help-0

[shell obsidian]

6P2

and then the b) would be the 6P3

[lone heart]

@shell obsidian Has your question been resolved?

[shell obsidian]

i'll need to confirm this later, this is the first question of the set and i solved the rest of them

can't just picture this in my head somehow 😅

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[velvet osprey]

What is the question ?

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@alpine sable Has your question been resolved?

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[alpine sable]

The ages of theatergoers vary quite a bit. For stage performances of Shakespeare's Othello, it appears that age is a normally distributed variable with μ = 50 years and σ = 12.
(a) What is the probability that a random audience member is younger than 35 years old?
(b) What is the percentage of visitors who are 65 years of age or older?
(c) What is the probability that a group of 10 randomly selected visitors is on average older than 55 years?
To encourage more young people to attend the performances, people under 35 years of age are given a 30% discount on the price of a ticket, not €20 but €14. The result is that three times as many young people come to the performance than would be expected based on the calculation in question (a).
(d) What is the average price of tickets sold after this action?

Translated with www.DeepL.com/Translator (free version)

[alpine sable]

answer of a and b

answer of c

answer of d (this part, is the part, I don't get)

note: in answer d, there are some dutch words.

I understand the dutch words, but if you don't, I can explain what the texts says in english

so, the probability that a random audience member is younger than 35 years old = 10.56%

[lusty zenith]

wow

[alpine sable]

but in (d) says this: to encourage more young people to attend the performances, people under 35 years of age are given a 30% discount. The result is that three times as many young people come to the performance than would be expected based on the calculation in question a.

that means, 10.56 times 3 = 31.68%

why would the the chances keep the same at the elder people (older than 35 years old)?

[small trellis]

Why wouldn't it?

[alpine sable]

but then it wouldnt be 100% total

[small trellis]

Explain to me what this means better

[alpine sable]

I get it, because 3 times more younger people, goes beyond the 100% total people

then before

lets say for example:
10 young people and 90 elder people.

[small trellis]

And then 30 and 70?

[alpine sable]

no

3 times of 10 young people, becomes 30 young people.
so, 30 + 90 = 120 total people.

before 100% now, 120%

idk, how to explain, what happens next?

[small trellis]

That wouldn't be 120% though

It's always 100%

So 30 would be 30/120

so 25%

But yes, the elderly percentage does decrease

[small trellis]

Was this part of the problem? Or is this your own speculation?

[alpine sable]

and for the elder percentage becomes 75% of the new whole.

[small trellis]

Yeah

[alpine sable]

whats with this?
note: "prijs kaartje" means price of ticket.

[small trellis]

I wasn't following all the stuff

[small trellis]

Tell me this though

[alpine sable]

I thought that 120 would be a percentage

but its like, 120 as a whole unit.

120 people = 100%

[small trellis]

Yes, exactly

But you were saying this:

I don't see how that's the case, so I was wondering if the task was asking you this

[alpine sable]

when I saw this bit:
I thought that 31.68 and 89.44 are like percentages

but they are people, in decimals

[alpine sable]

I got this. that E(stochastic variable y) formula, is just how to calculate the expectated value.

.close

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[woven timber]

I have many routes a player can take in a game I'm making and each route awards them a specific score (ranging from 4 to 31, but mostly concentrated around 15) and I need to decide which difficulty challenge to present the player with in order to progress through that route. The difficulty of challenges I have range from 1 to 9 and I want each difficulty to have as close to an equal chance of being chosen assuming the player takes a random route. Is there any formulae I could use to find a corresponding difficulty for any route based on that route's score relative to the scores of all the other routes? All I have tried is trial and error with divisions on roots of the score but the conventration to 15 is causing issues and I'm not sure where to start, so any resources which might point me in the right direction would be amazing! Thanks so much in advance

[lone heart]

@woven timber Has your question been resolved?

[small trellis]

So the difficulty is supposed to be dependent on the score of the route, but simultaneously also being dependent on randomness because you want "each difficulty to have as close to an equal chance of being chosen assuming the player takes a random route"?

Unless you mean that each difficulty will have as close of an equal chance overall, not once the player has been selected a route?

[woven timber]

Sorry, no, I'll try and clarify what I meant. So, take every score and put them through this formula to get the difficulty and count how many times each difficulty is chosen. I want these counts to all be as close as possible

Hopefully that makes sense

[small trellis]

Right, so the scores should be evenly distributed as well

[woven timber]

The scores are not evenly distributed, that's the problem. But, the scores are fixed values, the scores of each route is the same no matter who is playing on what device etc. I pretty much need a way to convert a score to an evenly distributed value then I would just be able to multiply this value by something to put it into my 1 to 9 difficulty range

[small trellis]

The scores are not evenly distributed
Then I don't know how you can expect to get the same amount of each difficulty after the scores go through the formula which is supposed to match the score with the difficulty

[woven timber]

Say the distribution of scores was -(x-15)^2+100 (which is kinda close to the actual distribution), I would want the formula to convert these values to roughly x/2.8

In that case, I believe the formula would be (sqrt(-y-100)+15)*2.8?

