thanks for your help!
#help-38
feral dragon
honest scroll
np
feral dragon
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half lintel
what is classic definition for limits in multivariable calculus
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half lintel
<@&286206848099549185>
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unkempt wyvern
this resembles a p series no?
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this resembles a p series no?
unkempt wyvern
bruh i gotta clean my eyes
so after splitting and simplifying the expression i can apply the divergence test?
marble wharf
try it
unkempt wyvern
doesn't really get me anywhere since its non conclusive
so i think best is to do comparison or limit test
but i need to find something i can compare to
marble wharf
after simplifying this should look like something else familiar
marble wharf
yes
unkempt wyvern
okay andiknow that for a geometric series if a > 1 converges
wait i just noticed the question asks to find the series sum
which is the limit of that sum right?
marble wharf
yes
unkempt wyvern
so uh
i have (1/2)^n + (1/3)n
and i have the geometric series 1/a^n that i know converges
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next vapor
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next vapor
Those lines on top scare me
marble wharf
I assume its just the notation your course uses for modulo
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marble wharf
how would you do this if it were normal numbers
next vapor
Ok
I don't know how to continue
I know i should eliminate the 3 ed row
But i don't know what to do after
@marble wharf
marble wharf
what would you do if it were normal numbers
marble wharf
what about all the other ones
marble wharf
yes
next vapor
Ok let me cook
This is what i came up with
@marble wharf
I still don't understand what role does mod 13 play 😒
Like is there a difference
@marble wharf
?
marble wharf
cant check your calculations right now
but you should have done all your calcs mod 13 instead of "normally"
maybe the numbers were just coincidentally in a way that mod 13 didnt matter
sleek canopy
cant check your calculations right now
hey! do you remember me ?
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wraith hinge
it depends
sleek canopy
😮
dusty sleet
Which grade are you in?
wraith hinge
() or [] ??
dusty sleet
() or [] intervals
Because I believe you haven't been taught this kind of writing intervals
cloud latch
Hi
cloud latch
How do I get the recursive formula and solution? (I was absent during the lecture)
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winged terrace
do you know the recursive formula
for arithmetic
im stupid you said you missed the lecture
a_n = a_1 + (n-1)d is the recursive formula used for a sequence made of solely arithmetic
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mortal fiber
I don’t know how to solve this it’s for physics if someone could help me through it or give me tips that would be appreciated
mortal fiber
#4 btw
winged terrace
no i get that but i think what T is matters because of physics
if it doesnt matter then think about the normal force and gravity
queen delta
You're just asked to solve for m. Use standard algebraic manipulation to do so. Essentially, express m in terms of those other things.
winged terrace
and then think about how we can isolate the m
mortal fiber
theres two m's which im kind of confused about
winged terrace
yes so
mortal fiber
couldn't i just divide the left side of the equation by a?
winged terrace
F_N is a force right
mortal fiber
im pretty sure
winged terrace
well you would still have the m on the left side of the equation
mortal fiber
would i just then divide m on the other side?
winged terrace
you could do all that
wraith hinge
$$F_n is the normal force
winged terrace
but you could also think of the physics and how a normal force is a reactionary force
queen delta
When you get the chance, @mortal fiber, you should do a review of Algebra. You will really struggle with almost anything that applies math as a tool, otherwise.
wraith hinge
You're welcome
mortal fiber
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gentle sleet
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gentle sleet
Since i picked the bigger s^2 to be the num for F the df will be like that right?
for part b
12, 10
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gentle sleet
wont th enext step just be P(A u B) = P(A) + P(B) (assuming independence)
My friend did P(A u B) = 1 - P(A^c n B^c) and we are getting diff answers
Im getting 0.2395 and he got 1-(1-.1587)(1-0.0808) = 0.22667704
burnt mulch
wont th enext step just be P(A u B) = P(A) + P(B) (assuming independence)
$P(A \cup B)=P(A)+P(B) \boxed{-P(A \cap B)}$
solid kilnBOT
Civil Service Pigeon
burnt mulch
(remember that “independent” does not mean “disjoint”)
fuckkkk Im slow
worthy lark
Translation: Q and T are tangent points. If QR (not the radius) = 7TM and PQ = 8, calculate the value of "R" (radius)
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Translation: Q and T are tangent points. If QR *(not the radius)* = 7TM and PQ ...
