help-39

[severe quarry]

Because the coefficient of x^2 is 1, positive

[midnight haven]

yeah

[severe quarry]

Now, you also know two zeros

[midnight haven]

ah yeah that makes sense

everything in between would be negative

and the rest positive

[severe quarry]

You know it will look like this

[severe quarry]

Yeah

So you could right away conclude all of this, without any calculation

[midnight haven]

ive never thought of that

thanks

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[unkempt rapids]

Why is there positive and negative infinity limits, they will both end up the same answer no matter if it's positive or negative?

[unkempt rapids]

how will the infinity being negative change the answer

[trail shoal]

Whats the limit as x goes to infinity of |x|/(x+1)

For example

Find the limit as it goes to -∞ and +∞

[unkempt rapids]

1 and -1?

[trail shoal]

As you can see limits at -∞ and +∞ differ sometimes

Thats why they're 2 different things

[unkempt rapids]

yh i see now

but is it for only absolute values?

[trail shoal]

It can happen for many functions, this is why we dont know until we check

[old marsh]

y = (ln x) * x^(sqrt x)

Or y = x^3

[trail shoal]

For example lim as x goes to ±∞ arctan(x)

[unkempt rapids]

oh ok

ty i understand now

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[unkempt rapids]

why is the answer -2 I got 2/3 or is there a mistake in the answer

[midnight haven]

its -inf

[unkempt rapids]

how does it make the answer -2

[light helm]

can you show your work?

[unkempt rapids]

i thought it was the same

ok

[light helm]

where'd that first line come from

[unkempt rapids]

don't you have to divide everything by x^3

[light helm]

specifically the 4x^3 + 1

[unkempt rapids]

cuz x is leading to infinite anything divided by x is 0? so i cancelled it

[light helm]

no as in how did you even get
4x^3 + 1
in the first place

before attempting division by x^3

[unkempt rapids]

look

its the numerator

[light helm]

sry, didn't realise that was there too

i meant the other 4x^3 + 1

where did that come from

[unkempt rapids]

the square root of 16x^6 is 4x^3

[light helm]

not quite

[unkempt rapids]

oh

[light helm]

it'd be 4|x^3|

but where's that +1 coming from

[unkempt rapids]

well i cancelled it anyways

[light helm]

wdym

[unkempt rapids]

because i divided it by infinite so it became 0?

[light helm]

no as in how did you get it in the first place

before division

these are all questions adressing what you're doing before attempting division by x^3

[unkempt rapids]

i was trying to remove the square root of 16x^6 + 1

[light helm]

square roots don't work like that

$\sqrt{a+b} \redneq \sqrt{a} +\sqrt{b}$

[jolly parrot]

ℝαμΩℕωⅤ

[unkempt rapids]

then how would it be

[light helm]

divide by
-x^3 = |x^3| = sqrt(x^6)
directly

(from definition of abs val, for negative values)

[unkempt rapids]

ohh i understand now

i had to put an absolute value on x^3 and it will be
4x^3/2x^3-4x^3

[pearl pond]

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[regal sequoia]

"Determine the area A and the coordinates (µx, µy) of the center of gravity of
sector D of the ellipse if"

[regal sequoia]

am i right in thinking that the first step is to integrate x from 0 to 1 and integrate y from 0 to x?

[pearl pond]

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[sharp smelt]

I don't even understand the question

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[cursive fulcrum]

Hey! i was reading it lol

[sharp smelt]

sorry

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[slim basin]

Dont get this

[slim basin]

i tried figuring it out and got sin theta = 4

i know it's in quadrant 1, and I know that the x line = 3/5

Or

It could be the hyp = 5, and the x line is 3

which would make sin theta = 4

but that's WRONG

[solid ibex]

sin theta = 4/5

[slim basin]

i figured it out

thanks

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[midnight haven]

for this Diffeq, using the bernoullis equation

does this look right?

there shouldn't be a - on the right hand side

nvm

yes

okie, thankyou

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[midnight haven]

@midnight haven

you made a mistake in the last step

converting 1/y to y

wouldnt i just be taking everything on the right side, and flipping it on itself

1 to 1, x to x^-1, and ce^x/x to cx/e^-x

no

the terms are related by addition

you could have that it if they were in multiplication

so how would i convert them when flipping 1/y to y

when you flip y

say

you have

(1/y) = 1+ (1/x)

if you flip y

will you get y= x+1 ?

dude you are solving D.E

and getting stuck at algebraic operations

just think properly

tbf, probably 80% of mistakes in DE happen within the realm of algebra

tbf?

