help-26

[topaz sinew]

@stray wagon Has your question been resolved?

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[vernal ledge]

say 6 is over here and 7 is to the right of 6 (see image below)

_________
|1|_|6|7|
|_|_|_|8|

then the spot below 6 must be greater than 6
but there is no other number greater than 6, since 7 and 8 are already in the grid
the same happens when the grid is arranged in this manner

_________
|1|_|6|_|
|_|_|7|8|

therefore, 6 cannot be in that position

again, 6 cannot be here either (see diagram below)

_________
|1|6|_|_|
|_|_|_|8|

this is because any path we take from 6 to 8 goes through two unknown integers between 6 and 8, but there is only one unknown integer (7) between 6 and 8 to fill the spaces
with similar reasoning, we can say that 6 cannot be here either (see diagram below)

_________
|1|_|_|_|
|6|_|_|8|

therefore, 6 is in one of these positions (see diagram below)

_________
|1|_|_|6|
|_|6|6|8|

[long stirrup]

.reopen

[topaz sinew]

✅

[long stirrup]

it's a sequence of brackets
((()()))
from 1 to 8, an opening bracket means you write the number in the first open space in the top row and a closing bracket means you write in the bottom row

you can't close a bracket if there's no unclosed brackets

like this, you can't finish from this state and write a number smaller than 5 above 5

from the way they ask, you're suppsoed to solve it and then notice that it's catalan numbers that you've already seen before?

no idea how it's possible

it makes no sense beyond just being complicated

[topaz sinew]

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[fossil pilot]

can someone help me with chemistry?

[jade thunder]

#old-network

[fossil pilot]

close.

.close

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[signal rock]

I used cosine theorem but it got me a bad result

and you are supposed to use sin or cos theorems

[versed cairn]

use cosine law to find angle C in triangle ABC and then use it again in triangle BCD to get side CD

[topaz sinew]

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[nimble vault]

why is the best way to do this by set construction

[topaz sinew]

@nimble vault Has your question been resolved?

[smoky sparrow]

What do you mean by set construction?

[topaz sinew]

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[foggy bloom]

is this correct?

[ancient mica]

yes, right

[foggy bloom]

thanks

.close

[topaz sinew]

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[versed cairn]

tan theta/2 is not equal to sintheta cos theta +1 , (or maybe im missing something)

[fair thorn]

^^

[smoky sparrow]

You've misremembered the identity

tan(x/2) = (sin x)/(cos x + 1)

[foggy bloom]

ohhh

im gonna retry it

[smoky sparrow]

Yeah nw

[topaz sinew]

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[foggy bloom]

like this?

[smoky sparrow]

Yep!

https://www.wolframalpha.com/input?i=tan(arctan(8%2F15)%2F2)

[foggy bloom]

LETS GOOO

[smoky sparrow]

You can check it yourself also

[foggy bloom]

thanks

but idk what arctan is i dont think i made it that far yet

[versed cairn]

arctan is inverse of tan

like a and a^-1 cancel each other , similarly tan and arctan cancel out each other

[agile harness]

the inverse tan function

[foggy bloom]

so arctan is tan^-1

[agile harness]

yes

[foggy bloom]

man idk why there are so many names my brain gonna blow

[agile harness]

you’ll get used to it

[smoky sparrow]

There's sin, cos, tan and csc, sec, cot
Each one of those has an inverse, but in practice we don't write arcsec(x), we just do arccos(1/x)

So 9 in total

And we definitely don't do haversines or versines anymore

[topaz sinew]

@foggy bloom Has your question been resolved?

[pastel juniper]

keep in mind that arctan is not (tan)^-1 i.e. 1/tan

[foggy bloom]

ayo @pastel juniper only got 44 more to go man! but im stuck on this one idek where to start

[pastel juniper]

send it. also react with ❌ on #help-26 message to keep the channel open.

[foggy bloom]

its this one

cuz aren’t i supposed to change 8cos^4t to like cos^32t

[pastel juniper]

huh what?

[pastel juniper]

you can apply double angle identity on LHS

[foggy bloom]

idk in one of the problems i did last week thats what i did changed cos^2t = 2cos^2t

[pastel juniper]

[foggy bloom]

this is me with neil degrasse tyson lnext to my rocket ship

[pastel juniper]

bro is getting distracted now

keep going forward soldier 💪

[foggy bloom]

so the cos4t becomes cos^4(t) - sin^4(t)

[pastel juniper]

nuh uh

what does cos2t become?

[foggy bloom]

becomes cos^2(t) - sin^2(t)

[pastel juniper]

yup

[foggy bloom]

hmm

🤔

[pastel juniper]

so why do you think cos(4t) becomes cos^4t - sin^4t 😭

[foggy bloom]

cuz theres a 4 🥲

instead of 2

[pastel juniper]

uhh

nice logic

but no

take 2t = u for some time there, so what does cos(4t) become?

[foggy bloom]

huh

2t=u

[pastel juniper]

yeah just substituting

[foggy bloom]

so 4t=2u

?

[pastel juniper]

yeah

so does cos(4t) become cos(2u)?

[foggy bloom]

cos4t = cos2t

[pastel juniper]

...

