help-27

[winter patrol]

basic coordinate geometry

[safe fractal]

Okay so this line here is the x axis

[winged oyster]

that exercise from my calculus class D:

[remote sun]

You don’t need calculus for this, try reading the graph, what is g(x)? It’s the green line right, what about g(0) it’s the y value at x=0

[winter patrol]

this specific question requires no calculus knowledge whatsoever

[safe fractal]

So this line I painted in red is the x axis

We need to find where x = 0 is on it

since we're looking for g(0)

if we were looking for g(1), we'd have to find x = 1 etc.

x = 0 is for most intents and purposes at the line's origin, so here

No, moving vertically up or down to the graph of g(x) from this point we will get the value of g(0)

basically "how far up or down do you have to go from x = 0 to reach the green line representing g(x)"

[winged oyster]

up 2?

[safe fractal]

Yup

as such, g(0) = 2

if you had to go down it would be negative

Now as an exercise, what's f(2)?

[winged oyster]

Wait i can

1?

[safe fractal]

Not quite, how'd you reach that?

[winged oyster]

Use the of g(0) g(1) that you mentioned above, In that case x could be 2, to get to the intersection is 1

Is it wrong?, Could you correct me?

[safe fractal]

Let's start from the beginning

we need f(2) right?

So we first need to find x = 2

where is x = 2?

[winged oyster]

??

[safe fractal]

Yes

now, from that point, going up or down we have to reach the graph of f(x)

f(x) is in this case represented by the blue graph

[winged oyster]

Yes

Uhmm

4 up?

[safe fractal]

How come?

Oh, ignore what left or right of this point

we're only going up or down

to hit anything blue

[winged oyster]

Buttt

to The final point?

[safe fractal]

No, ignore that final point up there

Just go up or down from x = 2

[safe fractal]

to hit anything blue

[winged oyster]

Hmmm

[safe fractal]

Only vertically

Look

[winged oyster]

Oh

ok

-2

Yes?

[safe fractal]

You are at the lightgreen point

since that's where x = 2 is

and you are moving along the purple line to reach the blue line

so you get to this

And that point is your value

Yes, it's -2

[winged oyster]

like

[safe fractal]

therefore f(2) = -2

[winged oyster]

Uh

Wait

I always forget the final point, Just vertically until they intersect?

or only in this case

or always like this excs

[safe fractal]

Always just vertically

always

As an exerice tell what f (1), f(3), f(4), f(5), g(2) and g(-2) are

quickly

[winged oyster]

Uh okay

Thanks so much

Really

<3

[mystic scarab]

What are those?

You have to know that perfectly in order to understand and do calculus

[winged oyster]

Ok

Wait for me

im slow for this

[mystic scarab]

You have to make a lot of practice, indeed

Otherwise you'll find a hard time in calculus

[winged oyster]

i know :(

[safe fractal]

Those are my crocks!

[winged oyster]

f(1) = -1, f(3) = 0, f(4) = 2 , f(5)= 4 , g(-2) hmm = 1?

I'm not really sure of g(-2)

[mystic scarab]

Perfect for f, all four are correct 👍

In the same manner, you should also see that g(-2) is not 1 😅

[winged oyster]

How is this calculated?

[mystic scarab]

How did you get all those values of f?

It's exactly the same process for g(-2) 🤷‍♂️

[winged oyster]

Hmmm

So its 0?

[mystic scarab]

Yep

[winged oyster]

Uh

Perfect, thanks!

[mystic scarab]

As a similar exercise, for what value of x is f(x) = 2?

Observe that we now fix the y value at 2

And slide to the left or right until we get to the blue graph of f(x)

[devout snow]

@winged oyster Has your question been resolved?

[devout snow]

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[sterile tusk]

is (AB)^-1 = A^-1 B^-1 if A and B are both matrices

[sterile tusk]

nvm got it

.close

[devout snow]

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[graceful cosmos]

(AB)' = B'A'

For ' meaning "inverse"

[olive snow]

Also A,B has to be invertible and AB defined

[devout snow]

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[crisp mountain]

GIRL HOW DO I EVEN SYART THIS

[abstract zodiac]

Expected to have 12, but if you're talking about real roots strictly then you'll have to find the solutions.

[crisp mountain]

i just need to know the steps on how to do it

[astral lodge]

fundamental theorem of algebra

says that the amount of roots in a polynomial including mult. and complex roots is the highest degree of the polynomial

so, what is the highest degree term in this polynomial

[astral lodge]

read the question

[crisp mountain]

3x^12

[astral lodge]

!noans also

[devout snow]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[astral lodge]

degree

you're on the right track

[crisp mountain]

3

[astral lodge]

(the degree is just the number in the exponent of x)

[abstract zodiac]

nah bruh

[spring salmon]

They put what u said

The term with the highest degree

[crisp mountain]

theyre right the degree is just by itself

[abstract zodiac]

12 is the degree girl

[astral lodge]

!noans

[devout snow]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[astral lodge]

just go away bro

[crisp mountain]

GIRL GET OUT MY CHANNE;

[abstract zodiac]

toxic

[crisp mountain]

ok continue pls

[abstract zodiac]

it ain't your room + i was just trying to help

[crisp mountain]

