help-0

[feral iron]

I can use the previous camera angle then add/minis the new ship angle

[viscid cove]

lol not the best wording to the question but sure

[viscid topaz]

(-ship angle + 360 + 90) % 360 = camera angle

[feral iron]

Well idk how u did it but that works - many thanks

[winged patrol]

Can someone help me visualize some stuff

Ok so, if we're trying to find the area of a circle right, we use the equation on the top left

What I'm trying to visualize here is how each component of this formula interact with each other

the green area represents the imaginary shape that I'm trying to match up with the real shape to be able to calculate the area of the real shape that being the circle

So I was wondering, in what way does Pi make the green area expand??

[viscid cove]

is the green area like the slice of a pizza?

[winged patrol]

kind of, it's r right, the radius

right now we have the r

let's say the r is like 5 or something

and we square it, it becomes 25, right?

now what's the green area supposed to look like

[viscid cove]

Are you sure you're not talking about a sector?

[ionic jewel]

i think the easiest way to prove that equation (outside of integrals) is to fill it with isosceles triangles like so

A

heres with more sides

the area of one of those triangles is 1/2 base * height, where the height is the radius

so for n triangles, the area is number of triangles * 1/2 * base * circle radius

which equals r/2*(nb)

then you know the sum of the bases (which is n * b, or number of bases times bases), is 2pi*r by the formula of perimeter a circle

so you get area = r/2(2pi*r) = pi * r^2

[winged patrol]

I-

Like, I wasn't really trying to prove or ask where it came from

[ionic jewel]

thats the best geometric approach you are going to get though

[winged patrol]

I just really can't visualize how the green line changes as things applies to it to fill the real shape

[ionic jewel]

try working backward from what I showed then

[viscid cove]

that's not what they're talking about

[ionic jewel]

i mean

is there something better though?

[winged patrol]

like- like

[ionic jewel]

he cant magically turn a line into the formula for area of a circle

[viscid cove]

jesus

listen first

[topaz scaffold]

Slice it into slices like a pizza and make it into a parallelgram?

[viscid cove]

r is a line, so its area is irrelevant right. Are you asking what happens to it when the circle's area is squared?

[winged patrol]

this is gotta be hard to explain, heck, one sec

Like I'm asking about the process of how the green line slowly morphs into something else to cover the area of the circle so that we could use it to calculate the area of the circle

liek say

[topaz scaffold]

Apply calculus

[viscid cove]

ffs

[winged patrol]

What does the ^2 do, does it make the green line expand/rotate around the middle and cover the area and then you can use that?

[topaz scaffold]

Apply calculus

[viscid cove]

dont be pathetic

[topaz scaffold]

The ^2 doesn't really do anything

It's not that we're transforming the radius into the area

[winged patrol]

Oh?

[viscid cove]

which level are you on?

like, what's the latest topic you're learning in maths?

[winged patrol]

Convergent and divergent sequence

[winged patrol]

But how does it work though?

[viscid cove]

i think you have the whole concept of area wrong

[topaz scaffold]

^^

It's not a transformation

It's a way of expressing the area in terms of the radius

[winged patrol]

Can you elaborate??

[winged patrol]

Ouch

[topaz scaffold]

The area of a square is l^2

l isn't getting transformed into a square somehow

[viscid cove]

the area you're talking about is the path covered by the radius when rotating right?

[winged patrol]

yea

[viscid cove]

when the radius turns around the centre?

ok

well, that gives a slice of a circle . "a sector"

area of the circle is given when it covers the entire path.

[winged patrol]

I'm sorry but that's still not what I'm looking for, maybe I am just unable to communicate the idea of what I'm trying to get

[viscid cove]

that's unfortunate

[winged patrol]

this is how my head works about area if I give an example with a cube, right?

width length height

width multiplied by length gives

and then you multiply it by height which will stretch it up

[viscid cove]

gotcha

[winged patrol]

which will be like this

and now the purple area is the area of the cube

which will be the final answer, right?

[viscid cove]

umm that's the volume

[winged patrol]

now you can visualize how w x l gives this yea?

oh right.

heck

I didn't have the right word for it, sorry

English isn't really my first language

[viscid cove]

yeah, i understand though

[winged patrol]

Yeah so I'm confused on how ^2 on the circle part applies like this

and how the pi also applies to it

how does it "stretch" to cover the shape

[viscid cove]

ok, last try

tbh bunny did a good job explaining

do you understand what is happening here?

[winged patrol]

Yea, trying to fill the area with more and or thinner triangles

[topaz scaffold]

That one also works

[viscid cove]

do you understand what is happening here?

[winged patrol]

yoooou fill it with triangles so that it closest match the shape of a circle, and then curl it out to find the area?

[topaz scaffold]

Kinda

[viscid cove]

the outer circle of the triangle is 2pi*r in length

[topaz scaffold]

At the limit you'll get a perfect approximation so to speak

[hybrid grove]

hmmm this server does have a lot of math

[viscid cove]

do you know where it came from? the length of circumference

[topaz scaffold]

It's a math server mate

[hybrid grove]

oh ye forgot

[winged patrol]

Okay

got it, I'm working it out in my head

[viscid cove]

dang

well if you want here;

take a circle of radius 1

[winged patrol]

Yeaaa?

[viscid cove]

pi is the distance covered when you rotate the radius to the opposite side

[winged patrol]

OH

OH OKOKOK

[viscid cove]

Its comes out of no where, even in a circle of radius one. Because its the actual property at defines a circle

[topaz scaffold]

It's the property that defines pi

Not the circle

[viscid cove]

bruh, it goes both ways

[winged patrol]

wait

but then

wait so let's say that like, it has a radius of one right

and (3.14)(1)^2

[topaz scaffold]

No not really

[winged patrol]

won't the area just then be half a circle?

