help-10

[compact raptor]

couldnt we just do like

x=t and then instead of x in that y equation we could do t?

[sonic anchor]

so the end of that is how far we are right now

but they also want a parametrization

[compact raptor]

yeah

[sonic anchor]

and we use y in terms of x to actually find that

[compact raptor]

but any parametrization works right?

so does my idea work

finding y in terms of x using the example abvoe and then setting x=t

?

or no

[sonic anchor]

nope

it would not satisfy our differential equations regarding y

[compact raptor]

bruh

[sonic anchor]

y'=-4ky right

[compact raptor]

how can it be this hard there has to be a way

[compact raptor]

but what about the dt

[sonic anchor]

wdym

y' if y=3/25 * t^2

y'=6/25 * t

[compact raptor]

the dt beneaht it

[sonic anchor]

yes it means you are differentiating with respect to t

[compact raptor]

so we can just ignore dt here?

[sonic anchor]

so if y=3/25 * t^2 as you suggest

y'= 6/25 * t

which does not hold

[compact raptor]

where di d u get t^2

[sonic anchor]

you just said you wanted to take the expression y=3/25 * x^2 we found right

and just set x=t

[compact raptor]

oh

ok

[sonic anchor]

it would not satisfy the differential equation

[compact raptor]

so if we have y=3/25*x^2 what do we do

wcan we just plug in y

[sonic anchor]

i mean im trying to tell you

but you keep getting your own ideas 💀

[compact raptor]

okay

please

step by step explain this

with the bot thing that shows equations n such plz

[sonic anchor]

so the differential equation $x'=-2kx$

[warm shale]

Køter

[compact raptor]

ok

[sonic anchor]

more specifically the differential equation $x'=kx$

[warm shale]

Køter

[compact raptor]

why kx

why can u just ignore the -2

[sonic anchor]

is very popular and has the soluton $x=C * e^{kt}$

[warm shale]

Køter

[sonic anchor]

ok its kind of confusing notation

k is actually -2

hmm

start over so its not as confusing

[compact raptor]

ok

[sonic anchor]

$x'=cx$

[warm shale]

Køter

[sonic anchor]

$c=-2$ n our case

[warm shale]

Køter

[sonic anchor]

so we end up with $x=c * e^{-2t}$

[compact raptor]

do u know where this rule comes from

like where i could search it up?

[warm shale]

Køter

[sonic anchor]

just search y'=ky and it will pop up

there are proofs for it but i dont think its necessary for you

you could just differentiate the solution to build a bit of trust

[compact raptor]

wait

wouldnt c just be our point?

okay i get it now

thank u

[sonic anchor]

they are different c

[compact raptor]

that equation helps

[compact raptor]

ah ok

[sonic anchor]

so we have $x(t)=c * e^{-2t}$ and are trying to solve for c

[warm shale]

Køter

[compact raptor]

i get it now

[sonic anchor]

we use our expression $y=\frac{3}{25} * x^2$

[warm shale]

Køter

[sonic anchor]

to solve for c could you do that

[compact raptor]

wait

okay i get this

is k t in our case?

then what is the x

[sonic anchor]

no, x=t

k=-2

and C=k=c

ik its dumb

[compact raptor]

wait but

then why do we have

-2k

[sonic anchor]

$\frac{d}{dt} ke^{-2t}=-2ke^{-2t}$

[compact raptor]

why is the answers online this then?

is it because 5, 3 is the point?

[warm shale]

Køter

[sonic anchor]

we have a constant k on it we need to find

i guess they do coincide with the points but thats a coincidence

[compact raptor]

man

why is this problem so hard

[sonic anchor]

we need to actually solve for it using the expression $y=\frac{3}{25} x^2$

[warm shale]

Køter

[compact raptor]

how

do we solve it using that

plz help

[sonic anchor]

we have the point (5,3)

[compact raptor]

yes

[sonic anchor]

so $3=\frac{3}{25}x^2$

[warm shale]

Køter

[sonic anchor]

we have an expression of x

[compact raptor]

yeah

[sonic anchor]

so $3=\frac{3}{25}(ke^{-2t})^2$

[warm shale]

Køter

[compact raptor]

why does x equal that

[sonic anchor]

ok lets go over that again, because the notation is insanely confusing

i understand why it is

solution to the general differential equation $x'=ax$ is $x= k e^{at}$

in our special case a= -2

[compact raptor]

ok

why ae^at?

okay

is C the point we plug in?

since we get 5, 3?

