help-27

[devout snow]

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[devout snow]

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[formal yoke]

Hello, I need someone to explain what to do with the numbers inside

Like 36 ⁴|³

I basically don't know what to do with them

Actually, it would be nice if someone could make all the steps, my teacher doesn't have any notes about this so I'm kind of confused

I know that ⁴√ = -¹/⁴

So the ⁵√

But idk what to do with the rest

[weary pebble]

First of all apply the roots

[formal yoke]

I think I found out

Basically

[weary pebble]

4th root of 36^(4/3) = 36^(1/3)

[formal yoke]

4/3 x 1/4

[weary pebble]

yes

[formal yoke]

10/3 x 1/4

Yeahhh

[weary pebble]

yes

[formal yoke]

I'm such a genius

[weary pebble]

But it's not finished hten

[formal yoke]

Then I basically

4/3 x 1/4 = 1/3

That will be for 36

I'll do the same for the other numbers

[weary pebble]

yes but i believe you can do some things more

First write that down and we'll see after

[formal yoke]

You mean like

36 = (2² x 3²)

And so on?

[weary pebble]

yes

Exactly

And you'll find your answer

[formal yoke]

Yeah, I see

It's a whole pain I have to sau

Say

Anyways thanks, goodbye

.close

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[devout snow]

@undone mauve Has your question been resolved?

[devout snow]

@undone mauve Has your question been resolved?

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[jade ridge]

I know it shows the answer but im unsure how to get to it

[jade ridge]

I understand that VA is x = -4, +4 and that HA is y = 0 but not really what leads to the between and beyond

[patent marsh]

the question is asking what your y values will be with a given x value. For example:

$f(-7) = \frac{8(-7)}{(-7)^2 - 16} = -\frac{56}{49- 16} = -\frac{56}{33} $

damn I guess the bot is still down

now just do the same with the rest

[jade ridge]

OHHHHHHHH

[dense briar]

just plug in the

lol

[jade ridge]

my god im stupid

[patent marsh]

nah you're fine dude

it happens haha

[jade ridge]

I feel like that was obvious lmao

thanks man

[dense briar]

yo mellow

u good with calculus?

[jade ridge]

I have been stressing for a week before I remember these servers existed

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[neon bone]

help pls

i have no idea what to do

[fresh comet]

try splitting the fraction into 3 fractions multiplied together each with their own letter

[woven radish]

Mixnik

[fresh comet]

then try using laws of indices to simplify and then combine them together

[devout snow]

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[weak snow]

need help with last question

[hybrid snow]

The perpendicular slope is always the negative reciprocal of the original slope

I'm assuming you haven't learned vectors so

[weak snow]

nope

.close

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[final drift]

okay

so if its rounded to one significant figure, what is the maximum possible water intially in the fish tank

a.k.a., what is the maximum number which rounds to 70 when rouded to the nearest 10

@paper flume ?

[paper flume]

74

[final drift]

yeah assuming it is a whole number

we would say the 'upper bound' is 75

because anything less than 75 rounds to 70

meanwhile, what is the lower bound for the amount of water removed?

[paper flume]

65

[final drift]

the lower bound of the water removed, not the initial water

(we are referring to the 20 liters number here)

@paper flume can you give the lower bound of the water removed (not the initial water)?

[devout snow]

@paper flume Has your question been resolved?

[paper flume]

no

[paper flume]

im not sure mush

im set 9

[final drift]

okay so 15 would round to 20 right?

so we have an upper bound of 75 liters of water, and we take away at least 15 liters of water

therefore, we have at maximum 60 liters left

[final drift]

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[woven radish]

marc

marc

[devout snow]

@pearl flicker Has your question been resolved?

[devout snow]

@pearl flicker Has your question been resolved?

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[zenith portal]

I need help with doing statement reason for this problem

[zenith portal]

I have the given already

The rest of my statements are AD=BD, m<ACD=BCD, and m<CDA=CDB

Idk what the reason are for those are though

[gleaming socket]

m<CDA=m<CDB because CD perpendicular to AB hence both 90°

[zenith portal]

But what do i write as the reason

[devout snow]

@zenith portal Has your question been resolved?

[real grail]

just prove that the angles ACD and DCB are equal

CD is a bisects of ACB if :

ACB = ACD + DCB and ACD = DCB

[devout snow]

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[devout snow]

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[potent nebula]

how do i find the derivative of

[potent nebula]

y= 1/12 (2x - 5)^6 + (4 - 1/3x^3)^-1

[bleak sun]

chain rule

[potent nebula]

so i got

[bleak sun]

whats derivative of $\frac{1}{6}(2x-3)^3$ first ?

[woven radish]

cantprogram

[potent nebula]

is it

1/2(2x-3)^2

[bleak sun]

no

chain rule 😦

[potent nebula]

1/2(2x-3)^2 (2)

[bleak sun]

yes 🙂

[potent nebula]

yea

[bleak sun]

or just $(2x-3)^2$

[woven radish]

cantprogram

[potent nebula]

oh yeah

ok i got it

thanks

[bleak sun]

did u get it

nice!

