help-0

[alpine sable]

I dont think I can

[vale wigeon]

sigh ok fine

[alpine sable]

yeah... its annoying 😦

[vale wigeon]

i mean ok

i think i know what they're trying to get at here

if you expand (x+y+z)(1/x + 1/y + 1/z) what you get is

3 + (x/y + y/z + z/x) + (x/z + z/y + y/x)

and then you can apply c to each part i've put in parentheses, taking (x/y)^(1/3), (y/z)^(1/3) and (z/x)^(1/3) as your x, y and z (bad notation but i hope you get me

getting (that mess) ≥ 3 + 3 + 3

this is an overcomplication if you ask me

but whatever ig

[alpine sable]

sorry do you mind explaining this part again?

[vale wigeon]

yeah okay so like

x/y + y/z + z/x = u^3 + v^3 + w^3 where u = (x/y)^(1/3), v = (y/z)^(1/3) and w = (z/x)^(1/3)

and then by part c we get u^3 + v^3 + w^3 ≥ 3uvw = 3

[alpine sable]

I need help in making a voronoi diagram, specifically from my name

[vale wigeon]

@alpine sable can we take this to a less busy channel

[alpine sable]

ok i see

when Im solving these questions Im not meant to work backwards

Ohh

Srry

Will do

Which chanlle do you propose?

so do I just rewrite the steps forwards?

[vale wigeon]

i pinged you in #help-9, aero

@alpine sable if you want

[alpine sable]

okay thank you!

[alpine sable]

im so confused

i cant find the square root

so i cant find answer

[winter bay]

ah

time to learn something so beautiful

called factoring

[vale wigeon]

can't find the square root of what?

[winter bay]

they think they have to use the sqrt to find the zeroes

but they can factor

[vale wigeon]

the discriminant of your equation is 169, as far as i can tell.

[winter bay]

if u want u can explain this ann

[vale wigeon]

honestly im too tired

it's all yours

[winter bay]

ill take it then

@alpine sable so instead of taking the sqare root of this you can factor out the equation

or you can use the quadratic equation but theres no need for that

so lets look at only the coefficients

[alpine sable]

See I got 259

[winter bay]

u arent trying to find the discriminant i thought

u are trying to find what the values of c are

there should be 2

luckily both are real

because imaginary numbers exist...

but anyways we can factor this equation to find c

[alpine sable]

I am solving for x

[vale wigeon]

what's that other 7 doing there?

[alpine sable]

I have all a b c

[vale wigeon]

the discriminant isn't b^2 - 7ac

it's b^2 - 4ac

[winter bay]

^

but even then its just not rigorous to plug and chug for c here

we should do it as pleasantly as we can

so lets factor this polynomial

to factor a polynomial, we need to find 2 numbers whos product equals ac and sum equals b when referring to $ax^2 + bx + c = 0$

[ocean seal]

hiidostuff

[winter bay]

we are given what a b and c are for your quadratic, so what are they?

@alpine sable

[alpine sable]

The a b c are in the equation itself right?

This how my teacher did it

[winter bay]

yep

but whats cool is that we can factor $x^2 -4x - 21 = 0$

[ocean seal]

hiidostuff

[winter bay]

to find its answers way easier

so what is ac in this polynomial

aka the product of the first and last coefficients

or the number before x^2 times the last number shown

[alpine sable]

My problem really is just that I can’t find the square root

[winter bay]

you dont need to

im trying to show you another way of solving it but you are getting stuck on one idea

when theres a much easier way

[alpine sable]

Oh ok

[winter bay]

so refer to that polynomial

[winter bay]

what is this value?

remember if theres no number before a variable the number is just 1

[alpine sable]

Yea

Is my problem any different?

[winter bay]

nope

yo ucan also factor the original

whats the original again?

[carmine lion]

39th

[winter bay]

ask in a channel that isnt taken jett

6 thru 9 havent been used yet

anyways @alpine sable u can show the og problem to me

[winter bay]

alright

so if we have $ac^2 + bc + x = 0$, what is $a * x$?

[ocean seal]

hiidostuff

[winter bay]

in relation to your original problem

[alpine sable]

-30?

[winter bay]

mhm

so now you need to find two numbers

lets call these numbers k and n

to where kn = ax and k + n = b

aka kn = -30 and k + n = -7

pro tip: list out all the positive and negative factors of -30 and see which ones work out

[alpine sable]

u were right it was

i did the entire formula wrong

[winter bay]

oh welp

[alpine sable]

LOL

[winter bay]

i guess solve it like that

u will learn about factoring some other time...

whoa

[neat schooner]

whoops

didnt write the end sorry

[winter bay]

do you mean $\lim_{h\to 0} \frac{f(x+h) - f(x)}{h} = f'(x)$

[ocean seal]

hiidostuff

[winter bay]

the general definition of a derivative

[neat schooner]

nvm, i got the answer right now

thanks for trying to help me either way, I appriciate it!

[cinder sundial]

Can red be simplify to blue

3x and the bottom 12 both divided by 3

[oak chasm]

@cinder sundial No, if you divide the top and the bottom by 3, you have to divide the whole top by 3 and the whole bottom by 3.

