So now u know the coordinate of x for F ,u can plug in that in the equation of parabola and find the intersecting point
#help-23
opaque shard
-k^2+6k
royal kiln
U hv the length of other side now
opaque shard
im so smart
opaque shard
nah i got it
plush spruce
Hi
radiant ice
hi
plush spruce
I need to represent the volume between my two functions f and g
This is the problem:
Let S be a revolution solid obtained by rotating the X axis, the regions in between the curves $f\left(x\right)=x^2+1$, x=0 and the tangent of f in the point x=1.
flat frigateBOT
S0S4 - Feel free to ping
plush spruce
I need to represent that region S, but I'm unable to
As you can see the integral is made but nothing is shown
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plush spruce
.close
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pallid orbit
For the one on the bottom, anyone know how she got 20?😭
safe radishBOT
For the one on the bottom, anyone know how she got 20?😭
mighty mango
from 1992 to 2012 is 20 years
mighty mango
I’m confused how that number came up
-# idek if that answers your question
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placid quiver
need help proving $$\int_{0}^{\infty}\frac{1}{\sqrt{\cosh\left(x\sqrt{x^{2}+\pi}\right)}}\dd{x}=\frac{\pi}{2\sqrt{2}}$$
flat frigateBOT
zeta theta beta eta
safe radishBOT
need help proving $$\int_{0}^{\infty}\frac{1}{\sqrt{\cosh\left(x\sqrt{x^{2}+\pi}...
placid quiver
dont know where to start
well i did do one hyperbolic sub and i got stuck after that
opaque fern
Honestly this is so not going to be trivial
My mind is going to complex integration at the moment
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small sandal
im pretty sure it can be done with subs, start with a u sub $\u = x\sqrt{x^2+\pi}$ and then try a hyperbolic sub and see where that gets you
flat frigateBOT
KB
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brave wedge
Can somebody help me with this problem
safe radishBOT
Can somebody help me with this problem
brave wedge
Let a, b, and c be the lengths of a triangle. \ Prove that $a^2+b^2+c^2-2ab-2bc-2ca < 0$
astral glacier
Prove that it's what
brave wedge
oops
flat frigateBOT
Defy logic guy
brave wedge
that's better
ionic blaze
Let a, b, and c be the lengths of a triangle. \\ Prove that $a^2+b^2+c^2-2ab-2bc...
strangely familiar
brave wedge
yes
golden nebula
Uhh
ionic blaze
what even is that name
golden nebula
Wait sht I clicked it
brave wedge
Wait sht I clicked it
subconsious
golden nebula
I meant to reply to inform mods
brave wedge
oh
ionic blaze
yes
I think you can approach this with, take this with a severe grain, the triangle inequality and dividing it by 2, a+b>c, a+c>b, b+c>a
no that doesn't work
ionic blaze
that's the only approach
cosine law
brave wedge
what even is that
ionic blaze
what even is that
a^2+b^2-2abcosC=c^2 where C is the adjacent angle to side a and b of a triangle
vague phoenix
$a^2+b^2+c^2-2ab-2bc-2ca = -1(-a^2-b^2-c^2+2ab+2bc+2ca)$
ionic blaze
where the -a^2
flat frigateBOT
Minλ
flat frigateBOT
Minλ
vague phoenix
This is also similar to $(a^2-(b-c)^2-2a(b+c))$
ionic blaze
I think you can approach this with, take this with a severe grain, the triangle ...
the triangle inequality can be squared since a, b, and c are all positive
so: a^2+b^2+2ab>c^2, a^2+c^2+2ac>b^2, b^2+c^2+2bc>a^2
you can add them together to get
2(a^2+b^2+c^2)+2ab+2bc+2ac>(a^2+b^2+c^2)
leading to yeah just the above like
ionic blaze
the triangle inequality can be squared since a, b, and c are all positive
so: a^...
goofy it's as direct as it is altho I doubt this counts as a proof
brave wedge
that equals a^2+b^2+c^2+2ab+2bc+2ca >0 which is obvious
ionic blaze
that equals a^2+b^2+c^2+2ab+2bc+2ca >0 which is obvious
oh wait nvm I miscalculated woops
that's just (a+b+c)^2 with extra steps
flat frigateBOT
Minλ
ionic blaze
that equals a^2+b^2+c^2+2ab+2bc+2ca >0 which is obvious
r u allowed to use AM-GM or....
brave wedge
yes
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devout scroll
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tiny geyser
how to prove that for every reel t>0
safe radishBOT
how to prove that for every reel t>0
burnt notch
I guess that's doable by studying the behaviour of the function f(t) = -t•ln(t)
And finding the point of max (hoping it gives 1/e as y-coordinate)
tiny geyser
And finding the point of max (hoping it gives 1/e as y-coordinate)
thank you got it ❤️
.close
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outer pollen
<@&268886789983436800>
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sharp sandal
Game Setup
Set A = {2, 3} (only numbers allowed are 2 or 3)
Player 1 (first mover) and Player 2 (second mover) take turns picking numbers from A
Player 1 always goes first
They each play 2 rounds (4 total picks)
If the sum of all 4 numbers = 9, Player 2 wins. Otherwise Player 1 wins.
