help-0

[flint badger]

"Make this side 0"

now u can do that

x^2 + 10x + 9 = 78 right

thats what it is now

[barren river]

no u used an example and so do i

[flint badger]

oh

im confused

[barren river]

a

x2+4x-3x-12

x2+x-12=78

[flint badger]

no thats not the right way to do it

u did it dight here

[barren river]

one sec

[flint badger]

oh my god wait I just realized how stupid that was

[barren river]

X+4(x-3)

[flint badger]

u got it

nvm

@barren river u are right

[barren river]

bruh

[flint badger]

I forgot about original question XD

[flint badger]

so this is right

do u know what to do next

[barren river]

u said move the 78 to the left side

So it would be negative 78

[flint badger]

wait omg @barren river bro

this is so confusing, sry

(x-4)(x-3)

do this again

[barren river]

its (x+4) tho

[flint badger]

bruh

i wrote it wrong

ims uch a bad teacher

ok I guess ur right then

[barren river]

now u made me confused

[flint badger]

no

u were right

dont listen to me

u did it right, I just thought it was x-4 so I got confused

[flint badger]

What does this become

[barren river]

wdym

[flint badger]

remember u have to make right hand side zero

[barren river]

oh "what will this become"

[flint badger]

To solve the quadratic right

u are trying to solve for x, remember?

[barren river]

yes

yea uh

Confirming

X=9 or x= negative 10

[flint badger]

yes @barren river

now let me ask u

@barren river if u plug x back into the original triangle, which will make more sense

9 or -10

[alpine sable]

sorry but what am i supposed to do here?

[ashen anchor]

More context to the question please?

[alpine sable]

find the value of the area of the triangle

[flint badger]

This is altitude problem right

[fickle swift]

Hi, can anyone help me with this question?

ABCD is a rectangle
AB: 5 cm, BC=3,6 ​​cm
AM+BM= 13 cm
Required: calculate the perimeter of △AMD

[ashen anchor]

What have you tried?

[fickle swift]

The teacher gave me a hint and said that we have to use Thales and his hourglass theorm "idk what it's called in english" and also the Pythagorean Theorem

[ashen anchor]

You have to? I can probably solve it using other methods

[fickle swift]

i might find MD by using Thales and then find AM by using the Pythagorean Theorem easily

[fickle swift]

I think he said that because it's the methods we have learned

i was talking about this

[real crescent]

hi can someone tell me if this is correct please

[arctic wren]

try to find Y and W with respect to MD

[frank fable]

No clue but I like ur handwriting

[arctic wren]

,rotate

[fickle swift]

Y?

[fickle swift]

where

[arctic wren]

i didn't go that far, but as far i looked at it and remember my geometry classes would do that way

[real crescent]

lolz ty

[fickle swift]

I mean we don't have Y in the shape

[arctic wren]

no

[sick sorrel]

can someone help me find the slope - rate of change

[alpine sable]

Take any 2 random points on the line and do\
$\frac{y_2-y_1}{x_2-x_1}$

[ocean seal]

Quod Erat Demonstrandum.

[sick sorrel]

omg tysm 🤗

[alpine sable]

No problem!

[ocean seal]

lea

[alpine sable]

These type of questions actually feel paradoxical to me to be honest. Like the principal will change every 1 year or "triple the original sum" by that do they mean amount or internet? If they mean amount, we have to calculate interest as 2x else we would have to calculate interest as 3x. If you get what I mean.

[tight birch]

hello, if i have a variable inside an integral which is not related to the differential, can i just take it out?

in this case, x if not a function of y

[alpine sable]

in this case, yes, you can

[tight birch]

oh so it's like the thing in partial derivatives, where the "unrelated" variables can just be taken out the derivative sign?

[alpine sable]

exactly

[tight birch]

hmmm okay okay thanks

so this is still fine right

[alpine sable]

if neither of A, w or t is in function of v or vice versa, yes, you can

[tight birch]

💯 thanks!

[ashen anchor]

i scribbled this in the last couple minutes. I hope there's no typos

its using some analytic geometry

[fickle swift]

Thank you

[jovial terrace]

Can someone explain to me how we get to the answer (answer will be in the image below this message) when downsizing this?

I just can't get to that solution

[devout summit]

Dividing by 2x in both numerator and denominator

[jovial terrace]

How?

[devout summit]

4x=(2x)*2 and, 6x+2x^2=2x*(3+x)

[devout summit]

So, doing this gets rid of the 2x factor from both numerator and denominator

[jovial terrace]

oh

[charred nacelle]

can someone explain why it's 21 and not 32

[wind venture]

Its the highest factor

Pretty simple

[jade birch]

$5^{21}\cdot 2^{22}=5^{21}\cdot 2^{21} \cdot 2 = (5\cdot 2)^{21} \cdot 2 = 2\cdot 10^{21}$

[ocean seal]

.itsjustnai

[high bear]

hi can i get some help once everything is free'd up here

[charred nacelle]

where did 2^22 come from

I know it's the same value

Is this something I should just 'know'

[devout summit]

$4^{11}=\left(2^2\right)^{11}=2^{2\cdot 11}=2^{22}$

[ocean seal]

Euclid31415

[jovial edge]

Hi

How do I calculate this?

[warped phoenix]

thank you!!

now another question 😅

I dont see why this is wrong

[vagrant dust]

The player would need to require only 1 set to win the match. So if we calculate the probability of the player losing all matches(1/2 * 1/2 * 1/2) and then subtract it from 1 u will get ur answer.

[fiery berry]

?

How would I solve this without log

[jovial edge]

So I have calculated it correctly (the writing in blue)

How about this one?

[ruby badger]

Did i do the 1. And 2. Correctly?

[novel siren]

you forgot 7 in the first one

[ruby badger]

Oh yeah

But i did 2. Correctly right?

