help-0

[molten pivot]

Do you know how to tell wolfram to use the other branch of W

We need W_-1

[urban pine]

the info page says ProductLog[k, z] for principal value k = 0

[molten pivot]

Thanks ill try

This gives us the upper half of the curve

Maybe there was something in my algebra that missed the other half of the solutions

Lol

[urban pine]

nice job though!!

[molten pivot]

By swapping x and y we get the lower part

So all we need to do now is minimize the distance to the origin

,w plot (1+(1/e^(ProductLog[-1,-ln(x)/x)]^2)

Lol wolfram really don't like doing calculus on W

[ocean seal]

Results provided by WolframAlpha

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

Requested by Mr. Gamer#6658

[molten pivot]

Ignoring portion of domain over which it is not a real function:

The minimum is clearly at x=e

@tame willow you can work out the calculus yourself now probably!!

If you know the derivative of W_-1

Or you can derive it implicitly

,w d/dx ProductLog[-1,x]

[ocean seal]

Results provided by WolframAlpha

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

Requested by Mr. Gamer#6658

[urban pine]

@molten pivot i'm blanking on why the origin minimization is 1 + y^2

[molten pivot]

Yeah I was wrong on that actually, thinking of arc length formula haha

You would have to minimize x^2+y^2 to minimize d^2 (squared distance)

It's generally easier to work with squared distances than actual distances, so we can just minimize d^2 instead of d because squaring preserves order over the positive numbers

[urban pine]

oh lol! yeah it works out for d^2 still

pretty rad to basically work it out on a napkin

[lone heart]

@tame willow Has your question been resolved?

[tight locust]

What has not been answered?

I mean it looks like there's nothing really left to solve

[ocean seal]

Noby707

Noby707

[pliant dune]

have you considered reading #❓how-to-get-help

[cold grail]

Sorry I forgot.

[tame willow]

.close

[lone heart]

Channel closed

Closed by @tame willow

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[lone heart]

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.

[fierce prairie]

completely lost on this one..

[urban pine]

some wild optimization prob?

are they ending up eight yards apart along the perimeter? i'm thinking that must be the case or i think this will get out of hand really fast nvm

[lone heart]

@fierce prairie Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[upbeat gazelle]

I am having trouble trying to prove by induction that (1 + x)^n ≥ 1 + nx. I end up trying to show that (1 +k+1)^j+1 ≥ 1 +(j+1)(k+1) and I have no idea what to do from there

[rugged sun]

Hi

What variable are you using induction on?

x or n?

@upbeat gazelle

[upbeat gazelle]

I'm not sure. I know x is a real number and they are both greater than or equal to 1

[rugged sun]

So if x is a real number, how can we use induction on it?

What I'm getting at here is that we only need to use induction on one variable

[upbeat gazelle]

oh gotcha.

[rugged sun]

The variable that takes integer values

[upbeat gazelle]

Base case: n=1 x=1 (1+1)^1 ≥ 1 + 1*1

2 ≥ 2 therefore, n=4 x=4 is true for (1 + x)n ≥ 1 + nx

Suppose n=j x=k such that j ≥ 1 and k ≥ −1

[rugged sun]

So why are you substituting for x at all?

[upbeat gazelle]

of so I leave x and just use induction on n?

[rugged sun]

Yeah, exactly.

Induction works on some statement P(n) that depends on n

In this case the statement is for n=1 : (1+x)>=1+x which is true for all real x

We then assume for n=k (1+x)^k>=1+kx for all x

[upbeat gazelle]

Base case: n=1 (1+x)^1 ≥ 1 + x

1+x ≥ 1+x therefore, n=1 is true for (1 + x)n ≥ 1 + nx

Suppose n=k such that k ≥ 1 and x ≥ −1

We will show that (1 +x)^k+1 ≥ 1 +(k+1)x

[rugged sun]

Yeah, not all real x actually, you are right

The range on x you give is correct

But the point is that that is part of the statement we assume

[upbeat gazelle]

I guess I am just confused on knowing when an inductive proof is done because it does not feel like it has really proved anything

[rugged sun]

Do you mean you are confused when you need to use an inductive proof

Or are you not sure why you need an inductive proof at all

[upbeat gazelle]

no just how in this case to simplify the problem in such a way that it is evident the left side is greater than or equal to the right

[rugged sun]

The point is that the assumption we make is a piece of information we can use

So in what you wrote above

We start with the left hand side of the k+1 case

And we manipulate it using that piece of information we have to get the desired right hand side

So in other words, the k case implies the k+1 case

The k case enables us to obtain the k+1 case

[fallen verge]

Is there a way to show it using binom?

[rugged sun]

Yes there is

But we are using an inductive proof here

[fallen verge]

Ah i see

[rugged sun]

So let's look at the left hand side of the k+1 case

It is

,,(1+x)^{k+1}

[ocean seal]

Social Capital Gainer

[rugged sun]

How can we manipulate this so that we can use the k case?

We want to use it somehow

[upbeat gazelle]

I think that is what has me stumped because the only way I can think of to get rid of the exponent is to go to that root and that would not be helpful

[rugged sun]

Ok another way to do this

Is to start by writing the statement we have assumed to be true

,,(1+x)^k\geq 1+kx

[ocean seal]

Social Capital Gainer

[rugged sun]

How can you generate this here

What can we do to the k case to get that (1+x)^(k+1) piece somehow

How can we get that +1 in the power

[upbeat gazelle]

I'm really not sure

[rugged sun]

What do i multiply 4^6 by to get 4^7?

[upbeat gazelle]

so I multiply by k?

