$E(X) = \int ^{\infty} _{-\infty} x f(x) dx$
why is $E(Y) = \int ^{\infty} _{-\infty} x^2 f(x) dx$
#help-28
neon mulch
glossy valveBOT
manaclo
mighty ridge
that's not it
neon mulch
but in the solution they use $E(Y) = \int ^{\infty} {-\infty} x^2 f(x) dx$
glossy valveBOT
manaclo
neon mulch
i dont get why it works
mighty ridge
I'm looking at what's the name of the theorem for that, I don't know it in english
neon mulch
can you send the name anyway?
mighty ridge
in french it's called théorème de transfert
merry pecan
I've been given the values for AE and GK. AE = 20.3, GK = 9.1. How do I find the volume of the tank, starting with all the lengths. All I've been able to work out is the length of lines ED and CA.
merry pecan
<@&286206848099549185>
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@merry pecan Has your question been resolved?
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dark seal
I am not able to to this right?
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I am not able to to this right?
dark seal
thanks another time, and do you know if this is right?
I think yes, but I am not pretty sure
eager violet
Looks right
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iron vapor
i think we can think like a.e /c
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dense edge
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sharp vine
,w how many terms x(x+1)
glossy valveBOT
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vapid steeple
can some one help me figure this out? my dumbass cant figure out how to get 45 degrees +60k at all
raw turret
torn jolt
fading cargo
7th exercise, are the steps here alright?
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7th exercise, are the steps here alright?
fading cargo
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inland turret
Linear Equations - Algebra
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Linear Equations - Algebra
inland turret
anyone can explin this?
balmy peak
khan academy
torn jolt
anyone can explin this?
what do you mean
torn jolt
explain what a linear equation is ?
ok
what specifically do you need to know about linear equations ?
torn jolt
alr lemme read
if you want an easy-to-grasp explanation, look for khan academy
inland turret
alright thanks
The value of y from 6(y + 5) = 2(-2y - 5) is
from last test
.close
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loud haven
someone here with a lot of experience with block matrices and order of operations?
loud haven
x^+ is a vector with (1,0) as its entries (its dirac stuff, dont ask 😂 ), while
sigma_y is this
sigma * p =
how would i have to do the order of operations? Can one evalaute block matrices directly? Do i need to make everything in its 4 dimensional form? Do i need to calculate (sigma * p) * x^+ before anything?
fiery dove
mensional form? Do i need to calculate (sigma * p) * x^+ before anything?
loud haven
<@&286206848099549185> anyone?
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loud haven
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plucky parrot
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plucky parrot
using ti-Nspire software, can't solve that? Claims its missing an "("
onyx glen
what even is this
did you mean $\frac{\pi \cdot 3 \cdot \pi^2}{7 \cdot \pi \cdot \pi^2}$?
glossy valveBOT
Ann
glossy valveBOT
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plucky parrot
how do i put that to Nspire
$\frac{\pi \cdot 3 \cdot \x^2}{7 \cdot \pi \cdot \x^2}$
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plucky parrot
not working
well it is my attempt at solving big circle area/small circles combined area
$\frac{\pi3a^2}{7\pi a^2}
\frac{\pi 3a^2}{7\pi a^2}$
$\frac{\pi 3a^2}{7\pi a^2}3$
nono
$\frac{\pi 3a^2}{7\pi a^2}$
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lethal jolt
How does one prove that pi/4 = arctan(3/5) + arctan(1/4) ?
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How does one prove that pi/4 = arctan(3/5) + arctan(1/4) ?
brisk obsidian
$\tan^{-1}{x} + \tan^{-1}{y} = \tan^{-1}{\left(\frac{x+y}{1-xy}\right)}$
glossy valveBOT
Kookiemon
lethal jolt
Sorry, I don't follow. Is that result derived from compound angle? If it is I'm not seeing it 😩
(And I don't think I'm allowed to quote it, I have to be able to derive)
brisk obsidian
Sorry, I don't follow. Is that result derived from compound angle? If it is I'm ...
That is an identity.
lethal jolt
Could you please derive it from something else?
brisk obsidian
You aren't learning about identities?
lethal jolt
Nah this is high school work. And I've never learnt about inverse trig identities
brisk obsidian
There is no pretty way of proving that it equals pi/4. The given values do not lend themselves to easy angle measures.
lethal jolt
Then can you explain how the identity was derived? And thus I might apply it without needing to quote it
brisk obsidian
That proof requires using a Maclaurin Series which I think is beyond what you are capable of.
