help-0

[wanton frost]

8/125 and 2/5

find the common base

[waxen turtle]

uhhhhhhhhhhhh

Idk what the common base means

They're both like perfect cubes right

Fr

[wanton frost]

2^3/5^3 and 2^1/5^1

that works yeah

so (2^3/5^3)^t = (2^1/5^1)

common base achieved

[waxen turtle]

So cool

[wanton frost]

so we can distribute in ^t

we get 2^3t/5^3t = 2/5

[waxen turtle]

So t=1/3

[wanton frost]

yeah

[waxen turtle]

So cool

Now wat

[wanton frost]

so t is our decades

1/3 is a number

we have found the amount of decades

every 1/3 decades the population decreases by 3/5

[waxen turtle]

Oh

Is that the answer

[wanton frost]

it should be, yeha

[waxen turtle]

Yay

[wanton frost]

yay

[waxen turtle]

Ty

Omg i liek water fr

[waxen turtle]

Is this right fr

@wanton frost

@wanton frost

OK THEY MADE A VID ABT SOMETHING LIKE THIS FR

Do I try the same thing fr

[waxen turtle]

Idk how he got 3.5 tho

<@&286206848099549185>

[neon sun]

315 divided by 90

dunno why though

[waxen turtle]

Why

Oh

Anyways

[waxen turtle]

Idk how to do it

@neon sun plz help

<@&286206848099549185>

[neon sun]

well i think to understnd this as a whole you should delve into the study of half life formulas

[waxen turtle]

<@&286206848099549185>

[neon sun]

no way you skimmed over my advice like that 😔

[waxen turtle]

I will only live a full life

[neon sun]

if only you used this wit in your mathematics 🙄

[rotund shoal]

You just got help

[waxen turtle]

😔

[lone heart]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[lone heart]

@waxen turtle Has your question been resolved?

[neon sun]

bro who did the question

first of all confirm that their working is correct

[waxen turtle]

Wat

Wdym

Wat

[neon sun]

the working out is it right?

also when rounded to 2 decimal places shouldnt it be 1.01

[waxen turtle]

He skipped it

I mean like

The rounding

But

Sal khan did it

[waxen turtle]

<@&286206848099549185>

[waxen turtle]

<@&286206848099549185>

[waxen turtle]

<@&286206848099549185>

[quasi willow]

its 1.5^(1/10) because t is in decades so per year its gonna be a tenth of the amount it would be for a decade i think.

[waxen turtle]

Uhhh

How do I answer the question with that frfr

[quasi willow]

idk what kinda system ur working on, so either its as i wrote it or you gotta round off the value of what i wrote and calculate it

[waxen turtle]

I have to say the factor it grows by each year

[waxen turtle]

Plz return

How calculate

[quasi willow]

use calculator or insert as written

[waxen turtle]

How do I round thus

1.041

[quasi willow]

idk what your problem requires as it doesnt say in the problem

you know the number now you pick how you want to represent it

[waxen turtle]

😔

Hurray I got it right

.close

[lone heart]

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[ripe zodiac]

Without evaluating express each number as the trigonometric ratio of an acute angle

[ripe zodiac]

why is it sin 50 rather than - sin 50

isnt it in the 3rd queadrant?

where sin is negative??

[storm musk]

Yeah it is in the 3rd quadrant

[gray isle]

whos saying its sin(50)

[storm musk]

Yeah

Let me think for a sec

[lone heart]

@ripe zodiac Has your question been resolved?

[lean prairie]

nah ur

right

[ripe zodiac]

the answer sheet

is it wrong?

[lean prairie]

its -sin50

[ripe zodiac]

o ok

thanks

[lean prairie]

wait

nvm

sin(-50)

is the same as

-sin50

thats y

[gray isle]

yeh. answer sheet is wrong

[lean prairie]

yeah

[ripe zodiac]

answer sheet says sin50

ooo ok

thanks guys

[lean prairie]

answer sheet is jokeman

warrah

[ripe zodiac]

ill ask my reacher in class then

just to triple check

ok bye thanks guys ❤️

.close

[lone heart]

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[civic tinsel]

.open

o-

[civic tinsel]

Hello

I just need help with a quick simplification
Cuz i basically solved all the problem but I am stuck in the last part for some reason

So its basically :

-2ab - a^2

2a^2 - 4b^2

The line is supposed to be a fraction

[oak gulch]

take 2 outside the parenthesis on bottom?

[long axle]

$\frac {2ab + a^2}{4b^2 - 2a^2}$

[ocean seal]

Stephen

[civic tinsel]

ye but negative 2ab on top so its ... ?

$\frac {-2ab + a^2}{4b^2 - 2a^2}$

[ocean seal]

Not_

[civic tinsel]

that

[oak gulch]

yea you are right idk was just spitballing

realised after i pressed enter

sorry

[long axle]

Nah

[civic tinsel]

?

