help-17

[twin meteor]

Quixz

[tacit aurora]

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[candid otter]

alright. which is bigger, 1.299 or 1.325?

[tacit aurora]

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[candid otter]

hmm, it seems to me like you know what decimal expansion is

[tacit aurora]

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[candid otter]

don't forget to .close this channel

[vocal sleet]

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[dire plover]

I don't know what I'm doing

Just got back in class after 3 weeks (hospitalized)

precalc

[lone niche]

do you know unit circle
starting at right side, circling counterclockwise, sin is the y value, cos is the x value

[dire plover]

i dont know sin is y and cos is x

[lone niche]

well now you do

[dire plover]

ty

[lone niche]

you have a y value of s2/2 first at pi/4

then at 3pi/4

that’s a 45 diagonal line

and sin repeats every full loop (2pi)

[dire plover]

at pi/4?

[lone niche]

angle = pi/4 = 45deg

pi is 180deg

[dire plover]

where did u get pi/4?

[lone niche]

memorized that thats where sinx = sqrt(2)/2

[tacit aurora]

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[lone niche]

bruh

[dire plover]

wdym

[lone niche]

it asks at what x values does sinx = sqrt2/2

[dire plover]

and how did u get pi/4

[lone niche]

memorized

[dire plover]

ohh the table

45 degrees of what?

[dire plover]

legit in class rn

[lone niche]

yes use that

[dire plover]

okay

so

wat

[lone niche]

x = 45 degrees

[dire plover]

okay

so sin45 = sqrt(2)/2

[lone niche]

yes

and another solution is 135

ur table doesn’t show that

[dire plover]

how

oh

[lone niche]

unit circle

[dire plover]

i c

so i dont understand

the answer

[lone niche]

do you have the answer and are confused

[dire plover]

no

i dont knoe the next step

[lone niche]

ok we have x = 45 and x = 135

but remember sin(x + 360) = sin(x)

because 360 degrees is the same as 0 degrees

[dire plover]

mhm

[lone niche]

so you actually get an infinite amount of solutions

[dire plover]

why

[lone niche]

they can be written as 45 + 360n, 135 + 360n

[dire plover]

ohhh

[lone niche]

because you can add 360, 720, etc

[dire plover]

i see

okay

[lone niche]

and the angle is the same

[dire plover]

so the answer is 45+360n and 136 + 360n?

he already did this question onn the board

[lone niche]

(135)

[lone niche]

ah

[dire plover]

ok

yea

[lone niche]

they also probably want it in radians

which is the pi’s

[dire plover]

when u put 'n'

is that pi?

[lone niche]

n is any integer

you add 360 an integer number of times, angle no change

[wicked cobalt]

.kill

[lone niche]

same with subtracting 360

[dire plover]

okay, ty

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[rough barn]

Relative to the origin O, points P, Q, and R have position vectors i+j, i+k, and j+k respectively.
(a). Find a vector equation of the line joining O to M, where M is the midpoint of PQ.
(b) Let N be the foot of the perpendicular from R to the line OM. Find the position vector of N. Hence, or otherwise, find a vector equation of the line joining R and N.

for (a) i got OM = i + 1/2 j + 1/2 k
how should i do (b)?
how can i find the line joining R to line OM?
would it be (0, 1, 1) + t(1, 1/2, 1/2) ?

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[stray bay]

I have a number...
the number is: -1.52822847
and the question states: Do not round until the final answer. Then round to four decimal places as​ needed.)

[stray bay]

I do not understand what the question wants me to round to.

the fourth decimal? then why would it tell me to not round until the final answer?

[hard atlas]

if you round along the way you get a much bigger error

do the same calculations as before but round along the way

see what result you get

[stray bay]

-1.52822847 is my final answer.

I did not round at all during my calculations.

do I then round this number to: -1.5282

Ah, alright I see then, thank you

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[clear lake]

confused on 2

I know the scalars must all be 0 if it's independent

for that second equation why don't we do (c4-c3)v4

since A is independent lets say a1,a2,a3,a4 in F

a1v1+a2v2+a3v3+a4v4= 0

so a1,a2,a3,a4 = 0

now for B

we have new scalars right? we can't just use a1,a2,a3,a4 again

so c1,c2,c3,c4 in F

[clear lake]

and we write it like this

so does this mean a1 = (c1+c2+c3)?

aka c1+c2+c3 = 0

-c1 = 0

-c2=0

then wouldn't c4-c3 = 0 too?

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[lime gorge]

In before ur asked to find f’

Post the instructions

@vagrant rune

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[outer gulch]

(C) i think

[vagrant rune]

How

[outer gulch]

using newton leibniz theorem

one second ill send a ss

bottom half of parabola not included because x cannot be negative

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[indigo kernel]

this is the solution:

could someone explain why summing up the right hand sides gave those terms? ( 1 - 5x + x^2 -4x + 20x^2 + x^2)

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[indigo kernel]

<@&286206848099549185>

Is it because we want the RHS to only include x terms with a maximum exponent of 2 since the LHS has a maximum exponent of 3 on x? If I do that it gives me the same result, and I'm trying to relate it to initial conditions for recurrence relations, but I have no clue if that's part of actual theory

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[cold cypress]

is this correct?

the guy in the video made is 100 steps

[karmic imp]

Both the video and you did practically. The video just combined the terms into one fraction, then converted to terms of sin/cos, then canceled stuff out. You made them into terms of sin/cos, then canceled then combined the terms into one fraction

[cold cypress]

okay

thank you

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[odd oriole]

Hey, quick question that I'm struggling to google:
If I have the probability of two independent occurring, what's the combined probability for at least one of them to occur?
For example, two events both have a 0.93 probability, I would expect the probability for at least one to occur to be >0.93 right?