It's kind of the reason why we have identities in the first place. Someone did the work so you don't have to.
brisk obsidian
Then can you explain how the identity was derived? And thus I might apply it wit...
Is this for Geometry or Trigonometry?
lethal jolt
trigonometry
lethal jolt
Is this for Geometry or Trigonometry?
Actually this was found as a practice question for ext 2 maths. So I'm sure both methods would be accepted
brisk obsidian
One alternative would be this.
Hmm, but that would still involve a rotation of the point C and F that requires knowing the angle BAC.
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lethal jolt
Got it! Used complex numbers to represent the vector AC, then multiply i/4 to represent the opposite side of the 1/4 triangle. Add the two together and the argument is pi/4. Thanks for helping
brisk obsidian
Interesting method. 🙂
dull thicket
An Area is bounded by the graph of the function f(x) = e^(-x^2), the x-axis and the 2 straight lines x = a x=3a, a>0. Find "a" where the area is biggest?
dull thicket
so i been trying this for a bit and i assume i make some integral and somehow get the answer
but i have really know where to start this problem
I would be happy to elaborate if anyone needs it
torn jolt
Hmm sketching it will give you some sort of hilltop looking curve
It will have a maximum at x = 0, and then starts growing slower and slower from both ends as it approaches 0
I think knowing that should give you an idea of what a should be 
dull thicket
It will have a maximum at x = 0, and then starts growing slower and slower from ...
dont you mean minimum?
glossy valveBOT
♡LexQa♡
dull thicket
yeah i just noticed i mistyped the graph T_T
dull thicket
in my graphing software not here
torn jolt
Ah i see
torn jolt
Yeah. So anyways, I suppose you would have the "biggest" area maximising the area under that hilltop before it goes to infinity and minus infinity
Since I assume a is some constant here
dull thicket
yup its supposed be
my first instinct here would be to take the antiderivative but we get hint that says we should not do that
torn jolt
Yeah not taking the derivative means not doing any of what we just did lmfao
Because you can only really figure out what it looks like using the derivative
dull thicket
i made a very important typo
torn jolt
Oh what is it
dull thicket
my first instinct here would be to take the antiderivative but we get hint that ...
i didnt mean derivative but antiderivative, the hint is as follows: dont try to find the antiderivative
torn jolt
Ah okay
dull thicket
sorry about that
torn jolt
Then our approach is suddenly alright
Lmao
Anyways, now figuring out what the 'a' needs to be is the hard part
The 3a is the problem I think
torn jolt
Nah it's fine, we can bullshit our way through it without the choices
dull thicket
okay xd
how would we go about finding the area of the graph without integral/antiderivatives tho?
torn jolt
Also they said to not do the anti derivative because you wouldn't find one no matter how you try anyways
torn jolt
how would we go about finding the area of the graph without integral/antiderivat...
im thinking taylor series
fun times with erf(x) ig
dull thicket
that should work i think but, we also shouldn't have to as its not part of this courses curriculum
we have learnt taylor polynomials but not series
torn jolt
i am really clueless as to how you could ascertain a value for a
dull thicket
maybe i should just post the multiple choices and we can trial and error it?
brisk obsidian
$\frac{\partial}{\partial x} \int_{a}^{b} f(x) dx = f(b) - f(a)$
dull thicket
glossy valveBOT
Kookiemon
dull thicket
Dont mind the text parts
torn jolt
oh partial derivative, did not think of that
good idea kookiemon
did u even learn partial derivatives? @dull thicket
thats like calc 3 and taylor series is calc 2
so i assume no
dull thicket
yes, i passed calc 3 and 2 but not one bc i was sick twice on exams
torn jolt
what is this question for?
dull thicket
calc 1
torn jolt
lmao did they put that 420 to meme with you
dull thicket
yuuuuuup
dull thicket
This task is pain
nocturne creek
**Kookiemon**
a and b are what here?
brisk obsidian
It's not my question, but it is an optimization problem to find the largest are under a curve with the boundaries defined as a and 3a, solve for a.
y = e^(-x^2)
dull thicket
<@&286206848099549185>
brisk obsidian
I know what the answer is but I'm not exactly sure how to solve for it.
dull thicket
how did you arrive at an answer?
brisk obsidian
So going back to this being an optimization problem of the area under the curve of f(x). You take the derivative of the integral of f(x) from x=a to 3a.
Given that f(x) = e^(-x^2), the derivative of the area function should equal f(3a) - f(a).
Or
a'(x) = e^(-9a^2) - e^(-a^2)
Which should allow you to solve for a but it doesn't work so there is some fault with my reasoning.
