help-33

[jagged oracle]

Lol 😆

Lol

Bro knows her original name

[candid thunder]

Bruh

.close

[marsh citrus]

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[candid thunder]

Yup

[jagged oracle]

Imma delete it

Privacy is the 🗝️

[candid thunder]

@eager tinsel how do you guys even remember it?

[marsh citrus]

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[cold widget]

How do I do this a faster way that doesn’t require me to just list out all of the possibilities? Btw, T is tomatoes, b is beans, and c is carrots.

[spark otter]

first thing you need to notice is that the beds used for tomatoes on the first 2 summers entirely determine where the tomatoes gotta go next for all the other summers

[cold widget]

They just like alternate right? From first to second to third, then back to first etc.

[spark otter]

uh huh

since you have 6 choices for the tomato pattern

fix a tomato pattern

(for example 1,2,3,1,2,3,...)

and then compute the number of ways for that specific pattern

[cold widget]

Um sorry if I sound stupid and annoying asking this question but what do you mean by there are 6 choices for the tomato pattern?🥹

[spark otter]

well

There are 6 possible ways to place tomatoes on the first 2 summers

[cold widget]

OH

[spark otter]

and since those 2 summers entirely determine where the tomatoes go next

you have 6 tomato patterns possible

[cold widget]

Ooohhh I see what you are saying

[spark otter]

So fix a tomato pattern
(for example 1,2,3,1,2,3,...)
and then compute the number of ways for that specific pattern

[cold widget]

I’ll give it a go, thank you for the help!

[marsh citrus]

@cold widget Has your question been resolved?

[marsh citrus]

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[still temple]

Hello, I don’t understand what am i suppose to do here, and i don’t understand the number 60 Next to the A so i don’t know the steps to solving it.

[severe shore]

the 60 is an exponent

it means multiple A by itself 60 times

You probably need to diagonalize first

[still temple]

how should i do that?

[marsh citrus]

@still temple Has your question been resolved?

[severe shore]

You should learn matrix diagonalization

but it has to do with finding eigenvalues and eigenvectors

there are some good videos, especially change of basis + eigen values and eigenvectors from 3blue1brown

but I will try my best to explain it

[still temple]

Wow, My teacher hasn’t taught me this. All he told me was study matrices tranpose, adding and subtracting, and multiplying and inverse multiplication.

[severe shore]

are you allowed to use a calculator?

[still temple]

Yes

[severe shore]

like matlab or just a scientific

[still temple]

Scientific

[severe shore]

you can input your matrix into your calculator

[still temple]

That’ll get me the answer?

[severe shore]

on a TI84 its like 2nd + math or something

and then call the matrix A into the equation thingy

[still temple]

Oh Mat A

[severe shore]

and raise it to the 60th power as if it were a number

yeah something like that

and it should spit out the matrix*

[still temple]

I’ll try to find it’s step in calculator

But there isn’t anyway for me to solve this question in simple way?

[severe shore]

,w {{4, 0},{3, -4}}^60

[elfin berry]

Results provided by WolframAlpha

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

Requested by vehnil

[severe shore]

bruh

[still temple]

it’s alright

[severe shore]

oh wait

,w {{4, 0},{3, -4}}^2

[elfin berry]

Results provided by WolframAlpha

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

Requested by vehnil

[severe shore]

oh yeah okay

thats cool

basically A^2 is 16I where I represents the Identity matrix [ 1, 0 ; 0, 1]

which you would find out if you start trying to do A^60 by hand

so A^60 = (A^2)^30 = (16I)^30

[still temple]

i see

thank you

[severe shore]

np

good question

I wouldve done it the wrong way

[marsh citrus]

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[marsh citrus]

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[sour quest]

Hello

[sour quest]

I would like to ask about this Integral involving the Euler formula (exponential) of complex numbers. If you're curious, this is related to the inversion theorem for characteristic function (for probability distribution)

Questions:

• I am very confused so as to why for the first line, the numerator has minus sign and not plus. This is because as I know e^(itc) = cos(tc)+i*sin(tc)

• Also, I am confused on how to change the integration limit from "-T to 0" to "0 to T" (for the second integral). Do I have some kind of property involving even and odd function? Or am I wrong?

• Edit: I tried to fix by changing the minus to plus, I think it's a typo by the author. I somehow figured how to prove it, by changing the limit from "-T to 0" to "0 to T" by changing the sign of all the t's inside the integrand. And somehow proved this.

Any help would be appreciated, I just would like to really understand this proof.

[marsh citrus]

@sour quest Has your question been resolved?

[marsh citrus]

@sour quest Has your question been resolved?

[marsh citrus]

@sour quest Has your question been resolved?

[sour quest]

.close

[marsh citrus]

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[fleet bolt]

I have no idea on how to do it so pls help

[limber hearth]

Triangular identity

[fleet bolt]

. close

.close

[marsh citrus]

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[fleet bolt]

.reopen

[marsh citrus]

✅

[fleet bolt]

@wise lance

[wise lance]

Sorry, just close

[fleet bolt]

.close

[marsh citrus]

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[marsh citrus]

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[nimble wren]

find the number of primes contained in 12345678

[nimble wren]

hello

can you find the number of primes contained in 12345678

@marsh citrus

.reopen

.close

[marsh citrus]

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[nimble wren]

WHAT ANS

WOI

<@&286206848099549185>

[eager tinsel]

!15min

[marsh citrus]

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.

