help-36

[brazen plume]

Ig you can

Yeah

[normal goblet]

Alrrr

Perfect

I have another question

It’s different

[brazen plume]

I’ll try to answer it

[normal goblet]

I don’t know how to make the subject of something in a formula when it’s repeated

You know what I mean

[brazen plume]

How far have you gotten?

[normal goblet]

Here because I need to find e byitself and there is 2 e

2 separate e’s

[brazen plume]

Shift the 3e to lhs

And after that the 2e as well

[normal goblet]

So for this it will be k^2 x 3e?

[brazen plume]

Yeah

[brazen plume]

.

[normal goblet]

I think I did something wrong

[brazen plume]

2e would be negative, not 3ek²

It would be 3ek² - 2e = 5m

[normal goblet]

Oh okay

[brazen plume]

Now in the lhs, take the e common

[normal goblet]

Then shift the k to the other side?

[normal goblet]

So it’s just 1e

[brazen plume]

Yeah

[normal goblet]

ek^2=5m

[brazen plume]

No

Take e common means 3ek² - 2e = e (3k² -2)

[brazen plume]

Because e is common in both 3ek² and -2e

[normal goblet]

Where did the 5m go though?

[brazen plume]

Yeah I did not write it because I was showing the lhs

But e (3k² -2) = 5m

[normal goblet]

Ohhh that makes sense

[brazen plume]

Now just shift the 3k² - 2 to the rhs

[normal goblet]

So e = 5m (3k^2-2)

[brazen plume]

Yep

[normal goblet]

Oh okay perfect

And for the next one

[brazen plume]

Do the same as we did here

I gtg now

[normal goblet]

But it’s 2 stuff at the bottom

[normal goblet]

Alr thanks bye

.close

[final saddle]

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[naive shoal]

how do you do this

[atomic coral]

y = 3/11

x = (5/3)*(3/11)

[honest carbon]

No, you do it yourself. We can check

[atomic coral]

so x = 5/11

y = 3 *

[naive shoal]

no like i dont know what elimination is

so idk how to start

[atomic coral]

and x = 5

[naive shoal]

i need someone to explain the process to me

[tranquil pine]

!nosols

[final saddle]

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.

[atomic coral]

just + the 2 equations

[naive shoal]

dont give me the answer

[atomic coral]

3x - 5y + -3x + 6y = 3+ 0

y = 3

[naive shoal]

i just need to know the steps i need to take

[atomic coral]

now we find x:

3x - 5*3 = 0
3x = 15
x = 5

we good?

bro we good @naive shoal ?

[naive shoal]

so wouldnt i have 1y=3

if i added them both

then what do i do

[final saddle]

@naive shoal Has your question been resolved?

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[hard pilot]

what exactly happened to get this equation?

did they just divide by 10Log?

[hard pilot]

bestie, doesnt really help me

Yea, couldve just said yes

.close

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[topaz bramble]

how do i solve algebra 2 questions like g(f(x))

[topaz bramble]

.close

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[remote island]

How many different complex solutions does the equation x^23 - 2 - i = 0 have?
i'd appreciate help

[trail mango]

there is no equation here. did you mean to put an = 0 or is there a typo somewhere?

[remote island]

corrected, sry

[trail mango]

np. would you be able to answer this if the equation was, say, x^23 = 1 instead?

[remote island]

yeah i think it's 23, but i'm nlot sure why

in t'e case of = 2 + i

don't the valeus differ

[trail mango]

what values?

[remote island]

wiat

i'm stupid

i is a constant

another question

0 right

Arg(6i^6)

[trail mango]

LOL that image is comically low quality

[remote island]

ye sorry

[remote island]

is it correct?

0?

Arg is a real value

not imaginary

or

do I calculate 6i^6

[trail mango]

yea i would calculate that

[remote island]

so i only don't calculate if it's in the form iy?

[trail mango]

what does that even mean

[remote island]

standard form of a complex number is z = x + iy

here Arg(z) = x and Im(z) = y

[trail mango]

you mean Re(z) right?

[remote island]

It can also be called Arg, no?

Wait no

[trail mango]

no

[remote island]

Okay so I will calculate this

It's 6(i^2)^3 = 6(-1)^3 = 6(-1) = -6

So that leis on a negative axis

Thus the angle is pi

Correct? @trail mango

[trail mango]

yea

[remote island]

Next question:
Solve: (1/i + i/2 +i)^4

1/i = -i

so (-i +i + i/2)^4 = i^4 / 2^4 = 1/16

corerct?

