/sci/ - Science & Math

>>9485939
Pls, /sci/ help! Retarded studies major here, how do I learn quadratic equation factoring. I haven't taken an algebra class in almost 3 years.

I literally can't solve this without having a breakdown.

-4x^2 + 23x +6 = 0
like I'm stuck here
(-4x + ?)(x + ?) = kms

Is there a comprehensive trig reference book? Not for learning, just for reference

Why does a wire conducting current need to be perpendicular to a magnetic field to experience a force? Why is force 0 when the wire is parallel with the field?

>>9486370
just induces a current in the wire if it's parallel right?

Taking thermofluids, can someone explain to get the pressure at point 2, why you'd add P1, the pgh of water, oil, but subtract the pgh of the mercury?

>>9486527
something about where the water table is defined
sorry I took the envirosci version of this

>>9486124
>(-4x + ¿)(x + ?) = -4x^2 + 23x +6

factors of 6 are ±2 and ±3 or ±1 and ±6

so ?≟1
(-4x + 6)(x + 1) = -4x^2 +2x + 6 nope

so ?≟2
(-4x + 3)(x + 2) = -4x^2 -5x + 6 nope

so ?≟3
(-4x + 2)(x + 3) = -4x^2 -10x + 6 nope

so ?≟6
(-4x + 1)(x + 6) = -4x^2 -23x + 6 nope

(-4x + 1)(x + 6) = -4x^2 -23x + 6 was close so fix the signs

so ?≟-6
(-4x - 1)(x - 6) = -4x^2 + 23x + 6

>>9486129

>>9486129
>>9486660

>>9486370

Because [math]\mathbf{F} = q\mathbf{E} + q\mathbf{v} \times \mathbf{B}[/math]

cross products are 0 when the vectors are parallel.

Who is the sexiest cartoon milf?

I'm having a lot of trouble with a capillary surfaces class. We're learning about differential geometry, and I'm being asked to calculate the mean curvature of this surface:

[math]x<\alpha, \beta> = <\sin\alpha \cos\beta, \sin\alpha \sin\beta, \cos \beta>
[/math]

How do I do it? The homework tells me I need to take the cross product of the derivatives of x with respect to alpha and beta, but tafter working out the cross product, I'm getting a really ugly vector that I'm not sure how to take the magnitude of.

Please help, sci. I have no idea what the fuck differential geometry even is.

>>9486758
Related question, how would you go about plotting a vector field / surface like this in Matlab?

>>9486538
Actually I think it's just cause the overall change in height relative to point 1 is decreasing to the mercury, though I'm not even sure what is being used, the top of h3 I guess since that's the total transition?

>>9486838
hydraulic head = elevation head + pressure head
I think you've got pressure head covered so it's just where you're measuring from now

>>9486745

>>9486873
>Who is the sexiest CARTOON milf?

Did I say anime? No! Anime/Manga doesn't count. I've excluded it to Western Animation.

>>9486375
if its parallel I don't think its induces a current

>>9486674
thanks for the response anon

Probability question. We have an access point that serves N clients. The probability that the access point sends a packet to one of the clients in any time slot is [math]p_a[/math]. Independently, the probability that any client attempts to send a packet to the access point in a time slot is [math]\frac{1}{N}[/math]. Packets are only successfully sent if only one packet is attempted to be sent over the network in any time slot (i.e. either the access point sends a packet to a client and no client tries to send to access point or only one client sends packet to access point and access point doesn't send).

I need to write two expressions: one for the average number of successful packet transmissions from the access point and one for the average number of successful packet transmissions to the access point in any time slot. So far I have:
[math]N_s = (1-\frac{1}{N})^Np_a[/math]
[math]N_r = \frac{1}{N}(1-\frac{1}{N})^{N-1}(1-p_a)[/math]
where [math]N_s[/math] is average successful packet transmissions sent from access point and [math]N_r[/math] is average successful packet transmissions received by access point. Do those look right?

Why has nobody set off a private nuke or mini nuke in place of shooting, bombing, or driving over people with a truck?

Is it that difficult and expensive to create?

if there's a charge at the center of a gaussian cube, you find the flux through the cube by q/epsilon. if there's another charge outside this cube, does that affect the flux through the cube at all? the outside charge would mean there's flux on all surfaces of the cube from it, not even thinking about the inside charge, so I think it would affect the net flux. I would have to do q/epsilon - Σ(flux through each side of cube disregarding inside charge).
Is that right? If so how do I find flux through a plane given a point charge? The electric field wouldn't be uniform so it's not just E*A.

>>9486124
Learn perfect square it's intuitive. Try to actually understand that shit
OR just memorized the general equation for that shit that we solved decades ago.
You know the one normies like to make fun off but is the most efficient way of solving a quadratic problem.
>ps the solutions are the factors

How do I prove
[math] 1+ \frac{1}{\sqrt{2}}-\frac{2}{\sqrt{3}}+\frac{1}{\sqrt{4}}+\frac{1}{\sqrt{5}}-\frac{2}{\sqrt{6}}+\frac{1}{\sqrt{7}}+\frac{1}{\sqrt{8}}-\frac{2}{\sqrt{9}}[/math]
converges conditionally?
I know that the series which is all of the positive terms diverges and that the series of all the negative terms diverges, but this only ensures me that it either diverges or conditionally converges. How would I show the latter here?

>>9487172
of course it should be: [math]1+\dots -\frac{2}{\sqrt{9}}+\dots [/math]

>>9487172
pair the positive terms and use the alternating series test

since 1/√n > 1/√n+1 > 1√n+2 so 1/√n + 1/√n+1 > 2√n+2

So there's a model for a behavior pattern, that can best be described as "in any creative domain a minority of people do the majority of work". Does anyone knows which theory is that?

how do I manage to take capsules (size 00) I do the lean forward method but I gag before I swallow, I puke before even managing to attempt swallowing, any advice or help?

>>9487266
https://en.wikipedia.org/wiki/Pareto_distribution

>>9487306
Tank you so very very much.

How do I not get tripped up so much with trig terms in calc? That's literally my only issue.
How am I supposed to know limx->20[cot(X)] for example? I have the unit circle memorized, first quadrant anyways because that's all you really need. I know that it's asking for 20 rads and not degrees but i still don't know what to do with that and usually just skip the book problems because it just hadn't clicked.
Even if it's cos or sin instead of cot I wouldn't fucking know despite knowing the cos and sin bounds.
Can someone walk me through an example or some shit?

>>9485939
I got a trig test in an hour and 30 minutes. I should've studied last night but I went and met with friends and got drunk then I got home and smoked a bunch of weed and then I slept late instead of getting up to study. I memorized the unit circle at least, I can solve a triangle or whatever, but trig identities I can't really remember other than sin^2(theta) + cos^2(theta) = 1. Also sometimes the word problems fuck me up. I took an adderall. How fucked am I?

>>9487471
>I should've studied last night but I went and met with friends and got drunk then I got home and smoked a bunch of weed and then I slept late instead of getting up to study.
this is what it is to be a human

>>9487471
Trig identities are basically just derived from that simple equation, so you can figure them out, but next time fucking study, you can drug yourself up any other time.

Can someone explain the formula for finding relative extrema in 3-space in a intuitive or geometric way? My teacher briefly mentioned that it's the determinant of the Hessian, but I was really just wondering why the left term being larger than the right indicates an extrema.

[math] f_{xx}f_{yy}-f_{xy}^2 [/math]

Need a book on C#. Didn't find any on the wiki. Any recs?

>>9487681
In the single-variable case, how do you find a relative optima? You set the first derivative equal to zero. What this means geometrically is that, at the optima, there is almost no movement up or down if you deviate from that point a bit.
To find whether that point is a maximum point or a minimum point, you use the "Second Derivative Test". If the second derivative is positive, that means your function at the optima is concave-up, so your optima is a minimum. Likewise, if the second derivative is negative at the optima, you have a concave-down graph and thus a relative maxima.

Extending this to the multivariable case, we see that we can make similar arguments. You first find the critical points of the function (set both [math]f_x = f_y = 0 [/math]). Now, you want to find whether the critical points you found are relative max, relative min, or in the case in pic related, neither.
The [math]f_{xx}[/math] term tells you the concavity in the [math]x[/math] direction. Likewise, The [math]f_{yy}[/math] term tells you the concavity in the [math]y[/math] direction.
From my understanding, the square of [math] f_{xy}[/math] tells you the concavity in the neighborhood of your point.

