help-27

[primal gyro]

I forgot we're thinking big not home

[restive river]

💀

ya so youre right about this but you have to make sure just to check that the denominator doesnt do some finnicky stuff

like becoming 0

like you have to make sure that the denominator never becomes 0 for any n ever ever

[primal gyro]

ooh like n/(n^2 * 0) still be infinity

[restive river]

uhh that'd just be indeterminate

[primal gyro]

ooohhh i see

[restive river]

cuz infinity * 0 is indeterminate

[primal gyro]

ah okay

[restive river]

you dont want indeterminate expressions if you're saying that the result is ALWAYS 0

[primal gyro]

mmm amen brother

[restive river]

what i mean is that because it's /9 the cosine values never become 0

so you're chilling

[primal gyro]

wait what does the /9 have to do wiith this?

[restive river]

cause any number over 9 like 1/9 or 5/9

cos of that is never 0

cos is 0 for cos(pi/2), cos(3pi/2) and stuff

if you had an even number though you'd run into issues

like if you had /10

then 5/10 would become 1/2

and cos(pi/2) = 0

so you'd run into situations where the denominator is indeterminate with infinity x 0

[primal gyro]

did i do this wrong

[restive river]

kinda hard to explain but basically you're just checking to see if the denominator will ever be 0

wait

did you put pi

hmm

am i tripping

[primal gyro]

bap

isnt it bc like

[restive river]

nah i was right

[primal gyro]

o

[restive river]

wait

tf

wait yeah

im having a schizo moment

[primal gyro]

wait now imm confuzzled

[restive river]

the cosine graph touches 0 yes but you're only checking integer values of n

because it was a summation

the indexes only move up by 1

at a time

[primal gyro]

WAIT THEY DO?

WTF

[restive river]

wdym

[primal gyro]

they like

only move up by once at a time???

[restive river]

well usually in sums

[primal gyro]

I thought summation was like the ultimate god tier bombard where it hits every possible number to infinity

[restive river]

uhh it does just one at a time

[primal gyro]

huuuuuhhh

so what if it was summation to infinity as n = 0.5

then cos would eventually equal 0 and indefinite and the world falls?

[restive river]

like this sum if you wrote it out (expanded it) it would be cos(1pi/9)/1 + cos(2pi/9)/2 + ...

[primal gyro]

riiight i see

[restive river]

i dont know how that would work lol

[primal gyro]

ahh i see

[restive river]

i mean yeah i get wht you're saying

you're right if that happened

[restive river]

in that case you would try to use a different test

[primal gyro]

ahh okay

just out of curiosity would you take it to le hospital

[restive river]

wait no nvm i think because it becomes indeterminate sometimes the limit just wouldnt exist

[primal gyro]

ohh right okay

[restive river]

wait no it would be infinity

bruh

im high

sorry

[primal gyro]

limit of 1/0 is inifinity?

[restive river]

yeah

[primal gyro]

ohhh okay

[restive river]

not limit

just sum

i mean

1/0 by itself

[primal gyro]

incredible

nothing turned into everything

[restive river]

uhh idk i dont think that's good you can't make progress with that

[restive river]

sorry

[primal gyro]

how does the sum of 1/0 infinity

[restive river]

if you tried lhopital, you would get sine on numerator and product rule on denominator basically end up with the same shit that you started with just with sines instead of cosines

[primal gyro]

riiight makes sense

[restive river]

i mean

wait

ill just write it out

just saying but

you cant do l'hopital if its not 0/0 or infinity/infinity

[primal gyro]

ohhh good to know i thought you could always just do it

[restive river]

oh fuck sorry

wtf

@primal gyro sorry im so high rn

[primal gyro]

np loll

[restive river]

for the .5 thing

i think you'd still end up with indeterminate

idk wtf im tripping

[primal gyro]

ooooh ya makes sense

1/0 equalls

[restive river]

1/0 is infinity

[primal gyro]

oh

[restive river]

but you have like cos(...)/(0 * infinity)

0 * infinity is indeterminate

[primal gyro]

ohh right okay

[restive river]

i mean in your .5 case

if you ever have an n that's divisible by 4.5

n would be infinity and cos (npi/9) would be 0

@primal gyro sorry for the confusion, just forget this, the point was just to check if the cos in your denominator was ever 0

[primal gyro]

ahh okay

Thank yall!!

.close

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[restive river]

btw if youre confuseed about the going up by 1 at a time the ratio test asks for a_n+1/a_n

it's always going up in whole numbers

no decimals

[devout snow]

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[kindred yacht]

hi

[kindred yacht]

Its The First time I Am Solving Quadratic Equations. Can Somone Explain me How To do so?

btw this is Singapore Math

[rose wyvern]

they are already solved tho

[kindred yacht]

i dont think so

[rose wyvern]

for e.g. in (a)
x = 0 or x = 7

[kindred yacht]

these are the answers

[kindred yacht]

do i have to write both in the exam??

