help-23

[surreal plover]

i mean the only solution woud be x = -3 +- 4i

[fickle mantle]

Yes

Number 15

[surreal plover]

yo teacher might have messed up

[worldly lantern]

just write no real solution after proving D < 0

[worldly lantern]

even 3 is

imaginary

how did u solve 3

[surreal plover]

teach might have used the gpt ✌️✌️✌️✌️

[limpid lodge]

Oh then must be from quadratics. Js open the whole square.

[limpid lodge]

Then this yh. Idk wht else ur teacher can expect.

[worldly lantern]

see the 3rd ques

its also imaginary

[limpid lodge]

Wht r supposed to with these eqn? Whats the instructions.

[fickle mantle]

Solve the equations

[surreal plover]

yeah so the only solution is x = -3 +4i and -3-4i

[fickle mantle]

Could u actually help me w everything

I kind of forgot how to do it

[limpid lodge]

Oh yeah then prob js prove Discriminant<0 and say it has no real soln. As you must have done with 3.

[open wedge]

,rccw

[fickle mantle]

Actually I do m pe how to but idk how to get to the answer

Like number 14

[open wedge]

expand

[fickle mantle]

If I jus square rooted the 16

[radiant ice]

wow stuff i can actually do 😭

[open wedge]

fr 😭

[limpid lodge]

Lol

[radiant ice]

yes

[open wedge]

you can expand both sides

and turn into a normal quadratic

[radiant ice]

you don’t need to

number 14?

[open wedge]

oh i thought 17

but yea

at least i showed you how you can do 17 tho

[fickle mantle]

Huh

[radiant ice]

number 14 you can square root the 16

but remember when you add a square root what do you do

[fickle mantle]

Oh bc I get it

*oh nvm I get it

[open wedge]

where's your pfp btw?

[fickle mantle]

Plus or minus it?

[radiant ice]

ok now simplify

[radiant ice]

yea

[fickle mantle]

I’m on a break from fc

*dc

[open wedge]

yea ic

so anyways

$x = \pm 4 - 2$, what values of $x$ can it be?

[flat frigate]

1 divided by 0 equals Infinity

[fickle mantle]

How do I continue pls

[open wedge]

the only way the LHS can be zero

is if one of the factors are 0

so case working

[fickle mantle]

1. +4-2 and -4-2

[radiant ice]

do you know that if you multiply by 0 everything is 0

[fickle mantle]

Yes

[radiant ice]

which means that one of the factors have to be 0

[fickle mantle]

I don’t understand

[open wedge]

assume no factors are 0

will you ever get a 0 as a result?

[fickle mantle]

Huh

[burnt notch]

If A • B = 0, what can you say about A and B?

In words, what kind of numbers do you need if you want their product to be 0?

Hint: don't overthink

[fickle mantle]

Oh

Uh

0

[open wedge]

at least one of them is 0

[radiant ice]

now replace A with (x-1) and B with (x+8)

[quick tundra]

there has to be a zero right?

whats this abt?

[radiant ice]

since -2 doesn’t have an x it can never be 0

[open wedge]

yea

[quick tundra]

yeah

[open wedge]

r e a d
t h e
p i n n e d
m e s s a g e

and the full convo

[quick tundra]

ok

[fickle mantle]

Do you want me to expand?

[open wedge]

uhhh no

[radiant ice]

no

[open wedge]

A = x - 1

B = x + 8

so the only thing when (x-1)(x+8) = 0

is when at least one of them is 0

so

CASE WORK

[fickle mantle]

Or do you mean that guys rule

Where you get x alone?

I forgot the name of the guy

[open wedge]

?

[fickle mantle]

I forgot the name

[open wedge]

is that the guy who brings in the golden rules or smth?

[radiant ice]

there’s a rule 😭

[fickle mantle]

I actually don’t know what you want me to do

[radiant ice]

okay

[fickle mantle]

No

[radiant ice]

so A * B = 0

[fickle mantle]

The one where you have bracket =0

Do you make it an equation

[radiant ice]

what do you know about A or B

[fickle mantle]

So

[radiant ice]

yes

[fickle mantle]

Oh

[open wedge]

two cases

[radiant ice]

wait is it the zero product rule?

[open wedge]

🥀

[open wedge]

ya

that can be proven btw

[fickle mantle]

I think so

Idk the name

[open wedge]

so apply that

[quick tundra]

did u guys solve it?

uhm hello?

[radiant ice]

nah

[fickle mantle]

Ok

[quick tundra]

what answer did u get?

[fickle mantle]

3/2 and 1

[quick tundra]

what

[radiant ice]

ok so how did you get 3/2

[fickle mantle]

Oh mb it’s 1 and -8

Wrong qiestion

[quick tundra]

can we use quadratic in this gng?

[radiant ice]

quadratic is slower

[quick tundra]

then what method is better?

[radiant ice]

if you can

factoring

or completing the square

[open wedge]

🔥

[quick tundra]

hmm

[radiant ice]

so that means x = 1, -8

or x_1 = 1, x_2 = -8

[fickle mantle]

Oh

Erm how do I do this

[radiant ice]

does that say 9x^2=x?

