help-0

[tawdry flower]

that's impossible

$e^{-10k}$

[tribal geyser]

2% per year

[ocean seal]

kirafa

[tawdry flower]

aaaaaaaaaah 2% per year

[devout sigil]

That’s the rate of decline

[tawdry flower]

yeah there's something im not getting here

i thought percentage rate of decline would be "what percentage of the population has been reduced"

it could also mean "what's the decline rate", meaning "what is k"

but "k" doesn't change over time

[devout sigil]

Which answer is this then?

[tribal geyser]

That’s converted and then 2%

[tawdry flower]

and i assume you got "k" from part (b)?

[tribal geyser]

Yeah

[wet crown]

quick question, is Greatest common denominator greatest common factor

im stupid

[tawdry flower]

nope

related tho

[ionic jewel]

google search for greatest common denominator just brings up GCF for me

[wet crown]

cheers

had ocd

and like freakin out and shit

cheers

[tawdry flower]

im gonna tap out on this problem - my best guess is that the answer is "k"

which is roughly 2%

[near plover]

I'm confused with this, I know they are both subpaces.

[unborn dome]

can someone help m out with this?

[near plover]

Is this what the sum looks like for this?

@unborn dome can u use a different channel

[glass lichen]

No

[unborn dome]

yeah sure

[glass lichen]

the x's dont have to be the same

[near plover]

thanks kind sir

[glass lichen]

if I have spaces U and V with corresponding bases B and C, then U+V has basis BUC

[near plover]

damn

is there a proof for this somewhere?

[glass lichen]

I mean.. common sense can justify it

[near plover]

damn this is not immediate to me

[unkempt grail]

$||ax||^2 = a^2||x||^2$ ?

yes

[glass lichen]

$B={u_1,...,u_n} \ C={v_1,...,v_m} \x\in(U+V) \implies x=u+v, u\in U, v\in V$

[ocean seal]

Mosh

[glass lichen]

where u and v can clearly be written wrt B and C respectively

since B and C have been defined to be bases

BUC will guarantee span of U+V, but it has to be made indep

[void sphinx]

i tried wolfram on this but it gives me an imaginary solution, is there any real solution for this q?

[strong furnace]

try u=pi/4 - x

[void sphinx]

alright

[wary badge]

Maths is best

[void sphinx]

i got sqrt2/8 (sinx-cosx) + C is this right?

[strong furnace]

idk , did not solve it myself

[void sphinx]

nvm cos^2x/cosx = secx lol fuck me

[strong furnace]

yeah that seems wrong( should get -1/(4*sqrt(2))*(2sin(x)-ln(abs(tan(x)+sec(x))))

[void sphinx]

in terms of u i got

-1/4[2sinu - ln|secu +tanu|]

[strong furnace]

oh yes negative sign

yeah I mean u aswell

[void sphinx]

now to change u back to x is a bit

alright wait

the integral i got was -1/4 int cosu - sinu tanu du

[proud iris]

If I have a cube and I have a plane (area) which has a slope (alpha) and a rotation (beta). and I wanted to cut the cube with that plane, how would I know which Coordinates belong in which side of the new 3D shape.
(the origin (the slope and the rotation) are always at the same point)
sorry if this is not well explained, maybe the image helps

[golden nymph]

wtf is a rotation

like is it a rotation around a line of greatest slope?

which coordinates belong to what?

that's what I get from entering math servers

[strong furnace]

<@&268886789983436800> (Deleted message) @thorny barn

[proud iris]

give me one second I'll get you another because my explanation is bad

[golden nymph]

HWTA HAVE I DONE

WHY CALL MODERATORS

IM INNOCENT I SWEAR

who deleted what who

CONFUSION

[night geyser]

sigh

[proud iris]

@golden nymph the rotation is supposed to be applied on (around) the x axis of this image

[alpine sable]

i forgot how to do b lol, can someone help

[golden nymph]

what about hte slope?

why is slope different than rotation omg

[golden nymph]

me too I forgot too

it's s * log 5

but what's next

[alpine sable]

thats what i got

but

[golden nymph]

the question is broken

[golden nymph]

.

I odubt I cna help but i guess I will try

ploruto

[proud iris]

otherwise I wouldn't be able to rotate the area however I want

slope is delta y

[golden nymph]

yeah makes sense

but they look pretty much the same

and I don't even understand what you want to find

[proud iris]

when cutting the cube with that 2D area, I get two parts of the cube. right?

[golden nymph]

yup

[proud iris]

and when given x,y,z (coords) I want to know if it would be in the first or second half

[golden nymph]

oooooooooooooooh

I got it

umm

I can think of something and tell me whether you'd like that or not

we have a space

and a random plane in that space

we have a random point and we want to know at what side is this point from the plane

is that equivalent to your quesiton?? @proud iris

[proud iris]

lemme think 1 sec

yes

it is

[golden nymph]

alright

then let me see how will I approach this

I can think of sth rn but I guess it sucks

please stop

please

this is a math server

thank you

but I guess my way works only if the plane doesn't pass through the origin

I think we can have the vector equation of the plane

and the position vector of the point

[lime sparrow]

hi this may seem like a stupid question to u guys but im really terrible at math. would like to know why its 3m/4 instead of 3/4m?

[golden nymph]

extrapolate it to a line by multiplying it by a parameter

[golden nymph]

(3/4) m

[lime sparrow]

yeah like that i mean sorry

[golden nymph]

3/4m can be confusing

people may think it is 3/(4m)

[lime sparrow]

my bad

[golden nymph]

(3/4)m= 3m/4

they are equivalent

lo

l

lol

ok where were I

[lime sparrow]

sorry im not smart lol

[proud iris]

I'll research a bit what extrapolating is. Give me one second so I can follow you properly

[golden nymph]

solving for the value of the parameter at which the line intersects with the plane. If the value of the parameter is greater than 1 it is on one side and if smaller on other side

[slate heron]

$$
\frac12\times\frac32\times\frac{m}{1}=\frac{1×3×m}{2×2}$$

[ocean seal]

Louis

[golden nymph]

did you take vector equations of planes tho??

