help-0

[vale wigeon]

you've fallen victim to the freshman's dream

$(a+b)^2 \neq a^2 + b^2$

[ocean seal]

Ann

[tired hamlet]

yeah I get that I thought that the squaring just undoes the square root?

[vale wigeon]

$(\sqrt{x-3} + \sqrt{2x+1})^2$ is still not the same as $(\sqrt{x-3})^2 + (\sqrt{2x+1})^2$

[ocean seal]

Ann

[vale wigeon]

squaring doesn't distribute over addition like that

[tired hamlet]

oh so it's (x-3+(2x+1))(x-3+(2x+1))

[vale wigeon]

what

no?

okay look

can you tell me how (a+b)^2 expands?

[tired hamlet]

(a+b)(a+b)

[vale wigeon]

i said expand.

while it is true that squaring a number means multiplying it by itself, that's not what i asked for here.

[tired hamlet]

a^2+2ab+b^2

[vale wigeon]

great

so now, can you apply this to (sqrt(x-3) + sqrt(2x+1))^2?

[tired hamlet]

yeah I got it it would be $3x+2\sqrt{2x^2-5x-3}-2$

[ocean seal]

jb8!!!

[vale wigeon]

strange ordering of terms but whatever

yes that is correct

does this answer your question of "why would i get roots"?

[merry herald]

oh if thats it then thanks

[tired hamlet]

yeah thanks i got it. and just set that equation equal to 2x+8

[alpine sable]

anyone inte conditional possion distributions ?

[halcyon pulsar]

I've solved this question for more than 30minutes now
First I found the Area of the sector
And now finding the Area of the traingle inside the sector
I would next Subtract area of sector and traingle
But all of this is taking alot more time and wierd calculations than it should
Help me in solving dis •~•~•

[merry herald]

so we could just do 180-a-b-c-d=360 ?

[remote iron]

Solve radius

[halcyon pulsar]

What is the middle "1" for?

[remote iron]

its a 1

[halcyon pulsar]

For what?

As a length?

[remote heron]

,rotate -90

[remote iron]

they are unit squares

[halcyon pulsar]

Okie

[halcyon pulsar]

<@&286206848099549185>

[wispy olive]

I do not know the answer.

But according the rules you should ping once.

But your irritation is understandable.

[remote iron]

<@&286206848099549185> anyone able to help with my q?

[wispy olive]

Woah 1k+ Subscribers nice.

[remote iron]

Thank you!

[placid zinc]

If the center of the four squares is (0,0), then (-1, 1) is on the circle, and (2, 1/2) is on the circle

(x - m)² + y² = r²

[wispy olive]

I like Linux so I will sub too.

[remote iron]

oh that's true. (Kaynex)

wait, 2, 1/2?

[placid zinc]

,w system of equations (-1 - m)^2 + 1 = r^2, (2 - m)^2 + (1/2)^2 = r^2

[ocean seal]

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[placid zinc]

Looking like the radius is √185 / 8

[remote iron]

wait explain how u got those points?

cause i think somethings fishy

[placid zinc]

Let the center of the four squares be (0,0)

[remote iron]

center as in the center of the circle yes?

[placid zinc]

I know that the center of the four squares is not the center of the circle

(in fact it's 3/8 off)

Then (-1, 1) is a point on the circle

[remote iron]

are u saying the top left corner of the square is -1 1?

because i don't think u can do that since its not centred.

like in the circle.

[placid zinc]

I can do whatever I want and you can't stop me

[remote iron]

I am not stopping you lol.

[placid zinc]

Jokes aside, note that I am putting the squares on a Cartesian Plane, and ignoring the circle for now

[remote iron]

I am saying that how is it -1, 1 if its not on the circle?

Alright, but what are you making the centre then

[placid zinc]

I am defining that (0,0) is the center of the four squares

[remote iron]

Alright...

so then top left corner is -1, 1

[placid zinc]

Right! And that's a point on my circle

[remote iron]

sure...

[placid zinc]

And similarly, (2, 1/2) is also a point on my circle

[remote iron]

and bottom left is 2, -1/2?

-1/2 no?

[placid zinc]

You could also pick that one

[remote iron]

oh yes.

then...?

[placid zinc]

So I summon the equation of a circle that is symmetric over the x-axis:
(x - m)² + y² = r²

Note it has two unknowns, m and r. So I'll need two points to find them

[remote iron]

...

[placid zinc]

You seem underwhelmed

Oh, I just let Wolfram do the actual algebra from this point forward

[ocean seal]

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[placid zinc]

That is, I gave it the equation, with the two points subbed in

👻

[alpine sable]

2 tan theta into 2 cot theta =

[empty kindle]

how to find k?

[quaint trout]

what is k?

[vale wigeon]

i have a hunch that they intended for you to name the one value that the common ratio of a GP cannot be.

[empty kindle]

.?

[vale wigeon]

the common ratio of your GP is r here

what can it NOT be?

[empty kindle]

same with k?

[vale wigeon]

....

forget about k.

sigh ok i guess my attempts at making you recall this have not worked like i thought they would

it's 1.

the one forbidden value of the common ratio of a GP is 1.

[icy trail]

i think the average rate of change will just be the gradient of the line between t=3 and t=5

[lime lintel]

so i substitute it into the equation, then what?

theres no graph

[icy trail]

its just the gradient of the line between those two points

[lime lintel]

...?

10..?

ok wait

so when t = 3, n = 7.5 and when t = 5, n = 17.5

minus 7.5 from 17.5?

[icy trail]

gradient = change in output / change in input

[lime lintel]

so 10.?

[icy trail]

have you divided by the change in input

[lime lintel]

whats change in input?

how do u know which ones which?

[icy trail]

change in t

you could just replace n with a y and t with an x to do change in y / change in x but

the gradient for this question is change in n / change in t

[lime lintel]

OHHHHH

OH OKKK

THAT MAKES SENSE

right

thanks dude

[icy trail]

[slate fossil]

I need someone to check my answer

Number 5

[vale wigeon]

your answer (C) is correct

[slate fossil]

Ah thx

[wintry vortex]

So why is it different converting it back from decimal to degrees?

