help-0

[ocean seal]

Dogecode

[runic canopy]

That sounds so simple

May i post another question here? Or yall trying to solve this one

[grim delta]

when it works it is
But later you’ll find cases where you have to do more steps of lhopitals to get there, or where it doesn’t work at all and you need to use other methods

Fun stuff

[runic canopy]

Math is so interesting 😂 i am just behind and all which i hate so much

[grim delta]

there’s probably an integral here
I can’t remember how to do it though

[runic canopy]

What if limit is an inf? I heard that when that happens, it is better to graph first…

[wintry vortex]

this room being used?

[fathom sequoia]

no

if you see a question hasn't been asked for this amount of time it' spretty obviou

[wintry vortex]

xD true, just being curtious

how do i get Ax and Ay out of this?

I know to get the magnitude its r=sqrtAx^2+Ay^2

but idk how to find Ax and Ay

[wary stream]

Sine and cosine

Recall that sine is normally for y component and cosine is for x component

[high palm]

hey are you guys still using this?

@wintry vortex

@fathom sequoia

[wintry vortex]

yes sorry just trying to understand lol

[high palm]

all good

[wary stream]

https://www.khanacademy.org/science/in-in-class-11-physics-cbse-hindi/in-in-11-motion-in-a-plane-hindi/analyzing-vectors-using-trigonometry-hindi/a/2d-kinematics-vectors-analytical-ap1

That should help a lot

[wintry vortex]

I cant open that on here 😦 im at work lol

my net is just barely able to do discord

and sometimes stops being abel to do that

[wary stream]

That's explains everything vector wise

[fathom sequoia]

no

[wary stream]

The components and angle

[wintry vortex]

so to fibd Ax would I use sin(theta)=A

[eternal cave]

Is this right?

[opaque iron]

Guys I need help with something

[fathom sequoia]

Dont ask to ask

[wary stream]

Yes, but don't interrupt next time

[fathom sequoia]

and this chanel is busy

DM me if you want

[eternal cave]

I’m so sorry

[opaque iron]

I saw a minecraft video with a waypoint set and I want to use triangulation to find out the coordinates of it

[wary stream]

Not in this channel, ask in a different one

[wary stream]

Recall that I said x component is cosine

Not sine

[fathom sequoia]

ask on a different channel for gods sake

😠

[opaque iron]

Y’all have no chill

[fathom sequoia]

also your question is unasnwereable

no one is going to answer that

[opaque iron]

Why

[fathom sequoia]

because it's too broad

[wary stream]

It's not having no chill, it's the fact that you're interrupting

[eternal cave]

ITS NOT A STUDY QUESTION

[wary stream]

There is currently someone here getting help

[fathom sequoia]

'how do I find the meaning of the universe'

[opaque iron]

I can show the screenshot it also has how many meters away it is

[wintry vortex]

lmao

[opaque iron]

And the direction

[wintry vortex]

im just gunna talk through him lol

[fathom sequoia]

ask on a minecraft server

[opaque iron]

Like they would know how to math

[wintry vortex]

so it would be cos(theta)=A to find Ax?

[wary stream]

Yes

[wintry vortex]

and sin(theta)=A to find Ay?

im gunna reppost the problem since its so far up

[fathom sequoia]

if you direct message me your question with details I will help you

[wary stream]

Yes

[fathom sequoia]

if it's over grade 11 I can't

[wintry vortex]

would I plug thetaA in for theta?

idk if the tiny A and B change the problem

[wary stream]

The problem wants you to find Ax, Ay, Bx, and By then combine the components that are in the same axis, so Ax + Bx and Ay + By

Then find the resultant of that, using Pythagorean theorem

[wintry vortex]

A^2+B^2=C^2?

[devout sigil]

Yes

[wary stream]

Yes

[wintry vortex]

ok, where does the theta a and b come in to play?

[wary stream]

Magnitude is Pythagorean theorem

[wintry vortex]

ive never seem those before

[wary stream]

I'll give you how to do one component, and you handle the rest, okay?

$$A_x = A \cdot \cos(\theta_A)$$

[wintry vortex]

cos\theta =364 I did that

[wary stream]

Then fill in the values. If A = 364, and $\theta_a = 226.4$

[ocean seal]

dldh06

[wintry vortex]

To get Ax, was that wrong?

[wary stream]

Sorry

It's cosine

My bad

[ocean seal]

dldh06

[wary stream]

Fixed

$$A_x = 364 \cdot \cos(226.4)$$

[wintry vortex]

ok lemme do it real quick

[wary stream]

Make sense?

[ocean seal]

dldh06

[wary stream]

For Ax?

[wintry vortex]

well i see that i didnt know the proper formula now lol

[wary stream]

You can apply the same concept for Ay

And Bx and By

Except for B, you have a different angle and value to use

Compared to A

[wintry vortex]

dam got it wrong lol

A_(x)=364cos(226.4\deg )

got -251

did i mess it up somewhere in there?

[wary stream]

No that's right

If you can imagine, where is 226.4 degrees with respect to 0 degrees

Like which quadrant

[wintry vortex]

quarant 1 or 3

[wary stream]

226.6

[wintry vortex]

cause x is positive in those

idk

[wary stream]

If it was drawn like this

What quadrant is 226.6?

[wintry vortex]

3

bot left

[wary stream]

Yes, and what direction is x?

Positive or negative?

[wintry vortex]

positive

[wary stream]

No

[wintry vortex]

226.4? isnt that positive

[wintry vortex]

im confused lol

[wary stream]

If 226.6 is in quad 3

Then the vector points something like that, correct?

[wintry vortex]

yes

[wary stream]

So what direction would x be pointing in?

Look at where the arrow is pointing

[wintry vortex]

bottom left

[wary stream]

If you drew it along the x axis

What direction?

[wintry vortex]

the -251­° made sense then in that respect but it came up wrong

[wary stream]

If you drew the red vector along the x axis, it would be the blue vector, right?

