help-23

[rigid kernel]

when i put this into x=-b/2a I get 133.3

@drowsy moss

oh

I think I see my mistake

i swithced the 4 and the 3 lemme check

ok ye i got it

thanks @drowsy moss

how i end this

.done

.close

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[rigid kernel]

https://media.discordapp.net/attachments/903481106819612714/953861249886736394/761155030513352705.png

[rigid kernel]

I need help again with the same quetsion,

question 8

I made a formula for perimiter P = 4x+3y

And then isolated y

Then puitting it into the area equation

getting a(x) = -4/x x^2 + 200x

getting x= 150

which is one of the measurments

I can see on the answer book but,

The other is 100

and when I sub it in y = -4/3x + 200

I get 0

a similar question, I did the same thing and got the correct measurment for that

But idk what im doing wrong here

[drowsy moss]

you are combining two different measurements and it's confusing your process (which is correct)

you split the long side into two measurements to 4x+3y. but then used the area function xy which is the area of one of the smaller rectangles

[rigid kernel]

oh

should the area formula be 2x times y?

[drowsy moss]

either call the larger rectangle sides x and y, or the area function is 2xy

either should fix the problem

[rigid kernel]

ohh

yeah thanks that makes so uch sense

lemme try and see if i get the correct answer so I dont have to reopen

[drowsy moss]

relabeling as x and y would mean your perimeter function changes, so if you go that route be careful

[rigid kernel]

my width and legnth were always w tho

y tho

x and y*

[drowsy moss]

?

your length was x+x, not x

[rigid kernel]

ye

2x times y

for area

[drowsy moss]

yeah, that will work

[rigid kernel]

oh im getting

75

when I sub it into x=-b/2a

Do you know what im doing wrong

[drowsy moss]

right, because x is half of the whole side

[rigid kernel]

trhe dimensions should be 150 x 100

[drowsy moss]

yes

put your drawing up again

[rigid kernel]

but i got 75 as one of them

A = 2x(-4/3 x +200)

[drowsy moss]

if x = 75, what is the length of that long side of the larger rectangle?

[rigid kernel]

oih

im stupid

75+75

equals 150

[drowsy moss]

haha not really. You started in a sort of awkward place that made sense to you

sometimes that means dealing with that choice at the end

[rigid kernel]

thanks

now i find the other

thing

[drowsy moss]

yep

and it should work out

[rigid kernel]

ye i got 100

Now i substidute it back i equation

for

the area

ok ye I go tit

Thanks

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[velvet hearth]

why in partial fraction decomp

[velvet hearth]

with multiples of thje same fraction on the denom

like (x-1)^n

why do you split it the way you do

[knotty crypt]

bc partial fractions is "undoing" the combining of fractions. it's easier to see why that is the case starting with an uncombined fraction and then combining it and comparing with what you want to split up

[velvet hearth]

yaa

I understand that

i just forget why instead of splitting

(x-1) (x-1) (x-1) (x-1) you split in increasin gpowers

[quasi bison]

i mean you would have multiple copies of the same fraction

also consider what happens when the denom is just x^n

[velvet hearth]

is the easiest example just like

1/ x^n

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[velvet hearth]

trying to do b

what does the [-1,2] mean

[shy delta]

It means that

-1≤x≤2

If it was round bracket instead it would be < instead of ≤

[velvet hearth]

ohh yeah sorry im dumb

[shy delta]

👍

[velvet hearth]

i dont know what that means for the surjectivity and stuff though

this isnt surjective right?

[shy delta]

Surjective is an onto function

Injective is one one

[velvet hearth]

the answers say its surjective

but how is it?

the co-domain is [0,4]

[shy delta]

It is

Not injective tho

[velvet hearth]

but the image is [1,4]?

[shy delta]

No it's 0,4

[velvet hearth]

How?

oh nvm im stupid i get it

ill try the others i think my concept is loose my lecturer is very confusing

[shy delta]

,w y=x²

I wanted the graph

,w graph y=x²

[flat frigate]

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Requested by Di_Gram#9808

[shy delta]

-1 to 2 means it'll input all the values ranging from -1 to 2

You do know that 0 falls to the right of -1 right

A sub domain of -1,2 would be 0,2

So natural 0,4 would be achieved

[velvet hearth]

gotcgha 🙂

I sketched A and B easily

but i have no idea how to show that f: A --> B is bijective

i proved its injective

but how is it surjective????

e^z can describe any point in the complex plane

but the function A --> B only describes points outside the radius e^2??

so how is it surjective lol

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@velvet hearth Has your question been resolved?

[idle grove]

This looks like the domain of f(A) is f(A) it self so it must be surjective

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[stark maple]

So I’m working on this but I’m not sure what I’m missing

[modern thorn]

do u have an illustration?

