help-27

[karmic mesa]

but dont we compensate for repeated solution? like f(0), f(f(0))

[deft tapir]

We do

It all depends on the values b, c, d, etc

I'm not sure how to account for how many solutions those have

Cuz for all I know it could be 3

Oh I have an idea

[karmic mesa]

go for it

[deft tapir]

So as to account for the possible solutions, we can check for f'(x) = 0

[karmic mesa]

and then just draw the whole graph?

well

[deft tapir]

We get two values, aka a domain of images

Any value within that domain has 3 roots

[karmic mesa]

erm

why are we talking about root here

[brave plaza]

you can make a recurrence based on the number of roots in the interval (0,4) of the function f^k(x)

[karmic mesa]

.

[deft tapir]

So for example f(x) = 3

[karmic mesa]

is root and grapht the same thing

[deft tapir]

Has 3 intersections aka 3 solutions

[deft tapir]

A root is basically a solution

Altho roots are usually solutions for f(x) = 0

[azure badge]

in the question whats ment by a

[deft tapir]

The number of solutions I presume

[azure badge]

kk

[deft tapir]

Ooooo

If you look close

You'll notice that all 3 solutions to f(x) = 3 are within the interval [0 ; 4]

Meaning that they also have 3 solutions

And that applies to all solutions

[karmic mesa]

yeah that's my initial thought

and i found a= 3^8 +3^7 +...+3^0

not sure how you found 3^9

it's like a double of mine

[deft tapir]

Which means for f(x) we have 0, 3
For f2(x) we have 0, 3 and 3 other solution
For f3(x) 0, 3 and 3x3
f4(x) : 0, 3, 3³

I think you just end up with 3⁸ + 1

So 6562

[brave plaza]

not quite right

[deft tapir]

Why not

[karmic mesa]

why is my cam blurry

[deft tapir]

Rip

[karmic mesa]

well basically you draw kind of a chart

[azure badge]

dont u jst need to look for what values n to the power of 9 applies this

[karmic mesa]

like this

[karmic mesa]

it's not the power

it's the f(f(f(f(f(x))))) like that

[azure badge]

yeah ik

[brave plaza]

for f3(x) each of the 4 previous values in interval (0,4) yields 3 solutions, so we get f^3(x) = 0 for 14 values

in general any solution in (0,4) will yield 3 more on the next iteration

[deft tapir]

Yeah that's just 2×3×3×...×3 8 times

[deft tapir]

Yeah hence why I said 3³

3 solutions, give 3 solutions, which give 3 solutions

That's just exponents of 3

[brave plaza]

4 solutions give 3 solutions

[azure badge]

just find the zeros using midnight formula

[deft tapir]

That's kinda like counting probability

It's 2 × 3⁸ I'm pretty sure

[brave plaza]

let $I_k$ be the number of roots in the interval $(0,4)$, we have $I_{k} = 1 + 3 \cdot I_{k-1}$

[woven radish]

k

[brave plaza]

the number of solutions is $I_k + 1$

[woven radish]

k

[deft tapir]

Wouldn't that be 1 + 3^n

I'm not sure anymore

[brave plaza]

the solution to this recurrence is $\frac{3^k - 1}{2}$

[woven radish]

k

[brave plaza]

so we get $a_k = \frac{3^k + 1}{2}$

[woven radish]

k

[karmic mesa]

yeah that's what im saying about

[deft tapir]

Yeah I overlooked the fact that 0 doesn't generate solutions

My apologies

[karmic mesa]

thanks guys for ur helps!

.close

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[glad arrow]

Could anyone help me graph the last radical function for number 1A? I’m not sure how

[winter patrol]

if unsure, start with a table of values

for a)
consider using values of x such that
3-x
will be a perfect square

[glad arrow]

I meant for number 1A

[winter patrol]

oh

same idea

table of values

use values of where
x-3 is a perfect square

[glad arrow]

For the graphing I’m supposed to graph the equations on the left then plug in the x’s right? Because I did c-e then plotted those points first and it feels like I did something wrong

[winter patrol]

you don't need to complete the parts in the given order

plotting known points is a key component in graphing
there's no issue in getting those first

and for the graph of the first piece
that should connect down to the point you made at (-7,-7)
and you should also determine the x-intercept for that part

[glad arrow]

So the left top graph I should drag down till it reaches -7,-7?

[devout snow]

@glad arrow Has your question been resolved?

[glad arrow]

<@&286206848099549185>

[runic grove]

,w plot y = sqrt(x)

[woven radish]

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[runic grove]

Can you somehow translate and transform this graph

To get -√x-3 + 1

[glad arrow]

It’d be up 1 unit, right 3 units then flipped over the x-axis

Do you mind answering the second question about the -7,-7 point?

It keeps tripping me up cus it’s not being used but I feel like it’s meant to be

Nvm thanks everyone for the help

.close

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[foggy geyser]

How do I start w/ evaluating this limit??😭 #17

[foggy geyser]

Would I make both the tan into sin/cos

[dark tundra]

you can

[thorn perch]

do you know l' hopital?

[foggy geyser]

I don't think so

[dark tundra]

you can solve this without LH, but you need to know a special trig limit

[thorn perch]

ok, if not you can also solve it by manipulating it

[foggy geyser]

oh yea

we have these ones

if thats what u mean

[foggy geyser]

how would you manipulate it?

[thorn perch]

in that case, you should rewrite tan as sin/cos

what i would do is first prove lim x->0 of tan(x)/x, because you can separate the original limit into tan3x * (1/3tan2x)

you could also just directly substitute sin and cos

that might be easier

[dark tundra]

just split to sin and cos yeah

[foggy geyser]

like this?

[dark tundra]

Yeah

[thorn perch]

yep

[thorn perch]

now given these limits, how would you manipulate your current expression?

you want to get a limit in the same form

[drifting mauve]

lowkey i don't think this is necessary 🤔

[thorn perch]

i'm just working off what they know

[drifting mauve]

well

[foggy geyser]

theres like probably a way to do it our teacher doesnt teach us Im taking a high school class

[drifting mauve]

sure

[foggy geyser]

would i like separate it like this but then also like maybe separate the sines to get the eqn on my formula sheet?

