eg the first term you underlined is in x^(n+1) not x^n
#help-26
strange whale
strange whale
you don't give a crap about them
halcyon frost
huh?
strange whale
we're just interested in the x^n ones
halcyon frost
i get that we are interested in those ones
obviously they are the ones that make up the sum we need
mortal thunder
you don't give a crap about them
Lmao that's :sigma: attitude right there
halcyon frost
but then, what was the point of writing (1+x)^n * (x+1)^n if we just leave most of its terms out
strange whale
waste is not a problem, we're doing math, not recycling plastic
if you're so afraid of waste, you could try writing up all the equalities you get from all the coefficients of that expansion
halcyon frost
ok, maybe if i see the next step i will get why this is alright
halcyon frost
if you're so afraid of waste, you could try writing up all the equalities you ge...
right, shouldnt take long
theres only n terms in each sum
so?
what do i do next?
strange whale
theres only n terms in each sum
nah the number of terms varies each time
strange whale
what do i do next?
well (1+x)^n (x+1)^n is also just (1+x)^2n right
what's the coefficient of x^n in (1+x)^2n
halcyon frost
hmmm
strange whale
this is just plain old binomial expansion
halcyon frost
it should be the sum
strange whale
no weird tricks here
halcyon frost
so its just combinations of 2n taken by k
or i
however you wanna note it
right?
strange whale
yes
halcyon frost
ok...
strange whale
C^2n_n as arya said above
halcyon frost
mhm
but we also know that the coef of x^n
is the sum of the squares of combinations
right?
strange whale
yes
halcyon frost
so would that mean that the sum of the sqaures = c 2n taken by n?
since they are both, x^n 's coefs then they should be equal
hell, yea, i got a thumbs up
let me check if thats the correct answer
halcyon frost
chu-vandermonde?
mortal thunder
✓
halcyon frost
bro, vandermonde was enough ong
since when did they chued him
yup, it was the right answer
oki, now time to look at the link that @strange whale sent with the diff solution
halcyon frost
wow, i just really looked at this formula and this is so useful to know
ill hang thins formula on my wall
why do they never teach us these types of formulas
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round pagoda
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round pagoda
ms:
why is the answer plus or minus
i only got positives values as my answer...
(if u know could u explain simply pls)
restive inlet
show your work
round pagoda
show your work
i just use trig to work out the sides
but
cos(22.61) =p/6.5
To find p
and tan(22.61) = q/6
prime turtle
$\vec{a} = 6.5 \overrightarrow{e_r} = 6.5\cos(\theta) \vec{i} + 6.5 \sin(\theta) \vec{j}$
thorny flameBOT
Goëtia
round pagoda
$\vec{a} = 6.5 \overrightarrow{e_r} = 6.5\cos(\theta) \vec{i} + 6.5 \sin(\theta)...
i dont know what any of that means...
restive inlet
where's 22.61 come from
round pagoda
where's 22.61 come from
arctan(-5/12)
restive inlet
that's be -22.61, but cos of that will be the same
however
that isn't the only solution to
tan(t) = -5/12
i.e you'd need to consider the solution in another quadrant
round pagoda
i.e you'd need to consider the solution in another quadrant
quadrant 4?
restive inlet
arctan gives you a value in Q4
prime turtle
isnt arctan injective?
restive inlet
think about other locations where tan is negative
round pagoda
quadrant 2?
restive inlet
yes
prime turtle
tan(x) = -5/12
the 4th quadrant gives -22.62
the 2nd quadrant give also a negative tangent (because cosine is negative there)
so what you do is 180° + x = 180° - 22.62°
round pagoda
i see
craggy matrix
Is the solution 0 for the above problem.
topaz sinewBOT
Is the solution 0 for the above problem.
quartz flower
Yeah
1/n -> 0, the other craps approach to a constant (technically we dont need to care about that, you just need to show it doesnt approach infinity) so the whole thing collapses to 0
topaz sinewBOT
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obsidian crypt
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obsidian crypt
Help me solve
steep sphinx
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oblique nacelle
Imagine this circle's diameter is made of two line segments of length n and d. The lengths n and d are not fixed lengths but they add up to the circle's diameter. Forming a right angle as shown in my diagram at the point at which the segments are separated, at some point p, the object is split into two shapes, the slice of pie shape on the left, and the pacman shape on the right.
Express n in terms of d such that both areas are equal.
topaz sinewBOT
Imagine this circle's diameter is made of two line segments of length n and d. T...
oblique nacelle
This is maybe an easy problem, but a bit challenging for me, I had a dream about it and decided to try and solve it. Turned out to be a bit more tricky that I expected. So I don't know if my description is perfect or if its actually solvable in terms I wrote down. But I got an answer.