[vast shale]

Find the probability of both not happening

Then use complements

[odd oriole]

Ah right good point, been awhile since i've done this, let me do a quick google

@vast shale I think I got it, just a quick reminder, compliments is just being able to find either side of a probablity, so P(!A) = 1-P(A) right?
Then using my example for one of the events would be P(!A) = 1 - 0.93
Therefore probability of both not occurring would be to multiply them together, (1-0.93) * (1-0.93)
Then using compliments again we get 1 - ((1-0.93) * (1-0.93)) = 0.9951
Is that right?

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[odd oriole]

Just want to check that I understand this correctly

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[gusty pelican]

How to control for a confounding variable?

It seems that there are 2 ways of doing it:

1. Ablation: make 2 models, 1 with, and 1 without the confounding variables, and then compare
2. Correction: make 2 models, 1 normal, and 1 corrected for the confounding variable.

I'm not sure how to do the 2nd one. How to correct for a confounding variable?

[vocal sleet]

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[strange crater]

what is the context?

I've never heard of "ablation" TBH. the standard practice is to include the confounder in your model, that in effect will "control" for it

but actually it's more complicated than that so I'm not sure

[gusty pelican]

The context is, there are 2 variables that commonly accepted as related

but I think, in my specific data, they are actually not, only correlated due to confounders

but, how to proof that?

the context is: these are timeseries forecasting, not sure if that matters

[gusty pelican]

I don't think simply adding the confounder in my model would control for it, because I don't think this is a linear phenomenon

[strange crater]

yea I gave that advice assuming it was just a regression model

I don't have experience w/ time series forecasting so I don't know how to deal w/ that

you might try asking at stats.stackexchange.com

[vast shale]

unmeasured confounders can't be included as explanatory variables

[gusty pelican]

So, in a normal generalized linear regression, you just put in the confounder into the model, and that's the end of it?

[vast shale]

@gusty pelican you can look into including a smoothing function

[gusty pelican]

like MA?

[vast shale]

I think generally lowess is used but I'm not too sure about time series

[strange crater]

Here's what Frank Harrell has said in the simple case:
"In many cases the need to adequately control for confounding outweighs considerations about overall model predictive accuracy, so we adjust for more variables than we would normally include in the model and let the width of the confidence interval for the exposure variable effect get a little wide as a result."
he does bio/medical statistics though which is I think different from what you're doing

[gusty pelican]

I think it is better if I write a made up scenario:

Let's say I have hourly data of ice cream sales and temperature. And if I just analyze them, they are correlated. But maybe the confounding variables is time-of-day/business. During the day, is when people are out and about, and that's what makes them buy ice cream, not actually temperature. So how do I control for this?

[vast shale]

is this for an assignment or self learning

you could use time stratification

[gusty pelican]

for a job lol >.<

[vast shale]

[gusty pelican]

I usually don't do this kind of thing in my job, but now I need it haha

[strange crater]

so in that scenario, the variables are not "separable" so I don't think there's anything you can do about it. but don't take my word for it. since you used the phrase "what makes them buy ice cream", that seems like causal inference which is entirely different

[gusty pelican]

Yea, ideally, I want causal inference, but I know that's too hard, so would be happy with simply linear correlation.

[gusty pelican]

what do you my unmeasured?

[gusty pelican]

what do you mean by separable?

[gusty pelican]

like, create artificial classes such as: morning, noon, evening, night ?

[vast shale]

exactly what you think it means

[vast shale]

yes

[strange crater]

well I suppose you could get enough data on colder days, have data for all times of day, etc. to see if you can "separate" the effect of the two. depends on how high the correlation is between them

but yea, obviously daytime + hotter temperatures --> more ice cream

[vast shale]

https://online.stat.psu.edu/stat510/lesson/4/4.1

could be helpful in your scenario. Again, limited time series knowledge

[gusty pelican]

So ARIMA is for 1 variable

for multiple variable the equivalent is VAR

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

So I thought, I could just figure out how people doing generalized linear model regression do it, and then simply replace the GLM with VAR, right? the concept should stay the same even if I swap the models ( I think they should have very similar assumptions)

[vast shale]

are you using the vars package in R?

[gusty pelican]

I will use python, but I haven't done it. I'm still at the stage where I'm trying to figure out how to exactly setup my experiments lol

[vast shale]

you can include seasonal dummies as exogenous regressors

[gusty pelican]

so that's what I thought right, but what if it is not linearly correlated?
Like, the obvious way to do a daily periodic dummy is create a sine wave with period of 1 day.
But what if the ice cream sales shape is sawtooth for example?