[long axle]

Ur original thing was -2ab - a^2

[civic tinsel]

ye i tried but my brain ain braining

[long axle]

So factor out a -1 then put it in the bottom

[oak gulch]

oh yeah

i was on the right track then lol

[civic tinsel]

ooh

sry didnt notice

[long axle]

U good

But with regards to whether it can be simplified

Lemme see

[civic tinsel]

Wait so if I multiply the top part by "-1" and multiply bottom part it is valid ?
Or what is factor ? Sry education in my country is really bad but I really enjoy math

[long axle]

Yes multiplying top and bottom of original expression will yield the same

U said u tryna simplify this?

[civic tinsel]

Ye

[long axle]

Hmm

[oak gulch]

Maybe you just did the problem wrong, did you check your math?

[foggy pecan]

$\frac {-2ab + a^2}{4b^2 - 2a^2}=\frac{a\left( a-2b \right)}{2\left( 2b^{2}-a^{2} \right)}$

[civic tinsel]

Yea I am starting to suspect that 😓

[ocean seal]

Joanna Angel

[foggy pecan]

nth more can be achieved

[long axle]

Other than that factoring^, that shd be it

Send og problem

[civic tinsel]

its kinda long , but lemme try to write it down

How do i write down a square root ?

[long axle]

$\sqrt {x}$

[ocean seal]

Stephen

[civic tinsel]

What if its a sqrt on a fraction ?

[long axle]

$\sqrt {\frac {c}{b}}$

[ocean seal]

Stephen

[civic tinsel]

Nvm ill just take a pic lol

[long axle]

Aight lol

[civic tinsel]

there

--

The sqrt part I simplified to :

$\frac {2b-a}{2b+a}$

[ocean seal]

Not_

[civic tinsel]

then the common denominator was 2a^2 - 4b^2

So I ended up with :

$\frac {(2b-a)(a-2b)+8ab+2b(a+2b)}{2a^2 - 4b^2}$

[ocean seal]

Not_

[civic tinsel]

wait ....

[oak gulch]

should be (a-2b)(a-2b) I think?

[civic tinsel]

Omg ... I am so dumb-

😭 -

thanks

[oak gulch]

glad i could help fr

[civic tinsel]

nvm that wasnt the error

[oak gulch]

damn

[civic tinsel]

I saw where it is

[oak gulch]

Where?

[civic tinsel]

its the 2a^2 in the denominator

its without the 2

So then , i should be able to simplify it

$\frac {-2ab - a^2}{a^2 - 4b^2 }$

Nvm

still cant

[ocean seal]

Not_

[civic tinsel]

Bruh i cant figure out what i do wrong

[oak gulch]

You can ping helpers

[civic tinsel]

At this point i feel like its a useless mistake so I am trynna figure it out tracing step by step

[oak gulch]

I can't figure out how you get that common denominator

but it's been years since i learned this

just started learning math again a few months back

[civic tinsel]

wow cool , I got it by multiplying the first fraction by (a-2b) and the third fraction by (a+2b)
That gave the same fraction as the one below 8ab

But If I multiplied the denominator I also had to multiply the top part

$\frac {(2b-a)(a-2b)-8ab+2b(a+2b)}{a^2 - 4b^2 }$

[ocean seal]

Not_

[civic tinsel]

This converts too :

...

$\frac {2ab-4b^2-a^2+2ab-8ab+2ab+4b^2}{a^2 - 4b^2 }$

[ocean seal]

Not_

[civic tinsel]

And lastly that simplifies too :

$\frac {-2ab - a^2}{-4b^2 + a^2 }$

[ocean seal]

Not_

[civic tinsel]

I might be wrong tho

[oak gulch]

yeah makes sense

[civic tinsel]

But according to the book the answer is :

$\frac {a}{2b-a}$

[ocean seal]

Not_

[fickle sandal]

needs more factorising

[civic tinsel]

I SOLVED IT

i think-

[civic tinsel]

Ye I think i saw how

:>

So its :

$\frac {a(-2b-a)}{(2b-a)(-2b-a)}$

[ocean seal]

Not_

[civic tinsel]

And then we just cross out

And we have the result that is :

$\frac {a}{2b-a}$

[ocean seal]

Not_

[civic tinsel]

FINALLY

[oak gulch]

good job

[civic tinsel]

How do i close this chat ?

[civic tinsel]

ty ))

[oak gulch]

.close

[civic tinsel]

alr thanks
And thanks for the support while I figured out how to solve it lol

.close

[lone heart]

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[oak gulch]

ofc np

was fun

[lone heart]

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[lime holly]

I have to evaluate this based on logical correctness, clarity, opening, stating the conclusion, reasons and overall valuation

and give each one of those a grade between 0 and 4 (4 being the highest)

[tall topaz]

I mean it looks alright to me

Maybe the conclusion could be a bit clearer

[lime holly]

also i asked someone about the math proof yesterday they told me it was line 4 and they lied to me and i got it wrong

it was in fact 13

[lime holly]

i still think i dont understand proof by induction maybe

[tall topaz]

Oh

[lime holly]

i watched a video on it but idk

[tall topaz]

Damn so it was 13 lmao

[lime holly]

yeah...

lost 0.25% of my overall grade because of that guy

note to self dont trust anyone lmao

[tall topaz]

Rip

It’s Aight 0.25 isn’t that bad

[lime holly]

yea true

okay so for proof by induction

ok so the sigma notation is just to infinity since its n

i guess

[tall topaz]

Well anyway Proof by induction really just consists of 1) Proving it works for some number (in most cases n=1) 2) Proving if it works for some number k it works for the next number k+1. Thaits it.

