help-39

[storm thicket]

We can factor a negative from e^[-ix]-e^[ix] to make the e^[-ix] negative now

[frank goblet]

lol

i had an idea, then it went back to the beginning just with a sign error haha

[storm thicket]

I have a feeling we'll end with the same one if we expand cosine to its exponential form

[frank goblet]

you made a mistake somewhere

your solution is complex, it shouldn't be

[storm thicket]

Yeah in the cosine lol

Hm

Oh also the e^[2ix] on the denominator should be e^[x(i+1)]

[frank goblet]

hmm

[mossy bronze]

Hmmm

[storm thicket]

Its a disgusting one for sure

[mossy bronze]

Use this formula

[frank goblet]

i think not even wolframalpha knows how to lmao, it only has the result, not the steps

[storm thicket]

Dont say the answer pls

[storm thicket]

Okie Ill try

[frank goblet]

ok i thinkj it is likely not a standard substitution or int by parts

maybe there are other tricks

[mossy bronze]

Yes

[frank goblet]

the only other cool trick i know is feynman's trick or leibniz rule, but that doesn't seem to be usefull neither

[mossy bronze]

Do you notice how you can get rid of e^x +1?

[storm thicket]

This is awfully incorrect XD

[midnight haven]

make the e^-x e^x

[storm thicket]

Ok

[midnight haven]

i think i have an easier method

[mossy bronze]

Just simplify the expression

[storm thicket]

Oh it does work

[mossy bronze]

Yes

[storm thicket]

Simple integration by parts now:3

[mossy bronze]

Mhm

[storm thicket]

Hply hell that cancellation is amazing

[midnight haven]

right

[mossy bronze]

That formula helps when the limits of the integral are opposites in sign

Cancels out most of the time

[midnight haven]

it's called queen's rule here

[mossy bronze]

Oh yes I've been trying to remember the name for so long thanks!

[storm thicket]

Kings rule and queens rule

5 damn steps

Thanks for the help guys

.close

[pearl pond]

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[pearl pond]

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[tepid warren]

Can I just explain this as
(3/4)/(7/256x)=4(x^x)+256?

[austere quail]

Isn’t this one from a math quiz game on Roblox? I think I recognise this problem.

[tepid warren]

Yeah

It’s literally pain rn

[austere quail]

I don’t know where you got the x^x from, do you have any calculations?

[tepid warren]

I somehow got X=25.6

[tepid warren]

Isn’t there a 4x^x?

Or is it 4x^4x

[austere quail]

No that’s 4x^2

or 4xx

[tepid warren]

Oh yeah I’m dumb

But how do you solve it

The left side is 26x

[austere quail]

First of all, you can remove 2 square roots as sqrt(A) = sqrt(B) gives A=B

[tepid warren]

K

[austere quail]

Then, 25^0=1

[tepid warren]

Wiat 25^0 is 1?

[hollow gull]

yep

[tepid warren]

K that explains why I can’t solve it

So teh left side is 64x

Teh right side is 4x^x+256?

[austere quail]

No, not the 4x^x.

[tepid warren]

Sorry

4x^2

So the right side is 4x^2+256?

[austere quail]

yes

[tepid warren]

64x=4x^2+256

[austere quail]

Yes.

[tepid warren]

But I still don’t know how to solve it

..

Idk how to rewrite 4x^2

[austere quail]

You can divide both sides by 4.

[tepid warren]

So it’s
16x=x^2+256?

[austere quail]

256/4 is not the same as 256

[tepid warren]

My bad

It’s
16x=x^2+64

[austere quail]

Yes

[tepid warren]

O

X=8

Thx

Ima close it

.close

[pearl pond]

Channel closed

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[tepid warren]

Yup I’m stuck on another one already

[austere quail]

You can rewrite 2x+10 as 2(x+5)

[spare lark]

Make it under the same denominator

[tepid warren]

Uh

[tepid warren]

So you rewrite the denominator as:
2(x+5) and 1(x+5)?

[austere quail]

not sure what a denominator is (language barrier hits hard), but if it’s the lower side of the fraction then you’re right

[tepid warren]

K

[spare lark]

The bottom of the fraction

[tepid warren]

Yeah it’s the lower side of the fraction

[thick dagger]

denomoinator is the dlower thing

[tepid warren]

Do you have to reduction of fractions to a common denominator

[austere quail]

You could do that

[tepid warren]

Is it gonna be more complicated

[austere quail]

(I have another method in mind where you don’t have to do it)

[tepid warren]

Can you say it?

[austere quail]

I’ll write it down, give me a moment

[tepid warren]

Alright

[tepid warren]

Kinda hard to read it

[austere quail]

Is my handwriting that bad?

[tepid warren]

No

I don’t mean that

It’s just

Ehh

You know

I’m only 13

I can’t read it

Like

I don’t understand

[austere quail]

Which part do you not understand?

[tepid warren]

Uhh ima just try and explain in my way

So there’s 3 square root 9x+27/x+5

And you put it together and it’s 1

[pearl pond]

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[austere quail]

No, there’s 1.5 of them

[austere quail]

oh I messed this up dang it

[tepid warren]

1.5?

