help-10

[rich frigate]

By question

[topaz rapids]

Is K 2.4?

[rich frigate]

No

[topaz rapids]

What do u mean by constant?

[rich frigate]

For 3.2 metere length cost is 38

[topaz rapids]

Yes

[rich frigate]

If we put L=3.2 and C=38

We get k=38/3.2

[topaz rapids]

Ok

[rich frigate]

So k is constant it never change

[topaz rapids]

Yes

[rich frigate]

We need to find out cost of 2.4 meter length

[topaz rapids]

Yes

[rich frigate]

Now L=2.4 and k=38/3.2
Can you find C cost

[topaz rapids]

Do I just divide 38 by 3.2 then do the same for L

[rich frigate]

C=kL

So

C=(38/3.2) x 2.4

[topaz rapids]

Or is it k=Cx2.4

[topaz rapids]

Ohk

[rich frigate]

No it is C=kL

Where k constant

[topaz rapids]

Ok let me find the code

[rich frigate]

Ya

[topaz rapids]

Cost

Is cost 28.5

[rich frigate]

Ya well done

https://tenor.com/view/traduun-gif-27169151

[topaz rapids]

Do u have another question I can solve by myself

Or no?

[rich frigate]

Like proportional question

[topaz rapids]

Yes

[rich frigate]

Let me think

Let student and no. Of classrooms are proportional there is 4 classroom for 48 students how many classrooms for 192 students

[topaz rapids]

Ok

Give me 2 mins

16?

[rich frigate]

Very good

https://tenor.com/view/baby-scream-yeah-hockey-kid-gif-24698394

[topaz rapids]

I barely had to use the method it was kind of common sense

But thank you for the help I’m studying for checkpoint

[rich frigate]

Ya that's also right

Ok good luck

Bye

[topaz rapids]

Bye

@rich frigate I found another question I just want to know if I got it correct

[rich frigate]

Go ahead

[topaz rapids]

I got 5.555

[rich frigate]

No

You change liter to millilitre

[topaz rapids]

What was it

Ohk

That’s what I did wrong

[rich frigate]

Ya try again

[topaz rapids]

Ok

Is it 180

[rich frigate]

Yes

[topaz rapids]

Is it the same thing as 18

[rich frigate]

No

[topaz rapids]

Y

[rich frigate]

How it same

180 and 18 is different numbers

[topaz rapids]

Because while diving I could have cancelled 0

Dividing

[rich frigate]

Are you joking

I am not understanding

[topaz rapids]

I’m actually on the perc 90 I’m bugging nvm

Lol

[rich frigate]

What is perc

Percentage

[topaz rapids]

No it’s a drug

But I’m not on it actually

I have a question on indirect proportion now

[rich frigate]

Oh I get it

Let's do it

[rich frigate]

How you get proportion

[topaz rapids]

What do u mean?

[rich frigate]

We need proportion of women in parliament

[topaz rapids]

Yes

[rich frigate]

You know how we get proportion

Or about it something

[topaz rapids]

Do I just make it a ratio?

Like 89:39 for New Zealand and 224:126 for Spain

[rich frigate]

Ya something like that

[topaz rapids]

Ok

[rich frigate]

But we need proportion then we can compare both

[topaz rapids]

Ok

[rich frigate]

So we need to find out if there was 100 people in parliament how many women in it

In newzealand and in Spain

[topaz rapids]

Ohk I get

[rich frigate]

Which gives us percentage of womens

Which we can compare

[topaz rapids]

Ok

[rich frigate]

Can you do it

[topaz rapids]

I think so

[rich frigate]

Try it

[topaz rapids]

Let me return

Try

I am confusing myself I need help

Wait hold up

[rich frigate]

Ok

You know calculating percentage??

[topaz rapids]

Oh that’s all u have to do?

[rich frigate]

Ya

[topaz rapids]

Oh ok give me 1min

For New Zealand it’s is 32%

[rich frigate]

I will became a very confusing teacher 🫣😔

[topaz rapids]

Y

[rich frigate]

Ya for spain

[topaz rapids]

36%

U want to become a teacher?

[rich frigate]

Ya

[topaz rapids]

It’s correct right?

[rich frigate]

Ya correct

You got your ans8

Answer

[topaz rapids]

Yh

U will be a good teacher

[rich frigate]

Any other questions I have to go then

[topaz rapids]

No

[rich frigate]

Thank you ,you will make me cry

https://tenor.com/view/peach-goma-goma-peach-peach-and-goma-peach-goma-whatsapp-status-peach-goma-fight-gif-1555954360060729022

[topaz rapids]

Good day or night

Later

[rich frigate]

Night

Here

[topaz rapids]

Ohk good night

[rich frigate]

11 16

Ok good bye

[topaz rapids]

I added u so if I’m ever need help in the future

[rich frigate]

Oh np

[obtuse pebble]

@topaz rapids Has your question been resolved?

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[rigid sky]

how to integrate [x^2] from 0 to 2.4

[rigid sky]

can someone tell with steps

[wicked crown]

you integrate x^2 and then if f(x) = x^2 and F(x) is the integral of f then you do F(2.4) - F(0)

[rigid sky]

and how we split the limits

[wicked crown]

does that help you ?

