help-49

[cobalt nest]

^

[faint tree]

i cannot find anything in my textbook talking about this situation

[cobalt nest]

The vector lies outside the square, this event corresponds to the empty set, which is Jordan measurable and has probability zero

if P(empty set) != 0 ur violating the axioms of probability space @ancient ridge

[midnight plank]

@faint tree Has your question been resolved?

[ancient ridge]

I disagree as what you are saying because it sounds like you are trying to say that everything outside of the sample space is just wrapped up in some equivalence relation and labeled the empty set. I would prefer to not get pinged about this further unless the message is the relevant passage out of OPs book.

[jaunty canopy]

as in phi is a probability density function from $\Omega$ to $\mathbb{P}$

[grand pond]

LY

[jaunty canopy]

C is asking for $\mathbb{P}(([-7, 7]^{2})^{c})$

[grand pond]

LY

[jaunty canopy]

so it's not an event

at least that seems to be what they're going for

[cobalt nest]

everything outside the sample space is literally the complementary of the sample space come on

look at the definition he gave

[midnight plank]

@faint tree Has your question been resolved?

[jaunty canopy]

yh but it looks like the question wants B D F G I J

cus otherwise like...what's wrong with what OP put?

[cobalt nest]

thats what we're trying to figure out

[jaunty canopy]

as in i'm pretty sure it's probably not C cus they're explicitly asking for ([-7, 7]^2)^C

in R^2

which isn't in sigma

[cobalt nest]

Omega = [-7,7]²

[jaunty canopy]

yeah

well i think probably wait for OP to try everything except C and then see what happens

[cobalt nest]

then being outside the square doesnt make sense

[jaunty canopy]

yeah ik

if it is C, it feels more like english rather than like...actual maths

but oh well

[faint tree]

this is not correct either

[midnight plank]

@faint tree Has your question been resolved?

[midnight plank]

@faint tree Has your question been resolved?

[midnight plank]

@faint tree Has your question been resolved?

[sullen cosmos]

This all looks correct to me

[faint tree]

and i wish it was

[sullen cosmos]

Wait

Why didint you select C

[sullen cosmos]

BCDFGIHJ?

No confusing cause you have to select the events that can’t happen lol

[faint tree]

i did already; look above

i originally did BCDFGIJ

H corresponds to the top half of the square, minus the axes

so i dont think its probability 0

[sullen cosmos]

Ur right idk why I said H

[sullen cosmos]

This appears to be correct

[faint tree]

i wish it was

[sullen cosmos]

Mistake by the teacher?

[faint tree]

i think there's an error in the question...

im not sure ill have to check it i guess

[sullen cosmos]

Email your teacher maybe?

[faint tree]

i guess so

[sullen cosmos]

If an event has probability 0 then it doesn’t occur lmao

Imagine that’s it 💀

You were actually taking a riddle class

[faint tree]

i give up zzz

ill check in with my teacher

usually these dont contain mistakes but maybe this time there is

[sullen cosmos]

I’m very curious wether it’s a mistake or what his interpretation is

[faint tree]

well idk but its 4am for me

ill ask him tomorrow

[sullen cosmos]

Same

[faint tree]

well thanks for the help anyways

[sullen cosmos]

I see you are greek?

[faint tree]

i am not lmao

[sullen cosmos]

Greek in the discord bio 😔

[carmine sigil]

Not quite

[sullen cosmos]

Yea yea I know it was a joke

[carmine sigil]

Oh? Alr

[sullen cosmos]

Oh wait what if this is the interpretation?

Events that have P = 0 but are still in the SS

[carmine sigil]

That's certainly the interpretation

[sullen cosmos]

Wait nvm that’s been tried

[carmine sigil]

So my concern is it says φ is arbitrary

[sullen cosmos]

But that’s shouldn’t matter no?

[carmine sigil]

If φ is arbitrary, could it be the case that it features δ functions

?

[sullen cosmos]

What’s a delta function

[carmine sigil]

https://en.wikipedia.org/wiki/Dirac_delta_function

Thus we can choose to assign any measure 0 subset of the distribution space non-zero probability

[sullen cosmos]

But then there no one answer

[carmine sigil]

Like phi could be half the time it's a uniformly random distribution, and the other half it select (0,0)

[sullen cosmos]

But then you don’t have enough information to solve the question

I don’t think that really applies here, this is very likely a Probability I course

[carmine sigil]

I don't see an error with this at all

[sullen cosmos]

C is wrong

Since lying outside the square is not an event

[sullen cosmos]

^ I think this is right

[carmine sigil]

Maybe

[sullen cosmos]

P(outside the square) is undefined

[carmine sigil]

P(outside the square) = 0

Any event outside of the space of possible events has probability 0

[sullen cosmos]

Since P maps from Ω -> R

[carmine sigil]

Ah fair

I missed that

Nice catch

[sullen cosmos]

Yea but he tried them both anyways

[carmine sigil]

Broken question, hate those

Especially ones that are so damn pedantic about their answers.

[sullen cosmos]

Well usually someone else who does the assignment early would catch the error and it would get fixed pretty quickly

[faint tree]

well the assignment was released only 30 min before i made the post

this is the only question i didnt finish in that time

[sullen cosmos]

Be the goat of the class

Email the teacher say you think it’s wrong and it will be fixed

You are that student now lmao

[faint tree]

it seems like it yeah

well thanks for helping

at least i know im not crazy

im gonna sleep

[sullen cosmos]

Yea it will probably be fixed by the time you wake up

[faint tree]

.close

[midnight plank]

Channel closed

Closed by @faint tree

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[dreamy lichen]

Show that $\lim_{n\to \infty} \frac{b_{n+1}}{b_n} = 1\$ Where $b_n = \int_0^{\frac{\pi}{2}} \sin^n(x) \text{d}x$

[grand pond]

MæthIsAlwaysRight

[dreamy lichen]

oh and I can't use the wallis product because this is part of its proof

idk where to start, because i dont really know how can I work out the ratio of 2 integrals

[midnight plank]

@dreamy lichen Has your question been resolved?

