help-10

[timid silo]

Wait let me help u

The point on intersection is x=-5

So x<-5

[lone harbor]

huh

i hope u understood what i meant here

[timid silo]

Yh

[lone harbor]

x< -5 is an inequality that also defines R

[timid silo]

Literally draw the line x=-5

[lone harbor]

yea

that i dont get

[timid silo]

The region R must be when x<-5

OK you know what let me draw it out give me a sec

[lone harbor]

alr

[timid silo]

What is equation of line

Can't be asked to work it out

[lone harbor]

y=3x+15

[timid silo]

First inequality

2nd inequality

So the region that satisfies all inequalities is region R where all the colours are there

[lone harbor]

oh ok i c

i get it

yea

alr

[timid silo]

Cool nws

[lone harbor]

so coming back to the Question statement

how was i supposed to figure out that X<-5

was even there

[timid silo]

OK give me a sec

[lone harbor]

alr

[timid silo]

If you disregard x<-5

Then you see that region R is in quadrant 2,3 and 1

Where blue and red coincide

[lone harbor]

oh

[timid silo]

But region R is only in quadrant 2 and 3

[lone harbor]

id completely ignored tht part of the Q satement ngl

shit i always make these kinda mistakes

well thanks a lot for ur help richie

i finally got this

[timid silo]

Nws lol I've learnt smth as well m good for revision thx 😊

[lone harbor]

lil

lol

alr imma close this now and head to bed

[timid silo]

OK gn

[lone harbor]

its nearly 4 where i am

gn

,close

.close

[obtuse pebble]

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[small sand]

Hello,I'm stuck on permutations,this is the following problem:
Considering this permutation S7
Decompose it in separated permutations,transpositions and find the inverse.

[small sand]

this is what i've tried ,I have no clue how to start on the inverse though :/

[brave bramble]

Note that the inverse is just doing the transpositions again, but in reverse order

A general result from group theory:
(ab)' = b'a'

Where I'm using ' as inverse.

[small sand]

but doesnt that just give me 2415367?

and also are the first 2 correct?

[brave bramble]

(24)(15)(13)(16)(17)
Is the inverse of 2).

[small sand]

I needed the inverse of this

wait

maybe i remember

is it just by going right to left

instead of left to right?

[brave bramble]

That's the same as 2, I thought?

Anyway,
σ' = (16547)'(531)'(17546)'(2415)'

Then ' reverses the order of each

[small sand]

there is no way that's right 0.0

ohhh

i see what you mean

[brave bramble]

σ' = (74561)(135)(64517)(5142)

[small sand]

that easy?

[brave bramble]

Ye

[small sand]

are the first 2 right?

[brave bramble]

That should be the same as my inverse of 2)

If 2) is the same as σ

[small sand]

and how could i check that?

[obtuse pebble]

@small sand Has your question been resolved?

[obtuse pebble]

@small sand Has your question been resolved?

[small sand]

you can close this im going to sleep,ill come back tomorrow thanks 😄

[trail cloak]

Okay hope you got the help you needed :)

.close

[obtuse pebble]

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Closed by @trail cloak

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[obtuse pebble]

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[molten dune]

Hi

[molten dune]

I need help with a geometry problem

Oh shoot sorry

I need to find all the lettered numbers

I completely forgot I cropped that but out 🤦🏼‍♀️

[rare wyvern]

Hello! You want to start at the triangle with the two equations. If you look it has two equal sides making it isosceles.

[molten dune]

Bit*

Ok

[obtuse pebble]

@molten dune Has your question been resolved?

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[spice chasm]

guys i’m stuck

[untold sierra]

I saw your other question, so thought it might help if I said this here, since it will help with this question too

A good technique for questions like this where one term has x in the power and another term has, say, x+3 in the power is to get rid of the +3 and then divide, like this.

You can do a very similar thing here.

[spice chasm]

dang that’s smart

so i should expand each term?

[untold sierra]

It's a nice trick to remember. It makes these questions a bit nicer.

I personally would do that, yeah.

There are several ways of getting the answer though.

[spice chasm]

what do i from here

i got that 343•2^x=32•2401^x

[untold sierra]

That looks good so far, yeah

Divide all of the numbers with x's onto one side

And all of the other numbers onto the other side.

Then you can bring both of the x's together in the same way I did in my picture.

[spice chasm]

look

dang that’s smart

[untold sierra]

That should be it!

Perfect!

You can always put it back into the original equation just to check.

[spice chasm]

yea let me do that

[untold sierra]

But if you followed everything right, it should be fine.

[spice chasm]

i was stuck at the constant part with 32 and 243

i didn’t think of dividing by both of them

[untold sierra]

Yeah, it's something you need to get used to, but when you know the pattern, it becomes much easier.

A lot of the questions like this end up being very similar.

So you can reapply the same idea over and over and it should work out.

