help-10

[scarlet gale]

log will tell you which exponent.

So, if I have log_7(45), that'll tell me the exact exponent to take 7 to in order to get 45.

[worldly narwhal]

right

[scarlet gale]

Like, there's some number where 7^something = 45.

[worldly narwhal]

i get that

im just thrown off by this problem

like wtf are they doing

it's the 7

that's confusing the hell out of me

[scarlet gale]

Ignore what they're doing for now.

[worldly narwhal]

okay

[scarlet gale]

OK, so log_7(45) gives you the exponent on 7 that gives you 45.

So, if you fill that in, you get 45.

7^log_7(45) = 45.

Does that make sense?

[mighty torrent]

log in base 7 means that 7 is what you are exponentiating

[worldly narwhal]

can we take this problem step by step

[scarlet gale]

OK.

[worldly narwhal]

thx

[scarlet gale]

The first step is to know that log tells you the exact exponent to get a number.

Then you use that exact exponent as the exponent to get that number.

[worldly narwhal]

right

[scarlet gale]

So, 7^x becomes 7^log_7(45).

[worldly narwhal]

got it

[scarlet gale]

Because we fill in the exponent that gives us 45.

[worldly narwhal]

ok now i don't get this step

can u use the sign stuff

that weird stuff u did

[scarlet gale]

What sign stuff?

[worldly narwhal]

to get the pic

of what ur saying

like a picture

[warm shale]

Chai T. Rex

[scarlet gale]

Does that make sense so far?

7 to the power of some number is 45.

And log tells us that number.

[worldly narwhal]

right

i get this all

[scarlet gale]

It's like if you want to tell what you multiply 7 by to get 28, you do 28 divided by 7.

OK, so now we just fill in the something: [7^{\log_7(45)} = 45]

[warm shale]

Chai T. Rex

[scarlet gale]

Does that part make sense?

[worldly narwhal]

yes

that "something" is equivalent to the log745

[scarlet gale]

Right, the log is our tool to tell which exponent to use.

And so your answer is 45.

Their work in the middle line is confusing.

[worldly narwhal]

um

is the stuff in the parentheses just x

[scarlet gale]

No, the stuff in the parentheses is the number you want to get.

[warm shale]

Chai T. Rex

[worldly narwhal]

this is still so confusing for me to understand

[scarlet gale]

Do you have any questions?

[worldly narwhal]

like what math are you doing

i get the first part

butnot what ur doing

[scarlet gale]

We're doing arithmetic here. There's not variables in this problem.

It's like 43 + 23 is 66, but there's no variable at all.

You just do the arithmetic.

Same thing here.

There are no xs.

You notice that you're taking 7 to a power. You notice that log_7(45) gives you the exponent to use on 7 to get 45. So, you get 45.

7 to the power that gives me 45 once you calculate it.

If you have 7^2 = 49, there are three numbers there.

[worldly narwhal]

oh ok

ill ask my teacher

maybe im doing something wrong

[scarlet gale]

No, let's try one last thing.

With 2 * 5 = 10, you can make one of them x and solve for it.

Like x * 5 = 10, you do 10/5 to get x = 2.

Or 2 * x = 10, you do 10/2 to get x = 5.

Or 2 * 5 = x, you do 2 * 5 to get x = 10.

So, if someone leaves out one of the numbers, you can still figure out that number from the other two.

Does that make sense so far?

[worldly narwhal]

yes

apparently its an inverse property

[scarlet gale]

OK, so you can do the same thing with powers.

7^2 = 49

If you have x^2 = 49, you take the square (2nd) root of 49 to get 7.

If you have 7^2 = x, you calculate the power to get 49.

If you have 7^x = 49, you calculate log_7(49) to get 2.

So, with a power, you have taking the power, taking a root, or logarithms to get the left out number.

Does that make sense?

[obtuse pebble]

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[worldly narwhal]

ytes

thank you

[obtuse pebble]

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[white scroll]

help

[white scroll]

Hi I need help calculating two z-scores

here is that data:

I wanna calculate the z-score less than 50

and the z-score between 50-60

[low patio]

ok, do you know the formula for z?

[white scroll]

yea I do

[low patio]

ok, what is it?

[white scroll]

(x-mean)/standard dev

i forgot the symbols

[low patio]

ok, so you know mean and SD

so what are you having trouble with for <50

[white scroll]

idk how to do it if there is multiple values

I can do individual values

but i dont know how to do it when it asks

calculate z-score under 50

[low patio]

think about what the z score represents in terms of area

[white scroll]

hmm ok

should i gather the average?

of all values under 50

[obtuse pebble]

@white scroll Has your question been resolved?

[low patio]

no

just plug in the number 50

[obtuse pebble]

@white scroll Has your question been resolved?

[white scroll]

oh ok

how about from 50-60

how will that work?

[low patio]

z_60 - z_50

[white scroll]

ok ty

.close

[obtuse pebble]

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[open sorrel]

that's Euclid's Elements Common Notion 3
https://mathcs.clarku.edu/~djoyce/java/elements/bookI/cn.html

[dawn quarry]

Yes it is

But I need help I started off with the segment addition postulate I’m not sure if that’s the correct step

[candid yarrow]

Can you also send example 5?

[dawn quarry]

Sure

[candid yarrow]

to solve this, you can copy the 3rd step of example 5, changing the names of the points as appropriate

[obtuse pebble]

@dawn quarry Has your question been resolved?

[obtuse pebble]

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[unborn vigil]

Hi. Is there a task, or is it possible to do it yourself, in which you need to place different geometric shapes inside a limited space or inside another shape?

