help-0

[shadow sparrow]

sorry

[alpine sable]

same thing

[shadow sparrow]

Yeah

Kk

so $-4*2x^{-4-1}$

First one

[ocean seal]

Huntifer

[alpine sable]

Yeah

[shadow sparrow]

$-8x^{-5}$

[ocean seal]

Huntifer

[shadow sparrow]

Next one

[alpine sable]

Wait no

[shadow sparrow]

Oh wait

dur hur

lmao

https://tenor.com/QO8C.gif

[alpine sable]

lol

Now do it correctly

[shadow sparrow]

$-\frac{8}{x^5}$

[ocean seal]

Huntifer

[shadow sparrow]

[alpine sable]

No

$$-3\times(-3)=-9\neq-8$$

[shadow sparrow]

Sorry I feel dumb

[ocean seal]

Azaradichta

[alpine sable]

Oh wait it's 9

[shadow sparrow]

wait -3 and -3

what

[alpine sable]

$$\dv{x}(-3x^{-3})=3\dv{x}x^{-3}$$

[ocean seal]

Azaradichta

[alpine sable]

$$\dv{x}(x^{-3})=-3x^{-4}$$

[ocean seal]

Azaradichta

[alpine sable]

Overall,

[shadow sparrow]

oh

I was still doing the first one

Like simplifying it

[alpine sable]

Soryr

[shadow sparrow]

$-4*2x^{-4-1}$

[ocean seal]

Huntifer

[shadow sparrow]

applying power rule to 2x^-4

[alpine sable]

Yeah right

-8x^(-5) is right

[shadow sparrow]

Then I was simplifying it

okay

I was so confused

[alpine sable]

[shadow sparrow]

Ok so

-3x^-3

Gonna be

$-3*-3^{-3-1}$

[ocean seal]

Huntifer

[alpine sable]

yeah

[shadow sparrow]

Or in this case

oops forgot the x

[alpine sable]

😅

[shadow sparrow]

$9x^{-4}$

[ocean seal]

Huntifer

[alpine sable]

Yes

[shadow sparrow]

Then there is -4x which becomes 4

So

[alpine sable]

-4

[shadow sparrow]

Yeah

[alpine sable]

And then just write everything together

[shadow sparrow]

$-8x^{-5}+9x^{-4}-4$

[ocean seal]

Huntifer

[alpine sable]

Nice

[shadow sparrow]

So now to turn it into

the weird form that is "correct"

[alpine sable]

The above one is correct as well

[shadow sparrow]

Yeah I know, but the test wont count it as correct

[alpine sable]

In calc, you will encounter such things most of the time, the question having multiple answers

For example

[shadow sparrow]

Yeah I know, the testing thing we use only wants it one specific way though

so it'll fail you on a question if its in another form

for example

it wants it like this

[alpine sable]

$$\dv{x}\left(\frac{x}{1-x}\right)=\dv{x}\left(\frac{1}{1-x}\right)$$

[ocean seal]

Azaradichta

[alpine sable]

Ikr

Very sad

[shadow sparrow]

Yes

college math be very sad

especially tests

[alpine sable]

That's the thing for online, right?

[shadow sparrow]

yeah because 1 and x are interchangeable in those cases

[alpine sable]

Teachers don't mind this

[shadow sparrow]

Yeah

Its online college because covid

[alpine sable]

They both differ by 1

[shadow sparrow]

So if we don't enter something in a specific form

no credit

[alpine sable]

ic

😑

[shadow sparrow]

never doing this again

lmao

online college bad

Granted I didn't have a choice

[alpine sable]

[shadow sparrow]

So power rule applies with D too?

[alpine sable]

D what?

[alpine sable]

Oh yeah

yeah it works

Just simplify first and then go

[shadow sparrow]

You just do the same thing to the thing as before

so its

$\frac{5}{x^{2/3}}$

Then

[alpine sable]

No

[shadow sparrow]

oh wait

[alpine sable]

2/3

[shadow sparrow]

2/3 sorry

[alpine sable]

Yea

[ocean seal]

Huntifer

[shadow sparrow]

Denom is always the root of

And if its just sqrt x its 1/2

[alpine sable]

yes

[shadow sparrow]

So uh

Then

$5x^{-\frac{2}{3}}$

[ocean seal]

Huntifer

[shadow sparrow]

Then power rule

[alpine sable]

$$\sqrt[n]{x^m}=x^\cfrac{{m}{n}}$$

[ocean seal]

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

[alpine sable]

Wow it doesn't work

[shadow sparrow]

As yes

[alpine sable]

I have to change my preamble

[shadow sparrow]

the nonexistent denom

mafth

[alpine sable]

[shadow sparrow]

I swear to god

imagine

non-existant numbers

we are moving past imaginary

we are now using non-existent numbers in our calculations

[alpine sable]

There are numbers past imaginary

That you will learn later, (just as a side note)

[shadow sparrow]

Ah yes

the fairy numbers

so

[alpine sable]

[shadow sparrow]

5x^-2/3

[alpine sable]

Yes

[shadow sparrow]

so now

[muted raft]

what does cfrac do?

[shadow sparrow]

$-\frac{2}{3}*5x^{-\frac{2}{3}-1}$

[ocean seal]

Huntifer

[alpine sable]

It creates fractions like ½, ¾ etc.

