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[tough dove]

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[twilit relic]

Hi, is this the correct way to solve this equation here?

[alpine sable]

subtract 1 then raise both sides to power e

[sterile vale]

e^0 equals 1 and if you apply the equations as the exponents of e, then you have to raise everything, you cant divide them like ln(ax+1) and e^1

[alpine sable]

but i dont think it has any solutions

[twilit relic]

So on the rhs, I have to do e^(ln(ax+1) +1) and not like e^(ln(ax)) + e^1?

[alpine sable]

yes

u needed a multiplication sign not addition there

[sterile vale]

yea, exactly, but the bigger problem is that nothing equals 0 when it's raised by e

[twilit relic]

Ahhh ok thanks!

Yeah found something fishy and immediately knew it was something along arth error lol

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[silk crystal]

Before I ask my question, is it possible to write Latex in Discord?

[twilit relic]

Surround your expression with $ IIRC

[alpine sable]

$x^{69}$

[ocean seal]

♡LexQa♡

[alpine sable]

Yes you can

[silk crystal]

I am trying to recursively express an ARCH(1) process. ARCH(1) process is modeled as follow: $x_{t} = \sigma_{t} z_{t}$ where $\sigma_{t}^{2} = \alpha_{0} + \alpha_{1}\sigma_{t-1}^{2}z_{t-1}^{2}$ where $z_{t}$ is i.i.d. Using recursion, we can write an expression for any $x_{t+i}$, however I am struggling to do so.

[ocean seal]

LetečiDebjule

[vivid zenith]

An ARCH(1) process is a type of time series model used in finance to describe the behavior of stock prices. It is defined by the following equation:

$x_t = \sigma_t z_t$

where $x_t$ is the value of the time series at time $t$, $\sigma_t$ is the volatility of the time series at time $t$, and $z_t$ is a sequence of independent and identically distributed (i.i.d.) random variables with zero mean and unit variance.

The volatility of the time series is determined by the following equation:

$\sigma_t^2 = \alpha_0 + \alpha_1 \sigma_{t-1}^2 z_{t-1}^2$

where $\alpha_0$ and $\alpha_1$ are constants.

To express $x_{t+i}$ recursively, we can use the equations above to derive an expression for $x_{t+i}$ in terms of $x_{t+i-1}$ and $z_{t+i-1}$. We can then use this expression to derive an expression for $x_{t+i-1}$ in terms of $x_{t+i-2}$ and $z_{t+i-2}$, and so on.

Here is the recursive expression for $x_{t+i}$:

$x_{t+i} = \sigma_{t+i} z_{t+i}$

where

$\sigma_{t+i}^2 = \alpha_0 + \alpha_1 \sigma_{t+i-1}^2 z_{t+i-1}^2$

and

$\sigma_{t+i-1}^2 = \alpha_0 + \alpha_1 \sigma_{t+i-2}^2 z_{t+i-2}^2$

and so on.

We can use this recursive expression to compute the value of $x_{t+i}$ for any given values of $x_t$, $z_t$, $\alpha_0$, and $\alpha_1$.

[ocean seal]

! Enis

[silk crystal]

Yes, but I am looking for the expression which will include a sum in it. Is this possible?

[vivid zenith]

Yes, it is possible to derive an expression for $x_{t+i}$ that includes a sum. To do this, we can use the recursive expression for $x_{t+i}$ that we derived earlier, and then use the fact that the sequence of random variables $z_t$ is i.i.d. to rewrite the expression in terms of a sum.

Here is the resulting expression:

$x_{t+i} = \sigma_{t+i} \left( \sum_{j=1}^i z_{t+j-1} \right)$

where

$\sigma_{t+i}^2 = \alpha_0 + \alpha_1 \sigma_{t+i-1}^2 z_{t+i-1}^2$

and

$\sigma_{t+i-1}^2 = \alpha_0 + \alpha_1 \sigma_{t+i-2}^2 z_{t+i-2}^2$

and so on.

This expression shows that the value of $x_{t+i}$ at any given time is determined by the sum of the previous $i$ values of $z_t$, as well as the values of $\alpha_0$ and $\alpha_1$. In other words, the value of $x_{t+i}$ at any given time is determined by the past $i$ values of $z_t$ as well as the current value of $\sigma_{t+i}$.

[ocean seal]

! Enis

[silk crystal]

Just a moment

I am a bit confused. Firstly, shouldn't there be only one $z_{t+i-1}$ term, here there are two, one from the sum, and one when replacing $\sigma_{t+i}$. More importantly, however, $\sigma_{t+i}$ can still be recursively replaced. What I would expect to get is some sort of a sum that reduces to the initialization. Assume, we initialize, say, $x_{1} = \sigma_{1}z_{1}$, where we have some data estimate for $\sigma_{1}$.

[ocean seal]

LetečiDebjule

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[surreal lichen]

Show that if 𝑎,𝑏, and 𝑛 are integers such that 𝑛≥2 and 𝑎≡𝑏(mod𝑛), then 𝑔𝑐𝑑(𝑎,𝑛)=𝑔𝑐𝑑(𝑏,𝑛).

[surreal lichen]

Here's what I have so far

if a ≡ b then a ≡ r and b ≡ r

a = mn + r and b = kn + r

using the gcd with remainder theorem

gcd(a,n) = gcd(n,r)

[surreal lichen]

not sure abt this part tho

[coarse garden]

could i ask a question here?