[trail mango]

yes

[remote island]

"What's the trigonometric form of the number i"

So it's something like

actually

it's obvious

it's pi/2

i = 1(cos pi/2 + isin pi/2)

corerct?

ok next question

What's the dimension of a transformation kernel F: R^3 -> R, where F(x, y, z) = y

1?

Wait no

[trail mango]

is it asking for the dimension of the kernel of F?

very weird wording

[remote island]

ig

[remote island]

The kernel consists of all vectors where F = F(x, 0, z). Meaning that it can be represented as (x, 0, z) = x(1, 0, 0) + z(0, 0, 1) -> i.e., the dimension of the transformation is the number of vectors in the basis, i.e., 2

[trail mango]

yep

[remote island]

Ok determinant of

now

5 * 6 + 1 * 7 = 37

done?

[trail mango]

what a weird question

yea, done lol

[remote island]

what's the dimension of the transformation image F: R -> R^5, where F(x) = (x, 2x, 3x, 4x, 5x)

Isn't that just 1

x(1, 2, 3, 4, 5)

??

[trail mango]

yea

[remote island]

Okay

This question I have no idea how to do

Give the eigenvalues of an endomophism with matrix A in the canonical basis of E^2 space

[trail mango]

this question is a certified @grim nebula moment

[trail mango]

what is E^2 space?

[remote island]

ig

[trail mango]

one more chatgpt screenshot and i'm quitting this channel

[remote island]

why

[trail mango]

anyway. this question just wants you to find the eigenvalues of A

[blissful condor]

based

[remote island]

JUST

hwo do I calculate a determinant

of lambda

lol

[remote island]

Cause det of this is 8 * 9 = 72

But

I am to solve det (72 - lambda) = 0

[trail mango]

if you can work with the symbol 8 you can work with 8 - lambda just as easy

[remote island]

Why

A.h

lambda

is 72?

cause det(0) = 0

[trail mango]

and eh what are you talking about?

[remote island]

Am i allowed to post a chatgpt screenshot

det(A - lambda * I) = 0

is what chatgpt said

is hwo i find eigenvalues

[trail mango]

what is all this stuff and what you said below it?

[remote island]

.

[remote island]

det(A) = 72

if det(A - lambda * I) = 0, then A = lambda * I

[trail mango]

no

[remote island]

And I is just 1
[1 0]
[0 1]
i.e., its det is 1

det(lambda * I) = det(lambda) * det(I) = det(lambda)

[remote island]

why not

[trail mango]

there are more matrices with 0 determinant than just the 0 matrix

[remote island]

OVER

what do i do then

[trail mango]

write A - lambda * I as one matrix and take the determinant

[remote island]

and

I only subtract lambda from diagonals?

[trail mango]

sure

[remote island]

The first diagonal

I mean

The TRUE one

Okay

Something like this

Therefore

detA = (8-lambda)(9-lambda) = 72 - 8lambda -9lambda + lambda^2

Correct?

How does that help me thouugh

AHH

lambda^2 -17 lambda + 72 = 0

Lambda I calculate from theq uadratic equation

Answers are 8 and 9

Those are eigenvalues??

@trail mango

[lethal estuary]

what even is the matrix?

[trail mango]

yea if you did the algebra right

[remote island]

[8 7]
[0 9]

sorry not my pics

[lethal estuary]

yeah that's right then

[remote island]

Okay

In my notebook I have written

that I can find eigenvectors using eigenvalues

[lethal estuary]

yes

[trail mango]

didn't the question just ask for the eigenvalues?

[remote island]

the formula is
[A - lambda_i * I] * [x_1] = [0]
[x_2] [0]
[...] [...]
[x_n] [0]

[remote island]

yes

but like idk how to calculate eigenvectors

so i figured i might as well ask

[lethal estuary]

you find the nullspace/kernel of A - lambda_i * I

after plugging in the particular eigenvalue

[remote island]

How do I do that

[lethal estuary]

same way you find the kernel of any matrix

[remote island]

so from

{ (8-lambda)x + 7y = 0
{ (9-lambda)y = 0

I solve this sytem of equations, yes?

[lethal estuary]

yeah

[remote island]

Can i just plug lambda valeus

Oh wiat

that's what youj said

sorry

i was doing shit like
8x - lambda * x + 7y = 0
9y - lambda * y = 0
9(8x - lambda * x + 7y) = 0
7(9y - lambda * y) = 0
72x - 72lambda * x = 0

[remote island]

.

lambda = 8
->
(8-8)x + 7y = 0 -> y = 0
lambda = 9
(8-9)x + 7y = 0
-x + 7y = 0
x = 7y

So

the eigenvector is (7, 1) ?????

