help-36

[lyric summit]

so they both are necessary

lmdba 1

abd

lambda 2

-2+i

and

-2 - i

but

it is enough

you take oen fo them

to get the pair

exp(-2x)cosx, and exp(-2x)sinx

but in characteristic polynomila you need to get two lambdas

hence in your case the same

lambda = i and lambda = -i are generated

by

lmbda^2 + 1

[faint locust]

But if we only had one lambda, then couldn't we get y_1 and y_2 just like they did, taking real part for y_1 and imaginary part for y_2?

Or is that only a "trick" and in reality we use both lambda_1 and lambda_2

[lyric summit]

lok at such super simple equation y '' + 1 = 0

its fundamentatl system is

sinx and cosx

becasue

polynomial is lambda^2 + 1 = 0

[faint locust]

Yes

[lyric summit]

and lambda^2 + 1 = (lambda + i) (lambda -i) = 0

[faint locust]

Yes

[lyric summit]

oen of them egenrates sin and cosine

but polynomial must be of the secodn degree

[faint locust]

And the other one?

[lyric summit]

you can take one or the poethe rone, i alway stake + i

since i liek postive IM

lambad = i, then Re = cosx, Im = sinx,

if you take - i, you get the same bu tin opposite order

hence it is the same

[faint locust]

Wait, let's say we had y' - i = 0, then we have lambda - i = 0 as polynomial.

Then lambda = i

Does that mean we have two solutions there too?

[lyric summit]

we discuss real equati9ns right ?

[faint locust]

In this case I discuss complex one

[faint locust]

Oh you mean for the exercise

[lyric summit]

yes yoru first quesiton

you consider the real equation

here

[faint locust]

Wait, it just says "homogenous linear differential equations", I need to look in the definition

[lyric summit]

so it is in real domain

i do not thikn so you play with compelx ones

with compelx cofiicients

[faint locust]

Oh, true, it's with real coefficients

[lyric summit]

comloelx equaosn we trach after harmonic anaqlysis

[faint locust]

Ok then yes, we can't have lambda - i here

[lyric summit]

but now if youlay with ode, all is real

so you muyst write lambda^2 + 1

[faint locust]

So lambda^2 + 1

Yes

Thank you!

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[arctic forge]

Im learning factorization. So far, Ive seen how to factor by GCF, grouping, and monic and non-monic trinomials of degree 2 . Now, Im in a weird situation where I dont know whats next. I dont know what method to use for polynomials and trinomials with degree greather than 2. I would like some guidance please

[signal vector]

For higher degrees, it gets much more complicated, look at the cubic formula for instance and compare it to the quadratic formula

[topaz kindle]

Do you know formulas for a^3-b^3 and (a+b)^3?

[signal vector]

This doesn't work always, not all cubics can be factored this way

[topaz kindle]

Yeah but if its a question its worth trying

Bc there is usually a "nice" answer

[signal vector]

@arctic forge is this stemming from a question you were given or are you just curious about factoring cubics and higher degree polynomials?

[topaz kindle]

Finding roots of your polynomial is the only reliable way

[arctic forge]

latter

what about synthetic division and other methods

I need a reliable, provable way

to factor tricky polynomials

[signal vector]

And there is one, but it's really a lot lengthier

[topaz kindle]

Well cubic formula exist you can get roots from it and from that factor the polynomial

[arctic forge]

yeah but what about degree 4

or higher

[signal vector]

And for 5th degree and higher, you just give up because there is no formula that only uses nth roots, multiplication and addition

[topaz kindle]

And can never be

[arctic forge]

tell me please

[signal vector]

Search cardanos method for 3rd degree and ferraris method for 4th degree

[arctic forge]

my profressor told me to use synthetic division for factorization

[signal vector]

Thats only when you know one of the roots before hand

[arctic forge]

did I understand wrongly or is it another method commonly used?

[signal vector]

Yep

[arctic forge]

this is for trinomials or polynomials?

[topaz kindle]

For polynomials

[signal vector]

This is for polynomials

[arctic forge]

and what about trinomials?

[signal vector]

You can treat them as a polynomial in 1 of the variable and factorise, but it won't be a "true factorisation"

[arctic forge]

OKAY THANKS

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[hushed dust]

Does anyone know how to do this?

[dapper jolt]

try substituting root x^2 -3 = u or smn

[dapper jolt]

hmm nvm

did you try trig substitutions?