[slate heron]

@proud iris can't you use trig functions for your question? Why are we using vectors?

[golden nymph]

idk

I turned it into vectors

if trig can do it that'd be better

[proud iris]

idk I am not good at math. I'm the cs guy, but I am trying to solve a math(y) looking problem

[golden nymph]

but is the plane restricted to rotate around one axis only??

I just don't get why is there alpha and beta

[proud iris]

no, x and y. So the plane can change however it want

[slate heron]

@lime sparrow

[golden nymph]

alpha is when the plane rotates around x

so what about beta

I can't visualise what beta does

[proud iris]

the plane always has alpha and beta. This is supposed the be able every possible rotation and slope

[proud iris]

gimme 1 sec

[golden nymph]

I think four constants define how a plane looks?

so this is an angle. Tell me two rays that define this angle

[golden nymph]

.

lol is it me or I can't understand what is that lol

[neon horizon]

What is 59x + 59 = 2537 find X

[proud iris]

ohh really? in my head I only needed 2 xD

[golden nymph]

subtract 59 both sides then divide 59 both sides

[neon horizon]

But I cant find the answear

[topaz scaffold]

Use an unoccupied channel next time please

[neon horizon]

What do you mean by both sides

[golden nymph]

left and right

the equal sign separates the sides

[slate heron]

Ploruto do you know the coordinates of the square's points in the first place

[neon horizon]

But what is X?

[slate heron]

,w find x in equation 59x+59=2537

[ocean seal]

Results provided by WolframAlpha

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

Requested by Louis#6988

[golden nymph]

the one you trying to find

[neon horizon]

Thxxx

[proud iris]

yes, it always starts at 0,0,0

[slate heron]

No the other 7 points

[golden nymph]

yay a help

[proud iris]

do you mean the 8 points of the cube or the 4 of the plane

[slate heron]

8

[proud iris]

yes, it's always 0,0,0 to 3,3,3

so (0,0,0), (0,0,3), (0,3,0) and so on

[slate heron]

And by slope alpha, you mean the angle it's tilted above 0 right? Because in the illustration you drew 90 degree angle

[proud iris]

yes

that would be the shift in y from 0, 3 on the y axis

[golden nymph]

so is it like the slope times 3?

[slate heron]

Yeah can't you just use trigonometry

[proud iris]

can I ? I am not that good at math.

[golden nymph]

wouldn't trigonometry be suitable only at a constant cross-sectional area?

[slate heron]

Do you know the angles?

[proud iris]

yes

[golden nymph]

there is a beta somewhere that God knows what it does

[proud iris]

all angles are given

[proud iris]

okay, I'll download a 3d software to explain it better 1 sec

[slate heron]

I can't seem to conjure up a general form in my head but I'm sure you can apply trig to find the X,y coordinates for each angle

[golden nymph]

wtf

[slate heron]

I don't think that's very relevant

[golden nymph]

a rotation around a normal axis to the plane?

that literally does nothing

a plane is extendable to infinity by definition

[proud iris]

no not really. in my case it's around the origin. You are right

[golden nymph]

planes rotate around axes and not points

wdym origin

God help me 😩

I am a highschooler I don't have brains to understand enough

[proud iris]

my too. just use your hand

take you hand and make s slope of 90 deg.

and now move your wrist

that's beta

[golden nymph]

you mean a rotation around the x-axis?

[proud iris]

yesssssss

[golden nymph]

that's definitely not what's in the picture

Kidnap Mr. Harry

and english?

[slate heron]

Wtf

[golden nymph]

or why

[slate heron]

Garden?

[golden nymph]

exafctly

it says park

[slate heron]

Where the hell does garden come from

[golden nymph]

where are you ploruto

[proud iris]

there is no garden

[golden nymph]

I think garden is park??

[slate heron]

My pencil is 23 cm long. Find the diameter of the sun.

[proud iris]

here am I. do you get my idea now? The picture was not perfect, I know

[topaz scaffold]

,w My pencil is 23 cm long. Find the diameter of the sun.

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by RipeOrange#4907

[topaz scaffold]

Dang it

Would have been funny

[slate heron]

$$345-\frac{345}{4}-\frac{345}{6}$$

[ocean seal]

Louis

[golden nymph]

the picture was not relevant you should know

[slate heron]

That's the garden area

No

[proud iris]

but do you get it now? yes or no?

[golden nymph]

lol

[slate heron]

You have to understand how this works

[golden nymph]

ok

[slate heron]

Do you understand how this works

[golden nymph]

alpha is slope

so y/x

and beta is angle around

x

[slate heron]

Don't use the word slope if you have the angle instead

Are you trolling? @mortal escarp

[proud iris]

sorry, I am not native. I thought that was the right word, my bad

[golden nymph]

I'm confused as to why there are two different things describing what appears to be the same thing

[golden nymph]

I have a question

[slate heron]

He means the angle of alpha and angle of beta

Beta rotates around 1.5

Alpha rotates around 0

Of the whatever line

[golden nymph]

are you 13+

[golden nymph]

oooooooooooooooooohhhhhhh

[slate heron]

1+1 is 2, but 10+1 is 11

[golden nymph]

so the plane actually moves

???

<@&268886789983436800>

[slate heron]

Dude

[golden nymph]

say bye

[slate heron]

Why

Quite sad

[topaz scaffold]

Oof

[golden nymph]

me?

cmon wtf fr

[slate heron]

Lol yeah

He got instabanned

For asking 1+1

So sad

[golden nymph]

umm

internet safety?