[vast shale]

you should be able to average the seasonality - no idea though

i've just poked around time series before. I'd recommend joining the stats server and asking there

@gusty pelican i can also ask my professor tomorrow

[compact estuary]

!!!

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@gusty pelican Has your question been resolved?

[gusty pelican]

nah its okay, my meeting with my team is tomorrow

just wanna appear competent lol

[vast shale]

just throw in some buzzwords!

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[copper roost]

i got that it diverges, is that correct?

[copper roost]

it ended up being $\frac{7}{2}$

[twin meteor]

ᴊᴀᴄᴋ

[grand frigate]

show working

[copper roost]

nevermind its gonna converge

[copper roost]

here the work

[grand frigate]

okay

[copper roost]

accidentally plugged 1 in instead of inf

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[vast shale]

Ok I'm freaking out rn

The half life of silver-105 is 41.3 days. How much of a 12g sample would remain after 54 days? Round to three decimal places

[vast shale]

Every answer I put in is wrong

[lone niche]

do you have an equation for amount left at time t

[vast shale]

A(t) = Ag • a^2

A = 0.983357
and for the 45 one I got 4.610 g

[lone niche]

heres the formula wiki gives for half life

[lone niche]

the 45 one?

[vast shale]

uhh whatever the last question I did was

I forgot at this point

I've been so caught up in this one

[lone niche]

so
you can plug in all of the numbers here

that formula makes sense because when t = 0, N(t) = N_0, and when t = t1/2, N(t) = N_0/2

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[viral copper]

$\sum_{r = 1}^{\infty} \begin{vmatrix} r & 2r - 1 \ 0 & 2^{-r} \end{vmatrix}$

[twin meteor]

NEONPerseus

[viral copper]

How do I get one of the rows/columns to be independent of r

[hushed pewter]

sum of determinants?

[viral copper]

Yeah

[hushed pewter]

Why you trying to get independence of r?

[viral copper]

Because when you add determinants, only the contents of one row/column get added to one another

[hushed pewter]

why not just calculate the determinant? Seems like a simple one

[viral copper]

r2^{-r}

I suppose

Alright I guess I could do some generating function fuckery for that series

With newton's binomial theorem

$\frac{1}{(1 - x)^2} = 1 + 2x + 3x^2 \cdots$

[twin meteor]

NEONPerseus

[tulip nebula]

Determinant comes out to be constant=2?

[viral copper]

No it's r2^(-r)

[viral copper]

Now I just multiply with x and sub in half

That should work

[tulip nebula]

Oh mb

[viral copper]

No worries

@hushed pewter thanks for pointing that out often the most obvious things escape us

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[hushed pewter]

oh yeah

They get me all the time

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[viral copper]

Determine the number of symmetric square matrices of order 3 such that the sum of the diagonal elements is 1, with each entry being 0 or 1.

[viral copper]

nvm got it

.close

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[hushed pewter]

[viral copper]

Hello again

Just 3*2^6

I think

[vale snow]

How

[hushed pewter]

2^6 ignores symmetry

.reopen

[vocal sleet]

✅

[hushed pewter]

Your answer is sus, @viral copper

!show

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

[hushed pewter]

.close

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[vale snow]

I think answer is 3*2^3

[hushed pewter]

neon will never know I guess

[viral copper]

Oh fuck

.reopen

[hushed pewter]

.reopen

[vocal sleet]

✅

[hushed pewter]

[viral copper]

Symmetry

Weeee

So it's just 3*2^3

Right

[hushed pewter]

mhm

[viral copper]

Thanks 💀

[hushed pewter]

If it makes you feel better, I once wrote a two page proof for an algebra identity that took two lines

We all goof

But I'll still

[viral copper]

Oh well

Shit happens

[hushed pewter]

yup

[viral copper]

Thanks again

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[hollow monolith]

help 🥲

\[\lim_{-\infty} f(x) \]
\[\text{and } \lim_{-\infty} \frac{4}{f(x)-2}\]

[twin meteor]

ᑎᗩᑕᖇᗴᝪᑌᔑᗞᗩᗯᑎ596

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[proper oxide]

Trying to solve this hard homework question. Any help is appreciated and full working and solution would be nice thanks 👍

[brittle lion]

I think you can find $s(t)$ first, then differentiate it with respect to time twice to get $a(t)$.

\begin{align*}
v(t) = \frac{\dd{s}}{\dd{t}} &= e^{-s} \
e^{-s} \dd{s} &= \dd{t}
\end{align*}

Next, integrate both sides

[twin meteor]

Nayaka

[regal bane]

You can get acceleration by differentiating velocity

[brittle lion]

...with respect to time

ah

i get it

you can use implicit differentiation instead

[proper oxide]

This is my working but i am not sure if it id correct, can you loook to see if their id anything wrong thanks

[regal bane]

Oh mb didn't even notice that it was using s and not t

[shell yew]

wouldn't it be exp(s)ds = dt ?

