help-39

[fringe robin]

Length of train is just length contraction (or dilation here)
How has distance been obtained, cant tell you where i dont understand because I cant start it

[pearl pond]

@fringe robin Has your question been resolved?

[regal herald]

since the plane and the front of the train are approaching each other in the frame

(w+u)t represents how much the distance between them has decreased at time t [ or should i say it represents how far they have collectively travelled]

taking T to the time when the plane reaches the front

so (w+u)T represents the total length of the train (in the frame)

then the distance between them is the difference between the two

so (w+u)(T-t)

in short:

(w+u)t, distance travelled towards eachother at t
(w+u)T, total distance they will travel towards eachother before they meet

(w+u)(T-t), distance left between them at t

[fringe robin]

oh so for this bit i don't even need any relativity, just say what you see

[regal herald]

yeah

[fringe robin]

and it looks like the next bit is just equating but my ipad ran out

[pearl pond]

@fringe robin Has your question been resolved?

[pearl pond]

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[fossil warren]

why do we have to add the value of the initial position? aren't you already technicially getting that by integrating from 0 to 3?

[blissful cloak]

the integraiton means the distrance travelled from 0 to 3

but we need the strating value to "anchor" it

[wild fable]

u need to find da constant for x(t)

[fossil warren]

yep

[fossil warren]

wdym by "anchor" it?

[blissful cloak]

Imagine I told you I traveled 100 feet, and asked you "where did I end up?"

that makes no sense unless I also tell you where I started

[fossil warren]

OHH rightt so you would need to add the position you're already at in order to answer that

perfecttysm

.close

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[naive plume]

i found the line of y2 but then

i forgot what to do after that

<@&286206848099549185>

[fickle schooner]

I would approach this with vectors

[chrome plank]

they're both tangeant lines, so you could express them in terms of r

[naive plume]

huh

[naive plume]

whats tangeant

someone come back its due in 30 minutes 😭

[quartz rampart]

They meant tangent i believe

A line which touches a circle at exactly one point is a tangent to the circle

[naive plume]

i see

how

does that elp tho

uh i cut the thing in half to make 2 right trianges is this helpful or useless

[quartz rampart]

tbh idk, is that the full qs, are you given anything else as well?

wait is OA on the y axis and OC on the x axis

[fickle schooner]

Your circle is centered at (r, r) with radius r which can be defined by:
$(x - r)^2 + (y - r)^2 = r^2$

You can take one of your tangents $y = mx + c$ and substitute into that equation to eliminate either y or x.

Since it's a tangent, the resulting quadratic should only have one solution (indicating only one point of contact). For such a quadratic, the discriminant is 0

[jolly parrot]

StrangeQuarkAL

[fickle schooner]

I think that's sufficient to find r

I personally wouldn't do it that way cuz it's kinda tedious tbh

[naive plume]

yeah

[naive plume]

whats the EASIEST way so solve this

in the next 26 minutes

[fickle schooner]

Are you familiar with vectors?

[naive plume]

uh not rlly

this is a similair problem that i had to do

and my math guy wants me to do it ina similair way as to this

probably

[quartz rampart]

i think we can prove AOC congruent to ABC

ig it doesnt help tho

[naive plume]

huh

[naive plume]

i thought it does

i was thinking like

"how does math guy want me to do this"

and last time there was pythagorean theorem and alla that stuff

[quartz rampart]

im not sure, maybe it could let me try some stuff

[naive plume]

and like stuff about 1 2 and root 3

like the lengths of a 30 60 90 right tirangle

[quartz rampart]

oh wait i got it

its a square

[naive plume]

uh

really..

[quartz rampart]

like do you know the property of tangent makes right angle with radius

[quartz rampart]

not the entire Quad

[naive plume]

did not know that

[quartz rampart]

ok nvm, if you did you could use it here and then distance bw centre and point would be sqrt(2)r by pythagorean theorem

[naive plume]

oh kay

[quartz rampart]

hmmm, this seems tough without the property

[naive plume]

aw shucks

[fickle schooner]

Fairly easy way:
You know both y1 and y2 and therefore you can find point A and C (they are y and x intercepts respectively). If you show that AC passes through the circle's origin (r, r), simply finding the intersection of y = x and AC would be sufficient to get a value for r.

[naive plume]

wha

[fickle schooner]

which part is confusing

[naive plume]

finding the intersection of y=x and ac

[fickle schooner]

Oh yeah, (r, r) lies on y = x and AC right?

[naive plume]

really

how can u be sure

[fickle schooner]

for y = x: sub in the point (r, r) -> r = r which is true so it does lie on y = x

AC is the one that needs some work

[naive plume]

okay

wait

yk im finding the length of r?

[fickle schooner]

The two kites in the diagram are similar

[fickle schooner]

yeah I do

[naive plume]

2??

[naive plume]

oh

woah!

OH I GET IT

[fickle schooner]

neat

[naive plume]

wait

i get the concept

but

i still dont get how to find it.. 😭

im a tad slow at these things

[fickle schooner]

what part are you unsure about?

I can elaborate

[naive plume]

how od i find the length

of the isdes of the kite

[fickle schooner]

You can find them in terms of r by finding the intercepts
For example, the left side of the top kite - its length is (y-coordinate of A) - r

[naive plume]

okay

wouldnt i need to find the length

of AB

then minur r

[fickle schooner]

Yes, AO = AB

just find A and C

[naive plume]

a= (0, 8sqrt3 -6)?

[fickle schooner]

seems so

[naive plume]

c= (0, 2sqrt3)?