[potent nebula]

yeah

thanks

[bleak sun]

u can .close

[potent nebula]

.close

[devout snow]

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[gleaming lava]

u busy

[bleak sun]

no im cantprogram

[gleaming lava]

umm

can you help me i guess

[devout snow]

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[gleaming lava]

The surface area and volume of a cube have the same numerical value. how many answers can you find?

[gleaming lava]

hello

can somebody help me with this

<@&286206848099549185>

[bleak sun]

dont ping

!15m

[devout snow]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[gleaming lava]

sorry

[bleak sun]

what is formula for the surface area of a cube

[gleaming lava]

do i wait again another 15 mins

[bleak sun]

.

[gleaming lava]

i do not know

[bleak sun]

ok so google it

[gleaming lava]

that much

when ever i google it its hard to understand what its saying im not a complete smart mind

[bleak sun]

ok

https://youtube.com/playlist?list=PLt3hChjBw-gGs0L4-tXGfx0tNQ93t01xf

[gleaming lava]

fine

now i understand

[bleak sun]

whats formula for surface area of a cube

[gleaming lava]

one moment please

is it formula 2

[bleak sun]

no

[gleaming lava]

you asked for what formula

is it

gtg thanks for the help

.close

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[wheat sparrow]

Apologies for the delete, had to do a quick revision but I'm solving a problem that involves implicit differentiation and related rates. While I semi-understand the basics, I am sort of confused on how to proceed. Do I follow up by using the quotient rule?

[violet wind]

what's the /dt and /2t?

[devout snow]

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[wheat sparrow]

dt is differentiating in respects to t and 2t is the adjacent angle

[bleak sun]

id first write an equation for the angle theta in terms of t

so whats A(t) = ?

[bleak sun]

u basically got to it here

?

whats A(t) in terms of x(t) and y(t)

or Theta(t) if that makes it easier to understand

urm why did u delete ur message

[wheat sparrow]

would it be d(theta)/dt if xt = 2t or yt = 4t^2? genuinely very confused here

[bleak sun]

ok so

A(t) = arctan(y(t)/x(t))

agree?

[wheat sparrow]

ye

[bleak sun]

whats y(t)

and x(t)

[wheat sparrow]

are you asking for the derivative of both terms

[bleak sun]

in terms of t

ok i gtg but u just differentiate with respect to t, thats about it

to find $\frac{d\theta}{dt}$

[woven radish]

cantprogram

[bleak sun]

cuz u have A(t) in terms of t

[devout snow]

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[scenic jungle]

a. Calculate the probability when the condition is at most 2 teachers pass! ```

Why my result is different while using excel?

[devout snow]

@scenic jungle Has your question been resolved?

[scenic jungle]

<@&286206848099549185>

[violet wind]

0.4^3 is .064, you wrote .64

also you're finding probability of exactly 2 teachers, not at most 2

[scenic jungle]

So?

[scenic jungle]

In my calculator says 0,64

[scenic jungle]

At most 2 teacher , it can be 1 or 2 teacher

So i wrote 2 teachers

[devout snow]

@scenic jungle Has your question been resolved?

[scenic jungle]

<@&286206848099549185>

[devout snow]

@scenic jungle Has your question been resolved?

[willow shell]

what does support level mean in here?

is that the probability?

for at most 2 teachers my answer was binomcdf (5, 0.6, 2)

which gives you 0.31744

but this is assuming that the support level just means probability

[scenic jungle]

Yes is it probability

[scenic jungle]

What the formula of this , can you give me it?

[willow shell]

oh i just use my calculator for this

[scenic jungle]

Can you check my ans ?

[willow shell]

with trials / n = 5
p= 0.6
x = 2

ah well i do not know the calculation so i can't check it for you

i'm allowed to use my calculator for probability questions :(

[scenic jungle]

How did you type in yr calculator

Steo by step

[willow shell]

in the distribution menu there's a function called binomcdf

i use a TI-84 Plus CE-T

[scenic jungle]

So the true ans on my excel right

[willow shell]

yeah

[scenic jungle]

But my teacher won't let me use it

[willow shell]

that's what i got as well at least

[scenic jungle]

My teacher using this method for the answer

But which part i doing wrong

[willow shell]

ah i'm sorry i can't help you with that :( maybe someone else can

[scenic jungle]

Oh okay

[scenic jungle]

But i have 1 question, maybe out of topic , can i send it? Maybe you can help me 🙂

[willow shell]

i doubt i'll be that helpful but yeah sure 😭

[scenic jungle]

If given the set of sample space S = {1,2,3,4,5,6,7,8}, which consists of 3 sets, namely A
= {1, 2, 3, 4}, B = {2, 4, 6}, and C = {2, 3, 5, 7}.
Define:
a. 𝐴 ∪ 𝐵 ∪ C =
my ans : {1,2,3,4,5,6,7}
b. 𝐴𝑐,𝐵𝑐,𝑑𝑎𝑛 𝐶𝑐
my ans :
𝐴𝑐 = {5,6,7,8}
𝐵𝑐 = {1,3,5,7,8}
𝐶𝑐 = {1,4,6,8}
c. (𝐴 ∪ 𝐵) – C =
my ans : {1,2,3,4,6} – {2,3,5,7} = {1,4,5,7}
d. Use DeMorgan's Law to find (𝐴 ∪ 𝐵)𝑐 and A𝑐 ∩ 𝐵𝑐
my ans : ????