to be fair

that is true

but you are aware of the fact that you have done a mistake

only through you telling me

i dont see how this is wrong

<@&286206848099549185>

[midnight haven]

i don't know how to explain this

btw

reopen the channel

.open

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[pearl pond]

✅

[midnight haven]

when you take ( 1+ (1/x)) to the other side

you get 1/( 1+ (1/x))

not 1+ (1/x)

right

is that not what i wrote

no ?

you wrote the opposite

okay here

if it was just 1/(1/(x+1))

then it would have become x

but there is 1/(1+1/x)

right

so i cant divide 1/1 and 1/1/x

no

you can't split it

so is this is, no further reduction

yes!

you can take x as l.c.m in the denominator

ah ok, i see

thankyou

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[slow marten]

Please solve this using Alligation Method, in solution it is solved by making equation

[pearl pond]

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[hollow hull]

let $a in R*, n in N, u = (1+ia)^n + (1-ia)^n$

[hollow hull]

prove that u in R

help please

[jolly parrot]

ATAE

[hollow hull]

edit: a in R* and n in N

[dreamy ibex]

are you aware of the bionomial expansion? @hollow hull

[hollow hull]

no

[dreamy ibex]

can you express the terms in euler's form?

[echo reef]

Wsp

[hollow hull]

how

i dont think we can use it

[fluid axle]

really there's much easier than that gumball

[dreamy ibex]

hmmm am wondering alternate ways as well actually

[fluid axle]

you know conjugates atae ?

[hollow hull]

yes

[fluid axle]

yeah then spamming conjugates works very well here

try showing that conj(u) = u

[hollow hull]

i will try it

[fluid axle]

if you've shown that, then gg u is a real number

it's a one-liner if you remember how conjugates work with sums and products

[hollow hull]

but i haven't studied that before I think it might be off topic

[fluid axle]

what, conjugates?

[hollow hull]

that if conj(u) = u then its a reel numver

no sorry

mb

[fluid axle]

it's really trivial to show anyway

[dreamy ibex]

true

[hollow hull]

thank i solve it

[pearl pond]

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[silver oracle]

is this correct?

answer b?

[indigo pewter]

yes

[silver oracle]

c?

[indigo pewter]

yes

[silver oracle]

d?

lmk if you want me to send the graph here

[indigo pewter]

yes

[silver oracle]

d?

one more after this

[indigo pewter]

yes

[silver oracle]

d?

[indigo pewter]

yes

[silver oracle]

ty

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[mystic fog]

Is it true that if a semigroup S has a unstable sub semigroup, then S is unstable?

[mystic fog]

@mossy dagger

• <@&286206848099549185>

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[hearty anchor]

Hi, i'm having my highschool finals next week

[hearty anchor]

but i cant quite crack this one excercise

So this trapezoid has a right angle DAB

and ADC

CD equals BC

and sin of the angle ABC equals 4/5

I'm supposed to find tan of the angle ABD

please cue me in on this one i've been sitting on it for almost an hour

[light helm]

construct a perpendicular line from C to AB

[hearty anchor]

oh i see

so a/sin alpha

a/sin alpha=1/x

then a=4/5x

by a i mean the legth of DA

no, my bad

the other way

[light helm]

what's x representing here

[hearty anchor]

its pretty late here

x is the legth of dc and cb

pardon me

so a/sinalpha=x/sin90

[light helm]

I'd just assign a numerical value to it for convenience

the ratios between sides will still be the same, angles won't be affected

let L be the point where the constructed line meets AB

since you know sin(ABC) = 4/5
you could assign the lengths
CL = 4 and BC=CD = 5

[hearty anchor]

ooh yeah

makes a lot of sense

okay now pythagorean and im set

so LB is 3

and the tan should be 4/8=1/2

thank you so much man

you're the boss

[pearl pond]

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[velvet meadow]

find if it exist, the limit of the recurrent sequence:
$\a_1 = 5, \quad \frac{a_{n+1}}{a_n} = \frac{n+1}{3n}$

[jolly parrot]

milanesa de pollo

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[restive pike]

ii

[restive pike]

confused on how the surface area is smaller than the length

[pearl pond]

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[restive pike]

<@&286206848099549185>

[pearl pond]

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[pearl pond]

@restive pike Has your question been resolved?

[restive pike]

,

[restive pike]

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[frail dune]

Could somebody help?

[frail dune]

Im suck at part b

[smoky musk]

!status

[pearl pond]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[frail dune]

2

[smoky musk]

Show your progress on part b so far

[frail dune]

its messy

Ive wrote down all the givens

[smoky musk]

Hint, what is the value of $P(A \cap B' \cap C)$?

