help-49

[grand pond]

Serphic

[midnight plank]

@noble elbow Has your question been resolved?

[tepid lodge]

huh

so $F_4(5)=5$ and $F_5(5)=5$

[grand pond]

DiamondPanda16

[tepid lodge]

oh wait are you trying to just find $a, b, c, d$ such that $F_a(b)=F_c(d)$ but its not trivial like this case

[grand pond]

DiamondPanda16

[noble elbow]

yes

i was thinking the golden ratio could be a potential way to make something silly happen but i dont know how i would exactly

do anything concrete

[tepid lodge]

oh so you're allowing non-integers

cuz normally factorial of non-integers isn't defined like that

you wouldn't say 4.5! = 4.5 * 3.5 * 2.5 * 1.5 * 0.5

[noble elbow]

im aware that it's defined used the gamma function, but honestly i think it would be even more ridiculous to generalize a 1.5 factorial

i mean that might actually be more of a useful question to ask though

[jaunty dagger]

Nieves

Dog

[tepid lodge]

that's actually a really interesting question

im gonna ask this in #math-discussion where all the smart people are

[noble elbow]

yippie!!

[midnight plank]

@noble elbow Has your question been resolved?

Channel closed

Closed by @noble elbow

Use .reopen if this was a mistake.

[midnight plank]

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.

[twilit field]

I suppose I can just set z=1 and obtain $x^2+y^2=1$, should that suffice

[grand pond]

What a wonderful world it is !

[dawn dagger]

what a task

[twilit field]

This looks much haarder

I don't get what $P_0$ is , a point in the plane?

[grand pond]

What a wonderful world it is !

[twilit field]

ooh, so the plane is given by $\xi u + \eta v$?

[dawn dagger]

\xi

[grand pond]

What a wonderful world it is !

[twilit field]

basically the span of those vectors, that's it, right

[dawn dagger]

yea i think so too, in the plane spanned by u and v

[twilit field]

hmm

okay

well, I suppose I could start by writing the cone in its vector form

$(x,y,x^2+y^2)$

[grand pond]

What a wonderful world it is !

[twilit field]

let $u=(x_1,y_1,z_1), v=(x_2,y_2,z_2)$

[grand pond]

What a wonderful world it is !

[twilit field]

so we have $(x,y,x^2+y^2)= (\xi x_1 + \eta x_2, \xi y_1 + \eta y_2 , \xi z_1+ \eta z_2)$

[grand pond]

What a wonderful world it is !

[twilit field]

Fine so far?

[midnight plank]

@twilit field Has your question been resolved?

[twilit field]

<@&286206848099549185>

[dawn dagger]

shouldnt it be sqrt(x²+y²)

[twilit field]

ooh, right

[dawn dagger]

or basically $(\xi z_1+ \eta z_2)^2 = z^2$

[twilit field]

how did you get that

[dawn dagger]

well if sqrt(x^2+y^2) = z

and sqrt(x^2+y^2) = \xi z_1+ \eta z_2

[twilit field]

yes

ah

this doesn't prove the intersection is a conic, does it though

[dawn dagger]

you can plug these in into x²+y²=z² and try to see if it simplifies into a conic equation

in terms of xi and ita

[twilit field]

hmm

yeah, that would do the trick

$(\xi x_1 + \eta x_1)^2 +( \xi y_1 + \eta y_2)^2 = (\xi z_1 + eta z_2)^2$

[grand pond]

What a wonderful world it is !

[twilit field]

How's that a comic though

[dawn dagger]

then something like xi^2(...) + xi(...) + xi * ita(...) + ita(...) + ita^2(...) = 0

[twilit field]

but x_1,x_2 etc are variables

[hard umbra]

what happened to P_0

[dawn dagger]

i thought these were the coordinates entries of u and v

which would be constants

[twilit field]

hmm

fair

those are

oh right

[twilit field]

Converted it

[hard umbra]

what?

[twilit field]

I think P_oP is just any vector in the plane

P_0 is just a constant

no

[hard umbra]

yes P_0 is a given point

you haven't yet written down a coordinate in the given plane in terms of the given data

and then you're jumping into subbing things into formulas without a clear foundation

[twilit field]

Any coordinate in the plane is a linear combination fo v and u

[hard umbra]

no

that is wrong

[twilit field]

huh

why

[hard umbra]

lets say i pick P_0 = (3, 4, 5), u = (1, 0, 0), v = (0, 1, 0)

then P = (5, 5, 5) is on the plane

P_0P = 2u + 1v

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[twilit field]

.reopen

[midnight plank]

✅

[twilit field]

huh what

[twilit field]

so basically any point on the plane is a linear conbination of these two + another point

[hard umbra]

imprecise, write it out

[twilit field]

$P = \xi ( x_1,y_1,z_1)+ \eta ( x_2,y_2,z_2) + (x_3,y_3,z_3)$

[grand pond]

What a wonderful world it is !

[hard umbra]

where x_1, y_1, z_1, x_2, y_2, z_2, x_3, y_3, z_3 are?

[twilit field]

real constants

[hard umbra]

but what are they

how did you get them

[twilit field]

Isn't that given to me

[hard umbra]

given where

[hard umbra]

do you see any of x_1, y_1, z_1, x_2, y_2, z_2, x_3, y_3, z_3 in this problem?

