help-0

[severe sluice]

somehow he refuses to believe me

(this is probably the last time i will believe that the helper ping will do something)

[plucky storm]

he wanted a derivation for the formula

[lone heart]

@opaque rapids Has your question been resolved?

[plucky storm]

english isn't his first language, i think he had trouble finding the words for "derivation" or "finding"

[lone heart]

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[rigid flint]

Hello. Not sure how to go about asking for help, but I’ll try to be as coherent as possible.

I have a spreadsheet of items where each row is an item with multiple attributes as columns. Some of the rows are items that are “valid” and the rest, “invalid”.

Based on the attributes, how best should I go about figuring out the relationship between the attributes and how they are valid or invalid?

I’ve experimented with linear regression and correlation matrixes to find pull factors and commonality.

Apologies if this doesn’t make much sense. Happy to share the sheet with anyone if you’d like to help out.

Thanks.

[lone heart]

@rigid flint Has your question been resolved?

[rigid flint]

<@&286206848099549185>

[lone heart]

@rigid flint Has your question been resolved?

[lone heart]

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[visual badger]

a is -15i +20j b is 24i+10j

[harsh swallow]

what's the question?

[visual badger]

c

find vector AB

i keep getting 39i -10j

[harsh swallow]

ok

and what's the problem?

[visual badger]

its not right

[harsh swallow]

wait

what

[ionic trail]

Send what you did

We'll see where you're wronf

[harsh swallow]

i did the question

and also got the same thing

[ionic trail]

Kinda sus

[ionic trail]

Got the same

[visual badger]

hmm then wrong ms

ight ty

.close

[lone heart]

Channel closed

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[lone heart]

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[errant marten]

hello friends I have question

[errant marten]

look this problem

shouldn't the answer be n - 1?

if I understand what "relative prime" even means correctly

[cloud thicket]

What do you think relatively prime means?

[echo socket]

Yes any n and n-1 whole numbers are always coprime

[errant marten]

I would think that they are numbers which do not divide n

[cloud thicket]

No that's not what it means

[echo socket]

If integers a,b are coprime, it means that gcd(a,b) = 1

[cloud thicket]

It's numbers which share no divisor with n

[echo socket]

(the same as a and b having no common divisors)

[errant marten]

oh

well then

I mean if n is the product of 2 primes

then

then surely, the only numbers which do share divisors with it are p and q themselves right?

since p and q are primes

?

[echo socket]

No

[devout summit]

Not necessarily

[echo socket]

p and n = pq are both divisible by p clearly

Same with q and n

I'd just write n-1 as the answer right away to the question

[devout summit]

That's not it

[errant marten]

the thing is the answer isn't n-1

that's what I wrote as the answer, but i was wrong

[echo socket]

Oh wait

Number of positive integers

Nvm

[devout summit]

All the numbers which do share a factor with n either have "p" as a prime factor or "q" as a prime factor or both

Hence, total number of positive integers not exceeding "n" which share a common factor with "n" is [(number of multiples of p not exceeding n)+(number of multiples of q not exceeding n)] - (number of multiples of pq not exceeding n)

Hence, subtracting this from the total number of positive integers not exceeding "n" gives us the number of remaining positive integers which are coprime to n

[errant marten]

bro

oh wait I see actually

since we've multiplied q with p

there are a number of q multiples of p

same with p

[devout summit]

Yep

[errant marten]

so the answer would be n - p - q + 1?

[devout summit]

You got it

[errant marten]

nice!

thanks dud

[devout summit]

Read more about totient function if you are interested

[errant marten]

thanks I will, for some reason I've already visited the wiki page before lol

[lone heart]

@errant marten Has your question been resolved?

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[plush herald]

how should I go about solving this limit without using L'Hospital?

[glass lichen]

recognize it as a derivative.

[plush herald]

I don't quite understand what you mean, can you please elaborate?

[echo socket]

The function that you're taking the limit of, it looks like a derivative of some other function

[harsh swallow]

the limit definition of derivative

[echo socket]

Yeah

[plush herald]

oh, this one?

[harsh swallow]

yeah

[plush herald]

I honestly still don't see how that's useful

[echo socket]

This might help to see

[plush herald]

so, f(x) would be 2^x in my case, right?

[echo socket]

Yeah

The question is now pretty easy as far as you derivative of 2^x

[plush herald]

so I can just derivate f(x) to get the limit?

and plug 2 into f'(x)?

[echo socket]

Yes

[plush herald]

damn

that's really cool

thanks a lot guys!

[echo socket]

No problem

[plush herald]

.close

[lone heart]

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[lone heart]

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[glossy iris]

may someone please help me with finding x and y?

I already calculated y using pitagoras theorem

[raw shard]

find the dimensions of the entire triangle

then subtract 8 from the base

well

[placid zinc]

Call the missing bottom bit "h".
Can you get h using similar triangles?