[foggy bloom]

oh wait

why is it u

[pastel juniper]

i named it u :)

[foggy bloom]

oh

[pastel juniper]

name whatever you want

[foggy bloom]

yes its cos4t = cos2u

[pastel juniper]

alright

now what does cos2u become

[foggy bloom]

should be like a voice call

[pastel juniper]

i dont do vcs 🗿

[foggy bloom]

cos2u = cos^2t -sin^2t?

or

cos2u = cos^2u - sin^2u

yes that one

[pastel juniper]

exactly

[foggy bloom]

🗿

[pastel juniper]

dont guess things from now on 💀

[foggy bloom]

hmm

[pastel juniper]

now substitute back the value of u in there, what do you get?

[foggy bloom]

back in where

in cos4t

[pastel juniper]

uh

what was u

in terms of t

[foggy bloom]

u=2t

[pastel juniper]

now put that 2t in place of u in cos2u = cos^2u - sin^2u

we are reversing what we substituted

[foggy bloom]

oh so cos2t = cos^2(2t) -sin^2(2t)

[pastel juniper]

i still see a u there

[foggy bloom]

there we go

[pastel juniper]

nah

wasnt it cos(2u)?

[foggy bloom]

wait. o

yes

i just switched it

edit

[pastel juniper]

so 2*2t?

[foggy bloom]

OH cos4t = cos^2(2t) - sin^2(2t)

[pastel juniper]

yeah so we found out that cos4t is not equal to cos^4t - sin^4t but actually cos^2(2t) - sin^2(2t) 👏

[foggy bloom]

letsss goooo

now i need to put it into the formula

[pastel juniper]

also look at the question. there's no sin term in RHS, how do you think we can convert sin^2 to cos^2?

[foggy bloom]

to find tan^2 then divide by sin^2

[pastel juniper]

no

what

[foggy bloom]

oh wait my bad

i just realized what i said

to be honest i dont know the only thing i can think of is to draw the triangle and plot the opposite/hypotenuse and find the adjacent side

[pastel juniper]

sin^2 + cos^2 = 1

[foggy bloom]

how did everyone here get so good at remembering things bro i swear i forget stuff i learned 2 seconds ago

[pastel juniper]

lmao, happens

[foggy bloom]

wait but then i must change the “sin^2(2t) on the LHS to = 1-sin^2(2t)

ur like albert einstein

[pastel juniper]

from sin^2 + cos^2 = 1, we can write sin^2 in terms of cos^2 as sin^2 = 1 - cos^2

and since we need to get rid of that sin^2(2t) term, we can use that here

[pastel juniper]

nope

[foggy bloom]

if ur not like eistein idk what that makes me

[pastel juniper]

a learner

[foggy bloom]

i need to rewrite thisnreal quick cant read my paper anymore

this is where i am right now

i just substituted in for sin

@pastel juniper u there

.close

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[wide junco]

i want to find the partial derivative for X of this implicit function

[wide junco]

is the only way to do this involving e and ln x?

[odd pagoda]

I dont know about only, but its very likely the best way

[thorny flame]

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

[wide junco]

lets say i do this, how do i get x^2 out? ln(x) could then be negative

[odd pagoda]

if x is negative then you have a problem with what x^(x^2) should be in the first place anyway

[wide junco]

so can i do it without specifying anything about ln's domain?

[odd pagoda]

this isnt a problem with the ln

this is a problem with x^stuff

well ok, x^stuff is defined with ln in the first place usually

[wide junco]

no we dont deal with complex numbers

okay thanks a lot

.close

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[sharp fable]

I'm not sure whether I've drawn the wrong diagram

Cuz I don't see how BF would form an angle with SD

[wicked bolt]

probably meant angle formed when they are layed on top of each other

as in like angle between vector SD and vector BF

[naive grotto]

is 0 negative or positive

[agile harness]

neither

[naive grotto]

thnx very very much

[sharp fable]

Can I assume vector GC = FB?

[naive grotto]

?

[naive grotto]

im not profecional but i think yhea

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@sharp fable Has your question been resolved?

[sharp fable]

Is this right?

[topaz sinew]

@sharp fable Has your question been resolved?

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[topaz sinew]

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[severe lichen]

okay so i got y^2/9 - x^2/25 = 1

but

i need it to be within the parameters (-pi/2, pi/2)

how do i do that

cause my equation graphs like this

but im supposed to have this

[shell aspen]

solve for y

[severe lichen]

isolate y?

ok

how do i do that

[shell aspen]

how do you reduce powers

[severe lichen]

sorry not 4 im thinking of something else

just square both sides

[shell aspen]

reduce

[severe lichen]

how do i get rid of everything else

y^2/9 = 1+x^2/25

[shell aspen]

isolate the y^2

[severe lichen]

y= sqrt(9+9x^2/25)?

oh it worked

thanks

[shell aspen]

yup

[severe lichen]

.close

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[karmic cloak]

How

[icy sky]

do you know the formula for the volume of a cone?