sharp sandal
how can we write this in a similiar way to this ∀a∈A(∃b∈A (a+b=5))
that says player 2 wins always
this is what AI come up with ∀a1∈A(∃b1∈A(∀a2∈A(∃b2∈A(a1+b1+a2+b2=9))))
but if a2 can be random aswell this doesnt hold
brave wolf
but player 2 doesnt always win
if P1 plays 3 then P2 can play either:
a) 2, then P1 plays 3 and P2 loses (no matter what he picks, it will be over 9)
b) 3, then P1 plays 3 and P2 loses again.
which one are you trying to express btw:
- Player 2 wins every possible game
- Player 2 can win every game, if he plays optimally
sharp sandal
∃ but this implies that it should be chosen acordingly
sharp sandal
which one are you trying to express btw:
1) Player 2 wins every possible game
2)...
this one
brave wolf
1 or 2?
sharp sandal
2
brave wolf
idk what you mean by this one
sharp sandal
sory
brave wolf
okay so no matter what P1 plays, there is a move that P2 can play, such that no matter what P1 plays next he can find a move that wins him the game
so basically what the AI said
forall a1 in A (no matter what P1 plays)
exists b1 in A (there is a move P2 can play)
forall a2 in A (such that no matter what P1 plays next)
exists b2 in A (he can find a move)
a1 + b1 + a2 + b2 = 9 (that wins him the game)
brave wolf
this is what AI come up with ∀a1∈A(∃b1∈A(∀a2∈A(∃b2∈A(a1+b1+a2+b2=9))))
so this should work
buoyant shadow
should it be ≠9
brave wolf
the ∀a1 and ∀a2 basically says that we consider every possible move played by P1
∃b1 and ∃b2 says that B has the freedom to pick the best possible move
brave wolf
should it be ≠9
P2 wins if the sum is 9
sharp sandal
forall a2 in A (such that no matter what P1 plays next) cant we call this one as exists as well
brave wolf
forall a2 in A (such that no matter what P1 plays next) cant we ca...
no, because you have to consider all the possible moves that P1 can play
brave wolf
if everything was forall, it would mean that every game is won by P2, no matter how badly they play
with this forall-exists-forall-exists, it means that if P2 plays optimally, he can win
if everything was exists, it would mean that there is some game, where P2 wins (so perhaps a game where P1 plays very badly)
.
.
maybe think about how would you check whether the statement "P2 can win, if he plays optimally" is true
you'd probably start by considering the cases:
P1 plays 2, then as P2 I can play 2, now P1 plays either 2 or 3...
P1 plays 3, then as P2, I can play 2, now P1 plays either 2 or 3...
notice that we have to consider all the possibilities for P1, while for P2 it suffices to find that one optimal move, it suffices to show that one such move exists
sharp sandal
so player 2 can only win if player 1 doesnt play an optimal game
ok i think i kinda understood do you have any advice for this kind of questions what should i study
brave wolf
so player 2 can only win if player 1 doesnt play an optimal game
well, yes, thats what actually happens in this game. If P1 plays optimally, P1 wins
brave wolf
ok i think i kinda understood do you have any advice for this kind of questions ...
depends, what was the question?
Were you supposed to:
- translate it to those ∃ and ∀ or
- find out whether P2 can win if he plays optimally
sharp sandal
ye
brave wolf
so which one xD
sharp sandal
i have to construct this type of propositions using those symbols
brave wolf
i see
well, then that's translating natural language into first order logic
you can probably find some exercises online by searching that phrase
or since you already use ai, you could prolly ask it to generate more similar exercises
though ai isnt always accurate
sharp sandal
yes thank you so much for youre help
brave wolf
np
safe radishBOT
yes thank you so much for youre help
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storm citrus
Can I get help with TinkerCAD circuits here and OpAmps as Comparators
opaque fern
Can I get help with TinkerCAD circuits here and OpAmps as Comparators
Usually, no. but I can help you just this one time but don't take it as a precedent for the future
storm citrus
ty
sorry for the bad circuit lemme explain lol
so all the way to left is just the voltage divider to get my threshold voltage, 2.56 volts
in the middle is just another voltage divider but with a LDR so i can see the cut off and what ever
the power pack on the bottom right is set to 2 volts, which if in+ is greather than in- (the threshold) i want 2 volts to run through to the light
but when i run it I don't get 2 volts through my light
opaque fern
Can you give fhe pinout to the op amp
opaque fern
Ok first issue im noticing
opaque fern
While true that ideal op amps can output theoritically infinite gain in an open loop system, this is not the reality in practice
Youre output is limited by the power rails of the op amp
If your op amp's V+ is 2 V, the maximum output is going to be 2 V too
The input signals you are feeding are 2.58 ans 8.79 V
Even disregarding the gain, this is too much
storm citrus
yep, and the 8.79 can be increased or decreased by the LDR.
storm citrus
Even disregarding the gain, this is too much
too much for the IC741?
why is it too much?
storm citrus
so if my V+ was 10V it would work fine?
storm citrus
that is true
opaque fern
Consider adding a current limiting resistor in series with the LED
Connect the 9 volts of the battery to the power rails of the op amp
opaque fern
Consider adding a current limiting resistor in series with the LED
Assuming 9 volts power supply, 7 volts is going to drop across the resistor
storm citrus
sorry, when you say power rails, do you just mean +v and -v?
opaque fern
Choose a reasonable resistance based on your desired current (e.g., 50 mA)
opaque fern
sorry, when you say power rails, do you just mean +v and -v?