[topaz scaffold]

Circles existed before pi mate

[topaz scaffold]

Yes and no

[viscid cove]

lmao just stop

[winged patrol]

how does the ^2 apply to this? :0

[viscid cove]

ok ok

now, you've made an error here

[topaz scaffold]

There has to be a square here cause it's an area

[viscid cove]

wow

way to explain it

[topaz scaffold]

Thanks man

[viscid cove]

now if i may...?

[topaz scaffold]

Go ahead

[winged patrol]

yes please

[viscid cove]

so, we just turned the radius r to make half of a circle

1 in this case

pi is not the area but the length of the broken ring

its in green,

[winged patrol]

GASP

AH

[winged patrol]

it's the exact same thing as w x l on a square

just with a curve

[viscid cove]

no no no

calm down haha, its a little different

[winged patrol]

okok sorry xD

[viscid cove]

well yeah a little, but no one is talking about the area rn

istg

lmao ornage

[winged patrol]

Yeeeeah sorry if im a lil dumb ._.

and uh, hard to understand stuff

[primal ether]

this is a bit to explain in text

[viscid cove]

nahhh

[topaz scaffold]

It's Ripe man

[primal ether]

beanie i recommend an animation video

[viscid cove]

ikr

[winged patrol]

give

[topaz scaffold]

2b1b

Yessss

[winged patrol]

pls i beg 🥺

[viscid cove]

but wait lets end that

i need closure dammit!

[primal ether]

sure

[viscid cove]

:'(

[viscid topaz]

https://www.youtube.com/watch?v=a2L27dTOyHk ?

[primal ether]

||https://www.youtube.com/watch?v=WUvTyaaNkzM||

[sleek elbow]

yay good vid

[viscid cove]

bruhh

yall throw calculus at everything eh

[topaz scaffold]

Well because the area of a circle is derived using calculus

[winged patrol]

you can continue pls

[topaz scaffold]

You don't actually need to know any calculus for this explanation tho

[winged patrol]

like, I want alotta comparisons so it's easier to think back to it

[primal ether]

there are proofs without calculus but its really best explained with it

[viscid cove]

but there are better ways to build intuition

[sleek elbow]

can confirm

[viscid cove]

anyways, let me talk with my self for a bit

[topaz scaffold]

That's the best one I've ever seen

Makes the most sense to me

[orchid laurel]

is this the help channel?

[viscid cove]

good for you

[orchid laurel]

im new here.

[topaz scaffold]

And is also realistic

[sleek elbow]

@orchid laurel one of them yes

[topaz scaffold]

Yep, and all the ones beneath this

[orchid laurel]

can I post my question here to get help with ?

[viscid cove]

there are other channels

equally helpful

[sleek elbow]

yes if its not in use @orchid laurel

[orchid laurel]

is this question in use?

by anyone

[viscid cove]

its in use

yeah

[orchid laurel]

oh im sorry.

[viscid cove]

[ionic jewel]

doesnt have to be, i posted a non-calculus proof earlier

[viscid cove]

ikr

[ionic jewel]

<@&268886789983436800> i guess

[viscid cove]

i'm so disappointed with the hivemind here

[topaz scaffold]

Oof

[tall wing]

lol

[topaz scaffold]

NOOOOOO

[tall wing]

alright

[viscid cove]

LMAOOO

[sleek elbow]

lmao

[tall wing]

banned

[viscid cove]

oof

[sleek elbow]

read rules oof

[tall wing]

you can't ask for help on exams :|

yea

[topaz scaffold]

That's the funniest one yet

[winged patrol]

i'm sobbing

[topaz scaffold]

Must... go... overkill...

[viscid cove]

cringe

[winged patrol]

not any um other stuff

[viscid cove]

?? no i wasnt replying to you

this is a mess

[river glade]

How do you reach the first answer?

[viscid cove]

my guy

[river glade]

I tried all the combinatorics formulas, nothing works

[viscid cove]

its in use rn

[river glade]

I thought you guys were just fighting but ok

[viscid topaz]

Fighting is a use

[viscid cove]

bruh this one's for the lurkers, i'm too anxious

so, in a semicircle of radius 1, the broken ring is pi

so the complete ring is 2xpi

i.e circumference

now, if the radius is 2

we consider there are two circles

circle one

circle two

"the length of the ring" is the circumference, for 2 it it is (circum of 1ring times2) 2pix2

similarly, for any value of r. There can be r different circles each with radius 1. The total "length of rings" will be

r times (circumference or length of one ring)

r times 2pi

so 2pi x r gives the circumference of any single circle of radius r

[alpine sable]

hi all im v confused on this

if anyone has any idea pls ping me ❤️

[viscid cove]

https://tenor.com/view/baby-angry-eating-mad-grumpy-gif-14328548

fine, that's all

[winged patrol]

I see! I think I kind of got it

what's the difference between 2pir & 2pir^2?

[viscid cove]

yay!

uhh

fine

so 2piR gives the length of the ring or perimeter

pi r^2 is the area

[winged patrol]

Oh!

So like

^2 somehow fills the.. space up?

or well like, expand into the middle

[viscid cove]

no no

i mean yea but a circle doesnt inherently have the definitions of units we use for area

"cm square, meter square"

so we need to turn our circle into a rectangle to see that

[winged patrol]

I am so sorry but I'll need to go now, my eyes are giving out, it's 4:24AM

Thank you for helping me understand it so far ;-;

[viscid cove]

haha no problem!

[winged patrol]

You're very appreciated 😭

[viscid cove]

if you understand the circumference, there are lots of vids on youtube very straightforward with the derivation of area

thanks, good night!

