Expression Definition and 999 Threads

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 [FONT=Helvetica] 3^3 * 3^( i8pi/ln(3) ) = 27 * (3^ i8pi - 3^ln(3) ) = 27 *( 3^25.1i -3.34) [FONT=Helvetica]= 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

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 Verify that the indicated expression is an implicit solution of the given first-order differential equation. Find at least one explicit solution y=∅(x) in each case.Homework Equations \frac{dX}{dt}=(X-1)(1-2X); ln(\frac{2X-1}{X-1})=t The Attempt at a Solution I know I need...

Homework Statement I've come across the type of sum in several places/problems but seem to be making no progress in trying to simplifying it further. We have a finite series of some exponential function. \sum_{n=0}^{N}e^{-na} Where a is some constant, a quantum of energy or a...

Hi all! I'm studying electrical generators, and while I was trying to come up to the expression of EMF induced in a conductor I got two different results following two different ways, and I can't find the error. With sinusoidal B, with e=bvl I get an RMS value E=2K_{f}f\phi, while with...

Homework Statement <Indefinite integral sign here>[r^2 -2r] / [r^3 - 3r^2 + 1]dr or the second example in the "Substitution" section here: http://people.clarkson.edu/~sfulton/ma132/parfrac.pdf Homework Equations nada. The Attempt at a Solution Nothing to really attempt, I just...

Find expression for event "exactly one of A,B,C occurs" Homework Statement Let A,B,C \in F be three arbitrary events. F is a σ-algebra. Find an expression for the event "exactly one of A,B,C occurs". The Attempt at a Solution Define i,j,k s.t. i,j,k \in \{1,2,3\} \wedge i \not= j \not=k...

Homework Statement I am trying to solve the following two systems of equations and at every attempt I get completely stuck. x2 + y2 = 1 -x + √3y = 0Homework Equations not applicableThe Attempt at a Solution the answers have already been given to me but I have no idea how to get the answers...

Homework Statement I am trying to find when the square root of the expression 25+8a^2 is rational, where the number a also needs to be rational. \sqrt{25+8a^2}=b, where a and b are both rational numbers. I am trying to get an expression for a in terms of some other number m, which would always...

Good Day, I need some help with the following problem. I do not know how to generate a linear equation connecting y and x from the expression below as the 4 seems to complicate things \(3^y = 4(3^{x-2}) - 1\) Could some one please care to give me some advice? Thanks in advance.

Can anyone help me simplify the expression \frac{\delta g_{\mu\nu}}{\delta g^{\kappa\lambda}}? I haven't seen a term like this before and I don't know how to proceed. It seems like it might be the product of some kronecker delta's but I'm not sure.

1. The problem statement. AC voltage is expressed as 240 cos(2765t - 45°). Im trying to find the: Peak Voltage: RMS Voltage: Average Voltage: Peak-to-Peak Voltage: The Attempt at a Solution Peak Voltage: 240v RMS Voltage: 170v Average Voltage: 0v Peak-to-Peak Voltage: 480v...

\frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2}(\frac{x - 3}{x - 2})^{-\frac{1}{2}} \cdot \frac{1}{(x - 2)^{2}} \frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2}(\frac{x - 3}{x - 2})^{-\frac{1}{2}} \cdot \frac{1}{(x - 2)^{2}} \\ \frac{1}{(\frac{x - 3}{x -...

Homework Statement ~AB+AB~c+ABC Homework Equations AB+A~B=A [b]3. The attempt at solution ~AB+A A+B

Homework Statement Given successive terms of numbers starting from the 1st term: 11, 21, 35, 53, 75, 101,... What is the general expression of the nth term? where n is positive integer Homework Equations /The Attempt at a Solution Can't find a good attempt.

I have to simplify (or get it in terms of tan I guess?) \cot (\frac{2\pi }{3} - x) I'm not sure how to get the reference angle and subtract the angle 'x' from it to get an expressional value...how would I do this?

Simplify (x+3)1/2 - (x+3)3/2 i honestly am so lost on this one how i approached it was (x+3)1/2 [1 - ((x+3)3/2 / (x+3)1/2)] but again, i have no idea what I'm doing.

Hii Every one, In one paper I read that, {\displaystyle \sum_{j\geq1}\left(\frac{c*m*logm}{2^{\left(\frac{j-1}{2}\right)}}\right)}^{j}<=m^{o(logm)} with the explanation "Since the sum is of the same order as its largest term". c>0, m>=2. m is an integer. Can anyone pls...

Hii Everyone, Plz tell me a tight upperbound for \frac{x}{1-x\left(1-y\right)} where o<=x,y<=1 regards, Bincy