[stark maple]

Yah

[modern thorn]

can i see

[stark maple]

Sure

[stark maple]

Sorry it was taking a while to load

[modern thorn]

wdym with ml1

angle 1?

[stark maple]

Yah

Same thing with 3 and 4

[modern thorn]

Is the O here supposed to be D?

[stark maple]

Yah

Here I wrote it out

It’s more clear

[modern thorn]

yep i guess your reasons are correct

just make sure to raise the typo concern to your prof.

[stark maple]

Do you know what I would out for the past reason or is it the same as the 6th one

[modern thorn]

they are not equal bot congruent

it’s a cpctc postulate ig

[stark maple]

Ok so for the 6th reason I should remove the equal part?

[modern thorn]

yepz To be safe, you could replace it with congruent since that’s what the postulate is known for

[modern thorn]

Same

[stark maple]

Alright cool thanks

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[ebon thorn]

idk how to answer this

[lean otter]

you need to look at the table

it's that simple

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[ebon thorn]

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[toxic stone]

my option is A, may i know if i am right? tqvm

[quasi bison]

yes

[toxic stone]

tqvm @quasi bison

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[true cobalt]

hey

[true cobalt]

can someone help me visualize this?

I mean understand step by step whats happening ?

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[true cobalt]

<@&286206848099549185>

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@true cobalt Has your question been resolved?

[true cobalt]

lol

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[paper magnet]

Hey does anyone know what NAN means? I was doing online homework when I came to the solution that an answer DNE, however when I put DNE it said I was incorrect and told me NAN was the answer. I have never seen NAN before and I was wondering if it also meant DNE.

[hushed copper]

That usually means Not A Number, DNE I guess would be Did Not Evaluate

Not a Number, as in the computer couldnt get to the result

[paper magnet]

@hushed copper Thank you

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[ancient escarp]

dne is does not exist

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[warm pendant]

can someone please provide the solution to this

[ancient escarp]

what have you tried

[safe radish]

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[warm pendant]

convert s to tn theta

[tall bough]

If 2 wasn't there it would be easy

use the trigonometric substitution for sqrt(x^2+1)

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[brazen shard]

guys is this definition valid for a vector space?

[stoic dune]

As vector addition?

[remote hamlet]

What is the main question?

[brazen shard]

ive been given 3 definitions

the question is if this is valid for a linear* space

[remote hamlet]

Could you show all text of the question? If it's not a hassle

[brazen shard]

its in german though

[remote hamlet]

Oh ok

Now it's better

Do you have the set of axioms you need to check?

[brazen shard]

I think so yes,

there are 8 axioms right?

[remote hamlet]

Maybe, it depends how they are numbered

[brazen shard]

(a+b)+c = a + (b+c)
a + 0 = a
a + b = b + a these?

[granite quail]

no additive inverse xd

[brazen shard]

explain?

[remote hamlet]

• addition axioms ( (V,+) is an abelian group)

• scalar multiplication axioms:
  (ab)v = a(bv)
  (a+b)v=av+bv
  1v=v

• distributivity axiom
  a(v+w)=av+aw

Did I leave something out?

[granite quail]

Sqrt(a^2+b^2) is equal to 0 in reals if and only if a=b=0

[brazen shard]

im so confused

😦

[granite quail]

In a vector space, you need to have an element -v for every element v such that (-v)+v=0

however, this operation is close - it is actually associative and commutative and distributive

[brazen shard]

okay

[granite quail]

and the zero defined there isnt the zero for that addition law, unless you take only the positive reals

[brazen shard]

what do you exactly mean by reals?

[granite quail]

real numbers

[brazen shard]

oh

[brazen shard]

okay so that is the additive inverse attribute

the first line is just very confusing

that a + b = sqrt a^2 + b^2

[granite quail]

in general algebra, you are allowed to define your operations however you want, but if you want to call them something

they better damn satisfy properties which are similar enough to addition and multiplication of real numbers to be called addition or multiplication

[brazen shard]

okay i see

[granite quail]

notice there is a different symbol for plus there

[brazen shard]

right

so the + is just a symbol

[granite quail]

its an operation

[brazen shard]

alright

so the first line isnt satisfied

[brazen shard]

because of this?

[granite quail]

yes

in fact, even if you chose the "zero" to be any real number

this "addition" would still not have inverses

[brazen shard]

oh i see now

because of the second definiton 0 isnt a real number

[granite quail]

You define the "0" to be the actual zero

[brazen shard]

okay but here 0 is a vector right?

[granite quail]

which you couldnt do, because then it wouldnt act as a 0, a+0 wouldnt be a

[brazen shard]

okay

i kind of understood

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@leaden grove Has your question been resolved?

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[lean otter]

Hello

[lean otter]

Would somoene please help me to understand why in this function it is considered bad to integrate with respect to x?

It is the example of area between curves.

[pulsar condor]

The bounds change as you move along x

And you're given them as functions of y

[broken yew]

I'm not sure that's the issue?

