fair enough
#help-0
vale sapphire
Okay, let me recollect here
d(1/x) is not 1/h for any particular value h. d(1/x) is how much 1/x changes when you give it a little nudge, a nudge of dx for instance
So, you could think of it like 1/(x+dx)-1/x
the little change in 1/x when dx gets really small is what we call d(1/x)
wooden sapphire
right
vale sapphire
But yes, the main point is that if dx is really small, if the variation is truly tiny, that rectangle in the top-right becomes very small
negligibly so
So you're only left with the green and red rectangles
sorry, got confused myself for a second
Before dx was added, the red area was there but not the green one
After dx is added, ie the green area is added, that red rectangle is no longer there
What 3b1b is saying, is that (neglecting the top-right rectangle), what you gained in one place must have been reflected in the other one
i.e the areas of the two rectangles must be the same
wooden sapphire
did you get to the end where he tells you to come up with d(1/x)/dx?
well, the end of the section of the video
vale sapphire
it's been a hot minute since i watched this
wooden sapphire
I understand the concept of what is happening here. What I don't understand is how the fuck you're supposed to come up with d(1/x)/dx using this image.
wooden sapphire
uhhhhh
ahh, see I don't even know
I can write out in words what a derivative is
vale sapphire
he gives you the width and the height, who cares if it's symbolic, the formula you learned in whatever-th grade still applies
wooden sapphire
is it a trick question?
wooden sapphire
are you telling me that d(1/x)/dx is the area of the red/green rectangle?
wooden sapphire
the red rectangle is d(1/x)/dx.
buoyant kayak
what is the formula for area of a rectangle
buoyant kayak
what is the width of the red rectangle
vale sapphire
correct
buoyant kayak
what's the height
wooden sapphire
d(1/x)
buoyant kayak
yes
so area is?
it's signed
oops
height is d(1/x) but remember this is a negative area
keep that in mind
i guess it's technically -d(1/x) huh
vale sapphire
yeah it is
wooden sapphire
I'm stuck
buoyant kayak
this is not a trick question
you know the width
you know the height
put them next to each other
that's the area
can you tell me what the area is
wooden sapphire
x * d(1/x)
vale sapphire
correct
buoyant kayak
remember it's negative
wooden sapphire
-x * d(1/x)
vale sapphire
actually correct
wooden sapphire
dx * 1/x
buoyant kayak
right
vale sapphire
what do you know about these two areas?
wooden sapphire
they're equal
buoyant kayak
yes
vale sapphire
write that and solve
buoyant kayak
so solve for d(1/x)/dx
buoyant kayak
if it helps you can show your work and we can point out what's wrong
wooden sapphire
I see it
so...
the issue I guess
was that I was trying to simplify the problem by substituting
but I was substituting something that wasn't equivalent
I'm still stuck on why that is exactly
buoyant kayak
what did you substitute
wooden sapphire
I substituted d(1/x) for 1/h
buoyant kayak
vale sapphire
what is h
buoyant kayak
f(x)=1/x, so if you wanted f(h), sure, that's 1/h
wooden sapphire
h is dx
buoyant kayak
but as systems already said
vale sapphire
h is dx
if dx is 0.01, 1/dx is 100
by writing d(1/x)=1/dx, you are telling me that when i go to the right by 0.01, 1/x increases by 100
it's a really simple formula
unfortunately it's wrong
wooden sapphire
the only answer my brain can come up with is that you can't put dx as x in d(1/x) because the function doesn't behave the same at every point. To get an accurate representation of how the function would behave at x+dx, that's what you have to plug in.
I can't tell if I'm lost at this point because I am that stupid or because I've subconsciously given up
buoyant kayak
d(1/x)=dy, dy != 1/dx
wooden sapphire
what is the ! for?
buoyant kayak
does not equal
buoyant kayak
so why do you think it does
wooden sapphire
I don't anymore
buoyant kayak
wooden sapphire
d(1/x) is (1/x+h) - (1/x) right?
if I stop thinking about the diagram it makes a shitload more sense
h being an infinitely small number
lone heartBOT
Available help channel!
fringe dome
A hypothesis test using 95 percent confidence has a significance level equal to
wintry lotus
What do your notes say a significance level is?
lone heartBOT
@fringe dome Has your question been resolved?
tacit arch
A hypothesis test using 95 percent confidence has a significance level equal to
Do what Buxy suggested
lone heartBOT
@fringe dome Has your question been resolved?
alpine sable
In this function. I have found the secant slope which I believe to be 2 but what about the tangent slope?
alpine sable
How should I think
abstract fractal
Do you know how to take a derivative?