[twilit field]

in the problem statement

no

[hard umbra]

so how are they given?

[twilit field]

as vectors in r^3

*R^3

[hard umbra]

all you needed to say was let P_0 = (x_3, y_3, z_3), u = (x_1, y_1, z_1), v = (x_2, y_2, z_2)

[hard umbra]

you got confused here before by what they were

im trying to get you to clarify what your variables mean

[twilit field]

oh

[hard umbra]

don't just conjure up names out of thin air and expect people to know what you're talking about

what is the coordinate representation of P?

i.e., what are its x-, y-, and z-components

[twilit field]

$P= (x_3+ \xi x_1 + \eta x_2, y_3+ \xi y_1+ \eta y_2,z_3+ \xi z_1 + \eta z_2)$?

[grand pond]

What a wonderful world it is !

[hard umbra]

yes

now this is what you substitute into the cone equation

[twilit field]

This is confusing me

My LA course thought me that a plane can be spanned by 2 vectors

why is the third one required

[hard umbra]

did your LA course really tell you that?

what do you call the thing that is spanned by 2 vectors?

[twilit field]

Atleast that's what I understood

[twilit field]

A 2D subspace

[hard umbra]

okay, a subspace

what is one of the axioms of being a subspace

[twilit field]

or a 2 dimensional vector space

It must have the zero vector

ah

makes sense

thanks

[twilit field]

so that gives me $(z_3+ \xi z_1 + \eta z_2)^2 = (y_3+ \xi y_1+ \eta y_2)^2+ (x_3+ \xi x_1 + \eta x_2)^2$

[grand pond]

What a wonderful world it is !

[hard umbra]

and why is this a conic?

[twilit field]

I should probably begin by expanding it

[hard umbra]

maybe

do you know what conic equations look like though?

[twilit field]

Only in their standard forms

like the ones centered at the origin of the xy plane

[hard umbra]

you don't know that for example any quadratic equation will define a conic section?

[twilit field]

no

[hard umbra]

welp

i guess its just expanding for you

[twilit field]

Or I could accept this for now

[hard umbra]

probably

the expanding isnt particularly insightful or fun

[twilit field]

yeah

Thanks!

.close

[midnight plank]

Channel closed

Closed by @twilit field

Use .reopen if this was a mistake.

[midnight plank]

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.

[somber canopy]

I saw a question

[somber canopy]

$\int_0^{2025} \fractionalPart{\sqrt{x}} dx$

[grand pond]

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

[lyric charm]

there is no dedicated fractional part command

[somber canopy]

fractional part of the square root of x

[lyric charm]

if you want curly braces you will just have to type \{ ... \}

[somber canopy]

I see

[lyric charm]

anyway ok point taken, whats your progress on this

[somber canopy]

so

I wanted to uh

I was trying to solve it and somewhere I went wrong

I cant figure it out

so I took

[lyric charm]

well show what you've got then

[somber canopy]

$u = \frac{\sqrt{x}}{45}$

[white gate]

$\int_{0}^{2025}\left\lfloor \sqrt{x} \right\rfloor,dx$

[grand pond]

kronium_

TargetVN

[white gate]

This?

[somber canopy]

no

bruh u dont know what fractional part is

[white gate]

i dont

[lyric charm]

not gonna be of much use here

[somber canopy]

${x} = x - \floor{x}$

[karmic trench]

write the function on keyboard

[grand pond]

kronium_

[white gate]

oh

[lyric charm]

wait i replied to the wrong thing

[white gate]

LMAO

[lyric charm]

this sub won't help much

[white gate]

i thought of the wrong thing

[somber canopy]

wait i'll rewrite the question

[white gate]

im more known to the floor function than fractional function
i do know that tho, just forgor the notation

[lyric charm]

$\int_0^{45^2} (\sqrt{x} - \floor{\sqrt{x}})\dd x$

[grand pond]

ann.in.a.teacup

[somber canopy]

$\int_0^{2025} {\sqrt{x}}$ $dx$

[white gate]

anyways this

[grand pond]

kronium_

[lyric charm]

this is your thing

[white gate]

use it

[somber canopy]

yes

wait

I uh

I made it a bit different

so what I did was

first I did

$u = \frac{\sqrt{x}}{45}$

[grand pond]

kronium_

[somber canopy]

and I converted everything to the u world

[lyric charm]

i think this is going to just make your life more difficult than necessary

it's a bad route

[white gate]

you can just use the exact relation between floor and fractional function

integral of floor function is easy to do

[lyric charm]

$\int_0^{45^2} (\sqrt{x} - \floor{\sqrt{x}})\dd x = \int_0^{45^2} \sqrt{x} \dd{x} - \int_0^{45^2} \floor{\sqrt{x}} \dd{x}$

[grand pond]

ann.in.a.teacup

[lyric charm]

like this

the first one is very straightforward

the second can be done almost geometrically and converted into a summation

[somber canopy]

Can you teach me how to evaluate floor and ceiling functions

I meant integrate

cuz i got no idea how to turn it into a summation function

[white gate]

it depends on the property of the function

[lyric charm]

ok right so

[white gate]

here, if sqrt(x) is in [n, (n+1)) then floor(sqrt(x))=n

[lyric charm]

you know that floor(t) = 0 when t ∈ [0,1), and 1 when t ∈ [1,2), and 2 when t ∈ [2,3) etc. yes? @somber canopy

[somber canopy]

yes

[lyric charm]

you mean x is in that interval

[lyric charm]

ok right

[somber canopy]

yes

floor means

it rounds to the lower integer

[white gate]

fixed

[lyric charm]

now i'm going to do the following: break up the interval [0, 45^2] into sub-intervals based on where the floor function jumps

which is going to be at every perfect square

ie 1^2, 2^2, ... up to 44^2

[somber canopy]

wait

wait

wait

tell me the function

right now

[lyric charm]

what function

[somber canopy]

type it in LaTeX

[lyric charm]

i was about to type the latex.

