help-0

[strong furnace]

this is what happens when you try to copy without understanding how it works , also stop spamming here

[gaunt magnet]

this is called learning

not copy pasting

[candid thistle]

I got ittttt
I got the math problem right

Turns out I didn't have to use similar triangles

(kinda)

Oh wait nvm I did the exact same thing as the stack exchange thing 🤦

I'm satisfied with it though

[stable leaf]

but there is a channel made just to spam this latex

#latex-testing

[candid thistle]

they should call it #latex-texing :P

[sick phoenix]

IM SO CONFUSED

[west solstice]

yeah wtf is it asking?

[rigid smelt]

Welp techinically this question is lacking information

[west solstice]

We dont have any functions

[rigid smelt]

Unless theres some place in the question that we cant see that says V is the vertex of the quadratic

We do

f is

[candid thistle]

Is there any other info in that question?

[sick phoenix]

nope

it’s just like that

:”))

[rigid smelt]

but welp its quite clear that they want us to just out of the blue know that V is the vertex

[sick phoenix]

apparently there’s 3 abs

[rigid smelt]

anyway, lets just go with that

[sick phoenix]

ans

[rigid smelt]

you should also talk to your teacher about the ambiguity of the question

anyway

when shall a function has an inverse?

[candid thistle]

oops

[sick phoenix]

ok so i checked

and the ans was all the ones that starts with x

[rigid smelt]

like i said

@sick phoenix

[sick phoenix]

oh i kind of get it now

[gaunt magnet]

hi

channel in use or may i have it

[rigid smelt]

its free i suppose

[gaunt magnet]

ok

then

[candid thistle]

If I have two similar triangles with side lengths a, b, c and x, y, z (corresponding respectively) would ax = by = cz?

[snow nest]

by similiar do you mean congruent?

[candid thistle]

No, similar

One is a scaled version of the other

[rigid smelt]

that depends on which sides is similar to which

[candid thistle]

a and x, b and y, c and z

[rigid smelt]

if they are correspondingly similiar

then yes

[snow nest]

maybe if the smaller triangle is placed exactly in the centre and both areequilateral triangle

[candid thistle]

it isn't an equilateral triangle. I know that for sure

[snow nest]

what type of triangle is it?

[candid thistle]

isosceles

[rigid smelt]

it doesnt have to be a special triangle or anything

[snow nest]

is the smaller one directly in the centre?

[candid thistle]

one has side lenghts 6, x, and x. The other (bigger) has side lengths x, 8, 8

[snow nest]

can you send a screenshot?

[candid thistle]

uhh ok

[rigid smelt]

as long as the sides are correspondingly similar, the equality is correct

welp just dont mind me then

[snow nest]

i'm sorry

i think waler is correct

geometry was never my strong suit

[rigid smelt]

similar triangle has nothing to do with location of triangles or how they are placed

if its similar, they have a common ratio

[candid thistle]

So how will I find x

[rigid smelt]

establish a ratio

[candid thistle]

x:6 = 8:x

x/6 = 8/x

[rigid smelt]

yeah

and then just solve for x

[candid thistle]

48 = x^2

omg! that was way easier than i thought

im getting kinda better at this (i hope :P)

[covert agate]

why is eulers totient theorem true

[alpine sable]

What is 2+9

[ionic jewel]

i feel like if you are at the level of math where you are using this you know how to look up a proof for it

[covert agate]

true

was watching a video as you were saying

[deep scroll]

If $kx=y$ and $kp=q$ then under what condition will be $x=p$ and $y=q$?

[ocean seal]

Fulminare

[low topaz]

Is there an equation to find an angle of a triangle

[ionic jewel]

trig, yes

oh god transparent looks so bad

[alpine sable]

Oops

[alpine sable]

Yes many

[low topaz]

Also a triangle without a right angle

[ionic jewel]

yes

theres like 40 million relevent theorems

[alpine sable]

Also triangle with 4 sides

[ionic jewel]

circles are just edgeless squares

[low topaz]

So how could i find the answer

[ionic jewel]

wheres the question

[low topaz]

What

[alpine sable]

The problem you are trying to solve

Do you have one

[ionic jewel]

theres lots of ways to find triangle angles, itll depend on your problem

[alpine sable]

For example, if you have an equilatetal triangle we know all angles are equal

And the total sum of angles in a triangle is 180, so if we divide 180 by 3 we get the measure of one angle

And therefore all angles

[low topaz]

What about a triangle like this

[alpine sable]

Depends on what is given. If we have A and B we can easily find C

Or any of the two angles

[river moon]

yeah i agree

[alpine sable]

A+B+C=180

[low topaz]

But what if non of the values for the angles are given and i only have the values of the sides

[low topaz]

Then 180-A-B=C

[alpine sable]

Law of cosines

[alpine sable]

Yes, that works if you're looking for C

$\cos(C) =\frac{a^2+b^2-c^2}{2ab}$

[ocean seal]

Em

[low topaz]

is C the angle we're trying to find

[alpine sable]

C is specifically the angle C

$\cos(A) =\frac{b^2+c^2-a^2}{2bc}$

[ocean seal]

Em

[alpine sable]

B has a similar formula

Or, once you find these two, you can do 180-A-C=B

Alternarively, you can do law of cosine for first angle, law of sine for second angle and subtract the two from 180 for the last angle

[low topaz]

What is the law of sine and the law of cosine

[alpine sable]

I gave you law of cosine for 2 angles

Law of sine is $\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}$

[ocean seal]

Em

[alpine sable]

If you have sides b, c and you found the angle C using the law of cosine, you can find angle B

[low topaz]

$\ 5

[alpine sable]

$\ 5$

[ocean seal]

Em

[low topaz]

Wow

[alpine sable]

What?

