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#help-49
sudden halo
so; I want to solve tst.
I'm thinking I can use djikstra's algorithm if I can get a hamiltonian graph of neurolinks, hatch positional, and unrelated position of the unpicked 2.
how should I weight the hatch vertices of a path?
https://algorithms.discrete.ma.tum.de/graph-algorithms/spp-dijkstra/index_en.html
for combinatorics, there's 20 combinations per this; excluding the 2, and 56 combinations including it.
https://www.calculator.net/permutation-and-combination-calculator.html?cnv=6&crv=3&x=39&y=14
if you're unfamiliar with the mechanic, step 38 - 42.
https://ff14.toolboxgaming.space/?id=577833117590361&preview=1#38
midnight plankBOT
so; I want to solve tst.
I'm thinking I can use djikstra's algorithm if I can ge...
@sudden halo Has your question been resolved?
sudden halo
I think this covers it?
midnight plankBOT
@sudden halo Has your question been resolved?
stable nexus
?
midnight plankBOT
@sudden halo Has your question been resolved?
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@sudden halo Has your question been resolved?
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@sudden halo Has your question been resolved?
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@sudden halo Has your question been resolved?
barren estuary
yo can i use this now
rough birch
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summer hearth
What is the shortest way to describe this?
(y+1)*(x-1)+x
midnight plankBOT
What is the shortest way to describe this?
`(y+1)*(x-1)+x`
summer hearth
I think this can be easier expressed.
summer hearth
It is longer.
keen herald
x(y+2) - y - 1
next rover
is this for code golf?
next rover
you don;t often see wanting to make a short expression shorter outside of code golf
summer hearth
You are defining code golf with code golf.
next rover
it's when people compete who can make the program shortest
summer hearth
`x(y+2) - y - 1`
Hm, so no shorter way.
keen herald
xy + 2x - y - 1 has 9 characters
That's the shortest I've found in terms of character count
summer hearth
Thanks. Felt like I am missing something. Looks like binomial.
last slate
Hi
muted steeple
last slate
I dont really understand how to get this result
grizzled blade
Huh
last slate
Why does the a or (1-a) stay the same, and what exaxtly happened to the lnX
grand pondBOT
last slate
ln(x) turns into 1/x doesnt it
grizzled blade
Yes
last slate
Is the lnX i sent the same as ln(x)
last slate
And the X in 1/x is the X thats in front of the ln ?
grizzled blade
Yes
last slate
I mean in the lnY example, it turns into 1/Y
grizzled blade
Yes
last slate
So i wonder why the 1-a stays
Is it a factor ?
I thought it would be removed or something
grizzled blade
$\vec{\rightarrow} = e^{-\ln (x)}$
last slate
Im not sure what the matter is with the e to be honest
last slate
Dont we just do the derivative thing
last slate
I just have a sheet that says ln(x) = 1/x , there is no e there
grizzled blade
f(x)=ag(x)
f'(x)=ag'(x)
Here is g(x)=lnx
last slate
When derivating, dont constants get dropped ?
grizzled blade
No
Not if the constant is multipied by the variablr
f(x)=5+x
f'(x)=1
5 gets dropped here coz it's not mulitpied by the variable
f(x)=5x
f'(x)=5
f''(x)=0
last slate
I seeeee!!! ππ»ππ» thank you:)
May i then ask you what would happen if it was
ln 10 ?
Would it turn into 1/10 ?
grizzled blade
It's a constant
last slate
Like instead of lnX -> 1/X
grizzled blade
,w derivative of ln(5x)
grand pondBOT
grizzled blade
if it's just x then 1/x
If it's a function like ln(f(x))
U need to use chain rule
ln(f(x))'=1/f(x) * f'(x)
grizzled blade
Try the derivative of ln(argsinh(e^sinx)) as simple exercise
last slate
i dont even know what argsinh means π
grand pondBOT
grizzled blade
Try derivative of ln(sin(x))
It's 10 times harder tho
,w plot ln(argsinh(e^sinx))
grand pondBOT
grizzled blade
I call it the Bunny-ears function
last slate
Try derivative of ln(sin(x))
Isnt that just 1/sin(x) ?π
grizzled blade
No
grizzled blade
,w derivative of ln(sin(x))
grand pondBOT
last slate
May i ask how you notice that you have to use the chain rule when seeing ln(sin(x)) ?
grizzled blade
No
grizzled blade
Solved
tropic cradle
midnight plankBOT
https://cdn.discordapp.com/attachments/903486480075354182/1044369502109958265/im...