@lethal estuary

[lethal estuary]

yes but you can confirm yourself

[remote island]

How

[lethal estuary]

what does it mean for a vector v to be an eigenvector of A?

[remote island]

idk

[lethal estuary]

Av = lambda * v

[remote island]

Okay so

[remote island]

Wait

whic' lambda

both??

[lethal estuary]

no... you have 2 lambdas and 2 eigenvectors that go with those lambdas

they are separate

[remote island]

huh

[8 7] * [0 1] =
[0 9]

The number of oclumns must equal the number of rows

[remote island]

So how can that be true

The only way it works is if you have 1x1 matrix and multiply it by a vector in 1D lolz

[lethal estuary]

They are compatible for multiplication

I recommend you learn these concepts first, instead of applying formulas

[remote island]

Why would they be compatible for multiplication

I know how to multiply matrices

[remote island]

And that's a condition for that

Wait

It's [0
1]
isn't it??? @lethal estuary

Isn't the answer just vector

(7, 9)

Well

If my lambda is 8

[remote island]

and I multiply it by

I don't get (7, 9)

Am I fucked? @lethal estuary

@blissful condor could you pls help me since cwatson died a tragic death

[blissful condor]

i’m too sick rn sorry

not thinking right

[remote island]

@trail mango could you plz

[remote island]

get better

white willow bark extract

is amazing

aspirin is bad for you

[trail mango]

sorry i have to mourn cwatson's tragic death

[remote island]

If you can't multitask

How are you going to handle mournign two deaths at the same time

<@&286206848099549185>

[remote island]

Question:

[cedar bobcat]

where

[remote island]

I know the lambda values

So I tried to confirm that they're right by

Av = lambda * v

[8 7] is A
[0 9]

Lambda is 8

[remote island]

Eigenvector is (0, 1)

And it seems that it's wrong

Av != lambda * v @cedar bobcat

[cedar bobcat]

can't help with eigenvectors and eigenvalues yet

<@&286206848099549185> someone help bro

[frosty cedar]

Hello

[tranquil pine]

!15mins

[final saddle]

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.

[cedar bobcat]

if you have time to be annoying, maybe help this guy

ok thanks

[remote island]

My brother in christ

I have found

that for eigenvalue 9

I do get (63, 9) and (63, 9) in both

[cedar bobcat]

i have 0 clue what you mean atm

[remote island]

I am saying

That in all likelihood the eigenvalue 8 is wrong

The quesiton is why

[remote island]

It has been calculated from and it's seen that I didn't make mistake with ergard to the eigenvalue

[cedar bobcat]

fine

[remote island]

My brother in christ

I have foudn my mistake

The correct eigenvector is
1
0
not
0
1

[cedar bobcat]

give me approximately 2 business mins to check why your values would be wrong

[remote island]

My dyslexia was my doom

[cedar bobcat]

oh u already

ok good

[remote island]

Dude

It's correct now

GG

[cedar bobcat]

have you considered simply stopping being dyslexic?

[remote island]

Alas, we have won a battle, but not a war

[remote island]

I'm too much of a pussy for an rng reroll

You'd have to kill me brother

And hope reincarnation is real

May I be reborn as a cat

Wait

Are cats dyslexic

[cedar bobcat]

you know ur a pretty cool dude

[remote island]

Dyslexia is a learning disability where your brain processes written language differently
Cats sure process language differently than humans

[cedar bobcat]

add me so we can discuss the liklihood of cats being dyslexic

[remote island]

Looks like I have to hope that I get reborn as a human

[cedar bobcat]

also uh maybe you should close this channel now

[remote island]

Done

[cedar bobcat]

before some highschooler mod comes by

[remote island]

Okay

next question

Find the distance between points A(2,3, 4) and B(3,4, 5) in the space E^3

Gotta find the formula

[cedar bobcat]

should be fairly straight forward

square root of the sum of the differences squared

like pythogreas

works for 3 dimensions too

[remote island]

are you sure?

[cedar bobcat]

yes

[remote island]

so

the answer is sqrt(3)

[cedar bobcat]

ye

[remote island]

Find the distance between lines x + y = 0 and x + y = -1 in the space E^2

Okay

This is my plaun

If they intersect, then the distance is 0

If they don't, then they're parallel

If they're parallel, then they're seperated by a constant distance

Then we take a point (0, 0) as an example

Calculate the distance to the second line

[remote island]

So just subtract them from each otherand we see that they don't intersect

cause 0 != 1

[cedar bobcat]

yep yep they're parallel

[remote island]

Now

[cedar bobcat]

take x=0 for both equations

the distance would just be the distance of y's, right?

