help-0

[hearty orbit]

@alpine sable Just normal equations?

[alpine sable]

uh yeah ig

[hearty orbit]

but what do you mean by constructing a formula

like y= ax + b

[alpine sable]

No

Like

This tones + this = g

[hearty orbit]

Like 5x + 3 = 1?

[marsh elbow]

xy+yz+zt+tx = 55
x; y; z; t are positive integers. How many solutions does this equation have?

can someone please explain this

[wheat rivet]

anyone know how to do this?

[jade birch]

x(y+t)+z(y+t) = 55
(x+z)(y+t)=55
Does this help?

[marsh elbow]

@jade birch but what are the number of solutions?

[jade birch]

Because they are all positive integers

you only have to look at

x+z=5 and y+t=11
and also
x+z=11 and y+t=5

[marsh elbow]

oh thank u so much

@jade birch so that means we have 2 solutions?

[jade birch]

No

[marsh elbow]

then

?

[jade birch]

How many solutions does x+z=5 have? Where x and z are both positive integers?

[marsh elbow]

oh

thank u

damn im brain dead rn

thanks once again

[jade birch]

What'd you get?

[marsh elbow]

this one would have 4 solutions @jade birch

[jade birch]

and y+t=11?

[marsh elbow]

1 10
2 9
3 8
4 7
5 6
6 5
7 4
8 3
9 2

10 1

[jade birch]

So?

[marsh elbow]

these r the number of solutions

[jade birch]

Those are the solutions, and there are 10 of them

[marsh elbow]

oh

yeah

my eng

thanks

that was really helpful

[jade birch]

Now, x+z=5 and y+t=11 have how many different solutions?

Calculate that

And then the same for x+z=11 and y+t=11 and then add the two up

That'd be your final answer

[marsh elbow]

yeah

finally i got it

tx again

[copper summit]

is -4^{2} =16 or -16

because my calculator says -16 but i learned that if its ^ {2} so its always positive

[jade birch]

-16

It's because

$(-4)^2\neq - 4^2$

[ocean seal]

.itsjustnai

[jade birch]

in the first one

its

$((-1\cdot 4)^2)$

[ocean seal]

.itsjustnai

[jade birch]

which is obviously 16 right?

but in the second one you have

$-1(4^2)$

[ocean seal]

.itsjustnai

[jade birch]

which yields you -16

the 4^2 IS positive, however it is multiplied by a -1

[copper summit]

ok ty

but wait a sec

so g(x)= -x^2 -ax

g(x)= 16

x= -4

the -x^2 is -16

ya?

[jade birch]

yes

-(-4)^2=-(16)=-16

[copper summit]

yes ok

and a=4?

[jade birch]

well

16=-16+4a

[copper summit]

wait no its 8

[jade birch]

There you go

[copper summit]

ty so much ❤️

[jade birch]

Np

[echo python]

This is kind of computer science problem, but I hope you all can help me you out: Currently trying to simulate reflections, but how can I calculate a lines 180° angle based on a start and end point?
so lets say the coordinates are (0,0) and (4,4) should be 45°, (0,0) and (0,10) 90°, (4,4) and (0,0) -45° etc.

for context: I'm trying to get the angle of the white lines based on a 5x5 area where the red line hits the white line. it basically gets the first and last white pixel and gets their coordinates https://i.imgur.com/kam0jCg.gif

[jade birch]

Isn't (0,0) and (4,4) the same angle as (4,4) and (0,0)?

[echo python]

oh yeah, my bad

meant (0,4) and (4,0)

[jade birch]

If I recall correctly, it had to do something with tangent of the slope

I gotta look it up though

[ionic jewel]

try drawing out the triangle to see

you can make a right triangle and know all 3 sides, which it's easy to use trig to get either angle

it's probably gonna be arctan((y-y_0)/(x-x_0))

[jade birch]

Yeah, this is a better idea

[echo python]

Alright, thanks a lot

[ionic jewel]

it's literally the arctangent of the slope but it's better if he finds out why himself

[thorn kindle]

K

[jade birch]

Ohhhhh right

Yeah I know I know

[jade birch]

But the reason I said this

Is because I got confused by the lines and thought he was looking for the angle at which the red line hits the white ones

[echo python]

Im a calc ab middle school sophomore

edit: calc ab isn't the right name

[jade birch]

ap?

[echo python]

tbh I have no clue what it's called considering I'm not a native english speaker, but it's basically just graphs, linear algebra and chance maths

[jade birch]

well not ap then, ap is advanced placement

[inland hawk]

hi

emm

i need help in something

I need help to identify the property or properties of each exercise.

[inland hawk]

same this

[chrome monolith]

Any vids on limits and continuity

I dont understand the topic

[jade birch]

try YouTube

[inland hawk]

help

[chrome monolith]

😐🤨

[inland hawk]

identify the mathematics properties of each exercices

?

[jade birch]

Khan academy?

[inland hawk]

that's the question

[chrome monolith]

Idrk any good youtubers for it

Ill check him out

[inland hawk]

im watching but i dont understand some parts

[loud nexus]

anyone know if exist any tool for arithmetic calc?