I made a graph in Geogebra where I plugged in each of the optional answers you gave and found it is 6 though.
That answer does not coincide with a'(x) above which you can visually see in the graph.
I'm trying to figure out what I'm doing wrong.
\begin{align*}
Area &= \int_{a}^{3a} e^{-x^{2}} dx \
Area' &= \frac{d}{dx} \int_{a}^{3a} e^{-x^{2}} dx\
Area' &= e^{-x^{2}} |_{a}^{3a}\
Area' &= e^{-9a^{2}} - e^{-a^{2}}
\end{align*}
glossy valveBOT
Kookiemon
brisk obsidian
In my mind, this should have worked but it doesn't.
dull thicket
i have no idea tbh
im still stuck trying to find a calc 1 way of actually being able to actually try begin to get an answer
brisk obsidian
The method I showed is Fundamental Theorem of Calculus (Part 1) which you would learn about in Calc 1.
$\frac{d}{dx} \int_{a}^{b} f(x) dx = f(b) - f(a)$
glossy valveBOT
Kookiemon
brisk obsidian
And the optimization should be fairly straightforward but I do not get the correct the answer and I'm trying to figure out what I'm doing wrong.
brisk obsidian
👀
nocturne creek
I might say a lot of weird stuff cuz im still learning this
But to find the maxima
dull thicket
nocturne creek
We need to put the derivative =0?
And if you do that you actually do get
Option 6
Now if you want to check if its maxima or minima, i think you need to find the second derivative and see there(?), Which you find out depending on the sign
nocturne creek
**Kookiemon**
Oh yes i actually had a different derivative
Absolutely not sure if this is correct or not tho
brisk obsidian
Gahh, I forget to use the Chain Rule. 😛
dull thicket
sooooo
if you use the correct derivative and FTC we will get the answer now right?
which should be six
brisk obsidian
nocturne creek
In order to check whether a= that is maxima or minima, do we need to find out the 2nd derivative and input this there?, Also is my derivative correct 😭
nocturne creek
In order to check whether a= that is maxima or minima, do we need to find out th...
Oh but i forgot if area was to be minimum it has to be a=0
But a>0
So a=0+?
dull thicket
sorry i was away for a couple of min
dull thicket
In order to check whether a= that is maxima or minima, do we need to find out th...
considering we already know that 6 is the answer and got 6 it would be very surprising if it wasnt
nocturne creek
considering we already know that 6 is the answer and got 6 it would be very surp...
I mean people get the right answers by the wrong deductions all the time
dull thicket
fair enough
brisk obsidian
Well, there are only two solutions for a and only one of them is greater than zero.
dull thicket
I mean people get the right answers by the wrong deductions all the time
perhaps a dumb question why did you write e^(-x^L) ? where does the L come from
brisk obsidian
That's a 2, his 2's just happen to look like an L.
nocturne creek
Okay since x=a
dull thicket
aaaaaaa
nocturne creek
perhaps a dumb question why did you write e^(-x^L) ? where does the L come from
Its a skill issue with my handwriting
dull thicket
i suffer the same skill issue 😔
dull thicket
Would that be correct?
i think so ?
dull thicket
wait we know the answer is 6 right and 6) is 1/2 sqrt(ln3/2)
right
and you have at the third last sentence 8a^2 = ln3
solving for "a" would give us sqrt(ln3)/2
torn jolt
Hello
dull thicket
right?
torn jolt
What's happening @nocturne creek
dull thicket
hi
torn jolt
Give me a run down
nocturne creek
Is this wrong
torn jolt
How did u make it e^a
nocturne creek
That is from the ftc i think
Or as my teacher made me learn, a case of leibnitz rule🗿
torn jolt
Also I don't think it makes sense, that's just a definite integral that should be 0 no?
When u are taking its derivative
nocturne creek
Also I don't think it makes sense, that's just a definite integral that should b...
Thats what i thought too, but for some weird reason the answer matches
The reason i thought itd be 0 is cuz a and 3a are constants
torn jolt
Yes
Exactly
Either you inadvertently did something in a similar way to how it should be done, or u just did something I have no idea about
Maybe @nocturne creek
Integrating from a to x
Might be an idea
nocturne creek
Integrating what
torn jolt
You might as well say that you don't know what 3a is
Also shit with erf(x) is just big no-no territory I don't want to get into
brisk obsidian
But when 3a=x, 3da/dx=1, im just confused what happens to da/dx
The integral is "separate" from the Area function, Area(a).
