help-49

[glass gust]

I love questions like these ( keep working dont mind me)

[pearl tulip]

act could u help me out

what should i do from here

?

[glass gust]

ok so

we still have a common factor in the first polynomial

[pearl tulip]

oh yeah

[glass gust]

what is the greatest common factor between 6 and 27

[pearl tulip]

um

3?

[glass gust]

yes

[pearl tulip]

okay

so 3x

is factored out

[glass gust]

so what do we have now

[pearl tulip]

wait

yes i got confused lol

um

give me a sec

[glass gust]

take your time no worries

[pearl tulip]

$3x(2x - 9) 7(2x - 9)$

[grand pond]

probablycrashing

[pearl tulip]

got it?

[glass gust]

yesI believe so

[pearl tulip]

is that right

ok

[glass gust]

but we are not done uet

yet

[pearl tulip]

ya

hmm

wait

[glass gust]

there should be a plus sign between the (2x-9) and 7

[pearl tulip]

2x - 9 = 2x - 9

oh my bad

$3x(2x - 9) + 7(2x - 9)

$3x(2x - 9) + 7(2x - 9)$

[grand pond]

probablycrashing

[glass gust]

what I would do to make this easier is make (2x-9) = a

so now we have

3ax + 7a

[pearl tulip]

wai

wouldnt it be 3xa?

[glass gust]

$3ax + 7a$

[pearl tulip]

instead of 3ax

[grand pond]

POTATO

[pearl tulip]

i see what you did

[glass gust]

both work, but exponents are alphabetical

[pearl tulip]

im just wondering

[glass gust]

not exponents sorry variables

[pearl tulip]

oh i see

wait thats actually really smart

[glass gust]

in standard form, its about the degree and alphabetical

[pearl tulip]

ok i see i see

i got it i got it

3ax + 7a

[glass gust]

so from this expression, what can we factor out?

[pearl tulip]

hmm

and a?

[glass gust]

yes

[pearl tulip]

HOLY COOK

[glass gust]

so what would our expression be

[pearl tulip]

$a(3x + 7)$

[grand pond]

probablycrashing

[glass gust]

YES

[pearl tulip]

OMG

[glass gust]

now remember

[pearl tulip]

OMG

[glass gust]

we set a equal to something

remember to plug (2x-9) in

[pearl tulip]

ya

ya

ya ya

OMG

BRO POTATO

UR A LEGEND

[glass gust]

once you do that, YOUVE FACTORED THAT

[glass gust]

🙏

[pearl tulip]

HOLY COOOOOOOOOOOOOOOOOOOOK

OMG I LOVE MATH

[glass gust]

My class went over that unit last week, and ive done this kinda factoring back in gr 8

[pearl tulip]

THIS IS SO COOL

[glass gust]

ME TOO

MATH :)))

[pearl tulip]

MATH IS MATH !!!!

[glass gust]

math is math

[pearl tulip]

same lol i js lowk forgot it BAD

[glass gust]

lmk if you need any more help regarding factoring

[pearl tulip]

ty bro

[glass gust]

(or any math, depending)

[pearl tulip]

friend request hol on

ty

[glass gust]

🙏

[midnight plank]

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[verbal cairn]

how could I determinate the convergency of the summatory from n=1 to infinite of cos(1/sqrt(n))

[verbal cairn]

I am not able to do the integral test with that function

[green reef]

use nth term test

if a limit of a_n to inf doesnt equal to zero or dne then the series diverges

it cant be used to see whether the series converges tho, only tells u that the series diverges or not

[verbal cairn]

the problem is that

it came with a 1-

[green reef]

yeah so

the limit tells u that cos(1/sqrt(n)) is 1 as n approaches inf

so the limit doesnt equal to zero so

the series diverges

[midnight plank]

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[cedar vortex]

need a hint here

[cedar vortex]

any help is appreciated

I got up until

$\sum _{m=k}^{n }\left(\frac{c\left(n,m\right)}{m!}\sum _{n=0}^m\left(c\left(m,n\right)\cdot \left(-1\right)^{n-m}x^n\right)\right)$

[grand pond]

nosqldb

[cedar vortex]

c(n,m) denotes the amount of permutations of [n] that have m cycles

wait sorry it hasn't been 15 minutes

<@&286206848099549185>

[midnight plank]

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[midnight plank]

@cedar vortex Has your question been resolved?

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[jade raptor]

how do u graph this

[jade raptor]

the one in pencil is mine and thats how i thought i was supposed to graph it but it’s wrong

😭

[opal tiger]

Make a table and plot the points

[jade raptor]

is there a way you could graph it though by seeing how the equation changes the parent function

like how +5 shifts it up five

on the test i wont have a calculator

i mean most of the making a table is simple

w/o a calc

[midnight plank]

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[robust flare]

Can someone explain Q4 b)? I don’t understand how the answer for EFF = 7.1429 and C/Y = 100,000

[nimble copper]

what does EFF and C/Y mean?

[robust flare]

EFF is effective rate and C/Y is compounding per yr

[nimble copper]

well the compounding per year isn't 100,000, it's infinite (that's what continuous compounding implies)

I imagine these are supposed to be inputs into a calculator

[robust flare]

Yes

[nimble copper]

you can stop pinging me now

[robust flare]

I’m sorry!

