/sci/ - Science & Math

>>10413642
Why can't I build muscle?

>>10413642
Italiano di merda, di quanto cazzo ti odio.
Negro negretto crepa frocetto

Who's the most powerful Touhou?

>>10413653
You're probably genetically incapable of building muscle.
>>10413857
Hecatia.

>>10414019
How can I fix it? I want to build muscle

Would it be correct to choose the particular solution here as [math] y_p = Ae^t + Bt [/math]?

>>10414236
You need a constant term or you'll never be able to cancel the derivative of Bt.

Brainlet-tier question: does the brain directly control anything other than muscles?

What kind of extreme autism results in this kind of behavior
https://www.youtube.com/watch?v=Ycm4ZIJL1dI

>>10414075
Go to the past, find a strong man, and have him cuck your dad.

>>10414350
I wish. Sometimes that's feasible now or in the future would help though

>>10414371
something* lmao

>>10414294
fluoride in the water

What's a good chemistry book that covers everything from the utmost basics (naming conventions, etc) all the way up to iochem/ochem?

Anyone know what a hold is on a college account?
My account is going to be on hold on March 1st if I don't complete my advising, but there are no appointments until March 8th.

>>10414236
Use a polynomial up to t^3

Any recommended sources for revision/relearning how to read circuit diagrams? I’m really out of practise.

A football player throws a ball vertically in the air. The speed is 5,0 m/s when the player slips the ball in the position 1,7 m above the floor.
What is the highest point the ball reaches?
I have a hard time figuring this out without m. Could someone nudge me in the right direction?

>>10414670
You know the ball's initial velocity and its acceleration after being release (g, downwards). Just integrate -g with respect to time to get velocity as a function of t, then integrate again to get position.

>>10414678
Thanks, man. I'm grateful.

Will readin VNs or manga in my free time help improve my reading comprehension and speed for when I study actual textbooks like signals and systems and applied electromagnetics?

>>10414808
No.
But reading hard literature, like James Joyce, Thomas Pynchon, McElroy, Rios and others helps a lot.
I'll recommend starting out with either Portrait of the Artist, or Waiting for Godot, or something Grillet wrote.

For set builder notation, if I say some object is a member of the set, it is a member of the set iff P(x) is true? Or is it a member of the set iff P(x) and x is bound to this set of numbers? Like how would I turn a set into an equivalent logical statement. I have to consider what's on the left of the predicate too right? This seems really obvious but I am starting to second guess what I originally thought.

>>10414966
>something is an element of a set if and only if it satisfies a condition
No. See Russell's paradox. See also the axiom schema of specification.

>>10414977
I am not sure why I specifically stated that x is bound to a set of numbers but thanks.

why do some people eat so fucking loudly???
How are they able to give off an incessant and loud smacking/chewing sound whenever they eat while everyone else eats quietly? I don't fucking get it.

>>10415377
Smacking your lips simply isn't a faux pas in Asian cultures, so I don't think they notice. Not even trying to be racist

This waveform has the following regions in time:
t <= 0 f(t) = 0

0 <= t <= 2 f(t) = 5t

2 <= t <= 6 f(t) = -5t + 20

6 <= t <= 8 f(t) = 5t - 40

t => 8 f(t) = 0

Now I'm supposed to find the laplace transform of this. I can write out the step functions, but after that I'm stuck.
Only thing I know is that L{u(t-a)} = e^(-as)/s but how do I apply this when the step functions are being multiplied by some slope?

>>10415680
All you have to do is start from the definition of the Laplace transform, and then break up the full integral into a sum of integrals over those regions. Don't use any pre-canned results for Laplace transforms.

>>10415686
How would I integrate something like 5t*u(t-2)e^(-st) dt ?
That u is getting me fucked up

>>10415695
Don't use step functions. Just do the integral over each region separately. Do the integral from 0 to 2, then 2 to 6, then 6 to 8.

>>10415699
thanks

What is the purpose of harmony? Why playing different notes at the same time sounds better than playing just one note? Aren't harmony and overtones the same? Couldn't you build an instrument that had the same overtones as a harmony?

