help-49

[spiral rock]

Lose what, its digital

Oh

[robust isle]

losing the file

it happens

[twilit field]

you can just go back to springer's website

[spiral rock]

I have a personal library

[twilit field]

and downlaod it again

[spiral rock]

Like a big storage device at home

Anyway thanks, I will find some time to read it

Working on AG

[twilit field]

I'll close this now

[spiral rock]

.close

[midnight plank]

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[night gyro]

if i said he needs to qudriple root it

[lyric charm]

"quadruple root" is not standard terminology

[night gyro]

what should i use instead

[lyric charm]

you're looking for "take the fourth root"

[night gyro]

Patrick needs to take the fourth root

[lyric charm]

and it is the same for any other degree 4 and up: fifth root, sixth root, twenty-ninth root...

[night gyro]

i see

.close

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[night gyro]

hello i got the answer correct but for this shouldnt i convert to cm cube first as 1L=1000cm cubed

[night gyro]

why are we not converting

[midnight plank]

@night gyro Has your question been resolved?

[sharp coral]

they calculate the mass by multiplying the density in g/cm^3 by the volume in liters, so we have mass in g*L/cm^3. then when we divide by the total volume in litera the L cancel out

[night gyro]

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[quaint shoal]

How would I do this?

[quaint shoal]

i need to use the derivative rule

[spiral rock]

this looks a lot like the derivative of $\sqrt{x}$

[grand pond]

ExpertEsquieESQUIE

[quaint shoal]

is that because it’s in this format f(x)-f(x+h)?

[spiral rock]

yes

[quaint shoal]

and f(x) is sqrt x

[spiral rock]

yes

but its not quite the derivative

[quaint shoal]

Like that?

[lament knoll]

almost

[quaint shoal]

put the 1/2 back into a sqrt?

[gusty falcon]

wouldn't you need to first show

how it's related to the limit definition of a derivative

before well computing that

even if it's just one line apart

[grand pond]

mmmm7

[lament knoll]

i didn’t saw the minus sign, then yes it’s good

[quaint shoal]

is the limit - because u turned f(x+h) -f(x) into f(x)-f(x+h)

[gusty falcon]

i just "factored" out a negative yeah

so that it matches

the more "canonical" limit definition of a function

aka the one you're more familiar seeing

,, f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}

[grand pond]

mmmm7

[quaint shoal]

ohhh now I see

[fair basalt]

im 13 and I don’t know what the fuck is going on 😭

[lament knoll]

?

[fair basalt]

I don’t get any of this

[gusty falcon]

Lol

[quaint shoal]

you’ll have it soon enough

[spiral rock]

well you are barely old enough to be on discord

[gusty falcon]

depends on the country too, no?

[fair basalt]

Well im still allowed

[fair basalt]

America

[gusty falcon]

sure

[quaint shoal]

okay so it’s just this?

[gusty falcon]

f(x) = sqrt(x)

you can just ignore

the negative for now

it's just the "negation" (the negative) of whatever the derivative of sqrt(x) is

[quaint shoal]

ohh so calculate it out and then negate it

got ittt

[gusty falcon]

yes

[quaint shoal]

perfect I understand now

I have one more question I’m stuck on

if u wouldn’t mind

,rotate

[gusty falcon]

what's the question?

[quaint shoal]

bottom one, Ive got tangent slope but what do I do to get f’a and f(a)

[fallow scarab]

your answer should be in terms of a

the normal line will depend on a

[quaint shoal]

i don’t think I’m following

[fallow scarab]

pretend a=1 for simplicity. find the normal line at x=1

oh no your slope of normal is incorrect

use algebra and put it into point slope first

[quaint shoal]

slope would 2/5?

[fallow scarab]

yea there you go

[quaint shoal]

hmm so what’s after that

[fallow scarab]

.

[quaint shoal]

Like that?

[fallow scarab]

oh no i misunderstood the problem

you're already done

or almost at least. this is the normal line. find the slope of the tangent line and that'll be f'(a)

[midnight plank]

@quaint shoal Has your question been resolved?

[midnight plank]

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[leaden seal]

hi this is a physics question but the bit im stuck on is maths and I think its proportion

[leaden seal]

can someone explain the bit in red idk why its 2/2.5

[flat veldt]

Try finding the length of all the sides of triangle FAB then use a trig ratio

Omg truss analysis

[leaden seal]

i have done this

in red

on the FBD

I don't understand the ratio

[flat veldt]

Firstly draw out the triangle

[flat veldt]

Yeah

[leaden seal]

and then

...

[flat veldt]

Gimme a sec to sketch

[leaden seal]

ok

[flat veldt]

Okay terrible sketch but
We're only interested in knowing what value of F will make it balance the downward vertical force 6kN so we need to find bkN using trig ratios

[leaden seal]

Ok

[flat veldt]

Btw what grade or college year is this from

[leaden seal]

Wait thats it?

[flat veldt]

Yeah just b=6kN
Then F×trig ratio= b

[flat veldt]

Yeah

[leaden seal]

how dowe work out trig ratio

was my question

[flat veldt]

Use the acronym SOHCAHTOA

[flat veldt]

Here we have an angle and the hypotenuse
We need the opposite so we use SOH [sin theta= opposite/hypotenuse]

[flat veldt]

You get b using Pythagoras' theorem first mb
Then plug that in here

[leaden seal]

actually

we have all three sides

[flat veldt]

Yeah I just saw that

Mb

[leaden seal]

so how do I know its soh then?