But, the distribution isn't actually -(x-15)^2+100, so I need a way to do the equivalent for the actual distribution

Sorry if I got that wrong, but hopefully it atleast shows what I mean 😅

[small trellis]

So the formula isn't linear. I see

I wonder if it's anywhere near close to achieving what you're trying to achieve

Don't you know what score you want to be attributed to what difficulty?

Start from there, no?

[woven timber]

Not sure what you meant, but here's the actual distribution of scores (score on left, occurrences on right). So, I need to convert the numbers on the left to a number from 1-9 with an equal distribution, unlike the distribution of scores

[small trellis]

But you know what those numbers should be, right?

[woven timber]

Hm?

[small trellis]

The occurances

You know what the outcome should be, right?

Specifically

[woven timber]

30

Because there are 273 routes and 9 difficulties, so each difficulty should appear 273/9 ≈ 30 times. But, how do I cause this from the scores given?

[woven timber]

I've graphed the score occurrences, so this is the graph I need to flatten

[woven timber]

<@&286206848099549185>

[lone heart]

@woven timber Has your question been resolved?

[lone heart]

@woven timber Has your question been resolved?

[lone heart]

@woven timber Has your question been resolved?

[lone heart]

@woven timber Has your question been resolved?

[surreal meadow]

the scores almost seem irrelevant at this point

couldn't you just make it so that every route has a 1/9 chance of giving you any given difficulty?

[small trellis]

@surreal meadow "find a corresponding difficulty for any route based on that route's score relative to the scores of all the other routes"

[woven timber]

Well no because I want higher scoring routes to give a higher difficulty challenge

[woven timber]

Otherwise people would always just go the route that gives the highest score for the lowest difficulty

[lone heart]

@woven timber Has your question been resolved?

[alpine sable]

@woven timber Ah, easy one

You said there was 9 difficulty levels

Just divide the number of routes by 9 to figure out how many routes each difficulty level has

[woven timber]

mhm

[alpine sable]

Then, sort them by score and pick that number of lowest scored ones for difficulty one, then the next ones for difficulty 2 etc

This way, the higher score, the harder the route and there's pretty much as much routes for each difficulty

[woven timber]

Oh wait... yee I was really overthinking it haha

[alpine sable]

Good thing I'm a programmer

You can do .close now

[woven timber]

😅 Ye, thanks so much, this has been doing my head in. Been looking into stuff like https://en.m.wikipedia.org/wiki/Histogram_equalization for ages lol

.close

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[rigid ravine]

The environmental festival has its own logo (see picture). Angle x relates to angle y as 5: 8. How big is angle x?

[alpine sable]

Try to find 360° relative to x and solve from there

Ping if you need clarification

[rigid ravine]

So x would be 37.5?

[alpine sable]

I didn't actually go through the math, let me check

[rigid ravine]

kk

[alpine sable]

Sorry, I was helping someone else at the same time. Yes, 37.5

[rigid ravine]

Ok nice

[alpine sable]

You're supposed to do .close when you're done

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[distant epoch]

is the following correct in terms of how you would write an equation? 2^(4x+1) mod 20 = 12, x ∈ N

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[acoustic wave]

How would I go about reducing sin(theta + pi/2 - arctan(-x))/cos(theta - arctan(x)) into a tan expression?

[lone heart]

@acoustic wave Has your question been resolved?

[acoustic wave]

<@&286206848099549185>

[cursive bolt]

<@&286206848099549185> can anyone tell me what's the ans of this is it 1/2

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@acoustic wave Has your question been resolved?

[acoustic wave]

.close

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[sterile oyster]

$\int\frac{sin(37x)}{1+cos^{2}(37x)}dx$

[ocean seal]

Raged

[sterile oyster]

At first I set u=37x, but I got stuck down the road

could we first simplify using half angle rule?

[thorn kindle]

Yeah let u = 37x. Then du = 37 dx.

[sterile oyster]

ok so then we're left with

[thorn kindle]

cos^2 = 1 - sin^2

This is

1/37 * sin(u)/(2-sin^2(u))

[sterile oyster]

$\frac{sin(37x)}{74-sin^{2}(37x)}+C$

[ocean seal]

Raged

[sterile oyster]

?

[thorn kindle]

No

First do the u sub

[sterile oyster]

so does dx = 1/37 du?

[glass lichen]

yes

[sterile oyster]

I'm not sure what to do with it next

<@&286206848099549185>

[magic geyser]

show what u have

[sterile oyster]

$\int\frac{sin(u)}{2-sin^{2}(u)}dx$

[ocean seal]

Raged

[sterile oyster]

$u=37x$
$du=37dx$
$dx=\frac{1}{37}du$

[ocean seal]

Raged

[magic geyser]

now

what will u do

think of a goniometric identity

how can u write sin^2x as

btw dx should be du

[sterile oyster]

I think I figured it out thanks

.close

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[solid sphinx]

h= xTan66
h= (x-20) tan60
h=?

