help-0

[cloud kiln]

Cant I just get the inverse of this function and calculafe the inverse’s domain?

[vale wigeon]

it doesn't have an inverse

[alpine sable]

how do i solve this simultaneous equation using substitution method?

[reef dust]

Substitute value of one variable from one of the equations into other

[alpine sable]

but in this case both x and y variables have diff values so do i use lcm to make them same?

[vale wigeon]

that sounds more like elimination

isolate one of the variables in one of the equations

if you're not sure which to pick, you can go with isolating x in equation 2 for this one

[alpine sable]

so 2x + 5x - 3y = 10 ?

[quartz oxide]

I think the channel is occupied rn

[fiery berry]

Oh

[quartz oxide]

Post at #geometry-and-trigonometry

[vale wigeon]

no, that is not at all what i said to do and also this is bullshit

[fiery berry]

Btw that's wrong

You want to either substitute out x or y

Eg 5x = 3y - 1

[alpine sable]

chill i was sick for some classes and i have an exam coming up so i missed some concepts 😭

[fiery berry]

What grade is this?

[alpine sable]

8th

[vale wigeon]

when i call something bullshit it's not to express anger

it's to express that it is bullshit

let me be more clear

i want you to take the second equation and solve it for x

[alpine sable]

2x = 10 - 4y?

[fiery berry]

Yes

Dived by 2

Then it should be easy to sub im

In

[alpine sable]

x = (10-4y)/2?

OHHH

[fiery berry]

Can just do x = 5 - 2y

[alpine sable]

yee

tysm

[fiery berry]

Ok

Np

[vale wigeon]

yes and now put that into the other equation

5(5-2y) - 3y = -1

[alpine sable]

got it ty

[white kiln]

i need help on number 3.

plz

[vale wigeon]

is "True" supposed to be your answer?

[placid zinc]

Note the answer to 1 is indeed false, but your reasoning is wrong. It's asking if A is a subset of B.

I don't know how we can expand on "true" for #3

[short turtle]

is this channel occupied? if not can any1 help me with this?

[austere violet]

.

[short turtle]

the ans is log3root3

but i kept getting logroot3 only

[vague coral]

$\sum_{n=1}^{\infty} \frac{(-1)^{2n}}{2^n} \log(3)$

I hope I'm not wrong

[alpine sable]

the n=1 term should be positive?

[vague coral]

yeah I saw my mistake

or no

[alpine sable]

it will never be positive now

never be negative

[vague coral]

I'm struggling with this lol

[alpine sable]

1/2 - 1/4 + 1/8 - 1/16 ... is (1/2 + 1/8 + 1/32)- (1/4 +1/16 ....)

[alpine sable]

can i see what you are doing?

[short turtle]

yea ive done this step

[alpine sable]

the first infite series is (1/2)/(1-1/4) = 2/3
the second infinite series is (1/4)/(1- 1/4) = 1/3

so yeah it should be 1/3

[quartz oxide]

I did it and got log3/3
Bruh

[short turtle]

the ans is log3root3

but idk how

kept getting logroot3

[austere violet]

ANYONE KNOWS BOUT EQUATION OF STRAIGHT LINES

[vague coral]

._.

[austere violet]

.

[reef dust]

R u using formula for infinite geometric series ?

[short turtle]

nope

[austere violet]

.

[alpine sable]

i think its 1/3 log 3

[short turtle]

for this one it does not uses the sigma notation thingy

[short turtle]

yea the ans is 1/3log3

[alpine sable]

oh thought u said root 3

[short turtle]

ow i wrong type i said log3root3

[alpine sable]

the formula is a/(1-r)

[austere violet]

...

[short turtle]

w8 not a-1/1-r?

owh im wrong then

[alpine sable]

no. For a geometric series a, ar, ar^2, ar^3 .... the sum is a/(1-r)

[short turtle]

oh i got it, thanks jacobp

[alpine sable]

no problem. this is my first time helping someone out

[alpine sable]

paste question?

I wish there was someone who could give me a lesosn on differnetial equations

[reef dust]

Keep in mind that -1<r<1

[vale wigeon]

the geometric series formula applies to any r between -1 and 1, not just between 0 and 1.

[wary stream]

Square brackets means it includes zero

[alpine sable]

lol mb i read it wrong

[wary stream]

Also, as a tip, you don't have to delete the question you asked. Other people could have had a similar question like you. One of the main times you should delete a post is if you multi-post in multiple channels

[alpine sable]

o ok srry i wont next time

[gaunt ether]

a man has to reach a flagpost 10m away from him. He travels 1m, then travels 1/2m and keeps on travelling half the previous distance. At this rate, how long will it take him to reach the flagpost? (it takes him 1s to travel 1m, 1/2s to travel 1/2m and so on.)

[uncut tapir]

Ok, so you're adding 1 + 1/2 + 1/4 ... What type of series is this?

[gaunt ether]

umm.....geometric?

[wary stream]

I think they mean if it's either a series that converges or diverges

[gaunt ether]

converges

so umm...how to solve it?

[uncut tapir]

No I meant this

[gaunt ether]

oh.

[uncut tapir]

Because you know the type of the series, do you know the formula for the nth term and/or the sum of the first n terms?

[gaunt ether]

yeahhh...😅😅no...

can u help?

[uncut tapir]

Start with the formula for just the nth term

[gaunt ether]

i actually haven't really studied series...i just came across this problem in a book 😅😅

so can u pls explain how to solve...

[sage bronze]

i may be wrong but wont it just take 10 seconds as his speed is constant at 1 m/s @uncut tapir

[uncut tapir]

First find a formula for the nth term of the series

Then find a formula for the sum of the first n terms

Then take the limit of the sum of the first n terms to infinity

[alpine sable]

can someone explain what aRb means?

[uncut tapir]

This seems correct as well. Wondering what the purpose of the question is

[gaunt ether]

no but like, he travelling in a certain manner right? it is like that zeno's achilles paradox...

[gaunt ether]

btw, gaunter, how to find the 'r'

[gaunt ether]

is it 1/2?

[uncut tapir]

Yeah I guess the idea is to demonstrate the series converges and refute the paradox

[uncut tapir]

That's correct

[sage bronze]

lol

[gaunt ether]

@uncut tapir , what is (n-1)? bcuz isn't n infinity?