I am just wondering if anyone could try it and verify for me if I am wrong. I expect I am wrong because my answer is a bit more complicated of an expression that I anticipated. In my answer I used "a" for the left side length for the "slice of pie", and "x" for the pacman side.
||intuitively i start with assuming a > x because where n=d as drawn in my picture the pie seems to be 1/4th the circle, so, my answer should have a larger numerator||
||Using wikipedia article I drawn this diagram and used a formula for a chord in relation to radius and something called a sagitta, or what they labeled as "h"? https://en.wikipedia.org/wiki/Circular_segment#Arc_length_and_area||
||using wikipedia formula from that page. I then also use pythagorean on a triangle formed outside of the chord/near the middle of circle with sides "c/2" and "r-x". And I used "a + x = 2r"||
after simplifying I get the answer I shown above, but IDK if it is correct. I tried using deep thonk AI but it says a different answer than mine||it thinks the answer is "n = d ( 1 + sqrt 2 )" but I think that is maybe wrong, I tried using that answer in formulas but just end up with r=0 making me think it found an edge case and decided it was correct I guess.||
sweet shard
Why is there so much spoiled to help you
oblique nacelle
I just think math is fun, sometimes people might want to try stuff on their own in case they see this
sweet shard
Help channels are meant for you to receive help
oblique nacelle
yeah I would totally appreciate it! My question is again whether I have gotten it wrong as I suspect I did, and how else can I verify my answer? My numerator is larger so it seems intuitively correct but what else can I do to check it?
topaz sinewBOT
@oblique nacelle Has your question been resolved?
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@oblique nacelle Has your question been resolved?
topaz sinewBOT
@oblique nacelle Has your question been resolved?
oblique nacelle
I am more confident my solution is wrong as I don't think my system of equations has enough information to solve it.
i switched to solve for x, the left length in terms of a, the right side shape's length
but I do not think I have enough information here yet.
Part of my issue I guess is that it seems like there are so many ways to solve this.
and I think the area of the left object is not always based on the same formula depending on the ratio
oblique nacelle
I think this might definitely require trigonometry. I can imagine one side of the pie is length L. Starting from the center as x goes from x=a to x=2R the length L grows from R until it reaches a size of sqrt(R)
eternal cave
Why not use calculus?
oblique nacelle
might do but not sure its necessary
eternal cave
might do but not sure its necessary
Its quicker?
oblique nacelle
It might yeah, but this helps me work where my math is weaker, and I can use calculus too afterwards.
oblique nacelle
so i spent too much time on it and I just wrote a quick script that estimated correct ratio very quickly, guess its just x = 2a or pie side is 2/3rds of the total diameter. Kind of disappointed it was such a simple answer because my first guess was to just try random ratio like estimated it was 3/4ths the diameter
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wispy hedge
the range of arcsin is limited to -pi/2, pi/2 right
topaz sinewBOT
the range of arcsin is limited to -pi/2, pi/2 right
wispy hedge
so it can only provide answers in the first and 4th quadrant
so arcsin (√2)/2 would only be 45 degrees?
reef fjord
arcsin(sqrt(2)/2)*
wispy hedge
yea
and then the range of arccos is 0,pi
so it only provides answers in the first and second quadrant
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restive burrow
this is really hard
topaz sinewBOT
this is really hard
golden wigeon
this is really hard
First, where does the parent function $y = \sqrt x$ start from?
thorny flameBOT
King Leo
restive burrow
Isn't it (0,0) for the parent function? I think so, but I'm not sure if that helps here.
warped tiger
yeah
golden wigeon
Isn't it (0,0) for the parent function? I think so, but I'm not sure if that hel...
✅
Now where does this transformed start
warped tiger
for a parent function it usually starts at 0 except for exponential were it asymptotes at 0 instead
restive burrow
Umm, I think it starts at (3, 2)? Not totally sure though.
golden wigeon
Umm, I think it starts at (3, 2)? Not totally sure though.
To get from (0, 0) to (3, 2), you must go right 3 and up 2 units
Meaning the graph has been translated 3 to the right and 2 upward
restive burrow
Ahh, okay, so it's a right 3 and up 2 shift, got it!
golden wigeon
Ahh, okay, so it's a right 3 and up 2 shift, got it!
So do you know how to implement that shift into your y = ... function?
restive burrow
I’m not really sure how to do that. Could you show me?
golden wigeon
I’m not really sure how to do that. Could you show me?
Assuming f(x) = sqrt(x), use the vertical translation and horizontal translation
warped tiger
hold up can i jump in rq
restive burrow
Yeah, of course! Go ahead
warped tiger
alr so if you take any random function lets say F(x)=2(x-3)+5
the number 2 multiplying on x-3 would represent a
and the 5 would be d
the f dosent really represent anything other than it being a function and the fact that its being multiplied by a
restive burrow
Ahh, okay! So 'a' is for stretching, and 'd' is for shifting up or down. Got it!
warped tiger
and c your shift from left to right is always backwards so +5 is left and -5 is right
my advice is to just put down 2-3 points to find the shape of your line then you can go from there pretty easy
restive burrow
Do you care if I sc this for notes?
warped tiger
no ur good
restive burrow
Got it! So based on that, would the equation for my graph be something like ( g(x) = \sqrt{x - 3} + 2 ) or am I missing something?
thorny flameBOT
Nova cap
topaz sinewBOT
@restive burrow Has your question been resolved?
warped tiger
gang sorry but yeah you got that
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hallow plaza
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hallow plaza
Can someone help me with this please
golden wigeon
Do you know what the four variables represent?
hallow plaza
No
golden wigeon
No
y: vertical distance from the originx: horizontal distance from the originm: slope (calculated byrise / run)c:y-intercept (found by evaluatingyatx = 0)
Lets work on c first. can you try finding the point at x = 0?
golden wigeon
How do I do that?
Dyk what the y-axis and x-axis are?
hallow plaza
No
golden wigeon
No
Blue = y-axis
red = x-axis
So @hallow plaza can you locate the point where the graph touches the y-axis (in general, you can assume x = 0 is on the y-axis, and y = 0 is on the x-axis)
hallow plaza
X=5?
golden wigeon
- `y`: vertical distance from the origin
- `x`: horizontal distance from the ori...
