help-0

[torn isle]

,w dot product [sin t, 3 sin t, sin²t], [cos t, 3 cos t, 2 sin t cos t]

[ocean seal]

Results provided by WolframAlpha

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

Requested by XZR1005#0050

[torn isle]

What if we try in this order?

I don’t know how to type the ^2 here

[alpine sable]

,w int 2 sin³t*cost + 10 sint cos t dt, t = 0..2pi

[ocean seal]

Results provided by WolframAlpha

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

Requested by baetriarchy#6631

[alpine sable]

LOL

[torn isle]

Yea, it’s still 0

I tried manually😂

[alpine sable]

i think the answer is just wrong (?)

[torn isle]

Maybe

[alpine sable]

it happens

[torn isle]

Okay

.close

[lone heart]

Channel closed

Closed by @torn isle

Use .reopen if this was a mistake.

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sage herald]

i am, i dont even know

[alpine sable]

substitute x=asecθ

[sage herald]

lemme try that out

okok

i get it now

[alpine sable]

you can also keep some frequently observed trig subs in mind to help you solve questions

[sage herald]

tysm @alpine sable

.close

[lone heart]

Channel closed

Closed by @sage herald

Use .reopen if this was a mistake.

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rugged karma]

Need help with a lim exercise,
Can't post full picture cause it's not English but I will write all the information given:
Let f: R->R for which the limit when x->2 of (f(x)-1)/(x-2) = 2

Calculate the following lim:

[vale wigeon]

,rccw

[rugged karma]

What I have done so far:
Let g(x) = (f(x)-1)/(x-2) then you get that the lim of f(x) when x->2 is 1, finding the area of the abs values we get that the first absolute value is negative near 2 and the second is positive

The answer is given as -14 (which may be wrong, there are wrong answers in some exercises as it's not an official book) but I keep getting -12

[last ether]

Are those 4th, 3rs and 3rd derivatives?

[rugged karma]

No they are powers, sorry for not mentioning that

[last ether]

Maybe Ann can solve this lol

I might need paper for this and I'm currently at a dining table waiting for my sister to stop burning cookies

Which means I'm nowhere near scratch paper nor a pen

[rugged karma]

Hahaha okay no worries thanks anyway

[lone heart]

@rugged karma Has your question been resolved?

[lone heart]

@rugged karma Has your question been resolved?

[rugged karma]

.close

[lone heart]

Channel closed

Closed by @rugged karma

Use .reopen if this was a mistake.

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

Hi

[alpine sable]

I need help with triangle

I know that abc is 120° and ab is 8✓2 I need to find other side

[frigid path]

is that all the info you have?

[alpine sable]

Ye

[crisp pine]

I dont think that is enough information to define a unique triangle

[alpine sable]

Wait

Ok then

It's like

I have

Cons

Cone

And I know H

Wich is 8✓2

I wanna find base radius

And only thing I know is this

We know this

Its 120° one

[crisp pine]

Uhh do you know its area of something?

[alpine sable]

No

[crisp pine]

Oh wait are you trying to find AC

[alpine sable]

No

I'm tryna find

Cones base radius

[crisp pine]

Im not quite sure what you mean by the cones base radius sorry

[alpine sable]

Like

Idk many mathematical English terms sorry

Like cones has base as circle right?

[crisp pine]

Oh no worries

[alpine sable]

So I have to find that circles radius

[crisp pine]

Yeah

[alpine sable]

Do u get it?

[crisp pine]

Its just I can't see the cone you are talking about from the diagram

[alpine sable]

Wait

[crisp pine]

Ohhh

Is it a 3D drawing

Ok yeah I can help then

[alpine sable]

H is 8✓2

[crisp pine]

Yeah great

[alpine sable]

U get it now?

[crisp pine]

yes thank you 🙂

[alpine sable]

Oki

[crisp pine]

ok so in that diagram

the angle between H and R is 90 right?

[alpine sable]

No

How?

Between h and l is 120

Like top

Or no wait I'm extra confused

[crisp pine]

I think the angle between H and L is going to be 60, half of that

I was talking about H and the radius R

[alpine sable]

Why can u explain?

[crisp pine]

Well the whole angle at the top of the cone is 120

And then you are splitting it down the middle with the line H

[alpine sable]

Oh oh I get it now

Ty

So then what do we do?

[crisp pine]

Sure no worries

So are you happy with the angle between H and R being 90

[alpine sable]

Ye

Lol

[crisp pine]

Ok, so its a right angle triangle

And you have an angle(60), and a side(H)

Do you know trigonometry

[alpine sable]

A bit

Not that much

[crisp pine]

Ok no worries

[alpine sable]

But I can learn

[crisp pine]

Well if this question has been given by a teacher

Then I would expect it to be solvable using skills u have learnt

[alpine sable]

Nah no teacher involved

[crisp pine]

Oh cool okay

[alpine sable]

I'm just tryna learn by myself

[crisp pine]

Thats awesome

Well the last part of this Q uses simple trigonometry

[alpine sable]

Like 8✓2/sin60° ?