[uncut tapir]

This is just the nth term

[sage bronze]

shouldnt the sum formula be used here

[uncut tapir]

That's the next step to derive the sum formula from the nth term

[gaunt ether]

a=1, r=1/2 so, an will be (1/2)^n-1 right? so what is 1/2^n-1?

[sage bronze]

we havent been given the nth term weve just been given the sum

[gaunt ether]

ok so, what will be the next step?

[sage bronze]

i mean im lost as well

[ocean seal]

Gaunter

[gaunt ether]

what...is...'k'? 😅

[wary stream]

We don't need useless comments from the peanut gallery. If you don't get it, just watch

[uncut tapir]

It's just an index for the summation

[sage bronze]

alright

[gaunt ether]

oh yes...yeah...

this problem is much more complex than i thought 😅😅

[ocean seal]

Gaunter

[uncut tapir]

If you want a hint, try to solve this for S_n

[gaunt ether]

uhh...hehe😅😅thanks...though this mathematics(summation and series) hasn't been taught to me now...so...i didn't quite get it but anyways thanks...

[dense blaze]

find a where the function is differentiable for all x values \
\ $g(x)$ = \begin{cases}$ $ax$, & \text{if $x < 0$} \ $x^2 - 3x$, &\text{if $x \ge 0$} \end{cases}

[ocean seal]

