help-0

[wanton tinsel]

does that make it easier?

[raven rover]

It looks easier to work with, at least

[wanton tinsel]

true

[raven rover]

I wonder if expanding the sine sum and splitting the fraction is the way to go

[wanton tinsel]

sin(n + 1/2) = sin(n)cos(1/2) + sin(1/2)cos(n)

and then break the fraction up?

[raven rover]

That doesn't look super helpful 😦

[wanton tinsel]

yeah still the same issue with sin(n) and cos(n)

is there some way to use a substitution

[raven rover]

I'm not sure

[wanton tinsel]

ive never heard of using substitution with series anyways

[raven rover]

Maybe re-indexing but I don't see a way this helps

I wonder if you could just say that the terms decrease and alternate in sign every (X) terms

Without mathematically saying so

But that's not rigorous

[wanton tinsel]

yeah maybe

though the terms dont alternate in a set cycle

sometimes its 3 and sometimes its 4

[raven rover]

Yup

I have no idea

[wanton tinsel]

welp

[raven rover]

What if you started writing out a few of the terms?

I know it isn't telescoping, but

sin(1/2) / 1

sin(3/2) / 2

sin(5/2) / 1 + √2

[wanton tinsel]

eek

would love if this was absolutely convergent

[raven rover]

Yup

Does the sequence's absolute value not converge?

[wanton tinsel]

dont think so

pi/(1+sqrt(n)) would compare to pi/sqrt(n)

which diverges by p < 1

if im not mistaken

[pallid sail]

doesnt this absolutely converge

[wanton tinsel]

oop

i could be wrong

[pallid sail]

like by applying the squeeze theorem

oh wait

im dumb

squeeze theorem is only for arrays

[raven rover]

Why is the π hanging out there like that?

That's so stupid

[wanton tinsel]

right why didnt they put it in the front

maybe it is actually in the sin

sin((n+1/2)pi)

[raven rover]

That would be GREAT

Try interpreting it as that

[wanton tinsel]

i think i will

[raven rover]

If you do that, then sin( π(n + 1/2)) = (-1)^n

[wanton tinsel]

why else would they put the pi in the back

[raven rover]

They're stupid

They need to be clear with notation, damn it.

[wanton tinsel]

smh this was half an hour for a lack of parentheses

well thanks for the help

.close

[lone heart]

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[raven rover]

Feels like that, huh?

I hate that

Regardless, good luck!

[wanton tinsel]

thanks :D

[lone heart]

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[alpine sable]

dumb question, where does the 2ab come from lol?

[glass lichen]

(a+b)(a+b)=a(a+b)+b(a+b)=a^2+ab+ba+b^2

[open folio]

FOIL, and the outers are a and b, which make ab, and the inners are also ab, which make ab. ab + ab = 2ab

[raven rover]

@alpine sable Comes from here a^2 + ab + ba + b^2

[alpine sable]

u gonna have to explain that last bit lol

[wary stream]

It's just distribution

[raven rover]

a(a+b) + b(a+b)

a^2 + ab + ba + b^2

[alpine sable]

yes but, how

assume im braindead, which i am

[raven rover]

Distributing is kind of something we have to accept works

Not sure if this helps, but:

a(b + c) = ab + ac

In our case, some of these variables are the same

[alpine sable]

yes thats familiar to me

ohhhh

a(a+b) = a^2+ab

[raven rover]

yup

Exactly

[alpine sable]

idk why i didnt see that lol

ok thanks for the help guys

.close

[lone heart]

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[crisp tendon]

can someone help me

[crisp tendon]

how would i find the TSA of a cylinder if it gives me the volume and height

im used to doing it as 2 x 3.14 x r (r+h) so im kinda lost

[tidal mural]

surface area?

[crisp tendon]

my teacher calls it total surface area

[tidal mural]

I believe it wants you to work backwards from the volume to solve for the radius, and then use the radius to calculate the surface area.

[crisp tendon]

how would i do that again?

[wary stream]

What's the volume of a cylinder formula?

[crisp tendon]

i dont know

[wary stream]

Google would help with that

You can look it up

[crisp tendon]

its not showing me

[wary stream]

That simple

"volume of a cylinder"

[crisp tendon]

no

i need to find the tsa

using the volume to find the raius

radius

[wary stream]

You need the radius first

[crisp tendon]

this

[wary stream]

You have volume and height

With those two and the formula, you can find r

[crisp tendon]

how

[wary stream]

Plug in the stuff you know, find r

[lone heart]

@crisp tendon Has your question been resolved?