[remote island]

x + y = -1 -> x + y + 1 = 0

Numerator is |1(0) + 1(0) + 1|
Denominator is sqrt(2)
The answer then is sqrt(2)/2

[cedar bobcat]

woowo hold on now

[remote island]

??

[cedar bobcat]

since ur case is pretty simple

the first equation is y=-x

and the second y=-x-1

just graphing these should give you the answer

they're two parallel lines with distance

you guessed it

1

[remote island]

Dude

Since when do dyslexics graph stuff

Perhaps as a cat.........

[cedar bobcat]

fair

but u gotta see it

[remote island]

Why

[cedar bobcat]

because the second line is simply the first

but moved down by one unit

[remote island]

Dude

You're a genius

I didn't notice it

I just plug-and-chug

A Consequence of Industrial Society

Ok next

[cedar bobcat]

i am all ears

[remote island]

Vectors a, b,, c, have coordinates: a(3, 4, 2), b(0, 3, 7) and c (0, 0, -3) in the orthonormal basis. Calculate the volume of a parallelipiped spanned by a, b, c

Now wtf is the orthonormal basis

[lethal estuary]

no, 8 is an eigenvalue

[remote island]

Yeah we've solved it

I wrote the eigenvector the other way around

But ty

[remote island]

Do you have any idea hwo to solve this

Volume is a * b * c, no?

So like do a dot product, of, say, b and c

So like
0
0
-21
?

Multiply it by a and you get
0
0
-42
?

i got negative volume bruh\

@lethal estuary am I a magician or just stupid

[lethal estuary]

that's not true, no

[remote island]

What did I do wrong

[lethal estuary]

are these all homework problems, or what? they're pretty different

[remote island]

Last year's exam

I'm just solving it to prepare

[lethal estuary]

so study your course notes. presumably you covered volumes of parallelepipeds

[remote island]

We actually haven't

We're divided into two groups

The other group has, we haven't

The class itself is also divided into exams from lectures and whatever the lessons where you solve problems are called

So like we haven't done any problems like this, yet we have an exam from it tomorrow lol

Could you pelsae help me

Isn't the volume a * b * c

@lethal estuary okay, chatgpt just says that I need to use an absolute avlue

So the volume is 42 ig

But it also calculated b * c like this.
Is it retarded?

[cedar bobcat]

these types of questions are boring

u have to check notes written in class

get it from the other group

[remote island]

Too late for that

Could you at least please tell me if I'm correct

8 questions left

[cedar bobcat]

i don't know

[remote island]

Isn't it easy to check

[cedar bobcat]

say axb is the length of the cross product

what you get you do the scalar product with c

yeah i knew it

very boring, very long

[remote island]

Wouldn't say so

That it's long

Anyway

I have an interesting question

nwo

Two interesting questions

Is the question idiotic or am i just stupid

Find dimension of the vector space of all real matrices of fifth degree

My contention is that if we have a matrix with n rows and m columns

The degree of that matrix is max(n, m)

So like, if we have 5 rows and 6 columns, the degree is 6

On the other hand

[cedar bobcat]

you sure it is?

[remote island]

The dimension of a vector space is n * m

[cedar bobcat]

ive never heard of degree of matrix

[cedar bobcat]

ok nvm its pretty straightforward

take two vectors, calculate their cross product
then that resulting vector calculate its scalar product with the third vector

and there you go

hopefully it actually comes up in your exam

because its fairly simple

[remote island]

Wrong translation

Solved it

nvm

On a line x+2y = 8 in the space E^2 find a point that lies the closest to the point (1,1)

nvm

gg

thanky ou all

.cloes

.cloes

.close

[final saddle]

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[real juniper]

how do i find the closed form of this

[clear moon]

2^n * z^(2n)

is the same as (2*z^2)^n

does that help you?

[real juniper]

nah i have no clue what to do

[clear moon]

have you seen a geometric series before?

[real juniper]

yes

[clear moon]

so the sum from n = 0 to infinity of x^n is 1 / (1 - x)

by geometric series

this is the same thing but x = 2z^2

[real juniper]

so the closed form is

1/1-2z^2

[clear moon]

yes

[real juniper]

that was easy

i just dont know what closed form mean

[clear moon]

if you can get rid of the summation

and write it as a fixed answer without an infinite sum

[real juniper]

why is the closed form just the sum of x^n

i know the sum is 1/(1-x) of x^n

havent i just found the sum now

[clear moon]

is the question why the sum from n = 0 to infinity of x^n is the same as 1/(1-x)?