[sonic anchor]

so $x'=-2 * x$ and $x= k * e^{-2t}$

[warm shale]

Køter

Køter

[sonic anchor]

we dont just plug a point in

you've noticed a pattern and just tried to take a shortcut

[compact raptor]

this is actually confusing

[sonic anchor]

its $3=\frac{3}{25}(k * e^{-2t})^2$

[warm shale]

Køter

[sonic anchor]

at t=0

$25=k^2$

[warm shale]

Køter

[compact raptor]

ok

oh

[sonic anchor]

k=+-5

[compact raptor]

thats why k=5

[sonic anchor]

yes

and you do the exact same for y

$y(t)=k * e^{-4t}$

[warm shale]

Køter

[sonic anchor]

$k * e^{-4t}=\frac{3}{25} * 5^2$

[warm shale]

Køter

[sonic anchor]

at t=0

$k=3$

[warm shale]

Køter

[compact raptor]

ok i get it

[sonic anchor]

so if you just trust me that x(t) and y(t) are given like $k * e^{-2t}$ and $k * e^{-4t}$ it makes sense right?

[warm shale]

Køter

[sonic anchor]

so since i prob couldnt explain that part to you 100%, you can just look up that yourself

[frail mortar]

Pls help, the problem:"The graph of the quadratic function y= f(x) passes through the points with coordinates (0,2), (2,0) and (4,4). Determine f(x)"
Tried to solve by using this formel: f(x)=ax^2+bx+c, but failed to get the answer right, sorry for my english, english is not my first language, but anyway have exam in 2 days really need to solve this problem. If you can solve it please send how you solved from step 2 step, any help is really appreciated 🙂

[compact raptor]

yeah

[compact raptor]

so that our C?

oh wait

no

its our k

and since x=ke^at

we write it as

x=5e^-2t

[sonic anchor]

yes

[compact raptor]

and y=3e^-4t

but we write it

as x(t) and y(t)

[sonic anchor]

yea cuase its a function of t

[compact raptor]

ah thx

thank u very much

[sonic anchor]

yea np, i think i waffled the y'=ky explanation but just look that up if you really want

[frail mortar]

Hey, guys I didn't really get the "how to get help" instruction? Can i post my math problem here, if you are a helper?

[sonic anchor]

you post it in one of the available help channels

[sonic anchor]

#help-3

[frail mortar]

thanks!

[sonic anchor]

nvm it just got taken 💀

[frail mortar]

How do I know if the channel is available

[sonic anchor]

#❓how-to-get-help

[obtuse pebble]

@compact raptor Has your question been resolved?

[obtuse pebble]

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[untold bobcat]

Hi how can one determine the number of variables in the 2^19 compositions of 20. The question doesn't mention the number of variables but when i saw the solution it used four variables.

[forest sinew]

,rotate -90

[forest sinew]

summand?

what summand

also what composition

what a stupid question

@untold bobcat it sounds like theyre talking about like

it suggests to me that you would go through each number 1-20

and decide whether to write it or not

so maybe they mean 1+ 2 +3+4+5+...

or maybe missing numbers

[obtuse pebble]

@untold bobcat Has your question been resolved?

[obtuse pebble]

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[shadow lava]

would this 2^x have to go to the left of the limit? or could it still go to the right of the limit as a common factor

[shadow lava]

I've never seen it like this before where a common factor is to the left of the limit

[latent walrus]

you can factor things out of limits

you dont have to pull it out - it just makes sense to do so. you could leave it as lim[2^x * (2^h-1)/h] if thats what you mean but theres no need to

[shadow lava]

OK

I feel like I just watched a magic trick, but it's math

d/dx of e^x

do most people think about it like this where they fully understand everything going on? or do they just memorize d/dx of e^x = e^x

[latent walrus]

i think if people wanted to do it they could, but many probably just memorise d/dx(e^x)=e^x

[shadow lava]

OK thanks

.close

[obtuse pebble]

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[runic void]

Why is it specifically written 0 not equal to x element of R?

shouldn't it be true if it was for all x?

1*0 = 0

[unreal musk]

[well assumedly they would not have proven that 0*a = a, so they exclude it there - you can show that it's true from the axioms though]

[runic void]

ohh,

well, im getting started

literally first page in analysis

[unreal musk]

I see I would guess that they might get you to show that 0*a = 0 for any real a at some point, maybe?

At least from my experience they get you to deduce extra properties like that(!)

[runic void]

makes sense

I've taken some number theory classes, and an introductory proof class

is it good enough for real analysis?

but the proofs in number were only the major ones, infinitudes, fundamental theorem, Euclidean as such

[unreal musk]

I would think so, it depends on the way they introduce the course, but in general I think you get let into analysis gently, as long as you have good algebra skills and all

You don't really need too much to get into [introductory] real analysis in my opinion

[runic void]

i actually wanted to get in

but i wanted not trip in

well, basically i didn't spend enough time in pre-calculus

tho calculus concepts were intuitive

kinda tripped in problems because of pre calculus

so i'm trying to get all the pre-requisites done so not trip off

[unreal musk]

Ah, what did you happen to cover in calculus? Did you do like the epsilon-delta definition of a limit and all?