Wait no

I'm wrong

R/sin60°

[crisp pine]

You would need to use tan for this one

[alpine sable]

Oh tan

[crisp pine]

Arent we trying to find R?

https://www.youtube.com/watch?v=Jsiy4TxgIME

(Idk how much trig u know but khan academy is great for teaching maths to you in general if u are trying to learn yourself)

[alpine sable]

Ye ty I'm watching it en

Rn

[crisp pine]

Ok cool

[alpine sable]

Just let's finish this

First ok?

Imma watch it later

[crisp pine]

Ok yeah sure

well basically R is 8root2 * tan(60)

It will make more sense why when u watch the vid

[alpine sable]

I know trygonometry as in algebra

So im not too confused

[crisp pine]

Ok cool yeah

[alpine sable]

Umh I got 3.6

But the answer is 4

[crisp pine]

One sec

Ok

You are in radians

While the angle is degress

degrees

either way I didnt get 4

Ohh wait

we dont have H, we have L, my bad

I kind forgot the question

[alpine sable]

It's ok

So H is 8✓2

And we have to find radius

[crisp pine]

Wait

[alpine sable]

And as u said angle is 60° between h and L

[crisp pine]

isnt L 8 root 2

[alpine sable]

No

Height is 8✓2

[crisp pine]

DIdnt u say AB is 8 root 2

[alpine sable]

I said AB as in height

Like ABC triangle

[crisp pine]

Ah ok

then I stick by it being 8 root 2 * tan(6)

[alpine sable]

Hm but answer

Isn't right

[crisp pine]

Yeah that is odd, I'm not sure then

[alpine sable]

Can we find radius here?

Like sides

Let's say it's circle

Ah nah nvm I'm wrong

It's S formula

[frigid path]

I'm not sure that's right

[alpine sable]

Oh hi

Can u help me?

He couldnt I think

<@&286206848099549185>

[frigid path]

Yeah, give me a second

[alpine sable]

Ok

I can explain again if u want

[whole garden]

What do you need to find in this question

And what grade/year material is this so I can possibly help you even more

[alpine sable]

Idk

And I have to find radius

Of base circle in cone

[whole garden]

so R?

[alpine sable]

Ye

[alpine sable]

Here

We know this

And that Height is 8✓w

2

[frigid path]

Hey, uhh what's the answer again?

[alpine sable]

8✓2

[frigid path]

If you know it

[alpine sable]

Answer is 4 but idk how to get it

[frigid path]

So yeah, bear with me

[whole garden]

Alright so

[alpine sable]

Ok

[whole garden]

I believe you have to use the pythagorean theorem

[alpine sable]

I think so too but idk any other sides

[whole garden]

What sides do you have

[alpine sable]

I just know one side

8✓2

It's height of cone

[frigid path]

You have to find the length of the circular arc, that will be the length of the base circle

Therefore, by having 2 radius, you'll be able to express them by one radius (sorry for my english)

And then, you'll be able to use the
Pythagorean theorem

[alpine sable]

How to find circular arc?

Lenght

[frigid path]

have u ever seen this formula?

or something similar

[alpine sable]

Yes

[frigid path]

so yeah, that's what you need

[alpine sable]

That's just 2pR/3

What do I get from this?

[frigid path]

yeah, so that is the length of the base circle

now, we know that the length of the circle is calculated with what formula?

[alpine sable]

2πr`2?

[frigid path]

well, it's 2πr

[alpine sable]

Oh no `2

[frigid path]

yeah

[alpine sable]

Ok

[frigid path]

so yeah, since we know that those expressions are equal

2πR/3 = 2πr

[alpine sable]

Ok

[frigid path]

now, you can express either R or r

bc you need to find the r, you can express the "r"

and there comes Pythagorean theorem

[alpine sable]

I'm confused ngl

Sorry in little sleepy

[frigid path]

okay so

[frigid path]

you must get something like r = 1/3R

or R = 3r

R is BC, and r is AC

[alpine sable]

Ye ik that

[frigid path]

so yeah, and BA is 8✓2

[alpine sable]

Do I do Pythagoras now?

With 8✓2 and 3r?

[frigid path]

Well, what do you think?

[alpine sable]

I don't think so

[frigid path]

Well, don't you know all the sides now?

I think that you can go with Pythagoras now

[alpine sable]

Im mas confused bro how can I get answer 4 with 8✓2 and 3r

[frigid path]

well, look

BC=R, R=3r, so BC=3r

and AC=r

[alpine sable]

Bro I knew that ac is r whole gime

Cuz it's raidus mate

[frigid path]

Mate, what else do u need

[alpine sable]

So bc is 3 radius

[frigid path]

yeah

[alpine sable]

How do I find that radius is 4?

I have to find radius and in answers it says that it's 4

[frigid path]

Well, since we know that ABC is a right triangle

we can use the Pythagorean theorem

[alpine sable]

Ok do it for me and show me pls

[frigid path]

it seems like you're tired, but you must do it yourself

how else are you gonna learn?