[nimble copper]

the effective rate is the rate compounded annually, or just 75000/70000 - 1

,calc 75000/70000 - 1

[grand pond]

Result:

0.071428571428571

[robust flare]

Oh, that makes sense

How come it’s 100,000

Is it bc it’s always 100,000

[nimble copper]

i imagine this calculator can't actually take "inifinity" as an input

[robust flare]

Yeah, I don’t think it does

[nimble copper]

as C/Y increases, you get closer to the actual result

[robust flare]

I’m using the BA II calculator

[nimble copper]

so just pick as large a number as your calculator can reasonably deal with

(or just learn how to do it algebraically)

[robust flare]

Do you think using 100,000 all the time would work for C/Y with q’s like Q4 b)?

[nimble copper]

probably

[robust flare]

Or would it depend on the numbers

Like what if I get the same question but with diff numbers

[nimble copper]

i can't imagine it being off by enough to matter

[robust flare]

Would inputting 100,000 for C/Y work

[nimble copper]

try it with 100,000, then try it with something like 1,000 and see if it matters

[robust flare]

Let me try

I get the same answer when I input C/Y = 1,000

Thank you so much for your help! Cheers

[midnight plank]

@robust flare Has your question been resolved?

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[bitter tartan]

help pls i did something but idk if its right so far

[midnight plank]

@bitter tartan Has your question been resolved?

[tulip token]

seems right so far

[bitter tartan]

yeah idk what im doing

[tulip token]

are you confused as to how to solve the equations 2 = c + d and 6 = 4c+d?

oh wait

the red part is wrong

it's 3(2) = c(2)^2 + d

[bitter tartan]

oh i think i see what u mean

hold up

wait

wtf did i do

😭

[tulip token]

okay let's go over some basics

do you know how to solve the equation 2x + 6 = 2?

try solving it

[bitter tartan]

yeah

am i have a slow moment with those or sum

my brain might be working a lil different im tired been doing math for like hours now😭

[tulip token]

okay, what about if you tried dividing by 2 first?

how might you do that?

how might you divide both sides of 2x + 6 = 2 by 2?

[bitter tartan]

like by 2x

i dont think ik how to do that

[tulip token]

okay

do you know what "equal" means?

not just that it's written by = and it separates two sides

but what it actually means

[bitter tartan]

uh

like

the equation on the left

equals the right

like

i was finding x

and if i plug in

-2 back into the equation

it equals the 2

idk

LOL

[tulip token]

no

"equal" means that they're the same

[bitter tartan]

yehah

[tulip token]

like fundamentally that's what it means

[bitter tartan]

oh

LOL

[tulip token]

it aligns with ordinary English

so if you do the same thing to two things that are the same

you reasonably expect that the things remain the same, correct?

like if I take two identical oranges and decide to paint both of them purple in the exact same way

I expect to get identical-looking purple oranges

solving equations is the same thing

[echo dew]

is that her bf

[bitter tartan]

i thought we was doing math why we talking bout oranges🧍‍♀️

[tulip token]

I mean math is literally logic

[bitter tartan]

oh

true

[echo dew]

is that ur bf

[tulip token]

it's not just spamming symbols and saying omg I can do it quick

[bitter tartan]

idk who that is

in just tryna finish my hw

[echo dew]

saccharine is doing fine ignore that guy then

[tulip token]

so if you divide both sides of an equation by 2, you'd expect that it holds true still

[bitter tartan]

yeah i understand

[tulip token]

so if you have 2x+6 = 2, you can write: (2x+6)/2 = 2/2

and then simplify both sides: x + 3 = 1

the reason why I bring this up is that you have written:
4 = 4c + d
4/4 = 4c/4 + d
1 = c+ d

can you tell me what you did wrong here, knowing the information I just told you?

[bitter tartan]

i didnt divide the whole thing by 4

[tulip token]

indeed

in any case, that step wouldn't help much anyway

but it's kinda important not to do invalid steps, because it makes your answer wrong

So going back to the original problem, you have 2 = c + d and 6 = 4c + d, and you need to solve for c and d, correct?

[bitter tartan]

c4/4 is just c but is d/4 d/4 or what

[tulip token]

d/4 is just d/4, unless you want to write it an equivalently fancy way of 1624d/6496

[bitter tartan]

oh

it looks kinda similar

dis feels wrong

[tulip token]

I mean it's fine, just not particularly useful

you have to do a little bit better to actually solve this

also you wrote the part in red wrong again

it should be 2(1) = c(1)^2 + d

again, you have to be careful about what you write

[bitter tartan]

okay what i do wit this now

[tulip token]

as a side note, I'd highly recommend you review some math material on algebra 1 or something like that; if you're in a class talking about continuity and you struggle with things like equations, it's going to be a real struggle

so you want to solve for c and d now?

[echo dew]

i thought they'd be on a foundation year

[bitter tartan]

yeah

dats what i been tryna do

[tulip token]

so you should've learnt how to solve systems of linear equations a long time ago, but I'll go over one method:

if you have two equations:
a = b
c = d

then it is also true that
a-c = b-d

convince yourself of this fact

in other words, you can "add" and "subtract" the equations and you'll still get something that's true

[bitter tartan]

i probably did learn I just forget

[tulip token]

in this case, if you have 2 = c + d
and 3/2 = c + d/4

can you subtract these two equations?

[bitter tartan]

like from each other?

[tulip token]

yes

also spend some time thinking about why you can do this

[bitter tartan]

yes

if I subtract lets say d from 2=c+d itll be d-2=c and i can plug d-2 into c in the other equation to find d?