I put tan (0.238) in and it didnt give me a degree

Im doing their equation and its giving me itself as an answer 😖

WHERE DID THE DEGREE COME FROM?!?! this program explains nothing and its infuriating o_O

[alpine sable]

wdym the degree? do you mean where did 10.6° come from?

[wintry vortex]

yes

[topaz wedge]

What’s 1 unvigintillion minus 2 novemdecillion 1 nonillion and 1 quadrillion? I can’t use Siri cause it’s too big and doing it on paper is not possible.

[alpine sable]

it is written, if you type in your calculator arctan(0.191) it will output 10.8°

[wintry vortex]

okay that got it, what did the arc part of it mea?

mean?

Why did that work?

[alpine sable]

are you new to inverse trig functions?

[wintry vortex]

yes

[alpine sable]

okay

have you learned inverse functions in general?

[wintry vortex]

If I have it was a long time ago. Its been around 10 years since I did a math class.

Im relearning alot.

but this is the last of the classes I need for my associates 😮‍💨 Im a freakin aircraft mechanic lol, idk why they think i need calc

[alpine sable]

okay so you may remember that the inverse function of, say, $f$ is denoted as $f^{-1}$

[ocean seal]

Al𝟛dium

[alpine sable]

one clear example might be e^x and ln(x)

,w plot e^x & ln(x) from 0 to 10

okay wait

[wintry vortex]

I may be more screwed than I thought, that doesnt look like english to me 0_0

[alpine sable]

please let me know your doubts, was anything i said unclear?

[wintry vortex]

Okay, so im following that a inverse function negates the original function. thus F^-1 being the inverse of F but the e^x lost me completly

I still dont fully understand how its used practically though

[carmine lion]

think of any 1 to 1 function

i.e a function that passes both the horizontal and vertical line test

then draw the line y=x

[alpine sable]

i'm looking for a graph for you to see it's reflection with the line y=x

[carmine lion]

and try to reflect that function in this line

basically, an inverse is a reflection of a one to one function in the line y=x

y=x is a mirror

for functions and their inverse

[wintry vortex]

would that make the lines parellel?

[carmine lion]

hmm not quite

,w graph x^2 and sqrt(x) and x from 0 to 2

[ocean seal]

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[carmine lion]

its kinda hard to tell

wolfram bot bad at graphh

there we go

[wintry vortex]

so thats an inverse function?

[vale wigeon]

@topaz wedge it's not that hard to do it on paper. "1 unvigintillion" is only 67 digits long.
the answer to your question, if you want to know it so bad, is 999,997,999,999,999,999,999,999,999,999,999,998,999,999,999,999,999,000,000,000,000,000, which i am not going to spell out in full unless you want to hear a torrent of "nine hundred and ninety-nine footillion"

[wintry vortex]

Ya'll are saints for helping me figure this out btw ❤️

[manic glade]

is this the correct way to describe the set of all infinite sized subsets of B?

[vale wigeon]

no, this gets you only the countable ones

[manic glade]

thats the ones i need yes B is all even natural numbers

[carmine lion]

oi corylus

this channel is occupied

[manic glade]

i was just wonderin on which side the x subset B is supposed to be

[carmine lion]

please move to another one

[alpine sable]

yeah and well talking about inverse trig functions we have sin with the domain and image of [-π/2, π/2] and [-1,1] then it's inverse will be arcsin, with domain and image [-1,1] and [-π/2, π/2] respectively

similar goes with arctan and arccos.

,w plot sin(x) & arcsin(x) from -π/2 to π/2

[ocean seal]

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[wintry vortex]

So function if memory serves just means the line doesnt cross x or y a second time. So would an inverse function mean that it all intsects at some point? then does cross x and y a second time?

evil people invented math 0_0

ok so arcsin or arccos would just be the opposite of sin or cos then?

This whole question series has my brain in a knot

[surreal meadow]

this isn't the definition of a function

in simple terms, a function of x means that for every single x, there is only 1 y

that is, every x value in the domain of the function only has 1 value corresponding to it

that's why we do the "vertical line test", as it tells us wether an x value has more than 1 y value associated to it

[wintry vortex]

But doesnt it have a Y above and below X? or are we only talking intersecting with 0 x?

[surreal meadow]

i'm confused by the question

have you seen the graph for sin(x)?

you can see it crosses the x-axis multiple times, yet it is still a function

this is because at every x-value, there is a single y value

[wintry vortex]

Ok, I think i understand

[surreal meadow]

an inverse function $f^{-1}(x)$ is how we go from $f(y)=x$ to $y=f^{-1}(x)$

[ocean seal]

maximo

[surreal meadow]

so for example

if we have f(x) = x

the inverse function $f^{-1}(x)$

[ocean seal]

maximo

[surreal meadow]

can be found by setting y=f(x), y=x

well that's a pretty awful example

[lucid beacon]

So like, we do something to x and get a new number. The inverse function is going from the new number back to x

I don't know if that's technically correct but

[surreal meadow]

f(x)=x^2 is a better example

f(x)=x^2

y=f(x)

y=x^2

flip x and y

x=y^2

sqrt(x)=y

we have that the inverse of f(x)=x^2 is f^-1(x)=sqrt(x)

do you see what i did?

you're solving for y in the equation f(y)=x

[wintry vortex]

tbh, not really. I think my brains to fried to do much more tonight =/

Man, this was not the math for them to just plop me back into

[surreal meadow]

what exactly is confusing about it

[wintry vortex]

sadly all of it. But i think I at least get the basic concept of function and inverse function and how to find them on a calculator like my homework was asking

Sadly its already throwing new curveballs at me and idk if u have the energy to learn em

I was hoping to get a few more questions done just to whittle down at it over the week but I didnt make it very far haha

Thank you a ton for all the help ❤️

[hexed lintel]

hi

the first one is identity and change the voice

i dont understand that

[surreal meadow]

@hexed lintel i'll dm you a link to the english server

[hexed lintel]

k

[surreal meadow]

they'll be of more help than a math server i'm sure

[kind parcel]

Can someone help

[surreal meadow]

do you know how to find the slope of that tangent?