[alpine sable]

Bro just do it

I'm still gonna learn

I'm gonna solve other similar problema

[frigid path]

AB=8✓2, BC=3r, AC=r

you have everything you need

[alpine sable]

😭😭😭

No I don't bro

Just finish it and then explain

Pls

[frigid path]

do you know Pythagorean theorem?

[alpine sable]

Yes

[frigid path]

apply it!

[alpine sable]

Bro what

Pythagoras is

a'2+b'2

And

Fucking (8✓2)'2+(3r)'2 does not work

Can't solve it

[frigid path]

is that the whole formula?

[alpine sable]

=c'2

[frigid path]

AB=8✓2, BC=3r, AC=r

[frigid path]

are you sure those are the right sides?

[alpine sable]

What

[frigid path]

yes?

what seems to be the problem here?

[alpine sable]

Idk what u mean bro

Just explain

[frigid path]

so this is Pythagorean theorem

right?

[alpine sable]

Yes

[frigid path]

so, a=AB=8✓2, c=BC=3r, b=AC=r

[alpine sable]

Ye

If I just do r'2 it still does not work

[frigid path]

(8✓2)'2 + r'2 = (3r)'2

right?

[alpine sable]

Yes

[frigid path]

and what seems to be the problem now?

[alpine sable]

I can solve that

But

Answers not gonna be R

There's gonna be 2 answers even

Idk why u making me do Pythagoras I told u answer is 4 we can't get 4 like this

[frigid path]

solve it, please

[frigid path]

you are completely right

[alpine sable]

It's -+ 4'✓2

By 4 I mean like in root

Idk how to say in english

[frigid path]

are you sure about that?

[alpine sable]

Ye

[frigid path]

well, that's not the answer

[alpine sable]

What

[frigid path]

did you solve this equation?

[alpine sable]

Yes I did

I'm sure it's right answer

I checked it on calculator

[frigid path]

https://www.wolframalpha.com/input?i2d=true&i=Power[8Sqrt[2]%2C2]%2BPower[r%2C2]%3DPower[3r%2C2]

Are you sure that you're right?

[alpine sable]

Bro what

Wtf

How

Where did 128 come from

What

[frigid path]

what is (8✓2)^2?

[alpine sable]

Oh my gos

God

[frigid path]

yep

[alpine sable]

Ur worst teacher ever tbh

[frigid path]

omg thanks "<3"

[alpine sable]

There must be some other way to solve this

What is this

[alpine sable]

U welcome

[frigid path]

well, that must be the way

[alpine sable]

Damn

Ok thank you anyway

Good luck

[frigid path]

good luck!!

[alpine sable]

❤️❤️

.close

[lone heart]

Channel closed

Closed by @warped mirage

Use .reopen if this was a mistake.

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

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[neon hemlock]

is it possible to get the circumference of a circle without using 2πr

[dense sleet]

Why do you ask?

[gilded quarry]

if you have the radius

and the area

you can substitute

one into the other

and not have to use pi

[dense sleet]

The question seems like you have a problem that asks for circumference but you dont have r so you ask if there is any other way.

So i suggest if there is a proper problem that you are trying to solve send it instead of asking a part of it

[neon hemlock]

no im saying if theres a way to find circumference without pi

[dense sleet]

No

Pi is the ratio of circumference to diameter

[neon hemlock]

yeah i know that

just wanted to know if there was a way to find c without pi

[dense sleet]

What is c?

[neon hemlock]

circumference, just cba typing it out

[weary wyvern]

literally 2πr is the circumference

do you want another way to write π?

[dense sleet]

Where theres a circle theres a pi 🥧

[neon hemlock]

yes i know that

[weary wyvern]

you need to precise about what you want

[neon hemlock]

i dont know how my question can be more precise than this

[dense sleet]

No

I dont see how there would be

[weary wyvern]

circumference = $\ 2r\sqrt{6\cdot \sum_{n=1}^\infty \frac{1}{n^2}}$

[ocean seal]

giannis_money

[neon hemlock]

what's n

[weary wyvern]

just writing pi another way

[weary wyvern]

the index in the sum

[neon hemlock]

ohh

thanks

.close

[lone heart]

Channel closed

Closed by @neon hemlock

Use .reopen if this was a mistake.

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

[dense sleet]

:\

[weary wyvern]

bruh moment

[neon hemlock]

what

[dense sleet]

Couldve just wrote $$\Zeta (2)$$

[weary wyvern]

sure

[ocean seal]

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

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

For a

I got 551.25

I'm not sure if that's right or not

or what the question means

on the right

.close

[lone heart]

Channel closed

Closed by @tropic hinge

Use .reopen if this was a mistake.

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

<@&268886789983436800> underaged ppl

[night geyser]

dont "joke" in the help channels.

.close

[lone heart]

Channel closed

Closed by @night geyser

Use .reopen if this was a mistake.

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

.close

[lone heart]

Channel closed

Closed by @tropic hinge

Use .reopen if this was a mistake.