tropic cradle
did I do this right?
midnight plankBOT
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tropic cradle
<@&286206848099549185>
random linden
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@tropic cradle Has your question been resolved?
tropic cradle
<@&286206848099549185>
tropic cradle
?
peak thunder
Uhmmm
tropic cradle
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daring shard
need help with finding the crit numbers
midnight plankBOT
need help with finding the crit numbers
daring shard
after i derived i got stuck with x 1/2(1-x)^1/2=0
midnight plankBOT
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round prism
Would like help completing this, don't know how to proceed
$O(n^{3})\neq 19n^{2}+63n-22$ means that,\
$19n^{2}+63n-22 \eqslantless C \times n^{3}$, or:\
$0 \eqslantless C \times n^{3} - 19n^{2}+63n-22$, use c =1 prove that $n^{3} - 19n^{2}+63n-22$ is increasing, find with derivative.\
$\frac{df}{dn} =19n^{2}+63n-22 = \frac{d^{2}f}{d^{2}n}=38n+63$
midnight plankBOT
Would like help completing this, don't know how to proceed
$O(n^{3})\neq 19n^{2...
grand pondBOT
Nurech
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@round prism Has your question been resolved?
round prism
<@&286206848099549185>
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@round prism Has your question been resolved?
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@round prism Has your question been resolved?
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@round prism Has your question been resolved?
midnight plankBOT
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Available help channel!
ebon mica
if this was a right triangle with angle 38 and the hypotenuse's length as 5, would side length x be equal to 5(sin 38)?
midnight plankBOT
if this was a right triangle with angle 38 and the hypotenuse's length as 5, wou...
junior flower
be careful with degrees and sin, but yep haha
junior flower
yep π
midnight plankBOT
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stuck tapir
hey
stuck tapir
so I need help with physics
willow ruin
in a maths discord server?
stuck tapir
physics relies heavily on math
just asking. If there are none ill close
acceleration specifically
anyone have physics knowledge?
halcyon trellis
Just post your question
white sluice
where is ur the question
jagged saffron
look at the coefficient in front of the xΒ² to calculate the acceleration
stuck tapir
yeah thats where I got the time
but I need another variable for distance to find acceleration
jagged saffron
2.55 = 1/2*a
stuck tapir
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midnight plankBOT
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stable halo
midnight plankBOT
https://gyazo.com/5fc6957aed01e9547fdc9c236bc32ffb
@stable halo Has your question been resolved?
winter swift
$0 \le x\le 1$
grand pondBOT
Mehdi_Moulati
stable halo
Yea
winter swift
$0 \le x^{k+1}\le 1$
grand pondBOT
Mehdi_Moulati
stable halo
Okoi
winter swift
$\frac{0}{k(k+1)}\le \frac{x^{k+1}}{k(k+1)}\le \frac{1}{k(k+1)}$
grand pondBOT
Mehdi_Moulati
winter swift
$0 \le \frac{x^{k+1}}{k(k+1)}\le \frac{1}{k(k+1)}$
grand pondBOT
Mehdi_Moulati
stable halo
Oki
winter swift
and we know that :
$\sum_{k=1}^n \frac{1}{k(k+1) }= 1 - \frac{1}{n-1}$
grand pondBOT
Mehdi_Moulati
winter swift
if i still remember
stable halo
do we know that
winter swift
1 / k(k + 1) = 1 - 1 /n -1
yes and by induction
stable halo
yes and by induction
i do not know how to prove by induction
winter swift
the induction is :
we suppose that [\sum_{k=1}^{n} \frac{1}{k(k+1)} = 1 - \frac{1}{n+1}] is true and we try to prove that
[\sum_{k=1}^{n+1} \frac{1}{k(k+1)} = 1 - \frac{1}{(n+1)+1}] is also true
grand pondBOT
Mehdi_Moulati
stable halo
isnt that just 1 - 1 / n
winter swift
A proof by induction consists of two cases.
- The first, the base case, proves the statement for n = 0 without assuming any knowledge of other cases.
- The second case, the induction step, proves that if the statement holds for any given case n = k, then it must also hold for the next case n = k +β1.