[fickle schooner]

no

C is on the x-axis

[naive plume]

i wrot ie wrogn

(0,2sqrt3)

[fickle schooner]

yeah

[naive plume]

okay

then do i use

distance formula

[fickle schooner]

Nope

[naive plume]

i meant 2sqrt3, 0

[naive plume]

then what

[fickle schooner]

yeah that my bad I'm sleepy

[fickle schooner]

find the equation of line AC

[naive plume]

okay

y=4-root3x + 8root3-6?

@fickle schooner sorry for ping but im runnning outta time 😭

what do i do witht the equatoin of the line..

[fickle schooner]

I said it earlier

The intersection with y = x OR sub y = r, x = r

since (r, r) lies on AC

[naive plume]

uhh..

[fickle schooner]

How do you find the intersection of two lines?

[naive plume]

set equations to eachoter?

[fickle schooner]

Yeah, you have AC and y = x

y = 4 root 3x + ... equals to x

We established that the solution should be r

[naive plume]

okay

thanks

HE SAYS I NEED PROOF

that ac goes thru the middle

of hte circle

thisp pmo

[pearl pond]

@naive plume Has your question been resolved?

[pearl pond]

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[empty vine]

need help

[empty vine]

I completed this chart and I wanted to double check to make sure everything is correct

is this right?

[wet osprey]

Can you not ghost ping me

[empty vine]

please

check over

it is urgent

[wet osprey]

I’m not helping you even if I could

[empty vine]

please

why not?

[wet osprey]

Don’t ghost ping people

[empty vine]

Im sorry

But no one is helping

and your role says very active

[regal herald]

why are you in such a hurry anyway

[empty vine]

so i assumed u are active

[empty vine]

because this homework is due soon

and i need to hand it in

but i want it to be correct

[regal herald]

If its not contributing to something i dont see why you would be bothered, its a learning process. And if it does contribute to something, then we cant help anyway

[empty vine]

?

I dont understand

O

No i want to double check tho

[regal herald]

did you just ghost ping again?

[empty vine]

?

[regal herald]

i saw it

[empty vine]

no i deleted because I mistyped

I meant to ping my friend

to help

but hes offline

[regal herald]

right

[empty vine]

.close

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[turbid egret]

not sure how to solve the following linear system:
$$xcos(t) + ysin(t) = 0$$
$$-xsin(t) + ycos(t) = tan(t)$$

[jolly parrot]

diego

[turbid egret]

textbook i'm using gives the answers

$x = -tan(t)sin(t)$ and
$y = sin(t)$

[jolly parrot]

diego

[turbid egret]

but i'm having a real hard time figuring out how to get to that point

[regal herald]

from the first equation, x/y=-tan(t) if that helps you

see what you can do with it

[turbid egret]

alrightt i'll see where that gets me

thank u

okay i'm still not getting very far at all with this

i'm not very good with trig so this is really tough haha

[regal herald]

what did you try with it?

[turbid egret]

i tried multiplying both sides of the second equation by -x/y to see if that got me anywhere (it didn't) and tried setting the right hand side of the 2nd equation to -x/y to see if that helped (also didn't)

[regal herald]

alright ill give another push

use x=-ytan(t) in the second equation

[turbid egret]

i've tried that it gave me something like this $y(\frac{sin^2(t)}{cos(t)} + cos(t)) = tan(t)$

[jolly parrot]

diego

[regal herald]

what happens if you multiply by cos?

[turbid egret]

ohhhhhhhhhhhhhhhhhhhhhhhhhhhh

ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

i see now

i don't know how i didn't spot that 😵‍💫

thank you for the help

[regal herald]

no worries

[pearl pond]

@turbid egret Has your question been resolved?

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[slate kite]

I don't understand quadratic equations (Sorry if the questions are in Spanish, I'm Mexican and I'd like some help)

[slate kite]

Help? Please

[jovial kiln]

lets try this one then

could you translate this particular question?

[lone kite]

Got this from google translate:

[jovial kiln]

makes sense

lets wait till the OP respawns

[open rivet]

Pi=3.1416 💀

[quartz rampart]

3.14159.. so its correct enough

[open rivet]

Yeah but who tf rounds pi to 4 decimals???

[quartz rampart]

welll the area has 4 decimals so

it kinda makes sense

[jovial kiln]

@slate kite u here?

[midnight haven]

R = 49 cm

[open rivet]

Thats also insane, but w/e

[midnight haven]

[slate kite]

yes, sorry

okay, i don´t understand how can i solve it, i´m new in this

[jovial kiln]

lets try this one. is this accurate translation by the way?

[pearl pond]

@slate kite Has your question been resolved?

[slate kite]

Let me translate, i need to rectificate

16- Calculate the time it takes for a body to fall from a height of 90 meters (take into account that gravity is equal to 9.8)

[midnight haven]

You know the formula of area of circle?

[midnight haven]

Oh

[slate kite]

A= πr² (r=radius)

[midnight haven]

Well you know the kinematics equations?

[midnight haven]

You got the

initial velocity , u = 0 m/s
height , h = 90 m 
acceleration due to gravity , a = 9.8 m/s²

@slate kite stellar after which you can put it all in [2] formula to get time

[midnight haven]

@slate kite r u available?

[slate kite]

I'm solving it, I'm trying to see what mistakes I make when doing the quadratic equation

[midnight haven]

It wouldn't need much but your answer must be 18.36 s

[slate kite]

I'm not very good at algebra, but I'm trying to get better every day, my goal is to become as great as you

[midnight haven]

That's the spirit !!!

@slate kite Well did you got the answer by yourself?

[slate kite]

I managed to understand the subject, I have not mastered it yet; But I know that with time and dedication I will be able to be better

[midnight haven]

Yes , I mean that did you understood the question? And having any problem somewhere else?

[slate kite]

Not yet, I have no doubts or problems with this, thanks for the explanation

[midnight haven]

So should I explain it to you?