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

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[magic plank]

Help

[alpine sable]

what have you tried?

[lone heart]

@magic plank Has your question been resolved?

[magic plank]

Nothing ☹️

<@&286206848099549185>

[alpine sable]

have you at least done the base case?

[magic plank]

I know no calculus

But I needed this question to be solved

[alpine sable]

you don't need calculus here

[magic plank]

i'm asking u for help not to chat with u

If u know the answer say it, and i would be thankful

[alpine sable]

#❓how-to-get-help

if you wanted a straight up answer, you could have just googled it

[magic plank]

So, u don't know the answer?

<@&286206848099549185>

[alpine sable]

i do know the answer. but i would prefer to help you understand the answer rather than just copying down what I type and handing it in

[magic plank]

I'm not "handing it in"

anyways explain to me the question first

then explain ur answer

if u have time

[lilac carbon]

Have you tried using induction?

[magic plank]

I don't even know what that means

Guys just explain how u solved it

[lilac carbon]

In which case, may I ask how you came to the problem in the first case?

[magic plank]

I'm not an expert in math or anything I don't even care just explain the answer I'm very curious

[lilac carbon]

Search up ‘principal of induction’ on brilliant

Will do a better job explaining than we can

[magic plank]

Lmao ikr, well it's just a problem I saw and wanted to know the answer to because it looks simple but I couldn't solve it

[magic plank]

So it can be solved using induction ?

[lilac carbon]

Yes

It does say in the question ‘use mathematical induction’

It’s a very important tool

[magic plank]

Yes but ... I don't even know what that means, I'm so lazy to know tho

I'll do it tomorrow

[lone heart]

@magic plank Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fathom sequoia]

WHY THE FUCK DID THEY EXCLUSE 27 HERE

[abstract fractal]

Times greater than 24 don't matter, because the time resets after 24 hours. 24 hours after 12pm, you get 12pm again

So 27 hours later is equivalent to 27 - 24 = 3 hours later, assuming the day doesn't matter

[fathom sequoia]

Ok

.close

[lone heart]

Channel closed

Closed by @fathom sequoia

Use .reopen if this was a mistake.

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

why is desmos giving 0,0 as a point?

[alpine sable]

doesn't the restriction x=/=0 carry over when taking f(g(x))

[lime bobcat]

Yes, but it is a computer software.

It's treating the functions as algebraic fractions

[alpine sable]

so would the correct domain be (-inf,-4)U(-4,0)U(0,inf)?

[lime bobcat]

So composing

$\frac{5}{\frac{4}{x}+1}=\frac{5}{\frac{4+x}{x}}=\frac{5x}{4+x}\in\mathbb{R}(x)$

[ocean seal]

Categorist

[lime bobcat]

Treating them as algebraic fractions in R(x)

But as real functions, the domain is as you say

[alpine sable]

so it drops the restriction in R(x)?

[lime bobcat]

Yes, but because they're algebraic objetcs in principle, not function expressions

[alpine sable]

ah k

[lime bobcat]

It's like $\frac{x}{x}=1$ this is true in R(x) but it is false as the quotient of the function f:R→R, f(x)=x with itself

[ocean seal]

Categorist

[lime bobcat]

x/x is not defined in x=0

it is an evitable nondefined hole

[alpine sable]

k got it

[lime bobcat]

Yes 👏

[alpine sable]

ty

.close

[lone heart]

Channel closed

Closed by @terse urchin

Use .reopen if this was a mistake.

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fierce prairie]

explain?

[wary stream]

Don't give out answers, not the purpose of the server

?

[wary stream]

I could potentially be wrong, but the area of a quadrilateral like that is $$\frac{1}{2}d_{1}d_{2}$$

[ocean seal]

dldh06

[fierce prairie]

okay so 30?

thanks

.close

[lone heart]

Channel closed

Closed by @fierce prairie

Use .reopen if this was a mistake.

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

[wary stream]

I said potentially wrong. But that's the area of a quadrilateral from the research I did

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[mighty flower]

help

[mighty flower]

why cant y in y=mx+b be negative

[tacit arch]

Who says it can't

[mighty flower]

-y=mx+b

why cant we have ot written like this

[tacit arch]

Who says you can't

[mighty flower]

you can?

I did a question where the answer was -y=-5

and my teaecher said I was wrong

and that it was y=5

[tacit arch]

If the question is "solve for y" then yes you were wrong

But if the question was "solve for -y" then you'd be right

[mighty flower]

I am still kinda lost

[median oar]

Solve for y means y on 1 side

But if the question asked to solve for x that means x on 1 side

Now if it asks to solve for -y that means -y on 1 side

[median oar]

3y + 2x = 5
3y = 5 - 2x
y = 5/3 - (2/3)x

[median oar]

3y + 2x = 5
2x = 5 - 3y
x = 5/2 - (3/2)y

[median oar]

3y + 2x = 5
3y = 5 - 2x
y = 5/3 - (2/3)x
-y = (2/3)x - 5/3

[mighty flower]

wont that be

y=-2/3x+5/3

[median oar]