[tulip token]

you could do that too

that's a different method for solving, but that's fine

[tulip token]

,w solve 2 = x+y and 3/2 = x + y/4

[grand pond]

Results provided by WolframAlpha

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Requested by Saccharine#3780

[tulip token]

seems like you got the right answer for d

now try to figure out c

[bitter tartan]

🥲

that was not

that hard idk why

i struggled

i learned this before

its literally just plugging numbers in and solving

my brain was lagging fr

[tulip token]

you could've started with 2 = c + d and 6 = 4c + d without doing all the division

but good to see that you solved it basically on your own

[bitter tartan]

yeah thanks

.close

[midnight plank]

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[round palm]

Hi, dumb question but if i want to say that there's no linear combination of (vector x) that results in vector b

[round palm]

then i could show that the dot product of columns of A * (vector x) != dot product of solution vector * (vector x)?

[west iron]

You don't know what x is

That equation cannot be untrue for every value of x because when x is the 0 vector it becomes 0 = 0

[round palm]

okay what about (1,1,-1)?

then the left side is 0 and the right side is 1

which is a contradiction?

[west iron]

I don't see how finding a specific value of x that makes the equation false helps

[round palm]

it works though

i found it in some book but it didn't make sense to me rn 😭 so i wanted to like retry understanding it

[west iron]

,w det[[1,3,5],[1,2,-3],[2,5,2]]

[grand pond]

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Requested by a_mog

[round palm]

yeah apparently my result is supposed to show that for the chosen vector x, you have that the vector x is orthogonal to all vectors in the column space of A, but not to the solution vector b

not sure how this generalizes for everything though

[west iron]

well then you would want the dot product to be 0

[round palm]

it is 0

,w (1,1,2) \cdot (1,1,-1) + (3,2,5) \cdot (1,1,-1) + (5,-3,2) \cdot (1,1,-1)

[grand pond]

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Requested by kannaaaaaaaaaaaaaaaaaaaaaaa

[west iron]

ok then yeah that's sufficient

[round palm]

,w (4,5,8) \cdot (1,1,-1)

[grand pond]

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Requested by kannaaaaaaaaaaaaaaaaaaaaaaa

[west iron]

it's 0 with the columns of A but not with b

[round palm]

but it's just one value of x right?

(vector x) but yeah

[west iron]

ok yeah

[round palm]

oh wait is it kinda like a proof

where one contradiction deems the entire thing false?

[west iron]

The idea is basically for any vector y

Ay will always be perpendicular to x

Because Ay will be a linear combo of the column vectors of A

since b isn't perpendicular to x, Ay can't be b

[round palm]

what is x??

oh wait

Ax = b but you consider another vector y

[west iron]

yes the vector <1,1,-1> that you found should not be considered as an input

[round palm]

hmm let me think about it

thanks btw for now

[west iron]

np

[midnight plank]

@round palm Has your question been resolved?

[round palm]

wait Ay is perpendicular to x just because it's a linear combination of the columns of A?

i don't get the perpendicularity part tbh

[west iron]

the dot product of any column of A with x is 0

Ay is a linear combination of the columns of A

[round palm]

is that a fact i should just know?

[west iron]

Wasn't that the specific reason you chose x?

[round palm]

😭 not really, i guess we're not concerned with x at all rn right?

i was thinking something along these lines

if c1,c2, and c3 are column vectors and (x,y,z) is the "vector x"

then we know that xc1 + yc2 + zc3 = b

now i just dot product y on both sides?

so like x( y * c1) + y( y * c2) + z (y * c3) = y * b

but i'm confused cuz i didn't use values of "vector" x here right?

i just used y = <1,1,-1>

[west iron]

you're confused because of me using the same confusing notation you used

[west iron]

Here you talk about a vector x

and now you are calling the vector with those properties y, and you're confused because I called it x

[round palm]

yeah i mean i thought u called it y now?

so i'm calling it y too

[west iron]

no, you switched x and y from what I was doing

[round palm]

right i guess dismissing everything prior

is this argument decent enough?

only problem is the (x,y,z) which i didn't choose

was i supposed to just go with (x,y,z) = (1,1,1)?

[west iron]

(1,1,-1) is rigbt

right

[round palm]

yes but that's vector y

[west iron]

ok sure

[round palm]

i'm talking about like vector x

[west iron]

But you don't choose a specific x

[round palm]

if i don't choose a specific vector x

then this wouldn't evaluate to a number(?)

y*column vectors = number yeah

[west iron]

the point is you consider all vectors x at once

It always evaluates to 0 regardless of what x is

[round palm]

oh x is just scaling that number

wait

yeah okay that makes sense

so the dot product on the left = 0 and the right = 1

[west iron]

Yeah

[round palm]

what's the big picture of this again?

the "algebra" checks out yeah

[west iron]

All possible outputs are linear combinations of the columns

This is a 2-dimensional plane in space which can be defined by the equation <1,1,-1> • x = 0

in other words, it's the set of all vectors perpendicular to <1,1,-1>

by showing y•b ≠ 0, you show b is not in that plane

[round palm]

hmm okay i get it

am i supposed to always find suitable y like this?

[west iron]

idk the usual way is just to row reduce I think

[round palm]

oh yeah to show linear dependence

wait so y is perpendicular to all vectors in the column space of A right?

but b doesn't lie in the column space

okay

[west iron]

yeah

[round palm]

sure thanks

[west iron]

np

[midnight plank]

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[chrome hill]

Logz is single valued function or infinite valued function?

[sinful trout]

depends

if using complex or not

[midnight plank]

@chrome hill Has your question been resolved?