@astral lodge

[abstract zodiac]

bby

[astral lodge]

well, i mean

[astral lodge]

you have this

he gave the answer twice like a knucklehead so what is the highest degree

[crisp mountain]

3

[astral lodge]

also i'll link the wikipedia page

[crisp mountain]

https://tenor.com/view/btweers-gif-15395315896732285587

[astral lodge]

https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra

[crisp mountain]

OH ITS 12

GNNNN

[astral lodge]

yes

❤️

[crisp mountain]

ok maybne i am slow

[astral lodge]

wrong emoji my bad

[crisp mountain]

i got degree confused w the other thing

[astral lodge]

3 is the coefficient

[crisp mountain]

yes

[astral lodge]

yeeeep

alr gn man

hope you do well on your test/quiz/whatever

[crisp mountain]

wait so 12 is the root...?

like

[astral lodge]

amount of roots

[crisp mountain]

.

so i. have to find all. 12?

[astral lodge]

i suggest you read this

[crisp mountain]

oHHHHHHH

[astral lodge]

skip the jargon

[crisp mountain]

HELPPP MEEEE

[astral lodge]

read the question 😭

[crisp mountain]

sorry girl im slow at math, thank u for the help

[crisp mountain]

PLSSS

[astral lodge]

you're welcome

[astral lodge]

so you got it? or what

if im being an ass just tell me

i am not in the greatest mood rn lol

[crisp mountain]

No I GOT IT

[iron kindle]

!done

[devout snow]

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@crisp mountain Has your question been resolved?

[devout snow]

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[quaint ether]

how to calculate this one

[jade oak]

What have u tried

[quaint ether]

i don't know how to do this one

[vital sedge]

u-sub

[quaint ether]

u = ?

[vital sedge]

u = t/n

du = 1/n * dt

then you have gamma :)

[quaint ether]

so it'S 1

[vital sedge]

yuh

[quaint ether]

nono my bad

now partial int

yeah still 1

thank you bro

.close

[vital sedge]

np

[devout snow]

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[tired kindle]

Help how do i solve this

[vital sedge]

let log2(x) = t and solve for t from there

then at the end, resubstitute and solve for final values of x

[tired kindle]

Like that?

[vital sedge]

ye but you wrote it.wrong

it's t^2 = 3-2t

[tired kindle]

Oh ok

[vital sedge]

now solve for t

[tired kindle]

The power is confusing me

[vital sedge]

alright, you have t^2 = 3-2t right

do you know how to solve equations like this?

forget the log right now

[tired kindle]

Its just moving everything besides the t to the left side right

[vital sedge]

ye it will become t^2 + 2t - 3 = 0

which will give t = 1 and t = -3

and since t = log2(x)

this will give log2(x) = 1 and log2(x) = -3

[tired kindle]

How did u get 1

[vital sedge]

t^2 + 2t - 3 = (t-1)(t+3)

[tired kindle]

Oh yea

[vital sedge]

yeyey

[vital sedge]

understood what i did here?

[tired kindle]

Yea replace the x’s

[vital sedge]

ye, so now
x = 2^ 1 and x = 2^ -3

and thus:
x = 2 and x = 1/8

[tired kindle]

That?

[vital sedge]

Do you understand why x = 2 and x = 1/8

[tired kindle]

Ik why it becomes 2

And

2^3 is 8

And then it has to be a fraction

Because the -3

So 1/8

So basically this is how it goes?

Did i miss anything in my working out

[gray axle]

+2t??

[vital sedge]

you wrote -t instead of -2t in the beginning

[tired kindle]

Wait what

[gray axle]

U have t² = 3 - t

Look at next sentence

[tired kindle]

-2t ?

[vital sedge]

ye

[tired kindle]

Oops

[vital sedge]

how is your camera quality so unbelievably high

anyways yea that's it

[tired kindle]

Iphone12 pro max

[vital sedge]

crazy

[tired kindle]

lol

[gray axle]

Change ur profile

[vital sedge]

why

[gray axle]

Sometimes I see something

At first sight

[tired kindle]

I see a dog

[vital sedge]

me too

[gray axle]

Yes, after u focus

[vital sedge]

???

[restive river]

what did you see before you were focused

[gray axle]

I see the energy theory E = mc²

!done

[devout snow]

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[tired kindle]

Wait did u want me to change the +2t to -2t or the one before that so its 3-2t

Its 3-2t right

[gray axle]

$t^2 = 3 - 2t$ so $t^2 + 2t - 3 =0$

[vital sedge]

look at the original question

[vital sedge]

.

[woven radish]

SELVATOR

[tired kindle]

Ooh ok just making sure

Thanks guys

[gray axle]

!done

[devout snow]

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[tired kindle]

.close

[devout snow]

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[devout snow]

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[amber loom]

I really just need the answer.

[warm lantern]

Unfortunately we're not a ghostwriting service

What work have you done so far?

[amber loom]

honestly none at the moment i just have this question

[vital sedge]

you know the law of sines

use that

[warm lantern]

If you can't see where to use the sine rule, try first determining the angle ABC

[devout snow]

@amber loom Has your question been resolved?

[devout snow]

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[rough ether]

i have to calculate the limit of the series

[upper harbor]

what does C represent here? Combinations?