[rose wyvern]

yes

[kindred yacht]

how do i solve it

[rose wyvern]

if axb = 0
either a = 0
OR b= 0

[kindred yacht]

what about the x=7?

[rose wyvern]

a = x
b = x-7

[kindred yacht]

i still dont get it

[feral agate]

Either the factor (x) = 0 or the factor (x-7)=0

Each of those correspond with one solution each

[proud adder]

So we have x(x-7) = 0
We have to get rid of the x outside of the brackets, so for that we can divide both sides by x, so we will get
x-7 = 0/7 which is simply just 0

[feral agate]

Wrong

You can’t divide both sides by x

[proud adder]

?

[proud adder]

Why?

[feral agate]

Because you can only divide both sides by a non-zero number

You don’t know whether x is 0 or not

[proud adder]

Oh so just separate the eqn?, x-7 = 0

[feral agate]

Yes

[proud adder]

Ah ok, mb

[kindred yacht]

.close

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[devout snow]

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[untold bough]

solve 56 - 3t - 56e^(-0.5t)= 0

[untold bough]

t is a variable

[small urchin]

Hi

[untold bough]

huh

[small urchin]

I know i to solve this

[solar goblet]

what have you tried so far?

[untold bough]

nothint

its lambert function

and i dont know what it is

[small urchin]

Write t as a vasusl Numbe

[solar goblet]

$W(x) = xe^x$

thats all

[small urchin]

Like 3

[small urchin]

you cannon remove the t

[untold bough]

is there a way to plug W into a calculator

[solar goblet]

though i believe theres a way to solve this without lambert

[untold bough]

you can try

we havent learnt lambert yet and we are never going to

but somehow the question concocted this equation

yeah there is a question

[solar goblet]

is this the full question?

or just a step

[untold bough]

no

[solar goblet]

!xy

[devout snow]

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.

[untold bough]

its my final equation

middle one

(show the particle... 19th second)

using wolfram alpha answer was 18.665 so my equation is correct

[solar goblet]

use calculus

we can prove that ||the equation has 2 real roots||

[untold bough]

yeah one of the roots is 0

okay if i have the derivative of that expression

what do i equate it to

[solar goblet]

hm hang on

calc only proves the number of roots

let me think a bit

[untold bough]

okay fuck calculus i solved it

plug in 18 and plug in 19 to the integral

one value is negative the other is positive

means it cuts the x-axis between 18 and 19

and is a solution

.close

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[devout snow]

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[thorn aspen]

listen this is gonna sound crazy but i have a shit ton of math problems covering trig and two units of algebra 2 that im very lost on. It's a lot of problems and I would need work and all that. I don't have the problems yet but I'll get them around 8:30 am pst and i need them done by 6 pm pst. It's probably anywhere from 15-25 problems. This is because I'm sick and missing school a lot and I've missed a lot of lessons. If anyone is interested in this heavy workload (its ok if you arent) help is gladly welcomed. Thanks!

[devout snow]

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[devout snow]

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[random birch]

where did they get 6.67x10^-11 from? (it's in the last section of the solving)

[random birch]

6.67x10^-11 is being used in all questions too

[opaque nova]

I’m not a physics guy, so maybe someone can correct me, but I’m pretty sure that is called newtons constant or smth

And it’s just a constant, G

Looked it up, *gravitational constant

[random birch]

wait yeaaaaaaaaaaaaaaa,

im so dumb

sorry man, just a lil error

thank you for telling me tho

[opaque nova]

All good

[random birch]

close.

.close

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[untold bough]

part 1 looks like -3

[brisk ocean]

its 6

but how would i get 6

[untold bough]

make both terms same power

[brisk ocean]

why

[stuck field]

You can simplify a. further to get (x+1/x)(x^2-1/x^2)^4
In the second factor solve for the term with x^0 and x^2 and add those terms. The idea is that you'll have x^1 from the first factor and so on.

[restive river]

try to simplify it

[untold bough]

ysah i did this isn't ir -3?

[brisk ocean]

how do i simplify

[opaque nova]

If I may suggest an idea. Just combine the two things using perfect squares and use binomial thrm

[stuck field]

I didn't solve that, I won't do it.

[stuck field]

I just told you how?

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

Might wanna use that.

[brisk ocean]

still confused

[stuck field]

Do you know this?