[alpine sable]

hi all does anyone know this 1

[viscid cove]

sure

[alpine sable]

i think its a calc 3 optimization type problem w extrema but i am not entirely sure

[viscid cove]

it says price of the base is five times that of a single glass panel

uh what

[alpine sable]

yeah

[viscid cove]

lmao am i high or something

[alpine sable]

no u probably know better than me

[viscid cove]

ok, let me know if i go wrong

[alpine sable]

i was just saying the chpater this is associated with is applications of relative extrema

but i dont understand the chapter at all

which is why im confused on how to di t

do it*

yes

[viscid cove]

one sec

[alpine sable]

okkk

[ionic jewel]

@alpine sable still need help?

[viscid cove]

yeah..nah i dont have it

[ionic jewel]

its a bit ambiguous actually

is the slate 5 times more than the panels (for any size), or is it 5 times more per area

im assuming the first based on the wording but its a bit weird

[alpine sable]

yes

mmm

[ionic jewel]

well then, let c be the cost of a glass panel, the entire thing costs 9c

this is just an all around bad question

[alpine sable]

yeah ;/

but

i found a similar problem online w aoslution

should i send that

to see if it helps w this one?

[ionic jewel]

sure

[alpine sable]

im trying to look at that and see what this is asking

ok

here is the problem:

[ionic jewel]

its not even that i dont know the math, i just dont understand what the problem wants lol

[alpine sable]

and then here is the solution

i dont understand math or the problem LMAO

[ionic jewel]

thats the same problem with 1.5 instead of 5

whats the soln

[ionic jewel]

i see

so the problem means it costs 5 times more per area

not for the slate

[alpine sable]

ah i see

[ionic jewel]

the first function in their thing is the cost function

which you would change from 1.5 to 5

[alpine sable]

where does the 2 come from for yz and xz/

[ionic jewel]

the square has two sides opposite each other

both of which have the same area

yz for the first pair, and xz for the other

[alpine sable]

ah ok ok

and then Vx and Vy are the partials

so when u solve i assume that Vx and Vy are zero in this case too

@ionic jewel i have another quick question if its fine?

so for this problem

the blue is the solution and its right

and this is also what i ended up getting

but

how could u end up using the second partial derivative test to prove it?

these tests

[ionic jewel]

uh

that would just check that its a relative minimum if you wanted

[alpine sable]

so u take the x and y partial derivatives

and just check/

[alpine sable]

in this question im confused how they got that Vx

[glass lichen]

what Vx?

[alpine sable]

and when u say this, is the function we should use z^2 = x^2 +y^2 or the version with (x-4)^2 + (y-2)^2 .. etc

[alpine sable]

partial derivative of x

[ionic jewel]

the latter

We need to minimize the function f(x,y) = (x-4)^2...

[alpine sable]

ok ok i will use (x − 4)^2 + (y − 2)^2 + z^2

[alpine sable]

but yeah im still a bit confused abt this

[alpine sable]

nvm

this one

pls

;_;

[mortal marlin]

If someone has any problems, I'm available to help you guys 🙂

I'm in the voice channels

[glass lichen]

do you have a question..?

[alpine sable]

me does

[glass lichen]

ok, well just apply the resistor rules a lot to get the theoretical resistance

[alpine sable]

idk the rules

the teacher jus dropped this stuff

[glass lichen]

given you have opted to not even post a question...

that's as much help as I can give

[alpine sable]

;-; even idk

[alpine sable]

mosh, can i post my answer from above

to verify its right?

[alpine sable]

this problem

[glass lichen]

you have the solution.....

[alpine sable]

its slightly different tho

[grizzled mica]

You want total resistance?

[alpine sable]

yup

idk parallel or series or stuff

at all

[grizzled mica]

1+4+((1/2)+(1/3+2+1))^-1

Ig so

Or wait

[glass lichen]

dont just give answers....

[alpine sable]

yes but how do u get there

also im not sure how to get z from that solution i posted

[alpine sable]

for this problem

i got x and y

[glass lichen]

it's explained.

read it

they say plug in the point.

[alpine sable]

isnt that for x and y

[glass lichen]

yeah......

[alpine sable]

for z it just has the answer

[grizzled mica]

https://youtu.be/eFlJy0cPbsY

[alpine sable]

it doesnt say how they got z

[glass lichen]

"Plugging this into the equation..."

[alpine sable]

the substituting part right?

[glass lichen]

what???

[alpine sable]

Substituting y x = into 0 Vx = yields

[glass lichen]

. . . . . . .

[alpine sable]

i dont see it hahah im so dumb

[glass lichen]

read what you posted, and find where it says "Plugging this into the equation"

This is reading comprehension at this point

[alpine sable]

i dont see that anywhere in this picture

[glass lichen]

that isnt what you posted

[grizzled mica]

Wtf

[alpine sable]

thats a different problem

im not talking about this one

i finished this 1

ok so this server is on about uni stuff and college grade stuff

hm

im in 10th so id not know

im talking about

[alpine sable]

this

porb

prob

[grizzled mica]

@alpine sable what grade

[alpine sable]

im in 12th

[grizzled mica]

Oh I see

[alpine sable]

this solution is for the problem i just posted

except instead of 1.5 its 5

idk how they got that z value in the solution

bc it just has the answer and no explanation

[analog gulch]

I recently came across this, and I'm struggling for an answer: https://math.stackexchange.com/questions/4207069/average-value-of-a-random-grid-of-multipliers

It's quite the interesting problem

[violet canopy]

could I please get help with this question for my homework, just wanted to check if it is correct

[alpine sable]

yes! it's correct

[restive tendon]

just out of sheer curiosity, how would i write this in interval notation?