[hushed dust]

no, how?

[dapper jolt]

i mean in general you would take x = some trig value but here it doesnt seem to work

okay here you can try changing 9^root(x^2-3)=3^2root(x^2-3)

and that entire thing in brackets comes together

[lyric summit]

read and analyse:

the rest should be easy for you

[hushed dust]

I don't understand what you did with it

[lyric summit]

i did operations in my jmind at once

3^1

= 3

i took it out

in front of parenthesis

then i got the same expresiosn as is on lweft side

then i moved ot he elft

etc

i may write it in slow version

moemnt:

[lyric summit]

but because it is not private lessons so i wrote all very quickly

then i took 3 out

and next i moved it to the left side of the equation

and then i noticed the same big expression

and set it inside the parenthesis

i hope you udnerstood me 🙂 smiles

the rest i left for you to continue, but it is not hard to notice next steps i thikn

[hushed dust]

hmm

this?

[lyric summit]

too much on right side, 3 ( ... ) +6sqrx - 18

[lyric summit]

yes) correct

[lyric summit]

very nice and continue

[lyric summit]

no, not this way, first all, note that : 3^2 = 9

and do not multiply

[hushed dust]

hmm, then?

[lyric summit]

let me write it:

[hushed dust]

ah

thanks!

[lyric summit]

🙂

[hushed dust]

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[cinder finch]

how do I draw the Lewis Structure for Al_2O_6

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[tranquil pine]

Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost all real numbers are irrational.[1]

[tranquil pine]

what does

countable and uncountable mean here?

[tiny gorge]

if a set is countable it means there's a bijection (one to one correspondence) between the set and the natural numbers

uncountable means there isn't

[pastel cosmos]

• infinite set

[tiny gorge]

where is this quote taken from? aren't they defining the terms?

[tranquil pine]

they are-

[tranquil pine]

can you give an example

[tiny gorge]

well the above is already an example

[tranquil pine]

ok wait

[tiny gorge]

the rationals are countable, there's a standard proof which the book should have presented (or it's assuming you already know)

[tranquil pine]

wait wait, so Google said that correspond means to match exactly or be similar. So the part where I'm confused at is, Natural numbers don't have negative numbers, so how can they.. correspond with the rational numbers..? like, N ={0,1,2..}, Q={...-1,0,1...} so..like only the whole numbers correspond..yk

[tranquil pine]

it was wikipedia

[tiny gorge]

google's definition is not a mathematical one

[tranquil pine]

they probably do have the proof ig

[tiny gorge]

a bijection is an invertible function

to say that a set S is countable means that there is a function f from the natural numbers to S such that

[tranquil pine]

wait wait

[tiny gorge]

the list f(1), f(2), f(3), ...

has two properties:

[tranquil pine]

stop stop

[tiny gorge]

the values are all distinct, meaning f(i) does not equal f(j) if i does not equal j

and

all elements of S appear once in the list

[signal vector]

Another way of understanding countability is that you can list out all the elements of the set

For the rational numbers, there is a way to do that

[tranquil pine]

.-.

[signal vector]

However you cannot do the same for the irrational numbers

And in that sense, the infinity of rationals is smaller than the infinity of the irrationals

[pastel cosmos]

guys she said to stop

🫠

[signal vector]

Oops

[tiny gorge]

well she can always scroll back, it's not like messages disappear 😁

[tranquil pine]

why and how..?

[signal vector]

Do you know how the set of rationals is defined?

Any rational will be of the form p/q

[tranquil pine]

ye

[signal vector]

With p,q integers

Look at this table

Does this table contain every positive rational number?

[tranquil pine]

no

[signal vector]

Which one does it not contain?

[tranquil pine]

wait nvm u got the ellipsis

so ye

[signal vector]

Now I want to turn this table, into a long list

[tranquil pine]

well the table still will have no end tho

cause infinite numbers so infinite possibilities u]

[pastel cosmos]

but if you pick any positive rational number, that number is in that table isn't it?

[tranquil pine]

yessssssss trueeee

[signal vector]

So what, the list will just be infinite

Like the list of numbers 1,2,3,..

[tranquil pine]

uye

[pastel cosmos]

that means every positive rational number is in the table

[tranquil pine]

yes

[signal vector]

To make this list, start off at 1/1, then follow the arrows

Do you see that you can keep continuing like this and circle every number in the table?