$Area(a) = \int_{a}^{3a} e^{-x^{2}} dx$
glossy valveBOT
Kookiemon
brisk obsidian
So when you do the Chain Rule, it's just d(3a)/da
brisk obsidian
You don't need the + and everything after that.
dull thicket
sorry i was gone for 10 min what has happened
brisk obsidian
Just ironing out the fine details of how to solve the problem. In particular, it was how the Chain Rule should be applied.
dull thicket
aaaaa its so close
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dull thicket
im not making any progress tbh and im just considering closing this and working on another task
.close
torn jolt
I need to find $\Im((a+bi)^2)$ and $\Re((a+bi)^2)$. Expanding $(a+bi)^2$ gives $a^2+2abi-b^2$, is that right?
glossy valveBOT
3317
torn jolt
In this case $\Im$ will be $2ab$, but what's $\Re$?
glossy valveBOT
3317
torn jolt
$a^2-b^2$?
glossy valveBOT
3317
forest widget
you got it
sinful onyx
"write a quadratic equation with whole-number coefficients, where one solution is x1 = sqrt(3) + 1 / sqrt(3) - 1"
torn jolt
"write a quadratic equation with whole-number coefficients, where one solution i...
Hmm
What do you think
How should this be done?
sinful onyx
move the solution to the left so its x1 - solution = 0, then square it?
silver pasture
move the solution to the left so its x1 - solution = 0, then square it?
and what would be the roots of that equation?
sinful onyx
i have not
torn jolt
i have not
Do it and tell me the answer
sinful onyx
2 + sqrt(3)
torn jolt
2 + sqrt(3)
Exactly
Since we need whole number coefficients
We will need such a number that can be added to 2+√3 so that only the whole remains and multiplied to 2+√3 such that only the whole remains
The other number should be?
I mean
The other zero will be?
sinful onyx
2 - sqrt(3)?
torn jolt
2 - sqrt(3)?
exactly
It will be the rationalizing factor
Whenever they ask for whole number coefficient
Take the other zero as the rationalizing factor of the first zero
Now try formation of polynomial using the sum and product rule
ivory cairn
after you rationalize, you can also just move the 2 over and square everything
(x-2)^2 = (root 3)^2
sinful onyx
we didnt learn that
torn jolt
we didnt learn that
So like you dont know how to make a polynomial based on its zeros ?
sinful onyx
nope
sinful onyx
after you rationalize, you can also just move the 2 over and square everything
(...
but i do remember this
torn jolt
Basically
To make a polynomial based on its zeros
Assuming ß and ∂ to be the zeros
K(X^2 - (ß ∂)x + (ß+∂))
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torn jolt
K is a constant just in case there is a fraction in the x2 term, you can multiply the whole polynomial by the denominator
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silver valve
What is the value of this because if it is 10 then shoudnt you square the exponent?
torn jolt
Value?
silver valve
The value of the box
atomic blade
What is the value of this because if it is 10 then shoudnt you square the expone...
It is 10
But wdym square the exponent
silver valve
Like square the 10
silver valve
?
silver valve
then if you were to simplify this equation would you not power it to the exponent
or square it to the exponent
take the numerator
for example the first numbers
you wouldnt square it?
atomic blade
The numerator would become -12x^5y^7
The denominator is 4x^4y^4
Overall it's just gonna be -3xy^3
You have to use exponent laws
$$(a^b)^c = a^{bc}$$
@glossy valve boy you dead
dull thicket
hi so i need a bit off help im using the trapezoidal rule to calculate the definte integral of e^x^2 from 0 to 1
dull thicket
1,4 and its a bit perhaps a but to much
well 1,4806
i was wondering how much its usually is off?
its probably off by like 0.03
is that to much?
balmy peak
depends how many trapezoids you are using to approximate
balmy peak
so your n = 5?
yeah ur answer should be 1.48065
is ur question about the error bound of the trapezoid rule ?
dull thicket
no
balmy peak
what specifically then? ur answers correct
dull thicket
Calculate the volume of the body that appears when the area between the graphs of cos(x) for x in [0,1] and e^x^2 for x in [0,1]
balmy peak
u have to use trapezoid rule for this?
atomic blade
Bruh moment
balmy peak
just plug into ur calculator
dull thicket
and i couldnt find anything else
atomic blade
Yeah no e^x^2 is ass
balmy peak
Calculate the volume of the body that appears when the area between the graphs o...
is this e^(x^2) or (e^x)^2
?
dull thicket
first one
balmy peak
dull thicket
i think atleast ?
