help-13

[dire geode]

What you have is fine, just apply the expansion correctly

[marsh pond]

can you clarify what you mean by that?

you mean keep going with the following [3x3] matrices now?

or something else by "expansion"

[dire geode]

Your first row should have a sum of 4 3x3 determinants

[marsh pond]

oops!

ty

so how would you write this on an exam? is there a best practice? use arrows like this?

or doesn't really matter as long as you get to the correct answer

I gotta do this 4 times somehow

[dire geode]

What you have is fine

Just do it many more times for practice

[silver fable]

Why not just calculate det(A)² + 1

[dire geode]

A is a 4d vector

[silver fable]

Oh i forgot about that mb

[marsh pond]

which is the better way to write this answer?

I put 2 versions at the bottom

[silver fable]

you're writing determinants wrong

[marsh pond]

wdym?

I'm not finding determinants of B, C, D, E?

[silver fable]

you're writing matrices instead of determinants

[marsh pond]

det(B) = 4

det(C) = 1

det(D) = -1

det(E) = 1

incorrect terminology here?

[silver fable]

first line you wrote det(A) = 2B-C+D-E

just replace brackets with vertical lines

[marsh pond]

that's incorrect, or correct way to write it?

[silver fable]

you basically wrote det(A) is equal to a matrice

[marsh pond]

why? like this
det|A| = 2B - C + D - E

[silver fable]

noo replace [] with | |

keep det(A)

[marsh pond]

ooooo

OK OK

lemme try again

[silver fable]

no need, just something to keep in mind

but the 1st method is more detailed IMO

If the det of B,C,D and E are known use the 2nd method... it saves time
but if you have to calculate them then use the first "version" to show work

[marsh pond]

so no issues here right, this part is perfect

it's just how I proceed with shrinking the [3x3] into [2x2], i'm using the incorrect terminology?

[dire geode]

The notation you're using is inconsistent

You use brackets for both the matrix and determinant

[silver fable]

again u're writing matrices instead of determinants

[marsh pond]

oh

[dire geode]

Stick to what Adam is suggesting here

[marsh pond]

I always need to use || instead of [] for determinants?

[silver fable]

of course

how would u dintinguish between them if u don't

[marsh pond]

well, i got the correct answer,but i wonder if i would lose marks here

i always assumed what type of bracket you use is up to you

could also be round bracket

[silver fable]

round brackets are for matrices

[marsh pond]

OK

do we not call the 3x3 a matrix?

it is, but it isn't

[silver fable]

some profs care some don't

[silver fable]

it's not a matrix

[marsh pond]

3x3 is a determinant

[dire geode]

Do you not realize how confusing this is

[dire geode]

Wrong

[marsh pond]

lmao

[silver fable]

a det is a scalar

[marsh pond]

yes i know, which is where i am heading with the answer

but along the way i am demolishing the sports car

running into every tree and pothole to get to my answer

[silver fable]

The determinant of a matrix A is denoted det(A), det A, or |A|. submatrices. (wikipedia)

[dire geode]

...

You're just being deliberately confusing now

[silver fable]

u can risk losing marks fine xD

[marsh pond]

alright so, always always always show determinants with ||

|B|

this should actually be written as det(A) = 2|B| - |C| + |D| - |E| ?

[silver fable]

this is wrong too u should write det(A) = 2det(B) - det(C) + det(D) - det(E)

then u can use properties of determinants to simplify

[marsh pond]

lol that's what i wrote at the bottom to begin with, you said

^ this is what I had originally

[silver fable]

yeah i meant replace in the first expression

[marsh pond]

so det(A) = 2(det(B)) - det(C) + det(D) - det(E) is correct

[silver fable]

there's no brackets here

[silver fable]

yes yes

[marsh pond]

and as for how I "draw" the 3x3's

I should use || instead of []

not sure what to call those 3x3's

if they aren't matrices

[silver fable]

determinants

[marsh pond]

and not determinants

so what do I call them?

[silver fable]

wait which 3*3 u talking about

[marsh pond]

bc i trust @dire geode i just don't understand i'm getting different answers on this

the 3x3's here:

i know the brackets are incorrect

old screenshot

[dire geode]

The way you wrote them, those are matrices

[marsh pond]

yeah

so I wanna draw them with ||

instead of []

[dire geode]

Then do that

[silver fable]

those are matrices but they're supposed to bet determinants (with | |)

[marsh pond]

alright

[dire geode]

I already told you to use this notation

[marsh pond]

this works?

wait, I think I messed up here

technically these are not |B| - |C| + |D| - |E| yet

i'm just labeling the new 3x3's

lemme redo this, just to be super clear with notation

alright

i have two versions below

which is the preferred? i think it's the bottom, but just wanna triple check on this

@silver fable @dire geode brb, thanks for the help with this!

or maybe both versions of the answer could work, technically? if || represents the determinant, they are both basically saying the exact same thing?

