help-0

[dusk wedge]

Hey, just a quick question, is it possible to compute the eigenvalues of a matrix A = x \ocross x, where \ocross is the outer product, but without having to compute A (can be quite large).

[median tendon]

What other forms can we use it on?

[vale wigeon]

1/x is not defined for all real x. your example does not work.

[tough hatch]

you can't use lhopital's in the first place if f or g is not differentiable, lol

[vale wigeon]

(II) is not true. take f = 0 and g = any discontinuous function you want

[median tendon]

Ann i think he was providing an example to show that II was wrong

[pearl marlin]

Take sinx and 1/x

[vale wigeon]

learn4math, 1/x isn't defined for all real x.

you cannot have it be one of the functions for the purposes of this problem.

@dusk wedge sorry, this channel is busy right now. please move to a different questions channel or #linear-algebra.

[pearl marlin]

Counter example for 2nd

Ops i made mistake

G is not continuous every where

Apology

[dull onyx]

are u guys still using this channel

[tough hatch]

apparently not

[leaden thicket]

can anyone help me for this question please with solution

[sage bronze]

Use the identity $1+ tan^2 (x) = sec^2 (x)$

[ocean seal]

HELLOBELLO

[leaden thicket]

than?

[slate heron]

do you know how to subtract fractions?

[leaden thicket]

ya i think

[sage bronze]

Then do it with this

$\frac {tan^2 (x) - ((sec(x) \times (sec(x) +1)}{(sec(x) +1)}$

[ocean seal]

HELLOBELLO

[wild marten]

$\tan^2(x) +1 = \sec^2(x)$

[ocean seal]

Beluga

[sage bronze]

.

@wild marten

[wild marten]

I just gave a hint above

[sage bronze]

Ok

[wild marten]

oh wait, it does not work like that, answer could be -1 or tan^2(x) - sec(x)

@sage bronze

[sage bronze]

Its -1 ithink

[wild marten]

yeah, but its confusing. According to your bracket placement it is tan^2(x) - sec(x)

[fleet marsh]

should i be solving the de with separation of variables and then setting that solution equal to the kx*arcsin(x) expression and solve for k?

[vale wigeon]

no you're way overthinking it

just plug in y = kx arcsin(x) into the DE and solve for k

@fleet marsh

[fleet marsh]

omg

right

tyvm

[leaden thicket]

is it really you ?

[wild marten]

no lol

check my about

[leaden thicket]

Oh

[ancient bear]

Why do we write Ax + B and Bx + C instead of A and B like with the case of linear factors?

Is it because it's one degree lower...

Huh

[surreal meadow]

because B may not equal C

wait i misunderstood the question

Ax + B and Cx + D
instead of
Ax + B and Bx + C

[tough hatch]

because when we combine the dissimilar fractions, we multiply both numerator and denominator of either fraction by the denominator of the other fraction

which would indeed result in having not just the same denominator for both fractions but also a third-degree polynomial in the numerator

[ancient bear]

ohhh

in other words

so that these when multiplied give us the 3rd degree polynomial that we see on the left

got it, thanks

[hardy vault]

can someone help me

[tough hatch]

no

you still have to add the (now similar) fractions

[ancient bear]

yes, I know, but adding them won't change the degree

[tough hatch]

it won't, but (Ax+B)(x^2+2x+5) is not equal to x^3+5x^2+6x+21 contrary to what you said

not necessarily, at least

[crystal steeple]

hey fellas

im kinda dumb

but i need to find x

this is the last step

and heh

im asking in a diffrent channel

[tough hatch]

@crystal steeple btw stick to one channel lol

ok lemme help you with that

[crystal steeple]

oh ok

[tough hatch]

do you know how to deal with logarithms?

[crystal steeple]

yeah

but no matter how i try i cant do this

[tough hatch]

can you rewrite that equation as a logarithmic one?

[crystal steeple]

no.....

[tough hatch]

for example

2^x = 4

how do you turn this into a logarithmic equation?

log_base (result) = exponent/missing power

[crystal steeple]

ok so once i turn this into log

[tough hatch]

can you?

[crystal steeple]

yeah

i can

i did

[tough hatch]

so write it out here

[crystal steeple]

this?

[tough hatch]

no

[crystal steeple]

oh

[tough hatch]

is 8/10 the exponent of 9/10?

[tough hatch]

^

[crystal steeple]

OO

OK NVM

THNK U

but how do i put it in a calculator

[glass lichen]

If you have a log base button... or change of base

[crystal steeple]

im using casio 570 ms

[tough hatch]

find the button named log

[crystal steeple]

yeah found it

@tough hatch

[plucky crow]

the direction vector AB is -3, 5, 10

right

so for part c

c + ab = d

[tough hatch]

?

[plucky crow]

oh its taken

my bad

ill wait

[crystal steeple]

i clicked the log button

[tough hatch]

lol no need to ping me

ok

channel is free

[plucky crow]

@crystal steeple if you do 2^log2 it cancels,

so just use that logic

[tough hatch]

they just wanted to notify me.

i digress

[cosmic geyser]

smallest whole number than be split into 25%, 35% and 40% (whole number)

[fluid ember]

20

[wispy olive]

Can we? If yes, then how? If no, then why?

[topaz scaffold]

Yes

[amber urchin]

Hint : Area of a triangle is half of length of a side times the altitude

[topaz scaffold]

For the second one use Herons formula

Or actually just use Pythagorean theorem

[vale wigeon]

it's ||impossible. imagine dragging the apex of the triangle parallel to the base as far as you want in either direction; the height stays the same, and so does the area, but the perimeter can be made arbitarily large||

[wispy olive]

Heron's Formula?

[topaz scaffold]

Oof

[tough hatch]

[vale wigeon]

heron's formula lets you find the area of a triangle in terms of its sidelengths

[topaz scaffold]

My brain ain't working, sorry

[vale wigeon]

it's somewhat unwieldy unless it really is all you have to work with

[wispy olive]

I do not understand the big words you used.

[vale wigeon]

which big words?

[tough hatch]

triangle wasn't given to be a right triangle

[amber urchin]

I dont think you can find perimeter, knowing only 1 side and 1 altitude

[wispy olive]

Yeah exactly.

[topaz scaffold]

Yea you cant

[wispy olive]

But maybe I can.

[vale wigeon]

which big words, senku ishigami?

[wispy olive]

No?

Reason/s?

[wispy olive]

Well.

[topaz scaffold]

If there was more info

[wispy olive]

Apex, arbitarily large.