[glossy iris]

oh

yeah I can

I know how to solve this now

thanks

.close

[lone heart]

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[wild shard]

.help

[lone heart]

Commands:
clopen: .close, .reopen
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[mental hearth]

calc 2 - i feel like this problem is more complicated then i think but idk

[glass lichen]

WLOG, you can say $\lim_{n\to\infty}a_n=L<\infty$

[ocean seal]

Mosh

[glass lichen]

idk why you're computing a_n/n^2

[mental hearth]

brain just crashed

[glacial hedge]

you can just apply the ratio rule

wait nvm wtf am i talking about

[mental hearth]

no idea

given after one class on series

[glacial hedge]

I like where mosh is going with this

By the divergence test $\lim_{n\to\infty}a_n=L<\infty$

[ocean seal]

Elonmosqito96

[glacial hedge]

Because if this limit wasn't finite, the series would diverge (divergence test)

then $lim_{n\to\infty}{\frac{a_n}{n}} = 0$

[ocean seal]

Elonmosqito96

[glacial hedge]

Because we can treat this as $\frac{lim_{n\to\infty a_n}}{lim_{n\to\infty}{n}} = \frac{L}{\infty} = 0$

[ocean seal]

Elonmosqito96

[buoyant kayak]

\lim

[glacial hedge]

whups

[mental hearth]

i learned this stuff on monday so i might be slow to grasp it but if i remember diverge test is like if the sum doesnt equal zero then it diverges but it looks like you guys are using that for something else

[glacial hedge]

uh

so its

$\sum {n=0}^{\infty }:a_n$ diverges if $\lim{n\to\infty}a_n \neq 0$

[ocean seal]

Elonmosqito96

[mental hearth]

yea that makes sense

[glacial hedge]

also its important to note that

if $\sum _{n=0}^{\infty }:an$ converges then $\lim{n\to\infty}a_n = 0$

[ocean seal]

Elonmosqito96

[mental hearth]

yea i'd assume every convergent series has a limit of zero when it approaches inf

[glacial hedge]

mhm... so do you see how $\lim_{n\to\infty}{\frac{a_n}{n}} = 0$?

[ocean seal]

Elonmosqito96

[mental hearth]

yea

is this also a convergent series if =0 is true? ${\frac{a_n}{n}} = 0$?

[ocean seal]

Praxis

[glacial hedge]

nope

[mental hearth]

y not

[glacial hedge]

For example $a_n = \sqrt{n}$

[ocean seal]

Elonmosqito96

[glacial hedge]

$\lim_{n\to\infty}{\frac{\sqrt{n}}{n}} = 0$

[ocean seal]

Elonmosqito96

[glacial hedge]

But by the divergence test $\lim_{n\to\infty}{\sqrt{n}} = \infty$ and therefore the series $\sum _{n=0}^{\infty }:a_n$ diverges

[ocean seal]

Elonmosqito96

[glacial hedge]

In short if n approaches infinity faster than $a_n$ the limit will = 0

[ocean seal]

Elonmosqito96

[glacial hedge]

However, this does not mean that $a_n$ approaches 0 as n --> infinity

[ocean seal]

Elonmosqito96

[glacial hedge]

lol latex fail.. but I hope u get the point

[mental hearth]

yea appreciate it

how do i show $\lim_{n\to\infty}{\frac{a_n}{n}} = 0$?

[ocean seal]

Praxis

[glacial hedge]

for this problem or in general?

[mental hearth]

in this problem

[glacial hedge]

First, show that $\lim_{n\to\infty} a_n = 0$

[ocean seal]

Elonmosqito96

[mental hearth]

well because we know it converges, the limit as n approaches inf is 0 because of the divergence test

[glacial hedge]

mhm

one way u can procede from here is logical but NOT Rigorous.. but i'm pretty sure its fine for a calc class

$\lim_{n\to\infty}{\frac{a_n}{n}} = \frac{\lim_{n\to\infty}a_n}{\lim_{n\to\infty}n} = \frac{0}{\infty} = 0$

[ocean seal]

Elonmosqito96

[mental hearth]

thanks bro was thinking of that cuz we know lim a^n is 0 and that lim n is inf and 0 divided by inf is 0

whats the rigorous method

[glacial hedge]

um

not entirely sure but probably using epsilon delta version of limit

lmao

[mental hearth]

nvm lol

[glacial hedge]

xD

[mental hearth]

gonna close channel i know how to solve the other 2 problems on my hw

thanks a lot man 👍

.close

[lone heart]

Channel closed

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[glacial hedge]

yw

[lone heart]

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[crisp iris]

How to solve, step by step, the following inequality

[crisp iris]

2 < 2 - xe^(x) < 2 + e^(-1)

0 < -xe^(x) < e^(-1)
With x belonging to |R

[placid zinc]

Solve the equality first:
0 = -xe^(x)

[crisp iris]

S = {0}

[placid zinc]

What is S? Lol

Random solution set?

[crisp iris]

yes

[placid zinc]

Either way, you're right, x = 0 is the only root

So to the left of x = 0, is it positive or negative?

-xe^(x) is positive for x left of x = 0
Negative for x right of x = 0

[crisp iris]

positive.

[crisp iris]

Indeed!

[placid zinc]

e^(x) causes no sign switches, which helps think about it

[crisp iris]

yes, I used this property to reach the conclusion.

[placid zinc]

Other one is a bit harder, because solving the inequality algebraically is a mess

[crisp iris]

That's the one I am wondering about!

[placid zinc]

But notice that
-xe^(x) = e^(-1)
Has the solution x = -1

[glass lichen]

-(-1)e^(-1)

[crisp iris]

Yes, indeed!
I apologize, I got confused.

Thus, the solution to the enequality

0 < -xe^(x) < e^(-1)
With x belonging to |R

Is x ∈ ] - oo , -1 [ ∪ ] -1 , 0 [

x < 0 , while x ≠ -1

@placid zinc @glass lichen I got confused in my previous work for it got crowded on the sheet papers.
Thank you for your clarifications, I appreciate them greatly!

[crisp iris]

I, of course, jumped many steps as to how I reached the solution here, but I did go through all the steps in my work.