I thought the bot included it's package

[muted raft]

ah $\cfrac{a}{b}$

[alpine sable]

But it didn't

[ocean seal]

zslya

[muted raft]

huh

[alpine sable]

[shadow sparrow]

$-\frac{10}{3}x^{-\frac{5}{3}}$

[alpine sable]

Wait

The exponent was -2/3

[shadow sparrow]

oh

oops

[alpine sable]

So, it should be -2/3 - 1 = -5/3

[ocean seal]

Huntifer

[shadow sparrow]

[alpine sable]

Nice emoji, I don't have nitro

[alpine sable]

^this one

[shadow sparrow]

Kk

[alpine sable]

Yeah it's correct

[shadow sparrow]

Let me check it in the thing

yep

so

[alpine sable]

Congrats! You just acquired Level 1 knowledge of Power Rule!

[shadow sparrow]

it is correct

[alpine sable]

Orz

[shadow sparrow]

but it is in this form

$-\frac{10}{3x^{5/3}}$

[ocean seal]

Huntifer

[alpine sable]

Ofc

[shadow sparrow]

I get a B if I get just 25% on the exam tomorrow

So I'm not SUPER scared but

Pretty scared because I'm looking at this review and drawing blanks all over the place

[muted raft]

Ahh I see the purpose of cfrac now @alpine sable

[alpine sable]

be careful with powers the computer is stupid

[shadow sparrow]

So

[muted raft]

$\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1}}}$ vs $\frac{2}{1+\frac{2}{1+\frac{2}{1}}}$

[shadow sparrow]

If you're still around, here are some dummy ones

[ocean seal]

zslya

[alpine sable]

Wait

That is \dfrac i suppose

[muted raft]

hmm?

[alpine sable]

You got to apply chain rule

[muted raft]

what is dfrac now

[shadow sparrow]

Yeah

[alpine sable]

It's short for \displaystyle\frac

[shadow sparrow]

f(g(x)) = f'(g(x))g'(x)

[muted raft]

Ah

[shadow sparrow]

I can't do that in the form its in tho right now right?

[alpine sable]

If you don't use LaTeX on pc or somewhere, then you won't understand the usage of displaystyle

[shadow sparrow]

For a

Actually..

Can't I apply the same concept to A?

As with the power thing

[alpine sable]

Let $u=4x^2-4x+3$. By chain rule,
$$\dv{x}f(x)=\dv{u}f(u)\cdot\dv{x}u$$

[ocean seal]

Azaradichta

[alpine sable]

Makes more sense if you let y=f(x)

[muted raft]

I use latex on mac

[shadow sparrow]

$1(4x^3-4x+3)^{-3}$

[ocean seal]

Huntifer

[shadow sparrow]

I know this is probably ghetto but

[oblique stirrup]

what is √(2) times 2 exact value? forgot the rules

[shadow sparrow]

Pretty sure its not a real number and is a decimal

[alpine sable]

It's just $2\sqrt2$, or $2\cdot2^{\frac12}=2^{1+\frac12}=2^{\frac32}$.

[ocean seal]

Azaradichta

[oblique stirrup]

ok i thought so, thanks

thats a crazy command lol

[shadow sparrow]

https://tenor.com/bpm8Z.gif

[alpine sable]

$$\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}$$

[shadow sparrow]

So I'm assuming the way I tried it above was wrong?

[ocean seal]

Azaradichta

[alpine sable]

Yeah everyone knows power rule and Chen lu

[alpine sable]

When did you try?

I mean what?

[shadow sparrow]

$1(4x^3-4x+3)^{-3}$

[ocean seal]

Huntifer

[shadow sparrow]

This monstrosity

[alpine sable]

That's true

Now you gotta substitute u=the thing in the brackets

[muted raft]

$\dv{y}{x}$ hack

[shadow sparrow]

1u^-3

[ocean seal]

zslya

[shadow sparrow]

or just u^-3

[alpine sable]

Sorry i forgot

[alpine sable]

Yes

[muted raft]

[alpine sable]

Now use Chen Lu

[shadow sparrow]

Chen lu...?

[alpine sable]

Chain Rule

[shadow sparrow]

Is that a martial art I don't know?

[alpine sable]

[maiden path]

bruv

[shadow sparrow]

Wait how would you use chain rule here?

chain rule is d/dx f(g(x))

isn't it?

[alpine sable]

$$\dv{y}{x}=\dv{y}{u}\dv{u}{x}$$

[ocean seal]

Azaradichta

[alpine sable]

^ Chen Lu

[shadow sparrow]

the chain rule I have is

[alpine sable]

$$\dv{x}f(g(x))=f'(g(x))g'(x)$$

Ikr

[ocean seal]

Azaradichta

[shadow sparrow]

$\frac{d}{dx} f(g(x)) = f'(g(x))g'(x)$

yeah

[ocean seal]

Huntifer

[alpine sable]

I just put f(x)=y and g(x)=u

So that it makes more sense👍🏼

You can think of it as dividing and multiplying by du

[shadow sparrow]

uh

hmm

[alpine sable]

$$\dv{y}{x}=\dv{y}{\textcolor{yellow}{u}}\dv{\textcolor{yellow}{u}}{x}$$

[ocean seal]

Azaradichta

[shadow sparrow]

Yeah

Wait so dy

would be derivative of 1

?