[chrome hill]

Z is complex

[sinful trout]

i think inf valued

[feral sedge]

what does this question mean

[fast igloo]

logarithm of z

[fast igloo]

infinite

because complex numbers can attain values periodically

[tribal temple]

(Unless you’re restricting to a particular branch, as above, complex logarithms are multivalued)

[chrome hill]

So if I say the principal branch

It will be single valued?

[sinful trout]

probably

[midnight plank]

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[neat sandal]

Can someone explain what the process behind evaluating a limit like this would be? The professor wrote it down but I didn't understand it

[neat sandal]

As x approaches from the right what happens to sinx? Do we do it graphically or?

Also how would it differ approaching from the left

[last slate]

sinx becomes 0+

[last slate]

sinx becomes 0-

[midnight plank]

@neat sandal Has your question been resolved?

[midnight plank]

@neat sandal Has your question been resolved?

[ruby wigeon]

the limit doesn't exist there because for our purposes the logarithm is undefined for negative values

as for evaluating the limit, you can use the fact that (sin x)/x is 1 as x approaches zero

$\lim_{x\to0^+}\ln(\sin x)=\lim_{x\to0^+}\ln\left(x\cdot\tfrac{\sin x}{x}\right)=\lim_{x\to0^+}\ln\left(x\cdot1\right)=\lim_{x\to0^+}\ln x=-\infty$

[grand pond]

lifefuel

[ruby wigeon]

informally you can see this as "sin x behaves like x near zero"

graphically:

[midnight plank]

@neat sandal Has your question been resolved?

[neat sandal]

.close

[midnight plank]

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[ruby wigeon]

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[pulsar crystal]

can someone show me steps to compute integral of this , I tried it and I ended with erf(x) , (way advanced for a high school level)
what i'm I missing , how this supposed to be integrated ?

[orchid vault]

Well evaluate xe^{x^2} and -x separately

For the first one, u sub.

[pulsar crystal]

I did

[orchid vault]

Then show what you did.

[pulsar crystal]

okay x(xe^x² -1) is equal to xe^x² -x
integral of x(xe^x² -1) = integral of xe^x² dx - integral of x dx( which is equal to -(1/2)x² )
now we are left with integral of xe^x² dx , suppose u= x²
du = 2x dx
dx = du/2x
now integral of xe^x² dx is equal to integral of xe^u du/2x
simplify by x so we get integral of e^u du/2
which is equal to 1/2 integral of e^u du

I'm sure I did something wrong

but what ?

[orchid vault]

No you didn't.

It's correct so far.

[pulsar crystal]

well (Ironically) what is the integral of e^u du

[orchid vault]

What's the derivative of e^x ?

[pulsar crystal]

e^x

[orchid vault]

...

[pulsar crystal]

🙂 that's beautiful

thank you a lot sir 🫀

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[zealous prairie]

ok so packaged food is 32

and frozen food is 5

32:6 ia the same thing as 16:3

is the answer e?

<@&286206848099549185>

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[plain sparrow]

Anyone available to help?

[midnight plank]

Please don't occupy multiple help channels.

[last slate]

@plain sparrow close either one of the channels

[frail burrow]

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[wide flame]

Hi!! Why does this not work

[runic hamlet]

wdym with "not work"

[wide flame]

like why is that not allowed in math

to do that

[obtuse basin]

It looks like you are misusing a property of logarithms which tells you that ln(a^b) = bln(a); Here you would need the product (3x) to be raised to the power of x/2 rather than x alone

[deep bridge]

What's ur moms name?

[wide flame]

it is raised to the power of x/2 though

[runic hamlet]

the 3 isnt

[wide flame]

oh

okay so

it would look more like this:

hold on

yes!!

thank you!!

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[misty sun]

$(-\sqrt{\frac{2}{3}})^{2} + y^2 = 1$

[grave meteor]

do you want help or are you just experimenting

[grand pond]

Tomi

[misty sun]

I do want help

I just cant

find a way

to show this properly

so this is my equation for the question.

and I just need to solve for y?

correct?

[surreal moon]

What are you trying to find?

Oh. The y coord on the unit circle?

[misty sun]

the missing coordinate(y)

[misty sun]

yes

[surreal moon]

Then this is correct, yes

[misty sun]

so I can just

$\frac{2}{3} + y^2 = 1$

[grand pond]

Tomi

[misty sun]

and then

$y^2 = \frac{1}{3}$

[grand pond]

Tomi

[misty sun]

$y = \sqrt{\frac{1}{3}}$

[grand pond]

Tomi

[misty sun]

@surreal moon is this correct?

[surreal moon]

Oh oops. It's $\frac{\sqrt{2}}{3}$, not $\sqrt{\frac{2}{3}}$

[grand pond]

SWR

[misty sun]

ah

@surreal moon thank you

so then

give me 5 sec

$\frac{2}{9} + y^2 = 1$

[grand pond]

Tomi

[misty sun]

yes

I get it now

@surreal moon thank you for the correction

.close

[surreal moon]

Yes you got it

Just be sure you know the sign of y

[surreal moon]

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[undone ledge]

hi, i'm trying to use a summation formula to do a riemann sum, but i am not getting the same answer as doing it the long way, so obviously i have no idea what i'm doing... n = 5, and it goes into a formula where it's squared... with the i^2 summation formula [N(N+1)(2N+1)]/6 should be (5(6)(11))/2 which is 55... i thought that's already squared, but the 2/5 are not, so -(4*55)/25 + 5n all times the 2/5 but that doesn't work, i tried other things, not getting it, i don't really know what i'm doing wrong

[midnight plank]

@undone ledge Has your question been resolved?

