help-0

[pale kestrel]

It is certainly not the letter i for igloo

and then n

it is L

[eternal sierra]

So it is Ln

[strange shale]

Its L dude... Dont listen to the I conspiracy

Its just that l looks like I

lIlI

[eternal sierra]

Because my math teacher makes some mistakes, he’s a bio teacher

So just wanted to make sure

[pale kestrel]

apparently ln stands for

logarithmus nātūrālis

[strange shale]

Ah another Harry Potter spell got it

[eternal sierra]

He said there is no proof why e^lnx = e

But

There must be one

[pale kestrel]

there is none

[strange shale]

e^lnx = x (not e)

[pale kestrel]

because that's how you define ln

[eternal sierra]

But

Any way to prove it ?

[pale kestrel]

usually at least.

bruh

You DEFINE it that way

it's like proving the color white is white

[eternal sierra]

What if you multiply both sides by ln

[pale kestrel]

???

[strange shale]

Multiplying Ln doesnt make sense

[eternal sierra]

Y = e^lnx

I meant

[strange shale]

you mean lnY = ln(e^lnx) ?!

[eternal sierra]

Taking the natural log

Of both sides

Mb

Yeah

[pale kestrel]

what if I count to 3 to prove 3 is the 3rd counting number

[strange shale]

The formula ln(a^b) = aln(b) is derived from the definition of logs

[eternal sierra]

Then it simplifies to ln(y) = ln(x)

Thus y = x ?

[strange shale]

You are doing circular reasoning

[pale kestrel]

$$(x)(1/x) = 1$$

[ocean seal]

Shuri2060

[strange shale]

Study their Derivations if you want to get more clarity

[pale kestrel]

I just proved x times 1 over x = 1

idk, bad example

[eternal sierra]

But that is a simple expression, but for me when I see

[pale kestrel]

probably this is the better one

[eternal sierra]

e^lnx

I can’t just say oh it will simplify to x

Maybe I’m dumb

But the

[pale kestrel]

That's literally how you define the function ln

it inverts what exponentiation does

[strange shale]

Basically what you are doing is circular reasoning my friend!!!

[pale kestrel]

so yes, e^ln x = x is obvious by definition

ofc some ppl might take different definitions, in case you will be able to prove that fact

[strange shale]

We used the the definition to derive the formula you used for your simplification

And using that formula you derived the definition

[eternal sierra]

How do we prove the definitions then

[strange shale]

You havent proved anything because its circular reasoning

[eternal sierra]

Log(a^2) = 2log(a)

[pale kestrel]

How do you prove the color white is white

You don't.

[strange shale]

We dont prove definitions

[eternal sierra]

Then How was this discovered

It must’ve been some work

[strange shale]

We define functions ourselves!!

[strange shale]

It was derived with the definition

Read the derivations of properties of logs if you are curious

[eternal sierra]

So where did everything come from

Such that you don’t use other things

To find things

[strange shale]

The definition of logs... Which can be x^(log_x(y)) = y

Or you can say it as log_x(a) is the number such that if x is raised the power equal to that number we get a

This definition is enough to derive all properties of logs

Or formulas are we may call them

@eternal sierra Getting it?

[eternal sierra]

Yes

This is fun

Thanks

[strange shale]

Good

[strange shale]

I know right!!!

[eternal sierra]

Yeahh

[strange shale]

It is so amazing to see things in math with clarity.. In a system of proper formal pure logic

[lone heart]

@eternal sierra Has your question been resolved?

[lone heart]

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[willow stump]

Hey guys, does it make any sense that this equals 1?

What I did was say that this equals the imaginary part of (sin1+icos1)^90

Now (sin1+icos1)^90 is clearly i

So does that mean that that expression is 1?

[vale wigeon]

yes

[willow stump]

Oh damn thanks

Wait a minute

Does that mean the inverse of that expression

Equals 2^90-1?

Shit not the inverse

How do I say that?

The opposite? Sorry I don't know math terms, all the terms in that row of the pascal triangle except for those

[vale wigeon]

i don't know what you mean at all

[lone heart]

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[misty bobcat]

find a function $f: \mathbb{R} \mapsto \mathbb{R}$ which at point x = 0 has infinite derivative and in this point is: $\a)$ continuous $\b)$ not continuous

[misty bobcat]

any ideas ?

[ocean seal]

Michal

[pale kestrel]

you have any ideas?

[misty bobcat]

no, to be honest

[elfin ermine]

Infinite derivatives or the derivative is infinite?

[misty bobcat]

probably derivative is infinite, im not sure if i translated it correctly

[pale kestrel]

not even graph

of both cases

[elfin ermine]

Uh, what language is it

[misty bobcat]

Slovak

[elfin ermine]

Ah fuck

So infinte derivatives would be easy i think

[pale kestrel]

what

I think infinite derivative is easy but ok ...