[winter bay]

Why would u need a specific youtuber to learn math online

3b1b possibly has a vid on it can't promise anything tho

[chrome monolith]

Cuz some of them r bad

??

[chrome monolith]

Thanks

[native temple]

no

wait

x * 20 /?

I need to ask my question

[manic quail]

And you can ask your question here, so just do it, please.

[native temple]

Is this a vertical line?

[manic quail]

No.

[native temple]

so what is it?

[manic quail]

You cannot write a function that is vertical.

You can do it like x=5, but I don't know if Desmos graphs that.

[native temple]

hmmmm

okay is this horizontal? and do they cross?

[manic quail]

They cross, but that is not horizontal.

[native temple]

they cross at one googol?

[manic quail]

You can do y=1, then you get a horizontal line.

[native temple]

oh

[manic quail]

They cross around (4,-1), as you can see on the picture you sent.

[native temple]

oh

[inland hawk]

the commutative property also applies to radications ?

[native temple]

I thought they would cross as the line goes up

and

the 1st line goes down

[manic quail]

Two lines NEVER have more than 1 intersection.

[native temple]

oh didn’t know that

[manic quail]

Well, if they lie upon each other, some might say they have infinitely many intersections.

[native temple]

is it possible for seemingly parellel lines to cross at one googol?

[manic quail]

Sure.

[native temple]

or some high number

oh

I was trying to make that

[manic quail]

Like y=-0.000000000001x + 100 and y=1.

You can just add some more 0s or write it as -10^(-123091820954823) or something.

[native temple]

oh

here’s one

[inland hawk]

hi

;-;

i think i will fail math

i dont know properties of radications

oh

[manic quail]

What do you mean by radication?

[inland hawk]

sorry if i interrupted your talk xd

[manic quail]

No problem, what do you mean by radication though?

[inland hawk]

i was wrong

this

xd

im searching the properties

but i think what i need help with this

[native temple]

What even is this line I made lol

[inland hawk]

i dont know which properties aplicates there

[manic quail]

@inland hawk what language do you speak? There might be some good videos on YouTube that could help you.

[inland hawk]

spanish

i searched

[native temple]

Why is sqrt(2024 ) veritcal?

[inland hawk]

i think know a little bit of that, but i dont understand this

[manic quail]

Basically, there are three properties: Commutative, Distributive and Associative.

[inland hawk]

doing it yes

but hte properties

[manic quail]

Are you supposed to solve those?

Just calculate them, I mean?

[echo python]

I'm currently trying it out, but I think I'm doing something wrong, considering it doesn't give the right angles.

(10, 0) (10, 19) gives the angle 141.371, using atan*90

the issue may also be that I'm working with range 0 to 20 integer coordinates. here's my code in case someone might be able to understand: ```py
atan = math.atan((last[1]-first[1]) / (last[0]-first[0]))

[native temple]

Parathesis, Braces, something....Exponents Multiplication/Division, Addiction Subtraction @inland hawk

that’s the order of operations so

[manic quail]

@inland hawk what is your problem now? Do you have to calculate them?

[inland hawk]

hmm

i think what i was confused

because

[glass lichen]

39-25+25=39

[inland hawk]

explains the appropriate properties, that is what the sentence said

[ionic jewel]

what angle is (10,0) and (10,19) supposed to give?

[native temple]

checking my answer

@glass lichen

[ionic jewel]

oh should be 90

[inland hawk]

explains the appropriate properties and obtains the result of each exercise

[native temple]

@inland hawk Is C confusing let me solve it then do B

[native temple]

okay

[manic quail]

@inland hawk , well, when there is a number in front of the parenthesis, you can distribute that number. $3(9+4)=(3\cdot9 + 3\cdot 4)$

[ocean seal]

veryhappyperson

[inland hawk]

yes

[manic quail]

That is called the distributive property of multiplication.

[ionic jewel]

that should give some sort of division by 0 error in whatever you are using (py?) but the idea should work idk what's wrong with yours

[inland hawk]

ok

[signal wolf]

Solve this problem, you can use a calculator and the internet : D
Problem created by @signal wolf

A.- Imagine that you have a message app, which you can put as a maximum of 500 characters per message, how many message configurations are there? (It is assumed that the Spanish alphabet is used and accents with and without capital letters, also the period, comma and space, and in the message, also you cannot put 0 characters (that is, you cannot put anything)) [Write your answer as summation]

Answer =

2A.- Solve the summation with at least 10 digits of precision and the corresponding exponent.

Answer =

[inland hawk]

im still findin properties xd

thank you

[native temple]

Yes A(b + c) = Ab + Cb

[manic quail]

Why do people love posting 10 different questions into one channel? xD

[native temple]

because it’s convient

[manic quail]

'Tis annoying.

[native temple]

lol

[manic quail]

@inland hawk, Do you know what the Associative property and the Commutative one is already?

[inland hawk]

yes

[echo python]

0 degrees

[manic quail]

So what is your problem then, @inland hawk ? There are only those three.

[inland hawk]

i was confused

[ionic jewel]

atan(19/0) should be undefined

[manic quail]

So now you are no longer confused?

[inland hawk]

anyway, thank you

[manic quail]

Okay, great.