[opal shell]

do you know how to integrate x^2?

[rigid sky]

yes

[opal shell]

just as an indefinite integral

tell me what it is

[rigid sky]

x^3/3

[opal shell]

correct

now we have F(x) = x^3/3

[opal shell]

refer to this now

[rigid sky]

yea but that is greatest integer function right

[opal shell]

?

what do you mean by this

[rigid sky]

this is in []

greatest integer function

[trail quartz]

Hey

[opal shell]

ohhhhhhhhhhhh

[peak kindle]

HELP PLS

[opal shell]

you mean ceiling function

[peak kindle]

draw the parallelogram ABCD in the figure; O is the intersection point of its diagonals. The point K is outside the plane of the parallelogram. KA=KC and KB=KD. Prove that KO is perpendicular to (ABCD).

[rigid sky]

.occupied

[wicked crown]

!occupied

[obtuse pebble]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[opal shell]

ok that's more complicated

[rigid sky]

no its []

[trail quartz]

For integrating the gif split the limits where it becomes an integer

[rigid sky]

greatest integer not celing

[robust bloom]

ceiling or floor?

[opal shell]

ceiling is the same thing i believe

[rigid sky]

greatest integer function

[wicked crown]

by greatest integer you mean [2.4] = 3 right ?

because that is exactly what ceiling is doing

[rigid sky]

step function

no

[2.4] bcomes 2

[wicked crown]

what is it then

[rigid sky]

[-1.9] becomes -2

[wicked crown]

so floor ?

ok so ig its floor

[trail quartz]

Ik ill help with that wait

[rigid sky]

oke

[opal shell]

do you know the graph of the floor function

you can do this using riemann sums i think?

[rigid sky]

whats riemann sums

[opal shell]

you know how integrals calculate the area under a curve, how do you suppose they do this?

[rigid sky]

i nknwo that

i didnt know it had a name

[trail quartz]

First split the limits as 0 to 1 + integral of 0 to sqrroot2 + integral of sqrrot2 to srqroot3 + integral of sqrroot3 to 2+ integral of sqrroot5 + integral value of sqrroot5 to 2.4

root values take a major role here as the function is a x²

[rigid sky]

yes and inside the integrals

is it just

1.dx

or something else

i get confused there

[trail quartz]

yes the box is still here so we will find the value of it

remember a trick to find the value take a number between the limits and get its ans but ill say the answer is always the lower limit

[opal shell]

would my method work just for my own sake

using riemann sums

[trail quartz]

so the first splitted integral which is 0 to 1 would become 0

[rigid sky]

yes

and then 1,2,3,4,5

[trail quartz]

it will include some values and would not be right bcs the gif function removes the point values

[trail quartz]

yes , good there is your answer

[rigid sky]

okay thanks

🙏

.clear

[opal shell]

[rigid sky]

its ok

.close

[obtuse pebble]

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[hardy kindle]

Students can sign up for English, Portuguese and Chinese.

The entire course has 173 people. 67 people signed up for English, 53 people for Portuguese, and 71 people wanted to learn Chinese. 30 people signed up for both English + Portugese, 37 people chose both English + Chinese. 27 people chose both Portuguese + Chinese.
Moreover, half of people who signed up for two languages take all three!

How many people from this field have not signed up to learn any foreign language?

[hardy kindle]

Im getting the answer as 29, however the checker says its wrong

Not quite sure what im doing wrong

|E∪P∪C| = |E| + |P| + |C| - |E∩P| - |E∩C| - |P∩C| + |E∩P∩C|

and youll just subtract that from 173

right

all the values are given except for |E∩P∩C|

Moreover, half of people who signed up for two languages take all three!

so this would mean that (30+37+27)/2 is |E∩P∩C|

what am i doing wrong lol

[rich frigate]

No you are right

Ven digram makes it very easy

Have you tried it

[hardy kindle]

I originally tried doing it with venn diagram then did it this way to confirm my result

[rich frigate]

So both your answers are 29

[hardy kindle]

yes

[obtuse pebble]

@hardy kindle Has your question been resolved?

[obtuse pebble]

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[boreal patio]

Hello i need help with finding the global min and max of a multivariable function on some Area, like how do i do that?

[boreal patio]

I have
f(x,y) = x^2 - 3y^2
and i need to find global min/max on
A = {(x,y) | (x^2+y^2)^2 <= 4(x^2-y^2)}

[dark stirrup]

Check for critical points in your area, and then check for critical points on the boundary

[boreal patio]

How to find critical points in the area?

I have
(x^2+y^2)^2 < 4(x^2-y^2)

and i did
f_x = 2x
f_y = -6y

To find critical points i did
2x = 0
-6y = 0
But now i get one point T_0 (0,0) which is not in intA

@dark stirrup

[dark stirrup]

It's right on the boundary, which is still fine for a critical point to be on

I do no believe a critical point needs to be in the interior

[boreal patio]

Ok obviously, so besides (0,0) there are no other critical points in the intA?

