help-23

[vale vessel]

are you basically trying to prove that given (A -> Xk is safe), a new collision must occur in the path (Xk -> X{k+1})?

[chilly plover]

ok I think question 2 is true, I'll write some explanation

[cosmic sparrow]

i decided to run it and it SEEMS to work im still not sure

[chilly plover]

I take question 2 as:
if B and C are one A* step apart, then is any point on the line from A to C at most one A* step apart from the line from A to B?

The case where the lines are the furthest apart is when A is infinitely far away and the lines are almost parallel, so I will assume that the lines are simply parallel.

Let D be some point on the line from A to C.
Because the lines are parallel, there is a point on the line from A to B that is exactly one A* step apart from D. (the points have the same offset from the center of the tile)

So it is true for the parallel case, and in any other case, the lines are closer so it is true as well.

[cosmic sparrow]

i have no idea what your talking about but its 1 am

[chilly plover]

oh hmm

[cosmic sparrow]

if what you said is right then it proves what your seeing here? i tried to run it with this logic

[chilly plover]

If the "border strip" is all the tiles that are at most one A* step away from the line A to B, then the property is true. (I think this is the same as what I tried to say)

[cosmic sparrow]

what is a border strip and what is A* step away

[chilly plover]

You mentioned it here:
"one A* step in an 8-neighbor direction (up/down/left/right/diagonal by 1 tile)"
and "Is it true that the straight move from A to C can only touch new tiles in a small “border strip” on the side corresponding to the direction B\to C?"

A border strip is generally a line (strip) that is right next to (borders) something, in this case the line from A to B in the question.

[cosmic sparrow]

yes yes

but what is A* step away?

oh i understand i think

[chilly plover]

I don't know how to explain it besides how you described it at the moment

for example if you are at the black circle, then all gray squares are one A* step away

[cosmic sparrow]

yes i get it now

i just dont understand your proof its too complicated for me 😭

especially D

il try to get things straight its a bit late, can i get back to you later? i dont want to trouble you @chilly plover

il check your proof tomorrow and get things straightened

thanks

[chilly plover]

yes, but no guarantees in how fast I respond
(let me know which part you don't understand or if it is just all of it)

[vale vessel]

<@&268886789983436800> ? ^^

[junior smelt]

What the hell!?

[dry sierra]

What

[wispy berry]

okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

[native cape]

I got a question

It’s radicals

[broken forum]

probably better to open your own help channel else no one's gonna see u fr

what's bro's question?

[safe radish]

@cosmic sparrow Has your question been resolved?

[vale vessel]

!occupied

[safe radish]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[river needle]

for b.) how did they know f(2) is a minimum

[clever gale]

They differentiated f(x) and set it equal to zero in order to find the x-value of the extrema point

[river needle]

ik but that only tells u where the turning point is

it doesn't tell u whether the turning point is a minimum or maximum

[open wedge]

hm

[open wedge]

well then find $f''(x)$

[flat frigate]

1 divided by 0 equals Infinity

[river needle]

how does the second derivative tell me whether the value is a minimum or maximum/

[charred summit]

sub the x value where f'(x) = 0 into the second derivative

if >0 the graph is concave up

<0 concave down

= 0 inconclusive

[charred summit]

local maximum

[charred summit]

local minimum

[river needle]

hmm this is a lot of work for a simple question that's worth 3 points only

[river needle]

in the grading scheme, they have made no mention whatsoever of finding a second derivative

p.s differentiating f(x) a second time is a pain in the neck

but i suppose there's no other way

[charred summit]

what's the function?

[river needle]

.

[charred summit]

oh you already sent it here

[nimble vine]

graph

if allowed

[river needle]

nah not allowed in an exam

[nimble vine]

den no

[river needle]

damn

so u agree ts is bullshit?

[charred summit]

Calculating the second derivative for exercises like this is very usual tbf

[river needle]

for the record

i dont think we've been taught that

taking second derivative

then pluggin in value

[nimble vine]

no wait

[hallow swan]

No!Division by zero does not exist because there is no number that, when multiplied by zero, results in the dividend. 2/0=0 0x0<>2

[river needle]

wrong channel i think

[charred summit]

You can also find all f'(x) = 0, which are all candidates for maxima or minima. Then choose values slightly less and slightly greater than those points to determine the sign of f'(x). Then you can interpret sign changes from positive -> negative will be a local maximum, negative -> positive local minimum

No sign change --> neither max or min

But just taking the second derivative is easier imo^

[river needle]

alright thx

.closse

.close

[safe radish]

Channel closed

Closed by @river needle

Use .reopen if this was a mistake.

[open wedge]

😭

31st bait

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[round temple]

Hi I was just wondering if anybody can do these math problems for me

[round temple]

I did a rough translation but and it may not be accurate but I hope it helps

[charred summit]

No one is going to do them for you

Someone will help you solve them though if you're having trouble doing so yourself

[round temple]

Well I kinda don't understand the whole subject so yeah

[nimble vine]

!noans still

[safe radish]

The purpose of this server is to help you learn; please don't ask for direct answers. Ask for guidance, explanations, or feedback instead.

@round temple Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[oak dagger]

Is my parabola correct? Why does it seem incomplete

[shut storm]

,rcw

[shut storm]

you seem to not have taken any negative x-values. that's the only thing I can say

[hollow dock]

Parabola seems look ok

[shut storm]

and that is probably the reason it feels incomplete

but otherwise there's nothing inherently wrong with the parabola itself.

[safe radish]

@oak dagger Has your question been resolved?

[oak dagger]

No

[shut storm]

react to the bot then. the bot cannot read text responses.

[vagrant ice]

(ping)

[safe radish]

@oak dagger Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[covert talon]

Rlly quick question

The mark scheme said 2.2-2.21 so would i still get the mark or no

Bc i basically did what the mark scheme said to do

[vagrant ice]

,w 1.6 / cos(42 deg)

[flat frigate]

Results provided by WolframAlpha

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

Requested by sooouth.

[covert talon]

I got 2.15 bc rounded too early so

[vagrant ice]

you rounded too early

[covert talon]

O

[vagrant ice]

yeah you should keep 1.6 to like 6 dp

[burnt mantle]

you wouldnt get the mark

[covert talon]

So next time just round at the end right

[vagrant ice]

just to be safe

[covert talon]

Oh okok

[vagrant ice]

exactly!