[somber canopy]

The floor function you were talking about

[lyric charm]

$\floor{\sqrt{x}}$

[grand pond]

ann.in.a.teacup

[lyric charm]

this thing

[somber canopy]

right

[lyric charm]

it jumps whenever sqrt(x) = n [with n an integer] i.e. whenever x = n^2

[somber canopy]

WAIT NO WAY

HOW TF DID U KNOW IT JUMPS AT EVERY PERFECT SQUARE

[lyric charm]

i just told you

$\sqrt{x} = n \iff x = n^2$?

[grand pond]

ann.in.a.teacup

[white gate]

.

[somber canopy]

oh right

I always knew that

its just that I didn't intuitively understand it

[lyric charm]

ok rigth

right*

[white gate]

now u know :b

[lyric charm]

shall we move on then to the breaking-up of the integral

[somber canopy]

yes

[lyric charm]

$\int_0^{45^2} \floor{\sqrt{x}} \dd{x} = \sum_{k=0}^{44} \int_{k^2}^{(k+1)^2} \floor{\sqrt{x}} \dd{x}$

[grand pond]

ann.in.a.teacup

[lyric charm]

make sense?

[somber canopy]

could you stop writing it as 45^2

and just write 2025

[lyric charm]

i mean, the 2025 would have vanished anyway by now

[white gate]

45^2 makes it easier to imagine tho

[lyric charm]

this is the last time it appears directly

[somber canopy]

it really doesn't...

ok wait gimme a second to take it all in

[lyric charm]

take your time

[somber canopy]

Ah yes

I get it

because when k = 44

it becomes

44^2 to 45^2

45^2 is 2025

[lyric charm]

yes

thats the last piece in the summation

[somber canopy]

yeah heres the thing

Ik a lot of summation techniques

but the problem is

summing an integral seems more like a manual process and it doesn't look like theres a shortcut like an equation or smth

maybe there is, idk

[lyric charm]

this kind of is manual yes

there ain't much of a way around it either

[somber canopy]

👀 😭

[lyric charm]

$\int_{k^2}^{(k+1)^2} \floor{\sqrt{x}} \dd{x} = \int_{k^2}^{(k+1)^2} k \dd{x} = k[(k+1)^2 - k^2]$

[grand pond]

ann.in.a.teacup

[white gate]

built-in finite/infinite series inside an integral

pretty yummy

[somber canopy]

wait

wait

mhm

the first part of this integral

isn't that just

k(k+1)

[lyric charm]

??

wym "first part"

[white gate]

uh

[somber canopy]

because the square root from k^2 to (k+1)^2 is between k and k+1

when you take the floor function of that

you get the height of k

and the width of k+1

nvm

height of k

width of

[lyric charm]

the width is not k+1.

[somber canopy]

2k - 1

[lyric charm]

the width is the width of the interval

which is 2k**+**1

or (k+1)^2 - k^2 as i wrote it

[somber canopy]

WAIT WHAT

Ok

[lyric charm]

i left it unsimplified

[somber canopy]

im definitely cofused

[lyric charm]

$\int_a^b c \dd{x} = c(b-a)$ yes?

[grand pond]

ann.in.a.teacup

[white gate]

i mean u can just do this, its simpler than thinking about rectangles

[somber canopy]

yes

[white gate]

since floor(sqrt(x)) = k for k<=x<k+1, so just sub k in and integrate normally

[somber canopy]

wait

I def dont get it

look at this

It has a height of k

It has a width of

${(k+1)}^2$ $-$ $k^2$

[lyric charm]

that is horrible tex

for two reasons

[grand pond]

kronium_

[lyric charm]

1. those {} don't do anything
2. dollars are meant to enclose entire FORMULAS (expressions, equations etc) and not just pieces

but yes, the width is (k+1)^2 - k^2 and the height is k

you are correct on both fronts

[somber canopy]

oH WAIT

it is 2k + 1

idk why but I took the expansion of (k-1)^2

for some reason

and subtracted that from k^2

anyway width of 2k+1

[lyric charm]

the floor integral has now been reduced to $\sum_{k=0}^{44} k(2k+1)$

[grand pond]

ann.in.a.teacup

[somber canopy]

$\sum_{k=0}^{44} \int_{k^2}^{(k+1)^2} \floor{\sqrt{x}} dx$

[grand pond]

kronium_

[somber canopy]

now what

wait

[somber canopy]

Thats exactly what I was gonna do

[lyric charm]

btw you do know how to do $\int_0^{2025} \sqrt{x} \dd{x}$, right?