[spice chasm]

yea

[untold sierra]

Although there will always be some questions that can throw you off, but in general it should be fine!

[spice chasm]

so what other method can you use instead of expanding the terms

if you want to use the logarithm early on

[untold sierra]

You basically log both sides (It doesn't matter what base it is) Then you expand it out, bring all of the x's onto one side, then factorise and divide.

[spice chasm]

ok let me try

[untold sierra]

Go for it!

[spice chasm]

is this correct so far

[untold sierra]

What you want to do is get only one x on the left side. So you want to try to make it say "x= ......"

To do that, go back to the second line and then expand everything.

[spice chasm]

Ok

[untold sierra]

Then bring every term with an x in it on the left, and every term without one onto the right.

[spice chasm]

the thing is i have ln2 on the denominator

so do i just multiply that to the left

[untold sierra]

Start from the second line, since that would make it easier.

[spice chasm]

ohh i thought what u meant was the second line of my work

[untold sierra]

Oh!!!

Yeah, sorry. I meant the first line of your work, yeah!

[spice chasm]

i think i got it

wait no

[untold sierra]

It's close, but there are two mistakes, yeah.

[spice chasm]

yea i put the wrong sign in front of 3ln7

[untold sierra]

Yep.

And the ln2 next to the x in your second line of working disappears in the next line.

[spice chasm]

oops lol

[untold sierra]

But other than that, perfect!

Both answers will give the same result. And I checked, they are indeed correct.

Nice going!

[spice chasm]

ty bro

[untold sierra]

That's O.K! No worries!

I'll go now. Good luck in the future! 🙂

[spice chasm]

u2 bro

.close

[obtuse pebble]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[timid silo]

Hi

[timid silo]

So whos here

[rare wyvern]

no one

you can put your problem here

[timid silo]

Oh

[rare wyvern]

,rotate

[timid silo]

Btw

I lack prior knowledge and im in 8th grade just know

[rare wyvern]

alright

[timid silo]

So uh

What to do first

[rare wyvern]

For the first problem, you are going to want to find the Y-intercept, and the slope

[timid silo]

Yeah

I used

The 0 and 3

Is that good?

[rare wyvern]

yea, you can use any two points

[timid silo]

My teacher said Preferbly the ones closest to 0

[rare wyvern]

which one are you going to have be y1, and which one y2

[timid silo]

I have 3 as my Y2

If that makes sense

Here lemme send a updated screenshot

[timid silo]

,rotate

[timid silo]

Ignore the bottom

[rare wyvern]

alright, so that answer is your slope.

[timid silo]

But the question is

Is there B?

[rare wyvern]

B is the Y-intercept

the point where x=0

[timid silo]

Yep

Which i dont see a graph for this

[rare wyvern]

alright, so X is going to be our mugs because the number of mugs isn't going to change. X often is the independent variable.

so when X=0, what is the value of the other variable.

[timid silo]

Uhh

Also 0?

[rare wyvern]

When there are 0 mugs, how much is the other thing there going to be.

[timid silo]

3

Right?

[nocturne minnow]

Basically, what is the y value when x = 0

[timid silo]

@nocturne minnow sucks for you They got the easier problem

Anyways

[nocturne minnow]

They were both easy

[rare wyvern]

lmao

[timid silo]

Well

[nocturne minnow]

.

[timid silo]

They got the easier one to explain

[timid silo]

Ik

[rare wyvern]

no, so the collumns are related to eachother, when we look at where 0 is, what is in the bottom row

[timid silo]

@rare wyvern continue

[timid silo]

The cost

[nocturne minnow]

The other one, was just a plot form of the table, same concept

[rare wyvern]

so the cost where the mugs is 0 is the y-intercept

the starting value

[timid silo]

Oh

Well that was easier then i thought

But now i have to explain it in words

[nocturne minnow]

Just relate the price and the amount of mugs

[timid silo]

Ok

Uhh

[nocturne minnow]

For every mug you buy, how much does it increase/decrease in price?

That's it

[timid silo]

Ok….

Ok I got it I think

Ill send a image of what im about to write soon

ok look at dis

Ignore everything besides question 17

[rare wyvern]

,rotate

[rare wyvern]

thats good, but check over the Y-intercept in A.

[nocturne minnow]

Also your equation is wrong

[timid silo]

Not

[nocturne minnow]

It is

[timid silo]

Whats wrong?

[nocturne minnow]

The y intercept

[timid silo]

Its wrong?

How

[nocturne minnow]

The y intercept is the where x = 0

As mentioned before, mugs is the x value, cost is the y value

[timid silo]

But none of my X = 0 in there

[nocturne minnow]

What is the y value that corresponds with x = 0?

[rare wyvern]

on the table with all of the other values

[timid silo]

Well theres one with

0 mugs

[nocturne minnow]

.