[novel siren]

yes

[azure gorge]

hey i got 2 very amateur almost ridiculous math questions:

a) I pick 2 flowers every 17 seconds, how many flowers would i pick in 1 hour?
b) I pick 3 flowers every 17 seconds, how many flowers would i pick in 1 hour?

how do i solve this?

[lapis wigeon]

you have to figure out how many seconds are in hour

and then divide the time it takes through the total time you have

[azure gorge]

1 hour = 3600s
using the rule of three formula.

a)
17s = 2 flowers
3600s = x flowers

2 * 3600 divided by 17 = 423.53

I get approx. 423 flowers in 1 hour.

b)
17s = 3 flowers
3600s = x flowers

3 * 3600 divided by 17 = 635.29

I get approx. 635 flowers in 1 hour.

@lapis wigeon is this correct?

[lapis wigeon]

yes

[azure gorge]

thanks

[pine igloo]

anyone able to help me with differential equations (ODE)?

[alpine sable]

Don't ask to ask, just ask.

[severe marlin]

Anyone evaluating this without calculator easily?

[obsidian crane]

The powers multiply

Oh wait that's not a power inside

[alpine sable]

And you can just simplify to 6/4 then 3/2

[obsidian crane]

So , it becomes (25/4)^-3/2

[obsidian crane]

It's not that.

[severe marlin]

Right track

Go on

I’m on that part right now

but continuing is a problem

[obsidian crane]

Now you notice theres 1/2 in the power

that's square root

so it becomes

(5/2)^-3

[severe marlin]

but it’s a negative power

[obsidian crane]

now reciprocal

[obsidian crane]

you can assume the negative is with either 3 or 1/2 as 3 x -1/2 = -3 x 1/2

[obsidian crane]

it will become (2/5)^3

8 / 125 final answer

[jovial tulip]

i need help with a geometry problem

[severe marlin]

yes you are correct can you explain again

so what will become 25/3

[alpine sable]

Just wait, man.

My bro here is helping.

[jovial tulip]

ok

[obsidian crane]

you mean 25/4

[severe marlin]

This one

[jovial tulip]

i didnt say anythig

tho

[obsidian crane]

Just apply the power

2x2x2/5x5x5

[severe marlin]

I’m at (25/4) power -3/2 so far

What shall I do after

[obsidian crane]

Look

(25 / 4)^-3/2 = (((25 / 4) ^ 1/2) ^ -3)

Do you understand this ?

[severe marlin]

can you write it out?

I can’t understand the computer signs

Sorry to put you through this

I should know this

[jovial tulip]

^ = power

ok can i ask now tho?

[severe marlin]

@jovial tulip just a tip there are question channels up to 9

[jovial tulip]

ok

[severe marlin]

if they don’t reply here

Try the others

#help-2

#help-1

[alpine sable]

Yeah, I can help you if you wish bro

Wrong quote though

[obsidian crane]

@severe marlin

[alpine sable]

Meant to quote the geometry dude

[severe marlin]

@obsidian crane cheersss man

Appreciate that

lemme work that out

[obsidian crane]

👍

[severe marlin]

Lovely

Thanks king

I understand more if I see the questions written

And that’s very helpful

Appreciate that, correct answer aswell

[ember tartan]

can someone help me

..

[severe marlin]

@obsidian crane

Does it also work the same for the others

[obsidian crane]

No one will say 'yes' just write the question .

[ember tartan]

MB mb

..

[obsidian crane]

If they are similar questions yes, I'm not sure what exactly are you referring to.

[severe marlin]

Typically this one

just the same one basically

Without the negative power

[obsidian crane]

Yes it will work.

[azure badger]

guys unrеtard for a second pls

[severe marlin]

Also note we can’t use calculators

[azure badger]

Let P (x) be a square polynomial. The equations P (x) = x-10 and P (x) = 1-x / 10 have 1 solution. What is the discriminant of P (x)?

[alpine sable]

Bruh.

There are two pending questions my bro.

[obsidian crane]

It's a general rule
$(a ^ x)^y = a ^ xy$

[severe marlin]

@obsidian crane how is the procedure any different this time on this one? Fo you think you can write it?

[obsidian crane]

$(a ^ x)^y = a ^ (xy)$

uhh lol

sec

[severe marlin]

Just write it out lmao

the bot is hard

[obsidian crane]

Just remember this rule

[severe marlin]

Ty

[alpine sable]

Is there a way of simplifying $$-\frac{\left(x-n\right)}{f'(n)}+f(n)=\sqrt{f\left(\int_{0}^{n}\sqrt{1+\left(\frac{df(x)}{dx}\right)^2}dx\right)-\left(x-n\right)^2}$$?

[ocean seal]

3317

[alpine sable]

I just had this math shower thought in which I rectified the curve of a continuous function and applied that function over itself as if the curve was the axis of the independent variable, then de-rectified it , preserving angles and distances at best

[lofty bluff]

guys I have a question

[alpine sable]

Bruh

Do it.

[lofty bluff]

is this correct?

cos²(πx) = cos(πx)²

?

[obsidian crane]

no

[alpine sable]

Why?

[tight birch]

cos²(πx) = (cos(πx))² is correct

[lofty bluff]

it is right?

[azure badger]

do you mean squared argument?

or what

[lofty bluff]

the square is afecting the cos too?

[obsidian crane]

it seems like you're squaring the angle if that's the case then no otherwise yes

[lofty bluff]

yeah

for the square to affect only the πx

[tight birch]

$$cos²(x) = cos(x) cos(x) = (cos(x))²$$

[ocean seal]

aIex

[lofty bluff]

it should be cos((πx)²)

[lofty bluff]

ok

[tight birch]

same with all trigos\

[lofty bluff]

then how do you make the square only affect the πx

[obsidian crane]

you don't

can you give me an example where you would need to do that ?