These two steps establish that the statement holds for every natural number n. The base case does not necessarily begin with n = 0, but often with n = 1, and possibly with any fixed natural number n = N, establishing the truth of the statement for all natural numbers n β₯ N.
stable halo
ahhh
so like we says its true for n, must be true for n + 1, so therefore is true for all values of n + i where i is any value
winter swift
so like we says its true for n, must be true for n + 1, so therefore is true fo...
yeah
winter swift
i made a mistake
$\sum_{k=1}^n \frac{1}{k(k+1) }= 1 - \frac{1}{n+1}$
grand pondBOT
Mehdi_Moulati
winter swift
it's 1 - 1/(n+1)
for n = 1 : the sum equal to 1/2
for n = 2: the sum equal to 2/3
for n = 3: the sum equal to 3/4
winter swift
1/2 = 1 - 1/2
2/3 = 1- 1/(2+1)
3/4 = 1- 1/(3+1)
stable halo
OH
No i understanbd
wtf
that smart
so am i supposed to do something like that for mine
right?>
winter swift
you just need to prove this
$\sum_{k=1}^n \frac{1}{k(k+1) }= 1 - \frac{1}{n+1}$
grand pondBOT
Mehdi_Moulati
winter swift
if we prove that the sum is bounded then its' converge
winter swift
if we prove that the sum is bounded then its' converge
this to prove that your sum is converge in x in 0<x<1
to prove 1-1/(n+1) we will use the induction
stable halo
to prove 1-1/(n+1) we will use the induction
no but to prove it conveges
can we not just
prove it has a limit
winter swift
prove it has a limit
maybe but i'm not sure
proven nest
Could someone please explain how there can be multiple triangles in the Ambiguous case in the Law of Sines? Thanks
midnight plankBOT
Could someone please explain how there can be multiple triangles in the Ambiguou...
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foggy cave
proven nest
thank u
proven nest
do you want to close this channel?
yes
analog pebble
type .close
proven nest
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rain locust
midnight plankBOT
rain locust
can someone explain those coordinates on the unit circle please please?
for example on the top left, there's -1/2 and sqrt of 3 /2
is sqrt of 3/2 for sin?
ebon sky
theyβre the x and y coordinates of the point
muted iris
is sqrt of 3/2 for sin?
At 2Ο/3, yes
(x, y) is now (cos, sin)
when y is β3/2 then that's ur sine
so if it's like HEY what's the sine of 2Ο/3 or something u go over there and ur like hmm what's the y value
and then β3/2 is ur answer
midnight plankBOT
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kindred token
How to do this?
midnight plankBOT
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tender ocean
it might be helpful to annotate the diagram
do you know law of sines?
the only way ive been able to see is using it but im probably just missing something
maybe make 2 right triangles? by drawing a line perpendicular to SB that hits A
not entirely sure, but sometimes doing stuff like that helps
oh, it does help
this is a really clever question
call the point where that line you drew intersects SB "C"
what is the angle CAB?
so what do you notice about these 2 different right triangles?
hmm
i dont think those really work because you dont have any side lengths
updated diagram
have you learned about similar triangles?
there are two triangles in this diagram with the same angles
well, here we can use AB= 2 * AS
yea its a really tricky problem
well, the hypotenuse of ΞABC is twice the hypotenuse of ΞSAC
the sides of ΞABC must be twice as long as their counterparts in ΞSAC
sure, but we know that the longer leg of the smaller triangle (AC) is equal to the shorter leg of the bigger triangle (also AC)
non-hypotenuse side
aha, but we do
hang on, are you sure you marked your angles correctly?
theres no way that AB can be bigger than AS
well, either way, i have to go
i would look at your angles again, either way i think its going to be the same similar triangle trick
my general tip would be to first mark down everything you know, then give everything you dont know a name/variable, and annotate those
so you can see certain places where things overlap
midnight plankBOT
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raven flax
hi
raven flax
I have an integral of e^(-pi*x^2)
and I know that integral of e^(-x^2) is sqrt of pi
how do I procceed?
thank you
I got it,for anyone interested you just need to choose u = sqrt(pi)*x when you make substitution
.close
torn smelt
Hello!
Soooo vectors.
I'm trying to implement a noclip into my GTA server. It's working fine so far and everything works exactly how I want it. But it's missing the sideways movement.
Basically I want the sideways movement to be controlled by A to go to the left depending on the camera direction and D to got right.
