help-0

[inner sequoia]

wait

[surreal meadow]

this means that the value of f(0) coincides with the value of g(2), essentially saying that f was shifted 2 units to the right

[golden nymph]

to get g?

[inner sequoia]

OH

so f will be to the right of g

[surreal meadow]

no

[golden nymph]

no

[surreal meadow]

f is to the left of g

[inner sequoia]

nvm i got my directiosn confuse

[surreal meadow]

"f was shifted 2 units to the right"

[inner sequoia]

thought right was left

[surreal meadow]

so as to say that g is 2 units to the right

[golden nymph]

amaznig

[inner sequoia]

ikr

[inner sequoia]

the number in parentheses is X right?

[surreal meadow]

yes, these are both functions of x

[inner sequoia]

alr

lemme think abt this

f(x)=2x

g(x)=2(x-1)

x=1

f(1)=2

g(1)=0

[surreal meadow]

yes

now think about f(2) g(2)

[inner sequoia]

but why is g(1) a right shift

isnt 0 to the left of 2

[surreal meadow]

0 is below 2

g(1) and f(1) are ploted on y = g(x) and y = f(x)

the x values are the same

so they are not to the left or right of each other

[golden nymph]

are you talking about the graphical representation of addition in a function?

[inner sequoia]

oh yes i forgot that was a y value

[golden nymph]

or what is the topic

[surreal meadow]

the overarching question is "why does f(x-a) shift the function a units right and not left"

[golden nymph]

yeaaah

I like this one

A classic

[inner sequoia]

OH

but if the y values were the same

then the lower one would be to the right?

[surreal meadow]

then the x values show why f(x) is to the left of g(x)

yes

jnow

now

no

lower on the x-axis means left

[inner sequoia]

lower on the y axis

[surreal meadow]

lower on the y-axis means the number is lower as well

left on the x-axis means the number is lower

[surreal meadow]

go on with this thought

when the y values are the same

[inner sequoia]

heres what i mean

equal x value

[surreal meadow]

that's when the x-values are the same

[inner sequoia]

equal y value

[surreal meadow]

yes

[inner sequoia]

the one that previously had a lower y value, when set at an equal y value to the other function, will be to the right on the x axis

HOLY SHIT IM DUMB

if you subtract from x you are subtracting from the y axis bcs i was changing what y was giving me not what x was giving me

but x is the same

DAMN IT I DIDNT NOTICE

[surreal meadow]

don't think of it that way

that works here because this function is linear

[inner sequoia]

i am subtracting from f(x), not from x itself

f(x) is the y value

so lower y value

but if the y values are made equal

then the one that had the lower y value when the x value is equal will be greater

[surreal meadow]

this works here because this is a linear function

but think of it for f(x)=x^2

g(x) = (x-1)^2

you're not simply subtracting 1 from y, or the function, you're substituting x-1 for x

[inner sequoia]

in my head it still works

[surreal meadow]

take x = 50

[inner sequoia]

i am squaring a lower number to get y, meaning the y value is still lower

but if i square a higher number then i will get a higher y

[surreal meadow]

https://www.desmos.com/calculator/5omaafn2ce

[inner sequoia]

but if i set the x values equal then the previously higher y will be to the left of the lower y

[surreal meadow]

check out those functions

in some intervals, x^2 is higher

in some (x-1)^2 is higher

(x-1)^2 =/= x^2 - 1

[inner sequoia]

ik

but f(x) is the y value

and x+1 is greater than x

[surreal meadow]

yes

[inner sequoia]

but if i set both at equal y values then x will be to the right

because a lower number is being squared

so if x is equal then it will be lower

[surreal meadow]

not necessarily

take x = -3

[inner sequoia]

what

[surreal meadow]

(-3 -1)^2 > (-3)^2

[inner sequoia]

well yes but if its negative then its the reverse

[surreal meadow]

think of it from the plane's perspective again

doing x-1 means shifting every x value to the left by 1

[inner sequoia]

yes

[surreal meadow]

so the plane is moving to the left by 1, while keeping the curve stationary

[inner sequoia]

yes

[surreal meadow]

in other words, the curve is moving to the right by one while keeping the plane stationary

[inner sequoia]

mhm

[arctic blade]

@alpine sable hmm I've just thought, perhaps probability isn't what i want. it may give a nice [0,1] value, but it doesn't sound right. To explain further, I'm going to use this 'value' of how different/off-trend this mew value is to feed to another function to decide how to correct it.

I have three other ideas:

1. fit a curve to it, then find the squared difference between the predicted value from the curve and the actual value.

2. fit a curve and calculate the derivative, regarding the gradient as the 'trend' then somehow compare that to the new value

3. find the weighted mean, meaning newer values 'matter more', and somehow compare the new value to that.

Which do you think is best? Or another method entirely.

[alpine sable]

It's hard to say, although I don't think you need a value between 0 and 1 for that application

So maybe taking the squared error from the prediction would work fine

[inner sequoia]

what is difference between vertical stretch and horizontal shrink

[alpine sable]

Horizontal shrink doesn't extend vertically I guess

[arctic blade]

@alpine sable hmm, I'll continue researching. i could use a better time series model, like ARIMA or Bayesian. The main question, that if you could answer would be used in all of these applications, is that if i do somehow have a predicted value, and a real value, what's the best way to compare them?

a squared difference, a ratio, or some other way?

[alpine sable]

We usually use squared or absolute difference in machine learning

[arctic blade]

hmm, thanks 🙂

[alpine sable]

Absolute is more robust but not differentiable

Anytime

[arctic blade]

might give a few a go and try and experiment, see which works better

[alpine sable]

Yeah in the end it comes down to which works better in practice

[ripe mountain]

does anyone know a simple 3d function of two variables that has at
one point a minimum in one direction and a maximum in another direction

[surreal meadow]

what do you mean by that

[ripe mountain]

hmm i guess i can show this

[austere bridge]

a saddle point?