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[lone heart]

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[dire terrace]

How do i calculate (81)^2/3

[pine kettle]

You can use a calculator

Otherwise I would just do order of operations to simiplify

[dire terrace]

How would i do that

[buoyant kayak]

do you know how to simplify roots

and convert from exponential to root form

[dire terrace]

no

[buoyant kayak]

then why are you doing a problem that requires it

[dire terrace]

deltamath

thats why

[buoyant kayak]

i don't know what that means

https://www.youtube.com/watch?v=u2Z1hoXSrXk

https://www.youtube.com/watch?v=GipavLCnke0

[pine kettle]

omg

Use parenthesis bruh I thought you were asking $\frac{81^2}{3}$

[ocean seal]

sills

[dire terrace]

nvm i got it

.close

[lone heart]

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[crystal spear]

what multiplies into 64 but also adds into 16?

[wary stream]

What are the factors of 64?

[crystal spear]

1 2 4 8 16 32 and 64

[wary stream]

So then which two factors adds into 16?

[crystal spear]

ohhhhhhhh i got it

its 8 right?

[wary stream]

Yes

[crystal spear]

thank you lol

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[lone heart]

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[alpine sable]

how is f(x) =y in this proof?

[alpine sable]

<@&286206848099549185>

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

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[nova quiver]

I am currently studying the queueing theory and get some trouble with this question 😦

[lone heart]

@nova quiver Has your question been resolved?

[nova quiver]

<@&286206848099549185>

i have learnt about generate the steady-State Balance Equations by the Markovian Queues but i dont know the relationship about the 1/1+i

lambda0 P0 = Mu1 P1

[nova quiver]

<@&286206848099549185>

[lone heart]

@nova quiver Has your question been resolved?

[lone heart]

@nova quiver Has your question been resolved?

[lone heart]

@nova quiver Has your question been resolved?

[lone heart]

@nova quiver Has your question been resolved?

[tacit arch]

.close

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[pure inlet]

ho

[pure inlet]

hi

I need help

[glass lichen]

Don't ask to ask

[pure inlet]

wat

anyways

'

I need help solving sqaure

U dont need to give me the answer

just tell me how to solve it

step by step

and then ill try to solve it myself

[glass lichen]

That's a triangle, but what have you tried?

[pure inlet]

oh

[glass saffron]

Heres a hint: What are internal angles of a square?

[pure inlet]

Nothing idk how to solve it I didn't listen to anything my math teacher said and I need help now

[glass lichen]

Damn, that sucks

Should have listened

[pure inlet]

so I just need u to explain to me how to solve it

[pure inlet]

ik

[glass lichen]

Google

[pure inlet]

already tried

[glass lichen]

Welp, go ask your teacher

[glass saffron]

^ What are the internal angles of a square

[glass lichen]

For all I know, you won't listen to what I have to say if you didn't listen to your teacher

[pure inlet]

Well I don't wanna go do that bc he will ask me what I did to try to solve it then ill have to tell em I don't know how to do anything of it

[pure inlet]

i will

[glass lichen]

Yeah, and you just did that with me.......

[pure inlet]

thats what im trying to do listen now

[pure inlet]

idk

[pure inlet]

the sides idk

[glass saffron]

have you attempted to solve this?

[glass saffron]

ah, i'll rephrase:

[pure inlet]

no because idk how

idk how to start

i never listend

Do i do 3x + 3x

or something

[glass saffron]

I have drawn an angle, and labled it a

[glass lichen]

Triangle is obviously going to be better

[pure inlet]

why u put a line above it

[glass lichen]

Doesn't matter?

[glass saffron]

Its a more visually intuitive fact to consider the bisection of an angle than the sum of angles in a triangle, for a beginner to math

[glass lichen]

It isn't

[glass saffron]

eh, its up to opinion

[pure inlet]

U know i can see what your saying that lines doing nothing

[glass lichen]

Thanks captain obvious

anyway, just write out angle sum of a triangle and solve.

[glass saffron]

what do the angles in a triangle add up to?

[pure inlet]

idk how to solve it thats what i've been saying

[pure inlet]

6x

[glass lichen]

???

[pure inlet]

3x + 3x = 6x

[glass lichen]

Google "angle sum of a triangle"

[pure inlet]

180

yeah 180 complementary

[glass lichen]

So write an equation for the angle sum of this triangle.

[pure inlet]

and 90 supplementary

[glass saffron]

Right, and what angles do you have in your triangle?

[pure inlet]

square*

but idk

i need serious help

(3x - 2) x 180

do i do that

[glass lichen]

what are the 3 angles in the triangle?

Hint: 2 are clearly labelled, and 1 has a box

[pure inlet]

yeah 2 of them are 3x

the other is 90

[glass lichen]

yes

so write an equation

[glass saffron]

Okay, and what do we know that these add up to?