[nocturne minnow]

You are looking for the y value that corresponds with x = 0

What is that y value that is paired with x = 0?

[timid silo]

5.99

[rare wyvern]

so when your mugs(x) is zero, then the cost is going to be 5.99

[timid silo]

Wait..,

Yes

But whats B

Ohhh

Is B 5.99

[nocturne minnow]

As mentioned before b is the y intercept

Where x = 0

Meaning that b is the value of y when x = 0

[timid silo]

So

[timid silo]

So basically 5.99

[obtuse pebble]

Please read #❓how-to-get-help

[nocturne minnow]

Yes

[timid silo]

So B is 5.99

[nocturne minnow]

Stop asking 50 questions and read what I presented

If you follow the statements I presented, you should identify the proper value

[timid silo]

Ok so the answer for B is 5.99

Im following ur statement tho

[rare wyvern]

yes

[nocturne minnow]

As mentioned before b is the y intercept
Where x = 0
Meaning that b is the value of y when x = 0

[timid silo]

Im answering his question

[nocturne minnow]

All you need to do is to identify the value of y when x = 0

[timid silo]

Like 4 or 3 times I think

[rare wyvern]

he just wants you to understand it for further questions

[timid silo]

I dont understand

[nocturne minnow]

If you use that table properly, you don't need to question it every time

[timid silo]

Its kind of like 0,0

[nocturne minnow]

I mentioned before, during a test, you won't be able to question your teacher if it's the correct answer. You either know it or you don't based on the given info

So what is the y intercept, based on the given info, and don't question it

[timid silo]

Ty

Got to finish this whole page and its tooken me 4 hours to be half done

@rare wyvern what about this one I feel like its simple but maybe its not

[nocturne minnow]

Use the words given, $8 per hour

[timid silo]

Yeah

[nocturne minnow]

That means every hour, $8 is made

[timid silo]

Hold on im onto something I think

Since there is no 8 in earnings on the graph

Gotta create my own 8 correct?

[nocturne minnow]

Yes

You know it's between 5 and 10

[timid silo]

Yep

Ok i created a 8 and connected it to 1

I can erase the line if u want me to

[nocturne minnow]

Continue that process

For every hour, you increase by $8

[timid silo]

Ahh ok

Am I supoosed to continue this forever orrrr

[rare wyvern]

until the end of the graph

[timid silo]

Oh….

[nocturne minnow]

Then connect the points

[timid silo]

Ok done

[nocturne minnow]

Did you connect the dots?

[timid silo]

Yes

[nocturne minnow]

If this is what you have, you did not connect the dots

You are connecting the dots at every point you created

[timid silo]

Yeah im going up 8 every time

[nocturne minnow]

You created a dot at (1, 8) correct?

And then (2, 16)

And so on

Connect those dots with a line

[timid silo]

Yeah and so on

U cant see the lines?

[nocturne minnow]

It's a line like what you drew in on question 16

A diagonal line

[timid silo]

Ohhhhh

So I continue a little bit off the graph?

[nocturne minnow]

You can if you want to

[timid silo]

Then no

Now the question is

Whats the equation

[nocturne minnow]

Apply the same idea you did with question 16

[timid silo]

Y=8?

[nocturne minnow]

No

[timid silo]

Oh

I know what u mean

[nocturne minnow]

Recall that equation of a line is y = mx + b

[timid silo]

Srry

U mean where I created that line and got 15/-2?

[nocturne minnow]

Yes the same process you did for question 16, apply to that question

[timid silo]

Ok ill try even though 8 only connected with 40 out of all of those

[nocturne minnow]

You see how you drew two lines at each point? Where it intersects?

Draw a line through each intersection

[timid silo]

Uh

Yeah

[nocturne minnow]

So can you find the slope of that line?

[timid silo]

But it only intersects on 40?

[nocturne minnow]

What?

[timid silo]

Wait nvm

It intersects on none

[nocturne minnow]

Then you didn't draw it correctly

[timid silo]

Want me to redraw 2 of em?

Just to get a slope I guess

[nocturne minnow]

Those are the points you plotted

[timid silo]

Oh shit

[nocturne minnow]

Draw a line through them

[timid silo]

I didnt see that

[nocturne minnow]

You see how you drew two lines at each point? Where it intersects?
Draw a line through each intersection
That is what that means

[timid silo]

Ah ok ty

Like this?

[nocturne minnow]

Yes

[timid silo]

So now i create a slope

Not really use to sum like this but uhhhh alright

[nocturne minnow]

Recall what you did for question 16

And apply it here

[timid silo]

Ok

Done i think?

Went from 15 to 40

@nocturne minnow u here?

[nocturne minnow]

I don't see an equation

[timid silo]

Oh thats a old image mb

I think its 5 over and 5 up

[nocturne minnow]

The slop is also mentioned in the text

[timid silo]

8

[nocturne minnow]

Yes

What is the y intercept?