[flat veldt]

So you can just do fsintheta = b

[flat veldt]

Because we have an opposite side and the hypotenuse
Plus we are dealing with verticals so we just need to get b then get our equation for b in terms of F

[leaden seal]

b=2

[flat veldt]

No
That's the length of the rod b here is a force

And b is in the opposite direction as the 6kN force

[leaden seal]

wait

here is my question

we are using the lengths of the rod

not the forces.

[flat veldt]

To find sintheta

There's the force and the length diagram
The force diagram shows that bkN balances 6kN (equal and opposite)
The length diagram shows the length of each of the rods helping us to find the sines and cosines for determining the components of the force F (which has b as it's vertical component)

[leaden seal]

yes ok

[flat veldt]

If we picked the other angle we could use cos theta = 2/2.5
So it's the angle that was picked

!done?

[midnight plank]

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[flat veldt]

I almost thought no one learns about trusses they seemed so annoying

[leaden seal]

they are very confusing especially zero force members

[flat veldt]

That's not the value of theta and the value of theta is not really needed
The value of the ratio is what's needed

[leaden seal]

Thetaisnt 45

[flat veldt]

It's about 53⁰

[leaden seal]

so whys it FAB*the ratio

[flat veldt]

Have you learnt about components of a vector

[leaden seal]

xyz?

[flat veldt]

Like how every vector (v) in a 2D plane can be written as
v=vSin∅i+vCos∅j

[leaden seal]

Oh ijz

[flat veldt]

Yeah that

If F were to be v
Then what do you think b would be if we're using our selected theta(remember b is the vertical component)

[leaden seal]

Hmmm

[flat veldt]

You might want to add b there too

[leaden seal]

isn't b the same as F

both vertical

[flat veldt]

F isn't vertical

It's along the hypotenuse(rod)

[flat veldt]

Oops

[leaden seal]

loops indeed

[flat veldt]

I meant b (remember b is the vertical component)

[leaden seal]

Ik

what is f the hyponuse

[flat veldt]

Yeah kinda the force along it

[leaden seal]

okkkkk lets do this

[flat veldt]

Yes

[leaden seal]

now

[flat veldt]

What's the relationship between F and b

[hint: it involves theta]

[leaden seal]

this?

[flat veldt]

Yes

[leaden seal]

Cool

let me add this to my notes

[flat veldt]

Now let b stand alone

[flat veldt]

Yup now keep this equation in mind

Now we move to the length diagram

[leaden seal]

ok...

and this is the forces diagtram

[flat veldt]

Can you draw it out please

[flat veldt]

Great we know that 2 corresponds with b
And 2.5 corresponds with F

[leaden seal]

yes

[flat veldt]

So we pick our theta here

[leaden seal]

. :..

[flat veldt]

Yeah

We used sin ∅ in the force diagram so
We use sin∅ here too to avoid complications

[leaden seal]

ok

[flat veldt]

Perfect we can now put this value right here

[leaden seal]

ok writing

[flat veldt]

[leaden seal]

and here I see it now

1 more thing

[flat veldt]

Yeah?

[leaden seal]

you are a goat

and thanks alot

goodnight

[flat veldt]

Please don't

[flat veldt]

Gn

[leaden seal]

.close

[midnight plank]

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[flat veldt]

I almost gave up on statics

[leaden seal]

never give up

when you have a goat

[flat veldt]

[midnight plank]

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[vocal walrus]

https://cdn.discordapp.com/attachments/1387985927594315807/1423491624465600623/image.png?ex=68e08162&is=68df2fe2&hm=f2663fb8d662f199594cdc3443ad1f000064758b784a0c737d0ea7952a311613&

[vocal walrus]

are these like..... backwards??? or am i crazy

[dry pollen]

how did you get your answers?

[vocal walrus]

so if i want the domain of (root x-7) + 4 the x - 7 means it translates to the right which means it would be [7, infinity) ?

i don't know if it's different because it's inverse?

the + 4 only correlates to range no?

[dry pollen]

have you first found the inverse function?

because they are asking for the domain of that

[vocal walrus]

ohh wait so

[dry pollen]

alternatively, realize that the domain of the inverse function is the range of the original function

[vocal walrus]

move 4 to the other side and square both sides

then -7

f-1(x) = 3?

[dry pollen]

where did the x go

[vocal walrus]

i thought i have to solve for x

[dry pollen]

well yeah

so you let y = sqrt(x - 7) + 4

moving 4 to the other side and squaring both sides gives (y - 4)^2 = x - 7

so x = (y - 4)^2 + 7

so the inverse is actually f*-1(x) = (x - 4)^2 + 7

but there is a domain restriction on the inverse because the range of f is not all real numbers

[dry pollen]

then consider this

[vocal walrus]

so that's viable for every question?

if i want the domain for an inverse but it's not in inverse form yet it'll always be what the range is

[dry pollen]

yup

[vocal walrus]

i see

okay tysm

[dry pollen]

glad to have helped. anything else?

also sorry if I'm replying late, kinda juggling multiple help topics atm hahah

[midnight plank]

@vocal walrus Has your question been resolved?

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[proud abyss]

(diagram of look-ahead carry adder)

is this not the same as the diagram of full adder? how do both of these differ, then?

[proud abyss]

we renamed the variables, sure, but the expression is still the same, right?