[grand pond]

ann.in.a.teacup

[lyric charm]

it is easy but it must not be forgotten about

[somber canopy]

of course

$\frac{2}{3} x^{\frac{3}{2}} + C$

ah

wonderful Latex

[lyric charm]

your } became a ] right next to the two

[white gate]

https://latexeditor.lagrida.com/

[somber canopy]

Leslie Lambert and Donald Knuth

[white gate]

probably it makes it easier

[grand pond]

kronium_

[lyric charm]

this but evaluated at 2025 and 0 and subtracted

(and the +C cancels out)

[somber canopy]

yes

so tis just

uh

les see

$\frac{2}{3}$ x $45^3$

[grand pond]

kronium_

[lyric charm]

no, bad tex!

[somber canopy]

Peak tex

[lyric charm]

no.

$\frac{2}{3} \times 45^3$

[grand pond]

ann.in.a.teacup

[lyric charm]

again, dollars should NOT enclose individual pieces of an equation.

[somber canopy]

bruh

[lyric charm]

it screws up the spacing terribly.

[somber canopy]

You pulling commands out of your ass that I didn't even know existed

[lyric charm]

you should not be writing

$a$^$2$ $+$ $b$^$2$ $=$ $c$^$2$

there is never a situation where that's appropriate

[lyric charm]

there's a cheat sheet in #latex-help actually

you can familiarize yourself w/ that

[somber canopy]

I see

@lyric charm What about other functions such as

$\floor{x^3}$

[grand pond]

kronium_

[somber canopy]

or $\floor{x^2}$

[grand pond]

kronium_

[somber canopy]

or $\floor{e^x}$

[grand pond]

kronium_

[white gate]

i mean its not like there's a general solution, but there's a general approach, mostly study the property of the floor function and split the integral into finite sum

[somber canopy]

Target

which country u from?

[white gate]

🇻🇳

[somber canopy]

damn

nice

.close

[midnight plank]

Channel closed

Closed by @somber canopy

Use .reopen if this was a mistake.

[midnight plank]

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.

[last slate]

How dk i get z?
And is what i did correct?

[plain osprey]

is o center of circle

[last slate]

Yes

[plain osprey]

y is an inscribed angle and z is an angle at the center of the circle

and they are in the same segment

any idea what that means

[last slate]

Inscribed angle means?

[plain osprey]

no like

do you know what the formula states if you have those conditions

[last slate]

I dont think so

[plain osprey]

this is what i wanna get to, btw

[last slate]

Oh angle at the centre =twice the angle at the circum

[plain osprey]

yes

[last slate]

How do we know y is the angle at the circumference

[plain osprey]

wdym

[last slate]

Like how do we find the angle at the circumference

Arent there several angles tpuching the circumference .like angle a

[plain osprey]

yeah

i dont think i quite get what you mean

are u saying how do we know y is inscribed or

[last slate]

Yea

What is an inscribed angle

[plain osprey]

an inscribed angle is just an angle formed by two chords of a circle

[last slate]

Pk

Ok

[plain osprey]

or simply the three points that make the angle all lie on the circle

[last slate]

Oo ok

: The inscribed angle is half of the central angle that subtends the same arc.

Is it this?

[plain osprey]

yep

[last slate]

Ohh oki but then how does it relate to angle at the centre =twice the angle at the circum

[plain osprey]

u lost me again

[plain osprey]

u js stated it urself here but in a different way

[last slate]

Wdym?

[plain osprey]

say A is the angle at circum (or also known as inscribed angle) and B is the angle at the center

and both A and B intercept the same arc on the circle

then A = 1/2B or we can say B = 2A

same thing

[last slate]

Ohh

[last slate]

So this and the angle at the centre thing are both same?

[plain osprey]

yes

[last slate]

Ohh ok

Thank u very much

Have a nice day!

.close

[midnight plank]

Channel closed

Closed by @sick kelp

Use .reopen if this was a mistake.

[plain osprey]

u2

[midnight plank]

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.

[verbal sphinx]

Can someone critique my solution?

[lyric charm]

hmm...

how do we know there is a rock on step 500 - (k+1) for Sisyphus to pick up and take?

plus, he can only move a rock up to the nearest empty space, right?

so what all is in between steps 500-k-1 and 501?

if there's any empties in there, we can't take the rock up that high.

(also, a stylistic note -- this is obviously themed after greek mythology, but the god of the underworld is usually anglicized as Hades)

[verbal sphinx]

yes so I hear haha... I wonder why they posed the problem that way

[verbal sphinx]

Isn't this covered by the ground of iterating P k times?

[lyric charm]

hmm well like

actually

let me try to sketch it out

    498 499 500 501 502
... _O_ _O_ _O_ ___ ___ ... Sisyphus: 499 -> 501
... _O_ ___ _O_ _O_ ___ ... Hades: 500 -> 499 (only move)

sisyphus can't go 498 -> 502 here, can he?

the rock on 498 could be lifted only to 499

and to fill 502 you would need to take the rock from 500

[verbal sphinx]

damn ok so i've really screwed this up 😭

[lyric charm]

yeah looks like your strat doesn't get the... ball rolling

[verbal sphinx]

LOL

[lyric charm]

(ba dum tss)

[verbal sphinx]

hmmm ok

i'll give it some more thought then ig

tysm

[midnight plank]

@verbal sphinx Has your question been resolved?