.close

[lone heart]

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[lone heart]

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[snow berry]

help

[snow berry]

in a 30-60-90 triangle

if the shorter side is = 1

therefore it means he hypotenu is equal to 2 right?

[icy trail]

yes

[glass lichen]

yes.

[snow berry]

then what is the length of the other side

[glass lichen]

sqrt(3)

[snow berry]

root 3/2?

[glass lichen]

no.

[icy trail]

just root 3

[snow berry]

okk

[glass lichen]

if you've ever heard of pythagorean theorem..

[snow berry]

I have

but the special cases

what should we multiply hypotenuse to get the other side?

[glass lichen]

???

Question makes no sense

there's only 1 30-60-90 triangle, to which you can scale

[snow berry]

nvm

to solve for the abnormal side, be use root 3 by 2 multiphied by hypotenuse

[icy trail]

if you're given hyptenuse, you can get shortest side by /2, and medium side by times sqrt 3 then /2

[snow berry]

ah ok

[lone heart]

@snow berry Has your question been resolved?

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[snow berry]

.close

[lone heart]

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[gray isle]

factorials? how are factorials even getting introduced here

[raw shard]

y = sqrt(x-3)+2, switch the placement of y and x, then solve for y

wait a second you might be doing it right i didn’t check

i know

[gray isle]

replace x in that equation with f^-1(x) and y with x and you'll (almost) have your inverse function.

[raw shard]

x = sqrt(y-3)+2, x-2 = sqrt(y-3), (x-2)^2 = y-3, (x-2)^2+3 = y

[icy trail]

inverse is to "opposite" everything we've done. we see that the order of things we do is this: subtrac 3, sqrt that number, then add 2. to opposite everything, we subtract 2, then square that number, then add 3, so we get inverse=(x-2)^2+3

that only works for simple cases where you can easily see whats going on

but basically when you swich y and x and solve for y, you are "oppositing" everythnig you did like that

[gray isle]

you'll need to restrict the domain based on the range of the original function

[lone heart]

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[mental hearth]

How to measure the approximation error when you use a power series to approximate something

[lone heart]

@mental hearth Has your question been resolved?

[lone heart]

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[lethal tendon]

What's the problem?

[lone heart]

@rich basin Has your question been resolved?

[lone heart]

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[rich basin]

.reopen

[lone heart]

✅

[rich basin]

show that

@lethal tendon

here

I don't get how they come up with lHS

@alpine sable please help

[placid zinc]

Do we know anything else about ω?

[rich basin]

w = w^4

[placid zinc]

Well, that's how they come up with LHS

[rich basin]

what did they do?

[placid zinc]

Also note w² = w⁵

[rich basin]

yeah

[placid zinc]

They simplified w⁴ and w⁵

[rich basin]

oh okay

what how did they konw

@placid zinc how dod you think i should approach to finding the exact value?

I'm thinking of roots of coefficients

@placid zinc why is my answer different

[placid zinc]

How did they know that w⁴ = w? I thought it was given in part b?

[rich basin]

this is in question 2

(b) is in question 2

[placid zinc]

Okay so I assume you're all good with part c then

Your answer isn't different

You got the same A and B, even if they don't look like it

[rich basin]

yaeh

@placid zinc I'm more of trouble of finding the exact values of what they are asking in (d)

my solution got an inverse of the B times 3

but they got +-

[placid zinc]

You got the same A and B, even if they don't look like it

If you really want the exact same form, try using A + B = -3 instead, to get A

[rich basin]

but then that would be produce two answers still for A

and two answers for B

but in the solutions there are only 1 solution for each

[placid zinc]

A and B end up being the same

So the two answers are "one goes to A, the other goes to B"

[rich basin]

Are you sure tyhey are the same

if they have the same there are going to be 3 answrs then

[placid zinc]

Well, "the same" in that they are either of the roots to x² + 3x + 3

There's two roots, and you have two numbers, A and B

[lone heart]

@rich basin Has your question been resolved?

[lone heart]

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[alpine sable]

hi

[alpine sable]

can i get help here or

[severe sluice]

yes, do you have a question?

[alpine sable]

yes i need help im tryna find a quadratic regression equation

[severe sluice]

which step do you not understand?

[tacit drum]

Hey can I get some help?

[alpine sable]

my calculator isnt working, so i have no clue what to do

[severe sluice]

oof...

[severe sluice]

no, check out math help (available)

[alpine sable]

can i get help here or

[severe sluice]

yeah

what did you already do?

did you... uh, finish that table? (you know which one, right?)

hi?

anyways, just give me your x and y values and i'll guide you through this @alpine sable

[alpine sable]

oh okay

[alpine sable]

one sec

0.01775147929,
0.01615951616,
0.01563753007,
0.01376048162,
0.0111738279,
0.009780534351,
0.008381689233,
0.007681564246,
0.005839864761,
0.002978990279,
0.004071937564,
0.01007067138,
0.01531100478,
0.02056672761,
0.02202785876,
0.02260778128,
0.02451361868,
0.02457218078,
0.02762557078,
0.03121387283,
0.03338898164,
0.03349779278,
0.0341163311,
0.035,
0.03594438793,
0.03702346041,
0.03578374173,
0.03899268887,
0.04025974026,
0.03765880218,
0.03546099291,

[severe sluice]

that's a big table

[alpine sable]

these r my x values (above)

[severe sluice]

maybe you should use excel

[alpine sable]

my y values: 11.4,10.5,11.8,12.3,12.7,13.5,14.8,14.8,25,15,15.1,14.3,13.2,12.5,12.3,12.6,12.7,12.5,12.1,11.7,11.3,11.9,12.7,13.3,13.7,13.8,14.5,15.1,14.8,14.2,13.5,

[alpine sable]

i dont have excel

[severe sluice]

uhhhhh that's a large table...

maybe use google sheets

[alpine sable]

its 31 values

[alpine sable]

what do i do there? will i be able to find the a, b and c value for the quadratic regression equation ?