[untold gale]

they are the same

you are correct

why does this trouble you so?

[proud abyss]

because of the difference in their workings

[untold gale]

dude those are drawings on paper

there innerworkings are wood pulp

[proud abyss]

i did not mean it like that but okay

[untold gale]

im just making a joke sorry

look bottom line , regardless of how an and gate is constructed it still behaves like an and gate.... we use those symbols in digital design to represent specific behavior. Its a standard.... infact its such a strong standard that if you told me one of those and gates did something other than the logical opperation from wence it gets its name id tell you either I just experienced a glitch in the matrix or you need to change your diagram

[proud abyss]

that was never my question. i probably worded myself wrong, so that's not on you; but i think i am going to leave this as of now

thanks for your input

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[carmine sigil]

.reopen

[midnight plank]

✅ Original question: #help-49 message

[carmine sigil]

@proud abyss a full adder has a carry in

Oh, that second one also has a carry in

[proud abyss]

yeah

is just z

[carmine sigil]

That second one is mislabeled, it is not a half adder

That is a full adder

[proud abyss]

the first one is a look-ahead carry adder, the second one is a full adder

[carmine sigil]

Are you asking for the difference between a look ahead carry adder and a full adder?

[proud abyss]

i am not sure if i understand this correctly but,

basically, if we talk about how to do addition of n-bit numbers, we talk about a look-ahead carry adder; but if we talk about what circuit is required for it, we talk about a full adder? i am sorry, this is probably all too trivial; it is just it kinda threw me off when i was revising

[untold gale]

Full adder → circuit to add 1-bit + carry-in → sum + carry-out
Look-ahead carry adder → technique/architecture to add
n-bit numbers fast using generate/propagate logic; .

[carmine sigil]

So a full adder is any circuit that implements addition with carry in and carry out.

A look-ahead carry adder is a particular implementation of a full adder that has the feature where if an addition does not have a carry, then you get the answer a little bit faster.

[untold gale]

Look-ahead carry adder implemented using full adders plus extra gates for look ahead

[proud abyss]

all right, thanks a lot

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[twilit field]

how would I do this

[last slate]

What’s the general formula for a reflection?

In the group presentation for D_n

[twilit field]

s^{n}r where s is some rotation and r a reflection

[last slate]

I think that’s right I haven’t done group theory in a while

Anyway

What relations do you know

[twilit field]

hmm, so. just cancel out stuff now

[twilit field]

the thing is I don;t know how this formula is obtained

I don;t think we ever did it in class beyind D_4

[last slate]

Do you mean that you don’t know the generator and relation definition of D_n?

[twilit field]

No

We "derived" it geomtrically for D4 I think

Or a small groups and that's it

Eh, I'll do this later

migh aswell revise eveyrthing else first

.clsoe

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[still flax]

Hello I'm on d) and I'm wondering if theres a quick easy way to sketch inverse graph? or do I gotta repeat the process I did for c) again 🥲

also wondering if my explaination for c) is okay ?

[last arch]

There is an easy way to draw y=g^-1(x)

Recall that g(g^-1(x))=x

so if y=g^-1(x)

g(g^-1(x))=g(y)

x=g(y)

So the graph of y=g^-1(x) is the graph of x=g(y)

@still flax

[last arch]

Yea your explanation should suffice

[still flax]

ah okay so I can just draw it like reflecting on the line y=x?

[still flax]

ok thank you

[last arch]

Ye

[still flax]

alright thanks a lot

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[twilit field]

Trying to find a non-abelian group of order 9.$G={1,±2,±3,±4,±5}.$
\
Define $a\circ b = \begin{cases} b & \abs{a}≠\abs{b} \ 1 & a=-b\ a & b=1 \end{cases}$

[grand pond]

wai

[twilit field]

though I suspect this may not be associative...

okay, turns out no such group exists

https://math.stackexchange.com/questions/795102/elementary-approach-to-proving-that-a-group-of-order-9-is-abelian

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[twilit field]

😔

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[fair kayak]

guys ive been doing this question more than once and i get it wrong all the time

[fair kayak]

i dont get the logic

isn't the exponential the 'one year'?

one year has 4 quarters?

[bold peak]

Yes

So if you have q quarter years, how many years is that

[fair kayak]

t/q = 4?

wait

t=4q

it's still 4q?

[bold peak]

Uh no

You'll have more quarter years than you'll have years

[fair kayak]

oh yes

[fair kayak]

t/4 righttt

[bold peak]

q/4

[fair kayak]

why q

isn't t for years

[bold peak]

Yes you want to express t in terms of q

[flat veldt]

It says time (t) = q quarter years
Read as t=q × quarter years
t=q×¼

!done @fair kayak

[midnight plank]

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

[fair kayak]

holdon

[fair kayak]

ohhhhhh

okk i got it

[fair kayak]

thankyouuuu

[fair kayak]

thankyouuuu

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[languid rain]

how to get the limit of y after changing the order?

[errant lodge]

y = x/a

y = sqrtx/a

Solve and get the boundaries

[lyric charm]

brackets!

[errant lodge]

I mean, its in the question so the person should get it, no😔

[lyric charm]

nope, you should always write properly

[errant lodge]

I can, on paper

But i’ll try

[lyric charm]

y = sqrt(x/a)

[errant lodge]

Okay mate

@languid rain you got it?

[languid rain]

oh yes, thanks, i zoned out lol

i close right?