[magic geyser]

what

[solid sphinx]

How to find h if I don’t have x

[buoyant kayak]

what

[magic geyser]

you have

2 different equations for h

[solid sphinx]

Yes I was given 2 different equations for h.

[raw shard]

set the first h equal to the second h

actually what are you even solving for

wait never mind

[solid sphinx]

Yes yes. I got it. Thanks.

.close

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[twin gust]

I don’t know where to start, I can’t show the process

I think I have to use roots, because that is what I am studying now

[umbral orchid]

what is (a+b)^2

what is (a-b)^2

now divide one by the other

[twin gust]

wait a sec

[magic geyser]

numerator will be 10ab

[jaunty thicket]

ignore me

[magic geyser]

a^2+b^2+2ab=8ab+2ab

[umbral orchid]

yeah

[magic geyser]

omg

I mean denumerator

[twin gust]

that problem has the result, do I send it here?

[magic geyser]

ok

[jaunty thicket]

ok so (a+b)^2=10ab

[twin gust]

(sqrt 15)/3

it should be the answer

[umbral orchid]

yeah

sqrt(10/6)

[jaunty thicket]

so (a+b)=$\sqrt{10ab}$

[ocean seal]

Bubbles

[jaunty thicket]

and (a+b)(a-b)=8a

[umbral orchid]

you can divide first
then take square root

[jaunty thicket]

so (a-b)=$\frac{8a}{\sqrt{10ab}}$

[ocean seal]

Bubbles

[jaunty thicket]

right???

[umbral orchid]

ok so

[twin gust]

hm

[jaunty thicket]

did i frick anything up?

[umbral orchid]

(a-b)^2=a^2+b^2-2ab

[twin gust]

yep

[jaunty thicket]

yuh

[twin gust]

the double product

[umbral orchid]

so you directly get (a-b)^2=6ab

[jaunty thicket]

ig u could do that

but my way should also work

2 routes to the same destination

wait let me sympliby the radical

[twin gust]

let me understand something, I'm writing it on my exercise book

[jaunty thicket]

$\frac{8a\sqrt{10ab}}{10ab}$

[ocean seal]

Bubbles

[jaunty thicket]

$\frac{4\sqrt{10ab}}{5b}$

[ocean seal]

Bubbles

[umbral orchid]

where’s this coming from

[jaunty thicket]

WAIT

NO

IM SO DUMB

LMAO

i read it as a²-b²

ok

i see where i fucked up

so is it $\frac{\sqrt{10ab}}{\sqrt{6ab}}$

[ocean seal]

Bubbles

[umbral orchid]

yeah

[jaunty thicket]

$\frac{\sqrt{15}}{3}$

[ocean seal]

Bubbles

[jaunty thicket]

right?

[magic geyser]

sqrt(5/3)

[umbral orchid]

same thing

[twin gust]

yes

[jaunty thicket]

which when symplified is sqrt15/3

alr

nice problem

[twin gust]

.close

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[eager linden]

I need to tell whether an equation represents a direct proportion, then if so, identify the constant of proportionality. 3y=1/2x

[eager linden]

.close

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[amber iron]

Need help on doing this using an implicit function

setup: integral of integral of y^2/z dA

clearly this is incorrect, why?

formula i used

y^2/z dA --> sin(phi) * (sin(phi)*sin(theta))^2 / (cos(phi)) d(phi) d(theta)

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@amber iron Has your question been resolved?

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@amber iron Has your question been resolved?

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[sterile crescent]

(sin^2 x/x^2) != (sin/x)(sin/x) right?

[sterile crescent]

its sinsq x

<@&286206848099549185>

ping me when u respond

[oak chasm]

@sterile crescent sin/x doesn't seem to mean anything.

[ocean seal]

Chai T. Rex

[oak chasm]

Just by how fraction multiplication works.

[sterile crescent]

thanks

.close

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[oak chasm]

No problem.

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[glass tide]

what is this type of sequence called?

[glass tide]

1 + 2 + 3 +....+ n

and how can I compute it for n quickly?

[cursive badger]

algebraic sequence

and it's equal to n(n+1)/2

when summing from 0 to n

@glass tide

[glass tide]

thank you

[tiny minnow]

@glass tide if ur done do .close plz

[glass tide]

why do people insist on others doing that?

there are 5 open ones

and this one closes on its own after some time

[tiny minnow]

but it will get full

[tiny minnow]

u still need help or not?

[glass tide]

nope

.close

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[weary rose]

hey can someone please help me with factoring polynomials? here is a question for example 4x^4 y +8x^3 y

[charred flint]

you have to find what each term has in common

they both have a multiple of 4, three x's, and a y, so you can takes those in front

[weary rose]

they both have y

[weary rose]

oh you mean the greatest common factor is 4

[charred flint]

exactly

[weary rose]

so 4xy

4x^3y

[charred flint]

yup

and the leftovers are x and 2

so it factors into 4x^3y(x+2)

[weary rose]

ohh

are the leftovers

always multiplied

[charred flint]

yeah by the stuff they have in common

[weary rose]

ohh

thank you

explained way better than yt vids

btw

can i use this method to

do bigger polynomials?

something like 6 j^2 k^4 h^3 + 60 j^3 k^6 +36 j^3 k^4 h - 36 j^3 k^2

[magic geyser]

ye

[weary rose]

its kinda hard to find the gcf here

how would i start solving this?