[fickle mantle]

Yeah

[radiant ice]

okay so try setting the RHS to 0

[fickle mantle]

I got 0 and 1/9

[fickle mantle]

What’s that

[radiant ice]

yeah that’s the answer

[radiant ice]

right hand side

you did already

[quick tundra]

tranpose everything to LHS

[fickle mantle]

Oh

Uh what about 7

Do I take the 9 to the 1

Then square

Or square the one

[open wedge]

s

SQUARE

ROOT

[quick tundra]

BRUHHHHHHHHHHH

[radiant ice]

try square rooting both sides

[fickle mantle]

Yes that

[quick tundra]

do this

[modern shard]

Yo gg gng

[fickle mantle]

Uh

I got it wrong

I got -8 and -10

[radiant ice]

what did you do

[quick tundra]

1st one right?

or dif?

7 oh ok

lemme see

[radiant ice]

numba 7

[open wedge]

no

[radiant ice]

okay

[open wedge]

you're wrong at the square root step

LHS should be 3x

[modern shard]

Starting with �, move all terms to one side to make the equation equal zero: �. Then factor out the common term �, giving �. Using the zero-product rule, either � or �. Solving the second equation gives �, so �. Therefore, the solutions are � and �.

[fickle mantle]

Oh

[quick tundra]

what

[fickle mantle]

I minuses

[modern shard]

Mb

[fickle mantle]

Instead of diving

[quick tundra]

ye

[open wedge]

some weird characters found

[radiant ice]

do you know this

ax^2
when you square root both sides
it’s sqrt(a)x

[open wedge]

and the other side has a $\pm$ 😭

[flat frigate]

1 divided by 0 equals Infinity

[modern shard]

Gng

[open wedge]

!nosols

[safe radish]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[radiant ice]

!nogpt

[safe radish]

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

[fickle mantle]

Huh

[open wedge]

good job

[modern shard]

@safe radish he asked for it

[radiant ice]

let me write it in latex

[open wedge]

!nosols

[safe radish]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[open wedge]

!noai

[safe radish]

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

[open wedge]

and no excuses

[modern shard]

@open wedge tf

[open wedge]

read what the bot says

it's in the server rules, i can't do anything

[quick tundra]

wht happened?

[radiant ice]

[
ax^2
]

[
\sqrt{ax^2}
]

[
\sqrt{a}\sqrt{x^2}
]

[
\sqrt{a},x
]

[flat frigate]

! sniper3d107

[open wedge]

he used AI to generate his answer

which violated 2 rules of the help channel as shown

[radiant ice]

do you know this @fickle mantle

[quick tundra]

related to this help thing

[fickle mantle]

No

I kind of know it

[open wedge]

AIs are strictly prohibited if you want to help someone no matter what

[graceful quail]

Do we get the moderator ping 🤔

[open wedge]

i'd wanna do it if he did one more time

[radiant ice]

well retry the problem where a=9

[quick tundra]

one serious doubt @open wedge who will Ai for this easy stuff man

[lean otter]

imagine calling police for noai

[open wedge]

fr

[quick tundra]

loll

[open wedge]

anyways

getting too off topic now

[fickle mantle]

I don’t understand what ur saying

[quick tundra]

did u get it @fickle mantle ?

[radiant ice]

okay so we have 9x^2=1

you can see that 9x^2 is ax^2 right,

[fickle mantle]

No

[fickle mantle]

Yes

[radiant ice]

ok now

we need to square root both sides

[open wedge]

hell nah i got blocked by OP?

[radiant ice]

damn

[fickle mantle]

Root over 1?

[quick tundra]

one piece?

[fickle mantle]

Then divided by 9?

[radiant ice]

root over 1 and root over 9x^2

[fickle mantle]

Oh

[radiant ice]

because what you do to one side you do to the other

[fickle mantle]

Won’t that half the 9

[radiant ice]

well no

it will square root the 9

[fickle mantle]

Yes

9^1/2

Is that it?

[radiant ice]

yes

[open wedge]

that's different from 9*1/2 which halves the 9

[radiant ice]

what is 9^(1/2)

[quick tundra]

wha

ye

[fickle mantle]

Erm for questions like this

What’s the basic rule

Ik how to solve it but also DOTN n pe how to

I just guess what to do

[radiant ice]

i mean

[radiant ice]

like what to do first?

[fickle mantle]

Yes

[open wedge]

$ax^2 + c = 0$ then move $c$ to the other side and square root

[flat frigate]

1 divided by 0 equals Infinity

[open wedge]

$ax^2 + bx = 0$ then factor $x$ out

[radiant ice]

try and set right hand side to 0

[flat frigate]

1 divided by 0 equals Infinity

[radiant ice]

or this

[open wedge]

full quadratic means quadratic formula

[radiant ice]

,tex .quadratic formula

[open wedge]

or factor or complete the square if you can

[flat frigate]

! sniper3d107

[quick tundra]

very beautiful 🤤

[fickle mantle]

I d ok nt understand

[open wedge]

https://www.youtube.com/watch?v=E2eVZFy9yzk

[fickle mantle]

What’s the basic for solving questions like all these

[quick tundra]

we rlly dont need this

[open wedge]

i'd like to sing with this guy to remember the formula

[radiant ice]

i have the pop goes the weasel song

[open wedge]

.

[radiant ice]

well it’s different for some

[quick tundra]

see, you gotta see what all algebraic stuff applies in ur equation

[modern shard]

Yo guys why cant we divide with 0

[radiant ice]

!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).

[quick tundra]

like suppose the formulas for sqaures or cubes, sometimes squaring both sides

[fickle mantle]

Wait what’s examples of this

[quick tundra]

refer to #❓how-to-get-help

[fickle mantle]

Aw

[quick tundra]

examples of?