[severe sluice]

just do it the normal way?

[alpine sable]

idk what the normal way is tho

😭

[severe sluice]

oof

[alpine sable]

can we talk on vc or no

[severe sluice]

no, i'm in a lecture

[alpine sable]

oh okay

[severe sluice]

so basically you make an x/y table

2 columns

[alpine sable]

yes

[severe sluice]

and then you add a few columns
x^2, x^3, x^4, xy, x^2 y

calculate the sums

call the sum of the x column m
call the sum of the y column n
call the sum of the x^2 column o
call the sum of the x^3 column p
call the sum of the x^4 column q
call the sum of the xy colon r (why colon?)
call the sum of the x^2y column s

i hate the variable names,

we have

qa+pb+oc = s
pa+ob+mc=r
oa+mb+(number of points)=n

[lone heart]

@alpine sable Has your question been resolved?

Channel closed

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[alpine sable]

thankksss vmmmm i figured it out

[lone heart]

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[pearl solar]

i need to minimise a/sinx + b/cosx without using calculus

[pearl solar]

a and b are constants here

[rare verge]

hehe

use the unit circle

( acosx + bsinx ) / sinxcosx

so sinxcosx should be larger than acosx + bsinx

[pearl solar]

i can minimize the above one

[rare verge]

note that sinxcosx

equals

[pearl solar]

1/2sin(2x) ?

[rare verge]

1/2 (sin(x+x)- sin(x-x))

yes

[pearl solar]

but like, i am not able to minimise it

i am so lost

[rare verge]

hm

hm

i think its negative infinity

[pearl solar]

wait, i am so dumb, i meant the sum of absolute values

[gray isle]

minimise
$$\abs{\frac{a}{\sin(x)}} + \abs{\frac{b}{\cos(x)}}$$
?

[ocean seal]

ℝamonov

[pearl solar]

yeah

[rare verge]

then its 0

[gray isle]

amgm

[rare verge]

a can be 0

b can be 0

0 plus 0

[pearl solar]

a and b are constants

[rare verge]

0

[pearl solar]

a and b are some fixed constants

[rare verge]

then a and b approach 0

no

nvm

[gray isle]

you can't choose a,b
final expression will be in terms of a and b if possible

[pearl solar]

yeah

[alpine sable]

well

problem is where we try to maximize sin(x), cos(x) is hence minimized

and we want to maximize denominator

[rare verge]

i mean when sin(x) and cos (x) is 1 and -1 respectively

a and b can approach 0 to avhieve the minimized number

[alpine sable]

that does not happen for the same value of x

[pearl solar]

yeah

[alpine sable]

that would require sin(y) and cos(x) where y is pi/2 and x is pi

but we need both in terms of sin(x)

also the absolute value makes that useless

[pearl solar]

yeah

[alpine sable]

so we wont care about the sign

therefore lets consider angles on [0, pi/2]

[pearl solar]

makes sense

[alpine sable]

that will give a range of values we can use to minimize

lets try some examples

for x = pi/2 and x = 0, they are DNE

so they are open enpoints

[rare verge]

for example

[pearl solar]

so this one person is talking about am gm, do you think they will be minimised like that?

[alpine sable]

GM?

[rare verge]

am gm

hm

ok lemme try

[pearl solar]

arithmetic mean and geometric mean inequality

[alpine sable]

oh

[pearl solar]

but like i am not sure if it will give the minimum value

[alpine sable]

,w 2+(2/sqrt(3))

[pearl solar]

beacuse there will be sin and cos on rhs too

[ocean seal]

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[alpine sable]

,w 2sqrt(2)

[ocean seal]

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[gray isle]

hmm, amgm not entirely reliable here

[alpine sable]

so I suppose it is minimized when x = pi/4 and so it becomes sqrt(2)|a| + sqrt(2)|b|

[pearl solar]

but like, can we be sure?

[alpine sable]

Im sure

[pearl solar]

like can you explain?

[alpine sable]

ok

so we know that for (pi/4 , pi/2) it acts the exact same as (0,pi/4) since sin(x) and cos(x) switch values there

x = pi/4 is when sin(x) = cos(x)

and here

actually we can use a difference

,w graph |sec(x)| + |csc(x)|

[ocean seal]

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[gray isle]

do you have the exact wording of the question?

[alpine sable]

why not

looks like it to me

[pearl solar]

yeah just give me a sec i will send it

[alpine sable]

,w pi/4

[ocean seal]

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[alpine sable]

we see a minimum at x is nearly 1 on the graph above

so pi/4 seems reasonable

well it depends on a and b

you can change those and see where the endpoint lands

[pearl solar]

1 and 3 sqrt3

[alpine sable]

I thought the answer was supposed to be in terms of some unknown a and b

[pearl solar]

yes

[alpine sable]

wait what

bruh

now we have an actual function we can minimize

[alpine sable]

wait you said no calculus right?