[cinder sundial]

Ohhhh

My bad

Am I right

Just the right part

[alpine sable]

I don't think so

[cinder sundial]

Damnnn

[alpine sable]

it would be 3x-1/4 - x

if you eliminate the 3

just the right part only

[cinder sundial]

Wdym

So the answer is fine but can be simplify further

Ohh

I get what u said

Let me try

[alpine sable]

I am really bad at English when it comes to math

lol

[cinder sundial]

Am I right

That’s what U talkin bout

[alpine sable]

wait a minute

let me point this out for you

[alpine sable]

eliminate that only

[cinder sundial]

Ohhh

You’re so smart

[cinder sundial]

What I did here

Is illegal

[alpine sable]

yes, it is not right

tbh, I am just new to this concept as well

I really hope I am right about this

[jade birch]

Doing what Maji suggested is right

But considering your understanding of these algebraic operations, I would recommend you do the thing in the parentheses first

[alpine sable]

that's correct

[cinder sundial]

I have no clue bout it, I just know it could be canceled

[alpine sable]

remember that if something is stuck with another arithmetic on a quotient [for example (3x-1)/12], you can't eliminate only one of them

[cinder sundial]

I got u

But That one is legal right

[jade birch]

yes

[cinder sundial]

Got it, thank you so much

[jade birch]

$\frac{4+4}{2} = \frac{2+2}{1}$

[ocean seal]

.itsjustnai

[jade birch]

if this is what it says

I can't see it well

[cinder sundial]

It is

Am I right

[alpine sable]

mind you explain me where the -1 come from?

[cinder sundial]

It’s -3

From -3 in the middle of question

[alpine sable]

got it

wait

[jade birch]

it's correct

[cinder sundial]

Yessssss

[alpine sable]

yes, it is correct

[cinder sundial]

I reached the final answer

[alpine sable]

nice

you are correct

[cinder sundial]

Should I write it 5-x

[jade birch]

You learn fast

[cinder sundial]

Or -x5

[jade birch]

compared to a couple of days ago when I had to explain subtraction to you, this is amazing progress 👌

$5-x\neq-x5$

[ocean seal]

.itsjustnai

[jade birch]

$5-x=-x+5$

[ocean seal]

.itsjustnai

[cinder sundial]

-x5=-x * 5

Am I right

[jade birch]

Yes

[cinder sundial]

Ohhh

I’m too smart

Thank you guys

[pine lake]

Hello

[alpine sable]

hello, Jigger

[jade birch]

Hi

[pine lake]

Can someone help me

First i separate them

[alpine sable]

exponential, huh

I can try

[pine lake]

Then i factorise

[pine lake]

Indices

[jade birch]

Can you show how you did that?

[jade birch]

indices = exponents = powers

[pine lake]

Ok

[alpine sable]

yeah, show us the your solution first

[oak perch]

-48/16807

[pine lake]

Ok

Lemme take pic

[alpine sable]

7^2 = 7*7

[pine lake]

Dude

I don't know how to do this

The separate and factorise was for +

[jade birch]

Your idea of how to solve that is correct, but if you didn't reach the correct answer you probably have some algebraic error, which is why i wanted to see your work

[jade birch]

$7^{b+(-2)}$ does this help?

[ocean seal]

.itsjustnai

[pine lake]

No not that

[alpine sable]

how did you actually separate?

[pine lake]

• between 7^b-2 and 7^b

[oak perch]

? Multiply 7^(2-b) on both numerator and denominator......

[jade birch]

Factorising is the same with '-'

factoring*

[pine lake]

Correct?

[alpine sable]

yes

you separated them

[pine lake]

Then how to do

[jade birch]

yep

$3a^2-a=a(3a-1)$

[ocean seal]

.itsjustnai

[jade birch]

factor 7^b

[pine lake]

Hmm

[jade birch]

$\frac{a}{b} - a=a\cdot(\frac{1}{b} - 1)$

[ocean seal]

.itsjustnai

[alpine sable]

try to distribute out the same element

once you do that, you might have some other way to go

[deep magnet]

Hey guys, I have been given this formula
[a_n := n + 3n^2 + 2n^3]
for which I have to prove that it is dividable by 6. My idea was to show that it is the same as the multiple of 6. With some rearrangement I got to
\begin{equation*}
a_n := n + 3n^2 + 2n^3 = n (1 + n(3 + 2n))
\end{equation*}
but I dont really know where to go from there. Did I run in the wrong direction or am I just missing something

[ocean seal]

Loewenherz

[rustic barn]

do you know how induction works?

[reef sorrel]

@deep magnet that one unicorn is right, induction is the way to go

modular arithmetic would be overkill

[upbeat gorge]

Many ways to do this

You can do induction, you can factor, you can do case-by-case, you can do some combination of them…

[ocean seal]

Loewenherz

[deep magnet]

Not really sure how I would use factor here [n \cdot (n + 1) \cdot (2n + 1)] seems not really helpful

[ocean seal]

Loewenherz

[upbeat gorge]

you can show that either n or n+1 is divisible by 2, then show that one of the factors is a multiple of 3

[vale wigeon]

try to consider $a_{n+1} - a_n$; maybe proving \textit{that} to be a multiple of 6 may be easier.

[ocean seal]

Ann

[vale wigeon]

& if you have this and the divisibility of a_1 by 6, you can do some induction to show all of the a_n themselves are also divisible by 6.

,w simplify 2(n+1)^3 + 3(n+1)^2 + (n+1) - 2n^3 - 3n^2 - n

[ocean seal]

Results provided by WolframAlpha

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

Requested by Ann#0413

[vale wigeon]

ah, look how nice it is.

@deep magnet @upbeat gorge

[deep magnet]

I have to work through that and understand it, but thanks already

[vale wigeon]

work through what

the algebra, or the induction i suggested?

[errant dagger]

how do i prove that simultanous equations have no solutions

ive done like 10 questions wrong

[oak chasm]

@errant dagger Use algebra to get only pure numbers remaining and the sides of the equation will be like 3 = 5 or something.

