help-10

[chilly narwhal]

Right?

[grizzled shore]

equations have equal signs

[chilly narwhal]

Idk its just so weird

[grizzled shore]

(And inequality signs as well)

[chilly narwhal]

Let me see if I can find something that's similar to the question

My laptop died

I will return w this question tmrw lol it takes forever to charge

But tysm for your help guys!

Also one question

[high lily]

seems like what you want is expanding and distributive property

[chilly narwhal]

Ohhh maybe

I mightve skipped that section

But that does seem to make so much sense

[high lily]

i'd recommend avoiding stuff that mention foil

[chilly narwhal]

Got it

I wanted to ask do u guys have like a review channel? Like to review the server or something? You've been helping me sm I'd like to give u 5 stars somehow

[high lily]

no

[chilly narwhal]

Oh ok no worries! Tysm!

.close

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[timid silo]

Hey, so I'm following the formula used for the theorem, but its making no sense when I combine them.

[timid silo]

Ik the formula is (EC)(DC)=(AC)(BC), but combining the terms are confusing me

[leaden ginkgo]

can you show your working?

[timid silo]

The only reason why i got it right was because i guess

but

ill show u what i have

Oh wait oh, i got mixed up, I understand now 😭

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[placid smelt]

Why did they just not perform EROs to row reduce this normally to end up with an upper triangular form.

That way we can just see the diagonal as the product of 3 numbers and determine what value(s) K can be?

Won't that work too?

As A is invertible iff the det(A) is not equal to 0

[brisk matrix]

have you heard of cofactor expansion?

[placid smelt]

Yes

[brisk matrix]

if you put 0s as they did on the first column, the determinant becomes easy to compute

[placid smelt]

Yes but doesn't my way work as well?

[brisk matrix]

yes

[placid smelt]

For some reason my way isn't giving the same answer

I did r3 -> 1/2(r3)

to get

[3 5 7
6 k 14
1 2 3]

then I did

r3 swap r1

[1 2 3
6 k 14
3 5 7]

This leaves me with -2det([1 2 3
6 k 14
3 5 7])

Now I perform addition eros

I do r2 -> -6r1 + r2

to get

-2det([1 2 3
0 k-12 -4
3 5 7])

Then I did r3 -> -3r1 + r3 to get:

[brisk matrix]

did you take into account how you row operations affect the determinant?

[placid smelt]

-2det([1 2 3
0 k-12 -4
0 -1 -2])

[placid smelt]

yes

[placid smelt]

this is where I have gotten

I need the -1 in the third row to become 0

idk how to do that

[brisk matrix]

i think you might not be able to

given you have that k variable there

[placid smelt]

Yeah so this method is not possible here then?

[brisk matrix]

looking closer it might not be

i mean, the method does "work"

as in, it should produce the right answer

but getting it to upper triangular form may not be with the k hanging around

[placid smelt]

damn

why is linear algebra so painful bro

I really gotta put it into a form to use expansion

How did they know what these eros would be the best ones?

To allow for expansion in the second row

Or do we just try and see how we can easily add zeros or a column and row and then work from there?

[brisk matrix]

not really

you could expand right away

and just simplify

[brisk matrix]

it doesn't matter

you just want zeroes along a row or column

but then again

you could just have taken the determinant of the original matrix

it's just a little more work to do so

[placid smelt]

Yeah true

Alright well, ty.

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[cunning tulip]

Help

[cunning tulip]

idk how to do it

[prisma hatch]

tan x = -1/sqrt(3)

use arctan and u will get ur answer

@cunning tulip do you know what arctan is?

i wish to give you solution directly but

!nosols

[obtuse pebble]

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

[cunning tulip]

What’s arctan

[wanton hull]

tan inverse

[prisma hatch]

inverse tan

[cunning tulip]

oh

Ok

[wanton hull]

wont he be getting two ansswrs?

[prisma hatch]

yes

[wanton hull]

ok

[cunning tulip]

Thx

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[naive citrus]

Where can I learn more about this?

[obtuse pebble]

@naive citrus Has your question been resolved?

[naive citrus]

<@&286206848099549185>

[obtuse pebble]

@naive citrus Has your question been resolved?

[naive citrus]

<@&286206848099549185>

[obtuse pebble]

@naive citrus Has your question been resolved?

[prisma hatch]

@naive citrus why dont you ping helpers?

!15m

[obtuse pebble]

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.

[naive citrus]

Doing other homework and just kinda forgot oops

<@&286206848099549185>

[shut lagoon]

Isn't this Bézout's Identity for polynomials?

What do you want to learn about?

[naive citrus]

This specific case of if they're coprime they also satisfy being equal to h(x)

Honestly our teacher hasn't taught us this yet but gave us homework that included this so I just wanna learn in advance

[shut lagoon]

Not sure I have any ressources on hand except just looking up things related to the identity online, sry

[naive citrus]

Ah okay, thanks

[shut lagoon]

Maybe you could find someone more specialized in the Abstract Algebra channel too

Might have more insight and ressources

[naive citrus]

Ah alright, thanks for the suggestion!