[jolly parrot]

Xwtek

[frail dune]

but i dont have P(AnB')

[smoky musk]

Use $P(B'|A)$

[jolly parrot]

Xwtek

[frail dune]

i dont have it either

[smoky musk]

$P(X'|Y)=1-P(X|Y)$

[jolly parrot]

Xwtek

[frail dune]

oh wow thats a rule?

[smoky musk]

Yes, you can prove it.

[frail dune]

thats great

[frail dune]

it is 0.2

[smoky musk]

Now, what about $P(A' \cap B' \cap C)$

[jolly parrot]

Xwtek

[frail dune]

hm

is it 1- P(A n B' n C) - P(A n B n C)?

[smoky musk]

No, It's not

[smoky musk]

Also, I got a different answer.

[frail dune]

wait yh

it is 0.06

not 0.2

my bad

well

how do i go from there

[frail dune]

i know that P (A' n B') is P(AUB) but we dont have P(B)

wait

i think i got P(B)

[frail dune]

using that rule again

is it 0.365?

[smoky musk]

I don't think it's right? Step by step please?

[frail dune]

i still dont know how will that get us closer to finding P(B' n C)

[frail dune]

from here?

[pearl pond]

@frail dune Has your question been resolved?

[frail dune]

hey? @smoky musk

[smoky musk]

Oh, you're just calculating P(B)

[frail dune]

Mhm

[frail dune]

^

Also why is it so long wtf

[frail dune]

@mossy dagger part b? anyone?

[pearl pond]

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@frail dune Has your question been resolved?

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[frail dune]

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[fierce crystal]

https://www.desmos.com/calculator/9osxgwyiix

why doesnt this work for inverse kienmatics?

[pearl pond]

@fierce crystal Has your question been resolved?

[fierce crystal]

<@&286206848099549185>

[midnight haven]

hi

[fierce crystal]

howdy

[midnight haven]

can I help you?

[fierce crystal]

yes, would be very appreciated

[midnight haven]

I can do some graphing but, I will se what I can do

whats seems to be the problem

[fierce crystal]

im trying to replicate inverse kienmatics

and

[midnight haven]

Yikes

thats hard

I am sooooooo sorry

this is not really my place of expertise

[fierce crystal]

so im splitting the midpoint of the direct line into 2 to make 2 right triangles

[midnight haven]

OOOh

[fierce crystal]

then solve for thr angels of the line using arccos of (b/c)

but thats not working

[midnight haven]

so what you need to do is solve that triangle?

[fierce crystal]

basically yeah

idk why it isnt working tho

[midnight haven]

okay I have done more work in that area

[fierce crystal]

do you think u could help?

[midnight haven]

I am not sure

or the length of the bottom

[fierce crystal]

the length of the bottom is just the total distance of the direct line to the endpoint

[midnight haven]

aaah

[fierce crystal]

i have it defined as d_mid

[midnight haven]

I am new to this website

do we have the hieght?

of the triangle?

[fierce crystal]

no but we have the hypotenuse

which is just 5 because thats the length of the line

so base = d_mid and hypotenuse= 5

[midnight haven]

dang

the only thing we really need is the height

at this point

[fierce crystal]

we can find it easily

height=sqrt hyp^2 - base^2

[midnight haven]

thank you

Height=29.3619

Base=3.12846607781

Hypotenuse=6.25693215562

do we know the back?

[fierce crystal]

the back?

[midnight haven]

where the cursor is

I think I can try that one

[fierce crystal]

no no, hypotenuse is always equal to 5

[midnight haven]

thats not the hyypotenuse

[fierce crystal]

.

[midnight haven]

I am trying to find the legs

that dotted line is not the hypotenuse

nm

sorry

My bad

I was trying something else

My mistake

forget anything I said

did you get this?

91.85770813

as your answer for the height of the whole thing?

[fierce crystal]

?

the height of the right triangle?

[midnight haven]

I managed to get the area of the total

but thats unrelated

you are trying ot find the angles of both triangles right?

[fierce crystal]

yes

[midnight haven]

okay

well

[fierce crystal]

trying to recreate this https://www.desmos.com/calculator/4xyb3lgisa

[midnight haven]

now your trying to find the angles of this traingle?

did you solve the first one?

or is that still pending?

because if we have one angle

I can solve the others

[fierce crystal]

i think i did solve it but not for the right thing

[midnight haven]

well I think it is extremely difficult to find the angles on a triangle without at least one angle

it takes certain mathematical expertise that I dont have

[fierce crystal]

trying to find these angels while splitting the middle

[midnight haven]

okay

interesting

do we have the top?