sevenseas

find a where the function is differentiable for all x values \\ 
\\ $g(x)$ = \begin{cases}$ $ax$, & \text{if $x < 0$} \\ $x^2 - 3x$, &\text{if $x \ge 0$} \end{cases}
```Compilation error:```! Missing $ inserted.
<inserted text> 
                $
l.56 \\ $g(x)$ = \begin{cases}
                              $ $ax$, & \text{if $x < 0$} \\ $x^2 - 3x$, &\t...
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```

[dense blaze]

is this 0?

cuz the limit x^2 - 3x when x tends to 0+ is 0

and for a function to be differentiable, the limit of g(x) when x tends to 0- and 0+ has to = L, 0?

sry idk where the latex has gone wrong

[uncut tapir]

Yeah I guess it would have to be

[dense blaze]

i think the ans is -3 tho

i think they differentiate x^2 - 3x

im abit confuse here do we differentiate or find the limits here

[oak chasm]

What's the slope at x = 0 for x² - 3x?

The slope should be the same at x = 0 for ax.

If the slopes differ, then you can't get the derivative at zero.

@dense blaze

[dense blaze]

-3

[dense blaze]

ohh

im confuse when to use limits or derivative

can i ask here, does differentiability means the function has to be continuous?

[oak chasm]

Differentiability means that you can get the derivative at all points.

The derivative for the linear and quadratic parts are fine outside of x = 0.

Where they meet.

[dense blaze]

oh i see its nth to do with continuity?

[oak chasm]

If the slopes of both parts don't match, then the derivative can't be gotten since the derivative limit will be different on the left and right.

And a limit doesn't exist when the left and right limits differ.

[distant horizon]

Find derivate and sub in x = 0

[oak chasm]

So therefore the derivative doesn't exist.

So make the derivatives of both parts match so that the left derivative limit and the right derivative limit match.

Does that make sense?

Continuity is somewhat important, but not for this problem.

You need removable discontinuities and the rest continuous for it to be differentiable, but that's not a problem here.

[dense blaze]

yeah i see this makes sense, i think i keep getting confused limit at a point vs using limit to get the derivative

[oak chasm]

The piecewise function parts are all continuous and they meet at the same point (0, 0), so the whole thing is continuous.

[dense blaze]

ah okay ic thank u

[oak chasm]

Oh, I was slightly wrong. Looked it up and removable discontinuities aren't differentiable at the discontinuity.

So, yes, continuity is required, but not sufficient.

You're welcome.

[hollow pelican]

hi guys does anyone know how to solve this

[oak chasm]

@hollow pelican Use the constant multiplier rule to get 5 out of the derivative.

Then use the chain rule.

[hollow pelican]

what's constant multplier rule?

[oak chasm]

derivative of 5x = 5 times derivative of x

Like that.

[amber urchin]

d/dx(a*f(x)) = a * d/dx(f(x))

[hollow pelican]

ok

[oak chasm]

Here, derivative of 5 cos(2t³) = 5 times derivative of cos(2t³).

[hollow pelican]

is it like this?

[oak chasm]

Nope.

y = 5 cos(2t³)
d(y) = d(5 cos(2t³))
dy = 5 d(cos(2t³))

[amber urchin]

I suggest using parenthesis after sin, cos and other functions

[oak chasm]

You need to keep track of what's left to be differentiated.

See how the 5 doesn't go inside the cosine?

It goes out of the part that still needs to be differentiated.

There's another way that people write it, too.

y' = (5 cos(2t³))'

Where instead of d(part to be differentiated), it's (part to be differentiated)'

[hollow pelican]

ohhh

[oak chasm]

So, you can pick either way.

[uncut tapir]

You need to write y = 5cosu and u= 2t^3 (correct so far)

First mistake is you wrote dy/dx instead of dy/du and du/dx should be du/dt.

You do multiply dy/du and du/dt like you did at the end but you are missing some terms. It should be

-5sin(u)(6t^2)

[hollow pelican]

ahh ok

thanks

[alpine sable]

Write in polar form:
(Cos(1/2)-i*sin(1/2))^2

How should I think about the angle in this case?

[ancient saddle]

Hello, sin(x) is an odd function, so -sin(x) = sin(-x)

Also, cos(x) is an even function, so cos(x) = cos(-x)

[alpine sable]

Thanks but I'm still not sure how to think of the angle. I understand that i could write it as

(cos(-1)+i*sin(-1))^2

but not sure how to think of the angle as an integer.

[ancient saddle]

It's (cos(-1/2)+i*sin(-1/2))^2, so the angle is -1/2 rad

(e^(-1/2*i))^2

[alpine sable]

Omg

Lmao

Thanks

[lyric cedar]

Angle does not matter. When you write pi/2 or pi as angle it actually means 1.52 or 3.14 rad respectively

[alpine sable]

Thank you :)

[delicate widget]

anyone?

[lyric cedar]

380 * pi * 80 cms

[delicate widget]

o thank you

😂

[lyric cedar]

🤣 i knew it was a joke

But cant be sarcastically rude , so just answered it

[delicate widget]

hehe

[alpine sable]

What does the [-10^-5, 10^-50 by [-10^-3, -10^-3] mean?

[topaz scaffold]

That's like the x and y axis of the graph

The x axis goes from -10^-5 to 10^-5 and the y goes from -10^-3 to 10^33

[alpine sable]

is there a way to show this on the graph or do u just assume it?

[topaz scaffold]

On a graphing calculator you have to press window

And then enter in those values

[alpine sable]

got it thx

[whole nexus]

excuse me

is this right ?

How can it turn into this?

[reef dust]

Assuming value of cos is known
U can calculate sin with the help of basic relation between sin and cos

[whole nexus]

sorry i can't get it

[whole nexus]

how can u calculate it ?

[reef dust]

U know the relation between sin and cos ?

[whole nexus]

yes

umhh

[reef dust]

U have value of cos
So u can calculate sin

[whole nexus]

cos(pi/2 - x) =sinx ?

[reef dust]

sin and cos of the same angles

[reef dust]

Here pi/2-x and x are two different angles

sin^2 +cos^2 =1 ?

[whole nexus]

yes ofcourse

ah

i still can't get it

[reef dust]

Dump the value of cos in the eqn

[whole nexus]

Let me try

[whole nexus]

ohhhhh i;m so dumb, ty very much

[reef dust]

👍

[alpine sable]

DO=OC=OE
i need to find whats DO+OC+OE
can someone help?

[reef dust]

I think u mean OC instead of DC

[alpine sable]

oh yes my bad

[uncut tapir]

Yeah otherwise that would be impossible

[alpine sable]

ok i changed it do you know the answer?

[uncut tapir]

Yes, the area of the three shapes inside the square have to be equal to 64. You can write all the areas in terms of OE and solve

Assuming angle OEB is 90°

[alpine sable]

exactly we cant know that its 90 for sure

thats why i cant solve it

[pure hill]

I tried it doesn't get solved that way the x terms get cancelled out

[reef dust]

Yes

[amber urchin]

Maybe cosine formula will work?

[uncut tapir]

ODC is an isocoles maybe we can take advantage of that?

[reef dust]

Yea we can use some trig here

[uncut tapir]

Not sure how it helps but it must be relevant otherwise they wouldn't have side all those sides are equal

[amber urchin]

Right, we don't know the DOC angle

[uncut tapir]

If we draw a line upwards from O would that bisect DC