[scarlet steeple]

I ping helpers after 15 minutes still no use

[eager tinsel]

but please follow rules

[scarlet steeple]

You are right I guess

[nimble wren]

hello

please help em

[nimble wren]

this one i need

[elder crag]

sum of the first n terms can be looked at as:
11 + 22 + 33 +...+nn
or
2^2 + 3^2 +... n^2
Lets use sigma notation:
$\sum_{k=1}^{n} k^2$

sorry my latex isnt that good ahaha

,help

[elfin berry]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[nimble wren]

whats the ans there

[eager tinsel]

@elder crag surround it by dollar symbol

[elder crag]

i have to go sorry, if someone else is here that could help find a general formula for the sums of n^2 that would be useful

[eager tinsel]

$\frac{n(n+1)(2n+1)}{6}$

[elfin berry]

77²

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

[elder crag]

oof, well heres the formula

[nimble wren]

i solved alr

it was 17244536

lel u wrong

but the 2n+1

[marsh citrus]

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[alpine basalt]

The notation $sup_{n\in \mathbb N}a_n$ is just the supremum of the set formed by the sequence

right?

[elfin berry]

normalAtmosphericPa=101,325

[spark otter]

yes

[nimble wren]

Harmonic Divisor Numbers

Harmonic divisor number is a positive integer whose divisor have a harmonic mean that is an integer

For example, 6 is an harmonic divisor number because it has four divisors 1, 2, 3, and 6 whose harmonic mean is 4 / (1/1 + 1/2 + 1/3 + 1/6) = 2, which is an integer

Find the first 10 digits of the 2024th harmonic divisor number

@elfin berry what ans

help

[whole thorn]

$\sup_{n\in \bN}a_n = \sup{a_n \colon n \in \bN}$

[elfin berry]

mayer-vietorUs

[marsh citrus]

@alpine basalt Has your question been resolved?

[marsh citrus]

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[lyric peak]

need help

[lyric peak]

how to get a sa of a cone

[late geode]

apply the formula

[lyric peak]

its so confusing😢

[late geode]

which part

[lyric peak]

hold up lemme send a pic

[lyric peak]

😢

im confused on the whole question

like its just super hard to do

[late geode]

what's your issue with the formula

[lyric peak]

idk how to use the formula

i try my best

[late geode]

do you know what the variables
r, s
represent

[lyric peak]

radius and surface?

[late geode]

no

[lyric peak]

then?

[late geode]

r is the radius of the circular base
but s isn't surface

[lyric peak]

hm

[late geode]

s in the formula represents the slant height of the cone

[lyric peak]

ohhh

im mid class rn doing a test that i missed yesterday

its so hard

😣

[late geode]

wait, ur doing a live test? that stuff doesn't fly here

<@&268886789983436800>

[lyric peak]

its not live

its online

but i finished it

sorry i didn’t know i joined this server today

[idle ridge]

is this a graded quiz? are you supposed to be doing it by yourself?

[lyric peak]

no no its a practice quiz

[idle ridge]

you just said you were doing a test right now though?

[lyric peak]

yh i did but its a practice test

[idle ridge]

Okay

Well if you're in class, then maybe you can just ask the teacher then? I still don't understand

[lyric peak]

i already finished so it okay

[marsh citrus]

@lyric peak Has your question been resolved?

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[hybrid flint]

Just confused about what “use similar right triangles means in provlem 6

[lone wharf]

Maybe it’s saying to make a triangle to find the slope

[marsh citrus]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[hybrid flint]

Im confused about how you would use right triangles to find the slope instead of just slope formula

[lone wharf]

When you use slope formula it’s the same as making a right triangle and dividing the vertical distance by horizontal distance

[marsh citrus]

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[scarlet steeple]

Can someone verify my answer

If i am right

if wrong then please tell me how to fix it

[limber hearth]

The derivative is wrong

[scarlet steeple]

Oh

Anything else

[limber hearth]

$3*\sqrt{x^2 + 4^2} => 3\frac{2x}{\sqrt{x^2 + 4^2}}$

[elfin berry]

YakuBros

[limber hearth]

So its 6x on top

[indigo karma]

yea

[toxic dome]

HEY YAKU

[scarlet steeple]

3 6x / square root x 2 + 4 2

[limber hearth]

No just 6x

On top of the frac

[scarlet steeple]

Ok

Let me check and re check

[toxic dome]

this has to be simple right?

or am i just dumbasf

[limber hearth]

What is the question ?

[toxic dome]

i cant find the adjecent side

i hate triangles AHHHHH

[limber hearth]

Which angles ?

[toxic dome]

C-D

[limber hearth]

C-D ?

[toxic dome]

yes the other half of the adjecent side

oh wait

d-b

my bad lolz

[limber hearth]

BDA is 120

[toxic dome]

oh damn really!??

yeah i would have not figured that one out

[limber hearth]

The sum is equal to 180 since its on the same line

[toxic dome]

but how about the 90 degree part of the triangle does it not count?