[elfin ermine]

You could use $e^x$ and $\frac{e^x}{x}$

[misty bobcat]

i was thinking about 1/x but function is not defined at x = 0

[ocean seal]

Luca

[pale kestrel]

You need to think carefully about domain

yes

wait a sec

b) doesn't rlly make sense does it?

how the heck can a derivative be defined when the point is not continuous

it probably wants 1/x for that one

[misty bobcat]

derivative of e^x at point 0 is 1

[pale kestrel]

for a), think about inverses

[misty bobcat]

what about sqrt(x)

is defined at zero

but derivative is undefined at 0

[pale kestrel]

got a problem with x negative

[misty bobcat]

and also i have to verify this with calculations

[severe sluice]

how can a point not be continuous and still have a derivative?

[misty bobcat]

idk, its weird excercise

maybe i have to calculate with somehow with one sidee limits

[severe sluice]

or maybe they mean something like -1/x?

[misty bobcat]

i think so, something like that

and then i have to calculate one side derivation

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[hollow pelican]

for this question, do i let u to be e^t+3

[hollow pelican]

?

[alpine sable]

u dont

u can approach it in a different method

try change sqrt to 1/2 power first

[hollow pelican]

like direct integrating this

?

[alpine sable]

personally i wont directly do it, i would change the power

of e

and become (t+3)/2

[hollow pelican]

Ok

[alpine sable]

and the second step is let u=(t+3)/2

instead of the whole e

do u got it?

[hollow pelican]

ok

is it like this?

[alpine sable]

yes

so thats step 1

now instead of let u to be e^(t+3), let u be (t+3)/2

[hollow pelican]

ok

[alpine sable]

or like u wrote, let u be (t/2+3/2)

its the same

which doesnt really matter

[hollow pelican]

ok

[hollow pelican]

i am clueless if im correct

[alpine sable]

yes it is correct

so now u can directly integral

[hollow pelican]

ok

i think i got it

do i have to calculate out -2e^2?

for the constant

[alpine sable]

-2e^2 is already a constant

so ur answer is already finished

u are all correct now

[hollow pelican]

oh okay

[hollow pelican]

thanks so much

[alpine sable]

npnp

[dense holly]

Hi, can anyone help me with this? I don't know how to start

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[alpine sable]

if i got 2 complex number z1 and z2

[alpine sable]

is the argument of complex number z1/z2 equal to arg(z1) - arg(z2)

[pale kestrel]

if u dont care about domain of arg

then ok

[alpine sable]

what about modulus

what does that do

divide the modulus straight?

[pale kestrel]

yh

[alpine sable]

so its |z1|/|z2| ah alright

just wanted to check

(im just gonna leave this channel open and do some math with this quicktime to check if it works) thanks

@alpine sable be careful with the modulus

Especially the inequalities

[pale kestrel]

?????

[alpine sable]

uh i think i did something wrong

let me introduce my specific questino

oh lmao

its z2/z1 not z1/z2

lemme try again

argument is when you inverse the imaginary parts sign right?

uh no?

[pale kestrel]

🚫

[alpine sable]

argument is tan^-1(im(z)/re(z))

aka angle it makes with re(z)

I see

everything worked, great. thanks 🙂

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[alpine sable]

(btw yh ik i could have just divided the two numbers straight but wanted to just try this method too)

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[hollow pelican]

hi guys does anyone know how to do this?

[fair crater]

Kind of not math but what have you tried

[glacial perch]

i dont remember exactly but there's something like kirchoff's laws to solve

[fair crater]

Yes that would be the way

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@hollow pelican Has your question been resolved?

[raw shard]

not your channel

[lone heart]

@hollow pelican Has your question been resolved?

[lone heart]

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[tribal needle]

can someone help explain how to find the answers to this?

[lone heart]

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[harsh swallow]

7?

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@tribal needle Has your question been resolved?

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[burnt wren]

given -- a circle with centre O and a chord AB
CD is the perpendicular bisector of AB that is also a diameter intersecting AB at E
If AE = 4cm and ED is 3 cm find the radius of the circle
(sorry for the bad drawing )

[glacial perch]

take radius as r

write OE as r-3

use pythagoras theorem in triangle OAE

[burnt wren]

oh okk thanks

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[covert agate]

hi

[covert agate]

this is how you define concavity stuff right

take concave upward for example

after googling, it said ‘function is concave upward iff for every line segment on the curve, the segment is higher than the curve’

[covert agate]

i dont get how you arrive from that to this definition

<@&286206848099549185>

[lone heart]

@covert agate Has your question been resolved?