[wintry vortex]

im gunna say yes but im not really following why it would be dead set on the x axis

[wary stream]

That's the x component of the red vector

The blue vector is the x component

[fast wave]

@wary stream

why did my teacher use Cos

for the x components

[wary stream]

Because cos = adj/hyp

[wary stream]

In relation to theta

[wintry vortex]

si why would the x component be sitting directly on the axis?

wouldnt that make it 180° instead on -251°

[fast wave]

why tho

[wintry vortex]

that helped me alot with that concept

maybe youll find that particular cheat sheet helpful to

[wary stream]

Also, please read the #rules and #❓how-to-get-help , because this channel is busy and you are interrupting. As well as don't ping people either

[fast wave]

How do we know its cos = adj/hyp?

[wary stream]

That red vector is not aligned along the x or y axis so you want to break it down into the x and y components, and those components will lie on the x axis and y axis

[wary stream]

Because it's a trig function

That's the rule for cosine

adj/hyp

[fast wave]

no like for this component

the x component

how do we know its this specific trig function

[wary stream]

Look at the angle, determine which side is adj, opp, and hyp

[wary stream]

Then determine the trig function

[keen trail]

@dark granite I have 2 questions that im stuck at

[wary stream]

Not in this channel, please

[wintry vortex]

okso why did my answer not work for this problem them?

I did A_(x)=364cos(226.4\deg )

[wary stream]

Because, it's not complete yet

[fast wave]

Yeah I figured the sides that are adj, opp, and hyp im confused on why we are using cos?

[wintry vortex]

Is the magnitude R?

[wary stream]

-251 is not the final answer

[wary stream]

Look at the angle, in relation to the sides

Determine trig function based on that

[fast wave]

?

[wintry vortex]

would the magnitude be sqrt Ax^2+Ay^2?

[fast wave]

I'm confused

[wary stream]

No

[wary stream]

$$\sqrt{(Ax+Bx)^2+(Ay+By)^2}$$

[ocean seal]

dldh06

[wary stream]

Everything is given in the diagram and with all the info I stated

[fast wave]

ur re-stating the diagram information

i dont understand the diagram

[wary stream]

It's a right triangle

[fast wave]

the reason the COS is used

[wintry vortex]

Because thats how that trig function works

and woah thats an intense equation 0_0

[wary stream]

Look at the angle, if you want x, the side along x is adj

[wary stream]

It's just finding the x and y components of A and B

[wintry vortex]

doing it now, ill brb 😄 wish me luck haha

[fast wave]

yeah so how do i know its not tan

[wary stream]

Then summing the x components and y components, then Pythagorean theorem

[wary stream]

Can you not read that diagram?

Find theta

[wintry vortex]

tan(theta)=Oposite/adjacent

[wary stream]

Find the x axis, what side is that in relation to theta?

[wintry vortex]

You know it because thats how the trig function works, thats a great diagram to show it

ima save that haha

[frail light]

can any one help me in my work

[wary stream]

Ask in #help-4

[fast wave]

adj

[wary stream]

And you have the resultant, what side is the resultant?

[fast wave]

whats resultant

[wary stream]

The side that's labeled D

To be more exact $\Delta d$

[ocean seal]

dldh06

[fast wave]

my hyp

[wary stream]

So you just stated adj and hyp, what trig function?

[fast wave]

how do u know its D

[wary stream]

You want to break down d into dx and dy

You don't know dx or dy but you know d

[fast wave]

i dont understand

how do I know d ?

[wary stream]

Because it'll be given

Or it would have been calculated

[fast wave]

d isnt given in the diagram

[wary stream]

Yes it is

[fast wave]

where

[wary stream]

I stated d at first but then said

That

[fast wave]

what

how do i know its d is my question

[wary stream]

$$\Delta d$$ is the side you are given

[ocean seal]

dldh06

[frail light]

any one tell

[wary stream]

Don't ask here

[frail light]

why

[wary stream]

Ask somewhere else

[frail light]

no

[wary stream]

Channel is being used

So please ask in a different one

[fast wave]

1000 x 0.20 = 200% profit

[frail light]

huhhhhh

[fast wave]

where does it say im given that tho

1000 x 0.20 (0.20) is 20%

[wary stream]

Ask in a different channel

[wary stream]

The hyp

That's normally given

Trust me on that

[fast wave]

bro what

[wary stream]

You are given $\Delta d$ and you want the x and y components of that vector

[ocean seal]

dldh06

[fast wave]

oh ur right

[wary stream]

Does it all make sense now?

[fast wave]

yesss

[wary stream]

So all the confusion is gone?

[wintry vortex]

WOOOOOOO! got it, 10 mins of math later

[frail light]

is these correct

[wary stream]

Channel is busy

[wintry vortex]

ty dl 😍

[wary stream]

Can you not tell?

[fast wave]

no im still confused about a few of the examples

E70S is changed why

[wary stream]

That's base on where you have the right angle

What exactly don't you get here?

[wary stream]

Did that all make sense? On why you had to find the components of A and B then add them up?

[wintry vortex]

yes, i just didnt know the proper equations

the examples are lacking

[fast wave]

for the theta

how did know to use tan?

[wary stream]

It's basically breaking down the vectors in the components, then summing x direction and y direction, the magnitude of that value

[wary stream]

Because you are given adj and opp

Look at the angle theta, determine the sides given based on that angle theta

[wintry vortex]

Boat, i learned this around a month or two ago and its really all about your perspective on the triangle. when you know which side is hypontenuse, oposite, adjacent, then you can figure out which trig function to use

you look for the function that works with the sides that you know

tan would be oposite/adjecent

[fast wave]

ohhh

[wintry vortex]

do if you know the angle and the oposite then you would plug them in to solve for adjecent

[fast wave]

so i use the givens to find out the unknown

[wary stream]

Yes

[wintry vortex]

tan(theta) is the angle

so if u know the oposite and adjacent u can plug them in and solve for theta

solve for degrees and itll tell you the angle

sorry to off topic, but how would I find resulting angle?