[alpine sable]

No

$u^{-3}$

[ocean seal]

Azaradichta

[shadow sparrow]

Yeah

and u is 4x^3-4x+3

[alpine sable]

Yes

[shadow sparrow]

so what is dy and dx?

In this case

[alpine sable]

$$f'(x)\equiv\dv{y}{x}$$

[ocean seal]

Azaradichta

[shadow sparrow]

When I think of f(g(x)) I think of

3(2x^2+3)+3

As an example

Where f(x) is 3x+3

And g(x) is 2x^2+3

[alpine sable]

$$f(x)=(\underbrace{4x^2-4x+3}_{g(x)})^{-3}$$

[ocean seal]

Azaradichta

[shadow sparrow]

Yeah

So f(x) is denoted as ^-3?

[alpine sable]

and $f(x)=x^{-3}$

[ocean seal]

Azaradichta

[alpine sable]

Yes

[shadow sparrow]

I always forget that exponents can be the outside formula sometimes

sorry

so in this case

derivative f(x) is

-3x^2

[alpine sable]

Yes

[shadow sparrow]

Where you fill in for g(x)

Then multiply by the derivative of g(x)

[alpine sable]

Yes!

[shadow sparrow]

Yeah

[alpine sable]

💯

[shadow sparrow]

I was getting confused by the fraction thing

Because I have to see everything in numerical use, the conceptual stuff with derivatives confuses me for some reason

[alpine sable]

You will get it with time

[shadow sparrow]

So at this point I see d/dx and I'm just like, ah yes, its telling me to differentiate, I know that

[alpine sable]

Yeah

[shadow sparrow]

So in this case anyways

[alpine sable]

Remember the Liniati Lu, Pawa Lu, Koshan Lu, Chen Lu,

[shadow sparrow]

-3(4x^3-4x+3)^2 for the first part

[alpine sable]

Yes

[shadow sparrow]

then g'(x) is gonna be

12x^2-4

[alpine sable]

Yes

[shadow sparrow]

So

$-3(4x^3-4x+3)^2(12x^2-4)$

[alpine sable]

No

Multiply

[shadow sparrow]

oh oops

[ocean seal]

Huntifer

[alpine sable]

Yes

[maiden path]

whered u get these

[shadow sparrow]

So the reason you use u is just so you can simplify it easier then substitute after?

[alpine sable]

On bprp, Papa flammy, Dr. πam channel

[alpine sable]

You don't need to think about it, I suppose.it will just confuse you more

[shadow sparrow]

Well so like

[alpine sable]

Use the fg form as of now

[shadow sparrow]

$-3(u)^2(12x^2-4)$

[alpine sable]

Yes

[ocean seal]

Huntifer

[shadow sparrow]

So uh

[alpine sable]

$-3u^{-2}\cdot u'$

[ocean seal]

Azaradichta

[alpine sable]

Anyways, bye

Because I also have to do my work

Cya later @shadow sparrow

also add me as a friend if you don't mind

[shadow sparrow]

lol, no worries, yeah I'm praying I can manage tomorrow, we'll see, tyvm for the help!

did do

At the very worst

I get a C tomorrow

[alpine sable]

Thanks

[shadow sparrow]

[alpine sable]

Good luck

[harsh acorn]

is the answer 138

[tough hatch]

yes

[brave fossil]

how would i go about doing this>

<@&286206848099549185>

[vale wigeon]

don't multipost. i answered you in #discrete-math

[winter roost]

How do I go about showing that:

$$ \partial (B_\epsilon (x)) \subseteq { y \in X : d(x,y) = \epsilon } $$

[ocean seal]

Cursor

[winter roost]

I'm guessing I do some sort of contrapositive here

[vale wigeon]

i mean you could?

you need to show that a point on the boundary of B_ε(x) is exactly at distance ε from x

you can instead show that any point not at distance ε from x is either in the exterior or the interior of the ball, depending on whether it's further or closer than ε

[stark wadi]

Mike is running towards the last pie for sale at the school bake sale. Jack see Mike running and Jack decides to sprint for the pie. Mike runs at full speed, 5.3 meters/second, while Jack speeds up at a rate modeled by the function 1.5x^2 + 0.3x. The pie is 25 metes away from Jack when he begins to run. Mike is already 4 meters ahead. Who reaches the pie first? Explain how rounding an exact answer could affect the results.

[vale wigeon]

^ this person is getting help in #help-9, whoever wants to post their question can go ahead

[upper kayak]

hi

i'm having trouble understanding the concept of instantaneous rate of change

my confusion is similar to the arrow paradox

how can there be a rate of change where there is no change?

i could calculate the rate of change of the line y = x

[vale wigeon]

the instantaneous rate of change is not by itself a "bona fide" rate of change

rather, it's what you get in the limit as you take average rates of change in your function over progressively smaller intervals containing your point

[upper kayak]

so nigh-instantaneous is a better term?

[vale wigeon]

no

actually, 3b1b has a video in his essence of calculus series which addresses this very issue

https://www.youtube.com/watch?v=9vKqVkMQHKk

[upper kayak]

can you please link it? I've only watched about half of the first one

oh, thanks!