[lime holly]

i understand that part but i dont understand how they prove that it works for k+1

[tall topaz]

Okay your statement is that sum = n/(n+1)

Okay one thing I’d change in this proof is instead of assuming it’s true for n I’d say like t instead

So let’s assume the statement is true for t then we have $$\sum_{k=1}^t \frac{1}{k(k+1)} = \frac{t}{t+1}$$

[ocean seal]

Pure

[lime holly]

why is that

[tall topaz]

It’s like we already use n for the P(n) things when we say for any natural number n

So I think just for clarity it’s better to use a different name

[lime holly]

oh so thats like when they only use n they assume its true for "k+1"

[tall topaz]

Yep

We want to show it’s true when n=t+1 ie $$\sum_{k=1}^{t+1} \frac{1}{k(k+1)} = \frac{t+1}{(t+1)+1}$$

[ocean seal]

Pure

[tall topaz]

$$\sum_{k=1}^{t+1} \frac{1}{k(k+1)} = \frac{t+1}{(t+2}$$

[ocean seal]

Pure

[tall topaz]

That’s what we need to proof

But $$\sum_{k=1}^{t+1} \frac{1}{k(k+1)} $$ is just $\sum_{k=1}^{t} \frac{1}{k(k+1)}$ + the t+1 th term

[ocean seal]

Pure

[lime holly]

i dont think id take off a point for that though

or if i did maybe 3 instead of 4 in clarity

[tall topaz]

Yeah I think 3 for clarity

[tall topaz]

But are you following so far

[lime holly]

let me look at it one more time

[lime holly]

okay so just replace n with t+1

and then

[lime holly]

it becomes this

[tall topaz]

Yes and the first sum we already know what that is by inductive hypothesis

[tall topaz]

For this I mean

[lime holly]

so now we assume that it is true because it works for n = 1

[tall topaz]

Right so we’re just looking at

This line now

[lime holly]

yes okay so

uh

wait it it originally t^2 + 2?

[tall topaz]

Wdym

[lime holly]

how did n+2 become (n+1)(n+2)

[tall topaz]

That’s the t+1 th term

the sum from 1 to t+1 is equal to the sum from 1 to t + the t+1 th Term

And for the t+1 th term you just plug in t+1 to the expression

$\frac{1}{k(k+1)}$ plug in k=t+1

[ocean seal]

Pure

[lime holly]

wait i dont think i understand how they started the first line then

[tall topaz]

Right

[lime holly]

how come we added that

[tall topaz]

No notice the index

[lime holly]

OH

nevermind

okay so its just replacing the k from the original one

[tall topaz]

Yeah that’s the t+1 th term

[lime holly]

so in the next line they add n/n+1 to the t+1 th term

[tall topaz]

Yes because the first sum is n/(n+1)

[lime holly]

and since 1/k(k+1) is "true" as we assume

we switch it with

n/n+1

[tall topaz]

Yes

Then it’s just algebra

[tall topaz]

Until you get to this

Proving it’s true for t+1

[lime holly]

how does the result n+1/n+2 show that the theorem is proved

[tall topaz]

Do you agree that it proves for the case t+1

[lime holly]

1/(n+1)(n+2) is the t+1 th term and the result of adding it to the original statement is n+1/n+2

[lime holly]

i dont see how it is proven with the result

or is it because

1/2 or n+1/n+2

[tall topaz]

Because that’s what you should get when you plug in n+1 to the theorem

[lime holly]

okay i see

i do think it would be more clear if they used t

maybe i will take off a point for that then

[tall topaz]

Yeah

[lime holly]

thank you

[tall topaz]

Also I’d take off like 2-3 points for conclusion

[lime holly]

they should have said something like "therefore by proof of induction" then state what they were proving "is true"

right?

[tall topaz]

Here’s how I’d write it:
Since the statement is true for n=1 and for somen natural number t, n=t being true implies n=t+1, the statement is true for all natural number n by the principle of mathematical induction.

[lime holly]

ah i see

tbh i dont even know what correct proof is supposed to look like because she always makes us correct ones that have faults in them

[tall topaz]

I can write good proof

Tbh this is not considered wrong and most people are too lazy to write that whole thing anyway

[lime holly]

i have to do a self study module on sets and functions and use proofs so i could be back at somepoint lmao

[tall topaz]

It’s just if you really wanna be harsh then you’d deduct marks

Ist this first year uni?