[pure inlet]

how do i right it

90 + 3x + 3x

?

[glass lichen]

= what?

[glass saffron]

*write, but yes thats half of it

[glass lichen]

that's an expression, not an equation

[pure inlet]

or 90 + 3x^2

[glass lichen]

....

[glass lichen]

did I say this was wrong??

[pure inlet]

no

[glass lichen]

so why did you feel the need to change it?

[pure inlet]

if im dumb just say that

[pure inlet]

idk

[glass lichen]

90+3x+3x = what

[pure inlet]

96x

[glass saffron]

AH

[glass lichen]

where the fuck did 96 come from?

[pure inlet]

3 + 3 = 6

[glass lichen]

so?

[pure inlet]

then add it with 90

and put the x

[glass lichen]

what is the angle sum of a triangle again?

[pure inlet]

hmm'

90+3x+3x

is

[glass lichen]

omg

[glass lichen]

.

[pure inlet]

dont u have to add equal terms

[wary stream]

Sum of angles in a triangle

[pure inlet]

oh its 180

[glass lichen]

YES

So write an equation

[pure inlet]

how the hell do u get 180 from 90+3x+3x

[glass lichen]

That relates those 2 things in a non-stupid way

OMG

[glass saffron]

Yes, the angles in a triangle add up to 180
So if you have three angles: 3x, 3x, 90, then they must add up to 180

[glass saffron]

O_O

[glass lichen]

You know that, for any triangle, the angles sum to 180

[wary stream]

You were creating an equation relating the given info and the sum of all angles equaling 180

[glass saffron]

‎

[glass lichen]

For this specific triangle, you know the angles add up to 90+3x+3x

So $90+3x+3x=180$

[ocean seal]

Mosh

[pure inlet]

How

[glass lichen]

use your brain, and read what I just said

[pure inlet]

ok

[glass lichen]

.

[glass lichen]

.

[pure inlet]

what what

oh yeah

i remember my teacher said that

[glass lichen]

so now solve for x

[pure inlet]

hmm

[wary stream]

We also said that too, many times

[glass lichen]

to which there are resources available online

[pure inlet]

I just never noticed

😭

[wary stream]

Sum of angles in a triangle equals 180

[glass lichen]

Why wouldn't you read what the people trying to help you type?

[pure inlet]

i tried quickmath and mathway

[wary stream]

That was repeated in different forms, many times

[glass lichen]

Oh wait, cause you didn't listen to your teacher

[pure inlet]

ya think

even i knew that

[wary stream]

Those are calculators. Resources as in webpages that provide information

[pure inlet]

oh

oops

well

what were we on

oh yeah

[glass lichen]

.

[pure inlet]

i was solving for x

ok

how do i solve for x 😭

[wary stream]

Using math

[glass lichen]

algebra

[pure inlet]

ik that

[glass lichen]

You just asked how, so I don't think you do

[wary stream]

If you have 2x + 1 = 6, how do you solve for x?

[pure inlet]

ik u use math and algebra but idk how to solve for it

[glass lichen]

Google resources

[pure inlet]

add both like terms first?

wait

[wary stream]

Meaning?

[pure inlet]

u add 1 and 2?

idk 😭

[wary stream]

No

You need to review math

So resources

Are good

[pure inlet]

so

2x + 1 = 6

x =

wait dont say anything im thinking

3

x = 3

[wary stream]

No

[little drum]

,calc 3(2) + 1

[ocean seal]

Result:

7

[pure inlet]

&

7

HOW THE HELL IS x 7

[glass lichen]

Are you just chosing to not read?

[wary stream]

You definitely need to review algebra

[pure inlet]

I think i know that

[glass lichen]

Nowhere did anyone say x=7

[pure inlet]

^

[glass lichen]

Where did Ansh say x=7?

That was just showing you why x=2 was wrong

[wary stream]

That was to show what happens when you plug in x = 3

[wary stream]

It was x = 3

That's what they said

[pure inlet]

i said 3

[glass lichen]

Ok then idk why Ansh did x=2

,calc 3(3)+1

[ocean seal]

Result:

10

[glass lichen]

there you go, still wrong

[wary stream]

Ansh flipped parentheses

[pure inlet]

so i was right

[wary stream]

No

[pure inlet]

i said x = 3

[glass lichen]

10=6??

You think 10=6?

[wary stream]

2x + 1 = 6
My example
Ansh did x * 2 + 1

[little drum]

omg the equation was 2x +1 lmao

death by parentheses

[wary stream]

Still wrong btw

[pure inlet]

i ge tit

ill try to solve it

what was the question again

[wary stream]

2x + 1 = 6

Solve for x

[pure inlet]

ok

can u give me the first step how to do it and let me finish it myself?