Channel closed

Closed by @verbal sphinx

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.

[wet bridge]

dk where to start

[buoyant yoke]

what do you need to find?

whats the question?

oh, i see

i suppose you can just try finding all the angles you can first

[midnight plank]

@wet bridge Has your question been resolved?

[wet bridge]

the ones i can find doesn't give me the answer

[buoyant yoke]

which ones can you find?

[wet bridge]

i can fill out the known ones if you want

[buoyant yoke]

yes please

[wet bridge]

do you see a solution now

i still cant

[buoyant yoke]

i suppose we have to name some angle x

[buoyant yoke]

and then continue calculating from there

[kindred dagger]

this looks off to me…

[wet bridge]

switch bottom ones to 45-135

[midnight plank]

@wet bridge Has your question been resolved?

[midnight plank]

@wet bridge Has your question been resolved?

[spring wave]

The bottom gold line intersects the corner of the parallelogram

[midnight plank]

@wet bridge Has your question been resolved?

[visual ingot]

Too basic for this question

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[midnight plank]

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.

[tidal turret]

i) a + b = -b - c + b = -c

ii) a + b = -c

iii) -a - 2b -2c = -(-b-c)-2b -2c = b+c-2b-2c = -b-c

iv) -b-c = -b-c

(-c,-c,-b-c,-b-c) = c(-1,-1,-1,-1)+b(0,0,-1,-1)

HnT = <(-1,-1,-1,-1),(0,0,-1,-1)>

HnT = <(1,1,1,1),(0,0,1,1)>

S = <(1,1,1,1)>

.solved

[midnight plank]

Channel closed

Closed by @tidal turret

Use .reopen if this was a mistake.

[midnight plank]

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.

[grand pond]

938c2cc0dcc05f2b68c4287040cfcf71

[tidal turret]

det(A^-1) = 1/6

det(1/3 . A^6)

(1/3)^3 . det(A^6)

(1/27).det(A)^6 .det(B) . 1/det(A) = 32/9

(1/27).(6^6).det(B).(1/6) = 32/9

det(B) = (32/9) (6)(1/6^6)(27)

det(B) = (32/9)(1/(6^5))(27)

,w (32/9)(1/(6^5))(27)

[grand pond]

Results provided by WolframAlpha

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

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[tidal turret]

,w det {{k,-1,2},{2k,1,1},{-k,0,2}} = 1/81

[grand pond]

Results provided by WolframAlpha

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

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[tidal turret]

,calc 81*9

[grand pond]

Result:

729

[midnight plank]

@tidal turret Has your question been resolved?

[tidal turret]

solved in #linear-algebra

.solved

[midnight plank]

Channel closed

Closed by @tidal turret

Use .reopen if this was a mistake.

[midnight plank]

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.

[lethal path]

try $(0, \infty)$ or something

[grand pond]

south

[iron fern]

like plug in (0,oo) in the answer?

[lethal path]

also the problem with interval notation is that intervals are continuous, but the number of units must be a positive integer ofc

[lethal path]

yeah, if you can type it out properly

[lethal path]

I think this is a dumb question

[iron fern]

I got

like this?

it say wrong

I got (-oo,-9/2)U(-9/2,oo)

but it say wrong

is it right?

[tidal turret]

the values for t can't also make M negative because then we have negative minutes ,no?

[iron fern]

so its positive?

[last slate]

Hey I have a question

It’s abstract but could a human genuinely take time to read my thesis ?

[iron fern]

I don't understand

[iron fern]

i don't see why not

[last slate]

Okay

🙂

[iron fern]

PLS HELP

[last slate]

Can you give me

[iron fern]

[last slate]

Constructive criticism

On it too

[iron fern]

what is this, sociology?

[last slate]

It’s basically like

You know oxygen and other elements and chemicals

[iron fern]

can you help me on the question

[last slate]

You know how they have a fixed identity ?

An oxygen will always be an oxygen

Etc

Its identity doesn’t change

[iron fern]

you know O2 is oxygen

[last slate]

Yes

[iron fern]

and O3 is ozone

[lethal path]

this doesn't belong in the help channels

[last slate]

But what I’m saying

[last slate]

I need help south

Could you help me ?

[iron fern]

me need help too

[lethal path]

also your thesis doesn't really belong on the maths server

[last slate]

I know

[lethal path]

it's not about maths but philosophy

[last slate]

But every one else

Is so rude

Else where

I genuinely wanted someone to hear my thesis

[lethal path]

asking here isn't going to solve anything, sorry

[iron fern]

hey man I am not rude

[last slate]

You’re not melon

You were sweet

Thank you

You too south

[iron fern]

Yo south

pls help

idk how to solve

[lethal path]

IDK what the question even wants

I really have no idea

[last slate]

South

So basically

It’s the identity of existence

It’s fluid

[iron fern]

here is the full question

[last slate]

Okay nvm

I’ll dip

[iron fern]

can anyone help

[burnt flame]

you don't want to be dividing by 0

[lethal path]

they tried this already

[burnt flame]

ah...