[rough ether]

yes

[upper harbor]

shouldn't it be k + 2023 C k instead of that? given n C r, n > r

[drifting mauve]

weird notation 😔 i think that is the case

[rough ether]

the C=(k+2023)!/k!*2023!

[upper harbor]

alright

[rough ether]

idk thats how we write it in romania🤷‍♂️

i asked this before and people said to use sumn taylor series which i havent learned yet

someone recognized the answer should be 1/2022 but idk how

he said that the sum of that for k and k+i is 1/i-1

[upper harbor]

oh okay i might be getting something here

[rough ether]

he wrote this

and then vanished

))

[upper harbor]

ye nope i cant do this, hate series

[lunar harbor]

It follows directly by partial fractions after you rewrite the summand as 1/(product of linear factors)

Anyway imma be that guy and dip lol

But here’s this if you end up needing it: https://www.cut-the-knot.org/arithmetic/algebra/BinomialReciprocalsInPascal.shtml

[rough ether]

no worries man the link helped out a lot

thank you very much

.close

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[devout snow]

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[alpine citrus]

How to do d), using calculaor? the answer in 0.09 but i keep getting it wrong

[upper harbor]

what is the formula of standard deviation

[devout snow]

Show your work, and if possible, explain where you are stuck.

[alpine citrus]

We were taught to just input in the calculator for population standard deviation

And idk how to do it for sample standard deviation

[alpine citrus]

we dont use the formula just casio calculator

[elder nova]

sample standard deviation is the same as population except you divide by N-1 instead of N

so you sum (x-mean of x)^2 over all values of x, divide the result by N-1, and take the square root

[alpine citrus]

it's alr someone helped with this

.close

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[devout snow]

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[royal laurel]

Ridiculous

Bullshirt

Fk

[tall knoll]

what is?

[restive river]

what?

[royal laurel]

-65 + 64=1

Not 9

[soft umbra]

[royal laurel]

This is Bullshirt

[smoky gyro]

[royal laurel]

The stingiest

[tall knoll]

,calc 49 + 25

[woven radish]

Result:

74

[royal laurel]

Shirt

[smoky gyro]

gattem

[royal laurel]

You are right

My bad

[tall knoll]

i possess all knowledge

[smoky gyro]

this is why youre helpful*

[winter patrol]

also that'd be -1

[royal laurel]

Do aliens really exist

[smoky gyro]

do*

[tall knoll]

https://tenor.com/view/wouldnt-you-like-to-know-weather-boy-gif-15559185

[smoky gyro]

yes good job

[devout snow]

@royal laurel Has your question been resolved?

[devout snow]

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[devout snow]

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[ionic remnant]

hey bot

[ionic remnant]

how do i do pedmass

[glossy dew]

what do you get from
5 + 3?

5 - 3?

5 * 3?

i think you already know those

[astral lodge]

we are not your servants lil bro

[devout snow]

@ionic remnant Has your question been resolved?

[devout snow]

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[sharp sparrow]

im abit confused on how to match the graphs to the non-linear equation.

[sharp sparrow]

i dont really know where to start tbh

[pseudo basin]

these are all parabolas

[sharp sparrow]

yes

[willow thicket]

i would start by checking where the an eqn's graphs cut y and x axis

[sharp sparrow]

oh yeah i alr did that

[willow thicket]

then it should be alright for these questions

[sharp sparrow]

so do i just sub in the points

[pseudo basin]

think about the vertex also

[sharp sparrow]

or sum like that

.close

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[fringe nacelle]

Hey

[fringe nacelle]

Can somebody help me with 4) please. This is in our Geometric Sequences unit

.close

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[ruby jetty]

Please help me, I can't simplify this

[distant kite]

do you know what things you need to multiply?

[pseudo basin]

where are you stuck with the simplification?

[ruby jetty]

yeah

i know that i have to flip the second one

[distant kite]

yea just do it

[ruby jetty]

I cant get past the (x-4) squared

[lime plaza]

You can write the squared as (x-4)(x-4)

[ruby jetty]

is it then 6(x-4) times 6(x-4)?

[lime plaza]

No

Only (x-4) is squared not 6

so 6(x-4)(x-4)

[ruby jetty]

can you provide a full working out, I don't understand enough because Im only in year 8😭

And if this is on my exam i'm cooked

[lime plaza]

Just write the $(x-4)^2 as (x-4)(x-4)$ and simplify

[pseudo basin]

we don't do that here. you have to share your working and then we guide you for how to continue

[woven radish]

devthemasked

[ruby jetty]

ok i will try

[pseudo basin]

$(x-4)^2$ as $(x-4)(x-4)$

[woven radish]

Ann

[pseudo basin]

you can and should send photos btw

[lime plaza]

Why is your texit white?

[pseudo basin]

configuration setting

[lime plaza]

oh

[ruby jetty]

Haven't started yet

[lime plaza]

Is that a multiplication

[ruby jetty]

oh i forgot the flip

[pseudo basin]

when simplifying a fraction, you should keep the num and denom as products first and foremost, so that common factors may be cancelled out.

[lime plaza]

ok

[ruby jetty]

So do I cancel the (x -1)?

[lime plaza]

Yes

[ruby jetty]

Bottom one is the lastedt

[lime plaza]

why did you multiply (x-4) to 2

[ruby jetty]

Do I keep it factorised

[lime plaza]

You could cancel it

[ruby jetty]

Ok

[kind cairn]

Is this the channel to get help?