For boundaries i did with lagrange multiplier:

L = x^2 - 3y^2 + lambda((x^2+y^2)^2 - 4(x^2-y^2))
and then calculated
L_x = ... = 0
L_y = ... = 0
L _ lambda = (x^2+y^2)^2 - 4(x^2-y^2) = 0

and i got lambda = 1/2
so then x = +- sqrt(5/8) and y = +- sqrt(3/8)

but like i feel like thats not the full answer

Or thats wrong even

idk

But for example point (2,0) feels like a maximum but i didnt get it from the system of equations

<@&286206848099549185>

[obtuse pebble]

@boreal patio Has your question been resolved?

[boreal patio]

<@&286206848099549185>

I can send you my calculations if that helps

[obtuse pebble]

@boreal patio Has your question been resolved?

[boreal patio]

<@&286206848099549185>

[obtuse pebble]

@boreal patio Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

Please don't occupy multiple help channels.

[thorn carbon]

sorry

[gilded needle]

duplicate of #help-14

.close

[obtuse pebble]

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[rich fable]

yo

[rich fable]

so

can someone explain why sin(pi - x) = sinx

[alpine bison]

do you know summation formulas ?

[timid silo]

look at the unit circle and trace it around maybe

[rich fable]

i get it when x is in the 1st or 2nd quad

but how in the 3rd and 4th quad as well?

.close

[obtuse pebble]

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[light coral]

So ik about imaginary numbers but I'm still struggling with multipling them. Not sure if Im even supposed to tho

[unique bear]

what is $\sqrt {-6}$

[warm shale]

znsn

[unique bear]

after considering that you do the same for $\sqrt {-384}$

[warm shale]

znsn

[light coral]

ok so sqrt of -6 gonna come out as i sqrt 6 right?

[unique bear]

yup

[light coral]

so r we multiplying now or gonna simplify them further?

[unique bear]

we do the same for $\sqrt {-384}$

[warm shale]

znsn

[light coral]

yeah negative would come out as i for both leaving us with positive radicals

[unique bear]

yeah so we now have $-\sqrt 6 \cdot \sqrt {384}$

[warm shale]

znsn

[light coral]

oh wait so we got - from i^2 right?

[unique bear]

yeah

that's right

[light coral]

ok now just multiply?

[unique bear]

exactly

we got rid of the annoying negatives in the radicals, so we can freely multiply using the laws you have

[light coral]

so is it - sqrt 2304?

[unique bear]

yeah

but we could do something a bit easier

$-\sqrt 6 \cdot \sqrt {384}=-\sqrt {2\cdot 3} \cdot \sqrt {2^7 \cdot 3}$

[warm shale]

znsn

[unique bear]

then we have $-\sqrt {2^8\cdot 3^2}$

[warm shale]

znsn

[unique bear]

so instead of multiplying immediately, we could do prime factorization

to make the multiplication process and the square rooting process easier

[light coral]

ooooh that makes sense

[unique bear]

you could certainly prime factorize 2304, it's just easier to factorize it earlier

do you know how to take the square root from there?

[light coral]

the pairs r coming out right?

[unique bear]

yeah

[light coral]

hm so - 2x2x2x2x3

[unique bear]

👍

[light coral]

-48?

[unique bear]

yeah

nice

[light coral]

so about a+bi

[unique bear]

what do you think they should be?

[light coral]

lemme look at my notes real quick

[unique bear]

alr

[light coral]

nope im lost

[unique bear]

that's alright

so a would be the real part

and bi would be the imaginary part

first of all, do you see any i in -48?

[light coral]

no

[unique bear]

that means the imaginary part is 0, because $-48=-48+0i$

[warm shale]

znsn

[light coral]

oh wow

[unique bear]

yeah, if you're missing the i, the imaginary part is always 0

now what's the part of -48 that doesnt have an i?

[light coral]

sorry i dont understand ur question

[unique bear]

the real part of -48 would be the part without an i

[light coral]

oh ok

alright i think i got it

thx

[unique bear]

np

if you want to confirm it, ||a=-48 and b=0||

[light coral]

did and got it right

could easily search the answer but need to know how to solve it

u explained well a lot

cya

[unique bear]

cya

thanks

[unique bear]

you should do .close

[light coral]

.close

[obtuse pebble]

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[lost widget]

Isnt this limit infinity?

From MVT?

[wild swallow]

,w lim x->inf of ((2x^2)^2/2 - (x^2)^2/2)/x^2

[warm shale]

Results provided by WolframAlpha

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

Requested by tearfox

[lost widget]

Yeah

[wild swallow]

okay seems legit

[lost widget]

But in 0

The limit

I think it is 2

[surreal forge]

yes

[lost widget]

Yes I think they meant the limit to be in 0 not inf

Thx

.close

[obtuse pebble]

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[obtuse pebble]

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[obtuse pebble]

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[worn jetty]

im kind of confused with the difference between negative slope vs decreasing slope for rate of change

[worn jetty]

<@&286206848099549185>

[gilded needle]

decreasing slope, meaning the slope gets smaller as you move to the right?