[lofty bluff]

I am having an argument with a teacher

where she says that cos(πx)²

is only affecting the πx

but not the cos

[tight birch]

she's right

[obsidian crane]

wait it must be cos((πx)²)

brackets matter

[lofty bluff]

thats the debate

[novel kettle]

Can someone check if I did this right
Question: A shopkeeper bought 300 apples at 80c each.30 apples got rotten and the remaining were sold at the market for 20c each.
A: Find the buying price
B: Find the selling price
C: Find the gain or loss percent

[tight birch]

if you want to affect the πx only then she's right

[lofty bluff]

hmmm

[tight birch]

but i think this one's better

[lofty bluff]

i also think that it should be cos((πx)²)

[tight birch]

ya ya agree

[lofty bluff]

then my statement of cos²(πx) = cos(πx)² is not correct

[alpine sable]

does slope include x?

[tight birch]

no

[obsidian crane]

x is a variable

[alpine sable]

ok

[lofty bluff]

well

thanks

[forest orchid]

can someone help me solve this, i dont really understand how to do transformations

[waxen copper]

help

please

[novel loom]

to make sure
15x^5
----- (over)
3x^2
= 5x to the power of 3

[buoyant kayak]

yes

[ember tartan]

god...someone help me

._.

[buoyant kayak]

with?

[compact nexus]

I'm unsure where to post this, but would someone be able to help me observe the general case? I don't see it intuitively

[crimson blade]

i was watching a yt tutorial on how to answer a question, and he converted x to a half and im unsure why or how he did it. does anyone know?

[alpine sable]

you use u-substitution where u = x^2 + 1, which means du = 2xdx, so dx = 1/2 du

then you have $\int \frac{1}{u} \cdot \frac{1}{2} du$

[thorn kindle]

Wow

[crimson blade]

ohhh alright, somehow i never thought of that. thank you

[ocean seal]

bertaunth

[lethal lichen]

can anyone help me with part B?

im using the formula for the sum of n terms in a geometric sequence

but my answer using this formula is wrong

[toxic cave]

How can I convert an answer in mapping notation to its logarithmic form?

Mapping notation: (1/2x,y)

The answer which idk how to get: y=log2x

[mild plover]

If a question is
dy/dx | x=-1

Do I input x =-1 into the derivative?

[alpine sable]

yes

[mild plover]

So this just means find the Y value of the derivative at -1?

Slope of tangent line at that x value

[alpine sable]

yes

[mild plover]

Thanks!

[fringe jungle]

Can someone help with this?

[toxic cave]

Can someone help me with question 16b?

[alpine sable]

to stretch something horizontally by 3, we divide x by 3

https://tenor.com/view/lol-math-gif-5022798

[ebon ore]

guys i need help pls help me find the total distance christopher columbus travelled on his journey

[alpine sable]

this one's a little tricky, but to stretch by 3, we do: \
$y = \text{log}(\frac{1}{3} \cdot 6(x-3))$

[ocean seal]

bertaunth

[alpine sable]

Bertaunth, excuse me, but is there are topic that deals with streching graphs?

its the transformation of logarithmic functions

oh wait no that's for logarithmic funtions

its just transformations

Hmmm

So if I want to learn more about this subject I can just search mathematical transformation on google?

when we transform something, we can transform it by stretching, moving it, rotating it, etc.

yep

Thanks

[alpine sable]

this is because for log functions, we do this:

where k is the horizontal stretch/compression

so if we want to stretch something by 3, we say k = 1/3

which is where the 1/3 comes from

now we want to move something to the left by 9 units

[alpine sable]

here, d means the horizontal shift

so d = -9

so then we get \
$y = \log(2(x-3+9))$

[ocean seal]

bertaunth

[alpine sable]

the we have 6/3 here which is why there's a two in place of the 1/3 and the 6

[alpine sable]

then we simplify this to get \
$y = \log(2(x+6))$

[ocean seal]

bertaunth

[alpine sable]

@toxic cave

[slate kayak]

Is this correct

[alpine sable]

no the work stops here

and then you simplify

oh wait

no sorry

[slate kayak]

How do I simplify😅

Oh

[alpine sable]

i just realized you multiplied by the conjugate

sorry about that

[slate kayak]

Its ok

[alpine sable]

yeah it looks right

[slate kayak]

Thnx

[buoyant kayak]

which ones do you need help with

mmmmk

what is velocity in relation to position?

how do we get to velocity from position?

right

and we want the velocity to be zero

you're given position graphs

so when is the velocity zero?

if velocity is the derivative of position

?

[alpine sable]

wait no sorry you have to redo the calculations in the numerator

[buoyant kayak]

what does the derivative represent?

what

[flint badger]

what do you mean by

"after the main one"

[buoyant kayak]

have you taken calc?

so what is a derivative?

that's derivative notation

what is a derivative

what is the definition of a derivative

[flint badger]

lmao

[buoyant kayak]

lmfao

[flint badger]

just explain to him what it is man

refresh his memory will ya

[buoyant kayak]

slope of an equation at a point...

ring a bell?

[flint badger]

you're right when you say its an equation

[buoyant kayak]

so knowing that velocity is the derivative of position... when is velocity zero?

[flint badger]

lol

[elfin talon]

You can define it as the instantaneous rate of change in a function of time(or any function for that matter), although this definition is conventional and gets the job done, 3b1b called the phrase “instantaneous rate of change” oxymoronic

[buoyant kayak]

not my question but nice job friend

[elfin talon]

Then what is your question

[buoyant kayak]

i didn't have one

[flint badger]

what is the definition of a derivative

I thought he was about to give the

difference quotient

lmao

[buoyant kayak]

in terms of slope of the position graph

[flint badger]

anyway im gonma leave now have fun

[buoyant kayak]

when is velocity zero

[elfin talon]

I was gonna say that, good on you

[elfin talon]

When the position is constant

(By definition)

[buoyant kayak]

bro

[flint badger]

LOL

[buoyant kayak]

not my question lmfao

no

your answer was not correct

[elfin talon]

What

[buoyant kayak]

no

[elfin talon]

Actually bro

[buoyant kayak]

this is an exam?