[burnt mantle]

you would get M1 but not A1

[vagrant ice]

don't round intermediate steps that much

[covert talon]

Okok

Thank u

[vagrant ice]

no worries

[covert talon]

.close

[safe radish]

Channel closed

Closed by @covert talon

Use .reopen if this was a mistake.

[covert talon]

.reopen

[safe radish]

✅ Original question: #help-23 message

[covert talon]

Nvm I’m back

How do I o this I, rlly confused

[vagrant ice]

say 1 = n

how can you write 2 and 3 in terms of n?

[covert talon]

2n and 3n

[vagrant ice]

that's correct, but there's another way using addition

[covert talon]

5n

[vagrant ice]

no, don't use these

[covert talon]

wut

o

ermm

1 + n and 1 + 2n?

[proud tree]

well 2=(1+1)

similarly, how would you write 3

[covert talon]

(2+1)

[proud tree]

for any general n, can you express the nth term in this sequence

[covert talon]

(n+1)?

[proud tree]

you know that you always divide by 2

let's look at the numerator for some terms

for 3, it's (3)(4),
for 4 it's (4)(5),
for 5 it's (5)(6)

[vagrant ice]

to find the next number after n, it's n + 1 right

[proud tree]

can you see a relation here

[vagrant ice]

so what you need is the next number after the next number

[covert talon]

ohhh yes

[proud tree]

so how would you express the nth term

[covert talon]

n(n+1)?

wait

erm

[proud tree]

don't forget the 2

[vagrant ice]

oh yeah you forgot to divide by 2

yeah that's correct then

[covert talon]

n(n+1)/2

[proud tree]

👍

how would you express the (n+1)th term

[covert talon]

ohh

[vagrant ice]

yes, so that's correct for (number * next number)/2

how about (next number * next next number)/2

[covert talon]

n(n+2)/2?

[broken forum]

close

[proud tree]

look at this

[covert talon]

is it just (n+2)

/2

[vagrant ice]

you were closer with this attempt

[proud tree]

what would be the number after n?

[covert talon]

n+1(n+2)? idk

auggh

[proud tree]

yes but put brackets and don't forget 2

[covert talon]

oh so its

[vagrant ice]

there we go you have the right idea

[covert talon]

(n+1)(n+2)/2

[proud tree]

okay now add both the terms

[vagrant ice]

don't expand

you have [ n(n + 1) + (n + 1)(n + 2) ] / 2 if you add both fractions

which term is in common?

[covert talon]

the n+1 right

(n+1)

[vagrant ice]

right!

so you can factor n(n + 1) + (n + 1)(n + 2)

(n + 1) * (...)

a simpler example is something like $2 \cdot x + x \cdot 3 = x \cdot (2 + 3)$

[flat frigate]

south

[covert talon]

so is that x(3 + 2) = x (2 + 3)

[vagrant ice]

yes

$\cdot$ means 'multiply'

[flat frigate]

south

[broken forum]

well technically 2x+3x=x(2+3), factorisation is the important thing not commutivity

[vagrant ice]

yeah, factoring is the distributive law but you do it backwards

if you've ever seen a(b + c) = ab + ac but never realised what it means

what we're doing here is starting from ab + ca
= ab + ac
= a (b + c)

2 * x + x * 3
= x * 2 + x * 3
= x * (2 + 3)

[covert talon]

👍

[proud tree]

how's it going with this

[covert talon]

do u just

Foil it

[vagrant ice]

no, as I said, don't expand

[covert talon]

Or does it become 2n(n+1) (n+2)?

o

ok ok

[covert talon]

(2n+2)

[vagrant ice]

right!

yeah cause you just add n and (n + 2)

okay so $\frac{(n + 1)(2n + 2)}{2}$

[flat frigate]

south

[vagrant ice]

you can definitely simplify this

nearly there

[proud tree]

you think you could factor something out of this

[covert talon]

the

2?

2(n+1)?

[vagrant ice]

yep!

$\frac{(n + 1)2(n + 1)}{2}$

[flat frigate]

south

[covert talon]

o

Do u thenlike divide the exponent by the denominator

[proud tree]

exponent?

[vagrant ice]

that's not an exponent but yes

[covert talon]

the

outside thing

oops

[proud tree]

so what would be your final expression

[covert talon]

(n+1)(n+1)

[proud tree]

hmm

what more could you do

[covert talon]

expand

n^2 + 2n + 2

[proud tree]

you want to simplify it

[proud tree]

they both are the same thing

i mean the terms

[covert talon]

o

(n+1)^2

[proud tree]

👍

[covert talon]

ohh

is that like the fina thiing i need to show then

[proud tree]

yep

[covert talon]

ohh

so annoying wtf and only for 4 marks 😭 legit all the harder higher mark ones r easier than this for me tbh

tysm tho

.close

[safe radish]

Channel closed

Closed by @covert talon

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[lament kiln]

Do you know how to solve Raabe Duhamel or Mac Lauren?

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[granite dove]

we need to differentiate this expression wrt x
please help

[fathom adder]

Write it y = this

[granite dove]

yeah

[stray yoke]

You will get a differential equation

[fathom adder]

you will get y² - sin²(x) = y
2yy' - 2sin(x)cos(x) = y'

[stray yoke]

y = this
Then square both sides
Differentiate both sides wrt x
Solve the DE

[granite dove]

ohk got it... tysm

i'll just try and see if i get the ans

[fathom adder]

Assuming x belong to an interval where y is actually differentiable also

[granite dove]

yeah got it thank you so much !!

.close

[safe radish]

Channel closed

Closed by @granite dove

Use .reopen if this was a mistake.

[granite dove]

.reopen

[safe radish]

✅ Original question: #help-23 message

[granite dove]

I am sorry but I needed to ask one thing that how did you write that entire infinity series just as sin sq (x)

[mighty mango]

-# y^2 - sin(x)^2 = y requires differential equations...?

[mighty mango]

idk how they got this but

[brave wolf]

you could just do quadratic equation if u wanted to

[mighty mango]

when y = this

square both sides

[jolly bridge]

?