ANGLE?

sorry caps was on

[fierce crystal]

nah

all we have is the side lengths and 1 angle of 90 degrees

[midnight haven]

we have side lengths?

please give them

if they are equal

I can easily solve it

but if not

I cant, at least its really hard

[fierce crystal]

the base is defined as d_mid in desmos, the hypotenuse is always 5, and the height is sqrt(hyp^2-base^2)

[midnight haven]

I dont have the link

[fierce crystal]

.

[midnight haven]

Is this the first one we are trying to solve?

and if so, can you tell me the length of the legs on the triangle

[fierce crystal]

legs?

[midnight haven]

its a tem for the two smaller sides

[fierce crystal]

so side a and b?

[midnight haven]

I think so

[fierce crystal]

a is adjacent or the height which is sqrt(hyp^2-base^2) and the base is d_mid

[midnight haven]

so what is Hyp?

[fierce crystal]

thats my fault, i used hyp as a stupid variable name for the direct line

[midnight haven]

ooooooooooooh

[fierce crystal]

i forgot i even used that

[midnight haven]

now i get more

lmao

[fierce crystal]

my bad lol

[midnight haven]

lol

🙂

okay I am madly confused

I am so sorry

I am not sure this is exactly my level

I feels like this is on level 10000000000

and I am on level 10

I would try to call someone else for helop

[fierce crystal]

alr thanks a lot for trying your a real one @midnight haven

<@&286206848099549185>

[pearl pond]

@fierce crystal Has your question been resolved?

[fierce crystal]

.close

[pearl pond]

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[jolly parrot]

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

[pearl pond]

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[desert pelican]

Why is the y in x=3y+5/7y-1 a function of x?

.close

[sharp smelt]

you deleted your OG message

yeah, nvm

[desert pelican]

Sorry, I'm trying to fix this channel.

[sharp smelt]

you opened a new channel

[desert pelican]

I made a new one.

[sharp smelt]

you can't fix this, the bot may close this at any moment , it's fine

[pearl pond]

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[glossy hearth]

i am completeyly stuck with this trig equation, i need to find x

[dense plank]

what have you tried

[glossy hearth]

im not sure where to start, like do i first substract sin x

or do do i subtract and then sqaure root

[blazing cave]

factor

[dense plank]

yea factor the thingy

[glossy hearth]

how

[blazing cave]

take out sin x

[glossy hearth]

so 2 sin^2 x=-sin x?

[dense plank]

no

that's moving the sinx to the other side

[glossy hearth]

do i divide sin x then

[dense plank]

sinx is common from both terms right?

[glossy hearth]

i think o

so

so does it become 2sin^2 x=0

since i divide sine x

[blazing cave]

you don't want to divide sin x

[glossy hearth]

so how do i remove it

[blazing cave]

say u have an expression like 3a + a^2, you can factor the common term (a) in both to make a(3+a)

do the same thing here

[glossy hearth]

so 2 sin(sin x)

[dense plank]

its sinx+2sin²x

[glossy hearth]

yh that the orginal quetion

question

[dense plank]

yea factor it

[quiet wasp]

what are you factorizing with

[dense plank]

it will be (sinx)(???+???)

[glossy hearth]

sin x+ 2sin(sin x)

[quiet wasp]

bruh

[blazing cave]

extra note : sin^2 (x) is the same as sin x * sin x

[glossy hearth]

wait hold on lemme try again

gimme sec

sin x+(2 sin x)(sin x)

[quiet wasp]

go on

[glossy hearth]

sin x+2(sin x)(sin x)

[blazing cave]

then factor out the sin x in both terms

[glossy hearth]

how do you factor it out, im not that good in factoring

sin x(1+2x sin x)= 0

[blazing cave]

sin x (1 + 2sin x) = 0, yes

[glossy hearth]

so what do i do now

[blazing cave]

u have two numbers multiplied together equals to 0

it can only happen if at least one of them is equal to 0

so you divide cases :
sin x = 0, or
1 + 2sin x = 0

[glossy hearth]

ohhhhhh

[blazing cave]

[zero product rule]

[glossy hearth]

so its like quadratics

thx so much

[blazing cave]

yes

[blazing cave]

hoi 👍

[glossy hearth]

wait

but why the answers say its 0, 180,210,330,360

[blazing cave]

first, what are the solutions to sin x = 0 (the first case)?

[glossy hearth]

0

[blazing cave]

any other?