[tough hatch]

to determine the coordinates of A, just solve for the greater x in 4x-x^2 = 0

@kind parcel

[alpine sable]

you can find the differential for the curve

then input x as 1

then create the eqn of the tengent from that

tangent*

then equate that x to 0

then you can find the B coordinate

X is directly proportional to y, or varies directly with y, if x/y = k

For some constant k

You can find the constant and solve for y

can we chat privately? If it’s alright?

Nah

ok:)

So do you get how to do it? I can show you how the first is done

no I don’t get it. please give me an example

x varies directly with y, and we have that when x=24 y=8

Then x/y = 3, which is our constant k

Then, when x = 6, 6/y = 3, so y = 2

that’s it?

Yea

Unless I misunderstand what varies directly means, but I think im right

so the final answer is 2?

Yes

alr alrr thanksss

Np

[winter mango]

suppose we have a binary string of length 15, how many possible strings have exactly 6 zeroes?

are we supposed to use permutations or combinations in this question?

i feel like it should be permutations because the order in the string matters, but the answer seems to be combinations

[alpine sable]

permutations are a subset of combinatorics

But the order doesn’t really matter that much here

[winter mango]

sorry, how is that?

[alpine sable]

Like, you have no real restrictions on the order of the zeroes, since you’re computing all possible arrangements

[winter mango]

i think i understand, it's still sorta hazy though

[alpine sable]

Sorry, I shouldnt have engaged with this question since I don’t have the answer yet

But i’ll come back once I figure it out fully

[winter mango]

it's all right, i think you have the right concept i am just getting more used to this stuff

thanks for answering

[alpine sable]

Np

Ok I think it’s (15 \choose 6)

[ocean seal]

cpl

[winter mango]

yeah that's the correct answer, or 15c9 but they're identical

[alpine sable]

Depends on how you conceptualize it

is this linear

In use

[winter mango]

i think i get it now

[alpine sable]

Ok, im glad

[winter mango]

it's easier to visualize as a sort of successes and failures

that's why the order doesn't matter

[alpine sable]

Cpl could you help me in question 1, if finished.

[unborn dome]

can someone help me with this question im really confused lol

[alpine sable]

how do i express cosxsiny as a difference of sine functions

[alpine sable]

I have a question

[unborn dome]

can anyone explain if this video used the sum and difference identity to solve this problem?

[alpine sable]

Shoot

[glass lichen]

they clearly did use compound angle formulas

[unborn dome]

so its not sum or difference formula @glass lichen ?

[glass lichen]

it is...

[tough hatch]

to answer your question, yes, they did

[glass lichen]

if you read the ss you posted.. you'd see they used one

[unborn dome]

ah t

thank you

im doing a review sheet rn so im a bit confused on topics lol

[covert wagon]

https://cdn.discordapp.com/attachments/863840750277361675/874266589749477416/Screenshot_5.png

anyone here understand n and o

[native cloud]

Why is there a comma inside the root?

[wind bane]

what is the question?

commas are sometimes used in place of decimal points in other places if i recall correctly

[covert wagon]

thats why i didnt get it

[native cloud]

Did the question ask to simplify?

[covert wagon]

yes

thanks

[native cloud]

Without a calculator?

[covert wagon]

wait

[native cloud]

I would be very hard without a calculator;;;

[covert wagon]

not that kind of type

[native cloud]

Not sure how it can be more simplified

[covert wagon]

the answer is square 3/10 - square 2/5

[surreal meadow]

~.3

[covert wagon]

i search in photomath

thanks for helping

[native cloud]

Ohhh in fractions

[covert wagon]

oh that was fractions

im not good at english

[native cloud]

That's okay

[teal garnet]

can someone explain how these are equal?

[surreal meadow]

l'hopital

the theorem is essentially

[fallow ruin]

Only when you encounter 0/0 or ∞/∞ !

[tight locust]

lim x->inf (1/x) = lim x->inf (0/1) = 0

that was a 1/inf limit and it still worked

[tight locust]

any comments?

[sage bronze]

it doesnt always work

there will be exceptions

[surreal meadow]

he said this so as to say that it is only necessarily true when you encounter those two indefinite forms

[sage bronze]

exactly

[devout sigil]

Doesn’t it still works for 0 multiplied by +-infinity?

[surreal meadow]

which is simply 0 over 0

or infinity over infinity

as long as you can rearrange it as such

[fallow ruin]

Indeed, purely coincidental

[tight locust]

lim x->0 (sinx*x) = lim x->0 (sinx/(1/x)) = lim x-> 0 (cosx/(-1/x^2)) = lim x->0 (-x^2*cos(x)) = 0

[surreal meadow]

what's your question

[surreal meadow]

$\lim_{x\to \infty}x\neq\lim_{x\to\infty}1$

[ocean seal]

maximo

[tight locust]

of course not. you have to express it as a quotient. then you can use l'h
x/1 = x'/1' = 1/0 = infinity

[sage bronze]

what

[fallow ruin]

no, you didnt check the limits

first you must encounter 0/0 or inf/inf, then you can apply l'hopital

[sage bronze]

yes

[surreal meadow]

$\lim_{x\to 3}\frac{2x+1}{3x+1}\neq\lim_{x\to 3}\frac{2}{3}$

[ocean seal]

maximo

[fallow ruin]

excellent example

[sage bronze]

yes

[surreal meadow]

lets make this easier

if you can prove that lhop works for every f(x)/g(x), regardless of indeterminate form

then i'll cede that you're right

[tight locust]

that was never my claim. just that it didn't necessarily have to be a 0/0 or inf/inf limit

[surreal meadow]

and we never claimed that it had to be 0/0 or inf/inf?

[sage bronze]

its just not advisable to use it

on every f(x)/g(x)

without indeterminate form

[surreal meadow]

i'd like to see the proof you wrote up again though

[alpine sable]

did you just lh this

lol

[surreal meadow]

because if you can tell me that $\lim_{x\to 3}\frac{2x+1}{3x+1}=\frac{2}{3}$

then there's either something fundamentally wrong with math or your proof

[sage bronze]

they tried to

[ocean seal]

maximo

[alpine sable]

oh

[surreal meadow]

nono no one actually tried to

[sage bronze]

as in its an example that

lh doesnt

[surreal meadow]

just using it as an example of why lhop doesn't always work

[sage bronze]

work for all

yeah

sorry my communication skills are a bit rusty

[alpine sable]

If two sides are given in a Right angle Triangle, how to find all angles inside it?