[low topaz]

Its the letter 5

[alpine sable]

Just make sure to use $ at the start and end. Like quotation marks

The letter $5$

[ocean seal]

Em

[alpine sable]

@ionic jewel 's favorite letter

[robust verge]

Are these correct

No negations written yet

[alpine sable]

Lets suppose we have given slope of two line. Based of Slopes can we find at which coordinate they will intersect. ❓
exp: we have slope 0 and -1

[deep scroll]

Can we prove $sin^2 \theta+cos^2 \theta=1$ without using trigonometry

[ocean seal]

Fulminare

[vale wigeon]

you will have to state some definitions for sin and cos

without definitions nothing can be proved

[placid zinc]

That's kind of like saying "Can I eat pasta without using my mouth"

sin and cos are trigonometry

[vale wigeon]

absorb the pasta through the pores in your skin

[placid zinc]

Like a baby eats pasta, put it all over your face

[rancid blade]

then your pores are each a tiny mouth

[dark granite]

yes then let your skin absorb it like a sponge lmao

[dark granite]

I would be interested to see if you managed to prove any trig identity without using trig.

In all seriousness @deep scroll , to prove something you must first make at least one assumption. Without any assumptions, no proof can occur. This is why things known as Axioms exist. Axioms are things we take to be true without proof.

[placid zinc]

@alpine sable
Is that the question you're talking about in #discussion?

[alpine sable]

yes

[placid zinc]

If two lines have different slopes, they will intersect exactly once

If they have the same slope, they may never intersect (be parallel) or have infinite intersections (by both being the same line)

[alpine sable]

what if we draw another two line parallel two them.. and they will have same slope too. and they will meet somewhere else definitely. so what will be the coordinate of where they will intersect?

and we have given coordinates of initial lines

@placid zinc something likethis

how can i learn maths

by doing a lot of exercises

[alpine sable]

#rules

ok

[placid zinc]

Do you have an example you want to go through?

[alpine sable]

actually problem is we have given some polygon. for simplicity .. lets assume a triangle .. now we have to draw another polygon (trriangle) 1 unit away(like in above picture) parallelly. so waht will be area of new polygon.

i can find area of given polygon using shoelace method.. but i am not able to figure out new one.. coz in shoelace method we need cordinates.

[flint stratus]

hey help me Ahmad is a rice entrepreneur. He bought 5 sacks of rice at a price of Rp.
2,940,000. Then the rice is sold at a price of Rp. 8,000 per Kg. If every sack
Rice is written Gross 100kg and Tarra 2 kg.
a. Is ahmad in a state of profit or loss? Prove it with calculations.
b. At least how many kg must Ahmad sell in order to get a return on investment?

[alpine sable]

#❓how-to-get-help

please read

[flint stratus]

i read it

[alpine sable]

what is Tarra 2kg?

[low topaz]

How can there be cos without an adjacent side

[alpine sable]

@flint stratus i responded to you in the other channel

[alpine sable]

tarra would be the bag

gross = netto + terra

hi! i was trying to figure out a problem on a 52 card deck.
I need to find the probability of drawing 3 kings.

what is the difference between these two?

$\mathbb{P}(King_3|King_2|King_1)$

[ocean seal]

ColoR

[alpine sable]

$\mathbb{P}(King_3 \cap King_2 \cap King_1)$

[ocean seal]

ColoR

[vale wigeon]

the former makes no sense

did you mean P(king3 | king2 & king1)?

[alpine sable]

ah yes

[vale wigeon]

ie the probability of drawing a third king given you've already drawn two?

[alpine sable]

yes I had to write it that way right?
$\mathbb{P}(King_3| (King_2|King_1) )$

[ocean seal]

ColoR

[vale wigeon]

no

this makes no sense

| isn't an operation

[alpine sable]

i see

[vale wigeon]

also am i right to assume you are drawing 3 cards total

[alpine sable]

in case i have to draw two kings

$\mathbb{P}(King_2|King_1)$
$\mathbb{P}(King_2 \cap King_1)$

What would be the difference between these two?

[ocean seal]

ColoR

[vale wigeon]

the first is the chance of drawing a second king after you already know you have drawn one

the second is the chance of drawing two kings before you have drawn anything

[alpine sable]

the second one is the possibility to draw two kings, when I still have all 52 cards in the deck, did I understand correctly?

[vale wigeon]

...yes

[alpine sable]

I understand! thank you very much!

[alpine sable]

and theres a limit of g(x) as x-->2

would there be a limit that exists?

as it is approaching an asymptote

[rigid smelt]

yes

notice that (x-2)^2 always approaches 0+ as x approaches 2 from either sides

[alpine sable]

oh right

i just thought it does not exist as it is discontinuous at x=2 @rigid smelt

and why are u referring to "0+"

i mean 2?

[rigid smelt]

thats not always true, a function can be discontinuous at a point x=a but still has a limit tending to a

[alpine sable]

oh right

thank u

[rigid smelt]

because thats what it tends to?

[alpine sable]

u mean infinity?

[glass lichen]

(x-2)^2 approaches 0^+ as x approaches 2

[ocean seal]

waler

[rigid smelt]

since the denominator converges to a very small positive number

[alpine sable]

does 0^+ mean infinity?

[rigid smelt]

1/(x-2)^2 tends to infty

no

[glass lichen]

clearly not

[rigid smelt]

0+ implies a number that is really close to 0 from the right hand side

for example 0.000001

[alpine sable]

could the answer also be "infinity" instead of "0^+"

or is this a different notation i dont know about

[rigid smelt]

the answer to what?

[alpine sable]

as x approaches 2

[glass lichen]

the answer to what you asked is infinity...

[rigid smelt]

of?