[lime holly]

wait i actually understand this one today :D

[lime holly]

yes 1st year

"mathematical reasoning"

[tall topaz]

I guess learning logic first year makes sense

But I feel like sets and functions are more important lol

Anyway I should sleep

,ti

[ocean seal]

The current time for pure1144 is 03:10 AM (GMT) on Sun, 19/11/2023.

[tall topaz]

Good luck with maths

[lime holly]

goodnight and thank you :D

its only 10pm here

🇨🇦

.close

[lone heart]

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[tall topaz]

[lone heart]

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[alpine sable]

I have a question about what resources are the best for my self-study of math. My study will consist of Elementary Algebra, Discrete mathematics, Trig, Calculus, Statistics, and Probablility. I want to be really good at all the high school level subjects and then move on to undergraduate stuff. Resources can be anything although I love textbooks it can be videos, apps like Khan Academy etc. I just want it to be straight to the point and best for beginners in being thorough and not leaving stuff unexplained.

[raven rover]

If you're going to go through all of those subjects, go through Khan Academy

[alpine sable]

You think it's better than your usual textbooks?

[raven rover]

depends on the textbook tbh

I never rly read though many calculus textbooks or khan academy that much

[raven rover]

For price reasons, go w khan

[alpine sable]

This is what I'm using

[raven rover]

libre texts has some good stuff - I've used it before

It rly depends on you

[alpine sable]

Thx man!

I'll use both.

[alpine sable]

Do you think Khan is on a sufficient level to get my into uni eventually?

For practicing stuff that I missed in high school...

[raven rover]

It depends on how much you study and the uni

[alpine sable]

Uni has very simple admission tests with high school stuff

[raven rover]

and your high school too

[alpine sable]

My high school is highly regarded

Although my grades were not stellar they were pretty good.

Anyways. Thank you.

I'd also like to know about some great books later down the line for advanced topics

to compile them for when I need them and put the name and the author in a text file.

[raven rover]

you'll come across them when the time comes 🙂

[alpine sable]

So no worries lmao

I have a little less than a year to tackle this

And I'm going to a real mathy school ngl

Have a nice day kind stranger!

[raven rover]

np! likewise 🙂

[lone heart]

@alpine sable Has your question been resolved?

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[crude marten]

This is what I imagine

I dont know how to setup dz

limits for dz

I assume its this

[raven rover]

your z, y, and x coordinates depend on each other, so your bounds won't be simply the numbers

you'll need to describe the upper surfaces (ceiling) as z = z(x, y)

[crude marten]

I split the shape into a rectanngle and the upper shape

so all I really need to find is the upper boundary for z no?

[raven rover]

yup

for each point on the floor of the building, the height of the ceiling will vary

[crude marten]

The z bound will be a functionn of x and y

but Im nnot sure how to find that function

[raven rover]

That's the tricky part, you have two diff planes as your ceiling, so you may want to split up the building into two parts

[crude marten]

dang, how do I find the planes then

[lone heart]

@crude marten Has your question been resolved?

[crude marten]

<@&286206848099549185>

[thin lance]

Why do i keep getting pinged 😭

someone take this role away from me

[crude marten]

Its your calling to help people, also I think its cuz of the midterm season everyone is practicing

[thin lance]

Ohh

Yeah ill just leave the server

[lone heart]

@crude marten Has your question been resolved?

[crude marten]

no

.close

[lone heart]

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[placid zinc]

Have any thoughts on the question?

[gritty pond]

i think my bounds are wrong

also im not sure if i am using correct formula

for line integral

[placid zinc]

Formula for line integral? Well, it doesn't really matter since you use green's to get a double integral anyway

Forget the bounds for now - have you tried the sub?

[gritty pond]

nope

i forgot how to do change of variables

[foggy pecan]

$\int_{0}^{2}dy\int_{y}^{y+2}\left( f(x,y) \right)dx$

[ocean seal]

Joanna Angel

[foggy pecan]

and f function is yoru function

[gritty pond]

ahh i think i see

[foggy pecan]

since inside we run with dx, then nth is chaned since you have only expx

yes yes

very well

[gritty pond]

do we need to substitute?

[foggy pecan]

no need, it is elementary

[gritty pond]

idk why

[foggy pecan]

their hint was for dudes, who would liek to use other graph )

but we aer not afraid of what we have now

[gritty pond]

maybe you arent

haha

i think this is inner?

[foggy pecan]

yes, since dx was neutral fo rus

yes

nod dy

nwo*

very easy

e^2 you can take out of parenthesis if you like

very well

all ok

eys and soem terms are alike

so you can join them

yes, it is also possibel to make factoring y grouping, but not necessary

[gritty pond]

this is the weirdest answer

[foggy pecan]

i agree, but the clue is, the way fo dealin g with it

[lone heart]

@gritty pond Has your question been resolved?

[tall pilot]

Help2

[old heath]

Open your own channel

[tall pilot]

https://discord.com/invite/7jw7V6Zt

[thick basalt]

...

