guarantee that this is the closest approximate of the root of the eq

[knotty reef]

Here

[grizzled pagoda]

Alex

[sleek zenith]

yes i continued

and i got this

wair

[knotty reef]

It should be x1 rather than f(x1)

[sleek zenith]

?

[sleek zenith]

the formula is this

so it should be f(x_1) not x_1

[knotty reef]

huh but like everywhere it's this

[sleek zenith]

$f(x_2) = 0.73905$
$f(x_3) = 0.73554$
$f(x_4) = 0.73553$
$f(x_5) = 0.73553$

[grizzled pagoda]

Alex

[sleek zenith]

so at 5th iteration it is repeating with 5 decimals

so i assume this is the end

am i right?

[viscid granite]

Yea

[sleek zenith]

so, it is f(x_5) or x_5?

[knotty reef]

Yes

[knotty reef]

Try both of them

[sleek zenith]

ty

.close

[amber wasp]

Channel closed

Closed by @sleek zenith

Use .reopen if this was a mistake.

[knotty reef]

wlc

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[split sail]

If i have two lists A and B and they have the same number of elements and same mean, but different variances\

[split sail]

then i introduce list C where it's a merge of list A and list B

what's an expression for the variance of C?

,, \operatorname{Var} (C) =\frac{\sum_{x \in A} (x_a - \mu)^2 + \sum_{x \in B} (x_b - \mu)^2}{2n}

[grizzled pagoda]

!Kiz__

[split sail]

is that even right? 💀

that seems sketchy asf

i think it's right, but why can you even do that in the numerator?

[amber wasp]

@split sail Has your question been resolved?

[amber wasp]

@split sail Has your question been resolved?

[knotty reef]

Never knew stats was this scary

[wild vale]

well... I think that is it

your denominator might need to add -1

but that depends on what you are working with

but if you want Var(C) in terms of Var(A) and Var(B), you might want to simplify that further

[split sail]

[split sail]

why? i don’t think so

tbh

[split sail]

I want to express Var(C) in relation to elements from A and B

my grand goal is to show that Var(C) < Var(A) + Var(B)

[wild vale]

If that is your goal, then from what you have, maybe try expand that square term out

And notice that your sum of squares can be expressed in terms of variance

[wild vale]

because you need it to make it unbiased if it is sample

[split sail]

well hmm

i’m guessing we consider it as the population here

cuz “two lists”

[split sail]

right okay but my expression i have there

is probably right

tbh

bc i’ve done this question before and hmm i think i got it right

[wild vale]

it is

[split sail]

i just don’t remember the logic for it

for the numerator at least

[wild vale]

if you don't see how sum of square is variance, then try expand the square

or not

[split sail]

like i can justify it now that i’ve written it down but how do i make it from the group up

[split sail]

without expanding the squares?

[wild vale]

because $\sigma^2 = \frac{1}{n}\sum_{i} (x_i - \bar{x})^2$

[grizzled pagoda]

Nonstationary Nickname

[split sail]

well Var(A) * n = sum of squares for data points in A

same thing for B

[wild vale]

yeah, and you should have linear combination of variance

[split sail]

yes sure that’s the variance

[wild vale]

since coefficient is > 1, then your proof is concluded?

[split sail]

no i mean how do i make an expression for Var(C) from the ground up and make it somewhat similar to what i had initially

or rather what do i do from the get go if i had to compare Var(A) + Var(B) and Var(C)

$Var(C) = \frac{1}{2n}\sum_{c \in C}(x_c - \mu_C)^2$.

[grizzled pagoda]

!Kiz__

[split sail]

That’s where one would start naturally right?

[amber wasp]

@split sail Has your question been resolved?

[amber wasp]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[marsh fog]

can someone help

idk how to do this

[storm moth]

partial fractions

[marsh fog]

how would you get partial fractions?

i mean i simplified the denominator to 2x+t+tx^2

but i dont see a way

[storm moth]

quadratic formula to factorise

[marsh fog]

oh right

im dumb

.close

[amber wasp]

Channel closed

Closed by @marsh fog

Use .reopen if this was a mistake.

[storm moth]

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[proper umbra]

For

q2) I dont understand how they came up with the DFA (image 2)

q4) Could I just say that since its infinite its not regular because |w| = 2^x(3) where x could be any natural number and isnt bounded

q5) Could I just say that since w[i-10: i] implies that |w| = 10. Its finite so it has to be regular

[night jacinth]

q2) it's your typical "count something mod 3" automaton, but yeah they forgot to add some transitions

q4) so you're saying infinite languages can't be regular ?

q5) "w[i-10: i] implies that |w| = 10" what does that even mean ?

@proper umbra

[proper umbra]

w[i-10:i] is looking at the last 10 characters of the string w

[proper umbra]

shit I forgot in some cases they can be regular

[vernal surge]

w itself can be of any length, there just needs to be some substring of length 10 with more 1s than 0s

[proper umbra]

Say we had "count something mod 4" then it would have been similiar to this but without the q1 to q3 and q3 to q1 direct transitions and instead of 3 states it would be 4 states? with q_3 to q_4 being a, b and q_4 to q_3 being c and q_1 to q_4 being c and q_4 to q_1 being a, b?