[alpine sable]

what do you mean exactly? what would you like to make into an interval?

[ionic jewel]

probably the domain

[glacial hedge]

How do i find if this is true or false.... it seems false but how???

[restive tendon]

domain

[alpine sable]

o alright, so in that case you have to look for possible "restrictions" on the domain of the function

if you're working w real numbers, what values of x would be valid to input in sqrt(x)?

[restive tendon]

probably everything above 0

0 and above

[alpine sable]

yeah! so in your function you can do the same reasoning except that now x in my example is everything inside the square root of your function

[restive tendon]

so that would be

in terms of domain

everything below 7?

[cosmic knoll]

right

like ]-infinity, 7]

[restive tendon]

mhm

[alpine sable]

yeah! thats correct. so you have x <= 7 (an inequation) which as an interval is (-inf,7] cus those are all the valid values for x

[glacial hedge]

you cannot have [-inf, blah]

it must be (-inf, blah]

[restive tendon]

ohhh alright

[alpine sable]

(-inf,7] is basically whatchu said but noted as an interval

[restive tendon]

yeah because it doesnt include infinity

as that is a concept

right?

[cosmic knoll]

Oh sorry, where I live we use like I wrote. So then yeah (-inf, 7]

[alpine sable]

more specifically it would be

x E (-inf,7] i think

[restive tendon]

ok

how would i do this?

in precalc i had the most trouble with triangles and stuff

and pythagorean functions

so y e : P

[cosmic knoll]

I would use vector subtraction

[restive tendon]

we didnt learn about that so

whats another way

wait lemme try give me a bit

if someone wants to give me instruction thats cool too

[cosmic knoll]

Law of Cosines?

[restive tendon]

yeah sure

[cosmic knoll]

we know the 2 side and the angle

a^2+b^2-2abcos(80°)

this will be the square of the distance

[restive tendon]

ight

so do i simplify...?

or how do i do this

[cosmic knoll]

1. calculate a and b

[restive tendon]

how do i do that

[cosmic knoll]

a=4miles/hour * 8hour=32miles

[restive tendon]

mhm

[cosmic knoll]

b=3,5miles/hour *8 hour=28

c^2=32^2+28^2-2* 32* 28*cos(80°)

[restive tendon]

ah

and this will calculate the distance between the two

correct?>

[cosmic knoll]

nope

the square of distance

[restive tendon]

oh well yea

ok got it

thanks

[winter salmon]

i got 10-5i but it was wrong and im very confused now

[pallid sail]

show your work man

[ionic jewel]

(i-2)[(i-2)(i+2)]
= (i-2)[i^2-2^2]
= (i-2)(-1-4)
= -5(i-2)
= 10-5i

[ionic jewel]

that answer is correct

[glacial hedge]

how do i do this??

[ionic jewel]

this is false

remember the rules for how eigenvalues change as you row reduce a matrix?

[glacial hedge]

yes

but how does that help here?

[ionic jewel]

isnt there one that doesnt change the eigenvalues?

which means you could make that change on a matrix A and get a different matrix B with the same eigenvalues

[winter salmon]

oh i had a typo lol

[glacial hedge]

OH

yeha

ty

[winter salmon]

could someone help me for this one too, i don't really even know where to start

[cosmic knoll]

sqrt(2)(1-i)/2 -->
2/[sqrt(2)(1-i)]=
sqrt(2)/(1-i)=
[sqrt(2)(1+i)]/[(1-i)(1+i)]=
sqrt(2)(1+i)/2

[winter salmon]

ohhhhhhhh

forgot you could do that with the same denominator

[ionic jewel]

thr reciprocal of a complex number is its conjugate divided by its modulus squared

change that minus to a plus, then divide it all by 1/2 + 1/2 = 1

so you get the same answer as benpatrik but less thinking

[winter salmon]

o

its telling me to find a and b and i got a=-2 but i keep getting b wrong

[cosmic knoll]

b is 2sqrt(3)

because of (a+b)^2=a^2+2ab+b^2

so 2*1 *sqrt(3)i

[thorn kindle]

Wow nice job!

[winter salmon]

oh lmao im dumb i kept including the i with the b

thanks

[fathom ore]

this is indonesian language btw, please help me 😄

[cosmic knoll]

with which problem?

[fathom ore]

i dont understand all of that

🥲

[cosmic knoll]

oh then

fist i usually take everything up

[fathom ore]

mhm

[cosmic knoll]

lake 4a

5*p^(-2) *q *3^-(-1) *p^-1 * q^-(-1)

when we do that we change the sign

The we multiple everything which have the same base

[fathom ore]

oh

[cosmic knoll]

p^[(-2)+(-1)]=p^-3
q^(1-(-1) =q^2

5*3^-(-1)=15

15*q^2 *p^-3

in the end the numbers with negative exponent we change positive and take the reciprocal

15*q^2 /p^3

[fathom ore]

mhm

[cosmic knoll]

in 4b same

3^-5 *q^2 *q^-(-3)= 3^-5 *q^5
q^5/3^5

[fathom ore]

is this the answer of 4b?

[cosmic knoll]

yes

[fathom ore]

oh

[cosmic knoll]

we use that m^a *m^b=m^(a+b)

and m^-a= 1/m^a

try doing c and tell what you got

[fathom ore]

wait

6^2p^-2q/2^2 * p^-2

36p^-2q/2^2 * p^-2

36p^-2q/2^2 * p^-2
36p^-2q/4 * p^-2

36p^-2q/4 * p^-2
9p^-2 * p^-2

9p^-2qp^-2
9p^-4q

so the answer is 9p^-4q

is it right @cosmic knoll

[cosmic knoll]

almost

you didn't change the sign of the denominator

[fathom ore]

oh

🥲

[cosmic knoll]

here 9*p^-2 *q *p^-(-2)

the final solution is 9q

[fathom ore]

so the answer is 9q?