[austere quail]

the bot now thinks I have a question

[amber urchin]

guys

[tepid warren]

You mean there’s 1.5 of
Square root 9x+27/2(x+5)?

[amber urchin]

can anyone help me with my problem

[tepid warren]

Not now yet

[calm wing]

#❓how-to-get-help

[austere quail]

No, look at the upper line of the picture I sent. You can imagine the fraction part as a “blob”. You have a half of the blob plus a whole blob and that is equal to one. You can simplify it to 1.5 “blobs”. This is because 0.5 + 1 = 1.5

[tepid warren]

Oh I know why it’s 1,5

Cuz they have the same molecule?

[austere quail]

Yes, the “blob” I called the parts are both the same

[tepid warren]

But the left denominator is 2x then the right one

So the left fraction is 0.5 of the right one?

[austere quail]

Yes

[tepid warren]

Ohhh

[austere quail]

I’ll give an example:
1/4 + 1/2

1/4 = 0.5*(1/2)

[tepid warren]

So you can rewrite it as
Square root [9x+27/1(x+5)]x1.5?

[tepid warren]

That more clearly thx

[austere quail]

don’t forget the square root

[tepid warren]

K

So it’s like this?

[austere quail]

Yes, and that is equal to one

[tepid warren]

K

Time to do the hardest part

Calculate

[austere quail]

You can get rid of the 1.5

Do you know how?

[tepid warren]

Wiat lemmie write it rq

Is it like this?

I’m probably wrong

Or smth

Oh Wiat I’m dumb

You need to multiply the denominator

[austere quail]

What did we do before with the 4x^2?

[tepid warren]

➗?

Idk the English for that

[austere quail]

Yes, we can do the same here.

[tepid warren]

Divide

Yeah

[austere quail]

Yh

[tepid warren]

Uhh

Wait me a sec

Is it like this?

[mossy bronze]

Yes

[austere quail]

Yh, you could do that

[tepid warren]

Time to calculate I guess

Wait how do you rewrite the molecule

[austere quail]

Do you mean the square root?

[tepid warren]

Yeah

[austere quail]

You can square both sides

[tepid warren]

Idk how to rewrite the 27

Oh yeah I’m dumb

Ohhhhhhh

You have to do x^2 when there is a square root

I’m so dumb

.

I somehow got
243x+2187/2x+10

[mossy bronze]

2187?

[tepid warren]

Uh

(27^2)x3

.

Now I solved 1080/x+5

[tepid warren]

..

Ohh

[mossy bronze]

Its (3×sqrt(9x+27))²

[tepid warren]

Wait I know now

Is it

27x+81/4x+100?

[austere quail]

no

[tepid warren]

My head is dying rn

[austere quail]

I don’t think so

[mossy bronze]

U forgot to multiply by something

[tepid warren]

Multiply what.

..

I’m so confused rn

[mossy bronze]

What is the numerator squared equal to?

[tepid warren]

Is the numerator the upper part of the fraction?

[mossy bronze]

Yes

[tepid warren]

Uh 3

?

Idk

[tepid warren]

So is the denominator
2(x^2)+40x+100?

[mossy bronze]

Yes

Wait no

[austere quail]

How’d you get 2(x^2)?

[tepid warren]

Uh

Cuz I made the fraction to
3(Square root 9x+27)/2(x+5)

[mossy bronze]

Yes and what does (2x+10)² equal ?

[tepid warren]

4x+100?

[austere quail]

no

Look at what I sent before

[mossy bronze]

Apply the rule

[austere quail]

(it is 2ab, I messed up something while screenshotting)

[tepid warren]

2x^2+2(2x)x10)+10^2?

[mossy bronze]

(2x)² not 2x²

[tepid warren]

What does it stand for

[austere quail]

You also have to square the two

[tepid warren]

I am so confused

[mossy bronze]

Here consider a to be 2x not just x

[tepid warren]

So it’s 4x^2?

[mossy bronze]

Yes

[tepid warren]

I finally get it

[mossy bronze]

Good

[tepid warren]

So (a+b)^2 is

Wait a sec

4x^2+2(20x)+10^2?

[austere quail]

yh

[tepid warren]

K

[mossy bronze]

Nice now squre the numerator

[tepid warren]

K

3(9x+27)?

[mossy bronze]

!!!

[tepid warren]

So I got this fraction
3(Square root 9x+27)/2(x+5)

And now I know the denominator is 4x^2+2(20x)+10^2?

So is the numerator 3(9x+27)??

[mossy bronze]

Yes

But

[tepid warren]

Thank god I’m finally correct

[mossy bronze]

No wait

[tepid warren]

.

[mossy bronze]

I though it was 9

You're wrong

[tepid warren]

The numerator?

[mossy bronze]

Mhm

[tepid warren]

How do I rewrite it

[mossy bronze]

U didn't use this correctly

[tepid warren]

I’m so confused rn

When do I need to use ab^2

Uh

.