>>10414236
y(t)=(1/2)te^-t+(7/4)e^-t+(1/4)e^t+t-2
The Laplace transform is (s^2+s-1)/(s^5+s^4-s^3-s^2). The characteristic polynomial is s^5+s^4-s^3-s^2=(s+1)^2.s^2.(s-1). Write a/(s+1)^2+b/(s+1)+c/s^2+d/s+e/(s-1), convert to rational form, equate numerators, solve for a,b,c,d,e (=1/2,7/4,1,-2,1/4). The inverse transforms of the terms are:
1/(s+1)^2 -> te^-t
1/(s+1) -> e^-t
1/s^2 -> t
1/s -> 1
1/(s-1) -> e^t

why is maths so ugly

>>10416918
Because it isnt engineering

>>10416918
because you haven't learned any math

>>10416918
because ur dum dum

>>10417039
intuitive things don't need to be learnt though

>>10415749
Harmony is polyrythms going really fast. I guess your question is essentially asking why does the color yellow makes me feel good wich I couldn't answer apart from some evolutionnary mumbo jambo. And overtones are just your fundemantal frequency multiplied so you could probably make an instrument which sound makes you constantly mindful of a dominant chord for example (2nd, 4th, and 6th harmonics mainly i think which is kind of the case with the basson.)

Check out https://www.youtube.com/watch?v=pb37dJFPoFg by bartok.

The paired instruments at transposed intervals make chordal harmonies with the overtones you hear augmented chords with the clarinet pair for example

Is it normal to have some difficulty in an intro to proofs/abstract math course? I haven't gotten a grade below 90 yet on anything but some homework questions require a lot of pondering on my part and sometimes I misunderstand the question entirely. Am I a brainlet? I want to be a professor in the future (although I have back up plans).

Can somebody help me rephrase the following in the form of propositional calculus (the context is completely irrelevant)?

"We know that galaxies exist and consist of matter. Galaxies are held together by the sufficient gravity. Both matter and dark matter cause gravity. In order to hold galaxies together, the gravity caused by both matter and dark matter is needed. If dark matter didn't exist, galaxies wouldn't exist. Therefore dark matter exists."

>>10417676
>Is it normal to have some difficulty
Yes
>I want to be a professor in the future
Good luck if your name doesn't start with ((()))

>>10417901
>Good luck if your name doesn't start with ((()))
Not even a pol fag but I noticed this as soon as I became a math major.

I don't understand part c.) here, how do I get a range of values for v? Will reply to this with my work

>>10418428

>>10418432
Perhaps trying writing the position explicitly as a function of time?

>>10418444
so just consider t > 10 then?

Can someone explain to me how these are equal? I don't understand what algebraic manipulation can give you this.

[math] \frac{64}{z-0.8}-\frac{56}{z-0.7}=\frac{80z}{z-0.8}-\frac{80z}{z-0.7} [/math]

>>10418760
Do long division on the fractions on the right hand side

>>10413642
Can someone explain this?
Presumably you're supposed to see the answer in like 30 seconds, but I'm too much of a brainlet
It's realyl making me annoyed