alpine sable
yes and in this case it would be 3x^2 - 2
abstract fractal
Yes. Do you know what the derivative represents?
abstract fractal
The derivative is the slope of the tangent line at some x value
alpine sable
I should put them in the formula
abstract fractal
What x value is the line tangent to on the graph?
abstract fractal
So plug 1 in to the derivative
alpine sable
its 1
abstract fractal
That's the slope
broken pine
I can get to the answer unprofrofessionally
But whats the actual method ur supposed to use to get as high marks as possible
proven meadow
to solve for x?
broken pine
Yea to get the value of x
proven meadow
distributive property
2(x+y) = 2x +2y
each term in the bracket is multiplied by 2
broken pine
Whats the bracked
wary stream
No need to distribute, tbh
broken pine
Im not familiar with these english terms
broken pine
Ah i figured
proven meadow
so 2(6 + x²) would become...?
broken pine
Oh lol
wary stream
FYI distribution is an extra, not needed step
proven meadow
FYI distribution is an extra, not needed step
ya that is true
proven meadow
But whats the actual method ur supposed to use to get as high marks as possible
i mean he said this tho
broken pine
FYI distribution is an extra, not needed step
Is it needed to get an A on the question
wary stream
Actual method is just solving for x
You don't need to do extra steps
As long as you solve for x, that's all you need
broken pine
Mhm
And how would u do that
The way i did it was just that i knew that x² had to be 9
Therefore i knew the answer was 3
But how do you get to it profesionally or whatever
wary stream
The proper term is algebraically
broken pine
Also the answer is supposedly +-3
broken pine
The proper term is algebraically
Alright
lone heartBOT
Available help channel!
dry echo
Could you figure this out in your head?
lone heartBOT
Could you figure this out in your head?
dry echo
I wanna understand if I'm slow because I had to use pen and paper and manipulate that equation a bunch of times until I found it
Is there a quick way to figure it out?
vague coral
Could you figure this out in your head?
I can't lol
manic wind
You have to use systems of equations
vague coral
system of equation and it's done
dry echo
I just wanted to make sure if I was dumb
manic wind
I don't think there is a short cut unless it's super obvious
vague coral
the values aren't so obvious tho so we cant find it in our head
dry echo
I always have this feeling like I'm too slow or something
But it's probably just in my head lol
vague coral
maths is dumb
wintry lotus
wouldn't it be (6/(x^2))^(x)?
dry echo
Well, with all those roles
wintry lotus
haha
vague coral
dry echo
wouldn't it be (6/(x^2))^(x)?
Would you tell me your thought process tho?
vague coral
well not really
wintry lotus
^ pretty much that, since your graph doesn't appear to go negative, you will have x^(even) somewhere
vague coral
b = 2 or -2
then C = -3 or 3
but since the graph increases
positive values I guess
vague coral
dry echo
.close
pseudo isle
lone heartBOT
pseudo isle
can someone tell me why this happens?
tacit arch
Distributive property
pseudo isle
thank you so much
tight locust
Distributive property
You can easily prove this geometrically
Let me demonstrate with a rectangular argument:
This is fundamental
Now you know
alpine sable
of paper money: the 17 Yacley bill and the 5 Yacley bill. How many different combinations
of these bills total 453 Yacley?```
I don't know how to approach this questionCasework
Start with one 17 Yacley bill, see if 453-17*1 is a multiple of 5, then move on to 2 Yacley bills, etc.
shadow bloom
My name is chad, I've been shooting hoops since I was 5 and I got 17 peoples lunch money today, 7 had 8 dollers and 6 had 3 dollars and 4 had 12 dollars, how do I figure out how much lunch money I have?
shadow bloom
<@&286206848099549185>
glass lichen
<@&286206848099549185>
Don't ping right away.
glass lichen
How old are you?
shadow bloom
17
glass lichen
High schools don't have recess
glass lichen
Also that is very much, bar the stupidity of how it's written, an elementary age question
Just use a calculator and stop making a fool of yourself
shadow bloom
I failed my maths gcse
wintry lotus
Saturday recess?!
glass lichen
That too 
alpine sable
My name is chad, I've been shooting hoops since I was 5 and I got 17 peoples lun...