_ _
hallow plaza
How?
hallow plaza
Sorry. I'm really dumb
golden wigeon
Since x = 0, the first term of the right side cancels out
So we have y = c
And based on the graph, we know that y evaluated at x = 0 is 5
So we say that c = 5. we cannot say y = 5 because the graph clearly shows that y is going up
hallow plaza
Ok
golden wigeon
Ok
Now, lets find m
Pick two random points on the graph (ideally ones whose coordinates you know)
(and send a picture when youre done)
hallow plaza
golden wigeon
Can you label their coordinates in an ordered pair
golden wigeon
Now, you have two coordinates of the form:
$$a = (x_1, y_1)$$
$$b = (x_2, y_2)$$
Calculate the slope using:
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
thorny flameBOT
King Leo
hallow plaza
Imma leave open just incase bc I have lots more questions lol
golden wigeon
Imma leave open just incase bc I have lots more questions lol
Sadly the mods wont allow that
You need to close and reopen a new channel
!1q read for more info
topaz sinewBOT
It is suggested that you limit yourself to one question per help channel, opening a new one once your original question is answered and your original channel has been closed. This is to make your channel easier to follow for potential helpers and can bring attention to the fact that your question has changed.
signal osprey
we say that a limit $\lim_{x \to x_0} f(x) = L$ of the function $f: A \to B$ is meaningful only if $x_0$ is an accumulation point for A
topaz sinewBOT
we say that a limit $\lim_{x \to x_0} f(x) = L$ of the function $f: A \to B$ is ...
thorny flameBOT
nico.alesi
neon iron
yes
signal osprey
now the question, sorry Im slow
what if the type of limit is $\lim_{x \to \infty} f(x) = L$
thorny flameBOT
nico.alesi
signal osprey
the definition would be: it exists $\Leftrightarrow \forall \epsilon > 0, \exists x_0 > 0 / x \in A \wedge x > x_0 \implies |f(x)-L|<\epsilon$
thorny flameBOT
nico.alesi
signal osprey
now $x_0$ has a different role, the accumulation point would be $\infty$, so I don't need to specify anything?
thorny flameBOT
nico.alesi
topaz sinewBOT
@signal osprey Has your question been resolved?
signal osprey
<@&286206848099549185>
opal vault
**nico.alesi**
if there is an infinity, you can "say" infinity is an accumulation point of A U {infinity}
topaz sinewBOT
@signal osprey Has your question been resolved?
signal osprey
if there is an infinity, you can "say" infinity is an accumulation point of A U ...
ok so I am "assuming" $\infty$ is an accumulation point
thorny flameBOT
nico.alesi
signal osprey
.close
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dusty mason
I don't get why Fy is opposing Normal Force
topaz sinewBOT
I don't get why Fy is opposing Normal Force
dusty mason
Like where did Fy come from, and what does it even mean? Basically a man is pushing a sled
hallow tree
they change the coordinates
such that the normal force is the y axis
and the friction is the x axis
just tilt ur perspective and the rest follows
topaz sinewBOT
@dusty mason Has your question been resolved?
dusty mason
they change the coordinates
But why is Fy negative and not positive
like this shows smth different
<@&286206848099549185>
dusty mason
yeah
hallow tree
because we define upward as positive
so normal force is positive
N-(Wcos(15)+F_y) = 0
N - Wcos(15) - F_y = 0
dusty mason
I got that, but why did they make this positive?
for Fy then?
like Ay and By are positive
hallow tree
because they r pointing upwards
dusty mason
wait, so we were supposed to assume that the straight Fx force meant that Fy would be downwards negative?
hallow tree
if u know where F and F_x are going then u can see where F_y is going by vector addition
dusty mason
ohh its like opposite
hallow tree
but in general, when pushing a block upward through an incline, F_y is gonna be downwards
dusty mason
bcuz this one was straight up for Fy and left for the Fx forces
while this one is the opposite of those
dusty mason
but in general, when pushing a block upward through an incline, F_y is gonna be ...
oh alr
prisma raptor
what is angle B 😭
topaz sinewBOT
what is angle B 😭
prisma raptor
i think im just having troubles conceptualizing how the triangle pbk would look like
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pseudo mirage
I don’t even know where to start?????? xd
topaz sinewBOT
I don’t even know where to start?????? xd
pseudo mirage
I’m guessing I’ll have to use the Pythagorean theorem somehow
tender swallow
the ladder is 12 feet long
so halfway of that is 6 feet
and the height at the halfway point is 5 feet
pseudo mirage
So to find the angle then I would use the inverse of sin 5/6?
tender swallow
can you calculate theta using trignometry now
tender swallow
So to find the angle then I would use the inverse of sin 5/6?
yep
and x is just double of the third side
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patent anvil
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neon iron
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neon iron
Is my particular integral right, I chose Ctcos(3t/2) + Dtcos(3t/2)
topaz sinewBOT
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neon iron
<@&286206848099549185>
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lofty karma
lofty karma
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worthy storm
lofty karma
@worthy storm made the piecewise function then step function but dont know how to properly approach laplace transform on piecewise functions
worthy storm
do you have the formula for the integral definition of the laplace transform?
lofty karma
this one?
lofty karma
e^(-st)(1-t^3)dt from 0 to 1 since function is 0 for x>1
can i apply same definition to this aswell?