[pastel cosmos]

then ur answer should be yes right?

[signal vector]

She did say yes

[signal vector]

Here

[pastel cosmos]

but she said this

[signal vector]

Oh, your question was different

[pastel cosmos]

Was I confused?

[signal vector]

She did agree that every positive rational was there in the table and we explained how if the list was infinite, it didn't matter

[tranquil pine]

to her question? yea

[pastel cosmos]

oh

then I'm sorry to interrupt your explanation

[signal vector]

Anyways, do you agree that if we keep continuing we will end up circling every number in the table?

[tranquil pine]

yes\

[signal vector]

In doing so, you have created a list, starting at 1/1, then the next element in the list would be 1/2, then 2/1, then 3/1, and so on

[tranquil pine]

yes

[signal vector]

Now, we can generate all the negative rationals

[tranquil pine]

it helped too btw

[tranquil pine]

by..

[signal vector]

Our list currently looks looks like this:
(1/1), (1/2) ,(2/1) ,(3/1), ...

[tranquil pine]

yes

[signal vector]

After each number, let's just add it's negative

(1/1),(-1/1),(1/2),(-1/2),(2/1),(-2/1),(3/1),(-3/1),...

Now we have listed down all the positive and negative rationals

Just add 0 at the start of the list, and you are done

[tranquil pine]

yea

true

[signal vector]

So you have proved that the rationals are countable

[tranquil pine]

yea

[signal vector]

You can write them out in a list, its just infinite. The same you you would write out the natural numbers, also known as the counting numbers. Hence the name "countable"

[tranquil pine]

yea

you can write them out but, you cant write out the irrationals cause of the inifinite decimals

no cause

of the

infinite and non recurring

decimals

cause they cnt be expressed in fractions

so irrational set is bigger

so uncountable

okay so basically, the reason why the rational set is countable is because it can be written even tho its infinite coz fractions can be written while in the irrational set, no fractions-> no ease (infinite time prolly💀 for writing one irrational) hence the irrational set is uncountable

[signal vector]

Thats not exactly the reason, the reason for why irrationals are uncountable is a bit more complicated than the reason for why rationals are countable. The easiest way I know is by doing the following:
1)Proving the union of two countable sets is countable
2)proving that the set of real numbers is uncountable
3)since the reals are the union of the rationals and irrationals, if the irrationals were countable, then the reals would end up being countable too(because of point (1)). So, the irrationals aren't a countable set

@tranquil pine

[tranquil pine]

oh

i cant do them steps

but

thank you

a lot

for typing

all that

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[steady prairie]

we can solve this by using the equations of kinematics

v=u+at

u is 0 as he starts from rest

v=at , v= 0.40 x 20

v=8 m/s

this is the constant speed mentioned

in the questioon

[tranquil pine]

@steady prairie organometallic , grignard reagent ?

[steady prairie]

yes sir

[tranquil pine]

jee ?

i can just feel it hah

[steady prairie]

was a JEE guy

I qualified for the national defense academy , so I don't need JEE now lol so am trying to help people out

with whatever I can

[tranquil pine]

wow

sir can i add you ?

[steady prairie]

sure sure

[gritty minnow]

But they are asking for top speed?

Do u need velocity for that

[steady prairie]

yes , that is the top speed

see velocity and speed

are same and different

here they're the same

since he was accelarating at first

[gritty minnow]

So it's 8

[steady prairie]

but now isn't

so he has achieved

a maximum speed

[gritty minnow]

What for net displacement

[steady prairie]

second equation

s=ut+1/2at^2

but we know the velocity

and time

so we can use

v^2=u^2+2as instead

u was 0

we know we

s=v^2/2a

s=64/(2x0.4)

64/(0.8)

80 m

now lets not forget

the distance he traveled on constant speed

[gritty minnow]

Can u send all the equations?

[steady prairie]

1. v=u+at

2. s=ut+1/2at^2

wait

[steady prairie]

this might confuse

s = ut + (at^2)/2

this is what I mean

3. v^2=u^2+2as

these 3 will help

[gritty minnow]

Are those it

[steady prairie]

yes

[gritty minnow]

Is s distance

Or displacement

[steady prairie]

displacement

[tranquil pine]

disp

[steady prairie]

but since he isn't turning back or anything

can be considered distance ( just for saying)

[gritty minnow]

I get it now thank u

Do u mind if I send some more

[steady prairie]

@tranquil pine I have to go , mind helping this guy out?

basic kinematics

[tranquil pine]

yeah ofc no problem

[steady prairie]

@gritty minnow

go ahead

[tranquil pine]

try it yourself using the three equations first
just substitute the values

like for the first one

you want a relation between speed accele and time

so v = u + at would work

[gritty minnow]

V=4+24

28?