[worn jetty]

what if you dont do any calculations

im more of a visual person so id imagine how the slope would be

[stuck depot]

I can draw something in paint in a minute but a negative slope just means that the slope is negative. something like m = -5. a decreasing slope just means that the slope is getting smaller or decreasing over a distance. for example the slope is going from m=5 at x=0 to m=3 at x = 1. just because its decreasing does not mean its negative (refer to example)

[worn jetty]

oh okay

thanks

i also found a representation

is this accurate

i think i kinda get a sense of it now

[stuck depot]

yeah it is

[worn jetty]

thanks

ok so

when youre listing the intervals where a graph is negative or positive, increasing or decreasing, do you do [] if the function exists at the part where it is what its being asked for

like for this function if they ask for intervals where ROC is negative do i write (-inf, -3) U (3,0]? or (3,0)?

ok nvm the answer didnt include it

but why

[obtuse pebble]

@worn jetty Has your question been resolved?

[stuck depot]

no, because (-inf, -3) is increasing/a positive ROC

slope goes from practically 0 to inf

[worn jetty]

wait so ik u dont include it for that

but

[worn jetty]

this question

[stuck depot]

wait hold on I messed up

[worn jetty]

no worries !

[stuck depot]

okay so I think it would be (-3,3)

starts super positive at -3 then approaches a slope of 0 at x=0 where it continues to decrease all the way to x=3

[worn jetty]

wait

i meant intervals where the ROC is + lol

so shouldnt it be -inf,-3 and -3,0?

i was just wondering whether if it was inclusive brackets or not

for 0

[stuck depot]

positive would be (-inf,-3) U (3,inf)

but im not exactly sure to be honest

for the 0

i think it would not be inclusive

[worn jetty]

huh but i thought 3-inf is negative slope

[worn jetty]

oh thats okayt thankss

[worn jetty]

when you learnt it did they explain why

[stuck depot]

It was like 2 years ago so I’m not sure

I would just ask someone else to be honest

[stuck depot]

its negative slope but the slope is increasing

[worn jetty]

mb i meant a positive slope 😭

[worn jetty]

ah okay

thanks for your help tho

[obtuse pebble]

@worn jetty Has your question been resolved?

[obtuse pebble]

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[golden sierra]

I solved this using like replacing X for 2, and I know the correct answer is A. For the SAT, is there a faster or even a different way to solve it quickly?

“Polynomial long division” How would I do that in this instance?

[polar fossil]

,rccw

[polar fossil]

hehehe i love this kind of strategy, big fan of things like this

[polar fossil]

$\polylongdiv{8x-2}{x+1}$

[warm shale]

ヘイリー

[polar fossil]

but tbh that doesn't reallly tell you anything

here's how i'd do this

$\frac{8x-2}{x+1} = \frac{8x+8-10}{x+1} = \frac{8(x+1) - 10}{x+1} = 8 - \frac{10}{x+1}$

[warm shale]

ヘイリー

[obtuse pebble]

@golden sierra Has your question been resolved?

[golden sierra]

@polar fossil how do u know to do 8x+8-10

[polar fossil]

i saw the 8x and wanted it to match the x+1 pattern on the bottom

[obtuse pebble]

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[fickle kindle]

Is the ball supposed to follow the green line or nah?

[fickle kindle]

I'm trying to learn the math behind pool and predict the trajectory of the balls with angles and stuff

For some reason the ball is taking a different path

[polar fossil]

in a perfect frictionless world where balls were 0 size and didn't spin yes it would

[fickle kindle]

it is a perfect frictionless world

and they dont spin

[polar fossil]

but

they are not 0 size

[fickle kindle]

ok but it wouldnt change THAT much

would it

[polar fossil]

idk how much is that much

[polar fossil]

it's a flash game

[fickle kindle]

ok i kinda exagerated

but the blue line is the "actual" path

[polar fossil]

that is closer to reality as the ball would roll off the rim

[fickle kindle]

bro

[polar fossil]

it's not, as the balls do eventually stop moving

[fickle kindle]

this is a super simple project i got on github

i coded these lines

im drawing a line from the cue ball to the mouse position

then "mirroring" the line

[polar fossil]

elasticity

[fickle kindle]

cueX - 2(mouseX-cueX), cueY

[fickle kindle]

howd u find the code

💀

anyway

what do i do

[polar fossil]

you told me it was on github and it was called pool game, wasn't that hard

[fickle kindle]

ok thats true

[polar fossil]

wdym

[fickle kindle]

this is the only thing ive implemented in the code

[fickle kindle]

how do i predict the ACTUAL path of the ball

also i havent figured out how does the game detect colision so yeah

its pretty bad

[polar fossil]

you have several options

1. write a physics engine
2. simulate the physics engine the game is using
3. add a constant angle to correct for bounces
4. add a variable angle to correct for bounces

[polar fossil]

it's using a physics engine

[fickle kindle]

yea i know

but what part of the code

anyway

[polar fossil]

pymunk

[fickle kindle]

i have the so called "cue_angle"

[fickle kindle]

yes i know its pymunk

oh

[polar fossil]

[fickle kindle]

yea

ok

what does this mean

lmao

those are the ball's properties

right?