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
2
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worthy lark
burnt mulch
Hint: Power of a point, specifically ||TM^2 = MP * MQ||
worthy lark
hmm
but isn't the power of a point only applied to 2 chords or 1 tangent and 1 secant or 2 secants?
burnt mulch
Look up the tangent-secant case
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What step are you on?
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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
no idea what im supposed to do
mild thunder
Gotta plug in your (x+delx) into your function and set up that quotient (idk if that helps)
mild thunder
So you got the lim all set up? Just foil out the parentheses and it should simplify a bit
vagrant marsh
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vagrant marsh
7*(x+delx)(x+delx)
west pine
this would lowkey be pretty easy if you used the limit definition of a derivative
trim kestrel
havent gotten there yet
west pine
ah
trim kestrel
okay so x^2 + 2xdelx + delx^2?
west pine
im assuming thats the point of the assignment though
idk I have some questions from my teachers that have me spot when I can cheat a limit using a derivative
but yeah I see
vagrant marsh
yeah those questions can be quite tricky, but this one is explicitly trying to show derivative form, so im assuming its for an intro class
trim kestrel
its calc 1
west pine
yeah you'll learn it soon enough
trim kestrel
okay so how do i solve this though
trim kestrel
okay so x^2 + 2xdelx + delx^2?
Is this right so far?
Can I just replace delta with a different variable to make it easier to work through
mild thunder
You can replace delx with something if you want. And yeah that's right just remember you have a 8 multiplying that whole term
trim kestrel
You can replace delx with something if you want. And yeah that's right just reme...
okay so uh
7x^2 + 14xy + 7y^2 -6x +6yx -6y
i replayed delta with y
nvm this is just confusing
mild thunder
Okay, I'm glad you said it not me
Try h instead of y
And also it looks good until the last term with 6yx
mild thunder
Yeah, you see your earlier mistake?
mild thunder
7x^2 + 14xy + 7y^2 -6x +6yx -6y
Should end with "-6y"
trim kestrel
7x^2 + 14xy + 7y^2 -6x +6yx -6y
7x^2 +7y^2 20xy + -6x -6y
7x^2 +14xy +7xy^2 -6x -6xy
then uhh
do f(x+hx) - f(x)
7x^2 +14xy +7xy^2 -6x -6xy - 7x^2 + 6x
okay got it
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lavish cosmos
Unsure of how to tackle this, i don’t understand what it means to sell the bill at 4%
lavish cosmos
Only question 5
hallow spruce
it means the same as it means to buy at 6%
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naive otter
Hello
naive otter
I need help proving Taylor's theorem with Lagrange's form remainder from Rolle's theorem
<pls ping me>
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knotty locust
I need help proving Taylor's theorem with Lagrange's form remainder from Rolle's...
What's the full theorem statement?
solid kilnBOT
naive otter
What's the full theorem statement?
This one ^ Taylor's theorem
knotty locust
Have you tried induction?
naive otter
I can't
knotty locust
Why?
naive otter
I need help proving Taylor's theorem with Lagrange's form remainder from Rolle's...
I need to use Rolle's
knotty locust
I need to use Rolle's
You can use Rolle's theorem to prove the inductive argument
First prove the base case n=1
then assume it is true for n=m
and prove this implies it is true for n=m+1 using Rolle's theorem
naive otter
It's true for n = 1 , using Langrange mean value
knotty locust
But how will I compare ?
Show me what you've written in your attempt of proving the inductive step so far
naive otter
Show me what you've written in your attempt of proving the inductive step so far
I'm sorry but I haven't written I was just observing
knotty locust
Okay so write out the information that is given to you (the induction hypothesis, the assumption that it is true for n=m)
and then write out what you want to prove (the statement of the theorem for n=m+1)
naive otter
f(a+h) =f(a) + hf'(a) +...+ (h^m/m!)× f^m(a+øh)
Now I consider we re taking the m+1 th derivative where m+1<n-1 ,
So it just changes my last term of the eqn.
What changes should I make to the LHS?