It's more like we don't have a function right?

We would have to split the integral into 2 parts

The purple shaded bit needs to be split by square root into 2 regions to get a function to integrate over

And the the right of the purple... not sure if you might need to split that too

[lean otter]

Would you please tell me why this case is?

[broken yew]

Well just try writing down an integral for the purple region only

where you integrate wrt x

To do that... you need a function in x to integrate, right?

But that thing isn't a function

So you would have to split it into 2

You could notice the line of symmetry along the x-axis and proceed ofc.

[lean otter]

I notice that.

[broken yew]

So you are splitting the integral to 2 bits along the x-axis

[lean otter]

But I am sorry, I am unable to understand why I need to split it.

If you have time, then would you please give me an example?

[lean otter]

Or elaborate this?

[broken yew]

$\int^b_a f(x),\dd x$

[broken yew]

What exactly is f going to be

You see, you have this equation $x=y^2-4$

[broken yew]

which defines that parabola

but y is not a function of x

It fails the vertical line test

[broken yew]

So you are going to have problems figuring out what f(x) is

(if you split along the line of symmetry, this problem is solved)

All in all, integrating wrt x isn't impossible, it's just a hassle.

[lean otter]

Ohh, Now I am understanding.

So, should I need to split positive and negative part?

[broken yew]

well yes...... but suppose you had a slightly more complicated example

then this becomes even harder

just shift that curve up by 1 unit or something

Or if you had a cubic

some cubic in y

x = f(y) where f is a cubic

and you wanted to do something similar.

Then you can't use the symmetry argument

And it becomes even more painful to try integrating wrt x

========
So this example is telling you - if it is a pain to integrate wrt x, then think about wrt y instead

[lean otter]

Ohh. I realize now.

One last question:

[lean otter]

By here, you mean it will be hard for us to know where we should split it?

[broken yew]

By a slight miracle, we can split it along the x-axis

but this certainly isn't true in general

The problem is we don't have a function in x

We have x = f(y)

not y = f(x)

[lean otter]

I see.

Thank you @broken yew 😊

[broken yew]

In this example you will be stuck, is what I'm trying to say

unless you switch to integrating wrt y

[lean otter]

Yes, Here it will be hard time for us to determine where we should split it.

[broken yew]

Well even if you split it along y = -1

Finding the inverse function is very painful

Cubic formula involved

[lean otter]

Yes, now I realize 😀

Thank you @broken yew for being patient with me and helping me out 🙂

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[mighty valve]

i cant figure this out :<

[humble venture]

does r(0) = i+j+k in your solution?

[pulsar condor]

You're right in that you simply integrate component-wise

however you have not correctly dealt w/ the constant of integration

[mighty valve]

okay so what do i do

[pulsar condor]

Given $f'(x)=x^3$ and it's known that $f(0)=1$, how would you find $f(x)$?

[flat frigate]

Mosh

[noble condor]

ok

let's see

if f'(x) = x^3

then f(x) would be of fourth degree

that is $f(x)=ax^4+bx^3+cx^2+dx+e$

[flat frigate]

sunflame

[noble condor]

if f(0)=1

$ax^4+bx^3+cx^2+dx$ when $x=0$ is 0

[flat frigate]

sunflame

[mighty valve]

so if i did plug in r(0) i would get <0, 1, -1/4> how do i add a constant to change that

[noble condor]

therefore, e is 1

[pulsar condor]

@noble condor tf

[noble condor]

what

[pulsar condor]

You took the most overcomplicated manner

[pulsar condor]

you integrate properly

what's $\int x^3\dd{x}$?

[flat frigate]

Mosh

[mighty valve]

x^4 /4

[noble condor]

oh

thx for that

I didn't learn integrals

[mighty valve]

and if f(0)=1 then the constant is 1

[noble condor]

exactly

[pulsar condor]

no

x^4/4 +C

[mighty valve]

yeah

[pulsar condor]

so f(x)=x^4/4+C

so C=1

[mighty valve]

yeah

[pulsar condor]

so the x component of r(t) is t^4/4+1

repeat for y and z

[mighty valve]

OHH

[pulsar condor]

Each integral has a different constant to account for

[mighty valve]

so y component would be ((e^t) - 1)

or wait

[pulsar condor]

$\int e^t\dd{t}=$?

[flat frigate]

Mosh

[mighty valve]

e^t + C

[pulsar condor]

and when t=0, you need e^t+C=1

so C=?

[mighty valve]

yeah the y component has no constant :(

[pulsar condor]

yeah

so you were right

[mighty valve]

its the x component needs +1 and z component need +5/4

okay ty

[pulsar condor]

you need the z component to be 1 when t=0

so just add whatever needs to be added to ensure that

[mighty valve]

that makes a lot of sense, thanks for the help

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[full fiber]

So, I know that when writing congruence statements between two triangles, the order of the vertices matters

[full fiber]

What if the triangles are isoseleces?