[polar fossil]

yes

[fickle kindle]

so what

[polar fossil]

idk the specifics, i've never used pymunk

you'd have to check documentation and stuff

[fickle kindle]

no bro

arent u a mather

?

what math should i math

to get what i want

[polar fossil]

i mentioned your options here

[fickle kindle]

whats the easiest option to apply to the code

[polar fossil]

probably an undo button

[fickle kindle]

1. my ass
2. sounds hard
3. sounds doable
4. also doable

[polar fossil]

to reset the positions of the balls to how they were before you fired your last shot

[fickle kindle]

h u h

i used this website to analyse sum angles

i used 8 ball pool cus it has stuff like the ball trajectory, the cue ball trajectory

and stuff

[subtle sinew]

I forget the actual value but it's almost an elastic collision in pool, meaning very little energy is lost. The path off the cushion is a mirror, angle in is angle out

That's if you hit center of the ball

[fickle kindle]

THATS WHAT I SAID

[fickle kindle]

no

like

the cue ball hittin the border directly

[polar fossil]

it sounds like that's not the case for this game

[fickle kindle]

but in 8 ball pool would be?

[polar fossil]

watch some footage and analyse it

[subtle sinew]

If you are hitting center of the cue ball, into a cushion, angle into is angle out

[fickle kindle]

yes

i think it doesnt apply to this game im testing

[subtle sinew]

If you are hitting into another ball, at an angle, it follows the tangent line

[subtle sinew]

Then the physics is wrong in that game. Because what I'm telling you is the physics of the real world

[polar fossil]

try turning the elasticity to 1.0

also it is really hard to find top-down footage of pool wow

[subtle sinew]

Top down in what way?

[polar fossil]

like a camera positioned above the table

this is the best i could find but you can't measure angles like this

[fickle kindle]

guys

should the force applied affect the tragectory

trajectory

idk

[subtle sinew]

https://www.youtube.com/watch?v=vsTTXYxydOE&ab_channel=StuffMadeHere

Btw that video is nice

[fickle kindle]

dank je

gonna watch that later

[subtle sinew]

Like this isn't the greatest camera angle, but here

https://youtu.be/vsTTXYxydOE?si=D1t7SDLbGF9yFCQ9&t=753

[fickle kindle]

?

[subtle sinew]

Yes

[fickle kindle]

why

[subtle sinew]

The harder you hit, the shorter the reflected angle

Softer, more angle

[fickle kindle]

the green line is the calculated trajectory

and the blue """line""" was the actual path

i set the elasticty to 1.0

[polar fossil]

try changing the ball elasticity as well

maybe remove friction from the wall

[fickle kindle]

thats what i just said

[polar fossil]

zzzz

there's cushion elasticity as well

[fickle kindle]

OHHH

[polar fossil]

here's your knobs

[fickle kindle]

thats right

yea but now the balls bounce too much

it works tho

[subtle sinew]

You have to have the "goldilocks" range

[fickle kindle]

h u h

also

im thinkin here

to calculate the hit ball trajectory will be a pain in the ass

[polar fossil]

physics do be complicated

[subtle sinew]

The sweet spot

[fickle kindle]

although i found out that the red angle is always 90 degrees

idk if thats obvious

just found it out

[subtle sinew]

AC?

[fickle kindle]

DÂC

[subtle sinew]

Yes it's 90

Deflection angle is tangent if you hit at an angle

[fickle kindle]

you lost me there

[fickle kindle]

so

the so called "Cue Angle"

would be BÂC

or BÂD

[subtle sinew]

If you hit the cue ball into another ball, head on, it stops in it's tracks. If you hit another ball at an angle, the deflection is tangent

[fickle kindle]

what is tangent

[subtle sinew]

90 degrees

[fickle kindle]

for me tangent is oc/ac

[subtle sinew]

It's that

[fickle kindle]

oh

[subtle sinew]

That orange line I drew, that's the expected path of the cue ball

[fickle kindle]

and how do i calculate that?

is the green angle the cue angle?

or the pink one

[subtle sinew]

Wdym calculate it?

It's always tangent

[fickle kindle]

i wanna write a software that maths the math

[subtle sinew]

Also why are you trying to code this?

[fickle kindle]

and draws a line

[fickle kindle]

idk

angles

trigonometry

thought it would be an interesting experience

[sweet edge]

coding in what language

[fickle kindle]

im using python for simplicity sake

[subtle sinew]

Pool is one of the most difficult things to code properly, as there are tons of physics involved

[sweet edge]

python has trig shit built in with their math package iirc

[sweet edge]

^

yeah, don't reccomend

[fickle kindle]

yea im not coding a pool game

just drawing lines

[sweet edge]

fair enough

[fickle kindle]

and calculating angles

[sweet edge]

have fun with that

[fickle kindle]

are you being sarcastic

[sweet edge]

no

/g

[fickle kindle]

here

what is the "cue angle"

[subtle sinew]

No, it's literally difficult to do the proper math

[fickle kindle]

i asked 4 times 😭

[subtle sinew]

Are you asking about the angle of the pool cue?

Cue ball?