[open wedge]

good job

[fickle mantle]

The algebra basic

[open wedge]

solve for $x$: $x^2 + 3x + 2 = 0$

[flat frigate]

1 divided by 0 equals Infinity

[open wedge]

that's one kind of your question

[radiant ice]

like 9x^2=1
it can be solved by rooting both sides and solving

but 9x^2=x
you had to set the right hand side as 0 then solved

[quick tundra]

quad formula to be used ryt?

[open wedge]

yea but it's not neccessary

[radiant ice]

unless you factor

[quick tundra]

yeah

[open wedge]

if $x = 0$ then yk what it is, else divide both sides by $x$

[flat frigate]

1 divided by 0 equals Infinity

[open wedge]

done and dusted

[radiant ice]

or the ac, b method

[open wedge]

that's one method of factoring

[fickle mantle]

Oh ok

[open wedge]

tbh, it's called pattern recognition

[quick tundra]

ye

that word

[open wedge]

mathematics is not just about memorizing kinds of questions, it's about using your head to solve different kinds of problem

[quick tundra]

[quick tundra]

thats how great mathematicians got these formulas in the first place

did u get how to solve these types of questions @fickle mantle

[quick tundra]

did she solve this?

[open wedge]

that's just an example i gave

[quick tundra]

oh

[fickle mantle]

Yes

[open wedge]

solve the problem given above

[quick tundra]

yayy 👏

[open wedge]

also that's she/her

[quick tundra]

oh 😅

sorry @fickle mantle

[fickle mantle]

It’s fine

Idm

[quick tundra]

mhm

[fickle mantle]

I think I did smth wrong

[quick tundra]

wahts the question?

[manic patrol]

,rccw

[radiant ice]

,rccw

[radiant ice]

which one the top one or the bottom one

[fickle mantle]

Number 5

[open wedge]

so good so far

[quick tundra]

,rccw

[quick tundra]

this a tedious one gng ✌️

[open wedge]

it's called

[fickle mantle]

[open wedge]

applying the quadratic formula

if you can't factor then just use the formula

it's just that factoring helps you solve faster

[fickle mantle]

My answer seems wrong

[quick tundra]

what is ur answer

[fickle mantle]

Haven’t gotten it

The process

Is wrong

[quick tundra]

hmmm'

im trying too ill let ya know when i solve it

even im struggling with this what

😭

[fickle mantle]

Sorry

[quick tundra]

why u apologising

[fickle mantle]

Wasting ur time

[quick tundra]

no?

its okay

i dont rlly hv anything to do other than this gng

[fickle mantle]

I easily forget how to do things so I gave to go all Tyyy e way back even though I’m in a high grade

[fickle mantle]

Oh ok

[quick tundra]

lol

[fickle mantle]

Autocorrect is gonna kill me

[quick tundra]

lets not deviate from our main topic other wise it'd be breaking the rules (not tryna discourage you of talking)

u can dm me if u wanna talk :)

im not much help 😭

did everyone leave

[fickle mantle]

Ig

[fickle mantle]

Ty

[quick tundra]

lol

[fickle mantle]

I can solve some of the questions rn

But I want help w learning completing the square

[quick tundra]

yeah

that completing square is something that even i dont get sometimes

but ill try my best to help

[fickle mantle]

Ty

I have a question for this

[manic patrol]

,rccw

[fickle mantle]

The right side

I’d the 2(x-3)

Suppose to be in a bracket

So the - affects it all

I get c fused w the negative things

[radiant ice]

i like to think of -1

and distributing

[quick tundra]

hmm

[radiant ice]

so like pretend you already foiled 2(x-3)

which is 2x-6

now you have -(2x-6)

and then think about -1

so it’s -1(2x-6)

then you foil

[quick tundra]

foil

[radiant ice]

[quick tundra]

bros getting typo after typo

[open wedge]

[quick tundra]

😭

[radiant ice]

i’m tired 😭

[quick tundra]

same

but u skill diff

jkjk

[fickle mantle]

Tysm

[lean otter]

https://tenor.com/view/skill-issue-urge-resist-cat-gif-25536160

[radiant ice]

you can also think of it like this

[quick tundra]

wat'd u get as final answer

[radiant ice]

-2(x-3)

foil but it’s now -2

[quick tundra]

which is -1 * 2 👍

[fickle mantle]

Oo

[fickle mantle]

Still solving

[quick tundra]

mhm

[radiant ice]

i’m supposed to be sleeping

[quick tundra]

😭

ill give u advice can i

go sleep

🤫

sigma

[radiant ice]

🤔

idk if this is good advice

can i get a second opinion

[fickle mantle]

I’m stuck

[radiant ice]

can you show?

[quick tundra]

controversial ive heard it is but bigger risk = bigger reward

[quick tundra]

show process

no rccw 😭

[radiant ice]

,rccw

[quick tundra]

no bro

[radiant ice]

ez

anyways

[quick tundra]

this guy is unemployed

[radiant ice]

ok so

[quick tundra]

and uhm

[radiant ice]

😭

[quick tundra]

-4 is -2 , 2 what ??

[radiant ice]

ac, b factoring method

[quick tundra]

js factoring bro

[fickle mantle]

Mb

[radiant ice]

ok so you can’t do the ac, b method

[quick tundra]

what is acb

[radiant ice]

your last resort is quadratic formula

[fickle mantle]

Same

[fickle mantle]

Oh ok

[quick tundra]

the ultimate move 🤫

[fickle mantle]

I’m so hungry💔

[manic patrol]

gentle reminder to take care of your health and physique before doing good math!