[surreal lichen]

#❓how-to-get-help

.close

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[desert zephyr]

Pretty sure I am making a mistake so just to confirm. I am given a matrix A and that A^2 = -A. Does that mean A^3 = A^2 * A = -A * A = -A^2 = A? And also A^4 = A^3 * A so A * A = A^2 = -A? And if we go on like this we get A^n with n odd is equal to A and n even it is equal to -A?

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[dry ferry]

Yeah that's correct

[desert zephyr]

Awesome thx

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[desert zephyr]

Pretty sure to proof it is diagonlizable you can show that it has non zero trace

After that yes you get the eigen values and eigen vector to actually diagonalize it

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[junior warren]

how would i answer b

[junior warren]

i know for a i just take the limit

but im not sure how i answer for the sequence

[alpine sable]

Is the sequence in question:
[
a_n = \frac{3n}{8n+1}?
]

[ocean seal]

♡LexQa♡

[junior warren]

as far as i can see

yes

but from what can do mentally

would it not sum to infinity

[alpine sable]

I think

You are mixing up

A few stuff here

[junior warren]

possibly

we went over a lot today lol

[alpine sable]

I think you may be confusing the concepts of sequences with series a bit. Read back on what you studied possibly on those two topics

[junior warren]

well from what i can remember

the limit of an

a_n

is the first bti

bit

unless i am wrong

but the limit of a_n

would be infinity

so it would diverge

[alpine sable]

[
\sum_{n = 1}^{\infty}(a_n) \neq \lim_{n \to \infty} {a_n}
]

[ocean seal]

♡LexQa♡

[junior warren]

oh

oh

the limit determines convergence

[alpine sable]

Okay wait, this works for the nth term divergence test

[junior warren]

but they arent equal

[alpine sable]

Only divergence really

If it is not approaching 0

[junior warren]

so i am not supposed to take the limit of an?

[alpine sable]

Nah you are for part a and b for this question, but I was just talking about your explanation which seemed like it would cause you misunderstandings in the future

[junior warren]

right so for a it is the limit

and i think that is right?

bc it should be divergent

[alpine sable]

Yeah it should be correct

[junior warren]

ok now so for b

what would i do

i just dont understand the sequence part

it would be infinity maybe?

[alpine sable]

It's the same story

Also take it to infinity

[junior warren]

i got the same

[alpine sable]

Yeah

[junior warren]

that it diverges to infinity

but that is wrong

[alpine sable]

The same thing, but it is different meaning

Both limits would give u 3/8

[junior warren]

oh?

not infinity?

[alpine sable]

But the limit of the series tells you if it diverges or not, the limit of the sequence tells you if it converges or not

[junior warren]

oh i see

that makes sense but

i dont understand the 3/8

limits are my downfall

[alpine sable]

Uhh

It's basically

[junior warren]

is it like this?

[alpine sable]

[
\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{3n}{8n+1}
]

[ocean seal]

♡LexQa♡

[alpine sable]

Well
[
\lim_{n \to \infty} \frac{3n}{8n+1}
]
[
\to \lim_{n \to \infty} \frac {3\cancel{n}}{\cancel{n}(8+\frac{1}{n})}
]

[ocean seal]

♡LexQa♡

[junior warren]

ah

that also makes sense

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[rocky summit]

Hey all!

[rocky summit]

I'm having a little trouble keeping the terminology straight in my head. I just want to double check something

Another unnecessarily complicated definition XD

This says that "The subgraph of G induced by T" is the subgraph which INCLUDES the vertices of T, and deletes all others?

[vale wigeon]

yes, it's the subgraph of T that includes all vertices from T and no other vertices

and all edges in G that had both endpoints in T, and no other edges

[rocky summit]

Thanks Ann!

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[nova hamlet]

Hello

[nova hamlet]

Can you tell me how does 1 minus square root of 3 change places

The photo is uploading so you can see

[pseudo ice]

There’s a fact that $\sqrt{a^2}=|a|$ (the square root gives you a positive number, so if a were negative you’d need to “make it positive” to cancel out the root and the square)

[ocean seal]

chartbit

[outer lark]

@nova hamlet should be why they swapped

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[pastel island]

how do I get a 1

using -5 and -8

[tacit arch]

you just go through multiples

5, 10, 15, 20, 25 and 8, 16, 24,

[pastel island]

yea

I tried and I still cant get it some reason

oh wait

HAHA

thanks i wasnt thinking 1/8th of 4

@tacit arch thabks

you are my personal legend <3.broski always here to save the day

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[tidal badge]

Can someone just check to see if I’ve done this right ?

It’s numerical higher order differentiation using jupyter

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[digital field]

i need help with this i dont know how to find the area

[digital field]

<@&286206848099549185>

and this

<@&286206848099549185>

[bold lance]

Split it up into 4 different shapes

Work out areas separately

Then add

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[clear moth]

Dk where to go from there

Nvm

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[stiff basalt]

I was messing around and decided to write an infinite series using square roots. For example:

1 = x + sqrt(x + sqrt(x + sqrt(x + sqrt(x...)

1 = x + sqrt(1)
1 = x + 1
x = 0

At first glance, plugging x as 0 into the original equation does not seem that the equation would work. Does anyone know the specific reason why 0 is the solution for x? Is there a specific proof for maybe how this series is diverging?

[tacit arch]

you have to find the domain where $\sqrt{x + \sqrt{x+\ldots} }$ converges

[ocean seal]

riemann

[stiff basalt]

hmmm could you explain?