[glass lichen]

waler was giving the reason behind why

[rigid smelt]

no

[alpine sable]

sorry i just thought u were referring to this sorry

[rigid smelt]

does 0.000001 seems like infinity

[glass lichen]

I also would've assumed it was obvious that (x-2)^2 and 1/(x-2)^2 were different things

[alpine sable]

i also wouldve assumed mosh made a mistake and it owuldve been logical to think it was a common error

that he was referring to the truncas

instead of a quadratic

@rigid smelt thank u very much for ur help

[rigid smelt]

actually, what is a truncas?

i got thrown off reading that at first

but i skipped it assuming you meant function

[alpine sable]

a truncas is this

[rigid smelt]

oh a truncus

right

[alpine sable]

so should i reask my question?

does a limit exist as x->0

[rigid smelt]

i mean thats the same thing

basically all truncus has a limit approaching the vertical assymptote

👍

[dull onyx]

stupid question but when i need to find the domain of a function is saying that x not= a number enough or do i need to write x∈R too

confused asf

[rigid smelt]

usually yes

because usually when you write x!= something, we imply that x is any numbers except that "something"

[dull onyx]

oh okay

i wrote (x∈R/xnot= -1) is that fine

[rigid smelt]

sure

[dull onyx]

thank u<3

[rigid smelt]

but you could also write x∈R/{a}

bruh

[dull onyx]

i need tolearn how to write like that

[dull onyx]

ok thx😭

[vale bison]

How do I approch this one.
I am learning integration but I am stuck on this one.

[alpine sable]

Integrate?

[vale bison]

Yeah

How?

[alpine sable]

Really hard to simplify it

Will take some time

[shell widget]

try u = x^4 + x^2 + 1

might work

[vale bison]

Yeah

[shell widget]

cause the numerator kind of resembles the derivative of the denominator

[alpine sable]

Prefer to simplify

[vale bison]

It does but it isnt

[alpine sable]

But thats a good idea too

[vale bison]

Tbh I dont know how should I simplify it either

[alpine sable]

You can facto simplify

[vale bison]

The denominator will be neatly seperated due to formula but the numerator is tough for me

[alpine sable]

But thats a foolish idea

[vale bison]

You mean simplify by removing the common factors?

[alpine sable]

Yea factorise

But its foolish

But Ik (I know) that foolish idea can work

[alpine sable]

First the denominator is more

[vale bison]

Hmm will applying c and d work?

[alpine sable]

Idk

Need to try it

Brooo wait

Ok so

[rigid smelt]

uhh are you expecting a real answer? Because you might be getting a complex answer

[alpine sable]

ln(x^2+x+1)/2 + arctan(2x−1/√3)√3+C

Lemme write it neatly

[mortal marlin]

Hi, it's about a week I've been interested in the formula for the area of intersection of two circles of the same radius given the radius and the distance between the two centres. Now I'm studying the general case when the circles are not the same. However, here's the formula for the simpler case:

$$\pi r^2-2\sin^{-1}{\frac{x}{2r}}-\frac{\sqrt{4 r^2 - x^2}}{2} x$$
is the formula for the intersection of two circle of the same dimension $r$ given the distance between the two centres

[ocean seal]

OkkSte335

[alpine sable]

Proof

[vale bison]

Its not allowed to distrub when others questions are going on right?

[alpine sable]

Ohhh wait

[alpine sable]

yea I am still writing

Dont worry

[mortal marlin]

Ok sorry

I'm not used to this rule

[vale bison]

Yeah just use another channel

[mortal marlin]

ok

[alpine sable]

could you help me with this question?

[alpine sable]

Ofc

Give me a moment

[vale bison]

@alpine sable
Damn that was a lot of work

[vale bison]

Hmm
(3x)³-(2x)³

I think its simply the formula

Just apply the formula and substitute

[alpine sable]

Bro thats wrong

Completely wrong

Ok see mister kugel

[alpine sable]

i did that but i got (3x-2y)[9x²+4y²+3x * 2y]

how to go from here?

[vale bison]

How is that wrong?

[alpine sable]

Your proof is given

[alpine sable]

i can't substitute

[alpine sable]

Ok so

Wait

chill

I am writing it

[wary stream]

Is this supposed to be the perfect cube equation of 27x^3 - 8y^3?

[alpine sable]

Yea lol

[alpine sable]

The questions kinda wrong.....Ig

[native cloud]

Why don't you add 3rd powers in (2x+3y=113)

[alpine sable]

that's what i thought

OH WAIT

SORRY

[alpine sable]

hmm i'll try that

[alpine sable]

but i won't get what 27x³-8y³ is equal to

coz i'll get 8x³+27y³

[native cloud]

True

I think there is a problem with that problem

[mortal marlin]

@alpine sable Are you still there?

[alpine sable]

Yes I am

Please give me some time to prove you wrong

[mortal marlin]

Come to dms

[mortal marlin]

Ok go ahead

[manic glade]

if you guys are done, would like feedback on this

especially the bottom part

in the example they just concluded IcapJ=(c,b) but that seems wrong so i added the c,d option

since yknow, the second interval could be entirely within the first

right(?)

[alpine sable]

As I said

Draw it

[manic glade]

draw it as in lines?

i cant actually draw in this editor

i guess i can add a picture from elsewhere but how important is it

our teachers are pretty adamant that drawing are only to help you think and do not constitute proof

[jagged raptor]

you can just solve for y and substitute

no reason to do all this fancy difference of cubes stuff

[ripe thunder]

yap

[alpine sable]

Bro where did you get this question from?

kekw i got it for homework

Your teacher?

Which grade do you study?

[jagged raptor]

y = 12/x
2x + 3(12/x) = 113
multiplying by x makes this a quadratic in terms of x

[alpine sable]

Can someone write eq(41) in terms of u?

[ripe thunder]

but then you ll have to set 3 cases

[alpine sable]

Yea

Its correct

But draw it for furthur classification

[alpine sable]

9th

[alpine sable]

Question is wrong

Scam?

[strong furnace]

yes

[ripe thunder]

yea

[mint spindle]

Yeah i actually create a fake account to know what it is about... It is a physhing site which will hack your steam account

[alpine sable]

the instant i see http i'm out

I didnt click it though

It was obvious

[sleek elbow]

How do you go from here: $4cos(\frac{pi}{3}x + pi) - 3$ to $4cos(\frac{pi}{3}(x + 3)) -3$ ?