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[silver fable]

use the first version

[cedar kiln]

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[floral urchin]

Hello, working on my final project for AP Statistics and think we made a mistake with what hypotheses test to perform. We proposed a 2-samp-T-test, but since our data is recorded categorically (preference, see table) we cannot calculate Sx1 or Sx2 which is needed for the test.

I am relatively sure the correct test to perform is a chi^2 for independence, but that test requires 2 matrices of data, and i am not sure how to make the data we collected fit into that format

[floral urchin]

really in need of guidance of which type of test is appropriate

Ho: m = .5
Ha: m > .5

Testing to determine whether a majority of sample prefers fiji water to tap water in a single blind fashion

please ping me in any response as i have general notifications silenced

[cedar kiln]

@floral urchin Has your question been resolved?

[floral urchin]

<@&286206848099549185>

[fallen fable]

Calculate the sample mean (x̄) and the sample standard deviation (s).

@floral urchin

.close

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[fallen fable]

.reopen

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✅

[fallen fable]

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[kind parcel]

Technique in the calculator to find the nth row of pascals triangle?

[kind parcel]

I remember there was a way to do it

I just want the numbers of a row

[short blade]

what calculator is it

[kind parcel]

ti 84

[short blade]

also, do you know what "n choose m" means?

[kind parcel]

n choose r

yeah

[short blade]

then that

row choose column

[kind parcel]

oh i see

[short blade]

(0 indexed)

[kind parcel]

thank u

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[mortal ether]

can someone tell me the math he did to go from pi/6 to 5pi/6

and then to 7pi/6 to 11pi/6

[ebon juniper]

a quadrant can be divided into 3 parts, all being π/6. in this case, he did (π/6)*3 for the 1st quadrant then added (π/6)*2 for the 2nd quadrant

oops

[violet flume]

its because of the plus/minus

can you see why you should get 4 solutions out of that equation?

this one

[surreal cave]

$\cos\theta=\pm\frac{\sqrt{3}}{2}$

[wraith dagger]

XxMrFancyu2xX

[mortal ether]

I just know we have to go up to 2pi

[violet flume]

$\cos \theta = \pm \frac{\sqrt 3}{2}$

[wraith dagger]

jan Niku

[violet flume]

okay, thats a good start

[surreal cave]

where does cos(theta)=sqrt(3)/2?

[mortal ether]

cos is x right?

[violet flume]

hrm?

[surreal cave]

yep :))

[violet flume]

well that person solved it again for some reason using x instead

[mortal ether]

i meant how cos is x and sin is y

[surreal cave]

just showing that you can solve for cosine like you can x in any polynomial expression

[violet flume]

you can apply identities but its maybe easier to think of cos(theta) as just the horizontal component of that reference angle

oh, yea

thats what i mean

so using that logic, you can see how for basically any angle, you should get 2 solutions from one

[surreal cave]

anyways berry yes find a theta where the x-value is sqrt(3)/2

[violet flume]

if you just reflect the angle across the horizontal "axis"

youll find a place where the horizontal component is the same

[surreal cave]

yea but first find the terminal angle 😅

[violet flume]

(and the vertical component is negative)

ah

well the first just comes from unit circle

[mortal ether]

$\frac{\pi}{6}$

[wraith dagger]

linx

[violet flume]

all you need is one

[surreal cave]

[violet flume]

then you can find the other 3

[surreal cave]

now what about where cos(theta)=-sqrt(3)/2

[mortal ether]

thats suppoused to be different?

[surreal cave]

there's a negative

[mortal ether]

oh ok

[surreal cave]

because of our plus minus

there are two cases :))

[mortal ether]

$\frac{5\pi}{6}$

[wraith dagger]

linx

[surreal cave]

but we have two other sneaky solutions

[mortal ether]

$\frac{7\pi}{6}$

[wraith dagger]

linx

[mortal ether]

$\frac{11\pi}{6}$

[wraith dagger]

linx

[surreal cave]

yes! but do you understand the logic?

[mortal ether]

i just look at every point that has $-\frac{\sqrt{3}}{2}$ ?

[wraith dagger]

linx

[mortal ether]

or $\frac{\sqrt{3}}{2}$

[wraith dagger]

linx

[surreal cave]

ig that's a way, just do it whatever way your teaching taught you :))

but yes those all are the answers on 0<=theta<2pi

[mortal ether]

this is a self taught course

but yeah this seems easy

now i have to figure out how to do it with tan...

[surreal cave]

just find where tan is equal to that value

as a decent rule of thumb if tan=1 then your looking at the pi/4's and is sqrt(3) then your looking at pi/3's but if 1/sqrt(3) then your looking at pi/6's

[mortal ether]

but tan is weird... $tan\theta=\frac{y}{x}$

[wraith dagger]

linx

[surreal cave]

this is a decent rule of thumb but ofc always do your math logically hope in all that answers your question @mortal ether :))

[mortal ether]

i'm a little confused still due to the formating

is this just a memorization thing?

[surreal cave]

wdym confused by the formatting?

