help-38

[autumn trout]

it looks pretty not implied to me

[vagrant marsh]

because defining a function at infinity doesnt make sense

[autumn trout]

i didnt write the question

im just going off what it says

would it be accurate to say
F(inf) = 0
F(x) x->inf = 1

[vagrant marsh]

if you want to be truly pedantic, say "f(inf) doesnt make sense" as your answer

[autumn trout]

with what reasoning

i love being pedantic

[vagrant marsh]

because defining a function at infinity does not make sense

[autumn trout]

why noit

[vagrant marsh]

because infinity is a concept

unless you get to the crazy math stuff, infinity is to be treated as "<variable> getting arbitrarily large"

[autumn trout]

ok even if we do try to plug in inf, it still wouldnt equal 1 because the numberator is a larger infinity than the denominator right?

[vagrant marsh]

no, the limit of the fraction is 1

[autumn trout]

why

[vagrant marsh]

divide the numerator and denominator by t^2 and then take the limit

you get 1/1

[autumn trout]

inf^2 + inf > inf^2 + 1

large/small = inf

[viscid flower]

what are we supposed to be weighing in on

$F(\infty)=?$

[vagrant marsh]

1. does f(inf) make sense
2. the limit

yes

[solid kiln]

jan Niku

[viscid flower]

Unless its implicitly $\lim _{t \to \infty} F(t)$ then no

[solid kiln]

jan Niku

[viscid flower]

it doesnt make sense

[dull temple]

that's a pretty poorly phrased question

[viscid flower]

its obviously not on the extended set right

[dull temple]

like surely it isn't as simple as just saying oh it must be 0 because it's not in the defined range

[autumn trout]

yeah the professor constantly brings up pedantic points on grading so kinda annoying he puts this question on here

[viscid flower]

what class

[autumn trout]

stats

[viscid flower]

if thats the case then argue that it doesnt make sense

F(inf) is only implied to be the limit

its certainly not defined that way

thats my opinion

[vagrant marsh]

bring it up with the prof

they might have a similar debate and you should ask them to change it

[autumn trout]

thanks

[hallow wolf]

f(infinity) => lim x-> infinity f(x)

[wraith hinge]

@hallow wolf how can you put some undefined number into x?

makes no sense

[hallow wolf]

notation

[autumn trout]

its not an undefined number its not a number at all

[wraith hinge]

limx-->af(x) is not equal to f(a)

[hallow wolf]

when i say f(infinity)

i mean

lim x-> infinity f(x)

[wraith hinge]

yes

I thought

F(inf)

Which is wrong

[tepid hamlet]

reminder of definition of $\lim_{x\to\infty}f(x)$

[solid kiln]

∫oosh

[hallow wolf]

$$ \text{how about you remind yourself to shower today}$$

[solid kiln]

benadryl

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[bold anchor]

help

[bold anchor]

help

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[bold anchor]

i need help on dialations

[bold anchor]

hello

[sharp birch]

hi guys i am in grade 11

[bold anchor]

nice

[sharp birch]

i am learning functions right now

[bold anchor]

ok can u help in my math?

please im stuck on it

[upbeat tundra]

send it

[bold anchor]

ok

[upbeat tundra]

i actually dk what a dialation is

might need an expert

[bold anchor]

how to get expert

[gilded mango]

I'm pretty sure this is 9th grade math I don't think it's that complicated

it's asking for dilation, which is like changing the area of something, so you probably want 2 times the area based on the question

[upbeat tundra]

i aint ever learn what a dialiation is

[gilded mango]

the shape must be centered on the origin as well

[upbeat tundra]

im sure its not hard

[gilded mango]

@bold anchor Do you know how to make something twice the size of the original shape?

[bold anchor]

yes i can send a screenshot of what shape i made

[gilded mango]

Send it

[gilded mango]

It has to be centered on the origin

[bold anchor]

?

[gilded mango]

The origin is (0 , 0)

and that square would be like, 5x the size rather than 2 times the size

[stark leaf]

misinfo...

[stark leaf]

this was correct, but you should understand why

[bold anchor]

yeah i dont think that is what i learned in class

i know what to do its just sometimes gets to confusing

Can you guys help me get to a score of 90 by any chance?

[gilded mango]

We cannot, but you have to understand that the origin is in the middle of the coordinate plane, which is what youre drawing lines on

The square has to be double in size as indicated by the question, and also centered in the middle of the coordinate plane

Do you know how the coordinate plane measures where things are?