[inland hawk]

yes, i guess

[manic quail]

You're welcome.

[inland hawk]

ok

[manic quail]

ok

[native temple]

let me solve C for you

[echo python]

welp, you're right. For some reason Python returns infinite from 19/0

[native temple]

@inland hawk

see

https://tenor.com/view/the-simpsons-suspect-suspense-looking-around-danger-gif-12117781

Now...

Why is this horizontal?

[manic quail]

It isn't horizontal, you have just zoomed out very far.

The violet function is not even a line, @sick river xD

[inland hawk]

hi

emm xd sorry if i interrumped

but im confused in the property of this

i said conmutative

and

additive identity

[native temple]

Sorry Vertical

Why is the sqrt(2024)

which is 1 less then the square of 45

is vertical?

[native temple]

Negative numbers that’s what

[manic quail]

@inland hawk Well, I am not sure what to say here, I would not call this commutative, since subtraction isn't. Maybe they want you to say that 0 is the Identity Element.

[native temple]

10-1 is the same as 10 + -1 or -1(-10 + 1)

[manic quail]

@inland hawk I think you could call that Associativity, since you change the order in which the stuff is done.

[inland hawk]

ok

i just thought what if 0 is there it could be that

and this two ?

asociative, right ?

[native temple]

yes

obviously

what’s the issue

id it’s not about negative numbers it’s the associative property

look

[inland hawk]

xd

i dont know about this

[winter bay]

It does this because $lim_{x\to 0} \frac{n}{x} = \infty$

[ocean seal]

hiidostuff

[echo python]

ahh

[native temple]

It’s fine just google algebraic properties

and read 4 articles on it

[winter bay]

Bc its like how 1/2 is bigger than 1/10000000 because 2 is smaller than 10000000

So bc of that u can kind of infer that $\lim_{x\to \infty} \frac{n}{x} = 0$

[ocean seal]

hiidostuff

[wary harness]

Find the largest and smallest possible value of the total mass of:
a) 12 boxes, each of which, approximately 14 kg (in the nearest kilogram)
b) 8 packages, each of which weighs approximately 3.5 kg (in tenths of a kilogram)

Can some1 help me with this?

[alpine sable]

an eigenvector is a generator for a 1 dimensional invariant subspace of a linear operator

So if you have a line that passes through origin (a 1d subspace), applying the linear operator sends that line to itself (invariant)

[wary harness]

I tried a couple solutions but still didnt solve it right 😫

[alpine sable]

v eigenvector of T iff Tv is multiple of v

(and v nonzero cuz else thatd always be eigenvector)

[alpine sable]

no this is not correct.

take n=1. lim x->0 1/x does not equal infinity. the limit doesn't exist

lim x->1 1/x =1, think you mean x->0

[wary harness]

@alpine sable can u help me with this? I have like 30 mins dealing with this and I cant find the solution of it

[alpine sable]

this channel seems to be occupied, please read #❓how-to-get-help.

[wary harness]

I've read that

[alpine sable]

python does not calculate limits. it uses floating point numbers. its a different "number system" than R or Q

[wary harness]

<@&286206848099549185> can one of u help me with this? I've tried to solve this for like 30 mins and I cant solve it

[mighty ivy]

what does it mean with "approximately" 14 kg

[alpine sable]

well if each box is aprocimately 14kg to the nearest kilogram

[mighty ivy]

o like that

so each box is 13.5 to 14.4999... kg

[alpine sable]

need to elaborate on what nearest kilogram then, there might or not be a minimum

[winter bay]

I know what ur saying but I think u mean n can't equal 0

[alpine sable]

but in either case, the infimum of the weight of each box is 13.5 kg

[mighty ivy]

13.5 rounds to 14 so theres a minimum

[alpine sable]

idk. they said "nearest kilogram"

[mighty ivy]

yes

[alpine sable]

13 is as near to 13.5 as 14

[mighty ivy]

thats not how rounding works

[alpine sable]

rounding works however you define it to work

[mighty ivy]

you dont round 13.5 to 13

ok then

c o n v e n t i o n

there solved

[wary harness]

Hmmmm

[alpine sable]

depending of the convention there is or not a minimum

[wary harness]

Dont wanna be that guy but not helping

[alpine sable]

do you round 13.5 to 14, psy?

[wary harness]

Ye

[alpine sable]

okay

[wary harness]

U didnt know that?

[alpine sable]

no i didnt

you said nearest integer and 13.5 is as near to 14 as to 13

but lets ignore that

So, you say each box weights 14 kg rounded to nearest kilogram

[wary harness]

Ye

[alpine sable]

so the minimum each box can weight, by your rounding method

is 13.5 kg

do you agree?

[wary harness]

Omg ty

I realised how to solve it

[alpine sable]

yea

note that there is no maximum

[wary harness]

But not the b one

Im still thinking on how to solve b

[alpine sable]

its analogous

[dapper schooner]

I need help with this proof

I think I need to use the summation definition if a determinant, but I don't really know how to use that well.

[alpine sable]

Can someone help me?

