Terms Definition and 1000 Threads

Homework Statement If x is a real number, we define [x] as being the largest integer <= x. For example, [1.2] = 1, [-1.1] = -2, [1] = 1, [11/3]3 = 3, . . . Let {an}n>=1 be the numerical sequence defined by: a1 = 3; and an = a[n/2], for n>=2 (a) Give the terms a1; a2; ... ; a8 of this...

Homework Statement P(r) = 1-(2r2+2r+1)e-2r i know that p(r) is just the derivative of P(r) to find the median i would just integrate from o to r and set that equal to .5 but when you integrate youre just going back to P(r) from 0 to r so i get 1-(2r2+2r+1)e-2r = .5 how would...

cosh x= e^x+e^-x/2 sinh x= e^x-e^-x/2 Can someone explain why the hyperbolic trigonometric functions are defined in terms of the natural exponential function, e^x ?

Homework Statement http://img716.imageshack.us/i/captur2e.png/ http://img716.imageshack.us/i/captur2e.png/ Homework Equations Stuck on the last part The Attempt at a Solution http://img689.imageshack.us/i/capturevz.png/ http://img689.imageshack.us/i/capturevz.png/

Homework Statement Prove that if {r1,r2,...rx} is a reduced residue system mod m (where x=\phi(m), m>2), then r1 + r2 + ... + rx= 0 mod m. Homework Equations The Attempt at a Solution I've been able to prove it pretty simply for odd m and for m=2k where k is odd, but for m with higher powers...

Homework Statement Does this series converge or diverge? infinity\Sigman=1 (n!/e^n) Homework Equations The ratio test. The Attempt at a Solution lim n--> infinity ((e^n)(n+1)!)/(e^(n+1)) I don't know what to do from here...

\begin{bmatrix} 1 & \frac{1}{2} & \frac{1}{3} \ldots & \ldots & \frac{1}{n}\\ \frac{1}{2} & \frac{1}{3} & \frac{1}{4} \ldots & \ldots & \frac{1}{n + 1}\\ \frac{1}{3} & \frac{1}{4} & \right \frac{1}{5}\ldots & \ldots & \frac{1}{n + 2}\\ \vdots & \vdots & \vdots & \ddots &...

Hello :smile: Sorry if this is in the wrong place, I don't know where else to put it. Is there a way to write radians as decimals in terms of Pi? I'm currently doing Polar Coordinates with Argand Diagrams, and this is something I'm curious about. I've just done a question and come...

Homework Statement \ x = y^4 + y^2 + 1, y \geq 0 Find the inverse function of y in terms of x and its derivative dy/dx Homework Equations The Attempt at a Solution I don't really understand how to find y isolated when there is two y variables, this is the best that I have =...

[Homework Statement If 0<a<b, find the radius R and center (h,k) of the circle that passes through the points (0,a) and (0,b) and is tangent to the x-axis at a point to the right of the origin. Homework Equations ((x-h)^2) + ((y-k)^2)=R^2 (equation of the circle centered around (h,k))...

Hi, The divisor summatory function, D(x), can be obtained from \zeta^{2}(s) by D(x)=\frac{1}{2 \pi i} \int_{c-i \infty}^{c+i \infty}\zeta^{2}(w)\frac{x^{w}}{w}dw and I was trying to express \zeta^{2}(s) in terms of D(x) but I didnt succeed, could someone help?

Consider a one dimensional gauge theory where the field has mass. The term, m^{2}A^{\mu}A_{\mu} is the conventional mass term. What if you find terms in your Unified Field Theory lagrangian of the form M_{\mu\nu}A^{\mu}A^{\nu} ? In this case M_{\mu\nu} is constant. When it is...

Homework Statement <x|p^2|x'>=?Homework Equations <x|p|x'>=-ih d/dx dirac delta(x-x') I=Integral(dp|p><p|) The Attempt at a Solution <x|p^2|x'>=<x|p I p|x'>=<x|p Integral(dp)|p><p|p|x'> I know that <x|p|x'> = -ih d/dx diracdelta(x-x') so does that mean that <p|p|x'>=-ih d/dx diracdelta(p-x')...

Does anyone know the equation for the Force of Gravity in terms of density? I have been trying to plug in the equatin for the density of a sphere into Newtons Gravity formula and keep hitting dead ends. And if you can show me the math and reasoning behind it please.