[low patio]

Tangrams?

[candid yarrow]

sphere packing?

[unborn vigil]

To make it easier, imagine that you are playing tetris and before putting the figure in place, you perform mathematical calculations as a result of which you determine the best place to put the figure

[zenith raft]

tetris has many mechanics which makes that complicated

[low patio]

interesting. that's a complex problem that make it highly dependent on the situation. in the case of tetris, see this: https://dspace.calstate.edu/bitstream/handle/10211.3/116668/ToPaulJohnAlonte_Thesis2006.pdf?sequence=6

[spice citrus]

normally an algorithm called minimax is used for these kind of things (in cases where it's not possible to do the task by hand)

[unborn vigil]

Can you tell me about them?

[candid yarrow]

Could you elaborate on that?

[zenith raft]

i cannot because i do not know anything about that

[candid yarrow]

I don't play tetris, but I know that the pieces fall, so if there's a hollow hole in the bottom layers, then it can't be filled, leading to a suboptimal packing

[unborn vigil]

I think I formulated my question incorrectly. The correct question is, there are several different geometric shapes and a limited space, you need to fill the entire space with these shapes

[candid yarrow]

Can you give an example?

[spice citrus]

that does sound like tangram

[unborn vigil]

For example, there are 7 figures that fall out in the same amount and there is a playing field that needs to be filled with these figures, leaving no open spaces between the figures

[candid yarrow]

fall out in the same amount?

[unborn vigil]

Yes, that's right, you need to assemble a rectangle from the available shapes

[candid yarrow]

so, is it tangram except you use a rectangle instead of a square? (there can be triangles)

[spice citrus]

maybe post a picture of your problem

[unborn vigil]

Yes, the rectangle and the shapes are in the same quantity

[candid yarrow]

what shapes can the figures be?

[unborn vigil]

22 rows and 10 columns

[candid yarrow]

what shapes can the figures that you're trying to fit inside the rectangle have?

[low patio]

So you're trying to pack this 22x10 figure with the standard tetris shapes (I, O, T, S, Z, J, and L)?

[unborn vigil]

yes

[low patio]

by the way, this is likely a CS problem, which is cool too

[unborn vigil]

Look at the figures in the statistics column

[unborn vigil]

CS ?

[low patio]

it's actually quite a difficult computer science problem, most people interviewing for top tech companies could not do this easily

[empty cypress]

surely this would have been easier to just ask your question instead of having people running loops answering similar problems

[low patio]

https://github.com/emilwallner/Tetris-

[empty cypress]

it would be a "hard" interview question at FAANG for example

this is fancy bin packing though

[empty cypress]

this is a good paper for this specific issue

[unborn vigil]

I want to find out if it is possible to solve this problem using mathematical methods so that I can continue to study it.

[low patio]

You could try, but it's going to be very difficult and could frustrate you

Note that: there are many many different ways you can fill an empty rectangle with tetris blocks (also known as tetronimoes). can you think of a "trivial" way?

here is the answer for 2xn:

[unborn vigil]

What do you mean?

[low patio]

What if you just used the I block?

[unborn vigil]

I do not understand

[low patio]

Are you familiar with tetris and its blocks?

[unborn vigil]

Yes, I play tetris

[low patio]

that's good. can you think of a way to fill in a 2x4 rectangle with tetris blocks?

[unborn vigil]

Yes, if you stack them on top of each other

[low patio]

which ones?

J blocks?

[unborn vigil]

they will not be able to be folded without forming empty squares, but this will happen if only two figures S and Z fall out

[low patio]

what if I stacked two O-blocks on top of each other?

[unborn vigil]

It will be very high

[oblique kelp]

🤔
when Tetris experts on the all clears (=, in gameplay, clearance of entire gamefield with no residue) should be able to solve this

[unborn vigil]

now the meaning of tetris is to build a tower and clear four lines at the same time

[oblique kelp]

you would do T-Spins instead these days

anyway, that's too gamey here
I gotta flee

[obtuse pebble]

@unborn vigil Has your question been resolved?

[candid yarrow]

you can fill the entire rectangle with just O-blocks

or I-blocks, if the sides have the right parity

[obtuse pebble]

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[bright karma]

Does anybody know why the integral of this is arccos(x/a)+C

[bright karma]

i got -arcsin(x/a)+C

as the negative one can be taken out of the integrand and well, 1/(sqrt(a^2-x^2)) is arcsin

[meager glade]

Do you know what the derivative of arcsin(x) is?

[candid yarrow]

try graphing those two functions

[bright karma]

yeah i did they're different

by pi/2 translation

[bright karma]

yes

1/(sqrt(a^2+x^2))

[candid yarrow]

yes, that is included in the constant +C

so the two functions you got are really the same

[bright karma]

ah so they're equivalent, given C is solved for?

i was just wondering why arccos is so commonly used

[candid yarrow]

yes, when you use the initial values, and then determine C, it doesn’t matter whether you use arccos or -arcsin

[candid yarrow]

maybe because of convention

[bright karma]

easier to memorise the difference maybe?

[candid yarrow]

between what?

[bright karma]

when they teach students to memorise this

but yeah as youy said convention

thanks so much for the help

.close

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[violet compass]

I get that we split it into subsets calculate them then join them again, but stuck at the part where i actually have to decide what the subsets are suposed to be

[violet compass]

in turn i struggle with the rest of the proceedings...

[low patio]

I would post this in #point-set-topology

[violet compass]

very well.