Calc 1 here. We have covered epsilon-delta problems for polynomial functions, but I have decided to go a step further. I know that the epsilon for a given value of delta and a given value of the function's domain can be expressed like so:
[eqn]\epsilon = f(c+\delta)-f(c)[/eqn]
The first five degrees of polynomial functions can be expressed like so:
[eqn]f_{1}(x)=bx+a[/eqn]
[eqn]f_2(x)=gx^{2}+bx+a[/eqn]
[eqn]f_3(x)=hx^{3}+gx^{2}+bx+a[/eqn]
[eqn]f_4(x)=kx^{4}+hx^{3}+gx^{2}+bx+a[/eqn]
[eqn]f_5(x)=qx^{5}+kx^{4}+hx^{3}+gx^{2}+bx+a[/eqn]
This gives me the following formulas for epsilon corresponding to their respective polynomial functions:
[eqn]\epsilon_1=b\delta[/eqn]
[eqn]\epsilon_2=g\delta^2+(2gc+b)\delta[/eqn]
[eqn]\epsilon_3=h\delta^3+(3hc+g)\delta^2+(3hc^2+2gc+b)\delta[/eqn]
[eqn]\epsilon_4=k\delta^4+(4kc+h)\delta^3+(6kc^2+3hc+g)\delta^2+(4kc^3+3hc^2+2gc+h)\delta[/eqn]
[eqn]\epsilon_5=q\delta^5+(5qc+k)\delta^4+(10qc^2+4kc+h)\delta^3+(10qc^3+6kc^2+3hc+g)\delta^2+(5qc^4+4kc^3+3hc^2+2gc+b)\delta[/eqn]
Having these formulas to compare each other to, I set about attempting to find [math]\epsilon_n[/math]. I start by generalizing the polynomial functions:
[eqn]f_{n}(x)=m_0+m_1x+m_2x^2+m_3x^3+m_4x^4+m_5x^5{\ldots}{\space}m_nx^n[/eqn]
This gives me:
[eqn]\epsilon_n=(nm_nc^{n-1}+(n-1)m_{n-1}c^{n-2}+{\ldots}~1m_1c^0)\delta+(P(n)m_nc^{n-2}+P(n-1)m_{n-1}c^{n-3}+m_2c^0+{\ldots}[/eqn]
Where the function [math]P(n)[/math] represents the centermost value for a given row of Pascal's Triangle corresponding to the binomial expansion of the nth power.
It is here that I got stuck. Firstly, I have no idea why the Pascal's Triangle function disappears for the last term of the sum making up the coefficient for [math]\delta^2[/math]. Secondly, I have been unable to find the pattern used to determine the coefficents for higher powers of [math]\delta[/math] than 2. Any insight, or alternatively, explanations for why I'm retarded would be appreciated. Sorry if I fucked up the latex.

>>10419021
>but I have decided to go a step further
fucking nerd

>>10418801
C.

Every image is flipped 90 deg against the clock, never 3 minor colors, minor symbol is seemingly always "perpendicular" to the split in the circle

>>10419021
Correction:
[eqn]\epsilon_n=(nm_nc^{n-1}+(n-1)m_{n-1}c^{n-2}+{\ldots}1m_1c^0)\delta+(P(n)m_nc^{n-2}+P(n-1)m_{n-1}c^{n-3}+{\ldots}m_2c^0)\delta^2+{\ldots}[/eqn]

If pi never ends, why is it not considered infinite?
Unless it does end and we just don’t know the exact value yet

>>10419140
> If pi never ends, why is it not considered infinite?
Because that's not what "infinite" means.
> Unless it does end and we just don’t know the exact value yet
Pi is known to be irrational (proven by Lambert in 1761). All irrational numbers have a non-repeating decimal expansion.

If a number x has a repeating decimal expansion, that means
x=a+b/10^k+b/10^(k+d)+b/10^(k+2d)+...
=> x-a = b/10^k+b/10^(k+d)+b/10^(k+2d)+...
=> 10^k*(x-a) = b+b/10^k+b/10^(k+d)+b/10^(k+2d)+...
=> 10^k*(x-a) = b+(x-a)
=> (10^k-1)*(x-a)=b
=> (x-a)=b/(10^k-1)
=> x=a+b/(10^k-1)
which means that x must be rational.

>>10419140
Because 3 < pi < 4

How to get the Heaviside step function in this given?

>>10419234
try drawing the graph

>>10419031
both C and E do those

>>10419236
but I need to find the Laplace transform in this given.

>>10419234
(O(t) - O(t-1)) * -4 + (O(t-1) - (O(t-3)) * 0 + (O(t-3) * e^-t) then simplify? I'm new to it also, but it's not that complicated, right?

>>10419293
Dude Ikd why But it confuses me alot but thanks.

>>10419267
>the Laplace transform
Just break up the integral into the segments where we have functions.

Anyone good with model theory? How do I prove this shit?

>>10419533
Oops wrong image

Can this be simplified without actually evaluating the integrals? Sorry for phoneposting.

>>10420186
Fuck, the limit on top should be a to infinity, not x to infinity.

What is the animal with the biggest average longevity/volume ratio? Beside humans

is the internal direct sum basically just a disjoint (at most trivially intersecting) union of subsets?

>>10420186
assuming there are no blow ups in f(x) over the full number line, the bottom integral can be split from 0 to a and a to inf. Divide top and bottom by the a to inf integral and the ratio becomes 1/(1 + ratio of integrals). Doesn't really make it more solvable in general, tho.

a) is negative x-direction because of the positive phase angle?
b) line is lossless because of the the 2x is positive for the amplitude?
c) ^
d) frequency is obviously 10^9
e) Dielectric er is from up = c/sqrt(er)
up = f*λ and λ = 3*10^8 because it's lossless?