Yeah
storm citrus
mm okay, but do i need to add a resistor to the LED? Is there anyway i can just have the Comparator output 2 volts while still having relativley high input signals without it blowing up?
opaque fern
Btw you should ALWAYS connect a resistor in series with a diode (or an LED)
opaque fern
Your LED acts (effectively) as a short circuit when it is forward biased
Meaning you are just creating a short circuit that would create theoretically infinite current
storm citrus
ye okay
storm citrus
so just in regards to this, why doesn't it actually output 2 volts or roughly around 2 volts?
storm citrus
But this does
storm citrus
In reality that LED would be burning either way
im still a bit confused about this sorry
is that because more than 2 volts is going through the led?
opaque fern
Like
Op amps usually have input protection diodes internally. If you push a voltage higher than the op amp's power rails at the input, massive currents will rush through the op amp and fry it
I assume the reason it is displaying 44 mV is because the op amp is effectively outputting close to 0 volts
But I correct myself: the LED would not be burning in this case because the op amp would have fried itself before that
storm citrus
So would the IC741 be rated for a specific voltage?
storm citrus
just searched it up, so supply voltage is +/- 18 Volts
and does supply voltage mean V+ and V-?
if so, im confused as hell, cos all my inputs are between that range, and my V+ and V- are within that range as well at 2 volts
opaque fern
and does supply voltage mean V+ and V-?
Yes
opaque fern
if so, im confused as hell, cos all my inputs are between that range, and my V+ ...
The issue is that youre putting them at 2 volts
Increase it to 9 or 10
And add a resistor at the output
storm citrus
okay so i increased the power rails voltage to 10 volts
and i added a 1k ohm resistor
in my mind, if i didnt have that resistor, 10 volts should be flowing through that led now
here's what im trying to make btw
I changed it up a bit so i dont have an external power source now and i just have the 9v battery
now i would assume 9 volts or very close to to run through the led, but its only 2.53 volts
to me that is either A, because the IC741 physically cannot output 9 volts, or B its bugged
I bet u regret letting this circuit question slide Lex lol
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stoic raptor
wait idont get how can AB + DB = DC?
safe radishBOT
wait idont get how can AB + DB = DC?
primal bone
That's not what that says
You've got three non-parallel vectors in the same plane
Thus, one can be made by summing multiples of the others
(cf how you can make any 2D vector by adding multiples of i and of j together)
stoic raptor
Thus, one can be made by summing multiples of the others
how is that true though
i know parallel vectors can be expressed as scalar multiples of each other
but how is this also the case
<@&268886789983436800>
pastel vector
wait idont get how can AB + DB = DC?
take (0,0,0) and construct a plane
now plug in the value of (5,6,-x) in that equation of a plane
and solve for x
stoic raptor
huh
pastel vector
huh
?
bruh
dc should lie in the span of ab and bc
for it to lie in the same plane
hence he just wrote dc as a linear combination of ab and bc thus indicating that lies in their span (plane)
stoic raptor
wait so if all the points are coplanar, i can write one of the vector lines as a result of two others with scalar multiples?
stoic raptor
ohh so its a rule?
pastel vector
yes
stoic raptor
oohh so thats called span rule
oh that makes so much sense now
thanks @pastel vector and @primal bone i appreciate ur help!
pastel vector
yes
stoic raptor
.close
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pastel vector
thanks <@903843697127489576> and <@660973674870079488> i appreciate ur help!
youre welcome
lone void
Sir Isaac newton what were u doing under an apple tree at 3 in the afternoon
tawdry plover
Sir Isaac newton what were u doing under an apple tree at 3 in the afternoon
he wont share with you the secret sauce
pastel vector
he wont share with you the secret sauce
apple sauce
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shell jacinth
This is a graph problem, where we have 10,15 and 30 Vouchers for hotels A, B and C. We cannot spend 2 consecutive nights in a single hotel. We need to find a solution where we can find a way to spend 45 nights using these vouchers.
The slide claims that the solution is not possible, but from what I've seen if you repeat the sequence ACBCBCBAC 5 times you can spend 45 nights.
safe radishBOT
This is a graph problem, where we have 10,15 and 30 Vouchers for hotels A, B and...
shell jacinth
Am I missing something obvious. For example the solution is actually impossible for 55 nights?
blazing swallow
from the wording, it seems like you have to use all the vouchers
and 4C 5 times is 20 vouchers
oh no actually 10 + 15 + 30 = 55 so you're right 
tired trellis
For part (ii), I don't really understand how to find out whether the integral converges or diverges if we're not actually given the function.
safe radishBOT
For part (ii), I don't really understand how to find out whether the integral co...
thin bridge
which function
thin bridge
you have info about h(x) at the top
you can utilise the info about the definite integrals of g(x)
tired trellis
Oh like whether they converge or not?
So wait this is saying that g(x)=0 for all values except 3 and 5
so shouldn't h(x) converge to 0?
like how does the 0-infinity integral also end up converging to -24
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minor flax
<@&268886789983436800>
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outer pollen
<@&268886789983436800>
versed wave
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hoary seal
how do we answer this
safe radishBOT
how do we answer this
split kayak
i assume by "this" you refer to those with a red outline, right?
hoary seal
yes
split kayak
Id like to assume you know what ∠AOB is too
hoary seal
thats the angle
hoary seal
I am confused what are we tryna do?
the question sai find sin of that angle
sin is opp/hyp
split kayak
You can isolate |sin θ|
Yes, you could find the angle by a multitude of ways, but what this problem is expecting you to do is to find the value of sin with this formula
hoary seal
isnt it magnitiude because there is two vertical bars
split kayak
For this you have to compute the magnitude of the cross product of the two vectors associated to AOB as an angle, and divide it by the product of the two individual magnitudes.
hoary seal
what is magnitiude of the cross product?
first time hearing it
ohhh
nvm
the lenght of that vector ok
split kayak
what is magnitiude of the cross product?