[mossy bronze]

It should be like this

Then u continue

[tepid warren]

So the numerator is
3^2x 9x+27

Uh is that correct?

[mossy bronze]

Btw that's not an x after 3² that's the multiplication symbol

[austere quail]

We use the dot for that

[tepid warren]

K

[mossy bronze]

Yea ik, it's a habit

[tepid warren]

So it’s like this now?

[mossy bronze]

3^2(9x+27)

[tepid warren]

Yeah

The “x” after the 3^2 is the multiply symbol

[austere quail]

(Usage of the capital letter (X) can prevent misunderstanding)

[tepid warren]

K

So do I solve it now?

[austere quail]

you could do it

[tepid warren]

Yesssss

[austere quail]

If you want to (because this is in a videogame), you can also just use a graphical calculator to solve the problems.

[tepid warren]

Graphical calculator?

[austere quail]

If you don’t have one, nvm what I said

[tepid warren]

K

Uh

Is X=13?

[austere quail]

There is another solution

[tepid warren]

What is it

[austere quail]

But I think the game will accept 13

[gusty moss]

amon gus

[tepid warren]

The one that requires Reduce the fraction to a common denominator

Meh

Ima just do it tmr

2 am for me…

.close

Oh wait it need u to close it

[austere quail]

Oh yh

.close

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[hybrid basin]

Hello

[hybrid basin]

Why isn't b correct?

[next dove]

it should be $-c(\vec{y}\times{\vec{x}})$

[jolly parrot]

77²

[hybrid basin]

But what's the difference?

Both will enlargen the area by 3

[next dove]

it is valid in dot but not in cross product

[next dove]

I think that might change the vector y

and hence the cross product

cross product is generally calculated by solving a determinant
now I am not sure if you know about that property of determinant or not

[hybrid basin]

I do

Then how would (-cy) x x look like?

[next dove]

That if any row is multiplied a constant, for instance say c
then you can take the c out of that determinant but with the power equal to number of entries in that row

[hybrid basin]

So c^3?

[next dove]

oh wait I think wrote it in opposite sense

now I see

option B should be correct that way

I apologize
I misunderstood something before

[hybrid basin]

Oh I confused you mb

It says the answer was b

Thanks a lot though!

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[quaint lotus]

how do I figure out the step pattern for this

[hybrid basin]

!status

[pearl pond]

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

[quaint lotus]

💀

[quaint lotus]

what

https://tenor.com/view/luluwpp-gif-25648350

[cerulean ridge]

I think just finding the values of y when x = 0, 1, 2, 3, 4 should work

[pearl pond]

@quaint lotus Has your question been resolved?

[pearl pond]

@quaint lotus Has your question been resolved?

[pearl pond]

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[edgy jasper]

can someone check this

to see if its right

<@&286206848099549185>

[last moth]

Please don't ping Helpers before 15 minutes, they get a lot of pings (as said in #❓how-to-get-help)

[long eagle]

I just checked it

I think all thing is right

[pearl pond]

@edgy jasper Has your question been resolved?

[pearl pond]

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[tropic tangle]

I have an answer, but I am not sure if this is correct or not, could someone check to see if this is right?

[pearl pond]

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@tropic tangle Has your question been resolved?

[tropic tangle]

<@&286206848099549185>

[tropic tangle]

anyone?

[long eagle]

yeah

you are right

GA is approximately 14.66yards

The distance between Player A and Player B(AB) is 10 yards

Angle AGB = 65

Angle BGA =74

Angle G = 180-65-74 = 41

sin(A)/a = sin(B)/b = sin(C)/c => GA = 10 * sin(74)/sin(41) ≈ 14.66yards

[tropic tangle]

thank you!

[long eagle]

you are welcome

[pearl pond]

@tropic tangle Has your question been resolved?

[pearl pond]

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[split lark]

I am stuck pls help

[warm current]

https://tenor.com/view/jake-peralta-squinting-read-trying-to-read-brooklyn-nine-nine-gif-13387080

[split lark]

lol

wht happened

[warm current]

Estimate error in the approximation

I just had trouble reading that

[split lark]

hello

.close

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[split lark]

pls help how did they get 0 as the limit?

[west sapphire]

if x = 0 then (n+1)|x| is zero

for all n

[split lark]

is that something i would just have to recognize

?

@west sapphire

[west sapphire]

well anything times zero is zero

there's not too much to recognize

[split lark]

hmm i se e

thx

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[sharp smelt]

Suppose x and y are real numbers, and 3x + 2y ≤ 5. Prove that if x > 1 then y < 1.

[sharp smelt]

so I started by solving for y

$y = \frac{5-3x}{2}$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

now $x>1$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

finding the limiting value of y

we get y=1

now what do I do?

[cinder flower]

if x > 1 then 5 - 3x < ?

[hazy solar]

you can just manipulate x > 1 algebraically directly

[sharp smelt]

oh

[quiet tendon]

just figure out how to turn the inequality for x into an inequality for y

first step: x > 1 -> 3x > 3
what do you know about -3x? 5-3x? (5-3x)/2? y?