That’s the same thing yes

All of the above equations are all the same thing

[mighty flower]

oh so your basicaly simplyfing it more

[median oar]

Just with different things as the subject

[median oar]

Simplifying it in the sense for y

If you’re looking for -y

Then of course you want -y to be on 1 side

[mighty flower]

yea cuz if its positive you cant simplyfy it more

[median oar]

No you’re simplifying it because the questions asks to solve for y

[mighty flower]

yea my teacher was prob looking for just y

[median oar]

Not for -y

[mighty flower]

oh

so it can be negative

[median oar]

Don’t use this term

[mighty flower]

wait but is b is also negative than y intercept is positive

[mighty flower]

got it thanks

[ocean mulch]

wat

[mighty flower]

I needede to know if y in y=mx+b can be negative

[median oar]

Yes

[ocean mulch]

gotcha

[median oar]

y ∈ ℝ

[mighty flower]

thanks guys

.close

[lone heart]

Channel closed

Closed by @mighty flower

Use .reopen if this was a mistake.

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[abstract hollow]

Hello Im just stuck on inputting a given restriction with my answer. Since my notes didnt cover putting the answer using a given restriction

[tacit arch]

Try using shift identities

Or co-function identities

[median oar]

Try drawing a circle

[abstract hollow]

alright

cause i already rounded my answer to the nearest tenth

[median oar]

Kinda like this

I don’t have paper on me atm but this one is for sin θ = -1/2

You can kinda see the angles that would fit in your restrictions

[abstract hollow]

ohhhh

i see but how would i know what angles would fit my restrictions?

cause mainly my answer was Θ=1.8+360

[median oar]

180 deg < θ < 270 deg means it’s in that bottom left quadrant

So that’s cos 1/4 + 180 deg

[abstract hollow]

ohh i see

it makes sense now since i thought i would just copy and paste it in from the original equation

thanks

.close

[lone heart]

Channel closed

Closed by @abstract hollow

Use .reopen if this was a mistake.

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sharp moth]

I'm using the grouping method of factoring and I am having trouble understanding how to interpret these types of demonstrations

[sharp moth]

I can do the factoring itself but when they introduce the letters instead of numbers it confuses me

[wary stream]

It's just combining like terms

[median oar]

Think of the numbers just as a weird symbols like letters

[sharp moth]

Alright I think I'm starting to get this

Thank you

.close

[lone heart]

Channel closed

Closed by @sharp moth

Use .reopen if this was a mistake.

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

[sharp moth]

.reopen

[lone heart]

✅

[sharp moth]

What is this referring to?

Are a b and c coefficents

[wary stream]

The general form is $ax^2 + bx + c$

[ocean seal]

dldh06

[wary stream]

Yes

So you can compare the bottom expression with the general form

[sharp moth]

sorry took me a minute to get that one too thank you

.close

[lone heart]

Channel closed

Closed by @sharp moth

Use .reopen if this was a mistake.

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

[sharp moth]

.reopen

[lone heart]

✅

[sharp moth]

How did they arrive to the conclusion that BC and AD are the two integers they need

I am trying to learn how to connect mathematical proofs to words

so I can read the instructions better

[median oar]

I can’t tell which way this proof is going lol

[sharp moth]

Okay so should I send more

[median oar]

Can you send like the full thing

[wary stream]

Because (BC)(AD) = (AC)(BD) is applying the commutative property

[sharp moth]

So that makes BC and AD the integers they need?

[wary stream]

Yes

[sharp moth]

I'm understanding that a * c and m * n play a role but I'm not sure exactly what their significance is.

Their both equal to each other which somehow makes BC and AD the numbers were looking for? I guess I really am confused by what it means to be "looking" for those terms.

Are the terms that we're looking for in the form of (x -1)

or are they more like 9x or 10

[lone heart]

@sharp moth Has your question been resolved?

Channel closed

Closed by @sharp moth

Use .reopen if this was a mistake.

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[small swift]

@digital shard sorry it isn't letting me message the other channel

https://gyazo.com/365f18711b5b6aed7db97cee8e4e6581

[small swift]

How did you come to the answer you got?

[wary stream]

What's the guess for yp of the function t?

[small swift]

Oh hm.. It was in the other channel

Do you think you could take me through the process of finding it?

Very interested in learning how to do this systematically

So I can solve other probklems

[wary stream]

https://tutorial.math.lamar.edu/classes/de/undeterminedcoefficients.aspx

This is a good resource on yp

[lone heart]

@small swift Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[keen girder]

Question: why is the following incorrect?

[keen girder]

I dont understand why the red answer is incorrect

[tacit arch]

When you shift everything in binary, you change the value

2=0010 to 0100=4

[keen girder]

how would i show n+1 then

[tacit arch]

Flip bits

[keen girder]

but how would you show it abstractly without knowing n

for some arbitrary n

would be b0=1 if n is odd and b1=1 if n is even

[tacit arch]

Same way as in base ten

Linearly from b0 to b1 ...