[mighty mango]

y^2 = sin(x)^2 + that infinite series which is just y again

[granite dove]

yeah but even if i square what about the rest of the roots in there

[mighty mango]

so y^2 = sin(x)^2 + y

[jolly bridge]

there are no roots left the equation simplifies, see what car did!

[granite dove]

ohh wait i think i get it now... yeah

it's y all over again

thank you so much everyone

[jolly bridge]

elligant

[mighty mango]

absoltely

fuck

[mighty mango]

anyways, can i dm you?

[granite dove]

.close

[safe radish]

Channel closed

Closed by @granite dove

Use .reopen if this was a mistake.

[jolly bridge]

sure? about...

[mighty mango]

or.. nvm i can ask about the differential equation part in hlounge

about the requiring differnetial equations

bc you ?'ed

[mighty mango]

I dont see how this requires differnetial equations

it is just an implicit function... no?

[jolly bridge]

.it doesnt

yeah

he just differentiated what you did

[mighty mango]

.oh- so why did you ? me 😭

[jolly bridge]

y^2= sin^2 x + y

[mighty mango]

.and why did they say this

[jolly bridge]

.yeah that was confusing, "solve the de" doesnt make sense

[granite dove]

Maye she meant Differential equation.. maybe she confused it with integration by any chance

[mighty mango]

2y dy/dx = 2sin(x)cos(x) + dy/dx
this is very easy.... not a differential equation- i hope..?

[jolly bridge]

.(sorry i got confused by what you meant

[mighty mango]

.its okay!

[jolly bridge]

.this is called a differential equation but yeah we dont need to "solve" it , if we did we would get the question 🥀

[mighty mango]

.oh yeah i see

.alright ty!!!

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[mighty mango]

<@&268886789983436800>

check this amazing deal

[safe radish]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[dusky echo]

.close

[mighty mango]

the channel is already closed. you also cant close other people's channels if they're claimed.

[dusky echo]

Sorry

[mighty mango]

no dont worry 😭

[dusky echo]

nice pfp btw

are you using nitro?

[mighty mango]

ty! we should stop talking here

or... some pink person might... us

well- not ban but warn

so lets avoid the hustle

and stay silent!!!

❤️

[junior smelt]

Or send a

[mighty mango]

-# oh no!!!!! its a pink person!!!!!

[mighty mango]

-# that can only be done by one pink person

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[halcyon light]

does my work look ok?

idk if I understood this right

[light shoal]

yes, 3/8 is correct, and your reasoning is correct

however you stated it wrong at the end:

that probability of that event is 1/8

but that's only one of the three ways to get two heads and one tail

if you had said P(two heads and one tail) = 3/8, that would be correct

[halcyon light]

ohhh

ok

thanks

[light shoal]

yw

[halcyon light]

What about this one? Is it rly this simple?

[fathom adder]

Yeah, whatever its tail or head they play a symetric role

[halcyon light]

.close

[safe radish]

Channel closed

Closed by @halcyon light

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[steep magnet]

I dont really understand what theyre saying in the solution here

I think this means the derivative is negative between 0 and 2pi

But idk how they got that or what to do with this information

Wait I see now that tells us its a local max at 0 and min at 2pi

But I still dont see how they got that its negative between 0 and 2pi

[median vigil]

if theta varies between 0 and 2pi, what interval is theta/2 over?

[steep magnet]

What do you mean by interval sry

[median vigil]

like lower and upper bound

$0 \le \theta \le 2\pi$ therefore $? \le \frac{\theta}{2} \le ?$

[flat frigate]

cloud ☁

[steep magnet]

Ohhhh

0 <= theta/2 <= pi

[median vigil]

yes

and if its input is between 0 and pi, is sin positive or negative?

[steep magnet]

Positive?

[median vigil]

yes

so if sin is positive then -3/2 sin is...

[steep magnet]

Negative

Ok makes sense, but how do we then know that it becomes positive when theta < 0 or theta > 2pi

[median vigil]

you can do a similar analysis

[steep magnet]

Ok I think I get it

Thank you!

❤️

.close

[safe radish]

Channel closed

Closed by @steep magnet

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[acoustic zealot]

matrix multiplication:
i have
A =
(1 # 2 # 2
1 # 2 # 1)

and B =
(1 # 2
3 # 1
1 # 1)

C = A * B; my solution: C=
(5 # 10
12 # 4)

I did
(B0,0 * (A0,0 + A0,1 + A0,2) # B00,1 * (A0,0 + A0,1 + A0,2)
B1,0 * (A1,0 + A1,1 + A1,2) # B1,1 * (A1,0 + A1,1 + A1,2))

is it correct?

[peak estuary]

no

the fact that you havent even used every entry of B should make you suspicious

[acoustic zealot]

ok, that s what i exepted, i did some of these tasks, and all of my solutions were wrong

i though it should result in a 2x2 matrix so, why should i use Bi,2

[muted sapphire]

well you have to get a 2x2 matrix

[peak estuary]

well you still used all entries of A

[muted sapphire]

and use all elements

[peak estuary]

why did you use that

with the same flawed logic you shouldnt need all entries of A either

[acoustic zealot]

wait, i think i got it, let me retry

i will send the solution

(25 # 20
20 # 16)

[peak estuary]

no

[acoustic zealot]

i did A0 row times B0 column -> A0 row times B1 column
same for A1

[peak estuary]

you need to take the rows of A and the columns of B

[acoustic zealot]

i did A0,i times Bj,0

[acoustic zealot]

(5+10+10 # 4+8+8
5+10+5 # 4+8+8)

thats how i got to that result

[peak estuary]

from where are those 5 and 10 and 10

[acoustic zealot]

wait

[peak estuary]

did you use your wrong result for C?

[acoustic zealot]

A0,0 * (B0,0 + B1,0 + B2,0) + A0,1 * (B0,0 + B1,0 + B2,0) + A0,2 * (B0,0 + B1,0 + B2,0)
1 * (1 + 3+ 1) + 2 * (1 + 3+ 1) + 2 * (1 + 3+ 1) = 5 + 10 + 10

= C0,0 (in my solution)

[peak estuary]

no

each entry of A gets multiplied with one entry of B

A00*B00 + A01*B10+A02*B20

[acoustic zealot]

ah ok

[acoustic zealot]

that would result into C0,0?