I have no idea how to implement that properly into my math stuff
This is what I have so far:
If you have questions about what the code does at a specific point, just ask.
const pos = localPlayer.position;
const dir = GetGameplayCamDirection();
localPlayer.setCoordsNoOffset(pos.x + dir.x * speed, pos.y + dir.y * speed, pos.z + verticalSpeed + dir.z * speed, false, false, false);
function GetGameplayCamDirection() {
const heading = mp.game.cam.getGameplayCamRelativeHeading() + localPlayer.getHeading();
const pitch = mp.game.cam.getGameplayCamRot(0).x;
let x = -Math.sin(heading * Math.PI / 180.0);
let y = Math.cos(heading * Math.PI / 180.0);
let z = Math.sin(pitch * Math.PI / 180.0)
let len = Math.sqrt(x * x + y * y + z * z);
if (len != 0) { x = x / len; y = y / len; z = z / len; }
return new mp.Vector3(x, y, z);
};
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fluid solar
Show that if π,π, and π are integers such that πβ₯2 and πβ‘π(modπ), then πππ(π,π)=πππ(π,π).
midnight plankBOT
Show that if π,π, and π are integers such that πβ₯2 and πβ‘π(modπ), then π...
fluid solar
I have no idea where to start
lyric charm
let d be a common divisor of a and n, show that d is also a common divisor of b and n
then do the same but the other way around (or don't because it'll follow automatically - just switch a and b around)
fluid solar
so if d divides a and n, then d divided kn, so divides a+kn. So d is a common divisor of a + kn and b
if d divides a + kn and b, then d divides kn, so d divides (a+kn)-kn = a
wait what did i just show
midnight plankBOT
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@fluid solar Has your question been resolved?
slender flame
midnight plankBOT
warm magnet
Add 4r to both sides
snow iron
Add 4r to both sides to cancel out -4r, then divide 27 by 9 to isolate R . X=3
scarlet snow
bro solved for X which wasn't even in the equation
tired shadow
Add 4r to both sides to cancel out -4r, then divide 27 by 9 to isolate R . X=3
Don't do all the work for someone
snow iron
thatβs the method that helps me understand concepts the best
By seeing all the steps then asking questions about said steps
snow iron
Don't do all the work for someone
btw do u think u could help me with my question
tired shadow
That's not how we operate, however
scarlet snow
thatβs the method that helps me understand concepts the best
this may be true but we don't specialise to help you we need to help anyone that's comes to the server, and a lot of the time people will be satisfied if you just solve the question for them and produce an answer even if they dont understand the intermediate steps, they may not even try to understand them. Rather to truly help them we explain the steps to make them understand each one and slowly solve the question themselves, I personally ask specific questions to try and make what they are missing "click"
snow iron
this may be true but we don't specialise to help you we need to help anyone that...
mb fam π
snow iron
I was just scrolling through the text channels while I was waiting and saw this one without someone helping on it so I just did it
slender flame
what does x equal
scarlet snow
what does x equal
this isn't a calculator server, first explain what is confusing you about the problem
slender flame
i js dont get how to work it out
if it was only x and not 4x
i could do it
but its 4x so
snow iron
A fraction can be compared to division where itβs the numerator being divided by the denominator
you can start there what do you see about the fraction that could help you get x on its own
slender flame
ok i got it it was 6
midnight plankBOT
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midnight plankBOT
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wintry cave
How to factor x^4 - x^2 + 1
midnight plankBOT
How to factor x^4 - x^2 + 1
tired shadow
How to factor x^4 - x^2 + 1
What have you tried
tired shadow
Notice that xβ΄ = (xΒ²)Β²
So you have (xΒ²)Β² - xΒ² + 1
How can you rewrite this as a quadratic
wintry cave
(x^2 - 1/2)^2 + 3/4
wintry cave
Ik
tired shadow
Notice, if we do the substitution xΒ² = y, we get yΒ² - y + 1
wintry cave
Then?
tired shadow
Can you factor yΒ² - y + 1
wintry cave
Nope it has no roots in R
wintry cave
Then why my teacher asked me to factor it ? π
runic hamlet
well depends on the field
every polynomial over R can be factored into a product of quadratics and linear terms
wintry cave
every polynomial over R can be factored into a product of quadratics and linear ...
How though
runic hamlet
completely factor over C and then multiply conjugate pairs
runic hamlet
or set up (x^2+ax+b)(x^2+cx+d) and then compare coefficients
or you can even do something here as a geometric sum
pure lagoon
i got kind of stuck on this question
midnight plankBOT
i got kind of stuck on this question
pure lagoon
you cant really multiply the 2 so does that mean the orthagonal projection doesnt exist?
jagged saffron
Why have you taken a fraction and put it into a vector
midnight plankBOT
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gentle wolf
midnight plankBOT
gentle wolf
Can anyone help me figure out M1 ^-1, M2 ^-2 and M3 ^-3 with euclidean algorithm?
midnight plankBOT
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@gentle wolf Has your question been resolved?
gentle wolf
sadge
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gentle wolf
midnight plankBOT
gentle wolf
How does 6 and 7 become 1 and 2?
hard umbra
gentle wolf
ty
I am told to continue by multiplying by 3 on each side
I cant seem to figure out why
is it to make the "rest" 1?