I have been trying to find lift and drag coefficients in terms of pressure. So far I have found multiple equations. Below is what I have found after multiple research on the web. I am using these equations in LabVIEW. My input is going to be upper and lower surface pressure and I have to find cl...

My friends and I have a problem that seems simple enough, but has proven to be pretty hard. We need some help. Suppose you have an object in space with no initial velocity relative to the Earth. Now, due to the Earth's gravity, the object will begin to accelerate towards the Earth...

Homework Statement The capacitor in an circuit is initially uncharged In terms of R and C, determine the time required for the charge on the capacitor to rise to 50% of its final value. In terms of R and C, determine the time required for the initial current to drop to 10% of its...

Homework Statement I need to find the volume of the solid generated by revolving this region bounded by the curves about the x-axis. y = sqrt(x), x+y=6, y=1 Homework Equations The Attempt at a Solution I find the intersections of these curves I get: (1,1), (4,2)...

Can someone please help me out with mass terms in the general case for a lagrangian? It is known that for n scalar fields, any quadratic in these fields will be a mass term. For classical fields \varphi_{j} with the most general possible expression being M^{jk}\varphi_{j}\varphi_{k} , the...

Homework Statement How can I write cos(x) in terms of cot(x)? I tried using the pythagorean identities and fundamental identities but still cannot figure it out. The answer must start as the following: cosine(x)=... Homework Equations All the trig identies. I think it wants me to use...

If I have 2 cosine terms added together, how would I combine them into one cosine term? Ex: A) 3 cos(2t) B) cos(2t - pi/2) Thanks PS. I don't think the sum to product formulas work, I'm wondering how to combine them into a single cosine term?

Homework Statement Find a set of 3 exponents a, b, g such that the quantity [G]^a [h]^b [c]^g has dimensions of time. In other words: [T] = [G]^a [h]^b [c]^g (hint: you should get 3 algebraic equations in the 3 unknowns a, b, g which are not that hard to solve. Now determine the socalled...

(I know how to do this without the rotation matrices) Any suggestion would be much appreciated. Homework Statement Show that the relationship between the forces in the inertial (S') and non-inertial(S) reference frames, with a coordinate transformation given by \vec{r}=R \vec{r'}...

Homework Statement By considering the force-separation curve for two adjacent atoms in a solid, f(x), show that the Young’s modulus can be expressed on the microscopic scale as: Y = - \frac{1}{x_0} \frac{df}{dx}\right| |_{x=x_0} (the | is meant to go allt he way form the top to bottom of...

I'm curious as to the origin of the "1/2" in some of the basic equations in physics. For example, d=1/2at^{2}. If d=vt, and v=at, then d=at^{2}, yet in reality we need the "1/2". Why?

How to write "this per that" in mathematical terms? What is the mathematical equivalent of saying, for example, meters per second? If we want to say that something moves with the rate of 50 meters per 30 seconds--do we write this as a fraction or as an equation, or we can write as both? I...

Hi Guy's I am just starting out in topology and I was wondering if someone might know of a good link that may have venn diagrams of some important topological terms ie closure of A, int A, limit points etc. regards Brendan

Homework Statement bernouliis equaton P + 1/2 Rho v^2 + Rho g h = constant find the units of the three terms on the left hand side & show they are the same and then the units of the constant on the right The Attempt at a Solution all i can think to do here is check the SI units...

Homework Statement Question: Assuming that the frequency of vibration f, of a wire/string depends on the length l, tension T and mass per unit length m, establish a formula for f in terms of l, T and m.,f, l, T and m Homework EquationsDon"t know The Attempt at a Solutionnot tried yet can anyone...

Homework Statement Find the period T for a wave of wavelength (lambda) . Express the period in terms of pi, lambda , and g. Homework Equations T = lambda/velocity, lambda = velocity/frequency T= 1/frequency k (wave number) = 2pi/lambda V = Squareroot of (g/k) The Attempt at a...

Hi, I'm desperately searching for some literature which discusses the harmonic oscillator, preferably simple, in terms of the path integral formulation. I am unfamiliar with dirac notation and want something as simple as possible which gives general results of the harmonic oscillator in terms of...

Consider this equation: x^2 + 5 + 4x + 6 + 3x^2 + 3x = 0 We know that we can combine the like terms and write the above equation like this: 4x^2 + 7x + 11 = 0 Why were we able to combine the terms?