[runic void]

not that

i mean say usual calc 1 or 2

those concepts were intuitive and doable

but my algebra skills were poor at the time

soo i kind of had hard time doing problems

so majority of time i was doing pre-calculus while in calculus class

I have almost 2 months of vacation before taking analysis course

so i'm trying to get done all the pre-requistes

[unreal musk]

Ahhh I see I see - I'm not too familiar with what the exact contents of calc 1/2 courses are, but sound real good you're spending the time to prepare with the prerequisites!
Do they state what they are anywhere?

I'm sure you'll be fine though!

[runic void]

yep yep

[unreal musk]

Best of luck with it all!

[obtuse pebble]

@runic void Has your question been resolved?

[obtuse pebble]

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[robust yarrow]

for these ones, to solve using an inverse matrix would i have to put the equation in a matrix and solve for x and y?

[timid silo]

Ax = b => x = A^(-1) b

[robust yarrow]

A = [ 1 , 2 ]
[1 , -2 ]

[timid silo]

correct

[robust yarrow]

ok so then i would find the inverse of that and then multipy that by 2x1 [-1, 3]

[timid silo]

find inverse of A

[robust yarrow]

i got [ 1/2 , 1/2 ]
[1/4 , 1/4 ]

[timid silo]

inverse of A?

check again

[robust yarrow]

ok

im doing 25a btw

[timid silo]

ik

[robust yarrow]

oh

[timid silo]

inverse of A = adj(A)/determinant of A

[timid silo]

wait lemme solve

there

[robust yarrow]

ok i think i got it now

thank you for your help

[timid silo]

np :)

[robust yarrow]

.close

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[primal idol]

Can two level curves of a functiom intersect?

Can paraboloids be a good example of this?

[royal basin]

can they?

[primal idol]

I think so... its horizontal and vertical contour curves do intersect

[royal basin]

do you have a picture of the thing youre talking about

bc i think there is some confusion on your end as to what "level curve" means

[obtuse pebble]

@primal idol Has your question been resolved?

[obtuse pebble]

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[wet raft]

Hi, I'd like to compute the convolution product of rect3(t) and rect1(t) and I can't seem to get started

[wet raft]

$\int_{-\infty }^{+\infty }rect_3(\tau)rect_1(t-\tau)d\tau$

[warm shale]

Sam឵

[wet raft]

can I do that ??

$=\int_{-1.5 }^{+1.5 }rect_1(t-\tau)d\tau$

[warm shale]

Sam឵

[obtuse pebble]

@wet raft Has your question been resolved?

[obtuse pebble]

@wet raft Has your question been resolved?

[obtuse pebble]

@wet raft Has your question been resolved?

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[crude pawn]

Can someone show me the process to find the particular solution for dy/dx - 2 = -y if the initial condition is y(0) = -3

I thought i got it right but i put it into a slope field map and it just does not work 😭

[teal turret]

Open a new channel, this one is closed

[obtuse pebble]

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[ionic summit]

for the limit comparison test you want bn to be what the series is overall dominated by right

like as n gets very large

dont see where 1/n^2 came from

[lapis spruce]

What is the question?

Ok

Which part are u stuck on?

[ionic summit]

^

[tardy epoch]

where in this solution specificially?

[lapis spruce]

He separated the two terms

[ionic summit]

hmm? still dont see it

[ionic summit]

why we are comparing to 1/n^2

[nocturne minnow]

@tardy epoch

[lapis spruce]

^

[tardy epoch]

need 5 pings before i can be bothered /s

[tardy epoch]

the 2^n / 2^n "cancels"

what remains after dividing the top and bottom by 2^n ?

[ionic summit]

oh

and

well

that makes sense haha

but wanna double check my logic here I am not 100% comfortable with LCT yet

[ionic summit]

this is my logic

well actually no I guess thats not entirely true I am sorta confused on it

I mean comparing to 1/n^2 makes things nice

but like I dont really know an overall guide

if there is one

like for something like this I cant tell really what to compare to

[lapis spruce]

Have u learnt to do only direct comparison test?

[ionic summit]

Im more concerned on LCT

[lapis spruce]

https://www.youtube.com/watch?v=LBxYQ0TJxYM

[ionic summit]

that's not entirely helpful

Ive seen that

[ionic summit]

and got this out of it

but thats not true for

the one example I posted

• he covers like very simple cases

[nocturne minnow]

You pretty much want to take the dominating term in the numerator and denominator

[ionic summit]

yeee that's what Im thinking too

but 1/n^2 is not dominating

wouldn't the other part of it

[nocturne minnow]

2^n is just a constant

[ionic summit]

OH MY GOODNESS MY BRAIN IS OFF

dldh06

thank you

[nocturne minnow]

So it's pretty much C*n^2

[ionic summit]

wait

actually

sorry one other thing

so we got

1/n^2(2^n) + 1/n^2

1/n^2 is dominating because both are going to 0

and 1/n^2 goes there faster right

[nocturne minnow]

I don't get your question

[ionic summit]

well

we had the original term

of (n+2^n)/(n^2(2^n)) right

that got broken into

1/(n(2^n))+(1/n^2)

and as I think we both are thinking

to do the LCT you want to choose the term that dominates right

and 1/n^2 dominates because both are going to 0, but 1/n^2 does it faster

[nocturne minnow]

Yes

[ionic summit]

okay epic

one other thing

what happens if somehow

the first term

ended up being idk n^3/(n(2^n))

and that goes to infinity right, while the other one goes to 0

what is the dominating term?