[white gate]

try reduction formula

[dreamy lichen]

Reduction formula helps me prove that if the limit is 1, then the wallis product formula is right

i have these 2 formulas

[white gate]

ye

then you use squeeze theorem and thats it

[dreamy lichen]

wait how do i apply squeeze?

the ratio is (wallis product) / (pi / 2)

in the limit

and i dont yet know whether wallis product = pi / 2

[white gate]

$b_{2n+1}\le b_{2n}\le b_{2n-1}$

[grand pond]

TargetVN

[white gate]

it can be proven using sin(x) <= 1

[dreamy lichen]

right, i can believe this

so b_n is decreasing

that'd mean that
(b_(n+1) / b_n) <= 1

in the limit

the opposite inequality is tougher tho

[white gate]

$\frac{b_{n+1}}{b_{n}}\ge \frac{b_{n+1}}{b_{n-1}}=\frac{n}{n+1}$

[grand pond]

TargetVN

[white gate]

its not that tough

[dreamy lichen]

OH

That makes so much sense

i just needed to go one step further

thanks man

[white gate]

np

[dreamy lichen]

you saved me a lot of pain lol

.close

[midnight plank]

Channel closed

Closed by @dreamy lichen

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[spice scroll]

how do i prove RHSs are equal using taylor series?

[grim vector]

Consider the expansion of exp maybe

[white gate]

expand e^x and e^(-x) using taylor series

there will be some terms that cancel each other

[midnight plank]

@spice scroll Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[gusty falcon]

in a dataset strictly consisting of repeats

[gusty falcon]

is that data point technically all percentiles?

like [2,2,2,2,2] then 2 is the 50th percentile

and also the 89th percentile right

[hearty rune]

yeah

nothing else it could be

[gusty falcon]

right okay thanks

and uh

in a normal distribution for example

each percentile has the same number of “frequency” right

i mean isn’t that by definition

but the area under the curve just tells you how much of the data a specific datapoint is above or below?

[heady plume]

not exactly

Percentiles are equally spaced in terms of proportion, not frequency.

[gusty falcon]

wdym?

[heady plume]

for example, the area between the 49th and 50th percentile is 1% of the total area of the curve, but for a standard normal distribution, the curve is taller near the mean meaning that the data points are more densely packed in that region

[gusty falcon]

yeah but the area between consecutive percentiles are still the same

1% in specific

what did you want to say with the second line

maybe i’m not getting that

u mean two data points could be “nearer” if it’s around the mean

compared to datapoint around the “endpoints”

but both still are 1%?

[heady plume]

You asked if the frequency is same for each percentile right? I'm saying suppose an interval with range d corresponds to an area of 1% near the mean, and another interval with range d' corresponds to same area of 1% far away from the mean. Then clearly d' > d

[heady plume]

Yes

[gusty falcon]

hmmm yeah fair

wait then

what does frequency even mean then

in terms of a continuous distribution

yeah okay i guess i see how u use it

thanks

.close

[midnight plank]

Channel closed

Closed by @gusty falcon

Use .reopen if this was a mistake.

[heady plume]

You can't talk about the frequency of a specific value because the probability of any exact value is technically zero.

[gusty falcon]

yeah that’s right

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[twilit field]

Find $\int_{S} (x^2-y^2)dx dy$ where $S$ is bounded by the curve $y=\sin(x)$ and the interval $[0,\pi]$

[grand pond]

What a wonderful world it is !

[twilit field]

So basically $\int_{0}^{\pi} \int_{0}^{\sin(x)} (x^2-y^2) dy dx$

right?

[dawn dagger]

check your bounds

[twilit field]

both bounds?

oops

[grand pond]

What a wonderful world it is !

[dawn dagger]

yes

[twilit field]

Next, I want to find the volume of the pyramid bound by the 3 coordinate planes and the plane $x+2y+3z=6$

[grand pond]

What a wonderful world it is !

[twilit field]

So The region is $x \geq 0, y\geq 0, x+2y \leq 6$

[grand pond]

What a wonderful world it is !

[twilit field]

so $\int_{0}^{3} \int_{0}^{6-2y} 6-(x+2y) dx dy$

[grand pond]

What a wonderful world it is !

[dawn dagger]

looks correct

[twilit field]

thanks

.close

[midnight plank]

Channel closed

Closed by @twilit field

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[twilit field]

A solid is bounded by the surface $z=x^2-y^2$, the $xy$ plane, and the planes $x=1$ and $x=3$. Find the volume of the solid

[grand pond]

What a wonderful world it is !

[twilit field]

This is essentially the region between x=y and x=-y in the first quadrant

[latent elk]

What have u tried?

Well, honestly, there's nothing to try here... Since u just need to put these into a triple integral

[twilit field]

double, right

[dawn dagger]

you can do both

[zealous schooner]

if you do a triple integral you'd just be integrating 1

but writing it as a triple integral is easier

[twilit field]

It's this region, right

[dawn dagger]

with the constraints x=1 and x=3

[twilit field]

$\int_{1}^{3} \int_{-x}^{x} (x^2 -y^2) dy dx$

[grand pond]

What a wonderful world it is !

[dawn dagger]

looks aight

[twilit field]

Cool

Tq

[dawn dagger]

nq

[twilit field]

Now this

$\iint_{S} x^2+y^2$;$S= {(x,y) \mid \abs{x} \leq 1, \abs{y} \leq 1}$

[grand pond]

What a wonderful world it is !

[twilit field]

so using symmerty

$4\int_{0}^{1} \int_{0}^{1} x^2+y^2 dy dx$

[grand pond]

What a wonderful world it is !

[twilit field]

Is this fine>

[last slate]

what a wonderful world it is !

[robust isle]

your bounds are off

|x| <= 1 vs x in [0,1]

[last slate]

why is there two integrals

[twilit field]

This is a double integral

[twilit field]

hmm?

x is between -1 and 1

[robust isle]

yea

[twilit field]

Yes, I'm just integrating in teh first quadrant

and multiplying it by 4

[robust isle]

yeah didn't see the 4

aight

[twilit field]

thanks

[midnight plank]

@twilit field Has your question been resolved?