[obtuse pebble]

@naive citrus Has your question been resolved?

[obtuse pebble]

@naive citrus Has your question been resolved?

[obtuse pebble]

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[gloomy trellis]

Because they approaches in the same direction so

y=x

y=-x

[obtuse pebble]

@gloomy trellis Has your question been resolved?

[wooden marten]

y = x and y = -x are not the same line

[gloomy trellis]

Which is actually logically incorrect as we have infinite path to approach the point
so to check existance of limit we have to discuss limit of the function about every path.

[wooden marten]

yep

[gloomy trellis]

Thanks you

.done

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[timid silo]

what do i need to study multivariable calculus?????????

[timid silo]

hello

🤠

[uneven palm]

https://www.khanacademy.org/math/multivariable-calculus/thinking-about-multivariable-function/x786f2022:vectors-and-matrices/a/multivariable-calculus-prerequisites#:~:text=The biggest prerequisite for multivariable,Limits

[timid silo]

thanks

😑

.close

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[timid silo]

Based on the data from the picture, calculate the area of ​​the figure that consists of a triangle, a trapezoid and a right triangle.

[timid silo]

Nevermind figured it out.

.close

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[timid silo]

Why is my answer slightly off from answr key?

[timid silo]

Ans key answr in red ink

Mine in blue box

(Multiplying radicals btw)

[ornate ravine]

seems to me like you're right and the key is wrong

[timid silo]

Uhhh

Are you sure?

Could we get a 2nd opinion on this guys?

Similar thing happening with the problem before that

[fossil crag]

what is the original question?

[timid silo]

Original questions underlined in green

The one on top is 4b)

One on bottom is 4a)

Answer key for reference

[slow prism]

ok I see. Look at b), the y is not inside the radical

it's outside

[timid silo]

Uh

What

How did they write it, in reverse order?

[slow prism]

so the answer key and what you got are the same thing

[slow prism]

yes

[timid silo]

That is a stupid way to write it

[slow prism]

exactly

[timid silo]

But I also see what you see.

Mmmm

That makes sense now

[slow prism]

the way you wrote is the correct way

[timid silo]

So I did do it right

[slow prism]

yes

[timid silo]

Cool thanks

[slow prism]

but the answer key is also right

[timid silo]

If it weren’t for you this book would have thrown me off

[slow prism]

it's the same thing

[timid silo]

Ok, I’ll continue writing it the way I did.

Thanks

[slow prism]

yeah... when you take the variable out, you can put it anywhere you want and they chose to put it after the radical which makes it look confusing

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[river kindle]

Solving for values of p that hold this inequality

[river kindle]

can someone help me finish this problem I think it’s quadratic formula, I’m just a bit out of practice

[tacit gate]

goddamn

[river kindle]

what’s up

I should also preface I’m solving for values of p that keeps this inequality

[obtuse pebble]

@river kindle Has your question been resolved?

[obtuse pebble]

@river kindle Has your question been resolved?

[river kindle]

<@&286206848099549185>

[obtuse pebble]

@river kindle Has your question been resolved?

[obtuse pebble]

@river kindle Has your question been resolved?

[shell hatch]

@river kindle you have two unknowns, n would need to be in terms of p, and the probability of actually solving this seems very low without a computer. You could also set n to different values, but again… There are many solutions and most are extremely ugly. Did someone actually give you this problem?

Here are the solutions that solve the inequality: https://www.wolframalpha.com/input?i2d=true&i=8np+-+8Power[p%2C2]n+%2B+4p+-+n+<+0

Obviously I don’t think anyone is going to be able to help you do this by hand

Also note that some of those solutions aren’t possible

For example, your n can never be 0

It also can’t be +/- 2

Do you see why?

[obtuse pebble]

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[timid silo]

I have no idea on how to even proceed

Like sure you can write that the addition of all elements in set is not equal to 0

But what then

<@&286206848099549185>

[pulsar geyser]

Yea

[timid silo]

Hey

😊

[pulsar geyser]

Hello

[timid silo]

So any idea?

[pulsar geyser]

Um no

Im thinking of one but it doest equal??

[timid silo]

I mean

It just feels so

Different

I have never encountered this type before

[prisma hatch]

!15m

[obtuse pebble]

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.

[pulsar geyser]

I know

[timid silo]

Usually vectors have a certain form

[prisma hatch]

Read #❓how-to-get-help

[timid silo]

What

[pulsar geyser]

Wth

[timid silo]

Like polynomials are understandable

Functions maybe

[pulsar geyser]

True

[timid silo]

But x^n e^ax is a weird form

[pulsar geyser]

Ysa

Hmmm i get you

Yes*

[timid silo]

Putting this here again

[pulsar geyser]

Aight

Should we equal it to 0 ???