Just solve for the cross product, and then its magnitude
yea
hoary seal
Just solve for the cross product, and then its magnitude
thats a vector
magnitude is without direction
split kayak
Okay so lets get onto the same page
The magnitude of a vector v = (a,b,c), |v|
is: √(a^2 + b^2 + c^2)
Geometrically speaking its the length of the vector.
The cross product of two vectors, v x u is an operation that finds the vector perpendicular to the two vectors.
Which means that it takes two vectors as input and gives you another one in return.
Since "v x u" is a vector itself, you can also find |v x u| too
Which is just the magnitude of the result of that cross product.
And it happens to be that theres an identity that satisfies:
|v x u| = |v| * |u| * |sin θ|, where θ is the angle that forms between the two vectors.
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daring sonnet
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finite coral
Hm. I don’t think AC being radius is enough
Maybe show that the line passes through at one point exactly?
finite coral
This just shows that point A lies on the circle
I don’t know what method the teacher wants to see, but I think that deriving the equation for the line and the circle, substituting the y value into the circle, and showing that there’s only one point should be good
If you get what I mean
finite coral
I don’t know what method the teacher wants to see, but I think that deriving the...
And said point is A
You have proved that A lies on the circle,
You just need to show that l is indeed the tangent
Can anyone else confirm?
safe radishBOT
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hollow wadi
I need help determining this functions derivative f´(x)
safe radishBOT
I need help determining this functions derivative f´(x)
vague phoenix
Do you remember the derivative rule?
hollow wadi
Here are the forms we have given
vague phoenix
Cool, we gonna use $D(x^n)=nx^{n-1}$
flat frigateBOT
Minλ
hollow wadi
2*1/2x-1?
vague phoenix
First, what is derivative of x^2
hollow wadi
2x
flat frigateBOT
Minλ
smoky nacelle
Cool, we gonna use $D(x^n)=nx^{n-1}$
what is this notation called
is this lagrange
vague phoenix
is this lagrange
You are overthinking
vague phoenix
Okay, since 1/2 is a constant, it will multiply with derivative of x^2
hollow wadi
Here is what i got
vague phoenix
Yes that is correct
smoky nacelle
Not sure which notation is that
leibniz
vague phoenix
I am leibniz fan then
hollow wadi
euler ok
yeah its quite confusing because later on in the course they are given like this
smoky nacelle
lagrange is just more convenient so yeah
vague phoenix
Multiple derivatives
hollow wadi
or like this
smoky nacelle
because then its just annoying
vague phoenix
How come annoying?
smoky nacelle
try writing $\dv{f(g(x))}{x} = f'(g(x))g'(x)$ in leibniz lol
flat frigateBOT
Περσυ
hollow wadi
yeah like it would be much easier if it was just in the form of dy/dx for each question for us
astral glacier
Guys the help channel might not be the best place for this conversation
Oh nvm the helpee is involved
Carry on
safe radishBOT
smoky nacelle
Oh nvm the helpee is involved
zavier minimodding for 3 whole seconds 
/lh
astral glacier
vague phoenix
leibniz
Well in that case Lagrange is much helpful
I am not sure who would use Newton's one?
vague phoenix
its all time derivatives
Imagine differentiating 50 times with 50 dots
smoky nacelle
$\dddddddddot{f(x)}$ no way this works but lol
flat frigateBOT
Περσυ
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
astral glacier
Imagine differentiating 50 times with 50 dots
You don't usually do that many derivatives tbf
In physics the most you differentiate is twice
smoky nacelle
it works till $\dddot{f}(x)$ at least
astral glacier
Just the f inside percy
smoky nacelle
yeah i saw lmfao
flat frigateBOT
Περσυ
smoky nacelle
looks cursed
vague phoenix
$\dddddddddot{f(x)}$ no way this works but lol
I think your letter d button is stucked
smoky nacelle
i $= \dot{\iota}$
vague phoenix
You don't usually do that many derivatives tbf
astral glacier
You don't ever differentiate more than twice for anything meaningful tbf
flat frigateBOT
Περσυ
smoky nacelle
You don't ever differentiate more than twice for anything meaningful tbf
jerk :')
smoky nacelle
jerk is meaningful if youre in some field im sure
we def have triple integrals
im sure triple derivatives would be helpful somewhere
fathom jewel
You don't ever differentiate more than twice for anything meaningful tbf
Taylor series real
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restive portal
I'm trying to use some trig in my game project to find the most acute left side angle, and most acute right side angle, relative to a directed line segment, but I'm having trouble writing a function that works for all cases.
My current attempt is using atan2, which I yoinked from stackoverflow https://stackoverflow.com/a/31334882
double result = atan2(P3.y - P1.y, P3.x - P1.x) -
atan2(P2.y - P1.y, P2.x - P1.x);
However, this doesn't work for all orientations, when the vector is oriented different, I get completely different results, and I'm not sure how to compensate.
safe radishBOT
I'm trying to use some trig in my game project to find the most acute left side ...
opaque fern
I'm trying to use some trig in my game project to find the most acute left side ...