Then you could try Pythagoras

[pure hill]

I think the answer is 15

@alpine sable please verify if you have the answer..

[uncut tapir]

I get the same answer if I try Pythagoras

[pure hill]

Well this clicked to me first so I tried this
But yes Pythagoras theorum will give same result

[alpine sable]

i dont have it

[pure hill]

Ok no prob
But the answer is probably 15 only

[alpine sable]

we dont know if OEB is 90°

[uncut tapir]

You can do Pythagoras on the top triangle if you split it in half

[alpine sable]

thats what i got too when i assumed its 90° but we cant really know that

[uncut tapir]

Actually I think you can

[alpine sable]

can you explain how i need the asnwer

[uncut tapir]

DO and OC are equal so O has to be exactly halfway between them both horizontally

[alpine sable]

ok and?

continue

[uncut tapir]

You should be able to 'drag' O to where E is without breaking the DO = OC rule

OE would have to be perpendicular

[pure hill]

And the path will be locus of a perpendicular to AB

[uncut tapir]

Exactly

[pure hill]

Nice dude! I was having some problem deciphering this one

[alpine sable]

i mean, can i do it like in a test or something?

[uncut tapir]

I guess you can check your answer by making sure the areas sum to what they're supposed to

[pure hill]

Yeah this one is also a way to check this

If the areas are same then the assumption of OEB being right angle is correct

[uncut tapir]

Formally speaking, the point O has to be on the locus which bisects DC and AB

And the only way OE can equal DO and CO is if E also exists on the locus

[alpine sable]

so that means E is a right angle?

[uncut tapir]

Yes

That would be the definition of a perpendicular bisector

[ivory otter]

hi

[ivory otter]

is this correct?

[reef dust]

Yes

[calm solar]

is this an artificial intelligence? WoW

[ivory otter]

what

[static fern]

uhhhhhhhhh

if im given 2 r3 lines that are skew

and at some point there is a minimum distance between the two

how do i find where the minimum distance is?

i've figured out how to find the orientation and the length of the minimum distance (orientation with the cross product, length with the scalar projection)

but i still have no idea how to find rthe actual minimum location without bashing it into the distance formula and praying

(spoiler the algebra did not work out to something i could solve)

[alpine sable]

[ionic jewel]

I'm genuinely amazed this server doesn't auto delete invite links

[alpine sable]

<@&268886789983436800>

[tropic wagon]

[sly mantle]

b&

[alpine sable]

you have a band?

[sly mantle]

yes

roketto & the degenerates

[mystic sinew]

does it have more than one linear factor (that's real)?

I wasn't able to find the other 2 real linear factors

so I graphed it

and yeah

only 1 real root therefore only one real linear factor

[ionic jewel]

yes

[mystic sinew]

?

yes what

[ionic jewel]

presumably you were expected to use rational root theorem to find it, which they call sometime else?

[mystic sinew]

what

[ionic jewel]

to find -1/2

[mystic sinew]

are there any other real roots other than the one they gave us?

[ionic jewel]

no

[mystic sinew]

don't see no imaginary numbers here chiefe

wrong question?

[ionic jewel]

no it's right

it's not asking for the roots

[mystic sinew]

I don't understand what it means

[ionic jewel]

it's asking for the possible roots

[mystic sinew]

what

there aren't any possible real roots other than the one they gave

I proved that

[ionic jewel]

according to the rational root theorem those are all possible roots but I also don't think that's what they want

hmm

[mystic sinew]

I don't get this

it doesn't have any other real linear factors

only the one they gave us (which isn't an option

(you need to select one to submit

[glass lichen]

yeah... and?

you'll have a linear factor and an irreducible quadratic factor if you were to factorize the cubic

[mystic sinew]

yeah I got that

[glass lichen]

however what you found is that x=-1/2 is a root of the cubic

[mystic sinew]

they're asking for another linear factor right here though @glass lichen

[glass lichen]

yes

[stuck jolt]

Oh wait

Nvm

[glass lichen]

well it says a

[stuck jolt]

Yeah

[glass lichen]

and since it only has one, it's the linear factor

[stuck jolt]

I just saw

[mystic sinew]

ah shit

my bad

just notice

ah I need some sleep

I feel like an idiiot

[desert moon]

why can you let p2 = 0?

i did this but I set p1 = 0 and got a different result for the solution to the solution

linear algebra: first order 2 variable DE

https://tutorial.math.lamar.edu/Classes/DE/RepeatedEigenvalues.aspx

[wary stream]

You can have p2 to be anything, in this case, zero was picked because it made it the most simpliest

The overall concept is to not have an eigenvector to be the zero vector

[desert moon]

i did this but i let p1 = 0

so then I got a different solution. Is that solution also valid?

[alpine sable]

6.2801e-8 , what does the e mean ?

[wary stream]

How did you let p1 = 0? There's no p1

[desert moon]

6.2801x10^-8

[alpine sable]

-0 ?

[alpine sable]

6.2801e-8 = 6.2801*10 -8 ?

[wary stream]

First, rule don't ask in a busy channel, and that's calculator notation for $$10^x$$

[ocean seal]

dldh06

[wary stream]

$$6.2801E-8 = 6.2801*10^{-8}$$

[alpine sable]

got it

and sorry sir

[ocean seal]

dldh06

[desert moon]

1/2 p1 + 3/2 p2 =-3
you can say p2 = 2 - 1/3 p1
then you get vector ( p1 , 2 - 1/3 p1)

let p1 = 0 => vector is (0 , 2)

or you can say p1 = 6 - 2 p2, which is what paul did and got (-6 , 0)

[wary stream]

So you solved for p2 instead

[desert moon]

yeah

and then my solution for the coefficients to the solution was different too

and so all in all, a different solution

[wary stream]

That's valid solution

You just solved for a different variable

[desert moon]

uwu then

[alpine sable]

a water container has 13 900 mool of water, how many water molecule does the container have?

[wary stream]

This channel is busy

[wary stream]

What are you confused about, you can solve for either p1 or p2 and get valid answers

[stuck jolt]

Isn't this chemistry?

[alpine sable]

Math

[jade canyon]

6.02 × 10^23 molecules/mole

[stuck jolt]

Can we agree this is chemistry though?

Or am I crazy

[uncut tapir]

It is

[stuck jolt]

Ok, good

[jade canyon]

it doesnt matter…

[stuck jolt]

Yeah, I know but I had a doubt for a second

[uncut tapir]

It kind of does because you wouldn't be able to solve without the chemistry knowledge

[alpine sable]

You can't solve it without knowledge of math

[reef dust]

🤣

[wary stream]

It's just basic conversion

[alpine sable]

What conversion?

Could you show me

[wary stream]

Just use math

And conversion rules

Have the units cancel out, use fractions

[uncut tapir]

Use this constant from the given chemistry context to solve the maths problem

[alpine sable]

idk how thats why im asking

[knotty trench]