[tacit arch]

oh that's not your mistake

your mistake is substituting in 1 for x in one place but not another

you have to make the substitution simultaneously

[stiff basalt]

Wait I don't understand. What I was trying to do was to take the square root of both sides and I add that to the original equation so that sqrt(1) = sqrt(x + sqrt(x +...)

Then I can substitute back into the parent equation 1 = x + sqrt(1) because the second part is the same.

Does that mean i can't do that

[tacit arch]

you can't substitute for x in just one part of the equation like you did

when you get to here, it's wrong because you substituted for x in only one part of the equation but not all of it

[stiff basalt]

ohhh i see

.close

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[pearl robin]

how would I go about calculating the spectrum of Y(t)?

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[river axle]

i really need my work checked and some clarification on 14.

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[reef dawn]

Where do I start for this problem?

[outer lark]

I believe where the normal line that goes through the origin and that line intersect is a good idea

[reef dawn]

would that be y=-1/2x?

[outer lark]

yep

and where that line and your line intersect couuuuld be the answer

[reef dawn]

how do i find the point where they intersect?

[outer lark]

hmmmm if you think about what your actually working out when you use the equations

so the y values

if those are the same

they must be touchingand we set equation 1 equal to equation 2, then we can work out where the common point is on the lines if it exists

right

well

[reef dawn]

-1/2x = 2x+3?

[outer lark]

that is a terrible explanation

yes

[reef dawn]

answer is -6/5?

[outer lark]

not the answer

the x coordinate

[reef dawn]

do I plug it into either y= 2x+3 or y=-1/2x?

[outer lark]

its a common point between the lines, they intersect there, both equations should give the same y value

[reef dawn]

alright, thanks for the help

[outer lark]

,w plot y=2x+3 and y=(-1/2)x for -3<x<0 and 0<y<3

[ocean seal]

Results provided by WolframAlpha

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

Requested by Clarkie#5208

[outer lark]

looks pretty chill to me

[reef dawn]

.close

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[small whale]

okay this one i actually need help with

the debt amount is 1500 by the way

i'm not great with rewriting formulas

epsecially when log and natural logs are in use

[placid zinc]

Solve for (1 + i)^(-M) first

Then take the log, drop the -M, and quickly solve for that after

[small whale]

so do i multiply the (1+i)^-M first?

[placid zinc]

We can make a sub to have it be a bit easier:

$P = \frac{Di}{1 - u}$

[ocean seal]

Kaynex

[placid zinc]

And we solve that for u

[small whale]

so 1P-u=Di?

or technically P(1+i)(^-M)=Di?

[small whale]

i need more help 😭

okay so after that i should have ln(1500(1+i)(-m)=lnDi?

[placid zinc]

So you are multiplying both sides by (1 - u) in order to clear fractions

After this, you get:
P(1 - u) = Di

[small whale]

ohhhhh

and P is 1500

so 1500(1-(1+i))^(-M)=Di

i just don't know how to drop the M

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[queen cedar]

hi

[queen cedar]

im studying rings in modern algebra

with regards to part e

i know that q is a field

so its only ieals are {0} and Q

just not sure which ones are either maximal or prime or both

woudl really appreciate osome help

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[pseudo ice]

What's the definition you have for a maximal ideal?

(You should, hopefully, have that all maximal ideals are prime ideals)

[queen cedar]

for this particular question?

i got that {0} is the prime and maximal ideal of Q

because both a prime and maximal ideal of q have to be

proper subset of q right?

and the only proper ideal of q is {0}

[pseudo ice]

Yep, that's pretty much it, I'd say!

[queen cedar]

ah i see

thank you

i actually had a question regarding part c as well if you dont mind

[pseudo ice]

Yep sure - just reply to my message/ @ me when you drop it

[queen cedar]

oh its the same screenshot

sorry i meant this

so i understand that the set containing only the zero 2 by 2 matrix

is an ideal of m_2(r)

and i want to prove that the only other ideal of m_2(r)

is m_2(r) itself

so i let I be an ideal of m_2(r)

that is a non zero ideal

so there is a 2 by 2 matrix A in M_2(r)

i divide it in to the case where det A = 0 and det A != 0

if det A != 0

by definiton of a ring

there is a A^-1 in M_2(R)

and so A*A^-1 is in the ideal I

and from there we can conclude that the ideal I is in fact equalto the entire M_2(R)

so now i have the case where det A is non zero

sorry, det A is zero

but A must be a non zero matrix

so there is an entry of A that is non zero

and i say that we can prove that

the matrix [1 0;0 0] and [0 0;0 1] are in the ideal

im trying to show that the 2 by 2 identity is thus in the ideal

just struggling on that part

because i can only see addition as a means to get the identity but the ideal must use multiplicaitoj

@pseudo ice

[pseudo ice]

Let me help you with this - a ring (say A) is a field if and only if it has exactly two ideals, {0} and A

[queen cedar]

i see

so should i prove that M_2(R) is a field

[pseudo ice]

Is it a field, though? 😉

[queen cedar]

not sure...

im not particularly well versed on fields

but i see how that could make the problem much simpler

[pseudo ice]

Fields mean every nonzero element is multiplicatively invertible

Can you find a matrix that isn't zero, but isn't invertible?

[queen cedar]

oh yeah

[1 0; 0 1]

sorry

[1 0; 0 0]

is not invertible

but non zero

wait a field has to be commutative right?

matrix multiplication isn't commutative

so M_2(R) can't be a field...