[slate kite]

No thanks, I understand everything, thanks for the help

[midnight haven]

You can close the channel using .close

[slate kite]

Okay!

.close

[pearl pond]

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[pearl pond]

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[leaden osprey]

Is this right

[sacred nova]

the calculations seem right but for d it should be let x be +-2π, not let f(x)

[leaden osprey]

fixed ty

do i have to prove the unit circle thing

[fair creek]

very high effort 😭 but it appears everything is alright

[leaden osprey]

haha ty

[fair creek]

what do you mean by this though 🤔

[leaden osprey]

where i wrote prove

[sacred nova]

i doubt it

[leaden osprey]

also

did i mark everything right on the graph

[sacred nova]

like you’re asking if you have to prove the value of sine 11pi/6 ?

[leaden osprey]

yea like do i have to show something

[fair creek]

ah no, don't worry 😔

[leaden osprey]

ah okay

[fair creek]

it's like more personal preference from me but i firmly believe that it's not necessary to show it

[sacred nova]

I mean I’ve never heard of having to probe something like that, but has the teacher indicated that you should there?
it’s just something that’s easily plugged into the calculator
(if you have to prove it’d just be that sin 11pi/6 = sin (11pi/6 - 2pi) = sin(-pi/6) = 0.5 and a similar method for the other one

[leaden osprey]

ah okay yea i cant use the calculator for this haha

[sacred nova]

that makes sense

[leaden osprey]

also what about the marks on the graph

[fair creek]

handicapped i guess

[sacred nova]

i messed up the signs here but yeah

sin (-11pi/6) = sin(-11pi/6 + 2pi) = sin(pi/6) = 0.5 **

[leaden osprey]

perfect ty

[leaden osprey]

I’ve been confused whether I got these in the right spots tho

[sacred nova]

they are

[leaden osprey]

okay goodgood thank you

.close

[pearl pond]

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[sacred nova]

oh it wasnt easily visible but below the minimum on the left it should be -2pi/3 not -pi/3

[leaden osprey]

good eye! i fixed it thank u

[pearl pond]

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[cosmic saffron]

Assume x is 1 million (1,000,000)
and I only want 6 digits precision
that mean
p = 1
is enough?

[cosmic saffron]

my question is with
x = 1 million
are
p = 1
correct?

[pearl pond]

@cosmic saffron Has your question been resolved?

[pearl pond]

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[lone smelt]

How to know if a non-factorisable quadratic equation (D<0) is always positive or negative for any value of x? I want to know this for an inequality question I sent. I want to cross multiply the quadratic but not sure if the sign will change

[flat cedar]

When D<0, check the coefficient of x^2 (let a) to check. If a>0 it's always positive and if a<0 it's always negative

[calm wing]

(if D<0, the quadratic does not touch the x-axis, so there cannot be a sign change)

[lone smelt]

alright, thanks a lot

.close

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[lucid moth]

I got an answer but its completely different

First the location of C we set g(x) = 0

Which gives us x = +-2, so C is located at (2, 0)

Then we integrate g(x) with limits 2 and 0

G(x) = 2x - (x^3)/6
2[2] - ([2]^3)/6 - (2[0] - ([0]^3)/6)
4 - 8/6 = 8/3

Then to get V we take 4 - 8/3 = 4/3

Now for W we integrate f(x) between p and 2 and set it equal to 2(4/3)

F(x) = -8/x
-8/[p] - (-8/[2]) = 8/3
-8/p = -4/3
8 = 4p/3
p = 24/4
p = 6

Which is not what they got...

Which step did I do wrong?

[final ember]

what is f(x)

[lucid moth]

8/x^2

[light helm]

you differentiated instead of integrating

[lucid moth]

Oh 😭

Ok I fixed it and got the right answer

Thank you!

❤️

.close

[pearl pond]

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[heavy hill]

can someone check my working for this

[merry carbon]

,rccw

[heavy hill]

chartbit!!!! ❤️

[merry carbon]

Hiiii

[jovial kiln]

what is T5 and T6

[heavy hill]

i thought it was the term number

[merry carbon]

In order of ascending or descending powers of c?

[merry carbon]

On another note, how did that 21 turn into a 12?

[heavy hill]

💀

omg

i didnt even notice

[merry carbon]

It happens sometimes

It does give you a “nicer” number, at least, which seems what the question writer might have intended

[heavy hill]

yeah!! it does

[heavy hill]

i think its descending

[merry carbon]

That’s fairs, there doesn’t seem to be a “universal” way to order these (the questions I’ve seen always tell you which way they do it!)

[heavy hill]

ah!! okay, thank you so much for your help!!

also really nice seeing you again!!

[proper cradle]

Why is nobody using nCr

This is really weird

[merry carbon]

Always lovely to see you

[compact ridge]

different notation

[pearl pond]

@heavy hill Has your question been resolved?

[pearl pond]

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[molten ridge]

are the lengths of the tetrahedron equal to half of the circumference of the cylinder?

[toxic lichen]

yes

[pearl pond]

@molten ridge Has your question been resolved?

[molten ridge]

i got the height as (sqrt(3)*pi)/2. is that correct?

[toxic lichen]

does not seem so...

[molten ridge]

what did u get?

after unfolding the cylinder, this is what it should look like

cant i use pythag to find the length of the height?

[long yarrow]

if I am not mistaken a tetrahedron have equal side lengths right?

[pearl pond]

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[hearty thicket]

can someone show me how to do this one?

[hearty thicket]

i know x^3e^x = x^3*sum{0}{infinity} x^k/k!

but im not sure how to get teh terms for the power series

[frozen lantern]

uh

do yk how taylor series work?