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pulsar notch
I need to convert m/s² into km/h².
I've used wolfram alpha to try to figure out how this should be done, but I'm not really sure where it's getting these numbers from? Specifically, why is it using 12960 km/s² ?
topaz sinewBOT
I need to convert m/s² into km/h².
I've used wolfram alpha to try to figure out ...
pulsar notch
Nothing?
clear lodge
good. And what do you obtain if you divide a number by itself?
pulsar notch
1?
clear lodge
okay. So keep in mind those two facts now.
I assume you know that 1 km = 1000m
i also assume that you know that 1 h = 60 mins = 60*60 seconds = 3600 seconds
pulsar notch
Yep
clear lodge
so, since 1km=1000m, they are the same number, correct? they are equal.
Thus, if we divide them, we get 1.
$\frac{1km}{1000m}=\frac{1000m}{1km}=1$
thorny flameBOT
LordFelix
clear lodge
which means that if you multiply by those fractions, you're multiplying by 1
so you're not changing what you had
pulsar notch
Yeah that makes sense to me
clear lodge
okay. so we're gonna do the same with 1h=3600s
$\frac{1h}{3600s}=\frac{3600s}{1h}=1$
thorny flameBOT
LordFelix
clear lodge
now, i'm gonna rewrite your original multiplication
$\frac{12 m}{1 s \cdot 1 s} \cdot \frac{1km}{1000m} \cdot \frac{3600s}{1h} \cdot \frac{3600s}{1h}$
thorny flameBOT
LordFelix
pulsar notch
Ah, I think I might be understanding
clear lodge
and now, you abuse the commutative properties a bit to arrange the same units in the same fraction
so you're dividing metres by metres, seconds by seconds (twice), and thus those get simplified
and you're left with kilometers in the numerator, and hours squared in the denominator
thus you get your 12m/s^2 to be the same quantity (as you only multiplied by 1 three times), but measured in different units
pulsar notch
Ah yeah, that makes sense
I think I understand it now then
Ty for the help!
.close
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dapper sparrow
Im stuck, where would i go from here in this proof? Note: x is a non-negative real number and n is a whole number (N and 0)
topaz sinewBOT
Im stuck, where would i go from here in this proof? Note: x is a non-negative re...
dapper sparrow
The issue is x is a non-neg real number, so x^2 < x for x<1
so I cant just say x(k+x)<=x(k+1)
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tawny jay
I am stuck with differentiating xtan^-1(x), please tell me how to solve
somber oasis
Let u = x and v = atan(x). product rule says d(uv)/dx = u'v + u v'. here u' = 1 and v' = 1/(1 + x^2). so
d/dx [x atan(x)] = 1*atan(x) + x*[1/(1 + x^2)] = atan(x) + x/(1 + x^2)
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rose moss
Can anyone please help in this question shouldn't acceleration of a be 0
rose moss
As immediately after spring force would still act on it wouldn't it ?
somber oasis
As immediately after spring force would still act on it wouldn't it ?
cutting spring 2 kills its tension instantaneously so block A suddenly has only its weight acting, not the upward spring force it had moments before
recalculate the net force with T = 0
jade thunder
Wouldnt this depend on where you cut the spring
rose moss
Wouldnt this depend on where you cut the spring
Ya I think so too but it's not mentioned clearly
In the question
jade thunder
If you cut it right above A doesn’t spring 2 need to contract before B starts moving
If you cut it right below B then the 2nd spring needs to propagate downwards until A starts moving no?
rose moss
If you cut it right above A doesn’t spring 2 need to contract before B starts mo...
But i think they have cutted it right below B as acceleration of b is g/2
somber oasis
Wouldnt this depend on where you cut the spring
in the massless spring model used here snipping any point makes its tension vanish everywhere at that instant so B feels the change immediately
sour bloom
Wouldnt this depend on where you cut the spring
Yeah it does, it would propagate along the spring at a speed at most the speed of sound on the spring
But yeah ig the question is just ambiguous
jade thunder
Yeah right because the blocks don’t know what is happening at another point until something tells it
Otherwise you could use this to break the speed to light
sour bloom
Anyway the intent is that the spring force is instantly removed
rose moss
Anyway the intent is that the spring force is instantly removed
So are they just completely removing the spring in the question
jade thunder
I guess if you cut it right in the middle then by the time the spring propagates the force to both masses, that’s what they are intending
sour bloom
Bad question, may want to feedback
somber oasis
I assume this is a Physics 1 question
sour bloom
Possible improvement: spring is cut at attachment point at B and at attachment point at A
rose moss
I assume this is a Physics 1 question
Ya it's basic level im still in high school 🙂
somber oasis
Ya it's basic level im still in high school 🙂
Yea, it makes sense it doesn't matter then
Where it's cut
rose moss
Ohh so they are just making the spring disappear completely then right ?
jade thunder
I guess that works
I love physics when you can just delete stuff from systems instantaneously
rose moss
Ohkk tysm for all your help
jade thunder
Surely that wouldnt break any other laws of physics
sour bloom
Then again the spring is (usually) assumed massless
So when it's cut theres infinite acceleration that propagates the signal instantaneously
loud oasis
it's a bit like circuit analysis where the speed of propagation of changes (sound in this case, light in circuit analysis) is assumed to be infinite because the length and time-scales under consideration are much larger than ones where the speed of propagation makes a major difference
rose moss
Ohkk I don't understand anything you all are saying
somber oasis
Ohkk I don't understand anything you all are saying
It's not really important
Do you understand how to solve the question?
somber oasis
No problem!
topaz sinewBOT
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mortal oriole
??
mild saddle
!original
topaz sinewBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
mild saddle
or this is the original...?
fallow igloo
.solved
sleek haven
how do I talk about the graph on the left?
topaz sinewBOT
how do I talk about the graph on the left?