[scarlet steeple]

I am still confused is it 6x/ sqaure root of x^2 + 4^2 like what is the derivative

And why am i wrong

But what is 6x / sqaure root of x^2 + 4^2 the derivative or what

[limber hearth]

Of 3sqrt(x^2 +4^2)

[scarlet steeple]

I need the derivative of x + 3√x2 + 4^2 not 3√x2 + 4^2

[toxic dome]

what are u studying green dude that looks 100x harder than what im looking at

[limber hearth]

Maybe a way of pythagore

[scarlet steeple]

Calculus

And you

[toxic dome]

construction electrician

[scarlet steeple]

It is not that hard just this question

[toxic dome]

im failing lvl 2 AHHHHHHHH

[limber hearth]

The +1 in front was correct so i did not rementionned it

[scarlet steeple]

Oh so + 1 is right then 6x

[limber hearth]

6x/sqrt(...)

[scarlet steeple]

Ok

Is the final answer square root of 16/35

not sqaure root 2 km

[limber hearth]

Im checkin

[scarlet steeple]

What do you use to check for future reference

[limber hearth]

I check by hand so

Oh frick mb

I induce you into error

[scarlet steeple]

Oh

[limber hearth]

Your derivative was good

[scarlet steeple]

Ok fixed it

[limber hearth]

But with it i found 8sqrt(2)

[scarlet steeple]

Ok

[limber hearth]

Like the minimal is (-sqrt(2), 8sqrt(2)

[scarlet steeple]

Ok

thank you

@toxic dome You ask your question

After your question is done i will close this channel

.close

[marsh citrus]

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[marsh citrus]

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[grand tide]

someone explain no 20, and 23?

[indigo karma]

for 20 imagine it in 3d space

[grand tide]

angles presented like that cannot happen in 3d space?

im guessing since we’re not talking ab xyz coords therefore that cannot happen?

[indigo karma]

for 23 afe and cdf\

[grand tide]

afd

cfd***

[indigo karma]

yea

[indigo karma]

i guess thats a 3d object

[grand tide]

yup

[marsh citrus]

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[marsh citrus]

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[neat kite]

hi could someone help me with this induction question? im quite lost on this topic so any help would be appreciated!

[marsh citrus]

@neat kite Has your question been resolved?

[half violet]

Verify the base case at n=0, then assume that every case upto n-1 is true, and then try to prove for n using n-1. That's the basic idea of mathematical induction in general.

Σ ar^i(for n-1) = a(r^n -1)/r-1

Σ ar^i(for n) = Σ ar^i(for n-1) + nth term

Solve it and you'll verify that it's true : )

[neat kite]

thank you so much for the headstart! i didn't know about base case

can i also ask why we have to use n-1 in particular ?

[quaint hill]

the idea of mathematicla induction is that its a "domino effect"

basically, we're saying "this is true for n = 0, and whenever it's true for a given number (n-1), it's true for the next number (n)"

since its true for n = 0, it's also true for n = 1

since it's true for n = 1, it's also true for n = 2

and so on

this allows us to prove a statement for all natural numbers without needing to do infinitely many cases

instead, we just prove it's true for the base case (n=0) and then prove the "domino effect" inductive step (whenever it's true for n-1, it's true for n as well)

your class may instead present the inductive step as "whenever its true for n, it's true for n+1 as well"

these are equivalent; it's just a matter of indexing

[half violet]

Very well explained

[neat kite]

thank you so much for explaining as well!

[neat kite]

so it wouldnt matter if it were n-1 or n+1 ?

just as long as i solve the base case for n=0 and then add or subtract 1 to n

[quaint hill]

the point is that youre proving "if its true for one number, its true for the next"

there are two main ways to formulate this with mathematical variables

• assume it's true for a given n-1, and then prove it's true for n
• assume it's true for a given n, and then prove it's true for n+1

so its not quite "interchangeable" — you can't assume it's true for n+1 and then prove it's true for n

(i mean, you can for some cases, but that's backwards induction which is meaningfully different)

[half violet]

Not really, imagine the base case as the domino you're pushing first. You're verifying it to make sure you've pushed it.
Then you have to verify if the domino can fall over and push the next domino right? So you take a random case, let's say n. You assume that all dominos upto n and including n has fallen over, so the next step is to prove that the domino will fall over. Hence, you try to verify for the next case.

[half violet]

Man you type so fast

[neat kite]

ohh i see so it just depends on which direction i choose to approach

i think i'll have to search up more on this because i dont have enough background to fully understand how to prove but thank you again for your help😭 your explanations were really clear

[half violet]

Yeah it's a tough idea to grasp! Maybe look into the derivation of this using the well ordering principle, it's quite pretty ; )

[marsh citrus]

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[marsh citrus]

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[feral saddle]

hi! i need help with the steps of this problem. if you could do the problem and then explain it, that would really help me understand how to tackle more of these problems. thank you!!

[cloud field]

look for who has errors in their steps

[narrow pecan]

If the problem said: simplify cot… how would you do that? Does your answer match either of those?

[marsh citrus]

@feral saddle Has your question been resolved?