[thorn perch]

ok specifically this one

[foggy geyser]

yeah ok

[drifting mauve]

what's the limit of cosx as x approaches zero?

[foggy geyser]

ohhh

[thorn perch]

yeah u also need to know this

[foggy geyser]

like this right

[thorn perch]

yep

don't forget the 1/3

[foggy geyser]

would the lim x->0 of the 3x/2x part be 0?

but then that would make the answer 0

[thorn perch]

well, what happens when you simplify 3x/2x?

[foggy geyser]

1.5x?

[thorn perch]

u cancel out the x

[foggy geyser]

oh no wait

oh

[thorn perch]

yeah

[foggy geyser]

thank you so so much i have solved this thanks to your help!!

[thorn perch]

no problem

[foggy geyser]

.close

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[vivid estuary]

Define (d : \mathbb{R} \times \mathbb{R} \to \mathbb{R}) by
[
d(x,y)=
\begin{cases}
0, & x=y,\
1, & x\ne y.
\end{cases}
]

\noindent
Consider (f : (\mathbb{R},d) \to (\mathbb{R},|\cdot|)) defined by
[
f(x)=
\begin{cases}
0, & x=0,\
\sin!\left(\frac{1}{x}\right), & x\ne 0.
\end{cases}
]

\noindent
where (d) is the metric from (a) and (|\cdot|) denotes the absolute value. Is (f) continuous at (x=0)? Prove or disprove.

[woven radish]

Branshi (Hints only plz)

[vivid estuary]

So I'm a bit confused on this question

I want to try proving this with epsilon delta rather than with open set characterization

To do that for any epsilon > 0 we need to find a delta such that when d(x, 0) < delta, we have |sin(1/x)| < epsilon

We know |sin(1/x)| <= 1

[sand pumice]

what's the only possible choice you have for delta?

[vivid estuary]

delta = 1?

if delta < 1

[sand pumice]

yes

[vivid estuary]

but thats where I'm getting mixed up, what does it mean for delta < 1

does that mean it has to be 0

because d(x,y) only has values 0 and 1

[sand pumice]

yes

but 0 isn't allowed in the definition

[vivid estuary]

0 isnt allowed?

oh

because f(0) = 0?

mm so are we supposing x is not equal to 0 at all at the start of this proof?

[sand pumice]

hold on

i forgot you don't need 0<d(x,c)

[vivid estuary]

yeah thats for the limit I think

[sand pumice]

yes so 0 is the only point you can take

then what do you get when you consider |f(x)-f(0)|

[vivid estuary]

just 0?

[sand pumice]

yes

[vivid estuary]

hm ok I see that makes sense

[sand pumice]

so you'll have 0 for any choice of epsilon, so long as your delta is <=1

[vivid estuary]

why less than or equal to 1

thats what my professor had in his solution

but wouldnt it be strictly

less than 1

[sand pumice]

I'm talking about the choice of delta itself

[vivid estuary]

yeah

if delta = 1

oh

I see what you mean

[sand pumice]

👍

[vivid estuary]

ok that makes sense thank you for the help!

.solved

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[hasty zodiac]

What is the negation of "Bob likes men and women"

[hasty zodiac]

please ping me if you respond

[buoyant condor]

@hasty zodiac

Uhh you realise how "bob likes men and women" is the same as "bob likes men and bob likes women"?

So you can say p = bob like men q = bob likes women

And negate that

~(p ^ q)

[candid maple]

if the above was not clear enough, I'll drop a hint and leave continuing to the other helper.
hint: an AND statement is true when both of its premises are true. what conditions should its logical negation satisfy?

[hasty zodiac]

ok but hear me out

would it then be
Bob does not like men or bob does not like women, right?

[buoyant condor]

Yeah

[hasty zodiac]

let me ponder rq dont close the channel

[buoyant condor]

Take ur time

[hasty zodiac]

ok wait so

wait nvm i had a train of thought

😭

[buoyant condor]

Happens

[last parrot]

Bob neither likes men nor women

[buoyant condor]

❌

[last parrot]

Huh

[buoyant condor]

That's incorrect

[candid maple]

!nosols, and too strong.

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[last parrot]

Im i too strong for bro💀

Then the negation for and is or

If not explicitly

[buoyant condor]

De Morgan's law yes

[last parrot]

My discrete maths prof say that i can use two cases neither, or depends how strong you want

But if you need broad range then use or

[hasty zodiac]

"Bob likes men and women"
essentially implies that there exist a man and a woman that bob likes

so the negation is that for all men and women, bob doesn't like any of them

so for the sake of argument, if we say that there is only two genders male (men) and female (women)

then could you also say that the negation is
for all men, women: bob does not like men and bob does not like women

[buoyant condor]

A negation of a statement simply states that that statement is not true

[hasty zodiac]

im still wrapping my head around it a bit so apologies if i said smth dumb as bricks 💀

[last parrot]

And is both must correcy

[buoyant condor]

I don't know why you are bringing existential and universal quantifiers in the mix

[last parrot]

And or doesnt have the case where both is correct

[buoyant condor]

This is purely predicate logic we are arguing with

Not first order

[hasty zodiac]

pondering

🤔

[buoyant condor]

The statement at the end does not cover two other possibilities: that bob likes men and not women or that he likes women and not men. Both of which render the original statement false.

[buoyant condor]

When you say "there exists" or "for all women" you are arguing in first order logic

[hasty zodiac]

ok wait i think my brain's getting there

[last parrot]

And bob here is not x so cant use quantifiers anyways

Theres only one bob

[hasty zodiac]

aight got it

thx gng

.close

[devout snow]

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[last parrot]

All good

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[dense mortar]

Aight smellas so I have a lil question that is definitely NOT minecraft related...

Basically, we have a set of n different numbers. First we pick one of them and "mark" it. Then we choose a number from the set at random, until we get our "marked" number (yes, we can choose repeat numbers). After that we mark another number and start the process all over again, doing it α times, yaaaaay.

On average, how many tries would it take for us to complete this process?