[ocean seal]

Ladan

[mint spindle]

My browser blocks http

[alpine sable]

Wdym

[wary stream]

Factoring the GCF

[sleek elbow]

gcf?

[wary stream]

Pi/3

Greatest common factor

[sleek elbow]

oh

[alpine sable]

Bro ask your teacher if it is correct

i did

Bro jeez dude

Where do you study

country

You should get this inter-2

[wary stream]

Keep that in the DMs/different channel. These are math help channels, not off topic/personal discussions

[alpine sable]

The questions wrong.

[rocky atlas]

I got a question that I'm stuck for half a day

It's related to principal of mathematical induction

A series is given in trigonometry and I got to prove that it's equal to a given formula

Proving p(1) is as easy as ever. The problem starts when go on solving p(k) by adding the extra element of p(k+1) on both LHS and RHS where solving rha is hard

If anybody knows anything regarding this, please help. I'd be grateful for your help

[alpine sable]

yea'

I want help guys

No one wants to help you 😶

I helped others

You need to help me

What is......

what is your question

the value of x when

x+2=4

:O

Answer fast dude

eeuuuhhh euuuhhh

idk

BRUH

you tell me

[rocky atlas]

Your question is in google

But my question not available in the google even

[alpine sable]

your question

i will try to solve it

[rocky atlas]

I can give you the source if you'd like. It's actually a homework from a video in yutube

[wary stream]

The mods don't like it when you ask troll questions

[rocky atlas]

Mine? Thank you a lot

[alpine sable]

give it to me

[rocky atlas]

@alpine sable I dm you the link

[rocky atlas]

And i also gave screenshot of question

[alpine sable]

yes im looking in to it

[rocky atlas]

Thanks😁

[median osprey]

Hi

this questions annoying me

i know that we need to make sure all units are the same first

but thats where i am stuck

too many fractions

not sure how to solve it

[slate cargo]

/60kg annulate

/1h = /60 min

And it remains : 225mg = 225*10^6 ng

0.1L = 10^2mL

And after (225*10^6/60)/10^2) ng/ml

[median osprey]

im so lost

where did you get that 60

[slate cargo]

1h = ... min

[median osprey]

so you worked out the left side first

so you did this

right?

[slate cargo]

The unit is 255 mg.min-1.kg

[median osprey]

ok

im getting like 134973005.4 ng/ml

is that even right?

[alpine sable]

i found it

but ugly proof haha

[alpine sable]

correct

No need of absolute

Give fraction

Enough tbh

[median osprey]

im not getting teh correct asnwer

the correct answer is 37500

but idk how they getting that

im so confused

[ocean seal]

Saturn_Petas

[rocky atlas]

Thanks a lot but how did you do it? Tell me the solution please

I will see if it's as ugly as you said or not ..

[solar falcon]

Sin 20, Sin 170, Cos 85, which one is the biggest number?
This is not something I'm trying to solve myself, I just want to know how the community would go about solving this without using calculator.

[jagged raptor]

idk how far you've gotten, but writing sin((n+2)pi / 6) as 0.5sin((n*pi)/6) + (sqrt(3)/2)cos(((n*pi)/6) was one of the key things

can you show what you have so far its kinda hard to not just give away the whole problem without your work

[rocky atlas]

Ok I will take photo

Just stuck at this point. Hopefully my handwritten ain't that bad🙄

This is the previous page

[jagged raptor]

okay so from this last line

[rocky atlas]

Yeah I can't prove it in rhs

[jagged raptor]

it would be nice if $\sin\left(\frac{m\pi}{6}\right)+\cos\left(\frac{\left(m+1\right)\pi}{6}\right)=\sin\left(\frac{\left(m+2\right)\pi}{6}\right)$

if that is true then we're basically done right?

[rocky atlas]

Yeah

And that's like some intense trigonometry proof

[ocean seal]

michαel

[rocky atlas]

Actually I got proof of it from some other server..lemme show u

[jagged raptor]

$\sin\left(\frac{\left(m+2\right)\pi}{6}\right)=\sin\left(\frac{m\pi}{6}+\frac{\pi}{6}\right)=\frac{1}{2}\sin\left(\frac{m\pi}{6}\right)+\frac{\sqrt{3}}{2}\cos\left(\frac{m\pi}{6}\right)$

[ocean seal]

michαel

[jagged raptor]

so if we can show that it equals 0.5sin(mpi/6) + (sqrt(3)/2)cos(mpi/6) we're good to go

[rocky atlas]

Yeah

[jagged raptor]

now going back to your last line of work, distribute the pi in the cosine

[rocky atlas]

It's real work is from there

[jagged raptor]

then split the fraction in the cosine and use a cosine angle sum formula

[rocky atlas]

Like this

Thou it's not my proof

[jagged raptor]

thats more complicated than it has to be

uh let me send what i did

[rocky atlas]

I can reverse all the way to rhs thou

[rocky atlas]

Okay

They just put cosine and sin formula in place of number

And somehow made it in the formula of sinAcosB plus cosAsinB

[jagged raptor]

the first line of that is your last line ^

using the angle sum formula for cosine results in (sqrt(3)/2)cos(npi/6) - 0.5sin(npi/6)

there already is a sin(npi/6) not from that, so sin(npi/6) - 0.5sin(npi/6) = 0.5sin(npi/6)

then whats left is exactly what we showed to be sin((n+2)pi/6) in our "side work"

[rocky atlas]

Ah I ser

[rocky atlas]

Required to prove yh

[jagged raptor]

yeah that comes from here

you use the sine angle sum formula to show that

[rocky atlas]

Cos(a+b) formula?

Oh sin(a+b)

[jagged raptor]

you use the sine angle sum formula to show

$\sin\left(\frac{\left(n+2\right)\pi}{6}\right)=\frac{1}{2}\sin\left(\frac{n\pi}{6}\right)+\frac{\sqrt{3}}{2}\cos\left(\frac{n\pi}{6}\right)$

[ocean seal]

michαel

[jagged raptor]

then the cosine angle sum formula to go from your last line of work to the right side of this eq ^

[rocky atlas]

Thanks a lot even though m still a bit confused now, I will have to focus on what you did..

