help-39

[south ice]

https://tenor.com/view/made-by-cameron-circle-spinning-gif-17584286

[midnight haven]

omggg

[south ice]

Circular reasoning

[full wadi]

https://giphy.com/gifs/exhausted-never-ending-repetitive-8w1AOMBiUbNTmWAtYg

[full wadi]

Premium trying to help

[midnight haven]

Bro do u hate me

For no reason

Indeed

I figured

[full wadi]

Goodnight fellas 🙋‍♀️

[midnight haven]

Am a g not a b

[full wadi]

Goodnight fellettes

[midnight haven]

Warbeast

U they're

GNG GO TO SLEPPPP

War beast

[south ice]

Good night man

[south ice]

Did you figure out why it’s T’(t)/|T(t)|

Also I lowkey am confused on the difference between what direction a particle is going and how its turning 💀

They kinda seem like the same thing

This is so cooked bro

<@&286206848099549185> anyone please?

[sweet schooner]

What’s up man

How can I help you

You want some intuition here?

[south ice]

Thanks bro

[sweet schooner]

You are stuck on the second one’s intuition I take it?

[south ice]

@sweet schooner

[sweet schooner]

Just #1?

[south ice]

Wdym

For now it’s just that

[sweet schooner]

Okay

Let me write them down

And I’ll see how I can do this for you

[south ice]

Thanks man

[sweet schooner]

So for the first, the tangent. This is essentially a particle moving along the curve and you can see what the speed and direction is of that particle. So it gives the direction of the curve, and the slope of the point

The unit tangent, however is basically the same thing except we don’t really know what the speed is (we lose the slope) so we really only see the “orientation” or direction

[south ice]

So for the tangent unit vector , we are considering the direction of the velocity , correct ?

[sweet schooner]

Pretty much

[south ice]

Okay but

[sweet schooner]

Only the direction at a given point

[south ice]

Does the direction of the velocity always follow the path of the position function?

[sweet schooner]

Yes it does. Because we parameterized it and it’s a smooth vector curve 👍

[south ice]

So how come when you graph velocity it looks so different

?

It looks like a whole new curve

Or am I understanding it wrong

[sweet schooner]

Well it should be. The position function and velocity function, while one is the derivative of the other, are two completely different functions

And may not look similar at all in most cases

[south ice]

So if they don’t look alike how can you say that the velocity has the same direction as the position function? Is that not related to the tracing of the curve ?

[sweet schooner]

Well position’s direction really only tells you where you are from the origin

The velocity (tangent) shows you what direction you really are moving

[south ice]

What I’m saying is

for that should the trace from r(t_0) to r(t1) look the same as the velocity from r’(t_0) to r(t1)

[sweet schooner]

Not at all

[south ice]

Aren’t the velocity vectors supposed to be tangent to the entire curve tho

Maybe the length would be different

So that’s why

[south ice]

Wait so here the graphs would look alike?

[sweet schooner]

No not necessarily

The idea is that on a position curve, each point (probably will) have a different direction and magnitude

When you apply the tangent

[south ice]

But I thought the velocity would follow the same direction

[sweet schooner]

Ah! No. Only at a given point do you get the velocity. The position curve doesn’t really give you any immediate information about the direction

[south ice]

Oh

So we can’t identify the direction at which the particle moves just by looking at the position curve r(t)?

[sweet schooner]

Correct

That’s why we need the tangent

I mean technically you can, but for all intents and purposes, you cannot

[south ice]

So whenever I’m looking at a velocity function, can I confidently say that the trace of that velocity function is the true direction the particle is traveling in

[sweet schooner]

Not necessarily, the trace is how the velocity is moving over time

the velocity function will only tell you what the velocity is at a given point, and how THAT curve moves is the “direction”

I will draw a picture

Say this is your position curve. It just shows you where a particle is

T(s) measures your velocity at a point

Basically the velocity curve will encode the information of ALL T(s) at a point into a given graph

[south ice]

So neither graphs can give you an idea of the direction the particle is moving in?

[sweet schooner]

The velocity graph pretty much does

[south ice]

But you said it doesn’t necessarily

[sweet schooner]

Well think about a typical position vs time graph. if you graph the velocity vs time graph, do you really see exactly the direction? Maybe you do

I don’t personally. I just see how it changes

[south ice]

Look what I really do know is that the tangent vector to the position graph is the value of how instant the position is changing with respect to time

But only at a point like I could imagine a bunch of tangent vectors

[sweet schooner]

Thats exactly what I’m getting at

It’s kind of hard to do

[south ice]

Do parametric equations follow the same logic?

Because I was gonna say let’s consider f(x) = x^2 and f’(x) = 2x

To make it easier to talk about

[sweet schooner]

I was about to give that example

[south ice]

😂

Crazy

So like f(x) is position

Which is a parabola

[sweet schooner]

Correct

Indeed.

[south ice]

If I take the derivative at some time I’m gonna get a tangent line

That’s the instantaneous rate of change at that point

Now what do we know here?

[sweet schooner]

Correct. It’s analogous, and exactly the same idea, to the same principle but applied to a parameterized curve

[south ice]

Okay so

Looking at the parabola

Can you say that the U shape is the direction of the particle

[sweet schooner]

No you can’t right, because if we graph 2x, we see that the direction is negative for x<0

[south ice]

Okay isn’t U how the particle is physically changing positions tho

Like the U shape

[sweet schooner]

It is

Yes, relative to the origin

[south ice]

So why can’t I say that from the fist end of the U shape to the second end is the direction the particle moved

Like it went dow down down then bottom then up up up

[sweet schooner]

You can, thats basically what you’re doing. However, when you say down, it’s moving in a negative direction right?

[south ice]

Yes

[sweet schooner]

When you work in higher dimensions, that isn’t enough to characterize the movement per say

You can extend the argument, but then the velocity graph will have that information in it

[south ice]

Okay so regarding that

For each time t, the instantaneous rate of change will yield a tangent line right

[sweet schooner]

Yes

[south ice]

So that tangent line tells us what? Where the particle moves physically and its speed?