[surreal meadow]

have you heard of the pythagorean theorem

[sage bronze]

using trigonometry and pythagoras

[alpine sable]

When is L'Hopital's rule not applicable? When your limit is a finite number divided by zero or infinity divided by a finite number. The limit has to be indeterminate such as 0/0 or infinity/infinity.

[sage bronze]

yes it has to be indeterminate

[alpine sable]

no i was answering

[alpine sable]

But pythagoras theoraem is used to find the third side, how to find angles?

[surreal meadow]

law of cosines

or just trigonometry

that's probably easier

[sage bronze]

yeah

[surreal meadow]

SOHCAHTOA to be more specific

[sage bronze]

whats sohcahtoa

[surreal meadow]

sin = opp/hyp, cos = adj/hyp, tan = opp/adj

[ocean seal]

Chai T. Rex

[sage bronze]

ah

so its a acronym

[alpine sable]

find the perpendicular and base. then use tan inverse function to find your angle. the other angle will be 90-angle

[sage bronze]

ok

[sage bronze]

i was so confused XD

[alpine sable]

i use
PBP
HHB
SCT

[sage bronze]

I just memorized it😬

[devout sigil]

Ever heard of sine rule

?

[alpine sable]

thats pretty smart tbh. i just dont have memorised execpt tan

[alpine sable]

yes

[surreal meadow]

you'd need at least 1 angle no?

[alpine sable]

but that question was clearly not directed toward me

[devout sigil]

Yes but u can use it to find the ratio of lengths

Of the sides

[alpine sable]

tbh no offense itd be easier to use pythagoras since its a right angled triangle

[devout sigil]

Yes this is just for checking

[alpine sable]

and im sure a person who's asking this rudimentary question doesnt know what sine rule is/respectfully

anyways i gtg

[devout sigil]

A/sin a=B/sin b where a and b are angles in a triangle and A and B are corresponding opposite sides to their respective angles

How is it not applicable?

[surreal meadow]

you only know 2 sides

and a 90 degree angle

[devout sigil]

The two angles are complimentary

[surreal meadow]

oh i forgot about that 90 degree angle

[devout sigil]

Facing the non-hypotenuse

[surreal meadow]

yeah should be easy with law of sines as well

[devout sigil]

If my two unknown angles are a and b I can say b=90deg-a

Side A/sin(a)=side B/sin(90-a), u can expand with formula side B/cos a

[surreal meadow]

that's unecessary

[devout sigil]

Which is why I agree if u prefer pythagoras, but u can still use this

[surreal meadow]

hyp = leg/sin(a)

you already know all 3 side lengths

you can find 1 angle like that and just solve like you said for a+b=90

[devout sigil]

Because I know people who don’t even know Toa cah soh

[sage bronze]

🥶

i didnt know

[devout sigil]

@alpine sable maybe someone didn’t even know the correlation between complimentary angles

@sage bronze do u know sine rule or cosine rule?

[sage bronze]

sine rule yes not cosine rule

[devout sigil]

In that case u can still use my approach to tackle such a problem

“Doesn’t know what sine rule is”

[fickle cliff]

how x^2+x+1/4 = (x+1/2)^2 ?

[sage bronze]

are you familiar with the identity $(a+b)^2 = a^2 + 2ab +b^2$

[ocean seal]

HELLOBELLO

[fickle cliff]

yes

[sage bronze]

then try to identify a and b in $x^2 + x + \frac {1}{4}$

[ocean seal]

HELLOBELLO

[fickle cliff]

a=x^2 , b= idk

[alpine sable]

How do we find trigonometry ratios for specific angles

[sage bronze]

this channel is occupied rn can u pls try another one

[sage bronze]

ur close

[fickle cliff]

b=1/4 ?

[sage bronze]

ur close

instead of a=x^2 and b= 1/4

it should be a= x and b = 1/2

can u see why

?

[alpine sable]

simplification?

[fickle cliff]

sorry no

[sage bronze]

ok

if a= x^2 and b = 1/4

$(a+b) = (x^2 + 1/4)^2$ if a= x^2 and b = 1/4

[ocean seal]

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

[fickle cliff]

where did ^2 came from?

[sage bronze]

try to find values of a and b such that $a^2 = x^2$

and $b^2 = 1/4$

@fickle cliff

[ocean seal]

HELLOBELLO

HELLOBELLO

[fickle cliff]

i kinda understood

[sage bronze]

ok

so what did u get as values of a and b

[fickle cliff]

(x+1/2)^2 because x^2 + 1/4^2 can also be inside brackets and ^2 can be outside

$x^2 + 1/4^2=(x+1/4)^2$

[ocean seal]

motoboi

[sage bronze]

nono

see

$x^2 + x + \frac {1}{4} = (x)^2 + 2 \times x \times \frac {1}{2} + (\frac {1}{2})^2$

[ocean seal]

HELLOBELLO

[sage bronze]

from here

[sage bronze]

u can factorise using this identity

to get $x^2 + x + \frac {1}{4} = (x)^2 + (2 \times x \times \frac {1}{2}) + (\frac {1}{2})^2 = (x+ \frac {1}{2})^2$

[fickle cliff]

wait let me do it on paper

[sage bronze]

yeah

[ocean seal]

HELLOBELLO

[alpine sable]

This channel occupied?

[fickle cliff]

yes

ok so
in $x^2+x+1/4$ u converted $1/4$ into $(1/2)^2$ because $(1/2)(1/2) = 1/4$
the $x^2$ can be also written as $(x)^2$
$(2x1/2)=(x1)=x$
$(x)^2+(1/2)^2=(x+1/2)^2$

Now my question is that where the x in $(2x1/2)$ is gone?

