help-28

[lime ether]

do this

solve for the constants A and B

[clever helm]

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[lime ether]

partial fraction

$1 = A(1-y) + By$

[glossy valve]

knief

[lime ether]

let y = 0

then A = 1

let y = 1 then B =1

[clever helm]

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[lime ether]

$\frac{1}{y(1-y)} = \frac{1}{y} + \frac{1}{1-y}$

[glossy valve]

knief

[lime ether]

integrate that bitch

no you can use ln

[clever helm]

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[lime ether]

please use

\

but no

you're forgetting the chain rule mate

[clever helm]

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[lime ether]

yes the one with chains

[lime ether]

second part

the 1-y

has a -

[clever helm]

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[lime ether]

lmao

[clever helm]

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[lime ether]

no

try again

maybe differentiate to see why

also

again

please use \

[clever helm]

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[lime ether]

there ya go

\ln

so its not italicized

[clever helm]

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[lime ether]

oh brother

keep the ||

[glossy valve]

Kenzo

[lime ether]

nice

see

much better

[clever helm]

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[lime ether]

now log rule that bitch

[clever helm]

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[glossy valve]

Kenzo

[lime ether]

bruh

breh

[clever helm]

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[lime ether]

dawg

log(a)-log(b) = log(a/b)

you did this in preschool

[clever helm]

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[lime ether]

you did

[clever helm]

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[glossy valve]

Kenzo

[clever helm]

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[lime ether]

very good sir

now e^

[clever helm]

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[lime ether]

yuh but + C

[clever helm]

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[lime ether]

where?

[clever helm]

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[lime ether]

no

its + c before the e^

the c is supposed to be a constant multiple

Ce^shit

[clever helm]

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[glossy valve]

Kenzo

[lime ether]

nice

now solve for y

multiply that shit over

distribute

put all of the y homies on one side

factor out y

divide by the other dudes

and you're done

[clever helm]

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[lime ether]

which part

[clever helm]

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[lime ether]

exactly

distribute

you finished the first step already

good job

[clever helm]

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[lime ether]

bruh

[glossy valve]

Kenzo

[lime ether]

yes

fire

great job

now on to the third step

[lime ether]

^

[clever helm]

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[glossy valve]

Kenzo

[lime ether]

now the fourth step

[clever helm]

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[lime ether]

well thats just bogus isnt it

[clever helm]

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[lime ether]

i said factor out y

youve just created an entirely new expression

[clever helm]

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[lime ether]

bruh

breh

you can do it

[clever helm]

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[lime ether]

lmao

[clever helm]

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[lime ether]

homie

y(...)

[glossy valve]

Kenzo

[clever helm]

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[lime ether]

nice job kenzo

now what is the next step

[clever helm]

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[lime ether]

wtn

wth

[glossy valve]

Kenzo

[lime ether]

nice

great job

,w y' = 1.2y(1-y)

[glossy valve]

Results provided by WolframAlpha

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Requested by kniefy

[lime ether]

same shit

[clever helm]

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[lime ether]

oh was there an initial condition

its the same thing though dw

notice the - in the exponent

if you divided your entire thing here by e^1.2t youd get a similar structure

we had to solve for C though

[clever helm]

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[lime ether]

look up partial fractions

[clever helm]

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[lime ether]

its still correct

kenzo its not wrong mate

$y=\frac{Ce^{1.2t}}{1+Ce^{1.2t}} \cdot \frac{Ce^{1.2t}}{Ce^{1.2t}} = \frac{1}{\frac{1}{Ce^{1.2t}} + 1}$

[clever helm]

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[glossy valve]

knief

[gritty rose]

Also look up exponent properties

[clever helm]

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[lime ether]

if you solve for C you get 1/9

and the 1/e^{1.2t} becomes e^{-1.2t}

[clever helm]

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[lime ether]

partial fraction

just go look up a derivation

or something

[clever helm]

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[brazen escarp]

Hi I lost my old chat it’s been 7 min but I need help

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Please don't occupy multiple help channels.

[brazen escarp]

I can’t find it bro

What

I need a quick review for my inequalities test

<@&286206848099549185>

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[gritty rose]

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[brittle steeple]

i need help with financial maths

[brittle steeple]

Bob has 300 000 invested at a 5.5% annual rate. He wants to do 4 withdraws per year from year 1 to 5, 2 withdraw per year from year 6 to 13, 1 annual withdraw from year 14 and so on. Every withdraw is done at the beginning of the period. How can i determine the amount he is going to withdraw if every withdraw are equals.