[pseudo basin]

this is one of many, and it's currently occupied

get yourself an unclaimed one

see #❓how-to-get-help for instructions

[lime plaza]

Read the instructions and check if you have done all of that

[kind cairn]

ty

[pseudo basin]

,rccw

[lime plaza]

We can factorize more

[pseudo basin]

distributing the six into (x-4) was a bad idea

[lime plaza]

Yes

[pseudo basin]

not fatal, but not very good either

[ruby jetty]

so if I were to revert the distribution, what now

[lime plaza]

Don't multiply the factors

It will cancel

Can you further split 6 into a product which can be cancelled?

So there is a 13 and 2 in the numerator

[mystic scarab]

And most important thing...
don't use × for the product symbol 😅

Otherwise you confuse it with the variable x

[ruby jetty]

I don't quite get it yet but I will send you my working out

[lime plaza]

Ok

[ruby jetty]

This is if I were to revert the distribution

[lime plaza]

,rccw

[lime plaza]

Ok so can you split 6

So it can either cancel 13 or 2

[ruby jetty]

I don't get what you are saying

[lime plaza]

So like

We see there is a 13 and 2 in numerator

We need to like split 6 so basically we can split 8 as 4 * 2 similarly can we split 6

So something gets cancelled

[pseudo basin]

to say the same thing in a somewhat different light

we have already done as much cancellation in the variable part as we could

we're left with (x-4)(x-1) on the bottom and that won't cancel with anything else anymore

so all we are working with are the raw-number factors

i.e. dev is taking you through how to simplify $\frac{13\cdot 2}{6\cdot 3}$ essentially

[woven radish]

Ann

[pseudo basin]

@ruby jetty

[ruby jetty]

ok

[lime plaza]

How do you split 6 then

[pseudo basin]

(and the (x-4)(x-1) just stays there, untouched)

[ruby jetty]

so 26 over 18 (x-4)(x-1)?

[pseudo basin]

mmm

no, you can reduce the fraction 26/18.

[ruby jetty]

oh, then the final answer is 13 over 9 (x-4)(x-1) correct?

[pseudo basin]

yes but this is not how you would write it in plaintext

13/(9(x-4)(x-1))

but as a fraction, $\frac{13}{9(x-4)(x-1)}$ is correct

[woven radish]

Ann

[ruby jetty]

ok thanks!

do i close the channel now

[lime plaza]

yes

[ruby jetty]

.close

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[strong tiger]

just a small question:
can a first order non exact ODE have more than one integrating factors?

[wicked rover]

in general yes

[strong tiger]

i see

thats all i wanted to know i was confused because i got 2 different integrating factors for one DE

thanks

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[low coyote]

A fast search in Google

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[strong tiger]

what does existence theorem means

[fossil locust]

the existence and uniqueness theorem for ODEs

the actual name of this theorem is the Picard–Lindelöf theorem

[strong tiger]

ohh

[wicked rover]

picard is for first order specifically

[strong tiger]

is that the condition for exactness of ODE?

[wicked rover]

no

[fossil locust]

ah that's true

but you can always write any nth order DE as a system of n first-order DEs, linked DEs

[wicked rover]

u should rewrite B as first order DE

[strong tiger]

i dont have it in my notes

[strong tiger]

alright

[fossil locust]

well by 'always' there are definitely some smoothness conditions or something

[wicked rover]

morally correct

[strong tiger]

i dont have anything related to lindelof theorem in my notes

i should look it up

what it means

[fossil locust]

thank my prof for that idea

we came upon this nuance in class, someone asked, and he clarified

[strong tiger]

i should pay attention to my classes 😭

[wicked rover]

its morally correct in numerics

[strong tiger]

i understand it now

[wicked rover]

rewrite as first order system then use ur favorite first order system numerical solver

thats one reason we love hamiltonians

[strong tiger]

the only hamilton ik is the one who drives the race car 😭

i did solve the B part DE

i got y = e^-x^2 / 2

so that would mean i is false

i dont have an answer key so i cant check if my answer is correct what are you guys opinion?

[fossil locust]

I'm busy with other questions

[strong tiger]

oof alright nws

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[placid barn]

!helpme

[devout snow]

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

[placid barn]

I require help with my G.E.D. Studying. Most of the prep tests I find online are straightforward, although they have a few questions that most people I know can't answer.

Since most people I know who have HS diplomas and G.E.Ds can't do the math, I'm curious if the test is solely going to be very basic, and if I'm not overthinking this.