[brisk ocean]

yeh

diff of 2 squared

[stuck field]

Do you see how you could potentially use it in your problem

[brisk ocean]

no

well

if we change the first equation

nvm

idk

[stuck field]

(x+1/x)^5(x-1/x)^4 = (x+1/x) * (x+1/x)^4 * (x-1/x)^4

[brisk ocean]

wait

do i break up

[stuck field]

yes.

[brisk ocean]

the fiorst side

[tight peak]

did you people just break up

[stuck field]

[brisk ocean]

and with this diff of 2 squared?

[stuck field]

Correct.

[brisk ocean]

but

which one is a and which one is b

do i need to expand the brackets?

[stuck field]

yes you do.

You can now use the fact that

x^4y^4 = (xy)^4

So that.

[brisk ocean]

oh

so ((x+1/x)(x-1/x))^4

[stuck field]

And now you use difference of squares.

[stuck field]

||||

[brisk ocean]

what would their indicices be?

[stuck field]

Let a = x, b = 1/x what do you get

[brisk ocean]

i got it nvm

ok

so now i've simplified

how would i find coefficients for x^1

wait

i think i can get this

[untold bough]

i got it

you cant find x²

only x⁰

its 6

[brisk ocean]

i did so far (-1x4c2)

wait

i need to square -1

so is it ((-1)^2 x 4c2)

@stuck field do i do simplification process again with 8b)

[stuck field]

yeah sure

[brisk ocean]

hmm

it wouldnt be diff of 2 squares though right

id have to make both ^4

[stuck field]

I'm currently outside, I can't help you anymore. I'm sure someone else would take over, buy you try it regardless.

[brisk ocean]

oh ok

thank u for helping me

[stuck field]

Not immediately but after you make it ^4 it probably will.

[brisk ocean]

<@&286206848099549185> how do I do b and c

[untold bough]

same powrr

[brisk ocean]

?

wait

what did u get when u simplified?

coz i got (x^2-1/x^2)^4 (x-1/x)^5 (x+1/x)

[untold bough]

no

make it all 5

and leave (x + 1/x)^4 outside

[brisk ocean]

why

then we cant do diff of 2 squared

[untold bough]

you can

(x - 1/x)⁴(x + 1/x)⁵(x - 1/x)⁵

[brisk ocean]

wait

@untold bough

nvm

?

<@&286206848099549185>

[brisk ocean]

How do i get find the x^2 coeffient from this

[devout snow]

@brisk ocean Has your question been resolved?

[misty jolt]

I think you should instead group (x - 1/x)⁵ with (x + 1/x)⁵ to get differences of two squares
Then for the remaining (x - 1/x)⁴, expand it to get (x² + 1/x² - 2)²
Then expand the diff of two squares to get a 10th degree polynomial
After that you can put the 10th degree with (x² + 1/x² - 2)² but don't expand it, you can use inspection to see which ones will end up with x²

[brisk ocean]

wai

[misty jolt]

I'm not an expert in this kind of stuff so it'll still be complicated

But i think it's easier this way

[brisk ocean]

so whats ur simplified expression from the original

[misty jolt]

Haven't calculated it yet

But i got a feeling

[brisk ocean]

from b here

[brisk ocean]

wait isnt the first simplification this

[misty jolt]

Yes, but the one that i wrote was how i'd do it

But to simplify you can use pascals triangle

[brisk ocean]

What can i do from my simplification

[misty jolt]

Not sure really

I would just expand it because its a lot easier to just brute force it

[brisk ocean]

wait

why do i expand

@misty jolt how would i find the coefficient of x^2

[misty jolt]

Wait hold on

You can actually use a binomial series here

[brisk ocean]

?

<@&286206848099549185>

<@&286206848099549185>

[restive river]

yes[[[[[

@brisk ocean

put formula of binomial theorem @brisk ocean

[brisk ocean]

which is?

?

@restive river

[restive river]

idk this form @brisk ocean

apply NcR.x power n-r.y power r

[brisk ocean]

?

[restive river]

oof

get its general form first

@brisk ocean

[brisk ocean]

the general form i dont know

[restive river]

wait

its hard tho i am tryin

[brisk ocean]

Wait

NO way we just overcomplicated everything

[restive river]

what?

how

[brisk ocean]

Its so simple

We never needed to simplify

Everyone kept saying simplify simplify

but it was really just 9C1 x 5C1

[restive river]

no i dont think so

i think

wait ik the answer from the idea you gave i think

lol i am tryin

[brisk ocean]

yeh it is

the answer is 45 in the textbook answers

[restive river]

hmm

i failed oof

i was trying to expand it and make it one trm

[restive river]

oof i think i will google this question try to get a proper explanation

[restive river]

lol

i got that from simplifying

[brisk ocean]

.close

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[devout snow]

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[exotic dagger]

what is the rest?