[sacred sparrow]

and where are thee stuck

[sharp lagoon]

I'm not sure how you can determine that from the information given. For example, he's able to withdraw $1 each time without problem. Is he trying to deplete the account to $0 after a certain number of years or something?

[brittle steeple]

is for perpetuity

[sharp lagoon]

OK, but taking out $1 per withdrawal in perpetuity is possible, as is taking out $2.

[brittle steeple]

so at the start of year 14, the annual interest should equal the withdraws, so he can withdraw money forever

[sharp lagoon]

Oh, I see.

[brittle steeple]

it is supposed to be very basic financial mathematics, but with the formulas i learned, i hardly find my way through this

[sharp lagoon]

OK, so what formula do you have for regular withdrawals?

[brittle steeple]

TBH idk if im using the right one

[sharp lagoon]

We can test it.

[brittle steeple]

what formula should i use

i tried and it seems like the amount for the withdraws is too low, so by year 14, the interest on the invested money is higher than the withdraws

[sharp lagoon]

What formula did you try?

[brittle steeple]

i subdivised the work in 3 steps. first step is year 1 to 5. second year 6 to 13, third year 14+
lets do step one :
C ((1-(1+0.01375)^-20)/0.01375) * 1.01375

[sharp lagoon]

OK, what formula did you use that has variables in it?

[brittle steeple]

FVA due

i calculated for each 3 steps and added up the amount of Ps.
from year one to five, i got 17.62P, year 6 to 13.16P, from year 14, i got 18.18P. All Ps add up to 48P.
335 250 = 48 P
6931 = P

at the start of year 14, after his withdraw, he is going to generate way more money with his interets than he is going to withdraw

so its not the right amound. when its perpetuity, you are suppose to withdraw the interest

[sharp lagoon]

OK, so let's call the withdrawal amount w.

[brittle steeple]

in the formula i sent, its P?

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@brittle steeple Has your question been resolved?

[brittle steeple]

i still need help

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@brittle steeple Has your question been resolved?

[brittle steeple]

no but alr

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[grizzled dirge]

How is 5 correc

[sacred sparrow]

notice it's f(f(x))

[grizzled dirge]

Yeh

F(-1) is 0

[sacred sparrow]

yes

[grizzled dirge]

F(0) is

1?

[sacred sparrow]

but if you approach f(x) towards x=-1

then that limit is 2

lim[x->-1]f(x) = 2

regardless of whether you approach from the left or right

[grizzled dirge]

Isnt there no limit

At the

Point

Sharp points = no limit no?

[hollow herald]

Uhh there might be a li'l detail you're missing

[grizzled dirge]

Wat

[hollow herald]

$x \to -1 \implies f(x) \to 2^-$

[sacred sparrow]

why would there be no limit existing for sharp points

[grizzled dirge]

Cuz different slopes

Coming from each direction

[hollow herald]

now lim_{x \to 2^-} f(x) = 5

[sacred sparrow]

it's about the value of the function, not the slope difference

the function doesn't have to be smooth at that point

[hollow herald]

are we talking the same question what

[sacred sparrow]

if you approach f(x) with x->-1 you get 2 @grizzled dirge

[grizzled dirge]

this is the same thing right

But there is no limit at x=1 here why is dat

[hollow herald]

huh? who told you that T-T

[hollow herald]

!nogpt

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Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[grizzled dirge]

Its khan academy

😭

[sacred sparrow]

it's a different topic

it's about differentiability

so the limits of f'(x)

not f(x)

[hollow herald]

"derivative does not exist"

[grizzled dirge]

Ah

[sacred sparrow]

and please don't come with that xd

[hollow herald]

Did you bother to open the link and check the context?

[grizzled dirge]

So limits can be at sharp points

But derivitives cannot be at sharp points

[sacred sparrow]

so just be clear

here the limit is 3 for x->1

and back to the original task

lim[x->-1]f(x) = 2

regardless of whether you approach from the left or right

[grizzled dirge]

Yeah

[sacred sparrow]

k

so now we can look at the limit for f(f(x)) 🐧

[sacred sparrow]

a very crucial point to note here is

that if you approach from the left

you approach the 2 from below

[grizzled dirge]

Mhm

[sacred sparrow]

and if you approach x=-1 from the right

you also approach the 2 from below

which becomes crucial for f(f(x))

ok so f(x) goes towards 2

which means f(f(x)) goes towards?

[grizzled dirge]

f(2) goes to

2 or 5

[sacred sparrow]

exactly, but note the crucial part from before

we approach the 2 always from below

so only from the left side

[grizzled dirge]

So 5

[sacred sparrow]

which means the limit for f(f(x)) is 5

yup

sry gtg

but good luck

🙂

[grizzled dirge]

Thanks

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[ruby helm]

I'm unsure where to begin for this. Can I get a small hint?