[magic geyser]

it's a waste of time and ull never get asked such question

[bleak ridge]

,w gcf 6 j^2 k^4 h^3 + 60 j^3 k^6 +36 j^3 k^4 h - 36 j^3 k^2

[ocean seal]

Results provided by WolframAlpha

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Requested by PapaBread#3820

[magic geyser]

cheat

[weary rose]

this is from my practice sheet the teacher gave me

[magic geyser]

then he needs help

[bleak ridge]

[magic geyser]

it's like saying

[weary rose]

wish i could use this lol

[magic geyser]

solve the det of 9x9 matrix with no zeroes

[bleak ridge]

Just find the gcf one variable at a time

Including constants

[weary rose]

is constant the number infront of a variable

[bleak ridge]

Ye

[weary rose]

btw how do ik if something can't be factored anymore

[magic geyser]

3k+4p

[bleak ridge]

If there's no more factors

I'm not sure there's any sure way to decide if it's done

You just gotta stare at it and be like "yeah that's done" or "yeah I'm done with this annoying problem"

[weary rose]

they're both divisible by 1 but i dont think 1 counts

so is it done

[magic geyser]

lol

1*(3k+4p) 🧠

[weary rose]

thank u all

.close

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[alpine sable]

How do I solve this problem?

[bleak ridge]

Can't you split it

[magic geyser]

linearity

[alpine sable]

Im not sure how to split them

[gray isle]

linearity

[magic geyser]

Linearity

[bleak ridge]

$\int f(x) + g(x) dx = \int f(x) dx + \int g(x) dx$

[ocean seal]

PapaBread

[alpine sable]

Got it

Thank you

.close

[lone heart]

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[abstract pelican]

Hi! Can I ask why he took the derivative of this equation instead of doing x = a - y?

[raven rover]

I believe y’ appears to be used later in the calculation

Perhaps it was used as an aside (to help with computation later)

[abstract pelican]

Hmm. That kinda answered my question

But I kinda would like to know the thought process behind it. Anyways, thank you~

.close

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[wooden harness]

How do i do 24.2% out of $120?

[raven rover]

You can technically multiply these together

Know that k% = k/100

So 24.2% = 24.2/100 = 0.242

[wooden harness]

i needed help with turning the percentage into a decimal

like this

i got that

bc 126% is easy

but 24.2 is something new

[gray isle]

the idea is the same

24.2 is a number just like 126

how'd you convert 126% to 1.26?

[alpine sable]

100/100 is just 1 and then the other 26/100 is .26

and then just add em together

[wooden harness]

thats how the teacher showed us

[gray isle]

do you understand why 126% = 1.26?

[wooden harness]

imma be all honest, no

[gray isle]

do you know what % means

[wooden harness]

percent

[gray isle]

do you know what percent means

[wooden harness]

the percent means how much of the whole i need to figure out

.close

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[sick torrent]

How would u do a question like this?

[gray isle]

integrate, use the given condition to determine the constant of integration and hence the original function

[lone heart]

@sick torrent Has your question been resolved?

[sick torrent]

How

[gray isle]

have you integrated stuff before?

[sick torrent]

No

[sick torrent]

Can u wall me through it

[gray isle]

have you been taught any integration at all?

[sick torrent]

Usually I follow the questions in my textbook to solve but I can’t find it in my textbook

[sick torrent]

I’ve missed my classes

[gray isle]

so you haven't encountered anything with
$$\int$$
before?

[ocean seal]

ℝamonov

[sick torrent]

No

[gray isle]

your textbook should have stuff on integration

[sick torrent]

It does but I can’t find a question similar to this one

[gray isle]

don't have to find something similar / in the exact same format

just learn the concepts

[sick torrent]

Can u please just teach me how to do this question.

[gray isle]

i don't plan to teach you integral calculus from scratch

[sick torrent]

Not from scratch just this question like what u would do

So I can use it to solve my other questions

[gray isle]

you implied that you had next to 0 knowledge of integration

first try and get to a point where you can do
$$\int x^2 \dd{x}$$

[ocean seal]

ℝamonov

[sick torrent]

Huh

Solve that?

[gray isle]

would you be able to?

[sick torrent]

No

How would I?

[gray isle]

your textbook should have stuff on integration
start from the beginning of the chapter

[sick torrent]

Crap

[gray isle]

instead of blindly diving in to questions

[sick torrent]

Sir or ma’am. I’m desperate. Just please tell me what to do step by step.