[thick basalt]

Not server

He meant

#❓how-to-get-help @tall pilot

[lone heart]

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[shell narwhal]

how do i find A (very quickly)

[sour dove]

no way faster by hand then doing the algorithm. You just have to multiply everything out and add it up per cell of the matrix

[shell narwhal]

there must be a way

ok here then

the real question is

without calculations , find a basis for all the subspaces of A

[sour dove]

oh unfortunately that I dont' remember. I'm rusty on my linear algebra lol

[shell narwhal]

oh no :C

[sour dove]

I forgot how to find a basis for a matrix

[shell narwhal]

i know how

but only when there is a single matrix

[sour dove]

nah as far as I know you'd still have to multiply the matrix out

[shell narwhal]

in the question it says without calculating it

[sour dove]

oh well maybe there is?

hold on I'm seeing if i can find anything

the instructions seem to imply that you don't need to multiply out your matrix lol

can I see the whole problem instructions?

[shell narwhal]

its in french

but my translation is pretty accurate

[sour dove]

ok

[shell narwhal]

thx for helping me btw

[sour dove]

yeah no problem. Unfortunately I don't know if I"ll be much help. I've been meaning to relearn LA but I just remember the basics. Google isn't much help either

[shell narwhal]

could it have something to do with A=LU ?

[sour dove]

I would say wait around for another helper who knows LA better or post in #linear-algebra. That's a dedicated channel to LA concepts and problems.

[shell narwhal]

my exam is in 6 hours ;-;

[sour dove]

I also gotta get to bed, lol. Sorry I thought it'd be an easy answer

yeah I would post in #linear-algebra then

[shell narwhal]

i did already

[sour dove]

ok cool. Hopefully you'll hear back soon. Otherwise in like 10 min if nobody else drops by then close this channel and reopen another one

best of luck!

[shell narwhal]

ok thx

.close

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[sour verge]

.reopen

[lone heart]

✅

[sour verge]

This MSE post has your question. You might want to read through it to understand a bit more

https://math.stackexchange.com/questions/4022080/finding-bases-for-a-matrixs-four-subspaces-without-computing-the-matrix

@shell narwhal it has to do with how the second matrix has 3 pivots and how the rowspace is R3

[shell narwhal]

so

[sour verge]

Seems like it deals with LU factorization. This website seems like a good intro to understand how you'd go at it. https://www.math.drexel.edu/~jwd25/LA_FALL_06/lectures/lecture4A.html

[shell narwhal]

it only states that the rank of the first matrix = rank of the second matrix

ok but what happens ?

do i have to find A as one matrix ?

how does A = lu help me

[sour verge]

No you don't.

They want bases for the rowspace, columnspace, left nullspace and right nullspace.

[shell narwhal]

yhea

[sour verge]

For the rowspace, since the right matrix has 3 pivots, we know the rowspace has dimension 3, so any basis of R3 works (say the three conventional basis vectors)

[shell narwhal]

i don't understand any of this. thanks for trying to help me, but its very late, ill go to sleep. thanks again

[sour verge]

That is ok. Rest well for you test.

If you want to try looking for more about this, search up LU factorization.

[shell narwhal]

alright

thanks

.close

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[ebon pilot]

Im so stuck

[ebon pilot]

Please help

[subtle birch]

yeah that image is pretty clear

[outer pulsar]

Yo how do I do no.9 using the direct comparison test y’all

[stark crater]

Median=50th percentile. To find percentile look for value in y axis and find what x value gives that y value

[sharp thorn]

#❓how-to-get-help

[ebon pilot]

So it’s 45?

[stark crater]

55

[ebon pilot]

Hb this one

[stark crater]

Lower quartile means 25th percentile. Do same idea

[ebon pilot]

How about interquartile range?

[stark crater]

I believe that means upper quartile (75th percentile) minus lower quartile

I have confirmed that that is correct

[ebon pilot]

so it’s 68-45?

69?

[stark crater]

Think your first one is 10 too high

[ebon pilot]

Oh u right

59-45

[stark crater]

Yeah

[ebon pilot]

Oki

Tnqqq

What’s this

I know what discrete and continuous are but I’m not sure where to group some of them

[stark crater]

What you thinking so far

[ebon pilot]

Oh nvm I got it

Thanks tho

[stark crater]

Gg

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[cursive cobalt]

What is the least value of n such that every collection of n points in the plane, all with integer coordinates, must contain at least two points for which the line segment connecting the two points contains a point (other than an endpoint) with integer coordinates?

[cursive cobalt]

Is it 5?

<@&286206848099549185>

We can have a square of 4 dots then the fifth dot will always make a line segment

[mortal trellis]

why should 4 of those form a square

[lone heart]

@cursive cobalt Has your question been resolved?

[surreal fog]

not every collection of 5 points is "a square + fifth dot"

only some collection of 5 points is "a square + fifth dot"

it is certainly not 4 because of the counterexample {(0, 0), (0, 1), (1, 0), (1, 1)}

this is the square you're talking about

now add 1 more point and yeah, it will make a line segment

but can you prove that you can extend the "square" case to all collections of 5 points?

[lone heart]

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[surreal fog]

hint: explore the properties of all counterexamples for n \leq 4

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[wanton flare]

can someone explain me how to do this?