[peak estuary]

yes

[acoustic zealot]

ok, so my result would be
(9 # 6
8 # 5)

[peak estuary]

yes

[acoustic zealot]

ok, thank you 🙂
i will practise a bit more

.close

[safe radish]

Channel closed

Closed by @acoustic zealot

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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 trench]

The question:
Kenny is thinking of two numbers greater then 10.
He says: "The highest common factor (HCF) of my two numbers is 7"
"The lowest common multiple (LCM) of my two numbers is 84"

Write down the two numbers Kenny is thinking of.

What I want to know:
Short way to answer the question quickly and correctly using a venn diagram.

[brave wolf]

I'd start by fatorizing 84 into primes

[charred trench]

Wait gonna do it

[charred trench]

2, 2, 3, 7

[brave wolf]

okay, now the venn diagrams

each circle will represent one of the numbers and it will contains its prime factors

the intersection is gonna contain HCF

and the union is gonna contain factors of lcm

[charred trench]

Whats gcd?

[brave wolf]

oh sorry, GCD = HCF

greatest common divisor = highest common factor

[charred trench]

Oh k

[brave wolf]

okay so we will start like this

[brave wolf]

now we gotta put those somewhere

both 2's must be in the same circle, because if they were in different circles, then we would have to put them to the intersection part

but the intersection part has to be only 7

[brave wolf]

okay, this almost works. But both numbers have to be > 10

your left circle number is just 7

so you gotta move the 3 to the left circle

[charred trench]

But the only factors of 7 is 7 and 1 its prime

[brave wolf]

i think you misunderstood what i meant

lcm is the all the factors in both circles

hcf consists of the factors in the intersection

first num consists of factors in left circle, 2nd num consists of factors in the second circle

so we start by placing 7 in the intersection (this part is obvious, 7 is in the HCF and HCF must be in the intersection)

[charred trench]

Im just wondering how the 3 came to the first number?

[brave wolf]

in this case, your first number would be just 7

[brave wolf]

but the question wants both numbers to be greater than 10

so you must move 3 to the first circle, to make the first number 7*3 = 21

[charred trench]

So we place it in left circle due to that.

[brave wolf]

yep

[charred trench]

Ahh

[brave wolf]

if there wasnt the >10 condition, this would be also vaid solution

[charred trench]

So we got 21 and what would be the other how to work it out

[brave wolf]

corresponding to the numbers (7, 84)

[brave wolf]

look at this

second number is all the factors from the right circle

[charred trench]

So 2X2X7?

And that is 28

[brave wolf]

yep

[charred trench]

So the final answer is 21 and 28

Thanks.

[brave wolf]

np

[charred trench]

Shall I close now then?

[brave wolf]

hmm, @frozen veldt seems to be typing sth

[charred trench]

Yh rlly long

[brave wolf]

let's wait for a while

there is some caveats to this method, so i think he is going to point them out

[frozen veldt]

sorry

[charred trench]

.

[frozen veldt]

I have nothing worthwhile to add

[charred trench]

Right thats the caveats

[frozen veldt]

I just wrote my own solution

here it was

HCF = take the factors that are in both
LCM = take all the factors that are in both, with the highest power winning if they contain the same prime factor

we need both numbers to contain 7
we need both numbers combined to produce precisely 2, 2, 3 and 7

7 alone is not enough because it's not greater than 10

so maybe 7*2 works

now the second number has to have a 7 and a 3 but can't have a 2 so as to not contaminate the HCF

does 7*3 work? yes

but now the LCM doesn't work because we don't have enough twos, so we need

7*2*2 and 7*3 and that works because both are greater than 10

[brave wolf]

oh ic

[charred trench]

Its good gng

[brave wolf]

ill add the caveats myself then

Firstly, you must be careful not to do sth like this

do you know why this is wrong?

[charred trench]

Why cant the 2 go there?

[brave wolf]

Because if there is a 2 in both circles, then they actually belongs in their intersection

but they cant be in the intersection, since that would make the HCF 7 * 2 * 2 instead

[charred trench]

Ohhhhhh!

[frozen veldt]

I think a venn diagram is a weird way to visualize this

[charred trench]

I need this for test Im revising currently

[brave wolf]

It kinda is, but it works if you think of it as multisets instead

so for example we cant draw a diagram like this

[charred trench]

2 on both intersections

[brave wolf]

the corrected version would look like this

Yes, but note that the other 2 stays there. You always take them in pairs

we take one 2 from the left circle and one 2 from the right and bring them to the middle as a single 2

and repeat this process until there are no 2 same factors

[frozen veldt]

nevermind I think a venn diagram is a good way to visualize this

[charred trench]

Yea

[charred trench]

Coprime way and those other ways dont like them

[frozen veldt]

I guess for this reason I don't really like it so much though

because it's very easy to draw the diagram wrong

[brave wolf]

Yeah, similarly its easy to mess up the normal method too

if you arent used to it

[charred trench]

If you have a sharp eye you good

[brave wolf]

the only reason it feels weird to see the venn diagram for the first time is that we arent used to dealing with multisets

and thats exactly the same reason why the normal method may feel weird

[frozen veldt]

I don't know what the normal method is but if you just eyeball the gcd and the lcm then there's no way you'd get them wrong because reading the gcd and the lcm out of a prime factorization is something even a toddler can do

[brave wolf]

because reading the gcd and the lcm out of a prime factorization is something even a toddler can do
This is what i meant by the normal method lol

[frozen veldt]

I generally prefer guessing and checking in mathematics, works in a lot of cases like simple integrals

[brave wolf]

sure, but you gotta have intutition to guess effectively. and that intuition needs to be built somehow

[charred trench]

Intution is technically a gamble

[frozen veldt]

I wouldn't call it intuition that the gcd is easier to visualize than the lcm

[brave wolf]

but your chances are improving after every round 🔥

[frozen veldt]

that's pretty much the first observation you make when you learn these things

so it makes sense to start with the gcd

and after that it's pretty straightforward to fill in whatever you need to satisfy the lcm

[brave wolf]

Well, I've seen a lot of interesting observations from my classmates

the only problem was 90% of them were wrong

but ig this is offtopic now

If you have no other questions, I think you can close this now @charred trench

[charred trench]

Alright

.close

[safe radish]

Channel closed

Closed by @charred trench

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[acoustic zealot]

AES-Cryption:
could you correct my solution?
I mean, not if i there are misstakes, more if i generally did the correct steps

the green arrow are notes, i did while i was in the lecture. they have no connection to the current task

if the green highlighted number looks weird. i just did write 2B as a byte and bitshifted it.