[gray isle]

i suppose if you insist, you'd first want to learn what some people refer to as the (reverse) power rule

[sick torrent]

I can only learn from doing / seeing that’s why I use example questions as reference I can’t find any in my textbook they’re all different

[sick torrent]

I know the power rule

[gray isle]

power rule is what's is applied when differentiating something in the form ax^n
(reverse) power rule is what you apply when integrating (but its pretty much the same rule)

[sick torrent]

Oh

[gray isle]

$$\int x^\blue{n} \dd{x}= \frac{x^{\blue{n}\red{+1}}}{\blue{n}\red{+1}} + c$$ since
$$\dv{x}\br{\frac{x^{\blue{n}\red{+1}}}{\blue{n}\red{+1}}} = x^n$$

[ocean seal]

ℝamonov

[lone heart]

@sick torrent Has your question been resolved?

[sick torrent]

Oh

I see

My notifications aren’t working so I didn’t see this earlier

[sick torrent]

My question doesn’t have XD

*dx

[gray isle]

you seem to be lacking the basic knowledge / understanding

and i would highly recommend that you

start from the beginning of the chapter

and or search up an introductory video on integration on youtube

[sick torrent]

My assignment is due in an hour :/

[open saffron]

I think the approach they want is to use the power rule to find the general equation for f(x) and then can you can use f(-1) to solve for c

[sick torrent]

Why is this incorrect?

@gray isle @open saffron

[gray isle]

how are you getting 3.62

[lone heart]

Channel closed

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[sick torrent]

.reopen

[lone heart]

✅

[sick torrent]

Bc this

[open saffron]

This is wrong since the rectangle approach is approximation not the exact value

[gray isle]

they want riemann sum indicated in the image

[sick torrent]

Like the scale

[gray isle]

what scale

[sick torrent]

Like

From the first rectangle to the last

[gray isle]

they want you to find the sum of the area of the blue rectangles

[sick torrent]

I see

The first rectangle doesn’t really start at zero right?

[gray isle]

wdym

[sick torrent]

That’s where the first rectangle starts

[sick torrent]

What’s the x value? I’m not sure Idk Pi like that

[gray isle]

the markings are divided evenly

pi is just a number

[sick torrent]

Ik

But that point

What is it?

Nvm

I found out it’s pi/4

[lone heart]

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[restive sphinx]

hey guys can you explain me cancelation law by addition or a+c = b+c is a=b

[gray isle]

subtract c from both sides

also don't multipost

[lone heart]

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[restive sphinx]

thank you sir

but still i dont get it if i making an adition how im gonaa subtract

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[lone heart]

@alpine sable Has your question been resolved?

[open saffron]

Well we know that sin(x) is positive for (0,pi/2) and negative for (pi/2,pi)

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[alpine sable]

pretty simple question but what part of a logarithm can't be a negative?

[alpine sable]

also how do this

[jagged imp]

the argument and base both can't be negative

[jagged imp]

use a log law to combine the lhs into a single log and see if you can do it from there

[alpine sable]

so you multiply x and 2x^2 which would get you log2 2x^3 right?

[jagged imp]

👍

[alpine sable]

if you could help me with just one more thing that would be great

ok so i did log3 x - 2log3 7 which it divides x/7 right?

what do i do with the 2 infront then

cause ik it's supposed to be exponent of 7

so do i simplify it before i use the log law and make it x/49?

[jagged imp]

ya

[alpine sable]

so then it would become log3..

oh wait it's log base 3

i thought it was log base 2

mb lol

thx for the help

[jagged imp]

nw

[alpine sable]

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[austere jetty]

Hi folks!

[austere jetty]

I'm sorry for asking too much about LU factorization, but I sometimes get confused

Let's say I'm calculating Upper matrix, is it legal to make an operation like this: Row3=4Row3-3Row2?

Row3 being the row number 3 and the same for Row2

Like i don't know if it is legal to multiply 2 rows and then do the operation

[open saffron]

pretty sure thats legal, as you are doing two things, one you scale the row3 and minus by a scaled row 2 . I just personally wouldn't do that because means that you are way more likely to mess up, and also there times where need to operation by operation

[austere jetty]

and how could I avoid that?

sometimes it seems like the only way

Also another question, when doing the reverse elemental operations in the Identity (to get L), should I do them in reverse order?

[open saffron]

what do you mean its the only way, as it just doing two steps in a single step, so anything done in that way should be able to be done in two step, can give example?

[austere jetty]

This what I'm doing rn, I want to make zero the number 18 [4,3]

There is no number I can multiply to 19 that gives me 18

and I assume is better to avoid divisions

[open saffron]

you can do this row3 - row 4 and then you get a 1 in row 3 for that column and then you can get 0 in row 4 for that column by row4- 18row3

And sometimes fractions are unavoidable

[austere jetty]

hmm i see

i somehow never thought about applying an elemental operation to the row above and then work with that

[austere jetty]

About this question, should the last elemental operation of U, be the first one (reverse) of L?

[open saffron]

Do you mean for LU=A and then using L^-1LU=L^-1U?

[austere jetty]

No, I mean for calculating L

with the identity matrix

[lone heart]

@austere jetty Has your question been resolved?

[lone heart]

@austere jetty Has your question been resolved?

[lone heart]

@austere jetty Has your question been resolved?

[alpine sable]

hi there

Could someone help me with this numerical calculation problem?