[elfin talon]

If you think about it the position is constant at all the points

[buoyant kayak]

welp

[alpine sable]

bruh

[buoyant kayak]

that ain't allowed

okay

<@&268886789983436800>

[elfin talon]

What’s your take on this

[sly mantle]

b&

[buoyant kayak]

:)

[flint badger]

damn

LOL

[alpine sable]

holy shittt

[flint badger]

I was about to lose my shit when you asked him the "definition of a derivative"

[elfin talon]

Eggdog I know somebody who has your exact name

Wierd

And he had a pfp similar to yours

[flint badger]

well yea if hes an eggdog

he'll probably have an eggdog pfp, but this isnt the place to talk about it so anyway

[elfin talon]

Is it a thing?

[flint badger]

yea its kinda a meme

[elfin talon]

Ohh damn ok

Why did he leave

/get banned

I was gonna tell him

It was gonna tell him it’s a trick question the position is constant at all the points

[flint badger]

You cant get help

On a quiz

[buoyant kayak]

he got banned for offering money to complete his exam, and his question was not a trick question

it had a very obvious answer

[elfin talon]

And it is that all the positions are constant right?

[buoyant kayak]

not in the slightest, no

[toxic cave]

The answer book says that the answer is y=log2x

[onyx flower]

can 3sinxcosx be written as 3/2sin(2x)?

or nay

[south lava]

Can someone find the points of multiplicity for the question f(x)=2x^3 - 3x^2 - 3x + 2

[alpine sable]

3sin2x/2

[alpine sable]

-1

[south lava]

thank you

[unborn sleet]

Hello guys I’ve a question about the two’s complement of numbers like -4.25

How can I represent it, around internet I can’t find anything about the fractional part

Someone says that it has to remain as the normal binary conversion other says that it has to be complemented

[onyx flower]

nvm im just dumb

[alpine sable]

sin2x +2xcos2x

[shut temple]

Chain rule my dudes

[onyx flower]

yeah i realized xd

clod hands just mistyping

[azure badger]

hello guys can you help me with 1 problem

[molten elk]

How exactly did that go from the line before the underlined line to the underlined line?

[molten elk]

also it is given that h >= -1

[alpine sable]

because ih^2 => 0

[dry echo]

Here's my problem

This is my work

Did I do this correctly? If so, what should I be plugging in besides 0?

-4 and 4?

[dry echo]

Yeah this worked, I was confused because I'd gotten an interval in my work

Nevermind then ✌️

[alpine sable]

when some says "root over 9b minus c" how do you know if they mean √(9b-c) or √9b-c

what is the difference in speech?

[buoyant kayak]

$\sqrt{9b-c}$ could be said as the square root of the quantity 9b-c

[ocean seal]

a disappointing son

[oak chasm]

For twos complement of a fixed point binary number, you take the value, complement the bits, and add one to the bits as if they represented an integer.

With a fixed point number represented as an 8-bit multiple of 1/16, we have:

4.25 = 0100.0100
-4.25 = 1011.1011 + 0000.0001 = 1011.1100

[unborn sleet]

Several people on the internet do only the integer part, but the fractional part they left it as it was, 1011.0100, that’s bugging my mind

[oak chasm]

Similarly, the twos complement of -4.25 is:

-4.25 = 1011.1100
4.25 = 0100.0011 + 0000.0001 = 0100.0100

That's not a very wise move, as it will be slow.

CPUs are very fast at flipping the bits and adding 1 to the end to do twos complement.

[unborn sleet]

I completely understood your first explaination, the difficult part is why some people leave the fractional part untouched

[oak chasm]

There, you're flipping part of the bits and then adding 1 to the integer part, which isn't at the end, which is two operations instead of one.

I assume they just guessed at how it works.

It also makes dealing with negative numbers a real headache.

You have to handle the integer part and fractional part separately.

[unborn sleet]

Yeah

[oak chasm]

You have to make sure to manually carry if the fractional part overflows.

You have to borrow if the fractional part overflows the other way when subtracting a positive or adding a negative.

[unborn sleet]

So I have to think it as two different numbers, factional and integer part

[oak chasm]

You shouldn't.

That's not how they do fixed point arithmetic.

They treat it as an integer multiple of two to some negative power.

So, the power of two goes into the denominator.

Like integer multiples of 1/2 are 0000000.1 for example as 1/2.

Or 0000001.1 as 3/2.

Then addition and subtraction, you can use the standard integer instructions.

Multiplication and division, you have to adjust a bit with a bit shift.

These are very fast if you keep the integer and fractional part as one number you deal with together rather than two parts.

[unborn sleet]

So let’s say I have 3.5, to represent -3.5 I get first 0011.1000 then flip the bits and add one to get 1100.1000

[oak chasm]

0011.1000
1100.0111
1100.1000

Yes.

[unborn sleet]

I think treating the integer and fractional as tel numbers is very complicated

[oak chasm]

Yes, it adds a lot of work to treat them as two numbers.

[unborn sleet]

Cause if I do it for -3.5 I would get 1101.1000 that would mess up

They asked me to do with that method but I can’t wrap my head around that

It becomes too complicated

But if I have to do that, how could I subtract the fractional part

[oak chasm]

Well, you do it like on paper, with one change.

That has four digits past the binary point, so it's 1/16ths.

[unborn sleet]

Sorry, what do you mean with one change?

[oak chasm]

Well, you treat it as an integer multiple of 1/16.

So, let's say you have xxxx.1000 - xxxx.0100.

You do 1000 - 0100.

You check if it borrowed.

If it did, you borrow from the integer part's result.

Just like you'd borrow on paper.

[unborn sleet]

Dang so I have to treat the integer part as an addition but the fractional part as a subtraction?

If I understood

[oak chasm]

No, you subtract both.

But separately.

Then, you get the integer part first.

Then, you get the fractional part.

If the fractional part borrowed, you subtract one from the integer part's result.