[sweet schooner]

The direction it is moving in*

A bit of nuance in that, but it doesn’t tell you where it is going to be at, but where it is going

Think of the U shape again, the direction of the tangent at the bottom horizontal, however, it is goes up again

Same idea

[south ice]

Okay there are two things I wanted to ask

If the tangent lines are hugging the curve

Why is its graph a line

That’s the first question which basically concerns derivative functions having different shapes although their tangent lines are almost hugging the original curve

[sweet schooner]

Well, it is in the case of our parabola because the derivative is a line. For our curve, whatever it may be, it will probably be a curve as well

[south ice]

Sorry but why is it a line as in

What really does dictate the shape of the velocity graph ?

[sweet schooner]

If I’m being honest it’s just the function as a result of the derivative

[south ice]

Okay forget that, if we wanna examine direction of where the particle is going, (because this concerns the original question about unit tangent vector) does the entirety of the velocity graph show us that? Or only at one point? Is it even valid to say that the velocity graph shows us the direction the particle is moving in?

[sweet schooner]

Yes so, the velocity graph will take the information of our tangent at EVERY point.

And the velocity graph doesn’t necessarily show you “visually” but say the velocity graph takes on a coordinate at (-x,y,-z) then we know that the position function at those coordinates is moving in the negative x and z direction and positive y direction

[south ice]

Interesting

And for that logic we utilize the unit tangent vector ?

[sweet schooner]

Essentially, yes

[south ice]

Okay now what about the unit normal vector ?

And what do we mean when we say it represents the turning of the particle ?

What’s turning here as being different than direction ?

[sweet schooner]

It’s pretty much only encodes just the direction (or turning) we have no sense of magnitude about the “speed”

Because we normalized it and made it a unit vector

Hey man, I have an analysis exam tomorrow. I need to get some shut eye. If you want I can continue this tomorrow

[south ice]

No worries man get some rest

Thanks a lot

[pearl pond]

@south ice Has your question been resolved?

[pearl pond]

@south ice Has your question been resolved?

[pure raptor]

hello

whats this about

[lofty storm]

@south ice i can try to help you... but i wanna understand the peculiar point of misconception u r facing?

[pearl pond]

@south ice Has your question been resolved?

[midnight haven]

Hello ppl

[pearl pond]

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[ashen slate]

Hi for this gradient, do you only look at the m?

[shell brook]

yes

also

nice handwriting

[foggy scarab]

fr

donate me yo writing skills bro 🙏

[ashen slate]

Its my tutor's writing ^^

[ashen slate]

Ah okay thank youu

[pearl pond]

@ashen slate Has your question been resolved?

[pearl pond]

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[grizzled bolt]

How can I approach this problem?

my first instinct was integration by parts, let u =4x^5 and dv = e^-x^3 but i started integrating the dv and i realized you cant really do that so im kinda stumped... My next idea would be to let e^-x^3 be u so i can differentiate it and do it that way around but i dont really know how that'll play out so i figured i'd jsut ask.

[shell brook]

let x^3 = t

see where that takes you

[grizzled bolt]

ok so it should turn out like 4/-3integral(4te^t)dt cause the x^2 cancels with the -3x^2?

i think

[shell brook]

yup

[grizzled bolt]

i didnt get the splitting the x^5 factor thats so random

from there i think i can handle the rest

[shell brook]

you can rewrite x^5 as x^3 times x^2 substitute it cleanly

[rough stream]

The trick is trying a u-sub with whatever's in the e^(). You'll see that a lot

[grizzled bolt]

do u have any tips for spotting this / name i can write down so i can remember that double usubs like this exist?

[grizzled bolt]

o

[rough stream]

And if not the e^(), then the √ or the ln()

[grizzled bolt]

so problems with e^n^x just try to get rid of n^x with a sub first and simplify

[rough stream]

Even more general than that! See an e^()? Consider the sub.

[grizzled bolt]

alright ill write it down for sure

i dont wanna get caught on the midterm with a question like this and its just a simple trick like that before it becomes solveable

ty

.close

[pearl pond]

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[pearl pond]

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[blissful brook]

how do they take a moment about X?

X is just floating bruh

how they know these distances aswell?

[pearl pond]

@blissful brook Has your question been resolved?

[rough stream]

Indeed you need those distances. Question seems borked

[blissful brook]

.close

[pearl pond]

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[full wadi]

Using theta and 2a you know those distances @blissful brook

[blissful brook]

yeah i see it now

[pearl pond]

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[carmine zinc]

I'm fully stuck actually

The diagram I drew isn't to scale(the angles are only approximately correct)

apparently staring into a white abyss doesn't gift me any answers

[quasi bobcat]

wait so let me clarify: angle AOC is 43 degrees and angle APC is 18 degrees? And you’re trying to find angle BOD?

[carmine zinc]

yup

[weary gust]

i think its an intersecting chord theorem

[carmine zinc]

huh never heard of that, lemme look it up rq

[carmine zinc]

isnt that for intersection within the circle?

[weary gust]

o its a secant

intersecting secants?

smt like this

[carmine zinc]

yea

it is that

wtf ive never heard of this formula

[carmine zinc]

i do think this is outside the syllabus of the paper ive yoinked this from, is there another way to solve it?

[weary gust]

is line ad a straight line

[carmine zinc]

If AOD and COB were a straight line it could never converge

because then you'd have diametres

[carmine zinc]

That being said, singularly they could be but I don't see a reason why they should be diametres

[weary gust]

im not really sure 🙁 last time i did dis was like 3 yrs ago

r u from aus?

