Confusion Definition and 1000 Threads

As an exercise, I'm trying to compute the class number of K = \mathbb{Q}(\sqrt{30}). By the Minkowski bound, I just need to consider the prime ideals which divide 2,3,5. I've found that (2) = \mathfrak{p}^2_2 (3) = \mathfrak{p}^2_3 (5) = \mathfrak{p}^2_5 where...

I am confused of how to derive the Lorentz equation x = vt+x'/γ...if x' is the distance to an event according to O' and x is the distance to that same event according to O, then shouldn't the last term be x'γ not x'/γ, since x' is already contracted according to O, so to relate it to x, we would...

I don't know how to properly present my answer to find the limit of a converging sequence like (1/2)^n. I would just write something like this... y=1/x+1, x=∞ } y=1/∞+1=0+1=1 but the syllabus gives something completely different and my textbooks don't seem to cover this portion of the...

Shouldn't there be negative work done by the string?

This is actually a solved example of Thevenin's principle in my textbook and I understand all of it except the part that I'm attaching to this post below; the part where KVL (Kirchoff's Voltage Law) is applied. Homework Statement Find Eth in the circuit shown in the attached figure...

I am confused by the design of this AM receiver/tuner circuit. http://imgur.com/f9n05 I don't understand how the inductor and capacitors on the left design a circuit that resonates at a certain frequency, and I also don't understand why the resistor and capacitor in parallel after the diode...

For 2 vector spaces an orthogonal direct sum is a cartesian product of the spaces (with some other stuff) (http://planetmath.org/encyclopedia/OrthogonalSum.html ), and this orthogonal direct sum uses the symbol, \oplus. However, there's an orthogonal decomposition theorem...

The Seebeck coefficient is the differential drop in voltage per unit temperature across a conductor. Goldsmid says that there must be a temp. gradient across a junction for a seebeck coefficeint to be defined. This makes sense if the difference in the fermi level energy between two dissimilar...

Hi! I'm extremely confused by this problem. A car of mass 1200 kg starts from rest and travels along a horizontal straight road. The engine of the car develops a constant power of 54 kW. All the energy produced by the engine goes into increasing the kinetic energy of the car. The questions...

A book says," 0.00052 has two significant figures: 5 and 2" Now imagine a scale to measure length and suppose it's least count is 0.00005 we measure a length and it comes out to be 0.00052 where we are uncertain about the last digit. So if i am understanding the meaning of sig. figures right...

Hello. I know how to do implicit differentiation taught in calculus 1, but I'm confused by something regarding it. Take the example: y3+y2-5y-x2=4 If we do implicit differentation we get: 3y2(dy/dx)+2y(dy/dx)-5(dy/dx)-2x=0 dy/dx=2x/(3y2+2y-5) Now, it makes sense how to...

For the circuit shown, is the 3 ohm resistor in parallel with the 5 ohm resistor if the 1 ohm resistor is "in the way?"

I was reading my textbook and was confused on the terminology, is an orbit each of those boxes that you fill up with the up and down arrow, and the subshell is like s, p, d, f, g, h? I was also confused about what the shielding effect is. If anyone can enlighten me that would be great, thanks

x=t2 and y=t3-3t, find dy/dx and d2y/dx2 I understand how to get to dy/dx but an confused on how to get to d2y/dx2 can someone please explain in depth, I know the formula is (d/dt dy/dx)/(dx/dt) I don't understand where d/dt comes from and what it is. why do we not just derive it twice? I...

Homework Statement 6. If the exposure rate from 137Cs at one metre is 2.50 mGy/h, how many bequerels are present? Homework Equations Exposure is a quantity that expresses the radiation delivered to a point at a certain distance. I1d12 = I2d22 I1 = the radiation intensity at...

Layman here. Two questions on Virtual Particles. I am not trying to make some claim to spontaneous generation, just curious about how to expand the holes in my knowledge... which is about the level of a post grad engineer who likes to buy the popular physics books in stores to read. 1)...

Hi all. I have ran into a problem in converting from imperial to SI units, as follows. The ideal gas constant for air is often given in imperial units as R = 1716 \frac{ft*lbf}{slug*°R} where 1 ft*lbf = 1.356(10^{-3}) kJ 1 slug = 14.59 kg °R = \frac{9}{5}K Thus making these...