[tranquil pine]

mhm

you got it

[gritty minnow]

Ayy

Lemme try displacement now

[tranquil pine]

focus on what is asked and use the equations

[gritty minnow]

48?

[tranquil pine]

mhm didnt checked but you are going in right direction

[gritty minnow]

What about 2nd and 3rd one those can't be substituted with the equations

[tranquil pine]

so you know what is avg. velocity ?

basic defination of it ?

[gritty minnow]

Not really

[tranquil pine]

well it goes like this

you know speed = distance/time

avg. speed = total distance travelled /total time taken for it

so now look on y axis for distance

and on x for time

[gritty minnow]

For 2nd or 3rd?

[tranquil pine]

similar defination for avg. acceleration

[gritty minnow]

@tranquil pine I'm stumped

[tranquil pine]

do you have some class notes regarding this topic ?

refer that
cause these are not very tough problems

are struggling with the algebra ?

[gritty minnow]

I missed a lot of this

[tranquil pine]

or cant read the graph

[tranquil pine]

solving without it is just waste
try getting it from some friend

[gritty minnow]

Is it -12÷5

[tranquil pine]

which one ?

[gritty minnow]

2nd

[tranquil pine]

nah i dont think so

[gritty minnow]

I took 5 as y2

[tranquil pine]

okay tell me how much distance did he travelled

[gritty minnow]

And 0 as x2

5/-12

[tranquil pine]

?

[gritty minnow]

12?

[tranquil pine]

nope

read it like this

in 0.5 sec he reached 0cm from 12cm

hence 12 cm travelled

further in 0.5 sec he went from 0cm to 12 cm , so again 12 cm travelled

similarly from 1 to 1.5 sec

so tell how much in total ?

[gritty minnow]

36

[tranquil pine]

good

divided by

time

[gritty minnow]

Which is 2?

[tranquil pine]

yeah but look properly for how much time it is asked

in da question

[gritty minnow]

1.5

[tranquil pine]

right

[gritty minnow]

So 24

[tranquil pine]

idk how much
would be correct

lazy to do divide 💀

correct

[gritty minnow]

I think I get it now thank u

[tranquil pine]

yay

3rd one ?

[gritty minnow]

Do u know this one? 31

I'm thinking of using the s=UT 1/2at^2 formula

Not sure tho

[tranquil pine]

yeah

do it

correct

you got time given

a given

u givent

and s is asked

go for it

[gritty minnow]

1×3+1.5×9

3+1.5×9

16.5

?

[tranquil pine]

u is 2 and time is 4 sec
ut=8

how did you got 3 there ?

[gritty minnow]

Whoops confused t for something else

How is u 2 tho

Wait nvm

Got it

Read it wrong

[tranquil pine]

andddddd

dont forget that

[gritty minnow]

Imma do the whole thing again one sec

[tranquil pine]

it was initially at x = 1m

so add up that to final answer
because from origin it is asked

[gritty minnow]

2×4+1+16

8+17

25

Add 1

26

[tranquil pine]

you sure you calculated the 1/2 at^2 part correctly ?

recheck and you are good to go

alr i gtg

bye

[gritty minnow]

Bye thank u for ur help

[gritty minnow]

1.5×16

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[cedar sparrow]

dependent

wait

[steady prairie]

waht

[cedar sparrow]

4 as in total of two dice?

then it's independent nvm

you can't get a 4 and a 7

[steady prairie]

I questioned myself for a second

[cedar sparrow]

intersection is 0 so they're independent

[steady prairie]

lol

[cedar sparrow]

then it's dependent

like 4 + 3

satisfies both

yes

intersection is not 0

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[fierce wadi]

I need help urgently with this math equation, to make it easier, I got a hint that goes along the lines if using : 1/b-a (1/b - 1/a) or something like that, this is the equation :

[brittle lark]

Hello!