.close

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[proud abyss]

can someone please help me with this question?

[proud abyss]

(please ping if responding)

[errant lodge]

Give an output equation first

[proud abyss]

Z = P.R.S + (P.Q)(R.S') + P(R'.S) + P.R'.S' + Q'.R'.S'

[errant lodge]

You gotta simplify now

Factor R

And then S = 1 ig with boolean laws

So ig simplification will do your work

[midnight plank]

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[safe onyx]

Trying to find inverse of A

[safe onyx]

I think I am wrong based on desmos

[slender walrus]

you're doing some weird stuff with your row operations, adding/subtracting the wrong components

[safe onyx]

In which line? I can't spot it 😅

[slender walrus]

for the whole augmented side

[safe onyx]

Is the first row alright? It seems fine to me

[slender walrus]

no

how are you getting from

0 1 0
0 0 1```
to
```1 0 0
-2 -9 -2
-2 -10 -1```
in those two row operations

[safe onyx]

0 1 0 - (2 10 2) = -2 -9 -2

[slender walrus]

you shouldn't be using any of the values in the left side

[safe onyx]

I'm supposed to do
0 1 0 - 2(1 0 0) ??

is that what you mean

[slender walrus]

yes

[safe onyx]

ooh

that makes it a bit easier brb

Got it thank you!!

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[smoky briar]

how about this one

[gaunt nimbus]

hi

[smoky briar]

i get it x can't be 1

so we have solutions like if x>1

x-2 < 3x -3

[gaunt nimbus]

${x \neq 1}$

[grand pond]

k

[gaunt nimbus]

mhm

so u are splitting into 2 cases

[smoky briar]

1/2 < x

[gaunt nimbus]

ok

so ${x > \frac{1}{2}}$ and ${x > 1}$

[grand pond]

k

[smoky briar]

yeah what does this mean for our solutions

1 to infinity

but 1 isn't part of it

[gaunt nimbus]

(1, infinity)

[smoky briar]

yeah but 1 isn't inclusive right?

[gaunt nimbus]

ye

[smoky briar]

(1, infinity) means the 1 isn't the smallest one that is included?

[gaunt nimbus]

mhm

[smoky briar]

and for case 2: x < 1
(x − 2) > 3(x − 1)

x < 1/2

basically (- infinity, 1/2)

[gaunt nimbus]

ya

so whats the issue?

[midnight plank]

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[dry mural]

So i have this shape im trying t oget the moment of inertia of

[dry mural]

its a cut bi cylinder

i think this is the solution

but im sort of unsure

wait old integral

this one is the real one

[midnight plank]

@dry mural Has your question been resolved?

[dry mural]

matter of fact so far i just found my mistakes myself

this should be the correct one, well hopefully.

[midnight plank]

@dry mural Has your question been resolved?

[small jasper]

discord.gg/physics

[dry mural]

fair enough

[midnight plank]

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[limber acorn]

can someone verify I did this correctly?

[waxen musk]

what are you aiming to do here?

[limber acorn]

I am trying to show that S is closed under addition

[waxen musk]

is y' a derivative?

[limber acorn]

Yes

[waxen musk]

theres an issue here

this should be 2(6x^3+5)

[limber acorn]

Why would we multiply by 2 here?

[waxen musk]

because were adding the equations here, right?

or are you doing something else here?

[limber acorn]

so what I did was let u = y1+y2 in S
and then since by assumption, u is in S,
u' + 3u = 6x^3 + 5 right?

[waxen musk]

oh i see, youre going for contradiction

[limber acorn]

yes

[waxen musk]

i believe that works

you should make that assumption clear though

[limber acorn]

I should yeah

thank you

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[midnight plank]

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[sullen bolt]

can this be simplified further

[lyric charm]

it might be, but a better question to ask is where did this come from?

[sullen bolt]

i made a formula which takes 3 points on a plane and finds the exact formula of the circle

given points (x1,y1),(x2,y2),(x3,y3)

[lethal path]

yep, so what's q here?

[lethal path]

can you send the link to the Desmos graph?

[sullen bolt]

https://www.desmos.com/calculator/vkkxftqtyr

[lethal path]

https://www.symbolab.com/solver/step-by-step/\frac{\left(\frac{x_{3}^{2}-x_{1}^{2}}{y_{3}-y_{1}}\right)-\left(\frac{x_{2}^{2}-x_{1}^{2}}{y_{2}-y_{1}}\right)-y_{2}%2By_{3}}{\left(\frac{x_{3}-x_{1}}{y_{3}-y_{1}}-\frac{x_{2}-x_{1}}{y_{2}-y_{1}}\right)2} simplify?or=input

well this is never going to be a neat expression to begin with

[sullen bolt]

mmm yeah looks like it won't be very neat

[lethal path]

but the bottom is the negative of the sum of the coefficients of the cross product of (x1, x2, x3) and (y1, y2, y3) nvm it's not

[sullen bolt]

q is also equivalent to this

(pre simplication into the original question)

[lethal path]

on Maths Stack Exchange there are a few results on this

https://math.stackexchange.com/questions/213658/get-the-equation-of-a-circle-when-given-3-points

the neatest ways all involve matrix methods

[sullen bolt]

mmmm

im stubborn tho

guess this becomes a no matrix challenge

news: yes the formula works
news 2: too lazy to simplify that behemoth

uuuuf desmos is crashing

every 2 minutes

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[still flax]

Hello Im stuck on this integration problem and not sure what to do next. So far I integrated both curve equations and then found the area under the first graph. Now i'm not sure how to ensure its bounded by the bottom graph

[waxen musk]

just take the difference of their areas

[still flax]

I found coordinates in the previous questions as A (1,2) and B(2,2)

[still flax]

oh is it just that ?

[waxen musk]

since the integral finds the area to the x-axis