[timid silo]

So what is the slope 8/5 or something

Uhh

[nocturne minnow]

No

[timid silo]

At 0 of my graph?

[timid silo]

Oh its just 8

[nocturne minnow]

Yes

[timid silo]

Ok so were finding B right now

[nocturne minnow]

Look at the line you drew in on the paper

[timid silo]

E

[timid silo]

Ok

[nocturne minnow]

What is the value of y when x = 0?

[timid silo]

Well

If were being realistic since its hiurs

Hours

Its 0

[nocturne minnow]

So then the y intercept is?

[timid silo]

Both*

0

[nocturne minnow]

So then the equation of the line is?

[timid silo]

Y=8+0

Well technically 8 over 1 right?

Or no

[nocturne minnow]

What does 8/1 equal to?

[timid silo]

Well

It says Earns 8$ an hour sooo

It cant just be 8 alone right?

[nocturne minnow]

Recall that the equation of a line is y = mx + b

That x is important to include

[timid silo]

Yes so are X is 1 correct?

[nocturne minnow]

What?

[timid silo]

The equation is

Y=8/1+0

[nocturne minnow]

.

x is a variable

[timid silo]

Ohhhh

So its 1/8 not 8/1

[nocturne minnow]

y and x will always exist in the equation of a line

[nocturne minnow]

No

What is m?

You already said it multiple times

[timid silo]

M is our Y

And X is our X

[nocturne minnow]

No

[timid silo]

Just kidding

M is our slope

[nocturne minnow]

So you using y = mx + b

You know what m is and what b is

[timid silo]

Yep

[nocturne minnow]

Plug in those values

Aka replace m and b with the values you stated above

[timid silo]

So Y is actually 0 now?

[nocturne minnow]

No

[tardy epoch]

Are you getting trolled @nocturne minnow

[timid silo]

Uhh no man

Im serious

The values stated above

Hmmmpm

Oh our slope

[nocturne minnow]

Probably

[timid silo]

So thats just it right?

Y=8+0

?

[nocturne minnow]

.

[nocturne minnow]

.

[timid silo]

Oh

[nocturne minnow]

.

[timid silo]

Are X is 1 or 5

I dont know which one tho

[nocturne minnow]

It's a variable

Like y, that's a variable

Are you plugging in a value for y?

[nocturne minnow]

Is there a value for y here?

[timid silo]

Plugging in a value?

Ohhhhhhhhhhhhh

Well theres 1

Which is the number 1 right?

[nocturne minnow]

Where is 1 coming from

Recall that the equation of a line is y = mx + b

You have the values for m and b, plug those values into that equation

[timid silo]

Waitttt

[nocturne minnow]

As mentioned

y and x will always exist in the equation of a line

[timid silo]

Is the X also 8

[nocturne minnow]

No

Why are you saying x is also 8?

[timid silo]

Well

[nocturne minnow]

the equation of a line is y = mx + b

[timid silo]

Its going up by 8 every time

[nocturne minnow]

y and x will always exist in the equation of a line

Have you never seen an equation of a line?

Like y = 3x + 45

That's an equation of a line

[tardy epoch]

Don't think bolding will work on trolls

[nocturne minnow]

Where y and x still exist

[timid silo]

Hmm

Im thinking

Gimmie a sec

Omg

Is it 0?

Has to be

[nocturne minnow]

What is 0?

[timid silo]

X

[nocturne minnow]

Have you never seen an equation of a line?
Like y = 3x + 45
That's an equation of a line

Where on earth do you see x is 0?

x is still there

[timid silo]

Ahh

I dont know

I say

X is 5

[nocturne minnow]

Why are you saying numbers for x?

Have you never seen an equation of a line?
Like y = 3x + 45
That's an equation of a line

[timid silo]

Oh

[nocturne minnow]

y and x will always exist in the equation of a line

[timid silo]

Ohh

[nocturne minnow]

Stop guessing and read

[timid silo]

We dont have a X

So the equation is

Y=8x+0

[nocturne minnow]

Yes

[timid silo]

Correct?

@nocturne minnow i have 3 more short answers if u could just answer them for me ill be on my way to doing my project

[nocturne minnow]

No

[timid silo]

Awww

[nocturne minnow]

I'm done

[timid silo]

Please

Pleasee

[nocturne minnow]

You can either wait for someone else to help, or stop doing math and just ask your teacher for help

[timid silo]

Well this is homework

I guess ill do it on my own its pretty essy

Thx for ur hard work

[nocturne minnow]

As I mentioned before, you are lacking tons of knowledge that you need, so if it's homework, then you can ask your teacher tomorrow for help

They can help you one on one

[timid silo]

@nocturne minnow truth is I am a spirit and god made me come here to test you

You will never see me again

🙏

[rare wyvern]

...

use .close to close the help channel if your done here.

