Expression Definition and 999 Threads

1. Simplify the derivative 2. y = \frac{\sqrt{1-x^{2}}}{x} 3. f'(x) = \frac{x*\frac{-2x}{2\sqrt{1-x^{2}}}-\sqrt{1-x^{2}}}{x^{2}}=\frac{-x^{2}-\sqrt{1-x^{2}}}{x^{2}\sqrt{1-x^{2}}} I just don't know how to simplify this further.

Find the minimum value of $$|\sin x+\cos x+\tan x+\cot x+\sec x+\csc x|$$ for all real numbers $$x$$.

Hey, guys How can the following equation be entered into matlab: http://i074.radikal.ru/1304/fe/a8b8e0fccbe5.png Thakns.

Simplify $$\frac{x^2-4x+3+(x+1)\sqrt{x^2-9}}{x^2+4x+3+(x-1)\sqrt{x^2-9}}$$ where $$x>3$$.

The awkward expression 1 km/s per Mpc--the radius is better It's been pointed out that by historical accident we've been stuck with an awkward mix of units conventionally used to express Hubble parameter. If you parse the quantities km/s per Mpc you find that the length units cancel and you...

hi , how i can demonstrate the expression of metric kerr?

Suppose I have a particle on a line, and I know some function a(x) and the initial x, v, and a. How could I work out x(t)?

Homework Statement Write an expression for the force applied to the brake caliper in the braking system(hydraulic) of a bicycle. F= force applied to the brake lever a = distance between F and the pivot point of the brake lever. b= distance between pivot point and lever piston. d1= diameter of...

Find [FONT=MathJax_Math]$$x$$ such that trigonometric $$\dfrac{\sin (3x) \cos (60^{\circ}-x)+1}{\sin (60^{\circ}-7x)-\cos (30^{\circ}+x)+m}=0$$ where $$m$$ is a fixed real number. Hi all, I know the expression in the numerator has no real roots by checking it at W|A (plot the graph of...

Could someone please help me make this expression a little smaller? I'm sure there are things that cancels out or could be re written, but I generally suck at these things as I tend to break a few math rules along the way. Could I for instance cancel n against n in the two last cosine...

Homework Statement Simplify the following trigonometric expression: cscθtanθsecθ Homework Equations tanθ = sinθ/cosθ sin^2θ + cos^2θ = 1 cscθ = 1/sinθ secθ = 1/cosθ cotθ = 1/tanθ The Attempt at a Solution I just want to double check my solution. cscθtanθsecθ = 1/sinθ x...

Given that the equation $ax^3-x^2+ax-b=0$, ($a\neq 0,\,b\neq 0$) has three positive real roots. Determine the greatest value of the following expression: $$P=\frac{11a^2-3\sqrt3ab-\frac{1}{3}}{9b-10\left ( \sqrt3a-1 \right )}$$

Hi, I'm trying to figure out a few questions on a practice exam that I'm working on for my Intro to Logic Systems class and could use some help. One of the questions (and the others are similar) says: Determine the minimized realization in the sum-of-produicts form using literals of the...

[Java] Can't figure out this "Illegal start of expression" error From my Java code: [FONT="Courier New"]while (info.substring(j, j)) != " ") { name += info.substring(j, j); j++; } gives an "illegal start of expression" error

Hi. If I could get some clarification on the attached circuits that would be great. The question asks to find the boolean expression for C. I already know the answers, but I don't quite see how they got it. For the first circuit: C=A_bar The truth table looks like this: A C 0 1 1 0...

Problem: Prove that $27195^8-10887^8+10152^8$ is divisible by $26460$. Attempt: I grouped the last two terms and manipulated them algebraically and came to the point where I suspect I might have taken the wrong path...here is the last step where I stopped and don't know how to proceed...

What identity I need to use for simplifying this trig expression into one expression?$cos(3x)+4hcos(x)$ where h is a constant. Thank you for your help. Can you explain, too?

Greetings, I recently discovered Mathematica's Format function, and it has been of great use to me. However, there is one thing that I want to use it to do, that I have yet to be able to. I could do this easily, though, if there is some Mathematica function that works as follows... If I put a...