[mortal ether]

its hard to read when its like that

[surreal cave]

oh

$\tan\left(\frac{\pi}{3}\right)=\sqrt{3}, \tan\left(\frac{\pi}{4}\right)=1, \tan\left(\frac{\pi}{6}\right)=\frac{\sqrt{3}}{3}=\frac{1}{\sqrt{3}}$

[wraith dagger]

XxMrFancyu2xX

[surreal cave]

that a little better? @mortal ether 😅

[mortal ether]

thank you

yeah

[surreal cave]

hope that helps a little :))

[cedar kiln]

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[grizzled sapphire]

Find the order of $SL_2(\mathbb{F}_p)$ where p is a prime.

[wraith dagger]

random-internet-guy

[grizzled sapphire]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[grizzled sapphire]

1

wait how do you use this command

[tropic oxide]

you use this command when a helpee is not sharing their progress

you can just say "idk how to start" yourself

anyway you know what GL is right

[cedar kiln]

@grizzled sapphire Has your question been resolved?

[grizzled sapphire]

wait actually i just realized i meant SL not GL, sorry

[tropic oxide]

right ok

[cedar kiln]

@grizzled sapphire Has your question been resolved?

[clear berry]

I think it's GL, not SL cause GL is much easier to solve without the extra constraint

[cedar kiln]

@grizzled sapphire Has your question been resolved?

[grizzled sapphire]

i agree that it's probably easier to find the order of GL, but i'm currently thinking about SL here :<

[clear berry]

Maybe what you can do is find number of elements in GL2(F_p) and then removed those that do not have determinant 1

[woven depot]

If you know how to find the order of GL_2(F_p), then try and find the number of cosets of SL_2(F_p) in GL_2(F_p)

Then apply Lagrange's theorem

[cedar kiln]

@grizzled sapphire Has your question been resolved?

[grizzled sapphire]

actually nvm i solved this

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[bleak rain]

@stone shale come here

[bleak rain]

math discussion is packed

$\int_a^b \lim_{n \to \infty} \sqrt{\left(\frac{f(x+h) - f(x)}{h}\right)^2 + 1} ; \dd x$

[wraith dagger]

ally ❤ (glomed down)

[bleak rain]

are you here?

.close

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[crimson sedge]

hi

[crimson sedge]

ok so

i am expanding

I wanna know while I expand, do I need to do somethign with the - outside the parenthesis of them?

or do 9x^2 - 6x + 1 - x^2 - 2x + 2x -4 by just doing foil and only changing the begginging to a minus

[upper garnet]

just rewrite it as (-1)(x+2)(x-2)

[crimson sedge]

oh i got it

i can just use formua

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

i iwll get (x^2 -4)

then flip the signs

as the -1 is outside

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[vital sphinx]

Why is this not allowed?

[tropic oxide]

t = e^y yields dt = e^y dy

NOT dt = ye^y dy

[vital sphinx]

Ah yes, stupid mistake. Thanks!

.close

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[sonic thistle]

Arno Dorian

[cedar kiln]

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[marble sun]

Anyone can help?

[steady plank]

The line of symmetry of a quadratic is at x=the vertex, so $x = \frac{-b}{2a}$

[wraith dagger]

scam.io

The line of symmetry of a quadratic is at x=the vertex, so $x = \frac{-b}{2a}$

[marble sun]

Yep, I got r = -b/2a as a result

[steady plank]

Exactly

We now have 2 points for ST, (r, -5) and (8, 3)

[marble sun]

i found the gradient which is 8/8-r

[steady plank]

That is right

If ST can be modeled by $y=mx+b$, then $m=\frac{8}{8+\frac{b}{2a}}$

[wraith dagger]

scam.io

[steady plank]

I think using b for two variables is a bit confusing so let's actually use $mx+c$ instead

[wraith dagger]

scam.io

[steady plank]

You can just plug in 8 for y and 3 for x

[marble sun]

Sorry for more context

[steady plank]

This means that the intercept is $3 - \frac{64}{8 + \frac{b}{2a}}$

[wraith dagger]

scam.io

[marble sun]

Sorry how did you get that? From the picture I send, I got this equation for line ST

Give me a second for me to post it

[steady plank]

If you expand that last equation from your penultimate post, $ y = \frac{8x}{8-r} + 3 - \frac{3}{8-r}$

[marble sun]

then i sub x=0 from there to get y-intercept? But i am not sure if i am right for the equation of line ST

[steady plank]

Plug in 0 for x to get the intercept

[marble sun]

Yep from there I got (16ax - 80a + 3b)/(16a+b)

Then I sub x = 0

In return I got

(-80a + 3b)/(16a + b)

Is this correct?

[cedar kiln]

@marble sun Has your question been resolved?

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[bronze pivot]

how do i get the conjugate of 220 < 0

[bronze pivot]

is it also 220 < 0

coz if i had like 220<30

it would be 220 < -30

[livid hound]

your question makes no sense

[bronze pivot]

why 😦

[livid hound]

220 isn't less than 0
220 isn't less than 30
220 isn't less than -30

[bronze pivot]

oh

[livid hound]

is there more context?