[pseudo ice]

Hmmm was about to say, they're not commutative rings

Most of my experience is with rings that are commutative

[queen cedar]

im a little confused

can you just tell me if m_2(r) is a field lol

there must be a reason you brought up something being a field if it only has two ideals...

[pseudo ice]

Pretty sure it isn't, as per before - you can find non-zero elements that aren't multiplicatively invertible

[queen cedar]

oh i see

so M_2(R) must have an ideal that is not 0 and not M_2(R)

: (

[pseudo ice]

Whereas the definition is that (1!=0 and) every nonzero element has an inverse

[queen cedar]

so where should i go from here

if M_2(R) is not a field

i thought i was on the right track in my original approach

anybody still here lol

@pseudo ice ?

[pseudo ice]

That's actually a good question, for which I'm not so sure of

If it's not commutative then aren't the ideals separated into left and right?

[queen cedar]

i think so

just wondering

you said that

a ring (say A) is a field if and only if it has exactly two ideals, {0} and A

if a ring like M_2(R) is not a field as we have shown

do you think that means M_2(R) must have a one sided ideal?

not sure if that makes sense...

[pseudo ice]

Hmm, now I'm not quite sure what's true when your ring isn't commutative

[queen cedar]

darn

im really stuck...

appreciate the ehlp though, thank you

do you think we could go about

solving this through ideals generated by non zero matrices of M_2(R)?

if an ideal contains a matrix A

then <A> must be a subset of I right?

close

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[alpine sable]

Hm. Any domain restrictions?

[rocky grove]

Well we know 1 solution to this

Which is 0

That's a sure solution

Other than that, there is no other way that I know of that doesn't involve complex numbers

[alpine sable]

Because I don't think you can trivially find all the possible number of real solutions

[rocky grove]

Newton's method can work here I think

[alpine sable]

Let's ascertain the level of education this is for

What is this for? @alpine sable

it's a past math olympiad paper

from 2012

Do you know stuff like Newton's method?

no

lemme search it real quick

[rocky grove]

Counting them from the graph, it is 63

[alpine sable]

i read through it and i still don't understand it 😅

[rocky grove]

But there should be a mathematical way to express the number of solutions

[rocky grove]

It involves derivatives

[alpine sable]

i understand derivatives

[alpine sable]

Did u check every point of intersection between -1 to 1lmao

Respect

[rocky grove]

Well since both x/100 and sin(x) are antisymmetric, I counted the positive half and multiplied it by 2 and added 0's solution to it

[alpine sable]

Yeah but still wild

[spare plaza]

201

[alpine sable]

but the thing is there should be no calculus involved

[alpine sable]

how did you get that

[spare plaza]

Wait its infinity

If its real number

[spare plaza]

Is that the answer?

[rocky grove]

[spare plaza]

If it is then the question is wrong

[alpine sable]

the question was multiple choice

but the document itself doesn't show the multiple choice options

[rocky grove]

63 should be the answer

[spare plaza]

Gimme options

[alpine sable]

and the answer just states the option

[spare plaza]

Is there any infinity as a option?

If yes then its the right

If not then 201 is answer

[rocky grove]

No infinity is not correct

[spare plaza]

But 201 isn't correct one

[alpine sable]

the answer key doesn't have the number

[spare plaza]

How

[alpine sable]

it just has the option

[rocky grove]

Because x/100 grows above 1 after x=100

And goes below -1 after x=-100

[spare plaza]

Question says its real number and there are infinite real number that could satisfy thosr

[rocky grove]

Nope

The satisfaction of this equation is the intersection points of x/100 with sin(x)

[spare plaza]

Now say how many real number comes in between them

Infinity

[rocky grove]

Plug in x= 10

10/100 =/= sin(10rad)

Plug in all the numbers between 0 and 3.11...

[rocky grove]

X/100 for those numbers will not equal sin(x_rad) for those numbers

[rocky grove]

Sure but put sin(10rad) in your calculator and see what value it spits out

For the equation to be satisfied, sin(10rad) should give you 0.1.

But sin(10rad) gives you -0.544

And 0.1 =/= -0.544

Anyways

[spare plaza]

Hmm ic ic

Wait lemme solve it real quick

Here if its not the answer then i am quitting maths

[rocky grove]

Yep I was gonna type it out

[spare plaza]

Oh nice

@alpine sable solved

[rocky grove]

Good job

[spare plaza]

Ty

[alpine sable]

can someone explain pls

i'm very lost

[rocky grove]

Ok so

Sine is a periodic function

[alpine sable]

yes

[rocky grove]

Meaning that it repeats itself

It has a period

[alpine sable]

yes

[rocky grove]

Which is 2π

Now let's go over to x/100

Since sin(x) goes from -1 to 1

x/100 = 1 when x=100

[alpine sable]

so when x=100 or -100 there will be no more solutions

the range of x is between -100 and 100

[rocky grove]

When x/100 goes above 100 and goes below -100 yes

Yep

So to find the amount of times 100 can fit the period of sin(x), we divide it by the period.

100/2π = 15.9...