[obtuse pebble]

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[hearty flame]

Hey guys, just wanted to know if there is a formula for calculating the nth prime number?

[ember frost]

so far, no, not an efficient one at least

[hearty flame]

Oh ok, alright thanks 🙂

[ember frost]

https://www.youtube.com/watch?v=j5s0h42GfvM theres this, but its a comically inefficient one

[hearty flame]

Thank you

.close

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[warm trench]

how do i do the b part

[royal basin]

bran : currant : wheat = 8 : 3 : 1

currant = 20g

can you work out the amounts of bran and wheat here?

[oblique kelp]

(of course, bran + currant + wheat = cereal)

[warm trench]

Im not sure how to do that.theres nothing i can multiply by 3 to make 20

[oblique kelp]

20/3

[warm trench]

Unless its similar to the a part

[royal basin]

^ fractions exist

you can kind of circumvent fractions here however

currant : (bran+wheat) = 3 : 9 = 1 : 3

[warm trench]

Where i have to divide 3 by 12×80

[oblique kelp]

I would rather go all-in on the fractions, for you can also make everything adjusted to the currant

[oblique kelp]

this is correct indeed

[royal basin]

yeah if you don't care about a breakdown of how much of what you need you can combine bran and wheat into one

like i did just now

[oblique kelp]

^

ah; and then again, we are trying to calculate (bran + currant + wheat) here

[warm trench]

A bit confused🥲

[oblique kelp]

you can use fractions
if you don't want to, you can combine ratios

bran : currant : wheat = 8 : 3 : 1

currant : bran : wheat = 3 : 8 : 1

currant : (bran + wheat) = 3 : (8 + 1) = 3 : 9 = 1 : 3

can you calculate how much (bran + wheat) you need now?

you do not have to calculate each of them individually, because you will receive fractional results and that's not good for you

[warm trench]

Then how do we calculate

[oblique kelp]

currant : (bran + wheat) = 1 : 3

currant = 20 g

calculate the mass of (bran + wheat)

...can you do that step then?

[warm trench]

Nope my brain is not braining

[oblique kelp]

it's essentially 20/x = 1/3

(bran + wheat) is triple the mass of currant

[warm trench]

So 3×20?

[oblique kelp]

ye, or 60

20/60 = 1/3

so, you have (bran + wheat) (= 60 g), and you have currant (= 20 g)
cereal is (bran + currant + wheat)
where does that lead you?

[warm trench]

80g?

[oblique kelp]

and that is the final answer
if you have more questions (about this problem), send them

[warm trench]

nope this is the last one having this problem Thanks for the help

[oblique kelp]

fair

.close this if you really have no more doubts

[warm trench]

Oki

.close

[obtuse pebble]

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[celest musk]

hello, can somebody help please?

[celest musk]

"Prove that the plane R^2 is not a finite union of circumferences."

I don't even know where to start

of course a circumference is limited as its radius can't be infinite, therefore the plane R^2 can't be written as a finite union of circumferneces

But i don't know how to write this mathematically

[royal basin]

circumferences?

did you mean circles?

[royal basin]

wdym by "mathematically"?

[celest musk]

i used google translate

[royal basin]

from what language

[celest musk]

i dont know how to put it into words, write it formally

[celest musk]

italian

[royal basin]

"Each circle is a bounded set. The union of finitely many bounded sets is also bounded, while R^2 isn't."

[royal basin]

what does "nemmeno" mean

[celest musk]

neither

[royal basin]

ah.

right

[celest musk]

and i also have to prove that R^2 can't be written as a finite union of straight lines

[royal basin]

this is cleaned up from what you wrote, and it feels formal enough to me as long as you know (or can prove) that finite union of bounded sets is bounded

[celest musk]

i don't know how to prove that honestly

[scarlet gale]

You can probably do a proof by induction.

The base case being one bounded set. The inductive case having you add one bounded set to the previous union.

[celest musk]

okay thank you

[scarlet gale]

No problem.

[royal basin]

prove every bounded set is contained in a ball centered at the origin

then for each of our n bounded sets we have the radius r_i of such a ball. their union is contained in the ball of radius max(r_i) < +infty

[celest musk]

thanks

.close

[obtuse pebble]

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[lone fulcrum]

I made a proof for this question. Could someone please see if it is incorrect or incomplete in any way?

[zenith raft]

looks ok other than that it's written in word or something

[lone fulcrum]

Why would it matter where it is written?

[glacial pulsar]

therefore*

[lone fulcrum]

Oh yea thanks

[lone fulcrum]

anyway thanks for taking a look.

.close

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[icy heron]

I tried to solve this but to no avail

[meager glade]

what have you tried

[icy heron]

I tried to find the derivative of f’(x)

[meager glade]

what did oyu get

[icy heron]

I couldn’t finish it

didn’t know where to go after I tried some stuff

[meager glade]

what even is f(x) here

?

ah wait nvm i see what you did now

[icy heron]

It says the dy/dx of f(x) Is 4*sqrt(y^2+7x^2)

[meager glade]

i thought you got confused with f(x)=y, f'(x)=dy/dx

if we look at the differential equation

we have this nasty term

the root thingy

perhaps it would be easier to get rid of it first

[icy heron]

Yea I changed it to the power of 1/2 but I still couldn’t get anywhere with that

you can chain rule, but I didn’t know where to substitute what

[meager glade]

what about squaring it?

[icy heron]

Can you do that?

[meager glade]

why not?

the left side is just y' right?