Channel closed

Closed by @twilit field

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[dusty portal]

For context: I have absolutely no knowledge of physics, yet they have introduced these problems in class.\
So, I was working through my notes (which you're supposed to answer the questions and do the homework for), and I never saw this concept when I was reviewing on Khan Academy or from CollegeBoard. They introduced a physics concept, in which $\mathbf{r}(t)=[(v_0\cos(\theta))t] \mathbf{i}+\qty[-\frac12 gt^2+(v_0\sin(\theta))t+h]\mathbf{j}$, where $\mathbf{r}(t)$ is the position vector as a function, $\theta$ represents the angle of elevation of the projectile, and $v_0$ is the initial velocity. Can anyone explain why this is?

[grand pond]

;(

[dusty portal]

Or maybe I should post this somewhere else?

And ping me if/when you reply, since I'm working right now.

[obtuse basin]

Seems to be projectile motion

v_0 is the initial velocity, theta is the angle at which the projectile is thrown from the ground

@dusty portal

The only force acting on the projectile is the force of gravity, which is vertical, so the horizontal velocity stays the same, meaning the horizontal position is simply the initial position times time passed, whereas the vertical position obeys (initial height) + (initial vertical velocity)t - gt^2/2

[dusty portal]

I see.

So its just like $-16t^2+v_0 t+h$ like you would see in an algebra class?

[grand pond]

;(

[dusty portal]

Well, I know gravity can vary, but you get the point.

[obtuse basin]

Yeah

[dusty portal]

I see.

Thank you.

Let me write this down, I do want to study calculus-based physics but I'm not the greatest at it.

[midnight plank]

@dusty portal Has your question been resolved?

Channel closed

Closed by @dusty portal

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[graceful ferry]

Can someone give me a direction?

[graceful ferry]

I know from the given that r(A)=1 and that (1 -1 3) is a linear span of columns of A, but how to find the space of rows of A ?

[midnight plank]

@graceful ferry Has your question been resolved?

[midnight plank]

@graceful ferry Has your question been resolved?

[graceful ferry]

Basically how to find x y z here ?

,rccw

[runic hamlet]

what does Ax=0 tell you about the rows of A

[graceful ferry]

All I know is that the dimension of the amount of answers(?) for Ax=0 (2) is the same as KerA which is the same as n-r(A) (the amount of zero rows)
And this is how I concluded that r(A)=1...

[runic hamlet]

but you are even given how ker A looks like

surely you have to use that somehow

[graceful ferry]

Oh I'll see then

KerA is {(3 -1 1) (-1 -1 -1)} ,,
How do I use this? could I find ImA ? How to use the given that Ax=(1 -1 3) has a solution,,
I know it means (1 1 -3) is a span or columns of A but I'm confused by this since all columns of A looks like this: (x 0 0) so how can I get (1 -1 3)? Is thus where the trick is?

[runic hamlet]

that is not the kernel

that is a basis of the kernel

[graceful ferry]

Mb, I mean basis

And I mean finding the basis for ImA

[runic hamlet]

the columns of A do not look like this

thats not what rank 1 means

what does it mean that A*(3,-1,1)=0

let (a1,a2,a3) be the first row of A

[graceful ferry]

That 3a1-1a2+1a3=0 and so on.. ?

[runic hamlet]

now look at that equation

what can you do with it

[graceful ferry]

Uh I could move a2 to other side and now I have 2 unkowns

Idk

[runic hamlet]

ok I wanted a less specific statement. "I can solve for a1,a2,a3"

can you find another such equation?

[graceful ferry]

Yes -a1-a2-a3=0

[runic hamlet]

so thats two equations

for a1,a2,a3

solve them

[graceful ferry]

a3=2a1
a2=-3a1

(1, -3, 2) ?

[runic hamlet]

no

[graceful ferry]

(1 , 1 , -2) I MISSED THE MINUS

Can you please explain what rank 1 means ?

[runic hamlet]

the rank is the maximal number of linearly independent columns or rows

so here at most 1 row is linearly independent

aka, they are all multiples of another

[graceful ferry]

Oh okay ty

.close

[midnight plank]

Channel closed

Closed by @graceful ferry

Use .reopen if this was a mistake.

[graceful ferry]

Ugh that means (1 -1 3) is useless

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[jolly pebble]

Can someone help me intuit the central limit thm

[cobalt nest]

Go ahead

[jolly pebble]

Hii

[cobalt nest]

hiii

ask away we will try to help

[jolly pebble]

Yea so

We r taking N samples from any (ANY) distribution

And it's sum is supposed to follow

The same family of distributions?

The sum of samples

[nova yoke]

in the limit

[nova yoke]

one restriction: it has to be a distribution with finite variance

[jolly pebble]

And if u subtract N times the mean of the OG distribution and divide that by std deviation times sqrt N, then that expression will follow the same normal distribution

[jolly pebble]

What would be a case where this is violated

[jolly pebble]

Right, as N-> Inf.

[nova yoke]

cauchy distribution is one example

most distributions you deal with in practice have finite variance though

[jolly pebble]

Why does it violate it..?

[nova yoke]

it has infinite variance (its tails are too "heavy")

its pdf looks like a normal distribution but more spread out

[jolly pebble]

Ahh ok

So if we sample from the cauchy distribution

Then the CLT won't apply?

Can you help me intuit all this

[nova yoke]

right, iirc if you take a sum of iid samples from the cauchy distribution the result is still cauchy

it doesn't converge to normal in the limit

[jolly pebble]

Ohh

So

1. Why does CLT apply for finite variance case
2. Why it doesn't apply for indefinite variance case

[nova yoke]

what kind of intuition are you looking for? have you ever seen one of those animations where they show the distribution of the sum of the number of "heads" in a sequence of coin flips, as the number of flips increases?