You can tell if it borrowed if you're doing a - b and b > a.

Or you can use a CPU overflow flag.

If you're closer to the metal.

[unborn sleet]

Damn I think they’re making us do that since we will use CPU overflow flags in a few weeks

[oak chasm]

But never do this in real code if you can avoid it.

[unborn sleet]

Yeah, for sure

[oak chasm]

Treat the whole thing as one integer times a negative power of two.

[unborn sleet]

That would be a waste of time and too complex

You’re a saint @oak chasm

So let’s say I have
+4.25 = 0100.0100
-4.25 = 1100.0100

I subtract them

Right?

[oak chasm]

Yes, the integer parts first.

[unborn sleet]

I have to borrow

A 1

[oak chasm]

    0100
  - 1100
11110000

And then you subtract the fractional parts.

[alpine sable]

may i ask which topic y'all discussing

[unborn sleet]

So I repeat the ‘borrow’ beat?

Two’s complement @alpine sable

[oak chasm]

  0100
- 0100
  0000

[clever mountain]

binary?

[oak chasm]

So, you get 0000.0000.

[unborn sleet]

Yeah, @clever mountain

[clever mountain]

ah, cool

[alpine sable]

Oh cool

[oak chasm]

Yes, a method of doing subtraction with a strange representation of fixed point numbers.

[unborn sleet]

Damn, you’re the GOAT @oak chasm

[alpine sable]

This is sort of a cop-out answer, but I had to try and find your textbook to learn the rules of mapping notation. Basically, you follow those rules to get the solution

[unborn sleet]

One last question and I’ll try not bother you again

0
-1

We have to borrow

But where do we borrow it?

It may sound as a super stupid question

[oak chasm]

What are the full 8 or whatever bits?

[toxic cave]

you are my saviour tysm

[oak chasm]

This?``` 0000.0000

• 0000.1000

[unborn sleet]

Nono the previous one

Sorry no

[oak chasm]

Oh, for the integer part?

[unborn sleet]

This one

Yes

[oak chasm]

OK, those are the fractional parts.

So, let's do a problem like that.

[unborn sleet]

For the integer part

Ok, give me one and I’ll try to solve it

[oak chasm]

    0100.0100
  - 1100.1000
11110000.xxxx

That's what we get for the integer part.

[unborn sleet]

Here is my question, how do I borrow the one for the MSB

0-1

[oak chasm]

Then we get:```
0100

• 1000
  1100```with a borrow.

So, you borrow 1 from the integer part.

You get 1111 for the integer part and then you add that borrowed 1 in to the top of the fractional part to get 0100.

So, you get 1111.0100

Which is -1.25.

So, let's check that.

8.25 - 8.5 = -0.25

Hmm.

[clever mountain]

is this channel open now?

[alpine sable]

okay

so

30/100 x 60/1 = 1800/100 = 180 = ?

need help

[oak chasm]

@alpine sable Sorry, this channel is busy.

[alpine sable]

oh sorry

ill move on.

[oak chasm]

8.25 - -8.5 = 16.75

Forgot that we were subtracting a negative.

Looks like you have to check the sign of what you're subtracting.

If it's negative, you add the fractional parts. If it's positive, you subtract the fractional parts.

So, we should have added:```
0100

• 1000
  1100

So, we get 0000.1100 = 0.75.

And 8.25 - -8.5 = 16.75, which has an overflow, so you subtract the 16.

8.25 - -8.5 - 16 = 0.75

[alpine sable]

wanted to add that line 3 should say "Shift 3 units to the right"

[oak chasm]

@unborn sleet Does that make sense?

You have to look at the integer part's sign to tell whether to add or subtract the fractional part.

[unborn sleet]

Give me two numbers and I’ll try

[oak chasm]

OK, 13.75 - -4.5.

Should get 18.25 - 16 = 2.25

[unborn sleet]

So I’ll have to add the fractional part

If I understood

For the integer part I add

If I get a negative I subtract the fractional part

If I get a positive I add the fractional part

[oak chasm]

You have (13.75) - (-4.5).

So, you need to subtract the integer parts.

Then, you need to use the sign of the original second integer part to tell you whether to add or subtract the second fractional part.

A less complicated way might be to convert the numbers to the reasonable way to do it and back.

[unborn sleet]

Ok, 13.75 = 01101.11000

-4.5= 11100.10000

I subtract
01101
11100

I do not know how to subtract 1 from 0

[oak chasm]

Borrow.

[unborn sleet]

Where do I borrow it, there isn’t the bit sign equal to 0 repeated?

[oak chasm]

From the next more significant bit.

[unborn sleet]

Would it not be zero?

[oak chasm]

  01101
- 11100
   0001

[unborn sleet]

Yeah I’m locked here

[oak chasm]

You treat it as if the next digit on the top number is 1.

 101101
- 11100
   0001

[unborn sleet]

I did not know that

[oak chasm]

2 - 1 is 1, so:```
101101

• 11100
  10001

Well, you only have five bits to work with.

And then the bits beyond that do not matter. They can be anything.

So, you make them something that will work.

[unborn sleet]

Perfect

So I get 11110001

[oak chasm]

So, now you check the negative/nonnegative bit of the second integer part.

11100.

It's 1, so it's negative instead of nonnegative.

And that means you add instead of subtract the fractional parts.

[alpine sable]

this is not a troll question

[oak chasm]

@alpine sable Sorry, this channel is busy.

[alpine sable]

alr

[unborn sleet]

You are great

We said that if we had to borrow for the fractional part we would do it front the integer part?

[oak chasm]

Yes.

You subtract 1 from the integer part and use it in the fractional part.

Similarly, if the fractional part overflows the other way, you add 1 to the integer part.

[unborn sleet]

I would do it from the result we got from the subtraction of the integers?

[oak chasm]

Yes.

[unborn sleet]

Thank you so much

Do you have a pathreon or something?

[oak chasm]

No, not really.