@real juniper

[real juniper]

no, i know it is

but why is that the same as the closed form

[clear moon]

why are the two equivalent?

[real juniper]

yeah

[clear moon]

well an infinite sum can equal a finite value

you'd say the sum converges to 1/(1-x)

as you add more and more terms

[clear moon]

unless you mean you want a proof of why that is the closed form?

[real juniper]

yeah, coudl u

idk how to

[clear moon]

let S equal your sum

so S = 1 + x + x^2 + x^3 + x^4 + ...

then

S - 1 = x + x^2 + x^3 + x^4 + ...

S - 1 = x * (1 + x + x^2 + x^3 + ...)

that thing in parentheses is exactly S

so S - 1 = x * S

(1 - x) * S = 1

S = 1 / (1 - x)

[real juniper]

arh

ok

ty

[final saddle]

@real juniper Has your question been resolved?

Channel closed

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[fallen vigil]

could someone explain limits. so a universal cone is a limit? but cant we just pick the empty set as the universal cone always? im probably understanding something wrongly

[dusky olive]

categorical limits you mean

[fallen vigil]

yea

[dusky olive]

what do you mean by the empty set

you are correct that there is a connection between terminal objects and limits

[fallen vigil]

wouldn't L being singleton make it trivially true

not empty as the we can't have morphisms to it

[dusky olive]

the initial object in the index category is indeed the limit of the diagram, but note that L being final in the larger category does not ensure that the above diagram commutes

[fallen vigil]

nvm it wont work 😭

yea that, it wont commute generally

[dusky olive]

the connection you are seeing is not fictitious btw, the initial object in the index category (if one exists) really does get mapped to the limit of the diagram

[fallen vigil]

can i think of cones as having information of the index cat?

[final saddle]

@fallen vigil Has your question been resolved?

[dusky olive]

I didn't respond because I'm not sure btw, <@&286206848099549185> does anyone know cat theory better than me and can answer this

[final saddle]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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[lament grail]

Each year, the value of an investment increases by 0.49% of its value the previous year. Which of the following functions best models how the value of the investment changes over time?
Group of answer choices

A) Decreasing exponential

B) Decreasing linear

C) Increasing exponential

D) Increasing linear

[lament grail]

Is C right?

no i mean

D

[tranquil pine]

well is the amount it changes by a constant amount or does it change

[lament grail]

it's just how it's written

i dont get ur q

[tranquil pine]

Does the investment change by a constant amount every year

[lament grail]

idk

[tranquil pine]

or does the amount it changes by change?

[lament grail]

it's how they wrote the q lol

so idk what is ur question exactly

[tranquil pine]

Im asking you the question to see if you can understand the question theyre asking

??

[lament grail]

yes

[tranquil pine]

If you cant determine if the rate of change is constant or increasing then you need to touch up on your reading skills

[lament grail]

they're asking if it's linear or exp. increase

it'sincreasing tho

[tranquil pine]

yes they give you that

now reread the question

[lament grail]

how, it's math not reading

[lament grail]

ok

[tranquil pine]

and determine if it changes by a constant amount or not

[tranquil pine]

If you cant understand the question u cant do the maths???

[lament grail]

1.49^x

[tranquil pine]

and is that exponential or linear

[lament grail]

exp.

but why not 1.49(x)

oh yes

[tranquil pine]

every year it increases by more

[lament grail]

so exp.

[sharp goblet]

A = p(1+r/100)^n

[lament grail]

yes

if i put 1.49(x) and 1.49^x and compare

[sharp goblet]

,w y = (1+x/100)^n graph

[soft zealot]

Results provided by WolframAlpha

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

Requested by itzmecairo

[lament grail]

woah

[sharp goblet]

Lookz like expo

Rise

[lament grail]

ye

s

but the graph is in 3d

1.49(1)=1.49
1.49(2)= 2.98

1.49^(1)=1.49
1.49^(2)=2.2201

first one increased by 100%

second increased by 0.49%

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[tranquil pine]

Any idea

[frank ginkgo]

Hi

[final tangle]

read the bot message
repost your question in a new channel

[frank ginkgo]

Is the integral this One?

$\int{\dfrac{{x}^{8}+4}{{x}^{4}+2,{x}^{2}+2}}{;\mathrm{d}x}$

[runic needle]

$$ \int \frac{x^8 + 9}{x^9 - 2x^2 + 2} \dd{x}? $$

[soft zealot]

mayer-vietorUs

jandro

[tranquil pine]

This

[frank ginkgo]

Hahaha

Wait

[tranquil pine]

But with a

[runic needle]

so no dependence on n?