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[ruby helm]

<@&286206848099549185>

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@ruby helm Has your question been resolved?

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@ruby helm Has your question been resolved?

[queen verge]

Ever seen this formula?

Here, you can use Y = 1/(1 + X^2)

it is a monotone transformation, so it should be fine

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[brittle cliff]

i dont know how to solve II and III

[brittle cliff]

from II i understand the 1/k part but i cant go further than that

from III i can get to 6/k^2 but i cant process the rest

answer key:

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[next sail]

II is basically like sum of 1/k and that diverges

III is using the limit comparison test

i mean basically the second one is like sum of 1/k^2 which converges

[brittle cliff]

i think i need to study the method again since i forgot how to use it

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[bleak delta]

i need someone to explain to me for every single multiple choice why its right or wrong

[bleak delta]

bc i dont even know how to multiply those matrices honestly

let alone know their rank

also how are you even supposed to compute the determinant, that sounds crazy to me

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@bleak delta Has your question been resolved?

[undone flint]

@bleak delta
Hey

[bleak delta]

yo

ive asked you this before but didnt understand it

[undone flint]

Order of A is (n×1)

The Order of B is (1×n)

[bleak delta]

yes

[undone flint]

Then BA = (1×1)

AB = (n×n)

[bleak delta]

why

[undone flint]

Matrix multiplication rule ?

[bleak delta]

i got no idea what that is

can u explain it real quick?

[undone flint]

Yk right matrix multiplication can only be performed when the column number of first matrix = row of second one

[bleak delta]

oh thats some good knowledge ure giving me

ill write this down to remember it

thx

keep going tho

with the other multiple choices left

[undone flint]

So Rank AB and Rank BA are n,1 or lesser respectively

[bleak delta]

one sec

[undone flint]

So now we need to find det(AB) huh wait a moment

[bleak delta]

i gotta write it and then imma try to understand it

[undone flint]

You can read this page
https://brilliant.org/wiki/matrices/

[bleak delta]

yep yep, u already sent me this

thx tho

anyway, continuing, what about the other multiple choices?

[undone flint]

I'm thinking

[bleak delta]

oki

[bleak delta]

how do you know they are both lesser than 1

for BA i get it

bc its literally only 1 element

but how about AB

how do you know that its rank is lesser than 1

[undone flint]

I wrote N, 1 respectively

AB rank ≤ n

[bleak delta]

oh, so a) is wrong

?

[undone flint]

Yes

[bleak delta]

and b) is right?

ok, ill wait for you to figure out the next multiple choice

[undone flint]

See (AB)² = (AB)(AB)

[bleak delta]

mhm

[undone flint]

(BA)(AB) isn't defined afterall !

BA had order 1×1 and AB is of N×N

[bleak delta]

and also, the book sais that a) is right so

idk what to tell you

[undone flint]

a is right !??

[bleak delta]

yea

my proffessor didnt want to show me this exercise because he said it involves some more complex matrice knowledge

[undone flint]

Is b wrong or something?

[bleak delta]

nope

[bleak delta]

this one is also right

[undone flint]

It says you to point out the incorrect ones

So obviously a is incorrect

[bleak delta]

theres just one incorrect one

[bleak delta]

nope

[undone flint]

Huh !!

[bleak delta]

the rank is not the size of the matrice, its the biggest determinant thats different from 0

idk if that help us in any way but

im just pointing that out

[undone flint]

Ik

Also det(AB) = deta ×detb but these aren't square matrices

So this formula doesn't work !

@bleak delta d is incorrect right ?

[bleak delta]

i mean yea

d is obviously the incorrect one

i saw that first thing when approaching it

[undone flint]

Maybe you would like to take a look into the Cauchy Binet formula !

[bleak delta]

?

why?

what does it solve in this problem?

[undone flint]

The Knowledge is needed to answer this question!

[undone flint]

It solves problems like how you calculate the det

[bleak delta]

i know htat det(AB)=detAxdetB when its a square matrice

if thats what it sais

the hard part is to show that the others are righ

right

[undone flint]

Yes

Cauchy Binet shows us the way to calculate det of product of two rectangular matrices

TBH I don't have much knowledge regarding that, i actually have linear algebra in my next semester !

[bleak delta]

ight sure, ill google it

[bleak delta]

ah

oki

[undone flint]

You can close this channel

And open a new one

[bleak delta]

why

[undone flint]

Coz most people wouldn't be able to see the problem

[bleak delta]

sure, ill try that

[undone flint]

K byee cya !