[raven rover]

People aren't really supposed to ask for money/pay for this kinda help

But that's pretty cool

If money were to get involved I imagine it should be in DMs or something, not here.

[unborn sleet]

Dude this man is great

[oak chasm]

I can't really accept payment.

[unborn sleet]

It’s just a little appreciation for the amazing job

He gave me so much time and cleared all my doumbts

[raven rover]

Yeah - people here are really good at that

I don't understand it

[unborn sleet]

I’ll write down what he taught me for sure ahah

[raven rover]

You can probably ask him/her what you can do to pay them back, although I imagine it'll just be along the lines of

Be nice.
Help others when you can to return the favor.

etc.

Or, it may be nothing at all

[unborn sleet]

I’ll return the favour for sure when I can

[plush stump]

x = 4 for #7 right?

[drifting wadi]

you can arcsin(3/5) to find x

but make sure u use the angle in the second quadrant

so type π-arcsin(3/5) to find x

in calc

[oak chasm]

You can use the Pythagorean identity to get cos(x), remembering you're in the second quadrant for the sign of it.

Then, you have sin(x) and cos(x), and can get tan(x).

[plush stump]

cos(x) = 4/5

[oak chasm]

Yes, and tangent?

[plush stump]

1sec

12/25

[oak chasm]

Nope, tan(x) = sin(x)/cos(x).

[plush stump]

lemme reduce

that's what I did

3/5 / 4/5 right

[ocean seal]

Chai T. Rex

[oak chasm]

Dividing fractions is multiplying by the reciprocal of the bottom.

[plush stump]

oh yes, forgot to flip the bottom

15/20 then

[oak chasm]

Which reduces to what?

[plush stump]

3/4

[oak chasm]

OK, one small mistake. You're in the second quadrant, so cosine and tangent are what signs?

[plush stump]

cosine and tangent are negative

[oak chasm]

OK, so cos(x) = -4/5 and tan(x) = -3/4

And then you're done.

[plush stump]

but is x in the set tho

[oak chasm]

x is the angle. You only need it to tell you what quadrant it's in.

[plush stump]

OH

[oak chasm]

The angle is between π/2 and π, which is the second quadrant.

[plush stump]

nice nice, this one example online that said "verified" used the angle x and x/r as the same thing?

[oak chasm]

I'm not sure what they did.

[plush stump]

yeah well, they solved it oddly, and it was probably wrong

Thanks a lot! let me just solve 8 and get back to you on that

[oak chasm]

You're welcome. OK.

[unborn sleet]

If I borrow I give it to the MSB?

Of the fractional

Or do I have to do multiple borrows

[oak chasm]

Yes, you take from the least significant bit of the integer part and put that as an extra 1 digit in front of the fractional part.

[unborn sleet]

It’s like I add one bit

Great

I thought I had to do multiple borrows and subtract each time one, but it seemed strange since I could not do the same for the overflow

Since I could add only one bit

The overflow verifies only if I have 1+1 for the MSB of the fractional?

Or 1+1+1?

[oak chasm]

I'm not sure what you mean.

You'll only have to borrow zero or one times from the integer part.

[plush stump]

cos(x) = 1/5, sin(x) = 2/5

[oak chasm]

Almost.

cos²(x) = 1/5.

So, cos(x) = sqrt(1)/sqrt(5).

[plush stump]

ah yes you're right

[oak chasm]

And then you can use the Pythagorean identity again to get sin(x).

Then you give them signs based on which quadrant you're in.

The interval x is in is the first and second quadrants and the tangent is positive, so which quadrant are you in?

[unborn sleet]

Thank you

[oak chasm]

No problem.

[plush stump]

[0, pi/2] is the first quadrant right? so All are positive

[oak chasm]

Yes.

[plush stump]

so full answers are tan(x) = 2, cos(x) = 1/sqrt(5), sin(x) = 2/sqrt(5)

[oak chasm]

Good, now does your teacher want square roots on top of fractions only or is that OK with them?

[plush stump]

honestly not sure.

[oak chasm]

Oh, then if you hadn't heard that they wanted that, you should be fine.

[plush stump]

Thanks for the help once again!

[oak chasm]

You're welcome.

[tight locust]

if you select two random points in the unit square

and make a line between them

and repeat that process an arbitrary number of times

what will the mean of all those lengths be

^ a question posed to me by my math teacher

i'm not sure how to go about it

should i code it?

[charred flint]

is it a line on the sphere or through it

[oak chasm]

You could, but that would only give you an approximate answer, not the reason why it's true.

[charred flint]

one question is easier than the other

[tight locust]

any point within the square or on its edge is valid

[charred flint]

oops I misread that as sphere aaa

what class are you in?

[tight locust]

there's no guarantee that number is even algebraic though

[oak chasm]

Right, so you'd lose that as well.

Unless it happened to be an easily noticeable value.

[tight locust]

so idk how to go about it. i think an approximate answer would be good enough right?

honestly if i could just figure out how to code it that would probably be good enough

it's just for fun anyways

[oak chasm]

Well, you could use the Pythagorean theorem.

It has (x₁ - x₂)² for the x component of the distance. What would the expected value of that be?

[charred flint]

oh nvm I remember this problem, go and code it instead lmao

[clever mountain]

so it's a cube? and the lines are in it?

[oak chasm]

No, it's a closed square that contains the lines.

[clever mountain]

oh so it's just a 2d square?

[oak chasm]

Any point in the closed square to any point in the closed square.

Right.

And it's a unit square.

So, what's the expected value of the length of a random line in the square?

[clever mountain]

how many lines inside of it? as many until the number stabilizes?

[oak chasm]

Well, it will stabilize at the expected value, so you really only need one line.

[clever mountain]

right but then if you add another the value will change

[tight locust]

sqrt(1/2) is my guess

[oak chasm]

Well, let's get an expected value for the absolute difference in x coordinates.

Then the absolute difference of the y coordinates will be the same.

So, you'll have sqrt(2 d²) or whatever.