[tranquil pine]

Minus

[final tangle]

read the bot message
repost your question in a new channel

[tranquil pine]

It's x^4- 2x^2 +2

[frank ginkgo]

$\int{\dfrac{{x}^{8}+4}{{x}^{4}-2,{x}^{2}+2}}{;\mathrm{d}x}$

[soft zealot]

jandro

[tranquil pine]

Yeah

[frank ginkgo]

Its this ?

[tranquil pine]

Exactly

[frank ginkgo]

Ok

Let me take a look

[final tangle]

read the bot message
repost your question in a new channel

are these messages invisible?

[frank ginkgo]

Oh yes

[tranquil pine]

Oh

[frank ginkgo]

Yes

@tranquil pine open a new help

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[royal schooner]

is there sm way to derive trig values for 37

[royal schooner]

im supposed to remember its values. unlike other angles tho idk how to derive it

[blazing condor]

Ya…. You can use the McLaren series for sin of x

[hybrid heath]

Like $\sin 37^{\circ}$?

[soft zealot]

SWR

[royal schooner]

yes

[royal schooner]

uh we havent done that yet

is there no other way

[formal trail]

37 and 53 degrees are (approximately) the angles in a 3-4-5 triangle

[blazing condor]

There are a lot of approximative ways

[royal schooner]

yeah but without knowing that

[hybrid heath]

I can give you an exact value, but it would have imaginary numbers in it....

[royal schooner]

with trig identities/geometric properties

[final tangle]

sin(36°) is derivable

[royal schooner]

huh?

[hybrid heath]

!xy

[royal schooner]

how

[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.

[blazing condor]

Well it’s half the angle of 74*

[final tangle]

36 72 72 similar triangle shenanigans

[royal schooner]

this is it lol

[formal trail]

if it's an angle you're expected to remember then i think remembering which triangle it comes from is the simplest way

[royal schooner]

ig ill just remember this

[royal schooner]

aight

[final tangle]

still only approximate though

[royal schooner]

yeah we were given those values in class so should be fine

thx

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[autumn geode]

oops I need a lil help decoding this

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[autumn geode]

.reopen

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[gilded flame]

Somehow the answer has 4a instead of 2 sqrt 2 a, which is what I am getting?

[gilded flame]

That's the answer

I think I'm on the track, except for that sqrt2 not being a 2

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@gilded flame Has your question been resolved?

[gilded flame]

<@&286206848099549185> 🥲

[gilded flame]

<@&286206848099549185>

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@gilded flame Has your question been resolved?

[gilded flame]

<@&286206848099549185> 🥺

[fallen vigil]

aw im unsure too :(. ok thats all i shall say cuz not my channel now

🥺

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@gilded flame Has your question been resolved?

[gilded flame]

You can have it back, no one seems to be able to help me

.close

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[fallen vigil]

cant be saved

too deep in math well

[slow canyon]

y did u do 1-cosu = sin u?

[gilded flame]

= sin u/2

Isn't that a trig identity?

.reopen

[final saddle]

✅

[slow canyon]

i believe its 1-cos^2x = sin^2x

[gilded flame]

I think I messed up the half angle identity 😬

Thanks for pointing that out that's got to be it

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[slow canyon]

np!

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[final saddle]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

@tranquil pine Has your question been resolved?

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[elfin slate]

please help me with 47.

i couldn't pair 47. with any graph above

i was assuming that

f(x) = x+5

but is my approach wrong?

[elfin slate]

is this wrong?

[elfin slate]

if I use this, when x = -5, y should equal 0

but none of the graphs shown above show that

[tranquil pine]

if you know the graph of f(x), and if u make some kind transformation like in this case f(x+k), the graph will horizontally move k units leftwards

and this is your f(x)

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[waxen jay]

how do i find the limit of this

[waxen jay]

would this be indeterminate since 2sqrt(x) will go to infinity, and x ln(x) will go to infinity

im not so sure about whether or not x ln (x) goes to infinity tho

[dense coral]

both x and ln(x) go to infinity, so their product also goes to infinity

[clear moon]

this thing is definitely indeterminate

[dense coral]

mhm

[clear moon]

maybe before you jump into using l'hopitals rule, there might be a nice simplification you can make first

hint hint

you don't need l'hopitals here if you do some algebra

[dense coral]

L'H 😠

kidding, L'H is fine, but I prefer more standard algebraic approaches lol

[waxen jay]

im honestly not sure what simplification i could do here

[dense coral]

think about the sqrt(x) in the numerator

we tend to prioritize getting rid of square roots, because they're annoying

how can you get rid of it?

[waxen jay]

square it?