[stark leaf]

this is also misinfo

when you scale lengths by 2, areas scale by 4

[gilded mango]

the length and width become double the size

scale factor of 2 meaning the length and the width of the original square are increased by * 2

[bold anchor]

well thnaks for your fellas help

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[main olive]

how to find parallel vectors to a plane

[main olive]

ax+by+cz=d

i want to write a plane parametrically: plate[s,t]={i,j,k}+us+vt

where u and v are two directional unit vectors

but for that i need to find v1 and v2, two vectors that describe the direction of the plane

[zinc ginkgo]

Just shift the vector to a different point in the plane

[main olive]

wdym

[main olive]

what vector

[ionic pendant]

two approaches to that:

1. given the plane equation, the normal vector to the plane is (a,b,c). so find two linearly independent vectors orthogonal to that
2. find three non-colinear points in the plane from the equation and find two vectors pointing between them

[main olive]

how would i do the first approahc

(a,b,c).(i,j,k)=0

ai+bj+ck=0

that has infinite solutions

[ionic pendant]

you just need any two of them. so pick values for two components and solve for the third (twice)

[main olive]

ohh ok

ty

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[umbral steeple]

Anyone know how long it will take me to learn algebra 1 and 2?

[vapid lynx]

depends how fast you learn

it's standardly taught in 2 years in middle/high school, but it could easily be one, and if you are self studying for many hours it could be a whole lot shorter

[limpid belfry]

if you understand it easily it takes about 2 weeks to get used to it

if not id say like a few months

[umbral steeple]

How would I practice getting better?

[limpid belfry]

do many questions, also try to understand what you are even learning

[spare thorn]

Forever. Im not kidding. Im in college went through Calculus and learned so much new stuff about algebra. With math. There is always more

[limpid belfry]

competition questions help a lot with explaining (i.e. people that do solutions to comp questions online)

thats how i learnt algebra but it depends for people

[umbral steeple]

I’m pretty sure I can learn algebra 1 and 2 in a few months but what kind of math would I move on to learn after that?

[spare thorn]

Trig or geometry is what I would recommend

[limpid belfry]

trig and geometry, after that you could try probability

[umbral steeple]

How long would those take me to learn?

3-5 months?

[limpid belfry]

trig takes a lot of memorizing but for me it took a month

geometry has a lot though

depends how far you're going into geometry

[lusty lotus]

Do any of you know precalculus? I have this homework that is due at midnight and a few questions I can’t figure out at all

[spare thorn]

Probability is kinda useless ngl. You could watch a could youtube videos but you dont need to spend a year on it

[spare thorn]

If youre good at spacial reasoning geometry isnt hard

[umbral steeple]

So algebra 1 & 2/ geometry and trig could be learned in roughly a year?

[limpid belfry]

i mean they should see different fields of math just to try it out

[limpid belfry]

yeah about what it took me

[limpid belfry]

for me it is lmao

[umbral steeple]

Thxs

[spare thorn]

Its different for everyone

[limpid belfry]

geometry is something you cant rush on for me

after that you could go into calc though

[umbral steeple]

Just thinking ahead here but after the year of studying is pre calculus/ calculus worth studying?

[limpid belfry]

id say so

[umbral steeple]

More than stats?

[limpid belfry]

eh idk i ddint take stats

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[fallow cairn]

Hello

[fallow cairn]

this is my question

I have like 4 of these ixls to do

before friday

@deep shale

<@&286206848099549185>

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[fallow cairn]

mb

[urban surge]

So you would shift the graph 4 right and up 11

You can just look at one point to see this, you don't need the whole graph

[fallow cairn]

oh wait

I think i get it

it's this up 1

and right 5

I think that's wrong

I just be sleeping during this class ngl

thank u for the help

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[echo jasper]

plzzz

[echo jasper]

the last row only

its kind o fmath

like 55 mass number and i know i dont have proton number

3+ e mean that e number is 52 i think

but i dont think e number and mass number help finding

the

proton #

[ionic pendant]

Mn tells you what the proton number should be (look it up in the periodic table)

[echo jasper]

OH

ok thnxs

.clse

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[ionic pendant]

the e number should also be based on the proton number, not the mass number

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[frosty fern]

how exactly do i use this u-sub

[stark leaf]

you want to replace all instances of x with u

[dense breach]

might be easier to write it as x = 1/u

[stark leaf]

and you want to replace dx with something du

[night patio]

also im like 95% sure from inspection that this requires a little mental gymnastics after ur u sub

[frosty fern]

i did this and ended up making it worse

[night patio]

u would actually get the same integral back but negative ( i think from a glance)

[frosty fern]

maybe i messed that up

[night patio]

can you show your working

[frosty fern]

i erased it lol

ill try again

uh

how do i do du

[night patio]

wdym

also you forgot to write your differential

in your 2nd line

really your u sub should show the following

$du=-\frac{1}{x^{2}}dx$

[solid kiln]

Dootud

[frosty fern]

yeah i just dont usually write dx

[night patio]

or equivalently, $-\frac{1}{u^{2}}du=dx$

[solid kiln]

Dootud

[night patio]

you should fix that habit

[night patio]

we also can obtain our new integral bounds, so really after u sub our integral should be