[manic quail]

What kind of handwriting is that? xD

[alpine sable]

😑

[manic quail]

Let me convert it into LaTeX if I interpret it correctly: $$-x_1 +x_2 \geq 3, x_2 \geq 4x_1$$

[dapper schooner]

Forget my question then

[ocean seal]

veryhappyperson

[manic quail]

@dapper schooner Yes. xD Didn't see that, sorry. There is a linear algebruh channel though, there you will probably find better help.

[dapper schooner]

Thanks

[inland hawk]

?

[fathom heath]

the last answer is wrong but I keep getting the same answer as fxx.fyy-fxy^2<0

at these points

[dapper schooner]

<@&286206848099549185>

[drowsy scroll]

Teacher handwriting be like

[inland hawk]

;-;

[dapper schooner]

<@&286206848099549185>

[untold warren]

need a little insight

i dont think i 100% understand what it means for the function to be riennman integrable, is anyone able to help clear up my confusions with this q?

[manic quail]

The Riemann Integral is just the "normal" Integral, @untold warren .

[untold warren]

a function is riemann integreble when it is non increasing/decreasing between a set interval?

[manic quail]

What? No, a function may be increasing or decreasing, you can still integrate it.

[untold warren]

i see

what about monotone and such, having a hard time understanding the definition

it just means that its only increasing/decreasing between a set interval im assuming?

[manic quail]

,w plot (1-x, for 0 <= x <=1) and (2-x, for 1<=x<=2)

[ocean seal]

Results provided by WolframAlpha

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

Requested by veryhappyperson#1152

[untold warren]

havent a clue lmao

[manic quail]

MOnotone means it doesn't change increasing/decreasing in the interval.

[alpine sable]

who can tell me why 60 is wrong pls

[untold warren]

o thats it

also ive already wrote the graph

something like this for the piecewise function

[inland hawk]

need help pls to identify the properties of the exercices a and b

[upbeat gorge]

define what you mean by “properties”

[manic quail]

Okay. Proving that doesn't appear to be that easy, since you cannot just say it is continuous, @untold warren . You would have to show that the function is bounded, which it is, and that it is continuous almost everywhere.

[inland hawk]

mathematic properties

like assosiative

[untold warren]

in that case, is this function piecewise monotone?

i think it is in this case

[normal lagoon]

It depends on what you are allowed to use, you could show the upper and lower integral are the same. You could use that the function has one discontinuity at 1. (A function with at most countable discontinuities is Riemann integrable).

[untold warren]

ah wait nvm i could be wrong

[inland hawk]

mathematic properties
like assosiative

[untold warren]

not piecewise monotone since I cant divide up the partitions and have 2 different monotone functions

i think i got a good answer..

i can probably explain the piecewise as a sum of 2 riemann integrable functions, -x and a piecewise of +2 and +1

[limber lynx]

Suppose that a ≡ 2 (mod 17), b ≡ 4 (mod 17), and c ≡ 5 (mod 17). Using the algebraic properties of
modular arithmetic, calculate the least residue of a + bc (mod 17)?

im not quite sure what to do here, i understand my notes but this looks different than everything on it

[upbeat gorge]

Modulo is the same

Just multiply and add them

[limber lynx]

so i can just do 22m = 17?

wait no

[upbeat gorge]

nah

It’s 22 mod 17

which is

[limber lynx]

ohhhh

[upbeat gorge]

As long as all the moduli are the same, you can add, subtract, or multiply with no problems

[limber lynx]

okay, thanks

[upbeat gorge]

the problems come with division and with different moduli

[limber lynx]

wait, but it says a ≡ 2 (mod17), not a = 2 (mod 17)

so am i still solving for 22 (mod 17)

[upbeat gorge]

Yes

When you say a ≡ b (mod c), what it means is that when you divide a by c, the remainder is b, or in other words a=cd+b for some integer d

[limber lynx]

alright, im gonna screenshot that lol

thank you very much

[upbeat gorge]

wait srsly how are you doing modular arithmetic without knowing what modulo is

[limber lynx]

i missed one class cause i had to drive my brother to get his wisdom teeth removed

[upbeat gorge]

ah oof

[ruby lion]

Small Problem... I'm tryin to get get back to the formula of the area of the circle via fubini's theorem and it's not working so far.
0 < x² + y² < 1
so -1 < x < 1 AND x² -1 < y < 1 - x²
and I'm supposed to integrate 1 on these 2 ranges to get Tau/2 ( Pi ) as the result for the area.
Problem : that's not what I'm getting.
Help anyone ?

Oh wait forgive me I'm such a dumb mother fker, I forgot the square root

[wicked ember]

ah

[stray raven]

The price of a range of circular rugs is directly proportional to the square of the radius.

P = kr^2
A rug of radius 2m costs £60.

Calculate the value of k.

any idea?

<@&286206848099549185>

[upbeat gorge]

You’re supposed to wait for 15 mins before pinging them

[stray raven]

ohj

i didnt know myb

[upbeat gorge]

anyway you can just substitute them into the equation

and solve for k that way

[alpine sable]

help

[stray raven]

would i end up with
k= sqrt 60/2

[upbeat gorge]

No

Square r first, then divide P by your result

[hardy geyser]

<@&286206848099549185>

[upbeat gorge]

It’s multiplication of fractions, so cancel galore

[hardy geyser]

@upbeat gorge

[upbeat gorge]

Why plus?