So what does this mean? If the "total concavity" (determinant of the Hessian matrix: https://en.wikipedia.org/wiki/Hessian_matrix)) is negative, then the function couldn't agree on whether it was concave up or down, so it's a saddle point.
If it's positive, then you know that at least it's a min or a max. point, but to see which one it is, you ned to look at the sign of [math] f_{xy} [/math].

Hopefuly this helped a bit. For what it's worth, Khan academy has a really good article on this:
https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/optimizing-multivariable-functions/a/second-partial-derivative-test

How do I explain time dilation and length contraction without invoking math? In regards to length contraction, my book tells me it has to do with the arrival of light from different 'points' of measurement but anything farther than that flummoxes me

>>9487796
You don't. Stop watching popsci.

>>9487796
If I tried to bullshit it, how accurate would approximating length contraction as 'It’s very mathematically confusing, but the best way I can break it down is that things shrink along their direction of motion at relativistic speeds because the very light they shoot at you is being hurried. You don’t get the whole 10 meters of length; at the speed they’re going you get like 6m, or 3m of light'

>>9487801
How about you get off your high horse and stop telling me what to do?

>>9487796
>>9487801
>>9487833
>>9487835
Ahem, here's a rephrase for you gents:
How do I explain relativistic length contraction in an intuitive, non-mathematical way (aside from the same way I'd say 'the longer path light takes in the light clock means mathematically, that clock is running slower')?

>>9487877
time moves slower as you move faster I guess
I used the formulas I don't understand shit

>>9487896
no no see i get time dilation length contraction just absolutely baffles me. I know it's partly a consequence of time dilation but I have no idea how to link the two

Can you guys recommend me good lecture sets for intro to fluid mechanics? I'm getting assblasted by this shit, any help would be appreciated

>>9485939
Say I have a green sphere on a white floor, and it's moving in some (blue arrow) direction. How do I calculate the change in momentum given the angle of the walls (red) are represented as a normal (purple arrows)?
The sphere is not noticeably bouncy at all, so don't worry about that. The wall and sphere combined absorb all energy.
Also, don't think about gravity. This is a top-down perspective.

have i done something wrong with this calculation? wasn't expecring a straight up coulomb potential

>>9487922
> The sphere is not noticeably bouncy at all, so don't worry about that. The wall and sphere combined absorb all energy.
The component parallel to the surface is preserved, the component perpendicular to the surface becomes zero (i.e. the sphere rolls along the surface after the collision). If the sphere is initially travelling perpendicular to the surface, it will stop dead.

For the general case, the perpendicular component is scaled by the coefficient of restitution (which for something "not bouncy at all" is zero), the parallel component is preserved.

tell me /sci/, if X is a real valued random variable, would the following be correct?

[math]Y=u(X) \rightarrow COV(X,Y) \neq 0 [/math]

>>9487909
yeah idk man it's because of an inverse sqrt term I believe

what does it mean for a vector field to be differentiable?
Is [math]F(x,y)=(x^2,y^2)[/math] differentiable for example?

>>9486894
Of course Lois Griffin

>>9487916
pls help

>>9487994
idk about vector fields but for F(x,y) to be differentiable it has to be continuous everywhere, so any function through any point has to be continuous or something like that
it was a pretty cool definition if I remember correctly, I wish I tried harder in that class

>>9486124
Just calculate the determinant, find roots an plug them to the formula
[math](x-x_1)(x-x_2)=0[/math]

>>9488029
the way they proved it with limits was fking radical

>>9487950
btw this is supposed to be the potential due to the electron in hydrogen

>>9486758
What have you learnt about mean curvature? What is the formula for it? Did you define it in terms of first and second fundamental forms or in terms of principal curvatures or..?

>>9487459
I really doubt any question would ask for a limit that is not in terms of pi like that. The Trig functions are continuous almost everywhere, so in general, the limit will be equal to the value at the limit. This of course is not true in the case where you "divide by 0". For example, limx->pi (cot(X))= limx->pi (cosX/sinX) and clearly sinX tends to 0, while cosX stays bounded, hence the limit will tend to infinity. And to which infinity it tends to depends on which side you're approaching, so it would be wrong to say lim=infinity.

>>9487681
It all comes down to the Taylor expansion, and how well it approximates a function. When you expand a function in a small neighbourhood, you get progressively more terms with more derivatives, and each term gives you more information on how the function is behaving locally. Try Taylor expanding the functions at a local extremum. Since grad(f)=0 at the extremum, you will need to look at the second order term in the expansion to see how the function behaves close to it. But since we're in second order, you will see that there are 3 second-order terms, and how they interplay is why they come up in the Hessian.

>>9487994
Literally google the definition, but basically if there exists a vector v(x,y) such that lim |h|->0 [F(x+h_1,y+h_2)-F(x,y)-v(x,y)]/|h| = 0, for all x,y in the domain

>>9486894
Best Milf!

>>9488403
We learned about the fundamental forms.
The professor just began writing down formulas, without really explaining it, so I have very little idea as to how to calculate it (that, and the cross product I calculated is really ugly)

Hey guys got a question regarding resonance frequencies.

If we connect two speakers close to each other, one of them acting as a microphone (just outputting frequencies not real sound) and the other as a speaker;

we observe that the strength of the volume depends on the frequency of the current and peaks at a certain frequency.

I know this is due to mechanical resonance from the magnetic field in the solenoid etc. but when we hit peak output is that because the mechanical resonance frequency from the speaker is very close to the natural frequency of the microphone or is it opposite?

>>9488557
Let me try and rephrase that:

I have a speaker that experiences mechanical resonance and if the frequency of the current is changed, the amplitude of the speaker changes with it.

At a certain frequency it peaks. Is this due to the mechanical frequency matching the natural frequency?

Hey, guys and girls, so I want to become PA and I was wondering what minor and major would suit me best for me to go to a "Top 30" U.S. school? A lot of people take Biology or English but I don't want to be just another "bio major". Thanks :]P

>>9488608
I don't know, but is it possible there's a standing wave pattern that's self-reinforcing? If you move the speakers, is that frequency still the peak amplitude?

Omfg those poor people.... aoe blast wave 2 miles in diameter from the impact point..

>>9488553
Well, it's you just have to find all derivatives up to order 2 with respect to alpha and beta. Then you can find E,F,G,L,M,N using the definition which should not be too hard if you note that you do not actually need to calculate the norm of the cross product ever by looking at my pic

>>9488694
>>9488553
i meant derivatives with respect to alpha and beta at the bottom there

Created a loft from plane 3 to plane 2, but I cannot find a way to delete the rest of the material from around that circular face I made from the loft. how do

"Show that the norm [math] ||.||_{\infty} [/math] in [math] C[a, b] [/math] is not strictly convex.
As a counterexample, use [math] f(x) = x [/math] and [math] g(x) = x^2 [/math] in [math] C[0, 1] [/math] . "

But... Don't we have that [math] ||f||_\infty = ||g||_\infty = 1 [/math] and [math] || \lambda f + (1-\lambda)g|| = max_{[0,1]} \lambda x + (1-\lambda)x^2 =1 [/math] ?
It should be <1 for it to be a counter-example right?

>>9488694
Huh...
Never really knew you could write E, G, and F that way
I found that an easier way to calculate the CMC would be to realize that you are given the equation of a sphere, and so if you calculate the curvature, the sphere has constant curvature throughout, so the answer would just be 1/radius

Thank you for the explanation though... I might have to look at it for a bit more to understand it!

>>9486664
Is Mollweide's Formula useful in anyway? I recognize it's pretty cute but I'm wondering if I can use it someday.

>>9488819
Well how else are your fundamental forms defined? For me, E, F, G were defined as the inner products of the generators of the tangent plane, and L,N,M the inner product of the gauss map with the second derivatives of the generators of the tangent plane. Since the Gauss map is easily calculated by my pic earlier, then calculating mean curvature is essentially an exercise in derivatives and inner products

>>9488764
define "strictly convex"

would this be true?

