Expression Definition and 999 Threads

http://img138.imageshack.us/img138/7113/conewithflattip.png Help needed, I need an expression of the figure in the picture, it is like a conic but the tip is not a point but a short 1D segment (it s not a truncated conic), I accept anything ;-) skewed Conics, Sperical Harmonics approx, cubic...

Homework Statement Dear all I have a question concerning the Coriolis acceleration expression. I learned it as Ac = -2ω x v, where ω is the vector which indicates the rotation axis direction of Earth and v the velocity of a body that I want to check the Coriolis effect on. My...

Homework Statement Show that the following expression is true: 0.2*0.8 = -14dB + (-1.94dB) Homework Equations 1 dB = 10log10(x) (where x is a ratio of two quantities) 10log10(ab) = 10log10(a) + 10log10(b) The Attempt at a Solution 0.2*0.8 = -14dB + (-1.94dB) 0.16...

Homework Statement Homework Equations work = kqqq/(distance) The Attempt at a Solution http://i33.photobucket.com/albums/d86/warnexus/electrodiag.jpg

Hi, I have the next expression: \frac{iw+3}{(iw-3)(iw+6)(iw+1)} Now I want to find the real part of this expression via mathematica or maple, and for the love of god it doesn't work, what have I done wrong here?! the codes and their errors are in the attachments...

Homework Statement A quasi-3 level solid-state laser gain medium consists of a ground state manifold containing two energy levels within which a single electron can be promoted, with the second energy 10meV above that of the lowest level. A. Where the gain medium is not optically pumped...

Homework Statement Express the function f(x) = -2sin(3x) -4cos(3x) in the form of a general sine finction. Identify the amplitude, period, and phase shift Homework Equations sinx/cosx = tanx sin2x + cos2x = 1 The Attempt at a Solution don't know how to start don't...

I am trying to solve a problem that includes a function of the light hitting a certain area. My question is, how would I change a function G(x) of photons hitting a certain area to include just photons of a certain wavelength, say red light. I feel like this could be accomplished using a Fourier...

Hello, This is not a homework exercise, so I decided to post it here. Hopefully one of you could help. I would like to find an explicit expression for (I-A)^(-1), provided that A is a squared matrix (nxn) and A^k = 0. It is also given that I-A^k = (I-A)(I+A+A^2+...+A^(k-1)). I understand that by...

Can somebody check if I answer them right? Write the dual of the following boolean expressions: 1.x’(y+ z’)+z = x'+(yz')+z 2.x(y+ z)’y’ = x+(y'z')+y' 3.xy+ y’z’+xz = (x+y)(y+z)'(x+z)

Hello, I am supposed to find an expression for the general stress wrt height within a truncated cone of lower and upper radii a and b (a>b), pulled down from its vertical axis by a force of the same magnitude as that pulling it up. The diagram implies that the height between the upper and lower...

The "cosmological" proper distance from the origin, D(t), to an object at radial co-ordinate r at cosmological time t is given by D(t) = a(t) r(t) The corresponding "cosmological" proper velocity v of the object is given by v = \frac{dD}{dt} = \frac{da}{dt} r(t) + a(t) \frac{dr}{dt} Using...

$$ \cos[k_n(L-\varepsilon)]-\cos k_nL $$ I just read this for small epsilon this result can be further simplied by using the trigonometric identity for $\cos[k_n(L-\varepsilon)]$. Doing so result is $$ 2\sin k_nL $$ I don't see this? Can someone explain?

Homework Statement Simplify the following expression: \sum_{ \alpha_1 + \cdots + \alpha_n = k} e^{i(\alpha_1 \theta_1 + \cdots + \alpha_n \theta_n)} Homework Equations \alpha_n = k - \sum_{j=1}^{n-1} \alpha_j 0 = \sum_{j=1}^{n} \theta_j The Attempt at a Solution I am trying to simplify...

Homework Statement Are there any positive integers n, a and b such that 96n+88=a^2+b^2 Homework Equations The Attempt at a Solution It resembles the Pythagorean theorem but I'm not sure how that would help me solve it. I factored the LHS 2^3((2^2)(3)n+11)=a^2+b^2 How do I...

Homework Statement Differentiate V0 - iR - q/C = 0 to prove that di/dt = -i/RC. Homework Equations V0 - iR - q/C = 0 ^ derived from previous question for a circuit that had one battery with emf V0, a resistor of resistance R and a capacitor of capacitance C (all in series). di/dt =...