[pearl solar]

the question was something like this

[pearl solar]

i can easily do it with calc

[alpine sable]

ik

but earlier you said w out calc

[pearl solar]

yeah thats what i said

[alpine sable]

ok

[pearl solar]

but i am asking

if there is a better way without calc

[alpine sable]

nah not really considering taking derivatives of sec and csc are very straight forward

and the absolute value is meaningless on (0,pi/2)

so you could just take normal derivatives of a sec(x) + b csc(x) on that interval

plus all of the MCQs lie on (0, pi/2)

[pearl solar]

yeah

but like i could have just put the values and minimised

[alpine sable]

,w graph csc(x) + sqrt(3) sec(x) on (0,pi/2)

[ocean seal]

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[alpine sable]

,w pi/4

[ocean seal]

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[alpine sable]

,w graph csc(x) + sqrt(3) sec(x) and x = (pi/4) on (0,pi/2)

[pearl solar]

there should be 3sqrt 3 there

[alpine sable]

looks like its pi/6

Say y = csc(x) + 3sqrt(3) sec(x)

[pearl solar]

yes

but how :\

[alpine sable]

there is no easy way without calculus

like

doing the minimization problem is way easier than any geometric solution you try to come up with

[pearl solar]

yeah ig

so thanks

/close

-close

[alpine sable]

(╯°□°）╯︵ ┻━┻

[pearl solar]

.close

[lone heart]

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[brave dagger]

why dont laws of exponents apply on this kind of equation?

$\left(x^{\frac{1}{a}}\right)^{a}$

[ocean seal]

s1lversnake

[echo socket]

What do you mean, wouldn't it be x^1? (for nonzero a)

Btw technically this isn't an equation, just an expression

[brave dagger]

no, its not try on desmos
and ok, thanks for the information

i mean not x^^1

[echo socket]

Ah yes, it should be absolute value cuz you're taking taking a root there I suppose

Not for all values of a tho

Try a=3

[brave dagger]

yes

but

why doesnt it work on all

[echo socket]

Here you took 1.1

WHich is basically the same as 11/10, right?

[brave dagger]

yes

[echo socket]

So it's the same as taking 10th root of x^11

[brave dagger]

ah

but still, they theach the wrongf thing at school

thats kinda weird they say it applies for everything

[echo socket]

There are many things wrong about maths taught in school

[brave dagger]

for sure

.close

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[fallen rain]

Hello guys
I'm stuck on this question for a while, can someone help me with this question please?

[vale wigeon]

@fallen rain have you made any progress or are you stuck not knowing where to begin?

[fallen rain]

I had worked out that y is equal to √5/10

but I'm not sure with my answer

[vale wigeon]

what's y?

and how are you getting square roots at all?

@fallen rain ?

[fallen rain]

y*y=`/20

but I think that is wrong

[vale wigeon]

what's y?

[fallen rain]

number of blue counter

[vale wigeon]

okay then your equation is as wrong as can be

there are n blue counters and 3n red counters, thus 4n in total
the probability of drawing two blue counters without replacement is (nC2)/((4n)C2)

[fallen rain]

can I set blue as x and red as 3x
3x:x

[vale wigeon]

okay sure your x is my n

same difference

[fallen rain]

@vale wigeon is my tree diagram correct?

[vale wigeon]

you overcomplicated it imo

unless you're deathly allergic to nCr...

but also once you draw one of x blues there will be x-1 blues left and not x. and yet you chose not to reflect that in your diagram

[fallen rain]

o yeah

I think I got it

thank you

.close

[lone heart]

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[rich basin]

@placid zinc I don't quite get it, they seem to hszve very different values

[lone heart]

@rich basin Has your question been resolved?

[rare verge]

whats ur question

[rich basin]

@rare verge This is the question and below is my working out, i used simultaneous equaiton

but I don't get why is it wrong?

[lone heart]

@rich basin Has your question been resolved?

[rare verge]

u have the whole question tho

[lone heart]

@rich basin Has your question been resolved?

[rich basin]

@rare verge the whole quesrion is higher

@rare verge this is the wghole question

<@&286206848099549185>

[rare verge]

ok

lemme c

use fifth root of unity?

[rich basin]

my main queries is why is my working wrong

what is wrong with simultaneous equatinos

[rare verge]

cuz it involves complex roots?

[rich basin]

i'm confused can you further elaborate

is it because ia m producing more solutioons?

[rare verge]

i mean u arent wrong?

u just need to double check ur ans to make sure they add to neg 3

[rich basin]

I have 4 solutions

but answers have 2

which I'm rather confused

[rich basin]

any ideas why 4 solutions

[placid zinc]

But you don't. Two numbers are the exact same, the other two are the exact same

They look different, but they should have the same decimal representation

[rich basin]

@placid zinc could you please prove using the ,w command

I don't quite see it being the same

seems so diffenrt

[placid zinc]

You proved it yourself

[rich basin]

what how?

[rich basin]

@placid zinc in mod arg form they are different

the modulus of both of them are different

[rich basin]

@placid zinc do you know how we can differentiate

between the two

[lone heart]

@rich basin Has your question been resolved?

[supple tundra]

help needed?

[lone heart]

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[ionic musk]

if a+b=5 and a^2+b^2=19
then what is (-2ab)^2=?

help

[lone heart]

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[analog olive]

square (a+b) , use value of a^2 + b^2 in it.. you will get value of 2ab

[ionic musk]

Is it correct?

[echo socket]

Is it 15 + 2ab = 25 on 3rd line?

Cuz it should be 19 + 2ab = 25 as far as I'm converned

[ionic musk]

it's 19

sorry my writing is ugly

[echo socket]

Yeah it's fine I probably shouldn't have asked that either cuz there's 2ab = 6 in the next line

[echo socket]

So yeah this is correct

[ionic musk]

thank you

[echo socket]

But you could do it in less steps

(-2ab)^2 is the same as (2ab)^2

So you could square both sides in the equation 2ab = 6 right away

[ionic musk]

i see

[lone heart]

@analog olive Has your question been resolved?