[carmine zinc]

nop

[carmine zinc]

Me too 😭 I've done barely any geometry in high school

[weary gust]

yer it sucks shouldnt be too much of a problem if its not in syllabus

[quasi bobcat]

ok but hear me out it kinda looks like that “angles in the the same segment” property so rn im just staring at it waiting for an epiphany to happen

[carmine zinc]

you mean "Angles subtended by a chord of one length are always equal"?

[quasi bobcat]

the one from this picture

[quasi bobcat]

oh yeah that

[carmine zinc]

I don't know how that would help then

[quasi bobcat]

yeah i’m stuck too but let me think about it for some time

[carmine zinc]

idk i guess i have like no intuition for geometry, but acc to this, you'd have 7 degrees? that feels wrong

[quasi bobcat]

7 degrees? where’d that come from?

[carmine zinc]

from that formula

[quasi bobcat]

might want to check your reasoning there…i don’t think the formula was applied correctly

[carmine zinc]

? a is 43, b is x and c is 18

no?

so $43-x = 36 \Rightarrow x = 7?$

[jolly parrot]

Supernova

[pearl pond]

@carmine zinc Has your question been resolved?

[pearl pond]

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[sturdy musk]

help?

[strong quest]

yea

[sturdy musk]

where does the 4 come from?

[glacial bluff]

260 / 65 = 4.

[sturdy musk]

oh, thanks

.close

[pearl pond]

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[sturdy musk]

.reopen

[pearl pond]

✅ Original question: #help-39 message

[sturdy musk]

why do i minus 260 by 260?

[tulip meteor]

To get a 0

[strong quest]

to get a 0 as remainder

[sturdy musk]

why not 26 by 26?

[hollow magnet]

26 is not a multiple of 65

why are trying to see how many times 65 "fits in" 26. Its clear that this is less than 1. We then try how many times 65 fits in 260. this is 4 (since 65*4=260) so we then know that 65 fits 0.4 times in 26 since 260 = 26*10

[glacial bluff]

normally, when doing long division, you want to subtract an integer multiple of the divisor.
unfortunately, 26 < 65, and while 26 can be kind of nicely expressed as a fractional multiple of 65 (26 = 0.4 x 65), long division does not deal with subtracting fractional multiples of the divisor.

[sturdy musk]

thank you guys

.close

[pearl pond]

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[pearl pond]

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[green aurora]

Can someone help me with one specific topic first? I want to understand how to derive the pmf of Y=g(X) when (X) is discrete, using the CDF method. Could someone explain it first intuitively, then practically with the formulas and a simple example?

[green aurora]

For example, if Y = X^2, could someone first explain intuitively what is happening, and then show the practical method step by step with the formulas?

Actually

I want to start with transformations of random variables, meaning Y=g(X), and understand intuitively what the transformed random variable actually is before moving on to CDF, pmf, and pdf. Could someone explain it first in a simple intuitive way, and then with a basic example?

<@&286206848099549185>

[sonic patrol]

In your mind what is a random variable

@green aurora

[pearl pond]

@green aurora Has your question been resolved?

[green berry]

@green aurora

[green aurora]

Is a function

[sonic patrol]

In that case, doing Y = g(X) is just function composition

[green aurora]

Okay

[green aurora]

Help pls

[green aurora]

Can someone help me with one specific topic first? I want to understand how to derive the pmf of Y=g(X) when (X) is discrete, using the CDF method. Could someone explain it first intuitively, then practically with the formulas and a simple example?

[sonic patrol]

You don’t have to repeat your message it’s ok

The pmf of Y is P(Y = y)

For that, you look at all the values x where g(x) = y

And then you sum over the probabilities

So sum_{x such that g(x) = y} P(X = x)

[green berry]

this is the line of possible values ​​of X

if you choose for example x = 0.15 in that case

the transformation says like: “ok, then the new value is y=x^2"

[green aurora]

@sonic patrol is this what you were saying?

[sonic patrol]

it's related yes

[green aurora]

but why is the blue arrow pointing towards the green dot?

[sonic patrol]

you'd have to ask alee

[green aurora]

@green berry

[green berry]

its (0.15,0.15^2)

the blue arrow means I take the value of X and bring it onto the graph of the function y = x^2

it means the transformed value is y = g(x) = x^2 , so I sign it on the Y-value line

so the yellow dot on the line is the value of the new variable Y

taking other values ​​on the line of possible values ​​of X you get other possible values ​​of Y

[green aurora]

but why is there only the graph for x>=0?

@green berry @sonic patrol

[sonic patrol]

well it doesn't have to be, it depends on the range of values that X takes

[green aurora]

or because must g(X) be invertible?

[green berry]

Let me add that the same interval of X does not always become the same interval in Y

for example in this case if we choose values of x close to 0, y changes a little while close to 1 if we change a little x, y changes more

So the function can compress or expand the pieces of the axis

So when you look at these intervals of x and y you have to think that the transformation changes the "geometry" of the values, and therefore also changes the distribution

[green aurora]

???

i dont understand

@sonic patrol

[pearl pond]

@green aurora Has your question been resolved?

[pearl pond]

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[uncut trench]

I have no clue how to calculate standard deviation here

[uncut trench]

For mean i have 1550

[rough stream]

They just want a formula
Var(X) = E(x^2) - E(X)^2

[uncut trench]

Really?

[rough stream]

Where E is the expectation, so E(X) = sum x / n

[uncut trench]

We never learned such a formula 😭

[rough stream]

Let me think if I can relate it a bit closer to the sums

[uncut trench]

Oh wait im dumb i didnt read the book

[rough stream]

Oh cool!

[uncut trench]

Its about 39.5

.close

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[pearl pond]

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[pearl pond]

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[proper nova]

<@&268886789983436800>

[rigid sphinx]

Hello?