I'm sry but I really don't know how to do this induction step here...
knotty locust
I'm sry but I really don't know how to do this induction step here...
Is there anything you can say about f^(m+1)(a+thetah)?
naive otter
Idk it's the Lagrange's remainder
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unreal cove
İ know there is an occurrence in general in mathematics when squaring or square rooting relations but where exactly do i need to add ±?
unreal cove
Where am I supposed to add the ± ?
İ know there is an occurrence in general in mathematics when squaring or square rooting relations but where exactly do i need to add ±?
solid kilnBOT
Katrro
spring warren
after square rooting
unreal cove
you are always supposed to add ± after square rooting?
this must be for even functions only though right
even exponents*
spring warren
you are always supposed to add ± after square rooting?
Not always supposed to add it after square rooting
unreal cove
Why
spring warren
when you have something like y = x^2, there are 2 solutions so you'd take the plus or minus
unreal cove
for y²=1-x²
spring warren
but when you something like x = sqrt(16) you'd only take the positive value
unreal cove
You need to add a ± when squaring both sides
unreal cove
but when you something like x = sqrt(16) you'd only take the positive value
Also when you take squares of both sides
A bit like how you need to add +C everytime you integrate
Right
spring warren
if you take squares of both sides you dont need to add it
unreal cove
that makes no sense
unreal cove
for y²=1-x²
How about this
spring warren
wdym
unreal cove
this is a relation and to turn it into a function i need to square root both sides
but then so i would need to do
spring warren
yes
unreal cove
y = ±sqrt(1-x²)
spring warren
yea thats right
unreal cove
so when I am i supposed to add a ±
spring warren
when you have y^2
it's because sqrt(a^2) = |a|
so for a relation like y^2 you get plus or minus
spring warren
I'm not sure what you wrote
unreal cove
sqrt(a²)= |a|
So a is either a=a or a=-a
But the problem is
Sqrt(1-x²)
it is not even
spring warren
y^2 = 1 - x^2 is a circle
spring warren
sqrt(a²)= |a|
So a is either a=a or a=-a
|a| = a or -a
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drifting storm
guys pls help
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guys pls help
wraith hinge
what have you tried
drifting storm
i copied the working from my teacher but i don't really understand
why do we pick a = 1 and a = -5 as the answer?
drifting storm
why not pick a = 4?
wraith hinge
if we pick that
that means
from condition
that 4<= x <= 7
which does work for 4
but for things higher than thst it doesnt
for example
x= 5 doesnt work
bcz f(5) = 26 > 16 (the range for f(x))
i will send you a dm of demonstration why a=4 doesnt work if you want
i just explained briefly
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shut valve
Pls help cause wtf is this
My teacher says to use the box method which I forgot HOW to DO
solar jackal
basically spli the expression into terms
the expression is 3x+6
then the terms are 3x and 6
put each term in a box
then take a number or a variable which is common for both yterms
the common numer is 3
3x and 6 both are divisible by 3
so take 3 out
then divide all the terms with the number you took out
divide 3x by 3 and 6 by 3
ur left with x and 2 as the quotients respectively
and ur ansser is 3(x+2)
did you get it?
solar jackal
its okay
shut valve
shut valve
Everyday☹️
shut valve
6x..?
solar jackal
YES!!
shut valve
YAY
solar jackal
now what about 20ab divided by4ab>?
shut valve
5
shut valve
Uh 4ab (6x + 5)?
solar jackal
YESSS
shut valve
YIPPEE
solar jackal
great job!!
shut valve
Thank you
solar jackal
sure
never perform algebra orally even if ur good at it bcus ull end up doing silly mistakes-
solar jackal
yeah this is algebra
x y z thingy
did u get the solution?
first take a common factor of 25 and 40
and then a factor of the variables ie xyz and x respectively
solar jackal
sorry for peeping but the drawing at the back is fire
and your anser is...........
CORRECT!!
great job
shut valve
YAY
solar jackal
ur gonna be great at math
just practice everyday
math comes with practicce
thats why i love it
btw what grade ru in-
im in 10th
shut valve
8
solar jackal
k byee take care
shut valve
Thank youu
solar jackal
yww
wind estuary
how to convert fraction into decimal?