[jolly pebble]

I've seen a few animations

Particularly of that little toy with beads

[nova yoke]

as far as mathematical intuition, when you add independent samples from some probability distribution, the distribution of the resulting sum is the convolution of N copies of the original distribution (where N = the number of samples)

and the convolution of the normal pdf with itself is the normal pdf again

[jolly pebble]

Galton board iirc

[nova yoke]

so it's kind of a "fixed point" for the operation

[jolly pebble]

Convolution as in the convolution operation?

[nova yoke]

yea

[jolly pebble]

why is this so

[nova yoke]

just works out mathematically, it's pretty easy to show

[jolly pebble]

Hmm ok

Idk why im not able to like

"get" it

I'm trying to make it intuitively click

[nova yoke]

as for how you might guess that is a solution to "what distribution convolved with itself gives itself again" without already knowing it, there's probably some cool way to deduce that but offhand i can't recall how

[jolly pebble]

Hmm kinda the way we got e^x

[nova yoke]

yea maybe kind of analogous

[jolly pebble]

Ok so again

Take any distribution

Sample from it repeatedly

And umm

Ah ok

[cobalt nest]

Lévy distribution too

[jolly pebble]

So can we just say that

It's cuz

It's very unlikely to get sums that sum to the largest possible sun

Sum

Random sums will be closer to the average

[jolly pebble]

I think I get that this is the intuition here

But like why

[cobalt nest]

hedge, whats the confusion u have here

[jolly pebble]

Is there any property here

I mean

[nova yoke]

this is true (and is basically the content of the law of large numbers), but from that alone you wouldn't be able to conclude that the limiting distribution is normal

[jolly pebble]

What is the sort of underlying logic that goes "If we take sum of a bunch of samples, we will with a higher probability get sums which lie in the middle of the distribution than the rare cases where the sum is the largest or smallest possible"

[jolly pebble]

right that would be my second question

But as u said that seems more of a mathematical technicality

Which we can get to by uhh algerbraing our way there

[cobalt nest]

The Law of Large Numbers states that as the number of samples n increases, the average of the samples converges to the expected value (mean) of the distribution

[jolly pebble]

Righttt

[cobalt nest]

Extreme sums (either very large or very small) are rare because they require all the individual samples to be extreme simultaneously

[jolly pebble]

And what makes that rarer than the mean-ish values?

And why does this not work for the cases you mentioned

Where variance isn't finite

[cobalt nest]

ur violating the conditions of CLT 🙂

[jolly pebble]

Yea that's what I'm askingz why r they the conditions for the clt

[cobalt nest]

aaah i see

you want to know the idea behind CLT?

thats your main question?

[jolly pebble]

Yes

I'm trying to intuit the CLT

[cobalt nest]

aight okey i'll think of some intuition and get back at ya

[nova yoke]

yea like i said, it comes down to the convolution property and the fact that the normal pdf is a fixed point for that operation

not sure if there's a less technical explanation for why in the limit you would get something of the form e^(-x^2)

[jolly pebble]

Honestly I think my question has

Boiled down at least rn I think it has boiled down to

Just understanding why the law of large number holds true

I mean

Rn I feel like GIVEN the LLN, it OBVIOUS that the CLT will hold

[nova yoke]

no i wouldn't say that actually

the CLT is a lot less elementary than the LLN

[jolly pebble]

Yea I just have a FEELING

[jolly pebble]

Hmm

So like why does the LLN hold

[nova yoke]

the LLN is just saying that as you take the sample mean of a bunch of iid random variables, the variance of the result gets smaller, and in the limit the result "converges" (in various technical senses) to the mean of the distribution

like if you flip a large number of coins and compute the fraction of them that are heads, you'd expect the fraction to be close to 1/2

[jolly pebble]

Isn't this the "consistency" assumption

[nova yoke]

and you'd expect that as you increase the number of coins, you're more likely to get a result close to 1/2

[nova yoke]

wdym by this?

[jolly pebble]

I mean that that will only be true if the estimator for the mean is consistent

[nova yoke]

well the sample mean is consistent

[jolly pebble]

Ohh

[nova yoke]

because expectation is linear

[jolly pebble]

The sample mean is by default a consistent estimator for the population mean?

Makes sense

I mean seems trivial now that I think about it

[jolly pebble]

Oh? It's required to be linear?

[cobalt nest]

it is by definition

[jolly pebble]

And wdym when u say expectation is linear

[nova yoke]

$$E\left[\frac{1}{n}\sum_{i=1}^n x_i\right] = \frac{1}{n}\sum_{i=1}^n E[x_i] = \frac{1}{n} n\mu = \mu$$

[grand pond]

Bungo

[jolly pebble]

Ahhh rightt

[nova yoke]

it's defined as a particular sum (or integral) right?

[jolly pebble]

Omg I'm tripping it's literally the sum of vals

Divided by n

n

[nova yoke]

and integration is linear

[jolly pebble]

N

[jolly pebble]

Rightt

So given it's linear

It has to be consistent

I mean even if it was quadratic

[nova yoke]

for the mean yes

[jolly pebble]

It would have been consistent I suppose

[nova yoke]

if you want an unbiased estimate of the variance you have to tweak the 1/n to 1/(n-1), for example

[jolly pebble]

Sum of squares for example? It's also consistent?

[nova yoke]

and for other parameters there may not be any obvious unbiased estimator at all

but the the mean is simple regardless of distribution

[jolly pebble]

Omg u made me remember another query I had

Please explain that to me

The whole degrees of freedom shenanigans

[cobalt nest]

kekw x))

[nova yoke]

well the math works out the way it works out
but maybe the intuition here is that when you compute the sample variance, you need to know the real mean but you can only compute the sample mean, so that introduces a bit of "noise" into your calculation that you have to compensate for

[jolly pebble]

Yes but why is it n-1 qnd not like n-2 for example

That's what I don't get

[nova yoke]

ah i can't give you a simple intuitive reason for that, you just do the math and that's what happens

that doesn't mean there isn't a simple intuitive reason, i just don't know it offhand haha

[jolly pebble]

It's something something degrees of freedom something

[cobalt nest]

degrees of freedom are closely tied to the number of independent observations or parameters in a dataset, minus the number of constraints.