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midnight plankBOT
glossy garnet
I suggest you read the rules in #βhow-to-get-help and not ping random users for help
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midnight plankBOT
glossy garnet
yes you already have an open channel
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restive igloo
Help pls
surreal marlin
Anything
restive igloo
what tools are you allowed to use for this?
anything
what are you planning on using?
strong sonnet
anything
This looks like a google interview task
so, well, a programm written by me
but if you are not in that field, there must be some smart solution too
restive igloo
This looks like a google interview task
so, well, a programm written by me
yeah idk how to do thatπ
restive igloo
but if you are not in that field, there must be some smart solution too
yeh, any ideas?
strong sonnet
yeh, any ideas?
trial and error?
restive igloo
trial and error?
wait do you understand what the a pointer primes are
they say add the sum of the digits and that should be the next prime
11 + 2 = 13
strong sonnet
yes
midnight plankBOT
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bold night
Let $f_n(x) = \frac{nx}{1+n^2x^2}$ for $x\in[a,1]$ where a is fixed in (0,1). Is this uniformly convergent?
midnight plankBOT
Let $f_n(x) = \frac{nx}{1+n^2x^2}$ for $x\in[a,1]$ where a is fixed in (0,1). Is...
grand pondBOT
todadqa
midnight plankBOT
@bold night Has your question been resolved?
fallow scarab
use the definition of uniformly convergent
bold night
? in what way?
fallow scarab
? in what way?
in the only way possible?
i can't think of how to use the definition incorrectly
try it and share your attempt
grand pondBOT
todadqa
fallow scarab
restive quiver
Does anyone here know how to tackle similarities in triangles?
midnight plankBOT
Does anyone here know how to tackle similarities in triangles?
twin basin
Does anyone here know how to tackle similarities in triangles?
Could you be more specific? Do you have an example question or some definition or theorem you want clarifying?
midnight plankBOT
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brave bane
i feel really stupid for asking this but i am not sure what to do with the 2x. I need to find X
midnight plankBOT
i feel *really* stupid for asking this but i am not sure what to do with the 2x....
warm magnet
What kind of polygon is that
Identify that first
Then use the interior angle sum formula
brave bane
Heptagon, 900
warm magnet
So the sum of all those angles gotta add up to 900
brave bane
mhm! i understand that, im just not sure where to put the 2x in the equation
warm magnet
Legit just add them up
160 + 2x + 125 + 110 + 112 + 147 + x = 900
Combine like terms
brave bane
would my equation be 3x+654=900?
my brain deflates everytime i ask a question dear god
midnight plankBOT
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brave bane
well if weβre going with that, would my answer be 3x=246?
midnight plankBOT
gloomy fiber
split crystal
help pls any one
midnight plankBOT
help pls any one
warm magnet
The radius is just half of the diameter
muted iris
(Ο(12/2)Β² * 5)/3
warm magnet
But also "use 3 for Ο" π they got real lazy
muted iris
(Ο(12/2)Β² * 5)/3
(Ο(d/2)Β² * h)/3 see
muted iris
But also "use 3 for Ο" π they got real lazy
LMAO
warm magnet
The volume of a cone is the volume of a cylinder divided by 3
If you don't know how to divide by 3 then idk man
split crystal
i kown how divide
muted iris
Just plug the stuff into the formula
split crystal
r=12ft then h =5ft right?
fallow scarab
12 ft is the diameter
split crystal
12 divide by 3 then right?
muted iris
No
fallow scarab
No
fallow scarab
How does radius relate to diameter?
muted iris
Once you have your variables organized plug them into the equation
warm magnet
bruh
muted iris
lula what is a radius
warm magnet
The radius is just half of the diameter
Man I sure hope someone gave you how they're related
Man I really sure hope
split crystal
lula what is a radius
the radius if the distance form the center circle
fallow scarab
The radius is just half of the diameter
@split crystal did you see this
split crystal
240 is my answer right?
fallow scarab
And the diameter is j double the radius
And this
fallow scarab
240 is my answer right?
Show your work
split crystal
fallow scarab
r=12ft then h =5ft right?