[covert agate]

im moving this to calculus channel

.close

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[forest turret]

i need it in y = mx+c

[hearty crown]

find the gradient first

[forest turret]

i have

[hearty crown]

c is the y-intercept

which is

1

[forest turret]

my friends have said its y=2x+1 but i dont know how to get 1

[hearty crown]

c is the value of y where the lines touches the y axis

in the first graph it crosses at y=1

so c is 1

[gaunt herald]

Ok so like you need to pick 2 points

[hearty crown]

then just plug in m and c into the y = mx+c equation

[gaunt herald]

Change in y/ change in x

[forest turret]

can you guys go throught the next one so i get it

[hearty crown]

the next one do the same

[forest turret]

coz i cannt understand it

[hearty crown]

but remember the gradient will be negative

just do the question step by step

1)find the graident (change in y/change in x)

2. find value of y-intercept from the graph

[forest turret]

what points do i pick

[hearty crown]

3)write the equation y=mc+x and plug in the values of m and c

any point it doesnt matte

[gaunt herald]

Any point that will make a triangle

[hearty crown]

r

[gaunt herald]

Not too long not too short

[forest turret]

pick one for me

[gaunt herald]

A normal triangle so that it could be easy

Like

If u want to make it easy as possible

Make sure that the lines

Are crossing the boxes like

Gimme a sec let me draw

[forest turret]

ok

[hearty crown]

an example

[gaunt herald]

Uhh sorry for the qualityy

[forest turret]

i dont now how to get c still

[gaunt herald]

Its the point where the line crosses the y axis

Where is the line crossing the y axis?

[forest turret]

what 5,0

[gaunt herald]

U need to get change in y and then divide it by change in x

So since u got and made a triangle that has as i mentioned the line is crossing the box in half

[forest turret]

so i have got y =-0.5x+c

[gaunt herald]

Waitwait

The formula is y2-y1/x2-x1 where is x2?

Y2 is like the furthest point from y axis

[forest turret]

can u write the co ordinates

like for y2 y1 x2 x1

[gaunt herald]

(0,1) and (2,5)

Okayy soo

We got the coordinates right?

[forest turret]

yh

still 0,5

-0.5

[gaunt herald]

Here

From @lethal tendon is the one who made it while explaning it to me so yeah

[forest turret]

what is the 1 for

c

[gaunt herald]

Yesss the "+ y" is when the line crosses the y at which point

It will be negative if the line has crossed below 0 y axis

[forest turret]

so its

1=-0.5x+c

which makes c 0.5

[gaunt herald]

Nono

[forest turret]

oh

[gaunt herald]

Again let me give u a better and easier method

You saw the triangle we did right?

[forest turret]

yh

[gaunt herald]

Okay so i want you to get their coordinates

Point 1 coordinates and point 2 as well

[forest turret]

(0,1) and (2,5)

[gaunt herald]

Yesss exacty

[forest turret]

so its 0-2 and 1-5

[gaunt herald]

Ok now here which is y's?

[forest turret]

to get the gradient

[gaunt herald]

Nono we need change in y

[forest turret]

o

0

[gaunt herald]

Nope

In the coordinates

Its (x,y)

Always

[forest turret]

ok

[gaunt herald]

Got it?

[forest turret]

so 1,5

[gaunt herald]

Ok so again which is y's?

Exactly

Now i want you to sibstract y2 which is 5

5-1?

[forest turret]

gradient is 0.5 right???

[gaunt herald]

We got change in Y now

No

[forest turret]

oh

[gaunt herald]

Gradient is 2x

[forest turret]

how

0-2

1-5

-2/4

[gaunt herald]

Since we got the 2 coordinates (0,1)(2,5) we need to get change in y so
In the coordinates always
(X,y)
The formula for gradient is
Change in y/ change in x
Y2-y1/x2-x1

Always get the second point first put it first

So now
(0,1)(2,5)
Change in y is
5-1
And change in x is
2-0

[forest turret]

can u solve it and do all the calculations on the paper so i willl know how to do it

[gaunt herald]

Sure but u will have to understand itt

[forest turret]

ohhhhhhhhhhhhhhhhhhhhhhhh

[gaunt herald]

We are closeee

Just last step

[forest turret]

i get it

but

[gaunt herald]

And now since we have change in y and change in x

Yeah?

[forest turret]

yh

[gaunt herald]

What is the formula?

[forest turret]

?

y+2x+c

[gaunt herald]

Nuuu

The formula

Forgradient

[forest turret]

2

[gaunt herald]

YESS

And you gotthe gradient

Y=2x + ?

[forest turret]

yh

[gaunt herald]

Where does the y cross?

[forest turret]

c

[gaunt herald]

At...

[forest turret]

1

[gaunt herald]

YESSS

there u go u did it

U still didntget it fully?