[lone heart]

@keen girder Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[flat ore]

if I write -1^0.5 it would be -1 right? does exponentiation have higher precedence than unary operators?

[vale wigeon]

it has a higher precedence than unary minus

[flat ore]

alright I see

[vale wigeon]

which is essentially the only unary operator that attaches on the left

[flat ore]

so if I wanted i, I would have to write (-1)^0.5

[vale wigeon]

guess so.

[flat ore]

thanks

.close

[lone heart]

Channel closed

Closed by @flat ore

Use .reopen if this was a mistake.

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vale wigeon]

why didn't you negate (a-ε, a+ε) ⊆ A?

[molten pivot]

Looks like you're missing a "not" somewhere

Yeah

Yeah

[vale wigeon]

"negation" means logical negation

nothing to do with swapping plus or minus in this case

[molten pivot]

Negation distributes over the entire logical statement:
1: for all a in A
2. ...is a subset of A
not(1 and 2) = not(1) and not(2)
So then the negation of 1 is "there exists some a in A"
And the negation of 2 is "is not a subset of A"

There's probably a more rigorous way to write that but whatever

Yeah

The empty set doesn't have any elements so asserting that it has a subset with elements is nonsense

[vale wigeon]

no actually

the empty set is open

any statement of the form "for all a ∈ ∅, ___" is true

it's called vacuous truth

[molten pivot]

But are a+e and a-e in A

[vale wigeon]

okay so

let A = ∅

give me an element of A and i'll give you an epsilon such that (a-ε, a+ε) ⊆ A. @molten pivot

0 is not a member of the empty set.

{} is not a member of the empty set.

yes, exactly.

so my response is always going to be that the thing you gave me isn't a member of A
and so, despite never giving you any epsilons, i haven't broken my promise

this is called vacuous truth

http://wikipedia.org/wiki/Vacuous_truth

not really.

yes

which means that the empty set is open

because (O) is true for it

as my analysis teacher once said, "Elements of the empty set have every property you could possibly think of. It's just existence that they struggle with."

yes

or alternatively if it makes you feel more at peace

you can demonstrate that the negation, which starts with "there exists a ∈ ∅ such that ...", is false no matter what follows this.

do you agree that if the negation of a statement is false, then the original statement is true?

yes but that's the exact opposite of what i asked you to agree/disagree with + you didnt really answer my question

no

would prefer not to have to pore through vaguely suicidal gifs

but no, the a in the first sentence of the problem statement and the a in (O) are not related at all.

in the first case a is the left endpoint of the interval (a,b). in the second it's an arbitrary point in the set A.

this is not something to be overthought. i promise.

no you're overthinking it now

ok so like let's back up a bit

do you know what an interval is and do you know how interval notation works

yes or no

so no to both

an interval is the set of all points on the real number line between two specified points called the endpoints

one distinguishes between open and closed intervals based on whether the endpoints of the interval are included themselves or not.

closed intervals include both their endpoints while open intervals include neither.

one may speak also of half-open intervals, which include one endpoint but not the other

as far as notation goes,

open intervals are denoted with (round brackets) while closed intervals are denoted with [square brackets]

(half-open intervals are denoted with a round and a square bracket according to which endpoint is the one included)

the interval (0, 1) is an open interval, consisting of all points strictly between 0 and 1

paraphrasing their set-builder notation:

$(0,1) = {x \in \bR : 0 < x < 1 }$.

[ocean seal]

Ann

[vale wigeon]

well this is the definition, so

you wish to show that, for every x in (0,1), one can find epsilon such that (x-ε, x+ε) is fully contained in (0, 1).

but 0 ∉ (0,1).

for every x in (0,1)

0.00000000001 is in (0,1).

not to mention that this:

0- any real number
will be less than 0
is false as stated (though i do get your point)

this does not make for a proof

all you've done is proved that (O) holds when we look at the element 10^-10. (there is a fancier way to say what exactly it is that you proved but i am not interested in taking this detour)

no we haven't.

my whole point was that we haven't.

just picking one specific value of x doesnt do shit

have you

ever

proved

a

FORALL

statement

before

right

well then you should know that, unless the set you're quantifying over is FINITE (which in this case, being an interval, it ISN'T), you CANNOT prove a statement that begins with "for all" by examples alone.

instead you should take an ARBITRARY x in (0,1) and show that there exists an epsilon (which you are allowed to express IN TERMS OF x) such that (x-ε, x+ε) is contained in (0, 1).

you are wrong

i can show you an example of this logic breaking down

[molten pivot]

Not to interrupt but if you need another way to look at it you could consider the statement that "there is no minimal element of A"

[sly mantle]

.01 is a specific value that x may be

[storm tusk]

Read arbitrary as an unspecific value

[sly mantle]

arbitrary means x may take any value in (0,1)

we must show smth true for each such x

no, .01 is a specific value while x is an arbitrary one

maybe theres issue in comprehending what (0,1) means?