Point d

Do you know about it?

Or can you check my answer on point a-c is it correct?

[willow shell]

oh yeah no sorry i've never heard of that 😭

[scenic jungle]

Oh okay 😦

[scenic jungle]

.close

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[supple knot]

• Ask your math question in a clear, concise manner.
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[devout snow]

@manic falcon Has your question been resolved?

[devout snow]

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[high aspen]

Can someone pleeease tell me how to solve this because i spent 15mins and i don’t even understand it

[devout snow]

Please don't occupy multiple help channels.

[midnight dirge]

lol

idt u can

[prime egret]

[wicked turtle]

what is there to solve exactly?

[high aspen]

idk

does someone understand

[midnight dirge]

here

https://en.wikipedia.org/wiki/Collatz_conjecture

[high aspen]

Bruh my friend sent me this

[midnight dirge]

now uk why

[high aspen]

he said it is a question he doesnt understand

.clode

.close

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[uncut crow]

i have a problem for everyone

f(x) = 7x

[high aspen]

kekw

[prime egret]

I’m listening

[uncut crow]

that's all

[prime egret]

Too advanced

[uncut crow]

[midnight dirge]

yes

[devout snow]

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[teal mantle]

could someone pls explain me what im supposed to do here. my shitty ass uni gave this as an assignemnt. i just want someone to kinda explain me what to do here.

[devout snow]

@teal mantle Has your question been resolved?

[devout snow]

@teal mantle Has your question been resolved?

[elfin hill]

You should write the equations of the Second principle of dynamics

[teal mantle]

shouldn't i just be finding the derivative for part a?

cuz its supposed to be related to derivatives

[vast rain]

I don't know what conditionally stable means

but surely stable systems are in a local minimum of the potential energy function yeah?

conditionally stable might mean where the potential energy function has a derivative of zero

i.e. you can stabilize the thing if you constantly offset the little perturbations

[devout snow]

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[visual raptor]

someone told me to do this

look up until the first step i get it

but i don't understand how we got to n=4

they told me to just equate the constants and forget x for a bit

but 3/5 also plays a role no?

<@&286206848099549185>

[vast rain]

hmm I think the cheap trick is just to plug in a value of x and solve for n

like if you plug in x = 5/3, you get 2^n * (5 + 5n/3)^2 = some number which might be solvable?

[visual raptor]

wdym

[vast rain]

in that you have a calculator so you can solve that equation for n through some iterative method

oh wait that doesn't work

nevermind

[devout snow]

@visual raptor Has your question been resolved?

[visual raptor]

so the constant = nC1 * 25 = 100

why not nC1 * 25 * 5/3 = 100

.close

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[orchid glade]

im trying to figure out the sum of squares of the first n natural numbers

[orchid glade]

and i landed upon the series 1 3 6 10

their second difference is one

but i have not idea on how to figure out their sum

[lunar pollen]

I believe you can use this formula, no?

[orchid glade]

my teacher gave it to me yes

but i wanna reach it

[lunar pollen]

As in the derivation of it?

[orchid glade]

yes

i tried the sum of odds over

[lunar pollen]

Take a look at this: https://math.stackexchange.com/questions/2030416/intuition-behind-the-formula-for-sum-i2

[orchid glade]

then the mirror method but...

[lunar pollen]

Pretty good intuitive explanation

[orchid glade]

welp i have limited wifi plus thats not me getting there i just want help with the qn i asked rn

[orchid glade]

.

[devout snow]

@orchid glade Has your question been resolved?

[devout snow]

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[nimble plover]

hey can i get helped?

[jovial mauve]

[nimble plover]

just a second

i dont think the translation is ok

[sonic smelt]

Is 60 the perimeter of ABCD or the area?

[jovial mauve]

BC is a point on E side?

The first line itself doesn't make any sense.

[sonic smelt]

Probably meant E is a point on BC side

[jovial mauve]

Yeah

[devout snow]

@nimble plover Has your question been resolved?