[last parrot]

So firstly probability of pick a marked number in a single draw is P=1/n

Expected value also 1/P

Which is 1/(1/n) =n

If N is total number of a tries then E(N) =a.n then

[last parrot]

a.n tries would be my last answer

[winter torrent]

i think a(n+1) if you're including the draw where you mark it

[last parrot]

Isnt it an?

[winter torrent]

if we imagine n is 1

then each trial will take two draws

[last parrot]

This is not picking with replacement from a set of different n?

[restive river]

um wouldnt picking any number suffice to mark it making that P of that = 1

[last parrot]

Great point

[winter torrent]

First we pick one of them and "mark" it. Then we choose a number from the set at random, until we get our "marked" number

i interpret that as picking two for n=1

[last parrot]

What if that point is also included as one of n rocks?

[winter torrent]

once to mark and once to get the marked number

[winter torrent]

also

after that we mark another number and start the process all over again
are we choosing from n-1 numbers here? or does our original number go back into the pool?

[last parrot]

I think we are picking with repeats and looking for average?

[dense mortar]

Nahh we don’t include that one

[last parrot]

For example if we have a coin then we throw the probability of head is 1/2 not 1/3 right

[winter torrent]

oh then it's a * n

what about the other question that came up?

[last parrot]

The average of tries

[restive river]

by complete meaning marking all of numbers then picking them each once after marked ?

[dense mortar]

By complete I mean after we pick the final marked number, where marking the number doesn’t count as choosing it. We could just assume that every time it’s just the number one that is marked I guess, doesn’t change the probability

[restive river]

you want to do this process n times, for all numbers or just a times irrespective of how many times repeat process

[dense mortar]

Just a times

[restive river]

ok

[dense mortar]

More so like, you write down your lottery numbers, which can repeat, and randomly choose the numbered balls from the bin until you get all your numbers, where if you don’t get your number you just throw the ball back in

[devout snow]

@dense mortar Has your question been resolved?

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[haughty acorn]

can any1 tell me why the n here should be -1/2 and not -1 i checked on internet and the asymptote was y = x-1/2 not y = x-1 , chatgpt told me its because i ignored the very small terms under the sqrt and instead of x(1) it would've been x(1/2x) so y would be x-1/2

[haughty acorn]

and y = x-1/2 is the correct asymptote of the function but i dont get why n is not -1 and its -1/2 i tried to force out x out of the square root and since x goes to inf |x| = x so x -1 -x = -1

[devout snow]

@haughty acorn Has your question been resolved?

[thick schooner]

u can't use the limit difference rule here

which is presumably how you got -1

,, \lim_{x \to \infty} \qty(|x| \sqrt{1 + \frac 1x + \frac {1}{x^2}} - x) \neq \qty(\lim_{x \to \infty} \qty(|x| \sqrt{1 + \frac 1x + \frac {1}{x^2}} )) - \qty(\lim_{x \to \infty} x)

[woven radish]

slayla

[haughty acorn]

but why

[thick schooner]

you need the limit of at least one of the functions to exist

to even use the "rule" or whatever you want to call it

by exist i mean the limit should be a finite real number

in this case both individual limits don't exist, so it's outside the conditions required to use said "rule"

infinity + finite number = infinity
finite number + = -infinite

but we're dealing with the infinite - infinite case, which is an indeterminate form

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[blissful harness]

hey

[blissful harness]

could anyone help me with proving that the circumcircle of BCX intersects line AX at its midpoint?

BX and CX are tangent to the circle in the diagram

Apparently it can be done with "striaghtfoward" angle chasing but I tried for almost an hour and still haven't found anything

[swift valve]

As in circumcircle intersets AX at D? Just making sure D is the midpoint here

[blissful harness]

no no the circumcircle intersecting AK at its midpoint (not marked on the diagram)

[swift valve]

Hm, do you have any intuition as to why angle chasing could help prove the result?

[blissful harness]

that what the book said

[swift valve]

I'm refreshing my geometry, so you'll have to give me a sec

[blissful harness]

thanks ❤️

[last parrot]

Lets go timmy

[swift valve]

Do you have any explicit way to determine anything about the circumcircle? E.g, radius, centre, bla bla bla

[swift valve]

Thanks bud

[blissful harness]

Nah not really

[deft tapir]

It would certainly help to have a demonstration, aka a diagram of the circumcircle

[swift valve]

You sure you don't have any formulas for circumcircle stuff handy?

[blissful harness]

I'm drawing a sketch of what i have so far

[blissful harness]

eh I tried proving the midpoint of AK and points B C X to be concyclic but it didnt work

[deft tapir]

Is M the center point of BC?

[swift valve]

Have you tried converting this onto a cartesian plane?

Defining some origin would be helpful

Think about a good origin

[blissful harness]

no i've not learned any computational geometry to do that

[swift valve]

Hmm, computational geometry? You know how to define lengths and distances and allat in R^2, yeah?

That should be all you need

Everything else is derivable

[blissful harness]

does it help solve this problem tho

[swift valve]

Hey man, never know until you try

If you can show some congruence or similarity, I think this problem can be solved easily

But

It's probably easiest in some coordinate system

[blissful harness]

hmmm

okay i'll try

[swift valve]

What are your thoughts on where you should place the origin

[blissful harness]

The circumcenter of ABC maybe

[swift valve]

Mmm solid

Justify

[blissful harness]

I think I solved it?

wait nvm

I SOLVED IT

how do i close this thing

/weather clear

/close

hmmm

[last parrot]

Do .closr

.close

[blissful harness]

.close

[devout snow]

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[spring oasis]

what would be the bridge between cavalieris principle and riemann integral

[vital sedge]

"bridge"?

fubini's theorem?

[devout snow]

@spring oasis Has your question been resolved?

[spring oasis]

care to elaborate

[spring oasis]

cavaleris theorem says that for the cross sectional areas at height h of a solid, if you sum them from minimum height of the solid to maximum height of the solid you get the volume of the entire solid, it also says that no matter the positioning of the cross sectional areas at height h in tridimensional space the volumes will still be equal to each other if the cross sectional areas at height h are the same

I was trying to relate this two terms together because

cavalieris principle was stated like way earlier than riemann integral and riemann sum appeared

so maybe it laid some insipiration to riemann perhaps?