[ripe mountain]

that one is the part c for the problem

here's part a: Draw a rough sketch (three-dimensional of course) of the graph of a simple function
of two variables that has an absolute minimum at a single point (say, at (0,0,0)).

that would be an answer to the part a

where the absolute minimum is at (0,0,0)

[ripe mountain]

my teacher said the most stragithforward answer to this problem has something to do with a 3d funciton that resembles a pringle, but i'm not exactly sure what he meant

[alpine sable]

Dhm

Ehm

Ask @soft ocean

[austere bridge]

a function like this?

[alpine sable]

Yes

[ripe mountain]

that's x^2-y^2 right?

[austere bridge]

yeah it is

[ripe mountain]

does that have a max and a min though?

at one point

[austere bridge]

sure it does

from one direction, it looks like this

it's a minimum

[surreal meadow]

what's part b?

[austere bridge]

but if you look from the other way, it's a maximum

[ripe mountain]

that's a maximum?

oh wait

it is at that point

because there's nothing else "below" it

[ripe mountain]

Draw a rough sketch of the graph of a simple function of two variables that has an
absolute maximum at a single point.

that would be the answer

[surreal meadow]

what's part c?

[ripe mountain]

this is part c

[surreal meadow]

can you send the words verbatim

[ripe mountain]

Draw a rough sketch of the graph of a simple function of two variables that has at
one point a minimum in one direction and a maximum in another direction.

[fair vine]

it doesnt say absolute, wouldnt sin(x+y) do?

[surreal meadow]

then yeah, x^2-y^2 looks like what you want

[ripe mountain]

yeah i think that also would work

[ripe mountain]

hmm okay thx

[alpine sable]

For future reference that's called a saddle point

[ripe mountain]

in general?

[ripe mountain]

a point with a max in one direction and a min in another direction?

[alpine sable]

Yea

[ripe mountain]

ohh okay thx

[alpine sable]

https://en.m.wikipedia.org/wiki/Saddle_point

Anyway just a fun fact

[ripe mountain]

3d is so cool man but there's so many things i need to think about lmao

i need to evaluate this where x=0, did i do this okay?

[placid zinc]

No haha. Can't just sub in half the limit

[ripe mountain]

what confuses me about this is it's basically infinity * zero, which would be indeterminate, does that affect the problem

[placid zinc]

Oh wait, you only care about where x = 0?

[ripe mountain]

for this particular case, yeah

[tight locust]

1^inf = 1

[ripe mountain]

oh so i didn't even need to do any ln stuff

?

[placid zinc]

Yeah basically. 1^h = 1, no matter what h is doing

[tight locust]

yes because this is exact 1

tending 1 is a different matter entirely

[ripe mountain]

wdym tending 1

[tight locust]

well the typical example of a 1^inf limit is this

(1+1/x)^x

as x approaches infinity

so the base approaches 1 as the exponent approaches infinity

hence tending 1 and not exact 1

[ripe mountain]

ah

so because x=0 here i don't have to worry about that in this particular case?

[tight locust]

yes

[ripe mountain]

so i'd just evaluate the limit to 1^infinity and say 1^anything is 1, so L=1

[tight locust]

yep

[ripe mountain]

ooh i see thx

[tight locust]

you should recognize this limit

[ripe mountain]

it's pretty common i assume?

[tight locust]

it's called e

[ripe mountain]

ohhh yeha

okay thank you

[frail crater]

What’s 1+1-2x2-23

[alpine sable]

Do you understand pemdas

[frail crater]

No

[alpine sable]

You evaluate parentheses first, then multiplication and division, then plus and minus

[inner sequoia]

is there diff between reflection along y or x axis

bcs when i check calculator reflecting using g(x)=f(-x) and reflecting using f(x)=-f(x) are exactly the same

[surreal meadow]

yes there is a difference

plot sin(x) and try it

and then plot cos(x) and try it

[dawn galleon]

Parametric equation= (-1,2,5) + s(4,0,-1) + t(-1, -5, 1)
Scalar equation = 5x + 3y + 20z +101=0
Vector equation= r . (5i+3j+20k) =101

did i do these right

<@&286206848099549185>

[surreal meadow]

^

[dawn galleon]

its hasnt been answered for hours

so i pinged after hours

so ye

[surreal meadow]

i think you're smart enough to understand that that's not logical

[dawn galleon]

no

no one answered so i posted it again

now i can use the helpers role

[surreal meadow]

now you can use the helpers role in 15 minutes

[dawn galleon]

yes my next helper role will be in the next 15 mins

[surreal meadow]

you clearly didn't read #❓how-to-get-help

[dawn galleon]

i did it says ping helper role after 15 mins

[surreal meadow]

you may use the <@&286206848099549185> tag once

fuck me

your scalar equation looks wrong

[dawn galleon]

No how

[surreal meadow]

which leads me to believe that your vector and parametric are too

[dawn galleon]

do not guess

[surreal meadow]

its not a guess

[alpine sable]

Parametric looks fine

But scalar is definitely wrong

[dawn galleon]

5x + 3y + 20z =110

now?

[surreal meadow]

looks good

[dawn galleon]

and my vector equation is good too?

[surreal meadow]

yes

[stable leaf]

what is a scalar equation?