[cosmic knoll]

yes

[glacial hedge]

How do i do this? I know theres the formula... but thats sorta cheating cuz this is a differential equations class

i get something really ugly

[fathom ore]

alright tysm, ill try learn the number 5 myself :D

[cosmic knoll]

ping me or dm me if you need help

Vin

[alpine sable]

can someone help me interpret 39?

Hopefully I can do the rest after this

[glass lichen]

do you know interval notation?

[alpine sable]

Are you speaking about the less than symbol and such?

[glass lichen]

I asked about interval notation

since 39... has interval notation

[alpine sable]

I'm not sure if I do

[alpine sable]

Yeah I do

[glass lichen]

ok so what does x in [1,2] mean?

[alpine sable]

Hm I'm not sure.

[glass lichen]

$x\in [a,b]\iff a\leq x \leq b$

[ocean seal]

Mosh

[alpine sable]

Wouldn't you generally need an equation beforehand?

So X = Y within inverval

[glass lichen]

No

it's set of points such that x is in [1,2] and y is in [1,2]

nowhere does it say x=y

[alpine sable]

I now understand the texit message

[glass lichen]

good...

[alpine sable]

Okay so where 1 =< X =< 2

and same for Y

[glass lichen]

yes, cause you said you knew interval notation, I thought you would be able to convert b/w inequalties and intervals

so sketch the region marked out by those requirements

[alpine sable]

Something like this?

[cosmic knoll]

Yes

[glass lichen]

yes, it's a unit square in that location

but obviously shaded in

[cosmic knoll]

but with the internal

[alpine sable]

Yes Gotcha

Thanks for some reason it wasn't intuitive for me

[glass lichen]

then 40 will be similar argument

[alpine sable]

I'll try and send a picture

I got this..

[cosmic knoll]

this is incorrect

this would be x=1 and 0<=Y<=1

[alpine sable]

so 0 =< x =< 1 which means , to me , that there is some X within that boundary and 1 =< y =< 2 which means , to me , that there is some Y within that boundary and that line is where both X and Y exist

Wait I might be completely messing it up

Is it just a dot at (1 , 1)

and if not then I am kind of lost

[cosmic knoll]

It more like set of points where the boundary condition is met

like (0;1) is right

[glass lichen]

repeat what you did for 39

just with x being on [0,1] instead

[alpine sable]

red would be x being 0 - 1 and y 1 - 2

Okay I got it I think lol

[glass lichen]

yeah, it's the square bounded by those intervals... just like the last one

[alpine sable]

Thanks a lot @glass lichen @cosmic knoll

[vagrant kayak]

hey

can anyone help me

can anyone explain conditional probability

[alpine sable]

#❓how-to-get-help

[fathom ore]

👍

[cosmic knoll]

You need help?

[fathom ore]

nope, i answered all of them correctly

😄

[cosmic knoll]

Congratulations

[dawn galleon]

u have to graph the points first on desmos

after you plot it, we would need it to create a function to model that data. Because its temperature over the year it would be periodic, so we might start with something like y = Asin(b(x + c) + d, where A a and b are all variables that you'll need to change around to make it fit the data

and then

https://www.desmos.com/calculator/iksvngkmg9

graph i got

then

[alpine sable]

Hey, how would I do this? I'm a little confused as I don't think the numbers don't follow a specific pattern. Can anyone help me out?

[cosmic knoll]

Probability with conditions is easiest to conceive with sets.
A set where B ⊆ A and C ⊆ A

The P(B)=B/A and P(C)=C/A

P(B∩C)=B*C/A^2

P(B|C)= [P(B∩C)/A]/[C/A]=P(B∩C)/A * A/C=P(B∩C)/C

Other words what is the possibility to happen P(B∩C) if C Happened

[wheat condor]

can someone help me with this problem?

[primal ether]

Using factor theorem, if f(a)=0 then a factor of f(x) is x-a

so in this case use algebraic division to divide f(x) by (x-3)

then you get $2x^2-7x+5$

[ocean seal]

vvv

[primal ether]

then find the roots of the above by factorisation

[warped phoenix]

why is n greater than or equal to 2?

shouldnt it be greater than or equal to 1

since 1 will be the first term?

[sage jacinth]

its greater than or equal to 2 because (ex. f(1-1) => f(0)) if n an integer below 2

and f(0) isn't defined in this case

[vagrant kayak]

thank you sorry for late reply

[copper prawn]

im forced to used quaternions

can i convert to euler angles and back to facilitate?

or would that cause problems?

[tight locust]

just learn quaternions lmao

[copper prawn]

[alpine sable]

roots of the quadratic equation x² - x - p(p-1) = 0

Please answer

[copper prawn]

any good resources?

especifically for 3d rotations

and yes i did see 3blue1brown's series

[alpine sable]

Please tell roots of the quadratic equation x² - x - p(p-1) = 0

[tight locust]

,w x² - x - p(p-1) = 0

[ocean seal]

Results provided by WolframAlpha

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Requested by EndTimes#8053

[tight locust]

1-p and p

[alpine sable]

The value of p if the roots of quadratic equation 2x² + x + p = 10 are reciprocal of each other is?

[tight locust]

just use the quadratic formula

[alpine sable]

I am unable to solve this

ANy help?

[copper prawn]

@alpine sable bhaskara's formula bro

[alpine sable]

??

Can you help

In solving this

[copper prawn]

finding the roots?