[math]E(X\textbarX+a , X+b)=X[/math]

For X a random variable, a and b real numbers

would this be true?

[math]E(X \textbar X+a , X+b)=X[/math]

For X a random variable, a and b real numbers

>>9488764
Why is the last equality true?

>>9488829
They define it as in pic related

would this be true?

[math]E(X | X+a , X+b)=X[/math]

For X a random variable, a and b real numbers

>>9488844
i.e. conditional expectation of X given X+a, X+b

>>9488839
If we pick λ=1 for example, the max would be attained for x=1 in 1
I probably meant "inferior or equal"

>>9488853
>If we pick λ=1
Re-read >>9488841

>>9488859
Ohhh
My bad

>>9488844
There is a button you can press that says something like "math" or "TeX" and it gives you a preview of the latex in the reply box

Can someone explain which test charge is positive and which is negative and the effect the electric field has on these test charges?
I want to say the positive one is the left and the negative is on the right, however I'm unsure how to explain I came to that conclusion "correctly".

>>9488948
ok this was a dumb question. Electric field exerts a force.

Is the transpose of the product of two matrices A and B, equal to B-transpose * A-transpose, or A-transpose * B-transpose? Or does it not matter?
That is,
>(AB)^T = B^T*A^T OR A^T*B^T Or are they equal?

Fubini's Theorem:

If i'm integrating g(x y) = x*e^(xy) or a triangle that is defined by x <=1 and 2x <= y <=2, why must we integrate of both variables? Why can't we just do one? Especially in the second case, how does the double integral give us the area?

>>9489016
matrix multiplication is not communitive.

>>9489016
B transpose*A transpose
That's a theorem.

>>9489160
>>9489016
What's the proof for this? I just checked my textbook and it said they're leaving the proof out for "brevity". I intuitively know it has to do with matrix multiplication, I can't see a way to prove it with matrix algebra.
(AB)^T=B^T*A^T
(Anxm*Bmxo)^T = B^Toxm*A^Tmxn
So it's not defined otherwise.
lol I'm retarded

Is pic related [math]{\Theta}(\log\log(n))[/math] complexity?

Is it medically possible to surgically insert tubes between the ribs that go into the lungs, allowing you to breath through your ribs? Or could you open them up wide enough that you don't even need to use your diaphragm since the inside of your lungs will have enough airflow through them that it's constantly providing you with fresh oxygen?

>>9489502
Nevermind, it is [math]{\Theta}(\sqrt{\log(n)})[/math]

I've got 3 ongoing projects and I'm not sure what software to use for each:

>MBD of an RFID door lock using Arduino and a servo
MATLAB+Simulink/scilab/oracle/anything else?

>neural network driven maze-solving robot
straight up C on an Arduino or Pi/MATLAB/scilab?

>subwoofer for HiFi
winisc/anything else?

>>9489594
Might increase o2 intake a bit but ramming more air into the lungs won't increase their capacity. Also the risk for infection goes up. Probably possible though.

>>9489502
[eqn]
sum = n \sum_{k=1}^{\left \lfloor
\frac{\sqrt{8 \log_2(n)+1}-1}{2}\right \rfloor+1} \frac{1}{2^{k(k+1)/2}}
[/eqn]

>>9487950
>e^2
why?

Got a neat applications question for you /sci/.

Ever heard of a Fresnel zone? It's an ellipsoid between two radio transmitters which graphs the trajectory of a radio frequency over a given distance.

What I know:
I'm working in GPS coordinates (decimal degrees). I know the distance between points A and B in meters. I know the radius of the Fresnel zone at any given point from start to end. I know the height of the Fresnel zone at any given point. I know it's bearing.

What I don't know:
What I need to do is plot the Zone in 3-D space. To do this, I have to get one thing, which is a set of 4 GPS coordinates, coordinates which will represent points along the circumference of the Zone at any given point of it's center of symmetry.

What I planned to do, but so far have failed, is to step to any point along the Zone, and pick a bearing, and walk out for the distance of the radius, then plot a point there. I may be failing because this is a bad plan, or because I am executing it poorly. Is it a bad plan?

Lads, how would I show that the nonzero entries of RREF(A), A some arbitray matrix in mxn, forms a basis for RS(RREF(A))? I have no idea how to do this without numbers. Thanks.

Can someone help me understand the flaw in my logic about the area of a sphere? If we rotate a circle 180 degrees around one of its diameters, don't we get a sphere with area equal to the circumference times half the circumference (the arch that we get from flipping), or 2*sqr(pi)*sqr(r) and not 4*pi*sqr(r)?

I have a theoretical complex voltage I'm comparing to a voltage measured with a true RMS meter, do I take the real part of the voltage or the absolute value of the complex voltage to compare with the measured voltage?

>>9487721
>>9487732

>>9489766
Restating because >>>/s4s/6305952

For a directional derivative in the direction v, what is the difference between [math] \nabla f\cdot \hat{v} [/math] and [math] \nabla f\cdot v [/math]?
I've seen both used, but to me only first makes sense. We've already calculated the "derivative" and now only care about the orientation. Whereas the second multiplies it by some scalar, which would give the wrong derivative(?).

>>9489594
If there are no biological downsides to exposing lungs directly to outside air, why are they a giant bulky internal organ at all instead of just a layer of oxygen receptors on our skin?

Where does the definition of a cross product come from? It's such a symbolically weird operation. In the second and third row you have the components of your two vectors but in the first row you have three distinct vectors as entries?

>>9490998
There's
https://www.youtube.com/watch?v=eu6i7WJeinw
for some geometric intuition I guess.

>>9489985
Same anon. This is what I have gotten so far. My homework is to prove dim(RS(A)) = rank(A). Can anyone critique it?

>>9489252
From the definitions of matrix multiplication and transposition.

Transpose:
(A^T)[i,j] = A[j,i]
Multiplication:
(A.B)[i,j] = sum_k(A[i,k]*B[k,j])

=> (A.B)^T[i,j] = (A.B)[j,i]
= sum_k(A[j,k]*B[k,i])
= sum_k(B[k,i]*A[j,k])
= sum_k(B^T[i,k]*A^T[k,j])
= (B^T.A^T)[i,j]

=> (A.B)^T = B^T.A^T

>>9490998
Given 3-vectors a,b, solving the system of linear equations a.v=0 and b.v=0 for v gives you the cross-product formula up to a scale factor (any scalar multiple of v is perpendicular to a and b).

Also: consider Cramer's rule, and A.A^-1=I. If you have a matrix A and calculate the cofactor matrix C, A[i].C[j]=/=0 iff i=j. So any given row of the cofactor matrix is perpendicular to the other rows of the original matrix. And each row of the cofactor matrix involves the /other/ rows of the original matrix (so you don't need to know the third row of A to calculate the third row of C).

You can use this to calculate perpendicular vectors in any number of dimensions. In N dimensions, given N-1 vectors you can calculate an Nth vector which is perpendicular to all of them. Construct a matrix where the first N-1 rows are the original vectors (the Nth row doesn't matter); the Nth row of the cofactor matrix is the perpendicular vector.

I need a quick rundown for multivariable calc
I'm going to study it in the proper way, but I need to know some basic things like vector integration and shit to not get lost at fluids course

pls help

>>9493636
Check out http://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx

>>9485939
ELI5 Deepfakes. I have a Bachelor's in CS but forgot everything I knew about AI, because no one wants a thing they can't get someone with half your intellect to maintain if necessary.

>>9489790
It should work if you're walking "out" toward the outside. If your vector is perpendicular to the zone's center axis, and you do at least 20 separate angles, it'll give you a nice circle of points around that spot in the zone.

>>9490390
I don't understand your question. To me this seems to be just the dot product of the gradient of some function f with the direction vector v, written in two different ways. So there's no difference. Or perhaps the $\hat{v}$ is a unit vector whereas $v$ is not.

>>9490390
I don't understand your question. To me this seems to be just the dot product of the gradient of some function f with the direction vector v, written in two different ways. So there's no difference. Or perhaps the v-hat is a unit vector whereas v is not.

What do here senpai. This is the first section on derivatives but I don't think we have covered how to find original functions of derivatives. Also, what dramatic conclusion are we supposed to draw from (c) and (d)?

Basically I don't get anything except (a) and (b).

