Expression Definition and 999 Threads

This problem probably should be easy, but I don't remember learning the basic way to do these problems: Write the trigonometric expression as an algebraic expression: cos(arccos x + arcsin x) The answer is zero, but I don't know how to get there...

Homework Statement An electron in a one-dimensional box with walls at x =(o,a) is in the quantum state psi = A o<x<a/2 psi = -A a/2<x<a A) obtain an expression for the normalization constant, A. B) What is the lowest energy of the electron that will be measured in this state...

Hi, I've completed an experiment in which I measured the height of the water in the tank with time. I plotted my results on graph paper as a graph of height against time, resulting in a curve of decreasing gradient, slightly resembling that of the e^(-kx) graph. 1) I am asked to symbolically...

Good evening. Is there a way to take a decimal approximation and see if there is a relatively simple expression? I'm guessing there might be software for this, but I'm not sure I'm even asking the appropriate question. If it matters, the number I'm after is...

Homework Statement A long, straight wire, radius R, carries total current I. The current is distributed in the wire so that the current density is proportional to s, the distance from the center of the wire. (a) Write an expression for the current density J in the wire, as a function of s...

Homework Statement I have the following task: Homework EquationsThe Attempt at a Solution But I don't understand how to solve it. Can somebody help me?[/B]

Find the maximum and minimum of $x^3+y^3+xy(x^2+y^2)$ given $x,\,y$ are two non-negative real numbers that satisfy $x+y+xy=3$.

$ \left( \vec{r} - \vec{a} \right). \vec{r} = 0 $ Please check this: Then, $ r^2 - a.r = 0 $, then $ \left( r - \frac{a}{2} \right)^2 - \left(\frac{a}{2}\right)^2 = 0 $, then $ \left( x - \frac{a}{2}\right)^2 + \left(y - \frac{a}{2}\right)^2 + \left( z - \frac{a}{2}\right)^2 =...

The vector r, starting at the origin, terminates at and specifies the point in space (x, y, z). A surface is swept out by the tip of r if $ (\vec{r} −\vec{a}) · \vec{a} = 0 $. $\vec{a}$ is a constant vector... 1) I tried $ (r - a).a = 0, \therefore r.a = a^2$, but still can't 'see' what shape...

Homework Statement In your design of an experimental spring powered model car, you note that the speed of the car (mass Mc) increases as the car travels further. The exact relationship is that v(x) = C|x|, where C is a constant and x is the position of the car with respect to the starting...

Find a closed-form expression for $f(n)$ where $f(n)=1+n+n(n-1)+n(n-1)(n-2)+...+n(n-1)\cdots2$ for $n>1$ and $f(1)=1$. (So, $f(2)=1+2=3$ $f(3)=1+3+3\cdot 2=10$ $f(4)=1+4+4\cdot 3+4\cdot 3\cdot 2=41$ and so on.)

Can someone please show me, step-by-step, how cos(θ)sin(θ+φ)-sinθcos(θ+φ) simplifies to sinφ? I know I have to use trig identities, and I got to cos2θsinφ-sin2θcosφ but I'm not sure where to go from there. Thanks

Homework Statement Homework Equations The picture is all we know about the entire system, we need to derive an expression for the acceleration of ramp M. There is no friction anywhere. The ramp is free to move on the surface beneath it. The Attempt at a Solution I drew the free body...

Homework Statement AC'D+ AB'D + BCD' + A'BC 2. Homework Equations The Attempt at a Solution Would I start by inverting all the inputs? Would there be 3 Or's to this? I get from the truth table, to simplifying expressions with k-map, but I don't know how to turn it into a circuit. Can someone...

I was trying to compute the time derivative of the following expression: \mathbf{p_k} = \sum_i e_{ki}\sum_{n=0}^{\infty} \frac{(-1)^n}{(n+1)!} \mathbf{r_{ki}}(\mathbf{r_{ki}\cdot \nabla})^n \delta(\mathbf{R_k}-\mathbf{R}) I am following deGroot in his Foundations of Electrodynamics. He says...

$$\lim_{{x}\to{\infty}}\frac{\sqrt{3x^2 - 1 }}{x-1}=\sqrt{3}$$ I tried dividing everything by ${x}^{2}$ but not

Homework Statement Simplify (1/3 + 1/3y)/(1/y + 1/3) Homework Equations (1/3 + 1/3y)/(1/y + 1/3) = x In this case I am using x to represent the simplified expression The Attempt at a Solution (1/3 + 1/3 * 1/y)/(1/y+1/3) = (2/3 * 1/y)/(1/y + 1/3) = (2/3y)/(1/y+1/3) = (2/3y)/(3/3y + y/3y) =...

Homework Statement [/B] The total force on a moving charge q with velocity v is given by \mathbf{F}=q(\mathbf{E}+\mathbf{v}\times\mathbf{B}) Using the scalar and vector potentials, show that \mathbf{F}=q[-\nabla\phi-\frac{d\mathbf{A}}{dt}+\nabla(\mathbf{A}\cdot\mathbf{v})]Homework Equations...