[nocturne minnow]

Plug in a large value for n and see which one is bigger

[ionic summit]

so you want the bigger one?

so if both are not heading to 0

then you want the bigger one

[nocturne minnow]

Yes, because the larger dominates

[ionic summit]

just double checking cus idk my confidence is not the best on this

like re-iterating

that's only if both don't go to 0

wait

cus like

1/(n(2^n) is larger than 1/n^2

but 1/n^2 dominates

[nocturne minnow]

Tbh I don't remember, I helped where I could

[ionic summit]

ahhh okay

thank you

.close

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[humble marten]

How do I do these two?

[humble marten]

I don’t know whether I’m on the right track or not

[obtuse pebble]

@humble marten Has your question been resolved?

[humble marten]

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[lapis spruce]

are the two angles given equal??

[humble marten]

for which one?

[lapis spruce]

for the q

the two angles u marked

[humble marten]

i didnt mark thoise

those were given

[humble marten]

and yes they are equal

<@&286206848099549185>

[obtuse pebble]

@humble marten Has your question been resolved?

[humble marten]

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[shadow tangle]

please do not spam-ping helpers

[nocturne minnow]

Don't abuse the ping

It's not going to get you help faster

In fact, it's probably just gonna make people want to help you less

[humble marten]

well idk what to do i opened this 1.5 hrs ago

[nocturne minnow]

Then wait

People have waited for hours before

[humble marten]

i have waited hours

i opened another ticket for the same problem yesterday

didnt get answered

[shadow tangle]

It could help if you posted in the help forum and/or the appropriate channel

[humble marten]

this is the appropriate channel

[shadow tangle]

#geometry-and-trigonometry is also one

[obtuse pebble]

@humble marten Has your question been resolved?

[scarlet dove]

I'm assuming you're referring to the question marked 14?

I can see the triangles in question, what exactly is given besides some angles and side lengths?

[humble marten]

OM?

[scarlet dove]

I mean like do we know any triangles or angles are equal, similar, parallel, congruent, etc

[humble marten]

similar

[obtuse pebble]

@humble marten Has your question been resolved?

[obtuse pebble]

@humble marten Has your question been resolved?

[scarlet dove]

Which triangles are similar?

[rain canopy]

@humble marten can you send a less blurred photo please

[obtuse pebble]

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[sweet jacinth]

Need some eyes to check my calculations and help if I got something wrong.

[sweet jacinth]

Calculating a vector, its length, and its unit vector.

oh, ignore the * between 3^2 and (-3)^2 I meant to put +

<@&286206848099549185>

[obtuse pebble]

@sweet jacinth Has your question been resolved?

[sweet jacinth]

Sigh, looks like no help, going to close.

.close

[obtuse pebble]

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[shadow lava]

to rewrite this expression before I take the d/dx

can someone help me to see exactly what is going on?

I'm taking the 3 from the x^3 and moving it in front of ln, right?

[trim portal]

use chain rule

[sage geode]

Yeah

That 3 also gets squared

So it becomes 9 in front of the ln^2

[shadow lava]

actually I am just talking about simplification

from this to this

[trim portal]

oh I see

[sage geode]

[
\ln^2(x^3) = (\ln(x^3))^2 = (3\ln(x))^2 = 9\ln^2(x)
]

[shadow lava]

but if it gets squared, why does ln stay as ln^2?

[timid silo]

Basically [
\map {\ln^2}{x^3} = \parens{\map \ln {x^3}}^2 = \parens{3 \map \ln x}^2
]

[warm shale]

A Lonely Bean

[sage geode]

\3ln

[shadow lava]

this I understand

[timid silo]

Time to smash this

[shadow lava]

oh I think I get it now

(3ln(x))^2 = 9 * (ln(x))^2

the exponent is distributed to both factors

that can also be written as 9ln^2(x)

because the 3 and ln have both been squared

thank you

.close

[obtuse pebble]

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[timid silo]

how i do this pls ?

oh no i found

.close

[obtuse pebble]

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[obtuse pebble]

@vernal flower Has your question been resolved?

[obtuse pebble]

@vernal flower Has your question been resolved?