[karmic cloak]

Ok so I’m paranoid I have state testing and we haven’t learned this and if I don’t pass it I don’t graduate

Could u tell me the formula

[icy sky]

so the answer is no

the formula is $\frac{\pi r^2 h}{3}$

[thorny flame]

GarlicBredFries

[karmic cloak]

Ahhh nvmmm

I don’t even know what the first symbol is and what h and r represent

Is it radias and height

[icy sky]

yes, r is radius, h is height

the first symbol is pi

[karmic cloak]

Oh that’s pretty simple rhen

Ty for the help

[icy sky]

youre welcome

[smoky sinew]

you're*

[icy sky]

bruh what

[agile harness]

bruh what

[topaz sinew]

@karmic cloak Has your question been resolved?

[topaz sinew]

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[cunning willow]

(240/289)*(289/161)

cuz tan(2x) = sin(2x)/cos(2x)

[loud oasis]

that's a good start but it doesn't simplify to 8/15

[limber remnant]

i guess my teacher gave me the wrong formula?

tysm though

[cunning willow]

it worked?

[cunning willow]

np

[neon iron]

i mean it's a triangle with opposite 240 and adjacent 161 relative to angle 2x

so simply considering tan(2x) = opp/adj = 240/161 suffices

[cunning willow]

no cap

Ws in the shaaaaaaaaaaaaat

[topaz sinew]

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[polar drum]

how to solve this using integration by parts?

[polar drum]

i always get I_n=I_n

[merry phoenix]

!show

[topaz sinew]

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

[merry phoenix]

I havent followed that all the way through but I think youve made an odd choice of substitution

If you let x=sin(theta)

You should end up with $\int \sin^n(\theta) d\theta$

[thorny flame]

TayBee

[merry phoenix]

Which from there is just an implementation of the reduction formula with your limits from 0 to pi/2

[polar drum]

hm this is sopposed to be the result

pro means for

and (2k)!!=(2k)(2k-2)(2k-4)...

(2k-1)!!=(2k-1)(2k-3)(2k-5)...

[merry phoenix]

Yeah that sounds like reduction formula on sin^n(theta) with limits I think

https://www.youtube.com/watch?v=OIzzLi8yR0w Probably better explanation of how to apply it (indefinite integral) than I can provide

But your starting point is $\int \sin^n xdx = \frac{-1}{n}\sin^{n-1} x\cos x + \frac{n-1}{n} \int \sin^{n-2} xdx$

[thorny flame]

TayBee

[merry phoenix]

where $\int \sin^{n-2} xdx = I_{n-2}$

[thorny flame]

TayBee

[merry phoenix]

The difference for you and the reason you get the odd/even rule is because in the first part of your integration by parts, you can substitute in your limits of 0 and pi/2, and since it's sin x cos, one of them will be 0 for both limits, so the entire term cancels

Which means in your case

$I_n = \frac{n-1}{n} \cdot I_{n-2}$

[thorny flame]

TayBee

[merry phoenix]

An awful lot of work to get there but you basically now have a recurrence relation and if you run through the logic on that (work out what I_(n-2) is, then what I_(n-4) is and so on), combine that all together, then consider I3 and I2 to look at what happens 'at the end' when n is even and odd, and you'll end up with your overall statement for In

[topaz sinew]

@polar drum Has your question been resolved?

[merry phoenix]

How are you getting on?

[polar drum]

I am trying to do uderstand it but probably wont do it all the way cuz I’ve got to go to sleep so I’ll ask you if I won’t understand something

[merry phoenix]

Np, it's quite a long problem haha

[topaz sinew]

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[topaz sinew]

@polar drum Has your question been resolved?

[topaz sinew]

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[trim hound]

As x approaches infinity, (1+2/x)^x Lhopital problem

[sullen scarab]

is it necessary to solve this with l'hop?

[trim hound]

i presume so

using the indeterminate power rules

[sullen scarab]

there is an direct method to solve this

one

[trim hound]

what is that

[sullen scarab]

do you know (1)^ infinty form?

so in this questions

you can see

that

since x is approching to infinty

the base is approching to 1

AND power approching to infinty

is the ans

e^2

?

@trim hound

[topaz sinew]

@trim hound Has your question been resolved?

[trim hound]

not sure i’ll get back to u

[sullen scarab]

OK

take you're time

i have a forumla sort of

for this

[trim hound]

that’s correct

can u explain how u didn’t

did it

@sullen scarab

[sullen scarab]

yeap

so usually

when you got

(1)^infinty

type inderterminte form

like

(g(x)) ^ f(x)

where g(x) tends to 1 and f(X)

tends to infinty

you use

e^ (limit x tends to 0) f(x) (g(x) -1) )

to get the ans

so like in this let consider f(x) as x

and g(x) as (1+2/x)

so using this

we get

e^ (limit x tends to 0)(2/x)(x)

and x got cancel

and we got

e^2

as the final ans

[trim hound]

so whenever you have indeterminate form do you do e ^ lim x->0 f(x)(g(x)-1) every time?

[trim hound]

this

[sullen scarab]

only when

you have

inderterminate form like

(1) ^ infinty

[trim hound]

1^inf?