[forest turret]

wait what question was that

[gaunt herald]

First one

[forest turret]

ohh

[gaunt herald]

On the left

[forest turret]

i was doing te 2

[gaunt herald]

Hdhdbsbs

[forest turret]

can u help me with 2

[gaunt herald]

BOI

[forest turret]

im gonna kill myself

[gaunt herald]

I thought we were dong 1

Suresure

Nono man

[forest turret]

ur friend told me

[gaunt herald]

Yeah?

[forest turret]

ok number

2

0.5 is the gradient

[gaunt herald]

Ok let me check

[forest turret]

and c is 2.5?

did u go?

[gaunt herald]

Nono im here

[lone heart]

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[forest turret]

@gaunt herald is the best helper everrrrrrrrr

[lone heart]

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[vapid oak]

@gaunt herald@gaunt herald slope applies to m not x, if you apply it to x then the ratio as x changes isn't the same triangle

[vapid oak]

.close

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[vapid oak]

.reopen

[lone heart]

✅

[gaunt herald]

Yess

Isnt that what i did tho?

[vapid oak]

no

[gaunt herald]

I got -2x
M=-2..?

Can u explain it more if u dont mind?

[vapid oak]

yes, m = -2, I just saw that you put it together with x

[gaunt herald]

Ohh my bad

Its supposed to be mx=-2x

Thanks for reminding me

Appreciate it

Take care and stay safe @vapid oak ty againn :))

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.close

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[fathom rain]

How am I supposed to get the length of the side a by using the chart (no calculator)

[glass lichen]

trig

[fathom rain]

Yeah I know

but I only understand how I can do it with a calculator

[glass lichen]

set up an equation for a.

[fathom rain]

sin(70°) = a/2 ?

[glass lichen]

yes, and you know what sin(70) is from the table

[fathom rain]

oh fuck me that was easy

thanks

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[lone heart]

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[spare timber]

I'm stuck on this problem. I've been trying to solve for c, but every time i get a difference answer based on which 3 time stamps i use

[spare timber]

i can send my work if that helps

[pale kestrel]

plot the graph

[spare timber]

i have it on desmos

[pale kestrel]

and check it is actually exponential

the one from the data

[spare timber]

yes

ill send ss

[pale kestrel]

or if it has some scientific error

[spare timber]

its very odd and led me to believe its piecewise function, which doesn't make sense

and ive triple checked data points

[lone heart]

@spare timber Has your question been resolved?

[spare timber]

<@&286206848099549185>

[fair crater]

Wait, that graph

[spare timber]

yes>

[fair crater]

Is that of the transformed points or of the original

[round owl]

Well here you can already see that it's not exponential

[spare timber]

thats of the table

i was given in problem

am i interpretting question wrong?

[fair crater]

Why is the exercise asking for an exponential transformation...

[spare timber]

yea idk

[fair crater]

I think we're equally lost as you as to why

[spare timber]

should i ask my teacher then

[fair crater]

Anyway the graph seems linear

Yeah

[spare timber]

ok

[fair crater]

Also it's not piecewise linear

With piecewise linear you get too many parameters to play with

And so while your fit to this data is good

[spare timber]

mm

[fair crater]

The likelihood of it fitting to the next time this experiment is performed could be low

So a simpler model like just a linear model

Is usually encouraged if possible

It is only when it is clear there is a quadratic, cubic, exponential curve etc that such transformations are done

Else it's not really a wise use of data

[spare timber]

got it

[fair crater]

This (whether a certain modelling decision is wise) isn't very mathematical btw although you could make it mathematical at a very high level later on if you do high level stats

[spare timber]

im not at that level yet lol

very far from it

[fair crater]

Well for now, just use common sense

[spare timber]

yep

ok thanks for ur help

.close

[lone heart]

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[rancid moon]

So i thought of a problem that I don't know how to solve. It isn't for school, it just came to me and I was curious, but I don't know how to solve it. I tried, but arrived at a paradox. Here is the problem and my solution. What is the probability that a random point is the midpoint of two given points on the plane?

Here is what I arrived at: There are infinitely many points on the plane and only one that is their midpoint. Somehow you would have to devide by infinity? I don't think you can do that, but if you do I suppose it would be 0. So an event of probability 0 can't happen, and yet we can calculate the midpoint of two points. So I think I misunderstood something about infinity or an event with probably 0 is possible. I am very confused.

[wintry lotus]

Sounds like a Limit problem, if your number of options of points on your plane is not infinite (say whole numbers between (0,0) and (10,10)) then you'd have a % probability, as more points are added, the smaller the % becomes

[pale kestrel]

the plane doesn't have a midpoint.