[vale wigeon]

i am happy to explain what i meant, but i do not know which part(s) of what i said you don't understand.

[amber urchin]

Not enough data maybe, unless I missed out on smth

[wispy olive]

And I am lazy to google it.

[vale wigeon]

"apex" in this case just means the vertex opposite to the fixed-length side.

i.e. it's the vertex from which you would drop the altitude.

[wispy olive]

Oh.

[wispy olive]

Okay.

I see.

[vale wigeon]

"arbitrarily large" means "as large as you wish" or "larger than any number you could give me"

[wispy olive]

You have to make another point for it in 1 of the sides on the triangle?

[vale wigeon]

what?

what are you talking about?

[wispy olive]

Les say

Triangle ABC.

And les say

We take the height from angle A.

So it has to land somewhere on angle BC.

So that point.

Will be the apex?

[wispy olive]

Oh. What is it?

[vale wigeon]

there's something to be noted here

the altitude need not land on the side BC itself

[wispy olive]

Woah this is SICK!!!!

[vale wigeon]

it is extended until it meets the straight line which contains BC

[wispy olive]

But big :|.

[vale wigeon]

that is how you determine its length

[wispy olive]

Yes.

I mean thaat.

[vale wigeon]

here is an illustration, albeit using different notation than you.

[wispy olive]

Hmph?

[vale wigeon]

dragging C along this horizontal line will not affect the area of the triangle, no matter how far you go

however, the perimeter of the triangle will increase, as should be obvious.

also, regarding heron's formula

[wispy olive]

Would not it be this line?

[vale wigeon]

i did say this

[wispy olive]

?

Sorry I am dumb.

[vale wigeon]

yes, what you have drawn is an altitude.

[wispy olive]

Oh.

LMFAOO you just agreed that I am dumb.

https://tenor.com/view/kekw-kek-bttv-twitch-emote-gif-15123134

[vale wigeon]

here is what an altitude may look like for a very 'stretched-out' triangle, for lack of a better word.

[leaden thicket]

can you please help

[wispy olive]

Wow you were so smart in 8th grade then @vale wigeon ?

[vale wigeon]

eh?

[leaden thicket]

can you please help?

[wispy olive]

So you were very smart and intelligent in 8th grade itself?

Noice.

[amber urchin]

A+B+C = 180 degrees
B+C = 180 - A
(B+C) /2 = 90 - A/2

I dont remeber what exactly sin(90-A/2) is, but there may be a table on which one would that be

[vale wigeon]

did i say so at any point?

[leaden thicket]

a/2 is in all options

[wispy olive]

Um no?

But you agreed that I am dumb.

[vale wigeon]

i didn't??

[amber urchin]

There is a table what sin(90-x) is equal to

[leaden thicket]

sin(90-a/2) = cos(a/2) ithink

[wispy olive]

So I interpret from that information that you were very smart and intelligent when you were in 8th grade.

[leaden thicket]

sin(90-x) = cos (x)

[wispy olive]

Yes you do?

[amber urchin]

Then I guess that would be the answer

[wispy olive]

Anyway.

This is not the point.

[vale wigeon]

the "yes" does not apply to your calling yourself dumb.

[wispy olive]

Just appreciated you anyway.

[vale wigeon]

if it did, i would have said "yes, and what you have drawn is an altitude"

[leaden thicket]

yeh cos a/2 is answer, thanks

[vale wigeon]

but the lack of this and changes the meaning of my sentence enough to make it so that i take no stance at all on your dumbness, senku.

[wispy olive]

Wow.

Serious grammar.

I do not mind anyway bruh.

[pallid sail]

gamer even if she meant it u shouldnt get offended

this is the internet

[wispy olive]

Yeah exactly.

That Is why I said.

I do not mind anyway.

[pallid sail]

like anonymity allows people to say whatever they want

[wispy olive]

And I am dumb, even I know Lmfaoo.

[vale wigeon]

i don't appreciate having words put in my mouth, i will say that much

[wispy olive]

Sorry Ann.

I will just ask normal questions from now.

Thank you for the help.

[plucky crow]

1 mark??

i did it using the cross product

since its 1 mark there must be an easy way to do it right

that im missing

[surreal meadow]

yes, using the cross product

[plucky crow]

is there no other way

[gray isle]

consider certain properties of a parallelogram

and you should be able to get the area from something you obtained earlier

[plucky crow]

oh

hahaha

yeah i see

now

[surreal meadow]

did you do the area of the parallelogram/2 for part b?

[plucky crow]

no i did 1/2ab sinc

and i found the angle c using the dot product

truth is the cross product isnt even in my course xdddddd

[tough hatch]

they just gave u what u need lol

[plucky crow]

yes i realized that

[fading solar]

Please tell me
Sec theta + tan theta =x, then what is relation of sec theta - tan theta in terms of x

[leaden thicket]

can you send screen shot please?

[topaz scaffold]

You could add the 2 equations to get that 2 sec theta = 2x

Oh shoot nvm

[topaz scaffold]

Dont do that

There's an identity that's pretty close to the equation

[fading solar]

Tan^2 theta + 1= sec^2 tbeta

*theta

But i am not getting the answer

[topaz scaffold]

Yep

Use difference of squares

[fading solar]

Okk

[alpine sable]

Can somebody help me on this one?

I need to find the vector which is a linear combination of x1, x2 and x3

[alpine sable]

UP

[lusty plaza]

what have you tried?

[alpine sable]

i computed all the combinations of x1, x2, x3 and the other ones in an online calculator, and all of them are linearly dependent

[lusty plaza]

surely your textbook or teacher taught you a method for finding linear cominations of vectors?

[alpine sable]

im studying on my own

[lusty plaza]

https://www.youtube.com/watch?v=miih2rwEiOc

[winter mango]

i cant figure out a way to do this without just trying all the combinations in the answers

and seeing which ones don't have contradictions

[weary hazel]

??

[winter mango]

maybe you can do a matrix with a determinent of 0?