>>10420388
Nah. It's when you eenie meenie two subgroups and say that another subgroup(or the whole group) is isomorphic to their direct sum and also contains them.

>>10421094
1. Negative x direction because both the x and t coefficients inside the cos() are positive, so if you increase t you have to decrease x to get the same angle. v(t,x)/(2e^2x)=v(t+a,x-b)/(2e^2x) for positive a,b.
2. Lossy. v increases as x increases but the wave is travelling in the -x direction. If it was travelling in the +x direction, you'd have amplification. Lossless would just be a sinusoid without any e^kx factor.
5. Propagation speed v=(2*10^9*π)/(40*π/3) = (3/2)*10^8 ~= c/2. Assuming μ=μ0, v/c=1/sqrt(εr) => εr=c^2/v^2 = c^2/(c/2)^2 = 4.

How many different valuations are there for a truth table consisting of 7 options?

ctive function such that [math]f:\mathbb{R} \longrightarrow \mathbb{R}, f(x)=6-x-x^3 [/math]. Find the slope of the tangent line to [math]f^{-1}[/math] on the point [math](-4,2)[/math]
I've been with this one for a couple hours now, finding the inverse function seems almost impossible and after checking in an online calculator the inverse is a monster, i need help with this one sqt.

>>10421549
Is it possible to go to the possitive x-direction and still have 2e^(2x) as the amplitude or is this invalid?

>>10421868
> Is it possible to go to the possitive x-direction and still have 2e^(2x) as the amplitude or is this invalid?
It's invalid. The transmission line would be amplifying the signal. The amplitude has to either remain constant (lossless) or decrease exponentially (lossy).

With the wave travelling in the -x direction, the amplitude is 2e^(-2u) where u is the distance travelled, i.e. exponential decay.

>>10421856
compute the tangent line for f and flip it through the x=y axis

Bumping.

Just starting Propositional Logic. Is the truth table for the bog-standard logical distributive property (IE, two logical operators) the same as the truth table for a logical/algebraic operator mix (IE, one logical operator and one algebraic)? Or is there a better way to prove their equality than a truth table?

Can someone explain time dilation.

So if I do a 100m race with someone going at lightspeed ...I'm somehow faster

If some does 100 things in 10 nano seconds while I do 100 things in 10 minutes I'm the fast one.

If someone flying in an ultra fats jet pulls out his clock to check the time. His clock will run slower then everyone else.

>>10421094
Is this a DSP course? If so, might I ask what textbook you are using?

How much time do people typically study and do hw each day?

>>10424138
I study -1 hours.
I unstudy so I can study more.

>>10424138
1 hour maybe 2

Can someone redpill me on Tropical Geometry?

>>10424529
>>10424542
Seems rather short. Is this per class? How many units in a semester?

>>10424564
Tropical geometry is a relatively new area in mathematics, which might loosely be described as a piece-wise linear or skeletonized version of algebraic geometry, using the tropical semiring instead of a field. Algebraic varieties can be mapped to a tropical counterpart and since this process still retain some geometric information about the original variety, it can be used to help prove classic results from algebraic geometry, such as Brill–Noether theorem using the tools of tropical geometry.

>>10425589
>redpill me
lmfao you just copied the wiki page. I already read that. I wanted a more hands down explanation

>>10414289
glands

>>10424928
lol dont listen to them, in uni recommended hours to make the bsc in time is 8h per day and I can tell you that even if you dont need 8h daily it feels like it

2sin2x-cosx=1

Can someone show me the steps to showing x = 180 degrees?

Shit, I procrastinated to the point where I am on the edge of being expelled.

How to proceed?

A-B, where A is the empty set, and B is a non-empty set equals the empty set, right?

>>10427080
Well, A-B is the set of elements that belong to A and don't belong to B. If A is empty, no element satisfies the first criteria and we have an empty set.

>>10427091
denks

>>10425917
> Can someone show me the steps to showing x = 180 degrees?
You can't. There are 4 solutions in the range [0,2π) (and infinitely many solutions overall, given that the expression is periodic).