@sleek haven Has your question been resolved?
loud oasis
what do you mean? what specifically are you trying to describe?
sleek haven
what do you mean? what specifically are you trying to describe?
It's fine I just handed the work in
It just talking about the years and what their posistioning means
if it isn't grouped together it means it's an anomaly
for example 2015, was a year where the UK introduced a policy where the carbon floor tax was increased
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crimson pivot
topaz sinewBOT
crimson pivot
So first I factor the quadratic
true magnet
!status
topaz sinewBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
3
true magnet
what have you done so far
true magnet
So first I factor the quadratic to (x - 6)^2
can you try expanding (x-6)^2?
topaz ledge
So first I factor the quadratic to (x - 6)^2
-6?
drifting swift
so what you've got is $\sqrt{(x-10)^2}$ thus far
thorny flameBOT
Ann
drifting swift
how can this be simplified further
crimson pivot
I think its abosolute of x- 10?
So | x - 10 | ?
Because of the square root
Is that the final answer?
Also how does a square root get created
For it to turn into the absolute value
topaz ledge
That is how a function is defined
Each value can how only 1 output for it to be a function
topaz sinewBOT
topaz sinewBOT
Available help channel!
novel geyser
Anyone know where does this math came from? it's in France and I don't know the book's title
topaz sinewBOT
Anyone know where does this math came from? it's in France and I don't know the ...
neon iron
Anyone know where does this math came from? it's in France and I don't know the ...
Maybe a baccalauréat?
- Collection of BAC blanc
- Annals corrigées for Terminal (meaning last year high school) S (France)
- Or maybe a web such as MeilleurenMaths, Académie en ligne, etc
sturdy flint
Que: A source of monochromatic electromagnetic radiation having wavelenght 62nm is subjected to a cross-sectional area of 1.6nm^2. If rate at which photons are absorved is 1000 photons per second then calculate intensity of absorbed light in units J/m^2 and [divide your answer by 100]
topaz sinewBOT
Que: A source of monochromatic electromagnetic radiation having wavelenght 62nm ...
sturdy flint
!status
topaz sinewBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
I got an answer and would like my work checked.
but it is not correct answer as i checked from answer key
.close
topaz sinewBOT
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hallow rain
topaz sinewBOT
hallow rain
Can someone explain what b even wants from me 💔
I don’t know what it means by bandwidth or data throughput or how to determine how much throughput is required
I don’t think i learnt this idk though
mild saddle
i think the idea is to play a game of follow the arrows from A to B, and "score" the highest number of "points" available
hallow rain
Oh
Easy
So basically a Euler path but with this digraph
Like try to get as close to a euler path
So AECDB
Why tf is it worth 10 marks
mild saddle
now i have no idea what the second part of the question wants, but AECDB probably isn't the max here
mild saddle
ok hold up
i think i misunderstood the question @hallow rain
i recommend discarding everything i said
my apologies
hoary burrow
Dang
hallow rain
Lol Allg
mild saddle
so i've done a little bit of research, and i think i get the problem now.
those numbers on the graph are capacities
aka how much can flow from one node to the next along that direction
your job is to find the maximum amount of flow A can deliver with the following two rules:
- no edge can be overloaded
- the total amount of flow entering a node = total flow exiting the same node (except A and B, which should satisfy total out of A = total into B)
you should consider all possible paths one-by-one until every edge is saturated (I found four)
topaz sinewBOT
@hallow rain Has your question been resolved?
topaz sinewBOT
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cloud apex
topaz sinewBOT
cloud apex
This is a problem set, a take-home test that can use any resource as long as I explain it, I need help with 1 and 2.
timber jetty
cloud apex
Ty 😂
timber jetty
Alright, what have you tried?
fallow igloo
timber jetty
good start, do you have any idea where to use?
cloud apex
Do u plug in 8
timber jetty
Yes, I have a quick question for you.
Do you know how to find the tangent line of a quadratic function using derivative?
cloud apex
Quadratic
cloud apex
I would need to see a example
timber jetty
I would need to see a example
$x^2 + 5x + 7$ find the slope at x = 3
thorny flameBOT
This is sad 😢
cloud apex
No
timber jetty
yeah, that explains
cloud apex
Yea
timber jetty
I'm not sure about the criteria
timber jetty
Now do I plug in 8?
yes, you plug in 8 to find the slope at x = 8
cloud apex
Perfect
timber jetty
Quotient rule?
Sure
cloud apex
Thank you! I figured it out
fallow igloo
.solved :)))))))
Have a good one
sinful quest
can someone please help me solve this, i barely understood everything our teacher taught us
jade thunder
Look at the first one
sinful quest
yes
jade thunder
Oh open a new channel
sinful quest
huh
jade thunder
U deleted your own message so this one will die
sinful quest
oh
jade thunder
.
topaz sinewBOT
Available help channel!
spiral flint
|x-x^2|<=1
topaz sinewBOT
|x-x^2|<=1
clear python
Yes
nova hare
Can't you directly just write it as |x(1-x)| leq 1
topaz sinewBOT
@spiral flint Has your question been resolved?
pearl fog
do not troll in help channels
pearl fog
<@&268886789983436800>
stark canyon
im srry if you thought I was trolling.
pearl fog
tbf nobody really asked you for it
lime geode
im srry if you thought I was trolling.