[alpine sable]

It would be a 4x3 matrix

[glass lichen]

the co-efficient matrix will have det of 0 by FTIM since it's somewhat implied {x1,x2,x3} isnt a basis of R^3

[alpine sable]

ohh got it

x3 is a combination of x1 and x2

then i can do a matrix with x1, x2 and the other

since x3 was the linearly dependent term, it was obscuring the result

[winter mango]

yeah

3*3 matrix which seems more solvable

determinant 0 and solke mb?

solve*

[alpine sable]

Answer is letter C

All the others span R3, so they are independent, and only C spans R2, so it is dependent

[winter mango]

@alpine sable you have the solution on paper?

like with the method and stuff, wanna practise some vector stuff

[alpine sable]

hold up

I just tested all matrices until one was = 0

[winter mango]

ye

was wondering if there was like

a more systematic solution

like using a b c as the third vector

but this is simple enough

thanks my dude

[alpine sable]

To find the dependent vector you could make a system with the 3 eq if you didnt figure out just by looking

[winter mango]

sounds reasonable

[alpine sable]

No problem my man

[north goblet]

i have this issue. gotta find AD lenght.
It's not that hard as a problem i think but don't remember the formulas or the theory.
Anyone knows what can i look up for ?

i don't even know what to look for tbh

maybe doing a proprotion with the angles ?

[wary stream]

First, is this drawn to scale, because that 45 degree angle looks really wrong

And that is not the best way to denote 90 degress

[north goblet]

Ofc is not to scale as it doesn’t really matter

As well as u denote the 90degrees

How that even matter ? Lol

[wary stream]

It does matter because if you labeled that angle as 45, then the other angle at point D is 135 degrees and that does not work at all

[north goblet]

ADB is 45•

Mb

[wary stream]

And for this, the convention is to denote like this, with the square looking symbol, not an arc

[north goblet]

ok, can u help me with the data btw ?

or just wanted to act smart ass ?

[wary stream]

I had to get it the correct info first

[north goblet]

so, what can i look up for ? what formulas ?

[unborn dome]

can someone help me out with this question?

i know one of the answers is 6arcsin(5/8) / pi
but I'm not entirely sure how to get the second answer, do I just do the same thing but 6 - 6arcsin(5/8) / pi to have arcsin by itself?

[obsidian cave]

Of the lower triangle, you have all 3 angles, and one side length, you can use the sine rule

[ionic jewel]

if ADB is 45 degrees, then so is ABD, hence AD is the same length as AB

[obsidian cave]

Actually, the triangle is 90° 45° 45°, it's isosceles, AD = AB

Yeah what they said

[unborn dome]

uh should i take my question to another channel?

[wary stream]

Yes

[unborn dome]

gotchu

[wary stream]

An inactive channel

[north goblet]

ok let's do a step back because in scale u can see what i mean

difficult

to write on pc

draw*

the scale is around the height being 6 times the base

[wary stream]

Since triangle ABD has a right angle and angle ADB is 45, you can conclude that angle ABD is also 45

Therefore making it isosceles

[vital sleet]

If you are using chain rule here

what happened to the tan in the 2nd time differientating the inside?

[wary stream]

Ask in an inactive channel

[vital sleet]

oh wait

this isnt inactive

mb

[north goblet]

????????

u cannot conclude that what the heck

u can even see it

[wary stream]

Yes you can

[north goblet]

all right i understand gonna move to someone that knows what is talking about

[wary stream]

Sum of angles in a triangle equals 180

[unborn dome]

woah

[vital sleet]

what kind of question is this

[unborn dome]

@north goblet calm down, all you do is play arknights man

we gotta evaluate math step by step

[wary stream]

So 180 - 90 - 45 = 45, therefore ABD is 45 degrees

[wary stream]

I know what I'm talking about, you don't apparently

[obsidian cave]

Not to make anything bigger than it is but it's so funny to me that a person joins a math help server, gets told a triangles angles sum to 180, then just denies it and leaves

[unborn dome]

@obsidian cave what do you mean the earth is obloid and not flat? blasphemy I say

[frail gulch]

lmao what is going on in this channel

[ripe mountain]

How do you make a 3d function of 2 variables that has at one point a minimum in one direction and a maximum in another direction

[thorn kindle]

On an obloid earth the angle sum of the triangle is 270

[unborn dome]

lmfaoo

[thorn kindle]

Or it can vary actually. It just has to be greater than 180

Angle sum on a sphere is 180(1+4f) where f is the ratio of the enclosed surface area to the area of the sphere

So if f is small it approximates euclidean geometry

[thorn kindle]

log_a(b) = log(b)/log(a)

[nova heart]

okay, i feel like this should be easy but im so confused
i've got a table of user's percentage who use certain programming language
how can i know the given population out of it?
for example c++ is used by 12%, c# by 3% etc etc

[ionic jewel]

and what do you want to find?

if you know the total population you can just multiply it by the percentage

eg if 150 people took your survey, 150*0.12 use cpp

[winter token]

I am not sure if high school level stuff is allowed here but I need some help with this!

I need to find the inverse function of this, but I have trouble solving it for x... Can somebody help me?

[jagged imp]

high school stuff is most of what populates these channels so its definitely allowed

what have you tried so far?

[ionic jewel]

x = ln(e^x)

may help to condense into one log

[winter token]

I played around with properties of logarithms and exponents to see if I could get anywhere but I keep getting stuck...

I simply rewrote the function in different ways like

e^y = (e^x)/ (e^x-1)

And much much more forms that wouldn't help me get anywhere

[ionic jewel]

,w inverse of y = x - ln(1+e^x)

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by 兔子#6562

[winter token]

I'm convinced that wolfram alpha is wrong here, If you put both functions at desmos you can tell that is not the correct inverse

[ionic jewel]

,w simplify e^x/(1+e^x)

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by 兔子#6562

[ionic jewel]

ah there we go

[winter token]

According to my book the correct answer is f(x)=ln(e^x/1-e^x)

[ionic jewel]

this only has one variable, and should be easy to invert

i knew that simplified somehow

[winter token]

but I can't myself get to that

[ionic jewel]

divide each term by e^x

once you get them all in one log

$y = \log\frac{e^x}{1+e^x}$

[ocean seal]

bunny

[ionic jewel]

multiply the fraction by e^(-x)/e^(-x) to get what Wolfram gave you for simplification

can you get the rest @winter token

[winter token]

Hope so, wish me luck :Ρ

[ionic jewel]

i can latex it all out if you need, ping if you do

[winter token]

latex?

[ionic jewel]

the typesetting

[ionic jewel]

like this

[winter token]

That would help yeah

I am just kind of lost on where I start in this I don't need the entire procces

[ionic jewel]

okay one sec

[winter token]

$e^(x-y) = 1+e^x$

[ocean seal]

-KlariNoX-

[ionic jewel]

wait what is this

[winter token]

This is as far as I got, (x-y is an exponent)

[ionic jewel]

i dont think we want this

no we dont

ok here we go

Original thing is
$$y = x - \log(1+e^x)$$
right?