[sharp smelt]

that;s it?

[quiet tendon]

yep

[sharp smelt]

got it

thanks

.close

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[grand bear]

hello

[grand bear]

does anyone know what topic of calculus this is?

[hazy solar]

Just first/2nd derivatives test I think

and maybe fundamental theorem of calculus for some intermediary steps

[grand bear]

oh got it thank you

sorry

i remember my teacher talking about optimization here

or it might have been for a different question

[hazy solar]

Derivatives tests is a form of optimisation

more precisely, the critical points represent a form of an “optimal” point

[grand bear]

ohh

do you know what i would need to search to find similar questions to this?

is there like a specific name for these types of questions?

[obtuse tendon]

optimization problems derivatives/integrals

or max/min problems

[grand bear]

thank you

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[vernal grove]

Why did they get rid of the -2 in $\nabla f$ when applying the chain rule

[jolly parrot]

Calc III Victim

[vernal grove]

or is it a typo

I mean it still wont make a diff right because I could factor the -2 and the inside will still be 0 will outside its -400 instead of 200

[pearl pond]

@vernal grove Has your question been resolved?

[calm wing]

i think it's a typo

i also don't see where it could've gone

[vernal grove]

bet ty

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[silver sequoia]

Can someone please check my work?

Is the answer -25 or 25?

Is my writting readable tho

Please ping me, im gonna do another question

[vague island]

the answer is -25

maybe

[pearl pond]

@silver sequoia Has your question been resolved?

[silver sequoia]

Yea .. maybe
Imma just close for now

[silver sequoia]

Mm okie thanks

.close

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[chrome wharf]

hi

[chrome wharf]

can anyone tell me how to calculate

Y = 2x+3

like put it on a graph <@&286206848099549185>

[rich thistle]

you can do a table for it

[summer gorge]

!15mins

[pearl pond]

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

[rich thistle]

or just find the intercepts

[pearl pond]

@chrome wharf Has your question been resolved?

[storm frost]

x | 0, 1, 2
y |

Substitute the x values in the equation and get the values of y

[chrome wharf]

how to put in a graph?

[storm frost]

Take x, y pairs and put them on the graph

[chrome wharf]

k thx

.close

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[burnt crystal]

I managed to get everything but part a) correct and I'm not sure why

[pearl pond]

Please don't occupy multiple help channels.

[burnt crystal]

my faukt

[pearl pond]

@burnt crystal Has your question been resolved?

[burnt crystal]

<@&286206848099549185>

[pearl pond]

@burnt crystal Has your question been resolved?

[pearl pond]

@burnt crystal Has your question been resolved?

[cunning veldt]

ok so the function for that line is
y = x/50 + 2, since it starts at (0,2) and the rise over run is 0.4/20 aka 1/50
and in this case y is log P and x is t so the function/equation becomes
Log P = t/50 + 2

so if you wanted the equation without any tweaks itd be
Log P = t/50 + 2

but if you want it in terms of P itd be

P = 10^(t/50 + 2)

was that the equation the question was asking for?

btw if it wanted it in terms of a and b itd be
ab = 10^(t/50 + 2)
or
log(ab) = t/50 + 2
or
log(a) + log(b) = t/50 + 2

[burnt crystal]

Okay thank you I'll read through this when I get the chance but thanks for the reply

[cunning veldt]

youre welcome

[pearl pond]

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[dense iris]

For the ratio value

I can get the value of 2 or -2/3

however the mark scheme only has -2/3

why?

why is the 2 rejected

😭

[dusty flame]

Bro

Convergence condition

[dense iris]

ah fak i forgot that was a thing

so mod x has to be less than 1 right

mod r has to be less than 1?

is that it?

[cursive wraith]

yes

[dense iris]

ouch ok thanks

rip all my marks hahaha

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[main terrace]

if this is my answer can't I also get the 3 = (1/3)^-1 and get it together which makes (1/3)^n-1
same for 4 * 2^n = 2^2 * 2^n = 2^n+2?

[pearl pond]

@main terrace Has your question been resolved?

[main terrace]

<@&286206848099549185>

[last moth]

yes you can write it as (1/3)^(n-1) + 11(-1)^n + 2^(n+2)

[main terrace]

is that better?

[last moth]

It's not better or worse, just different

[pearl pond]

@main terrace Has your question been resolved?

[pearl pond]

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[vocal nebula]

if you sum the horizontal and vertical it would be the same amount how to find the b ?

[pearl pond]

@vocal nebula Has your question been resolved?

[spare lark]

So 5+7+B+3 = 11 + A + 9 + 5 ?