[sage bronze]

me confused now

wdym by this

[fickle cliff]

Im still not used to this bot ;-;

[sage bronze]

no problem

u can

just write

it

and send a picture

[fickle cliff]

yup wait a min

[tough hatch]

add a second $ to end writing in math

for example $2=3$, which is not true

[ocean seal]

motoboi

[tough hatch]

this is just boring text, $this is text in math mode which looks ugly$, this is normal text

[glass lichen]

dont use $\times$ and $x$ in the same thing

[ocean seal]

Mosh

[glass lichen]

but we know $(a+b)^2=a^2+2ab+b^2$, here $a=x$ and $b=\frac{1}{2}$

[ocean seal]

Mosh

[glass lichen]

so clearly the 2ab term is just x

[fickle cliff]

but its not $2x$ its just $x$

[ocean seal]

motoboi

[glass lichen]

yeah....

Im aware

what's your point?

[fickle cliff]

it needs to be $2x$ right?

[sage bronze]

when u multiply 2x by 1/2 u get x

[ocean seal]

motoboi

[glass lichen]

$2\cdot\frac{1}{2}\cdot x=x$

[ocean seal]

Mosh

[fickle cliff]

[dawn galleon]

this

<@&286206848099549185>

[fickle cliff]

#❓how-to-get-help
4. If your question has not been answered for a minimum of 15 minutes, you may use the <@&286206848099549185> tag once. Please do not try to bump your question using this ping unnecessarily. Do not abuse this ping. Do not individually ping users with the Helpers tag without their express permission.

[surreal meadow]

LOL pinged helpers again to explain what not to do

kinda funny

[fickle cliff]

oops sorry for that

[dawn galleon]

lol

[dawn galleon]

thanks for 1 more ping

[gritty pine]

is the default index of a radical 2?

[oak chasm]

Yes, if you don't see a number, it's 2.

[ocean seal]

Chai T. Rex

[gritty pine]

OOOH finally i understand

its like saying 1/2

[gritty pine]

2 is the index of the radical

[gritty pine]

now im understanding, thank you so much

[oak chasm]

No problem.

[fringe robin]

anyone?

[ionic jewel]

i feel this this is one of those integrals where you have to turn one or two of your sin^2(x) into 1-cos^2(x) so you can u-sub and solve

[fringe robin]

i did cos^6 x divided both num and den

and i just got ans

thanks

[dense tulip]

Hey guys so this is sorta like a theoretical question that came up in my mind that I need help with

because I have the idea

that it's probably wrong in some way

so basically using the pythagorean identity

sin^2+ cos^2 = 1

if we simply take the square root of both sides

we get

sin+cos=1

[surreal meadow]

nope

[dense tulip]

is that not correct?

[surreal meadow]

$\sqrt{x^2 + y^2}\neq x+y$

[ocean seal]

maximo

[dense tulip]

ohhh really?

[surreal meadow]

take x = 2 y = 3

[dense tulip]

man I didn't realize that

[dense tulip]

ok sure

[surreal meadow]

2 + 3 = 5, 4 + 9 = 13

sqrt(13) =/= 5

[dense tulip]

ohh I see

that's so weird

though

it intuitively sort of makes sense

[surreal meadow]

(x+y)^2 =/= x^2 + y^2

its called freshman's dream

[dense tulip]

but I guess mathematics is all about discovering the fundamental truths vs intuition

[surreal meadow]

yup

[dense tulip]

oh wow

so is that the same as the sqrt

thing I was talking about earlier?

[surreal meadow]

you basically did the inverse

[dense tulip]

oh I see

cause like I guess I just took sqrt of sin^2 as sin and cos^2 as cosine and just jammed them

together

lol

ok thank you so much for helping me realize this flaw in my reasoning!

I'm legit doing AP Calc stuff and I tried applying this and failed

[surreal meadow]

np 👍🏻

haha i forget rules all the time

in an ap calc test i had to work back on whether $x^ax^b = x^{a+b}$ or not

[ocean seal]

maximo

[dense tulip]

ohh lol

nice

yeah I like the fact we can keep rederiving

things in math

its really cool

[surreal meadow]

nono

i mean like i literally forgot

[dense tulip]

oh about the rule

yea happens to me

[surreal meadow]

and yeah i derived it quickly again cause its obvious

[dense tulip]

as well

[surreal meadow]

but yeah lmfao

[dense tulip]

ye

thx for the help dude

appreciate it

[surreal meadow]

np

[dense tulip]

hopefully physics is actually not harder

than calc

liek alg trig based

physics

[surreal meadow]

it's different i'd say

theres a bit more memorization and the actual applications can be tricky

but its a different kind of difficult

[dense tulip]

ah ok

so like more problem solving?

[surreal meadow]

well yes, but i'd also call math problem solving

it's a more constrained type of problem solving, you have to be more careful of the rules and definitions as well as applications

[dense tulip]

yea true

[dense tulip]

ahh ok

i see

I"m always really bad at applications like in terms of definitions

that are hard to place

[paper minnow]

Is it necessary to write a double or triple integral when talking about a surface or volume if you've made it clear and are consistent all the way through? Just wondering in case I accidentally write it in a test paper or exam

[surreal meadow]

I'd assume so. you can always just give an integral a name like $I=\iint_Df(x,y)dA$

[ocean seal]

maximo

[surreal meadow]

so you don't have to write the whole thing over and over again

[paper minnow]

This is just a pure notation thing, just can't be fucked writing double or triple integrals is all. So in a test or exam paper, I can write $\int_{\Sigma}dA$ instead of $\iint_{\Sigma}dA$ if I've made it very clear that $\Sigma$ is a surface?

[ocean seal]

Isaac

[surreal meadow]

i think they mean different things, or that it might not even compute, but I can understand your pain

its sort of like writing $\Sigma_DdA$ instead of $\iint_DdA$

[ocean seal]

maximo

[topaz scaffold]

No

[surreal meadow]

just mean different things yknow?

[paper minnow]

yeah, I keep seeing the generalized Stoke's theorem and I'm like "😩 Why can't I just write a surface integral with one integral sign instead of two? it would be so much easier"

oh, I think I see the potential confusion though, if it gets construed for something in measure theory or statistics, right?

[surreal meadow]

that’s just my thoughts, and i’ve only recently learned about this stuff, so my views may be horribly wrong. there might be a way to avoid more pointless writing though

[gray oxide]

What is f'(2)

If f(x) = 2sqrt(x)

This is my anwer so far but it's wrong so pls tell me where I went wrong

[surreal meadow]

do you know the power rule?