Like 1/8 ??
I dont understand the division I completely forgot abt basics... The division part is confusing me because its not even divisible so what will I do?? To get the decimal answer
granite light
look up long division
wraith hinge
turn it into 1.000/8
granite light
basically
1 = 0.8 + ?
0.2 = 0.16 + ?
0.04 = 0.040
1 = 8*(0.1 + 0.02 + 0.005)
1/8 = 0.125
that's long division. you can divide numbers in base 10, in base 2, in base 12, in base N, you can even divide polynomials. It's same size fits all
wraith hinge
!occupied
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wind estuary
do you know division
haha what if its not divisible... idk long division
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keen void
Sketch the definition area of the given function
trim joltBOT
Sketch the definition area of the given function
solid kilnBOT
Merineth
solid kilnBOT
Merineth
prime crystal
Would that be correct?
no
that'd make the expression inside the square root negative
keen void
x > 2 would not work
keen void
why can't x < 0 ?
prime crystal
try taking x = -1
solid kilnBOT
Merineth
prime crystal
yes
solid kilnBOT
Merineth
keen void
Since this is in the denominator of the fraction, it has to be greater than 0
such that
$\sqrt{y(3-y)} > 0$
solid kilnBOT
Merineth
prime crystal
yes
keen void
But at the same time the y(3-y) has to be greater than or equal to 0
Can i solve the above function for y?
prime crystal
But at the same time the y(3-y) has to be greater than or equal to 0
greater than 0 yes, not equal to zero
since its in denominator
solid kilnBOT
Merineth
keen void
That equals to zero when y = 0 and y = 3
So the same thing applies as our previous function
$3 \ge y \ge 0$
solid kilnBOT
Merineth
solid kilnBOT
Merineth
prime crystal
yes
solid kilnBOT
Merineth
keen void
the value inside the ln has to be greater than or equal to 1
Such that
$9x^2+4y^2-36 > 0$
prime crystal
why 1
prime crystal
yes
solid kilnBOT
Merineth
keen void
in that case
it should be as such
pretty sure this can be written in standard form of an ellipse
$\frac{x^2}{4} + \frac{y^2}{9} > 1$
solid kilnBOT
Merineth
keen void
so it has to be outside the ellipse cordinates of x = 2 and y = 3
I think we can sketch the image now?
CHARTBIT
<3
<3<3<3<3
I need you to give me a crash course in mult var calc before my exam on friday 
whole coral
Friday 
awwwww 
keen void
i've been strcitly studying algorithms and discrete math
but now when i did those exams i haven't even started on calc 3
whole coral
Awwwww 
keen void
my love
whole coral
Well, at least there's still some time 
keen void
yeaaaa
I'm locking in for the next two days
how do i determine if my defintion is compact or not?
whole coral
If the region that your function is defined is compact or not?
whole coral
Well, "closed and bounded" in this case should do it 
If you're happy with the "closed" part? 
keen void
I do see that my x can be 0 and 2 which means the line should be straight?
Which in turn should mean that since 3 > y > 0 should be dashed lines?
Like this?
Or i might be thinking of something else
Considering he says it's a "compact"
Which makes more sense tbh considering it doesn't go towards infinity
whole coral
I do see that my `x` can be 0 and 2 which means the line should be straight?
Whi...
Yep, they should be dashed, which then means that your region you have is not closed, as they've noted
As a tl;dr, because that line is dashed, the region is not closed (the longer version, I'd need to ask for the definitions you have 
)
whole coral
If all the boundary lines are solid, then you're closed, and if you don't have any parts that go off to an infinity, then you're bounded
So if you have both, that makes you compact 
keen void
How do i remember that ;-;
I got a serious issue where i completely forget everything i study in math ._.
whole coral
Well, good question 
I guess just look that you have boundary lines everywhere and they're not dashed, to figure out if your set under consideration is compact 
keen void
Hmmm
Bounded
Compact
Closed
Are those the three terms?
A set of points is Compact if and only if it is Bounded and Closed?
whole coral
A set of points is Compact if and only if it is Bounded and Closed?