As for how you get those solutions: first,
1. sin(2x)=2cos(x)sin(x)
2sin(2x)-cos(x)=1
=> 4cos(x)sin(x)-cos(x)=1
2. |sin(x)|=sqrt(1-cos^2(x))
=> 4cos(x)sqrt(1-cos^2(x))-cos(x)=1
=> 4c.sqrt(1-c^2)=1+c where c=cos(x)
=> 16c^2(1-c^2)=(1+c)^2=1+2c+c^2
=> 16c^4-15c^2+2c+1=0
=> (c+1)(16c^3-16c^2+c+1)=0
=> c+1=0 OR 16c^3-16c^2+c+1=0
c+1=0 => cos(x)=-1 => x=π is one solution. The other 3 require solving a cubic, which gives you 4 values for cos(x), each of which gives rise to 2 values for x (as cos(2π-x)=cos(x)). But only half of those are valid (the other half come from the fact that equation 2 only considers the magnitude of sin(x) and ignores its sign).

Solving numerically, the other 3 solutions are approximately 0.185 (33.3°), 1.194 (68.4°), and 4.508 (258.3°).

>>10413713
Ma che oh

Where can I find old papers online without paying ridiculous sums?

specifically

LX. On the definition of distance in general relativity
I.M.H. Etherington

I'm almost certain I've failed Calculus II for the semester.

Is it better for me to withdraw from the course before the withdrawal penalty, or stick it through to see all the material, bomb the final, and then re-take to do grade replacement?

Either way I need to take the course over.

>>10427297
there is nothing in calc II you cannot learn in an hour.

>>10427380
It's not that I can't do the work. I can, for the most part.

It's that my professor is an extremely tough grader, and the tests are significantly more difficult than any of the homework or review material.

That, coupled with a time constraint and my very, very, very bad testing anxiety is a recipe for disaster.
I have now failed 2 out of 4 tests. Next up is parametric/polar calculus & conics, and infinite series.
I don't know how I'll fare with those.

>>10427190
Thanks, I didn't know the
>|sin(x)|=sqrt(1-cos^2(x))
identity so wasn't able to progress.

what the fuck is a span

>>10428890
The span of set of vectors in a given vector space is the smallest subspace containing that set. (By smallest I mean that it is minimal with respect to inclusion).

>>10419021
I'd write the expressions in sum notation and using binomial coefficients.
[math]\displaystyle f_n(x) = \sum_{k=0}^n a_kx^k[/math]
[math]\displaystyle f_n(c+\delta) - f_n(c) = \sum_{k=0}^n \left(a_k(c+\delta)^k\right) - \sum_{k=0}^n \left(a_kc^k\right)[/math]
[math]\displaystyle = \sum_{k=0}^n \left(a_k \left(\sum_{i=0}^k \binom{k}{i} c^{k-i}\delta^i \right) \right) - \sum_{k=0}^n \left(a_kc^k\right)[/math]
If you get used to writing this way your work will be tidier, you won't mess up as often and you can apply the countless known properties of binomial coefficients:
https://en.wikipedia.org/wiki/Binomial_theorem
https://en.wikipedia.org/wiki/Binomial_coefficient
http://www.math.psu.edu/tabachni/Books/taba.pdf#page=35 (chapter 2 of Mathematical Omnibus; fantastic book by the way)
https://dms.umontreal.ca/~andrew/Binomial/

>>10427277
Copy the doi into sci-hub.

>>10428581
You can get that directly from the fact that [math]\sin^2(x)+\cos^2(x)=1[/math]. That and the sine identity for the sum of angles are pretty much the only two ones you'll ever need (and you can even deduce the sum of angles from Euler's [math]e^{\theta i} = \cos(\theta)+i\sin(\theta)[/math], if you ever forget them)

>>10428890
>>10428953
>the smallest subspace containing that set
Yes, and you can prove (in the finite-dimensional case at least) that this definition is equivalent to the set of all linear combinations you can make out of the vectors.

This guy at the gym was doing pic related and I asked him how much weight dod he count it as. Like, how does he calculate the weight. He responds
>well, the bar is 45, and it has three 45 lb plates on it, so it's 180 lbs
And I was like, well, what about accounting for the weight on the other end of the bar? Or that it's like a fulcrum? I wasn't trying to bust his balls I'm just curious how to calculate the weight and I'm sure he's not actually lifting 180 lbs. I would at least subtract half the weight of the bar.