[wild marten]

$2\sqrt{x} = 2 x^{1/2}$. Can you continue now?

[ocean seal]

Lester

[glass lichen]

f'(2), to actually answer the question you asked... is the derivative of f(x) evaluated at x=2

[gray oxide]

This is what I did but it's not wrong

When you derivate a constant doesn't that become zero?

[gray isle]

Um that is extremely bad notation that makes it almost impossible to decipher

[gray oxide]

Oh sorry I'll try to rewrite it

Gimme a sec

[gray oxide]

How do you want to read it line for line?

[gray isle]

Yes

With appropriate use of = signs

the first part of that pic is already nonsense

[gray oxide]

Idk if this is better but hopefully it is

[gritty pine]

can any tell me how he got sqrt(5^2) * sqrt(2^3?)

[gray isle]

Ok your work is still nonsense

[gray oxide]

Sick

[gritty pine]

he just took the M.C.M to get the 6sqrt

[gray isle]

The first thing you wrote is literally already wrong

[gray oxide]

So you can't take out the constant?

[gray isle]

Not like that

you should be starting with
$$f(x) = 2\sqrt{x}$$

[gray oxide]

But there are examples where that is the right move why is it wrong here? Is it becuase its an multiplication?

[ocean seal]

ℝamonov

[gray oxide]

Yea I did then I started to derivate from there

[gray isle]

No you didn't

for some reason you included the ' at the very start

Indicating the derivative was already 2sqrt(x)

and then for some reason erased the 2 from existence

[gray isle]

and then said more stuff that wasn't equal was equal

[gray oxide]

I wrote the f'(x) to indicate that I'm going to do the derivate of the function in an actual exam I would have to write more correct but here I already know what f(x) is equal to so I felt that I didn't need to be "grammatically" correct

But if I did something wrong then my bad

[gray isle]

you do, otherwise people won't know what your talking about

and assume you have no idea what you're doing

and won't know whether you actually understand or not

[gray oxide]

But I did write what f(x) is and what f'(2) is

But I see your point

I can't expect ppl to know what I'm thinking

Sorry

Ok so do you want me to rewrite it? And then continue from there?

[gray isle]

$f(x) = 2\sqrt{x} \
f'(x) = \dv{x}(2\sqrt{x}) =2 \dv{x}\sqrt{x}$

[ocean seal]

ℝamonov

[gray isle]

start with something like that

[gray oxide]

Is that d/dx?

[dreamy crow]

wrong pic?

[gray oxide]

No, that's the derivates definition

[gray isle]

d/dx is a derivative operator

[gray oxide]

At least that's whats it's called in my language

[gray isle]

what you posted is the limit definition of the derivative

[gray oxide]

And what is the d/dx?

[gray isle]

d/dx is a derivative operator

d/dx sqrt(x)
Is the derivative of sqrt(x) wrt x

[devout sigil]

@gray oxide d/dx is the gradient function of a function... when question is asking for d/dx(2sqrtx) it means find the gradient of the curve 2sqrtx

[gray isle]

$f'(x) = \dv{x} f(x)$

[ocean seal]

ℝamonov

[devout sigil]

Also u know power rule?

[gray oxide]

I think so

I'll search up what it means quickly cuz I don't know the English terms

[dreamy crow]

this

@gray oxide

[devout sigil]

Ok, u want to find a way to get the value of n

[gray oxide]

Yea

[devout sigil]

What is ur answer for n?

[gray oxide]

On the picture?

[devout sigil]

Yes but now u have 2[d/dx (√x)] right?

[gray oxide]

Yea

[devout sigil]

If u get what @gray isle said

So we can sub this into the picture, √x=x to the power of n

[gray oxide]

Oh

[devout sigil]

Now can u tell me what is n?

[gray oxide]

N would be 1/2

[devout sigil]

Yep!

And n-1 would be 1/2-1=-1/2 right?

[gray oxide]

Ok so aren't we supposed to derivate that? Or was that not a rewriting but a derivation?

Oh ye

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

[devout sigil]

nx^(n-1) is the derivative, for x^n it’s still the function itself and is not yet differentiated

Yes u are right

[dreamy crow]

the problem here is that you take the 2 out

[gray oxide]

Yes

[gray oxide]

I know that if I don't I would get the right answer now

But why wouldn't you take out the 2?

[devout sigil]

Ok when u take a constant like 2 out, always live it there till u fully simplified ur derivative

[dreamy crow]

becuase it is not a constant like you said

[gray oxide]

But 2 is part of what I'm supposed to derivate right?

[devout sigil]

Huh? 2 is a constant

[dreamy crow]

well not in the way he thinks it is

[gray oxide]

I'm thinking that it has no value after it is derivated

Becuase it is a constant it doesn't have a changing value

[gray isle]

the 2 is being multiplied to sqrt(x)

[devout sigil]

No, if u know the scalar multiple rule, we can take it out such that 2 d/dx(x^n) is what we have simplified to

[gray isle]

the 2 isn't by itself here

[gray oxide]

What I mean is if the multiplication sign was addition what would change?

[devout sigil]

U can factor it out to differentiate the variable

But u must not remove it

[gray isle]

the derivative of a constant is 0

[devout sigil]

Because it is part of the equation

[gray isle]

however you aren't differentiating a constant here

[dreamy crow]

that was what i was trying to say

[gray oxide]

You factored it out?

[devout sigil]

9 is a constant, 9x is not a constant, 9 √x is not a constant

Yes I did

[gray oxide]

Oooooooooh

Lmao right you derivate the X in 9x but you leave the 9 out of it

[devout sigil]

Yes

[gray oxide]

I get it now hahahahaha

[devout sigil]

So if I have d/dx(9x) I can say it’s the same as 9d/dx (x)

Nice

[gray oxide]

Ok thank you now I know why I got the wrong answer

[devout sigil]

No problem, I’m glad I have been able to help

[gray oxide]

But if it wouldn't be to much I have one last question

[devout sigil]

Good luck!