[spring oasis]

.close

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[woeful garden]

hi guys i am new I am doing math homework and need help the answer is done using calculator and my head i am told it's wrong but my math is accurate i checked and doublechecked could someone please help can i get help here

[summer summit]

!da2a

[devout snow]

Asking the actual question right away is more likely to get responses.

Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.

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

[woeful garden]

ok the problem set is 45.3, 45.6, 46.1, 46.5, 47.2, 47.3, 47.6, 48.1, 53.3, 54.9 and i need to find standard deviation

my answer was 104.3755632

[violet wind]

that is way way too big to be the standard deviation

[woeful garden]

it asks for the full number i get no rounding

[violet wind]

even if you square root it it looks too big

is this just the sum of squared deviations or something

[woeful garden]

so then what am i doing wrong i did the equation and math on pencil, paper, and calculator and got it 4 times in a row

[violet wind]

you're using the wrong formula then

[woeful garden]

same exact answser each time

[violet wind]

standard deviation is supposed to measure how far away from the mean the data points tend to be

[woeful garden]

right

[summer summit]

you should send a picture or screenshot of your work so helpers can see where you went wrong

[woeful garden]

so what is my mistake i can send a pic of my notes

[violet wind]

do these data points look like they're 100 units away from the mean?

how should i know

[violet wind]

this is the only guess i have based on how giant the number you got was

[violet wind]

oh so you did just add up the squared deviations

yeah you gotta average them

[woeful garden]

i thought i did do that

[violet wind]

looks like you just added them up

then after averaging you have to square root

[woeful garden]

i mean i was going according to a video youtube as my teacher provided no information on the lab and it's extra work required for a statistics college course

[junior mauve]

what's your mean though

[violet wind]

it looks like the formula you have there is for sample stdev though

so instead of dividing by n you want to divide by n-1

so not exactly averaging

[junior mauve]

I don't see you writing down the mean anywhere

[woeful garden]

ok i am confused

also i didn't write everything down just the parts that weren't easy to figure or remember

[violet wind]

ok that's a little suspicious

it looks like you used the median instead of the mean as well

[junior mauve]

the mean should probably be one of those things in the writing down

[violet wind]

unless they happen to be exactly the same

[woeful garden]

also it doesn't ask for everything i wrote just range mean and st deviation

[junior mauve]

that's exactly what I thought as well. you have the median written down but not the mean

in a calculation where the mean is key

[violet wind]

yeah and if you look at the actual calculations he uses the median

[woeful garden]

because the mean is well nevermind the time ran out it switched to a new set of numbers

[violet wind]

ok this time use the mean instead of the median

and then divide your answer by n-1 and then square root it

dreyuk out

[woeful garden]

i get 5 tries i must've hit the try button on my last try i mean i ran out of tries

i did use the mean not median the median was 47.25 correct and the mean was 48.19

but i thought you square root it before the n-1 as it's pemdas

[junior mauve]

then this does not add up. 45.3 + 1.95 = 47.25.

in fact every single one of your (x - mean) is done using the median.

[woeful garden]

i just followed exactly as the video said do i need to share that here to find out what i did wrong

[junior mauve]

we're telling you what you did wrong already.

not sure what new info the vid would give but if you want, no harm sending 'em

[woeful garden]

https://youtu.be/1dGZvM18Lt0?si=rLJ5K8vIyRP4X2uq

[junior mauve]

you followed the vid wrongly

[woeful garden]

where did i mess up following

[junior mauve]

the vid used the mean in (x - mean), as it is supposed to, instead of the median

you used the median instead

(which is the same mistake we've been telling you)

[woeful garden]

i swear i used the mean not median

[junior mauve]

^

[woeful garden]

tha's not what i added it was 47.2 and 47.3

[junior mauve]

and the median would be 47.25.

[woeful garden]

right and that's what i got

[junior mauve]

but that's the median

not the mean

and note that when I added (x - mean) back into x, I got the median

[woeful garden]

right i didn't use the median i used the mean of each number

[junior mauve]

I should have gotten the mean

[woeful garden]

like the video says

[junior mauve]

and I'm telling you that you accidentally used the median in your calculations

[woeful garden]

ok i won't argue i came to you for help but i just don't see what you mean

[junior mauve]

you said the mean was 48.19 and the median 47.25.

[woeful garden]

right

[junior mauve]

pay attention to those figures.

now, if I subtract the difference between x and the mean from x itself, do you agree I should get the mean?

[woeful garden]

i think i see what you think i did the math was wrote there because i ran out of room on the page next to median

it's grouped but not exactly the same

[junior mauve]

that's not the issue. the writing is not the issue

[woeful garden]

ok sorry then i just don't seem to grasp what your telling me then

[junior mauve]

because you didn't let me finish

now, going back to that message, do you agree?

[woeful garden]

no because the mean is all the numebers added then divided by amount of numbers

[junior mauve]

but see

x - (x - mean) = x - x + mean by algebra

and x - x = 0, leaving mean alone

[woeful garden]

now that just confuses me

i never was good at reading equations sorry

[junior mauve]

so (x - mean) is the difference between x and the mean, correct?

and a negative difference means that x is under the mean

do you agree?

[woeful garden]

no i don't how could the mean - x equal mean if it's just adding all the numbers and dividing by total amount of numbers

[junior mauve]

ignore that and focus on my latest group of messages.

[woeful garden]

ok may i ask a question this is 8th grade math isn't it

[junior mauve]

Idk what grade this is.

[woeful garden]

because i missed a that year in high school and they never made me retake it also i am in college now

i basically skipped a grade so i asked to know if i wasn't taught this because i missed that grade

[junior mauve]

I am unable to answer that for you

[woeful garden]

ok sorry just trying to figure out why i can't understand this

[junior mauve]

you should probably ask someone in your country about that. I am only here to aid with the math

[junior mauve]

anyway, coming back to this

do you agree?