>>9494560
c) that it has a negative slope at x=1
d) that it has a positive slope at x=-4
e) g' is positive from 4 to 6 so g is strictly increasing so the difference is positive.
f) No, g'(x)=1/3(x-3)(x+3) -> g(x)=1/9 x^3 - 3x + C where C could be anything. Without more info on g, we can't find g(2).

can somebody explain why the range for x = (negative infinity, 0) doesn't equal zero

>>9494681
Learn to speak English motherfucker.

>>9494707
why is there all that squiggly crap on the left side of the graph

>>9494681
because c is not defined for x=0

(b+c)/2 = x^a (1+sign(x))/2 for all x=/=0 = {x^a for x>0; 0 for x<0}

>>9494716
Rounding error dumbass. Learn to floating point.

>>9494716
https://www.wolframalpha.com/input/?i=%5Bx%5E(a%2B1)%2F%7Cx%7C+%2B+x%5Ea%5D%2F2

>>9492551
someone pls help

>>9494680
your answers for c) and d) had me going DURRR how did I not see that while e) is stated in much better terms than what I had in mind. Cheers!

>>9494749
thanks senpai
>>9494764
>Rounding error dumbass.
wrong because it should round it the same way whether it be neg or positive

>>9488658
Biomed Engineering?

>>9485939
>Solving op's pic
8 + 2 = 10.
3 + 3 = 6.
4 + 1 = 5.
4 + 5 = 9.
5 + 5 = 10.
7 + 1 = 8.
3 + 4 = 7.
5 + 2 =7.
3 + 2 = 5.
4 + 4 = 8.
2 + 4 = 6.
6 + 3 = 9.

>>9495076
Thanks anon

>>9495076
>3 + 4 = 7.
>5 + 2 =7.

>a prime number has four different factors

AHAHAHAHAHHAHAHHAHAHAHAHAHAHAHAHAHAHAHAHHAAHAAHHAHAHAHAHAHAHHAHAHHAHAHAHAHHHA

>>9495148
What are you trying to say?

What's the best resource to study math (as a hobby) for someone who never went past a college Math 101 course?

>>9495167
A prime number doesn't have any factor's. That's the reason it's prime.

You cannot add 3 and 4 and get a prime number.

>>9495190
njwildberger's youtube playlists

>>9495200
Thanks. Hope I'm not getting nae nae'd.

>>9495217
He's great for a hobbyist mathematician I'm not trolling. He has some idiosyncratic opinions on infinity but that doesn't really detract from his content.

His linear algebra playlist is one of my favorite things on youtube of all time.

>>9495191
>You cannot add 3 and 4 and get a prime number.
Why not?

>>9495230
>He's great for a hobbyist mathematician
He's a professor.

>>9495236
He's [a] great [person to watch] for a hobbyist mathematician.

>>9495234
Because a prime number has no factors.

>>9495266
>Because a prime number has no factors.
What does that have to do with adding numbers to get a prime number?

>>9495236
Yeah, in Australia

http://www.telegraph.co.uk/technology/2017/07/14/malcolm-turnbull-says-laws-australia-trump-laws-mathematics/

>>9495276
Those are called factors.

Sheesh, it's like I'm teaching middle school here.

For instance, there are no two numbers that add to equal 11. You could make an argument for one and 10, but one is more of a concept really.

explain these two IQ test questions

>>9494460
>https://i.4cdn.org/sci/1517959737662.png

>>9494473
>https://i.4cdn.org/sci/1517959799925.png

>>9487971
It can be zero in many ways. Consider a r.v. X with an odd pdf, and u the squaring function.

>>9495393
Question 26:
the two dots next to each other are mirrored around the y-axis and then shifted the row down every step
the two other dots move 2 rows up every step, if they would disappear, they are instead added 2 columns to the left in the bottom row
So the answer is the bottom left

The other question is probably trivial as well

>>9495420
Thanks, I see it now.

>The other question is probably trivial as well
probably, it's escaped me so far though

>>9485939

>The sum of all of the integer powers of two up to some finite upper bound n, is equal to the next highest power of two, being two raised to the power of n+1

This is elegant as fuck and it's fucking witchcraft.

>>9495647
>the sum of cubes to n is the square of the sum of the naturals to n

e.g. [math]1+2+3+ \cdots +n = \frac{n(n+1)}{2}[/math]
[math]1^3 + 2^3 + 3^3 + \cdots + n^3 = (\frac{n(n+1)}{2})^2[/math]

>>9495647
Except it's not. [eqn]\sum_{n=0}^{N}2^n =2^N-1[/eqn]
Which you can see just by writing this in binary.

>>9495726
>Except it's not.
Wrong.

>all of the integer powers

>>9495726
those are only the nonegative integers

>>9495760
>>9495768
ahh, I see. Very good.

>>9495647
[math]\sum_{B=0}^{A}(C-1)C^B =C^{A+1}-1[/math]
Its like magic!

>>9495760
>>9495837
fuck me, I shouldn't have copy-pasted

>>9495848

But even though at least one anon misinterpreted what I wrote above (and was happily contrite upon realizing his mistake), this post >>9495837 now has me curious. I have to parse it. Clearly it's a generalization (and yet also a restriction to naturals) on the above stated case (consider C=2, (C-1)=1).

I just really really like the C=2 case where the sum is turtles all the way down ending at some definite top point. The ugliness goes away and you get Zeno (the all-important bit about the negative exponents summing to one, causing that one-term to vanish) implied in the whole business. It's really cool, that form, tbqh.

NUMBER THEORY

Let d' = gcd(a+b, lcm(a, b)).
Let d = gcd(a, b)

Prove d' | d.
How the FUCK do you do this. You'll find d=d' btw, but the flip side of the proof is easy so I'm just asking for this half.
I'm thinking of using Fundamental Theorem of Algebra and maxes/mins, but not sure how.

I'm having lots of trouble in my probability class right now :( I'm not sure when to use combination or permutation and I always get confused on questions that deal with blackjack i.e. what's the probability neither you nor the deal dealer gets blackjack. If anyone could lend some insight that might help me I would really appreciate it! :^)

>>9496123
It's the same as the binary case. Just write the number in base C then multiply by C-1, and note that infinite repeating decimals of C-1 = 1 in all bases. It's just like 9*11+0.999... = 100.

>>9496131
multiplication is distributive over addition broheim

>>9496131
use the gcd algorithm???
d = ax + by
d' = (a+b)x + lcm(a,b)y = (a+b)x + |ab|y/d
d'|d => d = d'q
and then just do some algebra

>>9496182
d=ax+by+bx-bx= (a+b)x+by-bx
yeah I don't think this method is gonna work because I don't see a way of getting lcm(a,b) like this
maybe multiply by d/d
whatever

>>9496205
((a+b)+by-bx)*(ax+by)/(ax+by)
somehow needs to reduce to d'q

I read on here an explanation of why math is a branch of computer science. I need to upset some mathematicians, does anyone have it?

>>9496350
>I read on here an explanation of why math is a branch of computer science. I need to upset some mathematicians, does anyone have it?
https://existentialtype.wordpress.com/2012/08/11/extensionality-intensionality-and-brouwers-dictum/

>>9496131
>Let d' = gcd(a+b, lcm(a, b)).
>Let d = gcd(a, b)

d=x*a+y*b
d^2= x^2a^2 + y^2b^2 + 2xyab
divide out a+b from the first 2 terms
d^2 = (x^2a + y^2b)(a+b) + ab(2xy - x^2 - y^2)
divide d noting a/d and b/d are integral
d = (x^2a/d + y^2b/d)(a+b) + ab/d(2xy - x^2 - y^2) = N*(a+b) + lcm(a,b)*M
d' divides (a+b) and lcm(a,b) so it divides their linear combination so it divides d.
QED

>>9496464
nerd

>>9494882
>>9494882
>wrong because it should round it the same way whether it be neg or positive

Look at your image dumbass, it literally proves my point. It's computing x^54 then dividing by ±x both times giving the same results. While in >>9494681, it's computing x^54 then dividing by x and just computing x^53 and getting slightly different results.

from numpy import *
import matplotlib.pyplot as plt
x=array(range(-2500000, 0, 1))/1000000.0

plt.plot(x,(x**54/x + (x**54)/abs(x))/2)
plt.show()
>no error
plt.plot(x,(exp(54*log(-x))/x + exp(54*log(-x))/abs(x))/2)
plt.show()
>no error
plt.plot(x,(x**53 + (x**54)/abs(x))/2)
>error
plt.plot(x,(x**54/x + exp(54*log(-x))/abs(x))/2)
plt.show()
>pic related error

>>9496145
Here's a simple rule to help you remember the difference between permutation and combination. Compute permutation to find out how many ways you can arrange some objects into a sequence. For example the numbers 1,2 and 3 can be arranged into 3! different sequences. Use combination to find out how many ways you can choose k objects from a total of n objects, when the order does not matter. For example when choosing two numbers between 1 and 10, the options (1,2) and (2,1) are treated as the same.