[vocal nebula]

yeah?

i dont know

i need to find the b

i alredy tried that way

[random stirrup]

wdym sum the horizontal and vertical

[vocal nebula]

if i add the vertical

it will be the same amout as the horizontal

[random stirrup]

at any square?

because at the top right square 11 + A + 9 + 5 = 25 + A and 5 + A + 3 = 8 + A

and 25 + A ≠ 8 + A

What is horizontal and vertical

[vocal nebula]

the square

[random stirrup]

you have to explain better

[vocal nebula]

sorry my english is bad 😔

[vital anchor]

11 + A + 9 + 5 = 5 +7 + B + 3
11 + 2B + 5 = 5 + A + 3

is that whats happening?

[vocal nebula]

yeah

wait

11 + A + 9 + 5 = 5 +7 + B + 3 = 11 + 2B + 5 = 5 + A + 3

i think like this

[vital anchor]

the image appears to be a rectangle with 2 different pairs of side lengths

or were you told that all sides were equal?

[vocal nebula]

all sides were equal

From the picture above, the sum of all the horizontal blocks is exactly the same as the sum of all the vertical blocks. The B value is...

[vital anchor]

if thats the case, then youre right,
11 + A + 9 + 5 = 5 +7 + B + 3 = 11 + 2B + 5 = 5 + A + 3
it would be like this

you can start shifting numbers around to just get a single equation i guess

[vocal nebula]

what do i do after get the single equation?

[vital anchor]

you can get B on one side of the equals sign and everything else on the other, getting an equation for B

[vocal nebula]

okay

ill try it

thankyou

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[fresh cloud]

could somebody double check this for me

[fresh cloud]

this one as well

[gray bolt]

Yeah seems ok, there's no 89 in the first set

[pearl pond]

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[fresh cloud]

could someone check this one too 😭

[fresh cloud]

also i have no clue how to do this one

i assume its C

[charred mauve]

I would also do c

[fresh cloud]

what abt here

[charred mauve]

Females and drama

[fresh cloud]

yeah i did females and drama bc its the highest percentage out of all the others

[charred mauve]

👍

[fresh cloud]

pretty sure i got this one right too

dont trust myself enough though

it should be that one because its the only one thats not negative and the other options are all negative

[pearl pond]

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[pearl pond]

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[cedar scarab]

This is what I've tried. I'm just not really sure how they got definite values for everything.

[cursive wraith]

did you try writing down the diagonalization formula

A = PDP^-1

[cedar scarab]

The what

I've never even heard of that

[cursive wraith]

ok because that really solves all of your problems

D is the diagonal matrix with eigenvalues

and P is an invertible matrix with each column being an eigenvector

[cedar scarab]

Ah ok. I recall the teacher saying we need to self teach ourselves how to do diagonalization because our final is next class.

[cursive wraith]

yep...

without diagonalization good luck solving this exercise

[cedar scarab]

Fair enough. I shall look up a video on that.

[cursive wraith]

anyways that's the formula

[cedar scarab]

Shame this class is only 4 weeks. Teacher was actually decent.

So $D=\begin{bmatrix} 1 & 0\ 0 & 3\ \end{bmatrix}$?

[jolly parrot]

Narutoes

[cedar scarab]

And then $X=\begin{bmatrix} -1 & -1\ -2 & -3\ \end{bmatrix}$?

[jolly parrot]

Narutoes

[cedar scarab]

So then $A=\begin{bmatrix} -1 & -1\ -2 & -3\ \end{bmatrix}\begin{bmatrix} 1 & 0\ 0 & 3\ \end{bmatrix}\begin{bmatrix} -3 & 1\ 2 & -1\ \end{bmatrix}$

[jolly parrot]

Narutoes

[cedar scarab]

.close

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[mental heath]

how does this proof hold?

[gleaming heath]

why do you think it doesnt hold

[mental heath]

unless I am mistaken

let me write

the first statement i interpret as containing two contradictions

given some existent q less than p

(where p is defined)

if 5 is the value chosen as a first addend in defining p

then p=6

which implies q=3 or q=2

given that

there are multiple terms

[gleaming heath]

the assumption is that there are finitely many primes so you need to use all of them in p

so it holds because p = 5 + 1

on the assumption that 5 is the only prime

so if p is not prime, then we have found a new prime (i.e. 2 or 3)

if p is prime, then it is not on our list (i.e. it is not 5)

[mental heath]

oh

i see

such is stated before that

which i read but

[gleaming heath]

https://en.wikipedia.org/wiki/Euclid's_theorem

[mental heath]

so p is subject to variance

[gleaming heath]

well the assumption is that there are finitely many primes

so it supposes you have all of them

[mental heath]

then

p must

i see

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[gleaming heath]

p must be prime or not prime

and in both cases, we find a prime not on our finite list

[pearl pond]

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[midnight haven]

z

[midnight haven]

my brain

bouta boom

what type of language is this

second sentence wtf

nvm

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[copper nova]

.reopen

[real musk]

My friend says this is chain rule, we are taking derivatives and I don’t know where/how to start

[quiet tendon]

you differentiate the trig derivatives like you normally would, but multiply by the derivative of the argument

a similar example might be that d/dx (sin(x^2)) = cos(x^2) * 2x

[pearl pond]

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[pearl pond]

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[zenith basin]

Can someone please help me with this

[pearl pond]

@zenith basin Has your question been resolved?