[lilac portal]

@nimble plover , I only got the length of BE

BE = 20 cm

2AD + 2AB = 60 cm

AD + AB = 30 cm

EC + DC = 10 cm

AD = BC = BE + EC

BE + EC + DC = 30 cm

Let EC + DC = 10cm

BE + 10 cm = 30 cm

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[restive river]

hello, my professor in mechanics class wrote that: $\det A = \frac{(A \vec{a}, A \vec{b}, A \vec{c})}{(\vec{a}, \vec{b}, \vec{c})}$

[woven radish]

matcool473

[restive river]

If anyone can refer me to a proof or a reference to where I can find one, that would be very nice 🙂

[devout snow]

@restive river Has your question been resolved?

[vital sparrow]

What does $(\vec{a_1}, \vec{a_2}, \vec{a_3})$ represent?

[woven radish]

Sid

[restive river]

i think it's scalar triple product, @vital sparrow , but im not 100%

[devout snow]

@restive river Has your question been resolved?

[vital sparrow]

Oh right since the scalar triple product of a, b and c gives you the volume of the supposed parallelopiped and applying A to each of these "sides" and finding the resulting area would give you changed area, dividing the two would give you the "scale factor" that is the determinant of A.

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[mortal depot]

Theres a room with 4 showers. Each shower has a chance of 0.5 to be functional/work on a certain day.

You enter the cabin and heard that 3 showers are running. How high is the chance that the fourth one works aswell?

According to the solution its 1/5 because there are 4 configurations where 3 showers are running and only 1 configuration where all the showers are running.

I have trouble understanding why the solution is not 0.5 aswell. The probabilities are independent, so if three are running then that doesnt chance the chance of the fourth one being 1/2. Why is that approach not true?

[topaz axle]

like, your intuition is trying to solve a different problem

[mortal depot]

please elaborate

[topaz axle]

you don't know which showers are running, so you "hear" the 5 configurations they are talking about
if you figured out which showers are running, by looking, that locates you down to two, and then it's 1/2

[mortal depot]

I mean yeah you are right

but it still seems a bit weird to me tbh

but I think

if I rephrase it to "at least 3 showers are running, how high is the chance the 4th one is running aswell" it seems a bit more logical to me

[topaz axle]

if you lived in this specific dorm for a long time you would have the right intuition i think

you would be used to 3/4 showers working 4 times more often than all four

so no wonder the fourth one is probably dead as usual

[mortal depot]

yeah depending on how the question is asked I can see where the solution is coming from

it was good hearing your view on it thanks

(I knew it makes sense, but I didnt quite see how before)

[topaz axle]

it's supposed to be weird

i actively don't understand how looking at the showers lets you update like that

at least i forgot, maybe i knew once

[devout snow]

@mortal depot Has your question been resolved?

[topaz axle]

yeah keep it open maybe

[mortal depot]

I think I managed to get it done with a formula aswell now:

P(4 are running WHEN at least 3 are running) = P(AnB)/P(B)

Intersection of A and B must be "4 are running" = 0.5^4
P(B) = 0.5^3 * 0.5 * 4(3 are running, so we have to account configurations) + 0.5^4 (all are running, so no configuration)

Then we have 0.5^4/(0.5^4*(4+1)) = 1/5

I think the main trap is thinking of B as "3 are running", when its actually "at least 3 are running"

or that was the case for me at least

[topaz axle]

ok it's impossible to understand, it just doesn't map to experience, i accept it

"if you know that 3+ showers are running and you need to assign a probability if all four are running, what you should do is go and check which ones are definitely running, with that additional information you can make a better guess. Your guess is gonna be 1/2 btw, but go check ok"

where's the flaw dear chat

oh it's like, we're actually told that three showers are running in way A + one shower is either not running or running in a way B

that probably tells you enough to say 1/2 immediately

of course you're missing the info on how likely is B, which is kinda the point, but maybe it works if you define it

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[restive river]

i need help

[supple knot]

read #help-27 message

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[fallen wind]

Am I crazy or are none of these the right answer

[fallen wind]

For 33

[quaint citrus]

What did u get for ur answer?

[fallen wind]

5/3 x^3 - 2x^2 + 3x

[bleak sun]

y(0) = 1

[fallen wind]

originally it was that + C but if its y(0) then c is 0

ohhh

c is 1

[quaint citrus]

Show ur work for the integration

I’m seeing another mistake

Yk what

I’ll just say it

[fallen wind]

i dont see a problem with it

[quaint citrus]

What is the anti derivative of -2x

[fallen wind]

-x^2

[quaint citrus]

Look what u have

[fallen wind]

oh

thanks

[quaint citrus]

Np

[fallen wind]

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[woven herald]

it said find the cos of EHF
FG=9
HG=10
HF=7.5
EF=6
EH=5
so find Cos would something like this?
cos=6/7.5?

[woven herald]

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[bleak sun]

dude you've made like 3 channels and just closed them instantly

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[fast helm]

forgot how to do 32e

how do you find pt of intersection

[sullen geyser]

after you have found the equations of both diagonals,i.e. AD and BC,just equate it as linear equations in 2 variables

for finding the equation of the 2 diagonals,use the point slope formula

@fast helm

[fast helm]

yes

doing it rn

bro

im so dmb

couldve just used midpoint formula

😢

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[plain field]

how the answer has come -9,0,9

[pseudo basin]

where do you see "-9, 0, 9"?