[hardy geyser]

Oops

[violet swift]

anyone?

[alpine sable]

Still need help?

[violet swift]

yes please on 3c

[alpine sable]

ok 1 sec I just need to get into class

mind if you wait 5 more mins?

Just for registration and the introduction of the lesson and blah blah blah

[violet swift]

yea no problem

xD tyty

[hardy geyser]

<@&286206848099549185> what did I do wrong

[alpine sable]

He's right in terms of multiplication

Division is multiplication of the reciprocal

[pulsar willow]

Yes

[gleaming granite]

Where did your x^4 term go?

[pulsar willow]

How did you go from 2nd last step to last step?

That too

[gleaming granite]

@hardy geyserIt seems as though you're canceling terms when they're being added , instead of using expansion you can just use factoring, and cancel like terms out of the equation

[alpine sable]

Can't you just cancel from the initial expression

[pulsar willow]

If you factorise top quadratic and bottom, they should hopefully cancel out

[alpine sable]

not the initial

after you multiply the reciprocal

$\dfrac{\left(x^2-9\right)\left(x^2-1\right)}{\left(x+1\right)\left(x+3\right)}$

oh no wait

I've written it incorrectly

no wonder

[ocean seal]

Several people are

[alpine sable]

So you could factorise (x^2+9)

[pulsar willow]

and x^2-1

[alpine sable]

uh no wait we could leave that

when we factor (x^2+9)

we'll get

[gleaming granite]

bruh

yall need to chill

at this rate you're gonna solve the problem

[alpine sable]

(x+3)(x-3)

[pulsar willow]

Oh forgot that's not the point of this

[alpine sable]

which we could cancel (x+3)

[pulsar willow]

True

[gleaming granite]

the op hasn't even responded

[alpine sable]

I mean you could cancel out (x+1)

I mean just factor and cancel really

So at the end you're left with

(x-3)(x-1)

So it's one of the last 2 options

cause it's one of the distributed binomials

[alpine sable]

ok back to you

reposting for refrence

Have you done anything in the time being

[violet swift]

i mean

ive found a colliner line and u=-3 w=18

but it doesnt make 3:5 area with both trapzoids

[alpine sable]

Hm ok

[violet swift]

oh i think i got one pair

u = 3 and w = 6

[alpine sable]

im sorry if I keep leaving

my teacher is just talking

to us all the time

ok if you're happy with that you're happy with that

i'll just do it myself

afterwards

[violet swift]

o alr, im just tryin find the last pair

[potent marten]

How do you solve 5+5 because my teacher said i do it weird

[fading zephyr]

wdym solve?

[alpine sable]

troll

[small stag]

You have to first find the average of the two numbers

Then the number of numbers

Take the natural log of both

Find the sum of the natural logs

And raise e to that product

[fading zephyr]

then integrate it from 0 to 1?

[small stag]

@potent marten

Yeah pretty much, I just wanted them to do the last step by themselves

[craggy bronze]

is there a monotonic sequence that is not convergent?

[fading zephyr]

if it's not bounded and it's an increasing sequence

[pine lake]

Hello is this channel free

[fading zephyr]

i don't think so

[pine lake]

Ok

[craggy bronze]

thanks!

[small stag]

Bruh

[pine lake]

Can u help me with this question

Its about linear equation with quadratic

[craggy bronze]

does that mean that not all monotonic sequence are convergent?

[fading zephyr]

well

is 1,2,3,4,5,... convergent?

[pine lake]

Hmm

[craggy bronze]

oh sorry

thank you!

[pine lake]

@fading zephyr can u help me

[fading zephyr]

so, the volume is x^2y

[pine lake]

What they r asking to find the volume

So the equation i got is

6x² = 66

12x = 40

[pine lake]

Where did u get this

[fading zephyr]

it's the volume of a cuboid

base area times height

[fading zephyr]

where did YOU get this?

[pine lake]

Surface area of cuboid is 66cm²

@fading zephyr

[fading zephyr]

yeah but the sides are not all equal

the surfaces, i mean

it would rather be 2x^2 + 4xy = 66

[pine lake]

Cuboid with square base

They told that

[fading zephyr]

the base is square, but they said nothing about the height

it's not a cube, it's a cuboid

[pine lake]

Oh shoot

Sorry man

I didnt notice

[fading zephyr]

the cm shennanigans is also going to be a mess

[pine lake]

Can u explain how u got it

[fading zephyr]

it's better to convert to meters first

[pine lake]

Ok

[fading zephyr]

gimme a min to get my tablet and make a drawing

[pine lake]

Oh sure

[tired summit]

Yo

Question

how do u use the degree symbol on keyboard

[fading zephyr]

the channel is busy

try an empty channel

[tired summit]

ok

[fading zephyr]

@pine lake see, you have the top and bottom surfaces as squares

but the sides have area xy, as they are rectangles in general

and there's 4 of them

the 4 are identical because they have the same height, and the same base length (since the base is square)

[craggy bronze]

are all bounded sequences automatically convergent? @fading zephyr

[fading zephyr]

monotonous increasing, i think there's a theorem for it

[pine lake]

Sorry

Im back

[pine lake]

Lemme understand this

[fading zephyr]

should have 2 solutions for x

[pine lake]

Ok

[craggy bronze]

@fading zephyr

[fading zephyr]

i think so? this isn't my specialty

[pine lake]

So factorise this

[craggy bronze]

but what if a bounded sequence is not monotonic, it that possible?