I can help you with that

[fierce wadi]

also, I can't use common denominator and can't use big numbers, try solving ot cleverly

[fierce wadi]

thank you

[brittle lark]

First you have to take x as the common multiplier

And then we will factorise the denominator and all of them will be like a continuation of each other

Like: 3×7,7×11...

[fierce wadi]

can you give me how exactly, I'm not that good at maths lol

[brittle lark]

Yeah sure

One minute

this is our first step

Basically we took X as the common multiplier

Then

[fierce wadi]

oh ok I get it now

[brittle lark]

Then what we can see is that they both can be factorized into a continuation, like 3xn then nxn+4, n+4xn+4+4 ...

[fierce wadi]

yeah I just noticed that wow

[brittle lark]

So that we can use 1/b-a (1/b - 1/a)

So then we are going to name 3-> a and 7->b

[fierce wadi]

ohh okay

[brittle lark]

Here's our new equation

Now we're going to do what we should on the denominators of the first factors and leave the brackets

So,

Like that

[fierce wadi]

are we gonna use 1/4 to factor right?

[brittle lark]

yees

[fierce wadi]

okay good, I'm starting to understand

[brittle lark]

There you go mate :))

I hope you understand

[fierce wadi]

yes, I did, thank you soo much you can't believe how much I needed this help

[brittle lark]

You're welcome my friend

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[soft zealot]

UserName_copied.

[hollow flume]

How is 1/(s-2)^4 = 1/s^4 ?

[vital crag]

no one is saying that

a=2 implies there's a shift happening

that's why this term is here

[hollow flume]

I only understand it algebraically

And I don't understand 1/s^4

[vital crag]

https://sites.calvin.edu/scofield/courses/m231/docs/laplaceTransShifts.pdf

[hollow flume]

Ok but this doesn't help

Wait

[vital crag]

you see part A right?

[hollow flume]

Yh

[vital crag]

that e^(at) term

[hollow flume]

Ok but

What about 1/s^4

I know that 1/(s-2)^4

is F(s-a)

But what about 1/s^4 ?

Is it also F(s)

?

Holy shit this is not for me

yooo

YOOOOOOO

I got it

1/(s-2)^4

is the 1st shifting property

Where L(e^at*f(t)) = F(s = (s-a))

Which is 1/(s-2)^4

[hollow flume]

thank you for your time

.close

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[onyx sand]

could someone help me out with these first two

[onyx sand]

trying to go off intuition since im not sure calculations would get me anywhere

i dont see why they all wouldnt have infinite

must have to do with fxx?

wait its in R2

i am even more unsure now

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[sour vine]

Idk how to find integrating factor without being able to convert to linear form

[crude wing]

yo can someone help with some work?

@unkempt moon

[sour vine]

what u need help w

[crude wing]

its like a booklet

i can send it if you wanna check it out?

[sour vine]

post the problem

just do it in here

[crude wing]

like experimental probability simulation and that

okayyy

this one

if you want i can ss it and then send it?

[sour vine]

what problem do u need help w?

[crude wing]

it number 4

the flu

its*

did you see it?

[sour vine]

yes

what do you need help with

like what have you tried

[crude wing]

im not sure beacuse im still geting used to it

[crude wing]

like the answer for that question

thats all

[sour vine]

i cant do your hw for you!! I can help you though

[crude wing]

yessss

thats what i meannn

srry

do you guys do call?

[sour vine]

ill just explain

do you know how to use the number table?

[crude wing]

no thats what i was sttuck on

[sour vine]

you need to come up with a system where each number has a 15% chance of being "infected"

[crude wing]

like???

theres

4 childeren in the family

and 1 afected person

and there a 15% chance of catching it

thats all ik

and the confusing part is the random number table

thats what i was stuck on

[sour vine]

you use the random number table to create a 15% of something happening

for example if you want to make a 50% chance for something, you could say even or odd

[crude wing]

yes

[sour vine]

so you just need to do for 15%

[crude wing]

bro this is really confusing

can you explain on cal?

[sour vine]

sorry i cant

but you understand how to get 50% right?