[rancid moon]

Yeah

Two points

On that plane have one

Maybe i worded it badly

Sorry English is not my native language

[rancid moon]

Ah that makes sense, i haven't gotten to that part of math yet

In school i mean

[wintry lotus]

Right on! It is a great thought problem.

[pale kestrel]

'Choose a random Real number'

This turns out to be impossible.

No such probability distribution.

[rancid moon]

What? This is really interesting, i wanna know more

Is there a yt video about it or something i can read?

[pale kestrel]

https://math.stackexchange.com/questions/997173/can-you-pick-a-random-natural-number-and-a-random-real-number

[rancid moon]

Thanks

I guess my question was answered now, although i don't know enough to understand it

But, thanks still

Should i do .close?

.close

[lone heart]

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[alpine sable]

i need help is (2ab)*(a) = 2a^2b ?

[pale kestrel]

$$xy = yx$$

[ocean seal]

Shuri2060

[pale kestrel]

multiplication is commutative.

[blazing thunder]

in this case dont you mean distributive

a(b+c) = ab + ac

[alpine sable]

thank you

[pale kestrel]

what

[pale kestrel]

where do you see addition

[alpine sable]

so its 2ab^2

[pale kestrel]

what.

$$(2ab)*(a) = ???$$

[ocean seal]

Shuri2060

[pale kestrel]

This is your question correct?

[alpine sable]

tes

[pale kestrel]

its not.

Use the fact multiplication is commutative and associative

$$xy = yx$$
$$(xy)z = x(yz)$$

[ocean seal]

Shuri2060

[blazing thunder]

it would be 2*a*a*b

because it is all multiplied by each other

no matter how the brackets are here

shuri is right about commutative

|| also shuri please help me in my channel ||

[alpine sable]

so

its

2a^2b

.close

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[vestal crest]

just wondered if this is (1/1)^0=1?

[buoyant kayak]

answer is correct, reasoning is faulty

[vestal crest]

can you give me a reason then

[buoyant kayak]

you're just plugging 0 in?

[vestal crest]

yeah

[buoyant kayak]

0^(-2) is undefined

you're gonna get a 1^infty form

[vestal crest]

oh right

[vestal crest]

im not sure to which form i am supposed to convert it

do i substitute x^2

[buoyant kayak]

$\lim_{x\to 0}{(\frac{1}{\cos{x^2}}})^{x^{-2}}=L$

[ocean seal]

a disappointing son

[buoyant kayak]

take the ln of both sides

you'll get a different indeterminate form, see what you can do from there

[lone heart]

@vestal crest Has your question been resolved?

[vestal crest]

is there other way to do this? i have never done it this way so i dont really know what to do

[buoyant kayak]

not another way that i'm aware of

https://www.youtube.com/watch?v=thEnl_gCjXA

hour long video, has plenty of examples if you'd like to find some that are similar

i'm not sure your familiarity with manipulating limits to use l'hopital

[vestal crest]

yeah i dont have a clue

thanks anyways

.close

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[pale kestrel]

,rotate

[pale kestrel]

is that a 2 on the left of sin?

[open plaza]

Yes

[pale kestrel]

I dont get whats wrong with drawing a picture

its pretty quick to see geometrically

[open plaza]

I don't know what to draw
You can draw the picture if you want

[pale kestrel]

https://i.imgur.com/kkJ3veH.png

^ this immediately leads you to the result?

[open plaza]

No

[pale kestrel]

ok do you see where i got my picture from

[open plaza]

Well my brother had solved this but i can't understand what he has written

[pale kestrel]

Take triangle ABC. B is right angled.

tan A = 1, so AB = BC.

Let x = AB = BC.

Then AC = x sqrt2

(try to continue this)

This is what my diagram represents.

[open plaza]

Ok

This will help me thanks

[alpine sable]

Can sm help me

[wary stream]

Don't ask in an occupied channel
Read #❓how-to-get-help

[alpine sable]

Well sorry I don’t usually use this discord, but I’m really confused so can an1 help?

[wary stream]

Well, read #❓how-to-get-help

[lone heart]

@open plaza Has your question been resolved?

[lone heart]

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[arctic harbor]

Hello, I need to graph this function, would I first start with graphing the base function y=3^x

[arctic harbor]

I need to graph the transformations of this graph, I like to go step by step, however, what would I place for the parent function of this graph?

My assumption is that it is y=3^x but I'm not sure

[cursive badger]

yeah, I would take 3^x, move it right 4 and up 2, then flatten it in half about y=2 and flip it

or I would use -.5(3^x) as my reference in the first place

@arctic harbor

[arctic harbor]

okay thank you

.close

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[night folio]

Can someone please help me with this

[night folio]

I need the answer for this problem

[wary stream]

We're not here to give answers, we're here to help. If you want answers, go somewhere else

But anyways, what did you try?