At this point I have 2 right triangles right?

would I have 2 different degrees?

[wary stream]

What was (Ax + Bx) and (Ay + By)?

[wary stream]

No, it's based off (Ax + Bx) and (Ay + By)

[dark granite]

okay, what are you confused about?

There's a lot of messages here and I don't wanna read em all, so could you please catch me up to speed?

[wary stream]

Resultant direction

Currently

[wintry vortex]

i was trying to help boat with that message 🙂

[dark granite]

ahhh

[fast wave]

what is even going on her

[dark granite]

vector sums

[fast wave]

hereyeah

[wary stream]

But boat is confused on something

[devout sigil]

It’s one triangle

[wintry vortex]

So since I got -156 for Ax+Bx would I then add 360 to make it positive?

[wary stream]

No

[dark granite]

I'm reading it rn

[wary stream]

Negative sign helps determine quadrant for angle

Next Ay+By?

[wintry vortex]

-473

[dark granite]

@fast wave this is only a bunch of trig. Forget about vectors for a moment and just think about triangles

[wary stream]

Does this diagram make sense to you?

[wintry vortex]

Not really

[wary stream]

-156 is Ax + Bx along the x axis

498 is the resultant/magnitude

-473 is Ay + By along the y axis

The negative sign helped me point in that direction

A little edit, just added -y and -x

[fast wave]

yea

[wintry vortex]

ok i get the negative part but where did the 498 come from?

[wary stream]

That what the answer you got

[wary stream]

Here

498

[wintry vortex]

ohhhh

my brain is getting all twisted from math haha

[wary stream]

The reason 498 points that direction is because it's between the x(green) and y(blue) vectors

Make sense so far?

[wintry vortex]

yes

[wary stream]

You want the angle now

How would you find the angle?

The angle of where 498 points

[wintry vortex]

Im spitbaling and may be super far off here haha'

[fast wave]

why is it negative for the first question?

[wintry vortex]

convert156 and 473 to radians and use say sin(theta)=-158/498?

[wary stream]

Not exactly

[wintry vortex]

dam

[fast wave]

whys this negative

[wintry vortex]

i ws so confident

[wary stream]

This should help. You can do something called parallel shifting, meaning that a vector can be anywhere as long as you shift it parallel

[dark granite]

what do you mean by "this"?

[fast wave]

see the negative sign

why is it negative

the equation above said positive

[wary stream]

Notice how I shifted -473 to the left. That is valid

[fast wave]

then the signs swapped and the

[wary stream]

It's a parallel shift

[fast wave]

S went to E

[wintry vortex]

makes sense since its still on the y axis

[wary stream]

It's not on the y axis but parallel to the y axis meaning still in the same direction as the y axis

[dark granite]

this has to do with the direction of the vectors

[wintry vortex]

Yes! makes sense

im following

so now i just solve for the angle?

[wary stream]

There's theta, know what to do from here?

[wintry vortex]

arent those degrees right now?

wouldnt they need to be radisns?

[wary stream]

The values of -156, -473, and 498 are not angle measurements

[wintry vortex]

ok brb! gunna run it see if i can get it 😄

[wary stream]

In the problem you are given, they are unitless

[dark granite]

Can anyone else help @fast wave <@&286206848099549185> ? I'm not really sure where the confusion is and they've already been helped by someone else and they're still lost.

[wary stream]

Now be cautious when you get some angle result, because if you look, the magnitude vector is in the 3rd quadrant

[fast wave]

wydm

[wary stream]

Meaning that the angle is between 180 and 270 degrees

[fast wave]

like the East to East?

[wary stream]

So you have to make that result you get, fall between 180 and 270 degrees

[wintry vortex]

YOu sir are a saint and i got it right!

why between 180 and 270?

[wary stream]

As I said, look at where the resultant lies

It's between 180 and 270, right?

[wintry vortex]

alittle confused on that bit

[dark granite]

take a vector and multiply each component of that vector by -1 and you'll get the same vector just pointing in the opposite direction

[wary stream]

The yellow arrow, what quadrant is it in?

[wintry vortex]

3

oh that quadrant is between 180-270 got it

[wary stream]

What is the range of angles in quadrant 3?

[wintry vortex]

i didnt know they had a range per quadrant

i just learned what a quadrant was last week haha

im learning slowly but surely 😄

[wary stream]

This thing

0, 90, 180, 270, 360 etc

[wintry vortex]

oooo nice, ima save that to

[stoic hamlet]

9B

Plz

[wintry vortex]

oof wat nvm angie was here ill move 😄

[alpine sable]

1001/16

hello

[dreamy viper]

Guys whats 2x/3x =? (Fraction) in algebra

[alpine sable]

Im wondering if i did these correctly

[alpine sable]

Oh hi sorry im not sure

[jolly stone]

yep but simple math typo at b) 6/9 = 2/3

and a) did you approximate 4/9 as 0.4? you can actually leave it as 4/9 no worries

[alpine sable]

So i answeed correctly yes?

[jolly stone]

answer is not correct but your method is

[alpine sable]

is sin^2(x) the same as (sin(x))^2

[jolly stone]

yep

[alpine sable]

thanks

you too

[alpine sable]

Ah i see thanks alot

[zinc zephyr]

how do i find the geometric mean of 2 terms, the √ab doesnt work

or atleast im dumb

[jagged imp]

sqrt(ab) should give you the geometric mean of a and b

[zinc zephyr]

what if i need to find per se 2 terms

since it would give me 1 term only if sqrt(ab)

[frail light]

teach pls

step by step

[zinc zephyr]

and if i need 3, i would just find the 3rd term and do it again for 2 & 4

[jagged imp]

idk what you mean by per se 2 terms

If you mean how would you find the geometric mean of more than 2 terms, for n terms the geometric mean is the nth root of the product of all the terms

[zinc zephyr]

Im trying to find 2 geometric terms between 6 and 750

[jagged imp]

I have no idea what you're talking about, it might help if you post the exact problem you're working on

[zinc zephyr]

Insert 2 geometric means in the sequence between 6 and 750 this is all our professor gave

[jagged imp]

could be a gap in my knowledge but idk what your professor is talking about

sorry

[zinc zephyr]

yeah its pretty confusing how he teaches shit

[zinc zephyr]

can u give an example?