Or you can use RREF if you know that.

[errant dagger]

what is that?

[oak chasm]

Something you learn in a class called linear algebra.

@errant dagger What's an example problem?

[errant dagger]

@oak chasm

this one

I wanna prove that simultenous euqations have no solutions

so there not parralel and not intersect

[ocean seal]

Chai T. Rex

[oak chasm]

So, what are our simultaneous equations?

We do it by component.

[ocean seal]

Chai T. Rex

[oak chasm]

@errant dagger Does it make sense how I got those?

[errant dagger]

yes @oak chasm

i apologise for the delay in resposne

response*

im just struggling on how to show there are no solutions here

[ocean seal]

Chai T. Rex

[oak chasm]

Then, fill in what you get for those two into the third equation.

Make sense?

[errant dagger]

hmm

im not quite sure what you mean sorry :/

[oak chasm]

OK, take the first two equations. Do you see how to solve for the two variables?

[errant dagger]

yep i can solve for one of them

which will give an answer for the other

[oak chasm]

OK, what do you get for both?

[errant dagger]

and then should i plug into the third and prove that it makes no sense?

[oak chasm]

Right.

[errant dagger]

I see

[oak chasm]

Prove that you get something like 3 = 5.

[errant dagger]

sorry im being yelled at by parents rn ill do the math in 5 mins and check uo than you

[oak chasm]

OK, no problem.

[steady wave]

is this channel free?

[oak chasm]

Not right now.

[steady wave]

aight then.

[errant dagger]

ok so

lambda = -2u

for eq 1

sub into eq 2

-2u = -1 - 3u

[oak chasm]

Right so far.

[ocean seal]

Chai T. Rex

[errant dagger]

u = - 1

[oak chasm]

Right.

[errant dagger]

therefore lambda = 2

sub into 3

[ocean seal]

Chai T. Rex

[oak chasm]

Right.

Now, fill in those to the third equation.

[errant dagger]

we get -1 + 2 = 3

1 = 3

which is false and therefore there are no solutons to this system?

[oak chasm]

Right, so they don't intersect.

No solutions.

Now, are they parallel?

[errant dagger]

so i just need to prove that there is a contradiction

ill do that one now good idea

so if theyre parralel

the direction vectors must be scalar multiples of eachother right?

[ocean seal]

Chai T. Rex

[oak chasm]

Yes, so which are the direction vectors?

[errant dagger]

the ones with constant coefficients

(2 , -1, 1) = a(-4 , 3 , -3)?

[oak chasm]

Yes, solve for a.

[errant dagger]

(1) 2 = -4a

(2) -1 = 3a

(3) 1 = -3a

(1) a = -1/2

(1) into (2)

-1 = -3/2

thats immediately a contradiction

so no solutions?

[oak chasm]

Right.

So they're not parallel.

Yes, no solutions for a.

[errant dagger]

thank you very very much :))

you were talking about smth rref before

and linear algebra?

[oak chasm]

Yeah, it's reduced row echelon format.

[errant dagger]

we havent done linear algebra in class yet, but im usuing gaussian elimination for a lot of these system equation proble,s

[oak chasm]

Yeah, gaussian elimination is another word for it, I think.

[errant dagger]

How would I show no solutions using gaussian elimination?

[oak chasm]

You'd have 0 = 5 or something on one of the rows.

The variables would all be zeroes and the constant on the other side of the equal sign wouldn't be zero.

[errant dagger]

im gonna try and do the parralel lines thingy with RREF then rq

[oak chasm]

RREF is Gauss-Jordan elimination, which is a bit further than Gaussian elimination.

[errant dagger]

actually yeah

i think the single variable elimination might not be possible (or easy ig for me)

since i havent done any linear algebra and gaussian elimination is just reall simple

[alpine sable]

Hello, anyone able to help me solve this? Lisa’s age is twice her sisters age. The difference between their ages is 8. How old are Lisa and her sister?

[errant dagger]

hmm this might have actually worked

i eliminated into 0a = 2 i think

thank you :))))

[oak chasm]

No problem.

@errant dagger Is it OK for primal to use the channel?

Or do you have anything else?

[errant dagger]

yep, feel free, thank you sm for the help :))

[alpine sable]

thank you @errant dagger

[oak chasm]

You're welcome.

[alpine sable]

i need to show work also, im just super confused

[oak chasm]

@alpine sable How would you write "Lisa's age is twice her sisters age." in algebra?

[alpine sable]

i think like

2x + 8

[oak chasm]

OK, let's go over that.

[alpine sable]

okay

[oak chasm]

We have three numbers, Lisa's age, twice (2), and her sister's age.

Let's call Lisa's age L. Let's call her sister's age s.

So, we have "L is twice s."

Does that make sense?

[alpine sable]

yes

[oak chasm]

OK, "is" usually means "=".

L = twice s

Twice means to multiply something by two.

So, L = 2s.

See how I got that?

[alpine sable]

Ohhhhhhhh

this is starting to make more sense

yeah i do see how you got that

[oak chasm]

OK, let's look at the second part: "The difference between their ages is 8."

This part is a little trickier.

Which age is higher?

Lisa's or her sister's?

[alpine sable]

lisa because we still need to multiply her agee

L = 2()

[oak chasm]

OK, so "The difference between their ages". Let's do that part.

Difference is subtraction, so we have L - s.

"L - s is 8"

L - s = 8.

Do you see how I got that? It's a little trickier because of the difference.