[alpine sable]

any1 know what im doing wrong?

[vale wigeon]

$\sqrt{4 \times 7} \neq 4 \sqrt{7}$

[ocean seal]

Ann

[alpine sable]

ohh do i multiply the square root of 4 by the 2?

aka 2x2√7

[vale wigeon]

if you wish to put it that way.

[upper kayak]

okay, that video cleared up a lot of confusion

so it is indeed as he puts it, sidestepping the paradox

sneaky human devilry

i love it

[alpine sable]

where did the n go lmao

[vale wigeon]

1/n appoaches 0

[alpine sable]

ohh

so if n approaches infinity, 1/n approaches 0?

[vale wigeon]

yes

[alpine sable]

Ah

[lime lintel]

yall know what a phase is

and a period?

[calm grove]

What's the value of sqrt4)

??

[alpine sable]

i figured it out thx

[calm grove]

[calm grove]

You can remember like this
Imagine n as largest number possible as you can
Like n = 1000000 , then 1/n = 0.000001
And you can already see how close it is to 0
And as you increase the value of n more and more 1/n will go more close to 0

[alpine sable]

ahh

that makes a lot of sense

thanks

yo I was doing this problem

and i am not gettting how 1/4 got in

[gray isle]

where's the rest of it

[alpine sable]

here

[gray isle]

4 * 1/4 = 1

they're making preparations for chain rule

(without explicitly making a substitution)

[alpine sable]

ok got it

!

got it bruv

[slender turret]

Is the channel free ?

[jagged imp]

yah

[slender turret]

So i got to calculate the area of AMH

And i have something with x^4 at some point whereas f(x) doesn't (which is the area of the triangle)

The functions aren't translated correctly so check for the one upper

Anyone, help me ? Thanks <@&286206848099549185>

[surreal meadow]

assuming the graph lines are equidistant, you can find the x-value for M and plug it into the parabola function to find the y-value

with that you should have enough information to do 1/2bh for the triangle

[slender turret]

Like i have to look for which x the y = 7 ?

[lethal ore]

What's the question? Solved already?

[azure jackal]

can someone help me out with this question.

[slender turret]

I wanna know how do i calculate the area of AMH / where was i wrong

[lethal ore]

Pic? @slender turret

[lethal ore]

Got it

[slender turret]

yup

I reupload

[lethal ore]

Can I know what data is give?
The equation of that parabola is provided
The coordinates of A and B are given
I want the equation of the line AM
Is it given? @$name#9275

[slender turret]

A(-6; 0)

B(6; 0)

area -> f(x) =

$f(x) = -\frac{1}{9}x^3-\frac{2}{3}x^2 + 4x + 24$

[azure jackal]

^anyone

[ocean seal]

you are already dead

[lethal ore]

What is this? Equation of that curve?

[slender turret]

I have to prove that area is f(x)

of the triangle area

they say

I've done that but ion know why it seems bad

it is bad cause i have $x^4$

[lethal ore]

Can you translate the whole question?
I fell like you're missing something @$name#9275

[ocean seal]

you are already dead

[slender turret]

a/ Show that the area of the triangle AMH is equal to f(x)

b/ Calculate f'(x)

c/ Study the variations of $f$

[ocean seal]

you are already dead

[slender turret]

d/Find the coordinates of M for which the area of the triangle is maximum and precise this area (number)

[azure jackal]

<@&286206848099549185>

[lethal ore]

Is this the equation of the parabola? $y=-\frac{2}{9}x^2+8$

[slender turret]

oh yeah my bad

it was all above

i forgot that one

[ocean seal]

simply.nikhil

[slender turret]

yup

$M(x; -\frac{2}{9}x^2 + 8)$

[ocean seal]

you are already dead

[slender turret]

$B(x; 0)$

is that correct ?

[ocean seal]

you are already dead

[lethal ore]

Oh wait. Now I get it

[slender turret]

cause @surreal meadow said i could find the x directly but i think because of my english i didn't understand well

[lethal ore]

Give me a min

[slender turret]

kk thx ^^

[lethal ore]

$\text{Area}=\int_{-6}^{x}\left(-\frac{2}{9}x^2+8\right)dx$

[ocean seal]

simply.nikhil

[lethal ore]

You'll get the answer when you solve this @slender turret

[slender turret]

wow xD ion even know what's that

[lethal ore]

What?

[slender turret]

we didn't see that in school for now

it's next year i think

but is it hard ?

like maybe if i put this as an answer nothing is wrong since it's correct ?

[lethal ore]

Piece of cake if you pay some attention 🙂

[slender turret]

so what that symbol is called

[lethal ore]

Integration

[slender turret]

is it basic level of integration ?

[lethal ore]

There are two types of integration. Definite and indefinite
The one I've written above is definite integration

[mighty sinew]

using x in bounds and as an integration variable

[lethal ore]

Holy shot. Scratch that @slender turret
The problem isn't just solved here. It further goes on
I've missed one more part

[slender turret]

mmh

[lethal ore]

Dude

This is the most simple problem that I've ever scene. But as soon as I saw a parabola and this equations, I thought about integration. Which is absolutely unnecessary here. @slender turret

[slender turret]

rly 😭

is that was necessary ?