[jagged imp]

the geometric mean of the numbers 3,4,5, and 6 is $\sqrt[4]{3 \cdot 4 \cdot 5 \cdot 6}$

[ocean seal]

Sneaky

[jagged imp]

its 4th root since theres 4 of them

[sturdy shuttle]

If i 1223 of something and need to get to 2000 and i get a 1 point every 35 seconds and every 8 rounds i get 1 point on top of the other point how long would it take?

[frail light]

teach plssssss

step by step

like everyone one is ignoring me whyyyy

[zinc zephyr]

(15000 + 18000)/4 then simplify 15000:18000

its 5:6

then divide (15000 + 18000) by the sum of 5 and six

which is 11

[frail light]

is it correct

sir

[alpine sable]

yea looks like its correct

[wispy sorrel]

how does descartes rule of signs work for perfect square trinomials

[open lynx]

anybody got an idea on how to do this?

[alpine nacelle]

Don't you think we need the full exercise ?

[woven echo]

no man just imagine the dance party

its a really good one

[alpine nacelle]

yeah they dance really well

but it doesn't really help to define D(x, y) lol

[woven echo]

lol

[open lynx]

f

sorry you are right

[alpine nacelle]

well, there are a lot of implications to test, quite painful

(a) and (c) are equivalent

[jagged imp]

a seems to imply c for instance.

[alpine nacelle]

(d) implies (b) and (c) (and so (a))

a <-> c
d -> b and d -> c
b doesn't imply d nor c does
so the only left to check are b -> c and c -> b

if one implies the other, it's an equivalence as G and B have a symmetric role, so b->c is the only left to check, which ends the exercise

[open lynx]

can you explain why

i don't understand how to use negations

like what is statement a implying

[alpine nacelle]

not(D(G, B)) means that G and B didn't dance together

[open lynx]

ok

[alpine nacelle]

from here, (a) is equivalent to (c) is immediate, simple negation rule

and then you can start using common sense to check the others

[open lynx]

ok thanks!

[alpine nacelle]

(for exemple, d means that noboby danced, so naturally implies b and c)

[open lynx]

i kinda did it with a table

makes more intuitive sense

[lucid cedar]

I'm having trouble solving the differential equation $$x''(t)=-\frac{k}{m}x(t)+\epsilon$$ where $k,m$ and $\epsilon$ are constants. I've tried a variation of parameters, but that hasn't worked either. Can anyone help me out?

[ocean seal]

WasMachenWirDennDa

[alpine nacelle]

it depends on the sign of k/m

[lucid cedar]

k and m are both positive

[alpine nacelle]

I think it's the worst case lol

[lucid cedar]

ah shiet

any suggestions on how I should approach it?

[alpine nacelle]

lemme think

have you already learnt about diff equation of 2nd order ?

[lucid cedar]

not yet, but to be honest I'm willing to do anything to solve this at this point

so go ahead

[alpine nacelle]

x'' + k/m x = e
as usual, you start by solving x'' + k/m x = 0
t² = -km so t = +- isqrt(km)
and so the general sol is c1 cos(sqrt(km)x)+c2 sin(sqrt(km)x)

and to this you sum a particular solution

[lucid cedar]

yeah I got to that, and then when doing the variation of parameters you do $$x_P=u_1y_1 + u_2y_2$$ right?

[ocean seal]

WasMachenWirDennDa

[alpine nacelle]

you should check if there is a constant particular solution first

because there probably is

[lucid cedar]

do you mean if $x(t)$ is constant?

[alpine nacelle]

like x(t) = em/k

yeah

[ocean seal]

WasMachenWirDennDa

[lucid cedar]

thing is that wouldn't work with the problem it came from

[alpine nacelle]

it definitely gives a particular solution

[lucid cedar]

the differential equation arises from a physics problem with a spring

so $x(t)$ definitely isn't constant

[ocean seal]

WasMachenWirDennDa

[alpine nacelle]

when you solve a diff equa, you solve the homogene for the general sol and you add a particular

here, x(t) = em/k should be a particular

[lucid cedar]

but x(t) = em/k wouldn't correctly model the motion I'm trying to model with x(t)

[alpine nacelle]

x(t) is a function of the form c1 cos(sqrt(km)x)+c2 sin(sqrt(km)x) + em/k

[lucid cedar]

ohhh

ok

that makes more sense

now how would I go about finding c1 and c2?

[alpine nacelle]

any c1 and c2 give solutions here, so you need to understand the physics conditions of your physics problem

to know what coefficients are representative of your situation

[lucid cedar]

hm alright

thank you for your help

I'll see what I can do

[alpine nacelle]

you could check for initial situation

[ruby sparrow]

Can someone explain to me what I need to follow to solve this?

[alpine nacelle]

like if you have some condition on x(0)

or things like that

[lucid cedar]

initially, x(0) = 0

and I also have 2 more points

ok I think I now what I gotta do now

I'll give it a shot and let you know

thanks 🙂

[ruby sparrow]

I'm confused with the question here

[alpine nacelle]

which part are you trying to do rn potato ?

[ruby sparrow]

it's the part i) to be precise

so the big union and big intersection means the combination of all elements inside the set right?