[timid silo]

So basically we need to prove that any linear of combination of those

Are never 0

[pulsar geyser]

Hm. Yea

[timid silo]

Unless for all scalars being equal to 0

[pulsar geyser]

Ohhh i get it

You a boy or a girl?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[fading sluice]

can someone help me recheck

[high lily]

what's your reasoning behind your choice

[fading sluice]

oh wait it is true bc its SAS postulate

so it corresponds

[high lily]

that's one way to justify it

[gleaming ridge]

yep

[fading sluice]

tysm for yall help!

.close

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[teal turret]

What have u tried

[reef hatch]

i have done the Q and have gotten the answer but my friend is tellin me its wrong

[teal turret]

Can u send ur work for it?

[reef hatch]

i have taken peri of smaller semicircle (30.84) and then the peri of large semicircle(92.54). Then i have subtracted the small semicircle twice and added it back once for the peri of whole shape.. i have gotten the perimeter of whole shape = 61.7

[teal turret]

Hmm

Do u have this working on paper?

I feel like it would be a bit clearer to understand

[reef hatch]

1 sec

im sending

[teal turret]

,rotate

[reef hatch]

sorry for the horrible handwriting

im in a hurry

[teal turret]

For the smaller semi circle circumference, how are u getting the pi * r +d

[reef hatch]

isnt the formula pi*r+2r?

so i have just taken D instead of 2r

[teal turret]

I’m not seeing where the 2r is coming from

[prisma hatch]

@reef hatch !status

!status

[obtuse pebble]

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

[teal turret]

what

We are literally working on the problem

Phantom notice that

This has the same perimeter

[timid silo]

Hey this is his friend

currently its fast time

and we about to break fast

you know ramdan for the muslims anyway he'll prob be back in a few mins

[teal turret]

Oh ok

[teal turret]

Notice that to find the perimeter of the figure, u can use this

So it’d be (circumference of big semicircle) - (diameter of big semicircle) + (3 circumference of small semi circle)

Idk if that’s what u were getting at, but I gtg now, hopefully u can understand it

[obtuse pebble]

@reef hatch Has your question been resolved?

[obtuse pebble]

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[kindred musk]

Could someone help guide me intuitively for why dividing by an integral by another integral gives the average? How does the bottom integral become "volume."

[kindred musk]

It all seems so strange to me.

This is the understanding I'm trying to reason with.

We're summing up all the values of dx here, multiplied by an f. In 1-D, this would give us an weighted area?

Then we divide by the sum of all our small distances?

[brisk matrix]

the integral of 1 over a 3d region represents the volume of that region

[kindred musk]

Why is that?

[brisk matrix]

it’s akin to how the integral of 1 over some interval is the length of that interval

[kindred musk]

Hm, but why does the function f disappear in the bottom integral?

[brisk matrix]

in general, you can think as the integral of 1 over an n-dimensional space as the n-dimensional volume of that space

how did it disappear?

[kindred musk]

I'm familiar with this.

[brisk matrix]

b-a is exactly the integral of 1 from a to b

[kindred musk]

Well, there's no integrand.

[brisk matrix]

the integrand is 1

[kindred musk]

I see.

And why do we divide by volume to find the average?

That also doesn't make sense to me.

How is the top function like "total mass"?

[brisk matrix]

think about the average of a function over an interval

you sum up all the values of the function (the integral), and divide by the length of the integral

[brisk matrix]

f defines the mass at some point

so the integral over the whole space is the total sum of the mass at all points

hence the total mass of the space

[kindred musk]

I see.

And if we follow this analogy (physics), then average is density?

Because mass/volume is density.

[brisk matrix]

yeah

[kindred musk]

So if I divided the bottom function, by the top one, I'd get the density of the cube.

Hm.

[brisk matrix]

yes

[kindred musk]

Interesting.

I still don't completely get why, but I do understand it more. Thank you!

[brisk matrix]

a few examples may help it sink in

[kindred musk]

👍🏻

I just find it crazy how length is also "volume"

Because in single variable calculus, I remember doing questions that asked about volume of a disk or etc.

[brisk matrix]

they’re using volume loosely

[kindred musk]

And the function gave the volume.

Not the interval itself.

[brisk matrix]

volume here refers to some arbitrary n-dimensional measure of size

length, surface area, volume, etc.

[brisk matrix]

this is just another way to compute volume

[kindred musk]

But the interval here can't be volume then.

Because the function gives the volume?

[brisk matrix]

what interval

[kindred musk]

b-a

[brisk matrix]

this is literal volume

[kindred musk]

Hm?

[brisk matrix]

b - a is a length

[kindred musk]

Right.

[brisk matrix]

you’re not taking the integral of 1 here

so you should expect the length of the interval necessarily

[kindred musk]

I guess these are just two different definitions of volume.

[brisk matrix]

read what i sent above

they are using volume to refer to n-dimensional measure of size

in this conversation about the last picture you sent, we’re using volume as the usual 3d volume

[kindred musk]

I see.