[lethal ore]

$\text{Area of triangle}=\frac{1}{2}(base)(height)$

[ocean seal]

simply.nikhil

[lethal ore]

Use this formula for that triangle and you're good to go

[slender turret]

yeah but i can't find the base and height i gotta use vectors right ?

[lethal ore]

Listen

Send me the pic again. Just of the diagram

[slender turret]

yup

this ?

[lethal ore]

Base is AH

[lethal ore]

From A to origin it's 6 units
And from origin to H it's x units
So AH=(x+6)

Understood?

[slender turret]

yeah but i don't get it like

x+6 is the vector right ?

[lethal ore]

Nope.

[slender turret]

why ?

oh yeah i used the formula wrong right 🤦‍♂️

[lethal ore]

Here that's why I asked you the coordinates of M or H
But when I read the question I got to know that the point M or H are not constant
The coordinates of M and H are variables
H(x, 0) and M(x, y)

[ocean seal]

simply.nikhil

[slender turret]

yes

[lethal ore]

From the origin H is x units away in x direction and 0 units away in y direction
From the origin M is x units away in x direction and y units away in y direction

[lethal ore]

Now you understood this?

[slender turret]

yeah i know that it's correct

but the formula maked confusion

[lethal ore]

Forget this. Not necessary here

[slender turret]

kk

so y = -2/9x^2 + 8

right

[lethal ore]

Yep

[slender turret]

so in mathematical way how i describe Area like A = (...) ?

[lethal ore]

$Base=(x+6)$
$Height=\left(-\frac{2}{9}x^2+8\right)$

[ocean seal]

simply.nikhil

[slender turret]

yup

the thing is i had (x + 6) ^ 2 for base

before

and height again same

square

[lethal ore]

You've this formula

[slender turret]

i messed up with the formula

[lethal ore]

Sometimes shit happenes. Dw about it

[slender turret]

$\frac{(x+6)(-\frac{2}{9}x^2+8)}{2}$

[ocean seal]

you are already dead

[lethal ore]

Solve this and you'll be at f(x) in no time

[slender turret]

kk hold on

should i write in real life

or use latex

what is faster ?

[lethal ore]

You don't have to show me your solution

I'll be glad if you get it right for real

[slender turret]

for real ?

[lethal ore]

Ofc

[slender turret]

Ah ok ( i didn't know english say this expression too )

[lethal ore]

What expression?

Never mind

[slender turret]

for real

[lethal ore]

I'm not understanding what you're trying to say

Let it be

Have a good day bro.
I gotta hop now

[slender turret]

I gotta say thanks a lot for the help bro

Have a good day too

[soft condor]

How do I find the sfa and volume of a cylindrical tank with height of 15m length of 7m and half sphere on top?

Oh and it has a bottom

This my formula for volume pix3.5^2x11.5+(4/3xpix3.5^3x1/2)

Is this correct?

[woven dock]

π×3.5²×11.5+4÷3×π×3.5³÷2

Haha

Looks like the same as yours

[soft condor]

So its right?

How do I find the surface area?

[woven dock]

Do you know the formula for curved surface area of the cylinder?

It should be 2πrh

[soft condor]

Is this right?

Excuse my belly lmao

[woven dock]

Looks nice

Haha belly

[soft condor]

Hahahaha

[carmine lion]

LOL

[soft condor]

This chat just turned sexual so fast

[carmine lion]

ayo

dad bod

[woven dock]

Nope, it's just belly

[upper kayak]

Damn

That's some belly no

[quasi dust]

Am i okay to ask a question in here?

[carmine lion]

no

[carmine lion]

actually yes

sorry

[quasi dust]

Anyone able to help me out with this at all?

I have gotten it down to (c^15/c^-3)^1/2

I'm not sure where to take it from there. I'm not too sure if i have done it right so far?

This is essentially what i have gotten it down to

[glass lichen]

yeah.. so keep simplifying

[quasi dust]

Once it got to this point, i'm not actually sure what i do next @glass lichen

[glass lichen]

apply the other index rules

[carmine lion]

$c^{-3}=?$

[ocean seal]

abe

[quasi dust]

Index rules isn't my strong suit, i was thinking that i remove the c^-3 so i just have c^12

[glass lichen]

15-(-3) isnt 12

[carmine lion]

you can either diretly use the divisibility rule

or the multiplicative one

if you convert it to 1/^3

i'd do the former tho

since its direct and faster

[quasi dust]

@carmine lion So it would be c^-1/3 ?

[carmine lion]

$c^{-3}=\frac{1}{c^3}$

[ocean seal]

abe

[carmine lion]

anyway

if you keep applying the index laws

u should get an answer

[quasi dust]

Yeah. That's what i've done until here. I looked at the one you just posted actually, but i thought not to do that because then it's like C^15 / 1/C^3

I'm not really sure honestly, it's a mess for me in this part 😅

[carmine lion]

you can think of it this way

is there no division symbol

thats dumb

[glass lichen]

$c^{15}\divisionsymbol \frac{1}{c^3}$

[ocean seal]

moshill1

[carmine lion]

there

and then u flip it

[quasi dust]

@carmine lionAh okay, i get it. Thanks so much for that 🙂

[carmine lion]

if there is multiple fraction signs

try converting some to div signs

and see if that helps

[carmine lion]

can u help with a trig proof lol

$\tan(2x)\cot(x)=1+\sec(2x)$

[ocean seal]

abe

[carmine lion]

should i convert the LHS to sine and cosine

[glass lichen]

I mean my gut is work on RHS

[carmine lion]

rlly

how so

convert the 1 in terms of tan^2 and sec^2

[glass lichen]

cause I cant see a direct path from LHS

[carmine lion]

?