[hoary egret]

just the rest of the system of equation

[exotic dagger]

can you show it just to check

[hoary egret]

okay

gimme a min

@exotic dagger

[exotic dagger]

I am not 100% sure but I think it is because of log(z)

normally with simultaneous equations

the calculator can only solve it if the equations are in the form of
ax + by + cz = d for all 3 equations, here you have logz, rather than just a constant multiplied by z

[hoary egret]

so what must I do to solve this problem?

[exotic dagger]

you prob need solve it by hand

first move the constant logk to the left of the equations

and then notice you can substract equations so that you can get two new equations without log k, and then solve x and y in the usual way

[hoary egret]

why are you allowed to just subtract equations

[exotic dagger]

well it's like doing

x + 2y = 3

and I'm substracting equal stuff both sides

e.g. x - y = 1, then I can substract x-y from the left, and 1 from the right

so (x+2y) - (x-y) = 3 - 1

[hoary egret]

I see thank u

i can take it from here

.close

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[wooden cairn]

need some help please starting with part a

[devout snow]

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[cosmic pelican]

hi

[cosmic pelican]

Basically when i went to type sin^2 (x) on the calculator i just type sin(x)^2

what about sin2x how do i type that in the calculator

[lost laurel]

sin(2x)

[cosmic pelican]

oh like the 2 with the x

alr thanks😅

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[devout snow]

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[analog kiln]

I need help with understanding this

[analog kiln]

I don’t understand where the -14v as well as the other whole numbers are coming from after multiplying it by 10 which is the LCD. When I do that I get - 70/50

[untold pivot]

10(7/5) should be 70/5 right

[analog kiln]

Do you not multiply the numerator and denominator?

[untold pivot]

nope only the numerator, otherwise 70/50 would also simplify to 7/5 and that does not make sense

[analog kiln]

Ok gotcha so always just multiply the numerator?

In these sort of problems?

[untold pivot]

yes unless you multiplying two fractions, then you want to multiply numerator with numerator and denominator with denominator

[devout snow]

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[analog kiln]

.reopen

[devout snow]

✅

[analog kiln]

Just a quick question. The LCD is 6 in this problem. However when I get to the part of - 7y+5/2 because of the negative sign at the beginning of the fraction do I treat 7 and 5 as negative numbers or only 7?

[devout snow]

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[fast smelt]

what do they mean by w + T?

[devout snow]

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[devout snow]

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[slim hearth]

How can I solve for t?

[devout snow]

@slim hearth Has your question been resolved?

[slim hearth]

<@&286206848099549185>

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[devout snow]

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

[slim hearth]

here

oh wait my progress?

alr

wait

so ikr that the sphere's radius is 3cm, the cone's height is 10cm and the cone's side length (the side the sphere is making contact with the cone) is 4.98cm

i used trigonometric functions to get this far

[lunar harbor]

Consider the triangle made by the centre of the sphere and the two endpoints of the shaded area

Think of how you can find the height of that

[slim hearth]

hmm

like a right spherical triangle?

[lunar harbor]

It's not a right triangle

[slim hearth]

then should I try to split it in half and find a way to apply the pythagorean theorem?

[lunar harbor]

Yeah

[slim hearth]

hmm, its hard though as the only infos I can find is that one angle is 90° and one of the cathetuses is 2.49cm long..

[lunar harbor]

||Think of finding the area in two ways||

[slim hearth]

hmm let's see the other way then..
tan(ß) = (t/2.49cm)

and ß is unknown..

for the equiangular triangle found inside the cone we can determine that both angles are (180-28)/2° long each, but it doesn't help as we need to find the angles of a triangle whoose height is t..

[devout snow]

@slim hearth Has your question been resolved?

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@slim hearth Has your question been resolved?

[slim hearth]

hopefully som1 can find an answer to this soon, cause i got a math school leaving exam tmrw and i gotta know this kind of stuff ,_,

[slim hearth]

oh wait I think I finally figured out how to do it

so first we calculate the hypotenuse of that half of the triangle

which would be squr(2.49^2+3^2)

which is 3.9cm

then we use that to calculate the cathetus of that half of the triangle, which would be t

which is squr(3.9^2-2.49^2)

which is.. 3cm?

[slim hearth]

or wait.. am I just stupid or is t literally equal to half of the cone's side length (2.49), as we could imagine the sphere's part that is inside the cone as a smaller sphere cutted in half, and a sphere's radius is always the same in every side..?

[devout snow]

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[devout snow]

@slim hearth Has your question been resolved?

[misty jolt]

What is s

[devout snow]

@slim hearth Has your question been resolved?