[alpine nacelle]

big union is all elements of all sets together

big intersection is all elements that are in all sets

I'll give you a hint for i)

Show that A_i is included in A_{i+1}

[ruby sparrow]

hmm lemme think about this

@alpine nacelle okay so if based on what you said, A_{i+1} doesn't cover the -i in the beginning and A_i doesn't cover the i in the end

is it correct here?

[alpine nacelle]

"A_{i+1} doesn't cover the -i"
it does

A_2 has -1

[ruby sparrow]

oh i thought because the i+1 so the elements got shifted to right by +1

[alpine nacelle]

all elements of A_i are in A_{i+1}

[ruby sparrow]

so what is in A_{i+1} that doesn't include in A_i then?

[alpine nacelle]

-i-1 and i+1

[ruby sparrow]

oh

because it's i+1

so the range from both ends increase by 1

[alpine nacelle]

indeed

if A is included in B, what can you say about A union B ? and what about A inter B ?

[ruby sparrow]

since A is included in B, A U B means that it'll be B range only then right?

while intersection then it'll be only A range then since only those points intersect is it

[alpine nacelle]

indeed, now you can answer i) in one go

[ruby sparrow]

huh that's it?

[alpine nacelle]

(be careful: A included in B => A is the smallest)

[ruby sparrow]

yeah for the intersection right

oh crap

[alpine nacelle]

so what can you say about the big union ?

[ruby sparrow]

i just realized how dumb am i now kek

so the big union range starts from i = 1

so basically the range gonna be the entire thing then?

[alpine nacelle]

the big union is the union from all the sets A_1 to A_n

[ruby sparrow]

while the intersection gonna be from 1 to i

[alpine nacelle]

A_n including all the others, as we've shown

[ruby sparrow]

crap i didn't see the big picture lmao

okay i can imagine it now

thanks a lot melo

[alpine sable]

https://cdn.discordapp.com/attachments/486844875632017408/885517315322568735/unknown.png

[alpine nacelle]

square it

[alpine sable]

i did

and i get only x = 1 as answer

and i should get x = 1/2 as well

[ruby sparrow]

x = 1 is the correct one still tho

if x = 1/2 you wouldn't get 2 it seems

I mean the sqrt (2x-1) - sqrt (2x-1) = 0 there already right

[alpine sable]

jhin

[ruby sparrow]

unless u wanna assume that only but infinite solution if u move the sqrt to other side

[alpine sable]

1/2 is a correct answer as well

[ruby sparrow]

hmm

[alpine nacelle]

it's because you sqrt'ed too soon

squaring both sides, we get 2x + 2sqrt(x²-2x+1) = 2
x+sqrt((x-1)²) = 1

note that the square is inside the square root

[alpine sable]

yes

[alpine nacelle]

so it has 2 sol

[warped phoenix]

Can someone help me?

I made students S, adults A, and children below 12 C

[alpine sable]

wait why

doesnt it cancel

?

[alpine nacelle]

no, because sqrt takes only positive value in it, but here, even if x is negative, the square will make it positive

and the sqrt will be well defined

so that's the case you miss

because 1/2 - 1 < 0

[warped phoenix]

For my 3 equations I got

E1: 3S + 7A + 2C = 3150
E2: S + A + C = 600
E3: A = 150 + C

Solving through though I get S = -50, A = 400, and C = 250, for obv reasons this is wrong because S can't be negative, does anyone know what I did wrong?

[alpine nacelle]

but gives a sol

[alpine sable]

oh yea absolute value

[alpine nacelle]

yeah

[alpine sable]

that what happens when you dont do math in the vacation

[alpine nacelle]

can relate lol

[warped phoenix]

anyone?

[alpine nacelle]

E3 is A = 150+S

[warped phoenix]

🤦‍♂️

you're right

one sec

[ruby sparrow]

okay i got these 2

i think this one's easy to solve

just compare 2 equations it seems

you get the 10S + 2C = 2100 and 2S + C = 450

nvm it's worse

i get negatives even worse than him lmao

[alpine nacelle]

I think he'll be okay with solving the system, it probably was just his error with E3 which mislead him

[ruby sparrow]

yeah i think that's the only issue

[warped phoenix]

i thiiiiiiiiiink i got it

S = 200, A = 350, and C = 50

is now what I have

is that right??

[ruby sparrow]

makes more sense now

test it

[alpine nacelle]

it's right

[ruby sparrow]

yeah it is now

[warped phoenix]

awesome, ty!!!!!

[ruby sparrow]

you get 3150

okay melo

i think i still have 1 last question here

only this one's left in my unsolved question

i'm not that used to cartesian product so not sure how to simplify it

[alpine nacelle]

how do you call the set which A and B are subsets of ?

[ruby sparrow]

AUB?

[alpine nacelle]

nah, the set which contains A and A^c

[ruby sparrow]

oh

the Universal set

that one covers everything then

[alpine nacelle]

from this, the only subset missing from the universal x universal is AxB

it's Universal x Universal \ {AxB}

[ruby sparrow]

hmm

so it's U x U - (AxB)?

[alpine nacelle]

I think so

[ruby sparrow]

now just how do i reach this point tho

that's the only question left

i do see the A B inside the equation

but i thought you can't swap the sets inside the cartesian product

[alpine nacelle]

Let's call this set C

[ruby sparrow]

due to its properties

okay so assume the sol is C

[alpine nacelle]

no element from AxB is in C

[ruby sparrow]

yeah the only missing value

[alpine nacelle]

and no element from C is in AxB

these are disjoint

however, C union AxB is UxU

therefore, C = UxU - AxB

[ruby sparrow]

wow

so you just can't look at it directly

in the equation only

but look from what's not inside the equation instead right

[alpine nacelle]

you could also write C = (A^c x U) union (U x B^c)

[ruby sparrow]

oh right the difference set rule

[plucky crow]

Need help on the graph sketching part

[fair crater]