Hi all, I have a spreadsheet which says failure will occur in my composite piece when a load of 3500 lb/in is applied. If I were to tensile test this piece and the thickness has already been input (0.138 in) does this mean for every inch wide the piece can take 3500lb of force? That seems...

Disclosure: I am studying biochemistry so my thermodynamics education is lacking and I'm likely misinterpreting some of these concepts (that's why I'm here for help). I have always had trouble defining some properties as either intensive or extensive. I understand that extensive are...

I'm working on an online EECS course, and to be frank some of it is going straight over my head - but at the same time parts of it are far below my current knowledge, so I want to work and stick with it. The speaker is working through proving current and voltage - to arrive at Kirchoff's...

what will happen if i short neutral ac outlet wire with earth? please see the figure if you have any confusion.

I'm trying to learn the basic theory of neutrino oscillations at a postgraduate level. I have a few things that are bothering me. 1) All of the papers & textbooks I have looked at start out by just assuming that each neutrino flavour eigenstate is a superposition of the mass eigenstates...

Hi I am having trouble getting my head around the definition of a gradient. I know a gradient tells us the direction of steepest slope that one must follow to arrive at a maximum and I know it is defined as: However I haven't got a gutt feeling for it, I need these questions answering...

My question is about the nth derivative of e^ax cos(bx+c). Though i can calculate it easily but i am confused at one point. When we calculate the first derivative we put a = r.cos(theta), b = r.sin(theta) (every thing is ok till here) My confusion starts when we use (theta) = tan^-1(b/a) [tan...

Hi everyone! 1. Is a linear equation the same as a polynomial of first(or 0th) degree? 2. The book 'Mathematics for physicists and engineers' by springer(publisher) states that an example of a linear (DE) equation is 5.dy(x)/dx = x.y(x). Yet I read somewhere else that f(x,y)=a.x.y+b is not...

Hello, Suppose, in moving train Observer O is at middle point M, and two clocks is situated at A(rear) and B(front). O has a clock. I have confusion about time of A and B after synchronization. I have two scenario, please, tell me which one is right. (1) If we assume that one way...

If I have a recurrence equation of the following form: $$T(n) = T(km) = a, m = 1$$ $$T(n) = T(km) = T(k) + T(k(m-1)) + cn, m > 1$$ Where a is simply a constant, and k is an integer constant > 0. Now I begin substituting to find the pattern: $$T(k) = a$$ $$T(2k) = a + [a] + c2k$$ $$T(2k) = 2a...

Hello, Can anybody explain how the aerodynamic moment is calculated for an airfoil ? I was reading the first chapter in "Fundamentals of Aerodynamics" by Anderson & the formula for aerodynamic moment for the lower surface of the airfoil confused me. Is the aerodynamic moment calculated about...

I am a bit confused about electric potentials and potential energy. There are three key situations that are giving me trouble: 1) If an electron is midway between to protons, the potential energy is -ke2/r for both, and thus the total electric potential energy is twice that value. I see...

Here is what I have [SIZE="3"] A=xro+yr1 B=yro+xr1 I need to find A x B I am confused about do it because The components of A and B are in terms of vectors If A = 3i + 4j + 7k and B = 2i + 2j + 1k I would have no problem (these numbers are meaningless just giving an example)...

Ion naming confusion with the "bi" prefix I am little confused on when you use the "bi" prefix to denote the existence of a proton in front of an oxyanion. For example, I know that [HCO_{3}]^{-} is called bicarbonate as well as hydrogen carbonate. A problem arises when I try to define...

I know that Taylors theorem is used to expand f(a+h) in terms of f(a) and its derivatives in the interval (a,a+h), but my question is that can we use it to expand f(a-h) in terms of f(a) and its derivatives over the interval (a-h,a). If yes please give reason.

2nd order DE..."largest interval" confusion Homework Statement Determine the largest t-interval on which therem 3.1 guarantees the existence of a unique solution: y'' + 3t^2y' + 2y = sin(t) ...y(1) = 1 ...y'(1) = -1 Homework Equations theroem 3.1 is the one that states if p(t)...