[analog olive]

bruh lol

not even my doubt

.close

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[upbeat laurel]

Is being able to obtain a closed form for any natural n in
$$\sum_{k=1}^{m} k^n$$
Any useful? The sum I'm talking about is $1^n + 2^n + 3^n \cdots + m^n$

[ocean seal]

Duhon

[civic jungle]

https://en.wikipedia.org/wiki/Faulhaber's_formula

The generating function proof and the matrix proof are quite nice

[crisp grove]

Icy honorable

[upbeat laurel]

So it's good?

[civic jungle]

The methods are good yeah

[upbeat laurel]

Ok, I made one a bit back so I wanted to know, thx

.close

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[upbeat laurel]

How are you meant to know?

Like

I'm just confused

I mean, not like one single organization has all the knowledge of employment, tho if you ask the person they are likely to answer truthfully

Yeah, but idk how this relates to math at all

Yeah ik it's stats but I don't know how you are meant to find out the answer based on the alternatives

But then again, I'm not stats God

[lone heart]

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[upbeat laurel]

You can wait for someone else more experienced in the field

If u want

Yeah

.reopen

[lone heart]

✅

[upbeat laurel]

If they have an answer within a reasonable time then they can ping ya/dm you

[lone heart]

@tired pasture Has your question been resolved?

[lone heart]

@tired pasture Has your question been resolved?

[lone heart]

@tired pasture Has your question been resolved?

[harsh swallow]

@tired pasture what's the problem?

a census can sort of be considered as a survey

its not entirely the same

but when you hear a census

it's a count

of something

and they often do that by surveys

[scenic heath]

Isn't the government an organization? And said organization is distributing given data on their website.

[harsh swallow]

but the source of the data

is the survey

they got the data from the survey

asking people

[stray rivet]

can someone help me please?

[scenic heath]

is the government the secondary source

[scenic heath]

you can ask your question in one of the math help channels

[stray rivet]

i did

[harsh swallow]

the government is the one collecting the data from the survey

in the usa there's this census

i forgot what it's called

but a youtuber i watch kept telling people to fill in the form

so the government of the usa asked people stuff

did a survey

the data they got from that

is gotten from the survey

[scenic heath]

right I guess it isn't relevant to the question that the government distributes the information

@tired pasture it only asks about the source

[lone heart]

@tired pasture Has your question been resolved?

[lone heart]

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[placid trellis]

how do i solve this

[placid trellis]

ive tried to order it in ascending

150 151 157 165 169 p 170

[lone heart]

@placid trellis Has your question been resolved?

[placid trellis]

<@&286206848099549185>

[bleak ridge]

Do you know the percentiles formula

[placid trellis]

c=np/100

thus i found the answer using percentile rank

just curious why is that

[bleak ridge]

Why's wot

[placid trellis]

wot?

[bleak ridge]

Why is what?*

[placid trellis]

the question ask me to find percentile and not percentile rank

but i found the solution using percentile rank formula

ive wonder if i can find the answer using c=np/100

[bleak ridge]

You should be able to

[lone heart]

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[inner sequoia]

how to simplify

[inner sequoia]

I got 10g^5h^3(sqrt3h) but thats not one of the answer choices

[warm brook]

@inner sequoia can you send your work as to how you got that

[inner sequoia]

one sec

its kind of a mess rn so i'll organize it

[inner sequoia]

nvm i think i did some random shit during the process

bcs i redid it and got 4g^5h^3(sqrt3h) which is one of the answer choices

[warm brook]

mhm

[inner sequoia]

my bad

.close

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[dreamy dawn]

I have a question about velocity

[warm brook]

[dreamy dawn]

So how can i calculate the speed over time?

like i have no background in physics what so ever but how can i calculate zu the drop over time

[warm brook]

(final position- initial position)/time taken

that’s average velocity

[dreamy dawn]

So say the final position was 50m (meters) away and the initial position was where i am standthing you would take 50m-0/30 seconds yeah?

Becuase initial position is where i am standing

[warm brook]

mhm

[dreamy dawn]

then with that answer you can put it on a graph if you wanted to to make it more visual

[mortal mantle]

Yea it would be a linear line

[severe sluice]

linear line

[jagged imp]

What would be linear? Position against time? That's not nessecarily true given just an initial and final position

[severe sluice]

it might not be a line at all; what if they're accelerating? the pos/t graph would be a differently shaped curve

[jagged imp]

^

[severe sluice]

or maybe they ran backwards at some point

[dreamy dawn]

If it was going faster at the beging than it was at the end wouldn’t the line depending on the graph slowly turn into a curve?

[severe sluice]

yeah, it will

[dreamy dawn]

Okay i’m just trying to mess with velocity because i’m bored, i’m gonna try something really quick

[severe sluice]

position = integral of velocity w/ respect to time

and then just use a graphing calculator to calculate the integral

[dreamy dawn]

okay i only have the final and initial position what do i do

Initial is 0 and Final is 226.1 inches

[severe sluice]

you need the time it took

@dreamy dawn

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[crystal tiger]

If alice has 4 cats, but bob adopts 3 more, and annie loses 1, how many cats are there in total?