[proper nova]

someone already handled this

my bad

here he comes

[grim anchor]

what is 6+7

[crystal dew]

might wanna check delete logs then

ah no need then

[potent elk]

21

[proper nova]

you should ban @grim anchor

[honest oyster]

Too hard

[proper nova]

and $\infty$ years of ban

[jolly parrot]

1 divided by 0 equals Infinity

[potent elk]

Don't waste time in these channels tho lol

.close

[proper nova]

already closed

[potent elk]

Ah lol

[proper nova]

give him a timeout or smth

[crystal dew]

minimodding

[proper nova]

poor me can't apply for mods just because im a minor 🥀

[grim anchor]

10 didvide by 4

[proper nova]

blud

[grim anchor]

help me

[proper nova]

how old are you?

[grim anchor]

14

[proper nova]

and you still need help with 10/4?

[grim anchor]

60/1000

[tardy flicker]

he is tryna not get banned or stuff lowk ✌️

[proper nova]

he's still surviving

[grim anchor]

i need help

[proper nova]

imagine sending a GIF and asks for help

🥀

[shell brook]

what do you need help with

[proper nova]

he's trolling and the channel's closed

[grim anchor]

100/ 1589

[shell brook]

oh izzit, damn i didnt notice

[pearl pond]

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[warm patio]

Is there a function that has a derivative only on all irrational numbers?

[main oriole]

$\pi x$

[jolly parrot]

MarcoMa210

[main oriole]

guess what the derivative is

[warm patio]

on all irrational numbers

[main oriole]

ah

[warm patio]

this is surely non trivial

[warm patio]

(and nowhere else)

[main oriole]

f(x) hits all irrationals and nowhere else?

[warm patio]

f(x) has a derivative at all irrational number points

[misty stone]

what is the question

[warm patio]

Is there a function that has a derivative only on all irrational numbers?

[main oriole]

you could use the fact that the irrationals are uncountable and thus are a larger set than the rationals

build the derivative off of that and then get its antiderivative

[warm patio]

how

[misty stone]

I guess yes

[warm patio]

why

[misty stone]

let me think a example

[main oriole]

but then again the function $\pi x$ is rational at $x=\frac{1}{\pi}$

[warm patio]

what

[main oriole]

to get a function that hits only the irrationals it would have to be discontinuous

[jolly parrot]

MarcoMa210

[warm patio]

thats not what im asking

[main oriole]

that's an example

[misty stone]

you can look for Thomae function

[warm patio]

its continous

not derivable

the Thomae function is not differentiable at any point

[misty stone]

what about Weierstrass function

[main oriole]

you are asking for a function whose derivative does that

make a function such that its derivative is the thomae function

[misty stone]

This can be a situation seen in specially structured functions that violate the rules of continuity and differentiability.

[west sapphire]

https://math.stackexchange.com/q/905083

[misty stone]

your question isnt like that

[west sapphire]

(accidentally left off part 2, which is the part you need)

it seems to be true for D(f) as well, but I can't find a definitive answer either way, still hopefully this is a starting point

[misty stone]

I'm trying to help, but it's very difficult to convey what I'm thinking because it's not my native language Im so sorry ıf I understand you all badly

[west sapphire]

ah yea, i think this does what you need: https://math.stackexchange.com/a/106397

you can let G_1 be the irrationals and G_2 be the empty set

oh wait, you want it differentiable on the irrationals, not non-differentiable

[warm patio]

ah yeah differentiable

[west sapphire]

you can swap the roles then

well not exactly swap

you can let G_1 = empty set and G_2 = rationals

[warm patio]

oh yeah that would do

[west sapphire]

cool, both work (can be differentiable precisely on the rationals, or precisely on the irrationals)

i don't think i knew this until now

[warm patio]

interesting

[west sapphire]

i suspect it's highly nontrivial to prove it in the generality above, maybe there's a shortcut for the irrationals specifically

[warm patio]

idk it was just a question that popped up in my head xd

thank you very much tho

.close

[pearl pond]

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[west sapphire]

yw, cool question

[pearl pond]

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[signal hazel]

is this the correct way to think about this exercise or am I missing smth?

[full wadi]

I would do the number of pins (10^4) - forbidden by considering each possible position of 73 (3) x the permutations of them (10^2), so yours reads correctly

Ah yes minus the overlap

I would've missed that

[warm patio]

it is correct

[signal hazel]

is this is the correct approach then?

great thank you very much!

[warm patio]

yes

[signal hazel]

.close

[pearl pond]

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[pearl pond]

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[long nova]

help why for (i) is it x > 0 and not x greater than or equal to 0???

[plush bramble]

Where does it say x can't be negative

[long nova]

it doesn't say x can be negative

but why is it only x > 0

should it not be including as well?

[shut skiff]

Can I ask a physics related question?

[plush bramble]

!occupied

[pearl pond]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[plush bramble]

Does it need to be?

[long nova]

for how can it be greater than equal AND equal when x is only greater than 0

[long nova]

i think so

[plush bramble]

Why

[long nova]

because only at x = 0 is e^x = x +1

other than that its only always greater

[plush bramble]

So?

[long nova]

so it doesnt make snese

[plush bramble]

Why does e^x need to equal x+1

[long nova]

so it can satisfy the inequality

[plush bramble]

So?

Does it make the inequality false?

[long nova]

otherwise it would just be e^x > x + 1

[long nova]

yes i believe so

[plush bramble]

Why

[long nova]

correct me if im wrong

[shell brook]

💀

[plush bramble]

You're wrong about something, but you're avoiding my question so I can't correct you

[long nova]

because tangent means it only grazes on point of the cruve

so only at one point are the two functions equal

and that is point (0,1)

the y-intercept

[plush bramble]

And what does that have to do with x>0 implies e^x >= 1+x

[long nova]

i think the statement is completely false becuase e^x = 1 + x would only be true if x were ever equal to 0 but since it's only greater than, then therefore it should only be e^x > 1 + x

[plush bramble]

Yea that's incorrect logic

[long nova]

but then that would not make sense or help us at all because our end goal is to use squeeze theorem

[long nova]

how is that incorrect

[plush bramble]

"it should only be e^x > 1 + x"

4 >= 3 is a perfectly fine statement

[long nova]

what how?