[lone wharf]

Have you done what the top two msgs said

[feral saddle]

i know

[cloud field]

then do it

[feral saddle]

i wanna check though, just in case

[feral saddle]

i did

[cloud field]

!showwork

[marsh citrus]

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

[feral saddle]

Part A: Student B simplified the expression incorrectly. Step 2 is the wrong step. Correct Error or Formula Misused: In Step 2, Student B incorrectly transformed the expression into tanθ 1+tan 2 θ ​ ⋅ cotθ 1 ​ . The correct simplification should have been 1 tan ⁡ 𝜃 + tan ⁡ 2 𝜃 tanθ 1 ​ +tan 2 θ, leading directly to 1 + tan ⁡ 2 𝜃 1+tan 2 θ, which simplifies to sec ⁡ 2 𝜃 sec 2 θ.

is this right

[late geode]

do you have a pic of your work,it's hard to see what you mean

[feral saddle]

@late geode

[late geode]

I don't see the error correction, everything there is wrong

[cloud field]

sorry to say but theres nothing wrong in step 2

[lone wharf]

1/tanx + tanx = 1/tanx + tan^x/tanx = (1+tan^2x)/tanx

which is forrect

@feral saddle

[feral saddle]

how is everything incorrect?

[late geode]

How'd you get that first line

and near the end you're implying that
1/(tan(t)) is 1

[feral saddle]

oh

but student b is wrong though, right?

[lone wharf]

you want to find the step that's incorrect

[late geode]

yes, student B is wrong

[feral saddle]

wait, but doesn't step 3 simplify to step 4, which is correct?

[lone wharf]

yea

[feral saddle]

so it's either step 1 or 2

[lone wharf]

try out all the steps from 1-2 2-3, 3-4, and see which one is wrong

[feral saddle]

well i know 3-4 is good, is 2-3 wrong?

[lone wharf]

is it?

try the steps

[feral saddle]

yeah, it should be

[feral saddle]

could someone do part a and part b, and explain it please

instead of asking questions, cuz im not entirely sure

[undone ether]

student b is incorrect

they're correct until step 2

step 3 is wrong

as 1+tan^2(theta)/tan(theta)/cot(theta)

is 1 +tan^2(theta)/tan(theta)*cot(theta)

not sec^2(theta)/tan^2(theta)

[marsh citrus]

@feral saddle Has your question been resolved?

[feral saddle]

what about part b

[undone ether]

yeah so

1 +tan^2(theta)/tan(theta)*cot(theta)

1 +tan^2(theta)

sec^2(theta)

[feral saddle]

thats it?

nothing else

[undone ether]

yeah

that's it

[marsh citrus]

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[marsh citrus]

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[woeful condor]

Hi may i know how to do this. I tried but it was wrong.i have no ans for it

[woeful condor]

Then my lecturer said that i have to use 3x1 matrices for hill 3 cipher but i still got the same answer for key

[marsh citrus]

@woeful condor Has your question been resolved?

[woeful condor]

<@&286206848099549185>

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@woeful condor Has your question been resolved?

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[gilded ember]

can someone explain why this isnt binomial

[marsh citrus]

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[earnest sundial]

I want to find all complex numbers λ that solve
(3-λ)⁴+18(3-λ)²+81=0

I know (but only because I looked it up) that this is relatively easy if you know that
(3-λ)⁴+18(3-λ)²+81=(λ²-6λ+18)²

At which point you can take the square root on both sides and just solve the quadratic.
Turns out the solutions are λ_{1,2}=3+3i and λ_{3,4}=3-3i

But how would I figure that out in the first place? How would I solve an equation like this without using any tools beyond a pen and some paper?
Do I just have to guess quadratics until one of them works out? That doesn't sound like a viable method.

[earnest sundial]

another option to solve the original equation might be seeing that "there's a lot of 3s in there" and just guessing complex numbers that contain 3, 1/3, 9, etc. But that again seems extremely inefficient

[marsh citrus]

@earnest sundial Has your question been resolved?

[dusky viper]

the original equation is also a quadratic

just take (3-λ)^2 as ur variable

and its reletively simple to solve

[marsh citrus]

@earnest sundial Has your question been resolved?

[earnest sundial]

so substitute?

[dusky viper]

sure

[earnest sundial]

say we define x:=(3-lambda)²

[dusky viper]

yes

[earnest sundial]

then x²+18x+81=0

etc

okay that makes alot of sense

[dusky viper]

correct

[earnest sundial]

thanks, I didn't even think of that

[dusky viper]

all good

[earnest sundial]

seems alot easier than figuring out the square root of a polynomial

[dusky viper]

yep

[earnest sundial]

thanks!

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[versed hatch]

why do i need use radians, assuming thats what it means by "the sum of the internal angles is pi"

[versed hatch]

wait

i just realized i made a mistake oops

.close

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[versed hatch]

.reopen

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✅

[versed hatch]

i did not make a mistake

[versed hatch]

i got the radii of all the circles

and just did 1/2 pi r ^2

but that was wrong so idk why

wait

i forgot to divide by 2

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[limber hearth]

Sqrt(x) = x^ ?

[still temple]

1/2

[limber hearth]

Ok and what do you do with the quotient like a^n/a^m ?

[still temple]

subtract

but arent the coefficients different

so i cannot

?

[limber hearth]

You get the coefficient simplified together which gives 12/4 = 3

[still temple]

sorry i dont understand

[limber hearth]

Ok ima latex

[still temple]

a^n/a^m = a^n-m

but a has to be 12 or 4?