Do you get two separate ways to write the triangle?

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@full fiber Has your question been resolved?

[safe radish]

@full fiber Has your question been resolved?

[iron tulip]

yeah

although they end up being the same due to reflection symmetry

[full fiber]

Ok

. resolve

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[lean otter]

2a>b+c+d+e+f

3b>a+c+d+e+f

4c>a+b+d+e+f

11d>a+b+c+e+f

21e>a+b+c+d+f

41f>a+b+c+d+e

a+b+c+d+e+f=71

a=25

b=

d=

c=

e=

f=

[lean otter]

i need to solve this and i have no fk idea

need to find b, c, d, e and f

[feral linden]

It’s not a single solution

But infinitely many solutions

for example, 2a>b+c+…+f=71-a so 3a>71

Similarly 4b>71

5c>71

…

You can replace a with a’=a-71/3, b with b’=b-71/4, c with c’=c-71/5,…

You will get something like a’+b’+…+f’=a positive constant

And they are all non-negative

So part of a 5-dimensional hyperplane (in a “quadrant”)

[lean otter]

huh

im actually 14 y/o trying to understand this

[feral linden]

An example, you see this: x+2y+5z=8964, x>=14,y>=3,z>=8. It’s part of a plane (plane is of dimension 2 right?) in R^3

Just a random example

Your solutions has this form

But it’s part of a 5-dimensional hyperplane in R^6

Can’t directly calculate that for you, you need to calculate yourself

But it’s of that form

[lean otter]

huh

can u give me a answer? i need it 💀

[feral linden]

…

Okay…

a+b+…+f=71
a>=71/3,b>=71/4,c>=71/5,d>=71/12,e>=71/22,f>=71/42

Like I said , it’s part of a 5 dimensional hyperplane, infinitely many solutions

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

huh

it says wrong answer 💀

i need to put it like

A = 25
B = ...

[onyx fractal]

I think this can be answered with exact values yeah

the main thing I think is going to be simplifying the equations so that they're in terms of each other, if that makes sense

So if you have 3b>a+c+d+e+f, you can multiply the equation by 2 and the inequality still holds. So you have something like

6b > 2a + 2c + 2d + 2e + 2f

and because you know 2a>b+c+d+e+f,

it must also be true that

6b > (b + c + d + e + f) + 2c + 2d + 2e + 2f

so 6b > b + 3c + 3d + 3e + 3f

5b > 3c + 3d + 3e + 3f

so you can see we've eliminated that a term, and if you keep doing similar stuff you can eliminate more terms

[tame charm]

@onyx fractal

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@lean otter Has your question been resolved?

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[radiant jetty]

There are 10 basketball teams. Each team play each other team once. What is the probability that your team plays its rival team and last year's champions in its first two games (assume that your team and your rival's tea, were not last years champions)?

[radiant jetty]

I was thinking in perspective, your team faces 9 other teams.
_,_,_,_,_,_,_,_,_
If we specifically pick out the champions and rival team to be the first 2 (order not mattering)
and put it over the total different ways to play against the team (merging the first 2)
2 / (7!)

[tame charm]

“Last year’s champions” is referring to one team, correct?

[radiant jetty]

ye

last year champions is a team that is not your rival team and not your team but is a team of the other remaining 8

[tame charm]

Right

Ok well

First we’ll count the number of ways to face those two people first, and then we’ll worry about probability

So let’s call the rival team R and the champions C

[radiant jetty]

Right

[tame charm]

I like this drawing you have here

Ok so then we could have

C,R,_,_,_,_,_,_,_```

[radiant jetty]

You have
R,C,_,_,_,_,_,_,_ = (7!)
C,R,_,_,_,_,_,_,_ = (7!)

so 2*7!

[tame charm]

Yep

[radiant jetty]

is the total amount of ways that you can face R or C first

[tame charm]

I think that’s all we need for the top

Now the total number of ways is 9!

So the probability is…

[radiant jetty]

2*7!/9!

[tame charm]

Yep

And simplified, that is…

[radiant jetty]

2/9*8
= 1/9*4
= 1/36

[tame charm]

Yep, that’s it

Nice

[radiant jetty]

thank you

I have one more question if you don't mind

[tame charm]

Go ahead

[radiant jetty]

If 5 red balls, 4 black balls, 4 white balls are randomly placed in a row what is the probability that the balls at each end of the row are the same colour?

_,_,_,_,_,_,_,_,R,R,R,R,R = 8! * 5!
_,_,_,_,_,_,_,_,_,B,B,B,B = 9! * 4!
_,_,_,_,_,_,_,_,_,W,W,W,W = 9! * 4!
is what I'm assuming and total is 13!

I'm assuming it matters if the R,R,R,R,R are in diff orders?