[jolly pebble]

Right

[cobalt nest]

suppose there is n data points

so there should be n deg of fred right ?

the sample mean impose a constraint that xi - mu = 0

[jolly pebble]

I'm a bit confused here

[cobalt nest]

thats why in the variance we do : $s^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2$

[grand pond]

Goëtia

[jolly pebble]

Yea so why do we use N-1 instead of like N-2 or N-k

Or idk N/2 or N/k

[cobalt nest]

to do n-2, u need another constraint

do to n-k, u need k constraint on the data sampling

[jolly pebble]

Yea exactly, that's what I'm asking "why"

[cobalt nest]

look, dgrees of freedom matter because they quantify the effective size or flexibility of a system

[jolly pebble]

What's the sample-population adjustment have to do with the degrees of freedom

[cobalt nest]

More degrees of freedom generally allow a model to fit data more closely, but this can lead to overfitting, fewer degrees of freedom impose simplicity, reducing overfitting but potentially increasing bias

degrees of freedom affect the precision of estimates and the power of statistical tests. More degrees of freedom typically lead to narrower confidence intervals and more sensitive tests

[jolly pebble]

Thee intuitive reason for using N-1 for sample variance is that cuz we are sampling from a distribution, subtracting from the samples mean and squaring it will lead to underestimation of the numerator term in the variance

So we are trying to account for that underestimation by ourselves reducing the denominator

But this only gives us intuition for why the denominator should be reduced

[cobalt nest]

you could think of it that way

[jolly pebble]

Not for "by how much"

[cobalt nest]

The key point here is that s² is designed to be an unbiased estimator of the population variance σ²,this means that, on average, s² should equal σ² when computed over many samples

degree of freedom or whatever, n-1 can be derived exactly from the mathematical expectation

[jolly pebble]

I think there's some logic

Here

[cobalt nest]

let me derive it for ya rq

$\sum_{i=1}^n (X_i - \bar{X})^2$ this is the deviations right?

[grand pond]

Goëtia

[jolly pebble]

That is the variance yes

[cobalt nest]

$(X_i - \bar{X})^2 = (X_i -\mu - (\bar{X}- \mu))^2 = (X_i - \mu)^2 -2(X_i -\mu)(\bar{X} - \mu) + (\bar{X} - \mu)^2$

[grand pond]

Goëtia

[cobalt nest]

$E[\sum_{i=1}^n (X_i - \mu)^2] = n \sigma^2$ agree?

[grand pond]

Goëtia

[cobalt nest]

$\bar{X} - \mu = \frac{1}{n}\sum_{i=1}^n (X_i - \mu)$

[grand pond]

Goëtia

[cobalt nest]

$\sum_{i=1}^n (X_i - \mu)(\bar{X} - \mu) = \frac{1}{n} \sum_{i=1}^n \sum_{j=1}^n (X_i - \mu)(X_j - \mu)$ if $i \neq j$ then $$E[(X_i - \mu)(X_j - \mu)] = 0$$ since they are i.i.d agree @jolly pebble

[grand pond]

Goëtia

[cobalt nest]

last term here when applied the expected value to it is just the variance of the sample mean evaluating to : $\frac{\sigma^2}{n}$

[grand pond]

Goëtia

[jolly pebble]

Hmm

Thanks goëtia

[cobalt nest]

bringing everything together we get $E[\sum_{i=1}^n (X_i -\bar{X})^2] = (n-1)\sigma^2$

[grand pond]

Goëtia

[cobalt nest]

you got it why n-1 now? @jolly pebble

[jolly pebble]

Yes

But the connection to the DOFs is still unclear

[cobalt nest]

DOF?

[jolly pebble]

Degrees of freedom

[cobalt nest]

aah

well it just depends on the estimator

[jolly pebble]

Hm?

[cobalt nest]

u know of the MLE?

[jolly pebble]

Yes

[cobalt nest]

we divided by n

[jolly pebble]

So here we are not adjusting for DOFs?

[cobalt nest]

In linear regression, the degrees of freedom for the residual variance depend on the number of parameters estimated. Specifically, if you estimate p parameters (including the intercept), the residual variance is computed by dividing by n-p, suppose ur in simple linear regression y = ax + b + e (a,b parameters)

this is the residual variance

[jolly pebble]

I guess I'll have to read a bit Abt degrees of freedom on wikipedia

Thx a lot for ur help goëtia

.close

[midnight plank]

Channel closed

Closed by @jolly pebble

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[maiden forge]

i got a quick question

[maiden forge]

currently doing this question

[kindred dagger]

You need help factoring?

[maiden forge]

sort of

just got a question

are u allowed to put 1 outside the bracket?

like this 1(3x+1)

[kindred dagger]

Definitely

[maiden forge]

ah ok

[kindred dagger]

In fact, you should, because it makes factoring easier

[maiden forge]

I thought you weren't allowed to do that but thank you for clearing up the confusion!

wait so the answer would be (3x+1) (3x+1) ?

[kindred dagger]

You can simplify further

||a * a = a^2||

[maiden forge]

expanding?

[kindred dagger]

No

Since two of the same values are being multiplied

[maiden forge]

ohhhhhh

(3x+1)^2

[kindred dagger]

,w expand (3x + 1)^2

[grand pond]

Results provided by WolframAlpha

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

Requested by .king.leo.

[kindred dagger]

Nice

!done ?

[midnight plank]

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

[maiden forge]

.close

[midnight plank]

Channel closed

Closed by @maiden forge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[sand flume]

can someone explain how this interpretation differs from margin of error: is it only because we didn't multiply by a critical value. also why would we use standard error of margian of error to make a interval for a cofindence level?

[midnight plank]

@sand flume Has your question been resolved?

[midnight plank]

@sand flume Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[frank osprey]

I do not understand why it cannot be the case that A' has an enemy of B on its left or B has an enemy of A' on its right, so even if we reduced the number of hostile couples by 1, we would be adding at least 1 back, can anyone help me to understand it please?

[midnight plank]

@frank osprey Has your question been resolved?