[jagged raptor]

let me underline some stuff in my work to make it easier to follow

[rocky atlas]

Well it's not your fault, just my fault..I recently learnt those formulas

[jagged raptor]

oh okay

yeah work it out yourself

[frosty oasis]

mathematics!

[jagged raptor]

it will be easier to follow and see

[rocky atlas]

Yup

[frosty oasis]

mathematics!

[alpine sable]

.

[fierce relic]

Question: I have a basic elementery level Probabilty problem. I just cant seem to wrap my head around it.

if 3 people are born on the same year what is the Probabilty that they will have the same birthday? I think the probabilty should decrease with the increase in number? am I correct? or is it just 1/365 WHY IS THAT ?? THE PROBABILTY SHOULD DECREASE IF More people are there!!

[alpine sable]

.

[rocky atlas]

Well so do you think, answer should had been 3/365?

[fierce relic]

no! it should have decreased! i thought of that answer also

[rocky atlas]

It can be 1/(365 x 3) if it's decreasing

[fierce relic]

yes then is it?

i dont know that correct answer

[rocky atlas]

I am just taking guess

[fierce relic]

yes my common sense tells me that answer

[alpine sable]

27 * 31

= 20 * 30 + 20 * 1 + 7 * 30 0 7 * 1
=600 + 20 + 210 + 7
=837.
Does this work?

[fierce relic]

alfredd there is already one question going please wait for little

[rocky atlas]

I think 365 is a big number, let's think about two coin dropping, their probability of being same is .head or tails

[small bear]

Just to understand this what you meant, you think that if there are more people, they are less likely to share a birthday?

[fierce relic]

E X A C T LY

[small bear]

thats wrong

[alpine sable]

Someone else can answer it, there's no 1 question at once rule

[fierce relic]

yes i wanna know why

[fierce relic]

ok

[rocky atlas]

First probability is HT, Second TH , third HH and last TT so two/4

[small bear]

imagine one person in the world, they cant possibly share a birthday with anyone

when you add two people, they are likely to share

so this should immidietly tell you that your previous assumption is wrong

the best explanation comes from the birthday problem, i will link it here

[fierce relic]

nono!

[rocky atlas]

According to your assumption it should had been 1/4

[fierce relic]

birthday problem deals with the word "ATLEAST"

[rocky atlas]

But answer is 1/2

[fierce relic]

yes!

[rocky atlas]

You can use similar logic here I guess

[fierce relic]

i do not deal with the word atleast i deal with the word ALLL MEMBERS HAVE THE SAME BIRTHDAY

[small bear]

well that changes the question dramatically

indeed you would be correct

[fierce relic]

yes ! thats the confusion

[small bear]

the probability they all have the same birthday is $(\frac{1}{365})^n$ where n is the number of members

[ocean seal]

peaceGiant

[small bear]

indeed, a decreasing function

[fierce relic]

OH!

there we go!

my friend said it would be same! THANKS A LOT BOTH OF YOU

[rocky atlas]

I didn't do anything lol

[fierce relic]

You helped me solve the other problems in my book!

can we give rep or something lol

[fierce relic]

closed.

[austere pike]

Having big trouble with this one.
$$
\lim\limits_{x \to -\infty} \sqrt{x^2 + x} - \sqrt{x^2 - 5}
$$
Apparently the answer is $-\frac{1}{2}$. How the hell do I start, let alone completely solve this? I thought I could do limits pretty well.

[ocean seal]

k0nz

[small bear]

Multiply top and bottom by conjugate

[golden nymph]

so thats an infinity minus infinity situation

[golden nymph]

hmm thats actually a great idea lol

I wouldve made a mess and lhopital lol

yeah I guess this way it will also need (I guess one) lhopital rule

[austere pike]

ok, sec, I'll see if that makes it any more clearer to me

[small bear]

i think it should be doable without lhopital

however Ill let k0nz check for themselves first

dont wanna spoil the solution

[golden nymph]

k

[austere pike]

ok, that leaves me with:

$\frac{x^2 + x - 5}{\sqrt{x^2+x} + sqrt{x^2-5}$

[ocean seal]

k0nz
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[small bear]

you shouldnt have an x^2 on top

[austere pike]

oh oops yeah that cancels out

[small bear]

so if you now plug x=-inf, you get infinity over infinity, do you remember what you do to the x's when this happens?

*btw its also x+5 on top

[austere pike]

divide by the leading terms?

[small bear]

very good

look at the numerator

what is the leading term

[austere pike]

I'm not a naitive speaker, numerator is the top right?

[small bear]

yup

[austere pike]

well, x?

[small bear]

exactly

divide by x both on top and bottom

and be careful of its sign and how you deal with putting that x inside the square root

[tired geyser]

Hey, hi

[small bear]

try it yourself and if you struggle tell me

[austere pike]

we are busy here

[golden nymph]

what is that?

[austere pike]

please go somewhere else

[golden nymph]

you forgot to close a } for the denominator of the fraction

[austere pike]

yeah I noticed

[golden nymph]

ping me in the channel you will repost this in as I am interested

[vagrant rover]

1/2(3)-3

Can I multiple 3 * -3 instead of 1/2 * 3 ?