[iron fern]

oof my last try left

[burnt flame]

did they put u or did they use the union symbol

[iron fern]

union symbol

yes I did

it say wrong

[tidal turret]

t can be 0 and that is positive minutes

but t can't be less than zero because that indicates the days

[lethal path]

ah we could try that

my concern is that t = 0 doesn't give M = 0

but you should definitely try it, it really might be just that

[tidal turret]

t indicates days so it cannot be negative, it should start at 0

and t = 0 gives positive minutes so we are good there aswell by not having negative time

try [0, ∞)

[iron fern]

worked

how?

please explain

[tidal turret]

t is days right?

[iron fern]

yes

[tidal turret]

and M is minutes

[iron fern]

yes

[tidal turret]

we need t >= 0

because days can't be negative

and t = 0 is the starting point because

t = 0 gives positive Minutes

[iron fern]

yes

[tidal turret]

so there is no reason to exclude it

[iron fern]

alright

[tidal turret]

it was fun exercise though

[iron fern]

nah i hate this kind of question

🗿

[tidal turret]

it was tricky but days can't be negative so that's new

[iron fern]

I had to take math in college because it was requirement by my major

or else I would never take math again in my life

[tidal turret]

ye, is good that you go over it ig

is cleared so you managed, gj

[iron fern]

hey man any sites you recommend for calculus or youtube video

self learning

besides khan academy

that doesnt help nothing

[tidal turret]

khan academy , openstax has free pdfs for calc 1,2,3, Paul's online math notes, also Organic Chemistry Tutor on YouTube and professor leonard is good. maybe I am missing some resources

MIT opencourseware

[tidal turret]

[iron fern]

ngl a lot of people talk about pauls online math notes

[tidal turret]

is good has quick examples for a lot of topics, well made resource

calc 2 and calc 3 specifically

sequences and series, convergence tests, line integrals

[iron fern]

as a bio major i think calc 2 and calc 3 is unnecessary

I like sticking to human

[tidal turret]

oh okay, I am more related to cs, but maybe is unnecessary for bio

[tidal turret]

all good, everything is clear now? just study what your course requires and you will do fine

[iron fern]

yeah me finna go cry in my bed

because I hate math

🗿

.close

[midnight plank]

Channel closed

Closed by @iron fern

Use .reopen if this was a mistake.

[midnight plank]

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.

[sullen hollow]

is it root 3

[lyric charm]

how did you get sqrt(3)?

[sullen hollow]

uh

the radius is 2?

sorry

pytagoras

wait can u explain 😭

@lyric charm

[lyric charm]

ok you say Pythagoras

what are your legs?

[formal palm]

the radius is NOT 2cms

[sullen hollow]

1 and 2

[lyric charm]

right

[sullen hollow]

the whole hypotoneuse is root 3

and then im stuck

oh

[lyric charm]

is it?

[sullen hollow]

root 5

[lyric charm]

1^2 + 2^2 isn't 3

yeah

[sullen hollow]

yeah WHAT AM I DOING 😭

[lyric charm]

so the DIAMETER is sqrt(5)

[sullen hollow]

brain is not functioning

so root5 divided by 2 😭

[lyric charm]

yes

[sullen hollow]

wait

@lyric charm it doesnt specify right angle tho

[lyric charm]

inscribed angle thm

an inscribed angle in a circle is always half of its corresponding central angle, and the central angle here is 180°

[midnight plank]

@sullen hollow Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[midnight plank]

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.

[fiery arrow]

integral of cos3xcos2xcosx dx

[fiery arrow]

adjust 1/2 and 2 and use transformation formual

in cos3x and cosx

we get cos4x and cos2x

so integral of cos4x cos^2x dx

then what

im stuck here

cant us LIATE because both are trignometric

maybe some identity?

[midnight plank]

@fiery arrow Has your question been resolved?

[cedar coral]

well, you can use the identities for double angle or triple angle, or the identities for sum of angles.
cos(3x) = cos(2x+x)
cos(2x) = cos(x+x)

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[midnight plank]

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.

[timid drift]

Greetings

[timid drift]

oh wait nvm I get it

.close

[midnight plank]

Channel closed

Closed by @timid drift

Use .reopen if this was a mistake.

[midnight plank]

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.

[fiery arrow]

i dont see it

[fiery arrow]

howd that help

[verbal pumice]

this seems correct

what exactly do you have though as the integrand?

[cedar coral]

cos3x = cos2xcosx - sin2xsinx
cos2x = cosxcosx - sinxsinx
sin2x = sinxcosx+cosxsinx = 2sinxcosx
Thus, cos3xcos2xcosx = (cos2xcosx - sin2xsinx)(cosxcosx - sinxsinx)(cosx) =
((cosxcosx - sinxsinx)cosx - 2sinxcosxsinx)(cosxcosx - sinxsinx)(cosx)

you can simplify that to have everything in terms of powers of only sinx and cosx, which can be split and easily integrated with the id cos^2+sin^2=1

[lyric charm]

this is so ugly without any parentheses

[cedar coral]

kinda, yes

[lyric charm]

i like using the shorthand $c_n := \cos(nx)$ and $s_n := \sin(nx)$ and additionally drop 1 subscripts (so $c_1=c$ and $s_1=s$) for this sort of stuff

[grand pond]

ann.in.a.teacup

[midnight plank]

@fiery arrow Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[twilit field]

Need help with this

I'm trying to simplify the paramatization first

any hints

not sure how to get this

Got it

.close

[midnight plank]

Channel closed

Closed by @twilit field

Use .reopen if this was a mistake.