[obtuse pebble]

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[mystic violet]

I need urgent help with this question

[pine forge]

yes solve the ratios

[mystic violet]

I forgor how to do 💀

[pine forge]

solve for the value of x

take 4 out from neumerator and 3 out from denominator

then factor out the expressions

it would be easier else the number would get too large

doesnt matter how you solve it. you end up getting same answer

[mystic violet]

I got x's value as 224

[pine forge]

might be

[mystic violet]

For 4x and 3x they worked

But not for 2x

[pine forge]

solve the second ratio and see how it goes

[mystic violet]

Ok

[pine forge]

both should give the same else theres an error

[mystic violet]

x=104

[pine forge]

huh

how its different

[mystic violet]

The question might be wrong

Idk

I'm gonna close this and worry about this later I guess

.close

[obtuse pebble]

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[ruby pebble]

I'm a little confused about the two non-invertible cases
why does the vector [b, d] have to be a linear combinations of the columns of A
and why does it specifically have to be a multiple of [1, C]?

[glacial obsidian]

Because
[
\begin{pmatrix}
a_{11} & a_{12}\
a_{21} & a_{22}
\end{pmatrix}
\begin{pmatrix}
x\
y
\end{pmatrix}

x\begin{pmatrix}
a_{11}\
a_{21}
\end{pmatrix}
+
y\begin{pmatrix}
a_{12}\
a_{22}
\end{pmatrix}
]

[warm shale]

d឵

[obtuse pebble]

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[obtuse pebble]

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[grave wyvern]

Can someone help out with this lim it's +inf I solved it but the number solution is quite sus

[glossy yacht]

all the square roots are approximately the same as x tends to inf

[grave wyvern]

Never mind I did it all wrong

I,did rationalization on both sides

But left it in its place and didn't inverse it

My bad

[teal turret]

It’s ok I forgive u bro

[obtuse pebble]

@grave wyvern Has your question been resolved?

[glossy yacht]

take desmos and graph all the square roots

[obtuse pebble]

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[uncut jacinth]

how come in math s(t) is typically used for a displacement/position time graph?

[uncut jacinth]

what does s stand for

?

[neon eagle]

displacement

[uncut jacinth]

then why not use d

[rigid lintel]

space

s stands for space

[uncut jacinth]

oh interesting

thanks

[rigid lintel]

or spatium

in latin

if you want to be fancy

[obtuse pebble]

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[obtuse pebble]

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[sage dagger]

Hi, I don’t quite understand this, if anyone could explain it to me that would help a lot

[sage dagger]

I know that we have two functions occurring at the same time and that the intervals next to it describe the function

But I am lost where I need to find things for example f(a+3)

[glossy basalt]

it's actually a single function

[sage dagger]

Ohh yeah I forgot that it counts as one whole function

[glossy basalt]

yea

so for (a)

just change all "x" in f(x) into "a+3"

including the conditions

and simplify them

[sage dagger]

f(a+3) = 1/(a+3), (a+3)> 3

?

[glossy basalt]

yea, don't forget the second line of the function

[sage dagger]

Alright was just checking it was right

f(a+3) = 1/(a+3), (a+3)>3

           2(a+3) , (a+3)<=3

And then we have to solve the inequalities you said?

[glossy basalt]

nah, not solve, just simplify

[sage dagger]

Ohh okay

when there’s a comma in the equation just separating the two equations, do we ignore that when simplifying

[glossy basalt]

i dont really understand

and i think it's a yes?

[sage dagger]

Do we just assume it means addition in the equation for example

2x, x<=3

2x + x<=3

[glossy basalt]

$f(a+3)=\begin{cases}\frac1{a+3},&a>0\2a+6,&a\le0\end{cases}$

[warm shale]

OldBiscuit

[glossy basalt]

oh

the comma, the means "when"

[sage dagger]

o

ohhhhh

[glossy basalt]

some textbook would write it like this

$f(a+3)=\begin{cases}\frac1{a+3},&\text{when }a>0\2a+6,&\text{when }a\le0\end{cases}$

[warm shale]

OldBiscuit

[glossy basalt]

or

$f(a+3)=\begin{cases}\frac1{a+3}&\text{if }a>0\2a+6&\text{if }a\le0\end{cases}$

[warm shale]

OldBiscuit

[glossy basalt]

something like that

[sage dagger]

Where does the a>0 come from

[glossy basalt]

oh

a+3>3

[sage dagger]

Ohhh right

Okay that makes sense

So what’s the next step after simplifying

[glossy basalt]

it's done

[sage dagger]

Oh that’s all?

[glossy basalt]

yea, that's it

[sage dagger]

Alright tysm

[obtuse pebble]

@sage dagger Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

22. x-4, x + 7, 45; acute

45 is the longest side and acute is the triangle classification, and you're supposed to find the value(s) of x that make the triangle.

I can't seem to solve this one, I get an answer but it doesn't match the one in the answer key.

[timid silo]

so here's my thought process:
there's some theorem that says a^2 + b^2 > c^2 if acute, therefore

(x-4)^2 + (x+7) = 45^2

(x+7)^2

then you go on and get

oh.....

I forgot to square 45

let's see if that works

so after doing that bs I should get:
2x^2 + 6x - 1960 > 0

take out two to get

2(x^2 + 3x - 980) > 0

now I shall do quadratic formula

ok that worked

I somehow self diagnosed the problem

.close

[obtuse pebble]

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[civic sluice]

How should I go about the rest of this equation?