[brisk matrix]

that’s why they said “total volume”

[kindred musk]

Then a lot of things can be volume.

[brisk matrix]

you shouldn’t focus on the verbiage

they are just saying the bottom thing is the size

of the space

[kindred musk]

I see.

[brisk matrix]

the “total mass” and “total volume” are meant to help you visualize, they are not literally mass and volume always

[kindred musk]

Got it.

[brisk matrix]

don’t think of it as a rigorous definition of what’s going on

[kindred musk]

The physics definitions always trips me up.

I don't like how physical properties are applied to more abstract concepts when they don't always match everywhere. But, your explanation helped! Thanks again.

.close

[obtuse pebble]

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[reef hatch]

I need help with finding the perimeter.

[clear condor]

ok

what is the diameter of the mini circles

[reef hatch]

not given

[clear condor]

36/3

[reef hatch]

yea

12

[clear condor]

so

find the perimeter of a circle /2

[reef hatch]

i have taken peri of smaller semicircle (30.84) and then the peri of large semicircle(92.54). Then i have subtracted the small semicircle twice and added it back once for the peri of whole shape.. i have gotten the perimeter of whole shape = 61.7 i have done this much but my friend is arguing with me sooo i need some help :p

[clear condor]

what

[reef hatch]

have i done this right?

[clear condor]

Then i have subtracted the small semicircle twice

why

[reef hatch]

because the whole shape doesnt include the two top small semicircles as they are cut out it just includes one small one

[reef hatch]

yea that is the shape

[clear condor]

the large semi is 92.54?

[reef hatch]

yea

[clear condor]

2 pi r for the normal

so it is pi r for the semi

[reef hatch]

but isnt the formula pi*r+2r?

[clear condor]

the 2r doesn't matter in this equation

[reef hatch]

Oh

[clear condor]

cause uh

yes

[reef hatch]

that might be where im messing up

why is that tho?

[clear condor]

no 2r

[reef hatch]

yea i took that for the first perimeter.... because i can remove the two smaller semicircles from this in the end like i did

[clear condor]

no

ok

lets start with the big semi

pi r

then uh

do the 3 smaller ones

[ancient jacinth]

the weird squiggly bits are 3 semicircles

solve for the diameter of the semicircles

[reef hatch]

uhh so bascially

[ancient jacinth]

then use the formula you'd normally use to calculate the perimeter of a circle

but divide it by 2

[reef hatch]

i have taken the whole top semicirlce as one

and taken the perimeter

then i have taken the peri of smaller semicircles which are all equal

then i have subtracted the peri of smaller semicircles with the peri of top one.... in the end i have then added 1 more peri of the small semcircles for the bottom one

[ancient jacinth]

why did you subtract the peri

[reef hatch]

the top part

im removing the 2 semicircles from the whole semicircle

[ancient jacinth]

wow

hmm

[obtuse pebble]

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[reef hatch]

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[exotic creek]

anyone know where i went wrong?

they 0.9 instead of 1.8 for A idk why?

[high lily]

1.8/(2x-4) = 0.9/(x-2)

easier to apply chain rule,

but doesn't matter whether you convert that

[exotic creek]

i got the wrong answer at the end

[high lily]

your work is unclear after that first line

can you explain what you're doing there

[exotic creek]

wait i think i know where i made a mistake

give me one minute

[exotic creek]

i integrated ln(2x-4)

so i got 2/2x-4

[high lily]

integral is incorrect

[exotic creek]

its not?

i meant ln

[high lily]

still no

[exotic creek]

ln(2x-4)

differeciated is 2/2x-4

[celest fossil]

Yes but you want it to be 1.8/2x-4

[exotic creek]

yes

then i multipled 2 by 1.8

which is 3.6

1.8/3.6 = 1/2

[celest fossil]

It must be 0.9*ln|2x-4|

[exotic creek]

ahh

i must compare without multiplying it with 1.8?

[celest fossil]

If you differentiate 0.9*ln|2x-4| you would have 0.9 x 2 x 1/2x-4 and that is 1.8/2x-4

[high lily]

you can view/do things in a slightly different order
valid actions will lead to the same end result

[celest fossil]

The second ln is also wrongly integrated

[exotic creek]

i can do 1/2x-4 then i would get 1/2ln(2x-4)

then multiply with 1.8 which is 0.9

[high lily]

[celest fossil]

Try to differentiate 0.9*ln|2x-4| than you will see that you get 1.8/2x-4

[exotic creek]

yhyh

[high lily]

()

[celest fossil]

And the other one should be -2.4*ln|x+3|

[exotic creek]

yeah

Thanks

[celest fossil]

So your integral should be 0.9 x ln|2x-4| - 2.4 x ln|x+3|

[exotic creek]

👍

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[noble mantle]

I don't know where to begin

[stoic salmon]

can you show the figure or the question?