[ocean seal]

bunny

[winter token]

yes

[ionic jewel]

do you agree that is equal to
$$y = \log\frac{e^x}{1+e^x}$$

[winter token]

I need to solve that for x to find the inverse function

[ocean seal]

bunny

[ionic jewel]

using log rules

[winter token]

Uhh... which rule is being used here?

[ionic jewel]

$x = \log(e^x)$, then using that $\log(a) -\log(b) = \log(\frac ab)$

[ocean seal]

bunny

[winter token]

ohhh thats genius

yeah I realised what you did now

I think I got it from here, Thank you so much!

[ionic jewel]

okay now we want to simplify our $\frac{e^x}{1+e^x}$ by multplying it by $\frac{e^{-x}}{e^{-x}}$ to get $$\frac1{e^{-x}+1}$$

[ocean seal]

bunny

[ionic jewel]

ah this step there is a tricky one too ^

but alright, perfect

lmk i fyou dont

[winter token]

@ionic jewel I was able to solve it, though I have to admit I probably wouldn't have if you didn't show me how to simplify that fraction in the last text 😅

Thanks a ton for the help! I've been scratching my head for hours on this problem

[ionic jewel]

You're welcome, glad it worked out!

[idle stratus]

[Laplace transforms, Control Theory, Electronics] I'm trying to figure out why I need to subtract LsI_2 in eq1 and LsI_1 in eq2. It looks like I_2 doesn't run through the inductor why do I need to subtract it?

[wary stream]

I don't recall much about circuits but this looks like mesh analysis, do you know how that concept works?

[past sundial]

Can someone explain tan to me? (Imma move this to a diff channel cause there’s a discussion I realize)

[idle stratus]

yea it is mesh analysis. I am reading a textbook and this is an example problem... just trying to figure out how they got there

actually I got it... it makes sense because I1 and I2 are closed loops which I didn't think they were

[wary stream]

So in meth analysis, in that example the current convention is ccw, where the arrow enters the component, it's positive, and the other side, it's negative. So in the left loop, I1 enters the component so positive, while I2 enters from the opposite, hence negative. In the right loop, I2 enters the component so positive while I1 enters on the opposite so negative

[arctic delta]

is my math right here?

im fairly confident but at the same time i couldve overlooked something

<@&286206848099549185>

[astral dagger]

not completely

look at your second line, the implicit derivative is wrong

try to fix it

[arctic delta]

you mean the cos?

[astral dagger]

also the cos, I didn't understand if it's argument is a x

of if I'm seeing things

but more specifically the h/4600 derivative

[arctic delta]

what's wrong with it? seems right to me, dh/dt is the speed of the rocket

[oak chasm]

h/4600 = 1/4600 times h.

What's the derivative of h?

[arctic delta]

the speed

[oak chasm]

No, what's the derivative of the variable h?

[arctic delta]

hmm

well that'd be the derivative of h(t) then right?

[oak chasm]

It's dh/dt.

So, it's 1/4600 dh/dt, not h/4600 dh/dt.

That's one error.

The other error is you have tan(theta).

Somehow theta becomes x.

The derivative of tan(theta) is sec^2(theta) dtheta/dt.

[arctic delta]

ah somehow changed that

[astral dagger]

then remember some trigonometric identities

[arctic delta]

deriv of tan theta is also 1/cos^2

[ocean seal]

SubGui

SubGui

[arctic delta]

so something more like this?

also i did forget to do pythag for sec/cos theta last time just realized

[oak chasm]

Yes, except minor error, the cos^2(theta) is missing the closing parenthesis.

[arctic delta]

gotcha

[oak chasm]

@green cave I'm not sure this channel is open. Try #help-9.

[green cave]

oh srry will do

[arctic delta]

okay here's the revised version

the number does makes more sense in terms of the question

@oak chasm how's this

[oak chasm]

You can't get 0.75 from a number about 1/7 times a number less than 1.

Also, it's probably radians instead of degrees.

[arctic delta]

well that part is about 0.147

[oak chasm]

You're going to get a number close to 1/7 times 7/9 or 1/9.

[arctic delta]

well idk what i did wrong considering those are the correct numbers

maybe i could change the unit to radians

instead of degrees/sec

[oak chasm]

,calc 68/460 * 2116/2792

[ocean seal]

Result:

0.11203438395415

[arctic delta]

680 not 68

[oak chasm]

Yes, 680/4600 = 68/460.

[arctic delta]

oh right

[oak chasm]

So, 0.112 radians per second.

[arctic delta]

im in radians and i get 0.14

odd

[oak chasm]

How did you get 0.14?

[arctic delta]

wait a sec

okay i got that number

[oak chasm]

,calc 68/460 * 2116/2792 * 180/pi

[ocean seal]

Result:

6.4190973609213

[oak chasm]

6.42 degrees per second.

[arctic delta]

thanks, turns out i forgot to multiply the two numbers and the 0.75 comes from the 2116/2792

can't believe i made that mistake

[native temple]

this open

?

[arctic delta]

yes

[native temple]

I’m learning about toolkit functions never heard of it

What are they

(via self studying a pre calc testbook)

[vale wigeon]

a quick google search yields this https://math.libretexts.org/Courses/Monroe_Community_College/MTH_165_College_Algebra_MTH_175_Precalculus/02%3A_Functions_and_Their_Graphs/2.03%3A_Transformations_of_Functions

[astral dagger]

you also could use #precalculus to debate some more if someones interested

then you open this channel to another questions

[native temple]

Is self studying math good?

At least to get the basics in

[astral dagger]

the best thing you can do for sure

[vale wigeon]

this feels like a really non-sequitur reply

[native temple]

That’s literally the textbook i’m working in

[vale wigeon]

lmao

what a coincidence

it was the first google hit

but yes self-studying math is good i guess???? it depends heavily on what youre studying from

[native temple]

openstax pre calc textbook

[native temple]

That good

I understand learning from a course(a textbook is a course in book form)

Depends on how good the course is

and how much human feedback you have

(mine is from here…..)

but this is the information I have

[floral willow]

I have gotten to the stage where y/2x = 1

but can you tell me what the math principle is for this?

Not the answer, just what it's called.

I want to solve this myself as I'm sure it's not difficult

[placid zinc]

Good luck with it

[floral willow]

But what is this called?

[vale wigeon]

a good chunk of algebra is governed by the same principle

"do the same thing to both sides"

in your case, you can multiply both sides by something to progress towards the solution.