[proper oxide]

My t is negative though

[regal bane]

Logic looks solid

[brittle lion]

\begin{align*}
v(t) &= e^{-s} \[.8em]
a(t) &= \frac{\dd{v}}{\dd{t}} \[.8em]
&= \dv{t} e^{-s} \[.8em]
&= -e^{-s} \frac{\dd{s}}{\dd{t}} \[.8em]
&= -e^{-s} \cdot v(t) \[.8em]
&= -e^{-s} \cdot e^{-s} \[.8em]
&= -e^{-2s}
\end{align*}

[regal bane]

Implicit is a lot slicker though

[twin meteor]

Nayaka

[brittle lion]

dang i forgot about the question

nvm

[proper oxide]

😅

<@&286206848099549185>

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[vast shale]

I need help guys

[raven bough]

i can't even read the ques

[vast shale]

@raven bough

[wooden sky]

Yes

It’s e

@vast shale

[vast shale]

Thanks bro

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[pale siren]

HHey I'm struggling with this epsilon definition question

Here is my proof but the problem is with large values of epsilon

I'm sorry If I am the big dumb dumb

[vocal sleet]

@pale siren Has your question been resolved?

[pale siren]

<@&286206848099549185>

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@pale siren Has your question been resolved?

[pale siren]

<@&286206848099549185>

[abstract panther]

?

[pale siren]

I'm having issues with my proof

[abstract panther]

in what way exactly?

[pale siren]

so I don't know what happens when epsilon is like 5

or like big value

how can I talk about it then

[abstract panther]

So in mathematics it is customary to denote a quantity that takes an arbitrarily small value. And in this definition of an infinitesimal sequence, the meaning is precisely that no matter how small an EPSILON we choose, we can find such a piece of this sequence (i.e., specify such an N) that it will not get out of this boundary (plus or minus epsilon) later.

read it

[pale siren]

yeah

[abstract panther]

and let"s repeat

[pale siren]

but like what happens if epsilon is 5

[abstract panther]

what do you have equal to N?

[pale siren]

N would have to still be a way greater than itself

[abstract panther]

sorry I'm using a translator so I'll take a long time to explain to you

[pale siren]

okay

[abstract panther]

I can try but I think it will be a long time

It is clear that each epsilon needs its own N. Let's say if a(N) = 1/N2 and ε=0.01, then N = 10, and if we take ε=0.0001, then we will need N=100.

[pale siren]

yeah

[abstract panther]

I can't figure out what your problem is

[pale siren]

So if you look at the question, they give you a hint that the epsilon >= alpha and epsilon < alpha

and we are suppose to use this to consider what happens when the lnxx is evalauted at a negative

[abstract panther]

a-a-a-and you confused me ahahah

[abstract panther]

I began to doubt myself that I knew

sorry im not can help you

[pale siren]

algood

[reef scarab]

This is referring to the epsilon delta, isn't it? Maybe show that $\lim_{x \to \infty} e^{-x}$ converges to 0, so $\lim_{x \to \infty} e^{-x^{10}}$ also does

I don't think eps delta really is needed here

[pale siren]

this is the epsilon-N

[twin meteor]

Kiameimon | Welt Rene

[reef scarab]

ohhh

[reef scarab]

tbh tho wouldn't what I stated still prove the question? Or are you strictly requiring for an answer which uses the eps-N method?

welp, rereading the question, the latter seems to be the case

[pale siren]

.close

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[dire terrace]

How to calculate area that is closed with these two functions

[rugged orchid]

Do you want to do this analytically or use graphs to assist you?

[dire terrace]

I mean, I would rather to have a picture

[outer warren]

is that second equation correct?

[dire terrace]

Of some sort

[rugged orchid]

Then first graph the equations

[outer warren]

its strange to be explicitly given two fractions with y like that

[dire terrace]

Ahh, its x/3 + y/6

[rugged orchid]

I saw that and just thought ok lol

[dire terrace]

How to graph the quadratic one, do I just find x1 and x2 from the equation?

And go with that

[rugged orchid]

If you’re at the stage where you are integration

You should be able to graph any quadratic and linear equations

[rugged orchid]

To be honest as long as the graph is close enough it’s good enough

So have the roots on the right side of the axis

[rugged orchid]

Have the parabola facing the right direction

[dire terrace]

I stopped here

[rugged orchid]

Ok

Why have you equated the 2 equations

(Not that it’s wrong, but why did you do it)

[dire terrace]

To find limits of the area body

That's what professor did

[rugged orchid]

Mhmm

If you do that you don’t even really need the graph

[dire terrace]

So that is the analytical way

[rugged orchid]

Yeah

[dire terrace]

I get x = 0 and 3

[rugged orchid]

The graph just helps you visualise what you’re doing

[rugged orchid]

What do those 2 values tell you?

[dire terrace]

That is the limit of the integral right?

From 0 to 3

[rugged orchid]

Well yes, but why

[dire terrace]

Cuz the area goes from 0 to 3

On X axis

[rugged orchid]

Well, what I wanted you to say is that x=0 and x=3 is where the 2 lines intersect

[dire terrace]

Ohh

I do understand that

[rugged orchid]

That’s why it makes sense to have them as the limits on the integral

[dire terrace]

However I do not know which one is the upper function

[rugged orchid]

It doesn’t matter 🙂

We want to look at area

That’s always positive

Just take the absolute value of whatever the integral is

[dire terrace]

So it doesn't really matter if I write f(x) - g(x) even though g may be the upper one

?