Now let's consider the following

[alpine sable]

wait so the number of times x/100 intersects sin x is the same throughout all the periods

-100<x<100

[rocky grove]

Nope

I was gonna say now

sin(x) =1 at π/2

Which is less than 2π

So when we divide 100 by 2π, it means that x/100 goes under 16 peaks but doesn't complete the last period fully

This in turn tells us that x/100 intersects sin(x) 2 times under every peak

So in total, the intersections on the positive half is 2*16 = 32

And since both functions are odd, the right side is the same as the left side

So the entire interval is 2*32 = 64 intersections. However, this means we counted the origin twice

So we take 1 out of it

64-1 = 63

And that's the amount of intersections

[spare plaza]

Draw graph of those 2 function in a website

And u will understand

The no of cuts is the answer

[alpine sable]

ok thanks

.close

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[dusk panther]

Could someone explain this question.

[alpine sable]

Use induction to get to something that is basically 6(blah blah) where then you can prove it is divisible by 6

Informal explanation, can explain more rigorously if you don't get it still

[dusk panther]

I mean I know I have to show it's divisible by 2 and 3 to make sure it's divisive by 6 but I don't really understand.

[rocky grove]

Factoring is key here

[tiny cosmos]

Sometimes I get really excited to explain something when I understand it. Proof by induction is basically proving that the question is true when n=1, and then setting n = k and plugging in n = k + 1 to the function and proving that THAT is true

And when you prove the latter half, you are basically proving that it will be true for all integers

[dusk panther]

Yes I understand that bit but for this specific question I'm finding it difficult to prove it.

Because it doesn't work well.

[lyric stream]

factor

[tiny cosmos]

Let me write this out quickly

[dusk panther]

Alright.

[tiny cosmos]

nevermind Im brain dead

sorry champ

[novel field]

Test?

[dusk panther]

No.

I was doing this question at home just as practice.

[novel field]

Why is there a 7 marks?

[dusk panther]

It's from the book.

[dusk panther]

It's all good.

[tiny cosmos]

nvm Im a genius

[dusk panther]

Oh let me try it out.

But wait that is not a proof tho is it.

[tiny cosmos]

No idk man Im cooked its finals week

[dusk panther]

Oh wait I'll check later.

Thanks by the way.

Gym first haha.

Thanks mate.

.close

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[torn glacier]

hello, I need help. How can I solve the equation? f(x) = 54 if f(x) = 3^x - 27 (I know the answer is 4, but I don't know how to solve this).

[strange meadow]

$54=3^x-27$

[ocean seal]

ed

[strange meadow]

$81=3^x$

[ocean seal]

ed

[strange meadow]

$x=4$

[ocean seal]

ed

[torn glacier]

54 = 3^x - 27
54 + 27 = 3^x
81 = 3^x

How do you get x = 4?

[strange meadow]

3^4=81

[torn glacier]

aaa alright, thank you!

[strange meadow]

yw

[torn glacier]

.close

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[red crater]

I tried learning computing root by hand, can’t solve the root of 1033,7 can any show the solving steps so i see where my error is? Calculating to 32.15 would be precise enough

[red crater]

Even the first step im confused by, online it says to separate the first number into its own pair if the amount of numbers is odd but that results in the first number of the square root of it is
1 which is crazy cuz it begins with 3 as its 32.15

[alpine sable]

Oh, I forgot to write 5.

@red crater

[red crater]

Oh that makes sense! How do i know when to add 0s

As in the start and end

[alpine sable]

by start, are you referring to something like sqrt(196)?

[red crater]

as in 1033.70 added one 0 at the end and two 0s at the end of 329

[alpine sable]

basically in the sqrt computing algorithm, we have to pick the two forward digits. If we do not have any digits, we can write it as its decimal form and preceed.

*proceed

like 329 = 329.0 = 329.00

= 329.00000000000000000000

and then you can add the bars to the pair of zeros

[red crater]

So we keep adding zeros till its divisible like 642-*- and adding zeroes to 329 till its divisible?

[alpine sable]

Didn't quite get you. Try rephrasing or showing an example.

[red crater]

When you get to the last step in the solution you sent you add try if 329 is equal to or less than 641- * - and if you add one zero its now 3290 by 64- * - and thats not less than or equal to even if we put 1 in - place. Lastly you add another zero and now 64155 is a number less than 32900 so you add 5 to our root then subtract 64155 from 32900 and repeat?

[red crater]

Sorry to bother i can now calculate the rest of the digits and think i understand tysm for all the help n sorry for the confusion

[alpine sable]

oh thats good lol

[lone heart]

@red crater Has your question been resolved?

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[brittle sun]

Linear Algebra
I'm looking for a matrix/determinant calculator(Not sure that's the appropriate name) where I can feed the program a matrix and tell it which operations to do, and it'll calculate them automatically.

[brittle sun]

Does anybody know about such a program or a site, or simply tell me what I should be looking for? Because "Matrix operations calculator" isn't working

[pseudo ice]

Like this? https://matrix.reshish.com/

[brittle sun]

I don't think so? I can't find where I can make operations on a given matrix at least

[pseudo ice]

Take a look at the LHS, this side?

[brittle sun]

I did, where can I perform manual operations on a given matrix?

[pseudo ice]

What do you mean by that? As in you want it to show you the steps?

Does e.g. https://www.symbolab.com/solver/matrix-multiply-calculator not work for that either?

[brittle sun]

No. I want to perform elementary operations on a matrix, and see the outcome

[worn fox]

Like EROs?

[brittle sun]

I don't know what that means

[worn fox]

Elementary row operations

[brittle sun]

Just.. elementary operations
SUbtract a row for example

[brittle sun]

Yeah, sure

Preferably one that works with column operations as well

[worn fox]

Just do the operation to an appropriately sized identity matrix and times your matrix with it

[brittle sun]

Yeah but certainly there's a calculator that does this automatically?