[vale wigeon]

this is like trying to prove that all americans have $1,000,000 in their bank account by pointing at one particular joe smith who does

[sly mantle]

(0,1) is not a number

its the set of reals between 0 & 1, exclusive

this is how (0,1) is defined

it includes numbers like 0.1, 0.2, 0.5678, 0.999

for any value in this set, we must show theres a corresponding epsilon

showing it for only one value, 0.1, isnt enough

[vale wigeon]

.

[sly mantle]

for any value in this set, we must show theres a corresponding epsilon
maybe it helps to think of “any” as “every”

these usually have the same meaning

so ill reword it

for EVERY value in this set, we must show theres a corresponding epsilon

not all reals

[vale wigeon]

there are as many of them as there are reals, as it happens

[sly mantle]

just the ones between 0 & 1

[vale wigeon]

not that it matters for us

it's insane if all you know is proofs by example.

but the point is

there's no need for proofs by example

perhaps we could leave this problem for the time being and look at another problem to help rectify this conceptual gap you have?

namely, that of proving a "for all" statement that quantifies over an infinite set

[sly mantle]

heres another “for all” statement

you can try proving it or disproving it

[vale wigeon]

is it gonna be something number-theoretic

[sly mantle]

eh a bit easy

[vale wigeon]

i was gonna suggest some parity problem now

to get our feet wet if anything

[sly mantle]

for every integer n there exists an integer m such that m>n

yes

[vale wigeon]

i was talking to rokabe there

[sly mantle]

for every integer n there exists an integer m such that m>n
@obsidian kayak is this true? prove it if yes, find a counterexample if no

i dont follow that reasoning

[vale wigeon]

there is a kernel of truth in this word salad.

so we can always come up with an integer
thats bigger
by adding 1

given any integer n, the integer n+1 is bigger than n.

yes, exactly.

it does not

not directly

[sly mantle]

forgot to say im having breakfast so ann can take over

[vale wigeon]

idk if i can continue this

been getting me exhausted

...

are you suicidal right now?

ARE YOU ABOUT TO COMMIT SUICIDE OR NOT

ANSWER ME THIS IN FULL SERIOUSNESS. THIS IS A SERIOUS MATTER.

WHAT DO YOU MEAN, "PERHAPS"

ARE YOU OR ARE YOU NOT

is this all a joke on your part?

you're drunk and high and trying to do math?

[sly mantle]

dammit

if ur joking this is ur last chance to stop

[vale wigeon]

🔇 ?

[sly mantle]

if ur not then theres not much we can do to help, pls seek professional help any way u can

and u should not be here

ok

[vale wigeon]

you are being inconsistent and changing your story on the go.

[sly mantle]

pls see what i said, get professional help if needed, theres not much we can do

.close

[lone heart]

Channel closed

Closed by @sly mantle

Use .reopen if this was a mistake.

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

[sly mantle]

u did ur best

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[half dagger]

Need help with this question

[languid bolt]

hello

still here?

[half dagger]

Yo

[languid bolt]

ok so

i have 2 solutions for this

that has the same result

wait.. brb battery at 3%

[half dagger]

Alright lol

[languid bolt]

ok im back

ok i got no clue

[half dagger]

Ok rip

[languid bolt]

i think there is 2 tbh

rests

and tress

cuz like... scrambles like
setrs is not a word

[half dagger]

Oh i think your misinterpreting the question. It’s actually about perms and combs i should have made that clearer my bad….

[languid bolt]

oh ok

[alpine sable]

Still technically 2 soln. One where we consider each S to be unique and one where we account for repetition of S

[half dagger]

Yea my thought process is that because it is a six letter word and we have 5 letters to choose to make a word that means the possible outcomes are 2 “s” words and 3 “s” words

[tawny schooner]

Absolutely right

[half dagger]

Could you elaborate on the 3C2? I’m not really understanding that part

[tawny schooner]

When we select 3S words, we need to have 2 letters from T,R,E

[half dagger]

Ooooo i understand now

[tawny schooner]

So we need to find number of ways of selecting 2 letters from those 3 letters, so 3C2

[half dagger]

Alright

Thanks a lot for the help i appreciate it

.close

[lone heart]

Channel closed

Closed by @half dagger

Use .reopen if this was a mistake.

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

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[karmic vortex]

so i got y=-2sin(x-pi)+1 but if it’s right

[karmic vortex]

i cant figure out how to get what’s in the parentheses

[languid bolt]

it's not right

[karmic vortex]

what part is wrong?

[languid bolt]

can i zoom in discord pictures?

[karmic vortex]

yes

[languid bolt]

nvm ima just download the image

brb ima just solve it first

[karmic vortex]

ok

@languid bolt i got another possible answer

[languid bolt]

oh wait i forgot i was supposed to solve this

[karmic vortex]

LMFAO

[languid bolt]

ok so

what's your answer?

[karmic vortex]

y=3sin(pi/6(x+1))

??

is that right? or at least closer?