[timid silo]

Oh right before I leave earth

.close

[obtuse pebble]

Channel closed

Closed by @small folio

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.
• 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 hedge]

https://gyazo.com/c0fd7a0b7532cb3c08dd3169f0904b81.png

[karmic hedge]

I dont really understand what the question is asking

[royal basin]

you are asked to write down the equation that says "The distance from (x,y) to P equals the distance from (x,y) to Q"

and to then do some algebra to it to isolate y in it

@karmic hedge does that clarify the problem statement for you?

[karmic hedge]

I think so, 1 moment I will try it

Im not going to close the chat yet incase I get stuck

(x-1),(y-3)=(x+2),(y-5)

I dont know what to do next...

[daring rock]

🤔 what do those commas mean?

Try using the distance formula instead

[karmic hedge]

Ok I will try

[daring rock]

(distance from (x,y) to P) = (distance from (x,y) to Q)

using the distance formula

[karmic hedge]

yes I got the right answer, thank you!!

❤️

.close

[obtuse pebble]

Channel closed

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[timid silo]

i forgot how to do this but for,
[
x_1 + x_2 + x_3 + x_4 + x_5 = 21
]
How do i find all possible solutions to the system if $0 \leq x_1 \leq 3, \enspace 1 \leq x_2 \leq 4, \enspace x_3 \geq 15$

[warm shale]

♡LexQa♡

[timid silo]

i tried stars and bars, but that failed terribly

oh yeah

$x_i \in \bZ, x_i \geq 0$

[warm shale]

♡LexQa♡

[timid silo]

okay should've just said whole numbers

[next reef]

Take $y_1=x_1, y_2=(x_2-1), y_3=(x_3-15),y_4=x_4$ and $y_5=x_5$

[next reef]

$y_1+y_2+y_3+y_4+y_5=(x_1+x_2+x_3+x_4+x_5)-(16)=21-16=5$

[timid silo]

so it is 5?

hm

[next reef]

What 5?

[next reef]

For this system of equations, by stars and bars, 9C5 possible solutions are there.

Ignoring the upper bound*

[timid silo]

i believe that's incorrect though

[next reef]

How?

[timid silo]

the answer is C(10,4) - 20

[next reef]

I'm still not done with my work

[timid silo]

oh i see

[next reef]

[timid silo]

okay

[next reef]

There are upper bounds for x_1 and x_2

Writing them in terms of y's, $y_1 \leq 3$ and $y_2+1 \leq 4$

[next reef]

Finding number of possible solutions for the counterpart and subtracting it from the total should work

that is when, $y_1 \geq 4$ and $y_2 \geq 4$

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

alright thank u

i will look over this later

[obtuse pebble]

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[feral sentinel]

hi can someone tell me if theres a faster way to do this

its only 2 marks

[unreal musk]

My guess with no work is to e both sides of the original: $e^{y} = 2 + \sin(2x)$

[warm shale]

chartbit

[feral sentinel]

hmm why?

is it because ln and e will evaluate to 1

actually that probbaly is why lol

[unreal musk]

Then $y' e^{y} = 2\cos(2x)$, and $(y')^2 e^{y} + y'' e^{y} = -4\sin(2x)$

[warm shale]

chartbit

[unreal musk]

Actually that's much easier, there we go haha

[feral sentinel]

am i doing something wrong

[unreal musk]

e and ln cancel each other out

$e^{\ln(a)} = a$ for any $a$

[warm shale]

chartbit

[feral sentinel]

wait but i thought thats ln(e) not e^ln

ohh i see

[unreal musk]

Then implicit differentiate that twice

[feral sentinel]

,w differentiate e^y

[warm shale]

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[feral sentinel]

,w differentiate e^(2y)

[warm shale]

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[feral sentinel]

hold up

kinda confused

[feral sentinel]

how did u get the y' in front

[unreal musk]

,w diff e^{y(x)} wrt x

[warm shale]

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[feral sentinel]

oh oops

liek this

[unreal musk]

You're done there

[feral sentinel]

wut

i thought i had to find dy/dx and d^2y/dx^2 individually

[unreal musk]

$\dv{y}{x} \dv{y}{x} = \left(\dv{y}{x} \right)^{2}$

[warm shale]

chartbit

[feral sentinel]

ye

oh

[feral sentinel]

so now i need to show that this is -4sin2x

[unreal musk]

why?

[feral sentinel]

err

[unreal musk]

if that's for that first part, then this…

[unreal musk]

…and this…

[feral sentinel]

im actually blind

[unreal musk]

…are the same, no?

[feral sentinel]

yes

sorry

[unreal musk]

Don't worry, happens to many of us

[feral sentinel]

XD ok i got it

now for part ii hmm

ill need to differentiate once more i thinj

[unreal musk]

Think that's what they're saying too

[feral sentinel]

okay then now i need to sub x = 0 into every dy/dx

[unreal musk]

True but then you can find y easily, and dy/dx, and then d^2y/dx^2 and so on, yea?