Arithmetic question. Integers include zero, natural numbers, and their negatives. Do natural numbers include zero or just positive whole numbers?

[wary stream]

Use fractions

[uncut tapir]

You have molecules/mole and the number of moles given. Can you find a formula to find molecules?

[alpine sable]

I cannot

[fair crater]

This is a definition/convention question, there is no 'right answer'

[wary stream]

Like if I wanted to covert 3.45 meters to kilometers, $$\frac{1 m}{1} * \frac{1 km}{1000 m}$$

[ocean seal]

dldh06

[knotty trench]

Thanks.

[wary stream]

Notice how the units in the denominator and numerator cancel out and km is left

[alpine sable]

6,022 * 10^23 / 13900?

[uncut tapir]

The units of that would be molecules/mol^2

[wary stream]

$$\frac{13 900 {mol of H_2O}}{1} * \frac{something}{something}$$

[stuck jolt]

tex hated that XD

Maybe space render it?

Meh its fine

As it is

[uncut tapir]

Try text{}?

[ocean seal]

dldh06

[wary stream]

Whatever

[stuck jolt]

XD

[wary stream]

That says mol of water

[uncut tapir]

$$\frac{13 900 \text{ mol of } H_2O}{1} * \frac{something}{something}$$

[wary stream]

Fill out the something part

[ocean seal]

Gaunter

[stuck jolt]

Ah, that looks nice

[wary stream]

How do you cancel the mols in the numerator

What conversion ratio do you need?

[wary stream]

Thanks

[quartz stone]

g per mol

H2O is 18 or smth

[uncut tapir]

This is the original question

[wary stream]

You weren't the original asker

So no comments from the peanut gallery

[quartz stone]

Oh sorry

[stuck jolt]

Relax, he was just trying to help out

[alpine sable]

6,022 * 10^23 / 13900 * 10^4

[quartz stone]

I thought this was chill and you asked the question... 🤦

I'm too tired

[alpine sable]

How

[stuck jolt]

Ohhhh

[junior vigil]

maxwell equations

[alpine sable]

Yes

[stuck jolt]

I like these equations

[alpine sable]

Watch me

👌

[uncut tapir]

Can you see if you divide those numbers you would get the wrong units? Since you are doing

$$\frac{molecules}{mol}•\frac{1}{mol}$$

[ocean seal]

Gaunter

[alpine sable]

yes

How do you use the bot

$$2+2$$

What

[ocean seal]

Alex_

$$2+2$$

[alpine sable]

Ohhh

This bot is cool

[uncut tapir]

You need to do the opposite

[junior vigil]

$2+2$

[ocean seal]

Moosey

[alpine sable]

How do you use sigma

On the bot

[uncut tapir]

It's LaTeX

[stuck jolt]

You need to take a latex course XD

[alpine sable]

_

I mean

How do I get the bot to put sigma

[junior vigil]

$\sum_{n=0}^{\infty} \frac{x^{n}}{n!}$

[stuck jolt]

Lemme show you a good latex youtube course

That is how I started

[junior vigil]

hmm

[alpine sable]

$$sigma$$

Bru

[ocean seal]

Alex_

[alpine sable]

What

[wary stream]

$$\Sigma$$

[junior vigil]

oh

dumb

$\Sigma$

[ocean seal]

dldh06

Moosey

[stuck jolt]

https://www.youtube.com/watch?v=fCzF5gDy60g

[alpine sable]

$$\sigma F=mv$$

[ocean seal]

Alex_

[stuck jolt]

Check this out @alpine sable

[alpine sable]

How do I write this

[wary stream]

Capital S

[ocean seal]

Moosey

[alpine sable]

$$\Sigma F=mv$$

.

[wary stream]

Also, if you wanted to test latex, use #latex-testing

[ocean seal]

Alex_

[alpine sable]

O

Ok

$$2cos Pi/9, 2cos 7Pi/9, 2cos 13Pi/9$$

[ocean seal]

Alex_

[alpine sable]

Bruh

[alpine sable]

opposite doesnt work

[wary stream]

Use #latex-testing and Google commands

$$2\cos \frac{\pi}{9}, 2\cos \frac{7\pi}{9}, 2\cos \frac{13\pi}{9}$$

[alpine sable]

Yes

Oh

[ocean seal]

dldh06

[wary stream]

There

[alpine sable]

$$3$$

[ocean seal]

Alex_

[alpine sable]

lol

[uncut tapir]

What is your question Alex?

[alpine sable]

?

[wary stream]

Use #latex-testing

[alpine sable]

Ok

[stuck jolt]

Btw, I forgot to ask, how does one get the helper role?

[wary stream]

You can message the ModMail bot and ask

[stuck jolt]

Okay 🙂

[uncut tapir]

This channel is for asking questions.

[alpine sable]

What fraction method did i have to use for the mole stuff?

[wary stream]

Conversions

[alpine sable]

Can you show the thingy

[alpine sable]

this?

[wary stream]

Just plug in the stuff that makes the units cancel and you're left with what you want

[tame stag]

does anybody know where i should but the 3 points

[steady fern]

hi

[tame stag]

hi

[steady fern]

i from brazil, and i want study english

[tame stag]

idk if this is the best spot

[steady fern]

i understand u

sorry 4 thi

this

[tame stag]

it's ok

[steady fern]

Do you recommend any courses to study English?

[tame stag]

i really don't know i guess just try to find some good online tutorials and lessons?

[stuck jolt]

Maybe a math help channel isn't the best best place to ask these kind of questions?

You could go to #book-recommendations Though, I am sure people would help u 🙂

[tame stag]

ok but

does anybody know

where i should put the points

cause im a literal idiot

[stuck jolt]

Ok lemme see

[steady fern]

uuwl, sorry

[desert moon]

uwu

[stuck jolt]

Its ok 🙂

@tame stag

Just plug the points given on the graph

-4

Is at x=-4 on the graph

Then range goes from 0 to 4

including both 0 and 4

[tame stag]

ohh ok

[alpine sable]

im guessing the domain should be the possible x values for a function f(x), and the range will be the results from that function (y). So the x coordinates of the points should be within the domain: -4 <= x <= 2. And the range would be the set of y values, within 0 <= y <= 4

idk

[tame stag]

ty 😭👌

i got it 😌🤚

i just realzied what an idiot i am

anyways

ill get going thx

[alpine sable]

If the determinant is 0, is the area of ​​a transverse vector a and vector a 0 when it's a parallelogram?

[topaz scaffold]

I don't get your phrasing

Ah it should be

[alpine sable]

I think the area is 0 then because tje determinant=area of a parallelogram and if if the determinant is 0 then the area is 0 and it's a zero vector

[dire crystal]

any ideas on how to prove this 😦

[dire crystal]

nvm

[crisp quest]

hello, doing linear algebra. I was asked to do a 3x3 lower triangular skew symmetric

I don't understand why its all zero's and not 1's in the diagonal

[crisp quest]

<@&286206848099549185>

[placid zinc]

What's the question?

What do you mean "do" a 3×3 lower triangular skew symmetric?

[crisp quest]

we have to make a matric

matrix

answer can only be
[0,0,0]
[0,0,0]
[0,0,0]

[glass lichen]

If you had 1's on the diagonal, it'd be symmetric not skew symmetric

@crisp quest

since you'd have $I_3^T=I_3$

[ocean seal]

Mosh

[crisp quest]

oh ya because on the skew symmetric.. the diagonal must all be different?

[glass lichen]

Skew symmetric means that $M^T=-M$

[ocean seal]

Mosh

[crisp quest]

or no the symmetric

let me think about it

i transferred into the class today

this is me catching up on last weeks stuff

[glass lichen]

Basically you have 3 parts to consider: the lower triangle, the diagonal, and the upper triangle

[crisp quest]

yes so if its a lower triangular

you need 0's in the top right

and if its symmetric you have to do the lower side

yes

[glass lichen]