[slim hearth]

welp i just did my exam lool

thx everyone for the help ig 💀

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[prime narwhal]

so im at

0x+1y=3

so y would be 3

how do i solve for x

then it is 0

[polar chasm]

plug y = 3 in 3x-5y = 0

that gives 3x - 5*3 = 0

which is trivial

[prime narwhal]

that makes 0x turn into 3x?

how thought

0*3=0

[dawn lintel]

??

3x=15

What's x?

[prime narwhal]

5

[dawn lintel]

That's it

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[devout galleon]

Hello! Could someone check this for me. I am not sure if that's correct.

[final scarab]

,rotate

[devout snow]

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@devout galleon Has your question been resolved?

[devout galleon]

<@&286206848099549185>

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@devout galleon Has your question been resolved?

[stoic rock]

Im not a Helper bit I think Io can help

first one is correct @devout galleon

Second one I would switch to x=-7 x=0

[devout galleon]

Thank you

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[topaz axle]

yes

not really

[radiant anvil]

similar triangle

[restive river]

Well 120 squared + x squared = 144 squared find x

So, ur answer is wrong, x = 80

[winter patrol]

that question was flawed

lengths there are conflicting

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[mental edge]

,rccw

[mental edge]

So after we find w then what?

Say w=2

Then 2=z+2 ? Is that how it works

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[gentle hatch]

i have no idea what question b is asking me

I know that for a, one xintercept has a multiplicity of 2

and I know that K has to be a negative value as both ends of the graph are pointing down

[dense jay]

its asking you to write f in the form k(x-a)^p (x-b)^q (x-c)^w

[gentle hatch]

pqw are the exponents that would say the multiplicity right?

[dense jay]

yes

[gentle hatch]

alright, thank you

idk how to close this

[dense jay]

'.close'

[gentle hatch]

thanks person

.close

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[mental edge]

This is z=iconjz right?

But isnt it like saying p=p ?

<@&286206848099549185>

[sand dove]

it implies p=p

but that's just what you deduce from the modulus

what about the argument?

[mental edge]

Wdym? The angle?

Thats the ø

[mental edge]

But then isnt p=0?

[mental edge]

2 results

Oh its a line

I see wym rafilou2003

[sand dove]

?

2=2

is 2=0?

[mental edge]

Yeyeyeye i get it

Its a line

[sand dove]

yep

[mental edge]

Wait

[sand dove]

except

[mental edge]

Rafilou

Except 0

Ye

But wait

Look

Ive never seen such tarnation

Whats the meaning of that module

[sand dove]

|z1 - z2| is the distance between complex numbers z1 and z2

like if they were on a plane

[mental edge]

Its a i

[sand dove]

z2 = i

so z is at most at distance 1 with i

meaning

z is in the disk

of center i

radius 1

[mental edge]

Im confused

[mental edge]

Where are u getting this

The module is z-i

[sand dove]

for any two complex numbers z1 and z2

|z1-z2| is the distance between complex numbers z1 and z2

as if you looked at them on a plane

for any z1 z2

so |z-i| is...

[mental edge]

Uhm

Is?

[sand dove]

the distance between complex numbers z and i

[sand dove]

literally this sentence

[mental edge]

But how do I write it

[sand dove]

applied to z1 = z and z2 = i

[sand dove]

wdym?

[mental edge]

Uhm

Like

How do I find z

[sand dove]

.

[mental edge]

Yea

...

[sand dove]

what do you know about z already

[mental edge]

Isnt this a new z

[sand dove]

.

look at the first condition

[mental edge]

Oh

But its -i

[sand dove]

and?

if you know z, you know z-i

[mental edge]

So uhm

Its a line

But

It doesnt have 0

And

It stops at 2

Of radius

[sand dove]

no

that doesn't work

you're gonna have to give me

z = .....

based on the first condition only

[mental edge]

But its a line

[sand dove]

z is a point ON the line

[mental edge]

Uhm

[sand dove]

i wanna know how you can write it

[mental edge]

But isnt it every point on the line with distante < 1 from i

[sand dove]

<= 1 yes

but it's still not clear

[mental edge]

Oh its

[sand dove]

which points on the line

[mental edge]

Uhm

[sand dove]

have distance <=1 from i

[mental edge]

z=2e^i5/4pi

And z=2e^ipi/4

[sand dove]

where does this come from?

why a 2?

[mental edge]

Wait

No

With p >0 and <=2

[sand dove]

still unclear

ok

forget about second condition for now

write z

[mental edge]

Z is line y=x

Without 0

[sand dove]

that's the LINE z is on

so write what z equals to

[mental edge]

z=x+e^ipi/4

And 5/4pi

[sand dove]

x + ?

no

you said everything beforehand

z is on line y=x without 0

so z = ?+?i

[mental edge]

x+ye^ipi/4

[sand dove]

doesn't make sense

what are x and y

[mental edge]

Uhhh

[sand dove]

from the start

let's say z = x+yi

simple

[sand dove]

what can we say about x and y?