When you asked this
split crystal
which one
muted iris
the one we just replied to
fallow scarab
idk
If you don't know, don't keep calculating. Stop and and read what people are telling you
muted iris
ok ur math isn't following the formula you've been given
this isn't how u calculate it
split crystal
ok
split crystal
pie r^2h/3
split crystal
5
muted iris
What's the radius
split crystal
12
muted iris
No
Thats the diameter
The radius is half whatever the diameter is
The diameter is the distance across the face of the circle
split crystal
6 then
muted iris
The radius is the distance from the middle of the circle to the edge of the circle
Yes
So
Plug them into your formula now
Don't calculate it yet
We're going one step at a time
split crystal
pie (6)^2 (5)/3
muted iris
you forgot the divided by 3 thing
muted iris
also it says use 3 instead of pi because your teachers r lazy
split crystal
180
split crystal
ooh okay
i have this other question that a cone can i slove it you check it if its fine with u?
muted iris
ight
split crystal
i got for my answer is 40
split crystal
so am right?
fallow scarab
Yes
fallow scarab
Calculate the two volumes separately then add them together
split crystal
how you do the rectangluar prism ?
muted iris
Nvm.im braindead don't listen to me
Rectangular prism is like
Length times width times height
So it's 6 * 6 * 10
split crystal
so the rectangular all we do is just times it
fallow scarab
i i had got 962 as my answer
Gotta stop throwing random numbers and just show the work
fallow scarab
So it's 6 * 6 * 10
Like this
fallow scarab
for the rectangular prims i got 360
split crystal
and the cylinder i did was. v=(4)^2 (12) the multiply the 4^2 like this 4x4=16 and the 12 stay the same into i did was 16x12= 192 x 3=576 and add it with 360
i try to explain
muted iris
and the cylinder i did was. v=(4)^2 (12) the multiply the 4^2 like this 4x4=16 a...
4 is your diameter
fallow scarab
The radius is half whatever the diameter is
.
midnight plankBOT
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knotty viper
Hi all! I'm trying to prove the following, and I'm not certain where to start or whether I'm over-complicating this:
for k, n, m in Z, k mod m = k mod n mod m iff m | n
I feel like I could use some operations on the ring of integers modulo n and m to solve this, but I haven't been able to get anywhere.
I was thinking that by working with homomorphisms from Z -> Z/mZ and Z -> Z/nZ * Z/nZ -> Z/mZ, I could somehow prove that these are equivalent. This feels like I could use some aspect of of the CRT, but I'm at a bit of an impasse. Does anyone have any pointers for the best approach here, or another approach altogether?
Thanks in advance!
midnight plankBOT
Hi all! I'm trying to prove the following, and I'm not certain where to start or...
runic hamlet
I would just start by writing k=qm+r and k=tn+p and then p=lm+s and then try something with those
midnight plankBOT
@knotty viper Has your question been resolved?
knotty viper
Sure, we can reduce this as follows:
k=qm+r
k=tn+lm+s
qm+r=tn+lm+s
We want to prove that r=s, but I'm not sure how to derive any sort of relationship between qm and tn+lm
In particular, I don't see how we can assert any sort of meaningful relationship between q, t, and l
knotty viper
Oh you're totally right
In that case, let me rephrase:
for k, n, m in Z, m | n -> k mod m = k mod n mod m
I believe that this claim should be true
runic hamlet
well that follows easily from what you wrote down
write n=hm and then use that division with remainder is unique
knotty viper
Apologies, I'm still a bit fresh with formal definitions of euclidean division
(q-th-l)m = s-r
Are you saying that because we know that s < m, r < m, we can find that -m < (s-r) < m, which means that the only possible whole-number value for (q-th-l) is 0, which means that s-r=0, which means that s = r?
runic hamlet
a bit long
qm+r = (th+l)m+s
those are both divisions by m and 0<= r,s < m, so they are the same
so q=th+l and r=s
but I guess in the end that boils down to your argument
knotty viper
To clarify, what do you mean by "those are both divisions by m"?
runic hamlet
yeah that wasn't great wording
I just meant on each side it's the form something*m + remainder
knotty viper
Ah gotcha, that makes sense
The crux of this is that rewriting n=hm is only valid under integers if m | n, correct?
runic hamlet
well that's the definition of what m|n means
m|n iff there exists an integer h with n=hm
knotty viper
A follow-up question: if we were to extend this to all real numbers as opposed to just integers, I presume that for k, n, m in R, m | n -> k mod m = k mod n mod m (for some equivalent definition of modulo) would still hold, right?