[polar fossil]

even the game in question doesn't bother and just leans on the physics engine

[subtle sinew]

Pretty much, like in real life, there's spin

[fickle kindle]

i was diggin through the code and found this "cue_angle" variable

[subtle sinew]

If you hit top of the cue ball, into another ball, it actually deflects 30 higher than the tangent

[fickle kindle]

the number there is the cue angle

what could it be

[subtle sinew]

I'm assuming that it's based on this

[fickle kindle]

@polar fossil you have the code

[subtle sinew]

That blue angle

[fickle kindle]

dont u

[polar fossil]

yes

https://github.com/Tynab/Pool-Game/blob/main/main.py

[fickle kindle]

isnt it the same

[fickle kindle]

do you have any idea of what the "cue_angle is"

[fickle kindle]

yea what is that

[polar fossil]

yeah it's

[fickle kindle]

yes but what does that mean

[polar fossil]

[fickle kindle]

bet

[polar fossil]

it's an angle between the cue ball, the mouse position, and the x axis

atan2 turns (y,x) into an angle

[fickle kindle]

the blue angle?

also now the number bellow the cursor shows abs(180 - (90 + cue_angle))

[subtle sinew]

You're honestly sending yourself into a rabbit hole with a video game. You ideally would need to experience it yourself to understand it all but this link is to one of the papers and you can explore the faq and videos for everything else https://billiards.colostate.edu/faq/30-90-rules/conditions/

[fickle kindle]

ok thank you

[subtle sinew]

Good luck with your endeavors

[fickle kindle]

im goin to bed guys

thanks for your help

and patience

sleep well

.close

[obtuse pebble]

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[molten brook]

So in this problem, I understand how 1/2 is calculated

But what if I try to calculate it this way:

[obtuse pebble]

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[molten brook]

.close

Uh oh

I accidentally deleted the image ooo

How do I fix this omg

[obtuse pebble]

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[vital holly]

need help haha

[fathom flicker]

What confuses you about this?

[vital holly]

going about it

[fathom flicker]

Yes but what about it?

[sweet edge]

Do you know what it means for a limit to exist at a point?

[vital holly]

yes i think

[sweet edge]

explain

[vital holly]

i thought wrong

[sweet edge]

we can help you with that as well, so dw if ur understanding is wrong

ok,,, what does it mean to you for a limit to exist at a point?

[vital holly]

when the limit has reached the 0 or the middle number in the table

[sweet edge]

interesting

that's not quite correct

are you familiar with the idea of left and right sided limits?

[vital holly]

yes

[sweet edge]

okay, so for a limit to exist at point x=c, both the left and righ sided limits as x goes to c must be the same

so in ur problem, if the left and right sided limits as x goes to 1 is the same, then we say that the limit at 1 is that

so by looking at the graph, what does it look like that limit is going to?

[vital holly]

-1

i mean 1 😅

[sweet edge]

not quite

yes

yes

1

I replied not quite to the -1

1 is correct

now if the graph had a jump, then the limit wouldn't exist there

since the left and right wouldn't be the same

does that make sense?

[vital holly]

yes

[sweet edge]

nice

anything else?

[vital holly]

no, thank u

[sweet edge]

np

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[nimble iris]

could someone explain why this is the answer?

[nimble iris]

like is it literally just saying 0 8 8 isnt in A

wait no

idk

[obtuse pebble]

@nimble iris Has your question been resolved?

[restive acorn]

a1, a2, a3 are the column vectors of matrix A

That would be (imagine i wrote them as columns)

a1 = [1 , 0 , -5]

a2 = [0 , 2 , 4]

a3 = [-2 , -5 , 4]

So the object

{ a1, a2, a3 }

Is a set that contains 3 objects, namely those same 3 column vectors

The vector b = [0 , 8 , 8]

they ask you

Is b an element of { a1, a2, a3 }

In other words, is b one of the objects in that set

The answer is clearly no since b =/= to any object in the set

[nimble iris]

like for example would {1,0,-2} be a set

the a1a2a3

[restive acorn]

Yes that would be a set of 3 numbers

[nimble iris]

okok

[restive acorn]

The objects in that set would be

1, 0, and -2

3 is not in that set

But -2 is

[nimble iris]

yes

[restive acorn]

This question is as if i asked you is 3 an element of { 1, 0 , -2}

[nimble iris]

wait so if 0 is in a1 8 is in a2 and 8 is. in a3, then it would be true?

or does the order matter as well

[restive acorn]

No if a1 itself was [ 0, 8 , 8]

Note that it's the column vector

[nimble iris]

ohh

[restive acorn]

If this were the case then i would say yes

[nimble iris]

so it would be true if a1 was 0, 8, 8

[restive acorn]

Yes

[nimble iris]

ok

[restive acorn]

Because b would be the same as one of the elements of the set

[nimble iris]

yes

[restive acorn]

Therefore it would also be an element of that set

[nimble iris]

oh okk

[restive acorn]

In this case the three columns are obviously different from b

[nimble iris]

yes

[restive acorn]

b cannot be an element of that set

[nimble iris]

do yk how to find the # of vectors in {a1 a2 a3}?

[restive acorn]

There are 3

They are a1, a2, and a3

[nimble iris]

ohh

i see

[restive acorn]

Each of those objects is a single column vector

The collection of all three would be a set containing three vectors

[nimble iris]

ty!