[royal shard]

You have a rectangle and cut out 4 quarters of a circle

So we need the area of a quarter of the circle and subtract it 4 times

But notice that the circle quarters are all equal, so we pretty much do area of rectangle minus area of circle

[obtuse pebble]

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[vital frost]

unsure if angles are pos or negative. any hints

say for theta5 is inversecos of -0.5

<@&286206848099549185>

i have 60,120, 30 for all 3 angles

[obtuse pebble]

@vital frost Has your question been resolved?

[vital frost]

<@&286206848099549185>

15min

.CLOSE

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[timid silo]

hello guys

[obtuse pebble]

Please don't occupy multiple help channels.

[frigid prism]

.close

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[timid silo]

im sorry this was a mistake

.close

nvm

[obtuse pebble]

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[humble maple]

Hey, how would I prove this?

[upbeat island]

start with the more complicated side

lhs here

first thing that pops out to me is that we have a difference of squares

that's a big hint, see where that takes you!

[humble maple]

I think this is what I am looking for, is this correct? @upbeat island

[frigid prism]

ye

[humble maple]

Extraordinary

Thank you

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[onyx spade]

how to do this but for third order odes

[onyx spade]

more specifically in matlab

like i can wrap my head around and code a first order

this was my code for 1st order ODE

[y,t]=RK4(0.5,1,3,@(t,y)(y^2)/(1+t),-1/log(2))

function [y,t]=RK4(h,a,b,d,y0)
t=a:h:b;
y(1)=y0;
for i = 1:length(t)-1
k1=d(t(i),y(i));
k2=d(t(i)+h/2,y(i)+hk1/2);
k3=d(t(i)+h/2,y(i)+hk2/2);
k4=d(t(i)+h,y(i)+hk3);
y(i+1)=y(i) + h(k1 + 2k2 + 2k3 + k4)/6;
end
end
% d=@(t,y)(y^2)/(1+t)
% h=0.5
% a=1
% b=3
% y(1) = -1/log(2)

but im stuck at the starting point for 3rd order

% BOUT TO GO into depression
% v''' - vv'' + (v')^2 = 0, with initial conditions V(y=0)=0, -(V'(y=0))=1, V''(y=0)=-1.
% 0 < y < 10
% so let v'= w, v''= x, v'''= x'
% so now we have x' = vx - (w^2) = 0 = f(t,v,x,w)
% so v0 = 0 w0 = -1 x0 = 1
f= @(t,v,x,w) (vx-(w^2))
h=0.5
a=0,b=10
t=a:h:b

[timber fox]

I can't say I have experience with the a third order, but i've implemented a second order, and setup was referenced from https://www.youtube.com/watch?v=nJ_f1h49jfM and https://www.youtube.com/watch?v=TjZgQa2kec0. It mostly is the same idea just a couple extra steps, I can imagine it extends into third order.

[onyx spade]

thanks

.close

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[timber fox]

also asking around the physics discord might help as they might be familiar with numerical integration for your application

[onyx spade]

i see thanks

[timber fox]

also ,

def updateBodiesRungeKutta(bodies) : # * Working as intended , much better accuracy.


    Y = []

    dt = TIMESKIP
    t = 0
    NElements = 3

    for i,body in enumerate(bodies) :

        Y.append(body.position)
        Y.append(body.velocity)
        Y.append(body.mass)

    Y = np.array(Y,dtype=object)

    k1 = dt * f(t,Y)
    k2 = dt * f(t+dt/2 , Y + k1/2)
    k3 = dt * f(t+dt/2 , Y + k2/2)
    k4 = dt * f(t+dt , Y + k3)

    yout = Y + 1/6 * (k1 + 2*k2 + 2*k3 + k4)

    for i,body in enumerate(bodies) :

        body.position = yout[i*NElements]

        body.orbit_points.append((body.position[0],body.position[1]))

        body.velocity = yout[i*NElements+1]

def f(t,Y) :

    Yout = []
    NBodies = int(len(Y)/3)
    NElements = 3

    for i in range(NBodies) :

        tempv = Y[i * NElements + 1]
        tempa = 0

        for j in range(NBodies) :
            if i == j :
                continue
            else : 
                tempa = tempa + (_acceleration(Y[i * NElements + 0],Y[j * NElements + 0],Y[j * NElements + 2]))

        Yout.append(tempv)
        Yout.append(tempa)
        Yout.append(0)

    return np.array(Yout,dtype=object)

this is the (very unoptimized barebone) implementation for the second order in python

[obtuse pebble]

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[sinful kraken]

does second moment of area change depending on axis shift

[obtuse pebble]

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[maiden garnet]

Does anyone know what the theta(x) function could be here?
This is from the second table in the "Connections within the group of rounding and congruence functions and with other function groups" section on https://functions.wolfram.com/IntegerFunctions/FractionalPart/introductions/FloorRelated/ShowAll.html
Or maybe it is defined somewhere else, and I overlooked it

[obtuse pebble]

@maiden garnet Has your question been resolved?

[maiden garnet]

It's https://en.m.wikipedia.org/wiki/Heaviside_step_function

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[astral plover]

how do you do this i am completely clueless

[sinful kraken]

what is the question ?