$0 You cant shoot hoops.
lone heartBOT
@shadow bloom Has your question been resolved?
hasty elk
not to mention i'm pretty sure it's damn near midnight in Britain
glass lichen
It is
native elbow
hello !(solving problems involving radicals)
A woman walks 5 kilometers to the east going to school and then bikes 9 kilometers northward going to church. How far is she from the church to the starting point which is her house?
wintry lotus
Have you drawn it out?
native elbow
yes i actually have a solution already-
my solution:
c= √9^2 + 5^2
c= √81+25
c= √106
c= 106km
is this correct ??
it feels weird bc my final answer is a pretty big number-
wintry lotus
sqrt(106) sounds right
ocean sealBOT
dldh06
native elbow
idk either i just followed a yt video 🧍♂️
native elbow
oh
wary stream
I'm pretty sure that video didn't make it disappear
native elbow
here's the vid-
wary stream
Maybe if it was a squared number, like $c = \sqrt{81}$
ocean sealBOT
dldh06
wary stream
That's when it can disappear because sqrt of 81 is 9
native elbow
do u guys mind telling me how to properly solve for it then? So i would know next time
wintry lotus
because sqrt(100) = 10
wary stream
Sqrt(106) is a valid answer
You just need to know when it's a square number
Like 106 is not a square number
But 100 is
distant flare
≈10.29563km
wary stream
Eh, decimals aren't exact though
distant flare
yeah, which is why i used ≈
but often times teachers just want the answer like that
at least that from my experience
native elbow
okay so which part of my solution was wrong- and how do i correct it?
lone heartBOT
lone heartBOT
Available help channel!
frosty eagle
this is review, is this correct?
lone heartBOT
this is review, is this correct?
shadow bloom
Hey nerds
tacit arch
.close
somber basin
Im being asked to prove that the theory of an F-space is complete (where F is a specific infinite field). But the trivial vector space is a vector space over the reals... a complete theory with an infinite model can't have any finite models. So, why isnt that a counterexample?
pale kestrel
try an advanced channel
somber basin
How do I get permission to chat in those?
manic wind
somber basin
thanks
worthy adder
how do i solve this using shell method
lone heartBOT
how do i solve this using shell method
worthy adder
would the radius be r=x-1
worthy adder
that is the book work not mine
this is different from what i normally do since the about x=1 is touching the equatoion
glass lichen
this is different from what i normally do since the about x=1 is touching the eq...
Have you drawn the region to start...?
worthy adder
yes
glass lichen
So, like riemann said, show your work...
worthy adder
glass lichen
and your work..?
worthy adder
that is all because i dont know how to approach it
worthy adder
the textbook never show this kind of example
i already serch thru and far cant find anything
professor suck really bad at teaching
glass lichen
No, cause I really doubt you actually googled "shell method examples"
glass lichen
Shell Method is using cylinders...
worthy adder
i know but this one in particular is making go insane
glass lichen
The resource I linked has examples w/ cylinders.
worthy adder
yes but they dont have it with it rotating in the in the shaded area
do u get what im saying
glass lichen
no
glass lichen
you can just ignore the part of the region to the left
worthy adder
so radius is just x
glass lichen
Radius, as shuri told you already, is a difference of functions of y..
worthy adder
than it would be r=4x-x^2-1
lone heartBOT
@worthy adder Has your question been resolved?
abstract fractal
you can just ignore the part of the region to the left
How would you know from the problem whether it's the region to the left or right?
Edit: nvm I see. It's not that we're ignoring the left part, it just gets swallowed by the right part during the rotation, right?
pale kestrel
I would shade in on your graph
the relevant region
thats being rotated
Identify the closed region.
grizzled ridge
Is this arrow means psi is a mapping from M-dimensional real space to the Hilbert space? I this case, can I say that "psi \in H" ?
tacit arch
Is this arrow means psi is a mapping from M-dimensional real space to the Hilber...
look in the textbook for notation
psi is a mapping from M-dimensional real space to the Hilbert space?
yes
"psi \in H" ?
no. the image of Psi is in H
grizzled ridge
> "psi \in H" ?
no. the image of Psi is in H
Thank you. Do you mean it is "Psi \in H" ?
tacit arch
Thank you. Do you mean it is "Psi \in H" ?
no. look up the definition of image
snow wind
hi
snow wind
part b
it would be an honour if someone could explan it to me
i know one method is to just find the probability between 1 and 2 defectives
but why can I not use the conditional probability fomrula here
manic wind
Find the probability that there are more than 2 defective lamps
snow wind
why can i not use this formula for this case
is my question
they are independent events
manic wind
Yes they are independent events, so conditional probability doesn't make sense
The defection of lamp A won't affect the probability that lamp B is defected
snow wind
oh fuck
i see
thanks a lot
just to clarify
i can just do this right
P(X <= 2 | X > 0)
manic wind
Yeah
cunning trout
lone heartBOT
gray isle
what have you tried
cunning trout
I don’t know where to start from given all that information
desert cradle
they straight up gave you the roots
gray isle
iirc, you've encountered these types of problems before
there are multiple ways to approach this
since you're given the roots, you could consider applying something like factor theorem
manic wind
Do you recognize (x-a)(x-b)
cunning trout
I think I need help
cunning trout
Do you recognize (x-a)(x-b)
I think, I forgot a little
manic wind
Like others have mentioned, that's the factor theorem. When k is a root of a polynomial, (x-k) is a factor.