[austere pike]

did you mean to say $\frac{1}{2}*3 - 3$

[ocean seal]

k0nz

[vagrant rover]

yeah

wait no

$\frac{1}{12}(3)-3$

[ocean seal]

Dexter is VACCINATED x2

[vagrant rover]

Like that

[devout sigil]

U have to follow the order of operations, that is PEDMAS

[austere pike]

you have to multiply with 3 first

[vagrant rover]

are you sure?

because

I think it's the other way around

like 1/12(3)

[devout sigil]

No it’s correct

[vagrant rover]

Before (3)3

[devout sigil]

What do u mean 1/2(3) where did the 2 come from

[vagrant rover]

I mean 1/12

sorry

[devout sigil]

1/12(3) ≠ (1/12)(3)

1/12(3) means the 3 is in the denominator and not the numerator

[small bear]

I disagree

1/12 (3) would be interpreted as 3 on top

1/(12 (3)) would be bottom

[golden nymph]

I agree that confusing notation is better avoided

[austere pike]

alright peaceGiant, I genuinely don't know how to progress

[golden nymph]

altogether

[austere pike]

first of all, this is what I got:
$\frac{1 + \frac{5}{x}}{\sqrt{x^4+x^3}+\sqrt{x^4-5x^2}}$

[ocean seal]

k0nz

[austere pike]

did I make some stupid blunder

[small bear]

dividing on top and bottom means you divide the bottom as well

top is fine

[austere pike]

yeah I did

[small bear]

bottom you multiplied

not divided

[austere pike]

oh god

im stupid

[small bear]

also, the be careful with the signs, you cant divide by x as is inside a square root

you must leave the negative sign in front of the square root, and divide by |x|^2

which is x^2 or (-x)^2 , the same thing

[austere pike]

right

oh my god it worked

and then it becomes negative because it approaches -inf?

[small bear]

nopep

[austere pike]

hm

[small bear]

you shouldve got $\frac{1}{-\sqrt{1} - \sqrt{1}}$

[ocean seal]

peaceGiant

[small bear]

is it clear why?

[austere pike]

well, it's logical considering that you said you must leave the negative sign in front of the square root, then it all checks out

but I'm not sure how the negative sign end up there

[small bear]

say you have $-5 \sqrt{2}$, you would do $- \sqrt{2 * 5^2}$

[ocean seal]

peaceGiant

[austere pike]

right, yeah

[small bear]

does this make more sense or should i write it out?

ill write it out just in case

[austere pike]

thank you very much

I'm really slow

[small bear]

$\frac{x+5}{\sqrt{x^2+x} + \sqrt{x^2-5}} = \frac{ \frac{1}{x} (x+5)}{ \frac{1}{x}(\sqrt{x^2+x} + \sqrt{x^2-5})}$
$\frac{1}{ -\frac{1}{|x|}(\sqrt{x^2+x} + \sqrt{x^2-5})} = \frac{1}{ - \sqrt{\frac{x^2+x}{x^2}} - \sqrt{\frac{x^2-5}{x^2}}}$
$= -\frac{1}{2}$

[austere pike]

doing it all in one go is ballsy lol

[glass lichen]

It's pretty common

[small bear]

gimi like 3 minutes hahahah

[austere pike]

lmao

[ocean seal]

peaceGiant

[austere pike]

but how does $\frac{1}{x} = -\frac{1}{\abs{x}}$

[ocean seal]

k0nz

[small bear]

$x$ is negative (since x goes to - infinity), $|x|$ is positive, and $-|x|$ is negative, so $-|x| = x$

[ocean seal]

peaceGiant

[austere pike]

ooooooooooh

oh yeah, that does make sense

by using the absolute value you escape the ambiguity

[small bear]

we do that since we cant put x inside a square root, only |x|

and thus leaving the minus sing behind the square root

[fiery meadow]

Hello

Can I please get help with this question?

<@&286206848099549185> thank you very much i appreciate ur time ❤️

[tough hatch]

pls read #rules and #❓how-to-get-help

where did the numerator go?

[austere pike]

ok I think I get it, I just need to let it simmer in my brain a bit

big thanks!

[small bear]

1/x has the same sign as x, so it is enough to look at one of them

np anytime

[tough hatch]

i mean you evaluated the limit for the numerator but not for the denominator

lol

[small bear]

that part should be clear to k0nz

the write-up is focusing on the sign change

[austere pike]

it is indeed

man, it's funny how computer science works

the programming is incredibly easy but the math just destroys me

[fiery meadow]

thank you 🙂

i have, now i see, thank u for alerting me

[hot thorn]

can someone solve this for me??

[quaint pond]

could someone explain me this problem

not the solution

the problem

[hot thorn]

please someone solve this for me

i have my exams

[vale wigeon]

this is from an exam that's going on right now? @hot thorn

[quaint pond]

like i dont understand the instructions

[vale wigeon]

@quaint pond you might want to move to a free questions channel or #probability-statistics for the time being

[hot thorn]

no

[vale wigeon]

@hot thorn in any case this is not a "do things for you" server

[hot thorn]

I don't know how to solve this

so i felt like to ask it on my discord

[gloomy canopy]

why we get π/4 to h?

[hot thorn]

please can u take a look on my problem

it's a rather simple one

[glass lichen]

It really isnt

[hot thorn]

are u taking about my problem

or her ?

[glass lichen]

I responded to you clearly

As well as what I said would make no sense to their question...

[hot thorn]

just leave it i'll try it out myself

it's been months since i last opened my discord

[candid sluice]

you can probably evaluate the right-hand determinant as a vandermonde determinant

about the determinant of the left matrix im not really sure

[hot thorn]

thanks

i'll just skip this one

it's really hard

[ionic jewel]

5️⃣

[alpine sable]

Anyone know how to do this?

[shell heron]

make them have a common denominator

[alpine sable]

yeah how lol

3*b - 42
7b - 7b

this is what I have so far

[shell heron]

where did u get 7b - 7b from

[alpine sable]

multiplied 7 x b

to get common denominator

[shell heron]

yeah and then u get 3 - 6 / 7b

[alpine sable]

you have to multiply the 3 and 6 right

by 7 & b

[shell heron]

oh yeah

[alpine sable]

so then 3b-42/7b?

[shell heron]

yes

that is correct

[ionic jewel]

yes but please use parenthesis

(3b-42)/(7b)

[alpine sable]

is that it?

there's no more simplification?

the answer is 2 = (3b-42)/(7b)?

[shell heron]

multiply by 7b

rhs and lhs

then from there u can take over

[alpine sable]

14b?