Solve using the LU Factoring method the system

[lone heart]

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[alpine sable]

When is multiplying these matrices allowed? Which format does a matrix need to be able to multiply them?

[alpine sable]

just two of them

[honest bloom]

seriously google it. I mean that not angry.

that is a very easy question

[alpine sable]

oh damn thank you

I tried that yesterday but somehow couldn't find anything

[alpine sable]

yup

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[alpine sable]

okay, so it's possible if the the rows in the first matrix are the same amount as the columns in the second matrix right?

[wary stream]

No, it’s columns of the first matrix and rows of second matrix are the same. You have it flipped

[alpine sable]

oops, thank you :)

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[void swift]

I was wondering how to eval this limit?
After I extract the n from the numerator, I'm basically stuck and don't know how to progress.

[alpine sable]

How did you extract n from the numerator?

[devout summit]

Try converting it into limit of Riemann sum format and evaluate using integral.

[void swift]

Here is my work at trying to convert it into a Riemann sum:

By the way, I saw your message in the help channel I used yesterday after waking up, so thanks for that

[devout summit]

Yes. Correct

Now, what is f(x)?

[void swift]

We want to bring that i to the numerator, don't we?

Uhhh, let me try

[devout summit]

Not necessary

$f(x)=\frac{1}{1+x^2}$

[ocean seal]

Euclid31415

[void swift]

Apologies, I am a tad confused. Why/how did you just convert it to this?

Are you indicating that

$x=\frac{i^2}{n^2}$

[ocean seal]

Ev

[devout summit]

$x=\frac{i}{n}$

[ocean seal]

Euclid31415

[void swift]

???

[devout summit]

Yep

[void swift]

I'm confused as to how you just realised that i/n = x though

Like, that didn't come to me naturally

[ocean seal]

Euclid31415

Euclid31415

[devout summit]

Sorry, gtg now

[lone heart]

@void swift Has your question been resolved?

[void swift]

I think I'm beginning to understand, although I still have a question on why necessarily it's that $x_i=\frac{i}{n}$

[ocean seal]

Ev

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[midnight void]

hey guys

i got stuck while trying to compute the limit of this function

could you help me ?

[ocean seal]

Euclid31415

[devout summit]

The first two brackets reduce to 1

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[teal ridge]

i need help with finding the area of the triangles as well as S, i wasnt in when we did it and now im stuck

[lone heart]

@teal ridge Has your question been resolved?

[candid torrent]

wait

which question you need help with 4, or 5

[teal ridge]

area of triangle on 4

and coordinate of s and area of 5

ive never done this lmao

but some of it is logic

[candid torrent]

@teal ridge let's do this one step at a time from the beginning

[teal ridge]

ok

[candid torrent]

there's a line that passes through (9, -4) and is parallel to 3y - x = 2

what does it mean if another line is PARALLEL to another

[teal ridge]

mhhm

[candid torrent]

in terms of there slope

tell me

[teal ridge]

they have the same gradient

[candid torrent]

exactly

so what's the gradient of the line

well

3y = 2 + x

y = 2 + x / 3

[teal ridge]

mhhm

[candid torrent]

y = 2/3 + 1/3x

so the gradient is 1/3

[teal ridge]

yep

[candid torrent]

so we know that our line has a slop of 1/3

so we have

y= mx + b

y = 1/3x + b

so how will we find b

tell me

[teal ridge]

not a clue lmao

[candid torrent]

hint: use the fact that (9, -4) it passes

have a clue now?

[teal ridge]

-4?

im no good at this stuff

[candid torrent]

sub in

x = 9 and y = -4

so sub that into y = 1/3x + b

[teal ridge]

oh right

b=-7

[candid torrent]

don't just skip steps

show me step by step

that's the best way to learn

[teal ridge]

1/3 of 9 is 3

[candid torrent]

-4 = 1/3(9) + b

-4 = 3 + b

b = -7

i want you to show me like that

but yes

you got it right

good job 👏

next part

so next

ii

[teal ridge]

wait a sec let me write it all down

[candid torrent]

we have a nother line l_2

we have some info on it

it passes through (0, 0) and has m = -2

and intersects l_1

so how will we fine the point of intersection

[teal ridge]

mhhm

[candid torrent]

how about

we start by finding l_2

y = mx + b

what should we sub in first

tell me what variable

[teal ridge]

id do the gradient

[candid torrent]

mhm

[teal ridge]

so flipping the other gradient to get 3

[candid torrent]

so what's our equation so far

no

we're given the gradient already

[teal ridge]

what?

oh yes sorry

i was looking at the wrong one

[candid torrent]

AND HAS A GRADIENT OF -2

oh

that's alright

so y = mx + b

what's m

[teal ridge]

-2

[candid torrent]

so y= -2x + b

[teal ridge]

mhhm

[candid torrent]

now how do we find b

(the same thing)

(remember it goes through (0, 0))

[teal ridge]

sub in 0

[candid torrent]

for what varaibles

[teal ridge]

x and y

[candid torrent]

good

so 0 = -2(0) + b

so b = 0

[teal ridge]

mhhm

[candid torrent]

so our equation is y = -2x

[teal ridge]

i did part 1 and 2 and got it right

i just need part 3

[candid torrent]

so l_1 = 1/3x -7 and l_2 = -2x

now for part 3

[teal ridge]

mhhm

[candid torrent]

l_2 crosses the y axis at point C

do you know what this means?