[rugged sun]

Not quite

Do you agree that (1+x)^k is (1+x) multiplied by itself k times

[upbeat gazelle]

so it can just be simplified to (1+x)>= (1+x)?

[rugged sun]

Not really

What I am getting at is

We can multiply both sides of this inequality by (1+x)

Since (1+x) is positive, then the >= sign doesn't change and we get

,,(1+x)^k(1+x) \geq (1+kx)(1+x)

[ocean seal]

Social Capital Gainer

[rugged sun]

What does the left hand side become?

[upbeat gazelle]

(1+x)^2k

[rugged sun]

Nope that would be (1+x)^k (1+x)^k

We dont have that here

[upbeat gazelle]

(1+2x+x^2)^k?

[rugged sun]

I think you are guessing. let me ask you a quick question

What is

,,4\times 4^k

[ocean seal]

Social Capital Gainer

[upbeat gazelle]

no idea

[rugged sun]

So you agree that 4^3, for example, is 4×4×4

[upbeat gazelle]

yes

[rugged sun]

So what is 4×4^3

[upbeat gazelle]

4^4

[rugged sun]

Yeah

[rugged sun]

So what is this

[upbeat gazelle]

so (1+x)^k+1

[rugged sun]

Yes

,,(1+x)^{k+1}

[ocean seal]

Social Capital Gainer

[rugged sun]

To be completely clear

So lets put that in

,,(1+x)^{k+1} \geq (1+kx)(1+x)

[ocean seal]

Social Capital Gainer

[rugged sun]

Do you agree?

[upbeat gazelle]

yes

[rugged sun]

Nice

So the left hand side is what we want

Now we need to manipulate the right hand side

What do you think we can do?

[upbeat gazelle]

Wouldn't it be the same thing?

(1+x)^k(1+x)

[rugged sun]

I mean

The right hand sjde is currently

,,(1+kx)(1+x)

[ocean seal]

Social Capital Gainer

[rugged sun]

What algebraic manipulation can we do to that

What can we do with a pair of brackets like this

[upbeat gazelle]

I'm not sure because you cant say (1+kx)^2 because they are not the same thing. You could divide the (1+x) from both sides

[rugged sun]

We we put it in deliberately, we wouldn't want to divide it off again

If I gave you something like

(x+3)(x+5)

What could you do to that

Really simple thing

To do

[upbeat gazelle]

well you could just multiply

[rugged sun]

Yeah

Exactly

[rugged sun]

So lets do that here

[upbeat gazelle]

1+x+kx+kx^2

[rugged sun]

Nice

Now factor that x out of kx and x

[upbeat gazelle]

1+x+k(x+x^2)

[rugged sun]

Or in other words, add x to kx

That's what I meant

[rugged sun]

Here you factored k out, we want to factor x out

Instead of k

[upbeat gazelle]

1+x(1+k+kx)

[rugged sun]

Yes, that is correct, but we want to leave kx^2 alone, you will see why in a second

[upbeat gazelle]

so 1+x(1+k)+kx^2

[rugged sun]

Yes, good

So this is what we have so far

,,(1+x)^{k+1} \geq 1+(k+1)x+kx^2

[ocean seal]

Social Capital Gainer

[rugged sun]

This is almost what we want

The k+1 case

Except we have an extra piece, the kx^2

What can we do about that?

[upbeat gazelle]

no idea

[rugged sun]

So to give you another example

,,a \geq b+2

[ocean seal]

Social Capital Gainer

[rugged sun]

a and b are positive

Do you agree that

,,b+2>b

[ocean seal]

Social Capital Gainer

[upbeat gazelle]

yes

[rugged sun]

Therefore

,,a > b

[ocean seal]

Social Capital Gainer

[upbeat gazelle]

alright

[rugged sun]

So how can we use that here

,,(1+x)^{k+1} \geq 1+(k+1)x+kx^2

[ocean seal]

Social Capital Gainer

[rugged sun]

To get rid of that kx^2

[upbeat gazelle]

no idea

[rugged sun]

Ok

So kx^2>=0

Yes?

kx^2 is either positive or 0

Since k is positive

And x^2 is always positive (or 0 when x=0)

[upbeat gazelle]

yes

[rugged sun]

Ok

So on the right hand side, we have added a number which is either making the right hand side bigger than it would have been without it or leaves it unchanged

So if we just drop that term

,,(1+x)^{k+1} \geq 1+(k+1)x

[ocean seal]

Social Capital Gainer

[rugged sun]

Then the right hand side is either unchaged or is smaller

This is because

,, 1+(k+1)x+kx^2 \geq 1+(k+1)x

[ocean seal]

Social Capital Gainer

[rugged sun]

So we went to a smaller (or equal) number

Therefore, this is true

,,(1+x)^{k+1} \geq 1+(k+1)x

[ocean seal]

Social Capital Gainer

[rugged sun]

Does that make sense?

[upbeat gazelle]

yes

[rugged sun]

So that's it, we obtained the k+1 case out of the k case

We have proved it by induction

[upbeat gazelle]

ok thank you

[rugged sun]

No problem at all

Do you have any questions at all

[upbeat gazelle]

so we inherently know that the left side is greater or equal to the right side now?

[rugged sun]

Yes

We assumed that it is true for k

And that assumption means that it must also be true for k+1

As we have just shown

Since it is true for 1 then it is true for 2, since it is true for 2, then it is true for 3 and so on

[upbeat gazelle]

awesome got it

.close

[lone heart]

Channel closed

Closed by @upbeat gazelle

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[fierce prairie]

in response to #help-4 message
@fallen verge I had to go, but I don't quite understand what you did here

why is it 2p + 8 = 90?