[manic patrol]

,rccw

[fickle mantle]

If I eat now I’ll get distracted

[quick tundra]

nah id win, i eat crayons

[manic patrol]

take a full meal first, then come back later. math can wait, not your hunger.

[radiant ice]

for factoring it is ax^2 + bx + c = 0

where you need to find 2 numbers(let’s say m, and n)that mutiply to ac and add to b
where an+m = b
which leads to (ax+m)(x+n) = 0

[fickle mantle]

I got a test on Tuesday

[radiant ice]

what day is it today?

[quick tundra]

bro ik what is factoring bro.

[fickle mantle]

[vague phoenix]

wise word

[radiant ice]

that’s the ac, b method

i better sleep 💤

[manic patrol]

I don't think taking an hour off to eat lunch/dinner or whatever meal would harm your math, but sorry for the intrusion if that's the case. please proceed.

[quick tundra]

everyone knows it i js didnt knw it had name

[radiant ice]

ah

[vague phoenix]

seems good

[quick tundra]

crayons>>>

[vague phoenix]

you are on the right track skittles

[quick tundra]

@fickle mantle yayy u got it 👍

[fickle mantle]

No I can take ur advise. Only thing is, I watch videos while eating and it’ll distract me

[fickle mantle]

Number b6)

[quick tundra]

,rccw

[manic patrol]

I would like to just say I'm not asking you to eat while doing math, so watching a vid or two while eating, while unhealthy (depending on who you ask), is not wasted time on math anyway.

[fickle mantle]

Oki

[manic patrol]

and if you are afraid of running afoul of time you can always set an alarm.

[fickle mantle]

Lemme finish this then I’ll eat

[manic patrol]

but I digress, and I'm sorry for barging in with unwanted advice. please continue.

[fickle mantle]

Stop it’s not unwanted

[quick tundra]

u doin good thing mate, should be proud 👍

@fickle mantle

u done with ur doubt

?

or u still hv one?

[fickle mantle]

I see why I got it wrong

[quick tundra]

hm

[fickle mantle]

It was the 2-c

2-x

So said it’s suppose to be -(x-2)

Ok Im gonna eat

[quick tundra]

ok

[quick tundra]

okki

[fickle mantle]

Bye for now

[quick tundra]

cya

[safe radish]

@fickle mantle 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.

[worldly lantern]

put x =1 , y = 0

and solve the formed quadratic in terms of fx

also

putting x=0,y=0 we get f(0) = 0

that will solve it

answer is pretty funny

[wet ridge]

how we know it is quadratic

[worldly lantern]

!show

[safe radish]

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

[wet ridge]

yes f(0)=0 . but how we know fx is quadratic i cant get

why we assume fx is quadratic

[worldly lantern]

no

fx is not quadratic

when we put y = 0 in the given equation

we get a quadratic in terms of fx

that means instead of x

you solve for fx

[wet ridge]

but when i put y=0 i get f(0)=0

[primal gazelle]

this is all we get from y = 0 sub

yes

[worldly lantern]

no , keep x = x and y = 0

[worldly lantern]

guh , no

[wet ridge]

i did same

i guess

[worldly lantern]

!show

[safe radish]

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

[worldly lantern]

dang

mb chat

i made a mistake

[wet ridge]

f(x+0)(x-0)=(f(x)-f(0))x
f(x)x=(f(x)-f(0))x
f(0)=0

[worldly lantern]

right

i read the ques as
f(x+y)f(x-y) = RHS

mb

is the answer just f(x) = x

it can be one of the solutions

can it not?

[primal gazelle]

it is

[worldly lantern]

so its solved then or wot

[primal gazelle]

we want to find all solutions and justify that these are the only ones

[worldly lantern]

ahh right

i did somethinf

idk if it does anything tho

this might look crazy

but..

RHS looks like derivative

[primal gazelle]

f neednt be differentiable

[worldly lantern]

right

dang

[primal gazelle]

but this does provide some intuition

@wet ridge

notice that the solution space is linear

also if f(x) satisfies the functional equation so does f(-x)

write the function f as a sum of an even and an odd function and work with each of them $g(x) = \frac{f(x) + f(-x)}{2}$ and $h(x) = \frac{f(x) - f(-x)}{2}$

[flat frigate]

k

[safe radish]

@wet ridge 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.

[west hedge]

why the right hand side is 2^2 not (2.001)^2

[west hedge]

seems arguable

[split kayak]

Recall the def. of a limit

for a function $f: \R \to \R$, its derivative at a point can be written as: 
$$f'(c) = \lim_{h\to0}{ f(c+h)-f(c)\over h }$$

[cunning pasture]

Because it's x^2, not (x+h)^2

[split kayak]

assuming theres such derivative
h is just a really small quantity

if instead of solving the limit, we numerically approximate the solution, with, lets say, c = 2, h = 0.001

Youre left with

$f'(2
) \approx {f(2.001) - f(2)\over 0.001}$

[west hedge]

why it isn't f'(2.001)

you are not answering my question

[split kayak]

Look at how this is written

[west hedge]

the definition that you have thrown is the conclusion

im asking how it works

and why it is not f'(2.001) instead

[split kayak]

Its just how the derivative has been defined.

[west hedge]

im still in the state where it has not been defined

[split kayak]

?

If this step doesnt bring any doubts, then you already know the definition of a derivative.

[west hedge]

3b1b is helping viewers to invent calculus

[west hedge]

he leads to a rather conclusion suddenly saying this is equals to 2^2, which is rather arguable in my opinion

why it is not (2.001)^2?

could you explain?