dull thicket
cuz the functions only defined from 0 to 1
i have now found an estimate of the area which 0,6342
and now i gotta rotate it
which i really dont understand how to do
balmy peak
rotated around the y axis?
dull thicket
what method is that
my book rarely uses names for the method only describtions
T_T
balmy peak
2pi * integral from a to b of R(x)H(x)dx
or r u doing this using washer but in the y world?
actually that seems way harder
so im assuming shell
dull thicket
i was gonna use washer method but wtf is the difference
balmy peak
ur rotating around y axis no?
dull thicket
yeah
and i found the area but i couldnt really do the full integral
so im assuming i just add 2pi to the area
?
not add multiply
balmy peak
if ur doing washer method
the DE has to be perpendicular to axis of rotation
so if u were gonna use washer for this u'd have to do it in the y world
i.e. f(y)
balmy peak
yeah bec ur DE is parallel to axis of rotation in shell method
so we can just use f(x)
dull thicket
DE?
dull thicket
okay gotcha
soo since i have the area between graphs multiply it by 2 pi and get 3.9848
dull thicket
but i cant do the integral
balmy peak
can u not use a calculator for this question
balmy peak
theres no way they want u to use trapezoid to estimate the area between the curve lol
dull thicket
but even so the integral by defintion is just the area under a graph
then what should i do?
balmy peak
then what should i do?
u cant use a calculator ?
if not just solve the integral normally
because its gonna be
xe^(x^2)
dull thicket
i can use a calculator
dull thicket
im so confused
balmy peak
are u allowed to just plug it into ur calc ?
if not
solve normally
2pi * integral from a to b of (f(x) - g(x))*x
dull thicket
okay i plug the integral 0 to 1 for e^x^2 *cos(x)
balmy peak
2pi * integral from a to b of (f(x) - g(x))*x
use this
multiply by x
shell method
If u cant use a calc then notice that we have
xf(x) - xg(x)
and we can solve the integrall
of
xe^x^2 normally
balmy peak
multiply by 2pi
balmy peak
yeah
dull thicket
ehm i dont find the same formula you showed me though
are you sure this is a valid one?
dull thicket
but where is the additional x
dull thicket
okay ill do that
rare elk
Can someone help me simplify this?
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Can someone help me simplify this?
vast fossil
Notice that 64 = 4^3 and x^3 - 3x^2 + 3x - 1 = (x - 1)^3
barren iris
Does inversely congruent mean that they are not congruent?
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Does inversely congruent mean that they are not congruent?
barren iris
This is about two triangles, that were split from 1.
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barren iris
<@&286206848099549185>
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@barren iris Has your question been resolved?
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@barren iris Has your question been resolved?
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@barren iris Has your question been resolved?
south dirge
Does inversely congruent mean that they are not congruent?
This means that you can't get one triangle by only moving another triangle by some vector, but if you're also allowed to rotate him, then you can
barren iris
This means that you can't get one triangle by only moving another triangle by so...
Oh I see.
That's helpful
barren iris
This means that you can't get one triangle by only moving another triangle by so...
So does congruent mean you can get another triangle by moving around the vectors?
south dirge
So does congruent mean you can get another triangle by moving around the vectors...
Congruent means that you can get A1B1C1 from ABC by moving every point of ABC by some fixed vector like this
barren iris
Congruent means that you can get A1B1C1 from ABC by moving every point of ABC by...
Okay okay
But if I were to do that with non congruent triangles, you won't have another triangle
south dirge
Well usually congruent means that you can also rotate ABC, but not in your case i guess
south dirge
But if I were to do that with non congruent triangles, you won't have another tr...
Then they wont be congruent
barren iris
Okay
Yeah reading what I said again, I think I said that wrong
Immediate regret
Okay
Ty
south dirge
Np
barren iris
Are you used to geometric proofs?
My book has it where each proof has like a statement and then a reason. My only thought for this sort of problem is to just write out what I think is given
Like AB = DC where AB is from a trainlge ABC, and DC is from a triangle DCE
south dirge
I guess there must be 3 theorems when two triangles are congruent
If their sides are equal, two sides and angle between or two angles and side between or something like this
barren iris
I guess there must be 3 theorems when two triangles are congruent
There totally is.
So would it satisfy a proof to just write out theorems that have already been proven?
Or like how do you even know when you're done with a proof
Also, thank you for your help
south dirge
Or like how do you even know when you're done with a proof
It should look smth like this:
Theorem: if A and B are true, then C is true.