[icy heron]

Idk

[meager glade]

so if we square the elft side

we get (y')^2

[icy heron]

is that what we’re looking for?

[meager glade]

$\frac{dy}{dx}=4\sqrt{y^2+7x^2}$

[warm shale]

Flappie

[meager glade]

its a step in the right direction

[icy heron]

Ok

And I can differentiate it from there?

[meager glade]

try it

see what happens

[icy heron]

16y^2+112x^2?

[meager glade]

what is this?

what are your steps

[icy heron]

I just squared the whole thing

[meager glade]

yes but look at your left side

the left side is $(\frac{dy}{dx})^2$

[warm shale]

Flappie

[icy heron]

So what does it mean if it’s squared

[meager glade]

now what happens if we differentiate this?

with respect to x ofcourse

[icy heron]

Idk

[meager glade]

look at it like this

we have our function

$g(x)=\frac{dy}{dx}$

[warm shale]

Flappie

[icy heron]

Yeah

[meager glade]

then $g(x)^2=g(x)g(x)$

[warm shale]

Flappie

[meager glade]

if we differentiate g(x) w.r.t. x

$\frac{d(g(x)^2)}{dx}=2g(x)g'(x)$

[warm shale]

Flappie

[meager glade]

right?

simply the chain rule

[icy heron]

Hm

[meager glade]

so now if we fill back in our original function

we get

[icy heron]

This is a lot to think about

[meager glade]

$\frac{d((\frac{dy}{dx})^2)}{dx}=2\frac{dy}{dx}\frac{d(\frac{dy}{dx})}{dx}$

[warm shale]

Flappie

[meager glade]

or simply put

2*y'*y''

[icy heron]

So to make my differentiable function easier to use, we squared dy/dx, and that means that the differentiable function can be simplified through the chain rule? Or what

[meager glade]

the issue with our differentiable function is htat the root is super annoying to deal with

to solve that, we square both sides

[icy heron]

Ye

[meager glade]

then we differentiate as we normally would

the only thing you need to be careful of is that you dont say [(y')^2]=2y'

make sense?

[icy heron]

Ok

[meager glade]

[y'*y']'=y*'y''+y''*y'=2y'y''

$(y'y')'=y'y''+y''y'=2y'y''$

mayeb easier to see like this

[warm shale]

Flappie

[icy heron]

This is what I have

[icy heron]

Oh that does make sense

[meager glade]

here also the right hand side is wrong

y is a function of x, remember

[icy heron]

Wait so you’re replacing dy/dx as y?

[meager glade]

so $[y(x)^2]'=2y(x)y'(x)$

[warm shale]

Flappie

[meager glade]

dy/dx is y'

[icy heron]

Right

[meager glade]

y' is shorthand for dy/dx

[icy heron]

got it

[meager glade]

and y'' is shorthand for d^2y/dx^2

sometimes this is ambiguous if you have more than 2 variables

but here we only have x and y so its fine

[icy heron]

Ok, so now what

[meager glade]

what does the question ask for us to solve

[icy heron]

The second derivative of f

[meager glade]

where do you see the second derivative of f

solve for that

[icy heron]

oh so it’s already in the function? And I need to isolate it

Ok

[meager glade]

exactly

[icy heron]

Why does this work though, and does it have a name?

[meager glade]

what works?

we are simply differentiating if that is what you mean

[icy heron]

Ok, now what

[meager glade]

thats your solution

thats the second derivative of f(x)

aka f''(x)

[icy heron]

But I still have Y in the right side, how am I going to solve for x=1

[meager glade]

you have the formula for y'

couldnt you put it in there?

[icy heron]

Wym

[meager glade]

$\frac{dy}{dx}(x)=4\sqrt{y(x)^2+7x^2}$

perhaps you see it like this

[warm shale]

Flappie

[icy heron]

I’m confused

The question said to find the value of the second derivative at x=1 right

[meager glade]

yes

[icy heron]

That’s what this notation means

[meager glade]

one moment

im gonna write it out for you

[icy heron]

I definitely did not learn this, but I had no other way of seeing how to do this problem so I kinda need the help of walking through it

[meager glade]

$y''(x)=16y(x)+\frac{112x}{2y'(x)}$

this is the second derivative right?

[icy heron]

Ohhh yea

[meager glade]

maybe, im not sure

[icy heron]

I forgot that the y’ was just dy/dx again

[meager glade]

but this is how i would solve it

[icy heron]

Wait

But in the original equation I still can’t solve for x=1 can i?

[warm shale]

Flappie

[meager glade]

what happens wheny ou put in x=1

into this equation

*plug in

[icy heron]

I’d still have to plug in x=1 in the original equation

[meager glade]

first, plug x=1 into this equation i gave

[icy heron]

Oh is that just 3?

[meager glade]

nono

just plug it in

write it out

[meager glade]

exactly

sow hat are you still missing

which values

[icy heron]

So when I solve for 16y’(x)

[meager glade]

16y'(x)?

[icy heron]

It’s like this, but I replace y^2 with 3^2, and x with 1?

[meager glade]

$y''(x)=16y(x)+\frac{112x}{2y'(x)}\y''(1)=16y(1)+\frac{112*1}{2y'(1)}$

[warm shale]

Flappie

[meager glade]

we see on the right hand side

that we still have y(1)

and y'(1)

that we dont know

but we can find them

how?

[icy heron]

By puttin it into the original equation ig

[meager glade]

we know what y'(x) is

why why not just plug x=1 into that aswell

[icy heron]

Is it this

[meager glade]

no

what is y'(1)?