[teal turret]

U wanna make a right triangle

[astral plover]

What is the exact value

[teal turret]

Use those side lengths to make the lengths of the right triangle

[astral plover]

Hypotenus 1 and opp rad2/3 right

Idk what to do after tho

[teal turret]

Notice that it’s equal to $\frac {1}{\cos {[\arcsin {\frac {\sqrt 2}{3}}]}}$

[astral plover]

sorry i dont understand that

[warm shale]

Stephen

[astral plover]

arcsin?

[teal turret]

There we go

Arcsin is sin^-1

Same thing

[astral plover]

Oh okay thanks

i think i got

thanks

[teal turret]

Wouldn’t it be easier to make the hypotenuse 3?

O u got the answer?

[astral plover]

Thats truer

i think i got how to do

not yuet

[teal turret]

Use Pythagoras to find the 3rd side

Lemme do it on paper

Ok where are u now

[astral plover]

i got rad 7 for the side

with 3 as hypotenuse

[teal turret]

Yep

Keep going

[astral plover]

okay i got it

i was jus confused for a sec

thanks

[teal turret]

Np

[astral plover]

3rad7/7 right

[teal turret]

Yep

[astral plover]

i was doing the wrong work xD

Thanks

[teal turret]

Ah lol

[astral plover]

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[drifting shore]

Help

[teal turret]

Ok so what have u tried

[drifting shore]

8 is not correct

[teal turret]

Show how u expanded the denominator

[restive fiber]

1/b --> b^-1 ...

[teal turret]

Expand the 7^(2+t)

[warm shale]

Stephen

[teal turret]

Good, now see how u can manipulate the terms to get the answer

Move things around

[drifting shore]

Got it…

Why did that have to be so difficult 😭

[teal turret]

Lol

Nice job

[obtuse pebble]

@drifting shore Has your question been resolved?

[obtuse pebble]

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[tawny void]

How would I set this up?

[upbeat island]

ok i think i have something

first two lines say
A B = I
and
[ 1 1 1 ]* = B [ a b c]*

asterisks transpose so i don't have to type column vectors lol

i think if you right-multiply by [ a b c ]* things reduce nicely

A B [ a b c ]* = I [ a b c ]*
A [ 1 1 1 ]* = I [ a b c ]*

[tawny void]

Thats fine lol

[tawny void]

What did you get?

[upbeat island]

what did you get lol

[upbeat island]

the second line here should basically be it. does it make sense?

[tawny void]

I got 5,-2,0

Is that what u got

[tawny void]

^

[upbeat island]

yep!

[tawny void]

Can you check these 4 problems if they right

[upbeat island]

you can post them and i'll try. my linalg is kinda weak though

[tawny void]

Thats fine

Im pretty sure all of them are right

Besides the theory question

On the invertible matrix theory

[upbeat island]

first two are good
for IMT check here again: https://mathworld.wolfram.com/InvertibleMatrixTheorem.html
last one breaks my brain gimme a sec haha

[tawny void]

Last one is right I js need help with that theory one it messes me up

[upbeat island]

ok good

for the imt i think you're only missing the basis one

[tawny void]

I don’t think it should be C

Actually Idk

[upbeat island]

number 12. on that link matches
i'm not so hot at proving that

def get a helper if you want more details on that. it's prob worth it. IMT and all the equivalences are pretty important

[tawny void]

Lol

U don’t needa prove it

[upbeat island]

i had to at once point 😭

[tawny void]

😭😭

No way

.close

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[timid silo]

Is this right?

[teal turret]

Ye

[obtuse pebble]

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[sweet edge]

What would the image of this map be?

[sweet edge]

My intuition is to say that it’s just the span of x_1?

since u can write the map as something like
0 0
1 0
0 0

And then the column space is just span(1 0)

?

[fickle turret]

Do you mean span (0 1 0)^T?

[sweet edge]

Do I?

uhhh

I think I do

hm

[fickle turret]

Then it should be right

[unreal musk]

(Remember that x_1 is a scalar rather than a vector of R^3 of course)

[sweet edge]

Yes yes indeed

Okay thanks !

.close

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[fickle turret]

.choose

[drifting badger]

I feel like the notation of (x1, x2)^T instead of just writing it as a column vector is lawful evil

Threw me off for a second when I first saw the text

[obtuse pebble]

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[umbral hollow]

.close

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[proven flame]

yo how do I round to a penny again

[proven flame]

I got this number 72.2886

how I round to the penny

I think 72.29?

[wanton hull]

nearest 0.01 s

[proven flame]

so 72.29? since 86 rounds up to 100

[wanton hull]

,calc 68.52 + (68.52*0.055)

[warm shale]

Result:

72.2886

[wanton hull]

yep

[proven flame]

ok thanks

.close

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[timid silo]

How do I get started with this one?

[obtuse pebble]

@timid silo Has your question been resolved?