9 year old?

[slate heron]

Yeah I know

[golden nymph]

come on?

[topaz scaffold]

Oof

[golden nymph]

am I evil?

[slate heron]

No?

[golden nymph]

😢

idk man thought it was the right thing idk

[slate heron]

Yes it was

[golden nymph]

where are you ploruto-san

@proud iris

[slate heron]

I'm just saying it looks sad from his end

[tame falcon]

Yes, Discord ToS dictate that users under the age of 13 shouldn't use it for reasons of legal consent. Major servers are kinda obliged to deal with clearly underage users.

[proud iris]

I downloaded blender 1 sec

[golden nymph]

but ngl 9 year olds take dope stuff

[slate heron]

Hahahaha

Blender for this

[golden nymph]

I am sure we learned about zero in 3rd grade

and he taking fractions

[proud iris]

seems to be hard to understand for him so I wanna help him

[slate heron]

All the plane does is pitch and roll

[glass lichen]

almost like... curriculums are different across the world

[golden nymph]

yeah teh angles confuse the heck out of me

[tame falcon]

I encourage mathematical curiosity among younger users as well, but this is more of a Discord thing.

[golden nymph]

so it rotates arounf a line of greatest slope?

fk Im confused

I know how planes work

lol

but idk what the plane does

[slate heron]

The roll axis seems to be the middle of the plane

[golden nymph]

aurcraaft*

[topaz scaffold]

So why not just have x y and z basis vectors and then apply rotation matrices for alpha and beta?

[slate heron]

However the pitch axis being one of the edges of the 3d cube

[golden nymph]

I am not sure though it seemed to be 3 different things up till now tbh

[golden nymph]

is that what the alpha does or is it the beta

lol

[slate heron]

Alpha is pitch (but imagine the pitch axis to be at the tail of the plane)

Beta is roll

[golden nymph]

that makes sense

he said beta is about the x-axis

which is what you are saying the alpha does

[slate heron]

Yes... Which is technically true

[golden nymph]

which is the source of the confusion

[proud iris]

do you get it or do I have to continue to struggle in blender xD ?

[golden nymph]

All I get is that I want to die

jkl

jk

I am ok

somewhat

but didn't get it

[proud iris]

I got it

0deg to 30 deg on beta

10

30

the origin point is bot left in the back

@slate heron how would you go about solving this problem with trig?

[slate heron]

Probably plug in the angles into a tangent function, get a slope,

Then use the y = mx graph where m is the slope to find where the point's would exist on y=3

If you're turning that on beta, then use tangent again except I think there's more math into that I can't quite say for sure

It's a bit complicated for me to do in my head

[proud iris]

need blender? 😄

[slate heron]

No it's just

I guess you gotta think the cube from a eagles eye view when you do the beta

Except the origin is at 0,1.5

[proud iris]

wait, if the origin of the plane is 0,0,0 every straight cut should be possible be adjusting alpha and beta right?

or is this a mistake on my site

[slate heron]

Maybe I'm wrong by doing this with trig

Im not sure, sorry

[proud iris]

np. my head feels really weird. idk why. I am used to thinking all day hahaha. Math seems to be something different.

[golden nymph]

im back

ok

so I think it will be more than some simple trig as Louis said

that is beacuse the cross-sectional area is not a constant shape

and btw that rotation is nothing like you described

that is actually a rotation around the y axis

idk where you got the x from

my God that is complicated

I think my way to do it is

express the equation of the plane in Cartesian form in terms of the two angles

and given the coordinates of the point

find using the x and z the y coordinate on the plane

and then if the y of the point above that of the plane then the point is on the plane and vice versa

[golden nymph]

but that would be the big problem

so I need three points on the plane to define it

I have the origin

and beta is the angle from the x axis and a horizontal line on the plane

give me a formal definition of alpha

that's what I need

tell me exactly what is alpha

[proud iris]

okay one sec I'll try to express it as good as possible

[golden nymph]

I can consider a point at the same horizontal plane as the origin and which lies on the plane

I can use that to have the beta in my equation

(0,0,0) (cos beta,0,sin beta) and I need the final point

which will be on a vertical plane passing through the origin

[proud iris]

I can't follow you, but you don't have to help understanding it. I seem to have forgotten all math I learned until this point*
where should this last point be is there an image that can help me understanding it?

[golden nymph]

what Im saying is

give me a precise definition of alpha

I will tell you something

and tell me if I am correct

[proud iris]

okay

[golden nymph]

I start at the origin

move 3 units in the z direction

and rise alpha in the y direction

am I now a point on the plane?

if not

then I didn't understand what alpha is

[proud iris]

okay

[golden nymph]

is it an angle or ratio

[proud iris]

angle

i'll explain

origin is 0,0,0

now your point is 3,3,3 on y axis

[golden nymph]

x?

[proud iris]

alpha

xD

mb

[golden nymph]

this point is not on the y axis

this point is not on any axis

the y axis is when everything but y is 0

[proud iris]

if you have a triangle where the angle between two sides is 90. is that (sin of site a and b ) or (cos of side a and b)

I forgot but that's the explanation of alpha

[golden nymph]

wot

sin is a ratio

90 is an angle

don't confuse me

[proud iris]

sin-¹

[golden nymph]

yeah thatd be sin

so

is it

concentrate with me

the angle between the z axis and a line on the plane that lies on a vertical plane

?