[glossy hearth]

sin x=1/2 is 30 and 150

[blazing cave]

whoops it should be sin x = -1/2

[quiet wasp]

where did u get sin x=1/2 from

[glossy hearth]

from factorising

1+2sinx=0

[blazing cave]

1 + 2sin x = 0 becomes 2sin x = -1, i think you forgot the negative sign

[glossy hearth]

oh..

mb

[blazing cave]

also for this i mean that sin x = 0 has other solutions (not just x=0)

[glossy hearth]

would that be 180 and 360, since sin is the y axis

[blazing cave]

yep

[glossy hearth]

aight thc

thx again

[blazing cave]

hoi

[quiet wasp]

you didnt fknish

finish

[glossy hearth]

wait why

did i not finish

[pearl pond]

@glossy hearth Has your question been resolved?

[pearl pond]

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[clever ridge]

I need to solve the following equation and turn it into it's lowest terms 3/8 divided by 7

[jolly parrot]

faiyrose

[clever ridge]

Looks about right

So 3/27 correct?

1/7?

3/56* right?

And this is in its lowest term right?

3 isn't divisible by anything other than 1

So the reciprocal is just the inverse of a fraction?

Equalling to 1

So the reciprocal of 14 is 1/14?

[jolly parrot]

faiyrose

[clever ridge]

🙏🏽 thank you very much

That's all

.close

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[flint halo]

hello I need help with linear algebra

[flint halo]

specifically question 9

these are all of the answers

up to 9

I dont understand how to find the coordinates that corresspond to the basis B (fancy)

I understand for Av_1 because Av_1 = lambda v_1

but my thought process was maybe doing

(A-Lambda * Identity_mat) v_2 = v_3

then solve

but that is incorrect

because the coords dont match up

then i tried doing D = C^-1 A C and that doesnt work either

im just so flippping lost

[merry carbon]

How did you try doing this?

[flint halo]

well

A we are given right

and then the C matrix is our matrix that we found from the eigenvectors

after orthogonalizing them C^T = C^-1

so I tought since were trying to find a "Diagnolized matrix" (jordan canonical form?) maybe that would work

but it didnt

also if it helps the topic of this homework is on spectral theorem

[merry carbon]

,w [[1, 1, 1], [-1, 1, 0], [1, 1, -2]] * [[6, -4, 2], [-4, 12, -4], [2, -4, 6]] * [[1, -1, 1], [1, 1, 1], [1, 0, -2]]

[jolly parrot]

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[flint halo]

yeaa

[merry carbon]

Ah, hmm

,w [[1, 1, 1], [-1, 1, 0], [1, 1, -2]] * [[1, -1, 1], [1, 1, 1], [1, 0, -2]]

[jolly parrot]

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[flint halo]

this one is complicated bruh

[merry carbon]

Orthogonal but not orthonormal-

[flint halo]

yeah

wait

do i need to make it orthonormal?

:|

ill try that then get back to you if it works out lol

[merry carbon]

A bit pain but yea, also, who named these

Orthogonal matrices need more than orthogonality for their columns, they need orthonormality

That does however change the basis, but that doesn't stop you from finding C^{-1} "manually"

,w [[1, -1, 1], [1, 1, 1], [1, 0, -2]]^(-1) * [[6, -4, 2], [-4, 12, -4], [2, -4, 6]] * [[1, -1, 1], [1, 1, 1], [1, 0, -2]]

[jolly parrot]

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[flint halo]

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

you are goated

ty :3

https://tenor.com/view/azumanga-daioh-tomo-yomi-hello-hey-hi-squish-gif-27433490

https://cdn.discordapp.com/attachments/1197084298034024504/1235476862063345745/Mikusaysrowreduce.gif

i made dis 1 ^

[merry carbon]

Awwww

[flint halo]

.close

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[pearl pond]

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[chrome flame]

Probability of max 12 getting when 2 dice rolling at same time

[flint halo]

Isnt it 1/36

[calm wing]

!noans

[pearl pond]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[flint halo]

sorry

[chrome flame]

Lol

[flint halo]

i was going to expaing

[calm wing]

you can only get 12 by having 6+6

[flint halo]

explain

[chrome flame]

I do not think he is giving answer

[chrome flame]

Yes

So what do you think?

[calm wing]

so what's the probability of getting 6?

[chrome flame]

Probability will be 1 or 1/36?