[sullen scarab]

yes

[trim hound]

oh i see

and what about all other indeterminate power questions

[topaz sinew]

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[wise dagger]

How do I do this quesrion

[terse isle]

What does f^-1(20)=2k mean?

[wise dagger]

That the inverse of f(20)= 2k

[terse isle]

It should be that f(2k)=20

[wise dagger]

Ok

I understand that part

Switch those two

Then do I just plug it into f(x)

?

[terse isle]

Try it

See what happens

[wise dagger]

Uh not sure if I did it correctly

[wise dagger]

Had to erase what I wrote since I for some reason went for the inverse

[terse isle]

f(2k)=20 doesnt mean 2k=20

It should mean

20=(10k)/(1/2 k(2k)-6)+18

Sorry the format is bad I’m on my phone rn

[wise dagger]

Would the 10 also be a (2k)

[terse isle]

Make sure you plug in 2k for x

It hould be $20=\frac{10k}{\frac{1}{2}k(2k)-6}+18$

[thorny flame]

Luke

[wise dagger]

Like this ?

[terse isle]

The bottom has k^2

[wise dagger]

Canceled the k2 with the top k

[terse isle]

There is a 6 in the denominator, so I don’t think that is possible

[wise dagger]

Ah

[terse isle]

Try moving the 18 to the other side first

And then multiplying both sides by the denominator

[terse isle]

Can you solve the equation?

[wise dagger]

do I just bring the 10 over by subtracting to the other side to leave the k by itself

Or would I divide it?

[terse isle]

Expand 2(k^2-6)

Or divide both sides by 2

[terse isle]

Don’t factor yet

Move everything to one side first

[wise dagger]

Can’t I just divide both sides by 10

Wait nvm

Actually I’m lost

Usually the brackets the one with the power of 2 exponent

So I could just move the bracket by turning into a square root

[terse isle]

I would divide both sides by 2

To get k^2-6=5k

And then k^2-5k-6=0

Now you can factor that

[wise dagger]

Ohh ok I see it

[wise dagger]

6,-1

Alright thank you

I think this is the right answer

.close

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[chilly carbon]

Hi

I am looking for a formula for the radius of this curve.

[chilly carbon]

Looking for advice or possibly a formula for something like this.

[cursive patrol]

you can think of that shape as a portion of a sector of a circle

[cursive patrol]

actually, i am not fully confident i understand your question

what is "600" here?

[chilly carbon]

600 inches

Its a train track

like quite literally.

[smoky sparrow]

Ah cool, so r * theta = 600 if theta is in radians

It's the formula for the arc length of a circle given the sector angle theta

Yeah the theta in the picture

[smoky sparrow]

And if you split the triangle here into 2

2 * R sin(theta/2) = 590

Weird I don't think there's a solution

[arctic briar]

this is physically impossible

you go outwards by 10 and the extra distance is only 10 units?!?!

thats impossible

[smoky sparrow]

Yep that's impossible

Nice intuition

[arctic briar]

without the 10 outwards it would be possible actually

[smoky sparrow]

Cause the circle is tangent to the horizontal line there, so when you go out 10 inches the circle will start widening very quickly

[smoky sparrow]

I guess so

[arctic briar]

yea

[fickle sorrel]

,w circle "arc length"=600, "chord length"=590

[thorny flame]

Results provided by WolframAlpha

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Requested by epprfdrb

[smoky sparrow]

Here's a task for you: solve for theta (or r) in r theta = 600 and then sub it into the other equation

I get r is around 946

[cursive patrol]

hm. it would be funny if 590 and 600 were arcs of different circles

"funny". not that it makes sense

[fickle sorrel]

The curve doesn't have to be part of a circle, does it?

[arctic briar]

well how would u work out the radius with 1 line

[cursive patrol]

apparently they want the "radius of this curve"

[fickle sorrel]

Sure

Noneuclidean geometry?

[smoky sparrow]

They want a train track on a non Euclidean surface

Sure.

[chilly carbon]

Going to be honest I am not great at math I was just asking because I was not sure. My grandfather asked me.

It builds trains

[smoky sparrow]

Cool

[chilly carbon]

had something do do with the curve and asking me if there was a way to get the radius and I honestly wasnt sure.

Thats why I asked here if anyone had any direction in this just because I was lost trying to figure out if it was possible.

Was not sure if there was a good way to figure it out.

[cursive patrol]

the earth.....

[chilly carbon]

I am going to ask him in the morning for reference and see If perhaps I missed something.

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[hollow perch]

can anybody e help here

[hollow perch]

for h(x)

[fallow heart]

It should be an 8 instead of 4, because you have $$y = a(x-2)(x-3) + 1\newline$$ In order to find $a$, you need the curve going through the vertex, which means $$y = -1 \text{ when } x = 2.5$$

This gives us $$-1 = a(2.5 - 2)(2.5 - 3) + 1 \Rightarrow \ldots \Rightarrow a = 8$$

[dreamy pilot]

What is the question

[thorny flame]

Alberto Z.

[fallow heart]

@hollow perch

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[neon iron]

Example 1.17

Is this allowed?