[wary stream]

Apply algebra

[pure inlet]

and how do i do that -_-

[glass lichen]

GOOGLE

[wary stream]

If you can't solve something that simple, I suggest looking a resources

[glass lichen]

Ask your teacher

Ask your peers

[wary stream]

Get a tutor

[glass lichen]

Read the textbook

[pure inlet]

cant u just teach me here

[glass lichen]

This isn't a teacher/tutoring server

[pure inlet]

oh

[wary stream]

It's a basic concept that is all over the internet

[pure inlet]

what is this server then

[wary stream]

Videos can teach you

[glass lichen]

It's help/discussion.

[glass saffron]

Let us rephrase: what we'd really like to find from this equation is, for what value of $x$, does $2 \times x+1$ equal $6$

[pure inlet]

alr ima watch this real quick and ill come back and ill try to solve the equation

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

[wary stream]

Use \cdot instead of *, just to look better

[little drum]

2 \times x

[ocean seal]

cat cat >w< pspspspsmeowmeow🐈

[wary stream]

Or \times

[glass saffron]

thanks i was just looking for that

[wary stream]

$x$, does $2 \cdot x+1$ equal $6$

[ocean seal]

dldh06

[wary stream]

I think \cdot is better

[pure inlet]

ill brb ima watch this and ill come back to answer the equation byeeee

[glass saffron]

i like it more too, but a primary school student is going to be more used to the cross

[wary stream]

Once you leave primary school, x and times conflict a lot if written poorly

[glass saffron]

Yes, yes, of course!

in truth, i'd rather g36 didn't get confused over what the dot meant - his track record is quite poor

[wary stream]

Thankfully latex makes it visibly different

[wary stream]

I honestly think it's too late for confusion

[glass saffron]

in fact, despite using latex quite often, i actually forget the names for \cdot and \times

i dont use cross products, or cartesian products

im going to keep forgetting it >m<

[pure inlet]

I think i found it out

ok whats the question again

@wary stream

[glass lichen]

Scroll up

[pure inlet]

or i scrool up

2x + 1 = 6

ok

[wary stream]

Solve for x

[pure inlet]

2

x = 2

right?

[wary stream]

No

[pure inlet]

bruh

ok wait

[wary stream]

Plug in 2 and check

If x = 2, does that satisfy the problem?

[pure inlet]

idk

2x

?

[wary stream]

If x = 2, that means plug 2 for x

[pure inlet]

um

maybe i should re-watch the vidoe]

[glass saffron]

when x=2, this equation becomes
2*2 + 1 = 6
4 + 1 = 6
5 = 6
so, no

[wary stream]

My opinion is relearn how to solve equations

[pure inlet]

2x + 1 = 6

so u do 1-1 and 6-1

cross out the 1-1

6-1

=5

so

wait dont say anything

[glass saffron]

... that was a promising start, but you've dropped the 2x

[pure inlet]

2x = 5

so then

divid both by 2

[wary stream]

Let the kid do it on their own

[pure inlet]

cross 2/2

2/5

um

kinda doesnt work

so5/2

i think i already messed up

um

[wary stream]

How did you get 2/5 in the first place?

It was 2x = 5

If you divide by 2 on both sides, you shouldn't have gotten 2/5

[pure inlet]

ik

i did

oh

i didnt read it

i shouldn't of got it

wait so was 2x = 5 the answer -_-

[wary stream]

No

[pure inlet]

oh

[wary stream]

You didn't find x

[pure inlet]

ik

i was going to

thats why i divid both sides by 2

so 2/2

is

1

and 2/5

thatts not possible

so i already messed up

wait no i didnt

2/5 25

x = 26

no

not at all

um

[pure inlet]

wait

ok um

i dropped the 2x

how did i do that

ohhh

wait

so

2x = 5

what do i do after that

[wary stream]

Refer to video

[pure inlet]

ok

he grabbed the number from 2x

and divid both numbers by 2

from the 2x

2 so 2/2

1

and 2/5

isn't possible

so idk what i did wrong

[wary stream]

How are you getting 2/5?

[pure inlet]

because i divd both sides by 2

so 2/2

is 1

and 2/5

[wary stream]

But it was 2x = 5

[pure inlet]

are u thinking this as a fration?

2/5

[wary stream]

So where is 2/5 coming from?

[pure inlet]

2/5 is 2 divided by 5

i got the 2/5

because u have to divid both sides by 2

[wary stream]

As stated, it's 2x = 5

[pure inlet]

yes

[wary stream]

You divide by 2 on both sides

[pure inlet]

yes

so i divid 2x by 2

and 5 by 2

[wary stream]

So where on earth is 2 divided by 5 coming from?