[lone heart]

Please don't occupy multiple help channels.

[celest ridge]

What type of math is that?

[wanton flare]

discrete math

[celest ridge]

K one sec

[surreal fog]

what type are A, B, and C?

are they sets?

and what is "-"

set difference?

[wanton flare]

yes i think

[surreal fog]

then what does it mean to place two set symbols next to each other like "AB" or "BC"

what's the context

[wanton flare]

what do you mean?

[surreal fog]

A and B are sets. if A = {1,2} and B = {2,3}, then what is AB? AB = {1,2,3} (set union)? AB = {2} (set intersection)?

you first have to know what those symbols even mean

[wanton flare]

the problem also talk about pairwise disjoint

[surreal fog]

yes, and?

i could assume either, or assume a completely different operator, but i'll never know if that answers your question

you first have to know what the symbols mean

[wanton flare]

.close

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[sly sand]

Find the probability that a number selected from the numbers 1 to 25 which is not a prime number when each of the given number is equally likely to be selected.

[lone heart]

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[humble ferry]

What have you tried

[lone heart]

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[viscid rock]

hello! I am new to graphing in x,y,z plane, thus, I really don't know how to figure out the boundaries needed for finding the volume (double integration). Here's the problem where I am stuck with

Find the volume of a cylindrical column having as its base the area between the curves y=x, y=x^2, and cut off by the x-y-z+1=0.

Can you guys give me some tips/clue for this one?

[lone heart]

@viscid rock Has your question been resolved?

[viscid rock]

@obtuse sonnet

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@viscid rock Has your question been resolved?

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[wraith gazelle]

How do I do 35

[woven ledge]

how did these numbers come from 6 men and 4 women

like

js wondering

i dont understand

[lone heart]

@wraith gazelle Has your question been resolved?

[wraith gazelle]

Yeah man that's what been bothering me too

[woven ledge]

maybe ask the person who gave this to u?

[lone heart]

@wraith gazelle Has your question been resolved?

[wraith gazelle]

Cant

[lone heart]

@wraith gazelle Has your question been resolved?

[fair saffron]

I found 2.160.000

You sort both women and men seperatly which is 4! and 6! Then you multiply them.
4!×6!

Then we gotta place the men between women

3 spaces gotta be full like:
W m W m W m W
The m's here need to be men then we can choose before, after or between women to place the other three men

Which would be one of 5 spaces for three of them so
5³

The I multiplied 4!×6!×5³ which is 2,160,000

I guess I have something extra here and gotta divide somn idk what is

[lone heart]

@wraith gazelle Has your question been resolved?

[potent zenith]

Its 6! x 4! x 7C4

6! Ways for men, since they're already seated

Lets consider this arrangement

_M1_M2_M3_M4_M5_M6_

_ is places to seat women

M is Men already seated

There are seven places for women to sit in, hence the 7C4 (choosing 4 seats out of 7). And then 4! Because 4 women can sit in 4 places in 4! (Or 4P4) ways

@wraith gazelle

[potent zenith]

Close but we need to choose 4 possible seats out of 7 given seats, instead its 7C4 and not 5^3

So, its 604,800

[fair saffron]

Oh you place men first instead of women. Clever

[wraith gazelle]

Thanksss

I got it

.close

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[subtle blade]

could anyone help me solve this?

[subtle blade]

idek where to start

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[grim tiger]

I'm not quite sure what models are, and therefore I don't know how to get them

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.close

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[novel dock]

Without using stats software (I have done it, I need to show the calculations manually), please can someone help me how to calculate the R^2 manually. I have data of the course taken, and the entry requirements to each course, along with the median wage after graduation in a regression. My regression equation is y=intercept+coefficient of entry requirement*ent-req+ coefficient of each course. So how do I calculate each coefficient and R^2 manually?

[novel dock]

<@&286206848099549185> Anything, please!

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@novel dock Has your question been resolved?

[novel dock]

<@&286206848099549185> Please, anyone? I've found some sources with matrices, but please help

[last walrus]

@novel dock maybe this link will help: https://www.wallstreetmojo.com/coefficient-of-determination/

[novel dock]

@last walrus It sadly doesn't, as I have more than two independent variables firstly, and I have many categorical ones

[last walrus]

Ok so this formula should work for a general linear model. $R^{2} = 1 = \frac{SS_{res}}{SS_{tot}}$

[ocean seal]

pencentre

[last walrus]

idea: (1) find all residuals and square them and add them (2) find y-bar and distance for each yi to y-bar, square it, add

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[lavish lance]

$int \frac { x } { ( 1 - x ) ^ { 3 } } d x$

[ocean seal]

Albert Einstein

[lavish lance]

$\int \frac { x } { ( 1 - x ) ^ { 3 } } d x$

[ocean seal]

Albert Einstein

[lavish lance]

how to solve it?😍

[hasty creek]

substitution

[foggy pecan]

t = 1 - x <=> x = 1-t etc

[lavish lance]

is this ok:x<=>1/t

[foggy pecan]

no

t = 1-x is a way easier

t = 1-x <=> x = 1 -t, and hence dx = -dt

[lavish lance]

thank you,I work out with t=1-x

[foggy pecan]

then you get simple denominator and sum in nominator

yw

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[green swan]

can someone expain this for me

[green swan]

it is from this

[ocean whale]

It looks like it multiplied by the conjugate

To get rid of i in the denominator

So you muliply 1/(1 - i) * (1 + i)/(1 + i)

[green swan]

ohhh its simply like that

thank you so much

.close

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[alpine sable]

what's the differnece between the Gauss-Jordan method and Guassian Elimination Method?