[bleak delta]

thx for trying tho

cya

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[pale kayak]

How did they get VAR(X) as 2? I used both my classpad and normal writing it down method and got 1.6 or are the answers wrong?

[stiff musk]

show your work

i get 2

[pale kayak]

0.2 * (1-3)^2 + 0.2 * (2-3)^2 + 0.2 * (3-3)^2 + 0.2 * (4-3)^2 + 0.2 * (5-3)^2

I’m new to this topic idk much

[stiff musk]

yea that's the right formula

but if you compute it, the answer is 2

so you must be making a mistake somewhere

[pale kayak]

Ah alright let me try again.

Got it thanks

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[granite bear]

Hello , i am aiming to fix Cii

which is the last question, PAB is a trainagle where A and B is the intersection point of y=15 and the parabola

[nocturne shard]

what is P and what is Ci

[granite bear]

AB length is (2k^(2) +32)^0.5

[nocturne shard]

can you find the distance from P to AB?

[granite bear]

the graph I drew is 100% correct, but i cant prove its less than 40

[nocturne shard]

Denote d(P, AB) be the distance from P to AB
S = 1/2 * d(P,AB) * AB

[granite bear]

Yes I did it and I get an inequality

[nocturne shard]

d(P, AB) is simply y_P - 15

show me the inequality

[granite bear]

I consider to let U and U^2 to be the k2 +16

[nocturne shard]

that's the right approach

move the sqrt(2) to RHS then take cbrt both sides to find u

once u find u, its pretty easy from here

[granite bear]

I find u is 1.019.......

if i find u is a real number, does it mean there is a possibility of area is less than 40?

[nocturne shard]

... no

so, u < 1.019

what did you set "u" to be

[granite bear]

U = (2k2 +32 )^0.5

[nocturne shard]

so that means (2k2 +32 )^0.5 < 1.019

can you simplify this inequality?

[granite bear]

SORRY U IS 3.8387

[nocturne shard]

oh

did you let u = (k^2+16)^0.5?

if so then indeed u < 3.8387

[granite bear]

If I find this inequality has real root, does it mean it is possible that the area is less than 40?

[nocturne shard]

yea

spoiler: ||it has no roots||

[granite bear]

I am really appreicate your help

Yes I find it has no real root too xd

So its a disagreement

[nocturne shard]

yep

[granite bear]

thank you for your help

have a nice day sir

[nocturne shard]

np

[granite bear]

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[shrewd hamlet]

nah u put some brackets in the wrong spots

$(-13) + (-13) \div (-13) \cdot (-13) - (-13)$

[shrewd hamlet]

remember pemdas/pedmas?

[surreal wraith]

So I did 13 x 13

Ye but this is speed math

I’m supposed to do this fast

[shrewd hamlet]

well ur supposed to do it in the order that it occurs

division occurs before the multiplication so u do that first

[surreal wraith]

You multiply first

[full forum]

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[surreal wraith]

Would it be 0

[gentle salmon]

yes

[olive olive]

remember that 9 * 0 is 0

[surreal wraith]

What about this

I got 45

And -18

Got 63 x -20

The. Got -1260

I also need to do this math fast

Meant to be speed math

@olive olive

[olive olive]

so that's -20 * (45 + 18)

which is -20 * (63)

which is -2 * 630

[brisk perch]

@surreal wraith cant you use calculator? (pure curiosity)

[olive olive]

which is -1260

[surreal wraith]

No

[olive olive]

which means you're right

[surreal wraith]

I can but will not

[olive olive]

good job

[surreal wraith]

Not trying to get a belt

[surreal wraith]

Thank you

[olive olive]

@surreal wraith remember that once you're done using this channel you need to type .close

[surreal wraith]

I have some more stuff

So with this

I did 13 x 13 got 166

[olive olive]

firstly (-13)/(-13) is 1

• (-13) is -13

[surreal wraith]

Ohhhh

[olive olive]

so (-13) - 13 - (-13)

then it becomes -13 - 13 + 13

one of the terms cancel out

[surreal wraith]

So 13

[olive olive]

and you're left with -13

[surreal wraith]

To many 13

I’m lost

What do we do with the x - +

[olive olive]

firstly you do the section in red

because of pemdas or whatever acronym you use

[surreal wraith]

So it would be -13

[olive olive]

yes

because the division and multiplication cancels out

[surreal wraith]

So we have -13 +or - -13

[olive olive]

so that becomes (-13) + (-13) - (-13)

are you with me so far

[surreal wraith]

Yes

[olive olive]

good

[surreal wraith]

This makes so much more sense

[olive olive]

now (-13) - (-13)

we know that every number minus itself is 0

so we get (-13) + 0

which is -13 i think

[surreal wraith]

Ok

I’m going to find one like this and see if I get the right answer

I got -8

[glacial dirge]

-4+11+15+11-15-11-15=-8

[surreal wraith]

Ok

[glacial dirge]

Remember -(-13) is 13 and -(13+11) is -13-11

[surreal wraith]

This math is fun

[glacial dirge]

Yeah pretty cool, you got anymore questions?