[tardy epoch]

What's F'(x^3)

[timid silo]

x^3cot(x^3)?

[frigid prism]

yes

[timid silo]

∫x^2F'(x^3)dx

is that the end?

[frigid prism]

yep

nope

you want to integrate

[timid silo]

im not sure how

like i dunno. doesnt the problem just say express using the F'?

[tardy epoch]

No. Read the problem again

[timid silo]

oh, i see. but how do i integrate? substition with u = F'x or something?

[thick gyro]

you can see

this is chain rule

@timid silo

like how sin(x^4) becomes 4x^3cos(x^4)

[thick gyro]

if you want, you can try use u = F(x^3)

[timid silo]

huh, but it's integral not derivative

[thick gyro]

im saying that

this is reverse

chain rule

if you see 4x^3cos(x^4)

you can immediately tell

that the integral is

sin(x^4)

[timid silo]

wait, but if u = F(x^3) , du = F'(x^3)3x^2 dx
=1/3∫du

[thick gyro]

yh

[timid silo]

does that work with no u?

[thick gyro]

?

how would you integrate

$\int dx$

[warm shale]

doctor99268

[thick gyro]

what do you think the answer is

[timid silo]

oh, =1/3u

[thick gyro]

yh

and you just sub in F(x^3) back into that

when youre dealing with reverse chain rule

there are two ways

first way is called integration by inspection

which is just looking at it

and seeing it

like, how i saw that it was immediately gonna be 1/3 F(x^3)

second way is substitution

which is just the more mathsy way

if you cant immediately see what the answer is

[timid silo]

i see, do i just leave it as 1/3F(x^3) or do I need to go further?

[thick gyro]

no thats what they want to see

[timid silo]

right on

thx

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[bleak saddle]

Express as a trigonometric function of one angle.
cos 17° cos 53° − sin 17° sin 53°

[bleak saddle]

im not sure how to even attempt this and i also cant find any videos that explain how too

[royal basin]

do you know angle sum identities?

[bleak saddle]

not sure i do

[royal basin]

sin(x+y) = ?
cos(x+y) = ?

do you know the identities governing these?

[bleak saddle]

sin(17 + 53)= sin(70)
cos(17+53)= cos(70)
cos(70) - sin(70)=?

is this what you mean?

[royal basin]

no this is not what i mean

forget about your problem for a moment

i'm trying to see how much you do/don't know

[bleak saddle]

i understand that sin= y and cos = x

is that what your maybe referring too?

[timid silo]

wdym sin=y and cos=x?

[bleak saddle]

as in a unit circle or a point

[royal basin]

no again that is not what i am referring to.

[median dome]

bad wording

[royal basin]

$\sin(a+b) = \sin(a)\cos(b) + \cos(a)\sin(b)$

[warm shale]

Ann

[royal basin]

do you know this identity yes or no

[bleak saddle]

no

[royal basin]

okay then you will have to learn about angle sum formulas or compound angle identities

(those are both searchable words)

[bleak saddle]

ok ill look them up. thank you

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[hoary rain]

So, i need to check convergence by using the root test

but, because its the absolute value of the limit, can i just ignore the -1^n-1 here?

[brave bramble]

The root test checks absolute convergence

Not conditional convergence

[hoary rain]

on my bad

i meant ratio test

[brave bramble]

Same diff

These tests don't operate on alternating series, you start by ignoring the (-1)ⁿ

[hoary rain]

ok so i can just ignore, cool

so i worked it out, and i got 3/2 * lim(n^3/(n+1)^3

and the limit diverges, so this just diverges as well?

[brave bramble]

That limit goes to 1

Ignoring the 3/2 out front

I mean - your total answer will be 3/2

[hoary rain]

oh, yeah i'm stupid

yeah and 3/2 > 1

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[polar bone]

can anyone please explain how the two are equal?

[prisma hatch]

!show

[obtuse pebble]

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

[prisma hatch]

Why don't you evaluate it yourself?

[polar bone]

ahh it's because one produces positive value while the other gives negative and when squared, it's equal

[prisma hatch]

Ya

What's problem?

[polar bone]

i get it now

thanks

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[hard whale]

Stuck on this Ellipse question to do with transformation of the ellipse

[obtuse pebble]

@hard whale Has your question been resolved?

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[vital frost]

A robot is equipped with a sensor to determine if a door is
open.
Sensor performance:
p(z=open | open) = 0.6
p(z=open | not open) = 0.3
Initial condition:
p(open) = p(not open) = 0.5
Using Bayes Rule calculate the probability of the door being
open after one measurement suggesting that the door was
open.

[vital frost]

how do i find p(z=open) as thats my denomiantor in bayes rule

[frosty spoke]

you can find that with p(z = open and door is open) + p(z = open and door is not open)

[vital frost]

so 0.9?

ans says 0.45

P(z=open) = P(z=open | open) * P(open) + P(z=open | not open) * P(not open)

total law of probabaility

[frosty spoke]

it's asking for p(open | z = open), is it not?