[floral willow]

the teacher gave me this link:
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities#x2f8bb11595b61c86:linear-equations-variables-both-sides

but that doesn't help.

[vale wigeon]

you are familiar with "do the same thing to both sides", yes?

[native temple]

what does in terms of n mean?

I can’t help this person unless I know what that means

[floral willow]

Yes, I'm familiar with it.

The issue is that y numerator.

[vale wigeon]

'solve for x in terms of y' means the same as solving for x, except that the answer will be an expression involving y rather than just a number @native temple
but also you don't need to interrupt

@floral willow well why not multiply both sides by something?

[native temple]

okay

[vale wigeon]

say, multiply both sides by x?

you may be surprised at the outcome.

[floral willow]

Yes, I understand, but I'd like to read a link about it.

[native temple]

give me a minute

[floral willow]

I can't find it in Google.

It will stick better if I have a guide to fall back on.

[vale wigeon]

mm

i cant think of any guide to give you here unfortunately

this is the sort of stuff you learn by doing rather than by reading

[floral willow]

hmm, there must be some guide about this type of problem.

I mean, I already have the solution, but that doesn't help me if I don't understand the mechanics of the problem.

[placid zinc]

Imagine telling me to delete my hint, when they have the full solution in front of them 🤣

[floral willow]

Well, I was trying not to look at it, but since no-one is aware of any guides for this, I felt I had no choice.

But I did try not to look at it and solve it on my own.

[placid zinc]

"Rearranging algebraic equations" is the lesson title

[floral willow]

ok, let me try to google that, one sec.

[floral willow]

this link?
https://www.learninghub.ac.nz/maths/algebra-and-equations/rearranging-equations/

[placid zinc]

Yes that's similar

[floral willow]

What specific link were you referring to?

[native temple]

Here’s how to solve step my step

the principle of algebra is the golden rule

to do operation $n$ on $ Expression A$ do operation n on all sides of expression a

[ocean seal]

Nerdy_Coder

[native temple]

in other words simply do operations on all sides

like with fractions

to convert s fraction to it’s equivalent operate on both numerator and denominator

[floral willow]

I think I finally found a link:
https://serc.carleton.edu/mathyouneed/equations/index.html

I think what I was missing was this rule:
RULE #2: to move or cancel a quantity or variable on one side of the equation, perform the "opposite" operation with it on both sides of the equation.

[native temple]

oh

[floral willow]

Next is this -> "Solve for x in terms of y"

I think I can feel how to solve this problem, but I don't know how to explain what it means.

I'm trying to search for a link now.

ok, found one:
https://www.intmath.com/blog/mathematics/solving-for-y-in-terms-of-x-using-fractions-12488

thank you for the help!

[faint steeple]

hello!

I just want a sanity check, is this correct? my solution is in red

[dusk schooner]

hey i need a help for my assingment can someone help?

[ionic jewel]

,w complex conjugate of (z-i) = 6-2z

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by 兔子#6562

[dusk schooner]

,w If 5sinA = 4, then find the value of 5cosA

??

[faint steeple]

so my solution was wrong D:

[oak chasm]

@dusk schooner Sorry, this channel is busy. Try #help-6.

[dusk schooner]

dont ping

[faint steeple]

is there an explanation of how this solution was derived?

because I've clearly gotten

not sure how Wolfram went from that to z = 2-i

[vale wigeon]

what is x?

are you implicitly saying z = x + yi?

[faint steeple]

that's basically what I was trying to do yeah

[vale wigeon]

well then do it in full

2x + z + i = 6

2x + x + yi + i = 6

3x + (y+1)i = 6 + 0i

[faint steeple]

is implicitly saying z = x+yi incorrect?

I was just going off my notes which says that z* + z = 2x

based on a conjugate of x+iy + x - iy = 2x

[dusk schooner]

The abscissa of the point R that divides the line joining the points A(2, 3) and B(7, 3) in the ratio 3:2 is???

[vale wigeon]

@dusk schooner channel busy please move

[dusk schooner]

aight

[vale wigeon]

@faint steeple if you introduce the variables x and y for the real and imaginary part of z then you have to do so explicitly

otherwise nobody will know where this mysterious x comes from or what it has to do with z

[faint steeple]

ah, I see...

let me go back and try my solution again with explicit declarations then

and also in full as you said

thanks 🙂
may be back in a bit if I need help

channel's free now

[rich basin]

what is this

It is neither of them

I am really confused

[misty pebble]

Given that 0 < a < 360, then the equation sin(a) = cos(a) has how many solutions? How would I work this out?

[green cave]

||45°,(180+45)°||

[green cave]

Do u know the geometry of sime and cosine in unit circle

[slender marten]

Convert the problem into an equivalent problem, we may divide by cos(a), where cos(a) is non-zero. Then we can answer the equivalent question tan(a) = 1 on the interval 0 degrees <a < 360 degrees.

[misty pebble]

Would it then be four? It's equivalent in four spots

[green cave]

No, u have to notice abt the signs in the 4 quads

[misty pebble]

Oh, 2?

[proud estuary]

How do I solve this, not the answer, just how do I figure it out?

[gray isle]

first consider setting up a fraction

[slender marten]

Understanding that billion is 10^9 might help.

[gray isle]

then express 75billion in scientific notation
and apply exponent laws

[proud estuary]

I appreciate it but this is a question for my daughter and I have no clue how to even work it or what you guys mean, can you explain the steps?

[vale wigeon]

do you know what 'scientific notation' means?

(do not be afraid to answer no)

[proud estuary]

no

[vale wigeon]

ok, let's back up further

do you know your way around exponents?

[proud estuary]

nope sorry, like I said all of this is new to me.

[vale wigeon]

wait so...

even this

is foreign to you?

[proud estuary]

yes foreign to me sorry, like I said trying to understand to help my daughter.

[vale wigeon]

it would be a lot better if we could get your daughter on the line, but i suppose she may be too young

this is going to be very difficult

because you would basically need to learn about exponents before even beginning to approach this problem, as understanding scientific notation is impossible without understanding exponents.

[proud estuary]

any explanation is appreciated.

thank you anyhow

[vale wigeon]

trying to think about where to begin explaining this...

[slender marten]

I think you should direct this to a teacher or something.

There's only one way for you to be able to do it, learn maths yourself. I can give you resources but it will take you a long time, more than you are willing to commit, assuming we're not being trolled.

[proud estuary]

True but her teachers are not available. but again ty

[vale wigeon]

khan academy is decent for learning basic stuff like this. the key words are "exponents", "exponent laws" and "scientific notation".