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[devout snow]

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[frozen aurora]

let I be that integral

we get that $I=\iiint_{\mathbb{R}^3} e^{-((x-y)^2 + y^2 + z^2)} dxdydz$

[woven radish]

artemetra

[frozen aurora]

i want to make a substitution like u=x-y

would i have to make some other substitution in order to "compensate" for the y^2 term?

i am not sure how

1. the jacobian would look like in this case
2. how would the bounds change (i presume still R^3 though)

[frozen aurora]

like v = y or something

[fossil locust]

yeah the Jacobian with u = x - y, v = y, w = z

[frozen aurora]

nice that makes sense

[fossil locust]

and yes the bounds are still R^3 because the range of x - y is still all real numbers

[frozen aurora]

oki

[frozen aurora]

and then i can do spherical coordinates on those three

[fossil locust]

yeah so actually good thinking

[fossil locust]

you can still do this and I presume you can use the Jacobian for Cartesian to spherical

$\rho^2 \sin \phi$

[woven radish]

south

[frozen aurora]

yes

$$\implies I = \iiint_{\mathbb{R}^3} e^{-(u^2 + v^2 + z^2)} dudvdw = \int_0^\infty \int_0^\pi \int_0^{2\pi} e^{-r} r^2 \sin(\phi)d\theta d\phi dr$$

oops my bounds

[woven radish]

artemetra

[frozen aurora]

like that

i have no clue how to approach that integral tho tbh

i might wanna switch the order of these but to what

[fossil locust]

by parts for the e^(-r) r^2

[frozen aurora]

true

[frozen aurora]

wait so this equals to

$=\int_0^{2\pi} d\theta \int_0^{\pi} \sin(\phi) d\phi \int_0^\infty e^{-r} r^2 dr$

[woven radish]

artemetra

[frozen aurora]

right

[fossil locust]

yep!

[frozen aurora]

hmmm let me check my result

,w integral e^(-r) r^2 dr from 0 to infinity

[woven radish]

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[frozen aurora]

oh awesome

let's gooo

,w integral sin(phi) from 0 to pi

[woven radish]

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[frozen aurora]

yes

[fossil locust]

ayyyyy you did it correctly!

[frozen aurora]

so this whole thing is 8pi?

[fossil locust]

I hope so

can't be bothered to check

[frozen aurora]

tf

[fossil locust]

but then the determinant is unchanged by any shear transformation

[fossil locust]

yeah so the Jacobian is 1, I'm telling you that is correct

[frozen aurora]

this makes sense but where's the flaw in my method then?

[fossil locust]

um

[frozen aurora]

OH FUCK

[frozen aurora]

it's e^(-r^2)

not e^(-r)

[fossil locust]

OHHHH

I didn't notice absolutely

[frozen aurora]

so sad

it's a trap to make you think you need spherical

[sand dove]

but spherical is a good first idea

$$I = \iiint_{\mathbb{R}^3} e^{-(u^2 + v^2 + w^2)} dudvdw = \int_0^\infty \int_0^\pi \int_0^{2\pi} e^{-r^2} r^2 \sin(\phi)d\theta d\phi dr$$

[woven radish]

rafilou is not not born in 2003

[sand dove]

now of course you can split the integral into a product of 3

[frozen aurora]

oh you can still ibp that right

[sand dove]

and after an ibp

gaussian integral

yay

[frozen aurora]

i don't see how you would arrive at sqrt(pi)^3 from that but i hope you can

question

$\iiint f(x)g(y)h(z)dxdydz = (\int f(x)dx) (\int g(y) dy) (\int h(z) dz)$

[woven radish]

artemetra

[frozen aurora]

does this ALWAYS hold?

oh and the integrals should be definite

[sand dove]

all integrals should be definite yes

also... I realized

no spherical needed

[frozen aurora]

yep

[sand dove]

$$I = \iiint_{\mathbb{R}^3} e^{-(u^2 + v^2 + w^2)} dudvdw = \left(\int_\bR e^{-t^2}dt\right)^3$$

[woven radish]

rafilou is not not born in 2003

[sand dove]

so yippie

[fossil locust]

yeah independence of u, v, w

e makes wonderful functions

[frozen aurora]

alright this is very good to remember

feels like cheating

[sand dove]

mmmh

maybe not all definite but all absolutely convergent

just to be sure

[sand dove]

https://en.wikipedia.org/wiki/Fubini's_theorem

[frozen aurora]

aha i see

thank you!!

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[worn kettle]

I have an issue in linear algebra with transformation matrices, for whatever reason, the problems i do with it SOMETIMES give the right answer, obviously there is something that I am misunderstanding?

[lime plaza]

You didn't need to do that btw you could have asked the question anyway

[worn kettle]

didnt see this msg show which is why i went to another channel, mb

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[pure flower]

how do i solve this? using matrices is preferable i think but if theres anything better im gonna learn

i equate the determinant of the coefficient matrix to zero, which gives me one equation, but i need another

[pure flower]

also yeah this is just a totally theoretical question but i cant seem to find anything helpful

(ping me)

[devout snow]

@pure flower Has your question been resolved?

[pure flower]

<@&286206848099549185> ;-;

[blissful igloo]

do you know about cramers

[pure flower]

yeah i mean... maybe?

clearly not thoguh

just tell me the relevant condition, ill review it again in a bit

[blissful igloo]

so deltaz = 0 and deltay = 0

its lengthy i think

but thats it

you will get 2 eqns in a and b

oh

delta = 0

and delta(z) = 0

[pure flower]

I know the form $Ax=B$, not sure what yours are 😭

[woven radish]

Percy

[blissful igloo]

no

cramers is a method to solve 3 variable equations

it has some theory to it

[pure flower]

hold on

[blissful igloo]

like infinitely many solutions, unique solutions , no solutions

[pure flower]

yeah

[blissful igloo]

so for infinitely many solutions
delta is 0
delta is basically determinant with a1 b1 c1 a2 b2 c2 a3 b3 c3

you should watch a yt video

its easy you will easily learn it

i dont know anyother method

[pure flower]

yep that gets me one

im missing the other

[blissful igloo]

replace coefficients of z with the constants of the equations in the determinant

and equal it to 0

it should give you one more eqn

[blissful igloo]

this is called delta(z)

[pure flower]

hm

okay

ill figure out the theory later

[blissful igloo]

did tou get the ans

you*

[pure flower]

hold on

im not sure i get what you mean

or maybe i just messed up the lin eq

[blissful igloo]

ok ill try wait

[pure flower]

im supposed to find det of:

1 1 6
2 3 a+1
-1 -3 2b

?