[solar hazel]

[blazing swallow]

well, $2^2 \approx (2.001)^2,$ so you could write it as $\dv{A}{x} \approx (x+h)^2$ if you really wanted to
but as $h \to 0,$ $(x+h)^2 \to x^2$ anyways. intuitively, whether you hold onto the left side or right side of the rectangle, it will become a line at $x=2$ in the end

[flat frigate]

حسیب ♥

[blazing swallow]

imo there is a bit of convention here: we start at x, then go h units to the right. but you could start at x+h, and go h units to the left to get (x+h)-h = x

[verbal cloud]

Because they are very close and we are trying to illustrate f'(2), not f'(2.001)

It's an approximation so it doesn't matter since in the end we need to take the limit anyways

[blazing swallow]

in fact, consider $\alpha = x + h$, then $\alpha - h = x$, so $$\frac{f(\alpha - h) - f(\alpha)}{-h} = \frac{f(x)-f(x+h)}{-h} = \frac{f(x+h)-f(x)}{h}$$
so going from $x \to x+h$ or from $x+h \to x$ yields the same thing

[flat frigate]

حسیب ♥

[verbal cloud]

Intuitively yes but here x is fixed so you can only have h goes to 0

[safe radish]

@west hedge Has your question been resolved?

[split kayak]

Btw, if you have a continuous differentiable function for this, then the direction doesnt really matter.

[safe radish]

@west hedge Has your question been resolved?

[safe radish]

@west hedge Has your question been resolved?

[verbal cloud]

What else do you need?

[cedar badger]

so uhm, why do you think it should be f'(2.001)?

[cedar badger]

.

[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.

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.

[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.

[rose palm]

this my question

[austere spade]

what have you tried?

[rose palm]

I thought about it an i thought it was 4. because I thought "if the initial value of the seconds its in air is 4, then after 2 seconds it should be 6" but i was wrong

then i checked it online and it said it was the first one, but I didn't really understand why that's why im here

[fathom adder]

Whats the difference between the one you have and the one you search ?

[rose palm]

it was the same one

[fathom adder]

But what differs

[rose palm]

wait im confused what are you asking

i searched up the same question online

i got the answer on brainly, but I didn't really understand why that was the answer

[fathom adder]

Its the same path, so values will be the same, but they say to you smth about the time

What does it mean?

Math speaking

[rose palm]

no that was me, I was confused

i thought the 4 at the start meant that the ball was in the air for 4 seconds

at the start

they said that (t-2) should be the time for the second ball

[austere spade]

thats not correct

[rose palm]

yeah exactly

[fathom adder]

Yes

[rose palm]

i thouht that but when i checked it was wrong

[fathom adder]

Why is that the case ?

[austere spade]

the 4 means that at the start, the ball is 4 units in the air

[rose palm]

but I dont get why t-2 is the time for second ball when it is hit AFTER the first ball why is it -

[fathom adder]

If it is the same trajectory, then you will have same values but with just a time difference

[rose palm]

and why is it T minus 2 is t the starting time?

is T like the time the first ball was hit

[fathom jewel]

you want h=4 to start at t=2 now, instead of t=0 (starting point) maybe that helps

[fathom adder]

So when t = 0 for the first ball, its height is the same as the second ball at t = 2

[rose palm]

so t-2=0

[fathom adder]

You can easily make the experiment by yourself actually

[fathom jewel]

Do you have a ball and a timer?

[rose palm]

ye

[fathom adder]

You can throw the ball like up

And then 2sec later do the same

[rose palm]

yeah then what 😭

[fathom adder]

At 0 sec, see how the first ball will be at the same height as the second ball is at 2sec

[rose palm]

i mean the height is the same the ball is just hit 2 seconds after

[fathom adder]

Yep so thats why we shift

Only

[rose palm]

ohhh so like in a graph

[fathom adder]

Sure

[rose palm]

like you shift it -2 so right 2

[fathom adder]

Exact

[rose palm]

so after 2 sec

so the T at the start was the time for the first ball

and the t-2 replaces the T for the second balls time??

[fathom adder]

Yes

[rose palm]

oh okay

thanks man 🙂

[fathom adder]

You're welcome

[rose palm]

how to close this

.close

[safe radish]

Channel closed

Closed by @rose palm

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.

[tawny mulch]

Does anyone know how there are 2 integrals with 2 different y values and why there are 2 integrals being used?

[tawny mulch]

theres one section of the graph being completely disregarded and im not sure why

[burnt terrace]

This problem splits into two integrals because when you take cross-sections perpendicular to the y-axis, the left and right boundaries of the region change depending on the value of y.

[tawny mulch]

is there a way you can show this visually?

[burnt terrace]

Sorry man but I don’t have that power

[tawny mulch]

im a bit tad confused

[burnt terrace]

I didn’t download Math+

Costed $8

[tawny mulch]

😔

[burnt terrace]

Whenever the left or right boundary changes, you need multiple integrals.

[quiet plume]

More explicitly, from $y=0$ to $y=1$, the region is contained between $x=0$ and $x=\sqrt[3]{y}$. This corresponds to the red sub-region you highlighted.

From $y=1$ to $y=6.4$, the region is contained between $x=\ln(y)$ and $x=\sqrt[3]{y}$, which corresponds to the orange region you drew.\

Since the bounding curves change along the way, you have to split the integral, as Braydon explained.

[flat frigate]

Azyrashacorki

[quiet plume]

Also which part do you feel is omitted?