[proud iris]

yes if I get you right, yes

[golden nymph]

or in other words the angle of elevation of a line parallel to the yz-plane and lies in our plane

if yes then I have all I need

[golden nymph]

(0, sin alpha, cos alpha)

[proud iris]

what exactly is that now? sorry for asking

[golden nymph]

that's the third point

now I can formulate the equation of the plane

and I will tell you what's next

ok

,tex \sin \alpha \sin \beta \ x + \cos \alpha \cos \beta \ y - \sin \alpha \cos \beta \ z =0

I hope that works

sht

[slate heron]

It's backslash

[golden nymph]

yeah noticed thanks

now how to make the x move a bit to the right lol

[slate heron]

You can't with spaces

I guess you can make a new line

[ocean seal]

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

[slate heron]

But wrap every line with $$text$$
$$text$$

[golden nymph]

lol I just made \ space

[ocean seal]

Louis

[slate heron]

That works

[golden nymph]

nah this is boring

thx anyways lol

[golden nymph]

@proud iris

[proud iris]

yes

[golden nymph]

look

see that cute equation?

[proud iris]

yes

[golden nymph]

I'll tell you what to do

so you have a point

and you want to determine whether it lies above or below the plane

ok?

You substitute the x and z coordinates of that point in the cute equation

z my bad

and solve for y

that y is the y coordinate of the point lying on the plane with the same x and z as your original point

let's call it y-plane

so compare your y-point which is the original thing with y-plane

if the point is above the plane the y-point is greater than y-plane and vice versa

is that what you wanted??

[proud iris]

if I get it right yeah. lemme try to fully understand you equation and then I'll come back

just gimme a couple of minutes

[golden nymph]

my equation is just and equation of a plane

it just means that every point on the plane satisfies this equation

and alpha and beta are just your constants which you know the values of

[proud iris]

I'll have to code a ton of stuff to test it but I wanna thank you already. 👍

( @golden nymph the equation still works if alpha is negative, right? )

[golden nymph]

waaaaaaaaaaaait

umm

by generalisation it should but lemme think about it

yeah it should work

the greater y belongs to the one abpve

[proud iris]

I mean it doesn't have to be negative. instead of -90 I can write 270 so I shouldn't be a problem

[golden nymph]

and beta negative too

so whatever sht you put in the angles it will work

waaaaaaaaaaaaaait

wwait

wati

wati

[proud iris]

wait

[golden nymph]

wait

90?

[proud iris]

my bad

[golden nymph]

the plane would be vertical!

that and -90 are a special case

whatever the point is

the equation of the plane will return math error

[proud iris]

yeah I know, and I won't use 90 don't worry

[golden nymph]

you can visualise it to understand what I mean

yeah sure ok have fun with the plane of your lol youre welcome

[proud iris]

is ZozzTheBoss your internet alias ?

@golden nymph so if this gets published I can give credits to you for the math

[golden nymph]

yeaaaaaa

cool I guess

math by ZozzTheBoss

I like that lol

[proud iris]

so ZozzTheBoss or are you know for a different name?

[golden nymph]

yeah that works

[proud iris]

kk

[hardy acorn]

given the function f(x)=-2c+cx-x^2 and f-1(5)=-1. how would i find c

[sage bronze]

$$f(x) = -2c+cx-x^2$$
$$f^{-1} (5) = -1$$

[ocean seal]

HELLOBELLO

[sage bronze]

first find the inverse of f(x), then replace x with 5 in the inverse function and equate it with -1.

[ionic jewel]

see #help-2 for how to do that ^

since you multiposted against the rules

[alpine sable]

q4 2nd part

can somebody have a look over that question pls

[small bear]

in the first part you calculate all the possibilities, now for the second part, calculate all the combinations such that Miss X and Mr Y are together

then you simply subtract the first with the second part

[warm sky]

Does anyone have any good resources about reverse functions?

[gray isle]

wdym by reverse function

[alpine sable]

https://cdn.discordapp.com/attachments/326138757474680852/874498430263783474/unknown.png

can smo helpp

[gray isle]

What have you tried?

[sage vale]

can't figure this out

[empty raptor]

The normal of SD through A is half the length of SD

[grave ledge]

A plant fertilizer contains 15% nitrogen by mass. In a plant food container
soluble there are 0.285 kilograms (Kg) of fertilizer. How many grams of nitrogen are in the container?

[empty raptor]

0.285 * 0.15 * 1000 ? Either that or not enough information

[grave ledge]

thanks

[alpine sable]

Hey guys, I've solved 1.

but I'm not sure how to approach part 2

I'm not exactly sure what assumptions im allowed to make.

thus far, ive assumed that mu is the eigen value of p(A)

and have assumed that A does have a eigenvalue lambda

and then im trying to show mu = p(lambda)

is this the right approach?

[sage vale]

I'm struggling to even read that question...

not smart enough sorry

[gray oxide]

Quick question derivate is rate of change does it have a direction as in can it be negative or positive?

Or does it only say what rate something is changing at and not what direction?

[round citrus]

It does have a sign

[gray oxide]

Does that mean yes?

[ocean dew]

HELP! im trying to learn complex numbers on my own and i just didnt know to do this

its in french

but i need to find the modulus nd the argument

[supple tundra]

Yes. If something has a negative rate of change, it means that quantity is decreasing with respect to some other variable

[gray oxide]

Thx :)

[solar cradle]

@ocean dew expand out the square and and get it in the form $z = a + ib$ then multiply by the conjugate to get the modulus and use de Moivre's formula to find the argument

[ocean seal]

Billy Clintorus

[ocean dew]

@solar cradle thnks ill do that

[tight rover]

how can I solve that?

[ocean seal]

SubGui

[alpine sable]

I need help calculating how much I make an hour. I make 100,000 game coins every 15 seconds, can someone calculate how much that is per hour?