[hearty thicket]

yeah

is there a faster method than just to find all t he derivatievs of f and find a pattern

for the coeffecient

[frozen lantern]

i mean this has e^x so it couldnt be that bad

[chrome plank]

not really, that's how you do it

[hearty thicket]

i see

ok i will just keep on finding the derivative then

[pearl pond]

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[frosty grail]

Can someone tell me where I went wrong? I first found the derivative. From the third line, I used a trig identity for what’s inside the bracket

[frosty grail]

This question is on finding trig derivatives

[rancid depot]

how did you get from line 3 (the one with parens) to line 4

[proper cradle]

2cos^2x-sin^2x is not cos2x

[toxic lichen]

2cos^2(x) - sin^2(x) is not equal to 2(cos^2(x)-sin^2(x))

[frosty grail]

Oh

[rancid depot]

ohh i see

[frosty grail]

So it’s only if it’s common to both sin and cos

Oopsie

[proper cradle]

Should have just expanded honestly

[frosty grail]

So I shouldn’t have used an identity..

[proper cradle]

There isn't one

[frosty grail]

So is the correct answer just the expanded form of line 3?

[proper cradle]

Well till line 3

It's correct

And thats the answer

If you want all of them in jus sin

[frosty grail]

Like Ann said, I accidentally thought I could separate the 2 and just use the trig identity for cos^2x - sin^2x

[proper cradle]

Just write cos^2x as 1- sin^2x

[frosty grail]

Ok thank you

[proper cradle]

mhm

[frosty grail]

Hello again
I don’t get how to do B

[plush bramble]

are you given any equations for position of a pendulum

[frosty grail]

Yes

[plush bramble]

or did you learn any

did you try using them

[frosty grail]

It’s defined as h(t) = Acos(2(pi)(t)/T)

So I worked around with it

I found T to be 1.42 s

I said the amplitude is 8, but I’m not sure about that

Because it’s the maximum horizontal displacement

And I imagined that’s how high or low the sine graph would get

Is that correct?

[pearl pond]

@frosty grail Has your question been resolved?

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[runic zephyr]

Question:
find all points where f(x, y) is continuous.

Hello !
i have no clue how to calculate the limit.

[cobalt hinge]

!occupied

[pearl pond]

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

[cobalt hinge]

Lelel it’s fine

[rose basin]

relax we posted at the same time

[runic zephyr]

sorry bro 😦

[cobalt hinge]

Which one? The one as x->y?

[runic zephyr]

yes

but is it even x -> y ?
like isnt it supposed to be (x, y) -> (a, a) ?

[cobalt hinge]

Yeah.

Just simplified convention.

[runic zephyr]

oh

[cobalt hinge]

Sorry, I don’t really write too formally mathematical wise.

[runic zephyr]

because this is the solution but it doesnt make any sense to me

[runic zephyr]

its all right man thanks 🙂

[cobalt hinge]

Recall the limit definition of the derivative.

[runic zephyr]

true but arent limits in 2D world supposed to reach a certain point from all curves possible ?

[cobalt hinge]

What do you mean?

That’s for 3D.

[runic zephyr]

i meant 2d world for x, y

excluded f(x, y)

[cobalt hinge]

Hmm.

[runic zephyr]

it seems correct but its also glitching my brain because x is a parameter itself.
idk maybe i need to change my prespective

[lime anvil]

good intuition, but the function $\frac{sin(x)-sin(y)}{x-y}$ is continuous so this isn’t an issue

[jolly parrot]

Yusername

[cobalt hinge]

Eh.

Maybe treat one of them like a constant.

[runic zephyr]

but its not when x = y

[rough stream]

y is the only variable in the limit. x is a constant.

lim (x,y) -> (0,0)
Is like the "path limit"

Which I would tex if I knew how

[runic zephyr]

but isnt it supposed to approach the same number if the limit does exist ?

when you consider y = constant and x = variable you are only tracing one possible curve out of inifinite more

[rough stream]

y is the only variable in the limit. x is a constant

At least judging by the notation used above

[runic zephyr]

in solution that i provided yes i agree

but im saying that its not correct

because you are saying x = a and you change the variable y

you cant deduce that the limit exists because you got to an answer from one possible path

[pearl pond]

@runic zephyr Has your question been resolved?

[runic zephyr]

.close

[pearl pond]

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[pearl pond]

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[hoary musk]

Hello i need help with this math problemMake a calculation based on the data obtained:

You own a restaurant and regularly procure the resources necessary to keep the restaurant running.

Specifically, you procured 200 eggs at 2000 dinars, 60 litres of oil at 9000 dinars and 10 kilos of salt at 1200 dinars. The dependent cost of these goods is 100 dinars, the gross salary 300 dinars, the margin is 2% (16 dinars) and the VAT is 24,48 dinars.

Calculate the price you'll be selling an omelet at your restaurant.

[hoary musk]

😔

[rain vessel]

What is a VAT?

!original

[pearl pond]

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.

[hoary musk]

general consumption tax

It translated bad my bad

[rain vessel]

No worries

VAT is general consumption tax?

[hoary musk]

Nah

It was translated bad

[woven matrix]

VAT is value-added tax, which is sort of the sales tax of the US

[hoary musk]

Ohh i tpught it was something bad translated

Then its VAT

[rain vessel]

I see

[hoary musk]

We go to online classes and teach sent it in google classroom and idk how to solve it

[rain vessel]

I feel like some information needed is missing

Like for example, what are the ingredients needed to make an omelette

[hoary musk]

Egg oil salt

[rain vessel]

Also what do “gross salary” and “margin” mean in this context

[rain vessel]

Yeah, but what are the quantities.

[hoary musk]

the total pay an employee receives before any deductions are made

Thats gross salary

[rain vessel]

And margin?