[plain field]

9, 0, -9

look at the bottom on picture

[pseudo basin]

where do you see "9, 0, -9"?

i do not see any -9 there.

yet you insist it is somewhere.

[plain field]

sorry it's 9,0,9

[pseudo basin]

f(x) = x^2

Let us now evaluate f at the critical number and at the endpoints of [-3,3]

[plain field]

yaa

so we first put -3 in place of x

then f'(x) = 0

and then 3

is that correct ??

@pseudo basin

[pseudo basin]

it sounds vaguely correct but you butchered it.

[plain field]

sorry i am very bad at maths

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[fallen wind]

hi guys

[fallen wind]

im trying to evaluate this

i integrated it and i got - (cos x) ^ 4

but when i do -1(f(2pi) - f(pi/3)) i get 1/16 and i dont get why im not getting -15/16

for f(2pi) i get 0 and f(pi/3) i get 1/16

[jovial mauve]

This is right.

,w int_{π/3}^{2π} 4cos^3(x)sin(x) dx

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[jovial mauve]

Cos(2π) is 1

Sin(2π) is 0

[fallen wind]

oh

i wrote my graph wrong i said that at 2pi the coordinate is 0,1 not 1,0

thanks

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[high chasm]

Is my answer for ii correct?

<@&286206848099549185>

Anyone able to check plz?

[obsidian elbow]

There's nothing wrong with your answer i believe

[high chasm]

Notice

Noice

[obsidian elbow]

Find A^t first

Then Put A and A^t in B equation you would be able to prove that lhs =rhs hence B equation is true

That would be it for part 1

I cant help you at part 2 as i dont know how to do it

[high chasm]

Dw I’ll try myself

[high chasm]

And thanks I got a similar answer to this

Much appreciated

[obsidian elbow]

Nice

[high chasm]

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[scenic surge]

So I was using linear approx for tan(45degrees)

[scenic surge]

and got to 1+2(44-45) but then I saw a vid where the dude

converted into rad

before plugging in

do I HAVE to

do that

or would just plugging in degrees work aswell

He got 1+2(44pi/180-pi/4)

and his and was diff then mine aswell

[long kettle]

The problem is that the derivative of tanx is only sec²x when you use radians

So yeah, you need to convert to radians

[scenic surge]

oh wait ai did convert when I did that

lol im so slow

I dint even realize

ty got it.

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[bold storm]

I don't know where to start for part b of question 17

can u tell me what to google on youtube so that the khan academy guy can explain it to me

search*

[strange nimbus]

The mean is just the sum of something divided by the number of people or whatever.

So, you still have the old sum.

Just add in the two new students' times to get the sum with their times included.

Then, divide by the new number of students.

[bold storm]

oh thats a lot simpler than i thought it would be

thank you

[strange nimbus]

No problem.

If you don't still have the old sum and you only have the old mean, you can just multiply the mean by the old number of students to get the old sum of minutes.

That undoes the dividing.

So you get back the old sum.

Then, you can add in the two new times and divide by the number of students.

[bold storm]

😮

[strange nimbus]

Basically, get the old sum, make the changes to the sum, and divide by the new number of people or whatever.

[bold storm]

👍

@strange nimbus could you look at the bottom question for me?

i just divide the mean heights by the number of men or women

[strange nimbus]

Nope.

[bold storm]

and then i add the sums?

[strange nimbus]

You need the old sums first.

[bold storm]

oh right

[strange nimbus]

So, get the sums for the men and then separately the sums for the women.

[bold storm]

alright then thank you very much for your help

[strange nimbus]

You're welcome.

[bold storm]

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[modest spear]

This is basically just P(transmitted 0 given that received 0)

Right?

Since 0 already happened

Probability is this

Would this be correct?

Or am I missing something

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[modest spear]

<@&286206848099549185>

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[frail igloo]

hi, can someone help me think of this problem? how should i approach it? i expect an infinite value.

[main gull]

Factor out the numerator and denominator

And see if things cancel out

[frail igloo]

they don't.

[bleak sun]

what does it look like factored

[frail igloo]

(x-4)(x+2)/(x-3)(x-2)

[bleak sun]

oh so what you know happens at x=2

[bleak sun]

given this

[frail igloo]

you end up with an a value but it's supposed to be infinite.

[strange nimbus]

One way to handle it is to divide the top and bottom by the x to the highest degree (top or bottom).

[frail igloo]

i don't know whether it's negative or positive

[strange nimbus]

So, divide each term of the top and bottom by x².

[main gull]

Wouldn't this be the way to do it if the limit was approaching +- infinity?

[frail igloo]

basing that it's infinite off of this

[strange nimbus]

Well, the numerator goes positive forever when x > 4.

You can find that by finding the roots by factoring.