Might be better for you to consider sketching
$x^2$, then $x^2-16$ then finally $\abs{x^2-16}$

[ocean seal]

ShatteredSunlight

[fair crater]

I'm sure 2(x-4) is simple, but you could sketch that separately too

The + just means you combine the sketches

[plucky crow]

Yeah I know the graphs separately

Just compoundimg them idk

[fair crater]

Combine the respective y-values at each point

That's basically what + means

You might want to find the exact $y$ at certain points of $x$ then connect the dots

[ocean seal]

ShatteredSunlight

[fiery crest]

I was gonna ask but you go first Melo

[alpine nacelle]

I was gonna help Syphax, but if he's fine, I can help you

[fiery crest]

Okay so don't fully remember my partial fractions from calc 2

but I think I'm mixing together 2 cases here

[alpine nacelle]

squaring and cubing is almost surely unnecessary

[fiery crest]

the square and cube part

Yesterday i did a problem where it was 1 over (s+ smth)^3 and then I had to do it like this

But if it's not "identical" terms do I just take them individually?

so without the cube and square

[alpine nacelle]

the goal is that in the end, the RHS has the same denominator as the LHS

[fiery crest]

Alright so no squaring ro cubing

[jagged imp]

for (ax+b)^k terms in the denominator, you're gonna need partial fractions of ax+b, (ax+b)^2, (ax+b)^3, ... up to (ax+b)^k, but when k=1 thats just ax+b

[fiery crest]

it's only for identical terms you go ^1 then ^2 ^3 etc?

x/(s+2)^2 would be A/(s+2) + B(s+2)^2? for example

[warped phoenix]

hey guys im stuck again

[jagged imp]

ye

[fiery crest]

okay good good, then I do know it, memory just needs some defrosting

[ruby sparrow]

take the first and 3rd equation minus each other

eliminate the y out

baiscally try to zone out 1 variable by minus 1 equation to another

if it's close but not enough, u can times the entire equation up

[fiery crest]

So try to find z for example, then you can use the value of z you know to solve x+z = smth for example

and when you have values for two variables you can find the third

[ruby sparrow]

or there's a cheat way

just use system of equation solver

if u r lazy to calculate and don't have to prove

[fiery crest]

I'm very used to calculate these with matrices I've gotten bad at doing it normally

[ruby sparrow]

lmao same

matrices makes everything faster ngl

but he's prolly in high skl

so i doubt he needs to use it

[fiery crest]

So I'm doing it manually and it might get messy with fractions

what year are you? @warped phoenix

[warped phoenix]

junior in highschool

yeah

theres a lot of fractions regardless if i do elimination or substitution

i keep getting different answers

every method i try

[ruby sparrow]

x = 26, y= -3, z = 15

[fiery crest]

Let me try using a higher level math method and see what I get

[ruby sparrow]

that's what i get from calculator

[fiery crest]

then you can see which of your answers is the right one

[fiery crest]

boring

let me do my gauss

[ruby sparrow]

sorry sleepy xd

[ruby sparrow]

yeah how abt no

gonna sleep after all the sets and theory lesson from melo xd

he helped me a lot

[fiery crest]

your local time?

[alpine nacelle]

I'm gonna go to, I think

[fiery crest]

Is there an easy way to test if your A B C for the partials are correct? @alpine nacelle

[alpine nacelle]

re-develop

[sharp sable]

Number 4 I didn't understand the question help pls

[zinc zephyr]

i think you just have to map it on a graphing paper

i can already tell that A is the right angled one

since A and B both has 2 for the x coordinate and also B and C has 4 as their Z coordinate

You do need to map it in a graphing paper since it says "Show that A, B, abd C are ..."

[sharp sable]

Ohh

[sharp sable]

So I have to map it

[fiery crest]

You shouldn't have to

[devout sigil]

For the right angle gradient of one line is -1/gradient of other line if no sides r fully vertical/horizontal

If it’s vertical or horizontal either their x-coordinate key-coordinate are the same

[fiery crest]

isn't this determinant stuff?

[devout sigil]

Just these two things to take note of and u should be able to find the right angle easily if any

[lucid cedar]

you could define the sides of the triangle as vectors and calculate the angle using the dot product

[sharp sable]

OK thanks everyone

[tender linden]

i recently found this on discord, im just curious if anyone can solve it or if it's an actual thing?

[zinc zephyr]

Yes, it says you have to show that they are actually a right triangle

[alpine sable]

Any help?

[plucky crow]

(A+b)/2

Finds the midpoint

[alpine sable]

thank you!!!

[plucky crow]

Help

[alpine sable]

sorry cant help with that :/

[grand tartan]

c o n f u s e d

thats real exciting math here

[plucky crow]

Not u lol

[swift knoll]

anyone know what the Chanel for pre algebra is

7th grade here. 😄

[jagged imp]

you can ask in the questions channels (not this one specifically) or #prealg-and-algebra

[swift knoll]

oh ok

thanks

[wanton holly]

why isn’t this 5?

[thin panther]

✨old annoying mathematician✨

[flat vale]

cuz the numerator and the denominator are both inf

[devout sigil]

The numerator is approaching inf and the denominator is approaching negative inf?

[flat vale]

-inf/inf = 1

[fiery crest]

5 + inf is still = inf

[wanton holly]

Ah I see thank you

[fiery crest]

and x/x = 1, x/-x = -1

[thin panther]

Wow that’s confusing. I’m here to ask how to do long decision

*divisiln

*division

I forgot

[flat vale]

go ahead

[thin panther]

😃

[thin panther]

?

[fiery crest]

Can I steal a quick question first

[wanton holly]

Wait but why is it 5 then if it approaches positive infinity?