[wary stream]

Slope is wrong

That's 1 - -4 or 1 + 4

[night folio]

1- -4

[wary stream]

I'm stating

1 - -4 = 1 + 4

[night folio]

Oh

[wary stream]

Two negatives makes a positive

The rest of the process looks right, you just need to fix the slope and apply the proper slope value

[night folio]

This right?

[wary stream]

Looks like it

[night folio]

Bet thanks

[lone heart]

@night folio Has your question been resolved?

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[steady prism]

Help me please

[steady prism]

I’m doing graphing proportional relationships

[severe sluice]

....right

so what are you struggling with?

[steady prism]

And I have no idea what I’ve doing

Algebra

[severe sluice]

do you have a specific question, or are you asking about the .... uh, nvm.

[steady prism]

This stuff, I have no idea how to do it

[severe sluice]

do you know the formula for proportional relationships?

[steady prism]

Nope

[severe sluice]

y=kx

[steady prism]

So what if it was like, y is 13 times the value of x how would I write that?

[severe sluice]

y = 13x

?

[steady prism]

I’m here

[lone heart]

@steady prism Has your question been resolved?

[lone heart]

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[hoary wasp]

I need help with a calculas ab question

[hoary wasp]

I know it has something to do with derivative and i found the critical points which are pi/4 and 3pi/4

im stuck on what to do next to find the maximum value

like are they asking for the coordinate at the maximum? because on the graph of the derivative it doesnt go from positive to negative for it to be a maximum during the given interval

i asked a question first lol

i found out how to do the first 2

would the last part be finding the average slope between x=0 and x=pi and then using mvt to find where else that slope exists?

<@&286206848099549185>

[bright hedge]

we know that the mean value theorem says:

$f(b)-f(a) = f'(c)(b-a)$

[ocean seal]

Yottachad

[bright hedge]

if we rearrange this equation we get:

$f'(c) = \frac{f(b)-f(a)}{b-a}$

[ocean seal]

Yottachad

[hoary wasp]

yeah that average slope is equal to the derivative

[bright hedge]

that is, there is some c on the open interval (a, b) such that the f'(c) is the secant slope

[hoary wasp]

yeah but what do i do

[bright hedge]

well first find the thing on the right

[hoary wasp]

i got (2pi+1)/(pi)

as the average slope

[bright hedge]

okay

f'(x) = 2 - 2sin(2x)

so we want:

[hoary wasp]

yeah

[bright hedge]

$2 - 2\sin(2x) = \frac{2\pi + 1}{\pi}$

[hoary wasp]

yup

[ocean seal]

Yottachad

[bright hedge]

and we want 0 <= x <= pi right

[hoary wasp]

yeah

[bright hedge]

okay so we have

$2\sin(2x) = \frac{2\pi}{\pi} - \frac{2\pi + 1}{\pi}$

[ocean seal]

Yottachad

[hoary wasp]

wait howd you get that

[bright hedge]

i rearranged the equation before

i moved 2sin(2x) to the left and i subtratcted both sides by 2pi+1/pi

[hoary wasp]

whered you get 2pi/pi from

this is what i did

but then i got stuck

[alpine sable]

he transformed the 2

[hoary wasp]

how though

pi/pi wasnt multiplied on both sides no?

so how did the 2 change

[alpine sable]

2pi/pi is the same as 2

[hoary wasp]

oh oh oh

i got it

yeah

[alpine sable]

do u understand why he did that?

[pale kestrel]

?

[hoary wasp]

yeah so he can subtract right?

[alpine sable]

lmaooo

typo

[hoary wasp]

common denominator

[alpine sable]

sorry

wait

not typo

but brainfart

[alpine sable]

yes

[bright hedge]

yeah sorry im back

[hoary wasp]

so what happens next

[bright hedge]

it was because of the common denominator

so then we get: -1/2pi = sin(2x) i think

[hoary wasp]

it becomes -1/pi

and then yeah

what you said

[bright hedge]

so then just take arcsin() and divide by 2

so we get

2x = arcsin(-1/2pi)

so then x = arcsin(-1/2pi)/2

wait

okay okay

so we know that sin(x) is 2pi-periodic right

so when we take the arcsin() of both sides

[hoary wasp]

yeah

[bright hedge]

we have to add 2pi to the side that x isn't on (because it will be the same angle)

so we would actually get:

2x = arcsin(-1/2pi) + 2pi*n

[hoary wasp]

wait

what

you lost me on that one

[bright hedge]

if we add 2pi to an angle

it is the same angle

right

[hoary wasp]

uhhhh i dont know

my teacher never taught me that

[bright hedge]

😦

you know how theta = 0

and going all the way around the circle

[hoary wasp]

he hasnt told us that

[bright hedge]

(so 2pi radians)

is the same thing

[hoary wasp]

idk why he put this question on the quiz

[bright hedge]

quiz????????