[fallen verge]

They both walk almost around the rectangle

[fierce prairie]

okay..

hold on whats p

[fallen verge]

P is the perimeter

[fierce prairie]

?

2(70) + 8 doesn't equal 90

I'm likely misinterepreting you

[fallen verge]

Oh ohmy god forgot about that

I didnt solve the problem lol

[fierce prairie]

oh lol

[fallen verge]

The 8 probably means as the crow flies then

[lone heart]

@fierce prairie Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[safe mural]

would someone be able to help me with this please

[safe mural]

i think we get the expected value of X hat but i'm confused on how we get the value for that

and it should be equal to usual estimator?

[naive valley]

well expectation is a linear operation

can you apply that fact

[safe mural]

im a bit confused i'll see what i can do

[naive valley]

hint to get started: $E\left[\frac{3X_1 + X_2 + \cdots + X_{n-2}}{n}\right]= \frac{1}{n}(E[3X_1 + X_2 + \cdots + X_{n-2}]) = \frac{1}{n}(3E[X_1] + \cdots ???)$

[ocean seal]

Bungo

[safe mural]

oh alright that's great i'll work with that then

thank u

sorry so now i'm a bit lost

i've rewritten it as that

[safe mural]

i think i'm meant to be working towards proving that what we had here is equal to

sry trying to understand this but i think we're trying to prove that E(X~)=X-

so if i have this, i'd try to prove that

-E(X_(n-1))-E(X_n)+2E(X1)=0?

[safe mural]

sorry for the ping @naive valley but would this be correct? how do i go about proving this

[lone heart]

@safe mural Has your question been resolved?

[lone heart]

@safe mural Has your question been resolved?

[lone heart]

@safe mural Has your question been resolved?

[naive valley]

yes, the work in your screenshot is right

(sorry, was signed out for a while)

now just use the fact that all of the X_i's have the same expected value (because they are i.i.d.)

[safe mural]

ah alrighty thank you so much

[naive valley]

ah one small correction, $\overline{X}$ is $\frac{1}{n}(X_1 + X_2 +\cdots + X_n)$, not $X_1 + X_2 +\cdots + X_n$, so your third line is not quite right

[ocean seal]

Bungo

[safe mural]

i think E(X-) is just nX- so it should be n(all of that) right

which is just (all of that)

or is that unnecessary?

[naive valley]

on your third line, if you replace $E(\overline{X})$ with $nE(\overline{X})$ it should be correct

[ocean seal]

Bungo

[safe mural]

alright thank you so much for everything

.close

[lone heart]

Channel closed

Closed by @safe mural

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[tough pond]

|a-b|<|b|/2 implies |a| > |b|/2
how do i prove this

[tough pond]

k i see it now

.close

[lone heart]

Channel closed

Closed by @tough pond

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[foggy onyx]

hi

[foggy onyx]

how can i do apply combine like terms

[clear stump]

you combine shit that can be combined

[foggy onyx]

(fg)(x) = (3x-2)(x²+2x-3)
= 3x(x²+2x-3) -2(x²+2x-3)
= 3x³+6x²-9x-2x²-4x+6
= 3x³+4x²-13x+6

how can i use combine like terms on this ex.

[gray isle]

you already did

[clear stump]

You done combined them

[foggy onyx]

= 3x³+6x²-9x-2x²-4x+6
= 3x³+4x²-13x+6

on this part

[clear stump]

the second to last step

[foggy onyx]

like explain how to do combine like terms

ik its already combined but can you explain it

[clear stump]

6x^2-2x^2=4x^2

math

[foggy onyx]

wait lol let me review it

[clear stump]

-9x-4x=-13x

more math

[foggy onyx]

OH OK

LOL

GOT IT

ty @clear stump @gray isle

.close

[lone heart]

Channel closed

Closed by @foggy onyx

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[tidal zealot]

can someone explain what was done here

[tacit arch]

$\log(a^b) = b\log(a)$

[ocean seal]

riemann

[tidal zealot]

right

(1+2+3...2n)

is that an arithmatic

[tacit arch]

do you know?

[tidal zealot]

sorry?

wht do i do with the (1+2+3...2n)

[mellow tusk]

summation of 2n terms

[tacit arch]

do you know what an arithmetic sequence is/

https://www.cuemath.com/algebra/arithmetic-progressions/

see if you can use that for your sum

[lone heart]

@tidal zealot Has your question been resolved?

[tidal zealot]

bruh thats wht i did

but idk what happenes to the two

[tacit arch]

2n is your final term

[tidal zealot]

so is the answer B

[mellow tusk]

no

[tidal zealot]

theres an extra 1/2

how do i get rid of it

[mellow tusk]

wrong formula

why is that n/2

it should be 2n/2

[tidal zealot]

why 2n

[mellow tusk]

cause 2n terms

why did u do 2n+1 then?

[tidal zealot]

ok i get it

rthank

s

.close

[lone heart]

Channel closed

Closed by @tidal zealot

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[tidal zealot]

how is the range of this function from (0, infinity)

[mellow tusk]

cause x>2 ( mandatory condition )

fgx=x-2,
x>2 and x-2>0

[tidal zealot]

bro what rule is this?

[lone heart]

@tidal zealot Has your question been resolved?

[trim wagon]

Where do you want help with?

[trim wagon]

The property used here is this

[lone heart]

@tidal zealot Has your question been resolved?