[glacial sequoia]

when you say max 12

[chrome flame]

@calm wing

[glacial sequoia]

do you mean atmost 12

[chrome flame]

Yes max 12

No exact 12

[calm wing]

oh

[glacial sequoia]

right

[calm wing]

then yeah it's a different case

[glacial sequoia]

nah she said exactly 12

so theres only one case

[chrome flame]

Bro she 😂

[calm wing]

br

[chrome flame]

Neon

Given answer is 1

[calm wing]

exactly 12 -> needs to be 6+6 -> what's the probability of getting a 6?

[calm wing]

then it's at most 12

!xy

[pearl pond]

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.

[calm wing]

just send a picture of the whole problem

[chrome flame]

It is not English

[calm wing]

that's okay

[chrome flame]

At most 12?

[calm wing]

if it's ≤12, then prob. is 1
if it's =12, then prob. is 1/36

[chrome flame]

What???

I didn't understand

[flint halo]

what is your native language

[chrome flame]

Hindi

You wrote something unclear

Rolling a dice 6 times

And getting 6?

[calm wing]

none of us here understand what problem are you trying to solve

[chrome flame]

He wrote something and deleted

[calm wing]

well it's deleted now

[chrome flame]

I understand it now it will be sum of 0 to 12 so we will add all the possible probabilities and hence we got sum 1

[calm wing]

great! do you have any more questions? if not, type ".close"

[chrome flame]

.close

[pearl pond]

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[pearl pond]

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[snow latch]

Would the average grade across all classes of a student measured in percentage be a discrete or continuous variable?

[snow latch]

Seeing as it has a limit from 0 to 100 but it also won’t necessarily be an integer

Rounded to 2 decimal points at least

So 4 sig figs

[tall flint]

If it truncates at all, strictly speaking it'd be discrete

[snow latch]

Ok

[snow latch]

The other variable is hours spent on social media

[snow latch]

But considering the fact that grades are only displayed to 2 dps, finding the average will usually be around 2 dp if not 3

[tall flint]

So?

[snow latch]

Some definitions of discrete data say that they are only allowed to be integer values

[snow latch]

So it doesn’t cut off in that circumstance

By your definition, nothing is every truly continuous data

Putting pi on a graph makes it a discrete variable by that definition

Age is even to 10 ^x measures too small to graph

[tall flint]

Pi isn't a variable

[snow latch]

Sure it could be

[tall flint]

I'm not sure where you're going with this so I'm gonna step back, gl

[snow latch]

I’m just confused I’m sorry

[tall flint]

Please stop pinging me

[snow latch]

Ok

Would the average grade across all classes of a student measured in percentage be a discrete or continuous variable?

Seeing as it has a limit from 0 to 100 but it also won’t necessarily be an integer

4 sig figs

[pearl pond]

@snow latch Has your question been resolved?

[snow latch]

<@&286206848099549185>

[atomic scroll]

lol

[pearl pond]

@snow latch Has your question been resolved?

[snow latch]

<@&286206848099549185>

[pearl pond]

@snow latch Has your question been resolved?

[pearl pond]

@snow latch Has your question been resolved?

[urban coyote]

imo its continuous, because it could change as the student does more classes

and yea it mostly would be an integer

[snow latch]

yes

[pearl pond]

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[worthy cairn]

Hi

[worthy cairn]

I'm trying to fit a linear regression model, but I came onto a few problems. Firstly, it seems my model is underfitting:

I am trying to predict food expenses based on weight, height, income, savings, children and a few others factors.

It seems income and savings are the most impactful, but they are also highly correlated with perasonr = 0.94

[pearl pond]

@worthy cairn Has your question been resolved?

[pearl pond]

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[silent meteor]

I give up, sat 3 hours on this integral. Why can't I break down this integral properly? I keep needing to evaluate arcsin(-2) which is undefined.

[midnight haven]

are you sure the question is right ?

[sharp smelt]

What is this?

[midnight haven]

sin^-1(-2)

which dosen't exist

[sharp smelt]

that isn't defined on R

[midnight haven]

or is there any other mistake

[sharp smelt]

!xy

[pearl pond]

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.

[silent meteor]

The exercise is about pressure which is depth * weight density * area

[midnight haven]

why is there an extra -3 ?

[silent meteor]

that's in order to shift the function down by 3 units

then the -y resembles the depth

[midnight haven]

when you take -3 to the left side

if becomes y+3

it

that will solve your integral , you get lower limit as 0 and upper limit -1

[silent meteor]

Doesn't the - sign turn the function into 3-y?

[midnight haven]

the function turns into -(3+y)

[silent meteor]

You're right, I now notice

🤦‍♂️

thank you for clarifying!

.solved

[pearl pond]

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[tepid panther]

how do I do this?