You could imagine in this that the lower bound in $x$ is defined piece-wise by $$x(y) = \begin{cases}0; \quad &0\le y \le 1 \ \ln(y); \quad &1 \le y < 6.4 \end{cases}.$$ Therefore you need to split the integral like you would for any piece-wise function.

[flat frigate]

Azyrashacorki

[tawny mulch]

okay i understand where the red and orange regions came from, but what happens to the region on the left side of the Y-axis? shaded in cyan

if it was the integral from 0 to 1, wouldn't it count for the Black and Cyan region?

[safe radish]

@tawny mulch Has your question been resolved?

[safe radish]

@tawny mulch 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.

[rancid rock]

trinomial

[rancid rock]

anhone wanna help me wit em

[safe radish]

Asking the actual question right away is more likely to get responses.

Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.

[rancid rock]

is the factorized form of x^2-2x-15 equal to (x-5)*(x+3)

[tardy mango]

yes

[near sleet]

yes

[tardy mango]

you can check this yourself by expanding your factorisation and seeing if it matches

[near sleet]

i find for simple ones graphing helps as well

[rancid rock]

ty

[tardy mango]

you can turn off pings when you reply btw

unless you meant to ping the op and now me

[safe radish]

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

[near sleet]

sleep brain, sorry

[rancid rock]

.close

[safe radish]

Channel closed

Closed by @rancid rock

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.

[light sparrow]

Is there a way to solve this question without using psuedoforces?

[hard crest]

,rccw

[hard crest]

pseudoforces are going to be the easiest way i think, pretending that someone is pushing the block to the left rather than pushing the wedge to the right

[light sparrow]

Yeah it definitely is! I was just wondering if there was a way to do it without?

[hard crest]

um well "remains stationary" isn't really true at that point; you want it to move linearly

it becomes dynamics rather than statics which is harder

[safe radish]

@light sparrow Has your question been resolved?

[light sparrow]

How would you do it with dynamics

[hard crest]

uhhhh i guess you'd find the paths of the block and the wedge and ensure that the block's vertical velocity is equal to 0

[light sparrow]

Could you show me

[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.

[charred moth]

Can I get help with finding the velocity of this function?

[charred moth]

Is it a question where you find the derivative?

[light sparrow]

Is this a displacement function?

[winter whale]

are you dealing with projectiles?

[charred moth]

I tried making a function to represent a quarter pipe with a concave

I used an ellipse equation for it

And then made it equal to y

[safe radish]

@charred moth Has your question been resolved?

Channel closed

Closed by @charred moth

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.

[toxic plinth]

I know there are proper definitions for these things but i have been struggling. So the idea of openness for a subset A in R^n is just that A doesn't include any boundary points, more formally i can put a ball around it of radius epsilon and find another point inside A.
But there was this example of X = (1,3] U (4, infinity), and A a subset of X where A = (1,3]
A is considered open in this set because no matter how small the ball i still find an element of A and no elements outside of that?

[delicate shore]

yes essentially

A is open in X equipped in the subspace topology

a set U ⊂ X is open in X iff it is equal to V ∩ X for some open V (in ℝ)

[toxic plinth]

what do you mean by equipped in the subspace of topology

[delicate shore]

Do you know what the subspace topology is?

[toxic plinth]

yeah thats the definition we were given

[delicate shore]

That's the definition of the subspace topology

[toxic plinth]

no just started geometry last week

okay

Are the two definitions i desribed for openness, one thing or are there different types of openness

[delicate shore]

What is open depends on the topology of the ambient space, for instance your A is open when considered as a subset of X but not open as a subset of ℝ

[toxic plinth]

so to be open isnt a general thing but rather requires to the know the space we work in

[delicate shore]

yes

[toxic plinth]

okay thank you

.close

[safe radish]

Channel closed

Closed by @toxic plinth

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.

[stark hatch]

?help

[timber dock]

[stark hatch]

how to understand zeta function?
.

[vague phoenix]

Read books

[safe radish]

@stark hatch Has your question been resolved?

Channel closed

Closed by @stark hatch

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.

[amber furnace]

Guys how to make my substitution method equations with reasoning 🥹

[manic patrol]

hi OP, for future helpers, do you have any example questions where you need to do this, and what you have tried? it's easier if you have them!

[amber furnace]

Idk how to do ts

It's like 50% of my grade

I have to like make my own equation thingy

[vague phoenix]

Is this your exam ☠️

Give out 2 linear equations and subs or eliminate 👌

[amber furnace]

So

One moment my teaches looking at me

I have to like make one myself

[vague phoenix]

Yes

As long as you provide corect method

Make 2 simple equations

[amber furnace]

Can u make it for me

[vague phoenix]

Bro thats your exam 💀

Just make 2 different one in form of y=ax+b

[amber furnace]

Is

y = 2x + 3

Substitution

y = 2x + 3
x = y + 1

Elimination

2y - 3x = 3
Y + 3x = 1

Graphical

[vague phoenix]

Then easy

[vernal portal]

try this 3x-2y=6 and x-4y=4

use intercept form and get x,y intercepts

and u can plot the graph from that easily

[vague phoenix]

Yes

Then do it boss you can do that

[amber furnace]

What's inequality

4x - 2y < 10

[vernal portal]

a>b and a<b that is an inequality

[amber furnace]

Is ts correct

[vernal portal]

just draw 4x-2y=10 first

[amber furnace]

Yes

I wrote all the equations

What's the reason explanation part

I found out thanks chat

[harsh sapphire]

<@&268886789983436800>

[hard crest]

hi what

[harsh sapphire]

er this guys lowkey cheating

[radiant isle]

@amber furnace is this an ongoing exam youre taking?