You need to prove that C is true, for example.
Then you prove that A is true, then that B is true, and using theorem you say that C is true.
In your case you can just say that their sides or angles with sides are equal, so we can use the theorem, so they are congruent. In harder cases you will need to prove that sides are equal using something else, that is given, and only then use the theorem. That works for every proof problem in maths, not only geometry.
barren iris
It should look smth like this:
Theorem: if A and B are true, then C is true.
Y...
That was a very helpful explanation
Thank you so much
south dirge
No problem 🙂
barren iris
Where did you learn how to do proofs
south dirge
school, books, videos, on my own, right now I'm learning it in university 🙂
Like everyone, to be short
barren iris
school, books, videos, on my own, right now I'm learning it in university 🙂
Lik...
Mine is pure self study from one book rn
south dirge
It's cool!
barren iris
It's rough for me rn but I need to learn it!
Totally different from what I'm used to
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@barren iris Has your question been resolved?
untold sapphire
A is (-2,0) B is (0,4). Find the equation of the line, which passes through A and is perpendicular to AB
shrewd hamlet
Do u know slope formula
untold sapphire
kinda
shrewd hamlet
Calculate the slope from those 2 points
untold sapphire
would the gradient be 2
shrewd hamlet
Yea
untold sapphire
oh okay
shrewd hamlet
Now, to get the perpendicular line, we need to make that slope of opposite sign and reciprocal
So what’s opposite sign reciprocal of 2
topaz valley
negative reciprocal a better word for it?
shrewd hamlet
Oh yea thx
pliant crown
💀
shrewd hamlet
1 am error 404
shrewd hamlet
So our current slope is: +2
glossy valveBOT
shrewd hamlet
Yep, so we just took the negative reciprocal of our slope
untold sapphire
would it be -2
shrewd hamlet
Close but no cigar
untold sapphire
or +2
shrewd hamlet
Take the reciprocal
Of -2
Well +2, is our slope
Do u know what reciprocal is
For example
3 is reciprocal of 1/3
1/4 is reciprocal of 4
-5/6 is reciprocal of -6/5
U see what’s happening?
untold sapphire
yeah
shrewd hamlet
So what’s the negative reciprocal of +2
merry carbon
shrewd hamlet
It’s -1/2
untold sapphire
oh nice
shrewd hamlet
Reciprocal of 2 is 1/2 and so negative reciprocal of 2 is -1/2
Now, do u know point slope form?
merry carbon
What is the equation for the perpendicular bisector of AB for the given points A (-2,0) and B(0,4)? was this the question or was i reading it wrong?
untold sapphire
Now, do u know point slope form?
yeah i think
shrewd hamlet
What is the equation for the perpendicular bisector of AB for the given points A...
Idk if bisector is the word, it passes thru A tho
untold sapphire
by the way i dont even know what is a reciprocal
shrewd hamlet
Essentially it’s 1/(our number)
That’s all the reciprocal is
Reciprocal of 10 = 1/10
merry carbon
yeah
shrewd hamlet
Reciprocal of 1/15 = 1/(1/15) = 15
merry carbon
im good at trigonometry bad at probability haha
untold sapphire
Reciprocal of 1/15 = 1/(1/15) = 15
wait ohhhh
and when u get the negative reciprocal do you plug in to point slope form
merry carbon
a reciprocal is this Multiplicative inverse
shrewd hamlet
Yea now that we have the slope of the perpendicular line that passes thru A, plug in point A and the slope we found into point slope form
untold sapphire
Yea now that we have the slope of the perpendicular line that passes thru A, plu...
thank you i got it now
the answer would be y= -1/2x -1
untold sapphire
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knotty silo
Question what is a integral in terms of a derivative?
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Question what is a integral in terms of a derivative?
warm abyss
The antiderivative
knotty silo
I look it up on internet and seems to be the opposite of a derivative which is slope but I don’t get how that makes sense
eager violet
knotty silo
The antiderivative
What does that do? It only means the opposite of a slope but what is the opposite of an slope
woven sand
Not really opposite but the inverser
woven sand
If it helps, area under a graph wrt time usually represents a cumulative amount of something (cumulative distance, velocity, what have you) while the slope at a point is the rate of change
Yeah FTC makes that connection
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warm abyss
https://en.m.wikipedia.org/wiki/Fundamental_theorem_of_calculus
This might help you
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broken rain
Let A be a finite set, with |A| = 8
a) How many relations of A in A exist?
b) How many relations of A in A exist that are reflexive?