I'm not sure how to deal with this

[tame charm]

The drawing should be
R,_,_,_,_,_,_,_,_,_,_,_,R
B,_,_,_,_,_,_,_,_,_,_,_,B
W,_,_,_,_,_,_,_,_,_,_,_,W

[radiant jetty]

How come?

[tame charm]

Oh wait

I thought it said “ends of the row” nvm

[tame charm]

Yeah the question is ambiguous here

Not sure if order matters within the same color

[radiant jetty]

The answer is 11/39

I'm just not sure how to get to it

I believe there was a way to remove "duplicates?

in a word like "DATA"
the amount of unique 4 letter permutations would be
4! / 2!

which would be 12

2! for the 2 "A's"

[tame charm]

Ah yeah

That makes sense why it’s not 1/something

Ok so order doesn’t matter

[radiant jetty]

but the thing is if the end 5 is in a diff order but all same color it's okay

and then the front doesn't matter

[tame charm]

8!/4!4!
9!/5!4!
9!/5!4!

[radiant jetty]

maybe
_,_,_,_,_,_,_,_,R,R,R,R,R = 8!/(4!*4!) * 5!
_,_,_,_,_,_,_,_,_,B,B,B,B = 9!/(5!*4!) * 4!
_,_,_,_,_,_,_,_,_,W,W,W,W = 9!/(5!*4!) * 4!

do I not multiply by the factorials in case they are in diff orders

[tame charm]

Don’t multiply by the factorials at the end

[radiant jetty]

Righht ok

So 13! should be
13! / (5!4!4!)

instead

[tame charm]

Yeah

This didn’t seem to work out

Hmm

[radiant jetty]

Ye i'm not sure

this is a little difficult

I'll just ask my teacher later

thanks thoughh

.close

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[radiant jetty]

9 people are on a volleyball team, 6 are on court all time. If starting-line are randomly selected, what are the odds that the captain and both vice captains will start the game?

[radiant jetty]

The answer is 5 : 16

nvm

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[whole gorge]

For what values of k is this system compatible (rank of coefficient matrix = rank of augmented matrix = number of variables or rank of coefficient matrix = rank of augmented matrix < number of variables)?

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@whole gorge Has your question been resolved?

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[winged inlet]

not sure how to do b

[safe radish]

@winged inlet Has your question been resolved?

[winged inlet]

<@&286206848099549185>

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@winged inlet Has your question been resolved?

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[spring frigate]

In a different GIS-task you mapped an area that is frequently flooded from
a nearby river. You know that your Digital Elevation Model (DEM) has some
uncertainties in the height accuracy, which is expressed as Root Mean Square
Error (RMS). These uncertainties influence the calculation of height
differences. If you have two pixels, pixel_1=10 m and pixel_2=20 m, what is
the range of height differences if your DEM has a RMSE in height of:
0 m
3 m?

[spring frigate]

Hey guys, Could you help me with this question? To be honest, I'm not that familiar with the RMSE formula, so that's why I'm confused..

ranges I've found are like this:
For actual value=0; 7 < x < 14
For actual value=3; 5 < x < 12

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[spring frigate]

<@&286206848099549185>

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@spring frigate Has your question been resolved?

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[lean otter]

can someone wsalk me through

[lean otter]

i dont really remember

i think one side is a conjugate

like the a+bi

actually nvm

its the cartesian point

oh yeah

its the cos theta+ i sin theta thing

but isnt e^pi i /2 just i

oh so a is 0 and b is 1

thanks

!close

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[drifting cairn]

hello

[drifting cairn]

another quick question:

im unsure if what i did in f(u) was right

because i switched x^2 dx of 1/6du which are equal algebraically

but x^2 was being multiplied to to u^2 (2 +2x^3)^2

i dont know if i missed a step

or did the f(u) part wrong

nvm i got it

.close

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[oak storm]

yo how do you translate y=x²+3x+4 with (0 2)

[oak storm]

oh sorry (2 0)

Here

[pulsar condor]

So move it two units to the right?

[oak storm]

ye but how?

[pulsar condor]

Same way you do any other horizontal translation

[crisp linden]

https://tenor.com/view/just-do-it-shia-la-beouf-do-it-gif-4531935

[oak storm]

really

[pulsar condor]

Yes

[oak storm]

hold on a sec

is it x²-x+2 ?

[crisp linden]

yes

Though I don't know why you put it in the canonical form

[oak storm]

idk that's how I got the question

[pulsar condor]

$f(x-c)$ is $f(x)$ translated c units to the right

[flat frigate]

Mosh

[oak storm]

i was confused myself

thank you anyway 🙂

[crisp linden]

Mosh just gave you the method for translating any function horizontally

Compute that, put it into the standard form for polynomials

and you get the answer

[oak storm]

alright

thats cool thank you so much

have a very nice day

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[visual snow]

What happened here?