[hard crest]

looks like one given this

[harsh sapphire]

blud 😭

[amber furnace]

No

[radiant isle]

explain this then?

[hard crest]

don't you have a triad to work on this with

[amber furnace]

Ye

I wasn't cheating yo

I was just checking if what me and my mates writing were correct

Y'all helped me so I don't rlly need this channel now

[safe radish]

@amber furnace Has your question been resolved?

Channel closed

Closed by @amber furnace

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.

[hot stone]

Did I set up the problem right

Nope

I did not

Here

[proud tree]

ye this is right

[hot stone]

Yay

I assume this is just multiply top and bottom by sqrt(sinx)

[proud tree]

👍

[hot stone]

Tyyy

.close

[safe radish]

Channel closed

Closed by @hot stone

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.

[timber dock]

?help

[quick tundra]

whats ur doubt

[timber dock]

How to solve integral cos6x-sin5x/sin3x+cos4x

[quick tundra]

idk calc

[round mango]

What have you tried?
-# (also as a general tip for next time it's better to just post your question first, instead of starting with ?help)

[timber dock]

I didnt get the question still. I dont have any Idea to solve it.

[round mango]

Hm. This one is a bit beyond me, I'm not even sure it has a closed-form solution

[quick tundra]

question tuff 😭

[delicate shore]

I think a common trick is to write the denominator as f and try to express the numerator as a linear combination of f and f'

[timber dock]

how?

[delicate shore]

May or may not work for this particular question

Oh, nevermind, the coefficients are inside the sine and cosine

Ignore what I said then

Are you sure this has a closed form?

[timber dock]

idk

<@&286206848099549185>

[vague phoenix]

She is a helper bro

[timber dock]

.

[delicate shore]

Where did this integral arise? Are you looking to evaluate an antiderivative analytically or numerically?

[vague phoenix]

I think you use sin = cos(pi/2 - theta)

To make it uniform on first hand

Do both on numerator and denominator to remove sin

[timber dock]

i saw it in some book

[timber dock]

i didnt get it

[vague phoenix]

Wdym

For example sin3x = cos (pi/2 -3x)

And do the similar method to -sin5x on numerator

[timber dock]

pk. lemme try this

[vague phoenix]

But this is a complex problem, why would teachers give you this if you not master it yet

[timber dock]

i dunno

but what u have told is making problem more lengthy

[vague phoenix]

Then idk what else solve this

[safe radish]

@timber dock Has your question been resolved?

[safe radish]

@timber dock Has your question been resolved?

[timber dock]

<@&286206848099549185>

[timber dock]

.

[main matrix]

,w integral of (cos(6x) - sin(5x))/(sin(3x)+cos(4x))

[flat frigate]

Results provided by WolframAlpha

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

Requested by altanis_

[main matrix]

[main matrix]

Wait use parentheses. Do you mean cos(6x) - (sin(5x)/sin(3x)) + cos(4x) or did you mean this integral

[timber dock]

integral

[main matrix]

Which function did you want to integrate

[main matrix]

This

[main matrix]

Or this

[timber dock]

this

[main matrix]

Good luck

[timber dock]

tq

[timber dock]

thank u very much

.close

[safe radish]

Channel closed

Closed by @timber dock

Use .reopen if this was a mistake.

[split kayak]

Does this yield anything?

[split kayak]

the sin above and below might cancel, idk

[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.

[lilac wedge]

I'm sorry, I'm not too into math, but my thesis project (a robot arm) has a Jacobian matrix used for correction of the arm after it's initial movement, and in our paper we have it as a 3x4 matrix (mapping 3d coordinates xyz to motor commands, 4 motors). All over the internet, I find that Jacobian matrices can be non-square, but one of the major concerns one of the teachers had during the final defense was that a Jacobian matrix can only be square. Apparently he majored in something focusing on it, whereas I am a student who basically got the formula from the internet and have a surface-level understanding of it, so I wasn't able to refute him. I basically just showed him a google search saying they can be not square but he wasn't taking it.

We got by with minor revisions but when we go back for his approval I absolutely know the same thing is gonna come back again, and I really don't know how to explain it to him. Does anyone know how to explain it so I can actually argue back?

[delicate shore]

A Jacobian matrix can be non square

in general, if you have a function from a space with dimension m, to a space with dimension n, then the derivative is the best linear approximation of the function at a point, and linear maps from dim m to dim n is just an n x m matrix

It is square precisely when your original function is between spaces of the same dimension

[lilac wedge]

Maybe it has to do specifically with how we're using it? This is the specific equation we're using, but during the defense he basically paused our presentation to give a lesson on it (and im so sorry again it kind of flew over my head, I wish I took notes), saying that since we're inversing the matrix, the matrix ends up being square (?)

[delicate shore]

If you need the matrix to be invertible then it is necessarily square

however I see the pseudoinverse being mentioned and it makes sense for non-square matrices as well

[peak estuary]

its not like you are inverting J here

so who cares whether J is square

btw fwiw, you should generally rarely invert a matrix and instead solve a linear system instead

tho I suppose maybe for 3x3 it doesnt matter much

[peak estuary]

(computing A^-1 e is the same as solving Ax=e)

[safe radish]

@lilac wedge Has your question been resolved?

Channel closed

Closed by @lilac wedge

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.