oh yeah, I got it backwards, yes you need $m_{12},m_{13},m_{23}=0$ for lower trianglular

[ocean seal]

Mosh

[glass lichen]

but then since you need skew symmetry, you also need it to be upper triangluar

so that means everything off the diagonal is 0

[crisp quest]

yes

i got that part

[glass lichen]

then for skew symmetry, you need the entries on the diagonal to be their own negatives

so $m_{11}=-m_{11}, m_{22}=-m_{22},m_{33}=-m_{33}$

[ocean seal]

Mosh

[glass lichen]

but that's only true for 0

[crisp quest]

ok

[glass lichen]

so all your entries are 0

so M=0

[crisp quest]

yes

that now makes sense

thank you

[glass lichen]

also like normal, $M=[m_{ij}]$ if you're confused by the notation I used

[ocean seal]

Mosh

[kindred cave]

41795-2123

[crisp quest]

our teacher in class used it once today

but, he didn't really use it on the youtube lectures

[glass lichen]

Yeah it just means the (i,j)th entry of the matrix is $m_{ij}$

[crisp quest]

so maybe he did it more last week when i wasnt in the class

[ocean seal]

Mosh

[glass lichen]

so the entry in row i column j is m_{ij}

[little owl]

are there functions that only have a horizontal asymptote on one side? Also, is there a function with a horizontal asymptote on both sides but is crossed in the middle?

[topaz scaffold]

e^x

[glass lichen]

yes to both

[little owl]

oh yeah exponentials

could you give me an example of the second one?

[glass lichen]

I know one just cant remember the exact eqn

[little owl]

hmm

do you know how i could find one?

[glass lichen]

,w graph y=x/(1+x^2)

[ocean seal]

Results provided by WolframAlpha

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

Requested by moshill1#9771

[glass lichen]

shit graph

[little owl]

lol

[topaz scaffold]

arctan?

Oh wait that's 2 different asymptotes tho

[glass lichen]

$f(x)=\frac{x}{1+x^2}$

[ocean seal]

Mosh

[little owl]

ooo

ty

[topaz scaffold]

Cool

[glass lichen]

has a HA of y=0 but root of the origin

[eternal mantle]

what does the symbol in the middle mean

[oak chasm]

Greater than or equal to.

[eternal mantle]

thanks

[oak chasm]

No problem.

[halcyon sierra]

I'm on this question here and the step is saying to cross multiply, how do I go about this?

[glass lichen]

they mean get a common denominator and combine the fractions on the LHS

[halcyon sierra]

How does that lead to this?

I see how they have the same denominator, but idk how we've gotten there

Shouldn't the 2Tan(2A) be in there somehwere?

Oh I am such an idiot, don't worry Mosh, thank you!

[silent kestrel]

https://learnopengl.com/Getting-started/Transformations#:~:text=Because vectors are,and 3D space.
im a bit confused on this part
what does it mean by "position vectors"
are they different from normal vectors?

[uncut tapir]

It says on the page. A vector on it's own describes a direction and magnitude. A position vector describes a point from the origin vector with its direction and magnitude

[silent kestrel]

so a position vector points towards a point?

[uncut tapir]

Yes

[silent kestrel]

ah okay

[alpine sable]

Base case: Setting $n = 1$ yields $1^3 = 1 = 1^2$.\par
Induction step: Take $n \in \N$ and suppose that $\boldsymbol{\sum^n_{i=1}}i^3 = (\boldsymbol{\sum^{n}{i=1}}i)^2$. Then \begin{align*}
\boldsymbol{\sum^n{i=1}}i^3+(n+1)^3 & = \left(\boldsymbol{\sum^{n}_{i=1}}i\right)^2 + (n+1)^2(n+1)\
& =
\end{align*}

[ocean seal]

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

[alpine sable]

I have this but I can't find a way to get the LHS to $\left(\sum^{n+1}_{i=1}i\right)^2$

[ocean seal]

sanjay

[eternal mantle]

what do the R and the E symbols mean?

[alpine sable]

in R(eal numbers)

[placid zinc]

Remember what you are supposing

[eternal mantle]

what does the E mean?

[placid zinc]

You can transform Σi³ into (Σi)² freely
When the top is n

[alpine sable]

well yeah

[placid zinc]

Or wait, that's what you've done, isn't it?

[alpine sable]

yeah

I actually can get to $\sum^{n+1}_{i=1}i^3$ using that reasoning

[ocean seal]

sanjay

[alpine sable]

but I need this

[placid zinc]

I remember you need to do
Σi = n(n+1)/2

[alpine sable]

uh

didn't follow

[placid zinc]

Have you seen that formula before?

You'll need to use it here

[alpine sable]

I didn't

look one thing

(1+...+n)^2

when doing the induction step

we also can get to (2+...+2n)^2

but I don't know if this will help

[placid zinc]

Are you saying that
(Σ i)² = (Σ 2i)²?
You've made a mistake somewhere

[alpine sable]

I mean we would need to reach (1+...+n+(n+1))^2

but its wrong indeed

I see that formula now

[alpine sable]

this

wow this simplied so much

(n(n+1)/2)^2

thanks man

[placid zinc]

Np, glad it worked out!

[storm swan]

hi i need a bit of help on this

im a bit confused, what does it mean by apply the definition of periodic function?

[placid zinc]

It means "Use your unit circle"

[storm swan]

ohhh i see ok thank you very much

[placid zinc]

Or, it means "you can lower this by 2π and it won't change the answer"

[storm swan]

the step before told me to break it down into 6pi+ pi, so do i break it down further?

[placid zinc]

No, that's a good way to break it

[storm swan]

ah ic, im just not sure what to do for this second step

[placid zinc]

Because 6π won't change anything, so it turns into cos(π)

[lavish pecan]

can someone help me on a question with my hw

it gors like this

What type of function is indicated by the following equation? 4x + 5y = 20

[storm swan]

ohh i see so its just cos pi?

[placid zinc]

Beautifully done

[lavish pecan]

pls help i have a test tmrw

[placid zinc]

Linear

[lavish pecan]

yes but how do i find out if it is linear or not

[placid zinc]

ax + by = c
Is always linear

Anything that can't be written that way is not linear

[alpine sable]

is there a equation describing a cylinder? For example in the case of a sphere, the sphere is the set of all points whose distance from the center of the sphere is equal to it radius. given a point in R^3 I can determine if the point is on the surface or not. So I am looking for something similar for a cyclinder.

[lavish pecan]

oh

thank you

[mild kettle]

This is my answer is it right?

[glass lichen]

no

it's not even a function

[placid zinc]

Being able to freely rotate any cylinder makes this problem vague. Give me 3 points and I can likely match some cylinder to them

(rcosθ, rsinθ, c)
Describes an upright cylinder

[uncut tapir]

Or use cylindrical coordinates?

(z, r, theta)

[alpine sable]

I am describing the cylinder with a center position, a radius, and height. I tried the cylindrical coordinates look for any sort of relationship between a point on the cyclinder, and the given quantities I have.

[placid zinc]

(rcosθ + p1, rsinθ + p2, c)
Allows you to move the center to (p1, p2)

[uncut tapir]

You can describe a cylinder as a locus of all points at a fixed distance r along a central axis of length z I guess

Maybe that would help ?

[alpine sable]