[steel ermine]

24,000,000

100,000/15 = 400,000/60 = 400,000/(1min) = 24,000,000/(60min) = 24,000,000 per hour

[stable mauve]

I don't remember as much Algebra as I should. I'm teaching my son; we're doing well.

He has a line graph from -2 to 2.

The question states: write the letter of the point that represents -3/2
Read: negative 3 over 2

A is between -2 and -1, B is between - 1 and 0, etc.

What's this answer and can someone point me to a good resource to be able to teach this properly?

[alpine sable]

Khan academy is generally good

Also, this would be easier to answer if you sent a picture of the graph

[tight rover]

I don't know

I don't know, all the info I got is that:
$Let f(x)=x^2$

[ocean seal]

leonardomoura

[tight rover]

$g(x)=af(x-b)-c$

[ocean seal]

leonardomoura

[stable mauve]

@alpine sable

[alpine sable]

So for this one what I would do is actually divide -3 by 2

Which gives you -1.5, and is easier to place on the number line

[stable mauve]

That's what I was assuming. Google failed me. Thank you @alpine sable

[alpine sable]

You’re welcome

[ashen agate]

?

<@&286206848099549185>

[glass lichen]

#❓how-to-get-help

[carmine lion]

lol

for this question, im not gtting the correct answer for part a

i havn't tried (b) yet

should i integrate with respect to x or y?

[alpine sable]

@carmine lion

[carmine lion]

yes?

[alpine sable]

omg i had the same questions

In my test

[carmine lion]

???

[alpine sable]

But the problem is that i dont know english

[carmine lion]

im not doing a test

as u can see the watermark for "do not copy"

[alpine sable]

@carmine lion what site is that

[carmine lion]

its my class hw

[icy trail]

have you drawn the diagram?

[carmine lion]

yes

[icy trail]

looks like you'll have to integrate

[carmine lion]

i know loll

is the area from x=-5 to 1

what way should i integrate

with respect to x or y

[icy trail]

with respect to y

[carmine lion]

why

[icy trail]

because its the area from the curve to the y axis

[carmine lion]

so area = $\int_{0}^{6} (y-5) ,dy$

[carmine lion]

is that right

[ocean seal]

abe

[icy trail]

yes

nice

[carmine lion]

i know the answer is 18

because i used area = bh/2

[icy trail]

[carmine lion]

but my integral won't evaluate to 18

[icy trail]

oh dam

[icy trail]

idk if this is right

the area to the left of the axis is negative?

[carmine lion]

yes

so i split it into 2

[icy trail]

i think this should be x+5

because x+5 = y

[carmine lion]

so??

you just said integrate with respect to y

[icy trail]

mmmmm yes I'm confused now

[carmine lion]

uh

so what do i do

[icy trail]

i think we were right with the first integral that evaluates to -12

did you do your triangles right

0.5 × -5 × 5 - 0.5 × 1 × 1

= -12

[carmine lion]

where did u gt the 1*1

shouldn't it be the length of the triangle = 1-(-5)

and the height it 6-0=6

so area = 1/2 * 6 * 6

[icy trail]

there are two triangles tho?

[carmine lion]

wdym 2 triangles

[carmine lion]

do you mean that

or do u mean thee whole triangl

[icy trail]

that top area isn't between the y axis and the line

[carmine lion]

that?

[icy trail]

the top triangle should be (0,5) (0,6) (1,6)

yes

nice

remeber the larger area is negative

[carmine lion]

how do u know which triangle they mean

[icy trail]

it says between the line and the y axis

[carmine lion]

ok

so i take the abs(area from 0 to 5)

• area from 5 to 6

[icy trail]

you don't need the abs, we care that the area is negative

wait nvm i don't think we do

yeah that sounds good then

[carmine lion]

lol

wait so

the answer is 13?

[icy trail]

ye

[carmine lion]

ok so

similarly

for part (b)

its the weird cureved triangles right

[alpine sable]

i dont get it lawl

[icy trail]

mmm you should probably integrate it properly

[carmine lion]

im integrating properly

[icy trail]

nice

[carmine lion]

those are correct right?

the bottom area is negative

so i put a negative sign on its integral

[icy trail]

no they're both positive

its with respect to the y acis

axis

[carmine lion]

huh?

[icy trail]

they're both "above" the y axis

[carmine lion]

why

[icy trail]

a negative area would be to the left of the y axis

[carmine lion]

i dont get what u mean

oh

i see

so 28/3 u^2?

[carmine lion]

so i can do 1 integral

without separating

bruh ok

this gonna take some time for me to get better

[icy trail]

that's how most things work lol

[gaunt magnet]

write vector and parametric equations of the plane

someone solve this for me

thanks

[wild onyx]

What have you tried on this?

[hasty ferry]

alguien que hable español??

[gaunt magnet]

i did but cant even start

[gaunt magnet]

<@&286206848099549185>

[wary stream]

People aren't here to do your work for you

[gaunt magnet]

Lol that mosh kid reacted on purpose

[gaunt magnet]

no i just started calc and vectors so if u do it for me

basically im learning

[wary stream]

No, no one is going to do your work

[gaunt magnet]

so even if u teach me for hours, i wont understand

WtF

[wary stream]

You make an attempt

[gaunt magnet]

so how am i gonna do my homework now 😖

[gaunt magnet]

impossibl

e

[wary stream]

You show that attempt and where you are confused at, and we help

[gaunt magnet]

yes

so how to start

[small holly]

how do i do the third column (sin190)
i tried subtracting and adding 180 to 190 but it was wrong

the answer is 350 degrees but idk how they got 350 degrees

[ionic jewel]

360-10

[small holly]

why would they minus 10?

[ionic jewel]

ericW is typing an explanation presumably

[glass field]

yeah i can delete it though

[small holly]

alright

[ionic jewel]

no u got it

[glass field]

like the problem said, the unit circle is helpful for these (but only if you understand both it and how the sin and cos of angles represent y and x values etc)

is that helpful or no?