[midnight plank]

@frank osprey Has your question been resolved?

[midnight plank]

@frank osprey Has your question been resolved?

[midnight plank]

@frank osprey Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[regal knot]

I don’t get what I have to do next

[regal knot]

is it 99-70=29

then divided by 4

[carmine sigil]

@regal knot do you know how to convert this into a z-score and look up values in a normal CDF table?

[regal knot]

yeah

[carmine sigil]

Convert both of these values into a z-score. Then you have 2 points on a normal distribution which you can use to find the two unknowns: mean and stdev

[regal knot]

Don't I already have 2 points 70 and 99?

[carmine sigil]

Yes, you are using the those two points, except in the z-score world as well

There are two ways to go from a value to a z-score, one is using the normal cdf and the other using the mean and stdev

You're using the normal cdf to find the z-score, then using the formula to relate regular x coord (i.e. 70 and 99) to z-score via the mean and stdev, you are coming up with two equations and two unknowns

@regal knot still with me?

[regal knot]

Kinda?

so am I doing a system of equations to get rid of one of the variables

[carmine sigil]

You're doing the system to find both variables

Once you do that you can use them to find the z-score associated with 80 to answer the question

This one you need to use the mean and stdev

[regal knot]

but theres not exact value for 0.16 and .99 in the z score table

or do I just do the closest one

[carmine sigil]

You need to estimate

Using a linear interpolation

Or dead reckoning, if you don't need many digits of accuracy

[regal knot]

so i'd be like

1. 70= u + (-1.00) x Sigma
2. 99=u + (2.33) x Sigma

and then you subsitute

[carmine sigil]

Ummm

Those are not the correct z-scores.

At very least 99 is wrong

But yeah, that's the idea

[regal knot]

ohhh

i see

I'm suppose to use 16% and 0.15%? right then convest to z score

[carmine sigil]

16% is pretty close

-0.995

0.15% = 0.0015 is approximately z-score of 2.965ish

[regal knot]

I got -2.96 and -1

[carmine sigil]

How on earth would you get -2.96?

[regal knot]

its was suppose to be for 16% but it gets 0.16%

[carmine sigil]

(wrong tail direction)

Anyway, I need to go afk, best of luck, you're 95% of the way there!

[regal knot]

thank you

I think I get it now

.close

[midnight plank]

Channel closed

Closed by @regal knot

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[tight bison]

I’m not the smartest and I’m not that cocky but I’m almost 10000000% sure I did this correct

But the computer said the answer was wrong

Nvm

I completely forgot I u subbed

.close

[midnight plank]

Channel closed

Closed by @tight bison

Use .reopen if this was a mistake.

[vale zephyr]

"10000000% sure"

[tight bison]

😂

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[errant fable]

can you help me with this question

[midnight plank]

@errant fable Has your question been resolved?

[cobalt nest]

!status

[midnight plank]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[cobalt nest]

@errant fable

[errant fable]

6

[cobalt nest]

good

consider .close

[errant fable]

Sorry could i ask abot another question?

[cobalt nest]

oke

[errant fable]

how can I rearrange this to be able to put into the equation

[cobalt nest]

?

[errant fable]

i need to rearrange equation to be able to find values to put into this equation

[cobalt nest]

what equation?

[errant fable]

Partial sum for geometric sequence

i just dont know how to rearrange to in form of a * q^r

its okay i dont think im explaining well ill be able to figure it out

.close

[midnight plank]

Channel closed

Closed by @errant fable

Use .reopen if this was a mistake.

[cobalt nest]

its ok just take ur time to formulate ur question in ur own mother language translate it to english using AI, and post it here we'll do our best to help you @errant fable

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[last slate]

Calc 2: A reservoir is shaped like a sphere of radius 5 m. It is filled up to 8 m with water.
Compute the work required to pump the water to 2 m above the top of the reservoir.

My equation for work is (9800)(12-x)(25-x^2)(pi) integrating from 0 to 8. This does not give the correct answer but close to the solution answer. Where did I go wrong?

[midnight plank]

@last slate Has your question been resolved?

[cerulean solar]

where does the 0 to 8 come from

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[inland patio]

If the $\limsup a_n=y$ of a real sequence $(a_n)$ is negative infinity, why does this imply that $s_n\to -\infty$, where $s_n=\sup_{k\geq n}a_k$? The definition of $y=-\infty$ I'm working with is that ${a_1,a_2,\ldots}$ is not bounded from below (but it is bounded above) and no finite $\limsup$ exists, where the finite $\limsup$ is defined in terms of: \

For every $\epsilon>0$;\

1. there exists $N\in \mathbb N$ such that $a_n<y+\epsilon$ for all $n> N$;\
2. for every $N\in\mathbb N$ there exists $n>N$ such that $a_n>y-\epsilon$.\

My attempt; if $y=-\infty$, then ${a_1,a_2,\ldots}$ is unbounded. Suppose on the contrary that $s_n\geq M$ for infinitely many $n$, where $M$ is some real. I want to derive some contradiction, but I don't know how.

[grand pond]

psie

[midnight plank]

@inland patio Has your question been resolved?

[cobalt nest]

that would imply that there exist k >= n : a_k >= M, by the definition of s_n = sup_k>=n a_k

[inland patio]

are you sure that there exists such a k>=n such that a_k>=M?

[cobalt nest]

well for infinitely many n

to be sure

you can do

a_k >= M - e

honestly a straightforward proof would do it instead of by contradiction

[inland patio]

I just don't see how 😅

[cobalt nest]

s_n is the supremum of {a_n,a_{n+1}, ...} right

[inland patio]

I'm trying to prove the equivalence of two limsup definitions by the way

right

[cobalt nest]

s_n >= a_k

since lim sup a_n = -infty

for any real M

there exist N

k>= n > N : a_k < M

this implies

sup_{k >= n}a_k <= M

thus s_n <= M

[inland patio]

how would you motivate the existence of such an N? Sorry to bother about this 🙂

[cobalt nest]

pick k = n

no problemo

k >= n > N

oke?