[alpine sable]

yeah so with difference we need to subtract age

[oak chasm]

Yes, that's right.

And the difference is 8, which is a positive number.

So, to get a positive number with subtraction, you need to subtract a larger number from a smaller number.

That's why we didn't say s - L = 8.

That would be a smaller minus a larger number, which wouldn't be a positive number.

But 8's a positive number, so we need it to be a positive number.

Does that make sense?

[alpine sable]

yeah

so if we did s - l

s - L

we would get a negative and 8 would be negative but since we need it positive

we need to take the greater and subtract it from the smaller

[oak chasm]

Right.

[ocean seal]

Chai T. Rex

[oak chasm]

The first one has L by itself on one side.

So we can use a trick.

In the second one, we replace L with 2s.

L is equal to 2s, so they're the same number, so replacing L with 2s shouldn't hurt anything.

Does that make sense?

[alpine sable]

So basically

2s - s = 8

[oak chasm]

Right.

Now, use algebra to get what s is.

[alpine sable]

so we would

add 1 to s to get rid of it

and then + 1s to 2s?

so like

3s = 8

[oak chasm]

Oh, no.

We have 2s - s. When you have s by itself, that's the same as 1s. So, what's 2s minus 1s?

[alpine sable]

1s

[oak chasm]

Right, which is also s. So, we have s = 8.

Now we know her sister's age.

It's 8.

[alpine sable]

Ohhhh and Lisas age is twice her sisters age

[oak chasm]

Right.

[alpine sable]

so 16

[fringe rose]

Whats the answer to this

[ocean seal]

Chai T. Rex

[alpine sable]

L = 16

well

L = 2(8)

[oak chasm]

So now we know that Lisa is 16.

So we know both Lisa and her sister's ages.

[alpine sable]

perfect man

thank you so much

i owe u a huge one

[oak chasm]

You're welcome.

[alpine sable]

and dicypher can use the channel

[jade birch]

What do you think is the answer?

[fringe rose]

sorry I just found out

it was 2.1

[jade birch]

Yes

[fast jay]

What does the intersection between B and A and intersection of B and C represent in this example? https://towardsdatascience.com/solving-the-monty-hall-problem-with-bayes-theorem-893289953e16

I understand what happens and why we do it but just for my own sake not what the intersection of those actually means

[alpine sable]

Really need help with this question

I swear there is something messed with the question

@here

[alpine sable]

HELP

HOW DO I SOLVE THIS

[obsidian crane]

x = 180 - 55 - 90

y is given, its 90

[alpine sable]

but it's split

see

[obsidian crane]

oh wait

ok so

you got x

[alpine sable]

idk how to split

90

[obsidian crane]

180 - 90 - x
180 - 90 - 35

[alpine sable]

y = 55

x = 35

?

[obsidian crane]

yes (if i didn't mess up any calculations)

[alpine sable]

55+55+35

it equals 180

I mean

145

[obsidian crane]

x is 55, y is 35 the other is 90

wait

yea right, that ^

[alpine sable]

but

what's going to become of that other 55

?

isn't it added to the equation

[obsidian crane]

Both the big and small triangles have a 90 degree angle along with others

[alpine sable]

A loaded truck drives at 60 km / h to the landfill, 240 km away.

When the truck is emptied, it drives at 80 km / h back.
What is the total average speed of the truck?
(requires 2 decimals)

@obsidian crane oh, alright

thank you

but wait

@obsidian crane how do you split the 90 degree angle?

[alpine sable]

i think u find the time it needs to pass the 240km when its loaded and then find the time when its empty.Then the average should be the 240km + 240km/t1 + t2

thats like 68.57 i think

[rancid lantern]

Can someone help me with this 6b2+5b2–b2–10b2

[alpine sable]

Wrong formula

Nvm

how?

Its right

Someone told me it was wrong

[astral cedar]

Is octahedron here inscribed in tetrahedron??
My teacher claims its not

[obsidian crane]

I was afk
we don't need to split anything

In the first step we can find the value of x considering the bigger triangle

In the bigger triangle, one angle is 55, the other angle (which i was mistaking initially for y) is 90 and the third one is x

That's how we got the value of x

Now we can consider the smaller triangle and use the value of x for find y.

[alpine sable]

Can anyone help me understand how to find the angles a and b?

[ionic jewel]

p sure interior angles of a pentagon is 540 degress

540-120-90-90 = 240

so angle opposite a is 240/2 = 120

a = 180-120 = 60

[alpine sable]

the same goes for b right?

[ionic jewel]

yea

[alpine sable]

thanks

[elfin hazel]

yeah, since we assume the house is symmetrical

[alpine sable]

i guessed it to be 60 as well but it was looking at 120 and a as a half circle

idk if thats a bad approach

[elfin hazel]

technically this works too

then since the red line and the left wall of the house are parallel, the red angle and a are identical (ie. a=60)

[pastel jasper]

Is this occupied?

[boreal jetty]

what does that mean?

Does it just mean 0.1 kmh?

[gray isle]

10 kilometres per hour

[pastel jasper]

no

it means 1/kmh

[boreal jetty]

Why the -1 ?

[gray isle]

exponent laws

$h^{-1} = \frac 1h$

[ocean seal]

ℝamonov

[boreal jetty]

So it means 0.1 kmh, like prop said: 1 / 10 kmh ?

[gray isle]

So it means 0.1 kmh, like prop said: 1 / 10 kmh ?
no

[boreal jetty]

Now i'm confused.