Hmm. Immediately im thinking this is a normalisation issue
Cause your range is ultimately between -pi and pi right
vale dagger
√6=3
opaque fern
If you subtract two angles you can get e.g., 270 or something
restive portal
well, I was seeing results ranging from 0 - around 5.7 something
opaque fern
Implement behaviour that wraps back around the [-pi, pi] range
restive portal
but completely varies depending on the base segment I'm starting with
I'm assuming there's some completely trivial way to calculate it
opaque fern
well, I was seeing results ranging from 0 - around 5.7 something
5.7 radians?
,w 5.7 * 180/pi
flat frigateBOT
restive portal
I don't understand the trig functions enough to reason about them, so I've just been trying a bunch of inputs trying to identify a pattern I can work with D:
opaque fern
rawDiff = angle2 - angle1;
diff = Math.atan2(Math.sin(rawDiff), Math.cos(rawDiff)):
Try this instead?
opaque fern
Oh Its shorthand for what you already have inside those functions. Since I didnt exactly know the state of your workspace
restive portal
well, it's those angles that I'm trying to compute in the first place
restive portal
I'm not attached to my current approach whatsoever, I just have 3 points as inputs and I'm trying to find the angle between them
opaque fern
angle1 = atan2(P2.y - P1.y, P2.x - P1.x);
angle2 = atan2(P3.y - P1.y. P3.x - P1.x);
rawDiff = angle2 - angle1;
diff = Math.atan2(Math.sin(rawDiff), Math.cos(rawDiff)):
that appears to change the result to the absolute value of the same things I was getting
lemme test a different input
I think it miiight be working? I'll go try integrating it and check on the main dataset
thanks for your help!
hoary seal
how do we answer this?
safe radishBOT
how do we answer this?
covert rain
Which point ?
safe radishBOT
@hoary seal Has your question been resolved?
hoary seal
Which point ?
we can go from the first
covert rain
Mmm
<@&268886789983436800>
Where does it say "complete the sentences"?
There is a theorem you can use
hoary seal
yea?
covert rain
Which one do you think should be used?
hoary seal
sorry back
hoary seal
Which one do you think should be used?
I don’t know the thereoums
covert rain
Yes
hoary seal
Why did they put a modulus around the function
covert rain
Its just a function
covert rain
They want to study the function with the absolute value
If you remove the absolute value it becomes another function
,w graph y=x
flat frigateBOT
covert rain
,w graph |x|
flat frigateBOT
covert rain
Change the function as above
hoary seal
I see
covert rain
Yes
covert rain
I thought you just meant |x| , so Yes
covert rain
What are the options of the first one?
hoary seal
I’m not sure but we’ll come back to tha because it’s glitching
Let’s do the empty boxes first
hoary seal
The selection boxes and the one that asks for our input
covert rain
Do you know how to find the maximums and minimums?
hoary seal
Yeah
first derivative set it equal to 0
Second derivative at that point and see if it’s a max or min
covert rain
First you have to find the stationary points
hoary seal
First you have to find the stationary points
and then?
covert rain
Second derivative at that point and see if it’s a max or min
This
Then also the extremes of the interval and the points where the function is not differentiable
hoary seal
Then also the extremes of the interval and the points where the function is not ...
Wdym?
covert rain
You also need to check the points where f is not differentiable and also the endpoints of the interval because the derivative tells you the behavior within the interval.
safe radishBOT
@hoary seal Has your question been resolved?
hoary seal
You also need to check the points where f is not differentiable and also the end...
how do we do that?
covert rain
Do you have the derivative?
hoary seal
Do you have the derivative?
ill show u what ive done now
hoary seal
Do you have the derivative?
I just got one point
there needs to be more right?
<@&268886789983436800>
hoary seal
@covert rain
covert rain
Mmm what did you do
safe radishBOT
@hoary seal Has your question been resolved?
safe radishBOT
@hoary seal Has your question been resolved?
covert rain
Can u explain me the different ability part
Wdym
safe radishBOT
safe radishBOT
Available help channel!
wheat slate
I need help finding g, I kind of would like a walkthrough if possible
wheat slate
coordinates of rac is (-13.8i, 0j, 5.8k)
magnitude of rac is 14.96 cm
<@&286206848099549185>
frozen veldt
you want the dot product to equal zero yeah?
and you know that one of the components of F is zero
wheat slate
ya the y component
frozen veldt
yup
safe radishBOT
safe radishBOT
Available help channel!
trail lotus
the ratio is suppose to be found but I don't know where they specified the short time between flashes and the long time between flashes.
safe radishBOT
the ratio is suppose to be found but I don't know where they specified the short...
plucky elk
!show
safe radishBOT
Show your work, and if possible, explain where you are stuck.
plucky elk
as usual
trail lotus
ofc ofc
worldly lantern
can you relate the angle between the beacons to the time between flashes
trail lotus
I thought only the answer from 1:120 was right because it included the degree
trail lotus
can you relate the angle between the beacons to the time between flashes
okay so 120 degrees? time between flashes idk shorter time between 1st and 2nd
trail lotus
do you know that the total angle on a point is 2pi
2 
split kayak
Do you understand what the ratio refers to in this case?
trail lotus
Do you understand what the ratio refers to in this case?
ratio is the short time between flashes and the long time between flashes.