[mental edge]

The same?

[sand dove]

yes, x=y

so z = ?

[mental edge]

Wtf

[mental edge]

Idk bro aaaahhhh

[sand dove]

z = x+yi

x=y

z = x + xi

[mental edge]

Oh

[sand dove]

think simple

so z = x(1+i)

since z is not 0, x is not 0

now

we wanna solve |z-i| <= 1

|x + (x-1)i| <= 1

use def of modulus

sqrt(x^2+(x-1)^2) <= 1

so square, develop

2x^2 - 2x <= 0

2x(x-1) <= 0

easy solving, 0 <= x <= 1

x not 0

so 0 < x <= 1

and finished

z = x(1+i), 0 < x <= 1

[mental edge]

Damn

Look i tried this way too but

I got this not y=x

[sand dove]

?

look at real part

x= y

[mental edge]

Ye but immaginary?

[sand dove]

imaginary : y=x

[mental edge]

Why he wrote without sqrt

[sand dove]

bc he squared

[mental edge]

U did too

But sqrt still there

[sand dove]

when a and b are both non negative, a <= b is the same as a^2 <= b^2 right?

[sand dove]

bc I squared afterwards

[sand dove]

here

[mental edge]

Kk

[mental edge]

I understand with calculations

But didnt u say the distance from -i must be <=1?

[sand dove]

from i

[mental edge]

But its -i

[sand dove]

|z1***-***z2| is the distance between z1 and z2

[mental edge]

Oh

[sand dove]

so |z-i| is the distance between z and i

[mental edge]

And z1+z2?

[sand dove]

nope

[mental edge]

Im asking

What distance would that br

-z2?

[sand dove]

then it's like distance between z1 and -z2

or -z1 and z2

[mental edge]

Why is sign opposite

[sand dove]

because

-(-z2)

[mental edge]

I meant in general

Not in ur example

[sand dove]

|z1-z2| is distance between z1 and z2 you're ok with that or are you asking why there's a - in here?

[mental edge]

Im asking why z2 if inside the module is -z2

[sand dove]

ok

what's the distance between 3 and 6

how many apples do you need to add to a basket of 3 apples to make it 6 apples

[mental edge]

3

[sand dove]

yes, how did you compute that?

[mental edge]

3+3

[sand dove]

ok then another example because you don't see it yet apparently

what's the distance between 3647 and 5839

[mental edge]

Big

[sand dove]

how many apples do you need to add to a basket of 3647 apples to make it 5839apples

I want a number as an answer

not "big"

[mental edge]

5839-3647

[sand dove]

so you do get it

there's a minus

for distance

[mental edge]

Okok

[devout snow]

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[lofty elm]

SO im doing a)
-2+1.5/2 = -0.25
f(-0.25) = 1.406
so i replace [-2,-0.25]?

?

[devout snow]

@lofty elm Has your question been resolved?

[dawn lintel]

<@&286206848099549185>

[orchid sierra]

It would be helpful if you provided more context for this question

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[errant oyster]

Hi

[errant oyster]

I’m looking for somebody who understands vector calculus.

Its for my friend, willing to throw some $$ if so.

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[hoary anvil]

Is there a method for converting an arbitrary long decimal expansion into nested roots, if we know the exact value can be expressed in terms of radicals?

[hoary anvil]

Context: I wrote a python script to solve a quartic equation, and I got a decimal approximation between -0.18144910885888135 and -0.18144910885888133. Since the equation is quartic, I know it has an exact solution in terms of radicals, but is there a way to find the radical representation without requiring a closed formula such as the quartic formula?

Obviously there's infinitely many nested radicals that will produce decimals within that range, but we're looking for one with maximum "parsimony." Once we have a candidate (or multiple candidates) we can test it on further digits to potentially falsify it.

[uncut crow]

sounds hopeless

[hoary anvil]

🙃

[uncut crow]

🙃

without any knowledge of the form of the roots beyond that they are expressible with radicals, surely you can rig up infinitely many candidates no matter how much precision you have

and i don’t see how you’re going to reduce the candidate list down to 1

[hoary anvil]

Right, but how do we generate ones with maximum parsimony?

[uncut crow]

what’s parsimony?

[hoary anvil]

it's like Occam's razor

If we want to precise, we would have some kind of cost assoiciated with number of terms and how big they are, and we're trying to minimize that cost.

Maximizing parsimony is a common goal in physics, biology, and other areas of science.