[dawn galleon]

Ok good should it be
5x + 3y + 20z =110 or 5(-1)+3(2)+20(5) = 101

[stable leaf]

is ax+by+cz=d or whatever

is that what that is called

[surreal meadow]

yes

[stable leaf]

did you try graphing them

[dawn galleon]

no

[stable leaf]

i mena obviously you can also juts plug in numbers and i assume that works?

[surreal meadow]

why would it be the second one?

[dawn galleon]

idk i thought it might be 2nd one

[surreal meadow]

but why?

[dawn galleon]

idk

[surreal meadow]

.

[dawn galleon]

yes

[stable leaf]

@surreal meadow

do you have the answer?

I mean i got an answer that i believe is correct

[surreal meadow]

the answer to what?

[stable leaf]

the scaler equation

i believe it is right

[surreal meadow]

the one he gave was incorrect

[stable leaf]

the one i have

i just didn't wanna post it in here because I don't think you are suppose to give direct answer

[surreal meadow]

he already has the answer

you can share yours if you want

[stable leaf]

5x+3y+20z=101?

[surreal meadow]

looks good

[stable leaf]

maybe @dawn galleon just needs to plug a number into his equation and solve for the right side

[surreal meadow]

he already solved it

[stable leaf]

oh i see

[celest anvil]

what i tried

so i know from this graph

that the radius is 3

the height is the upper function 2-(x^2+1)^-2

the bounds are 0 to3

im doing something wrong or missing something

[dawn galleon]

is scalar 5x+3y+20z=101? or 5x+3y+20z=110

101 or 110?

[stable leaf]

101

plug in a poiint

point

and test it

see what you get on the right side

pick a, b, c

try them

[dawn galleon]

ye it should be 101 ty

[arctic wren]

Maybe this is a dumb question but why this function is differentiable ? How i can check that?
$f(x)= x^{2}, x \le 1$
$f(x) = 2x -1 x > 1 $

[ocean seal]

Guilhotina

[topaz scaffold]

I think you gotta do the top function minus the bottom function

$\int_{0}^{3}2\pi x ((2-(x^2+1)^{-2})-(x^2+1)^{-2}) ,dx$

[small bear]

you check the derivative of the top function from the right or 1+, and the derivative of the bottom function from 1- (the left)

[ocean seal]

RipeOrange

[celest anvil]

ok i'll try that

[small bear]

if they match, its differentiable, otherwise it isn't

[arctic wren]

ooo ty

another question

$f(x) = x^{2} , x \le 1$
$f(x) = x^{2} -3 , x>1$

[ocean seal]

Guilhotina

[arctic wren]

this isn't continuous in x =1 , right ?

[surreal meadow]

yup its not

[arctic wren]

ok

ty

[celest anvil]

can you calculate it? i can't

[topaz scaffold]

,w integrate 2\pi x ((2-(x^2+1)^{-2})-(x^2+1)^{-2}) dx

[ocean seal]

Results provided by WolframAlpha

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

Requested by RipeOrange#4907

[topaz scaffold]

Ah this just becomes $\int_{0}^{3}4\pi x (1-(x^2+1)^{-2}) ,dx$

[ocean seal]

RipeOrange

[celest anvil]

roger roger

[topaz scaffold]

This should be easy to integrate

Use the chain rule thing

No idea what it's called for integrals

Reverse chain rule (?)

[celest anvil]

ye thx

[tight locust]

u sub

[topaz scaffold]

Ah

[carmine lion]

im not sure if im doing this right or not

[red phoenix]

what are yuou doing?

[carmine lion]

integral of x from -1 to 3

but idk if that will find the area

[red phoenix]

integrals defo find area

consider just changing y wit hx

and finding the integral against the x-axis

it would be the same right?

[carmine lion]

yea?

[red phoenix]

doesn't this give you confidence in your answer?

[carmine lion]

but the whole thing would be negative

wait so am i right

[red phoenix]

it wants area

so you flip that thing to positive

be careful tho

[carmine lion]

can't i use dy's?

instead of doing y=x^2-2x-3

[red phoenix]

yes

[carmine lion]

integral of x from -1 to 3

so isn't this right then

and then i absolute value

[red phoenix]

2-secs

i want to check something

[carmine lion]

ok

[red phoenix]

yes, so you would get negitive both ways

what was your answer

[carmine lion]

i got what that

[red phoenix]

looks good

but remember you want area

[carmine lion]

so positive

ik

[carmine lion]

thing is

why doesn't it show a sideways parabola

thats the only thing im confused about

[red phoenix]

idk, i suppose you can just turn your head?

perhaps it can only generate curves with x

[carmine lion]

ah ok

[red phoenix]

perhaps it internally changes the y to x

[alpine sable]

hi

does this mean we accept it

[queen nova]

Dylan has a fish tank at home. He knows its height, h, is one inch less than twice the width, w, and the length, l, of the fish tank is seven inches longer than the height.

What would be the expression to represent the volume?

[alpine sable]

or we reject the advertismenet

[carmine lion]

jeesuz

people spamming in here

[alpine sable]

(w-1)* w * (w+6)

i wish my math was this easy

what are you 15?

are you even allowed on discord

am i getting trolled

[queen nova]

im 15 yea

[alpine sable]

I'm respectful?

[carmine lion]

idk

[alpine sable]

oh

[carmine lion]

it seemed like ur overreacting

[alpine sable]

are people who are 15 allowed on discord with discord ToS?