cunning trout
I’m still confused
manic wind
When you look for roots in a polynomial in the form (x-a)(x-b) ... you're trying to make y = 0, and the way to do that is for x - k to be 0.
cunning trout
Do you recognize (x-a)(x-b)
But it’s not in this form
manic wind
Well the factored form tells you the roots, and in your original problem it tells you the roots
cunning trout
True but how would I find the value of a b and c
manic wind
Is there anything you can do to go from (x-k)(x-h) to ax^2 + bx + c?
If you've done factoring this should look very familiar
cunning trout
We can expand it
manic wind
Yes
gray isle
don't forget about the scaling factor
cunning trout
What’s that?
gray isle
the a
considering factor theorem, your function can be expressed in the form
f(x) = a(x-p)(x-q)
cunning trout
That makes it like a cubic equation
gray isle
how does that make it a cubic
manic wind
a is a constant
gray isle
(i like to use p,q. avoid using variables that are already established in relevant formulas)
cunning trout
I don’t understand, what exactly are we trying to do?
I don’t understand because the chapter I did doesn’t talk about any of this
gray isle
the ultimate goal is to determine a,b,c
cunning trout
Yes
gray isle
factor theorem allows a simple way to determine a
and ultimately the entire quadratic polynomial in factored form
which you can then expand to identify the values of b and c
cunning trout
I still don’t get it
gray isle
do you understand factor theorem
gray isle
iirc based on what you've asked in the past, you've definitely done stuff on factor theorem before
cunning trout
Yh I have done some stuff in factor theorem
But what I mean is I haven’t properly started it in my book
Which is what’s asking me confused in this question
gray isle
its pretty much
p is a root of the polynomial iff (x-p) is a factor
zenith compass
lone heartBOT
zenith compass
can anyone tell me how to conclude that sqrt((a+c)^2+(b+d)^2) less than or equals to sqrt(a^2+b^2)+sqrt(c^2+d^2)
Though I can use am-gm ineq
But i am not sure if they are all logically equivalent
Also I wonder if there is a more straightforward way (perhaps dun hv to apply other theorems) to prove it
I am proving the general triangle inequality for complex number btw
If I have to make a formal proof
How to make it “formal”?
little drum
little drum
Use QM ≤ AM
tight locust
QM?
little drum
me thinking.. quadratic mean would be insufficient, need at least biquadratic mean lol
zenith compass
Ummm
hasty elk
pretty sure you just need manipulation and squaring to get rid of square roots
zenith compass
<:thinkies:827642567775748163> _me thinking.. quadratic mean would be insufficie...
Is that the root mean square
little drum
yep (realized you'd still need some manipulns tho)
little drum
can you figure the rest?
zenith compass
Umm use the cosine formula?
little drum
use whatever you would to show AB + BC ≥ AC ig
little drum
😑
zenith compass
Lol but I still don’t understand
little drum
well this'd be more intuitive ig, if you've done triangle law
zenith compass
Is it true that “$|u+v|^2=u^2+2|u+v|+v^2$”?
ocean sealBOT
Trenton
zenith compass
I rmb it is true for absolute value, but dk if it still apply on modulus of complex number
zenith compass
well this'd be more intuitive ig, if you've done triangle law
But somehow this method use theorems that proved by the sqrt(a^2+b^2) definition
tight locust
Just use the axiom that the minimal distance between two points is a line
Any path other than a line will necessarily be longer
oak perch
ocean sealBOT
zenith compass
And to conclude that it is equals to
zenith compass
$|x|^2 = x^2$
Ok
zenith compass
btw if you didn't know,
So now I am a step closer
Now I have to prove that u^2+v^2-|u+v|^2=-2Re(u(v bar))
zenith compass
Oh yes, x=3+4i is a counter example
little drum
thinkin
screams
why was I thinking vectors
nvm, just me being terrible at complex numbers :c
zenith compass
Now I have to prove that u^2+v^2-|u+v|^2=-2Re(u(v bar))
Now this change to |u|^2+|v|^2-|u+v|^2=-2Re(u(v bar))
hasty elk
why did we not just use a b c d again
hasty elk
ah
zenith compass
As abcd is kinda geometric interpretation
hasty elk
in complex numbers, $|z|^2 = z\overline{z}$
ocean sealBOT
Camilleone
hasty elk
have fun
zenith compass
Oh thank you
little drum
**Camilleone**
omg thattttttttttt
zenith compass
zenith compass
zenith compass
Umm
hasty elk
you went the wrong way lol
zenith compass
Opps
hasty elk
don't move the square in
hasty elk
use $|z|^2 = z\overline{z}$ directly to get rid of the squares
ocean sealBOT
Camilleone
odd herald
whats a+7x?