Do not randomly enter help channels dumping messages that do not serve to help the helpee.
Do not post AI generated content in help channels.
stark canyon
it's not ai'
it was saved on my pc from my last math assignment
so I decided to share with you guys
lime geode
And if you do it again you will be muted. If you want to discuss math go to #math-discussion or a relevant topic channel
grizzled osprey
how is this possible? isn't there only a finite amount of blue points? this is from the aops page for the chicken mcnugget theorem
topaz sinewBOT
how is this possible? isn't there only a finite amount of blue points? this is f...
clear python
Why do you think there's only a finite amount of blue points
vestal totem
...why
grizzled osprey
isn't is because the chicken mcnugget theorem shows that there are only (m-1)(n-1)/2 amount of integers that can't be expressed with mx+ny?
wintry meteor
how is this possible? isn't there only a finite amount of blue points? this is f...
X and y are positive integers
wintry meteor
how is this possible? isn't there only a finite amount of blue points? this is f...
What colour will the negative integers be
grizzled osprey
oh, all blue
grizzled osprey
well since it's like that i think it should be the midpoint of 1 and 7919 which means P is 3960?
wintry meteor
On the left it’s eventually all blue and in the right eventually all red
So you need to find where they happen, P is the midpoint between them
If that’s what you’ve done and calculated when all red starts correctly, then yes
grizzled osprey
oh wait, the rightmost blue is 7919 and leftmost red should be 81 so i think it should be 3919
ruby tree
Leftmost red isn't 81
topaz sinewBOT
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small maple
If A and B are independent and P(A)=P(B)= 0.5, what is P(ABc U AcB)?
my question is, do i have to check for mutual exclusivity every time?
cuz if i say they are mutually exclusive, i cna just let P(AB^cA^cB) = 0 so i just compute for P(AB^c) + P(A^cB)
but if i just jumped into using the theorem for the union of events, i'll get
=P(AB^c) + P(A^cB) -P(AB^cA^cB)
which after using independence of A and B, will give me a different answer than when i let that be 0
topaz sinewBOT
If A and B are independent and P(A)=P(B)= 0.5, what is P(ABc U AcB)?
my questio...
@small maple Has your question been resolved?
mint crescent
What is $P(AB^c)$ supposed to mean
thorny flameBOT
Civil Service Pigeon
teal lodge
Yeah that’s what I’m asking
The notation seems a little scuffed
But I think it’s meant to be P(A and not B)
teal lodge
If A and B are independent and P(A)=P(B)= 0.5, what is P(ABc U AcB)?
my questio...
But it seems that you wouldn’t need to know mutual exclusivity here because you know that they are independent, meaning $P(A) \cdot P(B) = P(A and B)$
thorny flameBOT
CVG
small maple
But it seems that you wouldn’t need to know mutual exclusivity here because you ...
yeah this is my thought too
topaz sinewBOT
yeah this is my thought too
small maple
What is $P(AB^c)$ supposed to mean
yeah it's P(A int B^c), sorry my prof does that
so i thought it was standard notation
teal lodge
Ok gotchu
thorny flameBOT
CVG
So essentially the question is find $P(A\capB^c\cupA^c\capB) if P(A) = P(B) = 0,5 and A and B are independent$
```Compilation error:```! Undefined control sequence.
l.49 So essentially the question is find $P(A\capB
^c\cupA^c\capB) if P(A) = ...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.```
teal lodge
Oh my
That didn’t work
Ok just P(A and not B or not A and B)
But if you can work out P(A and B) because of independency, you can definitely solve it
small maple
i mean it's pretty easy to solve but i just got hit in the head by the mutual exclusivity, so since A-B and B-A are always disjoint, that means i can just use finite additivity property?
so the idea here is that events cant both be independent and mutually exclusive, but A int B^c and B int A^c are different events and only A and B are assumed to be independent? so A int B^c and B int A^c can be mutually exclusive
i think every single theorem just got jumbled in my head
topaz sinewBOT
@small maple Has your question been resolved?
craggy marsh
Find the sum.
topaz sinewBOT
Find the sum.
wraith patrol
i dont think this is pre uni level tho
sinful viper
Find the sum.
wtaf is ts
craggy marsh
drifting swift
wtaf is ts
you are not helping for sure.
drifting swift
gng someone help with fractions 😭
!occupied
topaz sinewBOT
gng someone help with fractions 😭
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
drifting swift
Find the sum.