[carmine lion]

yes

[alpine sable]

no im just surprised

[carmine lion]

discord ToS allows >= 13

i think

[alpine sable]

oh okay

[carmine lion]

yea

[solar cradle]

Its not really any concern of us how old anyone here is, if they're using the channels appropriately then they're fine

It's discords job to enforce their rules

[wary stream]

If they're under age, the mods have to ban them

From the server

[alpine sable]

have u seen that linkedin math problem about telling how fast horses are from 3 rounds or wtvr

their question seemed like one of those math questions that circulate on fb

i'm like 30 in uni so i'm in no place to judge lol

but their question truly threw me off

like is this an IQ question

@tame needle great musician

[alpine sable]

great dj

[graceful harness]

oops sorry

didnt mean to interrupt

my bad

[queen nova]

Is this right? I got stuck on the last part

[alpine sable]

-16 is in the wrong place

[queen nova]

oh ok

[alpine sable]

-16 * -12 = + 192

[wary stream]

What do you mean wrong place?

[alpine sable]

if you expand (x-16)(x-12) = x^2 - 30x + 192

and that is not x^2 + 4x -192

so unless im understanding this wrong

[wary stream]

So you mean wrong sign

Not wrong place

[alpine sable]

well -30x != 4x

oh yeah

wrong sign

definitely

[woeful pulsar]

avoid giving answers directly

[alpine sable]

huh

[woeful pulsar]

like ensure you engage the person asking to see how they thought about the question

[alpine sable]

oh

okay sure

[arctic wren]

if the line r is tanget to f(x) = -x² and g(x0 0.5 + x²
The unique possible solution is for R= 0 , right ?

[queen nova]

what is this in simplest form?

wait I think I got it

x^2 +4x-42?

I mean

x^2+8x-42?

[woeful pulsar]

g(x)=0.5+x^2?
If you draw them out you should see the lines

[wary stream]

I'm doing it mentally but I did not get this, what's your work?

[queen nova]

uh wait

oh I think I see what I did wrong

is it x^2 + 4x − 12

?

[wary stream]

Sounds right

[queen nova]

got it ty

[arctic wren]

oo ok, another question is there a math symbol to represent that one line is tangent to a function at poin a ?

[glass lichen]

no, just use words

[remote lodge]

what does the n represent in a recursive formula?

[glass lichen]

the term number

$a_n=f(a_{n-1})$

[ocean seal]

Mosh

[remote lodge]

ok thanks Mosh

[tropic ice]

how do they go from first step to second?

[red phoenix]

they do a find of substitute

has h(x) = x^2 +2x

imagine you have h(g) = g^2 + 2g

now just add the (x)

so you have

h(g(x)) = g(x)^2 + 2g(x)

[tropic ice]

so

@red phoenix how do you know where the x goes

if im doing a(x) = x^3 + 4x
a(b) = b^3 +4b
A(b(x)) = b(x)^3+ 4b(x)

oh i see

why does khan subtract instead of add

[red phoenix]

because thats the h(x) = x^2 - 2x

my bad

[tropic ice]

and this is called find a substitute?

[red phoenix]

no

i meant kind of substitute

[tropic ice]

what did I do wrong here

oh

pretend its +10

apparently g(f(3)) is -5

oh

wait

gosh

im so stupid

i got the answer nvm

[queen nova]

I'm not sure if its 12 6 or 7

wait I figured it out

[tropic ice]

6

[oak chasm]

There's also a power of x.

@queen nova

[queen nova]

Can someone help me with this:

[wary stream]

Find the GCF

[flint stratus]

someone from indonesia?

[queen nova]

ok so thats 6x^2

[wary stream]

Divide all the terms by the GCF

[copper prawn]

Can Sigma be used the other way around?

instead of 1+2+3+4+5

5+4+3+2+1

[alpine sable]

not sure

but

if you're heading toward negative numbers, maybe

[ionic jewel]

not the notation, but addition works like that in general

you could do $\sum_{n=0}^4 (5-n)$

[ocean seal]

bunny

[copper prawn]

wack

i thought putting a lower number than n at the top would do the job

[ionic jewel]

you can't do a higher number on the bottom of the sum

,w sum from n=10 to 1 of n

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

just goes to 0, notation always requires lower to higher

[copper prawn]

oooooof

this functions gonna look terrible

its already got floored powers to the log of 10

thx

[gaunt magnet]

hi

quees

<@&286206848099549185>

[stark grail]

Can anyone guide me for this ques ? I cant do this TvT

[gaunt magnet]

bruh channel in use

[stark grail]

im sorry

[gaunt magnet]

<@&286206848099549185>

[oak chasm]

Shouldn't it be when x and y are zero?

The z intercept, I mean.

[craggy ember]

I need just strait help in general

[oak chasm]

@gaunt magnet

@craggy ember Sorry, channel is busy.

[gaunt magnet]

i got -14

[devout sigil]

@stark grail I can help u now... let’s move to #help-7｜zen1thxyz if u want?

[stark grail]

sure! thank you so much!

[thorn kindle]

[oak chasm]

12 + 2s + t = 0
-9 - s - t = 0

2s + t = -12
s + t = -9

2s + t = -12
2s + 2t = -18

t = -6
s = -3

z = 4 - 2(-3) + 4(-6)
z = -14

@gaunt magnet Got the same.

[thorn kindle]

[gaunt magnet]

Yay Nice ty
Do u get this for this ques

[oak chasm]

@Usman#0988 That looks fine.

[gaunt magnet]

thanks
i got
4x+5y-z-7=0
for this

[oak chasm]

Yes. To check your work, try [0, 2, 3], [0, 2, 3] + [4, -3, 1], and [0, 2, 3] + [-2, 3, 7].

@gaunt magnet

[versed prairie]

How to find whether this is a reflexive relation

[sly mantle]

unpack definitions

[versed prairie]

Are ya talkin to me

[sly mantle]

yes

[versed prairie]

The first explains why it is reflexive.