$\int_{\inf}^{0} \frac{ln(\frac{1}{u})}{1+\frac{1}{u^{2}}} \cdot -\frac{1}{u^{2}}du$

wait sec

[solid kiln]

Dootud

[night patio]

rewrite to the following

$\int_{0}^{\inf} \frac{ln(\frac{1}{u})}{1+\frac{1}{u^{2}}} \cdot \frac{1}{u^{2}}du$

[solid kiln]

Dootud

[night patio]

and then

$\int_{0}^{\inf} \frac{-ln(u)}{u^{2}+1}du$

[solid kiln]

Dootud

[night patio]

@frosty fern are u still here

[frosty fern]

yes

[night patio]

are you following this so far?

[frosty fern]

whered the negative go

[night patio]

flipped the integral bounds

[frosty fern]

o

yeah

missed that

[night patio]

everything makes sense so far

or still not sure

[frosty fern]

so did du just come from this

and moving stuff around

[night patio]

yeah

[frosty fern]

ok im pretty sure i follow then

[night patio]

what do you notice about my last result?

$\int_{0}^{\inf} \frac{-ln(u)}{u^{2}+1}du$

[solid kiln]

Dootud

[night patio]

versus

$\int_{0}^{\inf} \frac{ln(x)}{x^{2}+1}dx$

[solid kiln]

Dootud

[frosty fern]

its like the same thing as the starting problem

[night patio]

not quite

its the negative of it

[frosty fern]

well yeah

is that significant

?

[night patio]

yes

[frosty fern]

oh

[night patio]

observe that

we can apply a dummy variable principle

have u heard of that before?

[frosty fern]

nope

[night patio]

ok

so in definite integrals

whether you are integrating with respect to u, x, y, z etc. whatever

your final answer is always just a value

so it is invariant what variable u use

ie

$\int_{b}^{a}f(x)dx=\int_{b}^{a}f(u)du=\int_{b}^{a}f(z)dz=etc...$

[solid kiln]

Dootud

[night patio]

so similarly

$\int_{0}^{\inf} \frac{-ln(u)}{u^{2}+1}du = \int_{0}^{\inf} \frac{-ln(x)}{x^{2}+1}dx$

[solid kiln]

Dootud

[night patio]

so it is saying that actually, $\int_{0}^{\inf} \frac{-ln(x)}{x^{2}+1}dx=\int_{0}^{\inf} \frac{ln(x)}{x^{2}+1}dx$

[solid kiln]

Dootud

[night patio]

or $2\int_{0}^{\inf} \frac{ln(x)}{x^{2}+1}dx=0$

[solid kiln]

Dootud

[night patio]

so

$\int_{0}^{\inf} \frac{ln(x)}{x^{2}+1}dx=0$

[solid kiln]

Dootud

[frosty fern]

thats crazy bruh

so much more difficult than our classwork on this stuff

[night patio]

well i think highschool integration is just practise tbh

once u do enough practise you will get them down

i think the learning curve is quite steep early on

because there are a lot of techniques and concepts you have to learn at once

[frosty fern]

maybe difficult was the wrong word

but like

[night patio]

long

[frosty fern]

unrelated

we never did a proof

long too

lol

[night patio]

all of this boils down to a like 3 lines once u know where to go with it

anyhow, lmk if u still aren't sure about anything

but i think the main take away here is the dummy variable concept?

$\int_{b}^{a}f(x)dx=\int_{b}^{a}f(u)du=\int_{b}^{a}f(z)dz=etc...$

[frosty fern]

dont go

hold on

[solid kiln]

Dootud

[frosty fern]

he structures these assignments so that they review what we did in class (obv)

and what we did was improper integrals

where u have to take limits to solve them

noen of that is necessary?

[night patio]

sry im australian highschool curriculum so idrk what u guys call improper integrals

[frosty fern]

bc the problem looks like one of those

oh

[night patio]

is there a definition u guys have for improper integrals

[frosty fern]

basically just an integral that has inf as a bound

[night patio]

oh so unbounded 'area'

for this one? kinda?

technically it is unbounded area

but it boils down to 0

[frosty fern]

i feel like im supposed to do it that way

is it possible to?

[night patio]

well sure

i guess you can wirte the bounds as limits

besides that im not really sure, sry

[frosty fern]

ill send a pic of the basic formula thing

you ever learned this?