[worthy storm]

sure

[neon iron]

Ohhh

I had messed up the signs

Thank you

.close

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[empty saddle]

"Suppose we have a hypothetical new alphabet (unrelated to the English alphabet) with 9
letters, partitioned into 6 consonants and 3 vowels."

the attached image is my question

for n= 0, i have just 6 to the power of 5 which makes sense, and for n = 5, I have 3^5. (so repetition is allowed)
I thought first that for incrementing values of n, the power of 6 will decrease and the power of 3 will increase and I just times the result (e.g. for n = 1, 6^4 x 3^1....but this is incorrect somehow.

[topaz sinew]

@empty saddle Has your question been resolved?

[empty saddle]

<@&286206848099549185>

[empty saddle]

<@&286206848099549185>

[verbal crater]

is the answer for n=1 9375 by any chance?

[empty saddle]

nope

[verbal crater]

damn it

[empty saddle]

the number should be decrementing as n increases but man idk

[worn dome]

is the question still available?

[empty saddle]

yes

please help me

[verbal crater]

then is the answer 466560?

[empty saddle]

for n = 1?

[verbal crater]

yes

[empty saddle]

nope

[verbal crater]

wow ok fuck me

[empty saddle]

lmfao

like this is some bullshit math right here

idk wut to do

[verbal crater]

because i thought to multiply a 5! at the end of 6^4 * 3^1

because that vowel could be at any of the 5 positions

[empty saddle]

true

it even gives a hint such as this...but i find it pretty useless

i tried times 5...didnt work

[rancid hawk]

5400 for n=1

@empty saddle

[empty saddle]

nope

[verbal crater]

19440?

[empty saddle]

AY

how u do it?

[verbal crater]

oh wow i made a blunder

[verbal crater]

i mistyped this in my calculator

i put 5^4 instead of 6^4

[empty saddle]

wait so is it just

6^4 x 3^1?

[rancid hawk]

so the repitation is allowed ?

[empty saddle]

yea repition is allowed sorry

[verbal crater]

the hint basically gave it away on how you should do it

[empty saddle]

i said in the beginning of my question

[verbal crater]

you first have nPr(5, 1)

because you have to choose 1 position for the vowel out of the 5

[empty saddle]

yeaaaa....

[verbal crater]

then you multiply by normal

you have 3 options for one vowel

and 6^4 options for 4 vowels

multiply all those together

[rancid hawk]

do we have to consider using one vowel like I take A am I allowed to use it more than one times ?

[verbal crater]

the n is the number of vowels

[verbal crater]

look back at the question

now we're discussing about when theres only 1 vowel

[rancid hawk]

I understand that but my question is if I take AAAAA I use only one vowel right ?

[verbal crater]

thats 5

yes you have A as your only vowel but you used 5 of them

so still 5

[empty saddle]

so

whats the formula u used

im still so very confused by your explanation sorry

[verbal crater]

you first pick the positions for the vowels

for 1 vowel, you have to pick 5 positions for it

[rancid hawk]

so why 19440 is not correct ? 3C1 to select one vowel out of 3 then 5P1 to arrange one vowel at 5 different places and 6^4 for other consontants. Then the answer would be 19440

[verbal crater]

so how many positions possible? 5

[verbal crater]

i think its right?

[empty saddle]

it is correct

19440 for n = 1 is correct

[empty saddle]

ok so when n = 2 im assuming theres 4 positions?

[verbal crater]

no

nPr(5, 2)

[rancid hawk]

Just change 5P1 to 5P2 and then 6^3

[verbal crater]

yes

[rancid hawk]

3C2

[empty saddle]

so 5P2 times 6^3?

[rancid hawk]

yes

[verbal crater]

and times 3^2

3 vowels in position 1 and 3 vowels in position 2

[empty saddle]

wait its wrong 😂

[rancid hawk]

why that 3^2

[empty saddle]

to confirm i did

5P2 times 6^3 times 3^2

[verbal crater]

and what did you get?

[empty saddle]

38880

which is wrong

[verbal crater]

wha

[empty saddle]

not even trolling rn

[rancid hawk]

check this 3C25C24*6^3

[empty saddle]

where is there a 4

[rancid hawk]

25920

[empty saddle]

nah its wrong

[verbal crater]

is it 19440 again?

[empty saddle]

wth

ok

yea it is

TELL ME WHY

WHAT

HOW IS THAT POSSIBLE

[verbal crater]

huh i looked back at your hint and saw that choosing 2 positions for vowels from 5 is 10

and i thought 5P2 was 10

apparently they used 5C2

why P instead of C hmm

[empty saddle]

they are assuming its not distinct?

[rancid hawk]

because you are selecting any two positions out of 5 which can be any combination regardless of positions.

[verbal crater]

oh right it is indeed C not P

[empty saddle]

mmm

so

for n = 3

its

5C3 times 6^2 times 3^2?

[verbal crater]

5C3

[empty saddle]

oh right

[rancid hawk]

@verbal crater still I am in doubt that why that 3^2 if you can clear my doubt ?

[verbal crater]

2 positions

each position can have 3 possible vowels

so 3*3

3^2

[rancid hawk]

so shouldn't it be 2^3

[verbal crater]

that is 3 positions, every position 2 possible vowels

[empty saddle]

5C3 times 6^2 times 3^2

so i did this and uhh

its wrong

[verbal crater]

3 vowels right?

so why 3^2

[empty saddle]

so its

3^3?