12/4 would be like a^n/b^m

u get my confusion

[limber hearth]

$\frac{12x^{1/2}}{4x^3} = \frac{12}{4} * \frac{x^{1/2}}{x^3} = 3* x^{\frac{1}{2}-3}$

[still temple]

okay i see

[elfin berry]

YakuBros

[limber hearth]

Great

[still temple]

3x^-5/2

i got it right tysm

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[upper gust]

. (its \cdot)

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[loud vector]

Hi

[loud vector]

Can someone check my work so far

Also I’m not sure how to simplify this further

[marsh citrus]

@loud vector Has your question been resolved?

[spark otter]

It's pretty simplified already

just 2/2

and put everything on a single fraction

[marsh citrus]

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[loud vector]

.repoen

.reopen

[marsh citrus]

✅

[loud vector]

since its a fraction on fraction idk how to make it just 1 fraction with 1 bar

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[bitter radish]

a little confused on how to approach this question

shouldn't it be somewhere around 30 terms?

by the time I reach 32 it should already be under the 0.001 threshold

[pliant maple]

ur supposed to use lagrange error bound i believe

[bitter radish]

oof

have not learned

let me take a look

this?

[pliant maple]

yea

[bitter radish]

let me see if I understand how to plug numbers into this lol

what do they mean by given x value

[pliant maple]

oh no that's my bad, that's only for taylor series

[bitter radish]

oop okay

so i plugged the question into gemini and it told me to take the integral

but i'm not sure why

[pliant maple]

yea i don't see why either

[bitter radish]

this is what it spat out

[pliant maple]

maybe it thought you were testing for convergence?

[bitter radish]

but 🤷‍♂️

maybe

i don't understand why it would be taking the remainder of the integral

and not the original function

and hence why I'm confused that it's 1000+ terms

and not the aforementioned 32

[pliant maple]

well the problem with your approach is that you found the point where it doesn't add more than 0.001, but you need to look for the point where the sum is 0.001 off from the infinite sum

as in ur looking for how many terms it takes to equal to sum of the infinite series - 0.001

[bitter radish]

hmmmmmmmmmmmmmmmmmmmmmmmmm

so how does taking the integral solve that problem

or rather

what other approach is there

to find the total sum - 0.001

so |R_n| = |S-S_n| < 0.001 which means b_n+1 < 0.001

right?

so the b_n+1 term

that is smaller than 0.001 is

32

or am I tripping

[brave marsh]

It's not the next term you're adding you want to be less than 0.001, it's the whole added up tail of the series you're omitting in your estimation you want to quantify.

Since the terms are all positive and decreasing, the integral can give an upper/lower bound on the error.
It's kind of like how you can use the value of an integral to determine if a series diverges.

I do think that the integral should be computed from N, not N+1, this way you

1. get one of the actual choices
2. actually get an upper bound.

You can read up on this here

[bitter radish]

will do 🫶

[brave marsh]

Moreover, I think bounding by the last term is possible, but only in alternating series, since the tail's behaviour is limited by that last term.

[bitter radish]

ohh okay

i get it now

this makes more sense

thank you @brave marsh

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[lethal steeple]

<@&286206848099549185> may I know how to do this question

[idle ridge]

Please do not ping Helpers before 15 minutes have passed

[lethal steeple]

oh Im sorry

[violet orchid]

did you try derivate?

[lethal steeple]

i tried but I get more than one stationary point

[violet orchid]

i get an imaginary number lmao

flying ing XD

[lethal steeple]

wow 💀

[jagged oracle]

Bro

Derivate it correctly

[lethal steeple]

lemme try

[jagged oracle]

,w d/dx (3x^2+8)^(5/3)

[elfin berry]

Results provided by WolframAlpha

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Requested by oppailol.

[violet orchid]

auch

[jagged oracle]

I told him the derivate

Now he will understand fr

[violet orchid]

it was necesary?

xd

[lethal steeple]

Umm, thanks now I know how I got the deriavative but may I know how to find its like the coordinates

[violet orchid]

equal to 0

then you will obtain one of them

the repalce

SHOULD work

[lethal steeple]

aight lemme try

i get imaginary numbers

[violet orchid]

I said ti :v

[jagged oracle]

See only we have one critical point that is x=0

[violet orchid]

.

[jagged oracle]

The domain is real

You cannot input complex numbers

[lethal steeple]

oh I see

[jagged oracle]

Find its y

U got x=0

[lethal steeple]

aight

[jagged oracle]

Find y now

For that point

[lethal steeple]

y=0

[jagged oracle]

U need coordinates of the stationary point

U sure?

[lethal steeple]

nvm 32

[jagged oracle]

f(x)=(3x^2+8)^5/3

Yes

Ok so point is (0,32)

Now what we need next ?

Nature?

[lethal steeple]

I see

Thank you so much

[jagged oracle]

Okok

Welcome np 🤗

[lethal steeple]

I can do that 👍

[jagged oracle]

Okok

Cya

[lethal steeple]

byeee

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[jagged oracle]

Ok

[marsh citrus]

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[gilded ember]

how does the numerator go from that to that

[marsh citrus]

Please don't occupy multiple help channels.

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.

[gilded ember]

this is the question

[marsh citrus]

@gilded ember Has your question been resolved?

[marsh citrus]

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[still temple]

Is there any non graphical way to solve this:

$1 + e^{2x} = 10x + 2$

[elfin berry]

Edmund Cloudsley

[still temple]

one intuitive solution is x = 0

$1 + e^{2 \times 0} = 10 \times 0 + 2$

[elfin berry]

Edmund Cloudsley

[still temple]

feel free to ping me! I would be in another tab

Thanks in advance 🙏

[cloud field]

probably set it to 0 then newtons method @still temple

thats how i'd try

[still temple]

hmm newton's method

never heard of it

would have to look it up

Thanks for the suggestion though. Have a good day!