[proper umbra]

How should I approach this one then

[vernal surge]

I think try to come up with an NFA

[proper umbra]

and for q4) Idk how I would use pumping lemma

This is how they did q5

[vernal surge]

had a similar idea with an NFA in mind

[proper umbra]

alr lemme see if I can come up with an NFA

[proper umbra]

for the last 10 characters I came up with this to check if there are more 1s thn 0s. j represents amount of 1s and k represente amount of 0s

,rotate

[proper umbra]

p sure im not doing this correctly but idk how else to do this

self loop on 0, 1 for both btw

forogtot edit that

[vernal surge]

yeah.. doesnt feel very NFA like, maybe try building a DFA for language X first, it needs like 20 states I think (or you just say it has to exist because X is finite)

then you can just hook it up to an NFA

[proper umbra]

Damn I was trynna dodge that because it seemed pretty annoying

is there no other way without NFA/DFA

for something like this

[vernal surge]

I mean you know it has to exist

[proper umbra]

right

Im just wondering if something like this came up on my exam what would be the best way to answer it

[vernal surge]

for q5 specifically I would just take this shortcut and explain how I would expand it to an NFA that accepts A5. I dont think they would ever ask you to construct this, not with a number like 10

[proper umbra]

I see and what abt q4

Pumping lemma to prove its not regular?

If so how would I set it up

Im not rlly sure

[vernal surge]

yeah feels very unregular, you got the lemma at hand real quick?

[proper umbra]

one sec

They used Myhill-Nerode Theorem to prove its not regular but that was covered back then. In the current course they didnt rlly cover that theorem

This is how they did it

But surely its possible with pumping lemma too right

[vernal surge]

ok so I think ignoring the multiple of 3 part first will make it easier to get an idea

what if we take any p, then we choose w = 0^p 1^p, can you see where this leads us?

[proper umbra]

Ive proved thats not regular before p sure

[severe scroll]

I LOVE THE PUMPING LEMMA (also, what are you still stuck on, i came here with a dramatic entrance and the intention of helping but actually I can't really stay for that long sorry)

[proper umbra]

how would I use pumping lemma to prove this isnt regular

damn saw your message a lil late

[proper umbra]

we did this in class before

[vernal surge]

same idea I think

[severe scroll]

it's okay, uh so the key for the pumping lemma is that you find some absurd string that you can pump stuff into

[vernal surge]

just need to expand it a little

[proper umbra]

how would I expand it

[vernal surge]

to make this choice of w have a length of a multiple of 3

[proper umbra]

im ngl Im still not sure how I would do that do I just add that |w| is a multiple of 3?

and keep the rest

[severe scroll]

well you want to take a different w

[proper umbra]

oh wait

[severe scroll]

like your counterexample w will be different depending on the language

[proper umbra]

0^3n 1^3n ?

[vernal surge]

yeah

[severe scroll]

that's one way of doing it

[proper umbra]

oh betttt

alr tysm

should b easy feom there

I get it now

.close

[amber wasp]

Channel closed

Closed by @proper umbra

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[west thunder]

Hi I need some help on understanding a basic trigonometric identity:
(units are in degrees for simplicity)
sin(x) = cos(90-x) & cos(x) = sin(90-x)

What I am confused with is that this identity is different from the graphical interpretation of the sin & cos function. For instance, sin(x) is graphically = to cos(x-90) or the translation of cosine to the right by 90. However, cos(x-90) is different from the identity. Why is this so?

Appreciate any help

[torn furnace]

it might be easier to convince yourself that cosine is symmetric about the y-axis

[grizzled pagoda]

jan Niku

jan Niku

[wild vale]

I mean it is true

[torn furnace]

its true if you assume its true

what i mean to say is, if you can convince yourself of the easier evenness of cosine

[west thunder]

evenness?

[torn furnace]

then this identity follows immediately from other things they already believe

[torn furnace]

an even function is one such that $f(-x) = f(x)$

[grizzled pagoda]

jan Niku

[torn furnace]

cosine happens to be even

[west thunder]

right

thanks

am i allowed to ask a follow up question or no, sorry im new

[wild vale]

sure

[torn furnace]

abosulety not

[west thunder]

ok

[torn furnace]

just kidding

whats up

[west thunder]

one sec i needa formulate

actually its rather simple:

sin function is odd, but the same identity confusion with graph holds for me? How can one explain this?

[torn furnace]

same identity confusion?

[west thunder]

yes so
sin(x) = cos(90-x)

but graphically sin(x) = cos(x-90)

oh shoot

wait did I just

[torn furnace]

I'm not sure what you mean

isn't this the same problem as before?

what does this have to do with the oddness of sine

[wild vale]

I mean, since cos(90-x) = cos(x-90) and cos(x-90) = sin(x) you can conclude that sin(x) = cos(90-x)

[west thunder]

wow I feel like a dumb teenager now

(which i am)

thanks

[torn furnace]

[arctic fulcrum]

Bro has no self esteem

Ur life is done if u keep thinking that way buddy

[amber wasp]

@west thunder Has your question been resolved?

[amber wasp]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[amber wasp]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dire siren]

is the way to solve this 5 x 5 x 2 = 50?

because the first digit can be any of the 5, the second digit can be any of the 5, but the last digit needs to be one of the two existing?

i feel like im missing cases where the second digit is the first digit and the third digit therefore can be any of the 5 digits, but i dont know how to show that in a formula

[amber wasp]

@dire siren Has your question been resolved?

[dire siren]

for reference im learning about combinations and permutations

if that helps

[drowsy wigeon]

i think when you go 5x5x2 you are forgetting that the first 2 numbers can be the same

i would go by counting the cases that 2 numbers are the same digit then when all 3 are the same

[dire siren]

how would i show counting the cases where the 2 first numbers are the same?

[violet raven]

The first place has 5 choices

but the second has only 1 choice

since it is the one being repeated

and then

the last place 5 choices too

so its 5 x 2 x 1

and then u can consider all permutations