[verbal crater]

yes

[empty saddle]

isntead?

ok

just confirming

[rancid hawk]

this time it is 3^3 and I get it but in previous where n=2 2 positions and 2 vowels so should not be it 2^2.

[empty saddle]

ayyyy i got it

[verbal crater]

vowels can be repeated

so 2 positions, each position 3 possible vowels

[rancid hawk]

now I get it since you are taking out of 3 vowels

Why was I not even understanding that ahh!

[empty saddle]

ok guys theres a part 3

[rancid hawk]

2430

[empty saddle]

nope

[verbal crater]

well you have to split it into different cases

case 1 would be only 1 consonant

case 2 2 consonants

and so on

and then add em all up

[empty saddle]

so

ok lemme try

[rancid hawk]

you need to add all the parts of b) except where there were all vowels

[verbal crater]

basically yeah

[rancid hawk]

58806

[empty saddle]

thats right!

ok guys

can u explain why

this is not

1024

[verbal crater]

is it ever 5040?

[empty saddle]

nah its not

[rancid hawk]

i am getting 1260

[empty saddle]

thats not it either

;-;

i dont get

why for this one u can just do the permutation method

but when u try to do 7!/2!x2! for e, it doesnt work

there is a hint again

[verbal crater]

wait then what about 630

[rancid hawk]

Why not making a bundle of BDAA and then permute it as one with other 6

[empty saddle]

bope

nope*

[empty saddle]

i tried that but it doesnt work

[rancid hawk]

you read there written Twice

we have missed it completly

[BDAA][BDAA]BC= 4!/2!=12

@empty saddle

[empty saddle]

yea

thats why this is correct

but how to apply it to here

[verbal crater]

would it be 105 then?

[empty saddle]

my idea is to permutate it and then minus the 12

[rancid hawk]

yep !

[empty saddle]

no

[empty saddle]

but both 1024 and 1012 doesnt work

[rancid hawk]

1260-12

[verbal crater]

oh yeah i divided instead of minus

[empty saddle]

o

it worked!

wait where did u get 1260 from @rancid hawk

[verbal crater]

its 7!/2!*2!

[empty saddle]

wuttt

[rancid hawk]

7

7!/2!*2!

[empty saddle]

wth

all these time

[verbal crater]

after bundling the string BDAA

you'll have 7 elements

[empty saddle]

i thought 7!/2!x2! was 1024

im throwing

[rancid hawk]

I did not understand why are you doing the same thing as mine but not getting the same answer

[verbal crater]

do you not have a calculator

if you tried to calculate it by hand then what a chad

[rancid hawk]

where is the f) @empty saddle

[empty saddle]

theres no f)

thank god 😂

[rancid hawk]

https://tenor.com/view/oh-no-elena-cañero-reed-gina-rodriguez-diary-of-a-future-president-no-way-gif-22731202

so we are done

[empty saddle]

i had a caluclator

but it somehow displayed 1024 once

or im hallucinating

[rancid hawk]

you need to stop taking LSD!

[empty saddle]

LOL

yea

maybe

math got me cooking some lsd

[rancid hawk]

was fun solving those permuatation questions after a long time.

[empty saddle]

i hate combinations and permutations

[rancid hawk]

That's what I like the most

[empty saddle]

damn i will let u know if i have more LOL

[rancid hawk]

don't forget

[empty saddle]

.close

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[neon iron]

There are 2 boxes with balls and numbers written on them( all balls are of same size)

Box 1 contains balls with number 1,2,3,4,5
So i can represent it as
A = { 1,2,3,4,5}
Box 2 contains balls with number 1,6,7,8,9
So i can represent it as
B = { 1,6,7,8,9}

So if I transfer marbles of both boxes into another big box
So can i represent marble in that box as
A union B
?
Kindly state reason for ur answer too

[neon iron]

There are 2 boxes with balls and numbers written on them( all balls are of same size)

Box 1 contains balls with number 1,2,3,4,5
So i can represent it as
A = { 1,2,3,4,5}
Box 2 contains balls with number 1,6,7,8,9
So i can represent it as
B = { 1,6,7,8,9}

So if I transfer marbles of both boxes into another big box
So can i represent marble in that box as
A union B
?
Kindly state reason for ur answer too

[jovial grove]

Is that not the definition of union

[balmy roost]

I guess no because the ball 1 in box A is not the ball 1 in box B right?

[balmy roost]

but he just assigned these values to these balls

ball 1 in box A isn't ball 1 in box B

[jovial grove]

I’m assuming it’s not a dumb trick question

[balmy roost]

I guess it would be a union if you assign different values for ball 1

or if you treat two different balls with the number written on them the same ball it'd also be a union

[neon iron]

Nope, they are same
But i was trying to use sets in probability ( I am just at basics)
But then I realized that a element can't be repeated
So that's why I asked this question

[neon iron]

It would be a union but then probability of ball 1 would be 1//9
But it's obvious that 5 balls in A + 5 balls in B = 10 balls in large box

So actual probability is 2/10 or 1/5

[smoky sinew]

Unless the sets are disjoint dont think sets apply here

[neon iron]

Disjoint means?