[sly mantle]

@crystal tiger pls dont

[crystal tiger]

sowwy

[sly mantle]

.close

[lone heart]

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[crystal tiger]

.close

oops

.close

[little valley]

Core memory unlocked

[lone heart]

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[dreamy dawn]

How can i calculate projectile motion? i look it up on yt but no one has been able to really flip the switch in my head

[jagged imp]

what do you mean by calculate projectile motion

[dreamy dawn]

Say you throw a rock off a cliff, how long will that object stay in the air?

or say a cannonball is launched into the air, where and when will it hit its target

[jagged imp]

do you have access to calculus

[dreamy dawn]

No?

the class?

[jagged imp]

as in being able to use it to solve problems. I ask because calculus is used to model projectile motion the vast majority of the time. If you don't know calculus I can't really help you with this personally. I'm sure there's ways to do it without calculus but I don't know them. There's also the physics "suvat" formulas but thats just calculus with extra steps and I don't wanna use that personally.

[dreamy dawn]

ah okay

so i need to know calculus to solve these problems?

[jagged imp]

need is a strong word but unless you already have the equations of motion for said projectile motion I don't know how to solve these problems without calculus.

[dreamy dawn]

but you can with them?

the equations

[gray isle]

for simpler problems, suvat equations are sufficient

[dreamy dawn]

But are they harder?

Like i know neither of these things

i’ve heard of calculus i have never heard of suvat

My phone is actually having a stroke rn

[gray isle]

look up suvat and/or equations of motion

[dreamy dawn]

this?

[gray isle]

yeh

[dreamy dawn]

So from my understanding of finding projectile motion, you need 2 equations

But how do i implement these?

[gray isle]

depends on what the question is asking and what you're given

[dreamy dawn]

So what do i need to take i to consideration?

like say the cannon is on ground level and fires the canon ball at a speed of 10 meters per second

then in the video i saw he took angles into consideration at the angle he threw the rock

which was i think 30°

[olive cedar]

when you have this type of information regarding projectile information, you usually start by finding the x and y components of the speed at which the object was launched

[dreamy dawn]

which in this case is 10 meters per second

[olive cedar]

given that you know it was launched at an angle of 30 degrees and at a speed of 10m/s, you can use sin or cos functions to find the x and y components

[dreamy dawn]

No clue what either of those things are i’m gonna be straight with ya 😅

[olive cedar]

ok idk the way they want you to find the answer HAHSHHAHA cuz we were taught to use simple calculus

good luck tho

[dreamy dawn]

nobody wants me to find this out except myself

but i will go find out what those things mean so brb

ah okay so sin is the opposite angle of the triangle

[severe sluice]

@dreamy dawn you must know trig to calculate projectile motion (given an angle the projectile is fired at)

[dreamy dawn]

so in 30° the opposite angle is 5°

[severe sluice]

what is the opposite angle?

[gray isle]

you comments suggest that you are not well versed in trig

and it will be very helpful to start learning and/or review

[dreamy dawn]

how can i learn it?

[gray isle]

khan can give a basic introduction

[oak chasm]

https://www.khanacademy.org/math/trigonometry

[gray isle]

ah okay so sin is the opposite angle of the triangle
so in 30° the opposite angle is 5°
are nonsense

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[winter roost]

bless u for trying to help people on christmas

[tame shell]

.close

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[mint fulcrum]

lol how do i solve for x

[mint fulcrum]

i tried logs

log_x [x^(2x) ]= log_x[243] + log_x[x] => 2x -1 = log_x[243] => 243 = x^[2x-1]

still stuck lol

[vale wigeon]

is this even possible

it strikes me as something very nasty that probably cannot be solved by normal means

x=3 can be guessed though

[mint fulcrum]

nvm NVM

my friend told me

she just tried guessing with a cube roots lol

or cube values

anyways thank you lol

merry christmas

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[alpine zephyr]

are the no. of partitions available for 19 is 490?

[alpine zephyr]

sry for my bad english

is partition of 19=490?

[lone heart]

@alpine zephyr Has your question been resolved?

[alpine zephyr]

<@&286206848099549185>

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@alpine zephyr Has your question been resolved?

[severe sluice]

we don't understand what you're asking

[vale wigeon]

,w number of partitions of 19

[ocean seal]

Results provided by WolframAlpha

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Requested by Ann#0413

[vale wigeon]

@alpine zephyr

[alpine zephyr]

thank u so much!!!

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[knotty wren]

I tried simplifying it myself and i can't figure out how they reached the simplified version shown in the image. Can someone guide me?

[knotty wren]

here's my attempt (I left in the middle cause I didn't understand anything)

[charred flint]

seems like you copied the initial equation incorrectly

you'll have to move all the y' to one side then divide by what's in front of it

[lone heart]

@knotty wren Has your question been resolved?

[knotty wren]

its just one step ahead i think, i had already moved all the non-y' terms to the right

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@knotty wren Has your question been resolved?

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@knotty wren Has your question been resolved?

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[tawny fable]

Hi there

[tawny fable]

I have a prove or provide a counter example here

And I played with some examples

and it feels like its true

[severe sluice]

definition of linear independence, probably?

[tawny fable]

I can't see that

[severe sluice]

wait wdym?

[tawny fable]

I know the linear combination betta1v1 + .... + bettaMvm = 0 iff betta1 , .... , bettaM = 0

[glass lichen]

Yeah... apply that definition

Also beta*

[tawny fable]

beta*

Do you mean just saying

showing that the linear combination lambda * T is from the form scalar * S thus scalar must be 0 since S is linear independent

[glass lichen]

No clue what you said

Cause cT doesn't make sense... T is a set

[tawny fable]

Yeah

I was lazy to write the linear combination

like

lambda1 * alpha1*v1 + .......... + lambdaM * alphaM * vm = 0

[severe sluice]

i have no idea what you're talking about. if this is your definition of linear independence, seriously, check that again. i have a very obvious counter example: v1 = <2,2> and v2 = <2,2>.