As in I quite literally just feed it R1 -> R1 - R3 and it.. does it?

[worn fox]

https://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=roc

[brittle sun]

My browser's blocking it, classic

I might just program one myself in all honesty
Maybe I'll look for an ERO calculator? Could that work?

[worn fox]

That's what I just linked

[brittle sun]

My PC doesn't like that link, I'll look for other ones real quick

Welp, nothing. Guess I'm programming it
Ty for the help

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[loud rampart]

@boreal verge

[boreal verge]

so B right?

[loud rampart]

and c

[boreal verge]

well at B what type of angle is R?

[loud rampart]

uhhh

idk it just says 62 degrees

so ig thats the answer for angle s

[boreal verge]

like inscribed or at the center

[loud rampart]

but p idk jow

oh

inscribed

[boreal verge]

great

that means the arc it forms is how long?

[loud rampart]

uh

180?

😭

sorry

[boreal verge]

its twice the measure of the angle

[loud rampart]

ohhh

[boreal verge]

meaning 62 * 2 = 124°

the length of the srv

arc

now what type of angle is S?

[loud rampart]

inscribed too

[boreal verge]

meaning its measure is half of the arc

which is again 62°

remember the arc is larger than the angle in all inscribed angles

cause i kept mixing them up

so S is 62 degrees right?

[loud rampart]

yes

[boreal verge]

because both S and R determine the same arc

[loud rampart]

yeah theyre the same

[boreal verge]

now what type of angle is P

[loud rampart]

central

OH

so is it just half

of p and s

[boreal verge]

its the same as the arc

twice

[loud rampart]

oh

[boreal verge]

not half

cause its larger

its the same length as the ark

arc

however tf u spell it

[loud rampart]

oh okay

arc

[boreal verge]

so P is how many degrees?

[loud rampart]

62

oh

Wait

MB

i thought you said r

wait what

[boreal verge]

dw abt it

[loud rampart]

oh yeha

ummm

is it 124

[boreal verge]

yes good job!

[loud rampart]

oooh

[boreal verge]

this shit can be confusing sometimes

now C

[loud rampart]

literally

yes

[boreal verge]

what type of angle is SRU?

[loud rampart]

inscribed

[boreal verge]

meaning the arc is how long?

[loud rampart]

twice as long?

[boreal verge]

exactly

which is 40 * 2 or 80 degrees

[loud rampart]

ooh

[boreal verge]

now we know RU is a diameter right?

[loud rampart]

yup

[boreal verge]

which means it splits the circle in 2 180 degree arcs

lets consider the top one with RT in it

not rt sorry

TU

[loud rampart]

okok

[boreal verge]

we know its 70 degrees

[loud rampart]

mhm

[boreal verge]

oh i just realised thats the 3rd subcategory

lets do that first

then go back to 2

[loud rampart]

alrightt

[boreal verge]

so we can find out RT from subtracting from 180 70

which would result?

[loud rampart]

110

[boreal verge]

thats right!

now we basically do the same thing for RS

[loud rampart]

ooh

[boreal verge]

take the whole ark and subtract SU

arc

i wanna write ark it sounds so cool but why tf did english make the word arc like

[loud rampart]

LMAO

[boreal verge]

it seems like its underrated autistic cousin

[loud rampart]

just use it its okay

[boreal verge]

anyways what would SR be then

take ur time

[loud rampart]

is it 110 too

[boreal verge]

no, its 100

[loud rampart]

oh

i thought i had to subtract 70

[boreal verge]

remember US is 80 degrees whilst UT is 70

You have to subtract the one on the arc were looking at

[loud rampart]

ohhh

okay i get it

[boreal verge]

now RST is included and you just founs the determined arc so it shouldnt be that hard

for 4 i mean

is there anywhere you have a particular issue?

[loud rampart]

is the arc of rst 110

[loud rampart]

not sure yet

[loud rampart]

since rt is 110

[lone heart]

@loud rampart Has your question been resolved?

[lone heart]

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[alpine sable]

X = 1000
5/100 = x/(x+y)
5x + 5y = 100x

What formula is used here?

[alpine sable]

<@&286206848099549185>

[spare plaza]

Whats the exact question?
And what grade is this?

Dont type whole question just send the pic of question

[alpine sable]

It's not in English, i gotta translate

[spare plaza]

Send me i have translator

And which grade ?

[alpine sable]

10th grade chemistry. My question is related to the math part tho. Here's the full problem:

A solution consists of 5% of acid and 95% of water. According to that, how much water would be needed for 1L of acid?

Solution:
%(v/v) = (v/v)×100
5 = 1L/(1L+v)×100
5/100 = 1L/(1L+v)
5L + 5v = 100L
5v = 95L
v (water) = 19L
v (solution) = 19L+1L = 20L

I am able to calculate that if 1L is 5%, then 100% is 20L, yes, but i wonder about the equation

[spare plaza]

Did u get?

[alpine sable]

Yes, i guess so

Thanks

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[wooden mantle]

Would this be correct?

[wooden mantle]

I have to find a constant c, which makes vectors v and v+c*u orthogonal

[runic iris]

i think so

[vague coral]

correct

[wooden mantle]

Aight, thanks

preparing for my exam

.close

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[north saddle]

Why is gamma(3) * zeta(3) = 2zeta(3)? is there a rule on this?