[surreal wraith]

Taking notes on this

[surreal wraith]

Not for now

But more will come up

[glacial dirge]

Sure, you can dm me if you have issues with these. What grade are you in btw?

[surreal wraith]

Thank you req and @olive olive

[surreal wraith]

8th

[glacial dirge]

Same :))

[surreal wraith]

But you doing pre uni math

[glacial dirge]

Yeah, I take a part in many competitions even winning some. Im currently learning 10-11 grade in american or 3-4 grade in europe. I dont even have to study no more in 8th grade because i won a competition allowing me to pick whatever school i want haha

[surreal wraith]

3-4 in eu?

[glacial dirge]

Im trying to learn calculus soon hopefully

[glacial dirge]

In eu (in poland) we have 8 grades, then we go to other school where 9th grade is 1st grade

And there are 8 grades in primary school and another 4 in highschool

[surreal wraith]

So I have the number

[surreal wraith]

Ohhh

How do I do this fast

I don’t want to waste time

Or space on my page

[glacial dirge]

I mean

[ancient folio]

U could use logic argument

1001 = 1000 + 1

And 123123 = 123000 + 123

[glacial dirge]

Just by looking at it you can see that 1001*123 is 123123

Yeah listen to him not me idk how to explain this one

[ancient folio]

123000 = 123 * 1000

=> 123 * (1001) = 123 * 1000 + 123 = 123000 + 123 = 123123

=> 123123 / 1001 = 123

[surreal wraith]

Don’t get the middle part

[ancient folio]

All math about is just pattern

[surreal wraith]

Ohh

[ancient folio]

Which one

[surreal wraith]

I see it

I just need to look at it carefully

[glacial dirge]

@ancient folio , could you perhaps explain how sigma notation works ?

[ancient folio]

Just a repeater

[glacial dirge]

All the yt vids on this topic sucks

[ancient folio]

Whatever inside the sigma, it get repeat and add into the sum

[glacial dirge]

I mean yeah i get how the easier works

This would be 2+4+6+8+10+12

[surreal wraith]

What is that

[glacial dirge]

But what if i have bigger numbers

[ancient folio]

Yep

[glacial dirge]

Or more complex questions

[ancient folio]

Then u just need to repeat them

Or use a calculator

Since they could do it much faster than u

[glacial dirge]

Or formulas including the sigma notation

[ancient folio]

I dont think there's a generic formula for it

[glacial dirge]

How about negative numbers?

[ancient folio]

Its a math function

[ancient folio]

Same thing

U just need to iterate them

[surreal wraith]

What grade?

[glacial dirge]

Iterate?

[ancient folio]

Evaluate each one of them one by one

[glacial dirge]

So if i wanted to have -1+-2...+-12

Lets say

[ancient folio]

Depend, I study them at grade 5, but I study at school for the gifted

[ancient folio]

Easy

[glacial dirge]

How would it look in sigma notation

[ancient folio]

Look at this

[glacial dirge]

Grade 5? So u were 12

[ancient folio]

Since if i is even, (-1) ^ even return a +

[ancient folio]

No lol, I had a master degree already

[surreal wraith]

Nothing that your saying is making sense

[ancient folio]

While i is odd, then it return -

[glacial dirge]

The letter "i" always scares the shit out of me beacuse the squere root of -1 is technicly i

Xd

[surreal wraith]

I rehate math

[ancient folio]

Consider this one

At i = 1

What do u get

[glacial dirge]

Why are we raising (-1)to the first power

[ancient folio]

Just evaluate it

What do u get

[glacial dirge]

Wait

I am slow af

[ancient folio]

At i = 1, (-1)^1 * 1 = -1

Right?

[glacial dirge]

Yeah

[ancient folio]

At i = 2?

(-1)^2 * 2 = 1 * 2 = 2

[glacial dirge]

(-2)²*2

[ancient folio]

Now i = 3

[glacial dirge]

Why

Wait

[ancient folio]

A bit wrong

-1 doesnt change

[glacial dirge]

Yeah i see

[ancient folio]

We only change the i part

[glacial dirge]

So for i=3

Its

(-1)³*3

Right?