[gray oxide]

Can you prove that the 9 in 9x is wrong to be derivated? Can you use logic to show how it is wrong to do that or is this one of those rules that it just is like that?

[gray isle]

depends on what you're doing

[devout sigil]

Scalar multiple rule: d/dx(k•f(x))=k•d/dx(f(x)) where k is a constant

That should be in math textbooks?

[gray oxide]

I don't have the d/dx but I do have this

[gray isle]

Usually somehow erasing something from existence will not be valid

[devout sigil]

Because if u differentiate the constant together with ur function u would probably end up with 0 right?

[gray oxide]

Yea

[gray isle]

you could consider 9x as the sum of 9 xs

[devout sigil]

Thus it doesn’t make sense. If I have any two functions let’s say y=4x-1 and y=2x³+x, if u differentiate the constant together u will get dy/dx=0. Which is illogical because the functions are different

This is by assuming u applied product rule

[gray isle]

9x = x + x + x + x + x + x + x + x + x

[dreamy crow]

u have the rule in your page just saying

[gray isle]

there is no way to properly justify erasing the 9 from existence in d/dx 9x
To get just d/dx x

[devout sigil]

Ye so there are already quite a few “proofs” or explanations here.

[gray oxide]

Yea I know but I wanna understand the why and how not just remember it

But yes thank you @devout sigil @gray isle @dreamy crow @obsidian cave

I appreciate it really I do

[devout sigil]

Example y=8x² and y=9x². dy/dx of first function is 8(2x), where dy/dx of second function is 9(2x). This shows that if the functions are similar, just differing in their constant product value, the gradient function is proportional to it.

[gray oxide]

Ah I get ittttt

Alrighty thank you imma leave this channel open now cya

[devout sigil]

Np, have fun learning math 🙂

[surreal meadow]

if you understand the power rule $(f(x)\cdot g(x))'=f(x)\cdot g'(x) + f'(x)\cdot g(x)$ then the constant rule should be easy to remember

[ocean seal]

maximo

[gray oxide]

It's fun when you understand it :)

[surreal meadow]

$(c\cdot f(x))' = c'\cdot f(x) + f'(x)\cdot c$

[ocean seal]

maximo

[surreal meadow]

since the derivative of a constant is 0, you can simplify this to 0*f(x) + f'(x)*c

so c*f'(x)

[gray oxide]

But if it is 0 then wouldn't that take it out....?

[surreal meadow]

exactly

so you get 0 * f(x) + c * f'(x)

which means you're only left with c * f'(x)

meaning that (c * f(x))' = c * (f(x))' = c * f'(x)

[gray oxide]

Are you using the derivate definition here?

Nvm there is no division

[dreamy crow]

callidus do you know what the derivitve represents?

[gray oxide]

Change

[dreamy crow]

rate of change exactly

[alpine sable]

Questions I have none.

[gray oxide]

Lol

[surreal meadow]

think about it for just f(x)
f(x) = 1 * f(x)
f'(x) = 1 * f'(x)

[dreamy crow]

lmao

[surreal meadow]

and using the product rule

(1 * f(x))' = 1 * f'(x) + 1' * f(x) = 1 * f'(x) + 0 * f(x) = 1 * f'(x)

[dreamy crow]

do you understand now why you cant take the multiplier out or do you need a more visual proof?

[gray oxide]

I really don't understand and I really don't want to waste your time beucase I'm prolly not getting it today so thank you for what you've helped me with already.

I want to research this tmrw what do I search up for this?

[dreamy crow]

nah its easy

i can show you now

tell me what does the derivitve represent

[gray oxide]

You sure, cuz I'm slow

Alright

[gray oxide]

Rate of change

[dreamy crow]

exactly

so let me show you a hypothethical situation lets say we have a function 0x^2 and a function 12x^2

if we were to cross out the multipliers

we would get that both of the functions change at a rate of 2x

but

if we graph this

we can clearly see that that is not the case

[gray oxide]

Yep

[dreamy crow]

do you understand now?

[gray oxide]

Yea I do get that they are not the same

[dreamy crow]

exactly 0x^2 is a function that constantly stays at 0

therfore its rate of change is 0

[gray oxide]

Yes

[dreamy crow]

but 12x^2 does change at some speed

but if we were to omit the multiplier like you did we would end up saying that both functions change at the same speed

which the clearly dont

do you understand now?

[gray oxide]

I understand that with the multipliers they change differently but without the multipliers they change the same is that right so far?

[dreamy crow]

yes if you were to take out the multipliers you would be saying that a functions which y value constantly stays at 0 is changing at the same speed as a function whichs y value does actually increase which is nonsencical

[woeful remnant]

Would someone know the answer to this question. "The mathematical operation known as addition is modeled after what?"

[surreal meadow]

the channel is occupied @woeful remnant , please go to another channel

[woeful remnant]

Oops sorry

[dreamy crow]

@gray oxide do you understand my explination

[gray oxide]

Yes I do get it

But

Why do we take out the whole coefficient first?

[dreamy crow]

wdym

[gray oxide]

In your example

You took out the 0 and 12

[surreal meadow]

you don't

it's just for the example

[gray oxide]

To show that the function wouldn't be the same after you take it out

[dreamy crow]

yes im trying to prove that taking it out would be wrong

and why you leave it in

as you asked

[surreal meadow]

@gray oxide what exactly are you having trouble comprehending?

[gray oxide]

The thing is I actually dont know lmao so I'm gonna go back an read untill I don't know what I'm reading anymore gimme a sec

[dreamy crow]

okay take your time its fine

[gray oxide]

$f(x) = 2\sqrt{x}
f'(x) = \dv{x}(2\sqrt{x}) =2 \dv{x}\sqrt{x}$

[ocean seal]

!callidus

[gray oxide]

When the 2 was taking out of the function and derivated

That was my original problem

[surreal meadow]

this is why it doesn't matter

[dreamy crow]

ah okay

[surreal meadow]

you can leave it in

you can take it out

it doesn't affect the result in the end

[gray oxide]

Becuase I cannot derivate the 2, but only the sqrt(X) part?