[fading zephyr]

well

[pine lake]

@fading zephyr

Factorise it right

[fading zephyr]

the sequence -1, 1, -1, 1, -1, 1 is bounded from above and below

[craggy bronze]

if it's possible, can you also call it convergent?

[fading zephyr]

and it does not converge

[pine lake]

Hmm

[fading zephyr]

and yes jigger, factorize or use the quadratic formula or whatever you like

[craggy bronze]

so not all bounded sequences are convergent?

[pine lake]

Oh ok

And also another question

[fading zephyr]

i explicitly said bounded and monotonically increasing earlier, @craggy bronze

[pine lake]

So just ignore the 40cm?

[fading zephyr]

other sequences have different convergence conditions

wdym just ignore

i put it in there via substitution

[pine lake]

Oh i just saw that

Sorry

And also can i use cm instead of m cuz im not confortable with it

[fading zephyr]

you have to be careful with the units

you can do it in cm if you're careful

[craggy bronze]

all convergent sequences are bounded, right? @fading zephyr

that's my last question by the way

[fading zephyr]

seems like it

[pine lake]

Oh ok

Thanks!

[craggy bronze]

thank you so much!

good luck to you as well @pine lake

[pine lake]

You too!

[quiet lantern]

Hello, I need help understanding this

[fading zephyr]

what's troubling you

[quiet lantern]

so im isolating whats in the bracket and whats outside

-6x multiplied by -6x

= positive 6x^2

and then we add the minus sign outside the bracket

[fading zephyr]

that's already incorrect

from the first step

remember the order of operations

[quiet lantern]

BIDMAS

[fading zephyr]

mhm

so brackets first

we have -6x^2

what's next?

[quiet lantern]

yeah -6x multiplied by -6x ? thats within brackets

[fading zephyr]

no

[quiet lantern]

🤔

[fading zephyr]

you don't have (-6x)^2

the next operation is exponentiation

x^2

[pine lake]

@fading zephyr

[fading zephyr]

which is... x^2

[pine lake]

Can u explain to me how did u get the y

Cuz u substituted y

[fading zephyr]

you are told the total side lengths are 40cm

[pine lake]

Yes

[fading zephyr]

and the side lengths are x, x, and y

so 2x + y = 40cm

[quiet lantern]

give me a sec i'm trying to absorb that 😄

[pine lake]

Can i do it like

Add all the sides = 40

[fading zephyr]

it's possible i misunderstood what they meant by the total length of the sides

that looks ambiguous to mee

[pine lake]

4x + 4x + 4y = 40

[fading zephyr]

it could mean 8x + 4y = 40

yeah

it's either that or 2x + y = 40

[pine lake]

Yes

[fading zephyr]

i can't be sure from how the problem is written

but it's one of those two

[pine lake]

I think its 2x + y = 10

Because u simplified the equation

[fading zephyr]

that's not really a valid argument xD

but it is definitely a possibility

[pine lake]

Bro what r u

Ur living in maths

Damn

Anyways thanks!

[fading zephyr]

aight

[quiet lantern]

Do you know where can I read more about that topic 😄

[alpine sable]

Why does my eulers method chart for Lotka volterra have increasing peaks

[fading zephyr]

which topic?

[quiet lantern]

this, its not covered well in my book 😦

the difference between them

[fading zephyr]

i wouldn't know

like

-6x^2 is -6 multiplied by x^2

remember that multiplication can be made clearer with parentheses

[quiet lantern]

ahhh

[fading zephyr]

-6x^2 is the same as (-6) x^2

[quiet lantern]

so x^2 is separate

[fading zephyr]

yes

unless they explicitly put a parenthesis before exponentiating

like (-6x)^2

just follow the order of operations

[quiet lantern]

okay got it!! thank you very much

[chrome monolith]

How do i do this?

[vale wigeon]

do you know how to take partial derivatives in general

||just take the derivative as normal, treating all variables except y as constants||

[chrome monolith]

Uh

3x^2 + 4y^2 + lny

[spare fern]

No, read the hint that Ann gave again

[chrome monolith]

So treat x like a constant

0

8y

I forgot how to derive ln

[spare fern]

$\dv{\ln(x)}{x}=\frac{1}{x}$

[ocean seal]

The Godfather

[chrome monolith]

So 8y + 1/x ?

[spare fern]

Yes

[chrome monolith]

Bruh

Thanks

Wait

Why do you treat x like a constant

And derive the rest

[spare fern]

You are not only treating x as constant but everything except for y as constant

That's the definition of partial derivative

You are taking partial derivatives wrt y

[chrome monolith]

To treat everything but y as a constant?