Especially in biology because there's an established way to quantify the parsimony of a phylogenetic tree

[uncut crow]

welp i have no idea what that has to do with this

[hoary anvil]

We're trying to find a nested root with maximum parsimony

[uncut crow]

can you give an example

[hoary anvil]

I can try?

so let's say the exact radical representation of what we're looking for is this expression:

But we aren't given that expression, we're given a 100 digit decimal

how can we find that expression given the 100 digit decimal?

we might get multiple candidates, but we can test them on the next 100 digits

and hopefully that would rule out all but one

as you can see, the exact expression has three terms, a maximum root of 3, and a maximum depth of 2

this gives it a higher parsimony than, say, an expression with 420 terms, and 69th roots, with 37 depth

[uncut crow]

okok

still sounds hopeless without more assumptions on the form of the root

[hoary anvil]

I guess like for a real world example, I was working on a problem and I didn't realize a certain ratio was approaching 1 + root(3)

It would have been nice if there was a way to find that expression given the decimal values I had

for that particular problem, whether or not the ratio actually approaches 1 + root(3) is still an open problem as far as I'm aware. But there's statistical evidence for it.

[uncut crow]

like, no matter how good your approximation is, there will be infinitely many candidates of the form sqrt(a) that "agree" with the approximation

also, say, infinitely many rational numbers

[uncut crow]

you would need more assumptions like the numbers under the roots are integers or something to be able to make the candidates for roots of forms like that finite

[hoary anvil]

yes

This has to be a common thing mathematicians do though right? Like solutions are often conjectured before they're proven, and sometimes the conjectures come from the nature of the problem, but other times they just come from the numerical values.

Like the process for solving a problem might start with a 100 digit decimal, then using that to find a nested radical, then testing that nested radical on further digits, and then trying to prove that the nested radical is, in fact, the exact solution.

I'd assume this is something common enough that there'd be a search method

[uncut crow]

numerical stuff can certainly help make conjectures. never really seen anything like this

[uncut crow]

i'm curious what this problem was

[hoary anvil]

3 rowed chomp

https://www.math.ucla.edu/~tom/Games/chomp.html

n x n and 2 x n have trivial solutions, I was trying to find a general solution to 3 x n boards (which is an open problem)

at least as far as I'm aware

[uncut crow]

ic

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@hoary anvil Has your question been resolved?

[devout snow]

@hoary anvil Has your question been resolved?

[devout snow]

@hoary anvil Has your question been resolved?

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[orchid arrow]

I have to show that this series is convergent and has a limit that is an real number within that interval

How would you do this?

[cosmic gust]

$a_n = a_{n-1} + \frac{1}{e^n + 1}$

[woven radish]

Oğuzhan

[cosmic gust]

Maybe defining it like this is easier

Nevermind it doesn't work here

[orchid arrow]

The things underlined in red are things that we also know

Given the function above

Maybe it has something to do with the question

Those were basically things that we had to prove

Which I've done already

I'm fairly sure from f) I can get that the series is convergent, but idk how to get the limit

[cosmic gust]

Maybe remove the +1 on the bottom which would make the result an upper bound?

If it only needs bounds

Not sure

[cosmic gust]

Which I think gives e^(1/e)

[orchid arrow]

I've just begun doing these so I think I'll just ask my teacher today

I'll keep in mind what you said though

Thanks

.close

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[small urchin]

[
\lim_{{x \to \infty}} \left( \left(1 + \frac{1}{x}\right)^{x^2} \cdot e^{-x} \right)
]

[woven radish]

Gordon Ramsey

[small urchin]

how is it solved

?

[sick valley]

Hi

[small urchin]

Hi

[tiny hearth]

try to evaluate: $\lim_{x \to \infty}(1+\frac{1}{x})^{x^2}$

[woven radish]

Obotron

[sick valley]

,w lim x-> infinity of (1+1/x)^(x^2)

[woven radish]

Results provided by WolframAlpha

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

Requested by jandro0103

[small urchin]

So

[tiny hearth]

ok so we have 0 * infinity

take logs and l'hopital

[small urchin]

Or ?

[sick valley]

,w lim x-> infinity of e^-x

[woven radish]

Results provided by WolframAlpha

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

Requested by jandro0103

[small urchin]

Maybe I need to use notable limits

[sick valley]

Well

Wait a second

[small urchin]

Ok

[sick valley]

I'm in my office, I have to do something for a moment, 3 minutes

[small urchin]

Ok

[autumn fjord]

this diverges of course

use the limit definition of e

and note that x^2 asymptotically outgrows all linear functions

oh i thought you were the one asking

sorry

[small urchin]

I do not know what to do

[tiny hearth]

take log of the limit

[small urchin]

Or ?

[tiny hearth]

idk another alternative

[small urchin]

I don't know what this thing is

[tiny hearth]

you dont know what log is ?