[zenith basin]

<@&286206848099549185>

[frail root]

there are 2n+1 people, sitting around a circle, so there would be (2n)! possibilities for sitting.

and suppose n+1 women are already sitting around the circular table, which has n! possibilitie.
now there exist n+1 positions between women that you can sit men in there ( so you dont get any two man sitting next to each other ). so you would have to choose n positions from n+1 positions available which is C(n+1, n) = n+1
and then you can sit men in those positions with n! possibilities.

so your favorable condition has (n+1)(n!)(n!) = (n+1)!n! possibilities

then the probability is (n+1)!n!/(2n)!

[frail root]

.

[zenith basin]

ty

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[real musk]

So

[real musk]

In this case we have -csc2x as the derivative

And secxtanx

[real musk]

I understand exactly what you mean by this example, but I see (I’m using variables as trig placeholders)

G(x) = X + Y

But I have two derivatives,how can I turn that into ONE derivative for chain rule? @quiet tendon

[quiet tendon]

differentiate X and Y separately

term by term

and use chain rule for each

let’s say a(x) was cot, b(x) was sec, and c(x) = x², then g(x) = a(c(x)) + b(c(x))

so g’(x) = a’(c(x)) * c’(x) + b’(c(x)) * c’(x)

[real musk]

So -csc(x2) * 2x + sec(x2)tan(x2) * 2x? @quiet tendon

[quiet tendon]

close but derivative of cot is -csc²

other than that that’s right

[real musk]

Thank you brother

.close

[pearl pond]

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[real musk]

.reopen

[pearl pond]

✅

[real musk]

Dang it the channel randomly closed and I did not catch / nor can I find the thread of which it was in

1-cosx > 0, next?

@south inlet sorry had to go find it

[south inlet]

so you have $\lim_{x \to 0^{-}}\frac{|1-\cos(x)|}{\cos(x)-1}$ right?

[jolly parrot]

eugene_krabs_has_cake

[real musk]

Thank god ur still here

Yes

[south inlet]

ok so since this function isnt continuous at 0, you cant just say the answer equals $\frac{|1-\cos(0)|}{\cos(0)-1}$

[jolly parrot]

eugene_krabs_has_cake

[south inlet]

so you have to manipulate it a bit

so are you aware that for x > 0 |x| = x?

[real musk]

Yes.. @south inlet

[south inlet]

so are you ok with saying |1-cosx| = 1 - cosx?

[real musk]

Oh, then yes? That logic makes them the same function

[south inlet]

yeah

[south inlet]

so this turns out to just be a limit of a constant function

[real musk]

Ok..? Which means

[south inlet]

well what would be the value of $\lim_{x \to 0^{-}} -1$?

[jolly parrot]

eugene_krabs_has_cake

[real musk]

-1 - 1 would be -2 punchin in cos (-1) - 1 @south inlet

[south inlet]

why are you putting in cos(-1)

what im asking is, if a function is constant, ie the value of the function never changes, what would be the value of the function as x tends to any number?

[real musk]

-1 is a constant…I understand that, maybe it’s the wording

-1? If it never changes?

A function in my head is something like x+2 and subbing in for that

[south inlet]

yeah

[south inlet]

so this limit is just -1

the function will always approach -1

[real musk]

Ok, so in the context of this equation?

[real musk]

.

1-1 is 0, the limit is always >0?

[south inlet]

well $\frac{|1-\cos(x)|}{\cos(x)-1} = \frac{1-\cos(x)}{\cos(x)-1} = - \frac{\cos(x)-1}{\cos(x)-1} = -1$

[jolly parrot]

eugene_krabs_has_cake

[south inlet]

so the thing inside the limit is just -1

[south inlet]

which means the question boils down to exactly this limit

[real musk]

And finally, how did we go from 1-cosx /cosx-1 to it being reversed @south inlet

[south inlet]

i took a negative out the front

[real musk]

Man, I hate to keep asking the littlest things I’m just trying to understand, why did you factor out a negative if

1-cosx = -(1-cosx) = -1 + cosx

[south inlet]

basically what i wrote was 1 - cosx = -(cosx - 1)

and then you can cancel the cosx - 1 on top and bottom

[real musk]

.

I have two more questions to go over from my quiz similar and I’ll cal it a night after

I actually get this one from what I was told here

Of just setting them equal to each other this is continuous

Graph ✅

But this one?? @south inlet

Reflects a certain rule yes, how can we apply that

Why was the square root taken here

[south inlet]

im guessing thats supposed to say as t tends to 0

[south inlet]

taking out the square

$\sin(x) \approx x$ if $x$ is close to $0$

[jolly parrot]

eugene_krabs_has_cake

[real musk]

Following

[south inlet]

so $\frac{\sin^2(3t)}{3t^2} \approx \frac{(3t)^2}{3t^2} = \frac{9t^2}{3t^2} = 3$

[jolly parrot]

eugene_krabs_has_cake

[south inlet]

but since we are taking the limit as t tends to 0, then this is basically an equality

[real musk]

We are ignoring sin

[south inlet]

yeah

[real musk]

A bit confused still by the square root. But I will just include it in my solving process less questions asked

Last problem of the night

@south inlet here is our answer key I’m comprehending

[south inlet]

ok so its basically asking does $\lim_{x \to \frac{\pi}{4}} \frac{2\tan\left(x - \frac{\pi}{4} \right)}{x - \frac{\pi}{4}} = 1$?