Hello ! I have an upper triangular matrix for an operator T in which an eigen value has been repeated s times in total. Derive an expression for s . My thoughts : ( Let * imply contained in ) then :I know that : (a) Null T0 * Null T1 *...*Null Tdim V = Null Tdim V + 1 = ... (b) Will i...

Homework Statement I need to derive an expression for the displacement of light as a function of thickness of glass and the angles. I will post a screen shot of the formula to be derived but it can also be found here...

a=4,b=3 and c=-2 5ab/12-2cb:confused:

Evaluate the variable expression when a=3,b=1 and c=-2 b^2-4ac. This is new to me so please explain how to do this.

Homework Statement Which of the following is a correct expression for ∫1t(s-1)y'(s) ds I know the answer is: a) 1/2(t-1)2y(t) b) 1/2(t-1)2y'(t)+ (t-1)(y(t)-y(1)) c) (t-1)(y(t)-y(1)) d) (t-1)y(t)-∫y(s) ds Homework Equations The Attempt at a Solution I know the...

Homework Statement Claim: If n is a positive integer, the prime factorization of 22n * 3n - 1 includes 11 as one of the prime factors. Homework Equations Factor Theorem: a polynomial f(x) has a factor (x-k) iff f(k)=0.The Attempt at a Solution First, we show that (x-1) is a factor of (xn-1)...

Suppose that $U$ is open in $\mathbb{R}^{m}$, that $L\in U$ and that $h:U\setminus \left \{ L \right \}\rightarrow \mathbb{R}^{p}$ for some $p\in N$. If $L=\lim_{x\rightarrow a}g(x)$ and $M=\lim_{y\rightarrow L}h(y)$. Then $\lim_{x\rightarrow a}(h\circ g)(x)=M$. (Someone told me that this...

Homework Statement Write the vector expression for the acceleration a of the mass center G of the simple pendulum in both n-t and x-y coordinates for the instant when θ = 66° if θ'= 2.22 rad/sec and θ"= 4.475 rad/sec2 I have attached an image of the question. Homework Equations an =...

Homework Statement ABC'D + A'BD + ABCD The Attempt at a Solution Here is as far as I have gotten: BD (AC' + A' + AC) BD (AC' + A') According to Wolfram Alpha, the answer should just be BD. Can someone help me get there?

I saw someone write this: dW=Pd2V I think this doesn't make any sense mathematically; but I wanted to check. Is this mathematically meaningful at all? This I understand: dW=PdV W=∫PdV But for dW=Pd2V I cannot see how one could proceed. Here V is an independent variable; P=f(V).

Homework Statement Write an expression for the voltage across R3 in terms of V0, R1, R2, and R3. Under what condition is the voltage across R3 approximately independent of the value of R3? Homework Equations I uploaded a picture. I think Req = R1 + R2... and 1/Req = 1/R1 + 1/R2...

Work done by a gas (consider ideal for simplicity) is given by = = -pressure(external) . Change in volume Why is external pressure considered here? Take for example a closed vessel with weight on apiston having gas enclosed with 200 atm pressure, if the weight is suddenly removed the gas...

Hi guys I'm trying to find out the nature of this serie \sum_{n=1}^{\infty}\left[ e^{1/n}-e^{-1/n}\right] I know the ratio and root tests are inconclusive, just the comparision test works (it diverges) But with which expression shall I compare? Thank you so much

Hello Everyone, I am after an expression for the torsion stiffness constant of a rectangular hollow section (RHS) with varying wall thickness. I have done some research into finding an expression that allows for four varying wall thicknesses but have not found anything as of yet. The only...

Dear Physics Forums denizens, I have a tricky problem that I hope one of you can help me with. (It's for a personal project, nothing to do with school.) I'm looking for a closed-form expression for the sum of the first through m-th terms of a combinatorial number. For those of you...

Homework Statement I did two attempts. I find attempt no. 1 slightly fishy and attempt 2 more rigorous. Can anyone tell me what's wrong with attempt no. 1? The Attempt at a Solution Attempt no. 1: Attempt no. 2:

Hi all, I am working with some beta functions. I want to show that the following is positive and bounded between 0 and 1. Is it possible to show this? $$ \frac{ \frac{B( a + b , \frac{2}{ c} )}{B(a, \frac{2}{c}) } - \big\{\frac{B( a + b , \frac{1}{ c} )}{B(a, \frac{1}{c}) }\big\}^{2} }{...

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...