[compact copper]

How about subtracting area under curve of (2x-3)^2 + 1 from 2(2x - 3)^4

[still flax]

okay thank you

[compact copper]

Or is it the other way around, well I myself am not sure about that, just put a modulus

[waxen musk]

its this, cause (2x-3)^2+1 > 2(2x-3)^4 in the region

oh well

[grim aurora]

hey guyz im new

[waxen musk]

((2x-3)^2 + 1) - (2(2x - 3)^4), to be specific

[lyric charm]

hello and welcome to the server.

this channel is currently occupied with someone else's question

go to #discussion or #chill if you just wanna chat

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[compact copper]

Ahhhhh yeah I see, I was correct in being confused IG, so it was the other way around

[still flax]

got the correct answer thanks everyone

.close

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[grim aurora]

anyone wants help?

[waxen musk]

feel free to patrol the occupied channels if you want to help

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[exotic ridge]

this is the rest of the question, whive ive answered correctly so far

[exotic ridge]

ive managed to do the first part, proving that the expression equals -15, but I don't get where the '8 possible values' come from

[glad meteor]

given alpha, beta and gamma are integer $(1+\alpha)$ be integer too, and it's one of the factor of -15 from what you derived, find out what values it can hold.

[grand pond]

Nab

[exotic ridge]

<@&268886789983436800>

[exotic ridge]

thanks for that

to think that one simple hint of reminding me that since alpha is an integer, 1 + alpha is also an integer made me go from being clueless to being able to finish the whole question

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[twilit field]

Won't these only converge either if (x_n) and (y_n) converge to the same limit , or there are only finitely many term from one of the seqeunces

[runic hamlet]

yes

and?

[twilit field]

So I basically have to show that , that' what happens here, I suppose

[sinful topaz]

i dont see why they cant be sequences that converge to different limits

[twilit field]

Then we have two subseqeunces converging to different points if there are infinitly many terms from each seqeunce in u_n

[lyric charm]

are you claiming that if lim x_n ≠ lim y_n (despite both existing) then either u_n or v_n will be divergent?

[sinful topaz]

if they converge to different points, you can separate the sequences by some distance, then un and vn converge

[twilit field]

I'm claiming that for u_n to converge x_n and y_n have to converge to the same limits, or there are only finitely many terms from one of the seqeunces in u_n

[sinful topaz]

surely you just need to consider the 2 cases of if the limits are different or the same

[lyric charm]

I'm claiming that for u_n to converge x_n and y_n have to converge to the same limits
you are claiming, "If u_n is going to converge, then x_n and y_n had better converge to the same limit".

therefore, you think that if x_n and y_n DON'T converge to the same limit, then u_n MIGHT NOT converge.

do i read you correctly yes or no

[runic hamlet]

or

wai is correct about what he is saying

he is just saying it badly

[twilit field]

No

[sinful topaz]

when you say this second part, do you mean that un and vn dont take infinitely many terms from both xn and yn?

[twilit field]

Yes, if they converge to different points

[sinful topaz]

yeah, but you can prove this fact no?

you dont have to assume that

[visual tiger]

If x = lim x_n and y = lim y_n, are you saying "for u_n to converge we must have x = y", or "for u_n to converge, it must converge to x or y", or smthg else??

[sinful topaz]

i think he means if x doesnt equal y, then there are only finitely many n such that un = xn (or potentially yn)

[twilit field]

Yes

Just stating an observation

[midnight plank]

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[midnight plank]

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[tidal turret]

.close

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[lyric charm]

@tidal turret curious -- what is this (a : b) notation? i dont think ive seen it

[tidal turret]

gcd

[lyric charm]

oh huh

[tidal turret]

[lyric charm]

is there a similar one for lcm

[tidal turret]

let me see, ill ping u if I find it

[grim vector]

a comma away from doing french math

[lyric charm]

alright

[tidal turret]

[a:b]

examples

@lyric charm

[lyric charm]

oh yeah ok square brackets with a colon, got it

[tidal turret]

🔥 💖

[tidal turret]

you guys use comma?

[grim vector]

(a,b) = gcd(a,b) in some books

[tidal turret]

🔥 👍

[grim vector]

mcm is cool with cyclic group order you can show a cool proprety with it

Peak algebraic structure

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[balmy quartz]

not sure how to tackle this

i started off saying

let intersection of RS and PQ = X
RX = n(RS)

but then i realised i can't work out RS

we have the vectors for OP, OR and OT, but the rest are different i think (the sides don't look the same size)

[hidden kiln]

Let me try to solve this first before I guide you, pls be patient ye

other helpers can guide if you want

[balmy quartz]

<@&286206848099549185>

this is the working out but i don't really understand it

[hidden kiln]

okay i solved it

now

do you know about vector line equation?

[midnight plank]

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[balmy quartz]

wdym

can u give an example

[hidden kiln]

@balmy quartz you just closed the channel, use reopen

.reopen

[balmy quartz]

.reopen

[midnight plank]

✅ Original question: #help-49 message