The roots are -2 and 4.

[frail igloo]

right.

[strange nimbus]

And the leading term is positive, so it's +, -, + for the regions it divides it into.

You can do something similar for the bottom.

And then you have a positive over a positive.

[frail igloo]

oh neat

but i forget how to do the sign analysis

hat do you mean by leading? :C

[strange nimbus]

Sorry, I'm a bit tired.

[frail igloo]

so it's (x+2)(x-4)

hey, that's fine. i appreciate the help.

[strange nimbus]

Oh, the leading term is the term with the highest degree.

But I think I went about it the wrong way, since we're looking at x = 2.

[frail igloo]

oh i see.

[strange nimbus]

So, the bottom is 0 when x = 2 or x = 3.

So, we can do the sign thing again.

The leading term is positive, so it starts out positive until it hits the root.

So, +, x = 2, -, x = 3, +.

So, the bottom will be negative when you approach x = 2 from the right.

And then you use the value of the top.

And then you have +/- or -/-.

That'll tell you which infinity you have.

[frail igloo]

and that determines

ya

hmm but how do we know it's in that order... i see it goes +,-,+ in order of terms

[strange nimbus]

Oh, no, it's not the terms.

[frail igloo]

i mean the order of x=2 x=3

[strange nimbus]

It's the graph.

[frail igloo]

yea i know you're using this to determine the graph

[strange nimbus]

Oh, you put the terms in ascending order.

The roots, I mean.

So, since the two roots are 2 and 3, you put ?, 2, ?, 3, ?.

Then you fill in the first ? with the leading term's sign.

And then each ? after that, it changes.

This is because the U or ⋂ will hit the x axis and then keep going, changing the sign.

[frail igloo]

so if we had x = 7 and x=8

it would be ?, 7, ?, 8, ?

A S C E N D I N G

xd

[strange nimbus]

Right.

[frail igloo]

haha thank you.

[strange nimbus]

And then you fill in the first ? with the sign of the leading term.

No problem.

[frail igloo]

this was really helpful.

i don't think we learnewd it this way

or maybe we did

been a while

[strange nimbus]

One caveat is that sometimes, you have multiplicities (the same root multiple times, like with (x - 3)(x - 3)).

[frail igloo]

ohh right

[strange nimbus]

There, you write out ?, 3, ?, 3, ?.

Then, the leading term is positive.

So, it's +, 3, -, 3, +.

But there's nothing in between 3 and 3.

So, you can ignore that part.

[frail igloo]

i see. the graph kinda just touches it

[strange nimbus]

Right.

[frail igloo]

cool !

thank u friend

[strange nimbus]

You're welcome.

@frail igloo I just looked into it and I'm slightly off (though this works for quadratics).

Really, you want to put the leading term's sign on the far right.

Then it'll work for all polynomials.

,w plot (x - 2)(x - 3)(x - 4)

[woven radish]

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[strange nimbus]

As you can see, the leading term is positive, and the far right portion is positive, and then it alternates as you go left.

That's because the leading term can generate the largest part of the value when x is a really high positive number.

Like 0.0005x³ - 2x² + 4x - 3 will have the x³ term eventually make the most impact, far more than the other terms.

And so its sign will take over as x gets really high.

[frail igloo]

hmm so leading term goes to them end and then same order for everything else?

[strange nimbus]

Yes, leading term's sign on the end, then backwards, changing the sign each time.

[frail igloo]

leading terms sign

[strange nimbus]

Then it'll work for all polynomials.

[frail igloo]

okay. that's also helpful. your curiosity will probably save me some marks down the line. thank you for verifying this for me

am also exhausted xD

[strange nimbus]

You're welcome.

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[plush knot]

Hi people!

[west kraken]

hello

[plush knot]

Before I wanted to prove that

$$a \sin x + b \cos x = \sqrt{a^2 + b^2} \sin \left(x + \arctan\left(\frac ba\right)\right)$$

[woven radish]

Nonna

[plush knot]

(I was given this formula today)

I think I finally figured it out, I need someone to confirm what I did

Let's say a and b are the two coordinates of a point P in ℝ².
This means that P = (a, b) = (r · cos(ω), r · sin(ω)) (It's a bit like complex numbers in trig form)

Now, this is very awesome:

[woven radish]

Nonna

[plush knot]

Is this good?

[nova ibex]

looks good

[plush knot]

Omg, thank you so much
You have no idea how much time I spent on this today

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[wanton pumice]

part b can someone check my workings

[wanton pumice]

ive checked with desmos but im not sure if i wrote the correct steps

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[honest geode]

I'm so stuck on this question

[coral token]

equate the equations?

[honest geode]

how exactlly

[coral token]

like 3x+y = x^2+kx+6

may not work idk

[restive river]

Hmm

What are you guys planning?

[restive river]

Hmm, do you know about the determinant of a quadratic equation?