[slender marten]

Get her on the line, she can't be that young if she's learning about scientific notation...

[vale wigeon]

she may well be 11 or 12.

[slender marten]

They don't teach nothing in the UK then, I didn't see that till college (16-18 years old).

[ionic jewel]

I definitely learned scientific notation in middle school, so something like 11-13 sounds about right

but it was in some sort of intro to science class or something, not in algebra iirc

[slender marten]

(I told you, they don't teach nothing in the UK, what is going on.)

Maybe they did and I just forgot.

[green cave]

yes

[frail gulch]

I can try to give a brief explanation, but it will likely be specific to this kind of problem

Exponents are a shorthand way of writing "i want to multiply something by itself N amount of times". For example, 2^4 is the same as 2x2x2x2 which is 16.

On an unrelated note, its hard for us to comprehend really large numbers quickly. For example, if I told you to multiply 10 million by 20 billion, how could you do this in your head?

One way to do this is to try and write large numbers in a shorthand, easy to understand method, usually with some estimation and "rounding". 2,345,678 could be estimated as 2,300,000 which is the same thing as 2.3 x1,000,000 (2.3 million)

[floral willow]

I would start here:
https://www.khanacademy.org/math/in-in-class-7th-math-cbse/x939d838e80cf9307:exponents-and-powers/x939d838e80cf9307:large-numbers-in-standard-form/v/scientific-notation-old

If you don't understand that, then start at the very beginning of the math section.

It starts with 1+1 = 2, I think.

[frail gulch]

If you notice something about multiplying by 10s, each time you multiply by 10 you simply add a 0 to the end of the number. So 1,000,000 has 6 zeroes, and is thus equal to 10x10x10x10x10x10, or also 10^6.

If you convert large numbers to this kind of format, it makes dealing with large numbers a lot easier. That last time about 10 million x 20 billion? Its the same thing as 10^7 x 2 x 10^10, and now you can simply count the number of 10s and get the answer of 2×10^17.

[proud estuary]

ty all for trying to help, I am going to take your advice and look at khan.

[frail gulch]

Good luck!

[floral willow]

Khan is good enough for beginners from what I've seen so far, although it would be much better with real world applications. But then again, there are hardly no textbooks that cover real world applications. Anyway, be sure not to skip around, as the concepts build upon each other.

Is the second variable numerator a fractional exponent?

[wary stream]

You mean the $v_0$?

[ocean seal]

dldh06

[floral willow]

Hmm, I'm not sure how to write it.

[ionic jewel]

$v^2_0$

[wary stream]

That's a v with a subscript zero, known as naught

[ocean seal]

bunny

[wary stream]

So v naught

[ionic jewel]

oh is that how you spell it lol

[wary stream]

Yep

[ionic jewel]

i always though it was v not

lol

[wary stream]

,w naught

[ocean seal]

Results provided by WolframAlpha

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Requested by dldh06#2659

[floral willow]

Hmm, I'm not seeing any results for this on Google.

https://www.mathsisfun.com/algebra/exponent-laws.html

[wary stream]

It's just a variable

$v_0$ is a variable

[ocean seal]

dldh06

[floral willow]

I don't know what to do with it.

What do I search in Google to research this math process?

I tried "v naught", but it showed Physics.

[wary stream]

Because it is physics related

But treat it like a regular variable

Like $y^2$

[ocean seal]

dldh06

[floral willow]

Hmm, this is confusing, but let me try.

[wary stream]

It's just a variable, that's it

[floral willow]

I'm stuck at:
$v^2_0$ = 1/-5x_0$

[ocean seal]

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

[wary stream]

What happened to $v^2$?

[ocean seal]

dldh06

[floral willow]

Oh, wait.

I'm stuck at:
$v^2 + v^2_0$ = 1/-5x_0$

[ocean seal]

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

[wary stream]

Like I said treat $v_0$ as a variable

[ocean seal]

dldh06

[wary stream]

So like $y^2$

[ocean seal]

dldh06

[floral willow]

I still don't get it.

Any links to other examples, maybe?

Or at least the name of what this part of math is.

I know it's "v naught", but that doesn't yield results in Google.

[wary stream]

If you had $v^2 + y^2 = \frac{1}{-5x_0}$, how would you solve for v?

[ocean seal]

dldh06

[wary stream]

It's just isolating variables, but with different variable names

[floral willow]

let me try the example you just posted

[wary stream]

The example I posted is exactly the same as what you have, I just used a different variable

[wary stream]

Also, why do you have divided by $-5x_0$?

[ocean seal]

dldh06

[wary stream]

That's wrong

[floral willow]

The opposite of $v^2$ would be the square root, yes?

[ocean seal]

Willow

[wary stream]

Yes

[floral willow]

Does that fall under the Law of Exponents?

[wary stream]

Not sure what that's exactly called

[floral willow]

I don't know how I remembered that either. But I'd like to update my notes.

I don't see it listed here:
https://www.mathsisfun.com/algebra/exponent-laws.html

Hopefully, someone comes along that knows what its called.

[wary stream]

It's just known that the opposite of squared is square root

[jovial forum]

What's actually happening when we 'eliminate the third column'? I really don't get this (trying to put something in RREF for Linear Algebra)

[wary stream]

Ask in a different channel

[wary stream]

What's the term for the opposite operation of addition is subtracting?

I mean, you can apply law of exponents for that

[floral willow]

Back to this problem you posed.
I'm stuck at $v^2 = \sqrt{\frac{1}{-5x_0}}$

[ocean seal]

Willow

[wary stream]

Where's the y?

[floral willow]

I don't know what happens to it.

but one second please, an additional video resource was just posted to us students.

I'm going to try and watch it to see if it helps me understand.

[wary stream]

On what specifically?

[floral willow]

On this problem

Not your problem, but the original problem I posted

I guess other students were also confused

let's see if it helps

[wary stream]

Like I said, those are just variables

[tepid jungle]

Does this mean that the probability of X1, X2,.... of occurring is p?

and that the distribution is geometric?

[noble sinew]

No, means X_i is distributed with Geom(p). iid means independent and identically distributed.

[tepid jungle]

but isn't p of a geometric distribution the probability of success

@noble sinew

[noble sinew]

It is

[tepid jungle]

oh pr of success, the Xn is just each variable, which could be anything

thank u

[mortal void]

Using variables and operation symbols, express each of the following verbal statement

The product of two successive odd number is 35

someone help me with this, my tiny brain is so confused

[noble sinew]

How can you write an odd number? How can you write the next odd number? How can you write a product is equal to 35? Just combine all these and you are done.