[frigid prism]

isolate x right

[grand sky]

You can start by getting rid of all the powers

[frigid prism]

so you want to undo all that is covering x

[civic sluice]

How

[nocturne minnow]

Hint $a^{\frac{m}{n}} = \sqrt[n]{a^m}$

[warm shale]

dldh06

[nocturne minnow]

Try making a fractional exponent

Using that concept

[civic sluice]

Like that?

[nocturne minnow]

You still need the parentheses

You can't get rid of them, yet

[civic sluice]

Alright, now what

[nocturne minnow]

What should you do to "remove" the 3/5 exponent?

[civic sluice]

Yeah

I think I should know what something like x + 2 =8 is lol

[nocturne minnow]

If you have x^3/4 = 5 what should you do to get rid of the 3/4 on the left?

[civic sluice]

I don't know

[nocturne minnow]

Do you know how exponent properties work?

You want the left side exponent to be a 1, because x^1 = x

So what do you need to multiply by 3/4 to get 1?

[civic sluice]

4/3

[nocturne minnow]

And whatever you do to one side, you need to do to the other

[civic sluice]

So I should multiply both sides by 5/3?

[nocturne minnow]

You don't exactly multiply by 5/3, you raise both sides to 5/3

Because you have an exponent already so you need to raise that expression by some other exponent and those get multiplied together

[civic sluice]

So like this

[nocturne minnow]

Yes

[civic sluice]

Thanks

.close

[obtuse pebble]

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[ruby pebble]

howcome the determinant gives the area of the triangles? I thought it gave the area of a parrallepiped

[wary vigil]

they're doing 1/2 *

[ruby pebble]

yikes yea just noticed that lmao

thank you

also, I'm allowed to take out the coefficient vectors and put them in a matrix right?

[wary vigil]

what do you mean?

[ruby pebble]

after the first arrow, I get matrix multiplication

I'm allowed to just take out those coefficients and put them into one matric right? like what I did after the } symbol

[wary vigil]

i would personnally write it more like

$\begin{pmatrix} x & y \end{pmatrix} \begin{pmatrix} 4 \ 2 \end{pmatrix}$

[warm shale]

Katharine

[wary vigil]

but you can take the number bit

and use it to create the matrix

[ruby pebble]

ah ok

why write it like that though?

[wary vigil]

of which the determinant gives the area of the parralellogram span by the vectors

i find it much more clear

ever since watching a video

[ruby pebble]

I usually think of the coefficients at the weights

so that makes sense

but the x,y as matrices is a lil funny

to me

do you have that video

by any chance

[wary vigil]

to write down basis vectors as a row and the vector components as a column

it's a video by eigenchris

on relativity

[ruby pebble]

ahh so everything in it will probably fly over my head lol

but alright I'll do it that way anyways

thanks for the help

[wary vigil]

https://www.youtube.com/watch?v=kkJ6J1izNBM&list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQa&index=4

but there are videos before this one

[ruby pebble]

alr thanks I'll try to understand it lol

[wary vigil]

that talk about the history of relativity and such

without the maths

but if this video starts out in a place that doesn't make sense

then watching the first 3 will help

the first like 8 videos aren't difficult in terms of maths

[obtuse pebble]

@ruby pebble Has your question been resolved?

[obtuse pebble]

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[cyan forge]

Im in need of help

[uneven palm]

have you tried drawing it out?

[cyan forge]

I tried but I am brain dead

I have a feeling it is C

though

[uneven palm]

do you have a reason or just guessing

[cyan forge]

I guess 16 / 2 = 8?

[uneven palm]

yep

so why would it also be 4?

[cyan forge]

idk

[uneven palm]

exactly lol

I believe it's just 8

[cyan forge]

what the hell is a quartile

[uneven palm]

cut the list into 4 quarters

and the first one is Q1

for example:

[cyan forge]

ohr

so its 3?

[uneven palm]

yea

[cyan forge]

ok

can you help me with 7 more questions?

what the hell is a IQR-

[uneven palm]

gtg unfortunately

[cyan forge]

oof

[uneven palm]

you can send them tho

[cyan forge]

but I have to get them done today

[uneven palm]

someone else may come

[cyan forge]

what is this

[warm canopy]

Interquartile range

it is Q3 - Q1

[obtuse pebble]

@cyan forge Has your question been resolved?

[cyan forge]

a

but its hard

[warm canopy]

?

[cyan forge]

welp

I just need help finding the answer

[cyan forge]

can you help?

[obtuse pebble]

Channel closed

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[cyan forge]

.reopen

[obtuse pebble]

✅

[warm canopy]

youve been told how to calculate everythin you need to know

[cyan forge]

but

it has an even number of digits

[warm canopy]

you take the number exactly between two numbers

[cyan forge]

a

6 - 4 = 2 ._.

hello?