[safe radish]

@acoustic zealot Has your question been resolved?

Channel closed

Closed by @acoustic zealot

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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 radish]

@noble spindle Has your question been resolved?

[fathom adder]

?

[quasi timber]

[median vigil]

.close

[safe radish]

Channel closed

Closed by @median vigil

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[exotic anvil]

[This is a test]
Hallo can someone halp me with fractions they're very hard

[karmic merlin]

Sure, How can we help you

[exotic anvil]

.close

[safe radish]

Channel closed

Closed by @exotic anvil

Use .reopen if this was a mistake.

[hard crest]

have u tried putting them in a blender that should soften them up

[light shoal]

make them into a soup

[tight nova]

@exotic anvil why do you have three channels?

[keen tulip]

[median vigil]

it's not possible to open more than two channels

so idk what you're talking about

[exotic anvil]

I was doing a test

[exotic anvil]

@mods acadishon

[tight nova]

#help-28
#help-23
#「the-obsidian-twink-jesus」

[keen tulip]

blud

[tight nova]

Ou

Oh*

[median vigil]

do you think obsidian counts the same as help channels

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[tight nova]

No

[keen tulip]

blud

[tight nova]

Oh shit

.close

[keen tulip]

.close

[median vigil]

.close

[safe radish]

Channel closed

Closed by @tight nova

Use .reopen if this was a mistake.

Channel closed

Closed by @median vigil

Use .reopen if this was a mistake.

Channel closed

Closed by @keen tulip

Use .reopen if this was a mistake.

[keen tulip]

wtf

[median vigil]

beautiful

[rustic goblet]

.close

[tight nova]

@rustic goblet hello!

[rustic goblet]

anyhow, you can open two channels if you do it in quick succession

but you can't open three

and the second will tell you off if you don't close the first one

[tight nova]

I meant lance has three channels with his name in them

[rustic goblet]

he had no such thing

only two

[rustic goblet]

^

obsidian doesn't count as a help channel

[tight nova]

Ik

I'm only ever asking for help if #help-25 ever opens up

[rustic goblet]

why 25 specifically?

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[tight nova]

Look at my name

[tight nova]

.close

[safe radish]

Channel closed

Closed by @tight nova

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[still grove]

I understand that the max value is (1,2) and no points of inflection. Should the min value be (3,-2)? The answer key doesn't have any min value so I was wondering if it is a mistake or there really is no min value

[stoic dune]

f is continuous on [0,3]. Reconsider your graph

If f is only defined on [0,3], then you're correct about the min

[still grove]

would it look smth like this?

[stoic dune]

Yeah that looks good!

[still grove]

okayyy, thanks!

.close

[safe radish]

Channel closed

Closed by @still grove

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[long galleon]

So, some say dozenal is a better way to count, others seximal! Those who dare even more say binary is the best way to count. But, what if we've got it all wrong, and there's a better way to maths (maths as a verb like in Toki Pona) that isn't counting? Even if there isn't a better way than what we have now, what might alternatives look like? What I'm circling around, if the above wasn't a good enough description, is the primitive system. Not foundational/axioms. If there is no alternative either, or if this is just too hard to answer, then that's an answer too.

[still stone]

all number systems are kinda arbitary

i think

[long galleon]

I've thought about this a lot myself and personally have settled on binary though I'm not really asking about bases or looking to debate, sorry.

[open wedge]

Two line summary

[quasi bison]

so wait hold on, what are you looking for a better way to do, exactly?

[open wedge]

1. Human: base 10
2. Computers: base 2

[long galleon]

Is counting the only way to primitively represent math?

[long galleon]

^^^

[quasi bison]

not a numeration system, and not axioms, but what

what do you mean by "primitively represent math"

[still stone]

no one counts after learning algebra

[open wedge]

Apart when $\frac{n(n + 1)}{2}$ exists

[flat frigate]

1 divided by 0 equals Infinity

[long galleon]

This isn't my question sry.

[still stone]

your question is a bit vague

[long galleon]

Prety much is there an alternative to counting.

[still stone]

?? multiplication??

[quasi bison]

an alternative to what end

[long galleon]

There's a lot of debate about how to count with bases and stuff but I'm just asking if the idea which this is based on is wrong.

Answers too could just be that no there isn't an alternative or this question can't be answered.

[quasi bison]

i think that nobody here understands what you're talking about or what kind of "alternative" you are even envisioning.

and when i say "nobody here", i mean "maybe not even yourself".

[long galleon]

Yeah

[long galleon]

I will take that as there is no alternative

[long galleon]

By this I meant like primitive in daily life. For example, price tags and such use counting numbers.

[quasi bison]

ok and how are you going to get any sort of economic task done if numbers in any way, shape or form are out of the picture?

[long galleon]

"This is a stupid question" is a good answer and I'm leaning on this based of of what I'm hearing.

[long galleon]

Good point, ty. I can't quite think of something else, so, yeah I suppose that answers my question.

[austere goblet]

!done?

[safe radish]

If you are done with this channel, please mark your problem as solved by typing .close

[long galleon]

Just one minute

I have something which I'm evaluating real quick

I can think of ranges but those still rely on counting numbers to a degree even if they're quantized. Order can't be done either without in some way representing the value that ties back to coutning numbers. Geometry could be used but it's just a roundabout way of replacing counting numbers while sitll having the same fundemental idea. Permutations like in group theory honestly maybe could contend but that's for me to look into and would answer the question, though not sure about this once since I am not familiar with group theory really.

At most I can think of parity (valid contender!), but parity alone is way too basic to get any modern maths done.

[long galleon]

Tysm.

:3

!done

[safe radish]

If you are done with this channel, please mark your problem as solved by typing .close

[long galleon]

.close

[safe radish]

Channel closed

Closed by @long galleon

Use .reopen if this was a mistake.