[charred flint]

I don't think doing x and y separately works x_x

[oak chasm]

They're independent, though.

You may be right.

[charred flint]

yeah the square root of expected values makes it break

[tight locust]

So i was thinking

Maybe just use a random value generator

In the interval [0,1]

And then do that again

And then Pythagorean theorem it

For like 1000 iterations

[clever mountain]

import random
import time

import pygame
import math

run = True

white = (255, 255, 255)
black = (0, 0, 0)

width = 1000
height = 900


def length(v_1, v_2, distance_to_surface):
    value = 0
    for x in range(len(v_1)):
        value += math.pow(v_2[x] - v_1[x], 2)
    return math.sqrt(value) - distance_to_surface


def change_pos(pos, keys_pressed_var):
    speed = 3
    speed_count = 0
    if keys_pressed_var[pygame.K_w]:
        speed_count += 1
    if keys_pressed_var[pygame.K_a]:
        speed_count += 1
    if keys_pressed_var[pygame.K_s]:
        speed_count += 1
    if keys_pressed_var[pygame.K_d]:
        speed_count += 1

    if speed_count == 0:
        pass
    elif speed_count > 1:
        speed = speed / 2

    if keys_pressed_var[pygame.K_w]:
        pos = (pos[0], pos[1] - speed)
    if keys_pressed_var[pygame.K_a]:
        pos = (pos[0] - speed, pos[1])
    if keys_pressed_var[pygame.K_s]:
        pos = (pos[0], pos[1] + speed)
    if keys_pressed_var[pygame.K_d]:
        pos = (pos[0] + speed, pos[1])
    return pos


window = pygame.display.set_mode((width, height))
pygame.display.set_caption("Boids")

fps = 120
clock = pygame.time.Clock()

while run:
    for this_event in pygame.event.get():
        if this_event.type == pygame.QUIT:
            run = False

    clock.tick(fps)

    window.fill(white)

    pygame.draw.rect(window, (0, 0, 0), (100, 100, 700, 700))

    average = 0

    for i in range(10000):
        coord_start = (random.randint(100, 800), random.randint(100, 800))
        coord_end = (random.randint(100, 800), random.randint(100, 800))
        point = length(coord_start, coord_end, 0)
        average += point
        pygame.draw.line(window, (0, 255, 0), coord_start, coord_end)
    average = average / 10000
    print(average)

    pygame.display.update()
    time.sleep(1000)
pygame.quit()

[unborn sleet]

@oak chasm I found an error in the process
+4.25 = 0100.0100
-4.25 = 1100.0100

Subtracting the integer parto

0100
1100

subtracting the fractional part

0100
0100

0000

The result is 1000.0000 instead of 0000.0000

[clever mountain]

this was the average length

365.0328661311797

in pixels in a square that's 800 pixels wide

[tight locust]

,calc 365.032866/800

[ocean seal]

Result:

0.4562910825

[tight locust]

How many iterations?

[clever mountain]

1 million iterations

365.63005509551624

which completely filled in the black square

[tight locust]

,calc sqrt(1/2)

[ocean seal]

Result:

0.70710678118655

[tight locust]

Wow lol

Where does that number come from

[clever mountain]

lol

[tight locust]

,w 0.4562910825

[ocean seal]

Results provided by WolframAlpha

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

Requested by EndTimes#8053

[oak chasm]

4.25 - -4.25 = 8.5.

And since you're subtracting a negative, you add the fractional parts to get 1000. So, 8.5.

[unborn sleet]

We did not say if the second integer had a 1 we would subtract the fractional parts?

since id like to get zero i would have to do 4.25 + (-4.25) ?

[oak chasm]

The second integer was 1100.

So, for the fractional parts, you add them.

[unborn sleet]

I messed up

sorry

i did not understand the part 4 --

so we add if the number is negative and subtract if it is positive

+4.25 = 0100.0100
-4.25 = 1100.0100
tto get zero

Add the integer parts

0100
1100

but we would not have to subtract the fractional parts

?

also if the second integer has 1

[sick torrent]

Why is this wrong?

[dry echo]

I think you made an arithmetic mistake

[clever mountain]

this is what it looked like when i ran it

[clever mountain]

@tight locust

[dry echo]

How did you end up with 10 on the numerator? @sick torrent

4 * 5 = 20 not 10

[tight locust]

Mkv?

[clever mountain]

just what obs made it. its a kind of movie format look it up if you want.

for the record the length would have been

0.456625

of the length of the square

[unborn sleet]

So for a - (b) I subtract the integer parts, if the b has 1 as MSB I add the fractional parts if it has 0 I subtract them, for a + (b) I add the integer parts if b has 1 as MSB I subtract the fractional parts if it has 0 I add them @oak chasm

[late parcel]

Couldn’t x=-1 or x=4 be it?

Because an absolute can also be considered a local

[daring schooner]

Help?

[buoyant kayak]

you’re looking at the graph of f’

[late parcel]

Yes

[buoyant kayak]

not f

[late parcel]

I’m confused

So then how do you tell

[buoyant kayak]

you’re asked about the max of the function f given the graph of f’

when do you meet a maximum, in terms of the derivative?

[late parcel]

At the top

[buoyant kayak]

?

[late parcel]

Idk

[buoyant kayak]

what is the value of the derivative when you’re at a maximum or minimum

[late parcel]

The greatest

[buoyant kayak]

i’m talking about the derivative

you’re talking about the function

[late parcel]

I don’t know

[buoyant kayak]

the function is at a maximum, sure. but it’s derivative?

[late parcel]

I don’t know what the difference is

[buoyant kayak]

between the function and the dericative?

[late parcel]

The first derivatives gives you the min and max

[buoyant kayak]

what do you do to find the min and max?

take the derivative and…?

do what?

[late parcel]

Do the first derivative test

Find critical points

Check if it’s increasing or decreasing

[buoyant kayak]

what do you set the derivative equal to?