[pure inlet]

2x = 5

i got the 5 from there

and divided it by 2

oohhhh

woops

5 by 2

not 2 by 5

mb

wait

'what

[wary stream]

If you are stating 5 divided by 2, how did you get 2 divided by 5

[pure inlet]

im even more confused now

[pure inlet]

idk

[wary stream]

Here you said 5 divided by 2

[pure inlet]

yes

[wary stream]

Here it's 2 divided by 5

[pure inlet]

ik

[wary stream]

So then where is 2/5 coming from?

[pure inlet]

because your supposed to divid 2 by 5

[wary stream]

No

[pure inlet]

because im supposed to divid both of them by 2

?

🤨

[wary stream]

You don't do 2 divided by 5

[pure inlet]

so do i do 5 / 2

instead

yvbmtyuj76h67y7ul;'

[wary stream]

If you have 2x = 5

If you divide by 2 on both sides

How do you end up with 2/5?

[lone heart]

@pure inlet Has your question been resolved?

[pure inlet]

So

I’m back

I’m very confused

So I ended off with 2/5

Which I wasn’t supposed to get

So 2x = 5

Is good

And now I have to solve for x

Which idk what to do

Bc if I divide both by 2

2/2 is 1

And then 2 divided by 5

Which isn’t possible

So do I add the 1 to the 5

And get 6

So then it’s 2/6

Which is 3

So 3 = x?

@wary stream

[wary stream]

No

What?

[pure inlet]

Dang it

I really thought I had it

[wary stream]

How about a slightly easier one?
2x + 2 = 6

Solve for x in that one

[pure inlet]

It’s basically the same thing but ok

2x = 4

Divide both by 2

So 2/2 is 1

2/4 is 2

So x = 2

?

[wary stream]

2/4 is not 2

[pure inlet]

No?

Oh

I’m dumb

Wait

What is it then

2 goes into 4

2 times

[wary stream]

You're saying 2 divided by 4

That's different from 4 divided by 2

2/4 is 2 divided by 4

[pure inlet]

Phhh

Ohhh*

I meant 4/2

Is 2

[wary stream]

That's right for that example

Now do 2x + 1 = 6

[pure inlet]

Ok

I’ll try

2x = 5

Divide

Both by 2

2/2

1

5/2

Um

[wary stream]

Yes that's better

So what does x equal to?

[pure inlet]

2

5/2 = 2

[wary stream]

This example

[wary stream]

What? No

[pure inlet]

What is it

2.5?

[wary stream]

Have you never dealt with fractions?

[pure inlet]

Yes

Many times

[wary stream]

So why are you saying 5/2 = 2?

[pure inlet]

Um

Because 5/2 is 2.5

[wary stream]

But you said 5/2 is 2

[pure inlet]

Yeah but I took the .5 away

[wary stream]

You never said 2.5 initially

[pure inlet]

Ik

[wary stream]

You can't make decimals disappear

[pure inlet]

Oh

So it has to be there

[wary stream]

2 and 2.5 are completely different numbers

[pure inlet]

Well yeah duh

So x = 2.5

Do I round up the 2.5 to 3

?

[wary stream]

It's like saying with money, you're supposed to get $2.50 back but the server just gave $2 because they took the $0.5 away

[ocean seal]

dldh06

[wary stream]

No, you don't round either

[pure inlet]

Oh

Why is math so hard

[wary stream]

It's not if you understand what you're doing

And that was simple algebra

[pure inlet]

I guess

So back to this

2x + 1 = 6

[wary stream]

You did that already

[pure inlet]

1-1 cross it out

I did?

[wary stream]

Starting here

[pure inlet]

Oh

Well I’m at 2x = 5

Now this is the “hard part”

Hard for me

Ok 2x = 5

All I need u to tell me

Do I have to divide both by 2

[wary stream]

What do you mean have to?

[pure inlet]

Like do I have to do it to get the answer

[wary stream]

That's the only way to get x by itself

[pure inlet]

Oh ok

That’s all I needed to know

[wary stream]

What other way do you have to solve for x?

[pure inlet]

Idk

[wary stream]

Dividing by 5?

[pure inlet]

Idk

Is that a question

Or are u telling me that

[wary stream]

It's more a rhetorical question

[pure inlet]

Ok ima just go with it’s a question bc idk what rhetorical

[wary stream]

Rhetorical question is a question that doesn't need an answer

[pure inlet]

Oh ok

So 2x = 5

[wary stream]

Solve for x

[pure inlet]

Ok

Divide both by 2

2/2 = 1

Now before I get to 5/2

Does the 1 have to do with anything

[wary stream]

It's 1x = 5/2

[pure inlet]

What

Oh yeah 2 from 2/2 had the x

So x goes to 1

So it’s 1x

So now I do 5/2

5/2 = 2.5

So x = 2.5?