[rugged orchid]

It doesn’t matter if you write it as |f(x) - g(x)|

[dire terrace]

Gotcha

So from what I understood

With your help

[rugged orchid]

You could also show that both are continuous on the interval, and evaluate at some point on the interval to see which is the higher one

(Well they have to be continuous to be integrable anyway)

[dire terrace]

Before doing the all integral work I only need to find the limits, that is where the two intersect

[rugged orchid]

Yes

[dire terrace]

But what if those limits are only one part of the area?

[rugged orchid]

So you mean if it intersects more than twice?

[rugged orchid]

Ooh

You could rotate that by 90 degrees before calculating as well

But you can write it separately I suppose

[dire terrace]

Professor told us that as well

[rugged orchid]

Thing is that’s not a function

Functions have only 1 output

If you can’t rotate I’d say it’s a bit tough

We don’t know if that sideways thing is symmetric

But if we do know that we can integrate just the top part from -1/2 to 0

Multiply that by 2

Then add the integral between the 2 functions from 0 to 4

[dire terrace]

Okay last question

When I graph the quadratic function

It should intersect the linear one on x=0 and x=3

Cuz I got those analytically

[rugged orchid]

Yes it should

[dire terrace]

Now it makes sense

Thank you so much

[rugged orchid]

That’s what equating the 2 lines do

[dire terrace]

Yea yeah i got it

Thank you so much

[rugged orchid]

When you did 6-2x = x² -5x +6

👍

[dire terrace]

.close

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[rigid carbon]

Is my poisson notation correct?

Cuz how would I integrate this?

Wait I’m stupid u can’t integrate a poisson it’s discrete

[rugged orchid]

Why is it from 1

I mean…

[copper roost]

i mean it looks fine

[rugged orchid]

It’s still a valid integral

[rigid carbon]

Question is

[rugged orchid]

(Tho you are missing the dx)

[rigid carbon]

Yeah it’s just rough#

If a courier delivers 3 packages per hour on average, what is the probability that he will take more than an hour to deliver a package? (Round off your answer to two decimal places)

[shell yew]

have you defined x! for all positive real numbers ?

[rigid carbon]

so we use poisson

[lone niche]

gamma notation sucks

[rigid carbon]

so it would just be

1- p(1)?

seems incorrect

[copper roost]

p??

[rigid carbon]

probability of x=1

[rugged orchid]

P(X<1)?

[rugged orchid]

But time isn’t discrete

At least not for the purposes of this question

[rigid carbon]

poisson is number of occurances during a period

our period is 1h

and the occurances are 3

[copper roost]

what kind of math is this

[rigid carbon]

stats

[copper roost]

ohhh

ive been looking at it all wrong

[rigid carbon]

If a courier delivers 3 packages per hour on average, what is the probability that he will take more than an hour to deliver a package? (Round off your answer to two decimal places)

so lambda = 3

[rugged orchid]

Wait hold up I think I was wrong

[rigid carbon]

so in order to work out the p

[rugged orchid]

This should be discrete I think sorry

[rigid carbon]

it would be, 1-P(x=1)

0.85?

[rugged orchid]

Wouldn’t that be probability that exactly 1 package is delivered in 1 hour

[rigid carbon]

hm

so 1 - p(x=1) - p(x=0)

its P(X>1)

i think it could also be an exponential dist

yeah this is throwing me completely off

yes its exponential

[gaunt slate]

p(x=0)=e^(-3)

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[rigid carbon]

.close

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[vast shale]

?

[obtuse radish]

hi

ur supposed to msg here if u have a problem that needs help

if its by mistake type ".close"

[vocal sleet]

@vast shale Has your question been resolved?

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[graceful sorrel]

I need some assistance

[graceful sorrel]

How do I put together a 169cm squares , 144 cm squares and 25 cm square to form a triangle

[full arch]

notice anything about those numbers?

[graceful sorrel]

Hmm not really

[full arch]

you should

what happens if you take the square root of them

[graceful sorrel]

I’ll get 13 , 12 and 5

[flat whale]

this is called a "pythagorean triple"

[graceful sorrel]

A Pythagorean triple

What is that?

[flat whale]

https://www.cuemath.com/geometry/pythagorean-triples/

[graceful sorrel]

Thanks for explaining

I’ll go and do that

.close

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[snow path]

basically stuck at first part\

they pull out -1/2? why?

i mean i can set the inside to u already, right?

or is it because it helps for when you choose to set inside sqrt to u?

honestly i just noticed a u-sub is the best way to goa bout things

[viral copper]

They just did it so that the top is an exact derivative of the term inside the square root

[snow path]

and perhaps this is why they pullout -1/2

[viral copper]

You can do whatever you want it's the same thing

<@&268886789983436800>

Thanks

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[verbal lodge]

1**9+9

[snow path]

wait what

[verbal lodge]

maybe the ^ is not allowed

[snow path]

1*9+9=18?

[verbal lodge]

** not *

[snow path]

OH

MB

i see

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[vocal sleet]

Please don't occupy multiple help channels.