I see this shit posted often and it hurts my fucking head. Is there a correct answer or is it just a self-referential paradox?

>>9496961
>not getting the reference

>>9496961
The correct answer is C. Whatever you choose, it will always be wrong.

>>9497017
No, because there's a zero percent chance that if you select C you'll be right. Therefore C can't be the answer.

>>9497044
Exactly, so C is the correct answer.

>>9497057
There is no correct answer

>>9497074
Precisely, so you have 0 % chance of picking the correct one, i.e., C is correct.

>>9497080
There's no correct answer. Are you simple?

>>9497090
It there was a correct answer, you'd have a nonzero probability of selecting it at random. You say there is no correct answer: therefore for any answer you choose you have a 0% chance of being correct, i.e. the answer C, which indicates this facy, is the correct answer.

>>9497097
*which indicates this fact

>>9496161
Can you elaborate? I know a+b = (mins of each prime)(sums of extraneous primes) but I'm not sure how I can leverage that

i still dont understand what the fuck is electric, current, charge, electric potential, permitivty etc etc after doing these fucking vector calculus

help a brainlet

>>9490390
>>9494340
Yeah the v hat is the unit vector. My confusion is that, for example, if you suppose [math] f(x,y)=x^2+y^2 [/math] and [math] v=(5,0) [/math]. Then
[math]\nabla f\cdot v=(2x,2y)\cdot(5,0)=10x[/math], but
[math]\nabla f\cdot \hat{v}=(2x,2y)\cdot(1,0)=2x[/math].
Surely they can't both be the directional derivative as they give different values?

>>9496145
probability is all about (all the ways/combinations that i want) over (all the ways/combinations that the thing can have)

I want to get a full mark in my upcoming physics exam. It's gonna be about electric fields. I'm generally speaking good at math and I have tow weeks of time to prepare. What should my studying strategy be?

So let's say someone is a professor at a university X and in the course of their research they discover something that has immense commercial value. Will they get basically nothing out of it since the IP of their discovery belongs to the school?

How would I go about showing that, for all [math]n\in \mathbb{N}\cup \{0\}[/math]
[eqn] s_{n} = 1 + \sum_{i=1}^{n}\left( \prod_{k=1}^{i}\left( \frac{1}{2} + \frac{1}{k} \right) \right) [/eqn]
this sequence of partial sums converges?

>>9497872
does it suffice to show that the product converges?

>>9486664
>There isn't Brigss' formula
>There isn't [math]tan A+tan B+tan C=tan A tan B tan C[/math] iff [math]A+B+C=\pi[/math]
>There isn't generalized tangent of sums
>There isn't De Moivre's formula

>>9496131
First do it for a,b coprime
From that, it's easy to prove it for all ad,bd (a, b coprime)

We want to prove that [math]1=(a+b,ab)[/math], with [math](a,b)=1[/math]
Note that [math]p|a \rightarrow p \nmid b[/math].
[math]p|a \rightarrow p|ab[/math]
[math]p|a, p \nmid b \rightarrow p \nmid a+b[/math]

This is true for all p, and proves the thesis
(if (a,b)=d, the thesis is [math]d=(d(a+b),dab)[/math], equivalent to [math]1=(a+b,ab)[/math])

>>9485939
I have to find the rectangle with biggest area inscribed in a circle with radius r, now I know already that the rectangle is a square but how do I mathematically prove it?

>>9497872
Instead of considering the product from k=1 to i of
1/2+1/k
consider that the product over
1+1/k
equals 1+i.

That being said, you can also plug in your expression into Mathematica and it turns out that it falls of exponentially, and the sum over all i from 1 to infinity is actually 7.

>>9487796
Assume the speed of light is constant in all reference frames, then calculate what an observer would see who is A) at rest B) in motion.

Are there any groups known to be non-canonically isomorphic to their automorphism group other than [math]D_4[/math] and [math]D_\infty[/math]? That is, isomorphic through a map other than the map sending g to conjugation by g.

>>9497981
nice

>>9497872
[math]\displaystyle \prod_{k=1}^j \left(\frac 1 2 + \frac 1 i\right) \le \frac{3}{2}\left(\frac 5 6\right)^{j-2}[/math]

why would the observed power of thermal radiation emitted by a body decrease less for change in shorter distances from the body (i.e. < 1/d^2 proportionality)?

>>9498349
sin(x) * cos(x) is maximised when x = 45°, meaning area of the rectangle is largest when forming a square inside the circle.

in 4-space, can you rotate things about a plane just like in 3-space you can rotate things about a line?

>>9498651
why wouldn't you be able to?

>>9490390
The second is the directional derivative in relation to speed on the surface.

If you have some curve c(t) on the surface f, its velocity is v(t)=c'(t) and its direction is v(t)/|v(t)|=c'(t)/|c'(t)|. The change of f with respect to space is [math]\nabla f\cdot \hat{v(t)}[/math] and it's change with respect to the curve parameter (say time) is [math]\nabla f\cdot v(t)[/math]. You get [math]\frac{df}{dt} = \nabla f\cdot v(t) = \frac{\partial f}{\partial x} \frac{d x}{d t} + ...[/math]

Why does [math]1^{k^{e^{i\pi}}}[/math] "complete the circle" iff P=NP?

>>9498349
0=d/dx[sin(x)cos(x)] = cos^2(x) - sin^2(x) = 2cos^2(x) - 1
1/2 = cos^2(x)
1/√2 = cos(x)
x=45°

>>9498651
The right way to say it is that in any dimension, you can rotate in a plane or many orthogonal planes at once. A rotation may fix an axis or plane etc. or it may not.

>>9498696
? source?

How many subsets of {0,1,...,9} have the property that there are at least two elements and the sum of the two largest elements is 13?

I was thinking to count the number of subsets given that 4,9 was included and then multiply by 3 (for 5,8 and 6,7), but this introduces overcounting that I can't account for. How do I do this?

>>9498731
If the largest number is n, then you get (13 - n - 1)! possibilities.

>>9498708
Mathematics can't answer "why" questions, only "how" questions. It was a troll post.

>Use gradient direction and magnitude to detect lines in an image.
>Estimate the extent of the lines and their parameters.
>Plot the lines overlaid on the image.
i don't get what this means by gradient direction. by magnitude i assume it means the value of the derivative. i also don't get the "extent of the lines and their parameters".
the previous question was
>Write a function that finds the outline of simple objects in images (for example, a square against a white background) using image gradients)
which i found very easy to understand and completed with the sobel filter

>>9498731
>the sum of the two largest elements
There's no overcounting, because any of {5,6,7,8} in any set containing {4,9} would mean the largest two elements summed to greater than 13. But you can't simply multiple by 3 either, because the set with the smallest largest element of 6 has a larger set of subsets "beneath" it than does the set of subsets identified by their largest terms being {4,9}.

>>9498708
>iff P=NP
The only way anyone would know this is if they'd solved P?NP already. It's a troll question. General rule of thumb for "P=NP" questions is that they're troll question.

Trying to show directly that [math]\frac{(n+1)(n+2)}{2^{n-1}}[/math] is Cauchy. For all [math]\epsilon >0[/math], there exists [math]N\in \mathbb{N}[/math] such that for all [math]m,n \geq N[/math], [math] \left| \frac{(n+1)(n+2)}{2^{n-1}} - \frac{(m+1)(m+2)}{2^{m-1}}\right|<\epsilon[/math] WLOG let [math] m\geq n [/math] does this imply [math]\left| \frac{(n+1)(n+2)}{2^{n-1}} - \frac{(m+1)(m+2)}{2^{m-1}}\right| \leq \left| \frac{(n+1)(n+2)}{2^{n-1}} \right| < \epsilon [/math] ? I've done ones like [math]a_{n} = \frac{1}{2^{n}}[/math] before, but those terms in the numerator are making me hesitant .