[white juniper]

start with recalling a formula of sector area

[tepid panther]

so sector area = central angle(rad)/2 * radius^2

[white juniper]

yeah

[tepid panther]

then algebraic manipulation to isolate the radius?

[white juniper]

for the first one you want to isolate central angle

for the 2nd the radius

[tepid panther]

yeah, that's what I meant.. my bad

[white juniper]

alright

[tepid panther]

let me try and isolate central angle for the first one

@white juniper how's this?

10pi/25 would simplify to 2pi/5

,calc 2pi/5

[jolly parrot]

Result:

1.2566370614359

[tepid panther]

so ~1.3?

[white juniper]

you can stay with pi

dont need to round it

[white juniper]

see the other values were written with pi

[tepid panther]

yeah but at the top it says to round to the nearest tenth

so idk

it won't let me type the rest of 2pi/5

,calc 10pi/25

[jolly parrot]

Result:

1.2566370614359

[white juniper]

oh really

i didnt notice

[white juniper]

so yeah its correct

[tepid panther]

oh okay thanks

for the second one I got the radius as 4

[white juniper]

yeah its correct

[tepid panther]

,calc 24pi

[jolly parrot]

Result:

75.398223686155

[tepid panther]

75.4 for the last one?

[white juniper]

i dont think its 24pi

how you got that?

[white juniper]

(pi/12)/2=pi/24

[tepid panther]

I thought when dividing you multiply by the reciprocal?

so like 1/2 = 1*2?

that doesn't sound right but

[white juniper]

but only when its pi/(12/2)

[tepid panther]

oh

okay let me fix it

,calc 6pi

[jolly parrot]

Result:

18.849555921539

[tepid panther]

18.8?

[white juniper]

yeah

[tepid panther]

let me do this one now

,calc 8pi

[jolly parrot]

Result:

25.132741228718

[tepid panther]

25.1?

[white juniper]

yes

[tepid panther]

thank you.

[white juniper]

np

[tepid panther]

I got an 8.10

8/10

@white juniper This is what I put for this question.. was I wrong?

[white juniper]

looks correct

[white juniper]

nice

[tepid panther]

not good enough

we need a 10/10

[white juniper]

do you know were you make a mistake?

[tepid panther]

no idea

these were my answers

[white juniper]

i dont know

everything looks fine

<@&286206848099549185> is someone able to tell?

[midnight haven]

use formula to find arc length/ radius

[tepid panther]

which one?

l=rtheta?

are you saying #2 is iffy?

[midnight haven]

1 degree = pi/180 radians

1 radian = 180/pi

[tepid panther]

what formula do you want me to use though @midnight haven

and for which question?

[midnight haven]

2,3

that formula would do it

[tepid panther]

can you model a problem for me on #2, still unsure with what you're saying.

[tepid panther]

please

@midnight haven where'd you go?

[midnight haven]

someone else might help you better i had to go

[tepid panther]

can you still help or?

[midnight haven]

i cant rn

@mossy dagger please help him

[pearl pond]

@tepid panther Has your question been resolved?

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[sharp smelt]

if $f \in C[a,b]$ what can be said about $|f|$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

so firstly $f$ is continuous on $[a,b]$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

as this is $\in C^1$ I'm assuming it's once differentiable

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

so I can say $|f|$ is continuous

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[cunning comet]

depends on the notation you use.

[sharp smelt]

wdym

[cunning comet]

what is C[a,b] in your context?

[sharp smelt]

Continuous in [a,b] I guess

and C^n means continuous and differentiable n times in the interval

thanks!

.close

[pearl pond]

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[sharp smelt]

$f\left(x\right)=ax^2+bx+c$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[white juniper]

that is quadratic formula

[sharp smelt]

yeah, it's not that simple lol

[white juniper]

[sharp smelt]

I'm not yet done

[autumn fossil]

||(-b+-sqrt(b^2-4ac))/(2a) ezz||

[midnight haven]

[sharp smelt]

$f(\frac{1}{n})= \frac{n+1}{n^2}$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

for all $n \in N$

[midnight haven]

No way function

Big?

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[midnight haven]

Alright

[sharp smelt]

set of naturals

find the value of

please don't give any hints

[cursive wraith]

so you wanna find a,b,c ig

[sharp smelt]

I'm using thie channel as my rough note

[midnight haven]

So what question asking?