I don't understand what means with relations of A in A :c
hard siren
I don't understand what means with relations of A in A :c
the relation whose domain and co-domain both is the set A? means defined from A --> A
torn jolt
Let A be a finite set, with |A| = 8
a) How many relations of A in A exist?
b) ...
i don't know either, but i assume they mean functions/mappings
or maybe just "arrows", in general, where it can, for example, map only a subset of its domain (instead of its whole domain)
broken rain
Something like this?
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broken rain
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marble whale
can anyone give me any ideas on how to approach this pls
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can anyone give me any ideas on how to approach this pls
scenic yew
can anyone give me any ideas on how to approach this pls
create right triangles first
Are we allowed to assume that angle abd is a right triangle?
@marble whale
Because my plan is to make angle abd, cdb, efb, efd a right triangle
And since ab = sin(2x), and cd = cos x, triangle abd and cdb are similar triangles since they both contain line BD
Oh we are allowed to, since cd = cosx, it must be that bc = 1
marble whale
Oh we are allowed to, since cd = cosx, it must be that bc = 1
Wait a sec
marble whale
Are we allowed to assume that angle abd is a right triangle?
Yes
Wait lemme draw the diagram again
marble whale
Oh we are allowed to, since cd = cosx, it must be that bc = 1
Wait how??
How did you get to that conclusion?
scenic yew
Oh since CD = cos x
Since cos x = a/h
and a = CD
But since there are no fractions, it means that h = 1
cause CD/1 = cos x
marble whale
☠️
How did I not think of that😭
OK that's one bit done
Also I managed to find that the angle is between 30 to 45
Not including 45
scenic yew
Oh I was about to answer 45
marble whale
Oh I was about to answer 45
😭😭
scenic yew
Since we concluded that CD = cosx
It means that BD= sin x
And BD is part of triangle ABD
AB has sin 2x, angle adb must be 2x
Since bd = sin x, bad must be x
x+2x+90=180
3x=90
x=45
marble whale
Yep that's fine, thanks a lot!
scenic yew
Oh do you need AD's length just in case?
marble whale
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ivory moon
I forgot how to do this
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I forgot how to do this
smoky wing
lean gazelle
How do I solve this?
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How do I solve this?
torn jolt
We don't see b)
lean gazelle
We don't see b)
how about now?
torn jolt
Or a)
torn jolt
The question themselves? No
lean gazelle
its translated from danish, so sorry if its garbage lol
<@&286206848099549185>
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torn jolt
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frozen lark
can't see the inputs of the first two gates
frozen lark
very well
torn jolt
thats good
frozen lark
so first let me say that it's good to start from the output then go back to the inputs
like in the finish line we've got a not gate
so we have a one big bar up all the equation
torn jolt
im just confused
frozen lark
?
frozen lark
no worries son, i'm gonna show u the way of truth
torn jolt
the x bar is shorter then the y bar
frozen lark
wait step by step
first we've got a huge bar in up
after that there's an and gate
*or
sorry mistake
any ways so we have a huge bar and under it there is or so it's +
so it's like :
$\overline{something + somthing}$
glossy valveBOT
mino65
frozen lark
remeber :
or = +
and = * (multiplication )
you can say that x and y is equal to x times y
x*y
but see that there is a not gate up that and gate
so it becomes nand gate
so:
torn jolt
the triangle?
frozen lark
you know the logical gates symbols no ?
frozen lark
any ways it becomes :
torn jolt
the one above
marsh surge
[(x.y)bar + (x+y)]bar
torn jolt
has a triangle and the one below just has a line
frozen lark
as long as you understand it like that
yes
but don't name a triangle in front of the teacher he'll probably laugh at you
say not gate or inverting gate
that's more accurate
torn jolt
my teacher is already a joke
frozen lark
torn jolt
i already laugh at him he dropped my grade by giving the entire class 0s
marsh surge
my teacher is already a joke
in that case being a joke in front of a another joke is kinda worse
frozen lark
naa don't worry logical calculations are super ez you'll get them in no time
any ways so now we have that
$\overline{\overline{x\cdot y} + somthing}$
glossy valveBOT
mino65
frozen lark
don't care about that i'm used to a and b
the other something is what?
we follow the other line that goes through as an input for the final or gate
and what is that ?
it's x or y
so x + y
so our final equation well be like :
torn jolt
wait
frozen lark
$\overline{\overline{x\cdot y} + x + y}$
glossy valveBOT
mino65
frozen lark
?