[carmine lion]

ok so how would i do it

[glass lichen]

$\cos(2x)=2\cos^2(x)-1=\cos^2(x)-\sin^2(x)$

[ocean seal]

moshill1

[glass lichen]

$1+\sec(2x) \ =1+\frac{1}{2\cos^2{x}-1} \ =\frac{2\cos^2(x)}{\cos^2(x)-\sin^2(x)}$

[ocean seal]

moshill1

[carmine lion]

yeah i got to this step

[glass lichen]

so then you can divide num and denom by cos^2

[carmine lion]

i get 2/1-tan^2(x)

[glass lichen]

yeah

and multiply by tanxcotx

cause tanxcotx=1

[carmine lion]

ah i see

[glass lichen]

Yeah I feel that going right to left is easier, because if you did left to right you'd have to split the fraction by doing +1-1 on the numerator

[carmine lion]

a rare case of using RHS

interesting

[glass lichen]

There's no rare case

you should start from the side you think is better to start on, for me that was RHS

[carmine lion]

alright

will keep that in mind

[bronze basin]

Would someone be able to help me with integrating this please

(a/b) (x/b)^(a-1) e^(-(x/b)^a)

Probably easier if I just send a pic

(Done it now and got c - e^(-(x/lambda)^k)

[fickle bridge]

: The square of the cube of the square root of the square root of 16

can someone help

[eager badger]

sq(cube(sqrt(sqrt(16))

[fickle bridge]

oh ok thanks

[eager badger]

np

[limpid spade]

no

isn't square ^2 and cube ^3

square =/= squareroot (sqrt)

[glossy current]

$\sq{\cube{\sqrt{\sqrt{16}}}}$

Welp

Cant copy him

[fickle bridge]

is the answer 512

[glossy current]

$((\sqrt{\sqrt{16}} )^3)^2$

[ocean seal]

Darkness

[limpid spade]

oh Sq and cb are ^2 and ^3 didn't know

[woven dock]

$\left( \left( \sqrt{\sqrt{16}} \right)^3 \right)^2 $

Looks fun

[glossy current]

,ask ((√(√16))³)²

[ocean seal]

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Requested by Darkness#5004

[glossy current]

Nope

[fickle bridge]

256

[limpid spade]

you basically multiply the exponents

then put the roots in exponents

sqrtsqrt(16)^6

[fickle bridge]

64 ?

[limpid spade]

then 16^6/4

,w 16^(6/4)

[ocean seal]

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Requested by Fractalogist PRS#2374

[fickle bridge]

ok thank you

[limpid spade]

basically 4throot16^6

[fickle bridge]

thanks

[harsh acorn]

$$2018^{8012} (mod 7)$$

[ocean seal]

Hyl1s

[harsh acorn]

how can I calculate this by hand

all I know is $$2018^{8012} (mod 7)= 2^{8012}(mod 7)$$

[ocean seal]

Hyl1s

[strong furnace]

you can find the cycle of remainder for smaller powers manually, e.g. 2 mod7=2 4 mod7= 4 8 mod7=1 and finally you get 2 mod 7=2 again , find where the 8012th power lies and you'll get what they are asking for

[alpine sable]

uh

i want to make sure i do this right

Find the value of x

i think the answer's 42

[strong furnace]

that is correct

[harsh acorn]

so it is 4

[alpine sable]

nice

[strong furnace]

2^8012 mod 7 is 4 yes

[harsh acorn]

then it works

[harsh acorn]

btw this is right too right?

[strong furnace]

yes

[alpine sable]

do i subtract 106 - 43

for this answer

[strong furnace]

what is your reasoning?

[alpine sable]

idk i think thats how you solve it

[strong furnace]

what was your reasoning for the last problem?

[alpine sable]

the sum of it was 180 so

95 + 43 + 42

=180

[strong furnace]

can you interpolate a similar logic here?

[alpine sable]

106 + 43 = 149

• 31

( 31 )

[strong furnace]

what angle would 31 be?

[alpine sable]

x

[strong furnace]

is x the third angle in the triangle?

[alpine sable]

yeah

[strong furnace]

it is not

[alpine sable]

how would i solve it

[strong furnace]

find a relation between the third angle and x

the third angle is 31

[alpine sable]

180 - 31

?

[strong furnace]

yes

[alpine sable]

149

or you could have added 106 + 43

other way around

[strong furnace]

could have done that as well

[alpine sable]

ok thanks

sheeeeesh

[harsh acorn]

does remainder increases by 2 multiple when divided number is increasing ^2?

[strong furnace]

I don't understand wht you mean elaborate

[harsh acorn]

if x/10=y(remainder 3)
then x^2/10=z (remainder 6)

[strong furnace]

are you asking if y and z are equal for every value of x?