Prob nkt

Not*

[wary stream]

Or you could leave it as a fraction

Fractions exist

[pure inlet]

But then that would be improper right?

[wary stream]

If you had a value of 1/3

It's better to say 1/3 than 0.333333333

[pure inlet]

True

Wait then is x = 0.4

[wary stream]

How did you get 0.4?

[wary stream]

You just said x = 2.5 here

[pure inlet]

So 0.4 is a 2/5

So x = 2/5

?

[wary stream]

Why is it 2/5?

[pure inlet]

Wait

Nvm im dumb

I went back

I love how easy Math is 😭😭😭

[wary stream]

The math I'm showing isn't hard

It's your ability to understand the process

[pure inlet]

to a kid in 7th grade failing this is embarrassing

[wary stream]

Maybe a tutor would help or asking your teacher for help

[pure inlet]

Maybe I tutor

Maybe a tutor

Bc I’m not gonna ask my teacher

Because he’s the type to randomly say that Idk how to do math at all

[wary stream]

Your choice

Doesn't matter

[pure inlet]

Ok

[lone heart]

@pure inlet Has your question been resolved?

[lone heart]

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[obtuse cove]

Please ping me when you are ready to assist.

[tacit arch]

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

[obtuse cove]

Number 1?

[tacit arch]

explain where you are stuck.

[obtuse cove]

🤣

I need help figuring out what to do.

[tacit arch]

plot the points

[obtuse cove]

Ok... 🤣

?

[lone heart]

@obtuse cove Has your question been resolved?

[tacit arch]

Is this a new problem or are you still asking about #1

[obtuse cove]

I finished number 1.

I need help with number 2.

I need to be done with school before 5:30. 🙏

<@&286206848099549185>

Need help with the above post, thank you.

[tacit arch]

And where are you stuck

[obtuse cove]

I just need a step by step walk through.

[tacit arch]

Oh you just want the full answer?

[obtuse cove]

That works to. 😏

[tacit arch]

yea that's not what this server is for

you're supposed to show what you've attempted

if you want answers, hire a tutor

[obtuse cove]

You baited me huh?

Or you were being sarcastic. 🤣

[tacit arch]

it followed from this

[obtuse cove]

What followed?

[lone heart]

@obtuse cove Has your question been resolved?

[lone heart]

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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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[cinder sundial]

Can someone put it on calculator for me

What I get from my calculation is 2989/4320

[cinder sundial]

Which Approximate to 0.691

[bleak ridge]

Do you not know how to put it into wolfram

[cinder sundial]

But it’s different from the correct answer tho

[cinder sundial]

Yes

[paper holly]

im getting 3029/4320

[bleak ridge]

,w nCr(5,3)

[ocean seal]

Results provided by WolframAlpha

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

Requested by PapaBread#3820

[bleak ridge]

[wary stream]

Depends on how you're reading that handwriting

[cinder sundial]

Should I send the original question

[paper holly]

its pretty easy to understand

[wary stream]

Are you reading that as 840 + 1890 + 252 + 7?

Cause that's what I see

[bleak ridge]

,w 4 nCR(7,4)/nCr(10,4) + 3 nCr(7,3) * nCr(3,1) / nCr(10,4) + 2 * nCr(7,2) * nCr(3,2)/nCr(10,4)+nCr(7,1) * nCr(3,3) / nCr(10,7)

[ocean seal]

Results provided by WolframAlpha

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

Requested by PapaBread#3820

[bleak ridge]

Oh no

[cinder sundial]

Shit

[paper holly]

yess

[cinder sundial]

So there’s sth wrong in my calculation

[paper holly]

im also getting 2.825

[paper holly]

yess

[bleak ridge]

Or something wrong with mine

[paper holly]

no i got the same answer as u 👀

[wary stream]

,calc 840 + 1890 + 252 + 7

[ocean seal]

Result:

2989

[cinder sundial]

There’s a bag it has 7 white balls and 3 red balls, now we pick 4 balls out from the bag, then the expectation of white balls is?

[cinder sundial]

That’s the original question

[bleak ridge]

I wonder if wolfram would self destruct if you put that into its input

[cinder sundial]

My equation seems fine, I’m just having trouble to calculate the value

[paper holly]

try the calculation again

[cinder sundial]

The answer is 2.8

[paper holly]

yesss

2.825 right?