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[still temple]

it worked btw

[still temple]

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[lethal bridge]

how do i do this?

[still temple]

a im pretty sure ?

[lethal bridge]

no

[still temple]

becaus f(kx) is a stretch oof 1/k in the x direction

[lethal bridge]

its not

[still temple]

coooked

tmua is hard

[lethal bridge]

gg

[stark trail]

Sir its an exercise in u-substitution

[lethal bridge]

what am i subbing?

[lethal bridge]

sir what do i make u

[still temple]

caan i ask where u got this question btw ?

imma do alot of them icl

[stark trail]

in option d let u=x/k

[lethal bridge]

what makes u want to start with opt D first?

[stark trail]

u said its not a, i tried b and didnt like it and it made me think that d was correct

idk if d is correct but if you let u=x/k you will find out

i think it is

i havent actually solved it yet but just substitute the thing insde of f in each of the options until you find the one that works

@lethal bridge Did you clear the doubt?

[lethal bridge]

perchance

i think so

[stark trail]

you cant just say perchance

[lethal bridge]

[stark trail]

https://tenor.com/view/starwarsday-gif-5413758

[lethal bridge]

https://tenor.com/view/nah-id-win-gojo-nah-id-win-gojo-satoru-gojo-jujutsu-kaisen-gif-722934852497975468

[bitter dock]

You just take the input for f in the second integral and let that be u

Do that for every answer to check it

[lethal bridge]

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[gilded ember]

when i sub this value into the derivative it gives me 0.0828 not 0

[marsh citrus]

@gilded ember Has your question been resolved?

[sand verge]

hmm approximation of x value caused it...
like even if I sub x= -0.6339745962 then I got 0.00000000032🤷‍♂️

[marsh citrus]

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[hybrid wave]

wdym

[maiden folio]

(1+sqrt(5))/2

[hybrid wave]

((2+sqrt5)**2)1/6

is this right?

[maiden folio]

I think that is not the right answer.

[hybrid wave]

how about

(1+sqrt5)/2

@maiden folio

(2+sqrt5)**1/3

<@&286206848099549185>

[maiden folio]

wait 15 mins

[hybrid wave]

ok

?

[hidden dawn]

9 + 4sqrt(5) = (2 + sqrt(5) )²

[hybrid wave]

so the root is 2?

not 1/3

[hidden dawn]

this wont work

[hybrid wave]

oh

My answer is (1+root5)/2

I am not sure if it is correct

[hidden dawn]

There isnt rlly a clean answer

Its js gonna stay irrational with a root

[hybrid wave]

oh

I don't now how to make it simpliest

[maiden folio]

$9+4\sqrt{5}=\frac{2^3(9+4\sqrt{5})}{2^3}=\frac{72+32\sqrt{5}}{2^3}=\frac{27+45+27\sqrt{5}+5\sqrt{5}}{2^3}$

[elfin berry]

Sinami058

[maiden folio]

$=\frac{3^3+3\times 3 \times 5 + 3 \times 3^2 \sqrt{5}+(\sqrt{5})^3}{2^3}=\frac{(3+\sqrt{5})^3}{2^3}$

[elfin berry]

Sinami058

[maiden folio]

$\frac{2^3 (3+\sqrt{5})^3}{2^6}=\frac{(6+2\sqrt{5})^3}{2^6}=\frac{(1+2\sqrt{5}+5)^3}{2^6}=\left(\frac{1+\sqrt{5}}{2}\right)^6$

[hybrid wave]

there is a six in the front

[elfin berry]

Sinami058

[maiden folio]

$\implies \sqrt[6]{9+4\sqrt{5}}=\frac{1+\sqrt{5}}{2}$

[elfin berry]

Sinami058

[hybrid wave]

yes

[maiden folio]

that's my ans

[hybrid wave]

same as me

[maiden folio]

ok

[hybrid wave]

.close

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[silver nebula]

If $A$ is a matrix with zeroes on the diagonal and positive reals off-diagonal, prove that $A$ is invertible.

[elfin berry]

Nostradamus

[silver nebula]

I tried doing the same thing as Minkowski's theorem with positive real diagonal entries, negative off-diagonal entries and row sums all positive. It did not work.

[marsh citrus]

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[silver nebula]

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[copper pebble]

What do I have to do in b

[dry prawn]

it tells you pretty explicitly what to do

what's your working understanding of a probability distribution?

[copper pebble]

i fr dont know

what it is

i forgot about it on school holidays 😭

[marsh citrus]

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[copper pebble]

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[gilded ember]

if the part of the domain i highlighted was 2 instead of 1 what would i do

[marsh citrus]

Please don't occupy multiple help channels.

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[gilded ember]

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[drifting wyvern]

Wouldn't the deviation be

SD 2 < SD 1

I get their center is the same I assume because of the fact they're normal distributions so mean, mode, medians are in one place

I just don't get how their standard deviations are like that

Their spread I can understand visually I'd assume, unless there is some math behind this that Im missing out on

[brave marsh]

Higher standard deviation means the data is more spread out around the mean, so the second graph has bigger standard deviation.