[ancient ridge]

I don't know what you are calculating, but -55 * 8/125 + 10 = 6.48

[undone ledge]

why is it 8/125?

[ancient ridge]

2^3 = 8 and 5^3 = 125

[glass dome]

$\frac{2}{5} \sum_{i=1}^5 \left(5 - \left( \frac{2i}{5}\right)^2 \right)$ \
$= \frac{2}{5} \left( 25 - \sum_{i=1}^5 \left( \frac{2i}{5}\right)^2$ \
$= \frac{2}{5} \left( 25 - \frac{4}{25} \frac{(5)(5+1)(2(5)+1)}{6} \right)$ \
$= \frac{2}{5} \left( 25 - \frac{4}{25} \frac{330}{6} \right)$ \
$= \frac{2}{5} \left( 25 - \frac{44}{5}\right)$ \
$= 10 - \frac{88}{25}$ \
$= \frac{162}{25}$\
$= 6.48$

[grand pond]

Kaisheng21
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[undone ledge]

oh both of them * 2/5 of course 🫠

ok i think i get it

thank you

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[rich prairie]

I've actually got a question regarding constructing a formula for a game I'm working on with js. I've tried a few different approaches but I'm not the most math inclined, making finding a suitor quite the challenge🙏

The formula will be for damage calculation on the event of critical hit. PVP will work as 1v1 between two items, each item having their own unique power level. I would like to construct a formula that calculates a fair damage boost that is affected by the difference in power levels between items. For example, a power level 70 item getting a critical hit against a power level 50 item would get a smaller boost, for a baseless example, 70 > 115, whereas in the event the level 50 got a critical hit, the boost would be greater (for that specific level), another example being 50 > 155.

If two items of similar level face off, the boost would be relatively congruent for both as the level difference would be less. E.g. level 70 vs level 69 with the 70 crit, 70 > 180. Etc.

If anyone is good with constructing formulas any help at all would be appreciated. I'm aware this help request is fairly unorthodox 😁

[main current]

When you say "70 > 115", "50 > 155" and "70 > 180", where are you getting 115, 155, 180 from?

[midnight plank]

@rich prairie Has your question been resolved?

[rich prairie]

Ah, sorry, what I meant by baseless examples were that those numbers weren't based off of any calculations. Rather, they were more guide points to express the type of scaling I'm looking for when it comes to the power boost - They don't have to be met, they were more just for reference 😄

[main current]

You're using > as an output, got it.

[rich prairie]

Oh right it means greater than doesn't it 💀 my mistake

[main current]

Why not just (Defender's level - Crit's level)?

So the boost is lowered by 20 points, when the 70 hits the 50

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[rich prairie]

I considered that at first but I decided it would be best the boost doesn't be less than the initial power level of said item, or that's more of a debuff than a boost. It's also possible to add the difference (between the two items, 20 in this case) onto the items base damage, but that would mean that the closer in levels the items are the lesser the boost would be, which is counter to what im trying to achieve 🤔

[main current]

So you want the boost to be larger as the levels get closer?

[rich prairie]

Pretty much, or rather lower as the levels get further away, as that would allow a more fair experience for lower level players facing off against a higher level player who gets a critical hit

[main current]

But also not symmetric, as you want 70 hitting 50 to be a lower boost than 50 hitting 70

[rich prairie]

thats true.. I suppose I may need a different formula or a way of somehow inversing it in the event of the lower level item getting a critical hit. In terms of coding it, it makes sense in my mind, but mathematically I'm still lost so I apologise if I'm not making too much sense😅 I suppose I just don't have a solid foundation to start off of in determining how the damage boost will function but I only got as far as considering the difference in power levels when trying to build my own equation

[midnight plank]

@rich prairie Has your question been resolved?

[midnight plank]

@rich prairie Has your question been resolved?

[rich prairie]

stop it lil bro 😭

[midnight plank]

@rich prairie Has your question been resolved?

[midnight plank]

@rich prairie Has your question been resolved?

[rich prairie]

<@&286206848099549185> if anyone has some free time ^ 😄

[midnight plank]

@rich prairie Has your question been resolved?

[still sluice]

I’ve got an idea

You could use level * constant * 1/x as your damage function

Because it gets smaller when you increase

Use x then

Oops, I miss calculated

I can change it

Use a normal distribution which has level as it’s center(mean)

Yes like this

$\frac{1}{s * \sqrt{2 * \pi}} * e^{\frac{1}{2} * (\frac{x - l}{s})^2}$

$\frac{1}{s \sqrt{2 * \pi}} e^{\frac{1}{2} (\frac{x - l}{s})^2}$

$\frac{1}{s \sqrt{2 \pi}} e^{\frac{1}{2} (\frac{x - l}{s})^2}$

S is like 4 so

$\frac{1}{4 \sqrt{2 \pi}} e^{\frac{1}{2} (\frac{x - l}{4})^2}$

[grand pond]

TürkNaşko

[still sluice]

And l stands for level

[rich prairie]

I cant say i understand any of that but i will at the very least be able to plug it into my code and do some practical testing 🔥 ill take a look now i appreciate the help

[rich prairie]

Does the value of s change depending on the numbers or does it simply stay as 4?

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[mighty topaz]

3x + 1?

[midnight plank]

Please don't occupy multiple help channels.