[small holly]

im just confused at why i would need to know how sin and cos of angles represent y and x values

[glass field]

see how both 30 degrees and 150 degrees have the same y coordinate? like if you go along the line from the center of the circle to the edge

they will have the same sin as well

the same is true for 190 and 350

[gaunt magnet]

yes

i see

[small holly]

oh alright

[candid hill]

guys

can you give me the formula for kinetic energy?

i am studying our lesson advance]]

uwu

[oak chasm]

@candid hill This is more of a mathematics server. There's a physics server listed in #old-network that might help more.

[candid hill]

ohh sorry

i give you vodka huhu

[fallow hollow]

Hey there, got a proof problem:

I'm looking at a right now, but I've always sucked with proofs. Would this involve using the limit definition of derivatives? I know that dy = f'(x)dx, but I'm not quite sure how to use this definition in a way that doesnt seem circular

[austere bridge]

Yeah, you'll have to use the limit definition with $f(x)=x^n$

[ocean seal]

cgodfrey

[austere bridge]

(for part a)

[ionic jewel]

yeah i imagine the limit definition would work great

[fallow hollow]

So I can show that f'(x) equals
$nx^{n-1}$
for f(x) = x^n using the limit def, and then do I just plug that into the definition for the differential dy?

[ocean seal]

Vaporwave Morgan

So I can show that f'(x) equals
 $nx^{n-1}$
 for f(x) = x^n using the limit def, and then do I just plug that into the definition for the differential dy?
```Compilation error:```! Missing $ inserted.
<inserted text> 
                $
l.57  for f(x) = x^
                   n using the limit def, and then do I just plug that into ...
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```

[gaunt magnet]

Hello

check my work guys

and tell me

if i do right

[oak chasm]

@gaunt magnet Sorry, channel is busy.

[gaunt magnet]

oh no!

ok

[austere bridge]

I'm not too familiar with differentials, but I believe so, yeah. The hard part is using the limit definition to show that $f'(x)=nx^{n-1}$

[ocean seal]

cgodfrey

[fallow hollow]

Okay, thanks!

[tranquil sierra]

What's happening here in general? I'm sorta immediately lost

[ionic jewel]

multiply the second term by sqrt(x-1)/sqrt(x-1)

to get common denominator

[tranquil sierra]

Wouldn't that give me another 1

[icy trail]

where? you're multiplying the root by one, it dosent change anything

[tranquil sierra]

Ok, I'm completely lost

[wary stream]

Do you know how to find a common denominator?

[tranquil sierra]

HCF?

[broken nova]

$$\frac{1}{\sqrt{x-1}} + \frac{\sqrt{x-1}\sqrt{x-1}}{\sqrt{x-1}}$$

oooof

[woeful pulsar]

Well, worst case you can just multiply the two denominators together

[broken nova]

ignore that pls

[woeful pulsar]

$\sqrt{x-1}=\frac{\sqrt{x-1}}{1}$

[ocean seal]

Element118

A random flying SR-71

[woeful pulsar]

and then add the two fractions by just using the product of the denominators as the new denominator

or that

[broken nova]

There you go

[sharp lodge]

is square root 15's answer only 3.872, no other simplified answer?

[broken nova]

root 15 is the most simplified it can get

[tight rover]

$x=\fraction{{\sqrt9}2^3}{log{1024}2.4$

[ocean seal]

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

[wary yew]

I have a question I'm trying to figure out

What is 4,200,000,000 x 4,200,000,000 spelled out?

And then could you take that same number from the answer and multiply it by itself again? I'm trying to fo figure out how big an area in minecraft is if going from oneside of the map to the other is 4,200,000,000 blocks on the X coordinate and also the same 4,200,000,000 blocks on the Y coordinate but I want to find the number spelled out and I can't exactly seem to find an answer for that

[woeful pulsar]

do 42*42 and multiply by the appropriate power of 10 first

let's work it out step by step and see where it takes us

[wary yew]

alright i'm horrible at math but let's try it

so 42*42 x 10?

17640?

[woeful pulsar]

an appropriate power of 10

like 20 * 30 is 600 because 20 contributes one power of 10 and 30 contributes one power of 10

so there's 2 powers of 10 in total, which means the answer is divisible by 100

[icy trail]

42 x 10^8 x 42 x 10^8

[wary yew]

Sorry I'm just...really bad at math, no disrespect just trying to understand so give me a sec to read and try and understand this 😅

[icy trail]

so 42^2 x 10^16

[wary yew]

so 1.764E19?

[woeful pulsar]

that's one way to put it, let's write it in long and write commas for each group of 3 digits

[wary yew]

I would rather do that yes

I don't know how to do that though

you mean like? 1,700,600,400,190,000??

idk man 😰

[woeful pulsar]

the number wouldn't split up like that

it'll look more like this
17 640 000 000 000 000 000

remember the 19 is just part of the exponent and it isn't part of the digits

[wary yew]

oh I wasn't aware of that fact tbh

[wary yew]

so that number would be the answer to 4,200,000,000 x 4,200,000,000?

[woeful pulsar]

the numerical answer

[wary yew]

okay so

[woeful pulsar]

but what you want is in words

so we have to change it to words

[wary yew]

no not words just spelt out like that sorry 😅

See I'm using Minecraft as a template for this question

[woeful pulsar]

oh i thought you wanted it spelt in words lol

[wary yew]

and I'm trying to figure out if going from one side of the map is 4,200,000,000 right

and up is also 4,200,000,000

how many blocks

are in the entire area

like it's a square 4,200,000,000 blocks on every side

so how many blocks are with in