[cinder sundial]

2.8 is the answer on the book

[paper holly]

oh

something might be wrong with the equation

[cinder sundial]

The resolution of the book says, the expectation of white ball is 1 * (7/10)+0*(3/10)=7/10 if we only pick a single ball out from the bag

Then we multiply it by 4, (7/10)*4= 28/10=2.8

<@&286206848099549185>

[cinder sundial]

But I think my solution is also correct

[cinder sundial]

Right? Can someone check the equation for me

[lone heart]

@cinder sundial Has your question been resolved?

[cinder sundial]

.close

[lone heart]

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[lone heart]

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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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[lone heart]

@alpine sable Has your question been resolved?

[tidal mural]

So if 3/7 of the book is read, how much of it is left unread?

what fraction of the book is left unread?

So lets say that the length of the book is x. how can you state this in an equation?

I am helping you. Im not just going to give you the answer though

The whole point of this is to help you get to the answer yourself, not to just solve problems for people.

[subtle mantle]

Stfu quipcel

[winter bay]

ratio

[rapid thistle]

Yeah buddy you're not gonna have a great time here if you just expect to get answers outright

The point of the place is, as opfromthestart said fromthestart, you are guided but are expected to put some thought in

Better for you too tbh for when the test comes around

[tidal mural]

If you dont care enough to put in effort, neither do we.

[lone heart]

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[lone heart]

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

[serene moon]

hi

[serene moon]

i dont understand this

why is it saying then

[supple tundra]

Ok what don't you get?

[serene moon]

how is it possible to factor t-1 from the denominator

(t-1) and (1-t) arent the same thing?

[supple tundra]

(1-t) = -(t-1)

[serene moon]

ok i understand that now thanks

i just dont really understand what they are actually doing

like i dont understand what this sentence means

and the equations that preceed

[white crown]

it’s just saying you can find the velocity by taking the limit instead of using the first theorem which uses the “h”

[white crown]

first you learn the definition of the derivative (I.e., using the h), then learning to take the limit as it approaches some number instead of to 0 only, then you’ll learn derivatives

[lone heart]

@serene moon Has your question been resolved?

[supple tundra]

Let's suppose this is a position graph against time and we want to calculate the slope at t=1

Ideally we want a line which has the exact same slope as the graph at t=1

So we keep shkrinking the interval

my explanation is wack

lemme find a video

https://www.youtube.com/watch?v=ANyVpMS3HL4

[lone heart]

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[viral perch]

<@&286206848099549185>

[viral perch]

Help <@&286206848099549185>

What do wrong

[merry depot]

Remember:
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• Show your work, and if possible, explain where you are stuck.
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[marble coral]

The expression is 28 + 5h
5 hours means h = 5

28 + 5h = 28 + 5×5 = 53

53 < 60

You have to close channel now

[buoyant kayak]

don't do people's work for them

[marble coral]

Sorry

[lone heart]

@viral perch Has your question been resolved?

[lone heart]

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[zenith compass]

I try to inequalities of digits

But the outcome is problematic

Can anyone tell me why?

And how to do it properly

[tight locust]

ok the amount of digits a number has is floor(log_10(x)+1)

Equivalently

floor(log10(10x))

[lone heart]

@zenith compass Has your question been resolved?

[zenith compass]

so number of digits of $a=\floor{log_{10}(10m)}$ and that of $b=\floor{log_{10}(10n)}$?

[ocean seal]

Trenton

[zenith compass]

$floor(log_{10}(10m)/floor(log_{10}(10n)$

[ocean seal]

Trenton

[zenith compass]

Idk it is legal or not to write:

$floor(log_{10}(10m)/floor(log_{10}(10n)$

[ocean seal]

Trenton

[zenith compass]

$=floor((log_{10}(10m)/(log_{10}(10n))$

[ocean seal]

Trenton

[zenith compass]

$=floor(log_{10n}(10m)$

[ocean seal]

Trenton

[buoyant kayak]

\floor

[zenith compass]

Opps thx

so number of digits of $a=\floor{log_{10}(10m)}$ and that of $b=\floor{log_{10}(10n)}$?

[ocean seal]

Trenton

[zenith compass]

$\floor{log_{10}(10m)}/\floor{log_{10}(10n)}$

Idk it is legal or not to write:

$\floor{log_{10}(10m)}/\floor{(log_{10}( 10n)}$

[ocean seal]

Trenton

Trenton

[zenith compass]

$=\floor{(log_{10}(10m)/log_{10}(10n)}$

[ocean seal]

Trenton

[zenith compass]

$=\floor{log_{10n}(10m)}$

[ocean seal]

Trenton

[zenith compass]

Well basically as floor function is just a round down

So I am not sure if I can join two log function together

[little drum]

._.

da heck?