[dense idol]

we're really out here asking the same thing 3 times

[mighty topaz]

Wait

Bruh

Yup

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[ruby widget]

Im confused as to how to start this

ive tried some angle chasing

refleced the triangle over EA

and still have nothing

[runic flower]

try circle theorems?

[ruby widget]

i dont know any

which circle theorem do i need

ill just google it and try apply it

[rare cloud]

try joining OD

[ruby widget]

damn that did clear up a lot but i got 5a

instead of 3a

[rare cloud]

lol

check for mistakes?

[ruby widget]

oh wait nvm i got it

thanks

[rare cloud]

yeah idk why is it hard

[ruby widget]

howd u know to join OD tho

[rare cloud]

practice

[ruby widget]

oh okay

look for isosceles triangles?

esp when it comes to circles?

[rare cloud]

all problems might not be solved using isoceles

[ruby widget]

yeah but do u reckon

[rare cloud]

sometimes you need to look at whats goin on

[ruby widget]

that should be something i should

look out for?

[rare cloud]

practice more ig

[ruby widget]

okay

[rare cloud]

you'll understand the nature of questions

[rare cloud]

if yw some questions you can dm me

for opening ur mind

[ruby widget]

sure thanks, thatd be nice

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[nimble matrix]

I have a physics doubt. So there is this equation where T is temperature, ∆T is change of temperature. Tf=Ti(1+alpha * ∆T) ^(1/2) , the right side somehow simplifies to Ti(1+(alpha/2) * ∆T).
Is this correct?

[nimble matrix]

I have not yet studied thermodynamics and the teacher has written this so I decided to ask here, to clarify whether this is correct or not.

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[sand musk]

i need help finding values for X and Y

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[somber tartan]

What would you say why does the y-axis intercept exist in linearn functions?

[obtuse basin]

Because linear functions are always defined at x = 0

[somber tartan]

aight ty guys

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[simple spire]

Find the sum of all the real numbers x, such that 5*floor(x) + 21{x} = 521

[simple spire]

i just need someone to check if my solutin is correct

floor(x) is an integer, so 521-21{x} = 0 (mod 5)

21{x} = 521 = 1 (mod 5)

so {x} = 1, 6

solving for x, x = 100.1 and 79.6

the sum is 179.7?

<@&286206848099549185>

[simple spire]

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[orchid gazelle]

we could also just use quadractic formula to get the answer right ?

[orchid gazelle]

instead of doing all that

or is there any other way for splitting up the middle term

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[thick shoal]

f(x+y) + f(x-y) = 2f(x)f(y)

[thick shoal]

looking for insights, not a solution

f(x) = 0 works

for all other functions ive worked out f(0) = 1

the function is even

and f(2x) = 2(f(x)^2)-1

im stuck now

[thick shoal]

also lim x -> infinity of f(x) = 0 is given

<@&286206848099549185>

[midnight plank]

@thick shoal Has your question been resolved?

[thick shoal]

yo pls anyone <@&286206848099549185>

[worthy bramble]

I don’t know how to help this tbh

It look like it come out of no where

I have no context what it is

[thick shoal]

its from an imo long list

i wanna learn how to solve imo problems

apparently you are meant to use contradiction to show f(0) cant be 1

[novel estuary]

Can you explain the question properly

[midnight plank]

@thick shoal Has your question been resolved?

[thick shoal]

f(x+y) + f(x-y) = 2f(x)f(y)
lim x -> infinity of f(x) = 0
what are all functions f:R->R

[still sluice]

I will think but if you write like it’s equal to zero, it’ll be easier to read

$f(x + y) + f(x - y) - 2f(x)f(y) = 0$

[grand pond]

TürkNaşko

[still sluice]

$\lim _{x \to \infty } f(x) = 0$

[grand pond]

TürkNaşko

[still sluice]

$f(x) is an even function$

[grand pond]

TürkNaşko

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[neat mauve]

hi can someone give me a hand looking at some summation rules?

[neat mauve]

specifically if someone could just look at these two pieces and check for correctness

i can explain further on my thought process and stuff if anything is unclear

<@&286206848099549185> if anyone is available!

[midnight plank]

@neat mauve Has your question been resolved?

[neat mauve]

<@&286206848099549185> sorry, just checking again if anyone can help with this

[still sluice]

Hi

Your graph is true

Just

$j = e^{n \ln{4}} = 4^{n}$

[grand pond]

TürkNaşko

[still sluice]

I could show you how you can

You said an idea of this right

$\frac{\ln{j}}{\ln{4}} = n$

Right?

And you could set it to n

[grand pond]

TürkNaşko

[still sluice]

And then you can bring ln(4) to the other side

[neat mauve]

so my original sequence is
j = 4, 16, 64, ..., n
but i want j to increase by 1 not by a factor of 4

[still sluice]

$\ln{(j)} = 4 \ln{(4)}$

Wait when I get n

[grand pond]

TürkNaşko

[still sluice]

Raise both sides to e

[neat mauve]

so i did
$\ln(j) = \ln(4)^{1}, \ln(4)^{2}, \ln(4)^{3}, ..., \ln(n) \Longrightarrow \ln(j) = (1)\ln(4), (2)\ln(4), 3\ln(4), ..., \ln(n) $

[still sluice]

This happens so you could set your j to n if you want natural numbers

[still sluice]

You did leave a blank at last dollar sign

LaTeX is glitchy at usage of dollar signs

[still sluice]

They are true

$\ln(j) = \ln(4)^{1}, \ln(4)^{2}, \ln(4)^{3}, ..., \ln(n) \Longrightarrow \ln(j) = (1)\ln(4), (2)\ln(4), 3\ln(4), ..., \ln(n)$

[grand pond]

TürkNaşko

[still sluice]

It should work

Did it work

[neat mauve]

oh yea it did

[still sluice]

I could miss something but I think this is a true way to do it

[still sluice]

I saw your n here

[neat mauve]

okay i see, thank you! i just wanted verify if i was following the rules of ln and summations

[still sluice]

Thanks, I’m a math programmer too lol

[neat mauve]

oh perfect lol thanks for looking then i appreciate it!