$\sum_{n=1}^{\infty} \frac{\cos(2nx)}{(2n-1)(2n+1)}$
thorny flameBOT
Ann
drifting swift
is that your summation?
sinful viper
😭
craggy marsh
well how does general formula/writing the sigma for it help? ig you were trying to write cosx in terms of e^ix and all that stuff?
inland mica
Might be useful
Actually nvm
craggy marsh
Actually nvm
ig it might get out of scope of my exam too but still
ill see through it once
drifting swift
well how does general formula/writing the sigma for it help? ig you were trying ...
makes it easier to think about imo
if nothing else
also less risk of accidentally writing a term wrong and ruining your life because of it
also writing 12 lakh dots then a ∞ symbol is just ugly
anyway yes actually i think putting z = e^(ix) and then expressing this via powers of z is going to be good
craggy marsh
~~also writing 12 lakh dots then a ∞ symbol is just ugly~~
you know lakh and that system? mb i am going out of the context but still
drifting swift
i know that lakh means 10^5 and crore means 10^7, yes.
craggy marsh
anyway yes actually i think putting z = e^(ix) and then expressing this via powe...
but will it work? i doubt that fact
drifting swift
my foresight tells me it will, though i haven't yet sat down and worked it out the honest way.
craggy marsh
rather it might complicate it further, but i too thought that way
of e^ix and stuff
or maybe sm1 try to teach be basics of fourier and then this problem with it?
drifting swift
i think i have found some kind of solution.
drifting swift
probably lots and lots of convergence issues swept under the rug but i kinda dont care
craggy marsh
maybe it falls under complex analysis and stuff
drifting swift
also my handwriting degraded a little towards the end
yes this is definitely something complex analysis-pilled
smoky sun
it's actually a fourier series
craggy marsh
but ig i can somehow understand some parts of it and some other parts not so nicely
eternal sierra
Find the sum.
bro what is this 💀 i thought u were preparing for jee
craggy marsh
bro what is this 💀 i thought u were preparing for jee
jee itself man, but some dumbo gave it to me
idk why
maybe A++
eternal sierra
jee itself man, but some dumbo gave it to me
maybe he was trolling or smth
my friend asked me to integrate
1/(sin^3x + sin(x+a))
craggy marsh
maybe he was trolling or smth
😔 yes ig. they used fourier shi in it
@drifting swift try to explain a bit to me
i cant comprehend where that z popped outta nowhere
drifting swift
the z is basically just converting the fourier series into a power series tbh
my motivation is $\cos(\theta) = \frac{e^{i\theta} + e^{-i\theta}}{2}$
thorny flameBOT
Ann
craggy marsh
is it like a function of x or smth?
drifting swift
no it is a variable in its own right
yeah so if you apply that identity to your f(x)
or what i called f(x)
digital river
probably lots and lots of convergence issues swept under the rug but i kinda don...
convergence should be |z|<=1, which I think you respected fine
drifting swift
then you get that it separates into two summations that i called g(e^ix) and g(e^-ix)
drifting swift
convergence should be |z|<=1, which I think you respected fine
not sure about specifically |z|=1
craggy marsh
no it is a variable in its own right
try it with e^x expansions and try to explain
maybe ill be better to comprehend it wholly
drifting swift
too low energy to do that sorry
smoky sun
topaz sinewBOT
digital river
not sure about specifically |z|=1
wolframalpha is also unsure. it says |z|<=1 is good, but then also that you have branch points at +-1
drifting swift
yeah i dont wanna touch that w/ a ten-meter pole for sure
topaz sinewBOT
Available help channel!
drowsy gyro
topaz sinewBOT
drowsy gyro
i need help applying C.B.S
i dont know what to do with the power of 2 from the first "( )"
sharp pagoda
wth
drowsy gyro
i need to demonstrate that
sharp pagoda
you mean prove?
drowsy gyro
yes
sharp pagoda
which power you dont know, the one in the paranthesis or outside the paranthesis
drowsy gyro
i dont know how to move forward given the first paranthesis with the power of 2 ontop of a squared b squared c squared
m= multiplied
(a.m.a + b.m.b + c.m.c) all to the 2 is less than or equal to (a squared + b squared + c squared)(a squared + b squared + c squared)
this is c.b.s
<@&286206848099549185>
.close
topaz sinewBOT
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Available help channel!
neon iron
How to do (b)
topaz sinewBOT
How to do (b)
neon iron
not sure what to do
sharp pagoda
use quadratic formula
neon iron
oh ok
neon iron
use quadratic formula
wait how?
wraith patrol
did you recite factorization identities/formulas
neon iron
(b)
wraith patrol
b is cubic
exotic nest
oh
exotic nest
You can use the QF for the first one though
neon iron
how to get the last 2 awnsers
sharp pagoda
b is easier
wraith patrol
did you recite factorization identities/formulas
vestal totem
roots of unity
neon iron
You can use the QF for the first one though
i done a already
sharp pagoda
move the 8 to the other side, solve for the roots
wraith patrol
roots of unity
pls no
vestal totem
what
neon iron
its complex numbers im doing so how do i use this to do it?
sharp pagoda
there should be 3 roots in complex plane, 1 in real plane
sharp wyvern
i done a already
do you know about quadratic formula
neon iron
do you know about quadratic formula
yes
vestal totem
its complex numbers im doing so how do i use this to do it?
roots of unity.
sharp pagoda
hes asking for 2nd question
neon iron
roots of unity.
so how about do I do this?
neon iron
wraith patrol
theyre not gonna learn roots of unity anytime soon
neon iron
theyre not gonna learn roots of unity anytime soon
im doing engineering maths
so probably not idk
sharp wyvern
theyre not gonna learn roots of unity anytime soon
this is litterally it btw..
vestal totem
then do the factorisation ig
vestal totem
diff of cubes
wraith patrol
its probably in grade 8, just a peculiar factorization identity thats sued for cubic stuff
sum or cubes and diff of cubes ig
wraith patrol
im doing engineering maths
then youll see roots of unity sometime, its part of complex numbers
sharp pagoda
$a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})$
sharp wyvern
its probably in grade 8, just a peculiar factorization identity thats sued for c...