[alpine sable]

value of p

The value of p if the roots of quadratic equation 2x² + x + p = 10 are reciprocal of each other is?

[errant dagger]

@alpine sable vietas

r_1 = n, r_2 = 1/n

[alpine sable]

hm

[fathom ore]

wait @cosmic knoll

[fathom ore]

so i should delete this right

the 9p^-2qp^-2

[alpine sable]

what about this

If (k - 1), k, (2k + 1) are three consecutive terms of an AP, then value of k is?

Can anybody solve this

0

[civic abyss]

hey im trying to find out a power of a character from a anime can anyone help me out

[alpine sable]

The value of p if the numbers x, (2x - p) and (3x + 6) are three consecutive terms of an AP?

[prime badge]

do they punch someone or what

[alpine sable]

4

is this correct?

Please recheck

Mine is not coming that

[alpine sable]

IT is 3 probably

oh nvm

I read it as a +

??

Please solve it again

[alpine sable]

Solve it again please

[jovial forum]

I have to integrate ((5x^2 - 17x - 9)/(x-5)(x^2+6)) with partial fractions. This is what I have so far:

5x^2 - 17x - 9 = A(x^2 + 6) + (Bx+C)(x - 5) = Ax^2 + A6 + Bx^2 - 5Bx + Cx - 5C = Ax^2 + Bx^2 - 5Bx + Cx + A6 - 5C

I think I refactor them here then try and equate the two sides?

5x^2 - 17x - 9 = (A + B)x^2 + (-5B + C)x + A6-5C

Have I done this right so far, and if so, I'm having trouble determing the values of A, B and C, what's the best way to accomplish that?

[rigid smelt]

you shouldnt have expand and factor

there is a faster way to it

you can substitute values of x such that (x^2 + 6), (x-5) or Bx is equal to 0

hence you can eliminate some of the constants

[jovial forum]

So this step was far enough: A(x^2 + 6) + (Bx+C)(x - 5)

[rigid smelt]

yep, just stop right there and substitute in values of x to eliminate either some of the constants

for example x=5

you get to eliminate Bx+C

and your equation now has A left

which you can find

[jovial forum]

So if x = 5 then I'm left with 125 - 85 - 9 = 31 = A31, so A = 1?

[rigid smelt]

,w (125-85-9)/31

[ocean seal]

Results provided by WolframAlpha

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Requested by waler#0265

[rigid smelt]

yeah

and then try to eliminate B or C

to find the other constant

[jovial forum]

Awesome

[rigid smelt]

ofc C cant be eliminated

[jovial forum]

How would you go about doing that?

[alpine sable]

The middle term (s) of the AP whose first term is 2 and last term is 252?

[rigid smelt]

look at Bx + C

what do you think can be eliminated?

[jovial forum]

x = 0?

[rigid smelt]

but what will be eliminated

[jovial forum]

I think I would be left with -5c, so B is eliminated

[rigid smelt]

yes B is eliminated

you basically just have C now, since A is found

[jovial forum]

and A

[rigid smelt]

not really

theres no more A

[jovial forum]

oh A6 - 5C

[rigid smelt]

A is found remember?

[jovial forum]

If x = 0 are we not left with -9 = 6A-5C?

right, I see

[rigid smelt]

yes, but A is found

we know what A is

so we are only left with C

[jovial forum]

yeah sorry, I see what you mean

So solving that gives C = 3

[rigid smelt]

yes

so now its just B to find

which you can basically sub any x value in to find

[jovial forum]

So it will come to 4

A = 1, B = 4 and C = 3

[rigid smelt]

probably if you did your math right

[jovial forum]

Now I just intragrate (1/(x-5) + (4x + 3)/(x^2+6)?

[rigid smelt]

yes

[jovial forum]

woo

Thank you

I get it now, will just have to practice them a bit

[storm swan]

hello, does anyone know how to solve b,c, and d?

i need help understanding it

[prime badge]

what's your calculation

[storm swan]

<@&286206848099549185> sorry for the ping, i really need help

[fervent grail]

a+b+c=1 ab+bc+ca=2,abc=3 then find tha value of a^4+b^4+c^4/a^3+b^3+c^3

[storm swan]

sorry im a bit confused would you mind elaborating?

[small stag]

Let’s break apart ae

[ionic jewel]

[fervent grail]

?

[ionic jewel]

use parenthesis correctly

[storm swan]

so far im trying to use ade to try and find ae, but im not sure if i am doing it right

[fervent grail]

a+b+c=1 ab+bc+ca=2,abc=3 then find tha value of a^4+b^4+c^4 / a^3+b^3+c^3

[small stag]

Aurie dm me it’s a bit hectic here

[storm swan]

oh yeah sure ill do that

[ionic jewel]

do you not know how parenthesis work or is the original problem supposed to be like that

right now you have a $\frac{c^4}{a^3}$

[ocean seal]

bunny

[ionic jewel]

try (a+b+c)^3 and (a+b+c)^4

i suspect it will end up being the final fraction + stuff you know the value of

[fervent grail]

How can I find the value of (a+b+c)^4 ?

Oh sorry

I was trying to say how can I find my answer using it ?

[ionic jewel]

well let's try the other one first

,w expand (a+b+c)^3

[ocean seal]

Results provided by WolframAlpha

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Requested by 兔子#6562

[fervent grail]

It's equal to 1

[ionic jewel]

what?

yes

[fervent grail]

I mean (a+b+c)^3 = 1

[ionic jewel]

ur right

yes

now let's see if this works

can you pull out any of the other identities from it?