[bronze pivot]

< angle

its a phasor

$220 \angle 0$

[wraith dagger]

steamhahasteamhaha

[bronze pivot]

here

[livid hound]

angle 0?

[bronze pivot]

yeah

[lyric narwhal]

i think they mean 0 degrees

[bronze pivot]

yeah

[livid hound]

can you show the original problem

[bronze pivot]

its a circuit analysis problem

[crimson sedge]

in electrical engineering it a<theta means a exp(theta)

[bronze pivot]

i just need to know how to get the conjugate of $220 \angle 0^{\circ}$

[wraith dagger]

steamhahasteamhaha

[crimson sedge]

$a \angle \theta \equiv a e^{\theta}$

[wraith dagger]

Jester

[crimson sedge]

so the conjugate would be a < -theta

which is 220<0

[bronze pivot]

that's all I needed

thanks

lol

🤣

[crimson sedge]

no bro u ll encounter it later

its not all u need

[bronze pivot]

for now

we just started AC analysis

okay anyways

thanks

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[dry cargo]

Why x must = 0 ?

.close

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[hazy umbra]

need help

[steady plank]

Based on Kirchhoff's laws, the total voltage drop over each of the three parallel branches is 36V

You can find it from the battery or by using the fact that Capacitance = Charge / Voltage

[hazy umbra]

how can I find the charge of each capacitors?

[steady plank]

We also know that capacitors in series have the same voltage drop

For the first branch, C1 and C2/C3/C4 have the same voltages

[obsidian coral]

https://www.youtube.com/watch?v=zaT4JorVUz0&ab_channel=TheOrganicChemistryTutor

[crimson sedge]

some of my old notes

[steady plank]

That means voltage over C1 and voltage over the parallel section all add up to 36, so V1 = 18

Using V=Q/C, we know Q = 18C

C2, C3, and C4 can all be calculated by doing 18/2, 18/3, and 18/4 respectively

Since they all have the same voltages

C5-7 all also have 18 V since there are two sets in series again

And C8-10 have 12V drops since there are 3 in series

[cedar kiln]

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.

[steady plank]

From here it is quite trivial

[hazy umbra]

so u just need to keep on playing the V=Q/C and find your way out right?

I'm kinda getting it

[steady plank]

Yes

Capacitors have the same voltage in series and in parallel, so it is easy once you practice a lot

[hazy umbra]

alr alr bet

thanks

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[obsidian coral]

No

[cedar kiln]

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[trail sedge]

Below the z = x² + y² surface, above the xy plane and inside the x² + y² = 4xcylinder

Graph the remaining body and calculate this volume with a double integral. Help pls

[digital spade]

Which part

[cedar kiln]

@trail sedge Has your question been resolved?

[trail sedge]

Under the Z=x²+y² Above the xy plane The graph of the solid inside the cylinder x²+y²=4 and the double integral of its volume

sorry english is not my first language

[brittle stag]

x^2 + y^2 = 4 or x^2 + y^2 = 4x?

[digital spade]

first you need to find the limits of integration

for x and y

[cedar kiln]

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[tidal ravine]

Is it 8?

1 worker = 4.5

[lyric narwhal]

not quite

[tidal ravine]

Could you help me

[lyric narwhal]

check how many painter-hours are needed

there is a hint in the first line of the question

[tidal ravine]

27 divided by 6 = 4.5?

[lyric narwhal]

that would be if the number of hours were directly proportional to the number of painters

if there are more painters, will the house be painted faster or slower?

[tidal ravine]

Faster

[lyric narwhal]

so that means?

[tidal ravine]

hmm

1 worker = 4.5 hours?

[lyric narwhal]

you just repeated the same thing again.

[tidal ravine]

i don't get it

[lyric narwhal]

do you know what inverse proportion means?

[tidal ravine]

One + other - ?

Not sure thou

[lyric narwhal]

nope

okay

first tell me what a direct proportion is

[tidal ravine]

hmm

when it adds same value?

i dont remember honestly

[lyric narwhal]

nope

a direct proportion is when the ratio of two quantities stays constant

i.e x = k*y is a direct proportion

you see direct proportions in things like no of objects vs cost

[tidal ravine]

Ah

is it something like

[lyric narwhal]

for example, if each object costs $5, the cost would always be 5 times the number of objects u decide to buy no matter how many objects u buy

[tidal ravine]

1:2, 2:4?

Something like that

Is it

[cedar kiln]

@tidal ravine Has your question been resolved?