[woeful garden]

i don't know because almost non of what you say makes sense to me so i don't know

[junior mauve]

then I apologize, but I'm probably not the right helper to help here (through none of your fault)

I'll step back for others to try.

[woeful garden]

ok sorry i apologize i just am from USA and was failed by the school system i don't blame them i just don't always get the help i need or needed

[shy osprey]

Can u send the Question again?

[woeful garden]

yes

[junior mauve]

pinned.

[woeful garden]

ok the problem set is 45.3, 45.6, 46.1, 46.5, 47.2, 47.3, 47.6, 48.1, 53.3, 54.9 and i need to find standard deviation

[shy osprey]

Well do you know the formula?

[woeful garden]

no there's no textbook and no one to ask i got my information besides the problem and data from youtube

[junior mauve]

I will advise Yajant in that two of us have determined that the OP is using the median to calculate (x - mean) instead of the mean.
but I'll let you try anyway

[shy osprey]

Ahh thats useful thanks!!

[woeful garden]

if it helps the standard deviation is on my equation sheet

[shy osprey]

sure show it

i mayhave a different form of formula cuz of regional differneces but ill share it

[woeful garden]

ok can't find it i looked in my bag i must've lost it

[shy osprey]

sorry am actaully travelling right now so the pic maybe bad

[woeful garden]

sorry i just found it forgot i put it in my folder

[shy osprey]

oh okay well share yours then

[shy osprey]

oh thats for binomial distribution

we use that in probabilty Questions

[shy osprey]

this is for pure stats

[woeful garden]

yes and this math is Statistics 3 The Mean and Standard Deviation and Empirical Rule

[shy osprey]

for ungrouped data we use this

[woeful garden]

it's a lab seperate but part of my statistics course

[shy osprey]

oh

well so how do you want to proceed then?

[shy osprey]

we can get the answer with this

[woeful garden]

no clue i honestly am not that good at this stuff that's why i came her for help

i am good at math but the more complex the problem the less i understand

and she says to just statcrunch everything but that isn't in the lab

[shy osprey]

well lets go with this

as you were trying smth similar to this earlier in this channel

[woeful garden]

our teacher literally doesn't teach us how to it ourselves only how to find it using a app

[shy osprey]

well thats sad

so i assume that you have found the mean deviation?

[woeful garden]

no truer words ever spoken man

no not yet i am trying teach myself how to find it

[shy osprey]

ah i see

[woeful garden]

because the site went out and i was stucjk without it

not today but rececntly

[shy osprey]

i see have you found the mean ?

[woeful garden]

sorry about the typos getting a bit frusterated at the situation

yes i did

[shy osprey]

well what was it?

If you are a little confused in this method dw, there is another shorter one

[woeful garden]

it doesn't even apply i already ran out of tried and got a set of numbers\

[shy osprey]

I wasnt trying to introduce a new method as i thought that you might have made a great deal of progress so

lets use the other method

Here ill share you a Question which my teacher gave to me yest

[woeful garden]

i will be right back i am getting a call

[shy osprey]

okey sure

see this one example

seems pretty similar to your Question

( i am assuming you are allowed to use calculators)

[violet wind]

different formula though

and keep in mind OP is looking for sample stdev, not population, so his denominator is n-1

[shy osprey]

um who are you refering to rn?

[violet wind]

you

[shy osprey]

sorry i feel like its N

[violet wind]

there's two versions

population and sample

your version is the population version which is N

[shy osprey]

Um not sure about that

I think its supposed to be N here

Ill just cross check though

Wait isnt the Question For population sample?

@woeful garden is your questuon based on sample or population

[woeful garden]

Not sure it's based on chickens

[violet wind]

!xy

[devout snow]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

@woeful garden Has your question been resolved?

[woeful garden]

No

But i have to do something else for now

[devout snow]

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[acoustic summit]

Can someone help

[summer summit]

,rccw

[summer summit]

remember SOH-CAH-TOA

sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent

try and see if you can use that to solve for these

[devout snow]

@acoustic summit Has your question been resolved?

[deep timber]

Which question @acoustic summit

[devout snow]

@acoustic summit Has your question been resolved?

[summer summit]

@acoustic summit dont react ❌ to the bot if you aren't going to ask another question, if you have one that's fine but you should respond or say something

[devout snow]

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[smoky hull]

ive attached the relevant thms/defns. my question is: how can we say that y_k is asymptotically stable, since y_k is the estimation using an RK method for the Dahlquist test eq, so how can we say that it is even a fixed point (ie f(y) = y' = zy, and need f(y_k)=0 for fixed point), let alone say its asymptotically stable. what do they mean

[smoky hull]

I get that for y_k, an RK approx to y(0+hk) for the dahlquist test eq, we want that our y_k go to 0. But id have thought that just makes y=0 the asymptotically stable point ?

I’m talking about the sentence starting clearly

[devout snow]

@smoky hull Has your question been resolved?

[smoky hull]

Idk whether notation is general so lmk if I can clarify anything in that regard

there appears to be another defn of asymptotically stable i hadnt thought of, but this seems to get rid of dependence on the RK method entirely i think?

[sullen island]

what they're saying when they state {yk} is asymptotically stable is that the result you get from the numerical method matches the stability of that fixed point

i.e. take a y0 as in def 8

this will give you a perturbed solution y, which goes to the attractive fixed point y*as y->inf

if you start your numerical method with that same y0, and the solution you get from that numerical method also goes to y*, then it's asymptotically stable

[smoky hull]

so ur saying if we take the numerical methods sol, then y=0 is an asymptotically stable point?

[smoky hull]

wait

so a method is called asymptotically stable if it goes to the y* for large k?

oh cant be for large k right cuz they say k in naturals

lemme read what u wrote again maybe im mixing things up

[sullen island]

lim_{k->infty} yk = y*

I am talking for large k yes

[smoky hull]

so y do they say this

[smoky hull]

i agree with this

cuz were talking about the dahlquist eqs where the only y* is y=0

[sullen island]

yeah I figured

wikipedia does the same thing

[smoky hull]

says for large k?

[sullen island]

about the dahlquist eq etc...