[tidal zealot]

how did they know c =2

[trim wagon]

Well you can take c= anything it doesn’t matter as it’ll cancel out in next line

[lone heart]

@tidal zealot Has your question been resolved?

[lone heart]

Channel closed

Closed by @tidal zealot

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[spare crow]

Heyo . was just wondering how you calculate the rotation of a matrix

[keen socket]

wdym

[spare crow]

This has realy confused me cos i thought you would just match a term to get theta like sin theta = -1/Sqrt(2) and you would get Theta as the anticlockwise rotation of the matrix but..(show notes)

[uncut torrent]

Yeah thats what you do

[keen socket]

then its clockwise ???

[uncut torrent]

Sketch their graphs

If that helps

[spare crow]

the fact i got two didnt put me off as much as when i subed them back in in any form i didnt get the matrix ???

or i should say the value in that element of the matrix?

[spare crow]

iv'e got the answears and they say it is 225

[keen socket]

judging by the notes your using the edexcel fm book?

[spare crow]

yeah!

[keen socket]

right, theres a clockwise rotation matrix

which just changes the sign of the sin theta

[keen socket]

it should be in the formula booklet aswell

[spare crow]

so i should use the clock wise theta to get the origonal matrix values

[keen socket]

ok lets say sin(theta)=1/root2

[uncut torrent]

Or just

Plot them, then see when they both have the same value for theta at -1/root(2)

,rotate

[uncut torrent]

So it's an anticlockwise rotation 225 degrees, or a clockwise rotation of (360 - 225) = 135 degrees

[keen socket]

right but its much simpler to use the clockwise rotation matrix

becuz u can see its 135 degrees clockwise

[spare crow]

ohhh yeah

[uncut torrent]

Ig? I find it easier to find an intutive solution rather than have to remember another equation

Can do either tho

[keen socket]

and matrix questions in exams are much harder than textbook questions

[spare crow]

sure , so i can see the answer is 225 . but if i sub that into cos or sin i dont get the og matrix values

[uncut torrent]

True, chapter 6 was pretty easy

[keen socket]

135*

[uncut torrent]

Yeah, if you plug 135 into the clockwise matrix, it will give you the original

[spare crow]

it dosnt though?

[uncut torrent]

Thats the anticlockwise matrix

[keen socket]

thats anticlockwise

broski

[spare crow]

ohhhhh

wait

no still dosnt

[keen socket]

yh it does

[spare crow]

cos 135 is - root 2 / 2 . isnt it?

[keen socket]

which -1/root2

if u rationalise

[spare crow]

omg yeah

sos didn't see that

dammm thx!

that taken me like an hour

welp , thank you ever so much ! @keen socket @uncut torrent

[keen socket]

maybe use formula booklet **

[uncut torrent]

Nw, good luck with further :)

[spare crow]

thx lol, gonna be my entire summer. spose you've done it ?

[uncut torrent]

Just finished first year

[keen socket]

same

[uncut torrent]

Oh damn

[keen socket]

which one u find easy

like rate the fm exams

[uncut torrent]

Ooh

The pure was horrible

Stats and mechanics was kinda ok

[keen socket]

i d say Core pure 2, further stats, further mechanics, core pure 1

i fucked up core pure 1

[uncut torrent]

Yeah 💀 that tennis question

[keen socket]

tennis?

[uncut torrent]

The vector question?

Wait

what exam board are you

[keen socket]

edexcel

[uncut torrent]

Yeah same

[keen socket]

u mean paper 2 vector question?

[uncut torrent]

Only did one pure paper

[keen socket]

right maybe different spec

[spare crow]

what modules would u recommend? i wanna do mechanics and pure or decision

[uncut torrent]

I cant speak for decision, but I didn't find stats too hard.

[keen socket]

dont choose mechanics u ll regret

[uncut torrent]

😭

[keen socket]

even if u do physics

[spare crow]

lmao rly

[uncut torrent]

Its fun but yeah its evil

[keen socket]

cuz mechanics collision is different pain

[uncut torrent]

Ong

[keen socket]

mechanics in general was pain

[uncut torrent]

I only started getting full marks on those questions towards the end of the year

[keen socket]

dont be fooled by the spec, since it says kinetic energy and stuff

its only really 1 topic thats hard

but in the recent exam they put like 3 of them questions in it

and they happen to be the 11 markers or 12 markers

[uncut torrent]

Pain

[spare crow]

yeah

i keep putting this clip in my notes

https://www.youtube.com/watch?v=SmqKvuyNPA8

.close

[lone heart]

Channel closed

Closed by @spare crow

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[flat saddle]

Hold on

Does this make sense

I was a bit confused on how to do the Y1,...,Yk parts

[copper stone]

you can just prove it using induction

it would be much easier

you just have to prove the case Au(BnC) = AuB n AuC and the rest is trivial

[lone heart]

@flat saddle Has your question been resolved?

[flat saddle]

I have done that in a previous question

[copper stone]

okay so you can prove the general case with induction

[flat saddle]

Not sure how

I don't really know proof by induction

[copper stone]

oh if you didnt learn it then no let it go

[flat saddle]

I just want to know if my proof makes sense

[lone heart]

@flat saddle Has your question been resolved?

[flat saddle]

.close

[lone heart]

Channel closed

Closed by @flat saddle

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[vale wigeon]

Remember:
• Ask your math question in a clear, concise manner.

you have an exam going on right now?

and you want to cheat on it using this server?

that's against the rules

[abstract fractal]

We can't help

[vale wigeon]

cheating on exams is not allowed here

you can get banned if you try

[abstract fractal]

Nice try

[alpine sable]

Okay, what question are you working on?

and show us your work then

[lilac nest]

.