split kayak
Now, do you understand that the beacons can be thought as simply lines on a circle thats rotating and which might or might not be facing to the observer.
trail lotus
Now, do you understand that the beacons can be thought as simply lines on a circ...
yes, I think the diagram already established that
split kayak
If the rotation is always at the same rate, we can say that a full revolution takes. "x" seconds
How much does it take to cover 120º?
trail lotus
How much does it take to cover 120º?
x seconds
split kayak
I full revolution could never take as much time as a part of itself.
trail lotus
one full rotation!
split kayak
120º is not a full rotation
trail lotus
120º is not a full rotation
less time it would take than a 360 degree rotation..?
split kayak
Yes but this is not a definite answer. The time it takes to make a 120º degree rotation has to be a fraction of what it takes to make 360º; Which we already stated that we would call x
trail lotus
Yes but this is not a definite answer. The time it takes to make a 120º degree r...
answer C b/c 120 is 1/3 of 360 degrees? how is that short time between flashes though? degrees aren't time??
split kayak
I have 0 clue what you wrote, but yes, 120º is a third of 360º.
And that was mostly what I was going for.
trail lotus
I have 0 clue what you wrote, but yes, 120º is a third of 360º.
b/c means because
split kayak
The fact that a distance or angle rotation isnt time doesnt mean that you cant correlate them.
worldly lantern
answer C b/c 120 is 1/3 of 360 degrees? how is that short time between flashes t...
a little side note : degrees can be thought of as time if the thing rotates at 1° per unit time
trail lotus
a little side note : degrees can be thought of as time if the thing rotates at 1...
so what the problem really meant is that the short time (between flashes) was 120 degrees and the long time (between flashes) was 360 degrees?
worldly lantern
try keeping two pens at 120° and rotate them , to see the length of intervals in which they cross a certain point if you cant understand how the longer time between flashes will be calculated , cuz it isnt 360° sadly
trail lotus
try keeping two pens at 120° and rotate them , to see the length of intervals in...
would it be bigger than 360 degrees? smaller? i don't quite understand yet
worldly lantern
i suggest you either try to visualise the interval
or physically do it
to find out
it would be very unrewarding for me to give away the answer
trail lotus
i suggest you either try to visualise the interval
okay so the movement of both pens aren't unilaterally related to degrees but something else?
idk 
worldly lantern
they are , if you do it right
trail lotus
they are , if you do it right
how do u do it right??
worldly lantern
two pens, kept in the same plane, making an angle of 120° are to be rotated , the axis of rotation passis through the shared vertex and being perpendicular to the plane of the pens,
if done this way
they will simulate light rays of a lighthouse
trail lotus
two pens, kept in the same plane, making an angle of 120° are to be rotated , th...
so like this?
worldly lantern
is that AI lol
trail lotus
is that AI lol
i had to visualize somehow 😭
worldly lantern
so they will always keep the 180 degree distance away from each other?
120° not 180°
trail lotus
120° not 180°
yea typo wtv
worldly lantern
how much angle has the system rotated , when pen A crosses the starting point of pen B
trail lotus
how much angle has the system rotated , when pen A crosses the starting point of...
240 degrees?
worldly lantern
yes if we rotate clockwise
no if we rotate anticlockwise
trail lotus
so like this?
i js chose that direction bc that's what this model seemed to be doing
trail lotus
yes if we rotate clockwise
no if we rotate anticlockwise
would anti be less than 240 degrees?
worldly lantern
anti would be 120° precisely
trail lotus
try keeping two pens at 120° and rotate them , to see the length of intervals in...
so the longer time between flashes would be 240 degrees?
safe radishBOT
@trail lotus Has your question been resolved?
trail lotus
so c was wrong 
<@&286206848099549185>
primal bone
so c was wrong <:monkey:651816857153699840> <@&286206848099549185>
Dude you're basically spinning those lights at the same time
- After being flashed by beacon 1, how much more does that spinning thing rotate until you're flashed by beacon 2?
- Once flashed by beacon 2, how much does the thing have to rotate again till you're flashed by beacon 1 again? [THIS is the third flash the question refers to]
safe radishBOT
@trail lotus Has your question been resolved?
hoary seal
<< a*x+0*0 > , < a*0+0*w >>
why did i get this wrong
safe radishBOT
`<< a*x+0*0 > , < a*0+0*w >>`
why did i get this wrong
outer pollen
the standard product of two 2x2 matrices is a 2x1 matrix?
light shoal
what last one?
hoary seal
what the heck is an identity matrix
light shoal
surely this is defined in your book or notes somewhere?
vague phoenix
what the heck is an identity matrix
Major diagonal is 1, elsewhere 0
light shoal
a simple google search will tell you
vague phoenix
Bro you learned to this stage and can't get this identity
light shoal
you should probably go back and re-read whatever sections teach you about matrix multiplication and the identity
you're not going to get far with this exercise set otherwise
outer pollen
did you ask your lecturer about them?
outer pollen
why not your lecturer though, if I may ask? presumably they're the one who wrote your notes and are in the best position to explain them.
hoary seal
true
arctic raven
straight from the horse's mouth is always best, not to call your lecturer a horse
hoary seal
straight from the horse's mouth is always best, not to call your lecturer a hors...
haha yeah
just been focusong on my other assignments, havnt had the chance to ask him
Im so cooked
outer pollen
you can always shoot him an email, then go do your assignments while he reads and responds.
or walk straight up to his office during his office hours.
hoary seal
Yes, thats a great idea
arctic raven
<@&268886789983436800> bro
neat wind
Can someone help me be able to solve related rates on my own
safe radishBOT
Can someone help me be able to solve related rates on my own
worldly lantern
do you have a specific question
narrow ivy
narrow ivy
Well try keeping in mind the formulas for basic geometric objects
neat wind
Something like this
worldly lantern
narrow ivy
Something like this
Try drawing an illustration
narrow ivy
Try drawing an illustration
Once you've drawn the right picture finding what to derivative should be good
stoic torrent
Something like this
.pin
safe radishBOT
Something like this
narrow ivy
Notice that the angle increases each timestep
neat wind
by how fast is the ballon rising are they looking for d theta / dt ?
narrow ivy
by how fast is the ballon rising are they looking for d theta / dt ?