[pulsar condor]

double angle on sin(4x)

[visual snow]

kk

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[visual snow]

.reopen

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✅

[visual snow]

.close

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[lean otter]

how can i determine all functions that satisfy this and it says f(1)=2

[lean otter]

heres the work

[broken yew]

You can at least make a guess at a certain class of f which satisfy that equation

[lean otter]

i made it was exponencial but idk how to prove that

[broken yew]

its just a suggestion

so you can write down some f which work

[lean otter]

okok

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[spiral pine]

I was told the moment of inertia of a sphere is only an approximation, how come?

[pulsar condor]

context?

[spiral pine]

Hmmm hard to give since I don't really know what context to give

[pulsar condor]

who's saying it's an approximation?

[spiral pine]

a friend

[pulsar condor]

/ what are they saying is being approximated?

[spiral pine]

something with the radius having a small something

[unique cypress]

Unless its a perfect sphere using the formula it is an apporox? Maybe that?

[spiral pine]

I forgot the names in english

[old reef]

..

Anyone wanna help me ?

[spiral pine]

When deriving it

[pulsar condor]

yeah idk what you're reffering to

[spiral pine]

Don't think so but that would be true

[unique cypress]

? This is his channel rn

[pulsar condor]

Like obviously to find the MoI about the central axis, you pick infinitesimal dm elements and then integrate over the sphere

[old reef]

Well can u help me in my channel ? ☺️

[spiral pine]

Mol?

[pulsar condor]

Moment of Intertia

[spiral pine]

oh

[pulsar condor]

Didn't want to type it all out

[spiral pine]

np

[old reef]

U call Moment of inertia "I" not mol

[spiral pine]

He knows

@pulsar condorSo like the approximation is just the inifini small dms?

[old reef]

I do now

[spiral pine]

Could that be what he was reffering to?

[pulsar condor]

Cool, now wait for someone to offer to help you

I mean you model it as a sum of infinite point masses, then integrate over the collection of them iirc

[spiral pine]

iirc? sorry .-.

[pulsar condor]

if i recall correctly..

[old reef]

Tf are those abbreviations? Lol

[pulsar condor]

Didnt ask the peanut gallery

If you don't have anything actually useful to say, don't comment.

[spiral pine]

thanks

everyone

.close

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[gentle wagon]

Help

[gentle wagon]

Hi, have an old test paper here and I understand this question but in the equations written the second equation why is there 0.34 x 100

Please ping if you know

Like can't you just combine that

<@&286206848099549185>

[pallid nymph]

100 kg of 34% strength

[gentle wagon]

Yes but can't you just combine this

[pallid nymph]

so 0.34 * 100 is the amount of acid

[gentle wagon]

Would it be ok if it was written as 0.3x + 0.4y = 34

Or is that wrong

[pallid nymph]

hmm

0.34 * 100 = 34

[gentle wagon]

Yeah

[pallid nymph]

so theyre the same

so i see no issue

[gentle wagon]

Alright

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[lean otter]

what am i doing wrong

[lean otter]

im trying to integrate using the integration by parts method

[kind fractal]

Hello, you should do that multiplication inside the second integral of the first line

Then it's just the integral of a power function

[lean otter]

oh wow im dumb

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[lean otter]

hey

[lean otter]

so if i have an inverse function like instead of y = sinx, x = siny ( if that’s right) how do i do implicit differentiation?

is it just 1 = cosy * dy/dx? if yes, what’s y to replace it

is y just y = sinx?

[peak carbon]

you want to implicitly diferentiate in respect to what?

[crisp linden]

if $y = \sin x$, $x \neq \sin y$

[flat frigate]

Remavas

[crisp linden]

You can see that very simply

The range of sin is [-1;1].

[lean otter]

waiiit

[crisp linden]

as you see

totally different

[lean otter]

oh so how do u do inverse sin

[crisp linden]

google inverse sin

[lean otter]

derivative

[peak carbon]

can't really

you have to restirct the domain

[crisp linden]

but he wants an inverse function

so it needs to be restricted anyways

[lean otter]

help

[lean otter]

how to get derivative of inverse sin

[peak carbon]

i think thats a table derivative

[crisp linden]

it is

[crisp linden]

If you googled inverse sin

You should've found that the inverse function of sin is called the arc sine

$\arcsin x$

[flat frigate]

Remavas

[lean otter]

yes

i’m asking about the derivative

[crisp linden]

It's a table derivative usually

Else, https://www.cuemath.com/calculus/derivative-of-arcsin/

[peak carbon]

https://www.derivative-calculator.net/

i use this

[crisp linden]

I mean, the derivation is pretty interesting though

Basically an application of the formula for inverse function derivatives

[peak carbon]

i hate analysis xd

[crisp linden]

Apropos analysis, I have a calculus test tomorrow

I guess this counts as studying

[peak carbon]

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

[peak carbon]

it sure does

[lean otter]

.close

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[crisp linden]

although it is about integrals

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[lean otter]

given function f(x) = (log2(x)+x) / (x/b + 2*b) what could be the way to specify 'b' that maximizes f(x)?