[inland patio]

ah ok, you used the fact that limsup a_n=-infty means {a1,a2,...} is unbounded, makes sense 👍

[cobalt nest]

@inland patio consider .close if ur question is answered

[inland patio]

yes 👍

thanks for the help!

.close

[midnight plank]

Channel closed

Closed by @inland patio

Use .reopen if this was a mistake.

[last slate]

water is filled up to 8

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[noble vapor]

what have you trie

d

[warm inlet]

i really don’t know what i’m looking at

fighting the urge to use gpt

[white gate]

Use the point (1/2,4) to split the region into 2 parts

[dusty portal]

Nah, don't.

[warm inlet]

but would i integrate with x or y

[dusty portal]

Depends on your preference. I usually default to x.

[noble vapor]

x

[white gate]

Wdym of course it's x

You are not rotating anything so it doesnt matter

[noble vapor]

y works as well tho haha

[warm inlet]

if i split it in half wouldnt using y-axis be easier

bc it’s a straight line pmuch

[dusty portal]

They ask...tricky questions on exams sometimes. It should be an open response.

[noble vapor]

its the same basically

[white gate]

Yeah you use a straight line x=1/2 to split it

[dusty portal]

It's still using 2 curves. So, in terms of work, it's not necessarily better.

[noble vapor]

with respect to y you get square roots wich is uglier

[warm inlet]

rahhh i hate calculus

[white gate]

this is just the beginning :)

[warm inlet]

what…

[noble vapor]

it gets worse haha

[warm inlet]

8 units of hell and it’s only the beginning 💔

[white gate]

trust me, you'll love it when you get deeper

[warm inlet]

let’s pause on that one

[dusty portal]

Wait until you see real analysis. Then you'll cry tears of blood.

[warm inlet]

i already do

[white gate]

rip

[warm inlet]

okay so i split it

and i have no idea what im doing still

[noble vapor]

do you know how to find the area under a curve?

[warm inlet]

integrate

[noble vapor]

do you know how to find the area between two curves?

[warm inlet]

yeah

i was just doing it

[noble vapor]

okay what exactly are you stuck on then

[warm inlet]

they were always in line with either the x or y axis

and it told me what to use

so it was easy

[dusty portal]

Elaborate.

[warm inlet]

like

it was either super obviously y axis or super obviously x axis

[noble vapor]

ahh wel here its obviously x axis except if you like pain and want to work with roots, but it shouldn't matter which one you pick

[dusty portal]

Ok.

Well, try to figure out which functions you should integrate (i.e., which is greater than the other on the partitioned intervals?)

[white gate]

Most of the time choosing which axis only matters when it comes to volume of solid of revolution

This is area so it doesnt matter, plus, going for y is even harder

[warm inlet]

okay so would i find the area under 2 and then another 2 and then another 2?

[midnight plank]

@warm inlet Has your question been resolved?

Channel closed

Closed by @warm inlet

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[mint ravine]

can someone please help me on this question

[tepid lodge]

what's the question?

[mint ravine]

be patient my computer is lagging right now

nevermind i don't need help anymore

.close

[midnight plank]

Channel closed

Closed by @mint ravine

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[kindred dagger]

I need someone to check my work for #38

(original question is loading)

[olive matrix]

it's right

[kindred dagger]

Thanks

.close

[midnight plank]

Channel closed

Closed by @kindred dagger

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[crude slate]

i dont get this

[crude slate]

what did I do wrong with the formula?

[sharp coral]

,, \proj_{\vec b}\vec a = \frac{\vec a \cdot \vec b}{\vec b\cdot \vec b}\vec b

[grand pond]

cloud

[crude slate]

how do I find the orthagonal complemetn?

[sharp coral]

(projection) + (orthogonal complement) = original vector

[crude slate]

is there stil lsomething wrong

that im unaware of ?

[sharp coral]

what is $\vec a\cdot \vec b$?

[grand pond]

cloud

[midnight plank]

@crude slate Has your question been resolved?

[crude slate]

Oh ty!

Forgor negative

[lethal path]

type .close if you're done

.close

[midnight plank]

Channel closed

Closed by @lethal path

Use .reopen if this was a mistake.

[lethal path]

(and .reopen if you want to reopen)

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[fleet sonnet]

A tower stands vertically at the base of a hill that inclines upwards at 30 degree to the horizontal. from a point 25 metres from the base of the tower and directly up the hill the tower subtends an angle of 52 find the height of the tower giving your answer correctt to the nearest metre

[fleet sonnet]

how do i draw this diagram

i dont understand the part where it subtends an angle of 52

[tepid lodge]

if you draw a line between the top of the tower and that point

the angle between that line, and the hill, is 52 degrees

[fleet sonnet]

so is it angle of depression?

[tepid lodge]

no its the angle at the base

like

[fleet sonnet]

i drew the tower and thehill going up

so i draw a dotted line from the base tower

and then it ends at the point

where do i do the 52

[tepid lodge]

blue angle is 52

[fleet sonnet]

huh

oh

[tepid lodge]

sorry for the quality why is my Paint set to 77 by 128 pixels

[fleet sonnet]

ok so its inwards

where do i start

so the diagram is like this right

[tepid lodge]

yes except the tower needs to be taller

because if that dotted line was horizontal , then the 52 would be 30

[fleet sonnet]

okay

where do we start

[tepid lodge]

find the height of that point on the hill

and also the horizontal distance from the tower to that point

[fleet sonnet]

for height u would use sin right

[white gate]

construct OA to be parallel to the bottom line

[fleet sonnet]

okay

whats it for

if we make ir parallel

[tepid lodge]

im pretty sure the tower is meant to be taller

that 52 looks less than 30

[white gate]

oh

yeah true

the angle would be negative

[fleet sonnet]

ok so like this

cant u find the angles inside the triangle cuz it says its a vertical

hmm

[white gate]

probably lower the point down

[tepid lodge]

i meant

like

[fleet sonnet]

u want the 52 to be a bigger angle and 30 to become smaller?

would it rlly matter

i just need the logic behind it

[tepid lodge]

tower higher

[tepid lodge]

probably not, but you would get a confusing answer if the diagram is misleading

[white gate]

you can see what happens if it's higher

[fleet sonnet]

wait thats negative

oh

[white gate]

yeah it needs to be lower

[tepid lodge]

exactly

[fleet sonnet]

okay wait

so this is how it would look

[tepid lodge]

yess

[tepid lodge]

now draw a line straight down from that point with the 52 angle to make a triangle

[fleet sonnet]

okay

we name that y

so sin 30 = y/25

[tepid lodge]

yeah

[fleet sonnet]

then y= 21.25

[tepid lodge]

uh

what

what is sin 30

[white gate]

@fleet sonnet is law of sine allowed?