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[snow niche]

I tried using asymptotic estimates but I get it wrong

[grave meteor]

You might need to use lhopital or Taylor series expansions

[snow niche]

Why ?

[kind zealot]

What are you getting

[snow niche]

+infinity

The result should be 6/7

[lethal lava]

Wait it is wrong somehere the last step would give -6/7 as final ans

[snow niche]

What you use to do that

[lethal lava]

Like what step we are taught to find limits like that

I can send you complete steps if you want but i cant see where I am going wrong

[snow niche]

Noteble limits

[lethal lava]

Yeah we are told to remember limits of some forms like thats why i generated( epower x -1)/x in the denominator

Except here that x is x²

Similarly x-sinx/x³ would give 1/6

You can derive them individually though by using expansion or L hospital

Are you sure its not -6/7 ?

[dense idol]

wolfram gives -6/7 btw

[lethal lava]

Ya thats what i am getting at the final step that ln(1+x)-x/x² would give -1/2

[midnight plank]

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[twin ridge]

Can someone double check this for me please

[twin ridge]

I'm fairly sure it's right, just wanted to get a second opinion since it's due today.

[midnight plank]

@twin ridge Has your question been resolved?

[surreal moon]

Looks good

@twin ridge

[twin ridge]

Cheers

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[visual tiger]

the result is good

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[drowsy thunder]

am not sure how to approach this question

[midnight plank]

Please don't occupy multiple help channels.

[drowsy thunder]

i tried f(2)-f(1)/2-1

and got 7

[last slate]

What is the integral of x^3?

[drowsy thunder]

i just started calc 1 and have not gotton that far

[last slate]

?

[drowsy thunder]

i have not learnt integrals

[last slate]

Is this differentiation

[drowsy thunder]

i dont think so

[last slate]

What

2 1/2 is the answer right?

Let me check smth

[drowsy thunder]

yes

[last slate]

@drowsy thunder

I think this is mean value theorem

Have you learned this yet @drowsy thunder

[drowsy thunder]

oh

ok i will try it

[last slate]

@drowsy thunder

[drowsy thunder]

ye

am still working on it

[atomic magnet]

didnt you try this alr though by doing [f(2)-f(1)]/(2-1)

[last slate]

Shouldn't take this long

Are you confused?

[drowsy thunder]

ye

[last slate]

@atomic magnet

[drowsy thunder]

do i find the derivitive of f(2)-f(1)/2-1

[atomic magnet]

hi

[last slate]

Can you help them.

[atomic magnet]

hmm

[drowsy thunder]

it ok

i think i got it

thx

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[tacit jackal]

I am not sure why it yields u ^ - 1/2

[nimble copper]

do you accept that $\sqrt u = u^{1/2}$?

[grand pond]

Steakanator

[tacit jackal]

sqrt(4) would be 2, 4^(1/2) gives 2 as well

I suppose I do actually

[nimble copper]

well that's what sqrt means so I hope so

so you combine this with the fact $u^{-1} = \frac 1u$

[grand pond]

Steakanator

[tacit jackal]

ah ye

i see it now

[nimble copper]

mix em together and you arrive at your destination

[tacit jackal]

makes sense, that was stupid

thanks for explaining!

!solved

whats the command?

[vestal trellis]

close

[tacit jackal]

!close

[nimble copper]

.close

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[mint flare]

too hard for me pls can someone explain (√17x13-√17/13)/√17/13

[mint mauve]

0.99408284023

[mint flare]

how

[mint flare]

i think i wrote it wrong wait

anyone pls explain to me

how to

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[waxen silo]

could someone teach me what I am suppose to do here

[waxen silo]

I am currently revising and I have no idea what I am suppose to do

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[unreal osprey]

How do I start with number 3

[surreal moon]

Graphing might help

Or just examine limits on the left on right.

[unreal osprey]

How do I put it in graphs?

[wet pollen]

Just enter the expression sans the limit part into a graph as a function.

[unreal osprey]

For number 2, should I continue on checking if it is -inf or +inf? Or it's just DNE?

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[waxen silo]

can someone help me understand what I have to do here, I am currently revising and I don't know where to start

[waxen silo]

just 1a will be enough

[hearty rune]

break it up, do you know how you would show 0<=y?

[waxen silo]

sorry for the very late reply, I kind of forgot everything abt this so no

<@&286206848099549185>

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[orchid gazelle]

Isn't that supposed to be -2ab ?

[orchid gazelle]

Or am i missing something ?