[vast shale]

<@&286206848099549185> i need help

[obtuse radish]

!15m

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[obtuse radish]

!status

[vocal sleet]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

@vast shale Has your question been resolved?

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[karmic imp]

Are you asking about $cos^{2}(\theta)$ and $cos(2\theta)$?

[twin meteor]

dldh06

[karmic imp]

It's not the same, one is an exponent, the other isn't

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[honest knoll]

I have a problem in number theory: n,k is positive integers. Find all solutions such that 1!+2!+3!+...+k!=1+2+3+...+n. I can't solve it

[cobalt crypt]

mod 7

[honest knoll]

<@&286206848099549185>

[cobalt crypt]

what part of mod 7 do you not understand

[honest knoll]

what do you mean mod 7

[cobalt crypt]

consider the equation mod 7

[real geyser]

why specifically 7?

[cobalt crypt]

because it works?

give me a smaller mod that works and you can use that instead

[vast shale]

because snow big brain

[honest knoll]

what are the possible pairs of n,k

[cobalt crypt]

that is for you to determine

[honest knoll]

how?

[cobalt crypt]

this is already solving the biggest part of the problem

you consider the equation mod 7

[ 2(1! + 2! + \dotsb + k!) \equiv n(n + 1) \pmod 7 ]

[honest knoll]

i can't understand how can i use this

[cobalt crypt]

what are the possible residues of the RHS

[honest knoll]

what is RHS

[cobalt crypt]

right hand side

[honest knoll]

0,1,2,3,4,5,6

[cobalt crypt]

is it possible for n(n+1) to be 1 mod 7?

[honest knoll]

i think no

[cobalt crypt]

so which are possible

[honest knoll]

0,2,5,6 i think this

[cobalt crypt]

what about the LHS

consider for k>=6

[honest knoll]

3

[cobalt crypt]

so can you have LHS = RHS in that case

[honest knoll]

what

[cobalt crypt]

if k>=6 then the LHS = 3 mod 7

but the RHS can only be one of 0,2,5,6 as you determined

[honest knoll]

yes

[cobalt crypt]

so is it possible for them to be equal?

[honest knoll]

o no

thank you so much

[cobalt crypt]

exactly

so you just have to check k<6 manually

[honest knoll]

and manually i have solve for all the others

[cobalt crypt]

yes

[honest knoll]

its 1,1
2,2
5,17

[cobalt crypt]

great

[honest knoll]

but i couldn't found the way to put a max

thank so much i appreciate it

.close

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[cobalt crypt]

[vocal sleet]

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[ancient fern]

.reopen

[quiet lintel]

I need help with this math problem :))

[lyric glacier]

add all the percentages up and divide it by 18

[quiet lintel]

Okk

[lyric glacier]

for part 2

i have no idea

what is a deviation lmao

[quiet lintel]

Tis why I need help 😭

[lyric glacier]

lol

[quiet lintel]

<@&286206848099549185> I need help with this math problem still 😭

[vast shale]

Sorry but i dont know it too

[vocal sleet]

@quiet lintel Has your question been resolved?

[lone shoal]

To calculate the Mean Absolute Deviation (MAD) you need to calculate the

$(\sum{x_i - x})/n$

[twin meteor]

SenPyAI

[lone shoal]

x is the mean from part 1

[quiet lintel]

Okk

I think I get it now

.close

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[slate saddle]

struggling with this problem

[lusty fox]

!show

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

@slate saddle Has your question been resolved?

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@slate saddle Has your question been resolved?

[runic arrow]

That's more of a physics question than math isn't it

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@slate saddle Has your question been resolved?

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[gloomy cedar]

So for limits when doing series, does $(-1)^n*n^2/(2n^2)$

[twin meteor]

Meep

[gloomy cedar]

Can you just say it diverges?

[rose raft]

is n going to inf

[gloomy cedar]

Yea

[lone niche]

limit of the sequence or limit of the series?

[gloomy cedar]

Since 1 will just -1^n will just alternate between 1 and -1 and it’s insignificant whether or not the limit is 1/2 or -1/2

Series

[lone niche]

well if you write the terms you get 1/2 - 1/2 + 1/2 - 1/2 + 1/2, which has partial sums of 1/2, 0, 1/2, 0, 1/2...

[dull bear]

limit of the sequence is not zero

[gloomy cedar]

Ye so it would be okay to conclude diverges because it’s not 0

Alright thanks !

[lone niche]

yep

[gloomy cedar]

.close

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[hearty delta]

how would I solve this intigral?

is there a rule or something im missing

[karmic imp]

Just to ask, is that a 5 or S?

[hearty delta]

5

sorry crappy handwritng

[hushed pewter]

dwhat?

[gloomy cedar]

Rewrite it as 3^-n

[hearty delta]

thats the original question, im intigrating the sum from 5 to infinity

[hearty delta]

ok and then?

[hushed pewter]

geometric series sus

[lone niche]

you can get an exact value for the error though

no integral needed

[gloomy cedar]

Yea swr has a point

[hearty delta]

hmm?