[abstract fractal]

Don't help someone cheat

[vale wigeon]

joking about committing bannable offenses is frowned upon.

[alpine sable]

I'm not

[abstract fractal]

They're literally doing an exam rn

[alpine sable]

ok that just looks like an insult at this point

[lilac nest]

That means you don't even need help and you're just wasting everyone's time, which is against the rules too

[vale wigeon]

<@&268886789983436800>

ok now you are spamming

[abstract fractal]

<@&268886789983436800>

[mellow tusk]

great

drip tho

[lilac nest]

.close

[lone heart]

Channel closed

Closed by @lilac nest

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[vale wigeon]

<@&268886789983436800> before this channel closes for good: OP ( @static raft ) is a spammer and self-admitted exam cheater

[lone heart]

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.

[cunning trout]

I need help with part c)

[cunning trout]

Would this be P(1-t,-3) ?

[lapis ingot]

well just do the same thing as the other ones

but write it as a function of t

[cunning trout]

Because answer says P(1+t,-3)

[cunning trout]

So is this fine ?

P=(1-t,-3)

[cunning trout]

This fine?

Ok I got it, thnks

.xlose

Uh

.close

[lone heart]

Channel closed

Closed by @cunning trout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[flat walrus]

Hello! I am looking at inverse trigonometric derivatives at the moment and am struggling with a concept. I am aware that the derivative of arcsin x is 1/sqrt(1-x^2) and this is achieved as cos(y)=1-sin^2(y) hence 1-x^2. however 1-x^2 and 1-sin^2(y) are not the same thing so why is it allowed? sec(y) is not equal to 1/sqrt(1-x^2) when plotted. Can someone explain?

[mellow tusk]

how'd u get this

this is achieved as cos(y)=1-sin^2(y)

can u show ur derivation for sin inverse x

[flat walrus]

sorry i meant cos y = sqrt(1-sin^2(y))

y=arcsin x therefore x=sin y, dx/dy = cos y. [ cos^2(y)=1-sin^2(y) =1-x^2] therefore dx/dy=sqrt(1-x^2) therefore dy/dx = 1/sqrt(1-x^2)

but this implies that 1/cos(y) = 1/sqrt(1-x^2) but thats not true when plotted

[mellow tusk]

why isnt that true

u assumed y=sin inverse x

oh a sec

[flat walrus]

so its just the fact that we made the variable x = sin y and so under that condition the derivative works?

[mellow tusk]

cos^2(y)=1-x^2, ( we know x=siny ), how is this expression wrong

[flat walrus]

well i guess its just i plotted sec y and 1/sqrt(1-x^2) and they didnt equate thats all

perhaps i did something wrong

[mellow tusk]

yes, maybe

[lone heart]

@flat walrus Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[native cloud]

Guys, can anyone help me prove why 0^0 = 0?

[mortal trellis]

well you can't prove it because it's not true

limits of the form 0^0 are indeterminate

often it is convenient to define 0^0=1

[native cloud]

Oh, desmos wrong?

[mortal trellis]

did you plug in 0^0 into desmos?

[native cloud]

Yes

It told me 0

It's wrong?

[mortal trellis]

it tells me it's equal to 1

[native cloud]

Nvm

It's 1

My eyes were acting weird

Mb

[abstract fractal]

Only sometimes

:)

[native cloud]

So how do I prove 0^0 = 1? @mortal trellis

[mortal trellis]

you don't

it is convenient to define 0^0=1 in a lot of cases

[native cloud]

Can't you still use limits to prove?

[mortal trellis]

no, limits of the form 0^0 are indeterminate

[native cloud]

Not sure how but

[mortal trellis]

they can be anything

[native cloud]

So undefined?

Theoretical: Undefine, Actual: = 1?

[mortal trellis]

it's undefined unless we are in a context where it's convenient to define it as equal to 1

[native cloud]

Okie

Thanks

.close

[lone heart]

Channel closed

Closed by @native cloud

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[wanton hare]

yeah

[lone heart]

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.

[alpine sable]

is there any way to take a random number and figure out either what polygon(s) it is from or the value of n to where it is contained, or if its just a polygonal number?

without looping / testing every number

for say a large number like 32098402374, is it possible to find either the value of n or what polygon sequences it is in?

basically i need to tell if a large number is figurate really quickly

<@&286206848099549185> is this in any way possible to do?

[versed crater]

You have the first step

Multiply it by 2

To get rid of the one half

Have u heard of a ticker function

[alpine sable]

no i have not

[versed crater]

Why don't u just use recursion for this?

[alpine sable]

im not sure what that is

right now im just checking it against every polygonal number

[versed crater]

Don't some numbers fall under multiple

Catergories

[alpine sable]

yes

36 is in both square and triangle for example

[versed crater]

Hmm

I can't see how ro do this without looping

[alpine sable]

me neither

is there no possible way? even with a different system of math

[versed crater]

Are their infinitely many types of polygon numbers

Or only up to 1000

[alpine sable]

there are infinite types of polygons as well as an infinite number of polygon numbers

[versed crater]

So u can. Only determine the polygon when n is 1 from first glance

[alpine sable]

theres got to be some way to backtrack a number, or at least make it smaller while keeping it in the same row/column?

im having a script do the work, but when its working with big numbers looping through this many times it would take years to get the answer

[versed crater]

Every one of these can be written as a triangular number plus kn

Where k is s-3

AHH yeh I don't think there's another way

Where did u get this idea from

[alpine sable]

not sure

thanks anyways

appreciate it

.close

[lone heart]

Channel closed

Closed by @split pine

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[ocean ravine]

.