so I guess I'm trying to find the area???

length width height type of thing??

[woeful pulsar]

volume

is that what you are trying to find? @wary yew

[wary yew]

I guess??

I just want to Know how many blocks fill that area so yeah I guess Volume

[woeful pulsar]

yeah so all it is to multiply the mutually perpendicular length, width and height.

[alpine sable]

If I kept repeating the alphabet (starting back at A after Z), what would be the 250th letter?

If I kept repeating the alphabet (starting back at A after Z), what would be the 250th letter?

[warped blade]

hi guys dumb question here
0-(2(-5)) = -10 but 0-2(-5) = 10
am I right?
first I get -10 because in the first sentence the 2 is inside the parenthesis then i get the result and negate it but then i get 10 because the number that multiplies is negative (-2)

or in other words the sign besides the number determine its number even if that number was part of a calculation (?

[wary stream]

It should both be 10

[wary yew]

<@&286206848099549185>

[wary stream]

Not entirely sure how you got -10 in the first one

[warped blade]

yeah you're right i checked the calculator

xDD i'm dumb i'm sorry

but 0-2(-5) = 10

[oak chasm]

@wary yew How many blocks deep is it?

[warped blade]

is 10 because even though i'm subtracting in the first place i'm multiplying two negatives?

[wary yew]

4,200,000,000

[oak chasm]

No, Minecraft is not that many blocks high.

[wary stream]

Two negatives makes a positive

When multiplication happens

[wary yew]

it's a mod coming out called Dragon Block V, and the space zone is 2,1 billion blocks all directions

they really pushing the limits, and I go curious at how many blocks are actually in that area

[oak chasm]

OK, if it's in all three dimensions, then you multiply the height times the width times the depth.

So, the height, width, and depth are 4.2 billion.

[wary yew]

right

[oak chasm]

4.2 billion times 4.2 billion times 4.2 billion.

Cube 4.2 (multiply three of them together).

What's that?

[wary yew]

I got 7.4088 x 1028

[oak chasm]

No, that's not it.

What's 4.2 times 4.2 times 4.2?

Oh, sorry, let me recheck.

Yes, that's right.

7.4088 times 10^28.

[wary yew]

now what would that look like written out?

That's what I been trying to figure out lol

[oak chasm]

OK, so 10^28 has 28 as the exponent.

Here's how to use it.

It's positive, so the number will get bigger.

So, move the decimal point to the right, which makes the number bigger, 28 decimal places.

7.4088
74.088 (1 place)
740.88 (2 places)
7408.8 (3 places)
74088 (4 places)
Add 24 more zeroes.
74088000000000000000000000000 (28 places)

[wary yew]

74,088,000,000,000,000,000,000,000,000

?

[oak chasm]

No, that's way too many places.

[wary yew]

oof

ah 24 zeros

I added 28 decimals

[oak chasm]

No, you added more than 28.

Each zero is a decimal place.

You have over 30 zeroes at the end.

[wary yew]

OH

EACH ZERO IS A DECIMAL

like that?

[oak chasm]

Yes, that's good.

You move the decimal point until it's at the end (that's 4 of them). Then you add 24 zeroes (that's 24 more of them). 4 + 24 = 28 places.

[wary yew]

ah okay

Thank you so much 😄

[oak chasm]

If the exponent on the 10 is negative, you make the number smaller by moving the decimal point to the left.

No problem.

[wary yew]

got it thanks

[tropic ice]

needhelp

not sure where i went wrong

[glass lichen]

it's... not wrong?

[tropic ice]

oh

really

the answer looks so ugly

can i simplify it any further?

[glass lichen]

it's not that ugly...

[covert berry]

Prove that if $x + y + z = \frac{1}{x} + \frac{1}{y} + \frac{1}{z} (x,y,z \in \mathbb{R}^{+})$, then $x + y + z \le 3$.

[ocean seal]

moono

[covert berry]

I need to prove this to finish my proof of an inequality.

Nevermind, it is false. 😓

[robust verge]

Hello everyone, I'm new here and I'm actually self-studying what some people call "The Fundamental Concepts of Mathematics" or "Discrete Math"

I'm currently practicing direct proofs, and I was wondering if someone can tell me if the solutions I made for a few items are correct or need some fixing? ☺️ Thank you

[tropic ice]

get a notebook!!

[solar cradle]

Looks good, I don't see any errors, I would say one small thing is you may want to specify a = 2 k +1 for some k in Z, instead of saying for k in Z

And lined paper sucks imo lol

[tropic ice]

i got this thing called a remarkable 2 a week ago

and its so nice for everything

its like paper but just digital and all in one place

[cinder sundial]

It asks for the solution

But Z isn’t a variable

[plush wagon]

Example 28 , solution, line no.8

Please tell me what they mean by Xo/2 < Xo?

And X1 +1 /2 > X1

, rotate

[glass field]

@cinder sundial one way to do this is by having z = (a+bi) and then setting up 16-30i = (a+bi)^2 and then expanding and solving the system of equations

another way to approach it would be to use properties of complex arithmetic regarding angles and lengths, etc

i solved it using the first method

[cinder sundial]

about angles and lengths?

i dont get it, does complex related to angles and lengths

[glass field]

thinking of complex numbers as vectors in 2 space... if you multiply 2 complex numbers togetehr you add their "angles" and multiply their "lengths", yes?

[cinder sundial]

"vector" thats beyond my level

i'll try the first method

but its kinda weird tho

cuz Z is a known value and it asks me to find the solution

wtf

[glass field]

z is some complex number right?

[cinder sundial]

yes

[glass field]

where when yo square it you get 16-30i

[cinder sundial]

yes

[glass field]

so z = a+bi for some a and b that are real numbers, yes?