[hoary musk]

1 sec

[rain vessel]

Also, this is information is essential

[hoary musk]

the amount by which one thing is different from another:

Thats margin

[rain vessel]

What is it in this specific context

[hoary musk]

I do not know it only says that in text

That the teach sent

[rain vessel]

I’ll assume it’s saying profit margin, and each omelet must make 2% profit

Which is 16 dinar

[hoary musk]

Yes

[rain vessel]

We still need these quantities

[hoary musk]

Oh wait nvm

Someone set me the answer

Sent me*

One of my friends did it

Sorry for maybe wasting time

[rain vessel]

https://tenor.com/view/long-tears-gif-11087877242190144149

[hoary musk]

https://tenor.com/view/my-apologies-cheese-kitty-cat-sorry-my-bad-gif-1026852287997442026

[rain vessel]

Please close the channel if you are done

[hoary musk]

How

!close

[rain vessel]

Type .close

[hoary musk]

.close

[pearl pond]

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[fallen flare]

About the implicit function theorem. If the theorem applies, then the equation F(x)=0 has a solution set of (g(y),y) where g(y) expresses the basic variables (lets call them x) in terms of the free variables (lets call them y), but only in a neighborhood of a point c st F(c)=0. It's this last part that I don't get, why would the implicit function exist only for a neighborhood of such a point? What does this mean in practice? Mind you, I've gone over the proof of the theorem so I'm aware of the logical argument, I'm just unable to visualize what this means in application.

My book provides the following example with the unit circumference, could you help me understand from it please?

[pearl pond]

@fallen flare Has your question been resolved?

[last moth]

Let's consider the example they gave, x^2 + y^2 - 1 = 0. Then, expanding around the point (0,1), you can write y as a function of x when -1 ≤ x ≤ 1 but it fails for x outside that range. That's why you can only write y as a function in a neighborhood of x=0, not all x.

[pearl pond]

@fallen flare Has your question been resolved?

[fallen flare]

Well yes but any x belonging to the circle will fall in that range right?

oh well, I see that any x is valid for F(x,y)= x^2+y^2-1, but only in the domain where x is in the aforementioned range can we describe y in terms of it

thanks

.close

[pearl pond]

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[merry carbon]

Interesting that those who want everyone always forget the <@&268886789983436800>

[pearl pond]

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[shrewd mist]

Vibrations & Control Systems (yeah ik its physics but I have enough helping equity to ask this lmao)
Consider the first image (two blocks, two viscous dampers, two springs)

An impulse I is applied downwards on m2. The goal of my project (partially) is to minimize the maximum displacement of the lower mass, m1 by setting the values of the two viscous (linear) dampers, c1, c2. I'm also trying to perform modal analysis (ie. what damping coefficients make it over, underdamped, etc- but that's secondary)

My EoMs in matrix form are also attached (2nd image). The coordinate system is + downwards, hence a +ve forcing term. At this point I chucked these EoMs into MATLAB to solve the ODEs numerically and iterated through c1 and c2 values to get an optimal set of values for a defined set of k1,k2 m1,m2, and impulse. Fwiw, my m1 = 3.6, m2 = 8.9, k1 = 51500, k2 = 2150, I = 500. All units SI. The values aren't too important though.

With these parameters, and bounding c1, c2 between [0,200], I get an optimal value (value that minimizes the absolute displacement of x1) of c2 around 60, with no significant dependence on c1. However, if I bump c1 up by an order of magnitude to ~2000, the optimal value of c2 crawls up with it to ~120, and then increases somewhat proportionally to c1. Ie. with c1 at around 8000, c2 is optimized at 300.

For the damping analysis, I got the TF of the lower mass as such (images 3 and 4)

I'm kinda at a block at this point. This is a 4th order system, is there any way for me to determine if the system is underdamped or overdamped (ie. can we- either analytically or approximately get some damping ratio and check if its less than or more than 1)? More broadly, does the concept of underdamped and overdamped even apply to a system of order > 2?

The prof "hinted" at working/trying to get the poles, but I'm a bit lost as to what to do with them. For low values of c1,c2- my poles are all imaginary, for intermediate values, 2 real 2 imaginary.

(1/2)

[shrewd mist]

For high values of c1,c2- all real, but still negative. All I can draw from this is that it appears to be BIBO stable.

The primary problem I want to figure out at this point is how can I determine if the system is over or underdamped?

[pearl pond]

@shrewd mist Has your question been resolved?

[pearl pond]

@shrewd mist Has your question been resolved?

[pearl pond]

@shrewd mist Has your question been resolved?

[pearl pond]

@shrewd mist Has your question been resolved?

[pearl pond]

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[full cobalt]

I have 0 idea how to do dis

[toxic lichen]

do you know what it means for two angles to be coterminal to each other

[full cobalt]

Naw

Co means together ik

[toxic lichen]

in numerical terms, we say two angles are coterminal if their difference equals a whole number of full turns.

a full turn, of course, is 2pi radians.

does this ring a bell?

@full cobalt

[full cobalt]

Im jus learnin bout dis

So not rlly

[toxic lichen]

ok well i explained what it means for two angles to be coterminal.

so what you need now is to start from your angle of 19pi/6 and go down or up in steps of 2pi until you land between 0 and 2pi.

[pearl pond]

@full cobalt Has your question been resolved?

[full cobalt]

Where do i do dis

[pearl pond]

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[full cobalt]

@toxic lichen

[toxic lichen]

i don't know what you mean by "where"

like, where to do the working for it?

paper.

[full cobalt]

No i mean

U said start my angle at 19pi

And go down or up

In steps of 2 pi

Until i land beyween 0 and 2pi

How i do that

@toxic lichen

[toxic lichen]

ok

well

let's think about it

right now you're looking at the angle 19pi/6.

are you above the range [0, 2pi], already in it, or below it?