[hidden kiln]

If you know the direction vector v and position vector of a point on the line r0, you can have the line equation as such

Do this ring a bell

[balmy quartz]

nah, i know that r = r0 + a tho

so yeah

[hidden kiln]

r = r0 + ta

[balmy quartz]

tv + r0 = r

yeah

[hidden kiln]

you need a parameter t

[balmy quartz]

yeah a multiple

[hidden kiln]

So the first thing is to get line equation of all 3 lines

any idea how to find those

[balmy quartz]

what of PQ, RS, TU?

[hidden kiln]

yea find line equations PQ RS and TU separately

[balmy quartz]

yeah this is the part where i was stuck on the original question

[hidden kiln]

You are given position vectors for point A B and C

You can try find the position vectors for every single points first

Because through that we can get enough vector to form the line equation itself

This means you have to find all position vectors for all points, literally

So do you know how to do that

[balmy quartz]

yeah but for example for point B, we can't do 2c + 2a because the lines are different

same for C, Q, A

[hidden kiln]

You do know position vectors of A B C tho

Position vector for point A is a

Position vector for point B is b

Position vector for point C is c

[balmy quartz]

OR is a

[hidden kiln]

The question did said position vector for point A is a, not for R

[midnight plank]

@balmy quartz Has your question been resolved?

[midnight plank]

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[balmy quartz]

.reopen

[midnight plank]

✅ Original question: #help-49 message

[balmy quartz]

sorry, i went to the shops

anyways

i fucked up somewhere

it should be k = lambda = 1/2

but i get k = lambda = 1 = 2 ☠️ ☠️

i see it i think

OQ is not AB / 2!!

[midnight plank]

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[lime oracle]

helpp, we're supposed to round off to two decimal places.

how do i do that with this as my answer? T_T

1 hp =745.7 W
hp = 0.0649867374 W745.7 W / 745.7 W

8.7148650384108e-5 hp

or

0.000087 hp

[bold peak]

Two decimal places or two significant figures?

Although ig the convention might be different based on where you're from

[lime oracle]

two decimal places, if i do scientific notation will it be okay? or should i ask my teacher if its fine my hp will be just as is?

[bold peak]

Can you share the original question

[lime oracle]

we were only asked to do thisss, then i told my member to ask our teacher if how much to round off. she said 2 decimal places

theres no context in the original question bcs its just instructions on how to do the lab

[balmy quartz]

2 dp = in your end result, there should only be two numbers after the "dot"

1.68853 -> 1.69 (rounded to 2 dp)

63.131621 -> 63.13 (rounded to 2 dp)

[lime oracle]

but if i do 2 dp for horsepower, i would get 0.00 unless i do scientific notation but idk if scientific notation is allowed 🥹

[bold peak]

Yeah they seem to want sig figs

[bold peak]

You should ask yeah

[lime oracle]

okayyy thank uuuu ❤️

.close

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[leaden seal]

not sure why my last answer is wrong

[midnight plank]

@leaden seal Has your question been resolved?

[true urchin]

Two issues here:

You assumed all member forces tension, away from the joint (good practice). After solving
Σ
𝐹
𝑦
ΣF
y
​

you found
𝐹
𝐵
𝐷

−
19.8
F
BD
​

=−19.8 kN, i.e., compression. That means the contribution of
𝐹
𝐵
𝐷
F
BD
​

in the x-equilibrium must be taken with that sign (negative). If you keep the algebra consistent, the term with
𝐹
𝐵
𝐷
F
BD
​

changes sign automatically.

The horizontal component of
𝐹
𝐴
𝐵
F
AB
​

should add (not subtract) in the equation once the sign of
𝐹
𝐵
𝐷
F
BD
​

is taken into account.

Because of those sign/consistency slips, the computed
𝐹
𝐵
𝐶
F
BC
​

is too large.

[midnight plank]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[midnight plank]

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[elder drum]

i need help converting quadratics into vertex form

ex. -3x^2 - 12x - 8

[midnight plank]

Please don't occupy multiple help channels.

[elder drum]

:/

[midnight plank]

Please stick to your channel.

[rich yew]

Do you mind going back to the old one, or closing the old one?

[elder drum]

how come nobody came even after i ping twice

[rich yew]

Not everyone is fit out for the question.

[solemn scaffold]

Yall whats 19-987+759x[674]+84

[midnight plank]

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).

[rich yew]

[sudden yacht]

Don't troll!! <@&268886789983436800>

[sudden yacht]

Also, !occupied

[tribal temple]

Yeah don't troll here

Gonna close this one as it seems the other one has some progress

.close

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[hasty flume]

hi

[hasty flume]

what is the 1-costheta

whys that there

[midnight plank]

@hasty flume Has your question been resolved?

[hasty flume]

<@&286206848099549185>

[magic berry]

Are you talking about

$x\sin\theta+y\cos\theta=y$

[grand pond]

Miyagi

[magic berry]

They just isolate y

Then plug the result into the next expression

[hasty flume]

solved tyy

.close

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[leaden seal]

can someone explain where the bit in red came from

[jaunty ivy]

that whole working seems wrong

2nd derivative is not 6x-2

[leaden seal]

i think that working is for this question

[jaunty ivy]

anyways third derivatives are invoked analogously to how 2nd derivatives are used for determining if critical points are indeed min / max. we can tell if the sign changes (hence an inflection point exists at that critical point) if the third derivative is nonzero