[hearty rune]

,rccw

[hearty rune]

no

(a-b)^2=a^2-2ab+b^2
(a+b)^2=a^2+2ab+b^2
so
(a-b)^2=(a+b)^2-4ab

[orchid gazelle]

Wait lemme show what i got

[hearty rune]

you seem to be under a misconception

[orchid gazelle]

Ow

[hearty rune]

a^2+b^2 is not equal to (a+b)^2

[hearty rune]

as i showed here

[orchid gazelle]

Oop lol

[orchid gazelle]

I see i see

How is it 4ab though

[hearty rune]

look at the two equations i wrote

to get from the second equation to the first, you would need to subtract 4ab

which is where the 3rd equation came from

[orchid gazelle]

Owh i see i see

[orchid gazelle]

thank u for the help just watched a proof video of it

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[mossy dawn]

The radius of a cylinder pipe 2m long expands with heat at a constant rate of 1.2 x 10^-3mms^-1. Find the rate at which the volume of the pipe will be increasing when the radius is 19mm.

[mossy dawn]

using v=pir^2 x h, I can't find dr/dt

[surreal moon]

It was given to you

[mossy dawn]

isn't it just 1.2 x 10^-3mms^-1

[surreal moon]

Yes

[mossy dawn]

but then when I apply it to pir^2 x h, it becomes 2000pir^2

so wait no.

what I mean is that they go from v=pir^2 x height to V= 2000pir^2

and they they find its derivative and do exactly as I understand.

it is just like where does the 2000 come from

oh wait.

I get it

2000mm is the cylinderical height as part of the formula!

sorry, I misunderstood

thanks

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[surreal moon]

👍

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[vague reef]

I do not understand this proof

[vague reef]

The hypothesis states that $\ge n$ pigeons are distributed among k holes.

[grand pond]

schrödinger

schrödinger

schrödinger

[vague reef]

<@&286206848099549185>

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[uneven sandal]

if I have a sequence of functions on a compact set and the limit function is continues is the sequence then uniform convergent?

[uneven sandal]

the sequence of functions can also be continues

if thats needed

[surreal moon]

So like $S_n(x)$ are all continuous, and you want to know if $\lim_{n\to\infty} S_n(x)$ is uniform convergent?

[grand pond]

SWR

[uneven sandal]

suppose $S_n(x)$ are all continues and $\lim{n\to\infty} S_n(x)$ is also continues on a compact set K, does this imply $S_n(x)$ being uniform convergent?

[grand pond]

tobi

[uneven sandal]

its just my intuition and it feels correct

Idk if it is tho

[surreal moon]

I was just talking about this yesterday. I think it is yes also, but I'm not certain. Sorry.

[uneven sandal]

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.reopen

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✅

[uneven sandal]

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[plain phoenix]

Hello there! ☺️ I would like help in understanding the solution to a problem on the topic of continuity of functions. I'm learning a bit of calculus on the side as a hobby because I always thought maths was cool but was really bad at it in high school

[plain phoenix]

the problem is: Let D = {x_1, . . . , x_n} a finite subset of R. Prove that every function f : D → R is continuous

and the solution: Let x_i ∈ D, and let (a_n) be a sequence in D that converges to x_i. Let e_i be the minimum distance between x_i and all x_j ∈ D with j /= i. Then e_i > 0, and (a_n) has an end piece that lies entirely in U_ei (x_i). However, only x_i lies in U_ei (x_i)∩D and it follows that the sequence (f(a_n)) has an end piece (f(x_i)). Therefore (f(a_n)) converges to f(x_i), i.e. f is continuous in x_i. In the special case D = {x_1}, (a_n) is constant and therefore (f(a_n)) converges to f(x_1).

(the e is supposed to be an epsilon)

the part I'm not understanding is why the intersection of U_ei (x_i) and D is only x_i, if almost all sequence members of (a_n) from D lie in U_ei (x_i) and why it would then follow that (f(a_n)) has an end piece (f(x_i)). I would really appreciate if someone could explain it to me!

[runic hamlet]

what else should be in the intersection

[plain phoenix]

the end piece, no?

[runic hamlet]

lets say D={1,2,3,4,5}

you want a sequence of them that converges to 3

how can that sequence look like

[plain phoenix]

I suppose just 3

[wary thorn]

@runic hamlet isn’t it easier to do this without sequences?

[plain phoenix]

f(x) = 3

[runic hamlet]

well sequences or eps delta, boils down to the same idea

[runic hamlet]

well, it could also be 1,2,3,4,3,4,5,3,1,2,3,4,3,3,3,3,3,3,3,...

[wary thorn]

Take the minimum distance between two of the points (divide it by 2)

[runic hamlet]

but the point is, eventually it will have to be constantly 3

[plain phoenix]

ah, fair enough!

[wary thorn]

Now if you make a delta ball of that radius around any point, none of the other points will be contained in it

[plain phoenix]

yeah, I'm with you

[runic hamlet]

and thats exactly what they are doing in the proof

if the sequence converges to 3, then eventually for eps=0.5, all entries of the sequence have to be at most 0.5 away from 3

but the only viable point which is 0.5 away from 3 in D, is 3 itself

[plain phoenix]

is saying that e_i (= 0.5) is the minimum distance the same as saying that all entries are at most 0.5 away?

[runic hamlet]

well in this case the min distance would be 1. I assume your book is working with open balls

and therefore takes the min distance directly. instead of something like e_i/2

but then the intersection U_ei(xi) and D are the points in D which are less than e_i away from x_i

(at least thats what I am guessing the U notation means for you)

[plain phoenix]

the way I learnt it, the intersection of two sets A and B is the set of elements which are contained in both

[runic hamlet]

yes

[plain phoenix]

I just started learning about convergence yesterday, so this is all very new to me. I don't know anything about delta or open balls