zenith compass
Oh
little drum
how does that end up any different from the a b c d thingy, except a little difference by defining f(u, v) = (|u| + |v|)² - |u + v|²
odd herald
what is a+7x
little drum
Ansh, wanna take it from here?
nu :c I've never once been formally introduced to complex numbers
hasty elk
opps lol
hasty elk
_how does that end up any different from the a b c d thingy, except a little dif...
the two methods are more or less equivalent if you break things down, but this one is more concisely phrased
little drum
hence the |x|² = x² confusion (@_@;)
little drum
the two methods are more or less equivalent if you break things down, but this o...
noted that!
Also, is using this circular?
zenith compass
little drum
cause a little tweaking with argand plane and the usual triangular law shouldn't hurt
hasty elk
go on and expand that bad boy at the right, yeah
hasty elk
Also, is using this circular? <:thinkies:827642567775748163>
circular? huh?
little drum
I mean, using |u| + |v| ≥ |u + v| to prove |u| + |v| ≥ |u + v| lol
hasty elk
I mean, using |u| + |v| ≥ |u + v| to prove |u| + |v| ≥ |u + v| lol
that is very certainly circular
little drum
can't use geometric arguments in complex plane then, ig
unless we've shown the triangular inequality holds I think it can be, cause the inequality only concerns the real parts
hasty elk
_can't use geometric arguments in complex plane then, ig_
bite your tongue i totally use geometry to argue complex numbers
little drum
let's gooooo
zenith compass
But why the rightmost term is equals to Re(u + v bar)?
hasty elk
if you take a general $z = x + iy$, what is $z + \overline{z}$?
ocean sealBOT
Camilleone
zenith compass
Only the real part x
little drum
*twice
zenith compass
As yi -yi cancel out each other
hasty elk
by the way it's not $2(u\overline{v} + v\overline{u})$, check your constants
ocean sealBOT
Camilleone
zenith compass
So $z+\overline{z}=2Re(z)$
hasty elk
So $z+\overline{z}=2Re(z)$
no, again check your constants
ocean sealBOT
Trenton
zenith compass
This?
hasty elk
yes
hasty elk
by the way it's not $2(u\overline{v} + v\overline{u})$, check your constants
also, this
little drum
hasty elk
sure, but do you know why you can do it?
hasty elk
well...you could do it, but i really was more looking for a knowledge of how complex conjugate plays with multiplication
zenith compass
Oh
hasty elk
like, if you knew what $\overline{zw}$ was
ocean sealBOT
Camilleone
zenith compass
In general, $\overline{zw}= \overline{z} .\overline{w}= \overline{w} .\overline{z} =\overline{wz}$
ocean sealBOT
Trenton
zenith compass
Yay
hasty elk
yeah, that's it
hasty elk
that's the one that tells you you can get the third line here
(also the fact that $\overline{\overline{z}} = z$, but this is more or less trivial)
ocean sealBOT
Camilleone
little drum
what's the geometric interpretation of multiplication and division in complex plane though 
how to show bar{zw} = bar{z} bar{w} geometrically T_T
hasty elk
bar is a reflection
multiplication is a scaling plus a rotation
if you multiply $z$ by $w$, you scale $z$ by $|w|$, then rotate that position vector about the origin by $\arg w$
ocean sealBOT
Camilleone
little drum
unlike vectors where product leaves you with the magnitude 
hasty elk
yeah, that's down to the fact you have an additional structure
little drum
$zw = (z |w|) \qty(\cos(\arg{w})+ i\sin(\arg{w}))$
ocean sealBOT
hasty elk
yes
if you want to put it in that form
sure
personally i think it's easier to see using $re^{i\theta}$
little drum
yay! I see the rotation
ocean sealBOT
Camilleone
little drum
:o
hasty elk
but whatever works for you hahaha
little drum
will take time understanding rotation in terms of e^{i\theta} ig
hasty elk
have fun 😛
lone heartBOT
@zenith compass Has your question been resolved?