[restive acorn]

Yw! Goodluck with your classwork

[nimble iris]

thank you!

[nimble iris]

sorry another question, the number of vectors in the span is infinity, how come?

i read online that its "since there are an infinite number of linear combinations that can be made using these vectors." but im confused

[restive acorn]

Span of any collection of non zero vectors contains infinite vectors

The span is the set of all possible linear combinations of the vectors

A linear combination is when you take any arbitrary constants (scalar) and multiply them to the different vectors than add them

In this case

A linear combination of a1, a2, a3 would be

c1a1 + c2a2 + c3*a3

Where c1, c2, c3 can be any scalar constants

If we allow c1 and c2 and c3 to vary we will get an infinite number of different possible vectors when adding them together

Heres a simple example

Let v = [1 , 1]

Span of v would include

1 * [1 , 1]

2 * [1 , 1]

3 * [1 , 1]

4.5 * [1 , 1]

100000000 * [1 , 1]

0 * [ 1 , 1 ]

-5 * [1 , 1]

Pi * [1 , 1]

Etc etc etc

Just from a single non zero vector, we get an infinite number of objects in its span

@nimble iris

[obtuse pebble]

@nimble iris Has your question been resolved?

[nimble iris]

Got it!! Thank you so much!!!

[obtuse pebble]

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[hollow igloo]

is this how you solve this in complex plane?

wolfram alpha shows differents answers

im not sure where i have mistake

[obtuse pebble]

@hollow igloo Has your question been resolved?

[hollow igloo]

<@&286206848099549185>

[obtuse pebble]

@hollow igloo Has your question been resolved?

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[main arch]

<@&286206848099549185>

[obtuse pebble]

@main arch Has your question been resolved?

[obtuse pebble]

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[timid silo]

I have no idea where to start

[wild shoal]

so its important to create an expression for the length and width of the field

and in the top left you have the distance of the track as b

so what would you do to find the expression of the length and width?

[timid silo]

I tried this but um not sure if its the correct answer

[wild shoal]

so thats the correct first step

but it wants the area of the track around the field so what would you do from here?

[timid silo]

I have no idea bro I half the lessons

How do I get the area around?

[wild shoal]

so you need to do the total area (5a +4b)(4a+3b) - that expression that you just made so 20a^2+13ab+2b^2

[proper idol]

Is the answer 18ab + 10b^2?

[timid silo]

So thats the answer

[wild shoal]

yeah thats correct

[timid silo]

Is he correct or did u say the answer

[wild shoal]

no I just worked it out

[timid silo]

Oh alright thx

[wild shoal]

to confirm

[timid silo]

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[obtuse pebble]

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[dense imp]

I could use a quick jolt in remembering just how to get started on this integral

[elfin burrow]

complete the square

[dense imp]

and after that is it some kind of trig substitution?

[elfin burrow]

think so

not sure what you get exactly

[wild swallow]

arcsine

possibly

[elfin burrow]

yep

looks right

7-(r+2)^2 I think

[dense imp]

ok thanks, I think I get it

🙏

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[lunar rover]

Hey, I have a question that asks what is a vector that is ortogonal against the vector $v=(3,7)$ Im translating to english so I hope I typed correct.

[warm shale]

Totalani

[lunar rover]

so to get the ortogonal it says $u\cdot v=0$

[warm shale]

Totalani

[lunar rover]

I get it to $3x+7y=0$ and thats where Im unsure how to continue. I can solve for x and y but not sure if thats the correct way?

[warm shale]

Totalani

[drifting badger]

Assuming you have defined u = (x, y), then that should be correct, yeah

[lunar rover]

yea, so is that the answer?

[drifting badger]

The 'answer' would be the set of solutions, (x, y), for your equation 3x + 7y = 0

[lunar rover]

because when I look it up it says $u_1=7,-3$

[warm shale]

Totalani

[lunar rover]

wait

its en equation syustem isnt it

[warm canopy]

There are infinitely many options to pick.from

[lunar rover]

How do I pick? the question only states "not the zero vector"

oh right, it says name one

[warm canopy]

Pick whatever you want for x, then y is determined

[elfin burrow]

then you just need a nonzero vector <x, y> that satisfies 3x+7y = 0

any

[lunar rover]

yea sorry im a bit lost 😄

[elfin burrow]

try this

[lunar rover]

ok

like 5

hold on

so if I pick 5 I get $y=\frac{-15}{7}$

[warm shale]

Totalani

[elfin burrow]

there you go

and you can verify that those vectors are orthogonal

[lunar rover]

How do I do that

[elfin burrow]

dot product

[lunar rover]

ah

one sec

am I suppose to get the original vector (3,7) ?

[elfin burrow]

you wanted something orthogonal to (3,7)

you found (5, -15/7)

[lunar rover]

i feel so stupid

[elfin burrow]

now you can check that (3,7) . (5, -15/7) = 0

[lunar rover]

ah ok one sec

oh yea its 0

ok so basically find the vector that makes the other vector 0 ?