Homework Statement If x=2+2^{2/3}+2^{1/3}, then the value of x^3-6x^2+6x is Homework Equations The Attempt at a Solution The very first idea that comes to my mind is to substitute the value of x in the given expression. But that gets very complicated and long as well. Any other ideas?

I need to know how to identify the expression for the constant term in a power relationship. The power relationship is a relationship I imagined on a graph. On the graph both the values on the x and y axis's would be increasing. The power relationship is between square of rotational frequency...

error in defined expression for Fresnel equation in MATLAB (urgent please )?? hi i have code for plotting Fresnel equation but there's something i didn't understand it and gives error >>((( plotopt - plotting option (type 'R' for plotting reflectivity, % 'A' for absorptivity or 'RA'...

(3/x-2) - (4/x+2) / (7/x2-4) I got it down to... -x+14/7 but the book is showing x-14/7

I was wondering, if it is possible to obtain somehow a solution expressed with elementary functions from an equation, which is in non closed-form at first sight. For istance let us consider an implicit function F(x,y)=0 with Fx(0,0)≠0, which can't be explicitly solved for y. Nevertheless...

The answer is a number... Work done so far 3^3 * 3^( i8pi/ln(3) ) = 27 * (3^ i8pi - 3^ln(3) ) = 27 *( 3^25.1i -3.34) = 3^(3+ i25.1) - 90.26 If this is correct how can I convert this to a number...

Hello, Is there a better way to find n such that for every n>n0 |sqrt(n^2+3)-sqrt(n^2-1)|<ε? I have tried reformulating the expression on the left side so that only one of the square roots remains, to not much avail. The only way I could solve it was by squaring both sides. I did get the...

$t\vec{a}$ and $\vec{b}$ where t is a scalar times the vector a. How can I make $\vec{b-ta}$ look right? Solved $$ \overrightarrow{b-ta} $$

Homework Statement (a) A block with a mass m is pulled along a horizontal surface for a distance x by a constant force vector F at an angle θ with respect to the horizontal. The coefficient of kinetic friction between block and table is μk. Is the force exerted by friction equal to μkmg...

Hello, I have a problem to understand how the author made the following expansion: 1/sqrt{1+[2(r-r')*d]/(r-r')^2}≈1-{[(r-r')*d]/(r-r')^2+...} where all the letters go for vectors and the symbol '*' is the dot product. I suppose it is a Taylor expansion, but i just don't get it in...

I have conceptualized a method for generating serial binary data at rates varying randomly. This concept should be able to provide data at random rates with various characteristics.The most relevant application is generation of Random sensor data for testing C4I systems (Surveillance and...

Hi! In this paper: http://www.atm.ox.ac.uk/user/read/mechanics/LA-notes.pdf On the bottom of page no. 25 there is written, that: \int δWdt=-\int δVdt. Why is that? Can anyone explain into me? Thanks in advance.

Well, this is a task for those who prepares to enter a university. According to the textbook this task is among the easiest ones. I managed to simplify this part of the (4b^4 + 4ab^2+a^2):(2b^2 + a) = 2b^2 + a. Well, I can't proceed any further. Could you give me a hint?

I have attached the problem and my working. It would be much appreciated if someone could check through my working and let me know if I have slipped up anywhere. Thanks in advance Steve

Homework Statement If |z|=1 and |ω-1|=1, where z, ω \in C, then find the range of |2z-1|^{2}+|2ω-1|^{2}. Homework Equations The Attempt at a Solution Since |ω-1|=1 Squaring both sides and simplifying |ω|^{2}=ω+\overline{ω} Also simplifying the expression given in the question...

Homework Statement This question stems from this one: https://www.physicsforums.com/showthread.php?t=642712 I think I know how to solve it now. The only problem is I have to show how to factor this expression into the form WolframAlpha shows. -a^2 b + a b^2 + a^2 c - b^2 c - a c^2 + b...

Homework Statement \frac{x^2}{(x^2 -1)} Homework Equations N/A The Attempt at a Solution I know the solution is supposed to be 1+\frac{1}{2(x-1)}-\frac{1}{2(x+1)} and when I did long division, I got 1+\frac{1}{(x^2-1)} , so I'm making progress, but I'm not quite there. What should...

Hello everybody, I am trying to solve this problem but I can't find an answer reading my book :( Let z=F(u,w,x) where u=f(x,y) and w=g(x,y) (i) find a general expression for Dxz (ii) verify your answer in the case where F(u,w,x)=w3-2ux, f(x,y)=4xy-x+1 and g(x,y)=y+xy2 Many thanks

Homework Statement Here is the question: http://i1110.photobucket.com/albums/h459/granolup/Untitled.png It is assumed that the blocks are not moving. Homework Equations F=ma N=mg friction = umg The Attempt at a Solution I have started out drawing free-body diagrams for each...