[cinder sundial]

yes

[glass field]

our goal is to find the a and b

[cinder sundial]

i did

[glass field]

then youre done

[cinder sundial]

5-3i and -5+3i

wait

what

wdym

[glass field]

i think one of those is incorrect however

or both perhaps

[cinder sundial]

it asks for the solution of z^2-(1+i)z-(4-8i)=0

z=5-3i, -5+3i. z^2=16-30i

[glass field]

yeah thats right

i mean you didnt post the whole problem i guess?

[cinder sundial]

yes, i been asked to find the z's value first

[glass field]

so youre done, right? you found the z's satisfying the square you wanted

[cinder sundial]

yes

then i have to find the solution

find the solution of z^2-(1+i)z-(4-8i)=0

damn

whatever

[alpine sable]

is this channel done now or

[cinder sundial]

yes

[amber hollow]

the answer is c right?

[glass field]

id approach that one the same way @cinder sundial

set z = a+bi and solve for a and b

[cinder sundial]

but i already solved the value of z

but i dont know what the question mean, "it asks for the solution of z^2-(1+i)z-(4-8i)=0
z=5-3i, -5+3i. z^2=16-30i"

[glass field]

i mean from where im sitting it sounds like two different problems since z's satisfying z^2=16-30i are -5+3i and 3-5i... and the ones satisfying the other quadratic are different

[dawn galleon]

<@&286206848099549185>

[wispy olive]

Let me try.

[dawn galleon]

ok ty

[acoustic shadow]

Don’t ping helpers before 15 min,
In such q take any of the components as 0 suppose z=0 that means the intersection happens in xy plane

[wispy olive]

This is the answer.

And let me show you how to do this.

xD.

This is how you do this.

Just take a Graphing calculator, put the 2 equations and the graph will come.

[oak chasm]

How is a line a single point?

[wispy olive]

?

I think they mean the point of interesection.

[oak chasm]

It says to find the line of intersection of two planes.

You have two lines instead of planes.

[oak chasm]

You get a point instead of a line.

@reef pebble Sorry, channel is busy.

[reef pebble]

oh

[wispy olive]

And that image is not even understandable.

[wispy olive]

Yes, but I think they mean find the point where the lines intersect.

Grammatical mistake probably.

[oak chasm]

No, they definitely don't.

[wispy olive]

Then?

[oak chasm]

Do you see the x, y, and z in the first equation?

[wispy olive]

How can they intersect at a line.

[oak chasm]

Because they're planes, not lines.

[wispy olive]

Just make a line about the line.

[oak chasm]

Do you see the z in the fidrst equation or not?

[acoustic shadow]

This is NOT how you do it,where’s the math behind it ?

[wispy olive]

Oh it is going 3 variables? I am out.

I only know 2 variable linear equations.

[wispy olive]

Uhhh how? And why not?

I like how the person who asked the question just went away like that lmfao.

[acoustic shadow]

Because this is a math channel,where as a helper you’re supposed to tell the meaning of the q and how it’s done and it’s math

[wispy olive]

Oh.

Very well then.

If he comes.

And asks for it.

I will give 1-2 paragraph long explanation.

[unborn dome]

can someone help me out with this question?

[acoustic shadow]

That nobody knows where he left lol

[wispy olive]

Lol yes.

[oak chasm]

@unborn dome Sorry, channel is busy.

[unborn dome]

got it, sorry

[wispy olive]

Thank you for guiding me as I am a new helper!

[dawn galleon]

i got

[dawn galleon]

i didnt get that i got

[wispy olive]

Now let me tell you how you solve such equations.

[solemn grotto]

Mac catches a certain number of fish on their first day fishing. On their second day of fishing they catch one more fish than the first day. On their third day of fishing, they catch one more fish than the second day. If they catch 63 fish in total, how many fish did Mac catch on each day?

What would be the formula

[dawn galleon]

so
x+5y-3z-8=0
y + 2z - 4 = 0

rearrange the second as
y = 4 - 2z

then sub this into the first equation and simplify
x + 20 - 10z - 3z - 8 = 0

Answer = 13z-12

this what i got

[wispy olive]

So there are 2 variables and 2 equations.
Both of the equations form a line. The point where these 2 these lines intersect is what you need as the answer, probably(since in the question you mentioned the line where they intersect instead of the point where they intersect).

[wispy olive]

Wait. It has 3 variables?

Sorry, I have no idea about equations in 3 variables.

Maybe some other person can help you.

[dawn galleon]

ye i got 13z-12

i not sure if im correct

[wispy olive]

The formula should be -
x + (x + 1) + (x + 1 + 1) = 63.

[oak chasm]

@solemn grotto @wispy olive Sorry, only one question in a channel at a time.

[wispy olive]

So this becomes 3x +3 = 63.
=> 3x = 60.
=> x = 20.
Hence the answer is 20.

[oak chasm]

#help-5 is open if you hurry.

[wispy olive]

Ah alright.

[dawn galleon]

[wispy olive]

I answered the question anyway.

[dawn galleon]

charli.t.rex am i correct for my question

[oak chasm]

@dawn galleon Should be an equation.

I don't know how to do the problem, but I can probably check it.

You take two points on the line equation and see if they're on both planes.

[dawn galleon]

oh hmmm. oh

[oak chasm]

So, get an equation and we'll check.

[wispy olive]

I have no idea what It means but maybe this graph helps.

Or you can use Geogebra yourself.

[hardy mirage]

How can I solve this?

Oh nvm

Didn't see that ST is 4 cm

Sorry

[wispy olive]

Lmao.

Happens.

[sour cosmos]

Can anyone help me with converting a standard form equation to vertex ?

[wispy olive]

Yes.

Would you like videos on it?

Or a text explanation?