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

whatever

.close

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[delicate lark]

would this be (b), 6?

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[fervent ermine]

show that

[fervent ermine]

$ln(1+x)<x$

[flat frigate]

Bread

[fervent ermine]

Whenever x>0

So I know I have to define the function on the continous interval [a,b] and the differentiable interval (a,b)

The value of a would be 0 what value of b should I use?

[light shoal]

it's equivalent to $1+x < e^x$, which is true because the LHS is just the first two terms of the Taylor series for $e^x$, and the terms are all positive

[flat frigate]

OurBelovedBungo

[safe radish]

@fervent ermine Has your question been resolved?

[fervent ermine]

right so I can use basically any x as B is that correct?

[fervent ermine]

I am unsure what the talor series is as I haven't learnt it yet. do you care to elaborate?

[north rapids]

Not so necessary for figuring this specific thing out, but a Taylor series is an infinite sequence of polynomial expressions which when added together equal non-algebraic functions like e^x or trig functions (or ln(x+1))

It replicates the value of every order derivative of a function in order to get a curve that more and more closely resembles that function, sometimes only up to a certain range

[fervent ermine]

ok thanks lawyer

[north rapids]

If you want some reading maybe check out Paul’s https://tutorial.math.lamar.edu/classes/calcii/taylorseries.aspx, and there are a ton of YouTube videos and other things out there

[safe radish]

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[fervent ermine]

,close

[fervent ermine]

.close

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[jade gust]

So how do i properly answer these questions

[pulsar condor]

Check if they're closed

[jade gust]

right so do I just insert random values into them

[pulsar condor]

No, you argue of they're closed or not

If you claim they arent closed, then you give your counterexample

[jade gust]

okay but how do i show if they're closed or not

i mean how do i begin my argument

[pulsar condor]

Oh you mean that

Then yes, play around

[jade gust]

ok cheers

.close

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[jade gust]

.reopen

[safe radish]

✅

[jade gust]

actually i might keep it open cause 3rd one might cause me problems

ok ye so how do i begin with the 3rd

[uneven agate]

where is this from and what do you need help with

[jade gust]

I'm reading Abstract Algebra by Pinter

because why not

What else would a highschool student do

[pulsar condor]

Well trivially you'd require a*b=+-ab

[jade gust]

oh right

[pulsar condor]

So it's not an operation, cause it gives 2 values

[jade gust]

right makes sense

ok cool

thanks

.close

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[jade gust]

(i reworded the questions so don't worry i know there's some mistakes)

[safe radish]

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[ember sphinx]

erm

u learnt laws of logs

[kind river]

only a bit of it

[ember sphinx]

Ok well with logs you can bring what ever is infront of the log into the log by putting it as the power

so instead of 3log2

it can be log(2^3)

which is the same if you put it in ur calculator

so you can do this for both logs

so you will have log(2^3)+log(3^2)

that is just log(8)+log(9)

and when you add logs, you times by them, opposite of powers

so it will be log(8x9)

which is log(72)

72 is your answer

<3

[kind river]

oh reall thank you very much appreciated you explained it soo good can you also help me with one more aswell

[ember sphinx]

Yea sure

send it

[ember sphinx]

do you know how to 'take logs of both sides'

or shall i show

[kind river]

i dont think do you add them

[ember sphinx]

Not really

we are just kind of changing them

[kind river]

alright makes sense

[ember sphinx]

ok

so basically

can you tell me what log(100) is if the base was 10

well it would be 2

because

10^2=100

[kind river]

alright i understand

[ember sphinx]

thats what log is basically it tells you what the power is in order for us to get that number

so now u take logs

so log(10^x+1)=log31.62

but as previously stated

we can do (x+1)log10

because its the same

like we did in your previous question

and we know that log10 is just 1

so x+1=log31.62

x=(log31.62)-1

and put that in your calc to get x

[kind river]

so i should put x=(log31.62)-1 inside a calculator

[ember sphinx]

yes

[kind river]

its not letting me calculate it i think its because im on the google

[ember sphinx]

ill do it for you

x=0.4999

but since its says 1dp

its 0.5

[kind river]

ahhh i get this now thanks is this lal

akk

all

[ember sphinx]

.close

i think u need to do

idk

[kind river]

oh yeah i do thank you very much you helped me understand this thanks

.close

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[terse basalt]

Hello, I'm not sure how to start with this problem. This field is not conservative so how do I go about solving the loop integral?

[terse basalt]

We are studying multivariable conservative fields and 2d curls.

<@&286206848099549185>

[safe radish]

@terse basalt Has your question been resolved?