So here is the deal, I have pic related, I have to proof that both are equal, they obviously are, Ive calculated to n=6 and its works but thats obviously not a proof.
I know the left side is the sum of ln(1+1/1)+ln(1+1/2)+ln(1/n), so bc they are Ln, I can use the Logarithmic property and make it ln(1+1/1)*ln(1+1/2)*ln(1+1/3)*...*ln(1+1/n), you get the idea and thats where Im stocked, I dont know what else to do. And btw it goes to M number and not to infinity, if thats relevent
If I could get a little help thatd be cool.

>>9498807

[math] \left| \frac{(n+1)(n+2)}{2^{n-1}} - \frac{(m+1)(m+2)}{2^{m-1}}\right|< \left| \frac{(n+1)(n+2)}{2^{n-1}} \right| + \left| \frac{(m+1)(m+2)}{2^{m-1}}\right| [/math]

>>9498829
>I can use the Logarithmic property and make it ln(1+1/1)*ln(1+1/2)*ln(1+1/3)*...*ln(1+1/n)
Wrong.

>>9498834
then assuming m >= n, I can then say, for some N, that [math]\left| \frac{(n+1)(n+2)}{2^{n-1}} \right| + \left| \frac{(m+1)(m+2)}{2^{m-1}}\right| < \left| \frac{(N+1)(N+2)}{2^{N-1}} \right| [/math] ?

>>9498840
ok I think I wrote that wrong, so I get so I get Ln((1+1/1)+(1+1/2)+(1+1/3)+(1+1/n)).

>>9498854
>>9498829
Oops I forgot to change + to *
Ln((1+1/1)*(1+1/2)*(1+1/3)*(1+1/n))

>>9498848
Just bound both terms by ε/2.

>>9498871
how did you come to that?

>>9498829
∑ln(1+1/n) = ln(∏(1+1/n)) = ln[∏((n+1)/n)] = ln((N+1)!/N!) = ln(N+1)

sum from n=1 to N

>>9498873
>ε/2 + ε/2 = ε

>>9498886
Yes, but how can you just bound the terms by this?

>>9490998
just think about it as the area of the parallelogram the two vectors form.

>>9498901
By picking N big enough since n>N and m>N

(n+1)(n+2)/2^(n-1) < ε/2
for n>2 (n+1)(n+2) < (2n)(2n) so
4(n^2)/2^(n-1) < ε/2
n^2 / 2^n < ε/16
n / √2^n < √ε/4
√2^n = (1+d)^n where d=√2-1>0
so (1+d)^n = (1+n*d + n*(n-1)/2 d^2 + ....) > 1+n*d + n*(n-1)/2 d^2 > n*(n-1)/2 d^2
so n / √2^n < n / [n*(n-1)/2 d^2] = 2/d^2(n-1) < √ε/4
need n > max{ 8/(√2-1)^2 + 1, 2}
Identically we need m > max{ 8/(√2-1)^2 + 1, 2} so pick N > max{ 8/(√2-1)^2 + 1, 2}

QED

>>9498964
>need n > max{ 8/(√2-1)^2/√ε + 1, 2}
>Identically we need m > max{ 8/(√2-1)^2/√ε + 1, 2} so pick N > max{ 8/(√2-1)^2/√ε + 1, 2}

Forgot the 1/√ε

>>9498969
I guess I'm just not seeing how
[math]\left| \frac{(n+1)(n+2)}{2^{n-1}} \right| + \left| \frac{(m+1)(m+2)}{2^{m-1}}\right|< \frac{\epsilon}{2} +\frac{\epsilon}{2} < \epsilon[/math]. That seems like a pretty big jump.

>>9498984
[math]= \epsilon [/math] *

>>9498984
ε/2 + ε/2 = ε(1/2+1/2) = ε(2/2) = ε

>>9498992
I will rephrase. How is \left| \frac{(n+1)(n+2)}{2^{n-1}} \right| < \frac{\epsilon}{2} ?

>>9498881
ok I finally understood everything after many minutes of intense thinking, and I get this equality (1+1/n)=(n+1)/n ...but how did you go from (1+1/n) to (n+1)/n, whats the thought process?

>>9498881
thanks btw mate.

>>9498984
Break them up by the triangle inequality
|x-y| < |x| + |y| < |x| + ε/2 < ε/2 + ε/2 = ε
so |x-y| < ε

[math]\left| \frac{(n+1)(n+2)}{2^{n-1}} \right| + \left| \frac{(m+1)(m+2)}{2^{m-1}}\right|< \left| \frac{8n^2}{2^{n}} \right| + \left| \frac{8m^2}{2^{m}}\right|< \left| \frac{8n^2}{\sum_{i=0}^{n} {n \choose i}} \right| + \left| \frac{8m^2}{\sum_{i=0}^{m} {m \choose i}}\right|< \left| \frac{3!8n^2}{n(n-1)(n-2)} \right| + \left| \frac{3!8m^2}{m(m-1)(m-2)}\right|< \left| \frac{3!8n^2}{n^3} \right| + \left| \frac{3!8m^2}{m^3}\right| < \left| \frac{3!8}{n} \right| + \left| \frac{3!8}{m}\right| [/math]

Pick N such that for m>N
[math] \left| \frac{3!8}{m}\right| < \frac{\epsilon}{2} [/math]
You should be able to solve this.

>>9498997
>I get this equality (1+1/n)=(n+1)/n ...but how did you go from (1+1/n) to (n+1)/n

So do you get it or not? 1+1/n = n/n + 1/n = (n+1)/n

Or do you mean [eqn]\prod_{n=1}^{N}\frac{n+1}{n} = \frac{\prod_{n=1}^{N} n+1}{\prod_{n=1}^{N} n} = \frac{\prod_{n=2}^{N+1} n}{N!} = \frac{\prod_{n=1}^{N+1} n}{N!} = \frac{(N+1)!}{N!} = N+1 [/eqn]

>>9499016
yeah, I don't follow, sorry.

>>9499026
it was the algebra part, I sometimes choke on brainlet algebra. you got 1+1/n on the same denominator and added both together, to get (n+1)/n, I feel like a retard for not seeing. I got everything else from the your first post.

>>9498696
Because a state graph that's not already NP-complete can never modify itself to be NP-complete. If it's Turing complete it can emerge an inner state graph, or sub-state-graph, that might be NP-complete, but then that Turing machine is one computational layer of abstraction beneath it. Think of P=NP as the upper limit of all complexity, the boundary between the capacity for emergent complexity and convergent computation.

>>9499044
[math]\left| \frac{(n+1)(n+2)}{2^{n-1}} - \frac{(m+1)(m+2)}{2^{m-1}}\right| <
\left| \frac{(n+1)(n+2)}{2^{n-1}} \right| + \left| \frac{(m+1)(m+2)}{2^{m-1}}\right|< \left| \frac{8n^2}{2^{n}} \right| + \left| \frac{8m^2}{2^{m}}\right| = \left| \frac{8n^2}{\sum_{i=0}^{n} {n \choose i}} \right| + \left| \frac{8m^2}{\sum_{i=0}^{m} {m \choose i}}\right|< \left| \frac{3!8n^2}{n(n-1)(n-2)} \right| + \left| \frac{3!8m^2}{m(m-1)(m-2)}\right|< \left| \frac{3!64n^2}{n^3} \right| + \left| \frac{3!64m^2}{m^3}\right| = \left| \frac{3!64}{n} \right| + \left| \frac{3!64}{m}\right|
[/math]

1st inequality: Triangle inequality
2nd inequality: n+1< n+2 < 2n for all n>2
1st equality: Binomial Theorem on (1+1)^n
3rd inequality: All terms are positive so the sum is greater than one of it's terms
4th inequality: n/2 < n-2 < n-1 < n for all n>4

[math]\frac{3!64}{m,n} < \frac{\epsilon}{2} \\
\frac{3!128}{\epsilon} < m,n
[/math]
This is satisfied when [math]N>\frac{3!128}{\epsilon}+4[/math]

>>9499059
>>>>/g/

>>9499084
just seems like guess work to me. Everything after the 2nd inequality might as well just been plucked out of thin air, I don't see any rhyme or reasoning. It works, but I'd never be able to think this up.