Its already given in your problem
First find what is the question asking for
narrow ivy
Yeah
neat wind
so it'd be like 45 = opp / 150
narrow ivy
Yeah isolate the unknown
narrow ivy
theta = opp/adj?
btw this is tan(theta) = opp/adj
stoic torrent
its supposed to be tan(theta) not theta?
fair sigil
Is this a chat for lol
stoic torrent
Is this a chat for lol
stoic torrent
This was clear right ?
neat wind
would it not just be dh/dt = 150 sec^2(45)
stoic torrent
would it not just be dh/dt = 150 sec^2(45)
Yes!!
neat wind
This was clear right ?
yeah
narrow ivy
would it not just be dh/dt = 150 sec^2(45)
Yeah try pluggin in the calc
neat wind
0.14 rad/min
narrow ivy
yeah
narrow ivy
wait would that just be it
Change the 45 degrees to radians first since its in that unit
stoic torrent
Change the 45 degrees to radians first since its in that unit
not necessry
narrow ivy
dam really?
stoic torrent
dam really?
since you are js putting a trigo function over it and evaluating its value
doesnt matter if you take degree or rad
same answer
and trigo functions are dimensionless
narrow ivy
Oh ok
neat wind
ok lemme try another question if thats fine
stoic torrent
ok lemme try another question if thats fine
Sure!
stoic torrent
.pin
safe radishBOT
stoic torrent
first, try on your own and draw diagrams for better understanding
stoic torrent
its correct
neat wind
oh
stoic torrent
draw their velocities asw
neat wind
would i have to derive the pythagorean theorem or smth im kinda lost here
stoic torrent
would i have to derive the pythagorean theorem or smth im kinda lost here
okay
Im back
Uh
stable zephyr
would i have to derive the pythagorean theorem or smth im kinda lost here
atleast i did to find the dist (also yajant sorry for randomly messaging this)
you can use pythagoras again and turn it into a differential
stoic torrent
i am not really good on english here but is the distance the hypotenuse or the addition of the distance of car and cycle from intersection?
stable zephyr
and solve for dx/dt
neat wind
i am not really good on english here but is the distance the hypotenuse or the a...
the hypotenuse
stoic torrent
the hypotenuse
okay then followe velt!
torn kettle
Very easy peasy
stable zephyr
the hypotenuse
find s and then differentiate the pythagoras thm wrt t
i assume you can solve the eqn formed
torn kettle
You will find answer by using differentiation
stoic torrent
i assume you can solve the eqn formed
-# might have to elaborte a bit
neat wind
wait so just use pythagoras to find the current distance??
torn kettle
Yes
stoic torrent
You will find answer by using differentiation
-# yeah thats what the qsn is on !
torn kettle
-# yeah thats what the qsn is on !
Yeahh
stable zephyr
wait so just use pythagoras to find the current distance??
use pythagoras to find the hypotenuse which is the dist between car and motorcycle
neat wind
alr dist would be 1
neat wind
and solve for dx/dt
mb but where did dx/dt come from tho
stable zephyr
mb but where did dx/dt come from tho
by pythagoras theorem you get s^2 = x^2 + y^2 right?
so x is the base
so if you differentiate it with time
you can get dx/dt which is what you want to find
neat wind
okayy ic ic
ok if i differentiate that wouldnt i just get ds/dt = dx/dt + dy/dt
mb i feel like im asking stpid questions
stable zephyr
ok if i differentiate that wouldnt i just get ds/dt = dx/dt + dy/dt
nop
wb the s^2
well u will get those 3 terms ofc
but dont forget s^2, y^2, x^2
stable zephyr
yeah
neat wind
then i would just plug in the values?
stable zephyr
yeah
stable zephyr
i have ptsd from ts 💔
not a big deal vro
neat wind
2 ds/dt = 1.6 dx/dt + 1.2 dy/dt
grim cosmos
not a big deal vro
idk i js dont like it especially when he gives me sum weird ahh shape i dont know
grim cosmos
most of the time he says the formula but like sometimes he doesnt
stable zephyr
oh well
stable zephyr
thats why i was so confused
o
neat wind
well first we coudl just divide everything by 2 so it'd jsut be
stable zephyr
yeah
neat wind
s ds/dt = x dc/dt + y dy/dt
1 ds/dt = 0.8 dx/dt + 0.6 dy/dt
1(20) = 0.8 dx/dt + 0.6(-60)
stable zephyr
yeah
neat wind
[20 - 0.6(-60)] / 0.8 = dx/dt
ok well
i thought we were supposed to find ds/dt not dx/dt too
thats my mistake tho
cause its asking for speed
of motorcycle
neat wind
yeah ok
that was confusing
but i undersatnd it
thank you guys
i'll probably practice more tomorrow in office hours ors mth
how do I end this
neat wind
.close
safe radishBOT
safe radishBOT
Available help channel!