[hoary wasp]

if this is how its done then we arent prepared to do that question

yeah its a take home quiz

due tomorrow

[bright hedge]

well im sorry

but one of the rules is that the helpers must maintain academic integrity

[hoary wasp]

........

[bright hedge]

but i will say search up some vids about trigonometry

[hoary wasp]

he hasnt taught us this

welp

im getting wrong 100%

but thanks anyways and have a good day

[bright hedge]

unfortunately all the helper ranks can't help on quizzes

you too

.close

[lone heart]

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[wheat prawn]

Hey I had a question

[wheat prawn]

If 3 150 mg of a radioactive substance decays to 450mg in 73 weeks, determine the half-life of the substance to the nearest week. (logs)

how would you write that into the formula

i dont get it

[pure wasp]

What formula you using

[lone heart]

@wheat prawn Has your question been resolved?

[urban pine]

i think something like

A(t) = P e^(kt)

the amount A for some principal amount P and time t you can solve for k
and then (using that k) you can find t_half from

1575 = 3150 e^(k t_half)

[wheat prawn]

f=I(r)t/T

f= final

I= initial

r = rate

[wheat prawn]

what am i doing wrong

ill show my work

oh

[urban pine]

that's a lot to unpack

you're treating exponents very wrong here

[pure wasp]

Wow never seen that before

[urban pine]

• to cancel the 73 in the exponent you would have to take the 73rd power of both sides (but don't do that)
• you can't multiply 150 and 0.5 since 0.5 has an exponent
• i think time t = 73
• idk where you even got the 150

that's assuming your setup is correct

which i'm almost sure it's not

[wheat prawn]

150 is in the question

3 150's

[urban pine]

is that three thousand?

3 * 150 = 450, there would be no decay

[wheat prawn]

then how does the question make sense

if there is no decay

the answer says 26 weeks

[urban pine]

well you didn't really answer me

[wheat prawn]

ik i did it wrong

[urban pine]

the number is three thousand one hundred fifty?

[wheat prawn]

no?

[urban pine]

the question is entirely reasonable if the initial amount of material is 3,150. as i showed in the setup for my first response
but you said "3 150's" so are you reading this as "three 150's"? because then the question doesn't make sense as there is no decay

[wheat prawn]

Ohhh

yeah

Lmao

[urban pine]

lol

[wheat prawn]

i read it as 3 150's

cuz there was a space

[urban pine]

ye sometimes the thousand separators are non-breaking spaces

https://en.wikipedia.org/wiki/Decimal_separator#/media/File:Thousands_separators.gif

Space, the internationally recommended thousands separator.

anyway does the setup from before make sense?

[lone heart]

@wheat prawn Has your question been resolved?

[lone heart]

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[lusty charm]

what things, objects, processes, structures can you find at home that can be represented by a linear relation?

[wintry lotus]

anything that is a straight line. Walls, doors, floors, tables, counters, picture frames

[lusty charm]

okay, how so? can you explain why please?

[wintry lotus]

A linear relationship is basically anything that can be found with on y = mx + b, i.e. a straight line. Suppose the floor is y = 0 on the graph, your outer walls are x = 2 and x = 5, the roof is y = x and y = -x.

Guess latex took the night off

If it is circular, it isn't linear, it would be parabolic in relation

[lusty charm]

this is so advanced

does the heat of a kettle work?

like it gets hotter and hotter

or maybe the price of your property? does that work? i mean it goes up and goes down

[pale kestrel]

no.

[lusty charm]

oh how so?

[pale kestrel]

just pick things that are clearly linear

Your kettle does not heat linearly

[lusty charm]

but its a linear relation?

[pale kestrel]

If it did, I can just keep waiting

and eventually it'll be as hot as the Sun

[lusty charm]

ohh i see

[pale kestrel]

^ this is probably heating curve of kettle

there is a limit

[lusty charm]

ohh i see

so

a linear relation

[pale kestrel]

take what was suggested above

[lusty charm]

anything straight basieclaly?

[lusty charm]

yeah but its a little confusing

[pale kestrel]

If you have a perfectly cuboid bath

the water level as you fill it up

is linear over time

[lusty charm]

oh but this

the walls

why is it linear

how could it be represented in a linear relation

is anything that is straight able to be represented in a linear relation?

[pale kestrel]

yes

thats what linear means

straight line graph

[lusty charm]

what about the relation part

[pale kestrel]

you are relating 2 things

your roof is straight

as you go left

how much you go up

is linear relation

[lusty charm]

oh okay

so

roof can be writing as linear

relation

wall can

etc?