[night patio]

yeah thats kinda just rewritin the bound as a limit

well i haven't been taught it by a teacher but its just a limit

So according to that we should be writing $\int_{0}^{\inf} \frac{ln(x)}{x^{2}+1}dx=\lim_{t \to \inf}\int_{0}^{t} \frac{ln(x)}{x^{2}+1}dx=0$

[solid kiln]

Dootud

[frosty fern]

yes

[night patio]

the rest of the process is still the same

its just writing upper bound of infinity as a limit

[frosty fern]

ok

uh

ill keep trying it ig. we didnt even finish the lesson so i could just be missing smth basic

how long is this text channel avaliable

so i can see what u showed me

assuming i close it

idk where u went but thanks for the help

your way makes sense but idk if its what the teacher wants

may just go with it anyways

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[karmic dagger]

Why is my calculator saying that -.401+.4 is -.801

[stark leaf]

it's not

[karmic dagger]

What

[stark leaf]

you see that E-4

[karmic dagger]

Yeah

Doesn’t that mean it extends out decimals

[stark leaf]

it means it's saying -0.0008016032

[karmic dagger]

OHHHH

[stark leaf]

good day

[karmic dagger]

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[gusty agate]

help

[gusty agate]

how to proceed

nvm

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[echo jasper]

is it best

[echo jasper]

to convert

1.550 to

cm^3

put it in d=m/v

with our given density

and find mass

[carmine bone]

hi

[echo jasper]

convert 1.024x10^29 atoms to mol then use m=g/mol to identify what metal

hi

[carmine bone]

hi

[echo jasper]

sadly i follow these steps and get it wrong

[carmine bone]

you should go to the chemistry server

go to #old-network

find chemistry server

[echo jasper]

they have #help?

[carmine bone]

i assume so

[echo jasper]

O

Ok

[carmine bone]

i havent joined but its a network so i assume so

[echo jasper]

ill check it thanks

[sacred sapphire]

@echo jasper !showwork

!showwork

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[echo jasper]

o ig ot it right

thanks

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[cosmic plinth]

Can someone check if I proved this correctly

[dapper swift]

that's correct and nicely expressed

just one thing: you have already used k

so you should use another variable: since 7k + 4 is an integer, call this integer m

then we have 2m + 1 which is odd

[cosmic plinth]

ah ok

thank you

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[cosmic plinth]

Can someone check if I proved this correctly

[limpid dawn]

I think it's good

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[cosmic plinth]

thank you

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[uncut wind]

hi i was wondering if this proof of mine is hard to read?

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[somber ginkgo]

there are sections that i migt word differently, but on the whole i think it's fine

i think you could be a little more clear why if u write m as a sum of fib. numbers, why m doesn't include F_j

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[keen stag]

Let G be a bipartite graph on n vertices such that each vertex has degree either 3 or 4.
Show that there is a matching M of size at least 3n/7.

My steps:

x is the number of v with d = 3, y is the number of v with d = 4
x + y = n

SUM(DEGREES) = 3x + 4y
|E| = (3x + 4y)/2
|M|>|E|/max(DEGREE) = (3x + 4y)/8

(3x + 4y)/8 <3n/7 to hold, it must be true that y>3x/4

how I can not prove that y>3x/4 holds for any such graph.

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[scarlet charm]

I got this measure theory, and I have no idea where to start. I am not sure how to approach the construction of such a sequence mentioned in the problem

[trail ingot]

@lavish hornet this looks familiar

[scarlet charm]

you have seen something like this problem before?

[trail ingot]

yep

[scarlet charm]

Oh nice. Would you then be interested in helping me with the problem?

[trail ingot]

not really sorry

[scarlet charm]

💀

okay

[rough goblet]

props to OP for being polite

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[scarlet charm]

<@&286206848099549185>

[somber ginkgo]

just as a foreword

i have no idea what L1(lambda) is and i have not covered limits of functions in analysis either

[rough goblet]

limits of functions in analysis is probably different from functional analysis

[scarlet charm]

L1(lambda) is the Lebesgue measureable fucntions with real values is how I understand it

[rough goblet]

but i have no clue what the latter entails so

[somber ginkgo]

huh my idea doesn't work

[somber ginkgo]

wait is the integral taken over the reals?

[scarlet charm]

it is real valued så <infinty. But the integral could be over any set in the borel sigma algebra if that makes sense

so as an example, if u is the indicator function of the set A in the borel sigma algebra, the integral is just lambda(A) where lambda is the Lebesgue measure.

[somber ginkgo]

right ok

cus i have an idea which works if we integrate over like [0 infinity) or smth like that

[scarlet charm]

yeah? that sounds good

[somber ginkgo]

basically like imagine a triangle but that triangle gets shorter and longer

then our function -> like a constant

but the integral of all our intermediate functions < that

wait lemme draw a diagram

[scarlet charm]

I like the idea, it seems like it could be something. Hmm we just have to make sure we keep the integral of all u_n 20, and the integral of u is 25

[somber ginkgo]

something like this?

aside: u could also make this work for smth like [0, 1) by making it 'infinitely tall' at 1

but idk how u could construct such a function for i.e. [0, 1] but i'll keep it in the back of my mind

[somber ginkgo]

wait u could do the same thing but define f(1) = 0

cus we don't need u_n to be cts

[scarlet charm]

yeah okay this look solid. So we need a sequence of functions that does this. Do you have a construction in mind? Idk if we need like some indicator function stuff going.