[midnight plank]

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.

[graceful ferry]

Charaterestic polynomial is defined as det(alphaI-A) or det(A-alphaI) ?

[lyric charm]

for the most part it does not matter which.

the roots are the same in either case -- those two polynomials differ by a factor of (-1)^n

(where n is the size of A)

[graceful ferry]

If n is odd it matters , the signs change for the characterstic polynomial

[lyric charm]

what are you doing rn that requires you to keep track of this difference?

[graceful ferry]

Just say I'm asked to write down the characterestic polynomial

I'm asking in general

[lyric charm]

double-check which convention for the charpoly is used in your class

and go w/ that

otherwise it literally doesnt matter almost at all and adjusting is not hard even if necessary

[graceful ferry]

Alrighty

Because

I've seen videos of two different lecturers and each one defined it the other way

I'll just double check with a lecturer

.close

[midnight plank]

Channel closed

Closed by @graceful ferry

Use .reopen if this was a mistake.

[midnight plank]

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.

[pure vale]

Hey, I don't understand what this question is trying to ask

[pure vale]

English is not my first language so this just made it so much harder 😭

[white gate]

well, find "depth of milk"

"depth of milk" has already been pointed out by the figure

[pure vale]

So

its saying that I need to find the colored area?

[white gate]

no

find the length of red line

[pure vale]

Ohh

Well that explained it then, ty :DDD

[white gate]

np

!done

[midnight plank]

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

@pure vale Has your question been resolved?

Channel closed

Closed by @pure vale

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.

[tidal turret]

The medians $AD$, $BE$, and $CF$ of triangle $ABC$ intersect at the centroid $G$. The line through $G$ that is parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If the area of triangle $ABC$ is $810$, then find the area of triangle $AMN$.

[grand pond]

938c2cc0dcc05f2b68c4287040cfcf71

[white gate]

what is the property of a centroid

[tidal turret]

the point where all medians meet

[white gate]

the other property

[tidal turret]

divides each median into two segments of ratio 2:1

[white gate]

yep

so in this case, AG/AD = 2/3

using Thales' theorem, you can obtain AN/AC = AM/AB = MN/BC = 2/3

and what is the relationship between ratio of areas and ratio of sides?

[tidal turret]

(ratio of sides)^2

[white gate]

correct

[tidal turret]

I am rusty

[white gate]

tbh i dont really care if you are rusty or not :/

if you know that then its good, if u dont its fine

[tidal turret]

I got lost when you mentioned basic proportionality theorem

[white gate]

u can always do some research

[tidal turret]

but basically what I meant is that the ratio of areas is the ratio of the sides squared

AN/AC = AM/AB = MN/BC = 2/3

aAMN / aABC = 4/9

aAMN / 810 = 4/9

aAMN = 4/9 * 810

,calc 810 * 4/9

[grand pond]

Result:

360

[tidal turret]

no need to be aggressive, though thank u for the help

.solved

[midnight plank]

Channel closed

Closed by @tidal turret

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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

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

[fathom maple]

i dont understand the bounds in rectangular even could anyone help. Also after than i would need to convert those to polar

[buoyant yoke]

do you need to find the area?

[fathom maple]

nope

[buoyant yoke]

!original

[midnight plank]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[limber glen]

What is the question then

[fathom maple]

Q: describe the given region in polar coordinates

[midnight plank]

@fathom maple Has your question been resolved?

[fathom maple]

.close

[midnight plank]

Channel closed

Closed by @fathom maple

Use .reopen if this was a mistake.

[midnight plank]

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.

[twilit field]

Now The best I can do is $\int_{-\pi /2}^{\pi/2} \int_{0}^{1+ sin(\theta)} dr d(\theta)$

[grand pond]

What a wonderful world it is !

[twilit field]

which feels sus

[verbal pumice]

First quadrant should be 0 to π/2?

[twilit field]

Oops

$\abs{\int_{0}^{2 \pi} \int_{0}^{1+ cos(\theta)} dr d(\theta)- \int_{0}^{2\pi}\int_{0}^{1-cos(\theta)} dr d(\theta)}$

[grand pond]

What a wonderful world it is !

[twilit field]

oops, wrong integral

$2\int_{0}^{pi} \int_{1-cos(t)}^{1+ cos(t)} dr dt$

This feels off

[grand pond]

What a wonderful world it is !

[twilit field]

actually, I think I messed up big time by not drawing a diagram

$4 \int_{0}^{\pi /2} \int_{0}^{1-cos(t)} dr dt$

[grand pond]

What a wonderful world it is !

[twilit field]

Is this right

[midnight plank]

@twilit field Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[ionic magnet]

In a regular triangular pyramid, the height forms an angle beta with the plane of the lateral face. The distance from the middle of the height to the lateral face is equal to b. Determine the volume of the pyramid

[lyric charm]

do you have a diagram?

oh dear

[dry merlin]

Dear lord.