[harsh acorn]

no no i want to say that if x increases multiple x (^2) then remainder increases by multiple of 2

if x/10=y(remainder 3)
then x^2/10=z (remainder 3*2)

[strong furnace]

are you saying x^2 mod m = x+2 mod m?

[harsh acorn]

x mod m = x^2 mod (2m)

[strong furnace]

oh

[strong furnace]

that is incorrect but can you explain your reasoning?

[alpine sable]

what is the relationship between <1 and <8

i put alternate exterior angles

[harsh acorn]

they are equal

bcs 1=5 and 5=8

so 1=8

i know that $$x^2 (mod 9) = 7$$

[ocean seal]

Hyl1s

[harsh acorn]

but x cant be 4 and 5 bcs x>23

without putting numbers to x how can i find the value of x

[strong furnace]

x(mod9) can only take values from 0 through 8 you could manually check for what value of x<9 we get x^2 mod9= 7 and then find the minimal x x>23 for which x mod9= that x

[harsh acorn]

why x(mod9) can only take values from 0 through 8 ?

[strong furnace]

what does x mod9 mean>

[glass lichen]

can you divide a number by 9 and get a remainder of 10?

[harsh acorn]

no i cant

oh

[glass lichen]

right so you'll only get numbers from 0 to 8 as remainders when dividing by 9

[harsh acorn]

is the answer 31

oh yes it is 31

[alpine sable]

how to get the other numbers

[harsh acorn]

do you know which angles are equal and which angles' sum are 180

[alpine sable]

1 and 8 are equal

2 and 7 are equal

i think

[harsh acorn]

yes

there are more

[alpine sable]

2 and 6

[alpine sable]

4 and 75 degrees

[harsh acorn]

remember this rule too

opposite angles are equal

if angles made of 2 lines

so

[alpine sable]

so 4 is 75 degrees

[harsh acorn]

think red lines as 2 line

[alpine sable]

yes

[harsh acorn]

which angles are opposite

[alpine sable]

7 and 8 1 and 2 3 and 4 75 degrees and 6

[harsh acorn]

angles drawn by reds are equal to each other

same as blues

[alpine sable]

whats the answer

i got like

5 mins to submit

im fricked

[harsh acorn]

wait a min is this a test

[alpine sable]

no

😉

is 4 75 degrees

frick frick

[harsh acorn]

yes

[delicate charm]

no

[alpine sable]

welp

https://tenor.com/view/good-luck-thumbs-up-gif-12555456

[trim rose]

if A*A=1156
how can I get A?

[golden quarry]

Sqrt(1156)

[strong furnace]

+- sqrt(1156)

[real sinew]

,w sqrt(1156)

[ocean seal]

Results provided by WolframAlpha

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Requested by crabchurch#2749

[trim rose]

Thanks! I think i'm dumb

[real sinew]

Right it is positive 34 and -34

[frank nacelle]

is this channel free

[real sinew]

Yes

[golden quarry]

I think

[frank nacelle]

ok ty

I need help on this problem

I know that the volume of the barrel is 20 pi

and a.) is 10 pi

I don't understand b and c

[real sinew]

What class is this for?

[frank nacelle]

geometry

i have to do homework challenge problems

and i have no clue how to do the problem

[real sinew]

Just wondering because my first reaction is to use calc but not if it is for geometry class

[frank nacelle]

dang

[real sinew]

No it isn't

[bleak crow]

Hi beautiful 🌚

[frank nacelle]

bro?

[real sinew]

I'm not sure how to do it without calc

[frank nacelle]

dang

the hint was special right triangles

[real sinew]

What does special mean?

[frank nacelle]

like 30-60-90 triangles

[real sinew]

Oh ok

[frank nacelle]

or isoceles triangles

like their properties

[golden quarry]

Wait if the

Water is 1ft

It means that its 1/4th of the original volume

Rite?

[frank nacelle]

not really @golden quarry

[alpine sable]

is this correct or incorret

[frank nacelle]

because its lying down

the channel is taken

[alpine sable]

k

[frank nacelle]

the radii are different

[golden quarry]

Wait wdym

[frank nacelle]

so like

ill show you

[strong furnace]

they want you to figure out the area in 2d of one slice if you look at the circular part

[golden quarry]

Or u can use squares

[frank nacelle]

thats the difference

[frank nacelle]

sry i don't understand

[strong furnace]

when you take a slice of cylinder you get a circle right?

[frank nacelle]

yeah a slice parallel to base

[strong furnace]

yeah that was what I meant

in this case it would be a circle with less than half filled with water

the portion that is filled by water will have some area

we have to find that area

[frank nacelle]

oh ok

why is the hint to use a special right triangle

[strong furnace]

do you think you can take it from here?