[north saddle]

Gamma is the gamma function and zeta is the Riemann zeta function

Please @ me

[vale wigeon]

isn't Gamma(3) just equal to 2? @north saddle

Gamma(n) = (n-1)! for natural n

[north saddle]

Oh thanks!

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[vague coral]

what have u tried ?

[cloud berry]

i have to try something?

how do i try something

[wraith stirrup]

it's C

[vague coral]

well, trying to prove the sign of b^2 - 4ac

[vague coral]

indeed

[cloud berry]

ok but like why tho

[wraith stirrup]

Bcs if b*2 -4ac = or > 0 than it means that there will be 1 or 2 roots

[vague coral]

complete the square and you discuss the sign of b^2 - 4ac

[cloud berry]

oh k

mkaes sense

[vague coral]

that aint a proof tho... but you do you

[wraith stirrup]

the disriminant cant be negative cos square foot of a negative value does not exist

[vague coral]

complex numbers doesnt exist

[wraith stirrup]

6*2 -4×2×5 = -4

[cloud berry]

the equation has 2 roots

or na?

[wraith stirrup]

no

D<0

[cloud berry]

no real roots

[wraith stirrup]

..

[royal summit]

I need help

Whats the answer

Im doin quiz

[cloud berry]

go in another form

[royal summit]

What

[wraith stirrup]

No roots if D < 0
1 root if D = 0
2 roots if D > 0

[cloud berry]

#help-32

go there

[cloud berry]

ok so what is d

[wraith stirrup]

D is a short for discriminant : b*2 - 4ac

[cloud berry]

so i can say nothing about the equation

[wraith stirrup]

no

bcs there are any roots

[cloud berry]

so there are no real roots

[wraith stirrup]

No

[cloud berry]

so what is it

[wraith stirrup]

nothing

1

[cloud berry]

merci

[wraith stirrup]

derien

[royal summit]

Whats this

I was told to come here💀

[gray isle]

no you weren't

[royal summit]

What the

I read the help thing st it told me to ask my question here

Like tf

[gray isle]

no it doesn't

[wraith stirrup]

BRO

[wraith stirrup]

i told u the answer

[royal summit]

Tells me to here

[wraith stirrup]

what u want more

[royal summit]

What channel

[wraith stirrup]

the answer is 31

[gray isle]

you skipped steps 0 to 2

[royal summit]

Ik

My bad im dum 😭

[cloud berry]

so if there is one root

the answer is c?

.close

[lone heart]

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[alpine sable]

Hello.

I'm using this table, filled manually by hand:
Requests Price
0 0
1-99 10
100-999 25
1000-2499 50
2500-4999 75
5000+ 90
This means.. the more requests, the higher the price.

Now I want create a formula, to give just the number of requests and the result should show the calculated price. But not exactly as the table shows!

Lets say 50 requests ( would be price of 10 in the table ).. should result in a calculated price of around 17.5 or so. 50 is the half of 1-99 requests and 17.5 is the half way from price of 10 to 25.

5000/90 was just a placeholder ( my pricing limit ) but would be nice if the formula could calc even 15000 or 25000 by the given values.

You know what I mean ?

Actually my math skills aren't even enough to ask google for a solution. I think there is maybe one formula per line in my table needed. But I want learn whats behind this..

[tribal haven]

eh, in excel this is either a bunch of ifs or if you change the left column a little bit a vlookup

but yeah roughly one if statement/formula per line here, since the prices and thresholds are fairly arbitrary

and a small problem of not being very clear what behaviour you want if for example requests >5000 here

[alpine sable]

Okay this is a little confusing maybe and we should ignore the 5000+ part. The table ends with 4999 requests = price of 75

I know think this should be a math function with progressive or regressive curves or so. But I'm not sure how to look for that.

Maybe we can concentrate on just one line of the table

[tribal haven]

the (very) rough idea is as follows

let r be the number of requests

if r == 0
return 0
else determine the interval r is in
let low be the lowest value of this interval
let high be the highest value of this interval
(e.g. say r = 400 you have low = 100, high = 999)
let p be the price of this interval
let p_prev be the price of the previous interval
(in this case p = 25, p_prev = 10)
return p_prev + (p-p_prev) * (r-low) / (high-low)

[alpine sable]

yes yes.. hm this looks interesting. i need to think about it and try it out a little

[tribal haven]

implementing this in excel/other spreadsheets doesn't exactly feel easy but it's possible and that'll do what you've outlined it to do

[alpine sable]

okay thank you so far! maybe there is a function to use, but I want understand the math behind it

i will report back later if I could try this out a little

[tribal haven]

essentially you figure out which bracket it falls into,
and take the price for the previous bracket as the smallest possible price (we're at least 1 request over this quantity)

then we adjust that price towards our highest possible price (the price for the bracket we're in) based on how high we are in our bracket

[alpine sable]

yes

this is much information somehow and i will try to understand this all

is it allowed to keep the channel open ?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

i have a problem

your solution was a good start but it negotiate the result somehow

line 2 and 3 are the given values.. line 3-15 contains your formula in column B

[tribal haven]

oh i see, ye just corrected it

had it the wrong way in my head

[alpine sable]

damn thats it

THANK YOU VERY MUCH

i would never have done this alone. and now i will try to understand this better

thank you, my friend !

.close

[lone heart]

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[shy whale]

If you have (x) amount of money, each minute you bet (x/10) amount on a 50% chance, what is formula to determine the chances that after (n) minutes profit is made?