[smoky hull]

ah

[sullen island]

I didn't know what it was at first

[smoky hull]

mb mb

idk if these defns are general either, this is not a core module ygm

[sullen island]

if wiki talks about it it's general enough

took me a bit more searching than usual tho

https://en.wikipedia.org/wiki/Stiff_equation#A-stability

[smoky hull]

i was also wondering that, since this defn S_psi is used for the defn of A-stable, and we kind of define S_psi using that dahlquist eq, does that mean A-stable onnly applies to RK methods being used for the dahlquist eq or is it general

i asked ai and it gave me 2 answers

[sullen island]

well it seems specific to the dahlquist eq here

[smoky hull]

yea

[sullen island]

but you could generalize it to other equations surely

dahlquist is a good benchmark tho

[smoky hull]

i guess but youd be making a new S_psi so does A-stable,, and further L-stable mean smt else

[sullen island]

yea

what do they mean by psi here tho

prolly some ugly thing

[sullen island]

ok what's the def of Psi itself tho

[smoky hull]

idk if notation is general

[sullen island]

I figured it would be something like that but never seen this exact notation before yeah

[smoky hull]

tbh

the pset for this wasnt bad

yet to look at past papers though

so ig if i dont actually get it, it should be chill

at least this particular q of mine

[sullen island]

yeah they could have bothered clarifying their language here tho

even wiki does better at explaining

[smoky hull]

lmao

nah iirc ppl said this course was poorly written

had to use a lot of ai assistance to understand where theyre pulling things from etc

hmm

bru i still dont know what they mean by y_k being asymptotically stable for all natural k 😭

[sullen island]

{yk} k in N is notation for a whole sequence

[smoky hull]

ye

[sullen island]

they're saying this sequence produced by the numerical method is asympotically stable

[smoky hull]

as in all the step approx from y_0=y

[sullen island]

which I've tried to explain at the beginning

[smoky hull]

but for a point to be asymptotically stable we need f(yk)=0

and the other condition

u said it goes to 0

i agree

but dont we need exact

and also we need this

i mean if u dont see a clear explanation the notes may well be wrong to call the yk sequence asymptotically stable

[sullen island]

well they are wrong not to clarify their statement

which is what I've tried to do

like their "asymptotic stability of a sequence" is related to the asymptotic stability of a fixed point

[smoky hull]

do they mean like: it is asymptotically, asymptotically stable

idec atp lmao, i think its irrelevant

hope*

[sullen island]

idk what you mean with this double asymptotically really

[smoky hull]

asymptotically it is asymptotically stable

first asymptotically to say taking k to infinity, then the second one as part of the term 'asymptotically stable'

cuz that would sort the issue right?

[sullen island]

k->infty is already "asymptotically"

asymptotic = related to limits to infty, that's all it means

[smoky hull]

ive been thinking theyre saying the sequence is asymptotically stable, as in for all k

cuz asymptotic stability is a term given to 1 particular point

but ig if they mean taking k to inf

oh is this what ur saying

[sullen island]

well here they're talking about the whole sequence

i've said that already

[smoky hull]

i think confusion in what they meant by just saying a sequence has this property

[sullen island]

indeed

[smoky hull]

ig they mean the limit as k goes to infinity has this property

is what u said asw, now i see

just confirm if this is everything pls, wanna make sure im not overseeing anything

i think so yh?

-close

/close

[sullen island]

well maybe you have other questions idk

but as far as this sentence of the book goes I think we're clear

[smoky hull]

nah if this is fine then im good for now

[sullen island]

it's .close

[smoky hull]

perfect, tysm 🙏

.close

[devout snow]

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[devout snow]

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[willow fern]

Calculate for which value(s) of t the vectors

a =
\begin{pmatrix}
2 \
t-2
\end{pmatrix}
\quad \text{and} \quad
b =
\begin{pmatrix}
3 \
2
\end{pmatrix}

are parallel.

[woven radish]

lexi
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[shy osprey]

oh hello there

[willow fern]

It’s probably 5

[shy osprey]

well since these two are parallel, we can say that they should have same slope right?

[willow fern]

Cause I’m supposed to get (2,3)

[shy osprey]

think again

[willow fern]

-1?

Yea

[shy osprey]

Read the question again😓😓

It says parallel not perpendicular

[willow fern]

x1/y1 = x2/y2

[shy osprey]

yup!

well what is it?

[willow fern]

Ik what to do

I’ll just have to put the numbers

And do algebraic equation

It’ll be 3 1/3

[shy osprey]

Yeah!!!

[devout snow]

@willow fern Has your question been resolved?

[devout snow]

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[slim salmon]

Hi can someone verify this ?

Thanks

[violet arrow]

bro what are these homework 😭

[slim salmon]

I have like a few more questions too 😭 😭

[violet arrow]

https://klipy.com/gifs/chicken-tree

[slim salmon]

Its gonna be a long night

[violet arrow]

lemme try and solve it

from what i can see the partial derivatives are correct

[slim salmon]

Yup

[violet arrow]

so since its x=0 and y=0 its only differentiable at z=0

[slim salmon]

Yupp

[violet arrow]

so yh i dont see a problem

u solve it rly well

[violet arrow]

honestly your solving it rly well i dont think you need help 😭

[faint gorge]

it looks fine to me as well

[slim salmon]

😭 😭 😭

I make some really silly mistakes sometimes

[faint gorge]

i think sirman maybe needs your help

[violet arrow]

[slim salmon]

https://tenor.com/view/braindead-cat-brain-damage-gif-583403308765934478

My help?

[slim salmon]

Btw thanks guys

Appreciate it

[violet arrow]

[devout snow]

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[devout snow]

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[jade wraith]

i thought y = 2z would repsent a side or in this case the diameter. i thought radius would be 2x/2

[jade wraith]

why does the radius stay as 2x and not 2x/2

wait

is it bc

imma draw it and someone help me

pls

the base of a quarter circle is already equal to the radius right

[devout snow]

@jade wraith Has your question been resolved?

