Expression Definition and 999 Threads

I have $$\frac{(-1)^n}{(4^n)n }(-4)^n$$ (where n is a sufficiently large positive number, I think in this case it only has to be positive). Is $\frac{-4^n}{4^n}$ the same thing as $(-1)^n$? How is this the case?

How to find if a quadratic expression of the form 4x2 + 4.n.x - P ......(x,n and P are natural number) is a perfect square. For example, 4x2 + 64x - 31 Thanks.

I can derive $$a(k) = \int d^3 x e^{ik_{\mu} x^{\mu}} (\omega_{\vec{k}} \psi + i \pi)$$ for a free real scalar Klein-Gordon field in three ways mathematically: the usual Fourier transform way in Peskin/Srednicki, an awesome direct a = ½(2a) = ... way (exercise!), and as a by-product of a clever...

Homework Statement I want to know how he simplified this expression to tan (theta) Homework EquationsThe Attempt at a Solution

lim_(h->0^-) (e^(x+h)/((x+h)^2-1)-e^(x+h)/(x^2-1))/h = -(2 e^x x)/(x^2-1)^2 I know how to differentiate the expression using the quotient rule; however, I want to use the limit definition of a derivative to practice it more.This desire to practice led me into a trap! Now I just can't simplify...

I have this expression: $$\sqrt{ 1 - \frac{16}{\sqrt{x^2 + 16}}}$$ And the textbook simplifies it to $$\frac{x}{\sqrt{x^2 + 16}}$$ But I'm not sure how it does this.

My textbook has the expression $$\frac{4}{9} + 2 - 44 = C(\frac{11}{3})(\frac{17}{3})$$ and it simplifies it to $C = -2$ But I am getting $$(\frac{4}{9} + 2 - 44) * 3 = C187$$ which simplifies to $$(\frac{12}{9} + 6 - 132) = C187$$ and $$(\frac{12}{9} - 126) = C187$$ then...

Homework Statement Consider the electric dipole seen in the notes. (a) Using integration, derive an expression for the magnitude of the electric field produced by the dipole at any point along the x-axis. Electric Dipole: http://labman.phys.utk.edu/phys136/modules/m5/images/electr5.gif...

Evaluate $1\cdot 2^2 + 1\cdot 2\cdot 3^2 + 1\cdot 2\cdot 3\cdot 4^2 +\cdots+ 1\cdot 2\cdot 3\cdots 2015^2− (1\cdot 2\cdot 3\cdots 2016)$.

$\tiny\text{LCC 206 {r3} integrarl rational expression}$ $$\displaystyle I=\int \frac{3x}{\sqrt{x+4}}\,dx =2\left(x-8\right)\sqrt{x+4}+C \\ \text{u substitution} \\ u=x+4 \ \ \ du=dx \ \ \ x=u-4 \\ \text{then} \\ I=3\int \frac{u-4}{\sqrt{u}} \ du = 3\int {u}^{1/2}du -12\int...

I have this expression $$\frac {1} { e^x + \frac {1} {e^x}}$$ and it simplifies to $$\frac {e^x} { e^{2x} + 1}$$ And I'm not sure how to get this simplification or what rules to apply to get to this simplification.

I have the expression $$\sqrt{ a ^2 - x^2}$$ using trig substitution (with $x = asin\theta$), I get$$\sqrt{ a ^2 - a^2sin^2\theta}$$ which gets simplified to $ a \sqrt{ cos^2\theta}$ and then $ a cos \theta$ for $$- \frac{\pi}{2} \le 0 \le \frac{\pi}{2} $$ what I don't get is domain of...

Mentor note: moved to homework forum A store has been selling 200 DVD burners a week at $350 each. A market survey indicates that for each $10 rebate offered to buyers, the number of units sold will increase by 20 a week. Find the demand function and the revenue function. How large a rebate...

I'm trying to clarify my terminological understanding of things related to mathematical expressions. Actually, first I want to make sure I understand what an expression is and is not. From my current understanding, an expression is any number, variable, or combination of numbers and...

Homework Statement A particle moves along a straight line so that its acceleration t seconds after passing a fixed point O on the line is (2 - 2t) cm/s2. Three seconds after passing O, the particle has a velocity of 5 cm/s. Find and expression, in terms of t, for the velocity of the particle...

nmh{1000} $\tiny{\text {Whitman 8.7.28 integral rational expression}} $ $$\displaystyle \int\frac{t+1}{{t}^{2}+t-1}\ dt$$ $\text{book answer}$ $$\displaystyle\frac{5+\sqrt{5}}{10} \ln\left({2t+1-\sqrt{5}}\right) +\frac{5-\sqrt{5}}{10} \ln\left({2t+1+\sqrt{5}}\right)+C$$ $\text{expansion}$...