And I can't even understand what those bizarre symbols on the right means

Can you explain to me why this is reflexive

[sly mantle]

what does R being reflexive mean?

[versed prairie]

It should have an identity relation and it can also have sets that are related to themselves

The fact is, I can decode if the Ordered Pair is given but if they are given in the form of equations I am getting hella confused.

[sly mantle]

the wording's off

[versed prairie]

It's been a year since I've touched this topic So yeah it'll be a little distorted

[sly mantle]

recall R is a relation on Z. we say R is reflexive if each element of Z (ie integer) is related to itself via R

[versed prairie]

Hmm

[sly mantle]

use the definition of R. to prove R is reflexive, we must show that, for each integer x, 5 divides x-x

[versed prairie]

So here they've given A and xRy and they've said x-y is divisible by 5 which means x-y = 5m where m is the integer so if we substitute x instead of y in x -y we get a 0 and we'll get 5m = 0

Is this ryt?

Taking the 5 out we can write it as 5(m) = 0 and taking the 5 to the RHS we get m = 0

Is this enough to prove that this equation is reflexive

[sly mantle]

R is a relation, not an equation. we don't call equations reflexive

[gaunt magnet]

ok ty

[versed prairie]

Substituting 0 in m we get the eqaution x-x = 5(0)

Yeah rel not an equation 😅

[versed prairie]

This proves that the relation is reflexive doesn't it?

[sly mantle]

the crux of the proof is really just saying x-x = 0 = 5(0). the work done above is just to help you

[versed prairie]

Got it

They've just use weird symbols and equations which confused me 😂

[sly mantle]

also in the proof we should state that we're letting x be an arbitrary element of Z (ie an arbitrary integer) before doing any algebra

[versed prairie]

Oh okay

So the above derivation is valid isn't it

[sly mantle]

the crux of the proof is really just saying x-x = 0 = 5(0). the work done above is just to help you
what's left is to do a 'well written' proof using this as the argument

[versed prairie]

Hmm

So we have to take x as an arbitrary element of R and prove that x - y = 5m is reflexive

[sly mantle]

R is a relation, not the set upon which the relation is defined

[versed prairie]

on Z ...

[sly mantle]

reminder

use the definition of R. to prove R is reflexive, we must show that, for each integer x, 5 divides x-x

[versed prairie]

Here the R is defined on Z by xRy to mean x-y is divisible by 5

So yeah got your point

[sly mantle]

a way we can write the proof goes:
let x in Z. then we have x-x=0=5*0. this shows 5 divides x-x, which is to say xRx. thus R is reflexive

[versed prairie]

Understood

Thx for the help

[sly mantle]

you're welcome

[alpine sable]

is the bottom eqn true or false?

[placid zinc]

The equation is true. Canceling as shown is a faux pas

[alpine sable]

so why is it true then?

[solar cradle]

Its the chain rule

[placid zinc]

I mean I could give a proof, but most people are happy with "the limit definition agrees with it"

[thorn kindle]

Derivatives are fractions

[topaz scaffold]

I want to see the proof

[thorn kindle]

Basic rules of multiplication apply. It's that simple

[placid zinc]

dy/dx = du/dt when dydt = dxdu

[alpine sable]

wait wait wait, derivatives aren't fractions

i can explain

[devout sigil]

dy/dx is not a fraction

[thorn kindle]

y = ∫ du/dt dx

[alpine sable]

they aren't fractions, but we can manipulate them like fractions

[solar cradle]

"can"

[alpine sable]

derivatives are actually ratios

[thorn kindle]

And what are ratios?

[solar cradle]

They're introduced as if they are but they aren't really

[placid zinc]

It's very convenient to think of dy and dx as objects in their own right, but they don't really represent anything.

[thorn kindle]

Yes they do

It's the infinitesimal Δ

[alpine sable]

no, dy/dx is a ratio, but we manipulate them like fractions

fractions are part of a whole

[thorn kindle]

Ratios are fractions

[alpine sable]

but ratios compare two objects

ratios are not fractions!!!!

fractions are a part of a whole

ratios are not

[devout sigil]

It is the rate of change of y with respect to x. dy is a very small change in y and dx is a very small change in x

[placid zinc]

Let's use an example.
y = x²
dy/dx = 2x

What is dx here?

[devout sigil]

It is essentially found as a quotient

I remember reading this somewhere before

[thorn kindle]

The infinitesimal Δ

[placid zinc]

That's just words haha. What actually is it?

[thorn kindle]

Everything i can possibly communicate to you through a text message is just words lmao

[thorn kindle]

Unless youd like me to use emojis

[alpine sable]

dy and dx are ratios

you can think of two number lines

one corresponding to x and the other y

[placid zinc]

Fair point. But I can heavily quantify y, and dy/dx. Both are functions R → R

[alpine sable]

if you nudge x some quantity delta x, it corresponds to nudging y some delta y

and if you take the nudge to be very small, it becomes dx, thus the ratio with dy is dy/dx

[placid zinc]

How small is "very small"?

[thorn kindle]

As small as you want

[alpine sable]

yeah

as small as you want

[placid zinc]

So I could half Δx and get dx

dx must be a real number

[thorn kindle]

dx can be whatever you want. I actually have been required to use dx as a real number

[alpine sable]

bruh

this is one of the most important concepts of modern math

it's the concept of 'approach'

it

yeah

[thorn kindle]

hold on i can show you one of my textbook problems

[placid zinc]

Okay lol no need

I know that you can replace dx with a real number to get an approximation to a change in y

I would never say "dx can be a real number" though

[topaz scaffold]

What happened to the fraction arguments?