frozen lark
there is no beginning line
torn jolt
i got a math disability
i can't think mathmathically
when it comes to doing math in general im struggling with keeping up
frozen lark
then think like an engineer
engineers don't think of some crazy integration equation they just start from some little scraches and then make the way step by a step
torn jolt
is this for the top part
frozen lark
?
torn jolt
here wait i got an example
frozen lark
it's not like the sky will fall if you can't solve some logical stupid equation
torn jolt
frozen lark
sus
torn jolt
4th slide
frozen lark
McMystix you've been writing since yesterday what's there ?
marsh surge
i dont know where to start
what you can do is divide the sequence in branches
find the equation for the top branch (the AND and NOT gate) let that be A
then find equation of bottom branch
(OR gate) let that be B
then find equation of the middle branch (OR and NOT) in terms of A and B
in the end substitute values of A and B
and you will get the final equation for the output
torn jolt
makes more sense
marsh surge
McMystix you've been writing since yesterday what's there ?
phone typing = slow :/
torn jolt
thank you
marsh surge
np
torn jolt
i watched the lectures
frozen lark
wew
torn jolt
and im super confused
torn jolt
this guys a complete joke honestly when it comes to teaching lol that is my teacher
marsh surge
and im super confused
just refer to this whenever youre confused
torn jolt
thank you for this
frozen lark
yeah you said that you can't think mathematically but you don't need to
frozen lark
in ma class there is a classmate that is so trash in math ... he really is but he's super powerful when comes to the logic
my point is
marsh surge
bad at math != bad at everything
torn jolt
basically
frozen lark
don't blame yourself if you can't understand it very quickly
torn jolt
bad at math != bad at everything
i agree
marsh surge
watch videos on YouTube if your teacher isint good
torn jolt
ok that might help
ima just be honest with you
i just listened to the lectures
so i didn't take notes on it and i went back and watched some of it and yeah it makes sense now being able to get it explained by you guys
torn jolt
yep
marsh surge
practice a bunch
marsh surge
start with easier questions and then try to solve hard ones
there isint much thinking to do in these questions, just be careful to not make mistakes
frozen lark
bad at math != bad at everything
and about my classmate don't worry he usually copy from my paper during the math exams so he's fine
marsh surge
and about my classmate don't worry he usually copy from my paper during the math...
lmao 💀
frozen lark
and for the 2nd question i can show how to solve it but i think it'd be better if you get yourself used to the 1st question problem first
frozen lark
it envolves some Factorization
torn jolt
frozen lark
he simply gave you a table
frozen lark
that table shows you when the F gets the value 1 according to the variable x, y and z
so we need to find the equation of F
look
torn jolt
hold on
frozen lark
a simple rule
torn jolt
idk what im doing honestly
marsh surge
welp
torn jolt
i hand drew the logic gate
marsh surge
you need to know binary to solve this
frozen lark
ok this seems to be a little bit hard
but you'll get through
first here's a good explanation for this weird table that's called " truth table"
you'll get the idea of the binary as well
torn jolt
i know how to do those
frozen lark
i know but the guys says that he have 0 base in all of this and a trash teacher
torn jolt
i dont know how to do logic circuits
frozen lark
it's just like yes or no
torn jolt
im getting really distracted i was just sending a message to my teacher
frozen lark
heeee
torn jolt
i understand what truth tables are
you have different symbols
or and
or is like a symbol of a wheel
torn jolt
because i learned truth tables at the beginning of this class
frozen lark
wtf
torn jolt
and it took 3 fucking months for this class to start
so basically he told me to just go play video games until the class started
frozen lark
ok ok son calm down calm down
torn jolt
😦 im depressed now
torn jolt
lets just focus on the topic
frozen lark
your not some stinky depressed 15 yo teenager
torn jolt
so i can understand this i've gotten no where
frozen lark
17 me
marsh surge
because i learned truth tables at the beginning of this class
heh??
marsh surge
without learning binary first?
torn jolt
yes
marsh surge
weird
torn jolt
yep
frozen lark
wat da hail is going on with the educational system
torn jolt
this class makes me wanna give up and jump off a bridge
frozen lark
naa don't let some 0s and 1s take your life that's kinda shame
torn jolt
ok
frozen lark
just go and learn binary and everything will become bright
torn jolt
for the logic gate
frozen lark
you see your trash teacher started with the wrong thing
here is the series of what you should do
torn jolt
ill come back after i get a bit of a better understanding
frozen lark
first : learn binary, hexadecimal and other numerical systems
torn jolt
so i dont waste your time
marsh surge
binary
octal
hexa
logic gates
frozen lark
good