You're supposed to show, number of digits of [a/b] is equal to whatever-

$m-n- 1 < L = \floor{\log (10\floor{\frac{a}{b}})} \leq m - n + 1$

[lone heart]

@zenith compass Has your question been resolved?

[lone heart]

@zenith compass Has your question been resolved?

[zenith compass]

Umm I get sth a bit different

How does the 10 multiplying $\floor{a/b}$ come?

[ocean seal]

Trenton

[zenith compass]

is this proof ok?

[little drum]

where'd you start though lmao

[zenith compass]

I think this two contradicts each other?

[little drum]

you know.. there was a far simpler way to this...

Just write: $a = bq + r$

[little drum]

and conclude about the number of digits in q

[zenith compass]

This is the division algorithm?

[zenith compass]

Do you mean this

[zenith compass]

<@&286206848099549185>

[solemn grove]

write it in standard form

personally feel like it makes your life much easier

you’ll get a = x* 10^m and b in terms of y and n

a/b = x/y * 10^m-n or something

and you can look at the two specific cases

when (x/y) < 1

and when it’s greater than one

[little drum]

nuuu

a is a m-digit number

b is a n-digit number

[zenith compass]

umm

[little drum]

0 ≤ r < b

[zenith compass]

Yes

So a-r at most m-1 digit?

[little drum]

yeah

*m - digit

whenever you're stuck, consider taking examples

300, 288 => 300 = 288(1) + 2

clearly, 300 - 2 has m = 3 digits

[zenith compass]

1000=999(1)+1

1000-1 has 3 digits

While 1000 has 4

[little drum]

Yeah

[zenith compass]

Wait but according to the question, we take the floor function

So is that the value of r doesn’t matter?

[little drum]

no issues, forget the floor function for the time being

[zenith compass]

Alright

[little drum]

Euclid's division already take cares of floor issues lol

[zenith compass]

Ok

[little drum]

when writing a = bq + r, you already have 0 ≤ r < b

so a/b = q + r/b

where q is integer

and r/b is fraction

[zenith compass]

Ok

[little drum]

so

[a/b] is just q

[zenith compass]

R/b will be removed anyway

[little drum]

Yeah

Now, if bq is either m digits or m - 1 digits... and b is fixed at n digits => q needs to be (m - n - 1) or (m - n) digits

I'm getting these by writing b, q as polynomial in "10" with degrees n and k respectively

$b = 10^{n-1} b_{n-1} + 10^{n-2} b_{n-2} + \ldots + b_0$

[little drum]

where $b_i$s are the digits

[zenith compass]

Ok so they are the definition of the decimal system

But what is k

[little drum]

k is highest power of 10 in the decimal representation of q

and you show that k = m - n - 1, m - n - 2 are the only possibilities if a is m-digit

[zenith compass]

$q = 10^{k-1} q_{k-1} + 10^{k-2} q_{k-2} + \ldots + q_0$

[ocean seal]

Trenton

[zenith compass]

$bq=(10^{n-1} b_{n-1} + 10^{n-2} b_{n-2} + \ldots + b_0)(10^{k-1} q_{k-1} + 10^{k-2} q_{k-2} + \ldots + q_0)$

[ocean seal]

Trenton

[little drum]

$bq = 10^{k + n - 2}b_{n-1}q_{k-1} + 10^{k+n-3}(q_{k-1}b_{n-2} + q_{k-2}b_{n-1}) + \ldots$

[zenith compass]

So the digits of bq is at least k+n-1

[little drum]

yeah

okay digits

k + n - 1 = m - 1 gives k = m - n

[zenith compass]

$0<b_{n-1}q_{k-1}\leq81$

[little drum]

whaaa

[zenith compass]

They are digits

[little drum]

Yep

[zenith compass]

At most 9 for each

[little drum]

honestly, try convincing yourself on paper

rigor is best to be done on paper

[ocean seal]

Trenton

[zenith compass]

Ok i will try

[lone heart]

@zenith compass Has your question been resolved?

[zenith compass]

.close

[lone heart]

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[zenith compass]

I know a-b is the quantity of wine after one time

But why square when it is repeated?

I mean

If square

Why the denominator don’t have to square too

[glad sluice]

(a-b):b would be the ratio of wine:water after first time right?

[zenith compass]

Yes

[glad sluice]

so for every "a" parts, (a-b) is wine and b is water

so what would be the composition of 1 part

[zenith compass]

Umm

So what happen when the process repeat

[glad sluice]

we'll get there

[glad sluice]

using this, find how much wine is in "b" parts

and we're removing "b" parts from the initial "a" parts

so just subtract

[zenith compass]

b x (a-b)/b?

[glad sluice]

nope