[shell heron]

yes

14b = 3b - 42

and that is easy work

[alpine sable]

hm I don't know how to solve an equation if both the lhs and rhs have the variable

do I add 42 to 14b or something?

[shell heron]

u want the variables to be on one side and the non variables to be on the other side

in this case u want b to be alone in one side

[alpine sable]

yeah how do I get both 14b and 3b on one side?

[shell heron]

you can either subtract, add, multiply, divide

which one do you think is the correct one in this situation?

[alpine sable]

divide?

[shell heron]

why is that so?

[alpine sable]

because they're multiplying by b

and division is the opposite of multiply

[shell heron]

yeah but why not subtract by 3b on both sides, then u remove the 3b from the rhs and have all the variables on the lhs

[alpine sable]

ooh I can subtract 3b

okay

[shell heron]

yeah

[alpine sable]

for some reason I was thinking you could only subtract numbers and not numbers w/ variables

[shell heron]

u can imagine it as 14b = +(3b)-42

[alpine sable]

does the problem become 11b = -42 then?

[shell heron]

yeah but u can still simplify that

so that u get an answer for b

[alpine sable]

by dividing 11 in to 42

[shell heron]

yes

dont forget the -

[alpine sable]

-0.26?

no 42 / 11

3.81

[shell heron]

its not 42 its -42

[alpine sable]

-3.81

[shell heron]

and you should write it in a fraction

its easier and its simplified enough

[alpine sable]

how can you simplify 11?

[shell heron]

you cant, its prime

[alpine sable]

so how do I write it as a fraction

[shell heron]

like u did before

???

[alpine sable]

42/11

but you said to simplify it further

[shell heron]

you see that -42? yeah, its negative and not positive

i said its simplified enough

[alpine sable]

oh gotcha

[shell heron]

.

[alpine sable]

thanks a lot

[shell heron]

no problem

[frozen cedar]

Good job. It is best lesson for all kids

[humble flicker]

I need help factoring 5x^2-13x-6

Can you show how too pls

Ik how to factor just don't know how to factor this

[proud locust]

ok i can help for 5 min

igg after that

[proud locust]

multiply co eff of x^2 and the constant
so 5*6

thats 30

i mean -30

bc its 5 and -6

so now you have to split -13 such that it multiplies up to -30

so 1 number has to be negative and another positive

for the multiplication to give negative

[silver flicker]

how do i convert the volume of an explosion into newtons?

(i only have the volume of the explosion)

[alpine sable]

You might be able to compute the pressure

Although im not sure what you mean exactly by volume of an explosion

[oak chasm]

@silver flicker This is more of a mathematics server. You might get better help at the physics server listed in #old-network.

[silver flicker]

oh

[arctic blade]

How would I best go about weighting a non-linear least squares? I'm using scipy if anyone knows of a way to do it with this

could I just multiply the residuals by a factor?

[lusty plaza]

Does it make sense to say that a Rational number has a denominator? Do integers technically have a denominator of 1?

[ionic jewel]

yes this intuition is right

although it's not a formal definition

[placid zinc]

Note that π/2 is not a rational number, despite having a denominator

[lusty plaza]

yes

my question was more Q->denominator not denominator->Q

[placid zinc]

Fair haha. If it's in Q, it has a denominator or it's an integer

[glass lichen]

if it's in Q, then it's a sensical ratio of integers

[raw garnet]

How do I show that this is the ONLY solution with the uniqueness theorem for second-order linear ODEs?

[alpine sable]

can u state the uniqueness theorem?

[ionic jewel]

is sensical actually a math word

[alpine sable]

so just use it

[glass lichen]

No, just means the ratio makes sense

[ionic jewel]

(probably the coprime part?)

which ends up being important for whatever reason

[placid zinc]

Imma be lazy with my definitions if I want

[raw garnet]

Does this mean that if I can write the equation on the form (which I can) then it is unique? What about y'(t_0) = y'_0? is it zero because that 3' = 0?

[placid zinc]

Then the solution is unique, yes

[glass lichen]

that type of problem a) has a solution (existence) and b) has only one solution (uniqueness)

[glass lichen]

but no clue where you pulled 3'=0 from

oh there was something before the theorem

[raw garnet]

it says that y'(t_0) should be equal to y'_0. My problem has y(x) = 3, then y(0) is also = 3 and y'(t_0) = y(0) = 0?

[placid zinc]

Okay so you have noticed that you do have to get it into a certain form. That form is:
y" - (x²/e^cos(x))y' + (1/e^cos(x))y = 3/e^cos(x)

[raw garnet]

Yes so I get p(x) and q(x)

[placid zinc]

The point t_0 is also x = 0

So are p and q continuous in some open interval about x = 0?

[raw garnet]

yes

[placid zinc]

That's all you need! The solution exists and is unique in that interval

[raw garnet]

alright great, thank you 🙂

[vale fossil]

i’m struggling with this, i don’t understand the steps

can someone explain?

<@&286206848099549185>

[alpine sable]

Show the problem pls

[alpine sable]

The area of ABCD is given by $\frac\theta{360} \pi (OB^2 - OA^2)$

[ocean seal]

The Library of Babel

[alpine sable]

Do you see why? @vale fossil

[vale fossil]

yes

that i understand

i understand everything except the re arranging part

for the equation to be equal to the angle

[alpine sable]

That’s just algebra, I can write it out for you

Occupied

[vale fossil]

i still don’t understand the steps

[alpine sable]

Ok

Any one in particular?

[vale fossil]

from first line to second

[alpine sable]

Sure, gimme a sec

[vale fossil]

oki

[alpine sable]

I guess what you need to understand is that for any equation, you can always multiply both sides by the same thing, or add the same thing to both sides

That’s what we do when we move things over

I’ll write that out in the steps

For example this

To eliminate the 360 denominator on the left side, I multiply by 360

On both sides

[vale fossil]

yes, that i understand

[alpine sable]

So what part about steps 1 to 2 doesnt make sense?