[devout snow]

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[molten mauve]

I was trying to find where the xyz of every vertices would be on an equilateral tetrahedron where every vertices is 1 point away from the tetrahedrons center

I got the edge length of it to be ((√57601)-1)/160 but Im not sure if I did something wrong

This is the method used to find the edge length (sorry if it isn't organized)

[last parrot]

isnt the circumradius of a tetrahedron is sqrt6/4 * a?

for side length a

[molten mauve]

I'm not sure

I don't even know what circumradius is tbh

[last parrot]

ok

distance from centre to vertex

so if the distance is 1 point a way then let R = 1

this way you find a

which is 4/sqrt 6

[molten mauve]

Hmm

[last parrot]

so if 4 vertexes are 1 points away, then

coordinate of V1 here will be (0,0,1)

V2 = (sqrt8/3, 0, -1/3), and etc for other 2 vertexes

[molten mauve]

Mine might be different because its an equilateral tetrahedron

And the center point I'm using isn't at the base of the tetrahedron but the overall center

[last parrot]

it is the same term for a regular tetrahedron anyways

[molten mauve]

Idk

[molten mauve]

Mb

[last parrot]

no problem

[molten mauve]

Does work👍

.close

[devout snow]

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[last parrot]

all good man cheers

[molten mauve]

🍻

[devout snow]

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[shy hound]

I have recently started getting into mathematics, and I feel I have a half-decent understanding of Algebra2. (Factorials, Summation, imaginary numbers, ect.) And, I need help on what I should work on next to improve my prowis. [Please do Ping me if you respond]

[supple knot]

Just follow Khan academy

[shy hound]

What is that?

[supple knot]

https://www.khanacademy.org/

[red kestrel]

You did polynomials matrices ... ?

[supple knot]

Go in order until you see something new

[shy hound]

No, I don't beleive I am well versed on that.

At what level would you say Factorials, Summation, and Polynomial Matrices are?

I don't want to press the wrong thing in Khan

[shy hound]

⬆️

[supple knot]

https://www.khanacademy.org/math/trigonometry

[shy hound]

All those skills are compatable with Trig?

[supple knot]

Those are the next things you would learn afterwards

[shy hound]

Can we go and change course if it is not on the appropriate level?

[supple knot]

Yea

[shy hound]

9k

*Ok

[red kestrel]

I guess you can check khan avademy as he said
Or if u are well rounded in abstrait algebra enter into linear algebra

Once you have finished abstract algebra, you can move on to linear algebra: understanding how to manipulate abstract objects such as matrices, polynomials, and more.

[shy hound]

What would you recommend?

[red kestrel]

So for example u go from polynomials , fractions, vector spaces, linear maps, matrices, determinants

U can follow this order

[shy hound]

In Kahn, or something else?

[shy hound]

Yeah... I don't really know what to do here. 😅

I have never seen this anywhere beforehand. .

[shy hound]

Where are those skills located at?

[supple knot]

Did you watch the videos

[shy hound]

Not yet, but it seems ahead of what I am trying to reach for. It feels like taking a desperate leap instead of a dedicsted step. (If you understand what I mean).

[supple knot]

Then you need to decide on your own what you want to learn

[red kestrel]

I don't know about khan academy

[shy hound]

Do you know what grade it is typically discussed in?

[red kestrel]

What are u trying to reach for ?

[red kestrel]

First year in uni i guess

Which grade are u in ?

[shy hound]

A graspable step. I want to grow to have a great foundation of mathematics. I am not looking for impressive problems to solve to appear smart or intellegent immediately. I would like to work in a way that actually builds foundations.

[red kestrel]

Usually after u finish groups rings and field u can get into linear algebra

[shy hound]

Not university....🙃

I am typically placed in classes that far excel what I should at that timw.

[supple knot]

Still not really useful information

[supple knot]

No one here knows your skills

[supple knot]

If you want to do more of the same just google the same topics you mentioned and look for problems

[shy hound]

The most difficult work I have done yet: Factorial, Summation, Imaginary Units, complex equasions. Does this help?

[supple knot]

Do this

[red kestrel]

U can either work ur way out by learning theoritically concepts and solve theoritical exercices giving you a solid foundation of as u can say critical thinking i guess (im not good at english)

Or go straight to learning about concepts which help you solve problems

Cause u either go little by little and try to learn the concepts theroitically or go straight to tools whoch can help you directly with exercices

I hope u understand what i mean

[red kestrel]

Did u do groups rings and fiels ?

[shy hound]

Alright then!

[shy hound]

I had not yet. Should I start there?

[red kestrel]

What about calculus ? Where are u at calculus ?

[shy hound]

I tried some of it out in primary school. It has been a while since I have done it again, but I have touched bases ever so slightly.

[red kestrel]

Im not a major in maths tho so maybe you shouldn't lidten to me tho lol im just telling u the order we follow since the maths we learn is kinda advanced for now

But not as a major in maths

[tawdry notch]

The topics are still the same I guess

Math majors just learn them quicker and go further

[shy hound]

Ok.

[shy hound]

Should I start with the basics of calculus?

[red kestrel]

Yes

[shy hound]

🫡

[red kestrel]

U need to know some stuff in calculus before getting into more advanced algebra

[shy hound]

Is Algebra2 what you are refering too?

*to

[red kestrel]

Im not sure but probably

[tawdry notch]

Wait

Algebra 2 is lower lever than Calculus 1

[red kestrel]

I don't the name concepts in english

[shy hound]

That's what I was thinking. 😅

[red kestrel]

Oh

[harsh stream]

Whats algebra 2 i just went straight to linear alg is it American stuff?

[shy hound]

I was saying I had a fairly solid grasp of Alg2.

[tawdry notch]

Trigonometry and Algebra 2 are Precalculus

after Precalculus goes Calculus 1

and so on

[shy hound]

So I should start with pre-calc.?

[tawdry notch]

Can you do trigonometry?

If you can you only need algebra 2

[shy hound]

Not well...

[tawdry notch]

Did you learn it yet or not?

[shy hound]

No, I hadn't

[tawdry notch]

Uhh

Yeah you surely need Precalculus

[shy hound]

So calc.》Trig. Or Trig.》calc.?

*pre calc.