zenith compass
I think II is $Re(|u\overline{v}|)$
ocean sealBOT
Trenton
zenith compass
But I am not sure what to compare
lone heartBOT
@zenith compass Has your question been resolved?
little drum
Looks good, yes
ocean sealBOT
little drum
What you've written is essentially: $x^2 \leq x^2 + y^2 = \abs{\mu \overline{\nu}}^2$
ocean sealBOT
zenith compass
Ok thank you
Thank you Ansh, Camilleone, Cogwheels of the mind and EndTimes
.close
lone heartBOT
lone heartBOT
Available help channel!
fierce tartan
Can anyone help me ? What is the correct max value?
lone heartBOT
Can anyone help me ? What is the correct max value?
solemn grove
Can anyone help me ? What is the correct max value?
in terms of magnitude, you’ll get one other value that is maximum too i think,
4 *-sin(theta) = r
so if -sin(theta) = 1
sin(theta) = -1
you’ll again get a max value
lone heartBOT
@fierce tartan Has your question been resolved?
fierce tartan
So the correct answer is (-4,3pi/2)?
This is one of my profs presentation
Because according to the presentation, sine is fixed to be maximum when it is 1
fierce tartan
This is one of my profs presentation
I searched the max value of this one on google and it turns out that it is (7,3pi/2) rather than my prof’s answer. But what I think is that, she fixed the idea that sine is maximum when it is equal to 1 or pi/2
solemn grove
dw matey, i’ve done polar curves. basically the max value is when the differential = 0
you can think of it like that
for your example
it’s not necessary or wtv
but in general, for harder problems
dr/dtheta = 0
find theta
and plug it back into r
remember, we only care about the magnitude of r
so
solemn grove
This is one of my profs presentation
yeah no. but it’s only magnitudes you see?
fierce tartan
Ill confirm it to her tomorrow then Ill just follow her hahahahaha
solemn grove
it’s fine matey
your working looks alright to me,
but if it’s just a multiple , then you know. both,(pi/2) and (3pi/2) give you a maximum
just plug 3pi/2 in and see
you need to be able to adapt and see what do you need to get the maximum of the eqn as a whole
r = 3 - 4sin(theta) for example
you can’t get your max by plugging in pi/2
or for 2+ sin(3theta)
you need to know what to pic and stuff
maximum of sin function =1
minimum of sin function = -1
depending on the equation, you need to make choices
old pelican
With 4044 cookies in the form of equilateral triangles, Mynor arranges to place them in a peculiar way consisting of two rows with the same number of cookies. The ones in line top numbers them from 1 to 2022, as shown in the image.
Mynor eats all those cookies in the top row that occupy position 6n + 4, with n ≠ 0, that is, those in positions 10, 16, 22,. . ., 2020.
When Mynor finishes eating the cookies, what is the perimeter of the new shape?
old pelican
I don't really get the question itself, how am I supposed to calculate a perimeter if I don't have the measurements?
It's a really large shape though.
(Shadowed triangles = Eaten cookies).
I guess that I could calculate somehow the perimeter of the repeated shape in there.
old pelican
(Shadowed triangles = Eaten cookies).
I guess that I could calculate somehow the...
And then just multiplying it? Not sure if that's right.
old pelican
try the question for smaller numbers?
Oh, wdym?
pale kestrel
i dont see how that drawn helps
what happens to the perimeter when a cookie is eaten?
old pelican
New side of the shape?
pale kestrel
?
uh
If the perimeter is P
at the start
and I eat the cookie at 10
what happens to P
old pelican
P becomes a smaller number? Idfk, I don't understand-
pale kestrel
You think the perimeter decreases when a cookie is eaten?
refer to your 1st diagram
pale kestrel
(Shadowed triangles = Eaten cookies).
I guess that I could calculate somehow the...
what happens to the perimeter when the triangle 10 is taken away
old pelican
You think the perimeter decreases when a cookie is eaten?
Yes.
old pelican
what happens to the perimeter when the triangle 10 is taken away
oh, nothing
old pelican
idk i don't understand at all
pale kestrel
You have this bar
what is the perimeter of it?
right now as it is drawn in your diagram
No cookies have been eaten
old pelican
86?
pale kestrel
no... how did you get that
old pelican
that's the amount of cookies in the diagram
pale kestrel
how is that the perimeter though
what does perimeter of a shape mean?
thats perhaps the problem
old pelican
what does perimeter of a shape mean?
sum of all the sides?
pale kestrel
length around the outside
not all cookies are contributing to the perimeter
the cookie 11 adds nothing to it
old pelican
oh gotcha
old pelican
what is the perimeter of it?