[neon iron]

The whole point of asking was WHY elements can't be repeated in a set?
And if it can't then what's the point of union?

[smoky sinew]

Bc imagine this, you want the union of [0,1] and [1,2]

As in all numbers between those including those

It makes sense that the result should be [0,2] right

[smoky sinew]

They dont share element

[neon iron]

But 1 won't be repeated
That's only I am asking, why?

[neon iron]

👍

[smoky sinew]

Yes

1 wont be repeated

Bc we dont count duplicates

If we counted duplicates it would be [0,2],1

[neon iron]

So duplicates in sets are possible or not?

[smoky sinew]

No

[smoky sinew]

Bc we want sete to work like this

[neon iron]

You are Indian?

[neon iron]

But in intersection of sets it is possible no?

[smoky sinew]

Duplicates?

No

[neon iron]

👍

[neon iron]

Oh, thanks a lot mate

[smoky sinew]

This is one confusing set thing

[smoky sinew]

The no duplicates

[smoky sinew]

Lmfao

Anyways any more questions?

[neon iron]

There can't be duplicates, it's rule of axiomatic set theory or naive set theory or both?

[neon iron]

Wtf just bro said

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[cursive patrol]

so true

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

@smoky sinew multiset exists no?

[smoky sinew]

Yea

But in regular notion of set

We dont define dupes

[neon iron]

So where is multiset used then?

[main shale]

combinatorics I guess

[neon iron]

Oh, I have that chapter pending..

[main shale]

the thing is, in other applications where you want to handle repeated elements, you either handle that data separately (e.g. algebraic/geometric multiplicities of roots) or use a different encoding within ordinary sets

because the theory of sets is more common/well-behaved

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[steep anchor]

I have everything correct till 14+8 √3 = a+b √3. How do I find the values of a and b? In the book it says we get it by equating the like terms but I don’t know what that means. Please help

[steep anchor]

EXAMPLE 17

[pallid hound]

so basically you match everything

compare LHS and RHS

the right hand side is already in the form of a+b(sqrt(3))

so a = 14 and b = 8(sqrt(3))

only this way because rational numbers will be rational numbers and irrational numbers will be irrational numbers

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[viscid ferry]

2*f(x) + f(1-x) = x^3 , then f(6) = ?

[viscid ferry]

I can't do that question PLEASE help me it's urgent

[short acorn]

Do you know anything else of f(x)

Do they want a number?

[viscid ferry]

nothing else

just them

is it possible to solve

[short acorn]

U can solve by pluging in 6 to the equation and solving for f(x) algebraicly

[viscid ferry]

then how

I wasn't able to solve that

[short acorn]

U wont get a number, you get an expression

[chilly walrus]

hint: try x=0.5

you will then get 2*f(0.5) + f(0.5) = (0.5)^3

so you can solve for f(0.5)

[tranquil verge]

just try x=6 and then see what u need next

[chilly walrus]

x=6:
2*f(6) + f(-5) = (6)^3
x=-5:
2*f(-5) + f(6) = (-5)^3

you have two equations and two unknowns f(6) and f(-5)

[topaz sinew]

@viscid ferry Has your question been resolved?

[clever oxide]

I thought that couldn't be done, nice

That's it @viscid ferry

[short acorn]

Thats good work. I must be drunk....

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[unkempt nova]

wondering how to proceed with this question

do I have to multiply x0 by this transition twice

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[simple orchid]

Hello

[simple orchid]

Can someone help me understand this?

[maiden plover]

It’s saying that Moivres theorem is true for all complex numbers except for 0 due to technical reasons

In any case you would never use moivres theorem for 0

Does that answer it?

[simple orchid]

What about n?

Can n be all numbers?

[maiden plover]

Do you know what $n\in\mathbb{Z}$ means?

[thorny flame]

Philka

[simple orchid]

n includes all integers?

The latter part of the explanation says n should be ≤ 0 and n ≥ 1 provided z = 0

That part confuses me

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[simple orchid]

.close

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[livid sparrow]

can somebody explain this derivation to me

[livid sparrow]

https://byjus.com/physics/derivation-of-terminal-velocity/

I understood just before they start using trig

[simple orchid]

What's b?

[livid sparrow]

b si

b is

pCdA

its a constant

basically if there is a way to circumvent all this trig they use that would be cool

like from their integration is there a way to get vt = alpha or whatever they use

after taking it out of the integration

<@&286206848099549185>

[smoky sinew]

what do you not understand about the trig

[livid sparrow]

whats sech

and where are they getting this from

[smoky sinew]

hyperbolic sec

vc v=tanh(theta)

[livid sparrow]

whats that

is there an easier way to prove this

[livid sparrow]

whats vc

[smoky sinew]

i meant bc as in because

v=tanh(theta)