Yep, at least for now [in the context of subsets of R^n], "compact" means the same thing as being both "bounded" and "closed", so you only need to worry about checking the latter two
whole coral
Just relaxing and chilling really 
tomorrow I'm going out earlyish 
keen void
D:
going out early
euw
You can help me xD while u chill :p
"(a) determine the tangentplane to the curve S in the point A"
IIrc we determined tangentplanes with this
keen void
Since we have x y and z in our function. I either have to use the right one or we have to solve for z and use the left one
Right one should be easier c:
whole coral
Right one should be easier c:
It definitely is, you definitely don't wanna solve for z 
keen void
yeah that looked painful
We start of with finding the gradient c:
So deriving wrt x,y and z
shesh
Okay i have a guess
$\frac{df}{dx} = cos(x+yz)(x^2+y^2+z^2)^{1/2} + sin(x+yz)\frac{(x^2+y^2+z^2)^{-1/2}}{2}2x$
solid kilnBOT
Merineth
keen void
seems ok ? <3
whole coral
$\pdv{f}{x}$ for the curly partials (does $\frac{\partial f}{\partial x}$ for you)
solid kilnBOT
@whole coral
whole coral
seems ok ? <3
And yep 
whole coral
the ones for z are basically swapping y and z around
keen void
Yeah it seems like it
you are so smart ;-;
$\frac{\partial f}{\partial x} = cos(x+yz)(x^2+y^2+z^2)^{1/2} + sin(x+yz)\frac{(x^2+y^2+z^2)^{-1/2}}{2}2x\ \$
$\frac{\partial f}{\partial y} = cos(x+yz)z(x^2+y^2+z^2)^{1/2} + sin(x+yz)\frac{(x^2+y^2+z^2)^{-1/2}}{2}2y \ \$
$\frac{\partial f}{\partial z} = cos(x+yz)y(x^2+y^2+z^2)^{1/2} + sin(x+yz)\frac{(x^2+y^2+z^2)^{-1/2}}{2}2z$
I think this should be correct
So now since we got our Gradient <3
We just need to make the dot product between them and = 0
whole coral
Yep yep
keen void
So we insert my point A into each partial derivative in my gradient?
$\grad F(a,b,c)$ which should be this part?
solid kilnBOT
Merineth
whole coral
$\grad F(a,b,c)$ which should be this part?
Yep (it works out nicer than it would seem to!)
solid kilnBOT
Merineth
keen void
(noticed i had the wrong partial sign so just updated it)
$\frac{\partial f}{\partial x} = cos(6 + (-2)3)(6^2 + (-2)^2 + 3^2)^{1/2} + sin(6 + (-2)3)\frac{(6^2 + (-2)^2 + 3^2)^{-1/2}}{2}26$
UH
Did i mess it up?
solid kilnBOT
Merineth
whole coral
meh, maybe so, not sure where 
[
\pdv{f}{x} = \cos(6 + 3(-2)) (6^2 + (-2)^2 + 3^2)^{1/2} + \sin(6 + 3(-2)) \frac{(6^2 + (-2)^2 + 3^2)^{1/2}}2 (2\cdot 6)
]
solid kilnBOT
@whole coral
whole coral
Anyways, just working out stuff from this point 
keen void
Yeah i'm doing the simplifcation on paper
currently i got
$cos(0)(36+4+9)^{1/2} + sin(0)....$
solid kilnBOT
Merineth
solid kilnBOT
Merineth
keen void
= 7
Nice c:
if i'm not mistaken
the same applies to the other ones as well
with the sin(0)
whole coral
Yep, hence I said it's nicer than it seems
solid kilnBOT
Merineth
whole coral
Well, just doing the dot product $\pmqty{7 \ 21 \ -14} \cdot \pmqty{x - 6 \ y + 2 \ z - 3}$, which should be easy!
solid kilnBOT
@whole coral
solid kilnBOT
Merineth
solid kilnBOT
Merineth
whole coral
keen void
whole coral
solid kilnBOT
Merineth
keen void
Got the right answer
whole coral
(b) being? 
keen void
"Determine an apporximate value for f(B) if B is of distance 0.01 from A in the direction where f is increasing the fastest"
I think i have an idea
"where f is increasing the fastest" specifically applies to derivative of f
f'(x) = 0
iirc
or in our case it should be f'(x,y,z) = 0?
oh shit could it be when the gradient is = 0?
whole coral
oh shit could it be when the gradient is = 0?