<@&286206848099549185>

I need to get these 7 questions done today

[frosty spoke]

chatgpt

[cyan forge]

what?

I really need help

[frosty spoke]

same

[cyan forge]

you know this right?

dude,

this is really not helping me

its been 15 minutes

since I pinged helpers

and I still need helppp

[frosty spoke]

same

[cyan forge]

should I ping again>

[frosty spoke]

probably not

[cyan forge]

bruh

its been 15 minutes and nobody responded

[cyan forge]

its been so long, can I please ping helpers?

you know what

imma just

.close

[obtuse pebble]

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[frosty valve]

b

½×b×h?

but i got numbers instead of the form

½(1+2√2)(3+√2)?

[frosty spoke]

what's the issue

[frosty valve]

Idk how to find it in the form

(p+q√2)/r

@frosty spoke

[frosty spoke]

what did you get after multiplying everything out

[frosty valve]

it showed in form now

i think i made a typo

it was in number and decimals

ty

.close

[obtuse pebble]

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[wise trail]

x3+y3+z3=42

[wise trail]

HELLO

TTTtttTTTtttTTTtttTTTtttTTTtttTTTtttTTTttt

.reopen

@here

i found help

[teal turret]

Bruh I told u there’s nothing we can do with that if there’s no instructions

[wise trail]

. x3+y3+z3=k

but k=42

x3+y3+z3=42

[teal turret]

Ok, so what does it want u to do with that equation

[wise trail]

to find y

[thick gyro]

do you know what x and z are?

[wise trail]

no

[thick gyro]

then theres nothing you can do

[wise trail]

oh

[warm shale]

Stephen

[teal turret]

U can isolate y_3, but u won’t get a numerical answer for it

It’ll just be in terms of x_3 and z_3

[wise trail]

i found a way

42 dived by 3 is 14

[teal turret]

Wat

X y and z are equal?

[wise trail]

so wega find how something by the power of 3 is 14

ya

they added togather as the same

[warm canopy]

where did you get this problem from

[wise trail]

.close

[obtuse pebble]

Channel closed

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[teal turret]

Bro…

[warm canopy]

.reopen

[obtuse pebble]

✅

[warm canopy]

@wise trail are you looking for integer solutions?

[wise trail]

wt

ya

[warm canopy]

https://www.sci.news/othersciences/mathematics/sum-three-cubes-problem-number-42-07576.html

then give up

[teal turret]

WAT

[wise trail]

lol

[teal turret]

It’s x^3??

[wise trail]

i wanted to test you guys to see how smart u r

[warm canopy]

what a waste of everyones time

[wise trail]

sorry

[latent walrus]

[warm canopy]

you couldnt even state the problem statement correctly

[tardy epoch]

The only thing you showed is how much of a twat you are

.close

[obtuse pebble]

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[teal turret]

Why did u confirm this was what u wanted

#help-5 message

[wise trail]

sorry

.close

[obtuse pebble]

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[timid silo]

.close

.close

[obtuse pebble]

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[haughty oar]

Hello, i'm struggling a lot with this question :

Let :

[haughty oar]

Calculate:

I tried several approach, like "telescoping terms" or simply to develop it, but i don't find a good result

[thick chasm]

Looks like an AGP

It is an Arthimetico-Geometric progression

[haughty oar]

True, but the "k" in the power is bothering me

[thick chasm]

Use the formula of AGP series

Or simply compute it

Do you want the solution??

[haughty oar]

it would be lovely

thank you very much

[dark stirrup]

!nosols

[obtuse pebble]

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.

[nocturne minnow]

I'm 90% sure that someone already told you not to give out answers

[thick chasm]

Sorry dude. Won't do that

[tranquil sonnet]

Look up Gabriel’s Staircase, then try applying that here

[obtuse pebble]

@haughty oar Has your question been resolved?

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[pseudo lily]

Goofy question but why is 3(1-log5) = log8

[pseudo lily]

I forgor how to calculate

[thick chasm]

Base of log?

[pseudo lily]

I think it's common log

So base of 10

[fierce lagoon]

1 = log(10)

[pseudo lily]

yes

so uh

[fierce lagoon]

1-log(5) = log(10) - log(5)
= log(2)

And 3log(2) = log(2^3)

[pseudo lily]

oh yeah

I'm half asleep

Thanks tho

.close

[obtuse pebble]

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[hallow igloo]

I was wondering if this is a valid definition of an Interval:

Let a,b,c be real numbers, and I be a non empty subset of R.
I is an interval iff for all a,b in I where a<=b. If a<=c<=b, then c belongs to I

[lost tree]

I is an interval iff for all a,b in I, a is less than or equal to b?

[hallow igloo]

I’m supposing for all a,b in I, they satisfy:
a less than or equal to b

If a less than or equal c less than or equal b, then c belongs to I

I’ll edit my statement

Let I be a non empty subset of R, and let a,b belong to I such that a ≤ b

I is an interval iff, If a ≤ c ≤ b, then c ∈ I

[obtuse pebble]

@hallow igloo Has your question been resolved?