[tawdry notch]

precalc = algebra 2 + trig.

algebra 2 and trig are precalculus basically

and after precalc goes calculus 1

[shy hound]

Alright!

Thanks for helping me!

[tawdry notch]

You're welcome

[shy hound]

👍 👍 👍

.close

[devout snow]

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[tawdry notch]

It's like 9th grade in school I guess?

[devout snow]

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[ionic jasper]

How do i derivate this?

[last parrot]

Have you tried multiplicative formula in derivatives

F'=u'v +uv'

[ionic jasper]

Ye but it looks different than the given solution

[last parrot]

Let x^2-2x+1 be u and e^-x be v

[ionic jasper]

That is what they gave as solution

[potent dirge]

There are many reasons why that might be. Did they factor out an e^-x?

[ionic jasper]

Idk

[last parrot]

This one would give same results

[potent dirge]

Well yeah, it’s just product rule. But idk how much his prof simplified afterwards

[last parrot]

It is the final sol so yeah should work out

[ionic jasper]

Okay 1 sec

So this is correct?

[last parrot]

,rccw

[potent dirge]

You’re off by a negative

[potent dirge]

When you do the derivative of e^-x, you have to remember to use the chain rule, and multiply by the derivative of the exponent

[ionic jasper]

Ye i see

Forgot an -

So -e^-x

[potent dirge]

Yep, and you can choose to factor out an e^-x, and then collect like terms to have a simple, and compact answer

[ionic jasper]

How

[ionic jasper]

Poh

U can make the -e^-x to e^-x and just change it in the () i see

[potent dirge]

Ignore what I said

[ionic jasper]

Okay

Thanks

.close

[devout snow]

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[last parrot]

Ye freddie explained correctly

[devout snow]

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[mellow willow]

Is the reason why this is only in quarter 1 and 2 is because the angle I is below 1?

[last parrot]

Sin always positive in quarter 2 and 1

[mellow willow]

Ah ok

For this one I don’t know if it will have 1 or two solutions since they add exactly to 180 but those numbers are rounded

[last parrot]

Wait let me check

Only B1 is true

Because if assume B2 is true (161.84 degree), then B+A>180, which is wrong in a triangle

And the rest you did correct

So basically, the scenario only works for B1, even though both B angles satisfy condition of quarters

[vestal surge]

the angle values look gross holy....

[last parrot]

Not that bad tbh

[vestal surge]

25.8 is so unusual

[mellow willow]

I’m stuck on this one

I just don’t know how to add those two pyth identities

[vestal surge]

heres a hint

[winter patrol]

If ur going to convert, convert one not both
or just apply "the" pythag identity directly
s^2 + c^2 = ?

[mellow willow]

Omg it’s that same identity I keep forgetting

For this next one I know there is some way I can seperate these to get the answer I just don’t know how

[winter patrol]

missing a - sign
s^2 = s * s

[mellow willow]

Huh

Isn’t it already squared?

[winter patrol]

yes, but you want to split it

[vestal surge]

ahh yea i thought something was off

[woven radish]

ghost

[winter patrol]

and you need to fix your sign ^

[mellow willow]

I’m so lost

But isn’t this the pyth identity

[winter patrol]

yes, but you messed up your sign

you have c^2 - 1 here
(Not 1 - c^2)

which would result in -s^2

[mellow willow]

Ohhh

When I seperate tho I go two tans

[vestal surge]

how

[winter patrol]

how are you getting 2 tans

[vestal surge]

theres only 1 cos in the denominator tho

[vestal surge]

oh they are being multiplied

not added

[last parrot]

Thats not how it works

[winter patrol]

so many things wrong with that

[mellow willow]

I’m bad at fractions

how do you seperate fractions then

[winter patrol]

s^2 = s * s

[vestal surge]

sorry for the bad handwriting

[mellow willow]

But I thought you had to keep the denominator ?

[vestal surge]

i used the cos to divide 1 of the sin

from the numerator

[mellow willow]

Huh

[vestal surge]

they are in multiplication so you dont need to split like that

it happens in addition

[woven radish]

ghost

[ocean haven]

,rcw

[mellow willow]

I’m just very confused now

[vestal surge]

^

[mellow willow]

Because I don’t know what way to do it on my test

[vestal surge]

look

if that helps

..

[mellow willow]

Ohhh

So like the denominator for a and b in the second one is one

[vestal surge]

yeah

[devout snow]

@mellow willow Has your question been resolved?

[devout snow]

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[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[broken horizon]

idk how to progress

[jaunty mantle]

Are you doing part a or b

[broken horizon]

both i am on a )atm

[jaunty mantle]

Well it looks like X and Y are independent so maybe we just try do X >= X² first

And then we can just square the probability to account for Y as well

[broken horizon]

do i have to integrate x and x^2?

[jaunty mantle]

I mean

[broken horizon]

i dont really understand my approach

[jaunty mantle]

We want P(X >= X²) right?

[broken horizon]

yes

for y respectively

[jaunty mantle]

Or in other words P(X² - X <= 0) = P(X² - X < 0)

[broken horizon]

we want the blue area

[jaunty mantle]

We can let Z = X² - X and then now consider what the pdf of Z is

There’s a formula that you can derive to find how the pdf of X changes via a monotonic function

Have you learned about that?

[broken horizon]

no

[jaunty mantle]

f_Z(z) = f_X(x) |dx/dz|

You haven’t seen this before?

[broken horizon]

that the area is the probability ?

[jaunty mantle]

That’s the change of variable for the pdf

[broken horizon]

this is what i have so far

[jaunty mantle]

Z = X² - X inverses to X = (1 +- sqrt(1 -4Z))/2

So X² - X < 0 we need to solve this

Err hold up I’m walking around let me sit down

[broken horizon]

ok

x^2 < x

then sqr
x < sqrt of x?

[jaunty mantle]

okay:
F_Z(z) = P(Z < z)
= P(X^2 - X < z)
= P((1 - sqrt(1 + 4z))/2 < X < (1 + sqrt(1 + 4z))/2)

does that make sense why

[broken horizon]

no sorry
I guess i will have to look into this more

[jaunty mantle]

think about X^2 - X - z < 0