[alpine sable]

i rebutted it

because i am a master debater

[placid zinc]

Idunno. I started asking what a differential was and we've gone a long way since

[topaz scaffold]

Well uh

Ratios are fractions

[alpine sable]

no they are not

fractions are part of a whole while ratios only compare two objects

[devout sigil]

A derivative is a gradient function if u are a total noob. If not I can join this debate lol

[alpine sable]

bruh

derivative not same as gradient

[thorn kindle]

an actual textbook problem

[solar cradle]

That's just an approximation

[alpine sable]

it is not rigorous

it is not evaluate dy, it is to approximate delta y

[topaz scaffold]

And in the end its still dy divided by dx right?

To get your derivative

[devout sigil]

It is for a fixed point of a function

[devout sigil]

I meant this^^^^

[alpine sable]

no

[celest anvil]

don't you split dy/dx during u substitution?

[alpine sable]

no, there is no concept of dividing in differentials

[topaz scaffold]

Yea

[thorn kindle]

also separation of variables

[devout sigil]

In fact dy/dx is the gradient function of the tangents to the function at a given point

[thorn kindle]

if dy/dx = 1 then dy = dx then ∫ 1 dy = ∫ 1 dx => y = x + c

[topaz scaffold]

I don't know enough about this to argue so imma just watch

[topaz scaffold]

Btw forgot the constant for the y

[ionic jewel]

you don't need one

[dawn galleon]

[ionic jewel]

he subtracted the constant on the Y side from both sides and got a new unique (single) constant on the other side

[topaz scaffold]

Oh yea oof mb

[placid zinc]

So let me go back to it:
y = x²
So dy/dx = 2x

What is dx?

0.05?

A real number?

If not a real number, what object is it?

[topaz scaffold]

$dx = \lim_{x \to 0} x$ (?)

[ocean seal]

RipeOrange

[dawn galleon]

yes

[thorn kindle]

d/dx f(x) = lim Δx->0 (f(x+Δx)-f(x))/Δx

you need infinitesimals to make calculus work

unless you wish to reject the concepts of infinity and limits themselves entirely.

which is possible

there is a geometric construction of the derivative

[cloud zinc]

how can I find P(S and (C or S)) in the formula:

P(S | (C or S)) = P(S and (C or S)) / P(C or S)

[solar cradle]

S and (C or S) = S

It's easier to verify when you're familiar with set notation

S and (C or S) is the same as $S \cap (C \cup S)$ and since $S \subset (C \cup S) \Rightarrow S \cap(C \cup S ) = S$

[ocean seal]

Billy Clintorus

[cloud zinc]

thats for 2.b

[cloud zinc]

okay

so this is simply P(S | (C or S)) = P(S) / P(C or S)?

[solar cradle]

ye

[cloud zinc]

aighty

thx

[solar cradle]

npnp

[cloud zinc]

so this should be 5/12

however, my textbook says

ohh nvm

I put in the wrong number

[next hatch]

is it possible for an integral to be unsolvable?

was given this question

tried solving 3 and couldn't find any solutions

[oak chasm]

@next hatch It's not asking you to integrate them.

[thorn kindle]

the substitution won't work on 3 but that is integrable

[wild marten]

works on (2)

[next hatch]

i understood the question but thought hey lets try integrate them

[wild marten]

1+x^3 = u => du = 3x^2 dx

on (2)

[next hatch]

i chucked 3 into symbolab and it said no solutions possible

[ionic jewel]

,w integral of x sqrt(1+x^3) dx

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

there u go

[next hatch]

fuck symbolab

[wild marten]

(2) is solvable using u = 1+x^3

[ionic jewel]

not pretty, but it does work

[next hatch]

thanks lester i understood the question

[wild marten]

its in terms of hypergeometric function

[next hatch]

the what

hypergeometric what

[wild marten]

so I think they are not taught about this yet

[next hatch]

nope

definitely not

[wild marten]

you can search about it

[next hatch]

tf is that lmao

[ionic jewel]

oh well i didn't say he could understand it, just that it has an integral

[wild marten]

ohk

[next hatch]

ill pass on that lmao it looks too complicated

thanks though

[wild marten]

its pretty easy actually

[next hatch]

yeah but im doing biomed with this as an elective and no more electives after

so it probably won't be useful

plus im really behind lmao i gotta get my shit together

[wild marten]

you'll get it together, good luck

[next hatch]

thanks ill need it xx

[cloud zinc]

I got a wrong answer

so if it is 13/30 / 12

it is 13/360

in the book it is 13/28

[devout sigil]

Which question are u referring to?

[ocean seal]

Lester

[cloud zinc]

question b

2.b

[strong furnace]

bruh

nabla

[wild marten]

$13/30 / 12 = (13*12)/30$

[ocean seal]

Lester

[strong furnace]

frac{a}{b} works

[cloud zinc]

where did the 28/30 come from?

[wild marten]

I know that, but the OP wrote it in that way so..

[devout sigil]

It’s from C U S

[cloud zinc]

if P(C or S) = P(C) + (S) - P(C and S)

[solar cradle]

I messed it up, this is a cluster lol

[cloud zinc]

it is 12

[solar cradle]

You wont get 12 for a probability

[devout sigil]

I’m wondering why u must take into consideration C n S

Question stated “given that they might prefer the computer lab or the science lab”

[solar cradle]

So earlier you had P(S) / P(C or S), P(S) = 13 / 28, P(C or S) = 1

[devout sigil]

0<= probability <= 1

[cloud zinc]

P(S) = 13/30

[cloud zinc]

I had that formula down

[solar cradle]

Using the formula you wrote, you can see that if you're careful, P(C or S) = P(C) + P(S) - P( C and S) = (15 + 8)/ 28 + (5 + 8)/ 28 - 8 /28

Where are you getting 30 from?