[icy heron]

16?

[meager glade]

yes

so why do you have 32 there

[icy heron]

Cus the denominator is 2y’

I thought

Yeah

[meager glade]

it is

but you still have another 2 in front of it

[icy heron]

oh oops

[meager glade]

so now you are doing 2* twice

anyway

it seems like you understand it

[icy heron]

bro I Alr know I’m gonna do something like that on an frq on the AP text

yeah

[meager glade]

all we have now are just numbers

and we have the answer

[icy heron]

I’ll prob have to review this question some more

This isn’t an answer choice

If that two in the denominator wasn’t there it’d be C, but it’s not

[meager glade]

looks about right

is the question multiple choice?

[icy heron]

yeah

[meager glade]

hmm

[icy heron]

The answers are shown

[meager glade]

$y'=4\sqrt{y^2+7x^2}\y'^2=16(y^2+7x^2)\2y'y''=32yy'+224x\y''=16y+\frac{112}{y'}\y''(1)=16y(1)+\frac{112}{y'(1)}\=16\cdot 3+\frac{112}{16}\=48+7=55$

[icy heron]

Wait when I squared the right side I got 16

[meager glade]

im just writing it for myself to see what went wrong

[icy heron]

Multiplied by the expression, did I math wrong?

Ah

[meager glade]

youre right

[warm shale]

Flappie

[icy heron]

Yeah I realize at line 7 the equation changes the 224 to a 112 out of the blue

[meager glade]

can you see where your derivation diverges?

aha

[icy heron]

K think cus u suggested it

[meager glade]

maybe

[icy heron]

Yea, I think maybe you cancelled out the two in your equation you told me to fill in, but I didn’t get rid of the two in the denominator or smthn

[meager glade]

its fine

as long as you understand it

[icy heron]

I think that’s about it

I understand all the steps ye

[meager glade]

nice

[icy heron]

.close

[obtuse pebble]

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[dense summit]

Pls help

[alpine raven]

what do they mean by canonical form ?

[full rampart]

A canonical form is a standard way of representing an element or entity as a mathematical expression

[true summit]

not helpfull tbh

[true summit]

!show

[obtuse pebble]

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

[dense summit]

I dont know how to solve this completely, for example how can i convert this to canonical form

[true summit]

can you show an example of canonical form

[dense summit]

I have no idea , this is my first time i see something like that

So unfortunately i dont have any examples

[full rampart]

so what dose it mean?

[dense summit]

Well.. in google it says that

[full rampart]

nah rlly

[dense summit]

Anyways if no one knows canonical form maybe can you please help me how can i write center and paramaters

[full rampart]

ok

[full rampart]

in what shape

[dense summit]

Umm i just see what u see :/ , my math is already not too good so...

[full rampart]

well im only 16 and i cant help if i dont know the full qusetion

[true summit]

parabola has a centre?

that equation looks parabolic

[dense summit]

This is analytic geometry btw

As subject

[obtuse pebble]

@dense summit Has your question been resolved?

[obtuse pebble]

@dense summit Has your question been resolved?

[obtuse pebble]

@dense summit Has your question been resolved?

[obtuse pebble]

@dense summit Has your question been resolved?

[royal mulch]

@dense summit I can help if you are around

[dense summit]

Heyy yes

[royal mulch]

Are you familiar with the completing the square technique?

[dense summit]

No unfortunately

[dense summit]

oh you have a twitch account too 🙂 , i m gonna follow you lol

[royal mulch]

sure

ok well if we dont know how to complete the square it can be a bit tricky lol

[dense summit]

yeah i m watching you on twitch 😄

i m not sure

i was trying to create a twitch account to follow you lol

[dense summit]

btw maybe thats a bit easy question but, how do we draw line for that type of equations without using a computer software? (sorry maybe thats a bit high school question but still...)

[royal mulch]

1. Find the vertex.
2. Look at value for a (in our case it's negative, so open to left)
3. Found the Focus and directrix.
4. Profit

[dense summit]

.close

[obtuse pebble]

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[obtuse pebble]

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[hazy flint]

Quick and simple question

[hazy flint]

Are these just xy and px

[royal basin]

are these : meant to be division signs

[hazy flint]

Yes

Division signs

[royal basin]

ok then no, $\frac{x^3}{y^3} \neq xy$ ad $\frac{p^5}{x^5} \neq px$.

[warm shale]

Ann

[royal basin]

what was your goal with these?

[hazy flint]

So we’re trying to subtract them I guess

That’s the confusion I’m having since if it was just x^5 : x^3 we could just say x^2

But since they’re both different letters I don’t know

The question would be I guess

How do we subtract exponents from different variables

Or can we even do that

[timid silo]

you cant

unless there is an relation between them atleast

if they say that x = y then yeah we can treat y as x

else

no

[hazy flint]

Wait so what’s the answer then

[hazy flint]

Is it just =\ or is it something like p^5x^5

[timid silo]

no

i told you

if there is nothing that tie x to y

then there is no solution

[hazy flint]

So it’s just =\

[timid silo]

it remains as it is

false

let x = 1 y = 2 , is it ?

\

[hazy flint]

What about

[hazy flint]

Is this unsolvable too

[timid silo]

if p =x then it is x^10

else

no simplified form

[timid silo]

which?