Wont you need to

one sec I have the answer key

[lone niche]

you can find the exact value of the partial sum and also the entire sum

[hearty delta]

The prof wants us to use an intigral

[lone niche]

fair

[hearty delta]

i just dont know how to solve that intigral

idk what im missing lol

[lone niche]

you can integrate an exponential

antiderivative of a^x is a^x/ln(a)

iirc

[hearty delta]

is it just a rule you have to know

or is it derived from something?

[lone niche]

it's derived from, the derivative of a^x is a^x ln(a)

[hushed pewter]

$\frac{1}{3^x}=3^{-x}=e^{\ln(3^{-x})}=e^{-x\ln{3}}$

[twin meteor]

SWR

[hearty delta]

oh the e and ln cancel out

so they add e^ln3^-x

move the -x to the front

ok i get that part

but how do you intigrate that lol

[hushed pewter]

How do you integrate e^x?

[hearty delta]

is that just 1/-ln3 * e^-xln3

alr i understand now

damn

[hushed pewter]

And you can re-simplify e^-xln3 back to 3^-x

[hearty delta]

i got to calc 3 without ever running into this somehow

ok that makes sense

alr tyty

.close

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[hearty delta]

@hushed pewter if your still alive lol

[hushed pewter]

[hearty delta]

I hit another problem like that, i did that right right?

[hushed pewter]

Looks good

[hearty delta]

alr

no other simplification?

[hushed pewter]

Other than calculating the integral, no

[hearty delta]

alr let me try this out

one sec

YOOOOO

@hushed pewter thank you so much lol

idk why that took me so long to figure out

[hearty delta]

bro tbh

this software doesnt explain anything

idk how I was supposed to figure it out from that

wait how did they simplify it so much

like how did the ln cancel out

[vocal sleet]

@hearty delta Has your question been resolved?

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[wind belfry]

Hello, I am learning some pre uni math and stumbled upon this and it confuse me

[wind belfry]

I am not quite sure what happens here because of the expression

sry I don't learn in english and not sure of the right terms for everything

my book is saying that given this:

[wind belfry]

then this would be the sum, but it does not make sense to me

[lone niche]

a is a generic list of numbers

actually they made a mistake

it should be written $\sum_{i=1}^{n}a_i$

[wind belfry]

the n really confuse me here..

[twin meteor]

zfnQRZJT

[wind belfry]

oh

[lone niche]

n = number

[lone niche]

this means add all the numbers in the list together

[wind belfry]

because this would be like doing an + an + an + an + ... + an right?

[lone niche]

yeah

maybe the idea is for you to see that that's n*a_n

could be intended

[wind belfry]

ok, I was very confused then I think I understand correctly

[wind belfry]

I am not sure what that means

what is _?

[lone niche]

$n*a_n$

[twin meteor]

zfnQRZJT

[wind belfry]

ah okay

[wind belfry]

idk what would that give me, I think its a typo

at least in this context

[lone niche]

probably

[wind belfry]

can u tell me what this is called?

[lone niche]

wdym by give you

[lone niche]

sequence

[wind belfry]

ok so they are basically saying given that sequence "a natural question would be, what is the sum of the members(idk what u call it) in the sequence"
then they say a way to represent the sum is this:

so I meant, it doesnt seem right or leading me to anything so I dont see what it can "give me"

[lone niche]

if they ask you to figure out what the answer is

then they will give you the list of numbers

and you can just add them

[wind belfry]

yea I think I understand now, this was suppose to be the explanation and I got stuck on it a while cuz of the a_n

thank you!

[vocal sleet]

@wind belfry Has your question been resolved?

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[upbeat tulip]

SOS for the proofs

[vocal sleet]

@upbeat tulip Has your question been resolved?

[vocal sleet]

@upbeat tulip Has your question been resolved?

[vast gorge]

@upbeat tulip do u know what's injective means?

[upbeat tulip]

I know the basics that it means one to one

[vast gorge]

one to one onto function yeah meaning every value is asscoative with different value

!status

[vocal sleet]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[upbeat tulip]

I didn't even know that was a thing you could do

[vast gorge]

since the function gof is injective f must be injective

u might thing but that's wrong

f is not always injective

even if the function gof is injective

[upbeat tulip]

@vast gorge so ur saying the first is false?

[vast gorge]

yup, well I did my best try not give answer

[upbeat tulip]

no yea I appreciate it and will work my way to get there

For gof is surjective and g is surjective, I had that was true? Is that correct?

[vast gorge]

yup

[upbeat tulip]

Dubs. Absolute win

[upbeat tulip]

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[thin vale]

If I have a matrix B, and I diagonalize it, what is the special way that I can write the matrix C, which is $C=(B+I)^{-1}$

[twin meteor]

AustinU

AustinU

[half imp]

C*I*I

[thin vale]

I am in pain at this question

[half imp]

ah I see

maybe

first write B+I as a product of three matrices

[thin vale]

I'm not sure how I would do that

[heavy plover]

I = SS^-1

distributivity holds for matrices i think

[half imp]

hint: use B = SΛS^-1

[heavy plover]

so you can factorise it

[thin vale]

well I figured as much XD

yeah that part about I=SS^-1 is helpful

I'll try that out

[half imp]

||I = SIS^-1||

try without spoiler first

[thin vale]