😭

[real musk]

Lol

[jolly parrot]

eugene_krabs_has_cake

[real musk]

Ok

https://tenor.com/view/sleepy-tomandjerry-ناعس-onnato-gif-5120823

[south inlet]

so you can again use something quite handy

$\tan(x) \approx x$

[jolly parrot]

eugene_krabs_has_cake

[south inlet]

for x small

and when x is close to pi/4 then x - pi/4 is close to 0

so $\lim_{x \to \frac{\pi}{4}} \frac{2\tan\left(x - \frac{\pi}{4} \right)}{x - \frac{\pi}{4}} = \lim_{x \to \frac{\pi}{4}} \frac{2\left(x - \frac{\pi}{4} \right)}{x - \frac{\pi}{4}}$

[jolly parrot]

eugene_krabs_has_cake

[real musk]

So u can set them equal again

[south inlet]

yeah

since you are taking a limit, basically x - pi/4 is coming infinitely close to 0, so this is just an equality

and now you can cancel things down

[real musk]

2

[south inlet]

yeah

[real musk]

Did you factor this from bottom and top btw

Or just numerator

[south inlet]

just the numerator

[real musk]

Which gives u -1/1

I finally see it now

I have my internship morning + midterm tmrw afternoon thank you for all the help, I am going to bed @south inlet

[south inlet]

np

but just as an answer to the previous one (hopefully you got this conclusion aswell), f(x) isnt continuous at pi/4

[real musk]

@south inlet because 2 does not equal pi/4 ofc

[south inlet]

not that 2 doesnt equal pi/4 but because 2 doesnt equal 1

[real musk]

You mean this from its unit circle value? @south inlet

[south inlet]

no

just that the limit of the function as x tends to pi/4 doesnt equal the value of the function at pi/4

[real musk]

Where is your 1 coming from

[south inlet]

f(x) = 1

at pi/4

[real musk]

…

oh

I’m blind

Completely forgot about the second constant

Thanks again dawg .close

[south inlet]

np

.close

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[real musk]

Okay I lied

[real musk]

Got quotient rule down fine

Sinx / cos^2x

I see no identity’s for it, honestly I would have left it as is, where did he get secxtanx from

[unborn abyss]

$\f\sin{\cos^2} = \f\sin\cos\cdot\f1\cos = \tan\sec$

[jolly parrot]

hayley 🥥 🌴

[pearl pond]

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[next dove]

to eliminate r we found r as a function of h and substituted back in

r/h = 5/16

and this will be true for at point of time in the cone

you can prove this by the similarity of triangles

by similarity of triangles

yeah

but this might works in other cases too

was this information given in that question?

can you show the work for this problem?

where you get incorrect answer

here that is not applicable

in the case of cone both height and radius were decreasing at the same rate
but here in cylinder, only height is decreasing but not the radius

so equality hold for initial condition only

here let EB be the level of water at any general point
now consider triangles ABE and ACD:-
angle A is common in both of them
and since CD||BE and AC and AD are transverses, angle ABE=ACD and angles AEB=ADC
hence the both triangles are similar

hence, EB/EA = DC/DA

at any instant of time

exactly

yeah you're cooking

it is differentiation of Volume with respect to height

yeah

np

[pearl pond]

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Closed by @gleaming sundial

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[pearl pond]

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[sinful frigate]

where Is this come from? I have solid geometry book but there is no such formula in it please anyone check this and let me know about that link/topic name

[pearl pond]

@sinful frigate Has your question been resolved?

[pearl pond]

@sinful frigate Has your question been resolved?

[pearl pond]

Channel closed

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[pearl pond]

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!

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[echo glacier]

.closed

<@&286206848099549185>

[spiral pivot]

!15min

[quiet tendon]

!15mins

[pearl pond]

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

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

[spiral pivot]

!status

[pearl pond]

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

[echo glacier]

7

[spiral pivot]

thanks, care to explain further?

[echo glacier]

sir idk

[spiral pivot]

!show

[pearl pond]

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

[echo glacier]

im only 16

idk even this

our teacher never taught this

[next dove]

ever heard about Aritmetic progression?

[echo glacier]

ye

i think in 7th grade

or 8th

i forgot

[next dove]

whatever

do you know about the formula for sum of the first n squares?

[echo glacier]

no

thats why im here

i wont come here if i know them bro

[next dove]

so maybe they want it done by something else
that you know

[echo glacier]

yeah

it was done by someone else

i just want to know the answer

[next dove]

so you don't want the procedure?