[languid bolt]

closer but no

ok so

[balmy warren]

the 3 is correct

[languid bolt]

yes

[balmy warren]

inside the sin function is not

[languid bolt]

3 correct

[karmic vortex]

oh

[languid bolt]

ok so

$$y = A sin (B (x - D)) + C$$

[ocean seal]

MarveI

[karmic vortex]

my desmos isn’t showing the pi numbers

[languid bolt]

step: pi

[karmic vortex]

oh ok

[languid bolt]

ok so A is 3

[karmic vortex]

yes

[balmy warren]

period of wave is 2pi / B

[languid bolt]

^^

[balmy warren]

phase shift is D/B

[karmic vortex]

B=12?

[languid bolt]

C is the center

[languid bolt]

no

[karmic vortex]

i thought there was no C

[languid bolt]

yeah

C = 0

[karmic vortex]

okok

is B the point in between 3pi/2 and 2pi?

[languid bolt]

this is period of wave

[balmy warren]

take a point on the graph

and trace it until it repeats

that will be your period

[karmic vortex]

how do i figure out what this point is?

[balmy warren]

you have grid squares

[languid bolt]

i misunderstood his or her or their or "whatever your pronouns are" question nvm

[balmy warren]

there are 3 grid squares per division of pi/2

so what is the value of 1 grid square

[karmic vortex]

1/2?

[languid bolt]

no

[balmy warren]

no

$\frac{\frac{pi}{2}}{3}$

[ocean seal]

IntelligentCake

[karmic vortex]

pi/6?

[balmy warren]

what is this @karmic vortex

yes

so what is the period

[karmic vortex]

hold on gimme a minute

[balmy warren]

just count number of squares from start of cycle to end of cycle

then multiply by pi/6

[karmic vortex]

12 times pi/6?

[languid bolt]

simplify

[karmic vortex]

2pi

[languid bolt]

👍

[karmic vortex]

so that’s my period?

[languid bolt]

yes

period = 2pi / B

find B

[karmic vortex]

i thought that’s what we were figuring out?

[languid bolt]

yes

you found period

[karmic vortex]

but we need B

[languid bolt]

yes

2pi = 2pi / b

[karmic vortex]

so we haven’t rlly found the period

[languid bolt]

we found period

but we havent found B

[karmic vortex]

would it be 2pi/12?

pi/6

[languid bolt]

ok so

what is period

[karmic vortex]

2pi

[languid bolt]

so

$$2\pi = \frac{2\pi}{B}$$

[ocean seal]

MarveI

[languid bolt]

what is b

[karmic vortex]

how do i find B?

[languid bolt]

this equation

period of wave = 2pi/B

we found period of wave

find B now

[karmic vortex]

but B is a number

how do i find the number?

is it a point on the graph?

[languid bolt]

...

$$\frac{2\pi}{1} = \frac{2\pi}{B}$$

[ocean seal]

MarveI

[languid bolt]

what is B

[karmic vortex]

1?

[languid bolt]

yes

B = 1

[karmic vortex]

…

[languid bolt]

Period = 2pi/B

we found period in the graph

so then we can find B

[karmic vortex]

ok

so is 2pi included in our final equation?

[languid bolt]

no

[karmic vortex]

ok

[languid bolt]

B is included

[karmic vortex]

so 1

[languid bolt]

yes

[karmic vortex]

ok

[languid bolt]

$$y = 3sin (1 (x - D)) + 0$$

[ocean seal]

MarveI

[languid bolt]

so far we got this

now we need to find D

idk how to explain D

i'd say it's displacement from center

like.. how far the graph is shifted in the x axis

[karmic vortex]

ahh ok

1/2?

[languid bolt]

no

[karmic vortex]

wait no

i had my desmos wrong

i had x+1/2

not minus

[languid bolt]

so like... you can just find the displacement from center

[karmic vortex]

6?

[languid bolt]

wait no

this

the distance

[karmic vortex]

1.5?

[languid bolt]

forgot the label

[karmic vortex]

3/2?

[languid bolt]

1 grid is

[karmic vortex]

so it would be pi/6 plus half a grid

assuming half of pi/6 is pi/3?

i think that’s wrong

fawk

[languid bolt]

yeah i think so too

uhh

i can zoom in 🙂

[karmic vortex]

-pi/6

[languid bolt]

i was wrong, one grid is not pi/6

[karmic vortex]

🧍‍♀️

[languid bolt]

😄

ok so anyways

A = amplitude/height which is 3

[karmic vortex]

i have y=3sin(1(x-6)) rn

[languid bolt]

no

[karmic vortex]

ok

[languid bolt]

A = amplitude/height which is 3
2pi/B = period of wave
C = center which is 0
D = distance from center?

$$y = 3sin(1(x - D)) + 0$$

[ocean seal]

MarveI

[languid bolt]

and this is D

[karmic vortex]

???

[languid bolt]

si

[karmic vortex]

that’s the answer?

[languid bolt]

yes

[karmic vortex]

ok

lemme check

it’s right

i just finished my homework

that was my last question

now i got a 100

thank you so much