[fervent grail]

Umm I don't think so

[ionic jewel]

$a^3 + 3 a^2 b + 3 a b^2 + b^3 + 3 a^2 c + 6 a b c + 3 b^2 c + 3 a c^2 + 3 b c^2 + c^3$

[ocean seal]

bunny

[fervent grail]

a^2+b^2+c^2 = -3

But I don't think so it will be useful

[ionic jewel]

no

notice the 6abc term?

can that simplify?

[fervent grail]

Yup

[ionic jewel]

to?

[fervent grail]

6abc=18

[ionic jewel]

$a^3+b^3+c^3+3ab^2+3a^2b+3a^2c+3b^2c+3ac^2+3bc^2 +18 = 1$

[ocean seal]

bunny

[fervent grail]

Yup

[ionic jewel]

now the question is if we can find more

[fervent grail]

Yea

Hey I have one idea

[ionic jewel]

that is good

im not seeing a way to factor more

[fervent grail]

Let's take 3a² , 3b² , 3c² common from 6 expressions

And then substitute b+c=1-a , c+a=1-b and a+b=1-c

[ionic jewel]

but the idea is that you can isolate the a^3 +b^3+c^3 = expression, then do the same for (a+b+c)^4 to get your fraction

this would be significantly easier on paper, so you can play around with it from here

[fervent grail]

Hmm

[ionic jewel]

this is almost always how these types of problems are solved, i don't see a nice solution any other way tbh

could be missing something though

[wild marten]

AB = i + 2j and AC = 3i + 4j then use the formula for angle between 2 vectors

[gaunt magnet]

hi

i got this as my equation

am i correct

[ionic jewel]

yeah looks good

hole at -3, x intercept at 4, asymptote at 2

[wild marten]

coordinates of $\Delta KLM$ : L(4,5), M(1,5), K(1,1)
so, congruent triangle is option(d)
(why?)

[ocean seal]

Schrödinger's Smile

[thorn kindle]

Side lengths

[ionic jewel]

just wait until you hear about google

its 2pi*r but just Google questions like thid

if you just need the formula look it up, don't ask us

exam?

<@&268886789983436800>

[tame falcon]

Thanks.

[alpine sable]

it is literally a peridoic test

Exam...

#❓how-to-get-help

[rigid smelt]

lmao just right after the other person was banned

[tame falcon]

Oof.

[alpine sable]

lmao

Lets get another one

[ionic jewel]

c-c-c-c-combo

[stark nimbus]

A cafeteria has a fixed costs of Php8,000 per day and additional costs of Php60 per combo meal.
a. Find a mathematical model expressing the total daily cost incurred by the cafeteria as a function of the number of combo meals prepared.

this is my answer

f(x)=8000+60x

what do you guys think

[ionic jewel]

looks great

[stark nimbus]

Sketch the graph of the function is the next question,but im kinda iffy because when I put it in geogebra

[ionic jewel]

it's in y = mx+b form

the slope is 60, the y intercept is 8000

[stark nimbus]

it just looks like that,seems good?

[dark sun]

anyone tryna guide me through this question

[placid zinc]

"uniform distribution" meaning that the plant is equally likely to be anything between 5-12 cm

You want to get the pdf - which is just a constant function

The area under that function should be 1, which is what makes it a pdf

[ionic jewel]

not at all

that graph is zoomed in on the x intercept, which you don't want

[stark nimbus]

so what do i do

because i have to draw it on a paper,how would i do this

[ionic jewel]

i feel like it's more likely it just wants desired range divided by total range

i doubt this is in a class that covers pdfs

[ionic jewel]

the y intercept is 8000, and the slope is 60

the point they will be looking for is (0,8000), and about the right slope

so if you have both of those ur set

technically the geogebra one is right but they will know you just used a graphing software

[stark nimbus]

so (0,8000) and (1,8060) will be my points?

[ionic jewel]

sure

[grand karma]

This may be a silly question, but how would you calculate the growth rate of something both additive and multiplicative? Suppose you start with 0 and the growth formulae added one then multiplied by 2?

[woeful pulsar]

what do you mean by "growth rate"

like order of growth with big O notation?

[grand karma]

how could you express it without knowing previous terms in the sequence?

[woeful pulsar]

oh, you want a closed form?

[grand karma]

I don't really understand your terminology to be honest

Possibley?

[keen kayak]

A transversal intersects two lines m and n such that a pair of alternate interior angles is equal. Then, what can you say about the lines m and n?

[ionic jewel]

you want a closed form

and I'm not sure there actually is one

[keen kayak]

Any guess about my question

[woeful pulsar]

well if you write out the first few terms you get
0, 2, 6, 14
add 2 ->
2, 4, 8, 16

[keen kayak]

Like m and n are paralell

[ionic jewel]

ah i was just getting there

but does that hold for a generic a_n = b(a_{n-1}+c)

[grand karma]

What does underscore do?

[ionic jewel]

sequence notation

the nth element of the sequence a

[ionic jewel]

1 4 10 22 46...
this doesn't match anymore

why i wasnt getting anywhere starting at 1

[woeful pulsar]

add 2 and divide by 3

[ionic jewel]

witchcraft

[grand karma]

could you try and explain this to me? (sorry)

i don't really understand it

[ionic jewel]

it doesn't matter it was a question for element, but it looks like he has a closed form for what you were originally asking

although generally, that's not really something that comes up

[wind bane]

wait, just to clarify, you start at 0. the next term is 2(0+1) = 2 correct?

[grand karma]

yeah

well the values are arbitrary

[wind bane]

okay but the relation is the same

you start with some value x, then the next term is a(x+b) for some constants a and b, correct?