[pastel jasper]

My bad

the "unit" i hope its like that in english

is just kmh^-1

[gray isle]

$kmh^{-1} = \frac{km}{h}$

[ocean seal]

ℝamonov

[gray isle]

(kilometres per hour)

[boreal jetty]

Oh i get it. Why would they use the exponent like that? Why not just say 10 kmh?

Is it a physics thing?

[gray isle]

because 10 kmh doesn't represent kiliometres per hour

[boreal jetty]

Oh okay so it's a common physics thing to say 10 kmh^-1

?

[gray isle]

depends on the preference of who's writing

you could instead write \
$10 \frac{km}{h}$ or $10 km/h$

[ocean seal]

ℝamonov

[boreal jetty]

I see thank you. So $kmh^{-1} is not actually 1/kmh

$kmh^{-1}

so (kmh)^-1 is not actually 1/(kmh)

[gray isle]

so (kmh)^-1 is not actually 1/(kmh)
no
(kmh)^-1 IS 1/(kmh)

kmh^-1 is NOT the same as (kmh)^-1

[boreal jetty]

I see.

[gray isle]

in kmh^-1
following the order of operations, the ^-1 only applies to the h

[boreal jetty]

I see so therefore you will have 10 * kmh^-1 = 10* km * (1/h) = 10* km / h

where km is one variable.

is that right?

[gray isle]

wouldn't really call km one variable

but yes

[boreal jetty]

I guess you're right the k in km stands for kilo ie 1000

But thanks you very much for answering my math is a little rusty i can see.

You should have an award for your guidance. I can't believe my math is that rusty. (:

[frail grove]

We throw a dice 4 times in a row
What is the number of results when the sum of the numbers is pair?

<@&286206848099549185>

[jade birch]

A pair
even?

[boreal jetty]

Well we can throw a dice wich have 6 sides 4 times, so the number of states it can have is 6*4.

[frail grove]

Yes@jade birch

[boreal jetty]

Now if all of the dices a thrown, the lowest amount, the lowest amount can only be 4, and the highest amount is 24.

I'm no mathematician, but if we had for instance two coins 'heads or tails'. That would be four states, if they were a pair that would only account for 2 states

'Sum of the numbers is pair' What that does entail?

[jade birch]

First die toss: 1
Second die toss: 1
Third die toss: 1
Fourth die toss: 1
The sum off the numbers is 4 which is even

[jade birch]

error in translation, pair->even

[frail grove]

That's 1 way, what about the others

[boreal jetty]

So the sum is even and the states are 666. interesting question

666 i mean

[jade birch]

use \

[boreal jetty]

6 * 6 * 6

[jade birch]

or that

Hmm...

[boreal jetty]

Lol sorry, i will try to do that.

[frail grove]

I need to use permutations and combinations

[jade birch]

Hard question for me to answer...

[frail grove]

Formulas

[jade birch]

permutations

combinations wouldnt work because 1,2,2,1 isnt the same as 1,1,2,2

[boreal jetty]

\111 =1

1*\1*\1

[jade birch]

try latex $11111$

[ocean seal]

.itsjustnai

[jade birch]

doesn't bug

$ at start and end of math things

[boreal jetty]

1 * 1 * 1 =1
2 * 1 * 1 = 2
..
6 * 1 * 1 = 6
6 * 2 * 1 = 12

[glass lichen]

\cdot

[jade birch]

Whats this?

[boreal jetty]

It's basically decimal, but it's not

So states of this would be 1,2,3,4,5,6 1,4,6,8,10,12

and so on...

[jade birch]

@frail grove Do you have the answer?

[frail grove]

No...

[boreal jetty]

I mean i could program it and calculate the answer that way. If there's any other sophisticated math i don't know about it.

[frail grove]

Posted it on reddit

Hopefully i get a solution there

[jade birch]

I'm really curious about the solution...

[noble sinew]

what is the actual question? Prob of sum of 4 dice being even?

[jade birch]

no, just how many occurences there are

[boreal jetty]

Its the probability that the sum is an even integer.

[noble sinew]

well uh lets just calculate assuming amount (if prob we can just divide our answer to get the actual one)

so the possible values are 4,6,8,...,24

[boreal jetty]

No the original question was:

We throw a dice 4 times in a row
What is the number of results when the sum of the numbers is even?

[noble sinew]

yes?

[noble sinew]

the possible values are this

we then calculate amount each one can get

4 can only happen 1 way (1+1+1+1)

6 can happen either with 3+1+1+1 or 2+2+1+1 (variations of those). So 4!/3!+4!/(2!*2!)=10

[simple pike]

Do you set this up as 13,900=2000(1+r)^15?

[jade birch]

@simple pike go to another open channel

[simple pike]

ight mb

[frail grove]

@noble sinew but there's more ways than that 😕

[noble sinew]

you have to do it case by case

[jade birch]

Yeah, he's doing it one by one

[noble sinew]

8 can happen with (5+1+1+1), (4+2+1+1), (3+3+1+1), (2+2+2+2), (2+2+3+1) so can you calculate amounts here?

[jade birch]

Do you think that there might be a more elegant solution than this one?

[frail grove]

Yeah we might miss a lot of "scenarios"

[jade birch]

No, not that

If youre careful you wont with the die being thrown 4 times only

[noble sinew]

you wont miss any but kinda tedious to calculate

[jade birch]

But for, lets say, a die being thrown 8 times, the cases range from 8 to 48

[boreal jetty]

@frail grove Why do you want the question answered?

[alpine sable]

hey is this already on use

[jade birch]

@alpine sable yes

[alpine sable]

alr

[frail grove]

@boreal jetty because i have to solve it?