[obtuse pebble]

@hallow igloo Has your question been resolved?

[obtuse pebble]

@hallow igloo Has your question been resolved?

[upbeat plinth]

@hallow igloo that works but we need quantifiers on a,b after the iff

[hallow igloo]

So for all a,b,c in R (ect.) ?

[obtuse pebble]

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[fathom flicker]

I found the vector, y=<1, 1, -1>, and this vector is in the left null space of A.

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[opaque galleon]

do I have to change bounds in Integration by Parts?

[royal basin]

no in fact you shouldn't

[opaque galleon]

ok thanks

so only in trig sub

and trigonometric integrals?

[lost tree]

with any substitution

[opaque galleon]

so basically everything but IBP

[fathom flicker]

you never have to change bounds

[lost tree]

oh well but u dont have to

[royal basin]

no, it is in substitutions in general that bounds get recalculated.

[lost tree]

u can like undo ur substitution by replacing it with what u made the subsitution for

after u have the answer

[opaque galleon]

what I usually do is just get the indefinite integral first, then evaluate, is that wrong?

[zenith raft]

that's fine

[obtuse pebble]

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[timid silo]

What is the next step for number 2

[obtuse pebble]

Please don't occupy multiple help channels.

[timid silo]

.close

[obtuse pebble]

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[woeful shuttle]

how do i differentiate something with 3 x things? for example x^2sinxcosx

[frosty spoke]

product rule

[woeful shuttle]

but how?

product rule's only for 2 things

at least that's the only way i've done it so far

[loud tangle]

you might want to look at the generalisation

1 sec

[frosty spoke]

well you could also just repeatedly apply it

[loud tangle]

oh

wiki page die

[frosty spoke]

for example, if I have (uvw)', I can do product rule on uv and w, so I'd get (uvw)' = (uv)'w + uvw'

[woeful shuttle]

rip

[frosty spoke]

and i can expand the (uv)' to give vu' + uv'

so then it's

(uvw)' = uv'w + u'vw + uvw'

[woeful shuttle]

good god lol

that seems like a lengthy process

[frosty spoke]

well, you could also rewrite sin x cos x as sin(2x)/2

[woeful shuttle]

i didn't think about rewriting it, that's a good point

the actual question is e^-2x x^3 sinx

idk if i can rewrite that tho

[frosty spoke]

you can actually rewrite it, but that depends on knowing something else

but in this case, you should probably just go with the product rule

[woeful shuttle]

alright, i'll do that

thanks for the help :^)

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[obtuse pebble]

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[smoky dove]

could someone help me understand how to solve for p for this parametric

I understand it becomes a quadratic of p^2-px+1 but everything from there seems way too complex so I feel like theres a simpler way to do it

but I just can't get to it

[timid silo]

There is

Square the x

What do u get

[smoky dove]

x^2=p^2+2+1/p^2

ok wow

thank you

[smoky dove]

also just a general question

how do you like know when to square the x value to solve this and other stuff

[obtuse pebble]

@smoky dove Has your question been resolved?

[obtuse pebble]

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[pastel mist]

find the equation of the plane through (1, 0, -1) and (-1, 2, 1) and parallel to the line of intersection of the planes 3x + y - 2z = 0 and 4x - y +3z = 0

[pastel mist]

@void spade

[void spade]

find the equation of the plane through (1, 0, -1) and (-1, 2, 1) and parallel to the line of intersection of the planes 3x + y - 2z = 0 and 4x - y +3z = 0

[pastel mist]

.close

[obtuse pebble]

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[obtuse pebble]

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[full saddle]

I have no idea what I'm doing for these questions
Help would be greatly appreciated

[royal basin]

do you know how to calculate magnitude and argument for complex numbers?

[full saddle]

Magnitude is
Uh
The hypotenuse

And argument...
Angle?

[royal basin]

you are close but you've kind of missed the mark on both of these.

[full saddle]

But these aren't really in the right form
So I'm a bit confused

[full saddle]

Oh

[royal basin]

geometric intuition's all well and good but like

you should be able to write down the magnitude of $x + iy$ without a hitch

[warm shale]

Ann

[royal basin]

you should also know some properties of magnitude such as |zw| = |z| |w|

[full saddle]

Sorry
I don't think I was ever taught this stuff

And magnitude is calculated how exactly?
I know it's √(x²+y²)
But I'm not sure how I'd find x and y

I think I figured it out
Thanks @royal basin

.close

[obtuse pebble]

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[tall wind]

Hi, I'd like to check if my proof of a function being riemann integrable is correct. The details are here: https://math.stackexchange.com/questions/4652613/riemann-integral-of-finite-rational-activation-function?noredirect=1#comment9825899_4652613

[obtuse pebble]

@tall wind Has your question been resolved?