[thin panther]

Sure

[flat vale]

no it's 5 + inf/ 1 - inf

[fiery crest]

if you have x = +- 2 then you'd factor it as (x+2)(x-2) right

[devout sigil]

Numerator is 5+infinity

[fiery crest]

How do you factor it when your x = -2 +- 3i

[devout sigil]

Incorrect notation, pls use parabolas

[flat vale]

which then becomes inf/-inf

[flat vale]

bruh alr (5+inf)/(1-inf)

[thin panther]

Aight imma come back later this is too confusing

[fiery crest]

I get confused with the signs

[wanton holly]

Then my teacher is wrong

[devout sigil]

He is correct

[thin panther]

Kk I’m in 9th grade i don’t know this stuff

Baii

[devout sigil]

It is x/-x=-1 but x is infinity

[wanton holly]

Oh for positive infinity it approaches 0

[devout sigil]

No?

[wanton holly]

I’m just trying to understand her notes

E^-x approaches 0 I mean

So it’s 5

[flat vale]

yes it does approach to 0

[devout sigil]

Yes

Because it’s 5/1

[flat vale]

1/2, 1/4, 1/8, 1/16.....

the value gets lesser and lesser hence it approaches 0

[stuck jolt]

$\lim _{x\to a}\left[\frac{f\left(x\right)}{g\left(x\right)}\right]=\frac{\lim _{x\to a}f\left(x\right)}{\lim _{x\to a}g\left(x\right)}$

[ocean seal]

Captain_Mat01

[stuck jolt]

Just do that

[kindred nymph]

help pls

[rigid smelt]

if two variable x and y are said to be directly proportional to each other, then the following is true, x=ky where k is any real number

[vapid oak]

to expand on that, you basically know that

$m^2=k \cdot n^3$

and you can combine that with the information that m=4, n=2 satisifes the equation to find k

[ocean seal]

Omfish

[kindred nymph]

so whats m? i got 23 but im almost sure i did it wrong @vapid oak

[devout sigil]

Did u find k

[vapid oak]

m and n are both variables in this situration.

[kindred nymph]

no

[devout sigil]

U should

[vapid oak]

this question is basicallt saying $x^2=k \cdot y^3$

[ocean seal]

Omfish

[devout sigil]

4²=2³ • k

Find the value of k and sub n=8 into the equation

[kindred nymph]

ohh

[fiery crest]

okay this problem sucks ass

[magic lodge]

anyone know how to do this?

[fiery crest]

reverse transform to solve for y(t)

[fiery crest]

in 2018 his icome was 5% more than 2017, that's like saying 1.05 * 2017

if 2018 = x and 2017 is y
x = 1.05y

divide by 1.05 on both sides,
y = x/1.05
aka the 2018 income / 1.05

[crisp summit]

yee

68k

[fiery crest]

opposite

[alpine sable]

Hey! I need this help with quadratic polynomial
The question goes
p, q are roots of x^2-4x+2=0 then find p^2-q^2
i can find p+q and p.q
but how do i find p^2-q^2?

[jagged imp]

factorise p^2-q^2

so you can express it in terms of things you can find

[alpine sable]

@jagged imp If i do (p+q)(p-q) here then i dont know the value of p-q

[devout sigil]

Do u know whether p>q?

[alpine sable]

i dont

[fiery crest]

just solve the equation and get the roots of x

x = +- smth and that's your p and q

[devout sigil]

There is no need for that

[fiery crest]

if they need the value yes

[devout sigil]

Use ur value of p+q to get p=value-q and sub into p² - q²

[devout sigil]

Value of sum and product of roots is sufficient

[fiery crest]

how do you have the value for p+q in the first place

without knowing p and q

[jagged imp]

look up vietas formulas

[fiery crest]

that's annoying stuff

this just looks like a HS question

[devout sigil]

Research on sum and product of roots of a quadratic equation

[fiery crest]

why not just solve it? it's an easy quadratic equation

[devout sigil]

Lol first u don’t get integer solutions and second solving the pair of simultaneous equations is faster

[fiery crest]

p = 2 -sqrt2
q = 2 +sqrt2

p+q = 4

p^2 - q^2 = 0

Math majors always want to complicate things when you can just do it in steps

It's different if they have to write the expressions and not just play with numbers

[alpine sable]

Birb

[vapid oak]

this is not true

[alpine sable]

I got the answer

maybe

thanks

[fiery crest]

no

you didn't because I just did the worst mistake in math

[alpine sable]

really?

[fiery crest]

i just did the most unholy sin

[vapid oak]

||happens to the best of us||

[fiery crest]

(a+b)^2 != (a^2 + b^2)

[alpine sable]

yes

but i didnt do this

[fiery crest]

okay then good

[alpine sable]

this worked

the final answer i got is 8root2

[devout sigil]

Correct

My bad this is a faster way

[fiery crest]

stuff like this is why I do engineering and not math

I want to play with my numbers no just write expressions all day

[alpine sable]

$8\sqrt{2}$

[ocean seal]

April's cat

[alpine sable]

Latex is fun!

[fiery crest]

sqrt{4}sqrt{4}sqrt{4}sqrt{2}

if you want to piss the grader off

$\sqrt{4}sqrt{4}sqrt{4}sqrt{2}

[fathom sequoia]

you don't need to write it off by heart, you have desmos where you can copy and paste equations to latex

[alpine sable]

xd

[fiery crest]

i hate my life

this is meant to be the "solution"

[fathom sequoia]

wow that looks so hard I would also hate my life if I got htat question

what grade is this

[fiery crest]

university year 2

[fathom sequoia]

oh damn you are smart

[placid venture]

Hi guys, how do I approach this?

Like what even is f_Y(y)?

[jagged imp]

f_Y is the pdf of Y

so the idea for a is to find the pdf of y and use the formula for expected value on that

[placid venture]

so do I first invert the function? x=lny?

so f_Y(y)=lny

and that would be the pdf?

I'm guessing by notation, as pdf usually uses the lowercase f?

[fervent egret]

can anyone confirm that this is allowed?