Not quite in this case 
keen void
hmm okay
Well i do know it has something to do with derivative since derivative determines how fast something is increasing
and when the slope is 0 means it is at its highest point (at least in f(x) functions)
whole coral
Well, you should hopefully have been given something that $f$ increases most rapidly in the direction $\nabla f(A)$, and decreases most rapidly in the direction $-\nabla f(A)$
solid kilnBOT
@whole coral
keen void
Well yeah since we are in 3D the point where it increases the fastest is represented with a gradient arrow from origo to the point?
Or am I thinking of something differen?
keen void
Hmmm
But derivatives are a way to determine the speed at which a point is accelerating?
Probably badly phrased
When I derive a function I get a new function which describes the speed at which a given point is increasing or decreasing
whole coral
I mean, kind of, but more like if you consider the single variable case, when you sketch a curve and its derivative/the tangent at that point
whole coral
There's a tangent plane yea, of course a whole plane of directions in which you can move
That said, I'm not great at explaining multivariate stuff tbh
keen void
It’s okiii
I just have to practice as much as I can before exam hehe
I can’t be asked stressing anymore 🥶
whole coral
Awwwww 
yeah, the most you can do is just prepare for it
whole coral
keen void
LOL
So I want to find the fastest point where my function increases to begin with
And I’ve already determined the gradient
I’ve never determined the fastest point of a gradient before
Gonna have to look it up
whole coral
Also there was this #help-35 message which is effectively the same
Aha, it was someone else I mentioned increasing/decreasing fastest #help-24 message
whole coral
Awwww
whole coral
<@788085606483361802>
Are you at least happy with the statements here?
keen void
Yeah I think so :3
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steel zealot
s
wraith hinge
what
wraith hinge
can you explain your work
?
i dont understand where does p come from
and numbers aswell
chrome talon
can you explain your work
I assume they wanted to do a proof by contradiction and assumed n = 2p + 1
steel zealot
u can do proof by contradiction
how tho
wraith hinge
well no
steel zealot
what do i do next
lilac flame
so far i got to 8p^3+12p^2+6p+6 = 2m + 1
is the lhs even or odd?
true kestrel
just prove it by that odd + even = odd
steel zealot
so its even
lilac flame
right
solid acorn
I am currently doing Andrew Ng's Machine Learning course and I came upon the formula for the Cost Function. It was the squared cost function so I searched online about why we are using the squared one instead of the mod one.
https://datascience.stackexchange.com/questions/10188/why-do-cost-functions-use-the-square-error?rq=1
I was trying to understand the top answer of this thread but it just all went over my head. I really don't know about Statistics(the answer was talking about CLT and Normal distribution and lots of other probability and statistical terms), Linear Algebra, Multivariate Calculus etc. Can someone help me about what mathematical topic should I start from to understand all of it? My goal is to do machine learning. I don't just want to apply formulas but understand them atleast to some depth.
marble wharf
well statistics, linear algebra and calculus is a good start
solid acorn
well statistics, linear algebra and calculus is a good start
What order should I do them in? Can you give me some good sources for them, if you have any?
@marble wharf
marble wharf
for the most part you can just do them independently
pick up some textbooks, we probably have some in #book-recommendations
solid acorn
pick up some textbooks, we probably have some in <#716264872018706443>
thankyou!!
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solid acorn
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heady matrix
Quick Q what are these like half square parenthesis?
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Quick Q what are these like half square parenthesis?
heady matrix
https://en.wikipedia.org/wiki/Floor_and_ceiling_functions
Would make sense, C is a prediction of Cipher text size based off block size and P, plain text size.
charred trail
not very familiar with all this encryption stuff, maybe check if they have previously defined the notation elsewhere
heady matrix
not very familiar with all this encryption stuff, maybe check if they have previ...