[scarlet charm]

I see yes. We just need to have the integral of u_n be 20. hmmmm

[somber ginkgo]

well u'd have to define it piecewisely

but like yeah just something where u stretch the box infinitely wide

sorry i haven't really gotten into measurable functions yet so i can only suggest ideas

[scarlet charm]

but would this stretching keep the integral constant for all n?

[somber ginkgo]

as in just force the box to be that way

like 1x1

1/2 x 2

1/4 x 4

etc.

[scarlet charm]

Yes I see. hmmm so what with something like this for some a_n in R and A_n is in the borel sigma algebra

or maybe something like this, if one part is the "length" of the box and the other is the "height" of the box

[somber ginkgo]

yh potentially

[scarlet charm]

so if we stretch the "box" out, would that mean a_n and b_n would do the "reverse of eachother" if that makes sense?

[fresh crescent]

Hey there! Thank you for the problem, do you want a basic equation to see how I solved it?

If you have any questions go ahead

[scarlet charm]

sure, you solved the problem? That would be a great help MoosE!!

How do you get that 40n+25/2=20 for all n? in the last part of showing u_n

[fresh crescent]

Oh that was a mistake

I think

There is supposed to be a 12.5 in there somewhere

[scarlet charm]

hmm then how does the integral of u_n equal 20 for all n? I don't follow

[scarlet charm]

there is a 25/2

[fresh crescent]

Replace the 25/2 with 15.5

12*

12.5

[scarlet charm]

yes that is the same

then how do we get 40n+12.5=20 for all n

[fresh crescent]

That is my bad let me change it

[scarlet charm]

okay no worries, I will wait

[scarlet charm]

how does the integral of u give 20 always? I don't follow

[fresh crescent]

I made a new equation

[scarlet charm]

this is still not 20 for all n. Just n=1 dosen't hold.

sorry

40+(40-10)=40+30=70

I think we need u_n as something like this

[fresh crescent]

I’ll do one last try

[scarlet charm]

yes

[scarlet charm]

but now you have integral of u_n is 25

[fresh crescent]

Right

Try to solve the rest

[scarlet charm]

hmm okay

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[lavish hornet]

[lavish hornet]

▼

[lavish hornet]

This also grants you u ∈ ℒ¹ for free, since 0 is trivially λ-integrable.

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[cosmic plinth]

To get the partial derivatives Fx and Fy, can I treat t as a constant?

[cosmic plinth]

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[wraith hinge]

What is 2+2

[sleek canopy]

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[wraith hinge]

lol

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[fair forge]

can i assume T Linear trans.?

[fair forge]

i mean why cant they just write it properly

LT or L.T

it takes 1 second and it makes it correct

[nova spire]

Well you can at least state T is a linear transformation

[fair forge]

still it's not proper to do that

it's assuming ill understand based on further topics in the course

[nova spire]

If you wanna be 'proper' just show T(au + v) = aT(u) + T(v)

[fair forge]

thats a further proof

thats something i dont think should be okay to just gloss over

[nova spire]

Then prove it

Let u = (x1,y1,z1), v =..., and a any real number

[nova spire]

And prove this

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[molten mesa]

Quick question how or why is the radius the amplitude? I'm having a hard time imagining it. 🥲

[molten mesa]

My teacher says: "*Note that in the context of this problem, the amplitude will also represent the radius of the Ferris wheel!"

[clear cloud]

You hop in the wheel at t = 0

Do you agree that after one round you will end up at the same point ?

[molten mesa]

yep

[wraith hinge]

surely he meant diameter rather than radius?

[molten mesa]

How so?

[wraith hinge]

Think of it this way, when you reach the top of the ferry wheel, your vertical height (amplitude) will coincide with your ferry wheel's diameter

[molten mesa]

OH I SEE WHAT YOU MEAN.

Okay okay I think I got it, thank you both very much!

.close

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[vernal ermine]

Im having trouble getting the parent (y=3^x) into exponential h,k form

[vernal ermine]

picture of the parent graph on the right

[zinc ginkgo]

,rccw

[zinc ginkgo]

,tex .transformation rules

[solid kiln]

riemann

[vernal ermine]

uhhh

is that supposed to help

i still dont understand

sorry im not trying to be mean

[zinc ginkgo]

y = f(x)

[vernal ermine]

.close

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[vestal fiber]

is this true or false? I have no idea how to solve this

[wraith hinge]

yes its true

maybe also for 1 and 0?