[boreal jetty]

@frail grove I mean i could compute the answer for you. But in what way do you need it to be solved?

[noble sinew]

yep the easiest by far is making a simulation

but otherwise do what I posted

[frail grove]

Yeah I'm gonna need the proof too but computing the result might help as well

[boreal jetty]

Okay i can't help you there. I'm to stupid, good luck 😄

[noble sinew]

gave you the answer on how to do it

it involves combinations and permutations

[frail grove]

This?

It won't work with higher numbers lile 28 for ex

[noble sinew]

highest number is 6*4=24

[frail grove]

I mean you're definitely gonna miss a lot of cases

[noble sinew]

you aren't

"Sum of four numbers is even iff even number are odd Even numbers of odd would be 0, 2 and 4 Work out probabilities of this happening" is prob smarter, you didn't read his comment probably

[frail grove]

I did, but didn't understand it

[noble sinew]

it says if even amount of odd numbers is even, so 3+3+2+2 (here 2 numbers are odd) so the result is even

[frail grove]

2+2+1+3=8

2 is even 😕

[noble sinew]

1 and 3

2 odd numbers

2 is an even number

hence result is even

[frail grove]

So any sum of 4 numbers where 2 numbers are odd the result must be even?

[noble sinew]

where an even amount of odd numbers

so 0, 2 or 4

then find prob of even number and find total number of ways to arrange 4 dice rolls

[frail grove]

Oh so it should be like this: (odd, odd, even, even)?

[noble sinew]

(even,even,even,even), (odd, odd, even, even) and (odd,odd,odd,odd) are all even

[frail grove]

There's only 3 odd numbers

And 3 even numbers

[noble sinew]

?

[frail grove]

Odd numbers : 1,3 and 5

Even numbers : 2, 4 and 6

[noble sinew]

yes?

[frail grove]

So there's only one solution (odd, odd, even, even)

[noble sinew]

?????????????????

2+2+2+2 (0 odd result is even)

1+1+2+2 (2 odd result is even)

1+1+1+1 (4 odd result is even)

[frail grove]

Oh yeah i forgot that the number can be repeated 🤦‍♂️

Thank you for your time 😊 you're a legend

@boreal jetty @jade birch thank you for ur time

[vocal zealot]

anyone

knows

fphysics here

[boreal jetty]

@vocal zealot Ask a question.

[vocal zealot]

alright so the question is an electron with the velocity of v=3.5Mm/s comes in from the left perpendicular in a homogeneous magnetic field . B is 28 mikroTesla.
what is the
acceleration?

@boreal jetty

Do I use F=ma

in this case

[dire wren]

am i just interpereting this wrong or is this worded weirdly

[alpine sable]

i can help with this but make sure to ask your question in an unoccupied channel

[dire wren]

oh this is occupied

[fringe trout]

is this correct

[ionic jewel]

technically yes

pyramids have to have at least 3 triangular faces tho

[fringe trout]

yeah

[ionic jewel]

cant see how you could do it with two

[fringe trout]

so it is false

[ionic jewel]

i mean

its still true

every single pyramid is a 3 dimensional object with at least 2 triangular faces

[fringe trout]

but it implies there could be pyramid with 2 triangular faces

[ionic jewel]

hmm

depends how you read it i guess

false then if you go with that

[fringe trout]

yea

very trippy question

[chrome sierra]

hello ! can anyone help me determine wether each number is considered a combination or not?

[alpine sable]

it's a combination if order does not matter

so for #1 lets say the 5 swimmers are A, B, C, D, and E

so he can choose them in the order A, B, C

or B, A, C

and the order does not matter

because either way he has the same 3 people on his team

so since order does not matter, we have a combination

for #2, order does matter

for example the number 2579 is different from the number 9752

so if you choose a different order you get a different number

this is unlike the previous example where you could choose a different order but still end up with the same team

so #2, order does matter so this is a permutation not a combination

[lime lava]

I need help with this problem. I know how to do all of the equation solving but I don't understand when it comes to using logarithms which is what we're working on. Thanks.

[alpine sable]

so this is a function where you input #years and output cost in dollars

so you want to find how many years until the cost is 60 cents, or 0.6 dollars

you start with the output and want to find the input

the input is t the output is c(t)

so substitute c(t)=0.6 and solve for t

[lime lava]

So far I have solved the equation to the point 2.07=1.046^t

But I don't know the next step

[alpine sable]

so now we want to take the log base 1.046 of both sides

[lime lava]

I have no idea how to do that

[lime lava]

Hmm ok. So you take the base of the exponent and make it the base of the log?

[alpine sable]

yes

so how can we simplify on the right hand side?

[lime lava]

Uh I'm not sure

[alpine sable]

think of the logarithm as asking "to what power do i have to raise a to so i can get b"?

so what power do you have to raise 1.046 to so that you can get 1.046 to the power of t?

well, if you raise 1.046 to the t th power, you get 1.046^t

does that make sense?

if not i can try to explain it another way

[lime lava]

kind of

but once youve done that you would just have 1.046^t again?

[alpine sable]

no, the right hand side would simplify and you'd end up with just t

well i can try to explain another way

starting with 2.07=1.046^t
we convert this to log notation

log base 1.046 (2.07) = t

[lime lava]

Ok I understand that

[alpine sable]

so now we have isolated t

and we just use a calculator to get a decimal answer for the left hand side

[lime lava]

ok

[alpine sable]

(using wolfram alpha btw)

[lime lava]

ok

so t=16.177

[alpine sable]

now let's think about what this means

[lime lava]

Yeah so t=16.177 years

[alpine sable]

so t=0 means 0 years have passed and the year is 1991

t=16.177 means 16 years have passed

[lime lava]

So that means it will be .60 in 2007?