[late parcel]

Set it equal to zero

[buoyant kayak]

right

so you’re finding where the derivative in zero

that’s where your mins and maxes are

so look back at your graph of f’

when is there a min or max?

[late parcel]

I’m so lost it’s not even funny

I still have absolutely no idea if it’s not -1 or 4

@buoyant kayak can you tell me what it is and I’ll see if it makes sense

[tight locust]

Damn thats pretty fucking cool

What ide/language

[buoyant kayak]

you just told me you set the derivative equal to zero to find the mins and maxes

[late parcel]

Yes

[buoyant kayak]

so when you solve for that, it tells you the x values that the derivative is equal to zero

you’re given a graph of the derivative of f.

when does the function f have a min or a max? when this graph is what?

[strong vapor]

Is this correct? It’s a warm up acivity

[buoyant kayak]

channel taken

[late parcel]

@strong vapor not open

[coral pagoda]

If there exists an x so that f'(x)=0

[clever mountain]

python, i posted the code above i can dm it too you if you want

[tight locust]

What ide

[clever mountain]

pycharm

[late parcel]

Is it 1

[strong vapor]

How about this one?

[late parcel]

Is it 1

Or wait no

Idk honestly

[tight locust]

Looks good

[buoyant kayak]

yes, it is.

[late parcel]

How

I just guessed

[buoyant kayak]

what is true at x=1

on your graph f’

[late parcel]

It has a Y value of 0

[buoyant kayak]

so it’s equal to zero

[coral pagoda]

Oh. You're helping someone, not the other way around 🤦‍♂️

[late parcel]

What is equal to 0

Bro

[buoyant kayak]

which makes it a critical point, correct? when the derivative is equal to zero?

[late parcel]

How

No

[strong vapor]

This warm up activity is annoying

[sudden crow]

please i need help (lesson continuity)

[late parcel]

@strong vapor @sudden crow not open

Please stop

@buoyant kayak x is not 0 at 1

Please walk me through it again

I mean how can you find a critical point when your not even given the function

Or equation of the derivative

@buoyant kayak see number 12?

[alpine sable]

please help

[late parcel]

I did the first derivative test

And I graphed the first derivative ok the right their

That graph tells me that f has a local min at x=3

Right @buoyant kayak

[buoyant kayak]

that’s not what the graph of f’ looks like

[alpine sable]

im gonna get beaten by my dad

[buoyant kayak]

your derivative is gonna be a quadratic

[alpine sable]

cause of a literal iready

[late parcel]

@alpine sable please go to another channel

[alpine sable]

can someone just

okay.

[late parcel]

@buoyant kayak yes I know that

But still I graphed the derivative

The first derivative gives you the min and max

Well look at this question

It gives you the derivative of f

So why is it not -1 or 4

[buoyant kayak]

because you’re not trying to find the mins and maxes of the derivative

you’re finding the mins and maxes of the function f

not f’

[late parcel]

Ok so please walk me through it again

I have the graph

[buoyant kayak]

of f’

[late parcel]

I have no equation to set equal to zero

[buoyant kayak]

you don’t need one

how do you find the mins and maxes of f?

[late parcel]

Set the derivative equal to zero

[buoyant kayak]

so finding when the derivative is zero

[late parcel]

I only have a graph

[late parcel]

What do you mean by this

[buoyant kayak]

this is what i mean

[late parcel]

Ok

How do you do that on a graph

[buoyant kayak]

when you set the derivative equal to zero, you solve for x, you’re finding the x values where the derivative is equal to zero

[late parcel]

Yes

[buoyant kayak]

you have the graph of the derivative of f

[late parcel]

Yes

[buoyant kayak]

so… when is the derivative equal to zero

[late parcel]

How do you tell when it equals zero on a graph

[buoyant kayak]

?

[late parcel]

No stopping points

Only sharp turns

[buoyant kayak]

you’re not finding when the slope of your graph is zero

you’re finding where your graph is zero

the graph IS the derivative

[late parcel]

The derivative does not equal zero in this graph

[buoyant kayak]

the graph is the derivative

[late parcel]

The Y value happens to be 1 at x=0

[buoyant kayak]

so the slope of f at x=0 is 1

[late parcel]

But the question is what is the x

How

How do you see that

[buoyant kayak]

because of this

[late parcel]

Is that because of the Y value

[buoyant kayak]

yes

[late parcel]

Is the Y value relevant

Why

Why would you look at the Y value

[buoyant kayak]

…because it’s a graph of the derivative

[late parcel]

The question asks for an X value

[buoyant kayak]

the y value is the slope at a point x

[late parcel]

No

How is the Y value a slope

The Y value is the value the graph is al vertically

[buoyant kayak]

how do you find the slope of a tangent line?

[late parcel]

Umm I’m blanking

[buoyant kayak]

if i gave you the function f(x)=x^2, what is the slope of the tangent line at x=2?

[late parcel]

4

[buoyant kayak]

and you did that how?

[late parcel]

2^2

=4

Plug and chug

I remember now

[buoyant kayak]

you took the derivative and plugged in a point x

and the value of the derivative at that point is f(x)

which is the slope of the line

at that point

[late parcel]

Yes

How is this relevant

[buoyant kayak]

so… what is f’(1) in your shown graph

[late parcel]

0

[buoyant kayak]

so the slope is zero at x=1

and when the slope is zero… you’re at a critical point

[late parcel]

Is that it

[buoyant kayak]

that’s f(0)

[late parcel]

Or that

Which one is why

[buoyant kayak]

the one where f’(x)=0

[late parcel]

The second?

[buoyant kayak]

yes

where the derivative is equal to zero

[late parcel]

Ok thx

[buoyant kayak]

and you’re going from a positive slope to a negative slope

therefore it’s a maximum

[late parcel]

Thx

[near falcon]

how do i solve the area of a sector

[late parcel]

@buoyant kayak wait

What

That’s double negative slope

Oh wait never mind