[drifting wyvern]

Oh, what about spread then?

[brave marsh]

Standard deviation is a measure of spread, so you could say that they are more or less equivalent.

[drifting wyvern]

Like the spread is like how spread out they are?

Oh, so they're kind of similar

[drifting wyvern]

Is my observance here correct then?

[brave marsh]

Yeah. I don't think "spread" is a metric that is used often honestly. It might just be to get an intuitive feel of what it means

[drifting wyvern]

I see okay, if you don't mind could you also explain this

I don't get where you'd get these numbers and stuff for the "At least" and "At most"

[drifting wyvern]

Is there some formula Im missing out on, Im studying this packet and I don't see it mentioned

[brave marsh]

All the bounds they are giving you you can write as the mean +/- a certain number of standard deviations.

There's usually this type of info somewhere

[drifting wyvern]

Yeah I saw this earlier

Not the Z: part

[brave marsh]

Yeah forget Z, but like if you check for instance "Between 29 and 37" that translates to [M - sigma, M + sigma], so you can add up the percentages

[drifting wyvern]

Could you work it out for me using the numbers they gave so I can understand it a bit better?

I heard of the sigma thing in a math video earlier but I didn't really understand/dig into it

[drifting wyvern]

Wait hold up

Am I supposed to be doing sequences and series the unit first

That unit talks about sigma

So I assume Im supposed to do it first before I dig into statistics?

[brave marsh]

sigma is just the standard deviation

[drifting wyvern]

oh

Well, I'll reflect on it, thank you.

[marsh citrus]

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[hazy dragon]

i need an explanation as to when using Caushy's delta-epsilon definition for limits of functions, why the following is allowed to do in the proof:

[hazy dragon]

what we want alright

but why is delta able to be 7 or eps/11?

i mean isnt there an upper bound or something for delta, since it's depended on eps?

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[gilded ember]

it says normally distributed then it gives a mean and sd

[gilded ember]

i thought normal distributions have a mean of 0 and an sd of 1

[ivory sundial]

The standard normal does

But for a generic normal distribution it depends on two parameters that can be changed (the mean and standard deviation)

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[ivory sundial]

Plot sinx and cosx. Test some vertical lines, potentially try folding paper

[marsh citrus]

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[pliant birch]

Can i have some help with how they got all the different angles in the solution

im unsure specifically how they got pi/2 -theta and pi/2 - alpha

the others (theta, alpha, theta-alpha) all make sense

nvm got it

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[nocturne wasp]

1 d i have got the wrong answer

By inverse

[ivory sundial]

(x-5)(x+2)=0

[nocturne wasp]

Null factor

But it says use quadratic formula

I put (-3 sqrt(3^2-4x1x-10))/2

Which got me (-3 +- sqrt 49)/2

[nocturne wasp]

What have I done wrong

[late geode]

you messed up the value of -b

[nocturne wasp]

0 thanjs

Thanks

It should be 3

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[fickle shell]

I mean I got the right answer but I still dont understand it

[green estuary]

Apply distance formula

And you get an expression that gives the distance based on t

[fickle shell]

Why am I able to sub in sqrt((xt1 - xt2)^2 + (yt1 - yt2)^2)

[green estuary]

Because the parametric gives you the x,y values based on tje value of t. That’s why your final expression is also based on t

I think it’d be helpful to plot t = 0 and t= pi to illustrate it to yourself

[fickle shell]

Nah I think I get it now

Thank you!

❤️

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[gilded ember]

how do you approximate where a is

[marsh citrus]

Please don't occupy multiple help channels.

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[marsh citrus]

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[upper sigil]

How would I finish off this differential equation?
$\frac{dx^2y}{dx} = x - 1 \$

[upper sigil]

this was the original question

[elfin berry]

Tomi

[brave marsh]

Integrate both sides w.r.t. x

[upper sigil]

is it this step?

[brave marsh]

Yes

[upper sigil]

the integral of dx^2y/dx is just = x^2 \cdot y right?

[upper sigil]

how come v(x)dy/dx + P(x)v(x)y is just d/dx{v(x) * y)}?

[brave marsh]

v is chosen to have that property. When you multiply your DE by an integrating factor v(x), you'll always end up back in a form where you can write it out as a product rule of y and some function.

[brave marsh]

This is a very formulaic way of writing it down, but at the end of the day the main part is to find the integrating factor and recognize the product rule.

[marsh citrus]

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[marsh citrus]

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[slate stump]

Hi, I need help in understanding Markov matrices.
I know that a Markov matrix always has an eigenvalue 1, but does it also mean that it has an eigenvector to match it?
Since we need the eigenvector to be all positive I don't know if that's the case, and if it isn't, then doesnt it mean the eigenvalue 1 doesnt matter?

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[jagged oracle]

Anyone wanting calculation help

[jagged oracle]

We ball

[crystal lintel]

?

[marsh citrus]

@jagged oracle Has your question been resolved?

[nimble prairie]

?

[jagged oracle]

Hlo

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[sacred idol]

uh

ok

[marsh citrus]

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[elfin berry]

l'agit

[marsh citrus]

@vital quartz Has your question been resolved?

[slim spoke]

I've never done these problems before, but is $P(A \cap B) + P(A/B) = P(A)$?