[teal ridge]

thats the y intercept

[candid torrent]

y = -2x

what ist he coordinate

of the y intercept

[teal ridge]

y=0

no wait sorry

[candid torrent]

yeah so (0, 0) is where it intercepts

so graph these equations on desmos

https://desmos.com

and see the triangle it forms

I have to go now

just

you can use Heron's formula to solve for the area

google Heron's formula and try to figure it out

[teal ridge]

k ty

.close

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[amber iron]

not getting the right answer

|dF| / |dF * k| = 2 * 2 / 2z = 2/z

double integral over the region of 2x^2/z dA

conversion to polar --> x = rcostheta, y = rsintheta

z = sqrt(4-r^2)

so $\int_0^{2\pi} \int_0^2 r^3\frac{\cos^2(\theta)}{\sqrt{4-r^2}} dr d\theta$

[ocean seal]

ykj3

[amber iron]

= 8pi/3

still not getting correct answer

<@&286206848099549185>

Anything wrong I did with my substitution? correct answer is 64pi/3, so I'm off by a factor of 2^3

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@amber iron Has your question been resolved?

[lone heart]

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[slate hornet]

I need help finding the angle of flight

[wary stream]

Trig function using the resultant components

[slate hornet]

Tan^-1(y/x)?

I got -3.723

Is that correct

[wary stream]

Yeah, sounds right

[slate hornet]

Thanks

.close

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[sly stream]

Hi can anyone correct what i did wrong im 100%possitive i messed this up and im answering number 1 btw

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[mortal turtle]

I think you may have used the wrong formula. the formula should be $A = P(1 + r/n)^n*t$

[amber iron]

.reopren

.reopen

[sly stream]

Thanks i got it already and i use the correct formula but i didnt do it correctly

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[sly stream]

Thanks for your time💖

[sly stream]

.close

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[supple tundra]

is there an equivalent for the product of two general sequences?

[supple tundra]

Clearly, $\sum({a_n \times b_n}) \not= \sum{a_n}\sum{b_n}$

[ocean seal]

azeem321

[supple tundra]

But is there any formula for this sum?

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[analog garnet]

log _(5)(x)+\log _(5)(x+5)=k Im having trouble finding x

[buoyant kayak]

is that $\log(5x)+\log{((5(x+5))}=k$?

[ocean seal]

a disappointing son

[analog garnet]

sorry that’s the equation

[buoyant kayak]

lol alright

do you know the rule when adding logs with the same base?

[analog garnet]

kinda

[buoyant kayak]

what is it?

[analog garnet]

well no that why im asking ig

but i think you multiply it?

[buoyant kayak]

yep

[analog garnet]

but they have the same base

[buoyant kayak]

yes, which means you can apply the log law

$\log_c(a)+\log_c(b)=\log_c(a\cdot b)$

[ocean seal]

a disappointing son

[buoyant kayak]

from there's it's just a matter of converting from log form to exponential form

[analog garnet]

So I don’t know if I did it

I did the last problem like this

Idk if that is the right steps?

[oak chasm]

@analog garnet You seem to have changed the 5 to a 7 and then the 7 to a 3.

[analog garnet]

oh cause i was watching a video on how to do it lmao

let me redo it sory

[analog garnet]

thats the recent one

[ocean seal]

Chai T. Rex

[oak chasm]

Do those steps make sense?

[analog garnet]

sorta

[oak chasm]

Do you have the logarithm rules?

[analog garnet]

like input should be bigger than zero and stuff like

[ocean seal]

Chai T. Rex

[analog garnet]

no havent learned that yet

well my Prof. didnt go over that

[quaint trout]

You used it here

You combined the logs and multiplied x with (x+3)

[analog garnet]

oh lmao then yea

sorry im kinda retarted rn

[quaint trout]

log_b (y) is the exponent of b that gives you y. In this case, you have
log_9 (x(x+5)) = k
The log is k, so k is the exponent of 9 that gives you x(x+5), i.e.

9^k = x(x+5)

[oak chasm]

Multiplication inside the logarithm turns into addition of the two parts.

[quaint trout]

Thinking more in terms of definition of log than rules

[oak chasm]

I used rules 1 and 7.

[ocean seal]

Chai T. Rex

[analog garnet]

i did that kinda

[oak chasm]

OK, and then you take 9 to the power of both sides.

That's so that you can get rid of the log.

Rule 7 has a log in it.

And it lets you get rid of it.

[ocean seal]

Chai T. Rex

[oak chasm]

Does that make sense?

[analog garnet]

umm

kinda

and this helps me find x right

[oak chasm]

In your problem, yes.

But here, we're only getting rid of the logarithm.

[analog garnet]

ok

[oak chasm]

Logarithms have a base, the little number that's written below and to the right of log.