[alpine sable]

yes

starting from 1991, 16 years later is the year 2007

so your answer is 2007

[lime lava]

Ok that makes sense

Thank you very much

[alpine sable]

no problem

[chrome sierra]

yes^^ I’m kind of confused at number #3 and #4 though

[alpine sable]

@chrome sierra #3, they are choosing a committee (basically a team)

order does not matter

[buoyant inlet]

Hi!
I'm a 15 years old boy and I really really love physics and math.
I'm studying alone to cover more arguments that school ( I'm currently starting first order differential equations).
Do you have any advice on what to use to study alone?

[alpine sable]

#4, lets say there are points A, B, C, D, E, F, G

[alpine sable]

ask in an unoccupied channel please

also wow 15 and differential equations, kudos to you

[buoyant inlet]

Yes, sorry

[alpine sable]

#4, let's say you choose 3 points so make some triangle. if you choose the points in the order A, B, and C, you make the same triangle if you choose those points in a different order

so order does not matter as long as you select the same "team" of 3 points

[abstract sundial]

This is just a practice by the way, then I move on to the test which I will do alone

[alpine sable]

ok well i'll take your word for it

answer here would be C

for a function h(x) you input x and output h(x)

if you input 2, the output is h(2)

input -7, the output is h(-7)

domain is just a fancy word for input space

all of these answer choices are written in what i call "math legalese" you just need to know how to decode what it's saying

[abstract sundial]

Thank you @alpine sable

[warped wadi]

Hi! I had a quick general question. Can someone please explain the difference of squares method in factoring when there is a,b, and c? For ex: x^4-14x^2-32

[alpine sable]

difference of squares formula is

you wouldn't use this for factoring quadratics that have non-0 a,b, and c

[alpine sable]

this you can just factor like a standard quadratic

2*-16=-32, 2+(-16)=-14

or just use quadratic formula

now for the (x^2-16) part you can use the difference of squares

How did this happen?

[novel siren]

expend $\cos(a+b) = \cos(a)\cos(b) - \sin(a)\sin(b)$

[ocean seal]

cake party

[plush hatch]

What method can I use for calculating this integral?

I just need a hint to get the indefinite integral

[alpine sable]

factor out an x on the bottom

(x^4+8x)^2=x^2 * (x^3+8)

now use u-substitution

u=x^3+8

[plush hatch]

Oh shit

LOL

[alpine sable]

you good from there?

[plush hatch]

Yeah

Thanks!

[alpine sable]

np

[plush hatch]

I didn't see it too tired xD

[alpine sable]

@novel siren what r those identities stuff called?

Nvm found it :D

[novel siren]

trigonometric identities I believe

[alpine sable]

What is the procedure of 407 x 9?

[plush hatch]

9x400 + 7x9 ?

[alpine sable]

What's the procedure of 71 x 54?

[sullen cobalt]

is this open?

[wise dust]

Try to focus on x+31. Are you able to find the lower left hand angle using x+31?

[sullen cobalt]

wdym by that

[wise dust]

the red angle here

can you figure out what that is using x+31 and another fact?

Let me know if you can't figure out what the "fact" that I'm referring to is 🙂

[sullen cobalt]

x+31 + that red angle is 180

right?

[wise dust]

exactly 🙂

so try to solve for the red angle. what does that give you?

[sullen cobalt]

how

OHH

[wise dust]

x + 31 + red = 180

[sullen cobalt]

180- x +31

im dumb

[lilac wave]

2 + 2 = 5

its smort

[wise dust]

it would actually be 180 -x -31

[sullen cobalt]

because i moved it

to the other side?

[wise dust]

since you are subtracting 31 from both sides

[sullen cobalt]

yea

[lilac wave]

guys answer 1 + 1

[wise dust]

exactly!

[lilac wave]

I need help

[sullen cobalt]

alr ty

[gleaming granite]

7 atleast

[wide jolt]

3

[lilac wave]

Correct yall!

[wide jolt]

Can someone help me with one question

[lilac wave]

sure

[trim pecan]

Anyone know what one plus one is 🧍🏾‍♂️

[lilac wave]

ask me question

[lilac wave]

3

[trim pecan]

No Fr

What is it

[lilac wave]

1 + 1 is 3

[wide jolt]

Evaluate the expression -24 divided by -1/2

[gleaming granite]

I can't tell if this is a joke question or real, ULTIMATE TROLL

[lilac wave]

looks like I haven't learned atleast

[wide jolt]

Not trolling 🥱

[lilac wave]

rip me

[wide jolt]

I’m in the 7th grade 😇

[lilac wave]

same

[trim pecan]

He is being serious we take the same class we are confused 😂

[wide jolt]

Onb^

[gray gorge]

How old are all of you?

[gleaming granite]

kk

[sullen cobalt]

14

[wide jolt]

I’m 13

[gleaming granite]

-5 oops gota include units (year olds)

[wide jolt]

WAIT FR?

[lilac wave]

14 (waiting until August for my birthday)

[gray gorge]

Ok 👌

Good luck with your class boys

[sullen cobalt]

why?

tos?

[sly mantle]

tos

[gray gorge]

Yep

[sullen cobalt]

ai

[gray gorge]

Just checking

[gleaming granite]

@wide jolt do you know about keep it change it flip it?