Thats fine, are you aware of how this ceiling function would be calculated?
charred trail
yeah, its the smallest integer which will be greater than P/block size
mighty prism
because you are probably padding the plaintext
so you have to go up to a multiple of the blocksize
heady matrix
because you are probably padding the plaintext
yeah padding and other miscellanous factors that can alter ciphertext size
heady matrix
so you have to go up to a multiple of the blocksize
ahh but how many times?
mighty prism
ahh but how many times?
how many time what? i assume that you are applying a block cipher to your plaintext, then your plaintext has to consist of an integer number of blocks, hence the padding
ceiling(P/blocksize) gives you the number of blocks after that
so the length of the cipher text will just be the blocksize times that number
heady matrix
AES-256 with a block size of 16 bytes
mighty prism
AES-256 with a block size of 16 bytes
what are you trying to ask?
heady matrix
So if for example P was 50, block size was 16 wed have C = (ceiling(50/16)) * 16
sorry, Ive just never heard of this ceiling function
mighty prism
So if for example P was 50, block size was 16 wed have C = (ceiling(50/16)) * 16
yeah
mighty prism
sorry, Ive just never heard of this ceiling function
ceiling function is just the least integer greater, so you just round to the next integer, for example ceil(0.2)=1, ceil(1.9)=2, ceil(50/16)=4
heady matrix
ceiling function is just the least integer greater, so you just round to the nex...
ahhhh okayyyy. I get it now thanks.
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humble thistle
is the division of a vector by a scalar defined
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is the division of a vector by a scalar defined
humble thistle
or I can't say that
I have to say that it's multiplied by 1/c if c is the scalar
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gentle sleet
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gentle sleet
having trouble getting the bounds for v
ik one of them will be pi/2
nvm im braindead
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elder field
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sly basalt
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sly basalt
judge yourself by your school syllabus and help channels are for maths problems. please delete your messages
its okay use #discussion for that
tribal sonnet
You could try to factor the upper part (denominator?)
sly basalt
You could try to factor the upper part (denominator?)
after putting limit?
tribal sonnet
yh
sly basalt
@tribal sonnet I put x=1 and denominator becomes 0, so its (1-2a+b)/0 =8
i differentiate function using L'h rule and put x=1, it gives a=-3
so a-b becomes -8
but answer is wrong
tribal sonnet
Are we sure that (1-2a+b) = 0?
sly basalt
nova spire
Are we sure that (1-2a+b) = 0?
that's up to cali to justify it but yes
nova spire
i differentiate function using L'h rule and put x=1, it gives a=-3
what's the differential you get?
nova spire
yeah I figured that out on my own
I'm trying to understand what went wrong in this approach
let me just try something
wait no a = -3
something is wrong when you compute b
oh yep
sly basalt
is
(1-2a+b)/0= 8
(1-2a+b)/8= 0
(1-2a+b) = 0
correct way to deal
nova spire
"(1-2a+b)/0= 8" is kinda wrong to write in the first place
you need to say that since .../0 results in a finite limit
you can only have 0 as numerator limit
so 1-2a+b = 0
and no going to 1-2a+b = 0 by multiplying by 0
1-2a+b = 0 is correct
though something went wrong between
-6-b = 1
to
b = -5
sly basalt
so 1-2a+b = 0
that just means 8/0=8
nova spire
that just means 8/0=8
sorry edited
nova spire
that just means 8/0=8
so just to recap
something went wrong between
-6-b = 1
to
b = -5
and something else went wrong when computing a-b afterwards
sly basalt
wait i did 6-1 instead of 6+1. b comes 7
nova spire
b=7?
tribal sonnet
a-b = 4 then, right?
sly basalt
yes😭
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valid bridge
can someone explain what this means
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can someone explain what this means
left oriole
can you show more context?
valid bridge
on page 9, towards the bottom of the page
left oriole
ok s_0 = 0
so it's just saying that in the example, the transform was well defined for s > 0
by well defined, they presumably mean "finite"
valid bridge
yea i figured that
left oriole
which notation, this?
valid bridge
yea
left oriole
it's just a fairly clumsy way of saying it's well defined for s > 0, and s_0 happens to equal 0
gentle sleet
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gentle sleet
This would be correct?