[long galleon]

This was probably the dumbest interaction you've had all day, though if you were curious, the question which I was trying to ask (I have poor skills with articulating myself after the brain damage /srs) is if an alternative day to day representation of logic and all stuff math is regularly needed for existed or could meaningfully be conceived of. The answer is no, not really unless you want something extremely cumbersome. This has been in my head for several weeks.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[halcyon light]

can someone clue me in on what to do after

[safe radish]

@halcyon light Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[acoustic zealot]

Prove through Induction:

Am I missing something.
How do i prove this

[cunning shard]

yeah, it looks correct.

gut gemacht.

[acoustic zealot]

Wait

Thats the proof?

[cunning shard]

proof.

You basically, showed this

1. P(0) is true.

2. P(n) is true => P(n+1) is true.

so, since P(0) is shown to be true, it follows by (2), P(1) is true,

i.e., you get a chain of true statements, P(0), P(1), P(2),..., where the truthness is implied as follows,

P(0) => P(1) => P(2) => ....

[acoustic zealot]

Ah ok, i thought i have to get back to n(n+1)

Ok thanks

.close

[safe radish]

Channel closed

Closed by @acoustic zealot

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[cloud maple]

I think there's something wrong with this problem but I'm not quite sure what is it

[cloud maple]

Progress

I think equality is attained when (a,b,c) = (0,1,1) and its permutations

[safe radish]

@cloud maple Has your question been resolved?

[cloud maple]

<@&286206848099549185> hi

[idle aspen]

hi

[idle aspen]

phần dưới dĩ nhiên rồi còn j...

kiểu

<=> a2 ≥ 0 sẵn rồi ý

[cloud maple]

Tui thấy ngược dấu á

b^2+c^2≥2bc≥2

Bên trên thì lại có bc≤1

[idle aspen]

bc≤1 ?

[cloud maple]

1 ≥ b^2c^2(b^2-bc+c^2) ≥ b^3c^3

[idle aspen]

1 ≥ b^3c^3 với mọi b,c dương

okay ill leave this to an english helper

minimise question

[cloud maple]

okay

[idle aspen]

@hel

<@&286206848099549185>

[cosmic vine]

?

[idle aspen]

backread

[cosmic vine]

I can't read

[cloud maple]

.

[cosmic vine]

I don't know that lauguge

[cloud maple]

that is english bro wtf

[compact lodge]

lmao what 😭💔

[cloud maple]

Wait nvm

My inequality is wrong

The equivalent inequality is not actually equivalent 😭

.close

[safe radish]

Channel closed

Closed by @cloud maple

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[opaque fern]

\lm this is kind of a weird question but what do the coordinates entail here? Like, do we say [
s_1: (\varphi_1(t), \varphi_2(t)) = (-\alpha, \alpha)?
]
that don't make much sense tho idk

[opaque fern]

\lm $\varphi_1$ and $\varphi_2$ are meant to be basis functions that you can construct any function in that system with. So in the above case you would have [
s_1(t) = -\alpha\varphi_1(t) +\alpha\varphi_2(t)
]

[opaque fern]

but obviously in that case this wouldnt make sense

[safe radish]

@opaque fern Has your question been resolved?

[dark elm]

We have $f:\mathbb{R}^{2}\mapsto \text{Set of some functions}$ defined by
$$f((x,y))=x\varphi_{1}(t)+y\varphi_{2}(t)$$
If we let $p_{1}=(-\alpha,\alpha)$, we get:
$$f(p_{1})=s_{1}$$

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[flat frigate]

BBMaths

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[thin lion]

Hi is this rigorous enough for this?

[verbal cloud]

I would say yes

[thin lion]

alright tysm

.close

[safe radish]

Channel closed

Closed by @thin lion

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[thin lion]

Hello! Im back again

[thin lion]

I feel like with other parts of real analsyis, it all feels very rigorosu when writng but idk with series

like is this wht someone marking wants me to realise?

[proud tree]

are you sure (n+sqrt(n))/2^n<=1/2^n

[thin lion]

😭 oh waitttt

no

scrap that

lemme redo that

[vague zinc]

You could even make the first one less rigorous 😉 Notice the geometric series with 8/25 < 1

[thin lion]

wdym here

[vague zinc]

Well it's obviously not wrong, just unnecessary to use the root test once you've reduced it to a geometric series already

[thin lion]

Is that fine? Just as a rough idea here, I’ll put the series in after

[thin lion]

Oh yea true 😭

Could have just evaluated the geometric series tbh

[thin lion]

Wait no Idt this is correct either 😅

wait i do use root test for this right?

just cause of the 2^n

[vague zinc]

Have you learned ratio test (d'Alembert)

[thin lion]

ohhhhhhhhhhh

😭 yea

Is that the way?

[vague zinc]

Just evaluate here for n -> inf

That's the ratio test

And see if its <1

[thin lion]

oh wait yes sorry

u get 1/2 < 1 ?

so converges?

[vague zinc]

Yep

abs convergence

[thin lion]

ah i see

[vague zinc]

It's like 4 lines to prove its convergence

[thin lion]

yea i overthought it

not sure why i decided to randomly do comparison test in the middle of ratio test

alr tysm

.close

[safe radish]

Channel closed

Closed by @thin lion

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[topaz furnace]

i need someone help me explain this really fast

[topaz furnace]

when loga(b)=x, why a has to be greater than 0

[brave wolf]

if a was say -2, then the equation would be
(-2)^x = b

[topaz furnace]

just started logarithm so kinda confused

[brave wolf]

it would be the inverse of (-2)^x

[fathom adder]

Because it means ln(b)/ln(a) = x

[brave wolf]

are u familiar with exponentials?