[tidal ravine]

im confused

[obsidian coral]

.close

[cedar kiln]

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[tidal ravine]

.close

[obsidian coral]

I closed it

It's good

[cedar kiln]

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[steady elk]

suppose we have sample space with cardinality of 0 or simply saying null set then wont the probability of sample space become indetermined

[steady elk]

answer in brief plz

[tropic oxide]

most formalizations of probability spaces forbid the sample space from being empty

[steady elk]

y

i wanna see zero there

[tropic oxide]

for precisely the reason you stated -- if Ω = ∅, should P(Ω) be 0 or 1?

there really isnt such a thing as an experiment with zero possible outcomes lol

[steady elk]

w8 u r the1 frm tomorrow

[tropic oxide]

... from tomorrow?

[steady elk]

ohkkk im considering this true

[tropic oxide]

i'm not a time traveller lol

[steady elk]

[steady elk]

ok agreed makes sense

ty

.close

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[crimson sedge]

ik its not math but can someone help please

[obsidian coral]

,rotate

[obsidian coral]

Find the equivalent resistance of the circuit

[crimson sedge]

i did

[cedar kiln]

Show your work, and if possible, explain where you are stuck.

@crimson sedge Has your question been resolved?

[crimson sedge]

i dont know how to continue and with what

i found the equivalent resistance

and the numbers are just random

[obsidian coral]

What did you get as the equivalent resistance? Can you show your work on what you did?

[obsidian coral]

The last step is wrong

R1 and R23456 are in series

Not parallel

[crimson sedge]

and then what

[obsidian coral]

Find I

You have V and the equivalent resistance

Use V = IR

[crimson sedge]

I=18,8A

[obsidian coral]

Yes

[crimson sedge]

and then

[obsidian coral]

What do you mean "and then"?

That's the goal, wasn't it?

To find I

[crimson sedge]

no i need every I

and every charge

[obsidian coral]

Use the series and parallel rules

[crimson sedge]

what are those?

[obsidian coral]

How voltages and currents are in series and parallel

Like in series voltages sum and current is the same

[crimson sedge]

okay

[cedar kiln]

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[vital valley]

How to find area between the curve sqrt(4-x^2) and x axis

[vital valley]

Integration gives sqrt(4-x^2) in denominator

The bounds are -2,2 I think so can't substitute in integration

[royal loom]

if y=sqrt(4-x^2)

square both sides

see the shape this equation is representing?

there is no need for integration

[vital valley]

Uh nope

[royal loom]

if it was

y^2+x^2=4

perhaps

what shape would that be?

[vital valley]

Ah fuck, geometry

Circle?

Radius 2?

[royal loom]

be careful though, because this isn't actually a full circle

we don't have y^2+x^2=4

but we have something pretty similar

y=sqrt(4-x^2)

sqrt is only positive

so we only get the top half of the circle

[vital valley]

Ah

2pi?

Final area

[royal loom]

I believe so

[vital valley]

Damn, ok thank you very much

[cedar kiln]

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[turbid spoke]

what happen here?

[marsh schooner]

use a substitution u = ln(7x)

[turbid spoke]

when i can use subtitution?

[marsh schooner]

from start integral

u = ln(7x)

[buoyant latch]

do you know that $\int\frac{f'(x)}{f(x)}, dx=\ln|f(x)|+C$?

[wraith dagger]

Frosst

[marsh schooner]

forget about it

but use sub good way to

[buoyant latch]

why forget about it

[turbid spoke]

I don't understand how I can have a candidate for u to make a substitution

[marsh schooner]

u = ln(7x) than dx = x*du

after that we got integral 1/u

answer ln(|u|)+C

and back substation ln(|ln(7x)|) + C

sorry for my English

[turbid spoke]

dont worry

hummm so yes but how u can use subtitution , how can determine can use this method

[cedar kiln]

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[steel drift]

need help with this question, no one in my uni group seems to know how to do it

mark scheme ans says it is a half (going to be afk for a bit so apologies if i don't answer back right away)

[gleaming cloud]

if $r\colon [a,b] \to \bR^2$ parameterises a curve $\mathcal{C}$ then
$$\int_{\mathcal{C}} \mathbf{F}\cdot\mathbf{\dd{r}} := \int_a^b \mathbf{F}\cdot\mathbf{r}'(t) \dd{t} $$

[wraith dagger]

giannis_money

[gleaming cloud]

here you would param C piecewise

[cedar kiln]

@steel drift Has your question been resolved?

[steel drift]

That is the part that is confusing me honestly

[gleaming cloud]

parm each edge

[steel drift]

I did a similar question before where r was linked a parameter t

And just differentiated it to get dr

If I parm each edge, what would r' represent?

Or dt

nvm looks like i need to understand what parametision is in general first lol, thanks for you help @gleaming cloud

.close

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[dire geode]

What's your question

[crimson sedge]

How I do this

[dire geode]

Use implicit differentiation

https://youtu.be/xbviQHhU1rA

[crimson sedge]

Xye^xy-1dy/dx=2xe^1x-3ye^2y?