if 3rd derivative is 0 then the test is inconclusive and u need to check sign change manually

[leaden seal]

right okay so first i need to find the critical points

[jaunty ivy]

yes

for min/max, u need to find points where f'(x) = 0
for inflection points, u need to find points where f''(x) = 0 or undefined (division by 0)

[leaden seal]

so set first derivative = 0

and find the stationary points

[jaunty ivy]

yes

[leaden seal]

this seems to be the x value

[flat veldt]

[leaden seal]

,w solve 4x^2-3x^2

[grand pond]

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Requested by zarahx123

[leaden seal]

yes its 0

[flat veldt]

f(x) = x⁴-x³

[leaden seal]

yes

[flat veldt]

Differentiating that gives 4x³ - 3x²

[leaden seal]

oh

i read it wrong

mb

[flat veldt]

[flat veldt]

,w differentiate 4x³-3x²

[grand pond]

Results provided by WolframAlpha

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Requested by ishigamisenku_

[leaden seal]

how do we get the second x value

[flat veldt]

⚠️

You might want to recheck that:)

[leaden seal]

ok

actually

[leaden seal]

can you help solve it

oh

[flat veldt]

[flat veldt]

Sorry I can't server rules

!noans

[midnight plank]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[leaden seal]

ill do it

[flat veldt]

[leaden seal]

you can correct me

[flat veldt]

Yeah

[flat veldt]

Alright 👌

[leaden seal]

not sure what to do now

3rd derivative test?

[flat veldt]

You can check the derivative at the left and right of x=0

[leaden seal]

using first derivative test?

[flat veldt]

Yeah sure
Although I haven't used this test before

[flat veldt]

Yeah that's what I normally do

But the third derivative test seems better

[leaden seal]

and to do the third derivative test do i differentiate again?

[flat veldt]

Yes

[leaden seal]

and after this

[flat veldt]

I don't really trust this third derivative again I haven't used it before
I'd rather use this

[leaden seal]

hmmm

[flat veldt]

[leaden seal]

um

okay

let me do that

[flat veldt]

[leaden seal]

so i need to choose test points

[flat veldt]

Yeah

,w plot x⁴-x³ from x=-1 to 1

[leaden seal]

and

how do i know which points

[grand pond]

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Requested by ishigamisenku_

[flat veldt]

If the nearest stationary points to the one at x=0 are at x=-k (left) and x=l (right)
Then the test points should lie on the interval-k<x<l

[leaden seal]

so

becuase x-0

x=0

[flat veldt]

Yes

[flat veldt]

Go on

[leaden seal]

i can use -1 and 1

or even a decimal

like 0.5

[flat veldt]

Are you sure about using 1

Check the nearest stationary points at the left and right

[leaden seal]

hmm let me do a numberline

so these should be fine

[flat veldt]

Yeah

[flat veldt]

Oops you used the wrong test points

[flat veldt]

Here are the correct ones

[leaden seal]

wdym

[flat veldt]

The stationary point at x=0 only has one nearby stationary point which is x=¾
So we know that our test point on the right should be
0<x<¾

Which is why we can't use 1

[leaden seal]

why cant it be smaller than this?

i used the test points in red

[flat veldt]

Wdym

[leaden seal]

smaller than 3/4

[flat veldt]

No, look at it again you used -1 and 1
Not -½ and ½

[leaden seal]

i didnt put those values in

[flat veldt]

Because
If the nearest stationary points to the one at x=0 are at x=-k (left) and x=l (right)
Then the test points should lie on the interval-k<x<0(left). 0<x<l (right)

[leaden seal]

OH

[flat veldt]

Hmm

Lemme check this

[leaden seal]

i thought it was inbetween these intervals

[flat veldt]

,w 4(-0.5)³-3(-0.5)²

[grand pond]

Results provided by WolframAlpha

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Requested by ishigamisenku_

[flat veldt]

,w 4(0.5)³-3(0.5)²

[grand pond]

Results provided by WolframAlpha

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Requested by ishigamisenku_

[flat veldt]

Okay recalculate the bottom one

[leaden seal]

yh

i wrote it wrong

[flat veldt]

Np

[leaden seal]

so

it changes from neg to pos

[flat veldt]

Yes

[flat veldt]

Nope

[leaden seal]

oh

it doesnt change

[flat veldt]

https://cdn.discordapp.com/attachments/1018703621841494076/1424162900091605033/wolf.png?ex=68e2f28f&is=68e1a10f&hm=178dddc176f7d0fa467b7f37000f3cf68e435a70fbaec08b20f46d1de9cb7333&

https://cdn.discordapp.com/attachments/1018703621841494076/1424162829749190767/wolf.png?ex=68e2f27e&is=68e1a0fe&hm=89743df1467003ed3ab74a8c7446e2c4c2e44ec61e2e8da7c24036d65ff74ade&

They're both negative

[leaden seal]

yh

[flat veldt]

What conclusion can you draw

[leaden seal]

does that mean its a POL?

[flat veldt]

POL?

oh
Point of inflection

[leaden seal]

yh

[flat veldt]

Yes

[leaden seal]

okay 🙂

[flat veldt]

I forgot the word

[leaden seal]

its cool

[flat veldt]

!done ?

[midnight plank]

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

[leaden seal]

no

[flat veldt]

Why are you doing maths questions so late at night

[flat veldt]

What's remaining

[leaden seal]

its only 23:41

[leaden seal]

you are a goat

[flat veldt]

I know isn't that considered late

[flat veldt]

Lmao thanks

[leaden seal]

.close

[midnight plank]

Channel closed

Closed by @leaden seal

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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[last slate]

.

yo

[waxen musk]

Hi lnrd

What do we have today

[last slate]

yooooooo

[last slate]

so you know how this is the equation to find the limit transition of some system

but see here theyre adding x1+x2+x3=1 to the system idk what means