@honest geode

[honest geode]

no sir, i'm new to this topic

[honest geode]

hmm ok

[restive river]

Breh im 15 no need to give me respect

[honest geode]

i'm 13 👁️ 👄 👁️

[restive river]

Well first try to find the inequality

From the quadratic

[restive river]

Just 2 years younger

Doesnt matter lol

Determinant of an equation is b^2-4ac

[restive river]

Only indians call people sir online

[honest geode]

?

[restive river]

Never seen anyone call someone sir on discord except indian people

[honest geode]

so b^2 in this case would be x^2

[restive river]

B is the coefficient of x and a is the coefficient of x^2 and c is the constant term

Is the answer is greater than zero, there are two distinct answers

If its equal to zero, there is only one answer and the zeros are equal

[honest geode]

b would be 3, for which x are you talking about, the x^2 or 3x or kx

[restive river]

So we just need to find the inequality first

[restive river]

is that not the discriminant?

[restive river]

Quadratic

[restive river]

Kinda

My teacher called it determinant

I stuck to that

dumb teacher

[honest geode]

?

[restive river]

Ik, its in my mind now

[restive river]

?

[restive river]

Discriminant of the equation

Which is b^2-4ac

We need a value of k which will give a value greater than 0

[restive river]

Lemme write it for ya

This is what i was saying

[honest geode]

so coefficient of b is k

[restive river]

No, b is the coefficient of x term

Here in the equation given, instead of b, k is given as that coefficient

[honest geode]

you rewrote x^2 as k^2 right?

[restive river]

Nope

Lemme write it again

[honest geode]

so a is 1, b is k and c is 6 in the above one right as it is x^2+kx+6

[restive river]

Yes

Now if you try to find the discriminant

We get k>2√6

[honest geode]

what's the } bracket supposed to mean is it the same as =

[restive river]

It means multiply

[honest geode]

but you wrote k^2 } 24

so it means multiply?

or does it mean k^2 = 24

[restive river]

oh that

[honest geode]

yea

[restive river]

You mean > this?

[honest geode]

so sorry i thought it was a }

[restive river]

Lol

Cool’

[honest geode]

what's the h(1)(6)

[restive river]

Im so sorry for my handwriting

Its 4

Not h

[honest geode]

oh ic

so 4 ac and a is 1 and c is 6 i see

[restive river]

Yes

[honest geode]

so then you found that k>2 * root 6

but k has two possible values

[restive river]

No

K can be anything above 2√6 for now

[restive river]

Now, we solve this

[honest geode]

so k is 2* root 6 so replace both the values

[restive river]

No

Y= 3x +k

We need to find such a value of k that the graphs of these equations when we put the value of k intersect

At two points

The value of k is to be greater than 2√6

[honest geode]

so trial and error?

[restive river]

Nope

Put in y= 0

2x=k

X=k/2

Now you know the solution to the first equation

[honest geode]

second one also y = 0

[restive river]

Yea

[honest geode]

then -6 = x^2+kx

then x(x+k) = -6

and as x = k/2 replace right?

[restive river]

Wait

That would be too complex

What i want you to do is

Equate these two problems

You will get a set of numbers not a value

But thats fine

[honest geode]

x(x+k) +6 = 3x+k
right?

as both of them lead to zero

[restive river]

Yep

Solve the equation

And you get the set of values

[restive river]

0

That will be greater than 0

[honest geode]

both of these values are greater than zerO?

[restive river]

https://www.gauthmath.com/solution/6-4-A-line-has-equation-y-3x-k-and-a-curve-has-equation-y-x-2-kx-6-where-k-is-a--1703053816464389

Try to understand

[honest geode]

Thanks

there is domain in this wow

and sets theory

[restive river]

Yeah dude

[honest geode]

how did they get (k-3)^2-4(6-k)

did they replace the value of x with k/2

[devout snow]

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[devout snow]

@honest geode Has your question been resolved?

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[halcyon topaz]

what should i do next

[torn crane]

you can factor xy out

or zx or something, somehow

wait, you already did that

but why are you simplifying then?

what do you want to get. there's 3 variables here, I don't think *we can make it much better

[devout snow]

@halcyon topaz Has your question been resolved?

[halcyon topaz]

i want to simplify it

[halcyon topaz]

cause it is not the answer

[marsh moon]

i might be able to help u here but i seek some clarification is that 2-y or z-y

[halcyon topaz]

z

[marsh moon]

so thats a total of 3 variables right?

[halcyon topaz]

yeah

ping me if anyone can help

[marsh moon]

simplifying it sounds odd in a way
do you happen to know the actual result ?
anyway ,
this is what i could come up with not really a simplification but u get the point

[halcyon topaz]

ans is (x-y)(y-z)(z-x)

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[junior cloak]

is this like a determinant or something?

if so show the original matrix

often you can "prefactor" determinants through row operations

[devout snow]

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[midnight dirge]

i dont get this, namely the x * y in (xN)(yN) and the line below that

why does that need to happen for the cosets to act like a group

also how is that equivalent to (xN)(yN) = xyN

[devout snow]

@midnight dirge Has your question been resolved?