[blissful igloo]

that is equal to 0

that determinant is equal to 0

and just open the determinant

you will get one more eqn in a and b

[pure flower]

right then ig i messed up the lin eqs maybe

wait

yeah

idk

f

[blissful igloo]

ok ill give it a try

[pure flower]

;-;

[blissful igloo]

is the ans

a = -2

and b = 10

so 16

[pure flower]

yea!

[blissful igloo]

send your work

you probably made some error while opening determinant

[safe knoll]

btw if u havent learn Cramers or are uncomfortable , u can always just row reduce the augmented matrixx

and use the condition for when ur system has infinite many solutions (when an entire row is just 0s including b column)

[pure flower]

silly mistake got it

$-3+1$ is actually $4$ now

[woven radish]

Percy

[pure flower]

anyway 😭

[pure flower]

i committed a sin and asked gpt and it said something similar

what does that mean, exactly?

[safe knoll]

the * indicate any constant

[pure flower]

that's

something

[safe knoll]

u can probably watch a video on when a Ax=b augmented matrix has a unique solution/no solution/infinitely many solutions

[pure flower]

okay thanks!

ill check it out

[safe knoll]

im pretty sure this is the first thing u study in Linear Algebra (considering u are studying linear algebra)

[pure flower]

i mean not really this is just a high school exam of a buncha shit

thanks though i love you guys

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[loud bluff]

This is washer right? And the big radius is 1+√y right?

And the little radius 1+y^2?

hewp

[north roost]

yes

this is washer

[north roost]

yes

set up the integral

solve it

can u're done

[loud bluff]

Is the big radius also correct?

[north roost]

yes

[loud bluff]

And the bounds are -1 and 1?

Wait I feel like there's a mistake with the bounds

Ohh I got it the bounds are 0 to 1

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[mystic tendon]

This is a more abstract question. I'm working on a info spreadsheet for a game, and I'm trying to work out conversions between two "arbitrary" currencies - what I mean is they aren't tied to anything in real life, so I have to work them out through math alone. How would I go about this?

[wise scarab]

for some conversion rate $c$ and some amount of currency $x,y>0$, if they're related like $cx=y$, then, to go from $y$ to $x$, do $\frac yc=x$

[woven radish]

00100000

[mystic tendon]

I don't have the conversion rate and that's what I'm looking for

I can get some example points of the currency conversion rate, but it involves powers so I'm not sure if it would be useful

[valid silo]

Can you buy the same thing from both of them?

[mystic tendon]

I can tell because the rate isn't "fixed"

[mystic tendon]

nope

[valid silo]

What do you mean?

[mystic tendon]

like 20k of one currency is 1 of the other, but 1M of the first currency is 18.85 so it doesn't add up

theres some kind of conversion where the first currency is exponentially increced by a decimal power and I'm trying to find that power

[valid silo]

Can you send a graph plot of data points?

[mystic tendon]

I can plot out some examples. How many do you need?

Sorry I have to go

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[wise scarab]

if you know that $a$ of currency $x$ is $b$ of currency $y$, then $a=ex$, $b=dy$, so $ex=dy$ and thus $c=\frac ed$ by the earlier form we wanted it to be in

[woven radish]

00100000

[wise scarab]

oh

[devout snow]

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[ancient hill]

I don't understand what I did wrong i got 3/4 as an answer and the answer model got -3. they divided by
x^2 first and then filled in x = pi/2, i just can't see why what i did is "wrong" (filling in x = pi and then factoring out 4 pi squared). Someone help please.

Oh it's question 9b by the way

[inland widget]

3rd line where you calculate f'(pi), you go from (-4)^k to (-1)^k, the way you have rearranged the term is not right. There should be a 4^k term not just 4 on the right hand side

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[umbral raven]

How do I do these questions:

1. ln(2x - 5) = 1
2. 4 + 2ln(x) = 10
3. In(3x+2) - 4 = 0
4. log_10(5-2x) = -1
5. 2log_10(3x) = 4
6. log_3(4x) = 3

They're all solve for x

[dawn violet]

you should learn properties of logarithms

do you know them

[umbral raven]

I do understand them

[dawn violet]

okay did you try applying

[umbral raven]

like

log_bA = x

and stuff?

[dawn violet]

i dont understand that

but yeah stuf like that

[umbral raven]

Okay so for the first one

Would i switch in to e?

[dawn violet]

yes

[umbral raven]

so

e^(2x-5) = 1?

im so confused

[dawn violet]

no no

a=x^b

is the same as

b = log_x a

x being the base

[umbral raven]

so uh

a = 1
b = In
x = 2x-5?