[tawdry sphinx]

i don't thinks so but I'm no expert at that

[vale wigeon]

yes it is allowed

[tawdry sphinx]

was it like multiplication?

[vale wigeon]

the only operation here is intersection

intersection is associative

[tawdry sphinx]

no i mean ok it is associative

[fervent egret]

ok thanks

[mental pendant]

need help

[glass lichen]

Im gonna go with probably

[tawdry sphinx]

is that double factorial?

[glass lichen]

yes

I mean surely that ratio is positive cause factorial > 0 itself

[tawdry sphinx]

yeah that is > 0

[glass lichen]

everything is positive

so.. the total thing surely cant be negative

oh yeah

[tawdry sphinx]

oh ok that is a bit harder

then it should be < 1 right?

sry i mean this is < 1

or at least should be

oh wait

i read (2n+2)!! * (2n)!!

in the denominator

how did you get that?

[mental pendant]

<@&286206848099549185>

[tawdry sphinx]

look at A(n+1)

isn't it (2n)!! / (2n+1)!!

[tawdry sphinx]

sry don't know anything about that

oh wait ok I'm sorry, i need more sleep haha

you're right

yup

[flint bone]

My bad I didn’t read the previous message

[tawdry sphinx]

it's alright

thx man

$(2n-1)!! > 0$ so we could just multiply right?

[ocean seal]

NoRysq

[tawdry sphinx]

meaning we would have: $(2n+1)!! \times (2n)!! > (2n+2)!! \times (2n-1)!!$

[ocean seal]

NoRysq

[tawdry sphinx]

but now how would you go further

i thought we want it to converge?

and yes we don't know if the ineuqality is true and that is why we need to try and simplify

yeah

$(2n+1)!! = (2n+1) \times (2n-1) \times (2n-3) \times ... \times 3 \times 1 \
(2n)!! = (2n) \times (2n-2) \times ... \times 4 \times 2$

[ocean seal]

NoRysq

[tawdry sphinx]

i think this is the key

[blissful sequoia]

Someone solve this please

[tawdry sphinx]

$(2n+1)!! \times (2n)!! = (2n+1)!$

[ocean seal]

NoRysq

[tawdry sphinx]

can you not interrupt @blissful sequoia

[blissful sequoia]

Sorry

[tawdry sphinx]

@alpine sable

[cold root]

does this apply to all exact equations?

[tawdry sphinx]

and it should be: $(2n+2)!! \times (2n-1) = \frac{(2n+2)!}{2n+1}$

[ocean seal]

NoRysq

[ancient saddle]

Yes

[cold root]

so if it fails the test we wont be able to apply that right

and just use other methods

[tawdry sphinx]

is it solved?

so actually you should get: $\frac{(2n+1)!! \times 2n!!}{(2n+2)!! \times (2n-1)!!} = \frac{(2n+1)!}{\frac{(2n+2)!}{2n+1}}$

i hope this is right

[ocean seal]

NoRysq

[ancient saddle]

Yes, there are methods for non exact differential equations that have their own tests too

[tawdry sphinx]

i first expand it and then simplify it yes

but that seems weird

[cold root]

is there a name for that formula?

for the exact diff equations

or is it just that

[ancient saddle]

it's just that as far as I know

[tawdry sphinx]

as they don't move and just go on let's move to #help-9 @alpine sable

[cold root]

exact diff equations only apply to the first order?

[ancient saddle]

Yes

[cold root]

1st order and 1st degree?

[ancient saddle]

what do you mean?

[cold root]

1st order and 1st degree diff equations

im trying to find 5 things to discuss about it

[ancient saddle]

If by 1st degree you mean the exponent, it works for every degree

The method is for non linear ODEs

[cold root]

what does the O stand for

[glass lichen]

Ordinary

ie not partial derivatives

[cold root]

oh whut i thought exact diff equations use 2 partial functions

with respect to x and y

[ancient saddle]

the method uses partial derivatives, but that doesn't mean the DE is not ordinary

[glass lichen]

$\dv{x}{t}+p(t)x=q(t)$ for example is an ODE cause it uses regular derivatives

[ocean seal]

Mosh

[cold root]

i see

what are the nonordinary kinds of derivatives

the ones with higher orders?

[ancient saddle]

Non ordinary are multivariable

Maybe review DEs classification, or search about it so you can see it clearer

[cold root]

im still a newbie this is literally my 2nd topic

but aight

[ancient saddle]

Oh, then don't worry you will learn about it in the next classes I guess

[cold root]

btw whats a homogenous differential equation

or is it better to search it in yt?

i just finished variable seperable a few days ago

[glass lichen]

homogeneous (probably wrong) is when you can do a sub and make it seperable iirc

[ancient saddle]

Yeah maybe search a video about classification and homogeneous ODE

[ancient saddle]

And have you studied homogeneous linear ODE before?

[cold root]

yup

linearity and the other classifications i just forgot

btw

maybe im stupid but why wont it apply to linear diff equations

is it because of the two kinds of variables in the diff equation

[ancient saddle]

Basically, it's a classification for linear ODEs, a linear ODE is homogeneous when there are no terms that don't have a y or its derivatives

[cold root]

aight aihgt

[slim elbow]

What is 9 + 10?

[cold root]

so it will only apply to nonlinear diff equations right

[slim elbow]

My mom said it’s not 910

[ancient saddle]

exact ODEs, yes

[cold root]

because linear diff equations only have one kind of function?

[dusky bluff]

@alpine sable it should be 1

@alpine sable the form of expression is f(x)^g(x). Check rules for that forms. Or you can take log

[glass lichen]

taking log is probably easiest

since continuity rule will be applicable

has your teacher said "you must solve it this way"?

[clear musk]

n^(2/n)=exp(2log(n)/n) in + infinity it's exp(0)=1

[alpine sable]

Someone please tell me the clue

[dusky bluff]

@alpine sable do you need to find the limit or you need to show limit exist?