[dire geode]

That's formatted terribly

[crimson sedge]

What

[runic garnet]

Use látex or send a picture on paper

Or paint

So it can be interpreted less ambiguously

[crimson sedge]

@runic garnet @dire geode

[buoyant latch]

what happened to the end

[dire geode]

You did chain rule wrong. And you need to use product rule

[crimson sedge]

Dy dx

[buoyant latch]

i mean on the right

[dire geode]

Observe that xy = x times y(x)

[crimson sedge]

I didn’t use chain rule

[dire geode]

,tex .diff rules

[wraith dagger]

riemann

[crimson sedge]

Am I suppose to move exy to the other side

[dire geode]

You need chain rule and product rule for this problem

[buoyant latch]

the left side is correct

the right side isn't

well

the left side is a little bit wrong

i dont know why you've slipped a - on the exponential

actually

[crimson sedge]

Cus -1

[buoyant latch]

never mind it's very wrong

[crimson sedge]

Idk where I use them

[dire geode]

.

[buoyant latch]

what is $\frac{d}{dx}e^{f(x)}$

[wraith dagger]

Frosst

[crimson sedge]

Ex*exy?

Idk

[buoyant latch]

no!

that's equal to $f'(x)e^{f(x)}$

[wraith dagger]

Frosst

[crimson sedge]

Idk how to do this then

[buoyant latch]

try and prove that by first principles if you want to

[crimson sedge]

I have no idea what that is

[buoyant latch]

surely riemann has a good one

[crimson sedge]

That makes it more confusing

[buoyant latch]

have you seen this before

$\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$

[wraith dagger]

Frosst

[crimson sedge]

Yeah

But I need to do it with implicit differenation

[buoyant latch]

ok let f(x) = e^x

[crimson sedge]

And idk how that one helps

[buoyant latch]

ok

$\frac{d}{dx}e^{3x}$

what is this

[wraith dagger]

Frosst

[crimson sedge]

3xe^2x

[buoyant latch]

that is incorrect

you aren't messing up the implicit part (yet)

you're messing up the basic explicit differentiation

[crimson sedge]

What

[buoyant latch]

so try do $\frac{d}{dx}, e^{3x}$ by first principles

[wraith dagger]

Frosst

[crimson sedge]

@buoyant latch what did I do wrong

[buoyant latch]

you aren't even listening to what i've said

[crimson sedge]

I tried the other way

The limit thing made it more confusing

[vestal wolf]

You need to understand the limit thing first

That's what derivative is on the essence

[vestal wolf]

Just use the definition of derivative is and plug f(x)=e^(3x) here

He decided that you first need to know how this becomes to fully understand your question

The answer here is btw ||3e^(3x)||, not 3xe^(2x)

[buoyant latch]

if you blindly do calculations without understanding what you're doing, you will make mistakes and not realise it

you should have some sort of sanity check for the steps you're doing

a sanity check i would use here is that the derivative of e^(f(x)) should still have e^(f(x)) somewhere

yours randomly got a - in it

[vestal wolf]

He might be confusing the derivatives of a polynomial with the derivative of exponentials, imo

The reason I thought so is because his answer was 3x e^((3-1)x)

Anyways, I got work to do

Turtle out

[cedar kiln]

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[cedar kiln]

@half elk Has your question been resolved?

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[mint raft]

Can someone please help me with these two questions

[gritty galleon]

have u been taught trig?

[mint raft]

Yeah

Just finding these two questions confusing

.close

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[sweet tartan]

find domain and range of y=(3-x)^2-8

[cedar kiln]

@sweet tartan Has your question been resolved?

[teal rune]

-8 up to positive infinity

(3-x)^2 will never be negative. The smallest number this term will be is if you insert 3 for x -> (3-3)^2 = 0^2 = 0

Then, what's left, is the -8. DO that:
0-8 = -8

That's the smallest number you can get.
Otherwise, you can go as big as you want.

[cedar kiln]

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[echo vigil]

Im stuck

[echo vigil]

Basic calculus

The dy/dx thing

No.9

[dreamy sleet]

,rotate

[dreamy sleet]

which one is no. 9

[dreamy sleet]

Could you describe what you’re stuck on in words

[echo vigil]

The goal is to find the d^2y/dy2

Stuck on whether or not i should use product rule

[dreamy sleet]

You can use the product rule

I think it’s the only way here

[echo vigil]

Also what should i do when this happen

[dreamy sleet]

still product rule

[echo vigil]

Btw is this correct

This is what I've been using as a guide for product rule

[dreamy sleet]

this working out is correct

[echo vigil]

Should i just make this the first derivative then?

[dreamy sleet]

Can you work out what happens when you do that

[echo vigil]

When i do what

[crimson sedge]

hello backup is here

are you solving for x?

[echo vigil]

No

[crimson sedge]

ok

[dreamy sleet]

trying to differentiate a function using product rule

[echo vigil]

Im trying to get d^2y/dy^2

[crimson sedge]

mmmi haven't done that in my years of math

😦

[dreamy sleet]

“make this the first derivative”

[echo vigil]

I actually dont know what'll happen if i did that

They didn't give us anything if we want to check it

Just how the process is

[dreamy sleet]

Try it and send it here and let’s see if it’s right

[echo vigil]

Try to get the 2nd derivative?