[topaz furnace]

i havent learnt about ln

[topaz furnace]

yea

[brave wolf]

the main issue is that exponentials with negative bases behave very badly,
for example (-2)^1/3 would be -cbrt(2)

but (-2)^1/2 isnt even defined (you cant have square root of negative numbers)

who knows what (-2)^pi would be

[topaz furnace]

oh yeahhh, but some work, while some dont, why we have to conclude that a>0

[brave wolf]

(-2)^(28/81), which is very close to 1/3 would be around cbrt(2), which has opposite sign to (-2)^(1/3)

[brave wolf]

Yep

(-2)^x behaves so weirdly that we dont really want an inverse of that

[topaz furnace]

im still very confused 😵‍💫

[brave wolf]

my point is that $\log_{-2}{x}$ would be an inverse of $(-2)^x$

[flat frigate]

MathIsAlwaysRight

[brave wolf]

and (-2)^x behaves very badly

,calc (-2)^0.5

[flat frigate]

Result:

1.4142135623731i

[brave wolf]

okay ignore this, its wrong

[topaz furnace]

i thought that log-2(x) is that (-2)^n=x, why it is an inverse of (-2)^x

[brave wolf]

thats what inverse function means essentially

[topaz furnace]

new to me

[brave wolf]

dont worry about it then

its just the fact that log_(-2)(x) depends on (-2)^x, which behaves very badly

so if we defined log_(-2)(x), it would also behave very badly

so we dont even bother defining it

this is how badly it behaves

undefined, a little bit further around -1.4 and another bit further its around 1.47

[topaz furnace]

ohhhh no way

might explode

understand better now

by the way

[topaz furnace]

how can i write like this

[brave wolf]

its called latex, you can try it in #latex-testing

[topaz furnace]

oh coollll

[brave wolf]

it works by putting $ $ around your equations

and the equations have to be written in special syntax

for example fractions are done using $\frac{1}{2}$, logs with $\log{x}$, $\sqrt{\text{or u can do square roots}}$

[flat frigate]

MathIsAlwaysRight

[topaz furnace]

ohhhhh complicated

thanks for your timeee, im going to try it out, appreciate it a lot

[brave wolf]

np

[topaz furnace]

🔥

.close

[safe radish]

Channel closed

Closed by @topaz furnace

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[steep magnet]

I got the right formula but I was just kinda guessing

I kinda knew that s = ln(t) and t = 1 and t = 2 would be bounds, not really sure why tho

[light shoal]

isn't $\int_0^{\ln t}$ going to get you the region below the curve $s = \ln t$?

[steep magnet]

I also guessed that the missing bound would be 0, not sure why either

[flat frigate]

Bungo

[steep magnet]

I have no idea sorry

Heres the full solution

[steep magnet]

But yeah could someone maybe explain whats going on here

[steep magnet]

And here

Cause I got lucky with my answer but I want to understand what im actually doing

[vague zinc]

s is horizontal and t is vertical. You should start out by rewriting the curve to t = ...

[steep magnet]

Ok but what does s being horizontal and t being vertical tell us sry

I dont know what were doing

[vague zinc]

Just easier to interpret what 'above the curve' actually means if you rewrite them

[steep magnet]

Interpret it how sry

[vague zinc]

Well, it's harder to picture 'above' when the curve is written as s = ln t because 'above' normally refers to the vertical direction

That's why we rewrite to t = e^s

(It's easy to picure that you want t >= e^s)

[steep magnet]

Im so confused 😭

Ok i think im just going to try and find another video on this topic

.close

[safe radish]

Channel closed

Closed by @steep magnet

Use .reopen if this was a mistake.

[steep magnet]

If anyone has a good video pls ping me and send it

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[eager junco]

Hi, can someone explain to me how Rodrigues rotation formula works? Thanks

[quasi bison]

https://en.wikipedia.org/wiki/Rodrigues'_rotation_formula

this one? @eager junco

[safe radish]

@eager junco Has your question been resolved?

[eager junco]

Yes

[safe radish]

Channel closed

Closed by @eager junco

Use .reopen if this was a mistake.

[eager junco]

.reopen

[safe radish]

✅ Original question: #help-23 message

[eager junco]

I know basics operations of vector, but not much after that

[quasi bison]

did you read the wikipedia article at least

[eager junco]

Yes I did read it

But it just looks like magic

[quasi bison]

do you understand up to the point where v is decomposed into a component parallel to k and a component perpendicular to k

[eager junco]

What’s before that?

I know that the cross product gives one of the two perpendicular vectors

[quasi bison]

bad transparent copy-paste

this picture. do you understand the idea here y/n

[eager junco]

Is v rot the answer we are trying to get?

[quasi bison]

yes

[eager junco]

Ok, what about w?

[quasi bison]

$\bd{k}$ and $\bd{v}_{\perp}$ are perpendicular (by construction); $\bd{w}$ is perpendicular to them both (also by construction) and completes an orthogonal triad (because we want that to happen)

[flat frigate]

Ann

[eager junco]

Oh so is it v perpendicular cross v parallel?

[quasi bison]

v_perp crossed with k rather than with v_parallel.

that way $|\bd{w}| = |\bd{v}_{\perp}|$.

[flat frigate]

Ann

[quasi bison]

(but crossing with v_parallel would give the same direction)

[eager junco]

Oh I see

So v parallel + v perpendicular = v?

I think I understand diagram now

@quasi bison may i know how these vectors are calculated?

[quasi bison]

yes

thats what it means to decompose v into a perp and parallel component relative to k

[eager junco]

Got it

[quasi bison]

roughly speaking the recipe goes as follows:
\begin{enumerate}
  \item calculate $\bd{v}_{\parallel}$ by projecting $\bd{v}$ onto $\bd{k}$ (via dot products)
  \item calculate $\bd{v}_{\perp}$ as $\bd{v} - \bd{v}_{\parallel}$ (or via cross-product shenanigans as wikipedia gives)
  \item calculate $\bd{w}$ as $\bd{v}_{\perp} \times \bd{k}$ --- a vector of the same length but rotated 90 degrees in the direction of rotation specified by $\bd{k}$
  \item rotate $\bd{v}_{\perp}$ by angle $\theta$ in the plane spanned by $\bd{v}_{\perp}$ and $\bd{w}$
  \item add $\bd{v}_{\parallel}$ back in
  \item ???
  \item profit
\end{enumerate}

[flat frigate]

Ann

[eager junco]

Ok, according to the wiki, it says that v parallel = (v dot k)k

May I know which multiplication it is implying here?

Oh, nvm I forgot that do product returned a scalar

[eager junco]

I understand now till step four.

[quasi bison]

dot means it's dot product.

[quasi bison]

do you mean that step 4 is where you're stuck

or that you understand step 4 and are stuck with 5

[eager junco]

Stuck at step 4

[eager junco]

Do I use the 2D rotation matrix here?

What does span mean?