[surreal meadow]

what do you mean

you can derive a constant

$\frac{d}{dx}c = 0$

[ocean seal]

maximo

[surreal meadow]

the rate of change of a constant is 0

[gray oxide]

Yes

But seeeeeeee

I'm really sorry

[surreal meadow]

don't be

[dreamy crow]

its okay

[gray oxide]

But 0* sqrt(x) = 0 right?

[surreal meadow]

yes

[dreamy crow]

yes

[surreal meadow]

but look back at what i sent

[gray oxide]

Hmmmm

[surreal meadow]

there is a rule for the product of derivatives

[dreamy crow]

okay let me show you visually why the rate of change of a constant is 0

[gray oxide]

No I get that

[surreal meadow]

he understands that testing

do you understand the power rule call?

[gray oxide]

Yes

[surreal meadow]

ok

now look at how it works when we apply it to a constant and a function

[gray oxide]

It's this right?

[dreamy crow]

yea

[gray oxide]

Ok

[surreal meadow]

so for example, if c = 2

[gray oxide]

Yep

[surreal meadow]

(2 * f(x))' = 2' * f(x) + f'(x) * 2

and the derivative of 2 is...?

[gray oxide]

0

[surreal meadow]

so we get

0 * f(x) + 2 * f'(x)

= 2f'(x)

[gray oxide]

So ur using the product rule?

This thing wiat

[surreal meadow]

we use the product rule to show that constants can be "moved" outside of the derivative without issue

[surreal meadow]

that one

yes

[dreamy crow]

yes

[gray oxide]

Ok sick

Thank you very much

[dreamy crow]

okay do you understand now?

[gray oxide]

Yes fully I feel much more calmer about my exam hopefully you guys get rtx 3090s so you can sli them

[dreamy crow]

yes :D

[gray oxide]

Lmao alright srsly tho thx a lot cya

I'll be back tmrw for another mission to understand the maffs

[dreamy crow]

no problem :D

okay

[inner sequoia]

why does subtracting from x shift the graph right

[surreal meadow]

because if we subtract 1, the new x = 1 is the old x = 0

[ionic jewel]

because the y value previously graphed at each point is now graphed at each (x-h) which is left

[inner sequoia]

so if f(x) = 2x

and lets say 2x is 1

so if x is 1 then the point is at (1,2)

but if i subtract 1 from x

then (1,2,) becomes (0,0)?

[surreal meadow]

yes, if you had 2(x-1), x = 1 would now point to the old x = 0 value

[inner sequoia]

bcs if f(x)=2x

then f(x-1) will still equal 2x?

[surreal meadow]

because if f(x) = 2x, and g(x) = 2(x-1), then f(0) = g(1), f(1) = g(2), f(n) = g(n+1)

[inner sequoia]

why does it change the axis

[surreal meadow]

wdym?

[inner sequoia]

wait

f(x) = 3x

x = 4

f(4) = 12

[surreal meadow]

yes

[inner sequoia]

g(x-1)= what

[surreal meadow]

g(x) = 3(x-1)

or even g(x) = f(x-1)

[inner sequoia]

why is it 3(x-1)

[surreal meadow]

i thought you were following what I said above

[inner sequoia]

nope

[surreal meadow]

we just describe a function g as the shift of f(x) right 1 unit

[inner sequoia]

why would addition shift the graph left

[surreal meadow]

that's what I've been explaining

take f(x) = 3x

and g(x) = 3(x-1)

[inner sequoia]

ok

[surreal meadow]

f(0) = 3(0)

g(1) = 3(1 - 1) = 3(0)

so f(0) = g(1)

same thing happens for f(1) and g(2)

[inner sequoia]

g(1)=3(1-1) which is 3(0) which is 0

[surreal meadow]

yes

[inner sequoia]

so g(1)=0

[surreal meadow]

which coincides with f(0)

[inner sequoia]

so g(1)=(f(0)

[surreal meadow]

since we're subtracting 1 from x, its as if we're shifting the whole plane to the left 1

[inner sequoia]

ah

[surreal meadow]

or moving the function to the right 1

[inner sequoia]

bcs x is moving left

but the function stays the same

so the function increases

[surreal meadow]

yes, that's how they describe transformations in linear algebra too

[inner sequoia]

or moves right

[surreal meadow]

instead of moving a function they move the plane

so instead of moving the function/curve to the right, think of it as moving the plane to the left

since every x value is now instead x-1

so x=0 is now in the position of 0-1 = -1, 1 is in the position 1-1 =0

and so on

[inner sequoia]

ok so if
f(x) = 4x
x=4
and g(x) = 4(x-3)
then f(x)=16
and g(x)=4

wait

[inner sequoia]

ah so if f(x) results in (2,1), then it becomes f(x-1)=2,1 right

[surreal meadow]

right, think of g(x) as g(x) = f(x-1)

so for every single x

[inner sequoia]

is this right

[surreal meadow]

g(x) is actually f(x-1)

yes that's right

[inner sequoia]

but y = 4 now instead of 16

wouldnt that mean it was shifted left

[surreal meadow]

no

the opposite

since the sope is 4

a higher y comes at a higher x

[inner sequoia]

lower y = lower x

[surreal meadow]

yes

[inner sequoia]

but g(x) = 4 is a lower y than f(x)=16

[surreal meadow]

exactly

wait im confused

[inner sequoia]

same

lemme try again

f(x)=1x

g(x)=f(x-2)

if x = 2

then f(2)=2

g(2)=f(2-2)

[surreal meadow]

well the thing here is that the function is sort of shifted down as well

[inner sequoia]

g(2)=f(0)

but what does g(2)=f(0) mean?

[surreal meadow]

https://www.desmos.com/calculator/vnfswtaocf

look at this graph

[golden nymph]

the image of g at 2 is the same as the image of f at 0

[surreal meadow]

you'll see the points line up with each other on the x-axis since they are all taken at x=3

[inner sequoia]

oh wait

if f(0) = g(2)

[surreal meadow]

that's not the case

g(2) = f(0)

not the other way around

[inner sequoia]

g(2)=f(0)

[golden nymph]

wot

[surreal meadow]

for the example he gave, not the desmos

[golden nymph]

ok

[inner sequoia]

so if g(2) = f(0)

wiat