" engineering math " and he is doing complex numbers, im gonna say he also needs to know how to use cube of unity , unless he hasnt been taught about it yet
thorny flameBOT
Roy
wraith patrol
my idea was that, youll get (x^2 - 4 + 2x) somewhere on the right, here you use quadratic formula, youd still get complex numbers
neon iron
" engineering math " and he is doing complex numbers, im gonna say he also needs...
nah i havent
sharp wyvern
nah i havent
ahh then yeah what koni said
neon iron
$a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})$
is this correct?
sharp pagoda
yea
neon iron
why is only ab negative?
sharp pagoda
so that it cancels
neon iron
oh ye mb
wraith patrol
why is only ab negative?
expand it and itd make sense, i just recited it back then
sharp pagoda
now you turned a cubic into a quadratic + linear
neon iron
yes its right
wraith patrol
if you wanna refresh ur memory on these identities,
in sum of cubes, the sequence of +/-s is +, -, +
in diff of cubes, the sequence is -, +, +
given that you write the factors in this format of linear first, quadratic next ofc
topaz sinewBOT
topaz sinewBOT
Available help channel!
north heath
what happens if the integral diverges?
topaz sinewBOT
what happens if the integral diverges?
loud oasis
then it doesn't have a laplace transform
loud oasis
the values of s for which it converges (if it converges for some but not others) also determines the domain of the laplace transform
north heath
what if the limit doesnt exist
loud oasis
the limit of the integral not existing is the same as the integral diverging
loud oasis
it's called a transform because it is a function which takes in a function and returns a function
and we decided we wanted a special name for that type of function
and the utility of the laplace transform is that it turns differential equations (specifically initial value problems) into algebraic equations, which are generally easier to solve
topaz sinewBOT
topaz sinewBOT
Available help channel!
proud jungle
Guys what do these do
topaz sinewBOT
Guys what do these do
wintry flame
They use limits to define the derivative
are you asking for like, intuition on derivatives?
and what they are for?
proud jungle
hmm okay how do I know when to use each definition
proud jungle
and what they are for?
this is like the very first introduction to derivatives
wintry flame
those two are the exact same
otherwise what you'd usually see is
[f(x+h)-f(x)] / h
which would return a function (that is the derivative of f(x))
the one on the bottom gives you
that function
evaluated
at a point
x=a
proud jungle
Guys what do these do
Hmm okay, so now I’ve got to use these rules to estimate the instantaneous change
these seems wrong tho
I don’t really see how I use these rules definitions for part b
in both problems
wintry flame
For b
idk why u substituded a for -1
for some parts
but then just left a afterwards
also it seems you've really confused
what f is
$f(x) = x^2 +2x$
thorny flameBOT
holo_morph
proud jungle
idk why u substituded a for -1
Am I meant to plug -1 in?
wintry flame
so your plugging in -1 + h for one term
and then for the other term
just -1
For a hint
if I wanted to plug a into f(x)
then I would get
$a^2 + 2a$
thorny flameBOT
holo_morph
fathom echo
holo can you help me rq
proud jungle
$a^2 + 2a$
So lik that??
proud jungle
I’m like beyond lost
wintry flame
they already defined f for you
proud jungle
they already defined f for you
like this? 🤔
wintry flame
but you only got the first part of the definition
you did
f(a+h)/h
you need
[f(a+h)-f(a) ]/h
proud jungle
[f(a+h)-f(a) ]/h
wintry flame
to clarify, that -1^2 should be in parenthesis like (-1)^2
so that its 1 and not -1
thorny flameBOT
proud jungle
how does that look?
wintry flame
yep
I wouldn't say that specifically makes you dumb
everyone makes those silly mistakes
the conceptual understanding matters more
although those will hurt you on a test
proud jungle
yep
okay I think I got it now
Basically just plugging in
thanks for the help!!!
.close
topaz sinewBOT
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Available help channel!
modest mist
I'm trying to understand my instructors notes
So in the another example section,
S={Ai}ieI
This means that set S has a bunch of A sets right
modest mist
And the set Ai has A1, A2, A3 and so on?
Based on the index set cause its I = {1, 2, 3….}
topaz sinewBOT
@modest mist Has your question been resolved?
topaz sinewBOT
@modest mist Has your question been resolved?
rancid jasper
ehy
rancid jasper
not sure why this is right]
I thought the dimensions of column space = R^m
so i thought it was 5
so what im getting from this is if there is 1 zero row, then the dimension of column space is m-1?
jade jungle
if I recall correctly, the dimension of the column space of a matrix (or its rank) is the number of pivots it has in RREF.
a zero row has no pivot.
topaz sinewBOT
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Available help channel!
maiden trail
what method? should I use u-substitution?
topaz sinewBOT
what method? should I use u-substitution?
maiden trail
partial fractions? does that just mean split it up and keep the denominator?
hoary burrow
long division then partial fractions
The denominator's irreducible though
Or am I tweaking
maiden trail
(t+2)(t-2) ? is that what he means
spare smelt
wait
maiden trail
nevermind I think I figured it out
timber jetty
maiden trail
polynomial long division, then set up the integrand as the quotient plus the remainder over the divisor, the evaluate from there
:p
.close
topaz sinewBOT
neat patrol
i need help learning how to do the arthmetic sequence