[ocean ravine]

.

.

[gray isle]

what are you getting in online calc

[ocean ravine]

hm?

oh

[ocean ravine]

.

.

.

[gray isle]

the percentage box would be 0.85

yeh

[ocean ravine]

.

.

.

[lone heart]

@ocean ravine Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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 elk]

$$(fog^{-1})(x) = x+6 \quad \text{and}\quad g(x)=3-x \Rightarrow f(-4)=?$$

[ocean seal]

Gl1tch

[burnt elk]

I'm stuck with this question how do I solve it

[main kraken]

first find the inverse of g(x)

[subtle mango]

Try to find what is x when g^-1(x)=-4

[main kraken]

or that too

[burnt elk]

x - 3 right?

[burnt elk]

thats make sense too

[main kraken]

g(x-3) = 3-(x-3) != x

so no

g(x) = 3 - x
y = 3 - x
♻️
x = 3 - y
x - 3 = -y
y = 3 - x
g^-1(x) = 3 - x

[burnt elk]

then what should I do

do I get f when I subtract g^1 from fog^1(x)

wait

f(3 - x) = x + 6
f(-x + 3) = x + 6
f(x + 3 ) = -x - 6
f(x) = -x -9

f(-4) = -(-4) - 9 = 13

found it

.close

[lone heart]

Channel closed

Closed by @burnt elk

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[polar zealot]

how do i multiply a 3 x 2 with a 2 x 2 matrix

[marsh portal]

so what you can do is multiple each row by each colmun on each matrix

[vale wigeon]

that's a 2×3 matrix in green

so you can't

[marsh portal]

so start on the green matrix and multiple it down the first colmun with the first row of the red matrix

[vale wigeon]

(2×3) * (2×2) is undefined

[vale wigeon]

that sounds like red*green

[marsh portal]

yeah i forgto

i was trying to help

[polar zealot]

i want green*red

[marsh portal]

yeah thats impossible

[vale wigeon]

green*red is undefined.

[marsh portal]

theres not enough numbers to multiply

[crisp pine]

To multiply an nxm matrix by a pxq matrix, m must equal p, and the resulting matrix will be nxq

[lone heart]

@polar zealot Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[polar zealot]

thanks

[polar zealot]

.close

[lone heart]

Channel closed

Closed by @polar zealot

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[inland oriole]

I want to prove this.
some kind of base two multiplication
Do you have to prove it by multiplying the left side?

[lone heart]

@inland oriole Has your question been resolved?

[lone heart]

@inland oriole Has your question been resolved?

[lunar dawn]

wait so binary on the left = decimal value of the right?

is that correct?

[inland oriole]

I assume that’s it bc there is an equal sign

I just would like to figure out how to convert from base 2 with a decimal point to a base 10 number

[lunar dawn]

you would just multiply each digit(1 or 0). for instance $1011 = 12^0+12^1+02^2+12^3$

[ocean seal]

Karter

[lunar dawn]

which would equal $11$

[ocean seal]

Karter

[lone heart]

@inland oriole Has your question been resolved?

[inland oriole]

How do you do scientific notation with floating point IDEE 754?

[lone heart]

@inland oriole Has your question been resolved?

[inland oriole]

.close

[lone heart]

Channel closed

Closed by @inland oriole

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[lone heart]

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.

[abstract badge]

hey

[abstract badge]

$\forall x\in \phi$

[ocean seal]

dark

[abstract badge]

is an always true statement since there are no elements in phi

can someone explain this better?

i dont get it

why is it always a true statement?

[floral scroll]

?

[abstract badge]

is it not always a true statement?

[floral scroll]

Do you mean if you have a statement $P(x)$, then $P(x)$ is true for every $x\in \varnothing$?

[ocean seal]

Andrew071

[abstract badge]

yes

[floral scroll]

by the way, we usually use $\varnothing$ or $\emptyset$ not phi

[ocean seal]

Andrew071

[abstract badge]

oh ok

[floral scroll]

It's true because there are no elements in the empty set. So if you say every x in E is even, but E is empty, it's a true statement

It's called vaccuous truth

[abstract badge]

ok i see

thnx

.close

[lone heart]

Channel closed

Closed by @abstract badge

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[abstract badge]

i confused myself with how i formulated it

when you put it like you did it's clear

[lone heart]

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.

[tender dew]

Does anybody know how to generate easily pixel spline (discrete, rasterised)

I read some info on topic and usually it's done with things like gradient and antialiasing

it's not like it's not dooable, but I don't need efficient one, I just simply need ANY

[tacit arch]

is there any math here

[tender dew]

I'm asking about way of generating a spline, any curve

that goes discretly from A to B by not the shortest path

[tacit arch]

http://www.saccade.com/writing/graphics/RE-PARAM.PDF

https://stackoverflow.com/questions/4541442/drawing-aliased-pixel-perfect-1px-splines-catmull-rom-specifically

[tender dew]

math that comes for Brazier curves is just an overkill

[tacit arch]

brazier curves

[tender dew]

Yeah, I was wondering if there'll be something not so profound, but faster

[lone heart]

@tender dew Has your question been resolved?