[mortal void]

yeah its answer is x(x+2)=35

but i am not getting the numbers with solving this!!

[noble sinew]

Why not

How are you solving it

[vale wigeon]

what are you getting?

[mortal void]

this

[vale wigeon]

so you got x=5 and x=-7 as potential solutions.

that is correct.

[mortal void]

or am i doing it wrong

[vale wigeon]

the numbers which multiply to 35 are x and (x+2), as you should remember from the equation you wrote yourself.

[noble sinew]

Then the other number is just x+2 like we said

And you are done

[mortal void]

how can we put if on the equation tho?

[vale wigeon]

what do you mean?

[noble sinew]

You found x=5 is a solution - then the pair {5,7} is a solution for example

[mortal void]

okay so we put one at one time lol sorry

[vale wigeon]

you used the letter x for the lower of the two numbers you're multiplying

the other number is x+2

you should have understood this much when writing the equation

[mortal void]

i was getting confused cause i was thinking to put both of them at once

[alpine sable]

Hey

[vale wigeon]

find two different paths, with the same start and end points, such that the integral of F · dr along one path is not the same as the integral of F · dr along the other path

[limpid aurora]

yeah the part im stuck with is i don't know how to find two different paths

[limpid aurora]

sorry i still dont understand :/

[vale wigeon]

@native cloud channel busy please move

@limpid aurora you have a lot of wiggle room here lol

pick any two points you like, literally any two points

and connect them with two different paths

you might, for example, go with the straight-line path

or a three-segment path which first goes parallel to the x-axis, then parallel to the y-axis, then parallel to the z-axis to get from the first point to the second

those are just some examples of the possible paths you could take

don't overthink it basically

[limpid aurora]

ahhh ok

thank you

i think the problem is i can't visualize this lol

[vale wigeon]

do you want me to get you started with some example paths

[limpid aurora]

yes pls

[vale wigeon]

take A = (0,0,0) and B = (1,1,1)

the straight line path from A to B: r(t) = (t, t, t) where 0 ≤ t ≤ 1
the 'parallel to axes only' path from A to B: r(t) = (t,0,0) for 0 ≤ t ≤ 1; (1, t-1, 0) for 1 ≤ t ≤ 2; (1, 1, t-2) for 2 ≤ t ≤ 3
a twisted path: r(t) = (t, t^2, t^3) where 0 ≤ t ≤ 1

please note that you do not need to take these exact paths. if you think you can see a path that makes calculations easier, then by all means go for that instead.

and don't overthink it.

[limpid aurora]

ohh ok that makes sense

thank you!

[alpine sable]

Hey, i also attempted this ques , but taking the odd numbers as 2x+1 and 2x+3 , odd nums can also be represented like this but then the answer that comes after putting solutions of x , is wrong. Can someone tell if there's mistake?

[mortal void]

can you show it to us?

[alpine sable]

wait

[gray isle]

you're conflating the zero product property

[alpine sable]

hmm

so how to find values of x

[gray isle]

ab = (something that isn't 0)
doesn't necessarily mean that a = that something or b = that something

[alpine sable]

oh lol

yeah

true

[gray isle]

well you have a quadratic equation, (you could solve that using appropriate methods)

however

[alpine sable]

yes

mb

[gray isle]

since you're looking for consecutive odd numbers,

you should be able to find the solutions relatively easily in that form from the factors of 35

[alpine sable]

using complete the square is also another way ,ig

alright got the right answer, thx for pointing out my mistake

[turbid harbor]

anyone know how I can start this question? It was in our end of year exam (first year robotics) and i had no idea how to start it as you cant seperate the variables to diff sides easily?

i obviously gave it a full page try but looking back through notes i dont think you can just open up with a divide by tan x llol

hm maybe I could subtract y then factorise the right as y(2secx-1) ?

and divide by (2secx-1) might go try that while waiting for a tip here 😄

ok i definitely can't do that 😂 typing without thinking...

feck this question 😂

[wise sigil]

@turbid harbor Try multiplying the equation by cos x

[turbid harbor]

shall do 😄 ty

tanx is sinx/cosx no idea how this is gonna hellp but i trust you 😂

ooo ok

clever

[wise sigil]

Got it then?

[turbid harbor]

i think so TY 😄 definitely got a route to go down

[alpine sable]

Are you guys finished?

[turbid harbor]

i am not super experienced with trig identities tbf and dont jump to them

yes

🙂

[alpine sable]

I need to ask a question

I think i might have messed up

[turbid harbor]

that means you're learning 😉 shoot the question

[alpine sable]

I needa find the gradient for these

(1,2) and (3,6)

[turbid harbor]

the equation for gradient is m=(y2-y1)/(x2-x1)

[alpine sable]

ye

2-6/2-3

Correct?

[turbid harbor]

(1,2) and (3,6)
x1y1 x2y2

i think you got your x1 and x2 wrong

[alpine sable]

6-2/3-1

[turbid harbor]

yes i think 😄

[alpine sable]

Lmao i got confused with my

x1 and x2

[turbid harbor]

change in Y over change in X is an easier way to remember it imo bc then you know you need to subtract the ys and xs without looking at weird symbols like y2y1 😛

[turbid harbor]

easily done!

[alpine sable]

Gradient is 2

[turbid harbor]

you got it 😄

[alpine sable]

@turbid harbor let’s try with one more

[turbid harbor]

then try again in a day or 2 and in a week and a month to drilll it into your long term memory 😉 (something im bad at personallly but working on)

[alpine sable]

2,3 and 6,8

alr so

8-3/6-2

5/4

@turbid harbor correct?

[turbid harbor]

looks it bro! im a lowly first year uni student who did A levels 8 years ago and only brieflly touched on this stuff in first year 😛

so dont take my word as gospel, but yeh pretty sure you got it

[alpine sable]

Lmao im yr 9

[turbid harbor]

you could always use an online checker to double check your answers

[alpine sable]

And i keep being confused in the arrangements

[turbid harbor]

impressive mathsing like this in year 9!