[waxen musk]

This is a probability axiom

The sum of all probabilities is 1, by definition

[last slate]

yeah but

how do the variables represent the probabilities in a given system?

and why do we add that information to the system when solving for X

[waxen musk]

bar X is the probabilities of being in each state

So x1 is the probability of being in state 1, for example

[last slate]

like here right

[waxen musk]

Right

[last slate]

okay\

i see

[last slate]

what about the second part

[waxen musk]

Why we add that information?

Because its given to us whenever we say something is a probability space to begin with

[robust isle]

also if you just solve PX = X, there are infinitely many solutions

[waxen musk]

Do you know the three kolmogrov probability axioms?

[robust isle]

constraining it to a probability gives you one unique solution (assuming your markov chain is nice enough), and ppl like probabilities

[waxen musk]

Put simply its

1. No probability is negative
2. The probability of all outcomes is 1
3. The probability of disjoint sets is the sum of their probabilities

We always assume these to begin with

[last slate]

idek what an axiom is

[waxen musk]

Its an assumption, because we need to start with something in math

[last slate]

i see

[last slate]

ohhh

okay

well

[waxen musk]

Usually we consider them like definitions

[last slate]

but i just dont get fully the logic behind adding the x1+x2+x3

into the system

what does that do specifically

[waxen musk]

Specifically its that they sum to 100%

its directly because of axioms 2 and 3

We know no pop in x1 is in x2 or x3, no pop in x2 is in x3, so theyre disjoint

And this is all possible outcomes

[last slate]

i know they sum up to 1 but why add them to the system while solving it..

[waxen musk]

This is why

Everything where the probs dont sum to 1 is completely meaningless to us here

[last slate]

why constraint it with that specifically

[waxen musk]

Because another solution may say it sums to .8
Now think about what that told us, all 100% of my population is only 80% of the population?

It just wont make sense if its false

[last slate]

so were just basically using information we know to properly restrict the system?

like we know to restrict the system we need another independednt equation

and we know we have one through that

[waxen musk]

right, we need everything to be 100% probs or pops, if its not 100%, youre saying theres other possibilities, or too many possibilities

[last slate]

so the bottom row of our augmented matrix will all be 1?

[waxen musk]

yeah

think of this constraint as being necessary for it to be a probability in the first place

[last slate]

and do we always use that fact whenever we solve for a steady state matrix

[last slate]

wdym?

[waxen musk]

its very important to note that we need x1, x2, x3 to be disjoint and all possibilities to do this, but otherwise yes

[waxen musk]

it comes directly from axioms 2 and 3

[last slate]

this is related to planes and lines right

is that how it works too?

is that a better way to think of it

[waxen musk]

this has more to do with the fact that its a weighted sum than any hiding lines or planes

of course, there is always a sense that its a plane or a line or etc

but were just solving a system of weighted sums here

[last slate]

but were talkin about restricting our system with that

[waxen musk]

since x1, x2, and x3 are all possible outcomes, the probability of at least one of x1, x2, x3 happening must be 1

but also, since they are defined to be disjoint, the probability of at least one outcome must also be P(x1)+P(x2)+P(x3)

so it immediately follows that P(x1)+P(x2)+P(x3)=1

so now, what if you saw a solution which said P(x1)+P(x2)+P(x3)=80%?

then clearly, there must be some x4 case, but there logically cannot be such a case here

or what if your solution said P(x1)+P(x2)+P(x3) = 120%?

you must have overcounted

[last slate]

im not confused at the 100% part

of them equalling a 100

btw does the steady matrix give us an amount of some thing or a probability

[waxen musk]

it kinda depends on what youre doing with P here

here it gives a probability

i could have multiplied my raw populations by P and gotten an actual amount of each population in the states

[waxen musk]

so, since it must be the case, its another constraint

its just another statement we want to hold true

[waxen musk]

of course, in this case, id need x1+x2+x3 to sum to the total population

[waxen musk]

this is secretly the same thing when you realize you can divide by the total population in this constraint

so, if i think i understand the question:
we are only saying they sum to 1 here because we gave each x1...x3 as % of disjoint populations
but this assumption isnt always one we make, we may also want x1...x3 as raw populations, or something else

we only add this for a constraint if we know the former

simply because its just another equation we need to hold true

[last slate]

i see

[midnight plank]

@last slate Has your question been resolved?

[last slate]

can we ever be given a sytem where we dont need to use that

[waxen musk]

that x1+x2+x3=1 ?

we dont need it with raw populations

like if i have 25 people total, and x1...x3 are the raw pops

then it becomes x1+x2+x3=25

[last slate]

wait

[last slate]

im just not getting why every time the system just wont work out unless we add this

[waxen musk]

its not that it wont work out, it will give us the right answer...

but itll also give us bad answers with it

like we said earlier, we dont want x1+x2+x3=.8 whatsoever