OK. First of all, I'm novice at Physics so this question may be weird. Above, there are 2 expressions for strain-stress relations. Let's assume that all components in the matrix are variables, not zero, not E, nor not G in the first picture. The first one is written in 2D matrix form, whereas...

To find the horizontal asymptotes of a rational function, we find the limit as x goes to infinity. Given the rational function ##\displaystyle\frac{x + 1}{\sqrt{x^2+1}}##, we can find the limit by multiplying the numerator and the denominator by ##\frac{1}{x}##. This gives us ##\frac{1 +...

Given that we have the expression ##\displaystyle-\frac{1}{(x-2)(x-2)(x-3)}~\cdot~\sqrt{\frac{(x-2)^{2}}{(x-3)(x-1)}} ##, how do we simplify it, step by step? Specifically, I am concerned about the ##\sqrt{(x-2)^{2}}## term. Are we allowed to cancel this with the ##(x-2)## in the denominator?

Initially the expression A has 8 terms. So how is it reduced in the second line to 5 terms? Could you show me, please? Thank you. \begin{align*} A&=10^{28} -10^{22} +61\times10^{14}+12\times10^{21}-12\times10^{15}+3\times10^{9}-36\times10^{8}+9\times10^{2}\\ &=10^{28}...

The rational numbers $a,\,b,\,c$ (for which $a+bc$, $b+ac$ and $a+b$ are all non-zero) satisfy the equality $\dfrac{1}{a+bc} =\dfrac{1}{a+b}-\dfrac{1}{b+ac}$. Prove that $\sqrt{(c−3)(c+1)}$ is rational.

##m*\frac{G*16*π*ρ*ω}{c^2}*\int_{a_0}^{a_{1}}(da*a*\int_{y}^{H+y} (\int_0^R (\int_0^{2*π} (\frac{(r-a*Cos(α))*r^2}{(a^2+r^2+h^2-2*r(a*Cos(α)))^{3/2}}* dα)dr)dh))## This equation is related with this post https://www.physicsforums.com/threads/gravitomagnetic-experiment.824048/. It where helpful...

$$\frac{\cot^3\left({y}\right)-\tan^3\left({y}\right)} {\sec^2\left({y}\right)+\cot^2\left({y}\right)} =2\cot\left({2y}\right)$$ I tried the LHS but could get it to reduce.

I would want to change this expression to another one that would have P easily accessible. \frac{\left \lceil (n+1)^{P} \right \rceil}{\left \lceil n^{P} \right \rceil} As an example of 'accessible'; given (n+1)^P / n^P, I can make P more accessible by using log(). Then it becomes P *...

I need to show that the following expression, $$a^3b-a^3c+a^3z+a^3x+a^3y-a^2bx+a^2by+a^2cx-a^2cy-a^2zx+a^2zy-a^2x^2+a^2y^2-abcz-abcx-aczx-acx^2+b^2c^2+2bc^2x+c^2x^2-b^2c-2bcx-cx^2,$$ is positive given that: $1.$ $\ a,b,c,x,y,z$ are positive real numbers $2. \ \ a>b+x$ $3. \ \ c<b+y$ I...

Hello! I have in my notes an expression for the sheet resistance of a uniform conductor with length L, width W = L and thickness t. It is R_{\square} = \displaystyle \frac{\sqrt{\displaystyle \frac{\pi f \mu}{\sigma}}}{1 - e^{-t/\delta}} = \displaystyle \frac{1}{\sigma \delta} \frac{1}{1 -...

Homework Statement Getting an expression for the convective heat tarnsfer coefficient. Homework Equations See attached images The Attempt at a Solution I have been reading about the boundary layers. Here is an extract of my notes corresponding to thermal boundary layer and consequently my...

Say I want to find ##\delta \bigg( \sqrt{- \eta_{\mu \nu} \frac{dx^{\mu}}{d \tau} \frac{dx^{\nu}}{d \tau}} \bigg)##. Is the following alright: ##\delta \bigg( \sqrt{- \eta_{\mu \nu}} \bigg( \frac{dx^{\mu}}{d \tau} \bigg)^{-1/2} \bigg( \frac{dx^{\nu}}{d \tau} \bigg)^{1/2} \bigg)##?

A friend and I have been working on this problem for hours - how can the following expression be simplified analytically? It equals $\frac{1}{2},$ and we have tried the following to no avail: 1. Substitution of $x = \sqrt{5}$ 2. Substitution of $x = 2\sqrt{5}$ 3. Substitution of $x =...

Hello Forum, I am new to C programming and I have a few questions about the main() function. The main function does not take any arguments (nothing written between the round parentheses): main() or even main(void) . I have also seen the expression void main. Is that the same as main(void)...

Homework Statement I'm trying to find Arc Length of F(x) = (e^x + e^-x)/2 0< x < 2]Homework Equations L = integrate sqrt ( 1 + (dy/dx))^2)The Attempt at a Solution (dy/dx)^2 + 1 = 1/4e^2x + 1/4e^-2x + 1/2] I don't know how to take the square root of the above function so I can be able...