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full onyx
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full onyx
any idea how to make this shorter
chilly bobcat
D is circumcenter of ABC
AC passes through circumcenter, making it a diameter
angle subtended by diameter AC (which is ABC) is 90 degrees
undone sierra
D is circumcenter of ABC
AC passes through circumcenter, making it a diameter
an...
well this was derived from another rule which is the one being asked about
but i am sure its accepted
chilly bobcat
well this was derived from another rule which is the one being asked about
hmm, i remember getting it using exterior angle theorem
full onyx
D is circumcenter of ABC
AC passes through circumcenter, making it a diameter
an...
is it possible not to use circles
chilly bobcat
is it possible not to use circles
it is necessary for a short solution
full onyx
we havent learned it
full onyx
but yeah idk
chilly bobcat
i think we can do without circles
oh wait
yes you can
extend BD a bit
you can do something like this
using exterior angle theorem
$2\alpha + 2\beta = 180^{\circ}$
solid kilnBOT
granite light
that's actually a smart way to solve this
candid prawn
complex numbers
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complex numbers
candid prawn
The complex number u is given by u = -1 -i√3
*express u in the form r(cosθ + i sinθ) where r > 0 and -π < θ < π. give the exact values of r and θ *
candid prawn
*The complex number **u** is given by **u = -1 -i√3***
okay so i rewrote this as u = -1 - √3i
and to find 'r' i found modulus of u
so r = 2
and to find θ idk tf i did
tough mist
hey guys
i have the amc 12 coming up
from now to then
is it possible to qualify for AIME
whole coral
hey guys
i have the amc 12 coming up
from now to then
is it possible to qualify ...
!occupied
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hey guys
i have the amc 12 coming up
from now to then
is it possible to qualify ...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
whole coral
bruh
You need to go to the "math help available" channels, but seeing your question, it's more fitting for #discussion or #serious-discussion
whole coral
and to find θ idk tf i did
Anyways, maybe try explaining as much as you can?
velvet coral
You need to go to the "math help available" channels, but seeing your question, ...
why dont I have access to these channels though man?
sorry for interrupting, I will be gone in a sec
candid prawn
dw
whole coral
why dont I have access to these channels though man?
(because you have the studying role which blocks out the social channels)
velvet coral
(because you have the studying role which blocks out the social channels)
ah ok, thanks, nvm me
candid prawn
Anyways, maybe try explaining as much as you can?
okey so i plotted the point on a mini graph (just a sketch)
i plotted (-1, -√3)
so they both in the negative quadrant (?)
i calculated the key angle or idk what its called, by tan^-1 (√3/1)
which gave pi/3
theta = arg (u) = - π - π/3
= -4 π/3
which is apparently not good
whole coral
I mean, you're technically not wrong, but because they asked you to give your angle between -pi and pi
Acutally wait pause 
whole coral
theta = arg (u) = - π - π/3
Why -pi/3?
candid prawn
i calculated the key angle or idk what its called, by *tan^-1 (√3/1)*
it gave that when i did that ^
candid prawn
In particular, why negative instead of positive <:RooThink:532310138439073792>
wdym
idk what i did i barely understand the chapter 😭
chilly bobcat
its just basic trig tbh
whole coral
which gave pi/3
As in, you found this to be pi/3, why did you subtract this from -pi instead of adding it? What was the reasoning?
candid prawn
wait lemme try rq
idk if you get it but
but like, 1st two quadrants (anticlockwise idk) are 0 to pi, and starting 1st two (clockwise) are 0 to -pi
whole coral
I'm liking the sound of what I'm hearing
whole coral
And what did you get?
whole coral
Aha, but then, remember our diagram here now
whole coral
but like, 1st two quadrants (anticlockwise idk) are 0 to pi, and starting 1st tw...
And also what you said here too 
Whatever the angle you find as theta, you may wanna make it negative
candid prawn
Whatever the angle you find as theta, you may wanna make it negative <:sky_pikaO...
like, that angle bounded to the x-axis?
so - π - (- π/3)?
WHICH GIVES ME -2π/3
whole coral
Yep, also, as well-
candid prawn
😭
whole coral
whole coral
The orange is pi/3, and we want the theta, which we can get by going backwards by pi, so then pi/3 - pi
whole coral
so - π - (- π/3)?
Which is the exact same thing here
candid prawn
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