[full cobalt]

Is this on the unit circle?

[toxic lichen]

well yes but actually no

i would rather you think about the number line

and don't overthink it

@full cobalt you still here?

this question didn't really require more than at best a minute of thought imo

[pearl pond]

@full cobalt Has your question been resolved?

[pearl pond]

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[full cobalt]

Im not good at dis

[full cobalt]

And wym number line

[oak ivy]

uh ann is saying to reduce 2pi?

19pi/6 - 2pi

since if we increase or decrease by 2pi we will be at the same point

[oak ivy]

.

[full cobalt]

Wat

[oak ivy]

subtract 2pi

[toxic lichen]

i was hoping he would come to this conclusion himself or at least tell me that he is stuck without waiting half an hour

[oak ivy]

lol

[full cobalt]

I was doing another hw

Mb

[toxic lichen]

rghghr.

ok right

[full cobalt]

The hell is rgrhrgr

[oak ivy]

angry

[full cobalt]

💀

[toxic lichen]

nothing, just a keysmash

grumble grumble

that's all

[full cobalt]

So 19pi over 6

Minus 2pi

[oak ivy]

Yes

[toxic lichen]

yes

[full cobalt]

And that result

Is the angle ?

[toxic lichen]

work it out first

i would really appreciate if you tried to put some thinking into it, rather than just blindly following some directions you were given

[oak ivy]

Adding or subtracting 2pi will give us the same position on the circle

[toxic lichen]

cause if you encounter a different problem with a different number

i would NOT want you back at the "stuck idk what to do HELPPP" position

[full cobalt]

Fair

I got a decimal

3.665

[oak ivy]

huh

u get in terms of pi

[full cobalt]

I put it in my calc

[oak ivy]

dont

write it in terms of pi

[full cobalt]

Idk how

3.665 pi?

[oak ivy]

no

what is 19pi/6 - 2pi??

[vapid cave]

do it in pen and paper or ur mind

[oak ivy]

You don't need to use calculator

[full cobalt]

I don know how to do it without calc

[oak ivy]

Bruh just write it down

[toxic lichen]

do you know how to subtract $\frac{19}{6} - 2$ by hand?

[jolly parrot]

Ann

[oak ivy]

And subtract

[toxic lichen]

like forget the pi for now

and try to recall if you know how to add/subtract fractions

[full cobalt]

Do i add a 1 on the bottom?

[toxic lichen]

"add" is not a good word to be using.

but if you want to turn the 2 into 2/1, by all means, go for it.

[oak ivy]

LCM

[full cobalt]

So then it 17 over 5

[oak ivy]

huh

no

u can only add/subtract like fractions

[full cobalt]

19-2 17

[oak ivy]

meaning they should have same denominator

[full cobalt]

Ooo

[toxic lichen]

ok ok ok hold on yes

again

work it out on paper, not in the discord chat box NOR in your head

[oak ivy]

So convert that 2 so that it has the same denominator

[toxic lichen]

@full cobalt did you try to do it in your head there just now?

[full cobalt]

So 19 over 6 and 2 over 6

[full cobalt]

No...

[toxic lichen]

on paper, then?

[oak ivy]

uh

[full cobalt]

Yes.

[oak ivy]

it's 2/1 right

[toxic lichen]

also be mindful of the fact that 2/1 is not the same as 2/6

[oak ivy]

so how can u write that as 2/6

[toxic lichen]

so you really need to go over adding and subtraction fractions, converting to common denominator, all that stuff again

lemme get you a video...

[oak ivy]

how can u convert that 1 into a 6 @full cobalt ?

[toxic lichen]

https://www.youtube.com/watch?v=GvLIEiqxS6s

[full cobalt]

U said they shoulf havr same denominator

[oak ivy]

yes

so you multiply 1 with 6 to get it to 6

[toxic lichen]

https://www.youtube.com/playlist?list=PL0o_zxa4K1BXacPNb33YSOBXUA_PWZ8bf also more generally

[oak ivy]

but you also need to multiply the numerator with the same number

[full cobalt]

I jus changed it

[oak ivy]

Whatever you multiply to denominator multiply the numerator with same number.

[full cobalt]

So 2 times 6

[oak ivy]

yes

[full cobalt]

So 12 over 6

[oak ivy]

yes

[full cobalt]

19 over 6 minus 12 over 6

7 over 0

[oak ivy]

No

You only subtract numerator

Denominator stays the same

You only perform addition/subtraction on numerator

[full cobalt]

O alr

So 7 over 6

[oak ivy]

yes

now that's 7pi/6

[full cobalt]

And 7 divides into 6 3 times

So 3 over 1

[oak ivy]

huh no

[full cobalt]

Shi mb

[oak ivy]

That is the simplified

7pi/6

[full cobalt]

So das the answer 7pi over 6

Where did the minus 2 come from again

[oak ivy]

..

cause

if we add or subtract 2pi

We land up in the same point

[vapid cave]

yea

[full cobalt]

How do ik when to do dis

[vapid cave]

we just add or subtract 2pi until the angle is within the given range

[full cobalt]

So any question in that format

I jus add or sub 2pi

As a fraction

Finding a common denominator

[vapid cave]

and repeat until it’s in the range

[oak ivy]

So basically

What is 19pi/6

[full cobalt]

How do ik when its in range

[oak ivy]

Use calculator

What is 19/6

[vapid cave]

when it’s between the bounds

in this case between 0 to 2pi

[oak ivy]

I don't think they understand that

@full cobalt what is 19/6

[full cobalt]

A fractiln

[vapid cave]

in cases like this where everything is by pi just divide to make things easier for urself

[full cobalt]

3.167

[oak ivy]

Ok

Is that within 0 to 2

[full cobalt]

Its highet

[oak ivy]

Yes

So then subtract 2pi

so 19pi/6 - 2pi

[full cobalt]

Ohhhhh

Ok what if

Without the -pi

I do it like it is in calc

[oak ivy]

SO basically

[full cobalt]

And it happens to be between 0 and 2

[oak ivy]

u got 3.167

You write it as 3.167 pi

[full cobalt]

No i mean for a diff question

[oak ivy]

And that is higher than 2pi

[full cobalt]

Example

Wjhat if it happens to be within 0 and 2

Can thst happen?