Write the expression for the infinitesimal radial inertal force dfr "look at pic" Consider the non-uniform rigid disc of Figure 1. The density of the material is variable and depends on the radial position: p = p (r). Its analytical expression is p=po+p(1) and where Po and P(1) are known and...

I do not have access to the math calculators. Δ = 162*(a-b)*(a^2-b^2)*(a^3-b^3) -108*(a^3-b^3)*(a-b)^3 + 81*(a-b)^2*(a^2-b^2)^2 - 108*(a^2-b^2)^3 - 27*(a^3-b^3)^2 thanks

Homework Statement Simplify the following boolean expression: Homework Equations B'D' + A + BD + AD + B'C'D' + B'C + CD The Attempt at a Solution --line 1-- A(1+D') + B'D' + BD + B'C'D' + B'C + CD --line 2-- A + B'D' + BD + B'C'D' + B'C + CD --line 3-- A + B'(D' + C'D' +...

I have: Y_l^m= Ne^{im\varphi}P_l^m(cos\theta) where P_l^m(cos\theta) is the associated legendre polynomials: P_l^m(cos\theta)=(-1)^m(sin\theta)^m(\frac{d^m}{d (cos\theta)^m}) The problem is that i want to use this expression to apply on it the creation operator for the orbital angular...

Homework Statement Find the limit (without using L'Hospital's rule) \lim_{x\to 0} \frac{ln(1 + sin^2x)}{e^{2x} - 1} Homework Equations The Attempt at a Solution I tried various substitutions in order to rewrite the expression to a standard limit. Such as t = e^x, t = ln(x), t =...

Homework Statement Suppose P(x) is a statement with a free variable x. Find a formula, using logical symbols, that means "there are exactly two values of x for which P(x) is true." Homework Equations The Attempt at a Solution (∃x)(∃y)(∀z)(P(x) ∧ P(y) ∧ P(z) → ( x=z ∨ y=z) ∧...

Homework Statement (A.∇)B What does this mean and how do I go about trying to expand this (using cartesian components)?

Homework Statement 2n Ʃ (k) k=1 The Attempt at a Solution 2n Ʃ (k) = 2n(2n+1)/2 (This is just a shot in the dark.) k=1

Homework Statement The inversion of cane sugar proceeds with a constant half life of 500 minute at pH=5 for any concentration of sugar. When pH is changed to 4, the half life becomes 50 minutes. Deduce the rate law expression for inversion of sugar. Homework Equations t_{1/2}*a^{n-1} is...

A text I am reading displays the attached image. Can someone explain the general method for obtaining the velocity analogues of those terms (in parentheses) in 1.5? I know the second and third terms in parentheses in 1.6 and 1.7 are the squares of angular velocities, but can a general procedure...

Homework Statement FIGURE P27.43 shows a thin rod of length L with total charge Q. Find an expression for the electric field at distance x from the rod. Give your answer in component form. Homework Equations Equation for an electric field: E= \frac{KQ}{r^2} The Attempt at a...

I have a problem taking the log of this expression \prod_{i=1}^m[\frac{1}{\sqrt{2\pi v}}\exp{(\frac{-u_{i}^2}{2v_{i}})}] Now I would get \ln({\frac{1}{\sqrt{2\pi v}}})(\sum_{i=1}^m{\frac{-u_{i}^2}{v_{i}}}) The author gets, by ignoring the constant multiplicative factors, \sum_{i=1}^m...

I was trying a while ago to prove associativity of the XOR operator. That led me to the following problem: I am trying to prove \overline{(\overline{A}*B+\overline{B}*A)}*B + \overline{B}*(\overline{A}*B+\overline{B}*A) = B Obviously it can be solved by just creating a truth table...

Homework Statement Evaluate the following expression: \sum_{j}\sum_{k}\epsilon_{ijk}\delta_{jk} Homework Equations \delta_{ij} = [i = j]The Attempt at a Solution I don't have a solution attempt to this one yet, because somehow I completely missed out on what the permutation thing has to do...

Homework Statement Evaluate the following expression: \sum_{j}\sum_{k}\epsilon_{ijk}\delta_{jk} Homework Equations \delta_{ij} = [i = j] The Attempt at a Solution I don't have a solution attempt to this one yet, because somehow I completely missed out on what the permutation thing...