[normal bay]

hi, could anyone quickly walk me through how my teacher got her answers for the first 2?

[normal bay]

also, please ping me when you respond

[vague phoenix]

Integral of velocity is displacement , since ask from interval time from 0 to 5 so add domain in integral 0->5

The displacement is similar, but it doesnt have an absolute value since it only find the difference of final destination compare to your start point

[safe radish]

@normal bay Has your question been resolved?

[lean otter]

integral of velocity is displacement

integral of speed can give distance

[normal bay]

can you walk me through it in a bit more detail i think i get it conceptually but im confused at how she got 13

[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.

[quick wraith]

(Challenging) † For an irrational 𝑧 ∈ℝ \ℚ and 𝑥 > 1 define 𝑥^z sup{𝑥𝑟 : 𝑟 ≤𝑧,𝑟 ∈ℚ}, for 𝑥 =1
define 1^𝑧 =1, and for 0 < 𝑥 < 1 define 𝑥^𝑧 inf{𝑥^𝑟 : 𝑟 ≤𝑧,𝑟 ∈ℚ}.

[brave wolf]

what are the assertions of part b

[manic patrol]

I think you might benefit from showing the problem as an image, OP.

[quick wraith]

None

I deleted that bit

sorry

[brave wolf]

so what is there to prove?

[quick wraith]

okay

[manic patrol]

can you show part b) as well? it's connected.

and please don't highlight the text.

[quick wraith]

I already proved a and b

[brave wolf]

And have you tried anything?

Do you know what it is asking you to do?

[quick wraith]

no

(d)

(challenging) ✝️

That one

[brave wolf]

So basically they extended the definition of x^z to irrationals as well. Do you understand their definition?

[quick wraith]

The definition of irrationals? Sure

[brave wolf]

no i mean their definition of x^z for irrational z

do you roughly understand what it does and why it works

[quick wraith]

No, maybe we could start by proving c first

let me try

I will ping u back

@brave wolf

Okay, that problem seemed to be unrelated with irrationals

but I proved it anyway

[brave wolf]

Damn that was quick

but yeah it is pretty much unrelated

I'll try to explain the defn of x^z for irrationals then

[quick wraith]

thank you

[brave wolf]

or would you like to check ur proof of c first?

or can we go straight to d

[quick wraith]

also, it told me not to use tools other than the supremum definition I was given

as you can see there

[quick wraith]

It is fine. c is the same stuff as the previous problems

the interesting one is d

[brave wolf]

So this is their definition. Take e.g. r = sqrt(2), then
{x^r : r <= z} contains e.g. x^1, x^1.4, x^1.41, x^1.414, x^(239/169)...
Taking supremum of that then results in x^sqrt(2). This definition ensures that x^sqrt(2) is close to x^(rational (lower) approximation of sqrt(2))

oh and important part of why this works is that if i take the sequence
x^1, x^1.4, x^1.41, x^1.414, ...
with increasing rational exponents, the sequence itself is increasing for x > 1

thats why sup can be used to "find" the limit - x^sqrt(2)

if x < 1, we have to use inf, because it'd be decreasing

[quick wraith]

isn't the supremum just x^z?

[brave wolf]

no not really

it's the set of all the x^r, not r themselves

[quick wraith]

x^z, I mean

I am sure it is

[brave wolf]

if x was e.g. 2 and z was pi, the set would contain e.g.

{2^3, 2^3.1, 2^3.14, 2^3.141, 2^3.1415...

[quick wraith]

Yeah

[brave wolf]

so the least upper bound if this set wouldnt be just pi

it would be 2^pi

2^3 is in that set, that's 8. So obviously z = pi cant be the least upper bound

the least upper bound will surely be greater than 2^3, greater than 2^3.141, ...

[quick wraith]

okay

I have one last question

what guarantees {x^r : r < pi }to have elements like x^3, x^3.1

etc

all matching the decimals of pi respectively

perfectly

[brave wolf]

3.1 = 31/10, 31/10 is a rational number < pi, so if you take r = 31/10, the corresponding element of that set is x^r = 2^3.1

it contains loads of other stuff too

it contains
2^(-1/2) too

becuase -1/2 < pi

the notation A = {x^r : r < z, r in Q} can be read as
"The set A contains all elements of the form x^r, where r is a rational < z"

so in our particular case where x = 2, z=pi, it would contain e.g.
2^-1000, because -1000 is a rational < pi
2^2, because 2 is a rational < pi
2^3.14159, because 3.14159 is a rational < pi
2^(-1/2), because (-1/2) is a rational < pi
...

oh actually their defn uses <=, but it makes no difference, since no rational can equal to an irrational

[quick wraith]

well

Thanks

.close

[safe radish]

Channel closed

Closed by @quick wraith

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.

[hearty fox]

help me compare bk and ak

help me guys

[safe radish]

@hearty fox Has your question been resolved?

[hearty fox]

omg

pls help me

im stuck

[safe radish]

@hearty fox Has your question been resolved?

[quick tundra]

Holy geometry

[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.

[strong nexus]

In a game of billiards, the white ball is first played against the cushion at an angle of α = 50°. It then simultaneously hits two balls (all three balls are of the same size and weight) that are touching each other, and whose connecting line is perpendicular to the direction of travel of the white ball.

[strong nexus]

Using the conservation of momentum and energy, show that the angle of incidence is equal to the angle of reflection at the radiation band and that the magnitude of the momentum does not change. What momentum and energy does the band absorb?

Any ideas?

[gaunt belfry]

isn't this more physics problem?