[feral sentinel]

uhh do u mean i can find those easily after subbing x = 0?

or is there a shorter way

ohh

yes

[unreal musk]

y = ln(2)

$\dv{y}{x} e^{\ln(2)} = 2$

[warm shale]

chartbit

[unreal musk]

And so on, and so forth 🖼️

[feral sentinel]

oh oops i kinda did it

lemme take a look at the shorter way

[feral sentinel]

wait am i doing the same thing

[unreal musk]

Good question

[feral sentinel]

hm

[unreal musk]

Lemme see if I agree with your second derivative

[feral sentinel]

alrighty

[unreal musk]

Your first I do

[feral sentinel]

[unreal musk]

Hmm I get $\frac{d^2 y}{dx^2} = -1$

[warm shale]

chartbit

[feral sentinel]

hm

[unreal musk]

As then from this, and with $y = \ln(2), \dv{y}{x} = 1$

[warm shale]

chartbit

[unreal musk]

Get $2 \frac{d^2 y}{dx^2} + 2(1)^2 = 0$

[warm shale]

chartbit

[feral sentinel]

hm

i just subbed them into my previous equations

[unreal musk]

Hmm, can you circle the one you used for the second derivative please?

Oh hold up a minute

[unreal musk]

[feral sentinel]

oh umm its the one where i wrote "wtf am i doing"

[unreal musk]

$\left( \dv{y}{x} \right)^2 \neq \frac{d^2 y}{dx^2}$

[warm shale]

chartbit

[feral sentinel]

AH

[unreal musk]

Naughty

[feral sentinel]

that makes sense

ok lemme just redo

is this better

[unreal musk]

https://tenor.com/view/士力架sni-snickers-gif-12660428

[feral sentinel]

[unreal musk]

Let me check it though myself, it's getting a bit nuts to the third order

[feral sentinel]

[unreal musk]

Ouch, hold up

,w diff e^(y(x)) y''(x) + e^(y(x)) (y'(x))^2 wrt x

[feral sentinel]

uh

[warm shale]

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[unreal musk]

Aha, what I got too, me can do math

[feral sentinel]

oh no

oh

i thought mine was entirely wrong

[feral sentinel]

"me can do math" casually has graduate+ in ur roles

[unreal musk]

Well, not "entirely" wrong

[unreal musk]

Yeah, don't know how that even happened, how did I even make it out of a masters huh

[feral sentinel]

wow

so ur doing phd meth

[unreal musk]

I'm more a concept guy tbh, calculations I always mess up

[unreal musk]

Well definitely not the PhD part

[feral sentinel]

i heard in the real world u dont have to do manual calculations

soooo

its the concept thats more important (i think)

[unreal musk]

I get the third derivative as -2?

[feral sentinel]

hmmmmmmmmmmmm

wooot

[unreal musk]

From this, I get $2(y''' + (1)^3 + 3(1)(-1)) = 2(y''' - 2)$

[warm shale]

chartbit

[feral sentinel]

hm so my differentiation is wrong for the third one

[unreal musk]

Then RHS is -8, right?

[feral sentinel]

yes

okay lemme diff again

[unreal musk]

Typo

[feral sentinel]

hehhh

my one is -6 now

reeeee

i cant see wheres the mistake

[unreal musk]

y

How'd you get that 2

And no second derivative, heh?

,w diff (y')^2 wrt x

[warm shale]

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[feral sentinel]

OH

[unreal musk]

[feral sentinel]

wait but theres still a 2 right

it still feels wrong

am i doing it correctly here lol

ah

[unreal musk]

[feral sentinel]

,w differentiate (e^y) * (dy/dx)^2

[warm shale]

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[feral sentinel]

wut

[unreal musk]

"wrt x"

,w differentiate (e^y) * (dy/dx)^2 wrt x

[warm shale]

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[feral sentinel]

[unreal musk]

Expand it, you get $2 e^y \dv{y}{x} \frac{d^2 y}{dx^2} + e^y \left(\dv{y}{x}\right)^{3}$

[warm shale]

chartbit

[unreal musk]

https://tenor.com/view/look-at-what-you-could-have-won-win-prize-gif-16706292

[feral sentinel]

wait why do we differentiate the first one

[unreal musk]

What do you mean? remember that y and its derivatives depend on x

[feral sentinel]

OH WAIT

ok nvm i see it now

AH OK ITS CORRECT

tysm

i kinda gtg lol

thanks alot

[unreal musk]

No worries, hope that helped

Have a good one!

[obtuse pebble]

@feral sentinel Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[haughty drift]

is 0 raised to the power 0 is 1 ??