[alpine sable]

they look the same to me no?

[ocean whale]

In the REF, the stars can be any value still

In RREF, it's only a diagonal of 1s, 0s everywhere else in a square matrix, at least in that example

[alpine sable]

ohhhh

[alpine sable]

they have to be 0's right?

[ocean whale]

Yes

[alpine sable]

ty so much!

.close

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[green swan]

can someone help me solve this using the shown method?

[lone heart]

Please don't occupy multiple help channels.

[green swan]

.close

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[lone heart]

Please don't occupy multiple help channels.

[limber karma]

.close

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@jovial panther Has your question been resolved?

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[short kernel]

Hello

[jagged cobalt]

hello

[wild umbra]

hello

[ionic jewel]

this one got closed, so he actually does need a new one 💀

[jagged cobalt]

oh damn

[wild umbra]

😂😂

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[fringe lynx]

I do not understand this someone help please

[lone heart]

@fringe lynx Has your question been resolved?

[fringe lynx]

<@&286206848099549185>

[lone heart]

@fringe lynx Has your question been resolved?

[fringe lynx]

<@&286206848099549185>

[runic mist]

@fringe lynx for starters because Ha is not equal to, you are doing a 2-tailed test

Have you calculated sample means and SD?

[fringe lynx]

not yet

getting that

[runic mist]

Then you should have a formula to calculate the test statistic

[fringe lynx]

got them

Sample mean #1= 33.8 and stdev=4.87

Sample mean #2 =36.1 and stdev=4.51

and no i do not have the formula for that

should i search that up?

[runic mist]

Do you need to give any answers about the hypothesis testing?

[fringe lynx]

it just says to do this:

But I dont want you to give me the answer I just need you to explain on how I can do it

please

[runic mist]

It might want a confidence interval

That's what my formula sheet says

I'm studying for a test on this stuff rn lol

[fringe lynx]

I got no idea what x, u, s, and n would be though

[runic mist]

X is sample mean

u is population mean, but we don't know that so just put zero I think

s is sample standard deviation

n is number of items

[fringe lynx]

so x1 would be sample mean for sample 1?

[runic mist]

Yeah

[fringe lynx]

alright im going to attempt to put this equation together so give me a min

[runic mist]

I think it is only asking for the confidence interval so use the last formula

[fringe lynx]

ohhh ok

then what would tadf mean?

[runic mist]

That is your t value

You can either use a graphing calculator or look it up in a table

[fringe lynx]

the assignment says to use an alpha level equal to 0.10

[runic mist]

Yeah

[fringe lynx]

so where would i find it on here?

[runic mist]

You look up half of alpha because it is a 2 tailed test

[fringe lynx]

gotcha

and what about the adf next to the t?

[runic mist]

*should be the number above that actually

Degrees of freedom is 9 not 10 mb

A is alpha, your level of significance

Df is degrees of freedom, which is one less than the sample size so in this case 9

[fringe lynx]

so it would be (1.833)(0.10, (9)

[runic mist]

Are you using the entire confidence interval formula?

[fringe lynx]

just this part

[runic mist]

Yes then that is good

[fringe lynx]

alright them lemme try to put the formula together

so this

i got -0.70225 and 0.70225

should i put that in? @runic mist

.close

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[runic mist]

You don't need the .10 and 9

@fringe lynx

Only 1.833

Otherwise looks good

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[gritty pond]

can someone check my proof?

[lone heart]

@gritty pond Has your question been resolved?

[gritty pond]

Is this good?

also what is consensus on R+?

im getting conflicting answers

does it include 0 or no?

[tacit arch]

There isn't, just follow your book

[gritty pond]

what do u think about my answers on the image questions?

if R+ does not include 0?

in my case since it seems moer intuitive

[tacit arch]

ii depends on the convention your class uses

Follow that

[gritty pond]

yes i am using R+ not including 0 convention

in that case, looks good?

since i think e^x

does not include 0

[tacit arch]

Yes

Sure

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@vivid heath Has your question been resolved?

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[stable wadi]

hey i need help with a simultaneous equation again

[stable wadi]

2x + 3y = 8
3x - y = 23

i ended up stuck at -7y = -22

[sour verge]

If you got the -7y=-22 can't you just divide through by -7?

[stable wadi]

i was thinking i got -7y = -22 wrong

idk

[sour verge]

It might be. How did you get there?