[crude wing]

kinda

[sour vine]

you can say if the number is even, then case 1 is true

if number is odd, case 2 is true

and then it's 50% chance for case 1 and 2 since the numbers are random

[crude wing]

yeah

[sour vine]

let's say you wanted to make a 10%

you can say the condition is the last digit has to be a specific number

let's say 2

so if the last digit of the random number is 2 then condition = true

and that would make it a 10% chance because there are a total of 10 possible digits

[crude wing]

but we have 4 children and 1 afected person with a 15% chance of a person being infected and we need to do 20 tirals to find out the probability of a person/children catching the flu

[sour vine]

yes, the probability will be the same for each child correct?

so you need to create a system that will theoretically produce a 15% chance

and then do it 20 times to see how close to 15% it is

[crude wing]

what do you mean by a system?

[sour vine]

system = simulation

[crude wing]

ohhhhhh

[sour vine]

how can you simulate a 15% chance with that random number table

[crude wing]

thats what i need

[sour vine]

assume the numbers range from 0-99

[crude wing]

okay

yes

understanding

[sour vine]

so you know how to do that?

[crude wing]

nooo

thats why i need help

[sour vine]

ok so you have 100 digits

ranging from 0-99

[crude wing]

ye'=s

[sour vine]

srry im trying to find a good way to explain

ok so like we said before

if you want a 50%, you can set the condition "if the number is even"

u know what ill call if ur really having trouble send rq

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[magic sparrow]

I'm very confused by this question because

I can prove that formula, for all n, using induction

and I think without differentiating under the integral sign

(unless IBP is somehow doing that)

So I am confused if my work is wrong or if the question is just expecting me to use a different method?

[trail mango]

it is expecting you to differentiate under the integral sign

[magic sparrow]

but what if I dont want to

it's easier this way

[trail mango]

too bad

[rocky tusk]

unfortunate

[magic sparrow]

😠

Okay

New question then

How does it want me to prove that differentiating under the integraL?

I don't get that method

[trail mango]

well first it wants you to verify the hypotheses for differentiating under the integral sign hold

do you have those on hand?

[magic sparrow]

Well I have a few different theorems

I can tell you one that I think works here

[robust mulch]

where does the minus sign go

[magic sparrow]

x^-(n+1)

[magic sparrow]

if f(x,t) and partial_x f(x,t) are continuous on the interval of integration then

d/dx integral f(x,t) = integral partial_x f(x,t)

and they converge unfiformly

[trail mango]

ok those look pretty easy to verify

[magic sparrow]

yes

so it is justified

[trail mango]

i didn't write it out but i imagine yes this is true?

[magic sparrow]

no I wasn't question

so it is

not

so is it

It is justified

[trail mango]

what??

[magic sparrow]

I'm confused

what are you confused about

[trail mango]

https://i.imgur.com/NdeKeah.png

[magic sparrow]

I meant

"So it is justified"

not

"So is it justified?"

[trail mango]

oh

ic

[magic sparrow]

👍

[trail mango]

soz lol

[magic sparrow]

https://tenor.com/view/stickydacat-gif-26502121

[trail mango]

so now you can differentiate under the integral sign

have fun

[magic sparrow]

okay

but why do I even want to do that

I dont get it

[trail mango]

practice? idk

[magic sparrow]

No I mean

how does it help to prove the result

to just randomly differentiate

[trail mango]

well you need to be a little bit inventive

actually no i don't think you do here

[magic sparrow]

[vital surge]

differentiation under the integral sign normally solves an entire class of integrals, expressing solutions as something in terms of the changing variable

[magic sparrow]

but I'm saying I guess like

it wants me to prove: Integral (of thing) = thing

if I do

integral (derivative of thing)

how does that do anything to helping me prove the original inequality

[vital surge]

oh i see

[robust mulch]

i would assume you can use basic integral stuff to verify the first part

[magic sparrow]

yah I already did and I proved the second part with induction

I just dont get the method they want me to use

[robust mulch]

!show

[final saddle]

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

[magic sparrow]

well I dont have any questions about my work

its just simple induction and IBP

and its right

[robust mulch]

ah i see

[magic sparrow]

It just doesnt use the method of differentiating under the integral

[drowsy epoch]

I think it is, if the Integral is convergent

[magic sparrow]

i know it is 😭

[drowsy epoch]

ok mb

you got two wolves inside you, shoulda known better

[magic sparrow]

and you know what they're doing

[vital surge]

what variable do you want to differentiate with respect to?