I guess it's a little hard to figure because it depends where you grab the bar, how thick the plates are (the further out on the bar the weight is the "heavier" it is), how high you lift the bar (weighs more closer to the ground than it does 18" off the ground) but can someone give a rough or average answer?

Is anyone here familiar with smith charts?
Let's say I have 2 points on the smith chart
the first one on the far left, gamma = -1
the second on the far right, gamma = -1
since the far right is an open circuit and the far left is a short circuit, is the impedence of the far right infinite and the far left is 0?
then, what would the admittance be?

>>10431524
You're thinking too much about it you fucking lanklet. It doesn't fucking matter about the physics.

>>10431602
so would my admittance on the far right be 0, then admittance on the far left is 0?

>>10431605
I just did a test, I put one end of the bar bell on a scale. I put three 45 lb plates on the other end. The scale read 24 lbs. I then lifted the weights up to my chest while bent over, as you would while doing the exercise. The scale read 47 lbs. At that height I was only lifting 133 lbs. NOT 180.

tl;dr you are a brainlet and probably a liftlet

>>10431658
You didn't read my post. I literally just said the physics doesn't fucking matter. No one gives a fuck about the calculations. If you there are 3 plates on there, then you call it 3 fucking plates. No one does the fucking math you retarded lanklet.

>>10431694
You don't think it's important to know? If you switch to regular rows and load it up with 180 lbs you'll probably injure yourself and wonder why.

>>10431720
its literally not important, exercise is about improvement not absolute strength you retard
all you need to know is "can i do more plates than i did last time" not the actual amount of force involved

>>10431720
It's not fucking important. You also have no idea what you're talking about in your post. Those are two different movements/exercises and you've managed to branch off from your main point.

>>10431807
1.) It is important, because I wanted to know.
2.) My main point was that the dude was not lifting 180 lbs like he said he was, and I was curious what the actual number is.
3.) I am not a physical trainer but pic related looks awfully similar to the one I posted above. They may be slightly different exercises but I don't see a big difference.

>>10431834
>They may be slightly different exercises but I don't see a big difference.
>slightly different
>work totally different fucking muscles
go ask this on /fit/ and see what they tell you

>>10431834
>They may be slightly different exercises but I don't see a big difference.
>If you switch to regular rows and load it up with 180 lbs you'll probably injure yourself and wonder why.
Your whole thought process is fucking everywhere. You have no idea what your main point is because you keep flip-flopping like the retarded lanklet you are. Lift more than a month before fucking talking

>>10413642
>just started chem 1A
>first lab is split into two parts
>lab 1A is finding how precise/accurate different glassware is
>lab 1B is making salt solutions and finding the densities
I'm working on my formal lab report now. Should I make a lab report for each experiment or somehow combine them? Making two intros on the same report is kind of ugly, but combining the two experiments into one intro is not great either. I don't know what is standard. Thanks.

>>10431892
In what way is my thought process everywhere, what are you talking about?
>lift more than a month before talking
No U. I had a simple question and instead of answering it you attack me, and say the answer isn't important.

Let's say you know the power input into a piece of metal. How do you figure out the temperature that it heats up to?

>>10432116
You would need to know the specific heat capacity of the metal

>>10432612
And let's say you do?

What types of critical points of 2-variable functions exist? I know of maxima, minima, saddle points, as well as monkey saddle points. Is this list exhaustive? I know this relates to whether the quadratic form of the function is positive definite, negative definite, or indefinite. However, this classification doesn't actually make any distinction between regular saddle-points and monkey saddles. In fact, surely you could create infinitely many different types of saddles?

>>10432612
The specific heat capacity isn't relevant. That determines how quickly it heats up, but not the eventual (equilibrium) temperature.

>>10432116
The equilibrium temperature is equal to the ambient temperature plus the power input times the thermal resistance (°C/W). The thermal resistance is determined primarily by the surface area, the shape, and the airflow (which can be due to either passive convection, i.e. hot air rising, or forced convection, i.e. a fan). Commercial heatsinks vary from tens of °C/W for something the size of an IC to 0.1°C/W for something the size of a small brick (those figures assume passive convection).

This assumes that the cooling from convection dominates, i.e. the object is surrounded by a cool, dense atmosphere. This is the case for a heatsink a few tens of degrees above room temperature in "room" atmosphere.