[dreamy sleet]

You asked if this process was right, could you do that and then send it here so I know what you’re talking about

[echo vigil]

So for no.8 I'll use product rule?

[dreamy sleet]

Yes

[dreamy sleet]

also just noticed you wrote the root a bit weirdly in the first step

[echo vigil]

My bad it extend past the 2nd x

[echo vigil]

Give me few mins

I think its the same problem again

I can't cancel the -2/3 using the 2x

Or can i?

Idk honestly

[cedar kiln]

@echo vigil Has your question been resolved?

[cedar kiln]

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[slow vault]

How to do a please help

With solution

[crimson sedge]

do you know what a non-permissible value means

[dreamy sleet]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

@slow vault Has your question been resolved?

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[vestal agate]

guys is it confirmed to be a quadrilateral

[vestal agate]

?

[dreamy sleet]

you could try constructing it to scale

[cedar kiln]

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[dry cargo]

Do someone can take a look ? did I went something wrong for my collinear?

[dreamy sleet]

!show

[cedar kiln]

Show your work, and if possible, explain where you are stuck.

[dreamy sleet]

,rotate

[cedar kiln]

@dry cargo Has your question been resolved?

[dry cargo]

@dreamy sleet

[dreamy sleet]

You can’t divide by a vector

[dry cargo]

yea thats what why im confusing

i mean did i went something multipication wrong ？ or forumla

[dreamy sleet]

you need to take i component and j component of both sides

[dry cargo]

but question said u and v

[dreamy sleet]

oh, I meant u and v

[dry cargo]

it matter with component too ?

[dreamy sleet]

What I mean is that the u and v components on both sides must be equal

[dry cargo]

yea

[dreamy sleet]

so, set them equal and solve

[dry cargo]

i do know this but at the end i cant solve

[dreamy sleet]

can you write out where you get stuck

[dry cargo]

Is it clearly?

[cedar kiln]

@dry cargo Has your question been resolved?

[dry cargo]

my direction has no wrong right ?

cant i do 9mv = 18v ?

[dry cargo]

i didnt divide by vector this is the ratio between those direction

m is the ratio , that i try to find

[cedar kiln]

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[exotic zenith]

How would i do this

What does the n mean

[long arrow]

do common base

[long arrow]

variable you are supposed to find

[quick palm]

Get your bases the same.

[quick palm]

Exponent which requires to be solved

so the end of your working out should say n=.......

[cedar kiln]

@exotic zenith Has your question been resolved?

[crimson sedge]

Logarithmic function

[cedar kiln]

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[livid hound]

what was your reasoning for drawing that red line like that

[cedar kiln]

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[wide scaffold]

Why is that true?

[wide scaffold]

I can use A*adj(A)= |A|*I

[iron saffron]

A^(-1) = adj(A)/|A|
adj(A) = |A| A^(-1)
adj(adj(A)) = ||A| A^(-1)| (|A| A^(-1))^(-1)

|A| is a constant and we know |kA| = k^n|A|

adj(adj(A)) = |A|^n * |A|^(-1) * (A^(-1)) * |A|^(-1)

adj(adj(A)) = |A|^n * 1/|A| * A * 1/|A|

adj(adj(A)) = |A|^(n-2) * A

[cedar kiln]

@wide scaffold Has your question been resolved?

[cedar kiln]

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[marsh schooner]

yo guys really need you help

[marsh schooner]

how me find D ?

i got that

but dont know how defined integral

[long arrow]

you know polar coords?

[marsh schooner]

I don't know what area to integrate, what the coefficients should be

[marsh schooner]

no

[long arrow]

that's the circle

[marsh schooner]

yep

[long arrow]

with center (1/2, 1/2) and radius 1/sqrt(2)

[marsh schooner]

i got it

but how me know what the coefficients should be

i got stack there

[long arrow]

you mean bounds?

[marsh schooner]

ye ye

[long arrow]

of the integral

[marsh schooner]

sorry

[marsh schooner]

yes

[long arrow]

you can choose which bound is constant here

let's say it will be x

then

[marsh schooner]

hm

wait why i can choose that

[long arrow]

$$\frac{1-\sqrt{2}}{2} \leq x \leq \frac{1+\sqrt{2}}{2}$$

[wraith dagger]

Modus

[long arrow]

because either x or y can be constant in this case (aka we can change order of integration)

[long arrow]

these numbers are the red lines

now you can find 'y' from the equation of the circle

[marsh schooner]

i already got it

[long arrow]

so now you have your bounds

[marsh schooner]

with +-

[long arrow]

and you can integrate, but I'd recommend polar coords since this would be problematic a bit

[marsh schooner]

but that so big i was scary when find that

[marsh schooner]

did i do correct here ?