[plush bramble]

It is also correct to say 4 > 3

[long nova]

4 can never equal to 3 though

oh wait a second

i think im seeing ur point

[plush bramble]

Do you know in English words what the symbol means

[long nova]

no

[plush bramble]

$\ge$

[long nova]

only greater than or less than

[jolly parrot]

riemann

[plush bramble]

Greater than or equal to

[long nova]

is it the "or"

[plush bramble]

Is 4 equal to 3? No

Is 4 greater than 3? Yes

Therefore 4 is greater than or equal to 3

[long nova]

ohhh

its like ||

ah i see your point

let me consolidate this once more

ok so you're implying it could hold true if x > 0 and also x >= 0 right?

it really just depends on what you need then right?

[plush basin]

key word or

there are two conditions

[long nova]

yeah i get that now

ok thanks @plush bramble and @plush basin i appreciate your help

..close

.close

[pearl pond]

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[pearl pond]

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[dusky gulch]

yo chat I need help I wasn't here for class on this day what I do, I do NOT know what I'm looking at rn 💔

[pearl pond]

@dusky gulch Has your question been resolved?

[full wadi]

What is the name of your class?

Do you not know any of the blanks @dusky gulch ?

[dusky gulch]

Functions gr 11 MCR3U1

[dusky gulch]

I do

but im still cofnused

idk

[full wadi]

Which ones don't you know

[glacial bluff]

then, for future helpers, please explain where you're stuck and what you've tried (since you said you do know at least some of them).

[dusky gulch]

can u help me with the other images the blanks aren't as important

idk what to do on the other images

[full wadi]

Can you tell me Y in terms of X for Example 1?

[full wadi]

That would be the answer for (b)

[dusky gulch]

it says y = x^2

[full wadi]

Its says f(x) = x^2

[dusky gulch]

where

i only see y = f(x) and y = x^2

oh nvm I see f(x) = x^2

but how the heck do I graph that

[full wadi]

Using this can you tell me y

[dusky gulch]

for the table of values?

[full wadi]

Just the equation of y in terms of x

Using this

[dusky gulch]

does that say y - 3f or y = 3f

[full wadi]

=

[dusky gulch]

x^2 = 3f[-1/2(y+1)] - 4

?

isn't that inverse

[full wadi]

We aren't using y = x^2

We have f(x) = x^2

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full wadi]

So f(- 1/2 (x+1)) = (- 1/2 (x+1))^2

[full wadi]

@dusky gulch

[dusky gulch]

yeah?

.reopen

[pearl pond]

✅ Original question: #help-39 message

[dusky gulch]

but

isnt -1/2 (x+1) that part y?

[full wadi]

We don't know what y is yet

[dusky gulch]

i couldve worded that better mb

[full wadi]

we need to figure it out using that equation

[dusky gulch]

but it says y = 3f[-1/2(x+1)] - 4

why did u plug in the equation into f(x)

[full wadi]

So what is f(-1/2(x+1)) ?

Those square brackets are just for clarity

[dusky gulch]

when you say f(- 1/2 (x+1)) = (- 1/2 (x+1))^2
the (-1/2(x+1)) part equals x?

but how does it equal x

[full wadi]

Do you understand functional notation?

[dusky gulch]

yeah

f of x

[full wadi]

If I define f(x) = x^2 then f(100) = 100^2 and f(q) = q^2

So f(x+1) = (x+1)^2

[dusky gulch]

yeah I know how that works but

[tardy flicker]

Functions are like a inout-ouput things, if u say f(x)=x³ then then u can substitute x with anything u wany like x+3, x+4 and so on

Input*

[dusky gulch]

why did u plug this into f(x) = x^2

as x

when its part of y = ..

[full wadi]

Because that is how functions work

The definition f(x) = x^2 is defining a behaviour

Using x doesn't mean anything, it's a temporary variable used to represent this behaviour

It would be the same function if i wrote f(P) = P^2

[dusky gulch]

ohh okay

but

why did u just plug the part in the brackets

wait

why didn't you do f(3f(- 1/2 (x+1))-4 = (3f(- 1/2 (x+1))-4^2

instead of just f(- 1/2 (x+1)) = (- 1/2 (x+1))^2

*why did you leave out the 3f & -4

[full wadi]

This is where f is used

[dusky gulch]

OH

so basically it's saying take the value of f from the second equation and plug it into the first?

so like if u get smth like this again u should plug this into..

this

am I on the right track now

@full wadi would that be what I write in b or a?

[full wadi]

(b)

[dusky gulch]

what do I write in a then?

or do I write that later

because I didn't sketch the graph yet

why is it even at (a) then

[full wadi]

Using your table (the one u deleted) name the transformations happening in that equation for y

[dusky gulch]

So I would state the transformations for this?

[full wadi]

Yes, state the transformations happening to f(x)

Including what is happening on the interior, so what it means to go from x to -1/2(x+1) in the function

[dusky gulch]

what about the a and c value

[full wadi]

What a and c values

[dusky gulch]

can u word this simpler 😭

[dusky gulch]

3 and -4

but u said including

[full wadi]

You can post that table again so I can see what you're seeing

[dusky gulch]

so nvm

[dusky gulch]

because the equation is y = af[k(x-d)] + c

format

[full wadi]

So name the transformations that correspond to a, k, d and c

[dusky gulch]

the table doesn't say anything important it's just the basics of knowing transformations in equations

[dusky gulch]

Why doesnt it just say state the transformations of y = 3f(-1/2(x+1))-4 then

but it says state the transformations applied to the graph y = x^2 to OBTAIN y = 3f(-1/2(x+1))-4

[full wadi]

Because y is a transformation of f

And f(x) = x^2

So y is a transformation of x^2 graphically

[dusky gulch]

so saying that wouldn't the new equation be y = 3f[-1/2(x+1)]^2 - 4

[full wadi]

They're saying imagine you had an old graph showing y = x^2 and now you have a new graph showing this, how was this old graph transformed into the new

[dusky gulch]

i still dont get it, should this be important to know?