So -3

[ancient folio]

Yep

Here's the final answer

As u can see

[glacial dirge]

.

[ancient folio]

for each iteration, the i switch from being odd and even

[glacial dirge]

I forgot about those ()

(-1)+(-2)+(-3)...

[ancient folio]

Oh

[glacial dirge]

Yeah mb

[ancient folio]

Just put the negative outside

lol

[glacial dirge]

Oh yeah XD

So for i=1

Its -1¹*1

For i=2

[ancient folio]

The sigma return 1 + 2 + ... 12

Then they all get multiple by -1

[glacial dirge]

-1²*2

Right or wrong?

[ancient folio]

Right

[glacial dirge]

Yeah you could also add those ()

[ancient folio]

But u might want to write it as (-1)^2

Cause -1^2 could be misunderstood as -1*(1)^2

[glacial dirge]

I can never find the ^ symbol

What do i do if i want 1!+2!...+6!

For example

I dont even know how to approach this

[ancient folio]

Literally this

[glacial dirge]

Oh yeah

Doesnt seem hard now

[ancient folio]

lol

[glacial dirge]

Could you make a question for me

A bit harder

?

[ancient folio]

Here's one

Find the sigma function that would return this

[glacial dirge]

@surreal wraith remember to close the ticket if you are done **

[ancient folio]

Dont

It will close this...

[glacial dirge]

Yeah ik

But maybe some people are waiting yk

[ancient folio]

Dont u worry

There's at least a hundred empty channels

[ancient folio]

This one is a bit hard if u dont know power really well

[glacial dirge]

Okay so the thing i noticed that all odd numbers are devided

Idk if that changes something

I wrote a sigma function returning 1+2+3+4+5+6 and what now

[ancient folio]

Want some help?

[glacial dirge]

Yeah

[ancient folio]

x^(-1) = 1/x

[glacial dirge]

Yeah ik

I thought about it

[ancient folio]

So 2^(-1) = 1/2

[glacial dirge]

But how do i apply it to odd numbers only

[ancient folio]

Now combine with this

See the (-1) ^ i somehow make odd number to be negative while even is positive

[glacial dirge]

..

Idk

Could you show the answear

[ancient folio]

Here's the answer

[ancient folio]

Its a bit hard for beginner, I wouldnt figgure out if I were u, so just try

Its all about practice!

[glacial dirge]

How old are you btw?

[ancient folio]

I rather not to disclose this

[glacial dirge]

But you study/studied math?

[ancient folio]

Nope

Engineering

[glacial dirge]

Oh ok

[ancient folio]

But I do study abt Numerical Analysis

[glacial dirge]

Whats that, sounds fancy

[ancient folio]

Which is a branch of math dealing with problem using numerical method

[glacial dirge]

Ah i see

Sounds fancy, is fancy

[glacial dirge]

What do you mean you do a study

My english sucks i cant even find proper translations to ts..

[ancient folio]

A lot of mathematic dont consider it real math though

[ancient folio]

Well, my major is in engineering

But I do further study in math (numerical analysis)

[glacial dirge]

Get it

[ancient folio]

Like Im not major at math, but I study it regardless, Im just not that specialize in math

[glacial dirge]

Yeah, yeah

Ur from the usa?

[ancient folio]

Nope

I rather not to disclose it either

LOL

[glacial dirge]

Great, then what topics should i know before studying math

Just generaly not some bs i wont even use

[ancient folio]

Its really depend on whats future path you would choose

[glacial dirge]

Get a phd in math then sit on my ass acting like im smart

[ancient folio]

90% of jobs in this world dont even need the use of calculus

[glacial dirge]

Yeah ik

[ancient folio]

But most highschoolers study it regardless

[glacial dirge]

Nah but honestly id love to have my job connected to math

[ancient folio]

Would u call calculus useless then?

[glacial dirge]

Im in 8th grade, i know the most basic stuff about calculus

I could solce reallyyy simple questions

[ancient folio]

My take is...all knowledge is useful, so nothing is "bs that u wont even use"

[glacial dirge]

Yeah but schooling system sucks here tbh

We get thought a lot of bs in my opinion

[ancient folio]

Self-study then lol

[ancient folio]

Great

[glacial dirge]

Thats what im doing, khan acadamy comes in handy

[ancient folio]

Study string theory. 99.99% of people have no idea what it is, yet 100% agree if u study it, you're smart lol

[glacial dirge]

So what topics from highschool are acctually useful if my studies have something to do with maths

[ancient folio]

Calculus...