[turbid harbor]

just keep practicing, you're setting yourself up to do well in maths in the future 😄

[alpine sable]

Alr thanks

Do you think i should make someone else double check

[turbid harbor]

our university teacher for maths said to switch around topics more, as its easy to be "on a roll" on one subject and just forget it if you dont repeatedly do them

[alpine sable]

Alr thanks

[turbid harbor]

:)) GL

[turbid harbor]

definitely don't got it, gonna go watch videos on implicit differentiation tbh 😂

[wise sigil]

After the hint you should have sin(x) * y' + cos(x) * y = 2

[turbid harbor]

OOOOO i forgot sec(x)=1/cos(x)

thanks man 😄

[wise sigil]

With the equation in this form it's not too hard to realize that you should look at (sin(x) * y)'

[turbid harbor]

im gonna write some of these on post it notes around my house bc i reallly need to remember to llook for them more

[wise sigil]

You can also just divide by tan(x) and do the usual process to find an integrating factor for equations in the form y' + p(x)y = q(x) but you'll end up with the same result and it's more tedious

[turbid harbor]

it's bad that "y' + p(x)y = q(x)" confuses me 😂

got a feeling second year maths I will be coming in here crying a lot

:3

[floral willow]

@wary stream My current answer is $v = \sqrt{5x_0+v^2_0}$

[ocean seal]

Willow

[raw garnet]

Could someone help me with Nonlinear Differential Equations and Stability? I don’t understand the bottom part of the solution. I know how to get the determinant and the trace but how do we know that it is the only critical point and that it is ass. stable spiral point?

[velvet pelican]

i am not too good at this but critical points are points where both x' and y' are 0, in this case you get 2 simultaneous equations which give one solution x=2 y=3. As for the type of node you need to look at it's position in the trace determinant plane:

this one lies above det(A) = 1/4 (Tr(A))^2 and to the left of the y axis so it's a spiral sink

[raw garnet]

That is a great explanation and picture :). I just didn't copy the last part, is my plot wrong? It looks like a spiral source to me

[velvet pelican]

no the plot plot of the soutions is different to the diagram i gave

you plotted on the x-y plane and the diagram is of the trace-determinant plane

[raw garnet]

Ohhh I see, my bad

[velvet pelican]

no worries

[raw garnet]

Yea I recognize the D T plane picture

I’ll look more into it now, thank you for the help

[velvet pelican]

welcome

[alpine sable]

Hey

Can someone help me find the gradient

Of i

Im confused

[sterile gull]

What is confusing you?

[alpine sable]

how to find the gradient

I got the y intercept

[sterile gull]

Do you know how to find slope for a given equation?

[alpine sable]

Yes

[sterile gull]

Yeah so gradient is just another term for slope

[alpine sable]

Ik

i dont know tbh at this point

[gray isle]

you said you knew

[alpine sable]

ik

y2-y1/x2-x1

[gray isle]

Do you know how to find slope for a given equation?
Yes

[alpine sable]

To find the gradient its y2-y1/x2-x1

[gray isle]

assuming you intended the appropriate parentheses,
that's the slope from two points, not an equation

[sterile gull]

Yeah this is when you are given the two points

[gray isle]

are you familiar with the slope-intercept form of an equation of a (non-vertical) straight line?

[alpine sable]

y = mx+c

Am I right?

To find the intercept

[alpine sable]

Not really

[gray isle]

y = mx+c
many other places use b instead of c

is the equation of a line in slope-intercept form

it is called the slope intercept form because the slope and the y-intercept can be read from that equation directly

[alpine sable]

well so that’s the equation correct?

[jagged imp]

Isn't the point of this question to introduce slope intercept form by having them find gradient from rise/run and relate that to the equation? part b asks you to find a pattern that is obviously meant to be discovering slope intercept form

i don't think they're supposed to be looking at the equation for a), just the plot of the line

[gray isle]

ig

[alpine sable]

Im doing 3D

Back to this

[gray isle]

in that case, choose two nice points on each line and apply the slope formula, and/or rise/run

[alpine sable]

Any points?

[gray isle]

what i initially mentioned applies to part b)

[alpine sable]

3, 3 and -5,-1

Like that?

[jagged imp]

(3,3) and (-5,-1) but yes

[alpine sable]

Alr

So

-1-3/-5-3

[gray isle]

please use appropriate ()

[alpine sable]

My bad

-4/-8

I might have messed up

Yeah I did

Its -8/-4

[jagged imp]

yeah thats it

[alpine sable]

Yes im done

[ancient bear]

cool

[stoic pier]

hey i need help

how to do this ?

[urban pollen]

log 3.109 is equivalent to log 31.09 × 10^-1

then you use logarithm's multiplication rule (rule 1) to separate 31.09 and 10^-1

so you should get log 31.09 + log 10^-1, using the power law, bring down -1

then its 1.4926 - 1, so log 3.109 = 0.4926

[stoic pier]

oh uh thankyou vm

[urban pollen]

ah yea i saw the other channel HAHA sorry

[stoic pier]

never mind 🙂

[manic glade]

is it true to say that if A=2n, B=4n (n in N) and B subseteq C subseteq A
then |P(C)|=א?
and is it true to say that the power set of all infinite size subsets of an א_0 sized set is size א ?

[cosmic geyser]

i made a ski resort on a map, the ski resort is 200cm long on paper, I need a conversion for every 1 cm = x km on the map, i need it to be more than 80km in total

need help asap

[stoic pier]

iam here

but

idunno the ans lol

[cosmic geyser]

im trying to find out a website to figure it out for me but i cant :((

[sterile gull]

if you take 1 cm = 0.4 km then for 200 cm you'll have 200 * 0.4 = 80 km

I don't understand the more part tho

[cosmic geyser]

nvm

thx so much

[alpine sable]

homie can you reask the question powerset of a finite set is also finite

[cosmic geyser]

thank you so much, i hope everything goes well for you

[plucky crow]

is this channel taken?

[manic glade]

n in N is implied

[alpine sable]

lol ok then its wrong

|P(C)| = c

[manic glade]

c meaning what here

[alpine sable]

continuum

[manic glade]

whats that

[alpine sable]

size of reals

[manic glade]

so.. א?

[alpine sable]

no

[manic glade]

the wiki page says its א

[alpine sable]

if by aleph you mean aleph_0

aleph_0 is the size of naturals

2^(aleph_0) is size of powerset of naturals

[manic glade]

א_1

[alpine sable]

which assuming CH is aleph_1 = continuum = size of reals

[manic glade]

so it is true then

[alpine sable]

no

|P(C)| > |C| for all sets C

[manic glade]

right

[alpine sable]

so |P(N)| > |N|

and |P(N)| = |R|= א_1 > |N| = א_0

[manic glade]

which = א

[alpine sable]

WHAT DO YOU MEAN BY ALEPH

[manic glade]

the size of c

[alpine sable]

aleph is not size of anything