Last edited on 24 March 2017 - 02:46 PM by AlbertEinstein

Hello, students of Badlion!

In the small portion of time that you are not dedicating to getting a high rank on Arena PVP, come ask questions about your math and science homework here (no computer science–I was born in the nineteenth century).

I will try to answer your question. Otherwise, some brainiac on the server should feel free to jump in and answer.

Ask away.

-AlbertEinstein

Please, join the Physics Discord for expedited homework help!

https://discord.gg/x5Z2Yqf

Posted on 12 December 2016 - 08:07 AM

What do you think is the stupidest branch of math that cannot be applied anywhere?

Posted on 12 December 2016 - 09:18 AM

Ok sir when I get home

Posted on 12 December 2016 - 09:19 AM

https://en.wikipedia.org/wiki/Recreational_mathematics

Math like this makes you say "nice" or "nifty," but that's about it. It's not going to necessarily provide you with a rigorous, mathematical theory of quantum electrodynamics, but it's cool to think about.

Though, a great deal of math that might be seen as useless at the moment could become quite useful as new theory calls for it. I think complex numbers were once discarded as being stupid and useless when they were first discovered. After all, at first glance, who knows what sqrt(-1) means? Now they're fundamental and are core to most math curricula.

So I'm not sure what specific branch of math cannot be applied anywhere quite frankly. Sometimes new math is created out of a need for it in a theory. I'm pretty sure Isaac Newton independently (Leibniz did too) came up with calculus to help describe the physics he was working on. So maybe in the end, all math may be applicable. Time will tell, and maybe that "recreational math" might be put to good use.

Posted on 12 December 2016 - 09:44 AM

Posted on 12 December 2016 - 10:53 AM

Can i join your clan?

Posted on 12 December 2016 - 12:24 PM

OK, this looks like a centripetal acceleration/uniform circular motion problem.

The premise is that this car is traveling with uniform speed along a circle. As a result, it has to have a centripetal force (and acceleration) acting on it to keep it in this uniform motion along the hill.

At the top of the hill, we have to analyze the forces acting on the car. But since the question is only interested in the person in the car, we will only consider him. There are two main forces acting on the person: gravity (F_g = mg) and a normal force (N). The phrase "force exerted by the seat of the car" is an indication that they're asking for the normal force.

Let's have our coordinates in the y-direction (up-down) have up being positive and down being negative. Using Newton's second law (net force proportional to acceleration on a body, we have -F_g + N = -m*a_c. Let's look at our signs. N is positive because it's pointing up to help balance the gravity; F_g is negative because it's gravity and pointing down; and -m*a_c is negative because centripetal acceleration always points towards the center of the circle.

Now, let's remember that a_c = (v^2)/r, where v is the speed of the body, and r is the radius of the circle. Let's substitute all these values (also, F_g = mg) in and solve for N:

N = m*(g - (v^2)/r) = (60kg)((9.8m/s^2) - (10 m/s)^2 /(30m) ).

You should be able to do the arithmetic there.

Posted on 12 December 2016 - 12:26 PM

Sure, if you do the follow the instructions on the clan page.

Zaverus attempted the test, did a little over half, and either forgot about it or got bored.

Posted on 12 December 2016 - 12:58 PM

you were the one that did the lightbulb right

Posted on 12 December 2016 - 01:07 PM

No, blow dryer and digital clock.

Posted on 12 December 2016 - 01:54 PM

Idk man i'll see.

Posted on 12 December 2016 - 03:00 PM

Right

Posted on 12 December 2016 - 06:50 PM

Automatically Deleted

Last edited on 14 December 2016 - 06:52 PM by *deleted-191881

Automatically Deleted

Posted on 14 December 2016 - 07:03 PM

3. factoral
1. you could probs look up
2. idk

Last edited on 14 December 2016 - 07:21 PM by ThatOneCombo

Create a rational function with the following characteristics:
three real zeros, one of multiplicity 2; y-intercept 1; vertical
asymptotes, and ; oblique asymptote, y=2x+1

Posted on 14 December 2016 - 09:19 PM

1. Fluoroantimonic acid.

2. Quantum mechanics is the best theory we have at the moment for describing physics at a very small level. When you study physics on the scale of an atom, you can't use the classical mechanical (Newton's laws, etc.) properties to describe systems. As its name suggests, quantum mechanics deals with "quantized" properties. Quantized in this sense means that rather than have a large, continuous array of possibilities for values of, say energy, you have a discrete levels that systems can be in at one time, with nothing in between.

Quantum mechanics first became necessary when Max Planck was trying to describe black body radiation. A lot of theories accurately described high and low frequency limits of the spectrum, but none could unify it. Planck was able to unify these theories (he's the first one to use his constant: Planck's constant). Light before was thought of as a wave because the equations that describe electromagnetism (Maxwell's equations) reduce to the wave equation in a vacuum. Planck used a quantized theory of certain properties of the light (wave number) and eventually resulted his quantum theory of black body radiation.