[umbral raven]

i know how to like solve for x cause there's other questions on the worksheet I can do no problem it's just these like 6 that confused me

[umbral raven]

yeah i get that i think

but what does it tell me for #1`

[dawn violet]

what do you think

try applying

[umbral raven]

does it turn into...

2x - 5 = e?

and then

2x = e + 5

x = e+5/2

?

[dawn violet]

2x-5 = e

yes

[umbral raven]

okay and then I j solve for x?

[dawn violet]

yeah

[umbral raven]

aight

i think i got the rest then

apprecaite it thanks

[dawn violet]

:)

[devout snow]

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[devout snow]

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[proven salmon]

u keep flipping a coin until u get HHT. find expected number of flips

[proven salmon]

@runic prawn

Number of flips. does that include the 3 flips u need to get hht

[runic prawn]

yea

[proven salmon]

so is it 5?

[runic prawn]

idk tbh i didn't solve it

how did u get that

[proven salmon]

oops i mean 8 since it includes

Okay so to get HHT is a chance of 1/8 bc og 1/2^3

So average 8 times 1/8

Like if you flip a dice and hope to get 6

[runic prawn]

but the 8 trials are 3 flips each

[proven salmon]

right

...

[runic prawn]

soo it should be 24?

but the trials are not independent

it's a bit more complicated than that

[proven salmon]

I want to build a simulation in excel now to find out haha

I really wish I could figure it out man

that sucks

why so stupid

average was 6,1

[sand dove]

Here's my idea

for each value of n

x_n will represent the number of strings of Hs and Ts of length n that do contain "HHT"

[chilly hornet]

have you learned about markov chains?
Otherwise it's kinda hard to explain the solution

[proven salmon]

No

[sand dove]

markov chain is indeed a good idea too

[chilly hornet]

Is this a problem you're being asked to solve, or did you just come upon it yourself?

[sand dove]

mmh maybe my solution is more complicated

[proven salmon]

No @martingale gave it to me for fun

[sand dove]

bruh

[proven salmon]

yeah

x_n?

[sand dove]

I think my solution's kinda equally complicated (and it relies on the same kinda principle)

so if you wanna go the easy "markov chain" explanation it's alright

[proven salmon]

I want yours

how about both😍

[sand dove]

ok well I'll try my best to explain

the probability that you get HHT in fewer than or exactly n flips is x_n/2^n

afterwards the expected number of flips required will be $\sum_n (1-\frac{x_n}{2^n})$

no wait

[woven radish]

rafilou is not not born in 2003

[sand dove]

other way around yeah

and I'm still not sure frick

[proven salmon]

so n under sigma is ?

[sand dove]

I'm basing myself off of the expectation formula for discrete variables in N

[proven salmon]

like the answer

[sand dove]

$E[X] = \sum_{k=1}^\infty P(X\geq k)$

[woven radish]

rafilou is not not born in 2003

[sand dove]

valid for X having values in the set of natural integers

so if P(X <= n) = x_n

P(X >= n) = 1- P(X <= n-1) = 1-x_(n-1)

ok

$E[X] = \sum_{n=1}^\infty (1-\frac{x_{n-1}}{2^n})$

[proven salmon]

Uhm is this something related to discrete variables in N?

[woven radish]

rafilou is not not born in 2003

[sand dove]

this is specifically for a binomial law

we don't even know the law of X, and I doubt it's that

[proven salmon]

is k=n

[sand dove]

but if it answers your question, a binomial law is a specific type of discrete laws yes

[proven salmon]

ok cool

[sand dove]

uh I don't know what you mean by that

[proven salmon]

here you wrote k

[sand dove]

oh you haven't even encountered sum notation before?

k and n are just mute variables

[proven salmon]

what does k usually mean

[sand dove]

they're just "programmed" to go through all the values in some range

[proven salmon]

it's just like n?

[sand dove]

here k is programmed to take on all (integer) values from 1 up to infinity

and add them all up

[proven salmon]

just like n!

[sand dove]

here I just gave the role to a different letter

[proven salmon]

okay thought I missed something

[sand dove]

$\sum_{k=a}^b f(k) = \sum_{n=a}^b f(n)$

[woven radish]

rafilou is not not born in 2003

[proven salmon]

I do not understand this notation though what is _?

[sand dove]

$P(X\leq n) = x_n$

[woven radish]

rafilou is not not born in 2003

[sand dove]

makes more sense when you type it in latex

it's for denoting what goes in index

[proven salmon]

ooooh

[proven salmon]

okay so how did you arrive here?

[sand dove]

so, believe me when I say this, this formula

Can be obtained from

$E[X] = \sum_{k=1}^\infty kP(X=k)$

[woven radish]

rafilou is not not born in 2003

[sand dove]

you've seen this formula before right

it's just expectation of X

[proven salmon]

No sorry

[sand dove]

with X some random variable that outputs natural integers

[sand dove]

really?

[proven salmon]

I dunno why I havent learnt infinite series

[sand dove]

so how would you find the expected number of flips?

[proven salmon]

I tried a bit in my free time

[sand dove]

don't you have a formula for expectation at least?