36?
old pelican
38?
pale kestrel
im looking
pale kestrel
Not sure where this is from.......
I am trying to get you to see
the difference in perimeters
after taking 10 away
I don't see how you get 2 extra
The top side will not be 18.
old pelican
oh okie uh
pale kestrel
Ok so for the top side
how much of the perimeter is horizontal
I want to see how you got 18
I'm talking about after weve removed 10
old pelican
i mean i usually counted 10, 12, 14, 16, 18(etc.) because they were part of the border of outside
but now that i don't have one and the top it's not horizontal
i don't really have any idea of what to do
i though maybe of like something like this but idrk what to do with that little bump
pale kestrel
correct
all good, now what is the extra perimeter from the wedge
you marked the relevant perimeter yourself
remember these are equilateral triangles
pale kestrel
it is 37
old pelican
oh really?
pale kestrel
well yes i mean...
you marked it very clearly yourself
my point is though, why does it go from 36 to 37
what exactly changes
old pelican
the number of sides?
old pelican
the number of sides increases
pale kestrel
Very vague, be more specific
You marked on the diagram yourself
you marked what was new
old pelican
the number of sides increase because uh
idk how to explain this
because the sides get split into two? idfk
pale kestrel
Ok think about it this way?
what changes and what doesnt in the diagram
Everything else stays the same except at the 10 triangle yes?
old pelican
the top side, the rest of the sides are the same
pale kestrel
You dont even need to look at the entire top side
literally the only thing that changes is the triangle where 10 is at
old pelican
Everything else stays the same except at the 10 triangle yes?
yes
pale kestrel
When 10 is present
which of its sides counts towards its perimeter
and what about when its not
old pelican
the top side?
old pelican
the top side and the new little hole here?
pale kestrel
Yes my point is
when 10 is there you count only the top side
when 10 isnt there you count only the other 2 sides
old pelican
oh yea
pale kestrel
Can you see why eating the cookie 10 will result in the total perimeter increasing by 1?
old pelican
ye i get it thanks
pale kestrel
Now apply this to solve the Q
old pelican
okie
old pelican
With 4044 cookies in the form of equilateral triangles, Mynor arranges to place ...
so, if in total, mynor eats 353 cookies
([352*2]+[2*352])+2+2
?
[352*2] comes from the split of the eaten cookies into two sides
[2*352] is the space between them
kinda like this?
pale kestrel
im not sure about the final answer but as long as you have the right process 🙏
Just be careful what the end of this bar will look like.
old pelican
okie
the bar also ends like this
that's why i subtracted 1 from 353
that's all then
thanks
.close
fierce solar
if 3sin(x) + 4cos(x) = 5
deduce the value of sin (x)
lone heartBOT
if 3sin(x) + 4cos(x) = 5
deduce the value of sin (x)
fierce solar
I've tried dividing the equation by 5 and feel like i there might be a relation between it ans cos^2 + sin^2 = 1 but i cant go further
little drum
I've tried dividing the equation by 5 and feel like i there might be a relation ...
perfect feeling!!!
here's a hint: $$sin(x + A) = \cos A \sin x + \sin A \cos x$$
fierce solar
uh whats the dashthrough circle symbol i dont think I've taken it
gray isle
its the greek letter phi
ocean sealBOT
fierce solar
oh I'll to solve it and respond in a couple mins
little drum
wait a sec! I'm kind of curious
little drum
oh I'll to solve it and respond in a couple mins
how much on a rate of 1 to 10 are you comfortable with trigonometry?
it can also go beyond 10 out of 10 tbh lol, your call
fierce solar
~6 i guess
ocean sealBOT
little drum
square both sides and use (cos x)² = (1 - (sin x)²)
fierce solar
we've only taken a bit this year and the lesson was removed from last year's curriculum so they kinda crammed both years lessons and im kinda lost
little drum
then it's just a quadratic
lone heartBOT
@fierce solar Has your question been resolved?
little drum
$16\cos^2 x = 25 - 30 \sin x + 9\sin^2 x$
ocean sealBOT
little drum
$\implies 25\sin^2x - 30 \sin x + 9 = 0$
ocean sealBOT
little drum
right?