[tender dew]

I come up with something like that

I know that full shift in X would be equal to deltaX and in y to some deltaY

I know that one value is higher (generally speaking)

so I loop in dimension of higher value of delta

always increment one side till it's get it's value right

and the other one can be expressed as a table or column

that is the length of higher value of delta

and is filled with ones for length of lower value of delta

now if zeros are at even distances (have usually the same amount of ones between them)

then the curve will be linear

but any change, and merge of ones into twos and so one will result in more of a spline curve

now I don't need higher degrees to represent spline - if the function will be monotonic that would satisfy me

I also wanted to get rid of something like long intervals without jump

Altough I know actions on this column would be much easier to be done with that long jump

this can be represented by any translation

Obviously this will form a triangle

after figuring sign (for direction) and which side is longer the spline might be created

if x shift would be bigger than y shift, then we'd need to switch values of L and W for algorithm, but that can be easily figured out

In this case L>W

so we can say that in a loop incrementing in longer delta gets you in that direction

and sometimes a step in other direction has to be made as well

we can express how much by this column that can be rearranged to make linear shift or to make more of a spline

rearranging this simple column by hand can get a nice spline representation

But this column rearrangement takes a lot of action

This one was done by hand

but I think there is a way to get to it by cutting column into parts. shifting, readding, and so on in 2 more loops

that's a lot of information to process

<@&286206848099549185>

[tender dew]

I thought some random step would be needed to it and thus limit's operations but needs more complicated distribution function

but maybe that method won't bee needed

maybe some istribution over a grid

of ones

[lone heart]

@tender dew Has your question been resolved?

[elfin snow]

maybe try asking this in #computing-software @tender dew

[tender dew]

thanks for advice

[elfin snow]

:)

[lone heart]

@tender dew Has your question been resolved?

[elfin snow]

you should close this channel

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[visual dragon]

Hello!

[last ether]

Just post your question

[visual dragon]

ok, I need help parametrizing (?) conic lines

[last ether]

Well you're gonna need to post a specific question

Because like with conic lines, it depends

I'm assuming with any conic you wanna make a parametric for them

[visual dragon]

I need to discover the Vertex, Focal point and director line of one of each

[last ether]

You're gonna need to complete the square

For these

So like rearrange the terms

[visual dragon]

ok, I thought you weren’t supposed to do that in the Elipse but i’ll try

with that I should get the canonical equation right?

[last ether]

Wdym canonical

[visual dragon]

sorry, language barrier,

like this one in the case of the parabola

Idk how it’s called in english

[last ether]

I've never seen this before

Idk what the 4p is supposed to be

I can put it into elliptical/conic form

[visual dragon]

or like this one for the ellipse

what should I do now

[last ether]

This.

You could put it into x^2/a^2

[visual dragon]

ok, so I got to this

[hearty rune]

Can anybody explain the answer to this question in a more simpler way?

[last ether]

#❓how-to-get-help

Note how this channel's been taken

[hearty rune]

ok

[last ether]

I'm doing a different problem

I'm doing the first one

The first one

Note that the 3rd line got cut off. It's equal to -36

[visual dragon]

ok, but what should I do if i don’t have a common factor

[last ether]

You normally would

[visual dragon]

like in the case of the (x-2)^2

[last ether]

Wdym

[visual dragon]

.

[last ether]

You have common factors in the x

It's just 1

So you do nothing

[visual dragon]

ok

[last ether]

$(x-2)^2 = \frac{(x-2)^2}{1}$

[ocean seal]

Umbraleviathan

[visual dragon]

now I have this

hello?

<@&286206848099549185>

[alpine sable]

Hey

[visual dragon]

Hello!

[alpine sable]

What do you need help with

[visual dragon]

.

now I’m stuck with this one

ended up using these ones

[alpine sable]

Can you type out the question here

That you need help with

Cause you’re showing me a bunch of stuff

@visual dragon

[visual dragon]

I need to parametrize these lines and I’m not really sure how

[alpine sable]

What’s the question

Write it out her

Here

[visual dragon]

“Find the Focal point, Vertex and Director line of one of each following conic lines”

[alpine sable]

Do you know how to find the focal point

[visual dragon]

a/c right?

[alpine sable]

Yea

[visual dragon]

or is that the focal distance?

<@&286206848099549185>

.close

[lone heart]

Channel closed

Closed by @visual dragon

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[slender solstice]

Hi, I need help on a proof:
In rectangle ABCD, E is the midpoint of BC and F is the midpoint of AD. G is a point on AB( extended if necessary); GF and BD meet at H. Prove that EF is the bisector of angle GEH.

[slender solstice]

I tried drawing a diagram, but honestly it did not help much. I don't know if I did something wrong, but it honestly doesn't look like GEH is being bisected by EF

<@&286206848099549185>

.close

[lone heart]

Channel closed

Closed by @slender solstice

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[sudden torrent]

What’s the equation that looks like this

[tacit arch]

,w plot arctan(x-10)

[ocean seal]

Results provided by WolframAlpha

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

Requested by riemann#2529

[tacit arch]

,w plot arctan(3x-10)

[ocean seal]

Results provided by WolframAlpha

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

Requested by riemann#2529

[tacit arch]

,w plot 1/(1+e^(-x))

[ocean seal]

Results provided by WolframAlpha

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

Requested by riemann#2529

[tacit arch]

wtf

,w plot 1/(1+e^(-10x))

[ocean seal]

Results provided by WolframAlpha

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

Requested by riemann#2529

[tacit arch]

https://en.wikipedia.org/wiki/Sigmoid_function

disappoint, wolfie

[sudden torrent]

@tacit arch I’m asking about the one that is a straight vertical line

In the middle

[tacit arch]

read this

[lone heart]

@sudden torrent Has your question been resolved?