[magic sparrow]

x, I think I figured it out, but thank you for your help, I still prefer IBP 😭

.close

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[vital surge]

ah nice glad you got it

and ye it's a clunky seeming method at first

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[lavish jewel]

HI

[lavish jewel]

Heya! rick here lmo!

k anyway

how would we evaluate the expression (-243)^2/5

<@&286206848099549185>

[crude wing]

Hey

[wary egret]

Hi

[crude wing]

what do you need help with?

[wary egret]

Dont ping helpers b4 15 mins

[lavish jewel]

Mb dunce

[lavish jewel]

Ahoy peepee!

how would we evaluate the expression (-243)^2/5

@crude wing

[crude wing]

got it

one sec

[lavish jewel]

ok so we remove the denominator and square -243

[crude wing]

yes

[lavish jewel]

then after that we find the fifth root of it (59049)

and that would be 3

Thank you so much baby girl

[crude wing]

ahahhahahah lol

[lavish jewel]

Ily so much

[crude wing]

np bro

[lavish jewel]

.close

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[crude wing]

got you

[lavish jewel]

i’m male

and straight

sry

[crude wing]

ofc bro dw about it

what grade are u in?

[lavish jewel]

thanks bb

[lavish jewel]

10th

we do algebra in 10th grade in california

[crude wing]

oh shi same lol

[lavish jewel]

Ohhh lol

[crude wing]

not in cal

tho

[lavish jewel]

where

you know whay forget u

bye

.clsoe

.close

BLOCKed

thanks for ur help bbg

[wary egret]

??

[lavish jewel]

How do i close the channel bb

[wary egret]

Do you understand why

[crude wing]

lollllllll

[lavish jewel]

Yea

[wary egret]

.close

[lavish jewel]

sorry i’m straight

i did

i did that

[wary egret]

Do again

[crude wing]

bro rick is so cool

ahahahahahahaha

[tranquil pine]

thats how it is thru most of america

its already closed bruh

[lavish jewel]

my friend is doing ap precalculus in 10th tho

[tranquil pine]

oui, its possible

i did calculus I in 9th grade

it js depends on if u seize and opportunity

[lavish jewel]

my friend is doing math 8 in 11th grade tho

he doesn’t have middle school

so 9th he did 6th grade math, 10th was 7th math, 11th is 8th grade

and 12th grade is not even algebra

they don’t have math

[tranquil pine]

yep

varies

but like i said

most of america

the general benchmark is that

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[wild pawn]

8. 3.0 m [N30 o W] – 10.0 m [S20 o W]

[tiny gorge]

!original

[final saddle]

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.

[wild pawn]

that is the original

can't be any more

[shut gazelle]

Can you send an image of the question?

[tiny gorge]

i don't believe that's the original question

[wild pawn]

ok

see

8

i dont know how they got the angle

i got the distance

<@&286206848099549185>

[lavish jewel]

Hi daddy

[wild pawn]

HELLO

[lavish jewel]

can’t help sry

[wild pawn]

All good

[final saddle]

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[lost marsh]

what'd I do wrong here?

[tiny gorge]

,rotate

[tiny gorge]

comma for some reason

[lost marsh]

ah haha thanks

[tiny gorge]

you didn't integrate e^-x correctly

[lost marsh]

what is correctly?

cant see the mistake

[tiny gorge]

what's the derivative of e^-x?

[lost marsh]

-e^-x...?

[tiny gorge]

right

so that means the integral of -e^-x is e^-x, right?

(just doing the opposite of differentiation)

[lost marsh]

yeah

[tiny gorge]

ok

so what's the integral of e^-x (without the minus sign in front)

[lost marsh]

-e^x

[tiny gorge]

-e^-x

the exponent doesn't change

[lost marsh]

oh okay, im still trying to get it but then what?

[tiny gorge]

well you wrote e^-x, it should have been -e^-x

i.e. you're missing a minus sign

[lost marsh]

what about like this?

now it's a negative again

[tiny gorge]

it's right until the last line

-e^(-ln a) is not a

[lost marsh]

then what is it..?

[final saddle]

@lost marsh Has your question been resolved?