[glacial dirge]

Ive read a book on it

By michio kaku

I think so

Wait

[ancient folio]

Honestly, calculus is so fundemental to a point where almost all high-paying job use it

Engineering, Doctor, Economist, Computer Science, etc

They all have to study and use calculus regardless

[glacial dirge]

Whats its useful for?

Calculus*

[ancient folio]

Depend...

[glacial dirge]

So in 1st grade theh teach us that sums are useful for example for counting money

Yk

[ancient folio]

lol

[glacial dirge]

I need this type of explanation lmao

[ancient folio]

Well

For economist, calculus can tell the future market

Whether the price of a stock would go up or down

For engineer, it helps to calculate the action of machines, structures, building, etc

Well

For u, it gets u straight A lol

[glacial dirge]

wdym straight A?

[ancient folio]

Like the score?

[glacial dirge]

my teacher dgaf

if thats what you mean

so i have something simple af like this

and its x to 5th power / 5 + C

right?

@ancient folio

[ancient folio]

U should start with derivative

not integral

[glacial dirge]

why not

dumb question

[ancient folio]

Its abt principal

[glacial dirge]

so derivative of f(x)=5x to2nd

would be just 10x?

[ancient folio]

Yep

U should understand why is that first

U understand the formula

[glacial dirge]

yeah

[ancient folio]

But u dont understand where the formula come from

[glacial dirge]

right

where does it come from

then

[ancient folio]

A bit hard to explain

[glacial dirge]

so i should look somewhere else i suppose

[ancient folio]

Hmm

I could try

to explain it

You need to start with limit

Limit is even harder to explain to a 9th grader

💀

[glacial dirge]

try atleast

[ancient folio]

Is there a public VC in this server?

[glacial dirge]

no

you can call me privetly tho

[ancient folio]

Can u join this

[ancient folio]

💀

[glacial dirge]

wtf is this

[ancient folio]

A secretive VC in this server

Probably for smart people

[glacial dirge]

xd

[ancient folio]

[glacial dirge]

yeah maybe

[ancient folio]

kidding

[glacial dirge]

yh ik

[ancient folio]

VC private then

Im bored

Good way to kill the time is to teaching math

[full forum]

@surreal wraith Has your question been resolved?

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[scenic flame]

In set theory, if A = B, then, is it true that A^C = B^C? where ^C is the complement

[scenic flame]

I can't seem to find a general rule for this, even if I could see that it might make sense

[hot lily]

Yes

[scenic flame]

Is there some axiom to refer to?

Like " law of .. states that .. this is true"

[hot lily]

I feel like this is basic boolean logic that happens to apply to sets

If A = B, then !A = !B

[scenic flame]

yeah I guess I could just show its true by using boolean logic

[stiff musk]

you can prove it using the contrapositive

$A = B$ means $A \subseteq B$ and $B \subseteq A$, which is equivalent to $B^c \subseteq A^c$ and $A^c \subseteq B^c$ respectively

[glossy valve]

Bungo

[scenic flame]

thanks, I can move on from there 🙂

.close

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[storm hinge]

i need help figuring out what i did wrong

[gritty rose]

Why is the upper limit 2

[storm hinge]

ya um because when i set the function i got 0 for one of the bounds and couldnt find the other so i looked at my notes and saw a similar question with 0 to 2

[gritty rose]

Yea that method of copying numbers from similar problems in your notes doesn't always work

You should plot y and see where the intersection and the area to be revolved to find the limit

[storm hinge]

i always have a hard time finding the bounds without putting it into a graphing calculator and im scared that i wont be able to do it on the exam

[gritty rose]

Practice graphing functions

Especially polynomials, logs, exponentials, trig functions, rational functions

[storm hinge]

isnt there an algebraic way to find the zeros? like shouldn't i be able to set the function to zero and solve?

but whenever i do this i always only get one number not twp

[gritty rose]

Yes

It's more obvious if you plot though

[storm hinge]

okay then ill just have to practice memorizing my graphs

okay i got the answer thx

.close

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[sly onyx]

2+4+6+8+10+12+...+8n = 4n(4n+1)

how can I prove it using induction

[honest hill]

do you know how induction works?

[viral jasper]

It's not true, for starters

!original

[full forum]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[sly onyx]

yes I do

but not with jumps

[honest hill]

how is it not?

[sly onyx]

its a bit hard for me with jumps

[honest hill]

wdym jumps?