[grand karma]

yes

[wind bane]

okay. let me think about it some more.
fyi, this is called a recursively defined sequence, or a recurrence relation
recursion since the previous term determines the next term

[grand karma]

i see

[dull lance]

So your equation should be y= (x+1)^2-6(x+1)+6
Expand and simplify. You will get y= x^2-4x+5.

I got x^2 - 4x + 1

[ionic jewel]

,w f(n) = a(f(n-1)+b), f(0) = 0

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by 兔子#6562

[ionic jewel]

[dull lance]

um

So your equation should be y= (x+1)^2-6(x+1)+6
Expand and simplify. You will get y= x^2-4x+5.
I got x^2 - 4x + 1

[ionic jewel]

,w g(n+1)=a*g(n)+b

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by 兔子#6562

[dull lance]

my working

[ionic jewel]

Wolfram can do recurrence equations

here's your closed form

[wind bane]

hey i was in the process of figuring that out

[dull lance]

Wdym

Whyyyyyyyy

😭

[wind bane]

,w g(n+1) = a(g(n) + b)

[dull lance]

[ionic jewel]

it's the same difference, b = ac

it's just a constant

i multiplied it out then combined the constant

[wind bane]

okie. tru dat

[ionic jewel]

you can pull out the original b at the end if you want

yeah i know how to do this by hand but there's no way I'm doing more recurrence equations right now

had a class that was doing them the entire time basically, was awful

[ripe mauve]

someone help me please

[haughty gyro]

Calculate the price of 12 apricots for both shops..... and look up LCM

[keen kayak]

Hm find are with the help of heron's formula of a triangle who's perimeter is 140

Help

I need answer in 10mins

[vale wigeon]

why such urgency?

is this a test?

@keen kayak

[keen kayak]

Yep@Ann#0413

Yep @vale wigeon

[vale wigeon]

we do not help on tests.

[keen kayak]

If u can help

[shadow mango]

i believe you shouldnt be asking this then....

[vale wigeon]

it's against the rules of this server.

read #❓how-to-get-help

[keen kayak]

Ok

i'll find the answer

[fathom ore]

1+1=2

[deft creek]

0+0=0

[ivory thicket]

Hey, I just want to fully understand this question before I move on

in relation to logs & solving equations

[ocean seal]

Uncreeperble

[ivory thicket]

by what factor does I have to be multiplied by to add 20 d to the answer

[ocean seal]

Uncreeperble

[ivory thicket]

I know the answer is 100

but I dont know where the thoery behind that is

is it cause $ I = 10^2 changes into + 2*10 somewhere $

[ocean seal]

Uncreeperble

[ivory thicket]

so to get the answer to +20, you would simply do 20/10 then 10^ <<<<

so to get it to add 30 it would be 10 ^ 3 (30/10 = 3)

OK THANKS

I got it

[alpine sable]

Hey, how do you solve this?

[dull oak]

@alpine sable @Subw#1337

u idiot im just gonna cointact discord and get my account back

[woeful pulsar]

try using the hint, can you try a+a=0? To do so, you might want to try out (-1)*(-1)

[alpine sable]

Any idea where to start? I am trying cylindrical but cant evaluate the integral.

[vale wigeon]

you're taking x as the cylinder axis, right?

[alpine sable]

Yeah since y and z are in the constrained cylinder equation

but CYL is r, theta, z not x so does that matter?

[vale wigeon]

yours will be (r, θ, x)

if you insist on being inflexible about this then you will sign yourself up for some unnecessarily hard integration

[alpine sable]

nah you're a genius!

thank you i see it now

[vale wigeon]

x = x, y = r cos(θ), z = r sin(θ)
dV = r dr dθ dx

[alpine sable]

Yeah! I got that as well 😄

[vale wigeon]

your solid has r from 0 to 12, θ from 0 to π/2 by the looks of it

and you have 0 <= y <= 4x

so 0 <= r cos(θ) <= 4x...

hm

uh

hm hold on

this is weird

im gonna try sketching this once home

[ivory thicket]

(3x)^2 = 30*3^x-81

Okay I have got this to

[ocean seal]

Uncreeperble

[ivory thicket]

ok

sorry

[alpine sable]

This should have been 0 <= 4x <= r cos(θ), i got it now tysm! ❤️‍🔥

someone help me with math hw

<@&286206848099549185>

[sleek elbow]

@alpine sable #❓how-to-get-help

rule 5 I believe

[alpine sable]

I thought F_SR = F_RS since they form an action-reaction pair? How could one be larger than the other by Newton's third law?

[topaz scaffold]

Well if one isn't larger than the other than the rock wouldn't be moving

[alpine sable]

@topaz scaffold But Newton's third law states that they have to be equal...

[glass lichen]

The force the surface exerts on the rock is the normal force, the force the rock exerts on the surface is from gravity

since it's an inclined plane, the gravity vector gets broken down into its rectangular components, so only a portion of the gravity force is inline with the normal force

[alpine sable]

Oh okay

Thanks

[warm granite]

Does anyone know how to add a smoothing spline to a plot in R? Ive tried looking up youtube videos, but their a bit hard to follow. Would anyone be able to help?

[harsh acorn]

Do I factor this like this?

[alpine sable]

Thank you!

[alpine sable]

\

hey can anyone help me with b?

[old anvil]

Yes great!

[rigid smelt]

try constructing these lengths

now this seems like part a but longer

[alpine sable]

hmm

ohh ok i got it thank u

A 77-kg person is parachuting and experiencing a downward acceleration of 2.5 m/s^2 shortly after opening the parachute. The mass of the parachute is 5.2 kg. (a) Find the upward force exerted on the parachute by the air. (b) Calculate the downward force exerted by the person on the parachute.

[ocean seal]

n/c

[floral jungle]

anyone able to help?