[frank nacelle]

no

i understand what area is have to get but i don't understand how to get it

[strong furnace]

since part 3 and part 2 are essentially the same problem but with different values and different hints their might be a trivial solution I am missing , let me think

but saying a special triangle and trigonometry

is the same thing in a way

[strong furnace]

if you get the angle that the chord makes at the center you can get the area of sector and subtract the remainng area which would be a triangle

[real sinew]

I can tell you the answer is 20pi/3 - 5*sqrt(3) but that is using calculus

I dont know how else to do it

[frank nacelle]

oh ok

[golden quarry]

Lel i got 7.5

2.000000000000000

[blazing oak]

I am joking

[alpine sable]

Can somebody go to questions 2

I mean questions 1

[frank nacelle]

ill try to use this process

[alpine sable]

I need help with something in questions 1 😦

[frank nacelle]

wdym by angle chord makes at center

[strong furnace]

if a is the chord alpha is the angle the chord makes at center

[frank nacelle]

ok

thanks for the explanation

UGH i can't get it

[weary notch]

this is kind of a stupid like quick question but i cant find this online, what does | | mean in set theory? as in if i had a statement like | A | = | B |

[solar tapir]

Cardinality

The number of elements that belong to that set

[weary notch]

so like

the number of elements in a is the same as the number of elements in b

[solar tapir]

Yes

R = Results of a six-sided die

|R| = 6

[weary notch]

ah ok

so like

whats the difference between intersection and subset if its a set of one element

is the other thing im confused on

like A = {1,2,3} and B = {2} would A (upside down U) B = 2 and B C A be true

also thank you

im not rly good at math im doing this in the context of linguistics and was having trouble reading stuff

[solar tapir]

$A \cap B = {2}$

That's true

[weary notch]

ok

oh

that makes sensethanks

[vale wigeon]

\{2\}

$\{2\}$

[ocean seal]

Ann

Max Hetfield

[solar tapir]

Always forget about this

[solar tapir]

And yes $B \subset A$

[ocean seal]

Max Hetfield

[west ember]

Can anyone help me with 3 questions on my algebra assignment

[solar tapir]

Just ask

[west ember]

Ok

[alpine sable]

Someone who can help me with this?

[slow mason]

someone help me please

[gloomy lintel]

So what is the definition of the circumference?

It’s pi x diameter right?

[slow mason]

nvm

got a dif one

@gloomy lintel

[gloomy lintel]

So the circumference is pi x diameter

[slow mason]

yes

[gloomy lintel]

The diameter is 6, bc it’s 2 x 3

[slow mason]

yes

[gloomy lintel]

So the circumference is 6pi

So just work that out and see which one is closest to your answer

[slow mason]

this one

@gloomy lintel

[ocean seal]

Azaradichta

Azaradichta

[alpine sable]

@slow mason

I need some help

Examine how a sum figure with five fields must be filled in with the expressions n, n + 1, n + 2, n + 3 and n + 4, in order to make the sum horizontal and the sum vertical as large as possible.

Sum figure: Must give the same number horizontally and vertically. One number must be part of both sides.

[solar pebble]

@alpine sable what's a sum figured

[alpine sable]

Nvm it was easy

[rugged lynx]

which formula do i use to find the circumference of this circle?

[alpine sable]

diameter is 2 cm, just find the formula

d*pi i think

[harsh swallow]

probability of G given L

is that how you read that?

[dusk panther]

I think so

[harsh swallow]

so you know it's L

[radiant jasper]

Hello, I am poor please give money

I literally just need 5 dollars ong

[harsh swallow]

which means that you're only looking at the column of L

all other columns are not relevant

[radiant jasper]

Dammnn

she really just said

Math/Poverty

[harsh swallow]

this is literally not the place for any of this

[radiant jasper]

Ik

worth the shot

:(.

But fr tho im about to starve

[harsh swallow]

@dusk panther do you think you would know if you know you only have to look at the first column?

[dusk panther]

I’m not sure I thought that I would have to look at pretty much the chart as a whole to get the answer

[harsh swallow]

no

cuz given L

means that only the first column is relevant

cuz the second column is only M

and the last column is L + M

[dusk panther]

Oh yeah that makes sense

[crisp summit]

Guys i have a question

How can you speedmath in division

There's people that can divide a very large numbers in seconds

I bet there's a trick. That only those who had graduated in a speedmath course.

[dusk panther]

I’m sorry I wouldn’t know

[crisp summit]

@dusk panther i really do wonder lol

Like i can multiply big numbers in my head using 30 seconds

But i rly do wonder how they can divide.

[ionic jewel]

there's some tricks but a lot of it is practice and innate skill

[alpine sable]

I have a question

Is it right

I got

[blazing oak]

I really don’t know

How to solve this

[gray isle]

the work the missing the right edge

[noble kite]

Pls help

<@&286206848099549185>

[solar tapir]

What do you think?

Don't spam the helpers tag btw

[lime tangle]

thats an absolute value function

its a function

[solar tapir]

Why is not a relation?

[glass lichen]

cause it passes the vertical line test

[solar tapir]

Functions are also relations

[glass lichen]

Yeah, im aware

[dire dove]

How would I find s and t, if I have [x,y,z]=[4,7,-1]+s[4,8,-4] and [x,y,z]=[1,5,4]+t[-1,2,3]???

[velvet pelican]

@dire dove set the [x,y,z] equal then compare the i j and k components separately to get 3 equations

2 of them allow you to solve for s and t

then use the 3rd one to confirm

[ocean seal]

Erzis

[hollow zephyr]

how can I be sure that both sides are either bigger or smaller than 0?

[reef olive]

,w x'=x+t^2

[ocean seal]

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Requested by ᲼᲼᲼᲼᲼#5213

[alpine sable]

hi

need help

easy but im stuck