Channel closed

Closed by @sudden torrent

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[cinder sundial]

Is theta obtainable without calculator

[alpine sable]

Has making linear equations in two variables worked ? ...the unknown angle opposite to theta be x so sum of angles of the triangle OCD and sum of angles of ABDC quadrilateral

[cinder sundial]

Let me digest it

[vale wigeon]

this is what length-chasing gives me

there is a bunch of 30°-60°-90° triangles that can be exploited

eventually you get that BCD is equilateral

@cinder sundial

[cinder sundial]

Yes and theta will be 60-30=30

God, u had a good observation

[vale wigeon]

here is the approximate order in which i derived these things btw

[cinder sundial]

Do you use the “formula” a^2=b^2+c^2-2bccosA. To get the length of CD

[vale wigeon]

no

just the pythagorean theorem

[lone heart]

@cinder sundial Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[charred plank]

How can i solve this for x ?

[vale wigeon]

cos^-1(z) does not mean 1/cos(z)

(yes the notation is stupid i know arccos is better)

[charred plank]

So what does it mean?

[slender gull]

arccos just like Ann wrote.

It's an inverse trigonometric function.
When you write cos^-1 or arccos you are solving for the angle. Using the ratio.

On the contrary, when you write cos(something) you are solving for the ratio, using the angle.

[charred plank]

Ok ,

cos^-1(x)=?

[slender gull]

An example would help better, probably.
cos^-1(1/2) would be 60 degrees.

so, for your particular problem, you should add phi to both sides, and then take cosine.

cos^-1(x) is cos^-1(x) but
cos(cos^-1(x)) = x

[charred plank]

so i will understand ,
cos^-1(x) gives the angel based on the ratio ,
so when we cos(angel) we basicly solving again for ration ,
that is known as x .

am i right ?

[slender gull]

Yes.

That's right.

[charred plank]

thanks.

[slender gull]

You're good.

[lone heart]

@charred plank Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[primal quest]

Do you use the “formula” a^2=b^2+c^2-2bccosA. To get the length of CD

[primal quest]

.close

[lone heart]

Channel closed

Closed by @primal quest

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[past valve]

A circle has a centre O and a second circle passes through O. The second circle cuts the first at two other points A and B. Let P be a point on arc AOB and extend the line BP to intersect the first circle at Q. How to Prove that the bisector of angle APQ passes through O.

[past valve]

I drew diagram and tried constructing multiple things to manipulate any of the basic theorems I know but can’t get anywhere

Anyone have an approach on how to prove it?

[halcyon niche]

unless if i'm being stupid $\angle QOP = \angle AOP$ iff $O$ lies on the angle bisector of $\angle APQ$

[ocean seal]

jasoon

[halcyon niche]

let T be the midpoint of the arc AQ, then

∠QOT = ½∠QBT
= ½∠QAT
= ½∠AQT
= ∠AOT

i hate latex

forget latex this works

[past valve]

Would it be sufficient to construct radii OA and OB. Then construct common chord AB and chord OP.

Then we formed a cyclic quadrilateral ABOP

[halcyon niche]

sorry i don't really see what you're getting at

[past valve]

Let Angle OBA = x
Then Angle OAB = x since AOB is an isosceles triangle.
Angle AOB = 180-2x because of angle sum of triangle

Then Angle APB = 180-2x because they are subtended by same arc.

This means Angle APQ = 2x to be supplementary with line BQ.

Since ABOP is a cyclic quadrilateral the exterior Angle APT = x.

Therefore the bisector of Angle APQ must pass through O?

[halcyon niche]

that only proves that PT is the angle bisector of ∠APQ though

[lone heart]

@past valve Has your question been resolved?

Channel closed

Closed by @past valve

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[lone heart]

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.

[fair ingot]

Nilai dari=Score from

[lone heart]

@fair ingot Has your question been resolved?

Channel closed

Closed by @fair ingot

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[gaunt stone]

hi

[gaunt stone]

how may i get the sinusoid to match or get very similar to the dotted data

[vale wigeon]

y_1 ~ a e^(-b x_1) sin(c x_1 + d)

[gaunt stone]

what is it bro?

frend pls explain

[vale wigeon]

please do not call me bro.

type what i said into desmos

it will run a regression on your data

and produce a sinusoid that matches it as closely as it cna

[gaunt stone]

oh ok thanks

it gabeme this

@vale wigeon

[vale wigeon]

show your exact input

i think it may have been that you screwed up

[vale wigeon]

$y_1 \sim ae^{-bx_1} \sin(cx_1 + d)$

[ocean seal]

Ann

[vale wigeon]

this is what you should've had

[gaunt stone]

oh ok i try again

oh ok it works

but i need the formula now

ok thanks man

ill try to find it

@vale wigeon

[vale wigeon]

look in "parameters"

it literally gives you the values of a, b, c and d in the formula

[gaunt stone]

ohh ok thanks

[vale wigeon]

also if you consider my help unsatisfactory then don't spit in my face by thanking me with "ok thanks man"

[gaunt stone]

wait what?

npc

[lone heart]

@gaunt stone Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[lone heart]

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.

[stable night]

Let a, b be odd perfect squares\
Then, a = $(2m + 1)^2$ and b = $(2k + 1)^2$, m, k $\in \bN$ (by T1)\
a + b = $4m^2 + 4m + 1+ 4k^2 + 4k + 1 = 2(2m^2 + 2k^2 +2m +2k +1)$ (by basic algebra)\
a + b = $2(2(m^2 + k^2 +m +k) +1)$

[vale wigeon]

[stable night]

sorry one sec

[vale wigeon]

it's \bN if you want natural numbers