So, this is where I am stuck: ln\left(y\right)+y^{2} = \sin{x}+c_{0} I am confrused... :blushing:

I just need an explanation of this. Found it in a question. :smile: Also, photons when absorb by an electron in an atom, does the energy (if less than the ionisation energy) have to be exactly equivalent to one of the energy states and if it isn't what happens? You probably think I suck at...

can anyone tell me what space is, I know matter is energy and time is changes in the state of energy, so is space a static form of energy. I'd like someone to explain using simple terms if possible please.

Hi, I have a helium atom in the excited state of (1s,20p), and I am told that it has 4 corresponding atomic terms. I am supposed to "write down the quantum numbers of these 4 atomic terms". As I understand it, an atomic term is specified by the 2S+1LJ notation, where S is the spin quantum...

Iv'e scene the documentary about string theory and i just have a few questions about it.(laymen terms) : 1.How does string theory contribute to a unified field theory? 2.Is matter really made of "vibrationg strings"? 3.What does string theory actually mean or what has been the impact...

Homework Statement \frac { d^2 \theta }{d x'^2 } = -y *exp(\theta) eq. 1 mayb be integrated to yield exp(\theta) = \frac {a}{cosh^2(b \frac{+}{-} \sqrt \frac{a*y}{2} * x')} \theta = f(y,x') Homework Equations The Attempt at a Solution the exponent is throwing me off, but i probably...

Homework Statement f(t)= 4t t<1 f(t)= 4 t≥1 I need to write f(t) in terms of H(t) Homework Equations H(t-t0)=0 for t<t0 = 1 for t≥t0 The Attempt at a Solution I am not too sure how it is done, as what I read online, people can just immediately...

There are two blocks of equal mass M that hang from a massless, frictionless pulley. There is a small square block of mass m sitting on top of one of the blocks. When the block is released, it accelerates downward for a distance H until the block of mass m sitting on tip gets caught by a ring...

setting a sinusoidal voltage term, the ODE can be written as (d^2 i)/(d t^2 ) + 25i = A0 sin (ϖt) assuming that ϖ^2 ≠ 25, determine the current i in terms of the parameters (ϖ and A0) and the variable t when the initial conditions are i(0) = di/dt (0) = 0 i really don't have much of...

can someone tell me what to read in "layman " terms ,the main differences between quantum theory and relativity?

Explain the difference for each of the following pairs of actions in terms of impulses; (a) A golfer's long drive and a short chip shot; (b) a boxer's jab and a knock-out punches; (c) a baseball player's bunting action and a homerun swing

Homework Statement f(x) = \frac{ln(3x)}{6x}, a = \frac{1}{3}, n=3 Find T3 Homework Equations Taylor Series - f(n)(x)/n! * (x-a)^n The Attempt at a Solution So, I isolated ln(3x) from 1/6x. I created the series based off of ln(3x). f(0)(x)=ln(3x) ->f(0)(1/3)=ln(3(1/3)) =0...

Assume a raindrop falls from the clouds and the mass increases as it falls and the increase in mass is 3kg/m. Neglecting any frictional force, find the acceleration in terms of velocity and displacement. Initially when t=0 assume mass is negligible. I just want to ask if we were to neglect...

Homework Statement A sphere of radius R, centered at the origin, carries charge density ρ(r,θ) = (kR/r2)(R - 2r)sinθ, where k is a constant, and r, θ are the usual spherical coordinates. Find the approximate potential for points on the z axis, far from the sphere. Homework Equations...

whether or not it is shrinking or expanding the origin and how long the universe has existed and whether or not there is more than one universe ?

Homework Statement The roots of x^2 + bx + c = 0 are r_1 and r_2, where |r_1 - r_2| = 1. Express c in terms of b. Homework Equations x^2 + bx + c = 0 |r_1 - r_2| = 1 The Attempt at a Solution Im not even sure where to start with this problem, and i don't see how the roots...

Homework Statement A speciality coffee shop sells Cuban coffee beans for $5.50 each bag and Colombian coffee beans for $3.80 a package. 1.If the cost of sales is $1450 plus $0.95 per bag, write down the function which calculates the profit in terms of the number of bags of coffee beans sold...

Homework Statement A toy rocket consists of a plastic bottle which is partially filled with water. the space above the water contains compressed air. At one instant during the flight of the rocket, water is of density\rho is forced through the nozzle of radius r at speed v relative to the...