/sqt/ Stupid Questions Thread Superb Owl Edition

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 =
[/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.

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

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?

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

...

>Who is the sexiest CARTOON milf?

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

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

thanks for the response user

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.

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?

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

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?

en.wikipedia.org/wiki/Pareto_distribution

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?

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?

>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

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?

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: 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:
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

You don't. Stop watching popsci.

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'

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

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')?

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

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

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

> 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 Veeky Forums, if X is a real valued random variable, would the following be correct?

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

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?

Of course Lois Griffin

pls help

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

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

the way they proved it with limits was fking radical

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

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..?

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.

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.

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

Best Milf!

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?

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

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..

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

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

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!

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

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

define "strictly convex"

Why is the last equality true?

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

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

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

>If we pick λ=1
Re-read

Ohhh
My bad

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".

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

matrix multiplication is not communitive.

B transpose*A transpose
That's a theorem.

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?

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?

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.

[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]

>e^2
why?

Got a neat applications question for you Veeky Forums.

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?

Restating because