[sly onyx]

8 *1 != 8
but

2+4+6+8

[honest hill]

whats the base case

[sly onyx]

1

[honest hill]

show that its true for n=1

[viral jasper]

Oh, so for n=1, you are doing (2+4+6+8), and for n=2, you are doing (2+4+6+8)+(10+12+14+16)?

[honest hill]

yes

its to 8n

[sly onyx]

yes

[viral jasper]

I see I see

[sly onyx]

for 1 its 20=20

[honest hill]

LHS is $\sum_{i=1}^{4n} 2i$

[sly onyx]

the problem for me is in n = k+1

[glossy valve]

Bonk

[viral jasper]

Mind showing what you've tried for n=k+1?

[sly onyx]

everything I have tried was wrong

[honest hill]

take n=k, so 2+4+...+8k, then add 8k+2+8k+4+8k+6+8k+8 to the LHS and RHS

does that get you anywhere?

[sly onyx]

give me a sec

[honest hill]

also try going backwards

[sly onyx]

what am I suppose to do in the n = k+1

[honest hill]

you want to get to 4(k+1)(4(k+1)+1)

[honest hill]

you dont take n=k+1

you need to show n=k+1

[sly onyx]

ik

but how

i cant just replace k with (k+1)

[honest hill]

expand this

what does that give

[full forum]

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[vale cipher]

A point is drawn 10 units away from the origin along the terminal arm of the angle 5pi/3. find the x coordinate of tht point

[vale cipher]

im kinda confused

i think its suppose to be easy but im lost

i get that r = 10

its in the 4th quadrent

[honest hill]

make a drawing

[vale cipher]

ya i did

[honest hill]

can you show

[honest hill]

do you know that x=rcos(theta) and y=rsin(theta)?

[vale cipher]

is there another way of doing it

wait

WAIT

BRUH

does that come from

(x/r) = costheta

[honest hill]

do you know how to parametrise a circle?

[vale cipher]

wait i think i got it

so

10cos(5pi/3) = x

[honest hill]

yes

[vale cipher]

5 = x

ah

i got it

[honest hill]

,w 10*cos(5pi/3)

[vale cipher]

thank you lol

[glossy valve]

Results provided by WolframAlpha

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

Requested by .bonk__

[honest hill]

😄

[vale cipher]

tyy

.close

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[brittle fulcrum]

these are the formulas im supposed to use

[dense pulsar]

Hint the trick is to turn the i's into polynomial expressions.

[brittle fulcrum]

like multiply the 2/n to everything?

[narrow ermine]

Take the coefficient out and split the sum into two to get $$\lim_{n\to\infty} \frac{2}{n} \left( \sum_{i=1}^n \left(\frac{i}{n} \right)^2 + \sum_{i=1}^n 1 \right)$$

[glossy valve]

Azyrashacorki

[narrow ermine]

Can you deal with the sums now?

[brittle fulcrum]

yea

[full forum]

@brittle fulcrum Has your question been resolved?

[steel solar]

oh this is a nice riemann sum

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[fresh junco]

been stuck with this for a while
i tried to understand but i always come with the answer that the two variables are correlated as the one thats "NOT CORRECT"

[brazen moth]

can the correlation coefficient ever be larger than -1?

[hot lily]

Can you draw an approximate line of best fit?
Emphasis on approximate; it doesnt have to be exactly correct

[fresh junco]

im sorry i dont quite get it. Do you mean draw a line ?

[hot lily]

Yes

[fresh junco]

something like this?

[hot lily]

Nice

Now, can you give me an approximate slope of that line

[fresh junco]

not sure how to do that 😅
im new to this side of the subject actually ;-; (i come from a financial accounting background)

but let me try

[hot lily]

Also @fresh junco can you draw x-and y axes

[fresh junco]

one min

@hot lily

[hot lily]

x sholud be on the bottom right, but thats fine

[fresh junco]

the slope can be -2? im not sure if im right

[fresh junco]

yeah mb

[hot lily]

Slope can definitely be -2

The slope can be any real number

[hot lily]

Anyways, here is some info about the correlation coefficient: $r$:\
In all cases, $r \in [-1 , 1]$\
If $|r|$ is close to 1, there is a strong correlation. \If $|r|$ is close to $0$, there is a weak correlation. \ If $|r| = 1$, there is a perfect correlation. \

If $r \in [-1, 0)$, there is a negative correlation. \If $r \in (0, 1]$, there is a positive correlation. \
If $r = 0$, there is no correlation.

[fresh junco]

oh

ok ill keep this in mind

[hot lily]

You said this slope is -2. -2 is a negative number, meaning there is a negative correlation between y and x

[fresh junco]

yes

from ur statement there is negative correlation