[full wadi]

If I take y = x^2 and transform it to y = (x+1)^2, what is that called?

[dusky gulch]

uhhh idk ngl

what is it called?

[full wadi]

It should be in your table

[dusky gulch]

arent u just inputting a value as x which is x+1 in that case?

[full wadi]

Look at the third row

[dusky gulch]

d = -1 so a horizontal shift to the left by 1 unit?

[full wadi]

Now apply that sort of logic to the rest of the values

[dusky gulch]

The way u worded it was uh different ig, why didn't you just say state the transformations of y = x^2 to y = (x+1)^2

I think when you said "what is it called" got me confused

[full wadi]

Sorry about that

[dusky gulch]

Can you also tell me why the horizontal stretch by a factor of 2 is 2 and not -1/2 when k = -1/2 and not k = 2

[full wadi]

The - doesn't effect the stretching amount

[dusky gulch]

is it because it's 1/k

basically

cant u sya

say*

Horizontal stretch by factor of 1/2

then

okay so it must be the denominator always

[full wadi]

It is just 1/k (positive)

[dusky gulch]

U see where it says -1/2 and the fill in the blank page says

k < 0 = graph is reflected in the y-axis
k > 1 = graph is horizontally COMPRESSED
0 < k < 1 = graph is stretched horizontally

(in all of them it says "by a factor of 1/k")

the equation says y = 3f(-1/2(x+1))-4
k = -1/2
bring back "by a factor of 1/k"
we have 2 as k, isn't that greater than 1 (obviously), so why is the transformation stretched and not compressed

when the denominator only matters

nvm I thought about it

the -1/2 tells you that it is stretched but then the 1/k (k = the factor)

so if I had 3 it would be compressed by a factor of 3 right?

thanks

and just to clarify again the - in the -1/2 doesnt matter right?

[full wadi]

The -'ve means it was reflected

But the stretching factor is positive

[full wadi]

Actually reading what they say it should be by a factor of 1/3

But I agree that it makes sense to say it was 'compressed' by a factor of 3

[full wadi]

As here you say they all say a factor of 1/k

[dusky gulch]

negative or positive = reflection or no reflection

[dusky gulch]

so which is right?

either one?

[full wadi]

Use what they say

[dusky gulch]

if I don't would I lose marks 💔

feel like it'd be easier too

[full wadi]

I don't know how leniant your markers are, hopefully not 🙂

[dusky gulch]

so can the new equation be f(-1/2(x+1)) = (-1/2(x+1))^2 OR y = 3(-1/2(x+1))^-4 are they both right?

[full wadi]

They new equation is the y one

[dusky gulch]

so when you said

If I take y = x^2 and transform it to y = (x+1)^2, what is that called?

the y = (x+1)^2 is the new equation

right

[dusky gulch]

and if I add the f in the new equation is that fine

(and still able to simplify it into vertex form)

what do I do for the right of the table of values

i already did the left part

but idk what to do on the second table of values

[full wadi]

the top section would be your new equation for y

[dusky gulch]

yeah I figured that what about the x and the y

oh

like why is there underscores there

wth

[full wadi]

Im not sure

[dusky gulch]

im guessing it doesn't mean anything then

[full wadi]

You can put your answer in (b) next to the y

As the left table has the original y = x^2

[full wadi]

The top section should be in terms of f

[dusky gulch]

wdym in terms of f

[dusky gulch]

do I have to simplify to vertex

[full wadi]

This is your new equation

[dusky gulch]

but with ^2 right

[full wadi]

<@&286206848099549185> I need to do something can someone take over ❤️

[rotund nymph]

what is 'the above relation'

[red hull]

We need the relationship

[dusky gulch]

y = 3f(1/2(x+1))^2 - 4

[red hull]

Okay so just map ordinary points and plug them into that

Plug x=0 into that equation and then whatever value you get that is the y value

Do that for 0,1,2,3 etc

[dusky gulch]

replace x in the relation with the x values from the other table ?

[icy forge]

@dusky gulch I think what you need to do is

1.just write the relationship that you have got , by solving the main problem , in the uppermost rectangle
2. Write values of x like -3 , -2 ,-1 below x ( as same in the left table )
3. Write values for y besides it that you get by putting x

[dusky gulch]

ik now so on the right table the first value under x would be -3 and then i would plug -3 into the relation i have in the uppermost rectangle and that would be my first y value

[icy forge]

Yeah

[dusky gulch]

first one is -3 and -1

[dusky gulch]

thank u

and thank u a lot more @full wadi

[pearl pond]

@dusky gulch Has your question been resolved?

Channel closed

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[cerulean dome]

I think I made some mistakes

Can someone help me pls

<@&286206848099549185>

Sorry, ik I am not suppose to ping right away, but I am in a rush

[sterile python]

1st one correct

[full wadi]

(16) seems good, maybe you should say you slowed down as you approached it

[sterile python]

but write slow down before stop

[sterile python]

not go up down hill here but go back to the start place would be more concise

since distance increase decrease

go away from home then walk back home for instance

[full wadi]

You could say you were running back and forth between two points

slowing down to turn as you reach the ends

[icy forge]

Yeah

[cerulean dome]

but what do the curly lines represent?

[sterile python]

turning back

[full wadi]

This would fit

[cerulean dome]

alright, thanks guys

[sterile python]

no worries boss

!done

[pearl pond]

If you are done with this channel, please mark your problem as solved by typing .close

[full wadi]

How do you have 3 channels h

[cerulean dome]

idk

[sterile python]

two different h

[trail minnow]

h

[full wadi]

h

[trail minnow]

h^3

[iron basin]

are you sure the y axis shows distance?