[timid silo]

it's undefined

mainly bc anything divided by 0 is undefined

[gleaming ridge]

Honestly it depends on how you want to define it. There are books where 0^0 is 0 and some books where it is 1

[timid silo]

?

[timid silo]

for simplicity sake, you can say it is 1 for most cases tbh

[gilded needle]

another reason it's generally undefined is that x^0 is 1 for x > 0, so taking limit as x->0+ you'd deduce that 0^0 = 1. But on the other hand, 0^y = 0 for y > 0, so taking limits as y->0+ you'd deduce that 0^0 = 0

[bleak maple]

its undefined but sometimes we take it to be 1 as a convention to make formulas or equations more compact

[swift grove]

In an exam they will mark you wrong for 0

you write 1

[timid silo]

i mean 0^0 is sometimes defined as 1, but never 0

[swift grove]

simple if you're in school

its 1

[gleaming ridge]

For example in Tao where he defines power of a natural number, he takes n^0 as 1 for all natural number in particular for 0 also

[swift grove]

if you're doing further college or advanced maths in A level they would break it down into something more complex but right now it doesnt matter any number to the power of 0 is 1

1

[gleaming ridge]

I haven't seen it as 0 but I have heard somewhere I think in Math sorcerer that you can also extend the 0^n definition to include 0 and define it as 0

[mental solstice]

i think the only cases i've seen it treated as 0 is in some specific combinatorics identities

to abuse the terminology, it's almost always treated as 1

[gleaming ridge]

I'd say it's definition depends more on convenience than anything as Camilleone and others have pointed out

[haughty drift]

but how it is undefined ??

[gleaming ridge]

In analysis, you'd usually see 0^0 = 1 while in some some places like combinatorial proofs it is defined as 0

[gleaming ridge]

Look above at what Bueno said

[zenith raft]

0^0 = 1

ms snow why are you thinkspinning me TwT

[wild swallow]

0^0 = 1

[zenith raft]

we're breaking up if you don't agree

[wild swallow]

[obtuse pebble]

@haughty drift Has your question been resolved?

[obtuse pebble]

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[timid silo]

how is my answer wrong? i dont get it

[swift grove]

it should be 2 hours 20 minutes

[timid silo]

hm?

so 18 km = 2 hours

[high lily]

how are you getting what you got?

[timid silo]

the remaining is 3 km

9 divided by 60

is

0.45

so

60 minus 45 is 15

so

[high lily]

whut

[unreal musk]

(units)

[timid silo]

2h and 15

units

skull

[high lily]

it looks like you're doing random things and hoping for the best

[timid silo]

wait

so

wait

this is

this is speed x distance?

[foggy estuary]

last you have to divide 3 by 9

[timid silo]

i meant distance divided by speed

[high lily]

why are you dividing 9 by 60 and what do you think that supposed to give you

[foggy estuary]

by that point u gonna get ratio 1/3

[timid silo]

sorry i dont get it

[foggy estuary]

1/3 to 60

[timid silo]

this is eqution is distance divided by speed right?

equation*

[high lily]

t = d/s

[timid silo]

yes

so

distance here

is

21

[high lily]

yes

[timid silo]

speed is 9m/h

so 21x9 right?

[high lily]

no

[timid silo]

i meant

divide

holy shit

this is why i got it wrong

so now its 2.333333333

whats next?

i know that 2 is equal to 2 hours

0.333333333 x 60

is 19.999999998

so round that off

is 20

is this correct solution?

[obtuse pebble]

@timid silo Has your question been resolved?

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[halcyon socket]

can someone explain me the nature of series 1 / ( (n+1) * ln^2(n+1) ) ?

[royal basin]

$\sum_{n=1}^{\infty} \frac{1}{(n+1) (\log(n+1))^2}$

[warm shale]

Ann

[royal basin]

this?

[halcyon socket]

no

[royal basin]

oh? then can you write on paper what the correct series is

[royal basin]

but that's the same as what i wrote...

[halcyon socket]

sory 😄

[royal basin]

anyway

have you made any progress on this so far

[halcyon socket]

i've tryed with some comparisons

[royal basin]

comparison? ok, what did you compare to?

[halcyon socket]

harmonic series

i mean 1 / n

with that series

[royal basin]

and which way did the comparison go?

[halcyon socket]

idk i just said it is diverges

[royal basin]

so you do not even know which direction the comparison between your series and 1/n goes?

how can you expect to draw any conclusions from it?

[halcyon socket]

idk how to calculate this series, 0 idea

im at starting with series

[royal basin]

you could not tell me whether $a_n \leq \frac{1}{n}$ or $a_n \geq \frac{1}{n}$.

[warm shale]

Ann

[royal basin]

i would say that this means you didn't actually compare your series to 1/n.