[rich heath]

Wow yes

[wide jolt]

WTF IS THAT

Bro I haven’t learned anything during online school 😐

[gray gorge]

Bop it

[trim pecan]

Fr

[rich heath]

I have exams and i can already tell that i am going to fail

And final exams

[gleaming granite]

If you have a fraction like $\frac{3}{2}$ it's the same as $\frac{1}{2} \cdot 3$

[rich heath]

Congratulations to me

[ocean seal]

keto11

[sly mantle]

@trim pecan please refrain from using slurs

[gray gorge]

@trim pecan I can see the messages you deleted. Please no slurs, even if it's a joke

[rich heath]

Wait those kind of fractions exist-

[gleaming granite]

bruh

[rich heath]

wow that's cool

[gleaming granite]

wtf is this chat

[rich heath]

no

[gleaming granite]

why is it so active

[rich heath]

Maths

[wide jolt]

Bc I’m here 🥱

[rich heath]

Bc why not?

[lilac wave]

Guys i have hard question, I can't answer.
Hard question is (3 x7) 13/9 (123+11)

[gray gorge]

Welcome to #help-0

[trim pecan]

Ok

[rich heath]

It's easy

The answer is

[gleaming granite]

420.69 very ez pz lmon sqz

[rich heath]

I ma give up-

[lilac wave]

I see funni number lol, but correct

[rich heath]

e

I was so close getting it but alr-

I have a question

Can somebody help me with this?

[gleaming granite]

what's the question?

[rich heath]

Nvm i got it sorry

And tu

Ty

[lilac wave]

help, can ya help me how to solve speed of light 3 = ms ²

[nimble cove]

311.000.000 m/s

[lilac wave]

Oh thank you

[nimble cove]

If I can 🙂

School assignment or your research?

Private Call?

[gray gorge]

Ohm's law

Though idk if it's precisely an inverse proportion

[nimble cove]

Volt, Ampere, Celsius, Resistance, Watt = 1
Calculate with Ohm's law, change Celsius with Volt

[drowsy sedge]

I do not understand this at all

Anyone care explain it for me?

[alpine sable]

you need to subsitute x=2 into dy/dx which u differentiated correct to find the gradient of the tangent to the curve @drowsy sedge

[drowsy sedge]

Okay well what about for the rest of it

[gray isle]

theres nothing about subbing x=2

they applied slope in two different ways

[drowsy sedge]

hmmm

[alpine sable]

oh sorry my bad

[gray isle]

the fraction there gives the slope from a certain point on the parabola to the point (2,9)

(in terms of x)

similarly the derivative gives the slope of the tangent to the parabola at a certain x

[main slate]

Hey all,
I try to find a maths approach to find the number of number prime with another number.
So, I try to find a "modified" function π(n) (π(n) is used to get the number of number prime below a number n, but i personnaly want to find a maths approach to find the number of number prime with n (below n))

[gray gorge]

You mean this thing? https://en.wikipedia.org/wiki/Euler's_totient_function

[main slate]

Let me check the article

that s exactly what i want

[main slate]

thanks

[gray gorge]

np

[main slate]

👍

[acoustic bay]

Can someone explain this one to me?

[worldly wraith]

so the table basically gives you:

P(X=a, Y=b)

& if you wanna find P(X=a), you basically do this:

$\sum_Y P(X=a, Y= b)$

[ocean seal]

213

[gleaming pollen]

I need help with ALOT of homework

is anyone able to help

[worldly wraith]

im being very vague but oh well

[gleaming pollen]

its like 10 pages

Proportional Triangles

[acoustic bay]

hmmm, but then how do we find cov(x, y)

[tropic portal]

Hey little thing

Am I doing that D.E right?

[limpid spade]

cant read

[blazing rose]

how can i do this

i got $e^a(b + e^b - e^a)$

[gray isle]

product to sum laws for log

[ocean seal]

Josh.

[gray isle]

how did you get that....

[blazing rose]

so i started with ln(3e^2)

brought out the 2

so 2 ln(3e)

and e^a = 2 so i replaced 2 with that

and ln (3e) = ln (3) + ln (e)

[gray isle]

you're not applying power rule properly

[blazing rose]

oh

how do i do it right

[gray isle]

the ^2 only apples to the e

(and not the 3)

[blazing rose]

OHHH

makes more sense

thanks

[gray isle]

you may want to consider product to sum first

[alpine sable]

using the identity sin^2theta + cos^2theta = 1 and cot theta = 10/15 what is csc theta equal to
i got √325/10 is this right?

[main slate]

hi, i have checked the article. Do you know if there is a way to optimize the totient function. I mean that it could be slow to compute all divisors of a number n for very big n.

[gray gorge]

Well, it ultimately hinges on if you're able to do prime factorization efficiently

And that's rather difficult

[main slate]

ok, i will see what i can do

[rare bough]

r = 2cos(3θ)

How do you know which points to select

so i already got pi/3,-2 and 2pi/3, 2 0,2

I just feel like I'm doing this incorrectly

[alpine sable]

do you need to sketch a graph of this function?

[upbeat stone]

I need some help on a problem

If it uploads

[alpine sable]

system of equations word problem

[upbeat stone]

Is there a way I can speed this up

And make it faster

Then just guess and check

[alpine sable]

so lets call W the number of wins

[upbeat stone]

Ok

[alpine sable]

yes you can make a system of equations

W= number of wins, L=number of losses

so she's played 20 times total

[upbeat stone]

Yea

[alpine sable]

W+L=20

[upbeat stone]

Ok

[alpine sable]

for every win, she earns 3 points

[upbeat stone]

Yes