Assume there is a 50% chance to either double the money, or completely lose it all every minute.

If profit is made, how many minutes would it take to double the total money (x)?

[lone heart]

@shy whale Has your question been resolved?

[hot bay]

I have these questions

[shy whale]

uh

im using this channel

[hot bay]

Sorry

[lone heart]

@shy whale Has your question been resolved?

[lone heart]

@shy whale Has your question been resolved?

[shy whale]

HOW LONG DO I WAIT

FOR AN ANSWER

[lone heart]

@shy whale Has your question been resolved?

[lone heart]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[past bridge]

Hello guys

[past bridge]

I was working on some homework

and one of my questions was this :

I have no idea how to solve this, please help me
Thanks in advance.

[mortal trellis]

<@&268886789983436800>

[past bridge]

I forgot to mention, no calculators were allowed.

[worn fox]

you need to un-nest the radical on the bottom

[past bridge]

So I multiply by sqrt(2-sqrt(3))/sqrt(2-sqrt(3))?

[worn fox]

https://brownmath.com/alge/nestrad.htm

[past bridge]

Thank you so much, this helped me a lot. I believe the answer is 1 1/3.

.close

[lone heart]

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[boreal verge]

what is the question?

[last python]

I have this

Ive tried mny calculators

They give me the answer

But no steps

Is there a formula for this?

[lone heart]

@last python Has your question been resolved?

[sullen rover]

I need help on this question. Anyone able to assist me?

[cold hinge]

bro post your question in an open help channel

[cold hinge]

do you still need help

the answer is 0 btw

[sullen rover]

oh my bad i thought this was open

[cold hinge]

no

[sullen rover]

the instructions said post it in help-0

[cold hinge]

one of these channels are open

[sullen rover]

thank you

sorry about that

it wont happen again

[cold hinge]

nw and why is your profile an onlyfans girl 💀 💀

[sullen rover]

lmao it is my dream girl; i just did it to mess with my boys

[cold hinge]

bro hell nah she belongs to the streets 🙏 get your priorities straihgt brotha

[sullen rover]

i got my priorities straight

broke up with my last gf cuz she was unloyal

and now im single on my grind

[cold hinge]

das good but onlyfans girls are all hoes bro she aint no dream girl

[sullen rover]

she was for me in like 7th grade cuz she streamed fortnite and wasnt an only fans girl back then

[cold hinge]

damn fr

how the mighty fall

[sullen rover]

real

[lone heart]

@last python Has your question been resolved?

[last python]

How did you get it

[cold hinge]

factor out x^2 from the square roots

[last python]

huh

[last python]

Did you factor out x?

First thing

[cold hinge]

yes

hold on

the procedure before that was

[last python]

Pretty sure sum aint right in there

@cold hinge

[cold hinge]

sorry thats embarassing

ill try to see where i did wrong

[last python]

No dw

I didnt do it at all 😭

[cold hinge]

i seem to get the right answer after rationalizing and doing the same thing i did before

ignore the scribble in the middle, i was braindead

[cold hinge]

i see what i ddi wrong

omg im braindead

i factored out x-x somehow

but i could only have factored out x

🤦‍♂️

let me try it again with the same method

nah it doesnt work. i think these types of problems with square roots you have to rationalize first

i guess you would know that from experience

@last python

[lone heart]

@last python Has your question been resolved?

[lone heart]

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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sharp rock]

How would you show that this is continuous at points it converges?

[sharp rock]

have showed it converges on intervals (a,b)

<@&286206848099549185>

[lone heart]

@sharp rock Has your question been resolved?

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[cerulean breach]

i just dont know

[wary stream]

Also please delete your image in the other channel, it is cluttering that channel

[cerulean breach]

my fault

[karmic pulsar]

Do you know the Pythagorean theorem?

[cerulean breach]

yeah

a2+b2=c@

c2

wait no

y=mx+b

[karmic pulsar]

Wut

It's a²+b²=c²

[cerulean breach]

nah i was right the first time my fault

yeah

oops

[karmic pulsar]

The sides marked with 6, 8, and y form a right triangle...

[cerulean breach]

oh im so stupid

so i would do 6 squared plus 8 squared = y squared

then do the square root of y squared

[karmic pulsar]

That's right

[cerulean breach]

yay

ill tell u what i get in a sec holdon

i got 10 for y

[karmic pulsar]

Next, you have another right triangle 8, x-6, and z, put z in terms of x

[cerulean breach]

ohhh so would i cross multiply or no

wait i dont think i would

still pythagorean?

[karmic pulsar]

Yes

[cerulean breach]

ok

would it be 8^2 +Z^2=x-6^2

[karmic pulsar]

No, z is the hypotenuse

[cerulean breach]

ohhhhh

[karmic pulsar]

We're doing the medium triangle

[cerulean breach]

alright

so 8 squared + x-6 squared= z squared

[karmic pulsar]

Also, be careful with parenthesis, should be (x-6)²

[cerulean breach]

oh yeah

thank you

ill tell you what i got

when you say put z in terms of x wdym

[karmic pulsar]

z= something mentioning x

[cerulean breach]

ok

i have 28 +x = z squared what do i do now

[karmic pulsar]

I don't think that's right

[cerulean breach]

oh

i did 8 squared + (x-6 squared) = z squared and then i got 64 +x-36 = z squared and then i got that

[karmic pulsar]

Parenthesis!

[cerulean breach]

i fixed it

[karmic pulsar]

(x-6)²=x²-12x+36