[ionic magnet]

[lyric charm]

i think your beta is in the wrong place to

it should be PSO not SPO

[ionic magnet]

it has to be PSO

oh yes

i though that too

[lyric charm]

also you should make an extra diagram of just triangle PSO itself

middle of the height

not its foot

so b is also in the wrong place

OQ is 2b actually

[ionic magnet]

where b has to be

[lyric charm]

midpoint of OS, perpendicular dropped from that onto PS

[ionic magnet]

midline?

[lyric charm]

no

[ionic magnet]

from mid of height

to PS

any point?

[lyric charm]

no.

midpoint of OS, perpendicular dropped from that onto PS

[ionic magnet]

midpoint of OS perpendicular dropped from that onto PS

[lyric charm]

no

that line is very much not perpendicular to PS

[ionic magnet]

i know

now

[lyric charm]

PO isn't b cos(beta) btw.

[ionic magnet]

yes

i made wrong picture

any ideas?

because i actually have nothing

only that angle beta

and perpendicular b

okay i also know angle P

it’s 90 - beta

[ionic magnet]

подожди

[lyric charm]

а, так ты по-русски говоришь?

[ionic magnet]

да

[lyric charm]

можно оригинал тогда?

чтобы не играть в испорченный телефон с переводами

на всякий случай

[ionic magnet]

В правильной треугольной пирамиде высота образует с плоскостью боковой грани угол бета. Расстояние от середины высоты до боковой грани равно b.Определить объем пирамиды

[ionic magnet]

откуда?

[lyric charm]

в смысле?

[ionic magnet]

you

where from

[lyric charm]

а, я из Питера

[ionic magnet]

ахах

имба

[lyric charm]

??

[ionic magnet]

давно тут сидишь?

[lyric charm]

на этом сервере?

да, давно

[ionic magnet]

сколько

[lyric charm]

короче, все то, что я тебе уже сказала, остается в силе

[ionic magnet]

да я уже понял

но что дальше

[lyric charm]

OP = 2b cos(beta) выходит

выражаешь высоту, сторону основания и фигачишь объем

у меня с собой бумаги сейчас нет, так что начертить не смогу

[ionic magnet]

чо дома бумажки нету?

[lyric charm]

я сейчас не дома

[ionic magnet]

щащаща

[lyric charm]

мне до дома еще минут 30 где-то ехать

только тогда я тебе что-то начертить смогу

[ionic magnet]

ты кем работаешь

[lyric charm]

учительницей в частной школе

[ionic magnet]

кста SM будет b/sin(beta)?

[ionic magnet]

ого

класно

[lyric charm]

а что такое M?

можно еще раз трехмерный чертеж?

[ionic magnet]

прикольно

я туда уже литр коректора залил

[lyric charm]

ы

ну переделывай

[lyric charm]

ага, то есть M -- середина высоты

[lyric charm]

да

!nosols

[midnight plank]

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

[ionic magnet]

что значит?

[lyric charm]

у нас тут есть несколько команд для часто встречающихся напоминалок

скидывать готовые ответы тут не принято

здесь не ГДЗ

[ionic magnet]

да я уже читал правила

помню

[lyric charm]

некоторые кадры не читают

[ionic magnet]

пожди

[lyric charm]

короче я бы из O перпендикуляр на PS все равно бы опустила

[ionic magnet]

как ты сюда попала?

[lyric charm]

??

[ionic magnet]

блииин

[lyric charm]

моя твоя не понимать -- ты хочешь меня обо мне же расспрашивать или все-таки работать над задачей?

[ionic magnet]

откуда взялось?

[ionic magnet]

и то и другое

[lyric charm]

вот как раз тебе и собиралась объяснить

[ionic magnet]

из какого триугольника

[lyric charm]

опусти из точки O перпендикуляр на PS. назовем его основание K

[ionic magnet]

сделал

[lyric charm]

OKS и MQS подобны с коэффициентом 2

значит OK = 2b

и рассмотри потом треугольник OKP

угол KOP в нем будет бета

ааа стоп. я немного налажала

OP = 2b/cos(beta)

[ionic magnet]

как ты поняла что за 2

[lyric charm]

ну OS = 2*MS же

M -- середина OS

[ionic magnet]

ааа

понял

[ionic magnet]

почему

[lyric charm]

чертеж скинь?

[lyric charm]

там угол KPO = 90°-β

ну а третий угол прямой

[ionic magnet]

45?

[lyric charm]

??

прямой угол сегодня с утра был 90 градусов)))

[ionic magnet]

ну

и провели перпендикуляр

[lyric charm]

ты его не обозначил

угол PKO

он прямой

[ionic magnet]

обозначаю

[lyric charm]

в треугольнике OKP углы 90, 90-β и β

[ionic magnet]

откуда там beta

😔

[lyric charm]

чувак

[ionic magnet]

а

[lyric charm]

ты сам в угол KPO написал 90-бета

и был прав

)))

[ionic magnet]

ладно

дальше

подожди

аня да?

[lyric charm]

да

[ionic magnet]

меня дима

приятно

[lyric charm]

очень приятно...

[ionic magnet]

давай потом когда сможешь

дома

будет бумага

[lyric charm]

10 минут дойти

[ionic magnet]

хорошо

добавь в друзя

[lyric charm]

если готов подождать, я тебе чертеж воспроизведу

[ionic magnet]

окей