[proven salmon]

by figuring it out somehow :/

like this

ah maybe this is a bit unrealistic

[sand dove]

that's probability under uniform distribution

it's P(something)

what about E[random variable]

[proven salmon]

I have nothing on infinite series

I just understand it is an infinite sum

Like i read and understood this https://www.mathsisfun.com/algebra/infinite-series.html

That's where I am at

frick

I lack foundations😭

[proven salmon]

Should we just stop? I think I should learn that first

have a great one

@sand dove Hey you play chess! you're probably like rlly good

[sand dove]

Nah not that much

[sand dove]

Yeah it seems like it's the best thing

You're tasked in the question to find the expected vakue of something

[proven salmon]

Whats you're favourite time?

[sand dove]

But you haven't even encountered expectation yet

[proven salmon]

Yeah I better encounter that first haha

[sand dove]

Rapid

[proven salmon]

I have a problem when learning by myself

like i understand math on the mathisfun website soo easily

they explain every fucking thing

But they only cover basics and it's not enough

and everytime i go on other resources I spend sooo much time not learning anything

Do u have any tips for finding resources that suit you or what should i do?

[proven salmon]

Just say spend more time practicing that is probably the answer anyway

[sand dove]

I know Khan academy is at least quite varied in resources

They also spend a good deal of time explaining each thing

[proven salmon]

I see you're postgraduate

[proven salmon]

What helped you the most (resources) other than in school

[sand dove]

Tbh I haven't gained a lot of math knowledge from outside of school, but I definitely get better at a subject by finding more exercises on it online

I'll have to agree that learning stuff just from online resources is hard

I tried my hand at a few advanced concepts on my own and there's a moment where I just drop out

Reason is, you need to find a good balance between learning theory and practicing with exercises if yourself completely on your own

[proven salmon]

asking people about a subject really helps

okay

[proven salmon]

Is it hard to do exercises with advanced concepts?

[sand dove]

Best thing usually is to get somebody to teach it for you

[proven salmon]

ahhh I have a gap year next year so I won't be able to ask people for help.

Other than discord lol

[sand dove]

The harder a concept is, the more prework in theory you need to put in to even grasp exercises on the concept

[proven salmon]

ok thx. Hope I'll be able to ping u soon to say I finished the problem

.close

[devout snow]

Channel closed

Closed by @proven salmon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• 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.

[woven radish]

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

Lambda

[raven leaf]

basically if you have two different values of your parameters, you have two different points on your contour

in other words, each point is only used at once most

[woven radish]

Lambda

Lambda

[devout snow]

@reef tendon Has your question been resolved?

[devout snow]

Channel closed

Closed by @reef tendon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• 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.

[sudden breach]

Can i get help wid dis

[supple trench]

!showwork

[devout snow]

Show your work, and if possible, explain where you are stuck.

[sudden breach]

i have ua question

[supple trench]

or use any calculator if you wanna get the answer

[sudden breach]

What do i type tho

[supple trench]

,tex
\underline{\large{Geometric series calculator}} \[5pt]
\tikzmath{\a = 1; \r = 2; \n = 6;
\an = \a * (\r)^(\n - 1);
\sn = \a * ((\r)^\n - 1)/(\r - 1);
if abs(\r) < 1 then {\sinf = \a /(1 - \r);} else {\sinf = "undefined";};
}
$a = \a, r = \r, n = \n$ \[5pt]
$a_n = ar^{n-1} = (\a)(\r^{\n - 1}) = \an$ \[5pt]
$s_n = \sum_{i=1}^n a_i = \frac{a(1-r^n)}{1-r} = \frac{\a[1-(\r)^\n]}{1 - (\r)} = \sn$ \[5pt]
$s = \sum_{i=1}^\infty a_i = \frac{a}{1-r} = \frac{\a}{1 - (\r)} = \mathrm{\sinf}$

[woven radish]

vin100

\underline{\large{Geometric series calculator}} \\[5pt]
\tikzmath{\a = 1; \r = 2; \n = 6;
\an = \a * (\r)^(\n - 1);
\sn = \a * ((\r)^\n - 1)/(\r - 1);
if abs(\r) < 1 then {\sinf = \a /(1 - \r);} else {\sinf = "undefined";};
}
$a = \a, r = \r, n = \n$ \\[5pt]
$a_n = ar^{n-1} = (\a)(\r^{\n - 1}) = \an$ \\[5pt]
$s_n = \sum_{i=1}^n a_i = \frac{a(1-r^n)}{1-r} = \frac{\a[1-(\r)^\n]}{1 - (\r)} = \sn$ \\[5pt]
$s = \sum_{i=1}^\infty a_i = \frac{a}{1-r} = \frac{\a}{1 - (\r)} = \mathrm{\sinf}$

[sudden breach]

What the hel is that giant thing

I aint learn that yet

[supple trench]

you can change the input values and test

on #latex-testing

[sudden breach]

12% interest is 0.12 right

[supple trench]

when you're talking about "interest", you need to be clear whether it's

• simple interest
• compound interest
  apart from the
• interest rate
• its corresponding time period is also important
  when i'm looking at "12% interest", i wonder "interest rate 12% per annum"? or that's a monthly interest rate?
  "12% = 0.12"

[sudden breach]

Uh

For this ex question my teach gave

It said interest rate of 12% per year

[hybrid pond]

I would use the compound interest form for this

[sudden breach]

So what if this question says monthly