[devout snow]

@midnight dirge Has your question been resolved?

[devout snow]

@midnight dirge Has your question been resolved?

[stone stump]

well if xy is in some coset, then that coset is xyN

"to act like a group" is maybe not the best wording

I would rather say "to act like we expect"

we expect that xN*yN behaves "similarly" to x*y

instead of being completely random

[midnight dirge]

hm

ok that helped me understand a bit btr

thanks

💕

.close

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[glad valley]

When looking at the Schur Orthogonality relations. I am a looking for a few clarifications on whats actually happening.

1. Is basically what happening is (i) all inequivalent irreducible unitary representations such that all their entries are orthogonal and (ii) for a given inequivalent irreducible unitary representation, the only non orthogonal entries are when they the same in which case the inner product is 1/n?

2. Would this imply that all irreducible unitary representations of degree d have an orthonormal set ${ k\phi_{ij} | 1\leq i,j \leq d}$. And it would make sense for k to be the square root of d since then since all equivalence classes can be defined by representatives $\phi^{(1)}, \ldots, \phi^{(n)}$ with orthonormal sets for each phi in L(G) which implies that the sum of dimensions is less than or equal to the order of G due to linear independence in L(G). So there are finitely many equivalence classes?

[woven radish]

ohNoiAmHere

[supple knot]

Have you tried #groups-rings-fields

[glad valley]

i shall try that

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[winged wave]

hello Im not sure how I can go about proving this. I found that this statement is true if n = even

[winged wave]

this is a topic on graph theory

[topaz beacon]

consider the number of edges

[velvet vale]

Have you tried considering cases?

[winged wave]

like when n is even or odd?

[velvet vale]

Yea

[winged wave]

I did i find that this is true when n is even

[velvet vale]

You can come up with a proof just by explaining how you construct such a case

[winged wave]

it doesn't have to be induction, contrapositive, those kind of stuff etc?

[velvet vale]

I imagine you could by induction

[winged wave]

would that be consider formal enough?

[velvet vale]

But you don’t have to

If you can come up with an algorithm that makes one and prove the algorithms correctness then that suffices

At least that’s the way I’m thinking about this problem

Like how would you construct an example for n=6

[winged wave]

I only drew from 1 to 5 then saw that it's possible for n = even and not for n = odd

[winged wave]

just draw?

[velvet vale]

Gmmm but what would you draw

Like is there some sort of way you would draw it for the conditions to match

[winged wave]

oh is it even possible for n = 6

im trying to draw it and im stuck

[winged wave]

hmm not really. so if n = 6 then each vertex has deg = 4 then connect edges until it becomes true

oh yeah it is possible for n = 6

[velvet vale]

Yea

[devout snow]

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[gilded nova]

could someone help me

[gilded nova]

q = 0.25$

L = 1.0$

8+L=q

q+L=10.75

[uncut crow]

i think it should be more like
8 + l = q
0.25q + l = 10.75

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[spice island]

hello, how can I solve this?

[spice island]

what does is mean to take out the greatest common factor?

[dark dawn]

What are the factors of 12?

[spice island]

it has many

[dark dawn]

Not too many

Write them out

[spice island]

3 * 4

[dark dawn]

Mhm

[spice island]

1 * 12

6 * 2

[dark dawn]

Ok

And what sre the factors of 8?

[spice island]

8 * 1

2 * 4

[dark dawn]

Ok so we know

12 ~ 1,12,2,6,3,4

8~ 1,8,2,4

Which of those factors is the largest whilst being common to both numbers

[spice island]

I don't know

[dark dawn]

Can it be 8?

[spice island]

do you mean the largest number that is common to both of them?

[dark dawn]

Yes

[spice island]

4

[dark dawn]

There you go

So

If we had 12 and 8

And you take the factor 4 from each

What equation would you get

[spice island]

no idea

4 times something

[dark dawn]

Whats factors from 12,8 multiply with 4 to get themselves

[spice island]

I don't understand what you mean

[dark dawn]

Well 12 is 4*3

Right

[latent heart]

When you factor a number from something. It means you're splitting the number up. For example, if you factor 3 out of 12. Something multiplied by 3, must give 12

For example, if you want to factor 9 out of 36, it would become 9 * 4

[spice island]

yes I understand that

[latent heart]

If you want to factor 2 out of 8, it would become 2 * 4

[latent heart]

What Clarkie is asking here is, factor 4 out of 12, and factor 4 out of 8

[spice island]

4 * 3

4 * 2

[latent heart]

Now look at the answers

Which one do you think it is

[spice island]

but I don't understand what the greatest common factor is

[latent heart]

Okay, here's a quick explanation

[spice island]

I need to take that out and then multiply by somethign

[latent heart]

We have two numbers, lets say 6 and 4

if we list out the factors we get

6: 1, 2, 3, 6