[pale kestrel]

yh

if you change something

and the resulting thing doesnt change

that is technically a linear relation

You heating your kettle isn't going to change the size of your TV

[lusty charm]

yeah

[pale kestrel]

that's a linear relation.

Maybe your teacher won't accept it though.

[lusty charm]

i think i should keep it simple though

yeah

maybe stick to the walls and floor idea?

[pale kestrel]

yh

roof

[pale kestrel]

.

[lusty charm]

why would floor be linear relation tho

how do you do that

how do you represent

like what would be the labels

[pale kestrel]

its the same idea as no change tho

i think a better idea is the roof

[lusty charm]

yeah but i have to name more than one

[pale kestrel]

you move horizontally

you will move vertically

filling up your perfectly cuboid bath

Water level vs time is linear

[lusty charm]

i see

[lusty charm]

why perfectly cuboid?

[pale kestrel]

if its

round at the bottom

the bottom will fill up at a faster rate

than when near the top

cus it takes less water to fill the bottom

[lusty charm]

what does perfectly cuboid even mean

[pale kestrel]

square

[lusty charm]

oh ic

how would doors work shuri? would it be how much width vs height?

[pale kestrel]

idk

[lusty charm]

so would it just not work

what examples other than roof

[pale kestrel]

try #math-discussion maybe

[lusty charm]

alr

[lone heart]

@lusty charm Has your question been resolved?

[lone heart]

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[potent lantern]

Hi, I need some trig help.

sec \frac{\pi}{6}

how come we multiply the \frac{2}{\sqrt{3}} by \frac{\sqrt{3}}{\sqrt{3}}

[buoyant kayak]

rationalizing

[potent lantern]

but why sqrt3/sqrt3 specifically?

[buoyant kayak]

when rationalizing the denominator, you're trying to get rid of the sqrt

so essentially just whatever the sqrt in the denominator is

multiply by that

as $(\sqrt{a})^2=a$

[ocean seal]

a disappointing son

[potent lantern]

perfect thanks for the help

.close

[lone heart]

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[pale kestrel]

calculator?

[rich basin]

how can we solve this without a calculator?

[pale kestrel]

just search online how to invert a 3x3 matrix?

[lone heart]

@rich basin Has your question been resolved?

[vale wigeon]

@rich basin do you want help with the matrix inverse question or the basis question

if both, which one first

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@rich basin Has your question been resolved?

[rich basin]

@vale wigeon More so on the inverse matrices, because I've been wondering for 2 years

[vale wigeon]

have you ever done gaussian elimination / row reduction before

[rich basin]

sorry no, I can learn it right now

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[solemn cape]

I haven't started solving this one because it's an optional item, but I'd like to get the idea on how to solve it,,

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[opal herald]

99% of people can't do this

[hearty frost]

do you want help with this ?

[fading citrus]

@opal herald Use this channel if you need a hand, don't double post. And that's not a very constructive way to post either, if you need a hand with something post what you are having trouble with/your work so far.

[severe sluice]

the sector's area can easily be found

for the triangle

sin 120deg is pretty easy to find

~~also i just happen to be in the 99% of people who can't solve this @opal herald ~~

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[pale kestrel]

chop the triangle into half.

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[proper cipher]

i just dont get what we have to do i have a small brain and idk how to not calculate the holes

[arctic gust]

are the holes squares?

[proper cipher]

yes but i dont know what holes a) has

and i need to know how to calculate the side of the squares with the holes in it

[arctic gust]

i dont think there are any holes in a)

[proper cipher]

it says there are parts missing

[arctic gust]

maybe just the top part

[proper cipher]

OH

i thought it was a handle

ok anyways with b)

how do i calculate the side area with the holes being there

like not give the answer just how do i do it

[arctic gust]

in b, there is an open top part and there are squares on 4 sides (not on the bottom)

[proper cipher]

yes

how should i calculate the sides with the tiny holes in it

[arctic gust]

so thats 5 x 10^2 - 4 x 4^2

5 x 10 x 10 - 4 x 4 x 4

[proper cipher]

thats uh

500 - 64

i think

so thats 436?

cm

[arctic gust]

yeah

[proper cipher]

oh k

thanks so much man

[arctic gust]

yeah no prob

[proper cipher]

.close

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[harsh ocean]

What's the difference between $\int_{S} \vec{B} \cdot d\vec{S}$ and $\oint_{S} \vec{B} \cdot d\vec{S}$

[ocean seal]

JSGF

[harsh ocean]

?

[arctic gust]

i think it means its over a closed loop

[harsh ocean]

Yeah I know but does it change calculations or is it just context wise

[arctic gust]

its the same

but we use it to denote that it's been taken over a closed surface

the element itself is that of a closed loop