[quasi bison]

do you know how to rotate a vector in R^2 about the origin by a specified angle theta

[eager junco]

I think it’s by using matrix multiplication

[eager junco]

Do I relate this to polar coordinates?

[quasi bison]

ehhhhhh

overkill.

[quasi bison]

sure, you can express it in that way.

though maybe it's best that you brush up on your linalg.

[eager junco]

Ok, just wondering, is it hard to figure out why Rodrigues rotation formula works after developing a good foundation?

[quasi bison]

not very, imo

it'll be a bit of a bash/slog but not like... terribly difficult once you grasp rotations in 2d and linear maps in general

[eager junco]

Got it thank you so much for your help!

.close

[safe radish]

Channel closed

Closed by @eager junco

Use .reopen if this was a mistake.

[eager junco]

Have a good day 🙂

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[fervent granite]

We know that we can use summation for approximating areas under a curve $\f(x)$ by partitioning the area into rectangles of equal width deltax and the height defined as $\f(x_i)$, where $x_i$ is our endpoint (suppose right endpoint), $i$ is our index, and $i=1$. We do this for $n$ subdivisions, and the evaluation of our sum tends to the true area under the curve as $n$ is set to larger and larger integer values. In fact, we can evaluate the limit as $n\rightarrow\infty$ of this sum to find the exact area under the curve, leading to the integral.
We turn our attention now to the product. What can we do to find geometric purpose with the product?

[tardy mango]

You may find this interesting: https://en.wikipedia.org/wiki/Product_integral

[fervent granite]

Ah I do see the product with expression 1+f(x_i)deltax. My problem arises from the idea of geometrically drawing this. I understand that this is not an expression of area, but that’s where my capacity of grasping the expression stops. How would I go about drawing this, as is possible with drawing Riemann sums?

It would be one thing to just accept the expression, but I want a geometric motive for it that I can see on paper.

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[safe radish]

@fervent granite Has your question been resolved?

[dark elm]

If no-one gives a good answer there is this: https://math.stackexchange.com/questions/1140507/is-there-a-geometric-interpretation-of-the-product-integral

If you have questions about it, I think more people might help

[safe radish]

@fervent granite Has your question been resolved?

[safe radish]

@fervent granite Has your question been resolved?

[safe radish]

@fervent granite Has your question been resolved?

[open wedge]

!15mins

[safe radish]

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.

[open wedge]

stop spamming helpers

[fervent granite]

.close

[safe radish]

Channel closed

Closed by @fervent granite

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[trim lion]

From the top of a 12m high building, the angle of elevation of the top
of a cable tower is 60° and the angle of depression of its foot is 45°.
Determine the height of the tower

Guys I'm having problems visualising this and making a diagram which is important to do in the exam I need help in how you visualise this and also how to solve it

[limpid lodge]

Are you confused about angle of elevation and depression?

[trim lion]

Right and how to visualise it as well

[limpid lodge]

Depression is when you're looking down from a point

https://share.google/wqfVBKFUd55FhkYGq

[trim lion]

Oh

And elevation

[limpid lodge]

Elevation would be when you're looking up

https://share.google/Dkwa7KGGGUZ2qY1wv

[trim lion]

If i were to make a diagram of this question how will i?

[limpid lodge]

Start with a vertical line for the building

[trim lion]

Will it be smth like this

[limpid lodge]

https://youtu.be/bmU40g_mIwc?si=dAEmD0nauIemQ5M3

Try this

[trim lion]

Okay

Okay i understand it now thank you for the help

I'm closing now

.close

[safe radish]

Channel closed

Closed by @trim lion

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[covert talon]

What next

[brave wolf]

you didnt divide the 7

[covert talon]

It’s a plus

Oops

My handwriting

[quasi bison]

is it handwriting or finger-writing

or mouse-writing

[safe radish]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[quasi bison]

💀

!msgdel

[safe radish]

The original post of this help channel has been deleted, and it will abruptly close and possibly lock. (This is irreversible.) Please claim a new channel, and don't delete the first message of any future channel you claim.

[covert talon]

its cus im doing it on my apple pencil but for some reason it has some like autowrite thing

like it changes what i write

[quasi bison]

go open a new channel

[covert talon]

ok

.close

[pure agate]

Looks like a test.

[covert talon]

its a past paper

:p

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[cloud maple]

(Given a,b,c be non-negative real numbers such that ab+bc+ca > 0, prove the above inequality)

I instantly thought of using pqr method when looking at this, and the inequality also allows me to consider p = 1

But I still can't think of a way to work it out, especially the (1+√2)^2

[faint seal]

What’s the pqr method?

[cloud maple]

Let p = a+b+c, q = ab+bc+ca and r = abc

Substituting (ka,kb,kc) into the inequality and it still holds, so we just need to consider p = a+b+c = 1

[faint seal]

Yeah it’s homogeneous

The last term seems to be the most problematic

[cloud maple]

Yea

[faint seal]

Where is this problem from?

[open wedge]

i have a feeling this needs cauchy schwartz

-# t ngu bđt lm

[cloud maple]

https://www.scribd.com/document/472238275/a-b-2-b-c-2-c-a-2-pdf
A pdf that studies the term (a-b)^2(b-c)^2(c-a)^2 when using pqr

[cloud maple]

I dont think its possible lul

No way you can pull out the (1+√2) just using known inequalities

[faint seal]

Maybe you define a function and then find that its minimum value is (1+sqrt2)^2

[cloud maple]

Well there's this inequality which can help in defining a function

except its

too long

Also one more note: the equality is attained if a = b = c, yes, but there's one more case and thats the main reason (1+√2) appears

[faint seal]

[ \frac{(a^2+b^2+c^2)\left[(a-b)^2+(b-c)^2+(c-a)^2\right]}{2(ab+bc+ca)(a+b+c)^2} \ge \frac{(1+\sqrt{2})^2(a-b)^2(b-c)^2(c-a)^2}{(a+b)^2(b+c)^2(c+a)^2} ]

[flat frigate]

kheer257

[faint seal]

Yes so discount the case where any two are equal and then divide through by the numerator on the left

[safe radish]

@cloud maple Has your question been resolved?

[safe radish]

@cloud maple Has your question been resolved?

[safe radish]

@cloud maple Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.