How can I find the volume of a torus using Calculus?

>>9499107
welcome to real analysis, enjoy your stay

Is it provable (rigorously, through real analysis) that the length of a continuous curve described by [math]\ f(x)[/math] from x=a to x=b is the number [math]\int_a^b 1+f'(x)^2\,dx [/math] ? Or is that just the definition of 'length'?

I know about intuitive deduction but I'm wondering if there is any formalism in this and not just LE EBIN RECTANGLES [math] XD [\math]

How should I handle having 3-4 anki decks for different subjects? 2 in the morning and 2 at night?

>>9499241
>anki
Meme.

>>9499243
what do you suggest

>>9499107
There's more than one way of doing it. You could have also just done (n+1)(n+2)/2^(n-1) = 8(n+1)(n+2)/2^(n+2) < 8(n+1)(n+2)/((n+2)(n+1)n/3!) = 3! / n

How do I figure out of this thing converges? Ratio test didnt work for me.

>>9499205
[math] \int ds = \int \sqrt{ dx^2 + dy^2 } = \int{ \sqrt{ 1 + \left ( \frac{dy}{dx} \right )^2 }dx } [/math]

>>9499289
>3! / n
3!*8 / n

>>9499297
if i>0
(k^2 + i) / (k+i)^4 < (k^2 + i) / k^4
∑1/k^2 + i*∑1/k^4 = π^2/6 + i*π^4/90

Hi /sci/

Other than just brute forcing, how could I find solutions to this equation?

40 = n*f +(n-1)*s

all values (n, f, s) must be positive integers, f<s and n>5

>>9499331
uhhhh its"i" as in the imaginary unit.

>>9499096
It is a superset of math, but it's a superset in the same way an unpolished clump of carbon is a superset of diamond.

>>9499344
Best I've found so far is f=1.5, s=4, n=8

>>9499377
>f=1.5
>integer

>>9499379
>so far
>reading comprehension

>>9499344
Diophantine equations are a bitch

>>9499346

|∑(k^2 + i) / (k+i)^4| <= ∑|(k^2 + i) / (k+i)^4| = ∑|(k^2 + i)| / |(k+i)^4| <= ∑(|k^2| + |i|) / |k+i|^4 <= ∑(|k^2| + |i|) / |k|^4 = ∑1/k^2 + ∑1/k^4

>>9499344
You can get the trivial bounds
1<=f<=4
6<=n<=9
5<=s<=7

>>9499344
If n is even then nf is even and (n-1)s must even so s must be even.

If n is odd then (n-1)s is even and so nf must be even so f must be even.

So taking the bounds from >>9499402 into account, we consider either
n in {6,8} and s=6:
so 40=6f+30 (no solution) or 40=8f+35 (no solution).

n in {7,9} and f in {2,4}:
so 40=14+6s (no solution), or 40=28+6s (solution s=2), or 40=18+8s (no solution) or 40=36+8s (no solution).

therefore the only solution is (n,s,f)=(7,2,4)

>>9499425
>so 40=6f+30 (no solution) or 40=8f+35 (no solution).
should have been
so 40=6f+30 (no solution) or 40=8f+42 (no solution).

>>9499425
great, thanks

>>9499401
thanks

>>9499401
>|(k^2+i)| = |k^2| + |i|

>>9499473
dem triangle inequalities man.

Consider the recurrence relation

a(n) = a(n-1) + 2 * a(n-2) + 3 * a(n-3); a(1)=1, a(2)=2, a(3)=3

I wish to find a(100). Is it true that a(100) = 528187750095095583956959668907 (I found this value using Python, not analytical means.)

What is the closed form of this relation?

>>9497408
It's just a matter of definition. When we learned about directional derivatives we always used a unit vector as the direction. But some authors might consider the value of the directional derivative to also depend on the length of the chosen direction vector.

Apparently in more abstract mathematics the definition of the directional derivative is still valid even if the norm of the vector is undefined. See the wikipedia article for the limit definition of the directional derivative and some other notes.

How do I find the pointwise limit of this :
[eqn] f_{n}(x) = \begin{cases}
-1, & \text{for } x \leq -\frac{1}{n} \\
nx, & \text{for } -\frac{1}{n} < x < \frac{1}{n} \\
1, & \text{for } x \geq \frac{1}{n}
\end{cases}[/eqn]
Haven't seen many examples of standard sequences of functions let alone a piecewise.

>>9499823
>It's just a matter of definition
i guess. i was taught the unit vector one as well, which i find more intuitive, though i suppose the non-unit vector one also has the upshot of being able to handle v=0

>>9500232
draw a picture

what the fuck is this lower case "s"?
How can we have vo/vi (or more specifically, vi) in the expression when it was just integrated?
Looking at other proofs for differentiators, I haven't seen this "s" notation anywhere else...

Can anyone tell me where the 6 in 6*Cov comes from? I figure it's based on typical variance with 2*Cov but then how does that turn into 6 instead? 2 times the 3 from the Y2 random variable? What if there was a constant for Y1 as well?

>>9500668
https://en.wikipedia.org/wiki/Variance#Properties

>>9500681
Surprisingly that is exactly what I was looking for. I even tried looking up general variance expressed with covariance but I didn't think about looking on the wiki for variance itself because I'm a brainlet

Question: at which age human head achieves the size that can contain adult's brain?

I-it's for a sci fi

[math]
\begin{bmatrix}
a_n \\
a_{n-1} \\
a_{n-2}
\end{bmatrix}=
\begin{bmatrix}
1 & 2 & 3 \\
1 & 0 & 0 \\
0 & 1 & 0
\end{bmatrix}^{n-3}
\begin{bmatrix}
a_3 \\
a_2 \\
a_1
\end{bmatrix}
[/math]

Diagonalize
[math]
\begin{bmatrix}
a_n \\
a_{n-1} \\
a_{n-2}
\end{bmatrix}=
\begin{bmatrix}
5.63789 & -0.318944 + 1.22255 i & -0.318944 - 1.22255 i \\
2.37442 & -0.687212 - 0.889497 i & -0.687212 + 0.889497 i \\
1 & 1 & 1\end{bmatrix}
\begin{bmatrix}
2.37442 & 0 & 0 \\
0 & -0.687212 - 0.889497 i & 0 \\
0 & 0 & -0.687212 + 0.889497 i\end{bmatrix}^{n-3}
\begin{bmatrix}
0.0983786 - 2.416×10^{-18} i & 0.135214 - 3.32061×10^{-18} i & 0.124298 - 3.05253×10^{-18} i \\
-0.0491893 - 0.169309 i & -0.0676069 + 0.329414 i & 0.437851 + 0.172377 i \\
-0.0491893 + 0.169309 i & -0.0676069 - 0.329414 i & 0.437851 - 0.172377 i \end{bmatrix}
\begin{bmatrix}
a_3 \\
a_2 \\
a_1
\end{bmatrix}
[/math]

>>9499552

>>9500723

>>9500646
It's the phasor domain (aka a Laplace transform [aka the "frequency" domain])

[math] s= i \omega = 2 \pi i \times {\rm frequency} [/math]
Z = R for resistors
Z = 1/sC for capacitors
Z = sL for inductors

>>9499552
https://www.wolframalpha.com/input/?i=a(n)%3Da(n-1)%2B2a(n-2)%2B3a(n-3);+a(1)%3D1,++a(2)%3D1,++a(3)%3D3

>>9500232
Actually just draw a picture.
___/------
which goes to
___|------

I have 2 digits lets call them a and b
i have 4 spaces to put them
how many ways can i put them in?
i found it is 16=2^4= 4^2 but what is the formula exactly?
aaaa

aaab
aaba
abaa
baaa

bbaa
abab
baba
aabb
abba
baab

bbba
bbab
babb
abbb

bbbb

>>9500966
For the first slot you have two choices.
For each of these two choices, you have 2 choices for the second slot.
Then 2 choices for the third slot.
Then 2 for the fourth slot.