[sterile python]

it not identified clearly but the explanation correct

assumptions

[cerulean dome]

idk

[cerulean dome]

that's why I am stuck

[trail minnow]

[cerulean dome]

oops, speed i mean

[iron basin]

did the question say that y-axis is supposed to be speed?

it looks like you can name the axes to be anything

[full wadi]

I thought it was arbitrary

[trail minnow]

show question gng

[trail minnow]

whats arbitrary

[full wadi]

If that's the entire question then you get to choose the axis

So you're good

[cerulean dome]

yeah

[sterile python]

pick a random

[trail minnow]

2nd question lookin weird today

[trail minnow]

oh

[sterile python]

or pick any

[trail minnow]

ohk

👍

[cerulean dome]

so the second one can be: running back and forth from two places? @trail minnow@sterile python@iron basin@full wadi

[sterile python]

depends which place you start

[trail minnow]

y axis is speed or distance?

[cerulean dome]

speed

[sterile python]

.

[iron basin]

what terms did you learn for now?

as in distance, displacement, speed..

[trail minnow]

that seems wrong

[iron basin]

are you just allowed to name the axes anything?

[trail minnow]

you're speed increases and decreases with respect to time?

[cerulean dome]

so it's distance?

[trail minnow]

most likely

[cerulean dome]

yes it tells me to write a possible situation for that graph

[trail minnow]

but i think the graph shld be diff might js be me

[glacial charm]

the first one could be current vs time

[sterile python]

or speed whatever

[trail minnow]

current?? where did I come from

[full wadi]

Da river

[trail minnow]

wha

[glacial charm]

since we can name the axes anything as long as the graph matches

[trail minnow]

doesnt make sense

[full wadi]

@cerulean dome Just use this

Make sure you include that you start at some distance away

Because the graph doesn't start at 0

[glacial charm]

its for the charging of a capacitor a saturation curve dont think too much if its out of your scope for now

[cerulean dome]

y distance x time, right?

[full wadi]

Actually you get to choose

[trail minnow]

ok 👍 me dum dum

[cerulean dome]

https://cdn.discordapp.com/attachments/1318413159471513622/1383513412839145594/image0.gif

[glacial charm]

im not saying you're dumb bruh im js throwing ideas🥀

[full wadi]

You see this guy's profile picture?

He knows his stuff

[iron basin]

if you could specify it as "distance from a point" then sure

[cerulean dome]

https://tenor.com/view/lion-sigma-alpha-how-bro-felt-after-saying-that-sigma-lion-gif-13957304746104521882

[full wadi]

!done

[pearl pond]

If you are done with this channel, please mark your problem as solved by typing .close

[glacial charm]

whats with the gifs

[iron basin]

distance normally signifies "distance travelled"

[tardy flicker]

its .close

[cerulean dome]

.close

[pearl pond]

Channel closed

Closed by @cerulean dome

Use .reopen if this was a mistake.

[full wadi]

https://giphy.com/gifs/heyarnold-hey-arnold-nicksplat-l0DAGyhYqdLsPREJO

[trail minnow]

wha

[pearl pond]

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[sonic sleet]

324630 mod 99

[tardy flicker]

basically the reminder when 324630 is divided by 99

324630=99 x 3268 +98

so remainder seems like 98?

[pearl pond]

@sonic sleet Has your question been resolved?

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[eager jewel]

how to integrate this

not sure how to start

[worldly jewel]

use the sum formula to expand cos(x-a), then ...

[past basin]

would the product to sum formulas help in this scenario?

im not sure

[eager jewel]

ahh alr got it got it thanks 🪴

.close

[pearl pond]

Channel closed

Closed by @eager jewel

Use .reopen if this was a mistake.

[eager jewel]

that x-a x-b kinda threw me off

[tardy flicker]

what was that?

[feral comet]

nothing

don't worry about it

trust me

yes trust me

[pearl pond]

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[ashen slate]

Hii i still don't quite understand how to draw the graphs thing?

Is it when its x² its a U shape on the graph?

[viscid shale]

Take the "U" with a pinch of salt, but yeah

[left steppe]

well kinda

[viscid shale]

Its called a parabola.

[ashen slate]

Ph okayy

[left steppe]

big U

[ashen slate]

So if its x²-2x+1 what would it be, im still confused 😅😅

And whats the equation for the n shape?

[viscid shale]

You should start doing a bit of algebraic manipulation for those.

These kind of equations "ax^2 + bx + c" are called quadratic.

And there are multiple ways to express them.

[left steppe]

try plugging in x values (which returns a y values) and see what happens

[ashen slate]

Uh, so if its x=y² its n shaped?

[ashen slate]

Ou okk thankss

[left steppe]

err no

[ashen slate]

Wdym by plugging in?

[left steppe]

like x = -5

or x = 5

[viscid shale]

y = ax^2 + bx + c
Is both an equation, and what we sometimes call a "function"

If you choose some value x, then you can calculate its corresponding value y.

You previously mentioned: x^2-2x+1
Say we choose x = 2, we will get 2^2 - 2*2 + 1 = 1

[ashen slate]

So its located in y?

[left steppe]

for n shapes do you know how to do reflection

[viscid shale]

So, when x = 2, y = 1 > which you can plot like in a map

[ashen slate]

No

[left steppe]

do you know how to flip a graph

[ashen slate]

Ouhh okok thans

[ashen slate]

Never heard of it :'

[ashen slate]

Its a vertical but slightly tilted line?

[left steppe]

okay well to flip a graph it is to flip the sign of a

where ax^2 + bx + c

[ashen slate]

So if a is + it becomes -?

[left steppe]

yes

[ashen slate]

Ouhh

[left steppe]

for y=mx+b

you flip the m to a -

let me find an example

[ashen slate]

Okk

[left steppe]

notice how only the x values change on the points but not the y values on the points

this is called reflection across the x axis

[ashen slate]

Ohh!! Okok i got it now ;3

So if its x=y² the u is sideways?