[austere cedar]

Symbols here are a bit unclear. Is this a group? a doesn't seem to be defined

[crimson rover]

Think it's a derivative question

[austere cedar]

' isn't common

Oh I see

[crimson rover]

No but in highschool I used to use it non stop

Now it's kinda gross 😭

[vestal fiber]

can you explain

[austere cedar]

Then yes this is true.

[vestal fiber]

prime

[cosmic meadow]

The point is you prove it

[vestal fiber]

can someone explain

[crimson rover]

What kind of course is it?

[vestal fiber]

calculus brother

[crimson rover]

Theoretical or applied?

[vestal fiber]

calculus 1

[whole coral]

(not for 1, derivatives of constants are zero)

[vestal fiber]

i dont know the difference between theoretical or applied

[wraith hinge]

true

[crimson rover]

It changes how you'd answer the question

[crimson rover]

Oh yeah 0 is a counter argument right?

[cosmic meadow]

So did you try anything to understand that, @vestal fiber ?

[vestal fiber]

Ofcourse brother

But I don't know the answer

everyone says true but noone says why

[cosmic meadow]

Show what you tried

[crimson rover]

0 works if you don't include x=0

[whole coral]

Well, depends on what "all x" means, in particular the expression isn't really well defined when x is nonpositive

[vestal fiber]

I tried to understand what it meant, but after that I had no clue how to solve it

[cosmic meadow]

What is the derivative of a^x?

[wraith hinge]

"for all x" i mean 0^0 could be weird unlesss u define 0^0 = 0

[cosmic meadow]

What does 0^0 has to do here?

[crimson rover]

We were considering a counter argument where a=0

Which works everywhere but when x=0

[whole coral]

x negative doesn't work either, dividing by zero

[crimson rover]

Oh true

[vestal fiber]

a^x * ln(a)

[crimson rover]

But then you can rewrite a as something that doesn't let you input negative numbers

[cosmic meadow]

And when is a^x * lna = a^x?

[crimson rover]

Oh nvm actually

[cosmic meadow]

@vestal fiber

[vestal fiber]

I am thinking

i am thinking

I have no idea

literally

i am gonna give up

[cosmic meadow]

When is x * a = x?

[vestal fiber]

if a = 1

[crimson rover]

But that would still be true for the original function a^x; x can't be negative so its still true for negative x they don't exist for the original or the deriv

[wraith hinge]

a^x =/ 0 so devide by it

[cosmic meadow]

Good then

[cosmic meadow]

This is the same question

What does lna have to be

[vestal fiber]

1

lets goo

Siuu

[cosmic meadow]

And when lna = 1?

[vestal fiber]

when a is a variable

I think

i forgot

omg

[wraith hinge]

...

[cosmic meadow]

Ln = log in base e

What is log in base 10 of 10?

[wraith hinge]

ln(a) = 1

for what a?

[cosmic meadow]

Solve this unrelated problem first @vestal fiber

Log_10(10) = ?

[vestal fiber]

1

ln(1) = 1

[cosmic meadow]

No

Relax

[vestal fiber]

ln(e^1) = 1

[cosmic meadow]

No need the 1 but yes

So if lna = 1

[vestal fiber]

lfg

[cosmic meadow]

U can deduce that a=

[vestal fiber]

lets go

[nimble lynx]

hi

small help pls

[vestal fiber]

.close

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[arctic wyvern]

i have no idea what do after this. I just started Arc length 😭

[limpid dawn]

what a pain in the arc

[whole coral]

You can factor this, think about...

...what you just expanded...

[arctic wyvern]

tell me about it

[arctic wyvern]

but from what i’ve seen you have to expand add 1 and then play with the expression like i hate it here 😭

[whole coral]

Alright, let me give you an observation-

(a - b)^2 expands to a^2 - 2ab + b^2, and (a + b)^2 expands to a^2 + 2ab + b^2...

[limpid dawn]

,w D[(3/5)x^(5/3)-(3/4)x^(1/3)+9, x]^2+1 = (1/2)+x^(4/3)+(1/16)x^(-4/3)

your work seems off

,w simplify D[(3/5)x^(5/3)-(3/4)x^(1/3)+9, x]^2+1

[solid kiln]

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[arctic wyvern]

i hate calc idk what to do anymore

[solid kiln]

bacc the sigma😔🤞

[limpid dawn]

Your derivative y' is fine

Something went wrong when you squared it

actually no your y'² is also fine

[solid kiln]

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[arctic wyvern]

my homework wants an exact answer

and i hate asking software like AI cuz they’ll just say “it’s too complicated get rekt” LIKE YOURE SUPPOSED TO HELP

[limpid dawn]

ok your work was fine from the beginning

you just need to factor

as already pointed out lol i live in the past

[arctic wyvern]

😭

it’s ok

but when you mean factor which line of my work should i factor? i’m at a loss here

[limpid dawn]