fierce solar
yeah
little drum
$\implies (5 \sin x - 3)(5\sin x - 3) = 0$
ocean sealBOT
little drum
$\implies \sin x = \frac{3}{5}$
ocean sealBOT
fierce solar
alright thanks i'll revise it whole then tell u if i understood the concept
alright all solved
thanks for your help
little drum
:D
before you leave, I have a curious question
is that your cat flying towards the camera? in your pfp
vague coral
maybe
little drum
arctan transformation
little drum
$\int \frac{1}{100\qty(1+\qty(\frac{3x}{10})^2)} \dd{x}$
ocean sealBOT
fierce solar
_is that your cat flying towards the camera? in your pfp_
unfortunately no
i'll leave now so i wont disrupt u helping
little drum
btw .close before you leave (@_@;)
fierce solar
.close
lone heartBOT
little drum
tyvm
lone heartBOT
Available help channel!
sharp glacier
lone heartBOT
sharp glacier
Hi
I need to have the same base
But I forgot how I can do that
When I have the same base I can substract the exponent
We did this a long time ago in class but I forgot how to do it
harsh swallow
don't you have the same base?
harsh swallow
you have 5 x^m x^-2
harsh swallow
harsh swallow
alpine sable
$\int \frac{1}{100\qty(1+\qty(\frac{3x}{10})^2)} \dd{x}$
wont it be 10 outside?
sharp glacier
Where is the 5
harsh swallow
i didn't take the 5 into account the 5 is just in front
sharp glacier
Oh okay
harsh swallow
sharp glacier
Tysm
little drum
sylveon handwriting
sharp glacier
.close
sharp glacier
@harsh swallow quick question
lone heartBOT
<@160921656313905152> quick question
sharp glacier
What is the right answer for this
When the base and exponent are the same
Do we multiply the base and add the exponents
Or just keep the bases as they are and add the exponents?
harsh swallow
$10x^{10m} * 10x^{10m} = 10 * 10 * x^{10m + 10m}$
ocean sealBOT
Katharine
lone heartBOT
harsh swallow
yes
harsh swallow
i can't read it :S
lone heartBOT
Available help channel!
ripe rain
$\lim_{x \to \infty}\frac {x (log x)^3} { 1+x + x^2}$
lone heartBOT
$\lim_{x \to \infty}\frac {x (log x)^3} { 1+x + x^2}$
ocean sealBOT
Deep
ripe rain
Can we do it without l’hospital
alpine sable
i can't read it :S
ripe rain
Occupied
alpine sable
bro I'm here before you
lone heartBOT
harsh swallow
@ripe rain can you reopen?
ripe rain
.reopen
lone heartBOT
✅
harsh swallow
ok thanks
alpine sable
.reopen
harsh swallow
i'll ask you when we're done
alpine sable
bruh
harsh swallow
😄
alpine sable
okay
harsh swallow
,rotate
ocean sealBOT
harsh swallow
your du = isn't correct
alpine sable
finish deep and we'll discuss abt mine
harsh swallow
i asked him to reopen so that we can continue here
otherwise you'd have to open a new one
whole hasstle
alpine sable
Ur wish
harsh swallow
hassle
harsh swallow
if u = 3x^2/10
alpine sable
I shld find the calculus 2-integrals
alpine sable
lone heartBOT
alpine sable
Why can't this equal zero???
hasty elk
...because that vector is non-zero...?
solemn grove
because it’s not zero?
solemn grove
...because that vector is non-zero...?
^^
you know how to find det of matrix right ?
i, j and k are unit vectors in this case,
by definition they’re non zero
old pelican
i just don't really know how to get the dimensions of the triangle
hasty elk
hint: start by figuring out the edge length of a hexagon
fallen sparrow
use the hexagon area formula
fallen sparrow
hint: start by figuring out the edge length of a hexagon
as camilleone said
try to find the area of one small triangle
then add areas like -
12+ (6* area of one small triangle)
Area of a hexagon = (3√3* side*side)/2
lone heartBOT
@old pelican Has your question been resolved?
ripe rain
How do we show that Thomae function is continuous at all irrational numbers and discontinuous at all rational numbers
lone heartBOT
How do we show that Thomae function is continuous at all irrational numbers and ...
@ripe rain Has your question been resolved?
lone heartBOT
Available help channel!
stiff hornet
lone heartBOT
stiff hornet
I need help with all parts
lone heartBOT
@stiff hornet Has your question been resolved?
stiff hornet
<@&286206848099549185>
lone heartBOT
@stiff hornet Has your question been resolved?
stiff hornet
someone help
tacit arch
Do you know what discrete uniform distribution is?
stiff hornet
no
tacit arch
no
"data" means points of the form [(x1,y1), (x2,y2),...,(xn,yn)]
So all of the datum has probability 1/n
lone heartBOT
@stiff hornet Has your question been resolved?
upbeat kayak
Given a f(x) what is a sufficient condition for one of the roots to be between two numbers(let's say 2<x1<-1) and the other not to be