[spare fern]

Yes, when you take partial derivatives wrt y

[chrome monolith]

How do i even begin doing this

X = 0

[jagged imp]

pretty much exactly the same way you did the last question

[chrome monolith]

2

(xy)^3

What do i do there

[jagged imp]

=x^3y^3

[chrome monolith]

Then

$x^3y^3$

[ocean seal]

heyguysimhere

[chrome monolith]

2 + 3y2

$2+x^3+3y^2$

[ocean seal]

heyguysimhere

[vale wigeon]

8y + 1/y

[vale wigeon]

don't say things you don't mean

x turns into 0 when you take partial derivative wrt y

and no, $\pdv{y} (x^3y^3) \neq x^3 + 3y^2$

[jagged imp]

nope. you probably took the derivative of x^3y^3 wrong

[vale wigeon]

x^3 is a constant

[ocean seal]

Ann

[vale wigeon]

$\pdv{y}(x^3y^3) = x^3 \cdot 3y^2 = 3x^3y^2$

[ocean seal]

Ann

[chrome monolith]

Oh yh

Wait what

[chrome monolith]

How

[jagged imp]

because its what ann posted and not what you seem to have done?

[chrome monolith]

X^3 × 3y^2

Oh lololo

My bad

Thx ann

[vale wigeon]

lowercase x.

math is case-sensitive.

[chrome monolith]

Ok

[austere elk]

any help

[jagged imp]

,rotate

[austere elk]

Thank you

Here’s a better one

[sullen nova]

ola

[normal lagoon]

$\angle RTS = \frac{1}{2} \angle ROS$ where $O$ is the center

[ocean seal]

andreO

[austere elk]

Thank you @normal lagoon

[alpine sable]

Inscribed Angle Theorem, which has been provided to you by andreO

[austere elk]

Yup

I got one more if u don’t mind

[fleet stream]

Can someone help me with this, do I need to do the elimination method first before substitution?

[vale wigeon]

doing both elimination and substitution would be more work than necessary

are you instructed to use the substitution method here?

@fleet stream

[fleet stream]

yes, i need to find x and y

[vale wigeon]

no

that's not what i'm asking you

you need to find x and y, that much is clear already

what i'm asking is, does it say anywhere in the problem to "use the substitution method"?

[fleet stream]

Yep

[vale wigeon]

okay.

so then

[vital tinsel]

use only substitution

you don't use both

[vale wigeon]

^

pick one of the variables and isolate it in one of the equations.

if you're having trouble making this nearly inconsequential choice with no wrong options, isolate x in the first equation.

[vital tinsel]

actually, it might be easier to isolate y in the second

but it shouldn't matter

[fleet stream]

like 15x-3y=45

[vital tinsel]

since all the terms are divisible by 3

[fleet stream]

solve that first?

[vale wigeon]

it doesn't matter

just stick with one

[vital tinsel]

yes^

[vale wigeon]

kommy is suggesting a route that will cut down on arithmetic a little bit

[vital tinsel]

but in the end, the result is the same

solve for one of the variables in one of the equations, and sub it into the other equation

it doesn't matter which one you choose

[fleet stream]

3y?

[vale wigeon]

?

[fleet stream]

Don't i need to choose one variable?

[vital tinsel]

yes

it doesn't matter which one you choose

so you can do 3y

or you could do another one

[vale wigeon]

choose one

it doesn't matter which

[fleet stream]

3y

[vale wigeon]

that's not a variable

y is

[fleet stream]

And I start from that?

[vale wigeon]

you have two variables here. two unknowns. x and y.

[fleet stream]

So i have to get rid of 3?

[vale wigeon]

so now, take one of your equations and solve it for y.

[vital tinsel]

you have to isolate the variable

[fleet stream]

is it going to be y=15x-45?

[vale wigeon]

no

[vital tinsel]

when you do something to one side of the equation, you have to do it to the other side too

[vale wigeon]

you can't just surgically remove the 3 from this equation simply because you have a personal vendetta against the number 3

:P

[fleet stream]

so how do i do it?

[pine lake]

Ann can u help me after this

[vital tinsel]

@pine lake you could ask in another channel

[vital tinsel]

What were the steps you used to get to y=15x-45?

[fleet stream]

i just removed the 3 lol

[pine lake]

But i didnt post the question yet

[vital tinsel]

post the question in another channel

[fleet stream]

Do I do this?

[pine lake]

Yes ik

Wait @fleet stream

Ur the yesterday one

I taught u yesterday

[fleet stream]

yeah, im done with elmination

[pine lake]

Good

[fleet stream]

i still cant do the substitution

[pine lake]

Did u watch the vid i sent u

Cuz he covered everything

[fleet stream]

the video that you suggested is different

[pine lake]

What no

[fleet stream]

it only has 'y' and not like the one in my activity

[pine lake]

Oh ok

[fleet stream]

so i dont get it

[pine lake]

Sorry kommy

U can continue now

[vital tinsel]

it's ok

[vital tinsel]

I'm not entirely sure what you've done here. Do you think you could describe each step

sorry lol

[flat gust]

systems of equations eh?

[fleet stream]

i kinda did the solution that i did on elimination

should it be like this?