Homework Statement I am trying to show that ##a(x)[u(x),D^{3}]=-au_{xxx}-3au_{xx}D-3au_{x}D^{2}##, where ##D=d/dx##, ##D^{2}=d^{2}/dx^{2} ## etc.Homework Equations [/B] I have the known results : ##[D,u]=u_{x}## ##[D^{2},u]=u_{xx}+2u_{x}D## The property: ##[A,BC]=[A,B]C+B[A,C] ##*The...

I've come across an expression that looks like n(k) = ∫cos(x-y)f(x,y)dxdy Is there a name for this transform? I would like to invert it to obtain f(x,y) but I'm not used to the 2D integral on the RHS. I tried to turn it into a Fourier transform: n(k) = 1/2 ( ∫eixe-iyf(x,y)dxdy +...

There is a crucial bug on both WolframAlpha and Mathematica. When we give the input "Floor(sqrt(11.44-10)/0.2)" it gives wrong answer. The actual answer is six (6) but wolframalpha gives five (5). The problem is Wolframalpha calculates 11.44-10 incorrectly. Although the answer is exactly 1.44...

I can't figure out how to format a variable isomorphic expression in Mathematica so that it will look nice. The best I can do will put parentheses around everything and expand powers. For example, given the array ##\{2,4,4,3,3\}##, I'd like Mathematica to write...

Hello everyone, I am trying to develop a model for my PhD research, I don't want to get into specifics too much, but I have encountered the following problem. I need to write \psi \frac{\partial \psi^*}{\partial x} in the following form \frac{\partial}{\partial x}(\text{Some function}) This...

Homework Statement I have the expression ##a_2\overline{β} + a_3β## involving complex variables, where ##|β|≤1##. I was wondering, is it possible to determine for what ##a_2## and ##a_3## the expression is always real, for every ##β## satisfying ##|β|≤1##; or is there insufficient information...

Homework Statement I have the expression ##a_2 \overline{\beta} + a_3 \beta## involving complex variables, where ##|\beta| \le 1##. I was wondering, is it possible to determine for what ##a_2## and ##a_3## the expression is always real, for every ##\beta## satisfying ##|\beta| \le 1##; or is...

See the photo of the question+ mark scheme! I don't understand a question on finding an expression for the variance of something... Attempt at solution: also I worked out c as (3/2) previously, which is correct Var(U) = (3/2)^2 x Var(Xbar) = 9/4n^2 x a^2/18 I'll attach a photo of this too if...

Simplify the expression $\dfrac{\sqrt{1+\sqrt{1-a^2}}((1+a)\sqrt{1+a}-(1-a)\sqrt{1-a})}{a(2+\sqrt{1-a^2})}$.

Homework Statement https://www.dropbox.com/s/d3qdr96n27j8wa7/circuit.png?dl=0 The questions is as follows: For each circuit write the equivalent logic expression. Homework Equations (B' + C) * A (?) My Attempt at circuit 2 (A* (A' * C') * B') + (A * C * B) My Attempt at Circuit 1 The Attempt...

Homework Statement A positive charge +q is located at the point x= 0, y = -a and a negative charge -q is located at the point x=0, y=a (a) Derive an expression for the potential at points on the y-axis as a function of the coordinate y. Take V to be zero at an infinite distance from the...

How can you derive an expression from the given direction defined by dx=2dy=-2dz. This is just a part of a problem that I'am solving. I have no idea how to get a vector expression using the given info. please help. Thanks! by the way I'm trying to find the directional derivative of a certain...

Homework Statement Find ## \sum_1^{23} tan^{-1}(\frac{1}{n^2+n+1}) ## Homework Equations ## tan^{-1}x + tan^{-1}y = tan^{-1}(\frac{x+y}{1-xy} )##The Attempt at a Solution I think we have to split the question in a form of relevant equation given above. First thing what should I do?

Homework Statement http://www.inter-ped.no/skei/MAT1013%20Matematikk%201T%20%20bokmal.pdf Page 10 task 4 for a picture. The window above consists of a rectangle and a semicircle. The windows perimeter is 8.0m. What does the radius in the semicircle have to be for the area of the window to be...

1. prove that: X'Y'Z + X'YZ' + XY'Z' + XYZ = (X⊕Y)⊕Z Homework Equations Use postulates and theorems. The Attempt at a Solution X'Y'Z + X'YZ' + XY'Z' + XYZ (original expression) X'Y'Z + X'YZ' + X(Y'Z' + YZ) (distributive) X'Y'Z + X'YZ' + X.1 (complement) X'Y'Z + X'YZ' + X (identity)[/B]...

Homework Statement A bullet of mass m is fired into a block of mass M that is at rest. The block, with the bullet embedded, slides distance d across a horizontal surface. The coefficient of kinetic friction is μk. Find an expression for the bullet's speed vbullet. Express your answer in terms...

Hi there. I'm reading Jackson's Classical Electrodynamics. 1. Homework Statement In chapter 6, the equation for the electric field of a moving point charge is derived. I could follow the mathematics to get the electric field for the moving charge, which is given in equation 6.57 in Jackson...