that helps I look into it.

[mild kettle]

The answer was x+1?

[uncut tapir]

Seems like it would. In your example a sphere is also a locus but from a fixed point not a fixed line

[glass lichen]

yes, that's f(x) for x<4

[mild kettle]

oh sorry I thought you were giving me an answer

[glass lichen]

???

where would you get that idea from?

"is it right?"
"no, it's not even a function"

[mild kettle]

sorry im not very smart

[pseudo dust]

[rich basin]

Is this explanation true

for the x component i have a similar one but instead of mg sin(theta) i have

mg / (sin theta)

Similarly with the cos as well

[uncut tapir]

Why would you do mg/sin(theta)

[winged pebble]

can i get help here or is this active

because my math thing is easy for u probs

like

im dumb

[placid zinc]

You've posted the same question in multiple channels you don't need to post here as well

[winged pebble]

;)

[rich basin]

@uncut tapir so if you were to find the force x pushing the Fn

it would be sin(theta) = O/H

in which O is mg

and H is the Force x you want to find

and since you want to make H to variable

you wouls move the mg to make the lefthand side become mg/ sin(theta)

And then you can find the net force of it going down to be ma which would be H - Fr

[uncut tapir]

Where you went wrong is actually H is mg

[rich basin]

why?

mg is the opposite of theta

[uncut tapir]

Theta is the angle between the normal and the direction mg acts

[rich basin]

Whast do you mean the noral and the direction mg acts?

that theta would be 180 then

[uncut tapir]

Also the hypotenuse represents the longest side. You would be saying a force greater than its own weight pulls it downwards which would be impossible

In mechanics the normal is a direction perpendicular to the surface

Like just think about it physically. If you lie down flat there is 0 weight horizontally meaning it's impossible for the force of your weight to move you in any direction

Then friction always acts opposite and parallel to the direction you travel

[rich basin]

but this is not horizontally this is occuring diagonally

So the weight would have an effect when it would pull the object downwards

[uncut tapir]

Yes that's my point. It does have an effect but not the full effect

[rich basin]

yeah, but then this is what i'm calculating

[alpine sable]

I was able to think of a part of the solution thx to that. Realizing I wanted orientation I introduced a normal vector, and letting the center position be the center position of the base of the cyclinder. With the normal vector n, center position c, and any point x on the cyclinder in R^3, I check if the dot product between the vector x-c, and n is greater than or equal zero will guareentee does point are in view of c. Only problem is introducing the radius of the cyclinder to the equation.

[rich basin]

@uncut tapir But why would you use the theta the normal and the downwards force

You would only use it to find the Normal force

[uncut tapir]

The idea is you resolve forces in two directions. Parallel to the surface and along the normal

[rich basin]

I get that, but then how can we find the force pulling it downwards the slope

[uncut tapir]

The magnitude of the normal vector would have to equal r right?

[alpine sable]

no the normal would be at that the center position of the base.

I wish I can draw a diagram for this

to post here

[uncut tapir]

It would be mgsin(theta)

[rich basin]

so you are using the theta between the downwards force and the normal

[uncut tapir]

Yes

[rich basin]

Isn't that finding Normal force

[uncut tapir]

The normal would be cos theta

[rich basin]

What, it can't be

If you were using sin(theta) right

it would be sin(theta) = O/H

in which O = mg

and what are you trying to find?
the mising variable that is unkown is H

therefore you would be finding h

And H is not an x component since you can see the legend of the y and x axis here

This is using theta between the normal and the downwards force

[uncut tapir]

That's exactly right. H isn't an x component

[rich basin]

But that is why you would need to use the theta

in the incline

the incline thet

[uncut tapir]

H is mg, O is the x component

[alpine sable]

Found a solution

[rich basin]

Is this the theta from between the normal and the downwards force

[alpine sable]

kind of

[uncut tapir]

Yes

[rich basin]

You can't make H mg, because gravity only effects the system vertically

and not merely the model is bending gravity

[uncut tapir]

The hypotenuse is the vertical line

[rich basin]

Wouldn't the hyptonuse be the slant line

[uncut tapir]

Nope. The diagram is drawn badly I'll admit

Theta should actually be in the top corner of the triangle

[rich basin]

how can the slant be lower than the vertical line

[white kiln]

what is this i need help

[rich basin]

All slants within a right triangle are the largest values

[alpine sable]

I need help

pls

its 9th grade math

so its easy

[alpine sable]

ask away

[alpine sable]

#34. Evaluate 7x2x7x5 using properties of numbers. Name the property used in each step
btw the properties is one of these or more reflexive, symmetric, transitive, additive identity, additive inverse, multicativ identity, multiplicative idenity, multiplicative properity of 0, associative, comutative, distributive

[uncut tapir]

The side opposite the 90° angle is

[rich basin]

yes

[alpine sable]

pls?

[rich basin]

then why wouldn't you make H be the mg / sin(theta)

[alpine sable]

hello?

anyone?

no?

no one is gonna help me with my math hw?

[vague coral]

i dont understand

[alpine sable]

me either

[alpine sable]

dats y i came here

[vague coral]

7x2x7x5 = 14 x 7 x 5 = 98 x 5 = 490

[alpine sable]

i need properties, not 490

i already know dat

[vague coral]

I dont know, maybe associative ?

[uncut tapir]

Forget about the trig for a moment. You are trying to create a triangle with the normal, the direction of the slope and a vertical line. The slope and the normal are perpendicular by definition which means the vertical line is the hypotenuse

[alpine sable]

i need step by step properties

[thorn vortex]

i think it is commutative

[alpine sable]

step by step pls?

each step is different

[uncut tapir]

This question is not very well defined

[vague coral]

what step

that exercise is weird af

[alpine sable]

the text book isnt defined

[alpine sable]

textbook be wiered af

[vague coral]

which step are we taking to evaluate this

[alpine sable]

idk

[uncut tapir]

You need to help us help you. What kind of answer are you looking for?

[rich basin]

@uncut tapir So you are trying to make a right angle with the normal and the x axes?

[alpine sable]

PLS

[uncut tapir]

Yes exactly

[alpine sable]

the question doesnt say

[rich basin]

@uncut tapir What would theta be in the new triangle?

[uncut tapir]

It would still be theta. It's kind of a long proof but you're expected to just treat it as a given fact for mechanics

[rich basin]

Wouldn't this be using corresponding angles or something