I just did this twice, once for 360 and once for (16^2 - 8^2)

[vale fossil]

it’s how to get (16^2 - 8^) on the other side i don’t understand if i have to multiply divide add or substrat

and

i think that’s it

[alpine sable]

sure, it’s not too complicated

Whether you add multiply etc depends on how the number is related to the variable you’re trying to isolate

If you’re trying to isolate x and you have a*x, you divide

If you have a+x, you subtract

[vale fossil]

okay that makes sense

[alpine sable]

Usually, you try to get x alone with only things multiplying it by just adding and subtracting

And then you’re free to multiply or divide

That’s about it, although it takes maybe a bit of practice if you’re not used to it

[vale fossil]

fair enough, thank you. i’ll try to rearrange it again see if i can do it now and i’ll reach out in the chat if i have another issue

[alpine sable]

[scarlet heath]

How do I solve for this (ignore the work that was me starting it but wasn’t right$

[alpine sable]

Replace sin θ with x and solve the quadratic

[wary stream]

Zero product property

[scarlet heath]

Oh so I should move it to one side

And factor

[alpine sable]

Yeah, treating it like a polynomial works just fine

[surreal meadow]

uh that looks like a quiz

[alpine sable]

Oop

[glass lichen]

and yes, it looks like a quiz

[alpine sable]

Honestly i dont think sometimes

[glass lichen]

@sterile falcon is it an assessment?

[scarlet heath]

Just wanted to check I was rigtt he about these

Wasn’t too sure

[thin sparrow]

13 is correct

14 im not sure

[wary stream]

Pretty sure they're both wrong

[red phoenix]

um cos^2x =/= cos x^2

i agree, both look wrong

[thin sparrow]

oh nvm

im deaf

i cant see well

[scarlet heath]

My calculator treated them the same so I threw a leg out

Mind explaining why if you don’t mind?

[red phoenix]

cos^2x = (cosx)^2

notation thing

(sinx)^-1 = 1/sinx

[scarlet heath]

Wouldn’t that make it uh

Cos^2x^2

Because it goes to both?

[wary stream]

No

[red phoenix]

it doesn't go to both

[alpine sable]

Only goes to both in multiplication, not function application

[red phoenix]

really just a notation thing so you dont confuse (cosx)^2 and cos x^2

[scarlet heath]

Dang alright

Thank you!

[viral crag]

why when the angle CBA = 20 , the angle CDB is always 110

[red phoenix]

Is point A the center of the circle?

[viral crag]

yes

[feral crypt]

It doesn’t

They are independent of one another

[viral crag]

it does i played with the point D and the value of CDB is always 110

[feral crypt]

Oh that’s different

[viral crag]

but im struggling to understand why is that

[feral crypt]

It’s due to circle theorem

Let me see if I can find a pic online quick

[red phoenix]

The x,2x thing?

[viral crag]

ohhhhhhh waitttt i got it now

[red phoenix]

as C,B dont change

[viral crag]

well thanks guys

much love

[feral crypt]

Oh nvm then XD

Np

[honest hawk]

Im being an idiot here

What rearrangement needs to be done here?

[placid zinc]

In order to get F?

[honest hawk]

to isolate for I

Essentially, how does one get to I=3F/2

Im spacing out big time 😅

[placid zinc]

So like the upper picture does, you can subtract 1/3F from both sides. This isolates 1/i

[honest hawk]

Yup. I then get 1/F - 1/3F

[placid zinc]

1/F - 1/3F = 1/i
2/3F = 1/i

[honest hawk]

lmao
im an idiot

[placid zinc]

When both sides are simple fractions, you can simply flip both sides

[honest hawk]

that non-numerical denominator tripped me up

[placid zinc]

i = 3F/2

[honest hawk]

Thanks, haha. Appreciate it.

[placid zinc]

Np feel free to ask if you have any others

[honest hawk]

Will do!

[dark parcel]

Hi guys anyone knows how to separate the real and imaginary part of this?

[wary stream]

,rotate

[dark parcel]

<@&286206848099549185>

[uneven isle]

message deleted as I realized channel was occupied

[ripe mountain]

@placid zinc @tight locust so i know i could do this using 1^inf=1, but was the way i did it originally incorrect? using the ln1 * infinity = L logic

[alpine sable]

Any advice on solving problems that you haven’t practiced? Calculus 1 and pre calc? I’m only good on examples.

[limpid spade]

what problems

[alpine sable]

How do I find all possible combinations of x and y which are solutions to
5=4x+y (mod 26)

[placid zinc]

It's too many steps, but yes. @ripe mountain

[glass field]

i dont see an x or a y @alpine sable

[alpine sable]

Sorry my bad, updated now, thanks.

[glass lichen]

Ok well it wants you to determine y(0) and the derivative of y(x)

[urban escarp]

yeah

but i dont really know what to do when the function is also in integral

[glass lichen]

FTC

$\dv{x}\int_a^x f(t)\dd{t}=f(x)$

[ocean seal]

Mosh

[urban escarp]

alright ill give it a try

[glass lichen]

hint you need chain rule for it

[urban escarp]

@glass lichen Is this on the right path

<@&286206848099549185>

[surreal meadow]

,rccw

[glass lichen]

Not quite

$y'(x)=\dv{x}\int_0^{73x}(t^2-\frac{1}{t}y(\frac{t}{73}))\dd{t}$

[ocean seal]

Mosh

[glass lichen]

since derivative of a constant (67) is 0

[urban escarp]

would it work if i differentiated the stuff inside integral normally (just like there isnt an integral at all) and then sub in t=73x?

[glass lichen]

refer back to FTC part I I posted already

[glass lichen]

.

you do chain rule for the bound, then plug the bound in for the integration variable

[frosty jungle]

guys why is 2 + 2 equal to 2 * 2 equal to 2^2 equal to 2 tetration 2 equal to 2 super tetration 2 equal to 2 super duper tetration 2?