[elfin berry]

Емил

[slim spoke]

In that case, we know that $P(A \cap B) = 0.2$

[elfin berry]

Емил

[slim spoke]

Oh okay

They look correct to me

I think so

I just used Venn diagram lol

😂

sure

take ur time

[elfin berry]

l'agit

[slim spoke]

let me think 😭

sorry I might take a while 😦

Okay I got it I think

So we know that $1 - P((A \cap B \cap C)^c) - P((A \cup B) / C) = P(C)$

Therefore $P(C) = 1 - 0.5 - 0.2 = 0.3$

[elfin berry]

Емил

[slim spoke]

Therefore $P(C) = 1 - 0.5 - 0.2 = 0.3$
And also $P(A \cup B) + P(C) + P((A \cup B \cup C)^c) - 1 = P((A \cup B)) \cap C)$

[elfin berry]

Емил

[slim spoke]

So, $P((A \cup B)) \cap C) = 0.2 + 0.6 + 0.3 - 1 = 0.1$

[elfin berry]

Емил

[slim spoke]

And $P((A \cup B) \cap C) \geq P(A \cap B \cap C)$

[elfin berry]

Емил

[slim spoke]

So $0.1 \geq P(A \cap B \cap C) $

But probability must also be greater than or equal to 0 so it's in the interval

[marsh citrus]

@vital quartz Has your question been resolved?

[slim spoke]

kinda like this

I think

🙂 okay good

so u think my strategy is correct?

I think so

🎉

[slim spoke]

I wanted to calculate the overlapping region between $A \cup B$ and C

[elfin berry]

Емил

[slim spoke]

So if you add the red blue and green regions and subtract 1 you get the overlapping region between $A \cup B$ and C

[elfin berry]

Емил

[slim spoke]

There's probably an easier way but I didn't see it 😭

[marsh citrus]

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[fathom sun]

Let $z$ be a complex number such that
[\left| z + \frac{2}{z} \right| = 2.]Find the largest possible value of $|z|.$

[glacial hedge]

of ?

[elfin berry]

Dork9399

[fathom sun]

whoops

[lucid bridge]

Seems like a triangle inequality question

[fathom sun]

how would I go about solving the problem then?

[glacial hedge]

let r = |z|
r - 2/r <= |z + 2/z| <= r + 2/r
So the largest r you can hope for verifies ||r - 2/r = 2||
that's r = ||1 + sqrt(3)||
maybe there's a fitting z ?

[fathom sun]

so the answer is 1+sqrt3

?

[glacial hedge]

if you can prove a fitting z exists

answer:
||yes, take pure imaginary z||

[fathom sun]

can you explain how you turned r - 2/r into | z + 2\z|?

[glacial hedge]

reverse triangle inequality

[fathom sun]

?

[glacial hedge]

|a+b| >= ||a| - |b||

which also states equality happens precisely when a and b are in opposite directions

[fathom sun]

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[twilit mountain]

Consider f(x) = x(x-4)^3. a) Find the critical points of f. b) Determine Intervals on which f is increasing and intervals on which f is decreasing. c) Find all local maximum and minimum values of f if any. d) Find the candidates of inflection of f. e) Determine Intervals on which f is concave up and intervals on which f is concave down. f) Find the inflection points of f.

[twilit mountain]

<@&286206848099549185>

[red phoenix]

bruh

thats what i asked you

[elder crag]

!status

[marsh citrus]

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

[elder crag]

and

!noans

[marsh citrus]

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.

[twilit mountain]

f(x) = x(x-4)^3 = x(x-12x^2+48x-64)
f’(x) = 4x^3-36x^2+96x-64 = 4(x-4)^2(x-1)
Is x=4 and x=1 the critical numbers?
Then (4,0) and (1,0) is the critical point?

F is increasing on (4, infinite)?
F is decreasing on (-infinite, 1)?

Then I don’t know how to solve the next part using a table, do I use f’ or f”?

[marsh citrus]

@twilit mountain Has your question been resolved?

[slim spoke]

f(1) is not equal to 0, you have to plug in 1 to the original function instead of the derivative

Also f is still increasing between x=1 and x=4

[twilit mountain]

yes I plug x=1 and x=4 into the original function: f(x)=x(x-4)^3 and got y=0 for both so the critical point would be (4,0) and (1,0)? Is that correct? Also how did you know that f is still increasing between x=1 and x=4?

<@&286206848099549185>

@marsh citrus I am on step a) which I am unsure if I am doing it correctly or not

<@&286206848099549185>

[marsh citrus]

@twilit mountain Has your question been resolved?

[slim spoke]

f(1) = 1 * (1-4)^3 = -27

Also the function is increasing whenever the derivative is positive

So any number greater than 1 other than 4 would have an increasing f

[marsh citrus]

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[normal sigil]

hi

[normal sigil]

can someone help me

[marsh citrus]

@normal sigil Has your question been resolved?

[marsh citrus]

@normal sigil Has your question been resolved?

[lone wharf]

what have you done so far (I haven't taken calc)

so I don't think I can answer

[marsh citrus]

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[wispy ledge]

Can I get help with 2

[wispy ledge]

,rccw

[wispy ledge]

I got D

The answer is C for some reason

Doesn’t the current split for each branch in parallel meaning a lower current to each resistor

[desert dirge]

youre assuming the total current is the same in each case

is that true?

[wispy ledge]

Yea