I'm just a humble human being here, so if my question comes across as stupid, please forgive me! :) Newton's Third Law of Motion states that for every action there is an equal (in magnitude) but opposite (in direction) reaction. One of my A-level revision guidebooks state that the attraction...

http://imageshack.us/photo/my-images/440/49789320.png/ Assuming the indicated direction of motion, why is friction acting as shown in the tangential direction? Shouldn't it be acting in the opposite direction?

I am a bit confused. http://pokit.org/get/bedc0ac7e1d17e01d7d58b021b81663c.jpg The function is y=x(2t) and the point of it is to show the property of time-invariance.(which we should fail in this example, because it isn't time invariant.) Input signal is x1(t) Output signal is shown for...

Anyone who follows some of my posts knows I've fallen in love with GianCarlo Ghirardi's thought experiment. (apologises for the equations - I don't know how to work LaTeX). The experimental set-up is a 45 degree polarised photon goes through a birefringent crystal. On the other side of the...

1. Homework Statement Find the total charge on a circular disc of radius ρ = a if the charge density is given by ρs = ρs0 (e^−ρ) sin2 φ C/m2 where ρs0 is a constant. Are the two limits of integration from 0 -> a for ρ and 0->2∏ for φ? In the example given in the notes, ρ varies, instead of...

Bag contains 9 blue balls, 3 red balls. A ball is selected at random, colour recorded and NOT replaced. A second ball is selected at random, colour recorded. a) Draw tree diagram (no problem). Part 2 a) Find probability second ball is red (no problem, 0.25) b) Find probability both...

Folks, 1) If we have \int F \cdot dr that is independent of the path, does that mean that the integral will always be 0? 2) For 2 dimensional problems when we evaluate line integrals directly and use Greens Theorem for every piece wise smooth closed curves C, arent we always calculating...

People have written about mathematical creativity and the joy and beauty of mathematics. What about the sleazy underside of mathematics? Has anyone written essays about Mathematical Confusion? As I recall my teenage studies of mathematics, the most common experience was "getting stuck". I...

If I say, V = I x R V = 1 x 5 V = 5 volts Now, if I interchange the values V = 5 x 1 V = 5 volts When current is 1 amp and resistance was 5 ohms, the voltage was 5 volts. When I interchange the values then it is still 5 volts. How can I...

This is a general concern with finding temperature values at different processes in the cycle, however i do have an example i am stuck on, and can post that if needs be. anyway, if i was required to find the flow rate at outlet, which temperatures would i need to put in the SFEE as i know...

If I take the Dot Product of two vectors, say A and B, I get: AxBx + AyBy + AzBz And then when I add those terms, I get the magnitude, right? So when one of those terms are negative, that means I could end up with a negative magnitude? I thought magnitude had to be positive.

Hi, just a small doubt I'm having: I'm given a cross tabulation table, such as undernourished status versus gender of the child: -----------------------------undernourished -----------------------------yes--------no --------------------boy------37-------- 86 ---------gender...

So I am again stuck on a question I have been provided. The question is: Draw a FBD for each monkey. For each monkey, determine the rope tension that would allow the monkey to begin accelerating in the expected direction. (on a side note this is a pulley situation one monkey is 22kg and the...

Hello there. I'm new to the forums obviously. And I'm also quite new to physics. I've read many existing answers about how this works but I can't really understand how it would logically work out. From what I've understood. Gravity is not a force. Objects move in a straight line unaltered by...

I think I am missing the point of center of mass here but help me understand. So we calculate the gravitational acceleration on Earth with the Newton's law of gravitation equation, but what gets me confused is the fact that we look at Earth as a point mass. As Earth is "big and round", I...

This might be silly question for some people, yet better to ask than don't know the answer :(. so the thing is , i know that centripetal force holds a thing to keep running on a path, but when i think of Earth and all those planet which surround it, the centripetal force is gravity right ? and...

http://einstein1.byu.edu/~masong/emsite/S1Q50/EQMakerSL1.gif Hi guys, I have a little confusion about the Gauss' law in differential form over here, obviously, many textbook wrote it in the above form, but actually, the only place at which divE is not zero is at the locations where the...