[oak ivy]

Then don't do anything

It's already solved

[full cobalt]

And if ot dosnt

Then i add or sub 2pi

[oak ivy]

THen probably they will ask to find the angle >2pi

[full cobalt]

To make it within 0 and 2

[oak ivy]

Yes

0 and 2 pi*

[full cobalt]

And how do i do that

[oak ivy]

Add 2pi??

[full cobalt]

2pi +2pi?

[oak ivy]

If they give between 0 and 2pi and ask >2pi just add 2pi

Example they give u pi and ask to find a value >2pi similar to pi

Could you tell me what it is

[full cobalt]

2pi?

[oak ivy]

uhn o

[full cobalt]

Pi +2pi?

[oak ivy]

yes

[full cobalt]

Das how to get the angle of pi?

[full cobalt]

U changed it

[oak ivy]

To make it better suited

Yes that's it

Just divide fractions if u wanna see where it lies and put a pi

19pi/6

can be 3.167pi

which is >2pi

[full cobalt]

And if <2pi then sib 2pi from 19pi/6

Alr i got it now

Thx mask

[oak ivy]

ok

[pearl pond]

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[vernal hinge]

can someone help ques 84 i feel imposible to integral like normal

[vernal hinge]

do i have to change something

[pearl pond]

@vernal hinge Has your question been resolved?

[vernal hinge]

<@&286206848099549185>

[leaden cape]

I imagine you will need to split this region represented by the triply iterated integral into 2 regions.

[pearl pond]

@vernal hinge Has your question been resolved?

[pearl pond]

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[sharp smelt]

Trying to parametrize this surface

[sharp smelt]

I was thinking I'd once more start off with a parametrisation of the sphere and move from there

so I have $(3 \cos(\theta)\sin(\phi), 3 \cos(\theta\sin(\phi), 3 \sin(\phi)); 0≤\theta≤\pi ; 0≤ \phi≤ π/6$

[jolly parrot]

What a wonderful world !

[sharp smelt]

seems to work

.close

[pearl pond]

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[sharp smelt]

I'm supposing hyperbolic identities would be required here

.close

[pearl pond]

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[pearl pond]

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[feral trellis]

How come this NFA rejects 10? What stops you from going q1->q4?

[toxic lichen]

do you even GET to q1 in the first place

i do not see an arrow leading out of q0 that says 1

[stone warren]

q1->q4 is not labelled

[feral trellis]

Ah sorry there should be a 1 there

[stone warren]

epsilon is empty word, so they can reach q1

you can reach q4

you cannot terminate at q4

you still have a 0 edge to take

and no edges in NFA means it goes to a sink

which is not going to be terminal state

[feral trellis]

That makes perfect sense thank you very much!

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[rough forge]

hi can someone rate my proof?

[robust oar]

10/10

[merry carbon]

A /10

[rough forge]

ok it seems to be okaish

thank yall

.solved

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[celest heart]

definition of a lineair function:

f(u+v) = f(u) + f(v)
f(cu) = cf(u)

but dont really know what to do tbh

[open rivet]

plug it into the definition 🤠

you are probably thinking too much

[toxic lichen]

do you know what the function we call alpha f does

[celest heart]

so af(u+v) = a[ f(u) + f(v)] = af(u) + af(v) ?

[celest heart]

I wish I knew

[toxic lichen]

ok well you have to

otherwise you have zero hope of proving anything about an object which you don't even know what it is

[celest heart]

wait so maybe

alpha f just maps from 1 vector space to another?

[toxic lichen]

mmm incredibly vague.

[celest heart]

shit

Idk then ;/

[toxic lichen]

ok right

$\alpha f : V \to W$ is the function which maps each $v\in V$ to $\alpha \cdot f(v)$

[jolly parrot]

Ann

[toxic lichen]

ie $(\alpha f)(v) = \alpha f(v)$

[jolly parrot]

Ann

[celest heart]

Hmmm okay

[toxic lichen]

write out, carefully and without trying to overthink it,

what it would mean for alpha f to be a linear map

it is not hard and it does not require any heavy lifting at all

[celest heart]

so i start with (af)(u+v) and want to end up with af(u) + af(v)?

[toxic lichen]

so perhaps you do

[celest heart]

Hmmm alright

[celest heart]

so this?

[toxic lichen]

in the first line i think you have a stray equals sign at the very end

[celest heart]

ah ye true that one should not be there

[toxic lichen]

also your opening bracket looks too much like a c. yes, sorry, i am bashing your handwriting again.

other than that you seem good to go

[celest heart]

Hahahah any tips ;-;

for the handwriting again

I changed my 4!

[open rivet]

go slower 🙂

[celest heart]

but fr

c and ( or lowkey just the same

[toxic lichen]

no

[celest heart]

ill make the brackets bigger

[toxic lichen]

c is an arc of a smaller radius and greater angular measure

[celest heart]

yes!

Ill take notes of this too

Thank you guys :) really appreciate it

Wait ill close this in a sec i am trying a question that is almost the same

[celest heart]

Proof f+g is a lineair function

this correct?

[toxic lichen]

seems so

[celest heart]

Lets goooo

Thanks ann :) Have a wonderful day/night

.close

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[pale frost]

how can i find

[pale frost]

$\sqrt{-57 - 16i}$ ?