[hazy flint]

That’s the thing though

There’s nothing to really say p=x

[timid silo]

then no simplified form

[hazy flint]

We’re just given two different variables with exponents

[timid silo]

yes

then no simplified form

[hazy flint]

So what exactly does that mean then

[timid silo]

it means it remains p^5 * x^5

just like that

[hazy flint]

Ah okay

So these are the practice questions we were given

So this is the context

[timid silo]

yeah well

first one seems defined well

[hazy flint]

The same variables are pretty easy

[timid silo]

yeah

[hazy flint]

Just was confused when they started using different variables

[timid silo]

i mean you can write x^3 / y^3 as (x/y)^3

but it is the same thing

[hazy flint]

Hmmm I see

[obtuse pebble]

@hazy flint Has your question been resolved?

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[wanton dune]

let f be linear mapping from R^4 to R^2 fulfulling

[wanton dune]

deifne matirx f with respect to standart bases

how should i do this?

should i write those R^4 vectors into oine matrix?

4x3

[obtuse pebble]

@wanton dune Has your question been resolved?

[wanton dune]

<@&286206848099549185>

[tame narwhal]

you need to figure out how to calculate f(e_i), where the e_i are the standard basis vectors

[wanton dune]

hm and how should i do that?

[tame narwhal]

how do you think you might? use properties of linear transformations

[wanton dune]

well this isnt particulary helpful

[tame narwhal]

do you know what it means for something to be a linear transformation/mapping? if so, use that to figure out how to get standard basis vectors

[unreal musk]

Did they only give you f of three things?

[tame narwhal]

also, the matrix will not be 4x3

[wanton dune]

yes

[unreal musk]

Well at least you can find f((1, 0, 0, 0)) and f((0, 0, 1, 0)) if you find those “inner vectors” in terms of (1, 0, -1, 0), (-1, 1, 0, 1) and (1, 1, 0, 1)

[wanton dune]

Should I find linear combination of (1,0,-1,0)(-1,1,0,1)(1,1,0,1) from which I get (1,0,0,0) ?

[unreal musk]

Yep - then from there, you find similar for (0, 0, 1, 0)

[wanton dune]

Alright and when I’ll have them then what

(It is too late and I’m am lazy to calculate it xd)

[unreal musk]

Then you would be able to know f(those) - use linearity!

[unreal musk]

Relatable they’re somewhat easy to spot at least(!)

[wanton dune]

Hm what do you mean by linearity sorry for my lack of knowledge

[unreal musk]

Remember that f being linear means that f(au + bv) = a f(u) + b f(v)

(You may have seen it as two separate conditions, that f(u + v) = f(u) + f(v) and f(au) = a f(u) but hopefully you see they’re equivalent [here a and b being scalars and u and v being vectors ofc])

The idea is that you’re given “f(u)” and “f(v)”, so you can use those to find “f(au + bv)” by splitting it as the the linearity and putting in what “f(u)” and “f(v)” are

[wanton dune]

Alright I think I got it

So when I’ll get those vectors I’ll put them form f() and then use linearity to do what?

[unreal musk]

So like you’ll find $a,b,c$ such that
[
\pmqty{ 1 \ 0 \ 0 \ 0} = a \pmqty{1 \ 0 \ -1 \ 0} + b \pmqty{-1 \ 1 \ 0 \ 1} + c \pmqty{1 \ 1 \ 0 \ 1}
]
And similar but for $\pmqty{0 \ 0 \ 1 \ 0}$ as well

[warm shale]

@unreal musk

[wanton dune]

Yes

[unreal musk]

Then you know that
[
f\pqty{ \pmqty{ 1 \ 0 \ 0 \ 0} }= f\pqty{ a \pmqty{1 \ 0 \ -1 \ 0} + b \pmqty{-1 \ 1 \ 0 \ 1} + c \pmqty{1 \ 1 \ 0 \ 1} }
]
from where linearity should be apparent hopefully of how to use(!) again similar for the other one, $\pmqty{0 \ 0 \ 1 \ 0}$

[warm shale]

@unreal musk

[unreal musk]

Rather annoyingly, the fact they only give you three rather than 4, a bit as to how you find the image of the other two standard basis R^4 vectors

[wanton dune]

Yes it is a dumb problem

Alright I’ll be honest with you I am so tired I am dying so I’m gonna head out thank you so much for help

[unreal musk]

Awww, hope you rest well have a good one!

[obtuse pebble]

@wanton dune Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[sacred jetty]

Need urgent help

💀

@meager glade

<@&286206848099549185>

[devout yarrow]

Ok

[sacred jetty]

tysm

[devout yarrow]

First, note that there's a time diff

[sacred jetty]

ye 1.5 hrs

[devout yarrow]

How far has a slower car travelled within this time?

The

[sacred jetty]

i dont understand what you mean

@devout yarrow

[devout yarrow]

Like think of it this way

The slower car has a headstart

[sacred jetty]

so do i do 60x1.5?

[devout yarrow]

So how far does it get with this headstart?

80x1.5

[sacred jetty]

i mean 80x1.5

yes

[devout yarrow]

Ye

But were not done

[sacred jetty]

120

km

?

@devout yarrow

[devout yarrow]

Yep

[sacred jetty]

what do i do next

[devout yarrow]

Sry somebody's doing me

Dm

[sacred jetty]

doing?

[devout yarrow]

Dming

[sacred jetty]

ohhhhhh

[devout yarrow]

Bruh

[sacred jetty]

sorry

[serene dawn]

That is so unfortunate...

[sacred jetty]

pls continue

[devout yarrow]

Yes 120 km headstart

[sacred jetty]

next what i need to do?