[marsh schooner]

.

i need find D1 D2 D3 and plus that all integrals

Thanks, have a good day

.close

[cedar kiln]

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[left crystal]

Hello I need help with mathematic induction:

1³ + 2³ + 3³......+ n³ = [ n(n+1)/2]²

[south tundra]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[left crystal]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[left crystal]

4

[cedar kiln]

@left crystal Has your question been resolved?

[south tundra]

Could you show your work?

[spiral badge]

Why is 0+0 not 00?

[south tundra]

This channel is occupied

[left crystal]

Sure. My handwriting is kinda awful but

[cedar kiln]

Channel closed

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[left crystal]

.reopen

[cedar kiln]

✅

[cedar kiln]

@left crystal Has your question been resolved?

[cedar kiln]

Channel closed

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[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[lament yoke]

Hello

[lament yoke]

How can I find how many elements this set has?

if u answer,ping me

[cedar kiln]

@lament yoke Has your question been resolved?

[lament yoke]

<@&286206848099549185>

[echo veldt]

Sine is periodic and its period is 2pi, thus sin (x) and sin (x+2pi) are the same

[lament yoke]

ok,and so?

[knotty egret]

actually i want to know too

i feel like there is just infinite

because a sine graph is periodic

[echo veldt]

but sin 0 and sin 2pi are equal

[knotty egret]

so i just want to know why its not infinite

[lament yoke]

it's not,that's the interesting part

[knotty egret]

ye

[echo veldt]

adding 22 to n is equivalent to adding 2pi to the left

thus there are 22 members of the set?

[lament yoke]

why is that?

[lament yoke]

that's not the answet

answer*

[echo veldt]

there are a max of 22

[lament yoke]

no,apparently

[echo veldt]

how now?

[lament yoke]

it's not,idk why

that's why i asked

[echo veldt]

oh

dammit

complements

sin (pi-x)=sin(x)

[knotty egret]

is it 12?

lmao im trash

[lament yoke]

nah

[echo veldt]

that or 11

[knotty egret]

but ther is 0

so i think 12

[echo veldt]

but 0 = 11

so 11?

[knotty egret]

oh right

lmao

[lament yoke]

no,it's not 12.it's 11,but why?

[knotty egret]

ahh

ok

[echo veldt]

because 0 pairs to 11

[knotty egret]

yea

wait what

[lament yoke]

what do u guys mean?

[knotty egret]

11pi/11 is not 0

[echo veldt]

sin 0pi/11 = sin 11pi/11

[lament yoke]

oh,since it's periodic

[echo veldt]

kinda

[knotty egret]

oh right

or a sec i thought 11pi/11 = pi/2

lmao

[lament yoke]

it's 2k+pi

[knotty egret]

yea

[lament yoke]

that's the period

[knotty egret]

so it is 11

i thought of it as 0pi/11, 1pi/11, and so on

[lament yoke]

yeah,but i still don't quite get it

so did i

[knotty egret]

ok good

[lament yoke]

why did it stop tho?

[echo veldt]

no it's 0/11, 1/10, 2/9, etc

[knotty egret]

how

[echo veldt]

x + y = 11 mod 22 for sin xpi/11 and sin ypi/11 to be the same

[knotty egret]

umm...

ok

[lament yoke]

since n can be 0

[knotty egret]

ok

[lament yoke]

what's ur rationale here?

x+y =....

[knotty egret]

why does the denominator get smalle

[lament yoke]

so far i get the part that I pair those

[knotty egret]

r

[echo veldt]

not denominator

0 and 11 pair

[knotty egret]

ok

[echo veldt]

because you can reflect sine onto itself if you reflect it across the line y = kpi/2 where k is a constant that is equal to 1 mod 2

[lament yoke]

How about this one?

[lament yoke]

Oh, it's because sine is odd

[echo veldt]

yep

[cedar kiln]

Channel closed

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Use .reopen if this was a mistake.

[echo veldt]

i'd assume that that set is infinite

[lament yoke]

.reopen

[cedar kiln]

✅

[echo veldt]

i do have to go now

[lament yoke]

Why is that?

[echo veldt]

bye

[lament yoke]

Okay

Bye

<@&286206848099549185>

Anybody?

[lament yoke]

On this one

[cedar kiln]

@lament yoke Has your question been resolved?

[lament yoke]

can anyone help,please?

[lyric narwhal]

i would think this has infinite elements

since root 2 is an irrational number

so there is no periodicity

[lament yoke]

but why there were only two elements at the previous point?

[lament yoke]

.

[lyric narwhal]

there are more than 2 elements?

[lament yoke]

sorry,i asked the wrong question

so there are more elements

at that point

[lyric narwhal]

at what point

[lament yoke]

.

i am sorry if i am not being clear,it's night time

[lyric narwhal]

i dont understand your question

do you want me to explain the n(pi)/11 one?

or are you asking me something related to that one

[lament yoke]

so,why were there only 11 there and an infinity here?

that's my question

[lyric narwhal]

because for the first case 11 is an integer, so you can generate a periodicity