Like log₁₀₀(x) has 100 as the base.

And then you write that base.

And then you take it to the power of the logarithm.

[ocean seal]

Chai T. Rex

[oak chasm]

See how I wrote the base of the logarithm, and then put the logarithm itself as the exponent?

[analog garnet]

yea

[oak chasm]

Well, now they cancel.

[ocean seal]

Chai T. Rex

[oak chasm]

That's because of rule 7.

And you're left with just x.

[ocean seal]

Chai T. Rex

[analog garnet]

ahh ok

so i plug this in my problem

[ocean seal]

Chai T. Rex

[oak chasm]

What's the base of the logarithm there?

[analog garnet]

9

right?

[ocean seal]

Chai T. Rex

[analog garnet]

ok

[oak chasm]

But since you did that on one side, you have to do it on both.

[analog garnet]

ok

[ocean seal]

Chai T. Rex

Chai T. Rex

[oak chasm]

Then since the 9 matches the base of the logarithm in that exponent, they cancel.

You get x(x + 5) = 9ᵏ.

Does that make sense?

[analog garnet]

yes because they log cancels right?

[oak chasm]

Right, a number to the power of a logarithm with that same number as the base gets rid of the number and the logarithm.

It also works in reverse.

[ocean seal]

Chai T. Rex

[oak chasm]

Notice how the base of the logarithm and the base of the power match there too.

But back to the problem, you have x(x + 5) = 9ᵏ.

[analog garnet]

yea you foil next right?

[oak chasm]

Yes, expand it.

Then get it equal to zero. Then use the quadratic formula.

[analog garnet]

so it would be x^2+5x=9^k

then sub 9 right

[oak chasm]

Almost, subtract 9ᵏ from both sides.

[analog garnet]

ahh ok

[oak chasm]

Then it will be equal to zero.

Which the quadratic formula needs.

[analog garnet]

so would the problem be

x^2+5x-9=0

[oak chasm]

Almost.

x² + 5x - 9ᵏ = 0.

Don't forget the exponent on the 9.

[analog garnet]

ahh yea

ok then i do the (x+) and (x-) right?

[oak chasm]

No, use the quadratic formula.

[ocean seal]

Chai T. Rex

[analog garnet]

ok yea i dont know why i secound guess my self

oh yea ok im kinda remembering rn

[oak chasm]

For later, here's someone who explains logarithms really well: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs.

There's some videos to watch.

[analog garnet]

ok

thank you so much for helping me

[oak chasm]

No problem.

[analog garnet]

.close

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[native willow]

can someone get me started on this one?
i'm not sure how to approach this.
from the L² norm, i have:
║Tn║²=1=∫0,1dx
i think i'm supposed to use bessel's inequality,

i can show:
SUM|<1,Tn>|²=SUM|∫[0,1] 1*(Tn)dx|² <= ║1║²
through bessel, but i'm not quite seeing how to relate this to the inequality in question

also, does the space being of piecewise cont. functions factor into this in any way? why is it given as L²pc ?

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[native willow]

<@&286206848099549185>

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[native willow]

<@&286206848099549185>

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[barren glade]

<@&286206848099549185>

4

im having trouble factor the equation i need some help 😦

[magic geyser]

no ping

ping only after 15 minutos

[devout summit]

$\log_x9=\log_x3^2=2\log_x3$

[ocean seal]

Euclid31415

[barren glade]

oh sorry

[barren glade]

ik still can't factorise it tho

[ocean seal]

Euclid31415

[barren glade]

ohh

got it thanks

.close

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[hollow atlas]

I believe we use generative functions for this

But idk how to even start

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[fervent frigate]

start with n = 1 and substitute 3 to the value of a_0

then you can do the same for values of n>= 1

and you get the pattern

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[candid nova]

I need help on how to do this proof

[candid nova]

what do i begin by

prove E is dense by showing every point in X is a limit point or a point of E?

<@&286206848099549185>

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<@&286206848099549185>

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<@&286206848099549185>

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[candid nova]

<@&286206848099549185>

[candid nova]

<@&286206848099549185>

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[slim sparrow]

hey how do you transform 121/100=1.01^x to logarithmic function

[gray isle]

log_1.01 to both sides

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[cunning anchor]

how to pronounce a/b in english word?

[gray isle]

a over b,
a divided by b
and various other ways

[cunning anchor]

okay

so du/dx -> du over dx?

[gray isle]

no

[cunning anchor]

or du divide by dx

[gray isle]

no

[cunning anchor]

how

[gray isle]

it seems like you're getting into derivative territory

and that would be best represented in words as
the derivative of u w.r.t x

[cunning anchor]

[gray isle]

verbally people could say (in context) the letters d u d x

[cunning anchor]

so it pronounce as d u d x?

[gray isle]

in the right context yes

[cunning anchor]

alright thanks

.close

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[alpine sable]

hello

[alpine sable]

i think its B

but i am not sure

becasue it could be multiple as well

[placid vigil]

[alpine sable]

is this a joke

.close

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