,, (x^{2/3})^2 + 2\cdot \frac{1}{4} \cdot x^{2/3} \cdot x^{-2/3} + \left ( \frac{1}{4}x^{-2/3} \right )^2 = \left ( x^{2/3} + \frac{1}{4}x^{-2/3} \right )^2

[solid kiln]

bacc the sigma😔🤞

[limpid dawn]

it's like a² + 2ab + b² here

[arctic wyvern]

i hate this so much

[limpid dawn]

can you see it tho

So you actual integral

[arctic wyvern]

yeah i do but isn't that what i did

let me get a close up

[limpid dawn]

,, \int_1^{27} x^{2/3} + \frac{1}{4}x^{-2/3} : \dd x

[solid kiln]

bacc the sigma😔🤞

[arctic wyvern]

wait

that’s what i was supposed to factor 🤦‍♂️

[limpid dawn]

yes

to make your life easier

[arctic wyvern]

let me cry why didn’t i see it

[limpid dawn]

it's okay

my stupid ass didnt see anything

[arctic wyvern]

so in a sense it’s a perfect square?

[limpid dawn]

yes

cancels out neatly with the square root

[arctic wyvern]

hmm

i hate math

but i love it

[limpid dawn]

ok

[arctic wyvern]

ToT

i need to know when im going to use this as an engineer

ToT

[limpid dawn]

funny thing

you won't

[arctic wyvern]

...

[limpid dawn]

computers will do the work

[arctic wyvern]

🧍‍♂️

then what the fuck

im suffering at home almost cried

[limpid dawn]

you think you will calculate integrals

[arctic wyvern]

just for computers to do it

[limpid dawn]

as work

[limpid dawn]

it still needs someone who has expertise and can tell when somethings off and shit

[arctic wyvern]

oh

i just want to make cool bionic arms and artifical organs

[limpid dawn]

damn we are screwed

let me die

[arctic wyvern]

🧍‍♂️

erm

i won;t

you'll be a knew cyborg 😍

[limpid dawn]

you will resurrect me artificially

[arctic wyvern]

when im done with you

[limpid dawn]

damn you a crazy helpee

[arctic wyvern]

ok but thank you so much cuz i was suffering ToT

[limpid dawn]

what's ToT

i only know lol

[arctic wyvern]

ToT = 😭

[limpid dawn]

damn

[arctic wyvern]

when i don't feel like typing it

[limpid dawn]

you dead in german?

ah ok

,w translate tot from German

[arctic wyvern]

im not german 😦 they are cool af tho

[solid kiln]

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[lean thunder]

I want to find a formula of how many such squares will be there if the container square size is n*n.

[dense rock]

Assuming

only lattice points as vertices?

[vagrant marsh]

assuming the squares are on the lines

[dense rock]

so they have to have perpendicular sides

to the big square?

or parallel

[lean thunder]

diagonal squares are also allowed

[dense rock]

hmm

that makes it harder

ok one where all sides are parallel is just nc2

but im not sure abt diagnol squares

[lean thunder]

are you sure?

[dense rock]

im pretty sure

unless u can find a contridiction

[dense rock]

that is assuming all sides of that square is parallel to the big square

[lean thunder]

I thought it's 1+2^2+3^2+...+n^2

[dense rock]

and only lattice points

Here i will show my thought process

and you can correct me

[lean thunder]

ok

[dense rock]

so we need it to be a square

chooseing 2 lines to be parallel

they are our first sides of the square

now there is only one choice for the remaining sides

so it is nc2

wait

i did mess up

[lean thunder]

yes

its not correct

its sum of square of numbers from 1 to n

[dense rock]

well i derived it from the rectangle formula 😅

[dense rock]

is it?

is that for all possible

[lean thunder]

yes

[dense rock]

or is that for strictly parrallel and lattice points

[lean thunder]

<@&286206848099549185>

[lean thunder]

yes

[dense rock]

Well i have an idea of what one could do to find diaganol squares

Consider a lattice square

or gird

Consider each point to be the center of a diagonal square.

Now those on the edge of the grid can create 0 by 0 squares

we disregard those

moving in a layer

we can consider those lattice points

lines can extend from the center square to the edges a max of 1 unit

resulting in at biggest a sqrt 2 by sqrt 2 square

moving in another layer

we can see that the biggest is extending from the center 2 units

meaing they can make both sqrt 2 by sqrt 2 squares and 2sqrt 2 by 2sqrt 2 squares

we can do that til we exhaust all points

Now the parity of n is also a factor

so im gonna split into those with an even and those with an odd parity

i will also assume n means amount of lattice points per side

call the function f(x)

as the one to find diaganol squares

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[dense rock]

f(n) = 2^04(n-3)+2^14(n-5)+....2^n(n-n+1) if n is odd

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[copper robin]

I do not understand geometry, I have 3 ixls due tonight and need to finish them so I won't be failing.