Once we get to qm+r=tn+lm+s, however, the same line of logic would no longer apply
runic hamlet
Well you're skipping over the important steps of how you would actually define that stuff
Like there is no divisible relation anymore on R
Or well not an interesting one
knotty viper
D'oh, you're totally right
I was still in integer mode and thinking that we could define divisibility if the result is in Z
But then we can use the above argument
Plus that's not a very meaningful definition of divisibility in R
Cool, big thanks for all your help! I really appreciate it π
runic hamlet
And nZ is not an ideal anymore in R so taking modulo is probably yikes
I guess it's still a normal subgroup
So I guess addition still works
But multiplication is probably fucked up
knotty viper
Yeah makes sense
One more follow-up actually: is there a good way to approach this problem from a more abstract algebra-centric lens?
Or does that not just make very much sense in this context
runic hamlet
Well you would do the same argument just translated as ideals etc
Feels like working in Z is nicer tho
At least I can't come up with a more abstract way right now
Taking repeated modulo is a weird thing tbh
Like I'm not even sure if that is well defined if we don't take the (k mod n) to mean the least positive representative in the class k+nZ
midnight plankBOT
runic hamlet
You're welcome
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safe raft
What equation Is needed to solve part A?
midnight plankBOT
What equation Is needed to solve part A?
@safe raft Has your question been resolved?
Available help channel!
safe raft
would it be correct to assume that the force is attractive because the directions of the magnetic fields are opposite of these two wires?
i dont understand the equation F = qv x B so I am trying to think of it in another way
therefore, if the current flows were opposite, the magnetic fields would be the same, so then the force would be repulsive?
midnight plankBOT
would it be correct to assume that the force is attractive because the direction...
fallow scarab
would it be correct to assume that the force is attractive because the direction...
#old-network for physics server
safe raft
<#406129911992942593> for physics server
alright thanks !
snow iron
midnight plankBOT
fallow scarab
I was wondering why the absolute value of -3/2 was used
you should have learned at some point that cos(-x) = cos(x)
warm magnet
Works for sec(x)
fallow scarab
or does it work for Sin and Tan aswell
sin(-x) = -sin(x)
try to show something for tan(-x)
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final sonnet
midnight plankBOT
final sonnet
Here's what I got so far...
I don't know where to go from here
Oh wait!
I think I can just subtract 1 from the n of the second sum
nvm
If i subtract 1 from all the n's then it becomes an-1
but I don't think we can do that
<@&286206848099549185>
<@&286206848099549185>
midnight plankBOT
@final sonnet Has your question been resolved?
final sonnet
<@&286206848099549185>
dry merlin
by looking at the coefficients of x^n you should get relationships between a(n-1) and a(n+1)
final sonnet
hmmm
are you saying I should move one summation to the other side
and equate them?
dry merlin
not necessarily you can also look at the coefficient of x^n in the zero polynomial
midnight plankBOT
@final sonnet Has your question been resolved?
final sonnet
.close
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willow beacon
does anyone know how I would graph this?
midnight plankBOT
does anyone know how I would graph this?
dull yoke
Review ur multipliers
Ur given MPC
Remember that tax multiplier is 1 less than spending
willow beacon
Review ur multipliers
um what would that be?
dull yoke
U donβt know what spending and tax multipliers are?
willow beacon
not really no
dull yoke
willow beacon
ok so then how I would graph that then
in this situation I believe the increase would be 150 million and the increase in consumption would be 120 million
dull yoke
Howβd u get that
dull yoke
so I think it would be a aggregate demand that shifts right
Well this is right but ur numbers r still wrong
Read the link then come back
azure kraken
midnight plankBOT
azure kraken
Can someone help me with this one
last slate
{x + ln(1-x)} / {1 - sqrt(1-x^2)} = [{x + ln(1-x)} / {1 - sqrt(1-x^2)}] * [ {1 + sqrt(1-x^2)} / {1 + sqrt(1-x^2)} ]
last slate
you have to apply l'hospital eventually
azure kraken
${x + ln(1-x)} / {1 - sqrt(1-x^2)} = [{x + ln(1-x)} / {1 - sqrt(1-x^2)}] * [ {1 + sqrt(1-x^2)} / {1 + sqrt(1-x^2)}$
grand pondBOT
Yousssef
last slate
basically mulitply both numerator and denominator with (1 + sqrt(1-x^2))
last slate
[{x + ln(1-x)} / x^2] * [1 + sqrt(1-x^2)]
you will end up with this
the right side is 2 basically when limit x -> 0
we need to calculate for the left side
now ln(1-x) = -x - (x^2)/2 - (x^3) / 3 - (x^4) / 4 - ...
hence x+ln(1-x) = -(x^2) / 2 - (x^3)/3 - (x^4)/4 - (x^5)/5- ...
azure kraken
the right side is 2 basically when limit x -> 0
What do you mean with right side?
last slate
dividing by x^2 and then taking limit x->0 we have final limit to be -1/2 - 0 - 0 - .. = -1/2
hence -1/2 * 2 = -1
last slate
What do you mean with right side?