To the right

[left steppe]

yes

[ashen slate]

Ah!

Omg ok thank youu

[ashen slate]

I saw someone say this is y=x²-2x+1

Does the 2x not matter? Bc the graph didn't go to 2x jere? Just 1

[ashen slate]

Hi

[viscid shale]

It does matter, yes.

The 2x is the cause of why its shifted to the right

You should probably learn vertex form and root solution methods.

[ashen slate]

Oh!

Since the 2x is negative you flip it so it becomes positive 2x that's why its moved to the right?

[sterile python]

Yes but it face upward, if -x^2 face downward

[ashen slate]

Okay

[viscid shale]

Its quite more elaborate than that.

[ashen slate]

Oh ;-;

[ashen slate]

Ouh okay thankss

[viscid shale]

To clarify, if you write down the equation as $y = ax^2 + bx + c$

[viscid shale]

The value a tells you where the parabola points and how stretched is.

b vaguely tells you about the shift to the left or right
and c tells you the shift up and down.

Thing is, b doesnt only move the parabola left or right, it also displaces it up and down too.

So theres a specific balance between b and c if you want to keep it at the "normal height" of the the vertex touching the y = 0 line.

[ashen slate]

Oh okay

Thank youu

What does the b look like wjen its shift up / down 😅?

[verbal whale]

For vertical shifts, a and b don't change, only c does

[sterile python]

to be honest c do the most in shifting up and down

and to left write just add to x

[shadow elm]

you can complete the square for horizontal shifts

and tweak the x term

inside square

[viscid shale]

For clarification, b does move the vertex of the parabola up and down tracing a parabola itself.

C simply moves it up and down alone. > Which is what we formally know as a vertical shift.

[pearl pond]

@ashen slate Has your question been resolved?

[ashen slate]

Oh!

[ashen slate]

So c does up & down & b does left & right?

[ashen slate]

Oug okkk thanksss

[sterile python]

no

depends on c, shift of x

[midnight haven]

Parabloas not u

*parabolas

[ashen slate]

😭 ok then uhh

So if i want the parabola to go to the left i put lets say $x^2+3x+1$? Is it possible?

[jolly parrot]

Mugnes

[ashen slate]

Oh ok thank yiuu

[ashen slate]

Ah

[sterile python]

nah you got to use y = a(x-h)^2 +c

where h is shifting horizontally

[ashen slate]

This is so confusing

So to move the parabola to right/left its different formulas?

[ashen slate]

If i want to move the parabola more to the right do i just change the c & keep the 2 the same

[shadow elm]

complete the square first

yk how to complete a square?

[sterile python]

you use that formula when completing the square

[shadow elm]

or ykw

just put x = x-a everywhere

[pearl pond]

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[ashen slate]

No

[ashen slate]

Oh

[ashen slate]

Ah ok9k

[shadow elm]

yea

it shifts it a units to the right

[ashen slate]

Oh okay thank youuu

[pearl pond]

@ashen slate Has your question been resolved?

[tardy flicker]

Do .close if done

[pearl pond]

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[green aurora]

The question asks you to carefully sketch the graph. I know that by definition of this function, the absolute maximum must be at tau=0.

[green aurora]

What can I try to do?

[shadow elm]

youve gotta make the exact graph?

[green aurora]

I note that for tau to -infinity and infinity the function tends to 0

[green aurora]

no

[shadow elm]

rough sketch?

[green aurora]

the trend of the graph

[shadow elm]

alr

[shadow elm]

correct

now try finding some roots

put the above trig fxns to zero

and see if something works out

[green aurora]

I can also try to see if it's even

it's even!

[low matrix]

hey is there a specific name for this function

[green aurora]

autocorrelation function

[autumn trellis]

It's not defined at 0 btw

[green aurora]

but it doesn't always have the same expression

[low matrix]

what field is this used in?

[green aurora]

but autocorrelation function has maximum in 0

[autumn trellis]

I mean there will be a division by 0

The limit as tau->0 may exist but I'm just saying you need to indicate that the function itself is not defined at 0

[green aurora]

ok

given that the function as tau tends to -inf and +inf tends to 0, can I say that it is not periodic?

I just need to know if the function is always positive or not

[shadow elm]

at $-\infty$ it tends to 0 from negative side , so it will be below x axis

[jolly parrot]

parthisjoking

[shadow elm]

,rccw

[green aurora]

but it come out 0/0, did you use De l'hopital?

I mean the limits at 0

[shadow elm]

that does not matter that the first term is indeterminant

the other two will outweigh it

mostly

[green aurora]

but by any chance is the function asymptotic to -B^2 sin(4\pif_0tau)/(512\pi^3f0^4tau^3)?

[shadow elm]

dont have the physical strength in me to calculate thay

😭

sry

[green aurora]

I don't understand how you figured out how much the left and right limits were

in 0

[pearl pond]

@green aurora Has your question been resolved?

[shadow elm]

idk dawg

🥀🥀

what even are these functions

[green aurora]

but since the maximum is in 0, shouldn't the limit in 0 be finite?

[shadow elm]

mb

i was talking about limit at infinity

idk about 0

[green aurora]

ah okay

anyway

thanks

.close

[pearl pond]

Channel closed

Closed by @green aurora

Use .reopen if this was a mistake.

[livid spire]

hey

[midnight haven]

hello

[livid spire]

how are u

[midnight haven]

fine

?

[nocturne grail]

LMAO

!redir

[pearl pond]

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

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Remember:
• Ask your math question in a clear, concise manner.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[stoic imp]

where is the mistake

[dusky widget]

Why do you assume there is a mistake?

[stoic imp]

looks sussy

no mistake then?

[stoic imp]

so it's commutativ3

[dusky widget]

Is it? Math isn't a guessing game!!!

[shell brook]

i luv helpers having fun while helping