[jolly parrot]

jandro0103

jandro0103

[pale frost]

I would like to know how to calculate the square root of the discriminant

[tropic saddle]

comvert to polar form

alternatively, multiply out (a+bi)^2 and compare coefficients

[pale frost]

thx ill try both

[pearl pond]

@pale frost Has your question been resolved?

[pearl pond]

@pale frost Has your question been resolved?

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[pale frost]

<@&268886789983436800>

[pearl pond]

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[uneven radish]

i dont think i understand any of this

[pearl pond]

@uneven radish Has your question been resolved?

[jovial kiln]

you have to add the torque by gravity and torque by F then express it in the form of
I d^2θ/dt^2 = t_F + T_g
using newton's second law (I being moment of inertia)

then the simplifcation follows by subbing in values given

for second part, let -4.9sin(theta) = -4.9theta and 0.03125cos(theta) = 0.03125

you get θ'' + 4.9θ = 0.03125
which you can solve using characteristic equation of the homogeneous equation and finding the particular solution

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[mental imp]

I get how to do this question, but im confused about how come we can start it at the origin and everything still works out?

[pearl pond]

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[jovial kiln]

.reopen

i think u might need to reopen channel

[mental imp]

uh oh

ok will do

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[clear orchid]

Doing homework probability questions
Not sure how to show that the recursion goes to what i have for part d
How do i get from part c to d

[pearl pond]

@clear orchid Has your question been resolved?

[clear orchid]

<@&286206848099549185>

[pearl pond]

@clear orchid Has your question been resolved?

[clear orchid]

i just need direction for a show that question going from my final answer in part c to part d

[pearl pond]

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@clear orchid Has your question been resolved?

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[brisk pike]

hi

[brisk pike]

so yesterday i came here asking everybodys help to find a fallacy in the following argument:
Say you threw a body up (no air resistence). At the maximum height it can achieve, we know for a fact that its instantaneous velocity $v$ will be 0, and acceleration will be $a= -g$.
But we know of a formula, $a = v \frac{dv}{ds}$ where putting $v=0$ would imply that $a=0$

[jolly parrot]

rak³en

[brisk pike]

I still dont get the problem, so I am taking someones advice and will work through an example

lets say we threw it up with an initial veloctiy $u$, then $v(t) = u-gt$.

[jolly parrot]

rak³en

[brisk pike]

We can solve for $t$ from the second equation $s=ut - 5t^2$ (assume $g$ is $10$)

[long yarrow]

why multiply by v?

[jolly parrot]

rak³en

[brisk pike]

that way u get dv/dt

[brisk pike]

anyhow since we're going up we want to minimise $t$ so we choose $t=\frac{u - \sqrt{u^2 - 20s}}{10}$. Putting this in $v(t)$ we find $v(s)$ to be $$v(s) = u - g\frac{u - \sqrt{u^2 - 20s}}{10} = u - (u - \sqrt{u^2 - 20s}) = \sqrt{u^2 -20s}$$

[iron basin]

funny you think dv/ds is defined

hm

im not sure either

ill try too

[brisk pike]

0 is differentiable.

is this all correct?

anyhow differentiating the below once

[jolly parrot]

rak³en

[brisk pike]

so we find $a(s) = - \frac{10}{\sqrt{u^2 - 20s}}$

[jolly parrot]

rak³en

[brisk pike]

o

I see now

$v(s) = 0 \implies s = \frac{u^2}{20}$ but $a(s)$ is undefined for this

[jolly parrot]

rak³en

[brisk pike]

hmm

[iron basin]

this basically

[brisk pike]

well then how do I know for sure that the equation is defined?

I can say 'dv/ds' must exist

but in the scenario v=0 but I cannot solve for v or s then I cant really know whether dv/ds exists, does it?

<@&286206848099549185> 👆 is the final question

[iron basin]

dv/ds doesn't exist

but dv and ds do

[frozen lantern]

what are you doing

[iron basin]

thats why the integral form of this works

[brisk pike]

huh?

[brisk pike]

i am asking for help

[iron basin]

the third equation of motion

[brisk pike]

no idea what you're talking about

but

wait

yeah i cant turn the 3rd equation into an integral

[frozen lantern]

are you sure you can evaluate $\frac{dv}{ds}$ at $v=0$?

[jolly parrot]

Percy

[brisk pike]

thats impossible for all v(s) ?

i dont see whats wrong if we dont know the nature of v(s)

[frozen lantern]

do you have a $v(s)$ to evaluate

[jolly parrot]

Percy

[iron basin]

we don't really use the differential form much anyways

[brisk pike]

well i know that in free fall i do

but what if i dont (or its too complicated)

[frozen lantern]

what is it

[brisk pike]

i have done it for free fall I am asking more generally

[iron basin]

well

you could just integrate your way through it

[brisk pike]

[frozen lantern]

...so you're telling me you're sure dv/ds is defined at v=0 in free fall?

im not

[brisk pike]

no i know it isnt defined in free fall

I am asking IN SITUATIONS OTHER THAN FREE FALL

where i might not know what v(s) is

then how do i know that equation holds true or not

ofcourse if i know v(s) I can most probably just do what i did for free fall

[iron basin]

im not sure if you'll encounter such a situation

if you do you're welcome to discuss it here

[frozen lantern]

do you wish to overgeneralise $v\frac{dv}{ds}$ as being \textbf{definitely} 0 when $v=0$, despite $\frac{dv}{ds}$ not being defined for the \emph{one case} in which you can model it?

[brisk pike]

...............

[iron basin]

a dollar

[jolly parrot]

Percy

[brisk pike]

nvm

i am troubling myself for no reason

thanks for beating some sense into me

.close

[pearl pond]

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