[vital frost]

yh

using bayes rule

[frosty spoke]

so what did you get for p(z = open)?

[vital frost]

it should be 0.45

ill show u graphic

[frosty spoke]

okay so

I'm not sure what your question is then?

[vital frost]

hows dominator that

[frosty spoke]

how's the denominator what?

[vital frost]

P(A | B) = P(B | A) * P(A) / P(B)

thats bayes rule

so i can see top matches but bottom doesnt

i dont see how P(z=open) = P(z|open)(p(open) +P(z|cllosed)p(closed)

[frosty spoke]

do you agree

that p(z = open) = p(z = open and door is open) + p(z = open and door is not open)?

[vital frost]

dont quite understand

i see z=open in all parts of q

eq

[frosty spoke]

contemplate the equation carefully

think about what it means

do you not see why it's true?

[vital frost]

yh

[frosty spoke]

so you don't actually know why it's true?

[vital frost]

yh unsure

In summary, the probability of the event Z = Open can be found using the law of total probability by considering the probabilities of the event happening under the conditions that the door is open (D) and the door is not open (D').

thats what i thought

[frosty spoke]

really

you didn't just paste that from chatgpt

[vital frost]

no

textbook

[frosty spoke]

so it's not what you thought

it's what you pasted from the textbook

[vital frost]

yh

[frosty spoke]

good to know that you can't be honest about it

[vital frost]

so what does z=open mean

is it probability sensor thinks door is open

which then u check when door is open and door is closed then sum

@frosty spoke

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[dawn escarp]

Hello guys! Just a quick one!
What should be the sign right there in the box
< or >

[timid silo]

log is increasing, so >

the sign doesnt change

[dawn escarp]

And if it would be log 0.5 then it would change right?

[obtuse pebble]

@dawn escarp Has your question been resolved?

[timid silo]

yes

because $\log_a(b)=\frac{\log(b)}{\log(a)}$

[warm shale]

Toby

[dawn escarp]

Ohk thanks Toby!

[timid silo]

yw :D

[dawn escarp]

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[blissful meadow]

I got 1 as an answer not sure if that’s right.

[obtuse pebble]

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

[clear condor]

not correct

[blissful meadow]

I substituted t for 20 and P(t) for 1.23, and got that.

[clear condor]

0.005* 20 is what

[blissful meadow]

0.1

[ancient jacinth]

calculation error

show your working

[obtuse pebble]

@blissful meadow Has your question been resolved?

[ancient jacinth]

wrong

p(20)=1.23e^(0.005*20)

[obtuse pebble]

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[vital frost]

what does inverting projection matrix mean

[obtuse pebble]

@vital frost Has your question been resolved?

[vital frost]

<@&286206848099549185>

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@vital frost Has your question been resolved?

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[clever spoke]

I'm trying to find such a and b that the limit is finite but I don't even know how to begin this one

[obtuse pebble]

@clever spoke Has your question been resolved?

[steep flax]

What's tg?

[hidden compass]

Tangent, I guess

[steep flax]

Well guessing isn't good tho

[hidden compass]

I mean, it's tangent 😅

I don't believe tg could be other things actually

[steep flax]

Fair point

[steep flax]

Are you allowed to use l'hospital?

[latent fjord]

check if there is in-determinant form

[steep flax]

There r often ways to not use l'hospital and still determine the limit using quite adhoc seeming trig identities. It annoys the shit out of me cuz then they're just making u do trig under the illusion that u're doing calc.
So the first question to ask is if using l'hospital is allowed or not. If it is, things are much easier. If it isn't, things can go very south very fast.

[latent fjord]

fair point

that is indeed infuriating

[obtuse pebble]

@clever spoke Has your question been resolved?

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[loud harbor]

Surely OA+OB=AB, wouldn’t it have to be OB-OA? Same for 4b

[jolly ginkgo]

OA+OB=AB?

[daring cosmos]

resultant means sum of two vectors, so resultant doesn't mean AB

[daring cosmos]

<edited>

[jolly ginkgo]

I was asking them

If they are right or not

[daring cosmos]

I see, alright

[jolly ginkgo]

You aren't supposed so find AB

to*

[loud harbor]

Isn’t that what the resultant of two vectors is?

Like the line joining them together

[jolly ginkgo]

No

Resultant will be the vector OA and you starting OB from A

OA+OB

[loud harbor]

Okay thank you I get it now 🙏

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[floral patio]

if the question is asking me for the maximum value of this function, how do I format my answer. is the maximum value 11 or is it (3π/2, 11)

[gray turtle]

just eleven, 3pi/2 is the x coordinate where the value of the function is 11

[floral patio]

okay thank you

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[true talon]

calc 2 differential equations

[true talon]

Here is what I tried:

[hot sonnet]

mm maybe they want something like y = ...

[median dome]

you should simplify the expression

$\frac1{e^{-x}} = e^x$

[warm shale]

kheerii

[obtuse pebble]

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