[small urchin]

Yes

[tiny hearth]

$\ln(x)$

[woven radish]

Obotron

[small urchin]

I know

I don't know what the thing you wrote is

[sick valley]

Wait

Im back

[small urchin]

Pls help

[sick valley]

I analyzed the exercise

[small urchin]

Ok

[tiny hearth]

Let: $$L =\lim_{{x \to \infty}} \left( \left(1 + \frac{1}{x}\right)^{x^2} \cdot e^{-x} \right)$$ $$\ln(L) = \ln\left (\lim_{{x \to \infty}} \left( \left(1 + \frac{1}{x}\right)^{x^2} \cdot e^{-x} \right) \right )$$

[woven radish]

Obotron

[tiny hearth]

then you can take the limit outside the logarithm

[small urchin]

What is that

[sick valley]

Wait

Omg

[small urchin]

I can't do it like this

[tiny hearth]

why?

[sick valley]

Listen to me Gordon Ramsey

[small urchin]

Ok

[tiny hearth]

OH

WAIT ITS JUST e^x * e^-x

[sick valley]

Write x^2 as x • x

[tiny hearth]

which is 1

[small urchin]

Ok

Can I see all the steps?

[sick valley]

No

Wait

[small urchin]

😭

[tiny hearth]

$\lim_{x \to \infty} \left( 1+\frac{1}{x}\right)^x = e$

[woven radish]

Obotron

[sick valley]

Are you doing what im saying?

[small urchin]

Yes

[tiny hearth]

that first term is effectively e^x

[sick valley]

Ok

Put

1/e^2 out the limit

[small urchin]

Ok

Why?

[sick valley]

Now you have

What why

[small urchin]

Ah OK

No wait

Where does it come from?

Give me all the step pls

[sick valley]

You have $\frac{1}{e^2} \lim_{x\to\infty} \left(1+\frac{1}{x}\right)^{xx}$

[small urchin]

What

How

[sick valley]

Wait

[small urchin]

May I know why you did this?

No

[woven radish]

jandro

[small urchin]

What Is that !

[sick valley]

This

[small urchin]

.

[sick valley]

What I told you 3 minutes ago, you need to listen

[small urchin]

What

Where does e^2 come from

[sick valley]

$x^2 = x x$

[woven radish]

jandro

[small urchin]

That's not what I asked you

[sick valley]

$e^{-2} = \frac{1}{e^2}$

[small urchin]

But if there is x

[woven radish]

jandro

[small urchin]

What are you talking about

[sick valley]

Ah sorry

I've read wrong

[small urchin]

Why did you write 2?

[sick valley]

Wait

[sick valley]

I read it wrong 🥲

[small urchin]

Ok

Sorry

[autumn geode]

u should start by taking then ln of the inside to separate that product

[small urchin]

I can't use that method

[sick valley]

Anyway

[autumn geode]

u didnt learn it?

[small urchin]

No

[autumn geode]

well then why can u not use it

[small urchin]

Because I don't know him

[sick valley]

You have $\lim_{x\to\infty} \left(1+\frac{1}{x}\right)^{xx} \cdot e^x = e^{2x} = \infty$

[woven radish]

jandro

[sick valley]

Easy

[small urchin]

What are you saying

[tiny hearth]

??

[autumn geode]

thats not the limit

[small urchin]

Its all wrong

👍

[tiny hearth]

$\lim_{x\to\infty} \left(1+\frac{1}{x}\right)^{xx} \cdot e^{-x} = \lim_{x\to\infty}e^{x}e^{-x} = 1$

[sick valley]

Sorry

[woven radish]

Obotron

[sick valley]

It was e^-x

[small urchin]

Yes

[sick valley]

I think it was e^x

[small urchin]

...

It's e^-x

[sick valley]

Yes

[small urchin]

How you do it 😭

[sick valley]

Im fixing

[small urchin]

Ok

[sick valley]

Chill

Use this formula

[tiny hearth]

$\lim_{x \to \infty} \left( 1+\frac{1}{x}\right)^x = e$

[woven radish]

Obotron

[small urchin]

Is it 1?

But how

[tiny hearth]

$$\lim_{x \to \infty} \left( 1+\frac{1}{x}\right)^x = e$$ so $$\lim_{x \to \infty} \left( 1+\frac{1}{x}\right)^{x^2} = \lim_{x \to \infty}e^x$$

[autumn geode]

its not according to wolfram alpha

[woven radish]

Obotron

[small urchin]

But in fact everything is wrong

[tiny hearth]

the answer isnt 1?

[small urchin]

It's done with Taylor

[autumn geode]

no

[sick valley]

Can @tiny hearth Stop

[small urchin]

But what are you telling me

[sick valley]

You are an idiot

Its not 1

[small urchin]

Oh well, I think you're using gpt chat