$B+I=S(\Lambda(S^{-1}+I))$? or $B=S(\Lambda S^{-1} + S^{-1})$

[twin meteor]

AustinU

[thin vale]

$B+I=S \Lambda S^{-1} + I$ $\newline$ $=S \Lambda S^{-1} + S S^{-1}$

[twin meteor]

AustinU

[thin vale]

yet I am supposed to remove the addition

So

$S(\Lambda S^{-1} + S^{-1})$

[twin meteor]

AustinU

[thin vale]

which still has addition

so

[fluid obsidian]

Uh

[thin vale]

$S((\Lambda+I)(S^{-1})$)

[fluid obsidian]

Nic remove one bracket

[twin meteor]

AustinU

[thin vale]

this is the product of 3 matrices

I suppose

[fluid obsidian]

Now take the whole inverse

[thin vale]

but Lambda+I

[fluid obsidian]

Keep it as it is

[thin vale]

the whole inverse would be

[fluid obsidian]

It's still diagonal

[thin vale]

$S (\Lambda+I)^{-1} S^{-1}$

[twin meteor]

AustinU

[thin vale]

would you say that is how I could express C=(B+I)^-1?

as a product of 3 matrices

[heavy plover]

yes

[thin vale]

is there anything I can do to simplify the

[fluid obsidian]

Yea

[thin vale]

lambda+I inverse

part

[fluid obsidian]

I hope you took the inverse right

[thin vale]

you just swap the order and inverse it all right?

[fluid obsidian]

Yeah

You are right

[half imp]

yeah that's what I was thinking too

tbh I moved the inverse sign to the other S by mistake

lol

[fluid obsidian]

You know inverse of diagonal matrix

[thin vale]

it's 1/A right? for diagonal A

just reciprocal everything

[fluid obsidian]

What even is 1/A

Yeah reciprocal of elements

[thin vale]

bad notation meaning to reciprocal everything

[half imp]

reciprocal every entry yeah

[thin vale]

Okay so

I have a question

and first I need to type down lots of information

so bear with me

[fluid obsidian]

You are my favorite Austin dw

[thin vale]

$H=\frac{1}{2} \cdot \begin{bmatrix} 1 & 1 & -1 & -1 \ 1 & -1 & -1 & 1 \ 1 & 1 & 1 & 1 \ 1 & -1 & 1 & -1 \end{bmatrix}$ $\newline$ H is orthogonal. Suppose first that the columns of H are the eigenvectors of $B$ $\newline$ Suppose next that the eigenvalues of B are $\lambda= 0, 1, 2, 3$

[twin meteor]

AustinU

[thin vale]

yikes

[twin meteor]

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

AustinU

AustinU

[thin vale]

Okay so now we finally have all of the information for my question, if anyone is still here

I want to know what basic classes of matrices B and C belong to. options being singular, symmetric, orthogonal, positive definite, semidefinite, or diagonal <@&286206848099549185>

Since, B has an eigenvalue of 0 can't I say that it is singular? This I can see.

[lyric glacier]

im here

[thin vale]

hey, do you have any ideas?

[lyric glacier]

i meannnn

im in yr 8--

i guess i can help tho i got into olympiad

what do u need?

[thin vale]

read the question above, otherwise this is a help-channel so please don't interrupt

[fluid obsidian]

Help

[thin vale]

oh good faf you are still here

any ideas?

[fluid obsidian]

I doubt B is like this

[thin vale]

that is the diagonilization of B, since we know it's eigenvectors and eigenvalues

[fluid obsidian]

You seem to have forgotten 1/2

[lyric glacier]

:/

[thin vale]

I guess so

with the 1/2 then

doesn't change much

[fluid obsidian]

Ok lets see

You took the transpose for inverse good

[heavy plover]

doesnt the 1/2 go away when multiplying by S^-1 anyways

[fluid obsidian]

Can we choose more than one options

[fluid obsidian]

Actually we get 1/4 instead

[thin vale]

yes we can, we want to identify as many classes we can stick B and C into

I guess the approach should be going 1 at a time

Shall we start with singular?

[heavy plover]

yes

bc it has an eigenvector of 0

[thin vale]

B is singular

C is not

agreed?

[heavy plover]

yes

[thin vale]

Okay, next maybe we try diagonal?

can we tell from above that B or C are diagonal?

[fluid obsidian]

If $S= 2H$ then $S^{-1} = 2H^T$ so $S\land S^{-1} = 4 H\land H^T$

[thin vale]

is that about the 1/2? lol

[twin meteor]

fäf

[heavy plover]

why is one side inverse and the other transpose

[thin vale]

Okay, next we can see that the eigenvalues of B are =>0 so we can say B is positive semidefinite, but the eigenvalues of C are > 0 so C is positive definite.

[heavy plover]

oh S is orthogonal

[fluid obsidian]

H and S are both orthogonal matrix

[thin vale]

agreed with that?

[thin vale]

getting a bit off topic I think faf

[heavy plover]

idk that theorem but it sounds right

[fluid obsidian]

Okay so where are we

[heavy plover]

is a positive definite matrix one with only positive entries or a positive determinant