[dense coral]

well, you can't just square it willy-nilly

that would be changing the expression

[waxen jay]

then square the denominator as well?

ok yeah nvm

[dense coral]

nono

you can't just square everything

well, you could, but then you'd have to take the exponent out of the limit too

I was thinking of smth simpler

[waxen jay]

ok yeah im not too sure how else u could simplify that honestly

[dense coral]

here's something: how would you simplify 1/sqrt(2)?

what step would you take?

[waxen jay]

oh, multiply both the numerator and denominator by sqrt(2)?

[dense coral]

yes!

[waxen jay]

ohhh

[dense coral]

so what would you do for our limit here?

[waxen jay]

multiply the numerator and the denominator by sqrt(x)?

[dense coral]

yes!!

[waxen jay]

htank you!!!

[dense coral]

tell me what you get

or can you take it all from here?

[waxen jay]

i think i got it from here

thank you tho!

.close

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[dense coral]

[elfin slate]

OMG i didn't even read the question no wonder i was so lost

OMG had i known that the red graph is f(x).....

would've been so much easier

tysm

🙏

[tranquil pine]

lmao np

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[waxen jay]

Is there a trick I can do here so i dont have to do l hopitals rule as $\lim$ x -> oo $\frac{-\frac{2}{x^2+2x}}{-\frac{1}{x^2}}$

[soft zealot]

dingypine

[dense coral]

@waxen jay first things first, I would get rid of this nested fraction

oh hi smay!

[blissful condor]

match coefficients instead, notice that dividing by 1/x^2 is the same as saying we have a factor of x^2 in the numerator. did you put it into this form yourself, or was it given to you like this?

[blissful condor]

hello mountain friend

[dense coral]

hello mayday

[blissful condor]

can we get much higher

[dense coral]

higher!

btw, awesome post in #math-pedagogy

I'll let you have this one

I'll go find someone else to help

[blissful condor]

. reference

[waxen jay]

it was given like this

[trail mango]

[blissful condor]

okay yes there is a way to do it without l’hopitals rule, and they were being sort of tricky to give it to you like that

we want to rewrite this fraction

so that there isn’t any nested stuff

[waxen jay]

ok i see

so i guess i can just flip -x^2 and multiply it by the other stuff?

[blissful condor]

yeah, thats right (you should write it out still, so that i can see where you’re at/make sure things look right)

[waxen jay]

alright sounds good

alright ima write it out and take pictures cause thats way easier lol

[blissful condor]

that’s fine, i don’t expect you to tex everything lol

[waxen jay]

alright so just wrote it out

and multiplied it

[blissful condor]

actually need to make sure that your minus sign on the left doesn’t get misplaced

[waxen jay]

just factored it out

wait i think i forgot an x on the numerator

[blissful condor]

that’s not the issue, your form was fine before

but $-(\frac{1}{x^2+2x}) = \frac{1}{-x^2-2x}$

2x

[soft zealot]

smay

[waxen jay]

why did you put the - in the numerator tho?

denominator**

[waxen jay]

there already was one up here

[blissful condor]

sorry, i’m going off this picture

which has a minus sign out front of the top fraction

[waxen jay]

oh yes thats right

thats what the problem has

[blissful condor]

so it seems like we should get $$\frac{2x^2}{x^2+2x}$$ as the new thing we’re working with in the end

[soft zealot]

smay

[waxen jay]

oh yeah that makes sens okay

then you can factor out an x and just take the limit right?

[blissful condor]

do what you think is best from here, personally i would factor out x^2 in both numerator and denominator (it’ll leave a 1/x in the denominator that we won’t care about), and then try taking the limit

but a trick to doing these limits is just compare the highest order term

[waxen jay]

okay i see, thank you

i appreciate it

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[dense coral]

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[violet totem]

you have to make a force that cancel out (A+B)

first find the force of A

no

do it like this

because a goes 8 to the right and 5 up

what is b then?

no but almost, remember it goes to the left..

yes

what is A+B then

are you guys learning about vectors?

anyway the net for is a plus b

so you should know what a vector is?

I don't know how I can help you solve it when I don't know which level of math you're supposed to solve it with

https://www.youtube.com/watch?v=Ej3ZVxljJfo

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[violet totem]

you can not have something negative in a square root.

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@uncut vessel Has your question been resolved?

[uncut vessel]

No

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[full halo]

,rccw

[full halo]

Is this correct?

What does it mean for the graph that y=0 but x anything

<@&286206848099549185>

[copper terrace]

x can be any real no.