[echo glacier]

no

idk

bro

i cant even solve it

[next dove]

your teacher gave it right?

[echo glacier]

no

it was a quiz bro

in a game

idk what is ans

[next dove]

bro😶

This server is to help you learn math
not to give answer for a game

[echo glacier]

ok

[next dove]

maybe you should get to know about concept

[cunning veldt]

lol

[spiral pivot]

!noans

[pearl pond]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[spiral pivot]

We're happy to help you learn, and this is a very complicated question.

But we're not here to give answers.

For what it is worth, the first few natural numbers who belong to this class of number are 1, 6, 28, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190, 18600, 18620, 27846, 30240, 32760, 55860

[echo glacier]

ok thanks

[cunning veldt]

ok good to know its not supposed to be easy since i have no idea how to approach this tbh

[spiral pivot]

if you're interested in just getting an answer, you may be able to find one on the OEIS, A001599

[echo glacier]

oh

ok

OMG

OEIS

yea i remember

tahnk u sir

u are a child of god

[cunning veldt]

or you could also just use chatgpt
its not always 100% reliable but its a decent last resort

[spiral pivot]

don't even joke about that.

!chatgpt

oh, that's not one

!nogpt

[pearl pond]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[cunning veldt]

i never said its reliable

[spiral pivot]

In fact you implied it was unreliable, but still.

[cunning veldt]

im just saying if he wants a direct answer and cant find it anywhere, and this thing isnt that important anyway since its just a game, he COULD use it

yeah i do firmly believe its unreliable

like well above 50% of the time

[echo glacier]

wtf

didnt work

[spiral pivot]

I didn't say you wouldn't have to work for it

just if you want a solution, there is code at the bottom in multiple different languages that allows you to generate however many of these integers you want

[echo glacier]

bruh

i cant do math

i think chess is more easy

i can mate in 13

[cunning veldt]

then why you playing a math game💀

[echo glacier]

ofc

for fun

its for fun

but im actually depress

[cunning veldt]

then go on chess.com or something, if you aint even willing to put in a nudge of effort for the answer😭

[echo glacier]

no lol

i want to answer this

[spiral pivot]

Then answer it

[echo glacier]

more thrill

yea

im gonna bruteforce

im gonna start typing random numbers

[spiral pivot]

Good luck, with that.

[cunning veldt]

now i actually wanna find a non brute force way to solve this tbh

but i suck at number theory so its probably not happening sadly

[spiral pivot]

It's legitimately a very hard problem, and I don't know a good approach to figuring it out without brute forcing either.

[cunning veldt]

yeah its like suspiciously hard, feels like we're missing something

usually games like those never involve stuff that is that hard to prove or doesnt have a general rule

[spiral pivot]

Also actually calculating the 2023rd harmonic number seems like it would require a considerable amount of compute

[cunning veldt]

well im sure the problem relies on the fact that theres some neat pattern which makes you not have to actually compute the number/divisors/harmonic mean

i hope so atleast...

[spiral pivot]

Well, looking into it, it seems like perfect numbers are harmonic integers, but also some RMS numbers, but not all, and there are still multiple open conjectures about them on the oeis page.

[pearl pond]

@echo glacier Has your question been resolved?

[cunning veldt]

i dont think this question is getting solved anytime soon tbh😭

it doesnt seem like theres much known about these harmonic divisor numbers in the first place at all

[pearl pond]

Channel closed

Closed due to timeout

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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.

[glass bolt]

Why is the set convex?

[glass bolt]

My tutor just said the set of all x where f(x) >=c is convex so the function concave

No explanation

Because its a vector ofnpoints?

[cursive wraith]

the set is convex because it's an interval

oh wait

it's in R^n

well anyways if it's in R^n it looks like it's a closed ball

closed balls are convex

[glass bolt]

So like any two points is contained in the set

Line segment between two points

Is that the formal definition?

[cursive wraith]

the formal definition is indeed "for any two points inside the set, the points of the segment are inside the set too"

[glass bolt]

So its a convex set in R?

[cursive wraith]

I don't know what f is here

[glass bolt]

Or because its line segment between points in the interval is unobstucted

[cursive wraith]

is it a function from R^n to R

[glass bolt]

Neither do j

[cursive wraith]

or a function from R to R

ok it is a function from R to R I think

well here

An interval is always a convex set

by definition of an interval

intervals are the convex sets of R

so

[glass bolt]

But surely everything is a convex set of R?

[cursive wraith]

no

{1,2} is a subset of R

yet the segment that connects 1 and 2 is [1,2]

[glass bolt]

And that subset is convex requires the line segments within that subset to be within the set

[cursive wraith]

with 2 points of a subset A, you can create the line segment that connects them

[glass bolt]

Yes

[cursive wraith]

all of the points of that line segment must also be in A

for A to be convex

[glass bolt]

Ok

[cursive wraith]

this subset, A = {1,2} is not convex for example

[glass bolt]

Ty for the help

Why

[cursive wraith]

A only contains the points 1 and 2