[sharp smelt]

I have to find $\lim_{x\rightarrow0}f'\left(x\right)$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

so so start

• to start

[midnight haven]

So you have 2 different expression for your function?

ah it is for naturals and only for 1/n

Alright

Make sense

[sharp smelt]

no hints please

so I was thinking

[midnight haven]

It isn't hint, I don't know either

[sharp smelt]

I could start by finding the limit of this as $n \rightarrow \infty_N$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

where $\infty_N$ denotes the natural infinity

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

so the limit would be 0

hmm

but that doesn't help much

I guess I could start by deriving f(x)

[midnight haven]

Yeah because it make no sense since you say x=1/n
If n is infinity x is 0

[sharp smelt]

which is $2ax+b$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

now to find b

$c=0$

[midnight haven]

Why you want to find b?

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

The derivative is 2ax+b

[autumn fossil]

I have an urge to say a hint

[vital estuary]

me too

[sharp smelt]

please don't

[autumn fossil]

i wont

[sharp smelt]

I need to develop critical thinking skills

[autumn fossil]

ill make popcorn and watch

[vital estuary]

me too

[midnight haven]

What kind of hint? He haven't gave us complete question

[sharp smelt]

I have

[midnight haven]

So what about f(1/n)?

Why this expression exist

?

[sharp smelt]

$f\left(x\right)=ax^2+bx+c; f(\frac{1}{n})= \frac{n+1}{n^2}$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

that's just the question

[midnight haven]

So what we suppose to do?

Prove that limit for f(x) exists?

[sharp smelt]

find the limit of $f'(x)$ at 0

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[cursive wraith]

f(1/n) is given, but you haven't linked the 2 expressions f(x) and f(1/n) before

[midnight haven]

If f(x) undefined but f(1/n) defined then you want to prove it for all numbers by using f(1/n)

[autumn fossil]

do they need to be linked? There are 2 statements about f

[midnight haven]

👍

[midnight haven]

Yes

[sharp smelt]

was going to do that now

[cursive wraith]

meaning... the two combined together...

[hollow cobalt]

If f is a quadratic satisfying f(1/n) = (n+1)/n^2, you can just solve for a, b, c by obtaining values of f at 3 distinct points

[autumn fossil]

first is f(x) = ax^2 + bx + c for some a,b,c in R i suppose and the second statement is f(1/n) = (n+1)/n^2 for all n in N.

[sharp smelt]

I know

please don't give away hints

[midnight haven]

That's not a hints

[autumn fossil]

(also too complicated, there is simpler solution)

[pine moat]

why would you open a channel if you don't want help?

[sharp smelt]

I work better when I feel I'm being Judged

[midnight haven]

So how do we prove that limit exist for f(x)'?
Is it induction?

[pine moat]

interesting

[sharp smelt]

from this I've established f(0)=0

so c=0

[autumn fossil]

Wonderful, can I ask how?

[vital estuary]

https://tenor.com/view/cat-cat-stare-side-eye-side-eye-meme-ginger-cat-gif-9337430562745204577

[autumn fossil]

(its correct, dw)

[sharp smelt]

from this

[midnight haven]

There is no f(0) unless you prove that if true for f(1/n) then true for f(b)
Where b=1/1/b
Where 1/b in N :/

[sharp smelt]

I took the limit at the natural infty (I think something like that exists )

[autumn fossil]

There is, you dont understand the question

[autumn fossil]

ah i see

[midnight haven]

Ah well you right he just took limit of n

[cunning comet]

plugin 1/n in f(x) = ax² +bx+c and compare.

[autumn fossil]

There is some function f: R->R and the 2 equations are just properties of f

[midnight haven]

👍

[sharp smelt]

now $f(1)=2$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

and $f(\frac{1}{2}) =3/4$

[jolly parrot]

ƒ(Why am. I here)=I don't Know

[sharp smelt]

now I just solve two linear equations, and I'm done

huh,was expecting it to be much harder lol

[autumn fossil]

Can I show my solution now?

[cunning comet]

there is even an easier way.

[sharp smelt]

yes

[midnight haven]

Well yeah but isn't you want to prove each step?
I mean if you want to use n+1/n^2 for integers for example
Or that's totally irrelevant here?

[autumn fossil]

f(1/n) = (n+1)/n^2 = 1/n + (1/n)^2

f(u) = u + u^2 for u = 1/n for some n

and you get the expression straight away

[sharp smelt]

wait, what

just a minute

[autumn fossil]

f(x) = x^2 + x is not hard to prove from that

[midnight haven]

But u is a rational number

[autumn fossil]

u is not a random rational number, u can be any number in form 1/n

but that gives you at least 3 fixed points

[midnight haven]

Yeah but what is x? X could be real numbers

[autumn fossil]

(actually it gives you aleph 0 of themú)

and 3 fixed points define parabola