Cooling from radiation (i.e. black-body radiation) follows the Stefan–Boltzmann law; radiated power is proportional to surface area and the fourth power of absolute temperature (but note that if the surface isn't convex, some of the radiated power will be reabsorbed). So temperature (in K) is proportional to the fourth root of power. This dominates in a vacuum or near-vacuum or for objects which are hot enough to glow.

> What types of critical points of 2-variable functions exist? I know of maxima, minima, saddle points, as well as monkey saddle points. Is this list exhaustive?

A critical point has zero gradient, thus the directional derivative is zero in every direction. If the directional second derivative is always positive it's a (local) minimum, if it's negative it's a maximum, otherwise it's a saddle point. In a typical saddle point, it varies between positive and negative. But there are three other cases: always non-negative but sometimes zero, always non-positive but sometimes zero, and always zero. The first two are "horse saddles", i.e. saddle points which are also extrema, the last one is a "monkey saddle", i.e. a horizontal point of inflection in every direction.

The term "monkey saddle" can also apply to a specific curve, having the formula z(r,a)=r^3*cos(3*a) in polar coordinates (z(x,y)=x^3-3xy^2 in Cartesian coordinates); this has 3 "depressions" - one for each leg and one for a tail, hence the name. But any function of the form z(r,a)=f(r)*g(a) where f'(0)=0 and f''(0)=0 has a monkey saddle point (zero slope and zero curvature in all directions) at r=0.

So I'm trying to figure out some probability stuff, I think I have things right but people are telling me I'm wrong, and I want a second opinion to confirm I'm retarded.

So, I'm trying to figure out the chance that when you roll 11 separate 6 sided dice that none of the dice rolled land on either the 6 or 5 faces and that at least 6 land on the 1 face.

So the way I'm calculating this is just running both instances through a binomial distribution calculator and then multiplying the results together as follows

https://www.stattrek.com/online-calculator/binomial.aspx

First condition (none land on 5 or 6)
>Probability of success on a single trial
Input .3 repeating
>Number of trials
11
>Number of successes (x)
0
>Cumulative probability: P(X <= x)
0.01156101994 (not rounding because lazy)

Second condition (at least 6 land on on 1)
>Probability of success on a single trial
Input .16 with the 6 repeating
>Number of trials
11
>Number of successes (x)
6
>Cumulative probability: Cumulative probability:
P(X >= x)
0.00460879153 (not rounding because lazy)

Chance of first condition multiplied by chance of second condition to get chance of both conditions occurring at the same time
0.01156101994*0.00460879153=0.00005328233

Format as percent
0.00005328233*100=0.005328233%

So is this right or wrong, and if it's wrong why I am retarded and how would I actually calculate this properly? Am I supposed to consider the second condition as having a success chance of .25 on a single trial because I'm already accounting for the fact that nothing will land on 5 or 6 in the first condition?

>>10432887
Ok, I talked with someone and I think I have it figured out now, but since I already posted might as well post this for a second opinion anyway.

So since I'm already accounting for 6 of the dice landing on 1, that means that my other condition shouldn't be that 11 dice are not landing on 5 or 6 but that the remaining 5 are not landing on 5 or six so...

https://www.stattrek.com/online-calculator/binomial.aspx
First condition (at least 6 land on on 1)
>Probability of success on a single trial
Input .16 with the 6 repeating
>Number of trials
11
>Number of successes (x)
6
>Cumulative probability: Cumulative probability:
P(X >= x)
0.00460879153 (not rounding because lazy)

Second condition (remaining 5 don't land on 5 or 6)
>Probability of success on a single trial
Input .3 repeating
>Number of trials
5
>Number of successes (x)
0
>Cumulative probability: P(X <= x)
0.1316872428 (not rounding because lazy)

Chance of first condition multiplied by chance of second condition to get chance of both conditions occurring at the same time
0.00460879153*0.1316872428=0.00060691905

Format as percent
0.0006069190492*100=0.06069190492%

This right?

I feel constantly mentally too tired to do math and need uppers like coffee to get me to do it, but then I can't sleep at night. Anyone else have the same problem?

I want to study physics. Which of the following would be best to transfer to?
>Maryland
>Tennessee
>Indiana
>Purdue
>Michigan State
>Arizona