[fleet sonnet]

ye

im doing questiosn related to law of sine cosine

[fleet sonnet]

0.5

[tepid lodge]

oh-

[tepid lodge]

then you don't need the orange line, you can use the triangle that's already there

but its just easier without law of sine

[fleet sonnet]

oh

[white gate]

lmao

[fleet sonnet]

oh

so then u use law of cosine

to find x

[white gate]

sine is easier tho

[fleet sonnet]

wait i mean sine ye

what if i forgot about both these formulas

what do i do

without using them

u never nkow bruh i might forget during test

[tepid lodge]

then you do

this

wait lemme fix my paint first

[fleet sonnet]

okay

[white gate]

well

this also works

[fleet sonnet]

oh u split up

law of sine would be easiet right

[white gate]

ye

the one above is the 2nd easiest

[tepid lodge]

yes that

[fleet sonnet]

wait uhh

do we need to find x

oh ye we do

[fleet sonnet]

we find x using cos right

[tepid lodge]

yeah

y is sin(30) * 25, and x is cos(30) * 25

[fleet sonnet]

yes so 21.65

[tepid lodge]

then d is tan(22) * x, and h is y + d

[fleet sonnet]

oh

ye i get it

okay lemme calc rq

but ty

okay i get it

ty.

.close

[midnight plank]

Channel closed

Closed by @fleet sonnet

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[chilly cobalt]

hi! im prepping for a middle school competition and this was one of the questions last year, what do i do for b)?

[chilly cobalt]

(im supposed to find Q, by the way)

i think its gonna be something to do with pressure right? cause they put that its open to the atmosphere

also for a) i have d = this thing

[midnight plank]

@chilly cobalt Has your question been resolved?

[chilly cobalt]

<@&286206848099549185>

[midnight plank]

@chilly cobalt Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[slim eagle]

When deriving tangent equations for parabolas, why does the conversion using the slope form involve replacing ( a ) with (-a) (e.g. going from ( y^2 = 4ax ) to ( y^2 = -4ax )), while in the parametric form the conversion is achieved by substituting ( x ) with (-x)? What is the reason behind these different transformation approaches in the two forms of the tangent equations?

[grand pond]

The modest AI

[midnight plank]

@slim eagle Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[fleet sonnet]

how would i do this question A parallelogram has sides of length 3x7 cm and 6x8cm and the acute angle between the sides is 48. find the lengths of the diagonals of the parallelogram

[fleet sonnet]

why did they give 3.8 but the . is in the middle

instead of 24

vectors?

[slim eagle]

nah nvm

[fleet sonnet]

idk how to do it

where do i start

[slim eagle]

draw a diagram first

of the parallelogram

and indicate what you know about is given in it

[fleet sonnet]

okay wait a bit

[last slate]

what an modest ai would tell.

[fleet sonnet]

it should be like this right

[slim eagle]

do you know about the

parallelogram law of vector addition?

[fleet sonnet]

uhhhh

no

for vectors im still kinda new

but i know its like a+b

[last slate]

Thats why he is here lol.

[fleet sonnet]

is the vector

thats like the only thing i know

[flat plinth]

You could just do this with the cosine rule

[fleet sonnet]

whats the bottom one for

[slim eagle]

magnitude of diagonal

[fleet sonnet]

how

[slim eagle]

R

[obsidian wedge]

it is the resultant

[flat plinth]

This is much simpler

[slim eagle]

you can also derive it

if you want

[fleet sonnet]

i have no clue what that is

the question should be asking me to solve using cosine or sine law

[obsidian wedge]

Look it up

Oh

So you're restricted to those two ideas

[slim eagle]

oh

then use cosine law

[fleet sonnet]

not rlly but

idk

[flat plinth]

It's simpler so it'd make sense

[slim eagle]

simple

[fleet sonnet]

ye i want a simple way

[slim eagle]

use cosine rule

[fleet sonnet]

how

do i draw a diagonal

through mid

[slim eagle]

its pretty basic

now

if you know the formula

[fleet sonnet]

i know cosine law formula

[slim eagle]

its just plugging in the values now

[fleet sonnet]

does the 48 get split into 24 and 24?

[flat plinth]

Hear me out

[fleet sonnet]

okay

[flat plinth]

Draw the other diagonal

[fleet sonnet]

oka y wait

[flat plinth]

And use the fact that the bottom is also 6x8

[fleet sonnet]

yes

[fleet sonnet]

oh so then u just do x= 21^2 + 48^2 - 2x48x21 cos 48

that would be the same with the other way right

[flat plinth]

Yep

[obsidian wedge]

So there's (a-b)^2 instead in the cosine rule... The resultant seems more apt for this problem

[flat plinth]

Remember to root that

[fleet sonnet]

oh yeeee

root

[fleet sonnet]

huh

[obsidian wedge]

You won't get it

[flat plinth]

Lol

Poor kid

[obsidian wedge]

Algebraic Simplification

[fleet sonnet]

ye i dont get it

[obsidian wedge]

It's alright

[fleet sonnet]

is that uni grade lvl

or like y10+

[flat plinth]

Dw abt it you'll notice it after getting familiar with the rule

[obsidian wedge]

No

[flat plinth]

This

[obsidian wedge]

It's algebra

[fleet sonnet]

oh ok

[obsidian wedge]

The resultant is vector relatedhowever