[copper robin]

so these are my options atm

i dont understand most of these

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[split barn]

A bacterial colony doubles in size every 20 min. How long will it take a colony of 20 bacteria to grow to a
population of 10, 000?

[split barn]

ive just been trying to plug it into the decay formula

here hold on

what ive done so far is 10000 = 20(2)^t/20

trying to find hte t as how long it would take

[bright quarry]

yea looks good

your equation is correct

just solve for t

divide by 20

then 🪵

then multiply by 20 and you’re done

[split barn]

okay for the division part in the exponent how would i get rid of that

does inverse operations apply

[idle wolf]

You can multiply

[faint schooner]

log_2(500)=t/20

[split barn]

where does the (2) go

[bright quarry]

log_2 is the inverse of 2^

$\log_2(2^u) = u$

[solid kiln]

knief

[split barn]

any other way my curricular didnt have that

for the other problems they said to create a y1 and y2 into desmos but whenever i do that the x of the intersecting point doesnt give me the right answer when i put it back into the equation

[bright quarry]

please learn how to solve things analytically instead of graphically

[split barn]

ik but ur method isnt in my lessons

i usually dont use desmos

can i send ss?

[bright quarry]

yea

[bright quarry]

ahh man that’s dumb

your teachers are terrible

who teachers exponentials without logarithms

use khan academy

you don’t need them

[split barn]

bro lowkey im just tryna get through this class

[bright quarry]

you used 50

it’s 500

[split barn]

oh yea

oops wait

but its a e learning course for college

e learning sucks

[bright quarry]

khan academy is elearning

[split barn]

yeah i got 9891 ill round it to 10000 thanks

just do the period close thing right

[bright quarry]

what

[split barn]

to close the chanel

[bright quarry]

oh yea

[split barn]

channel

.close

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[crimson thunder]

ok erm im back with another question~

[crimson thunder]

thats erm what i did

and then i got lost ;-;

[wary basin]

first step is good

next step is how to simplify

[crimson thunder]

is this a new trend i didnt catch on 😭

[crimson thunder]

sorry if it takes me a bit to reply! i lag a lot at night

[zinc ginkgo]

1/(a/b) = b/a

[crimson thunder]

how do i-?

oh so now its

that chopped off bit says 3

?

[late laurel]

solve the complex fraction

[crimson thunder]

is this what i do next?

[late laurel]

is it 5

[crimson thunder]

OH &

7

MBMB

ok wait

how does it become this guys

oh i lied

i got it

[wary basin]

nice :D

[crimson thunder]

TYSM KIND TORTURED SOULS

I WILL REMEMBER YOU (if i ever graduate high school)

[late laurel]

sometimes no words say a lot

[crimson thunder]

❤️

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[subtle topaz]

A line is tangent to a circle.
It means a line just touches the circumference at a point so it forms a microscopic line of 2 pixels(without space) or
Does it means the line touches the circumference at a point so it forms a microscopic line of 1 pixel

[late laurel]

the line touches the circumference at a point as in point of coordinates

[subtle topaz]

oh ty

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[vagrant fossil]

Is y=2x+3 a direct variation

[prime crystal]

no

[vagrant fossil]

We can add 2x and 4

3*

Then it turns to y=5x

[prime crystal]

what

its 2x+3

not 2x+3x

[vagrant fossil]

Yea

[prime crystal]

yeah so how can you add 2x+3 into 5x

[vagrant fossil]

Idk

I mean

If both have x that would make it x²

Not just x

[prime crystal]

how

thats in multiplication

$x+x = 2x \ x \times x=x^2$

[solid kiln]

Astar777

[vagrant fossil]

So its not direct variation?

[prime crystal]

no

direct variation is a linear relationship between an independent variable and a dependent variable

y=kx

[vagrant fossil]

If x increase same toby

To y*

[prime crystal]

if it was y=2x then it would be direct variatiion

[vagrant fossil]

What abt y=2x²

I mean its direct right

[prime crystal]

nah

[vagrant fossil]

Why

Its the same

[prime crystal]

how

its not linear

its exponential

[vagrant fossil]

Uh

What abt

2x=4y

[prime crystal]

yes

y=(2/4)x -> y=(1/2)x

if its in y=kx form

its direct variation

[vagrant fossil]

How

Bro So confusing

It can be direct if y=kx

Im crying

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[last dawn]

Since 0 (false) and contradiction are not the same thing, why do we assume that A is automatically contradictory whenever A is false

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@last dawn Has your question been resolved?

[last dawn]

<@&286206848099549185>

[pulsar dust]

Hm wdym?

[last dawn]

0 doesnt mean contradicts, right?

Why do we then assume when a is false that it contradicts too

?

[west sleet]

A has two states true and false

If we want to find the value of not(A), it is one of the values true or false which is not the value of A

A=true
not(A)=false

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