[full halo]

Yeah but how to draw

y=0

[copper terrace]

draw x axis

coz y=0

is represented in graph like that

[full halo]

Ah

So its all x

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[tranquil pine]

Is someone ok with helping me with math for an hour or 2

[rustic sinew]

!da2a

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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/

[tranquil pine]

Someone help me with math for 1-2 hours i need help with studying

[green ibex]

!volunteers

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[tranquil pine]

.reopen

[final saddle]

✅

[tranquil pine]

How do i solve this

[rustic sinew]

!status

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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

[tranquil pine]

1.I don't know where to begin.

<@&286206848099549185>

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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.
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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

[tranquil pine]

.close

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[uneven goblet]

.reopen

.reopen

[tranquil pine]

halp

[tranquil pine]

how do you even get this

how do you get 0.559

do you cross multiply with a rational function or?

[marble hawk]

Divide both sides by 1.666

1.665

[tranquil pine]

makes sense tbh

but

wouldn't that give you (x-3)/1.665

or are you just using

elimination

to eliminate both 1.665

[lethal estuary]

1.665 / 1.665 = 1

[tranquil pine]

yes

i meant for

x-3

or do you just eliminate the 1.665

since it would equal to 1

and x-3)1 equals x-3

[lethal estuary]

yes, (x - 3) * 1 = x - 3

[tranquil pine]

can i just say x=3.6

i don't see the need to have 3.599

[lethal estuary]

it depends on how many significant digits they ask for

[tranquil pine]

they don't really specify for any

they just want the constant speed

x= speed btw

in miles

idk i also plugged it in my calculator and 1/1.665 is 0.6

[lethal estuary]

,calc 1 / 1.665

[soft zealot]

Result:

0.6006006006006

[lethal estuary]

I guess 0.6 would be fine

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[tranquil pine]

halp again

[tranquil pine]

ok guys

so let's say i wanted to calculate the total time in air for this graph

ball throw situation by the way

would i take the total distance from the y intercept to the next x intercept

in this case 0+3.349

since you know you're adding x

or would you have to add both x intercepts

that wouldn't make sense since you can't really have negative time

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[kindred lantern]

can someone help me how do calculate this integral without using complex numbers?

[kindred lantern]

yes...

[odd rivet]

ops

error function doesnt work here

[kindred lantern]

why?

[odd rivet]

you can change the dy and dx

order of integration

[kindred lantern]

yes

i tried

[odd rivet]

if you draw a picture

or use theta functions

[hybrid heath]

!show

[final saddle]

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

[hybrid heath]

If you change the order of integration, you need to change your integral bounds also

If you integrate dx first, then it's not from 0 to 1 anymore

[kindred lantern]

but in the beggining i changed

[swift chasm]

But look that at the end you have something dependent of x, it should be a constant.

[kindred lantern]

why?

to change the order of integration

is not just change the order of integral and the order of dx and dy?

[hybrid heath]

Look at the integral bounds of your dy intergral. They are functions of x. This is because the dy integral is happening first, and is being taken over a non-axis-aligned rectangular region. The exact bounds of your dy integral depend on your x coordinate. But if you integrate dx first, then this requirement will switch. The exact bounds of your dx integral will now depend on the y coordinate. Draw some generic 2D region and see how the limits would change depending on how you integrated over that region, or review your book, which I'm sure gives a more thorough explanation

[kindred lantern]

thank you @hybrid heath

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[sonic crystal]

I want to find the value of t in the arithmetic sequence t-5, 3t, 3t+1 but I’m stuck on how I would do that

To find the common difference I just subtract 3t - (t-5)?

[hybrid heath]

The difference between 3t and t-5 must be equal to the difference between 3t+1 and 3t, no?

[sonic crystal]

Idk I haven’t done this before lul

hello chart

[scarlet sequoia]

it's an arithmetic sequence, so to go from one term to the next, you add a constant that remains the same

How much are we adding to go from 3t to 3t+1?

[sonic crystal]

Just 1

[scarlet sequoia]

yes

how much are we adding to go from t-5 to 3t?

[sonic crystal]

Well it can’t be one right because t-5 + 1 is t-4?

[scarlet sequoia]

?

it's an arithmetic sequence

so it has to be 1

[sonic crystal]

Oh

[scarlet sequoia]

we always add the same amount to go from the previous term to the next one

[sonic crystal]

okay

So what do we do next?

[tulip coyote]

See here

[scarlet sequoia]

how much are we adding to go from t-5 to 3t?

[sonic crystal]

t-4 = 1?

[scarlet sequoia]

no

that's not how much you added

[sonic crystal]

3t - (t-5) = 1?

[scarlet sequoia]

yes

[sonic crystal]

oh okay

then just solve for t

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