(i'm using a_n to denote 1/((n+1) log^2(n+1)) for brevity)

[halcyon socket]

i think an >= 1/n

[royal basin]

you're wrong

in fact it's a_n ≤ 1/n

from which you can at least conclude that the comparison with 1/n tells you nothing

[halcyon socket]

so, how can i know the nature ?

[royal basin]

i'd suggest Cauchy's condensation test

also we should probably reindex the series so that it's $\sum_{k=2}^{\infty} \frac{1}{k \log^2(k)}$

[warm shale]

Ann

[royal basin]

just for convenience

[halcyon socket]

compare that ?

[royal basin]

no, you are confusing application with proof.

cauchy condensation test says that if $f$ is a positive, decreasing function then the convergence of $\sum f(n)$ is equivalent to that of $\sum 2^n f(2^n)$

[warm shale]

Ann

[halcyon socket]

oh i will try, thx a lot

[obtuse pebble]

@halcyon socket Has your question been resolved?

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[obtuse pebble]

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[timid silo]

how do we know its 1.7 on the x-axis

[timid silo]

for mean = n/2 so 200/2 = 100

the corresponding value of 100 on the x-axis is 1.7, iam not able to mark it

[spiral knot]

from the graph

draw a horizontal line passed by 100

until it touch the graph

[obtuse pebble]

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[obtuse pebble]

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[spiral knot]

and project it on the x-axis @timid silo

like this

[obtuse pebble]

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[wanton dune]

Please help me find the length of side c

[atomic bobcat]

show your work

[high lily]

how much trig have you learned so far?

[royal shard]

i would start with:
-divide the big triangle into two smaller right triangles
-I would put the line from the 60° angle to the longest side, such that we get two 90° angles

then get all the values in the upper triangle via trig functions

then do the same for the lower right triangle

[dim bobcat]

Hint side c common in both right angled triangles

[timid silo]

thanks so much, my internet connections vanished, i usually get stuck at this can you let me know how can i understand better because the second part is exactly going to be the same

i will open another channel

.open

[timid silo]

looks like that didnt help

.close

i usually used to add my questions i am on my channel if that didnt work it means due to my network connections maybe

[fading quest]

someone else claimed this channel, go and grab a new one if you need it

[obtuse pebble]

@wanton dune Has your question been resolved?

[obtuse pebble]

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[coarse orchid]

Help

[swift grove]

?

[coarse orchid]

How to solve this?

Note : "atau" means "or"

[next reef]

What have you tried?

[dim bobcat]

Sir long Musk what things have you tried till now?

[lost tree]

why is the 2 in superscript

is that the base

[dim bobcat]

Yes

[next reef]

Yes

[dim bobcat]

Seems like

[lost tree]

oh

[next reef]

It is the common notation in some part of the world

$log_a(b)={}^alog(b)$

[lost tree]

$\log_2\left[\log_2\left(2^{x+1}+3\right)\right]=1+\log_2x$

[warm shale]

SilverSoldier

[lost tree]

oh i see

[timid silo]

Strange

[obtuse pebble]

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[subtle whale]

Why is it different?

[nocturne minnow]

Is that chatgpt?

[subtle whale]

yes

[nocturne minnow]

It is not ideal to use chatgpt to do math problems

As it gets it wrong often

[subtle whale]

I am just trying to convert the units

[nocturne minnow]

.

Google can convert units

[subtle whale]

is it different to convert from
g/cm^3 to kg/m^3

than to convert from
kg/cm^3 to kg/m^3 though?

[nocturne minnow]

You don't need an ai to do that

Well, m^3, or anything to cube relates to volume

You'll just have a small number

,w 2 g/cm^3 to kg/m^3

[warm shale]

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[nocturne minnow]

,w 2 kg/cm^3 to kg/m^3

[warm shale]

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[nocturne minnow]

See, kg/cm^3 to kg/m^3 is larger than g/cm^3 to kg/m^3. Conversion process applies the same concept

[subtle whale]

Is that why this is wrong?

I'm not sure what's the correct way to do it

[subtle whale]

It's supposed to be 8.8x10^2 kg/m^3

But I am getting 0.088kg/m^3, where am I going wrong?

[high lily]

unit conversion is essentially applying multiplication by 1

note that since 1m = 100cm
then
1m^3 = (100cm)^3

hence you should be multiplying by
$$\frac{(100cm)^3}{1m^3} = \frac{1000000cm^3}{1m^3}$$
or equivalent

[warm shale]

ℝamonov

[subtle whale]

Aha, right, thank you

I want to find the value of uncertainty for this

By taking the log of both sides

So that I can follow something like this to find the error

Can anyone help me write the top equation in the format found in the 2nd picture 2nd line?

[obtuse pebble]

@subtle whale Has your question been resolved?

[subtle whale]

No

😔

[obtuse pebble]

@subtle whale Has your question been resolved?

[subtle whale]

?solved

-solved

!solved