[safe radish]

@terse basalt Has your question been resolved?

[safe radish]

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[lean otter]

How would I write down the division of 2 different shapes' volumes? For example the V of a cylinder and the V of a cuboid

[lean otter]

assume the cylinder is just dh and the cuboid is whl

[upper folio]

what do you mean?

as in the ratio of the 2 volumes?

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

no just

um

idk how to explain

[upper folio]

do you have the question?

[lean otter]

how do i shorten this down

like this little fraction

or more like

how do i expand it

to 2 V's

how do I have 2 variables corresponding each of these

and what would they be

[upper folio]

i'm confused do you have the whole question?

[safe radish]

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[kind dove]

can someone help me with order of these permutations ?

[remote hamlet]

Could you send the main question, for more clarity?

[kind dove]

its not in english

[remote hamlet]

What language is it written in?

[fiery merlin]

@kind dove Order in the sense of how many times you need to apply it to get to the identity permutation?

[kind dove]

But i need to find out order and parity of permutations in the set and then check if set H is subgroup of S_4

[kind dove]

im struggling with the composition

[fiery merlin]

OK, what does (123) mean?

1 → 2
2 → 3
3 → 1

or

1 → 3
2 → 1
3 → 2

[kind dove]

first

[kind dove]

Slovak

[fiery merlin]

OK, so let's start with id.

How many times do you need to apply it so that:

1 → 1
2 → 2
3 → 3

To find out, let's apply it.

[kind dove]

how to work with id ?

[fiery merlin]

We have:

1, 2, 3

id takes 1 to 1, 2 to 2, and 3 to 3, so you get:

1, 2, 3

[kind dove]

when there are no number ?

[remote hamlet]

So, to recap, H is a subset of S_4

Are you familiar with the notation (12), for instance?
I.e., do you know that it is used to denote a bijective function of the set {1,2,3,4} into itself?

[kind dove]

isnt id of order 1

[fiery merlin]

id replaces each number with itself.

Yes, the order of id is 1 because you get back 1, 2, 3 immediately.

Let's try (12).

1, 2, 3

becomes

2, 1, 3

Does that make sense how (12) does that?

[remote hamlet]

If you are aware that each (12), (123) and so on, represents a specific function from {1,2,3,4} into itself, then you just need to be at your ease composing two functions together

[kind dove]

how doo you know that id has 1, 2, 3 numbers ?

[fiery merlin]

No, you start with 1, 2, and 3.

Forget the permutation.

You have those numbers

1, 2, and 3, in that order.

1 becomes 1 in id.

2 becomes 2 in id.

3 becomes 3 in id.

So, after apply id to 1, you have:

1, ⋯

After applying id to 2, you have:

1, 2, ⋯

After applying id to 3, you have:

1, 2, 3

[kind dove]

uhm

[fiery merlin]

Does it make sense how I start with 1, 2, 3 and apply id to each of them in turn?

[remote hamlet]

Anyway, for completeness sake, note that, for instance, the function represented by (123), is exactly
1 -> 2
2 -> 3
3 -> 1
4 -> 4

[kind dove]

but i think there should be also 4 included, because we are working with S_4

[remote hamlet]

Also 4 is relevant, if you are in S_4

[fiery merlin]

OK, so include 4.

1, 2, 3, 4 becomes 1, 2, 3, 4.

With id.

[kind dove]

ok so id is order of 1

[fiery merlin]

Right.

So, let's apply (12).

1, 2, 3, 4 becomes what?

[kind dove]

then (12) (12) = id

[fiery merlin]

Right.

Just to check, you applied (12) to each number in turn and then did it again?

[kind dove]

yes

[fiery merlin]

So, the order of (12) is 2 because order means how many times to apply it to get the identity.

[kind dove]

i did it from right to left

[fiery merlin]

Right to left?

[kind dove]

yes

[fiery merlin]

Like the right (12), then the left (12)?

[kind dove]

yes

[fiery merlin]

OK, so what about parity?

[kind dove]

its number of inverses i think

[fiery merlin]

For that, you apply the permutation once, then you swap 1 into its correct place if it's not there. You swap 2 into its correct place if it's not there already, and so on. Then, the parity is just whether you did an odd or even number of swaps.

Like you go from 1, 2, 3, 4 to 2, 1, 3, 4.

Then 1 isn't in its right place, so you swap it to get 1, 2, 3, 4, and that has everything where it goes.

So, the parity is odd.

That's because you needed one swap.

[remote hamlet]

Do you only know parity defined through number of inversions, Michal? There are also some equivalent ones

[kind dove]

i know the definition only using inversions

but it need to look at it more

[remote hamlet]

Alright

[kind dove]

then the (13) will be same as (12)

but with even parity

am i correct

?

[fiery merlin]

Why even?

[kind dove]

hmm

[remote hamlet]

What sign did you get for (12) already?