[cloud zinc]

the total of the people

[solar cradle]

5 + 8 + 15 = 28

[cloud zinc]

plus 2

[strong furnace]

well then your P(S or C) changes to 28/30 then

[solar cradle]

oh i didn't see that 2 in the corner lol

[cloud zinc]

lmao

[solar cradle]

But yeah, then P(S or C) = 28 / 30

Then P(S) / P(S or C) = (13 / 30)/(28/30)

[cloud zinc]

S or C excludes the 2 right?

[solar cradle]

yes

[cloud zinc]

aight

is P(A and B) = P(B and A)

or is it not equal to each other?

[strong furnace]

they are equal

[cloud zinc]

oh so its it the same thing?

[strong furnace]

yeah the "union" and "intersection" operators are commutative and associative

[wispy shadow]

help

[topaz scaffold]

Just wondering, is this a test?

[dark granite]

what have you tried? You need to show us that you have at least attempted the problem Also, we don't help with quizzes/tests/exams.

[honest hawk]

Im an idiot

can someone explain or show the steps to how this works?

[topaz scaffold]

Try expanding the log

[honest hawk]

i was thinking that
so log(A)+log(10^B)

Im always stupid with logarithms

ill simmer on this

[topaz scaffold]

Assuming the log is base 10 this becomes log(A) + B

[honest hawk]

i agree

[topaz scaffold]

And then...?

[honest hawk]

Lets see.

Give me a second

just to make sure, the base 10 part of the log and the (10^B) part cancel out, correct?

[vale wigeon]

"0.A"

what does this even mean

[honest hawk]

I dunno--this was on a pre-made ANKI deck

am i doing this right? Sorry, the work is done via computer mouse

[topaz scaffold]

0.1 * A I think

[honest hawk]

(I might need assistance on another one later on if that's okay.)

[topaz scaffold]

You just need to figure out how they are approximating logA

Don't do the last step

Idk how they got the approximation tbh

[honest hawk]

Im not even sure i need this information for the MCAT

but might as well learn

[topaz scaffold]

Do you get a calculator?

[honest hawk]

lol, no

I wish

[topaz scaffold]

Ah that's probably why

[honest hawk]

Wish leads me to believe that something too complicated will not be given

the most ive seen on practice questions are the simple log rules needing to be used

[topaz scaffold]

The 0.A thing might just be a simple approximation instead of a more accurate one then

[honest hawk]

makes sense. Ill probably keep it on the backburner until a question that involves it comes up

[topaz scaffold]

Cool

[minor elbow]

is this channel free?

can someone plz help me?

[honest hawk]

I had another quick question, but go for it

ill just ask it when i get to it

[minor elbow]

ah ok

thx

i dont know what im doing wrong for this q

nvm

i got ittt

[topaz scaffold]

Cool

[honest hawk]

Well, hopefully this is more simple

I can take this one for granted because ive used it before, but trying to derive the proof

lmao all i got is this

[topaz scaffold]

What's log(1)?

[honest hawk]

wait a fat minute

oh crap

[strong furnace]

if I am looking at it right

the estimation assumes

scientific notation

so A in (0,10)

[honest hawk]

Should just be 0

[topaz scaffold]

Yep

[alpine sable]

could someone please tell me what the derivative graph would look like for this

[honest hawk]

oh duh, that makes sense

[topaz scaffold]

So you just get log A

[honest hawk]

jeez i need to make connections

[topaz scaffold]

When the graph is increasing it's positive. When it's decreasing it's negative

Neither would be 0

[strong furnace]

if you're still not sure about the logarithm thing the approximation is within ~0.2 of the actual value always

[honest hawk]

Many thanks! :)

[alpine sable]

is that as x approaches infinity?

so lets say a quartic is decreasing as x approaches infinity

[topaz scaffold]

The derivative will be negative

Probably negative slope too

[alpine sable]

XD

[topaz scaffold]

I gotta make sure yk

[strong furnace]

when working with just graphs of the functions its probably better to just look at the slope of tangent

[alpine sable]

Uh, what's the question? I just completed log today :/

[topaz scaffold]

What question?

[alpine sable]

Oh, got it.

[strong furnace]

do you know how to get the direction ratio of perpendicular line from plane equation

[alpine sable]

@honest hawk you can try new base introduction to make it easier I guess.

[gaunt magnet]

wait i did it do u get

[strong furnace]

that would be correct

[topaz scaffold]

Eh?

[gaunt magnet]

ty

[alpine sable]

Uh, it's just introducing a new base.

[dawn galleon]

hey someone check my vector equation

quick please

i get

r . (5i+3j+20k)

<@&286206848099549185>

[strong furnace]

thats an expression not an equation

you're lacking the right hand side

[dawn galleon]

i got (5,3,20).r = 101

[strong furnace]

right

[dawn galleon]

should their be an arrow on r

[strong furnace]

anything to show it is a vector

[gaunt magnet]

and must add the . before the r

[dawn galleon]

ok t

ty

and yes

i will add .

[strong furnace]

there's a . before the r?

[dawn galleon]

no it .

wait one sec

[strong furnace]

well you had one in your msg so idk what's new anyway yeah that should work

[dawn galleon]

so i need to add the dot rightZ?

[strong furnace]

man you need to just show r (dot product) (5,3,20) = 101

use whatever notations are in your book/course

[dawn galleon]

so the vector equation is (5,3,20) = 101

i dont need to do anything

[stable leaf]

i swear

did this question already get solved

[stable leaf]

^

[hardy mirage]

uh I've been stuck at this question for a while

if a line's gradient is 2 and y-intercept is -6, determine the x-intercept

I have no idea on how to solve it

someone please help

[tawdry flower]

do you have any formulas that might help you?