[devout yarrow]

Now, when u have this type of speed qns when one person has a headstart but the other is faster, u take the speedd difference

[sacred jetty]

so 20km/h is speed difference

[devout yarrow]

Yep

So the faster car will take 120/20 hours to catch up

[sacred jetty]

so 6 hrs?

wait why 120/20?

[fickle orbit]

bro

ur over-complicating it

so much

[sacred jetty]

JUST TELL ME WHY

[fickle orbit]

no both of u r

so the first car

has 80kmph

and 2nd has 100kmph

[sacred jetty]

yep

[fickle orbit]

we know theyre both multiples of each other

so think of the car going in leaps

[sacred jetty]

like 80 and 100

[fickle orbit]

of multiples

[sacred jetty]

just tell me everything in one go

[fickle orbit]

but the first car has a headstart of 1h

thts all

i told u everything#

[sacred jetty]

cus i gtg i have a class

[fickle orbit]

u need to knowe

just look back at what i said

[sacred jetty]

how

i dont understand😭

@devout yarrow

help me

[devout yarrow]

@fickle orbit wait fine ur method works too

[sacred jetty]

i dont understand his or her methods

[devout yarrow]

But if there's are really weird speeds

It's jnsustainable

[fickle orbit]

these speeds are perfect

quite literally

[devout yarrow]

Ik

[sacred jetty]

everything addict just continue with ur things

[devout yarrow]

I'm talking generally

[fickle orbit]

yea

u want it as a funciton of time

and two equation equal to each other

[sacred jetty]

@fickle orbit just let @devout yarrow explain

[fickle orbit]

but he wont understand probably

[devout yarrow]

I understand

Just let me explain OK?

[sacred jetty]

yes

go on

[devout yarrow]

Which method do u want

[sacred jetty]

urs

[devout yarrow]

Ok

U know speed = distance over time right?

[sacred jetty]

yes

ik all of those formulas

bro dont just leave in the middle of an explanation

[devout yarrow]

Ok

Then Time = distance over speed

[sacred jetty]

BRO IK THE FORMULAS

[sacred jetty]

......

[devout yarrow]

Now think abt it: they r going in the same direction thus the speed at which the faster car is catching up is 100-80=20 km/h

[sacred jetty]

yes i understand

u already explained that

[devout yarrow]

The faster car needs to catch up 120 km

[sacred jetty]

yep

[devout yarrow]

So the time taken to catch up is 120/20 = 6 h

[fickle orbit]

that makes no sense

[devout yarrow]

By this

[sacred jetty]

BRO JUST LET ME HIM EXPLAIN

[fickle orbit]

ok then enjoy the wrong answer bozo

LOL

[devout yarrow]

It's just a more abstract way of thinking

[spiral crane]

this is like the definition of a narcisist damn 😭 @devout yarrow you've got some golden patience my guy

[sacred jetty]

bro is he giving wrong answer?

[devout yarrow]

Thanks

We're not done

[sacred jetty]

im so frigging confused, who is giving the right solution😭

[devout yarrow]

Wait first just focus on my solution

U can ask other ppl later

[sacred jetty]

ok

continuue

[devout yarrow]

So we know it takes six hours after the departure of the second car for it to catch up

Yes?

[sacred jetty]

yes

[devout yarrow]

So, six hours after 7.30 am is?

[sacred jetty]

1:30 pm

[devout yarrow]

Yes!

Now circle it a write down the workings

👍

[sacred jetty]

yep done

now what

[devout yarrow]

Do u still want to know how to solve such qns in general?

[sacred jetty]

i have a class soon

so i cant rly sorry

[devout yarrow]

Oh

[sacred jetty]

but continue

[devout yarrow]

Then u should ask ur teacher

[sacred jetty]

this question

[devout yarrow]

?

[sacred jetty]

this is tuition work

[devout yarrow]

Oh

[sacred jetty]

my tutor not replying to my questions

and it due today

[devout yarrow]

OK then

I'll quickly tell u how to solve such qiestions

[sacred jetty]

ok

[devout yarrow]

Step 1: account for the time difference

So we yook 1.5 hours and multiplied by 80 to get the headstart

[sacred jetty]

just one sec

do you mind summarising what we did for this question quuickly

[devout yarrow]

Ok

[sacred jetty]

cus i dont have enouugh time to do myself

sorry

[devout yarrow]

So we took the time difference and found the headstart that the slower car got

Then we found the speed difference to find a t what rate the faster car was catching up

Then we divided to find the time taken

Then we used it to find the answer

[timid silo]

Hi @sacred jetty

Do you still need help?

[sacred jetty]

ummmmm not rly @devout yarrow saved my life😁

[timid silo]

OK

[obtuse pebble]

@sacred jetty Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[karmic mural]

What is the connection between vector functions and space curves?

[karmic mural]

not sure

is space curve

j somethng that can be defined witha vector?

or what

[low patio]

A vector-valued function 𝑟⃗ (𝑡) whose values are three-dimensional functions traces out a space curve, a curve in three-dimensional space

[obtuse pebble]

@karmic mural Has your question been resolved?

[karmic mural]

i c

ty

[obtuse pebble]

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[cyan copper]

How is ae 80° if ab is 100 bc is 80 bcd is 120 AED is 140

[obtuse pebble]

@cyan copper Has your question been resolved?

[obtuse pebble]

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[warped crest]

hey this is my friends problem and I forgot how to do sigma shit

[warped crest]

but it's like really really weird

I've got no idea

[unreal musk]

5 + 6 is 11

[warped crest]

thanks

[spring trail]

partial fractions?