[flat gust]

3x-8y=24
15x-3y=45

You're trying to solve this right

[fleet stream]

Yes

[flat gust]

Do you want to do it by substitution or elimination?

Doesn't really matter

[fleet stream]

It needs to be done with sub

[flat gust]

Oh

[fleet stream]

Thats the instruction says

[flat gust]

Well

[pine lake]

@fleet stream u can simplify the second equation to make it more easier

[fleet stream]

How do i do that

[flat gust]

Isolate y for one of the equations

Let's do that first

So

[fleet stream]

wdym by isolating

[flat gust]

Like make it into this form

y=mx+b

That's a lot simpler isn't it

So you have

[fleet stream]

yes ive been seeing that

[flat gust]

3x-8y=24 and 15x-3y=45

[fleet stream]

I choose one equation?

[flat gust]

Yep

Let's choose the second one

Agree?

[fleet stream]

I chose 15x-3y=45

Yes

[flat gust]

great

So

15x-45=3y

then

You know how I got that right

I just swapped it around

[fleet stream]

Yes

[flat gust]

When you swap things around it turns from -ve to +ve and yea

great

so then

[fleet stream]

Understood

[flat gust]

So how do we get rid of the 3

so that y

can be just there

like

just one y

how do we get rid of the 3

do you know?

[fleet stream]

No

[flat gust]

So

When it's for example 2y=x+1 you just divide the whole thing by 2 and you'll get rid of the 2 from y

Which will become

y=x/2+1/2

you know?

[pine lake]

Y at the left and x and numbers at the right

[fleet stream]

so i divide 3y with 3?

[flat gust]

Yes!

Correct

Let's do that

[pine lake]

Or vice versa

[flat gust]

15x-45=3y

[fleet stream]

Just 3y?

[flat gust]

Nope

Divide everything

by 3

[fleet stream]

Oh I only did 3y and 45 at my first try

[flat gust]

Well

That's wrong

So what will you get

[fleet stream]

so 3x-15=y

[flat gust]

Great

See it looks so much simpler now

Now let's plug that in

to the other equation

3x-8y=24

can you plug in y

?

[fleet stream]

3𝑥 − 8(3x-15)= 24

[flat gust]

So you already have y=3x-15

[fleet stream]

Is that right

[flat gust]

Exactly

Yep

So let's distribute that -8

You'll get?

[fleet stream]

Multiply to 3x-15?

[flat gust]

Yep

[fleet stream]

3x-24-120=24

[alpine sable]

is anyone here at the university level

:<

[flat gust]

Let me check if youre right hold on

You should have 3x-24x+120=24

You see how?

[fleet stream]

Yes because -8 multiply to -15

[flat gust]

Yep

Ok now you have that

Can you find x there

[pine lake]

@fleet stream did u find out the calculator checking method

[flat gust]

3x-24x+120=24

[fleet stream]

3x and 24x?

[fleet stream]

Nope

[flat gust]

Well yea you can 3x-24x

[fleet stream]

I nned to combine that right? the one with x?

[flat gust]

Of course

[fleet stream]

21x+120=24?

[flat gust]

It's -21x+120=24

[fleet stream]

I always mess up the signs lol

[flat gust]

Lol

Let's -120 from 120 and 24

You will get

[fleet stream]

-21x-144

or +?

[flat gust]

-21X=-96

It wil be this

[fleet stream]

Oh its substract

[flat gust]

Yep to get rid of that 120 there u can -120 on both sides

[fleet stream]

And then i divide -21 to -96?

[flat gust]

Yes!

[fleet stream]

is it okay even if its in decimal?

4.571

[flat gust]

mm hold on so it will be x=-96/-21

which is just the same thing as

x=96/21

Can we simplify that

96/21

[fleet stream]

by 3 right

[flat gust]

Yep

[fleet stream]

32/7

[flat gust]

Ok let me check on the calculator

[fleet stream]

that's the x?

[flat gust]

If we didn't do any mistakes

it should be

but let me check on the calculator

That is weird

[fleet stream]

is it wrong

[flat gust]

Yea

[fleet stream]

is it not okay if its in decimals?

[flat gust]

It can be

but the calculator says something diff

let me try to solve

[fleet stream]

Okay

[flat gust]

Oh wait

You got

3x-15=y

it's actually

5x-15=y

Let's try this again

[fleet stream]

Okay okay

[flat gust]

Plug it back into the second equation

[fleet stream]

3x-8(5x-15)=24

[flat gust]

yES

Yes

yes

[fleet stream]

-37x=-96?

[flat gust]

Exactly

x=96/37

that's your x

[fleet stream]

In fraction?

[flat gust]

Yep

calculator says correct

So we are correct

Now we have x

[tropic pecan]

Is it free?

[flat gust]

Plug x back to the first equation which you would then solve for what it y

[fleet stream]

15(97/37) − 3𝑦 = 45

Is that right

[flat gust]

The first equation

Not the second one

[fleet stream]

3(97/37) − 8𝑦 = 24

[flat gust]

3(96/37)-8y=24

It's 96

not 97

So distribute 3 to it

[fleet stream]

Oh sorry

Like the first one? But it's in fraction right

Do i still do the same

[flat gust]

ummm