[stable wadi]

so i multiplied first equation by x3 and second equation by x2 so i could get 6x on both sides

then i did

6x + 9y = 24

• 6x - 2y = 46

that bullet point is meant to be a minus

idk how it got there

[sour verge]

Well, first error : 9 - (-2) = 11, not 7.

[stable wadi]

oh

oops

so 11y?

[sour verge]

Yes.

[stable wadi]

oh i got it now

thank you

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[alpine sable]

Find the locus of midpoints of all chords of the fixed circle O such that these chords subtend right angle at a fixed point A which lies inside the circle and is not the center.

[rich quiver]

!status

[lone heart]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[alpine sable]

I dont know where to begin

@rich quiver

[rich quiver]

Let the eqn of circle be x²+y²= a²
Take the midpoint as (x1,y1) and write the eqn of chord using T=S_1

[alpine sable]

Oh please

No coordinate bash please

Only geometrical approaches

I completed by a coordinate approach

[rich quiver]

Let me think

Is locus a circle?

[alpine sable]

Yes

Can you comment on the radius and centre aswell ?

[rich quiver]

I just draw the figure and like i had a feeling that it will be a circle

[alpine sable]

Oh ok

[rich quiver]

Ok i will try

Centre is the fixed point

[alpine sable]

Yes

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[wide night]

how many solutions of (a, b) are there in this equation:

[wide night]

a and b range from 1 to 100 inclusive

[naive summit]

8->27
8->99
27->8
27->44
35->36
35->72
36->35
36->71
44->27
44->63
44->99
63->44
71->36
72->35
99->8
99->44

[wide night]

uhh are they solutions?-

sorry how did u get them?

thanks tho!

I just wanna know the steps sry Q-Q

[naive summit]

brute force programing...

[wide night]

wow-

dang thanks!

.close

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[calm anchor]

,rotate

[calm anchor]

Why is this incorrect?

[vast arch]

@calm anchor The second part isn't correct. It is not true that sin(x) = sin(x + pi)

[calm anchor]

I dont see where i did that

Ooh wait i see

[vast arch]

You have that 5v = 4v + pi + 2npi

[calm anchor]

But what should it be instead?

[vast arch]

Just the first part would be correct I think

V = 2npi

[calm anchor]

No, there are two answers

,rotate

[calm anchor]

f)

[vast arch]

Yeah you're right

Let me think for just a sec

This is really bad but I actually don't know

I'm sorry about that

[calm anchor]

No worries

[vast arch]

I'll come back if I think of something

[calm anchor]

It is difficult asf

Ive been stuck on this

For like two days

And i just cant get into a flow because i get stuck

<@&286206848099549185>

[slow fern]

no

[calm anchor]

Why?

[slow fern]

too lazy

[calm anchor]

I think it reset the helper ping

[frozen tiger]

what's the question '<'

[calm anchor]

Why is this incorrect

And what is the right answer?

[frozen tiger]

find the v that satisfies sin5v=sin4v?

[calm anchor]

Yea

I found the first one

But the second one is confusing

[calm anchor]

Here is the correct answer (f))

[frozen tiger]

I think, when you multiply 2pi to 1/9 that you get from 5v+4v and reciprocate it

It's a bit farfetched

but basically

well

not basically

4.5v+-1/2v=5v/4v

I have no idea

[calm anchor]

Hahahah

Same

Thx for trying

<@&286206848099549185>

Ill repost the question

,rotate

[calm anchor]

How do i get the second answer? (Solve for v)

Sin5v=sin4v

[lone heart]

@calm anchor Has your question been resolved?

[calm anchor]

<@&286206848099549185>

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@calm anchor Has your question been resolved?

[calm anchor]

rip

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@calm anchor Has your question been resolved?

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[fair spindle]

could you put the 8 outside of the integral

and inside would be 1/(1+x^2)

[ionic jewel]

yes

[alpine sable]

yah

[long axle]

The Limits are practically screaming arctan

[fair spindle]

yeah

and i forgot my trig

so how would you calculate 8arctan(sqrt3) - 8arctan(1/sqrt3)

[undone ledge]

can you write sqrt 3 in terms of tan

and 1/sqrt 3 in terms of tan

arctan(tan x) = x

[fair spindle]

do u mean tan x = sqrt 3 for example

oh i see

[undone ledge]

yeah

kinda

[fair spindle]

do u mean arctan(tan sqrt 3) = sqrt 3

[undone ledge]

no...

[fair spindle]

nvm

[undone ledge]

like which for what x does tan give sqrt 3

[fair spindle]

ah pi/3 right

[undone ledge]

ye

[fair spindle]

so 8pi/3 - 8something

i'm forgetting

[undone ledge]

now for what x does tan gives 1/root 3

[fair spindle]

oh since it's the reciprocal of the other onee

i'm gonna guess pi/6

cus that's the other angle

[undone ledge]

yep

[fair spindle]

alr thank u i got my answer

4pi/3

there's this one too

i know it has something to do with ln

but i'm not sure

[brisk oak]

replace 2^s with e^(x*ln(2))