[1 + sqrt(1-x^2)]
this one
grand pondBOT
last slate
put x = 0 there
azure kraken
[1 + sqrt(1-x^2)]
this one
I donβt have that
last slate
my method is different..
last slate
whenever there are roots at the denominator try to remove that
that's how I approach most of this problems and they do workout well evetually
last slate
Didnβt you use l,hospital rule?
nope..series expansion of ln(1-x)
it's simple
1/{a - sqrt(b)} = {a+sqrt(b)} / {(a+sqrt(b)) * (a - sqrt(b))} = (a + sqrt(b)) / (a^2 - b)
were you able to understand the above which I wrote just now?
azure kraken
Yeah I think I understood it
last slate
so now think about how you would proceed to do the same for 1/{1 - sqrt(1-x^2)}
azure kraken
So u took the conjugate
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@azure kraken Has your question been resolved?
fallow scarab
depends on your bounds. try a change of variables
https://mathworld.wolfram.com/Erf.html
the important equations are 1, 23, 24
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clear gulch
I have tried simplifying 125 to 5^3 and 25^x to (5^2)^x
5^2x + 5^3 x 5^2x = 630
5^2x + 5^2x+3 = 630
Thats all I could do I have no idea what to do next since 5 to the power of a number isnt 630
midnight plankBOT
I have tried simplifying 125 to 5^3 and 25^x to (5^2)^x
5^2x + 5^3 x 5^2x = 630
...
shy mesa
@clear gulch
clear gulch
Hi
shy mesa
Try to think of 2 powers of 5 whose sum is 630
shy mesa
Yup
swift frost
Ok so in here https://prnt.sc/IpCyJcibdox2
midnight plankBOT
Ok so in here https://prnt.sc/IpCyJcibdox2
swift frost
the answer is this https://prnt.sc/jzlFRPuB8UJ3
but then here https://prnt.sc/EaM-mFB-1b-8
we have this https://prnt.sc/ikntLZFHvLmH
why is the formula for one specific (x1 + x2/2) and the other question have adding the equations completely with distance formula despite both wanting the centre of circle equation
cobalt silo
One is the middle point of a segment and the other looks like the intersection of two lines that is the center of a circle
swift frost
which one's the intersected
cobalt silo
we have this https://prnt.sc/ikntLZFHvLmH
That, it's finding the intersection of the graphs of equations 1 and 2
swift frost
so distance formula should be required for intersection graphs but not ones for just a shape
cobalt silo
Wdym?
You solve systems of equations to find intersections
You use the distance formula to calculate distances
swift frost
I mean if the circle is passing through
cobalt silo
Ah yes
The equation of a circle looks like the distance formula because it's defined as the points at fixed distance from the center
swift frost
and what about finding coordinates of Q in https://prnt.sc/IpCyJcibdox2
cobalt silo
I'd find the slope of SR and get the line with the same slope that pases through P
Same with slope of SP and move it to R
Q is the intersection of those two lines
swift frost
Wait how do we find the slope
cobalt silo
(y2-y1)/(x2-x1)
knotty plover
im kind of stuck on what to do after this point
midnight plankBOT
im kind of stuck on what to do after this point
knotty plover
we have to use the method of substitution
(if you want the problem more clearly)
#7 and #8
glossy pelican
What is the doubt
knotty plover
Everything tbh
im not sure what to do next
ik what to do for 7
somewhat
I just plug in X
but for 8 im not sure
do I solve even further for it?
glossy pelican
do I solve even further for it?
Yes
spiral crater
Which question?
spiral crater
7/8?
knotty plover
7 and 8 yeah
spiral crater
Well for 7 we can rearrange the top one to be x+3y=6 β> x=-3y+6
Plug that into the second equation and solve
Do you know how to solve by plugging in?
5(-3y+6)+6y=12
Would you be able to solve for y?
knotty plover
yes
spiral crater
For question 8 we can rearrange -4x+y=-15 β> y=4x-15
spiral crater
For question 7 or 8?
knotty plover
8
spiral crater
Aight
knotty plover
I got X = -5
oh okay
and then you plug that into one of the equations
the. solve for y
get the ordered pairs
knotty plover
Ohh okay, Thank you so much
spiral crater
No problem
knotty plover
.close
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wet vector