[elfin burrow]

find a vector that makes the dot product zero

and you do that by choosing x and y such that 3x + 7y = 0

[lunar rover]

right

and since choosing x didnt matter I could pick anything

[elfin burrow]

yes

[lunar rover]

awesome

[elfin burrow]

if you chose x = 7, you would have y = -3

like in your example

[lunar rover]

right, that makes sense now

gonna do the other one which states find the ortogonal for the vector (-3,-7). let me do it and see if I do it right

so its basicly the same right, except negative, so -3x-7y=0

Gonna pick 5 again

think im doing something wrong witht hat

[elfin burrow]

what did you do?

[lunar rover]

I got it to (-3,-7) * (5, -15/7)

maybe im doing the dot produkt wrong but im not geting it to 0

[elfin burrow]

,calc (-3)(5) + (-7)(-15/7)

[warm shale]

Result:

0

[lunar rover]

ooof

yea I was doing it wrong

thank you again

I appreciate you taking the time

gonna go practice some more

[elfin burrow]

enjoy

[lunar rover]

.close

[obtuse pebble]

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[hollow ferry]

help me buddies

[hollow ferry]

What I got was

A. -4
B. 75
C. -8

But im strugglin

[restive acorn]

For B.

You have to use chain rule

[hollow ferry]

oh

[restive acorn]

you got 3g(x)^2 that part is right

But you have to multiply by derivative of the "inner function" g

so it's

3g(x)^2 * g'(x) by chain rule

[hollow ferry]

ah

[restive acorn]

You always have to chain rule (even when you dont think you do secretly youre doing chain rule)

[hollow ferry]

Thank you
So that would make it 75*-4?

[restive acorn]

Yes

[hollow ferry]

I get it now ty

i think I did the rest correct right?

[restive acorn]

Yea you did do the other one correctly

You got

h'(g(x) * g'(x)

Right?

[hollow ferry]

yeah

[restive acorn]

Yep thats good

[hollow ferry]

and for part A It was just

g’(x) + h’(x)

[restive acorn]

Correct

Derivative behaves nicely with addition

[hollow ferry]

yeah

alright thank you I owe you one

.close

[obtuse pebble]

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[timid silo]

I am confused with putting this into my graphing calculator

How do I put in 6sin^2(x-5...

i have a ti-84

[restive acorn]

Type it like this

6sin(x)^2 - 5cos(x) - 2

[timid silo]

could you put brackets around it

i feel like im doing something wrong

[restive acorn]

If you want to be extra sure add some more parentheses

(6)(sin(x)^2) - (5)(cos(x)) - 2

But the way i wrote it thefirst time would work

[timber pine]

are you supposed to represent sin^2x as 1-cos^2x

[restive acorn]

The calculator understands the order of operations

[timid silo]

how is he finding the answer using that though

im still confused even after putting it in

[restive acorn]

They have to use the calculator to.solve it so no they dont

[timber pine]

Oh

[restive acorn]

After graphing, you need to use the calculate menu in your calculator to find the zero in the interval

You do 2nd -> trace (calc)

That will take you to calculate menu

Then select the zero function from.that menu

Since youre looking for when that thing equals.zero

[timid silo]

am i supposed to be in deg or rad

[restive acorn]

Unfortunately it's a bit difficult to.explain what to.do from there via text

Degree

They asked for the answer in degree

You could do it in radian and convert

[timid silo]

idk if this is asking for too much

but could you do it in desmos and show me

[restive acorn]

This video may help

https://youtu.be/4sW7XxBw4Hg?si=tiKOxFsAb099EohH

[timid silo]

the desmos graph looks like that

but mine looks different

[restive acorn]

I would try to help more but im not at a computer

I would need to verbally explain from here

Hence why i gave that video

I hope it can help

[timid silo]

i just get

"error: no sign change"

[restive acorn]

You should look up tutorials "how to find zeros ti 84"

"Use zero function ti 84" etc

You have to click a point that is near the zero from the left and right

They ask "left bound" and "right bound"

Use the cursor to move to the left of the zero for left bound

Press enter

Then repeat to the right of the zero for right bound and hit enter again

Then it will find it

I recommend watching a video to see it in.action

Its hard to explain through text

[timid silo]

ohhh

i got one of them

i got -35.815

but how does that turn into the answer of

x= 60 or x=300

[restive acorn]

That is not in your interval

There are probably many zeros

So you have to find ones where x is between 0 and 360

You may need to change your window to do thay

By pressing window and setting x min to 0 and x max to 360

(Assuming youre in degree)

Desmos graphs in radian

[timid silo]

okay i got it

[restive acorn]

So thats why their graph is very different

[timid silo]

its 35.815

same thing but positive

[restive acorn]

If the other answers are correct (60 and 300)

That must mean theres an error in the way you entered the function

Otherwise theres an error in the key

Just make sure youre in degree

Alternatively use the desmos graph between 0 and 2pi and convert the radian answer to degree

[timid silo]

oh i finally got it

thank you

it was something with my window size

.close

[obtuse pebble]

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• Be polite and have a nice day!

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[hoary hull]

idk how to solve this ques. my friend sent me this. 2,1 and 3 are arc lenghts

[obtuse pebble]

@hoary hull Has your question been resolved?

[obtuse pebble]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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[lunar rover]

Hello