2*2*2*2 = 2^4

>>9500982
What if it was abc and 4 slots?

>>9500982
thanks mate
>>9501005
i guess 3^4, brainlet

>>9500966
how is this not nCr?

>>9501005
3^4

>>9500232
lim fn(x) -> sign(x)
proof: let N =⌈1/x⌉, then ∀n > N fn(x) = sign(x) and ∀n fn(0)=0

QED

>>9501017
>nCr?
what?

>>9500966
#digits ^ #spaces

>>9501031
>what?
https://en.wikipedia.org/wiki/Combination

>>9501017
Order matters: combination -> permutation
There's replacement: permutation -> exponential

>>9501031
n choose r, the number of ways you can choose r things from n possibilities
nCr = n!/(r!*(n-r)!)
4C2= 4!/(2!*(4-2)!) =24/(2*2) = 6 which is obviously wrong but why?

>>9501044
>n choose r
sorry didnt know
yes it indeed is.

>>9501041
Fuck I don't get it
I understood this at some but I lost
time to kms

>>9500959
so the answer is just going to be 1?

>>9500966
>I have two digits
so binary
>it's 4 bits
so it's [math]2^4[/math]

>>9501139
No, the pointwise limit function is going to be
-1 when x<0
0 when x=0
1 when x>0

>>9501162
hmmm...i'll have to ruminate on this for some time

>>9500761
thank you sir

>the laplace transform breaks up the time domain into moments
what the fuck is a moment

>>9501277
a moment is a specific quantitative measure, used in both mechanics and statistics, of the shape of a set of points. If the points represent mass, then the zeroth moment is the total mass, the first moment divided by the total mass is the center of mass, and the second moment is the rotational inertia. If the points represent probability density, then the zeroth moment is the total probability (i.e. one), the first moment is the mean, the second central moment is the variance, the third central moment is the skewness, and the fourth central moment (with normalization and shift) is the kurtosis. The mathematical concept is closely related to the concept of moment in physics.

how do I resist the urge to masturbate? When the thought gets in my mind or I see some HOT woman my dick goes gorilla and I can't think straight.

webm related

>>9501277
The Laplace transform of f(t) is just the Fourier transform of f(t)*H(t)*e^-γt where H(x) is the Heaviside step function H(t>0)=1 and H(t<0) = 0 (making it one sided) and γ>0 is an arbitrary damping factor so you can transform functions that don't go to 0 as t goes to infinity like constant voltages or sine waves inputs.

>>9501347
Pray to Saint Thomas Aquinas for the strength to resist degeneracy. Also pray for knowledge.

How does lack of sleep affect my ability to absorb and understand new concepts?

I'm dusty on my control theory and I want to revise some of the basics before next semester.

I'm looking for some slow KA/3B1B-type playlist that goes IN DETAIL over basics of control theory. More specifically, I want to gain a better intuition about the different meanings of the location of poles and zeros in the complex plane.

F.e. if I look at a root locus plot or at the location of the poles and zeros of a filter, I would like to have a better immediate understanding of the characteristics of the transfertfunction and/or which "device" (or model thereof) I'm looking at.

Anyone have a suggestion? All suggestions are welcome even if they don't fit the criteria exactly.

>>9499123
Start with a f(x) that describes a semicircle. Rotate it around the y axis. Multiply it by 2.

>>9501598
Get some fucking sleep, it's literally the best thing ever and there is no reason short of death that you should be putting off sleeping. And death is just permasleep so it's a win win.

Any Tips for studying statistics? I want to study this book: Blitzstein, Hwang. Introduction to probability.

SAW A CUTE GIRL DOING INTEGRALS AND I DIDN'T BOTHER TO ASK HER HOW IT WAS GOING AAAAAAAAAAA NOOOOOOOOOOOOOOOOO

given [math]\sum_{i}^{n} \left( \prod_{k}^{i} a_{k} \right)[/math], does this sum diverge if the product diverges? It should, right?

Brainlet here. Please help. Pic Related.

Rotating region R around the y-axis, which is bound by f(x), g(x), x1, and x2. I know I need to change f(x) and g(x) into terms of y. Is the outer volume (x2 squared - x1 squared) or (x2 - x1)squared? Is the formula for inner volume correct? Is anything correct? :(

Please help with this gravitation problem.
"Three point particles are fixed in place in an xy plane. Particle A has mass [math]m_{a}[/math] , particle B has mass [math]2.00m_{a}[/math], and particle C has mass [math]3.00m_{a}[/math]. A fourth particle D, with mass [math]4.00m_{a}[/math], is to be placed near the other three particles. In terms of distance d, at what x coordinate and y coordinate should particle D be placed so that the net gravitational force on particle A from particles B, C,and D is zero?"

This is somewhat a easy problem, but the solution says that [math]\vec{F_{AD}}=\frac{Gm_{a}^2}{d^2}\left ( 2.404 \measuredangle -56.3^{\circ} \right )[/math] but I don't understand how they got this

>>9502753
>This is somewhat a easy problem, but the solution says that FAD→=Gm2ad2(2.404∡−56.3∘) but I don't understand how they got this
Well what answer did you get?

>>9502756
Well for the x direction I found 1.73d, but the solution says its 0.716d. I don't know how the fuck they came with that vector and it's angle.

Are there any algorithms for accurately calculating rates with data bins? For example say I want to measure heart rate and get a number every 2 seconds, what's a good way to get an accurate result?

what sort of stupid algebra turned 2y * cos(x) into y * 2cos(x)?

>>9502831
also, the point of this screenshot is to find where the example is wrong.

>>9502831
Anon, even first graders know that 2*3=3*2

How can I teach myself Engineering Dynamics?

>>9502841
WHAT.
It's 2y * Cos(x). How the fuck is that equal to y * 2cosx

>>9502782
What is the number you get every 2 seconds when measuring heart rate?

Big bois, it was a long time ago I did complex analysis, but a can't figure out why the lecture notes state that
[math] \text{Arg}(1 + e^{it}) = \frac{t}{2} [/math] for [math] |t| <pi [/math].

I smell bullshit... Do you smell it too?
Please help this brainlet out.

>>9502853
commutativity of scalar multiplication.
pls.

>>9503582
I smell it too. Have a shitty paint drawing.

>>9503599
Actually, I read it too fast and didn't realize it's [math]\frac{t}{2}[/math] instead of [math]t[/math]. This might be true after all. It definitely works when t is pi/2.

>>9502837
sin magically changes to cos from step 2 to 3 and the constant of integration is added at the end for some reason

>>9503599
Thnx for the beautiful art, Big Man

>>9503602
yeah, I just checked Wolfram and it seems to be true, but do you have any idea to prove/intuitively confirm this shit? I don't want to use arctan or arccos because those shitty non-elementary functions make me sick.

>>9503612
new
>>9503612

TESTING THIS MDRFCKR TO SEE IF I CAN KEEP THIS DEAD THREAD ALIVE

>>9503613
Just figured out a proof using the half-angle formula for the tangent function, [math]\tan(\frac{t}{2}) = \frac{\sin t}{1+\cos t}[/math].

The argument of [math]1+e^{it}[/math] is the arctan of it's imaginary part divided by the real part, so we have
Arg [math](1+e^{it}) = \arctan(\frac{\sin t}{1 + \cos t}) [/math].
Taking the tangent of this just gives us the half-angle formula. Therefore Arg [math] 1+e^{it} = \frac{t}{2} [/math].

>>9503599
>>9503582

Draw a parallelogram
The sides are all one so it's a rhombus
Rotating about bisection of the angle brings it to itself
Therefore the opposite diagonal point goes to itself
Therefore it's on the line of rotation
Therefore the vector sum (the diagonal) is half the angle.

QED

>>9502753
Find the net force on A from B and C and negate it. This is F_AD.
Divide by G*4*m_a^2 and you have [math] \frac{ \hat{r}_d } {| \vec{r}_d|^2 } [/math]

>>9502837
Step 2 should have + C
Step 3: should still be sin(x)

also you don't need |y|

>>9503709
Ah thnx, that's a smart one. I didn't know about half-angle formula for tan.

>>9503895
Nice geometric proof. Zank you