😭

whats this

[warped crest]

So like
3/(n + 6)(n + 5) and I have forgotten all sigma shit

[spring trail]

same

but im sure the first step gonna be seperating those two

[zenith raft]

the usual shenanigans that manifest whenever chartbit and i have looked at the same channel

[spring trail]

does this even converge?

like ive reduced it to
{3/(n+5)}-{3/(n+6)}

oh wait -

so still might be

@unreal musk

if both of those 2 part diverge

i cant use them to compute this sum can i

[unreal musk]

They diverge separately if you take the sums separately, but you're supposed to notice something

(the emotes are a hint!)

Try writing out a few terms

[spring trail]

Together they converge i get that part

[spring trail]

rlly helpful ngl

😭

[obtuse pebble]

@warped crest Has your question been resolved?

[unreal musk]

Love doing the "help people without saying anything, only using reacts" thing

[timid silo]

Maybe this'll clear things up ...

you shouldn't have to go out very far to see what's happening

I think this is what chartbit's getting at.

[obtuse pebble]

@warped crest Has your question been resolved?

[obtuse pebble]

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[wind oar]

why would this first step be done? i dont get it

[wind oar]

like why is it possible to do that to find h

[tardy epoch]

They show you how

[wind oar]

i don’t get it though

[tardy epoch]

Which line exactly

Or equation

[wind oar]

when bc*ae/2 = 72 turns in 12h/2=72

wait a minute

oh man

AE is h

LOL

.close

[obtuse pebble]

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[rich roost]

Not sure exactly how to approach this

[rich roost]

mainlt looking for hints or a theorem i could use honestly

or maybe its trial and error but i doubt it

[royal basin]

you know n can't be prime or that would give you only two roots.

[rich roost]

yeah

[royal basin]

otherwise idt you can do better than trial and error

lowest n worth considering is 6

[rich roost]

id need like x^2 + x = n

but x to be small

compared to n at least

6 works for 4 but 8 is a stretch

[smoky vigil]

might be easier to consider factored form (even though it won't give you the zeros, it'll give you a good idea of relation between the zero divisors)

[smoky vigil]

it can't possibly have 8 solutions, there are only 6 numbers in the set lmao

[rich roost]

i know

more like

this works for 4 but for 8 i prob need a better way

than just trying

[smoky vigil]

think about your factor rainbows :)

i.e. list out your factors, and skip over the primes

[spice citrus]

Maybe numbers that are the product of the first k primes work nicely

[smoky vigil]

primeorial!

:)

[spice citrus]

At least 30 shows promise with 6 roots I think

*7

Hmm, 210 still seems to have 7 roots, nvm

Primorials dont work

[rich roost]

i think im gonna not do trial and error if i have to check that many lol

there has to be something better

[spice citrus]

I found a number

[rich roost]

maaybe some quadratic

oh nice

[smoky vigil]

it does work, you get x=0 and x=29 for free

[spice citrus]

Oh, whoops

[smoky vigil]

as for the others, 5*6=0

[spice citrus]

60 also works

[smoky vigil]

14 * 15=(2 * 15)*7=0

[spice citrus]

And 210 as well then

[rich roost]

i mean intuitively it makes sense but why

maybe induction could help

[smoky vigil]

well you get n-1 and 0 as solutions for free every time

that goes for all of em' though

[spice citrus]

I think you can prove all primorials have at least 8 solutions

Except 6

[smoky vigil]

primorials greater than 6

[rich roost]

6 has 4 p sure

[spice citrus]

Yeah, 2 and 1(?) Dont work eitger

[smoky vigil]

yeah i had a brainfart

[rich roost]

i mean 1 is a priomorial right its just the empty product

[spice citrus]

Yeah, what I thought

Gtg now, have a math exam lol

[rich roost]

feel that

thx for the help

i think i got enough info here so ill close

[smoky vigil]

ah

i figured it otu

()

[rich roost]

oh nvm

[smoky vigil]

(2 * 3) *5

[rich roost]

what do u have

[smoky vigil]

2* ( 3 *5)

well esentially

you can write all numbers in mod 30 as (2^k 3^l 5^m)p

[rich roost]

all numbers in Z/30Z?

[smoky vigil]

yes

[rich roost]

thats p interesting

roots in rings look so complicated in general its quite funny

yeah even 29, you can find one

as that prime factorization

just has to go up

[obtuse pebble]

@rich roost Has your question been resolved?

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[obtuse pebble]

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[timid silo]

this isn't necessarily a maths question more than an explanation. a friend of mine told me a trick to converting binary numbers but i'm mathematically illiterate and want to understand how it works.

[timid silo]

are screenshots allowed?

it's been a while since i've done math so i'm afraid a lot of what he said doesn't make sense to me

i'm not understanding what ternary is (google defines it as a system that has 3 as its basis) and don't get where the numbers are coming from

[alpine raven]

ternary = {0,1,2}

binary = {0,1}

[timid silo]

right, so ternary is the default numeric system we use?

[alpine raven]

no

{0,1,2,3,4,5,6,7,8,9}
this is what we use for everything

base 10

[timid silo]

i've never heard of ternary

what are its uses?

i only know of binary because i've started studying computer science

[alpine raven]

i have no idea

[timid silo]

i now realize my math is further behind than i thought

[alpine raven]

the main base used in computer science are mostly binary, hexadecimal I think

[timid silo]

so, where did he get these numbers from? for example the first set of numbers for 1011 in decimal (1*10 to the power of 3)

where'd that come from?

[alpine raven]

wdym

[timid silo]

in the screenshot. the last set of numbers at the bottom