[final saddle]

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[austere spire]

can anyone help me with this? not sure what it's trying 2 make me solve

[fathom walrus]

lol yea theres no equals sign

maybe try simplifying down?

maybe some things cancel

yea i think some things cancel

[austere spire]

yea this what i tried:

[fathom walrus]

when u factored out a 3

u only factored it out from 1 (21-18y)

u have to factor it out from both

[austere spire]

ohh yea wait ill fix

[trim crown]

18 squared = 324

You can turn the expression into a prefect square

[fathom walrus]

yea

once u get to (21-18y)(21+18y) thats just difference of squares too

[austere spire]

nice

[fathom walrus]

check and see if its correct if u can

[austere spire]

wait ill try

yea i think this one's better

thanks! ill close now

.close

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[uncut topaz]

Can someone help men how to get the null hypothesis and alternate hypthesis of no.1

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[uncut topaz]

Hello

[uncut topaz]

Can someone help men how to get the null hypothesis and alternate hypthesis of no.1?

<@&286206848099549185>

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@uncut topaz Has your question been resolved?

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[winter crypt]

how do u do dis

[winter crypt]

i did this much idk what to do after

!status

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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

[winter crypt]

2

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@winter crypt Has your question been resolved?

[winter crypt]

.close

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[feral hawk]

what does the B stand for in y=mx+b

[trim crown]

Y intercept

[young verge]

y-intercept

[feral hawk]

tysm have a great day or night

[trim crown]

You can see that by letting x=0

[feral hawk]

.close

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[strong crypt]

Linear Algebra

[strong crypt]

I'm just at a total loss at this point

I was thinking that the change of basis matrix would be made up of the two provided vectors and [-1 -1 2] as the span of this would represent R3

But wouldn't that just be the basis then...

like i'm just rlly confused on where to go

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[sturdy ocean]

.close

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[turbid sable]

So I was under the impression that with velocity time graphs to find displacement all I had to find was the area but I’m having trouble with this odd shape

The curve is giving me trouble

[halcyon shale]

you can't find exact displacement unless equation is given

you could only approximate the middle part to be a trapezium

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[tranquil pine]

So there are a few things i need to be checking, right?

1- I need to verify that the natural domain of those functions is simply connected
2- I need to verify if the partial derivatives of the components are equal
3-I need to verify that under any closed loop this will end up being 0

well i guess they are all iff statements?

2. runs on the assumption that 1) holds though

i think 2) and 3) are iff's with each other

so its probably sufficient to show either

i think all of those are simply connected as i think the domain of all of them spans R^3

so i guess just checking the partial derivatives now

[grim nebula]

i mean like no

it's sufficient to be a closed form over a simply connected domain to be conservative but you don't have to be

you just need to verify that there exists a potential

[tranquil pine]

ok

so i guess like

[grim nebula]

not closed => not exact

but closed could mean exact

[tranquil pine]

wdym by closed first of all

[grim nebula]

like

curl = 0 i suppose

[tranquil pine]

ah okay

and by like not exact you mean the derivatives being equal

p much

[grim nebula]

exact means is the grad of something

[tranquil pine]

oh ok

[grim nebula]

closed means curl = 0

so exact => closed

[tranquil pine]

yeah

[grim nebula]

but not necessarily the other way round

[tranquil pine]

contrapositive

[grim nebula]

over a simply connected domain it's true that exact = closed

but you don't require this

[tranquil pine]

so i can skip verifying if its simply connected by just proving the implication exact -> closed

[grim nebula]

there are still exact forms over a non-simply connected domain

[grim nebula]

well don't prove that

that's the poincaré lemma

[tranquil pine]

LOL

ok so uh

what should be i doing then

[grim nebula]

like just find the potential

[tranquil pine]

just guess a random potential function?

[grim nebula]

no you can work it out

like

[tranquil pine]

oh

integrate?

[grim nebula]

check if the curl is 0

if it isn't you're fucked

if it is

try to solve the system of PDEs

[tranquil pine]

[grim nebula]

like u_x = yz, u_y = xz, u_z = xy

[tranquil pine]

oh wait

[grim nebula]

pretty clear to see that u = xyz works

[tranquil pine]

those are easy

[grim nebula]

that's your potential

[tranquil pine]

just integate ig?

[grim nebula]

yeah

so that proves that 1. is exact

[tranquil pine]

wait but why check if curl = 0 even lmao since exact => closed cant we just directly find if it s exact

oh wait

i forgor how to implications work

[grim nebula]

i mean like

technically

it's dumb

because all your vector fields are defined on R^3

so you automatically get that closed => exact

[tranquil pine]

if it isnt i guess the issue is that you can end up with T => F?

[grim nebula]

checking that curl = 0 is enough

but like

i feel like this is overkill because you haven't proven the poincaré lemma