polar ibex
How do i find f'(-4)? i know how to find f(4) but idk how to differentiate this
simple galleon
How do i find f'(-4)? i know how to find f(4) but idk how to differentiate this
fund. thm. of calculus says the derivative is the opposite of the integral
polar ibex
Ok so f(x) is the antiderative of g(t)
simple galleon
,tex so if you take the derivative of $\\int_0^x g(t)dt\$you get $g(x)$
flat frigateBOT
bored amogi
polar ibex
is g(x) the same as f(x)
and it's like
g(x) * 1 or something for the deriative
??
simple galleon
ok so let me show you the fundamental theorem of calculus formula
(a is a constant)
polar ibex
if we take the derivative of the integral doesn it cancel it out
simple galleon
yeah it does
polar ibex
so f(t) = f(x)
simple galleon
no
f(t)=int from 0 to t g(y) dy
(replace y with any variable other than t)
again
f(t) does not take any derivatives
polar ibex
what is y supposed to be
simple galleon
f'(t) is a derivative
simple galleon
what is y supposed to be
basically just notation
itll correspond to the x on your graph
polar ibex
wait so in the context of f(x), f'(x), and g(x)
simple galleon
yeah?
simple galleon
close, replace -4 with x
polar ibex
Ok
How do i solve for this?
g(t) = f'(x)?? or is that still not allowed cuz integral is from 0 to x
simple galleon
you use the formula
simple galleon
g(t) = f'(x)?? or is that still not allowed cuz integral is from 0 to x
g(x)=f'(x)
you cant switch variables here
polar ibex
so now we solve for g(4)?
simple galleon
(alternatively it could be g(t)=f'(t) but it doesnt matter)
polar ibex
im not sure where we get g(x) from
simple galleon
so now we solve for g(4)?
-4
simple galleon
im not sure where we get g(x) from
alright so one more time
we are looking at f' (not f)
since f is an integral
f' is the derivative of an integral
polar ibex
Ok
simple galleon
the derivative and the integral cancel out
polar ibex
Yes
polar ibex
So when like a derivative and an integral cancel out it becomes g(x)
flat frigateBOT
bored amogi
polar ibex
**bored amogi**
Wait this is from the FTC 1
simple galleon
Wait this is from the FTC 1
yes
polar ibex
Ohhhhh
Oh yeah i js remembe r how i got that equation
Cuz i took the derivative of both sides
polar ibex
Yes
My hw is like 10 questions per unit and all the answers are 0-9 one of each number
BUt i got 2 answers = 0
8 and 1
question
safe radishBOT
@polar ibex Has your question been resolved?
graceful lichen
safe radishBOT
warm warren
well what have you tried
graceful lichen
some random integers values for x & y so that LHS = RHS
but didn't get a perfect pair
warm warren
.texsp{||subs $a = xy$ and multiply the given equations||}
flat frigateBOT
Annie Maqionde
graceful lichen
sin(xy) = xy
warm warren
sin(xy) = xy
when is this true?
graceful lichen
when sin is 0
warm warren
when is sin zero?
warm warren
in general nπ where n E Z
hm so substitue that
an easier method
would be to roughly plot the graphs of sin x and x
and see where they intersect
graceful lichen
hm so substitue that
Why substitute now when know it's nπ then it can be any value from this set
any one value for n actually
Right?
warm warren
Why substitute now when know it's nπ then it can be any value from this set
hm yes but your equation is sin x = x
for what value of n is this true?
its NOT true for all values of n
graceful lichen
yes when n = 0
warm warren
and when is $n\pi = xy = 0$?
flat frigateBOT
Annie Maqionde
warm warren
more properly, when is $xy = 0$?
flat frigateBOT
Annie Maqionde
graceful lichen
when both x and y are zero
graceful lichen
one of them can be nonzero
After multiplication non zero can make whole thing zero
warm warren
yes so this should give you a fairly good idea on how to find x and y. if sin xy = 0, then cos xy = ?
graceful lichen
yes
warm warren
now you'll have to see which of x and y is zero
graceful lichen
I appreciate your idea of subbing xy= a
warm warren
both cannot be zero(obvious from the question)
and you'll have to observe that cos 0 = ?
graceful lichen
Yes
warm warren
now $\cos 0 = x$
flat frigateBOT
Annie Maqionde
flat frigateBOT
Annie Maqionde
warm warren
in general (2n+1)π/2
we do not need the general forms
warm warren
in general (2n+1)π/2
and this is wrong
graceful lichen
okay okay
warm warren
x is one. correct
if x is one, find the value of y
graceful lichen
y= 0
warm warren
precisely
graceful lichen
Tan(xy)= 0
warm warren
are any other pairs possible?
warm warren
correct
and there you have your solution
do not interchange the values of x and y
!done
safe radishBOT
If you are done with this channel, please mark your problem as solved by typing .close
safe radishBOT
graceful lichen
.reopen
safe radishBOT
✅ Original question: #help-23 message
graceful lichen
Do we not have say cos(a) =/ 0 while cancelling
smoky nacelle
$\neq$?
flat frigateBOT
Περσυ
graceful lichen
Yes
graceful lichen
When subbing xy= a