Einstein's Nobel prize was on the photoelectric effect, which provided a basis for what is known as a photon. The photoelectric effect is the discharge of electrons when light is irradiated on atoms. The interesting aspect is that the energy of the photons didn't depend on the intensity of the light irradiated, but rather the frequency of the light. The higher the frequency, the more energy the photoelectrons would have (hence, E = h*v, h = Planck's constant). Einstein proposed that light comes in discrete packets called photons. In other words, rather than being a continuous wave, they are discrete, quantized particles in a sense. This introduced the concept of particle-wave duality of light.

But classical physics would never have predicted this. Hence, a new theory had to be made to explain these processes. Another important phenomenon that brought the need for quantum mechanics was the Stern-Gerlach experiment. This introduced the concept of spin (inherent angular momentum in particles). Particles were shot past a uniform magnetic field. The magnetic field should, in classical theory, make a continuous distribution of trajectories when the particles hit the other side (the magnetic field causes a force on the particles that pushes them around). Instead, they saw that there were two discrete, QUANTIZED regions of particles on the other side (up and down). This introduced the concept of spin-1/2 particles (electrons, protons, for example). The spin of these particles can be either up or down. Details aside, this warranted the incorporation of linear algebra into quantum mechanics.

Quantum mechanical observables (momentum, position, angular momentum, etc.) are described by Hermitian linear operators (Hermitian has to do with complex numbers and other things) which are often represented as matrices. We use math called linear algebra to describe these systems. Using this math, you can arrive at the famous Schroedinger equation that describes the time evolution of a quantum state. One of the reasons that quantum mechanics is so controversial is the fact that it's not deterministic. Instead, quantum mechanics uses probabilities to describe properties of the observables that I mentioned. This was proposed by Max Born. Einstein and some others actually disagreed with this aspect of quantum mechanics, believing that everything is deterministic and that there might be hidden variables that we're just missing in our theory. However, after some work, it was shown (by the help of Bell's inequalities) that Einstein was actually wrong and that none of the hidden variable theories could match the predictions made by quantum mechanics.

Something that you may have heard is called the Heisenberg uncertainty principle. This principle is stated in terms of standard deviations of two observables: position and momentum. The standard deviation, in this sense, is how the measured observable is different from its expected value. The statement is (delta x)*(delta p) >= h-bar/ (h-bar = h/(2*pi), h = Planck's constant). This means that you can never know exactly where an electron is in an atom and its momentum simultaneously. If you were to know exactly where an electron is, the delta x would be zero, but that would require infinite uncertainty in the momentum p!

All of this is pretty counter-intuitive! If you see a ball moving, you can obviously say how fast it's moving and where it is, but on as small of a scale as quantum mechanics, you just can't do that!

There's a lot of math behind quantum mechanics. If you're interested in that or want to know more about other aspects of quantum mechanics, just ask me. I barely scratched the surface of quantum physics with what I wrote here!

3. Factorial, as the other person said.

Posted on 14 December 2016 - 09:20 PM

In your own words, what is the Pythagorean Theorem

Posted on 14 December 2016 - 09:44 PM

Can you write a five paragraph essay including origin of quantum mechanics and how it evolved over time. Also mention where it is most often used.

Posted on 14 December 2016 - 10:17 PM

We begin by creating a function with a vertical asymptote of 2x+1 and y-intercept 1.

f(x) = 2x + 1 + g(x), such that f(0) = 1 = 1 + g(0) —> g(0) = 0. (1)

We also want large x to give f(x) ~ 2x + 1, so lim(x->infinity) g(x) = 0. (2)

Let's define g(x) = p(x)/q(x). From (2), we require deg q(x) > deg p(x) (3). Combining f(x) into one fraction:

f(x) = (2xq(x) + q(x) + p(x))/q(x) (4). From (3) and (4), we clearly have that the numerator of f(x) has degree deg q(x) + 1.

Now, assuming you meant three distinct zeros, one with multiplicity two, we must have that the degree of the numerator of f(x) is 2 + 1 + 1 = 4 = deg q(x) + 1 —> deg q(x) = 3.

Since g(0) = 0, we must have p(0) = 0. Thus, p(x) can be written as p(x) = x r(x), deg r(x) = 1 or 0, from (3). For simplicity, choose deg r(x) = 0 and r(x) = 1. Hence, p(x) = x.

So, f(x) = ((2x+1)q(x)+x)/q(x). Let q(x) = ax^3 + bx^2+ cx + d. Then, the numerator of f(x) is 2ax^4+ (2b+a)x^3 + (2c+b)x^2 + (2d+c+1)x + d. Let's choose the three distinct roots as j,k,l. Then, the numerator must factor as n(x-j)^2 (x-k)(x-l).

This gives a system of equations for a, b, c, d , when we choose our roots. Precisely, 2a = n, -n(2j+k+l) = 2b+a, n(kl+2jk +2jl+j^2) = 2c+b, -n(2jkl+j^2 k +j^2 l) = 2d+c+1, j^2 k l n = d.

Choosing j = 1, k = -1, l = 2, n = 2, we have a=1, b= -7/2, c= 11/4, d = -4.

So just one example would be f(x) = (2x^4-6x^3-7x^2+2x-4)/(x^3-(7/2)x^2+(11/4)x-4).