[livid sparrow]

oh ok

[smoky sinew]

do u know hyperbolic trig

[livid sparrow]

where did they get that from

[livid sparrow]

no

is it hard to learn

[smoky sinew]

i think theres an easier derivation

did your teachers send you this

[pastel juniper]

there's one using stoke's law

which is easier than this

[livid sparrow]

no im trying to do this for fun

like understading it on my own

[smoky sinew]

oh alr

find another derivation

imo

[livid sparrow]

okay

[livid sparrow]

if you know it can u send it

or like a website

[pastel juniper]

https://www.vedantu.com/question-answer/derive-expression-for-terminal-velocity-when-a-class-11-physics-cbse-5f5bf4a268d6b37d16e3b6f5

[livid sparrow]

there is this and a really simple af derivation cant find an inbetween

ok cool will go through rn

[pastel juniper]

the expression F = 6(pi)nrv is given by stoke's law

[livid sparrow]

yeah but problem with this is that it assumes

its a sphere

the other equation is more general

[pastel juniper]

yeah stoke's law is applicable only for spheres

[livid sparrow]

can somebody then

explain hyperbolic trig

really quickly and fast

enough for me to grasp that derivation

[topaz sinew]

@livid sparrow Has your question been resolved?

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[floral sage]

Anyone know how I’d solve something like this

[loud oasis]

the second derivative is the derivative of the first derivative

[floral sage]

Yeah I know that but do I just plug 1 in for x and 3 in for y once I have the second derivative?

[loud oasis]

yes

you'll also need the value of dy/dx, which you can also get from the given information

[floral sage]

Wait why do I need the value of dy/dx

[loud oasis]

when you take the derivative you'll need to do implicit differentiation/the chain rule because y is a function of x

[floral sage]

Oh well yeah

I thought you meant the numerical value of dy/dx at (1,3)

[loud oasis]

but you do need that

[floral sage]

Oh wait I see now lol

Dumb question sorry

[loud oasis]

no worries

[floral sage]

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[left fiber]

why is DS in a circle (for physics for example) radius * d theta in the theta hat direction?

[left fiber]

i don't get the theta hat direction part particularly

DS is the small length

i understand radius * d theta = small arc length, but im not sure why its in the theta hat direction and not like the R hat direction

[loud oasis]

if you're going along a circle, then the theta direction always points along the circle, and the r direction points outwards from the circle

[left fiber]

ahhhh okay

tysm

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[brazen inlet]

139

[brazen inlet]

Question 139, I’m confused how to do it

What’s the first step

[rose sierra]

Well you're given dy/dx and you want to find y, so try integrating the rhs

[shrewd lance]

it is variable saparable form of diffrential equation

[shrewd lance]

ye

[stone verge]

the idea is to find y or f(x)

[brazen inlet]

Yeah but I’m lost how to start it

[stone verge]

what happens if you integrate both sides

[brazen inlet]

You get f(x)=

Ik im just asking how to integrate it

[rose sierra]

(x^2+1)/x^2 is a bit tricky to integrate but try rewriting it

[brazen inlet]

I did, as x^2/x^2 +1/x^2

Simplified to 1 + 1/x^2, and then integrating that gets me x-1/x

[rose sierra]

+C

[smoky sparrow]

Yep

[brazen inlet]

And I need to set that to y(1)=-1

So it becomes

x-(1/x)-1

[smoky sparrow]

You're just missing the +C, which you can find from y(1) = -1

[brazen inlet]

Alr thanks I guess I made a mistake earlier

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[smoky sparrow]

Nw

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[hardy urchin]

hey so i have finished questions 1-2 but im needing help of number 3-4

[trail goblet]

the questions are unclear. please type them out or provide us with a better quality picture

[hardy urchin]

alr gimme a min

[trail goblet]

have you tried solving for items 3-4?

if so, please show us

[hardy urchin]

by items do u mean questions?

if so i have but i just ran into trouble

but ill tell you what i have solved:

the length of AC is 44.96m
the angle of C is 24.71
The area of ABC is 319.51 m^2

help

[hardy wing]

You can get the length of all the sides of the triangle ACE, which lets you get its area.

[hardy urchin]

how would i start

[hardy wing]

Do you have the length of all the sides of the triangle ACE?

[hardy urchin]

no

im only missing CE

[hardy wing]

You can start by getting them then.

Yeah, sine law

[hardy urchin]

alr wait hollup

wait i only have 1 angle tho

i also tried doing cosine law but still missing stuff

[hardy wing]

Okay,

We have AC, right?

[hardy urchin]

yes

[hardy wing]

So, sin(92)/AC=sin(ACE)/25

Agree?

[hardy urchin]

wait pause

[hardy wing]

What’s up

[hardy urchin]

Sin A/a = Sin B/b = Sin C/c

oooh wait im seeing it

[hardy wing]

Yeah, I didn’t plug in the numbers

But we have all apart from angle ACE

So you just plug

[hardy urchin]

so i re arrange the equation to find Sin ace

[hardy wing]

Yes

And then arcsine to get ACE

[hardy urchin]

whats arcsine

[hardy wing]

You get sin(ACE)

How do you get ACE from that?

[hardy urchin]

wait so i got currently sin92x25/44.96=sin c

[hardy wing]

Yes

Simplify the LHS

[hardy urchin]

ooooh alr i get it now

thank you