@uncut tapir Also is this theta

[uncut tapir]

You should get this

[rich basin]

Okay so this is using corresponding angles to find theta

I thought theta would be between the hyptonuses and C to D

I mean between B to D and C to D

[uncut tapir]

The diagram is drawn badly

You don't have to prove the two given angles are equal for every question like I said it's just considered a given

[rich basin]

Thanks, I understand now

[alpine sable]

Am confused why wrong

[uncut tapir]

Why have you got 4 solutions

[alpine sable]

I put all the points where it’s intersected

it says solutions plural

[dusky flame]

isnt it two points only

[uncut tapir]

But this is a linear function and a quadratic? Function. At most you should have 2 solutions

[alpine sable]

But how would I pick which points to be the solution? Is it just on a certain axis

[dusky flame]

look at the points of intersection

[alpine sable]

Oh man

the fraction and (1, 0)

[uncut tapir]

Yes

[dusky flame]

ye

[alpine sable]

Wow i’m so rusty

thanks

[rich basin]

@uncut tapir I still don't get how you would find the x component using the angle between the normal and the downward's force

[eternal cedar]

i need a refresher on logs

[uncut tapir]

Refer to this diagram. The weight is the hypotenuse. You want the force acting along the opposite

[ripe mountain]

I just need the common difference.

[eternal cedar]

1 is 5 i think

[ripe mountain]

That's the first term

[eternal cedar]

differs from 5 for each term

[uncut tapir]

You don't need the common difference

[eternal cedar]

not sure what you mean by common difference

that isnt necessary for solving arithmetic series

[ripe mountain]

Oh I must have misunderstood something

[uncut tapir]

Did they go over the famous story of adding the numbers 1 to 100?

[ripe mountain]

Nope

[uncut tapir]

Gauss noticed that 1 + 100 = 101, 2 + 99 = 101, ... and reasoned there are 50 such pairs which add to 101. So the answer was 50 * 101 = 5050

You basically just apply the same idea here

[alpine sable]

Up quick question what is recursive and explicit formulas don’t understand them yet

[eternal cedar]

am i allowed to ping helper since its been 15min

literally just joined the server so idk how stuff works here

<@&286206848099549185>

[lone heart]

#questions

For a list of rules about asking on this server, please see #❓how-to-get-help.

[lime gate]

youre fine to ping helpers

[eternal cedar]

ok

[alpine sable]

I finally arrived at a solution I been working on for a while. Leaving it here for anyone who might experience the same problem as me. I tried to be clear as much as possible

Someone pinged me on this channel

But idk who

[muted owl]

i got c as answer can anyone verify plz

[stable crypt]

Check mentions

[cinder shard]

Can someone explain the trick to this question?

I tried to set the two equations equal to each other, but I know there's a simpler way to do it

[feral crypt]

I've already done part A, I just need help understand part B. Thanks!

[ionic jewel]

g(x) can be described as f(x) flipped over then moved up 10

so if you want it to be in the same place you need f(x) = 5, cuz it flips to -5, then moves up 10 back to 5

@cinder shard I assume your setting equal to each other worked too?

[cinder shard]

I'm getting kind of a complex answer

(-6 +- root 84)/2

Assuming I use the positive value since this is for a practice SAT and u can only input positive values @ionic jewel

[feral crypt]

Is the answer 2 @cinder shard?

[ionic jewel]

the answers should be a little less than 1 and a little more than 7

[cinder shard]

my work

but as u can see, there must be a simpler and more time efficient way to do this, especially because 84 isn't a perfect root

[feral crypt]

is it 2?

[cinder shard]

idk

brain is too fried to come up with what root 84 equals

Not exactly what bunny predicted so im assuming i did it wrong

[feral crypt]

yeah it's much simpler

[ionic jewel]

,calc sqrt(10)+4

[ocean seal]

Result:

7.1622776601684

[feral crypt]

so essentially, you're trying to find a value for x when the two equations equal each other

so, you're going to equate the two equations and solve for x

[cinder shard]

that much I know, but there should be an easier way to do this

it also doesn't tell me to round

so I'm kinda suspicious if it isn't a whole number

[feral crypt]

it is a whole number

give me one sec

There you go, possible answers are 2 and 8

[cinder shard]

thanks for the explanation

I didn't cross out the 10's and that made it harder for me

[feral crypt]

oh haha, that'll do it

[cinder shard]

I tried to multiply everything by -2 to get rid of the fraction, but it just made it more complicated

[feral crypt]

yeah, typically SAT questions don't require that much work

it's mostly just understanding concepts rather than doing hard maths

[cinder shard]

yeah thanks for the help

[feral crypt]

np 😄

[maiden carbon]

kinda confused, the positive part of the graph is above the X line but that looks right

[ionic jewel]

@feral crypt that's wrong

oh

god

no ur right

i coulda sworn it said g(x) = -f(x) + 10

[jolly vine]

quick question
can a form still be called a quadratic function even if it has 2 squared exponents?

[lusty ibex]

you mean like this (x-a)^2(x-a)^2

[jolly vine]

yep

[lusty ibex]

nope then it becomes a quartic

[jolly vine]

oh alright, thanks!

[lusty ibex]

nws

[maiden carbon]

still need help with thi

[reef geyser]

can someone help me w these

[alpine sable]

How

[vale wigeon]

these look like questions from a test

[stable crypt]

On mobile its in the search button at the middle bottom of the screen

[vale wigeon]

@reef geyser is this a test?

and/or other timed, graded assessment?

[reef geyser]

nopeee just an assignment

[vale wigeon]

so it's homework. okay.

[reef geyser]

yup

[vale wigeon]

i would appreciate if you re-uploaded those pictures so that they're right-side-up

[reef geyser]

okay hold up

[vale wigeon]

okay

let's start with 10a

have you made any progress on 10a so far?

[reef geyser]

not really i’m kinda new to the chapter so it’s confusing

[vale wigeon]

so you're unfamiliar with the basic trig ratios?

i.e. sin, cos and tan

and what they represent in the context of right triangles

[reef geyser]

i know some of it

like i get the basic idea but i just get confused when it comes to questions

[vale wigeon]

well here we have a right triangle where one side is known to be 16cm, another side is unknown, and the third side is not labeled at all

we are also given that tan(θ) = 4/3

tan(θ) is the ratio of two of the sides. which ones?

[reef geyser]

OHH WAIT

i think i got the 1 st one

its 12 i think

[vale wigeon]

incorrect

[reef geyser]

WAIT WHAT

[vale wigeon]

you are saying x = 12, yes?

[reef geyser]

yup

[vale wigeon]

yeah, no, that's wrong.

[reef geyser]

wait so how do i do it

[vale wigeon]

and it should be painfully obvious that the side labeled x is longer than 16