[hardy mirage]

uh no

[stable leaf]

do you have an equation

[tawdry flower]

as a matter of fact you do - the equation of a line in point-slope form

$y - y_{0} = m(x - x_{0})$

[ocean seal]

kirafa

[tawdry flower]

You're given the gradient, which is "m". And you're told that the line passes through the y-intercept (in other words, the point (0, -6) )

[stable leaf]

i mean you also would have

y=2x-6?

right

[tawdry flower]

oh yeah

that's much simpler

LOL

[stable leaf]

and think what x intercpet means

(?,0)

[hardy mirage]

uuhhhh

may I ask

where do you get y = 2x - 6

[tawdry flower]

$y = mx + b$

[ocean seal]

kirafa

[tawdry flower]

m is the slope (or gradient) and b is the y-intercept

[hardy mirage]

then what is the y?

[stable leaf]

it is an equation

you pick x value

you get y value

input --- > output

[hardy mirage]

um what's the name of this equation?

[stable leaf]

linear equation?

in slope intercept form

[tawdry flower]

i think it's called slope-intercept form

the equation i gave before is called point-slope form

[stable leaf]

there is another form

and i really am not sure of the use of that one

ax+by = c

[tawdry flower]

I think that one's called standard form, but people tend not to use that so much

[stable leaf]

maybe to get the intercepts easily?

[hardy mirage]

hmm these two formula's usage is the same?

[stable leaf]

they are all the same

[tawdry flower]

for the most part, yeah

it might be easier to use one or the other

[stable leaf]

idk if you would call it a formula

would you?

[tawdry flower]

sure

i dont see why not

[stable leaf]

i guess it is

kinda

i was more thinking of just an equation but maybe they are the same thing

[manic glade]

does this look right?

[ivory otter]

Hey so im kinda confused, what is spearmans coefficient of rank correlation used for exactly

and how is it different from the normal correlation coefficient formula

[covert breach]

for rank correlation

[covert breach]

normal correlation is not for rank

essentially correlation is for ratio/interval data, whereas rank correlation is for ordinal data

[ivory otter]

Google search: "How to answer a question without answering the question"

[covert breach]

i mean i answered the question, idk what u want

rank correlation is used when u have ranked (ordinal) data, and normal correlation is used for actual values (interval/ratio data)

[severe sluice]

i don't quite understand this (if you continue using the same logic but you don't divide both sides of the equation by 3/2 in the first step, the result will be different)

<@&286206848099549185>?

[alpine sable]

i dont understand.. how will the resukt be different?

[ocean seal]

Unity's Particle System

[severe sluice]

(woops. meant 3/2.)

[alpine sable]

@severe sluice T is directly proportional to 2/3 times of E(total), and E(total) is equal to 3/2 times PV
So can't T be directly proportional to PV?

man can u not delete the soln before i read it xD

[ocean seal]

Unity's Particle System

[alpine sable]

Isn't the proportionality constant here not the same as that given in the text?

[red phoenix]

i agree

[tribal geyser]

Hey guys how do u do 14)c

Coz I thought u just multiply growth constant and 10

coz for k I got -In(0.9)/4

But the answer is 0.028..

<@&286206848099549185>

[tawdry flower]

i guess i can give it a shot

[devout sigil]

Me too

[tawdry flower]

in that case i'll leave it to you @devout sigil

(:

[devout sigil]

Nah u can do it man

[tawdry flower]

lol alright

[devout sigil]

We can compare answers u know (:

[tribal geyser]

lolol

please help lolol

[devout sigil]

Did u correctly find the value of k?

[tribal geyser]

Yes

[devout sigil]

What is it

[tribal geyser]

0.02634012891

[devout sigil]

Geez I’ll take the exact value

[tribal geyser]

-In(0.9)/4

[devout sigil]

Ah thanks that’s better

[tawdry flower]

To say that the population fell by 20% is to say that it was 80% of what it was before. So we want to find "t", such that $P(t) = 0.8P_{0}$. Re-write P(t) as $P(t) = P_{0}e^{-kt}$.

[ocean seal]

kirafa

[tawdry flower]

WHAT

[tribal geyser]

14)b lol

I mean c

[tawdry flower]

oh woops

[tribal geyser]

yep C)

[tawdry flower]

im dumb lol

lemme try that again

[devout sigil]

Bruh

[tawdry flower]

stfu im doing my best

.>

ok, let's consider the population after 10 years: P(10). According to the model we're given, we have $P(10) = P_{0} e^{-10k}$.

[devout sigil]

Bro ur faster than me I think I’ll leave this equation for u

[tribal geyser]

Yes I did that too

then so u multiply that by k?

[tawdry flower]

The percentage decrease in the population (compared to now) can be found through the ratio of P(10) to P(0), which is:

$\frac{P(10)}{P(0)} = \frac{P_{0}e^{-10k}}{P_{0}}$

so we get $e^{-10k}$

[ocean seal]

kirafa

kirafa

kirafa

[tribal geyser]

yes

[tawdry flower]

yeah, you can get it from there by plugging in k

[tribal geyser]

I did but the answer is 2%

[tawdry flower]

huh

maybe your choice of k is wrong?

or did you get that correct?

[tribal geyser]

No lol, I got that correct

[tawdry flower]

yeah im getting this wrong too

but idk what i'm doing wrong

hold up, the answer is 2%?

[tribal geyser]

Yesh

[tawdry flower]

so the population decreased by 2% after 10 years?

[tribal geyser]

Yes