[tawny fable]

maybe I had a typo?

idk

[shell widget]

If u have two linearly independent vectors, there doesnt exist any non-zero scalar such that multiplying any one vector by it creates the other

[tawny fable]

yeah

[shell widget]

so using this it should be easy to prove that its true

[severe sluice]

very specific: ||for every pair of vectors a and b, if there aren't any x so that ax=b, then there are no y so that alpha*a*y=beta*b ||

[tawny fable]

got it

thanks

.clode

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[hollow owl]

hi i need help pls

[severe sluice]

what's this notation?

[echo socket]

I think it's the notation for inner product

[hollow owl]

inner product

[shell widget]

Recall $||v||^{2} = <v,v>$

[ocean seal]

Sup?

[hollow owl]

ok but how I recall $||3v1-v2||^2$?

[ocean seal]

skidrow

[shell widget]

$||3v_{1} - v_{2}||^{2} = <(3v_{1} - v_{2}), (3v_{1} - v_{2})>$

[ocean seal]

Sup?

[shell widget]

and then apply properties of inner product

[hollow owl]

the given inner product is < , >

it is mean standard inner product?

[shell widget]

yeah

you'll have <3v1,3v1> + <3v1,-v2> + <-v2,3v1> + <-v2,-v2>

[hollow owl]

ok i get it but how i continue?

<3v1,3v1> = 3<v1,v1>?

[shell widget]

9<v1,v1>

and <v1,v1> = | v |^2

[hollow owl]

why 9 and not 3?

[shell widget]

because <av1,v2> = a<v1,v2>

[sly mantle]

real inner products are bilinear

[shell widget]

you are given everything u need to solve the problem

just use what u are given

[sly mantle]

actually all of the algebra needed for this is done by recalling real inner product properties

[hollow owl]

but a here is 3

[shell widget]

yes

but you also have <v1,bv2>

and so that becomes b<v1,v2>

[hollow owl]

so its ab<v1,v1>

[shell widget]

<3v1,3v1> = 3<v1,3v1> = 9 <v1,v1>

Yes

[hollow owl]

<3v1,-v2> + <-v2,3v1> = 2<3v1,-v2>=-6<v1,v2>?

[shell widget]

Yes

[hollow owl]

ok
I get <v2,v2>=-36

[shell widget]

u sure?

[hollow owl]

no

its+36

now i am sure

I need to sqrt it cuz its ^2 yes?

[sly mantle]

yes bc $\ip{x}=\norm{x}^2$

[ocean seal]

RokettoJanpu

[hollow owl]

ty

i have another question can u help?

[sly mantle]

go ahead

[hollow owl]

V Level 3 polynomial space
Check if the function defines an internal product

i dont understand the inner product

[sly mantle]

f & g are any degree 3 polynomials (which are functions)

f(0) is the value of f when evaluated at 0, etc

[hollow owl]

f(0) is like x^3?

just for example

[sly mantle]

no, if f(x)=x^3 then f(0)=0^3=0

f(1)=1^3=1, f(2)=2^3=8

[hollow owl]

ok but how i check liner symmetrical and all of this if i dont have the functions?

[glass lichen]

check it for generic functions

[hollow owl]

can u give an example? so i understand

[sly mantle]

to show symmetry we must show <f,g>=<g,f> for any polynomials f,g

the key to showing this is the fact multiplication of real numbers commutes

[hollow owl]

ok, but how I show this? what i put instead f(0) f(1) f(2) etc

[glass lichen]

Nothing

you keep f(whatever) and g(whatever)

[glass lichen]

you show it by definition of <f,g> and then commutativity of real numbers as Rok pointed out

[shell widget]

@hollow owl just so u understand, <g,f> = g(0)f(0) + g(1)f(1) + g(2)f(2) by definition of the inner product given

but since g(0),f(0),g(1),f(1),g(2),f(2) are real numbers, you can switch them around, just like (2)(5) = 10 = (5)(2)

g(0)f(0) = f(0)g(0) and so on

[hollow owl]

so i can refer f(0) as x and f(1) as x1, i dont rly care about the poly behind this?

[glass lichen]

??

no

just leave f(0) as f(0).

[sly mantle]

u dont know the value of f(0) bc f is an arbitrary polynomial

[shell widget]

he prolly means using a sub for convenience, better to let f(0) = A, f(1) = B, f(2) = C instead of using x's

[glass lichen]

Yeah but that's not needed, and draws away from the defn of the IP

[hollow owl]

ok i proof symmetrical now how i proof linear and positive

[glass lichen]

same way

do it by definition

[lone heart]

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[gusty oyster]

The interval [0,3] is partitioned into n equal subintervals, and a number xi is arbitrarily chosen in the ith subinterval for each i. Then:

$$lim_{n \rightarrow \infty} \sum_{i=1}^{n} \frac{2x_i +5}{n}$$

[ocean seal]

màe

[gusty oyster]

Can someone pls help

I plugged in 3i/n

And multiplied the whole equation by 3/n

Got 0

And that's wrong

[alpine sable]

This looks like an integral written as a riemann sum and a limit

[gusty oyster]

Thank you so muchhh!

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[abstract goblet]

could someone help me out with this ?

[charred flint]

do you see anything interesting when expanding (1+1/3)(1+1/3^2)?

[scenic heath]

try to multiply both the numerator and denominator by (1-1/3)

you should see how to continue

thats a nice problem