This is the derivative of an expression that contains terms of the form (partial derivatives)*differentials. Are you supposed to apply the product rule to the (partial)*differential terms? And with respect to what variable? I've tried different ways but didn't get the right result, so if anyone...

Homework Statement (a) Write the expression for y as a function of x and t in SI units for a sinusoidal wave traveling along a rope in the negative x direction with the following characteristics: A = 5.00 cm, λ =85.0 cm, f = 5.00 Hz, and y(0, t) = 0 at t = 0. (Use the following as necessary: x...

nmh{2000} index{expanded form} write each expression in expanded form and then find the sum $ \begin{array}{l}...

Homework Statement Homework Equations The Attempt at a Solution There is solved problem on change in water height with respect to time. I understand it but there is the b part of the question. It asks that what's if the top of the tank is open to the atmosphere? I think nothing would...

Hi. I have the following expression X=\frac{G\frac{x_1}{x_2}\gamma_Q}{\frac{1}{G}x_3 \gamma_P+1} where ##x_i## is an exponential random variable with mean 1. All other parameters are nonzero positive constants. Basically I want to find the probability density function (pdf) of ##X##. So I...

I was supposed to simplify the expression ##\ln |\cot {x}|+\ln |\tan {x}\cos {x}|## and apparently it’s wrong. Where’s the mistake? Is it not simplified enough or . . . ? ##\ln |\cot {x}|+\ln |\tan {x}\cos {x}|## ##=\ln |\frac {\cos {x}}{\sin {x}}|+\ln |\frac {\sin {x}}{\cos {x}}\cdot \cos...

Homework Statement http://imgur.com/AotzH28 Two long, straight conducting wires with linear mass density λ are suspended from cords so that they are each horizontal, parallel to each other, and a distance d apart. The back ends of the wires are connected to each other by a slack,low-resistance...

Homework Statement Find the general expression for the adiabatic relationship between P and V Homework Equations start with ##(\frac{∂P}{∂V})_s## expression for adiabatic relationship between V and T: ##(\frac{∂V}{∂T})_s = \frac{-C_v}{\frac{RT}{V}}## Relationship between S and T...

Homework Statement edit: I figured out my mistake Here's the entire problem. But I don't yet need help with all the steps. I'm getting off on the wrong foot (as usual)a We have shown in class that ideal gas adiabats have the form: ##P_I(V_i)^γ = P_f(V_f)^γ## with the heat capacity ratio: ##γ...

Let $a,\,b$ and $c$ be positive real numbers where $a+b+c=2012$. Find the maximum of $$\frac{(a^2+b^2+c^2)(a^3+b^3+c^3)}{a^4+b^4+c^4}$$.

Homework Statement Homework Equations Work energy theorem The Attempt at a Solution .5mv2 - .5mv2 = (kx - μmg)d final velocity is 0 ½mv2 =(kx - μmg)d solve for v2 ((kx - μmg)d2)m When this was wrong I tried integrating Fx but it was still wrong

Hi everyone. I'm trying to derive an expression of the velocity of an object in free fall on Mars, and I am having trouble. Here is what I've done so far: Drag on Mars can be expressed as $$F_d = \frac{C_d A \rho_M v^2}{2}, $$ where C_d denotes the drag coefficient, A the reference area, and...

Let $a$ be the smallest root of the equation $x^2-9x+10=0$. Find $a^4-549a$. Extra credit if the solution does not find the actual roots of the equation.

Hello all, as far as I can see this question is not posted already, my apologies if it is and please provide a link. But I'm watching this video on youtube: And at 22:38 there's an expression given for the uncertainty of an arbitrary operator Q, however I'm concerned the expression is incorrect...

Given: Ra[bcd] = 0 What permutations of bcd make this expression 0? TIA for your response.

Hello! Suppose a quartic polynomial with real roots where all its roots lie in the interval $$x \in \left[\frac{5}{8}a-\frac{3}{8}\sqrt{15a^2-16b}, \frac{5}{8}a+\frac{3}{8}\sqrt{15a^2-16b}\right]$$ where $a \in \mathbb{R}$ and $b<(15/16)a^2$. Is there a way to check that at least one of those...

I am not able to understand the mathematical expression of "change in Gibbs free energy", For a chemical reaction occurring at constant temperature and constant pressure, (ΔS)total = (ΔS)system + (ΔS)surrounding Considering that reaction is exothermic, ΔH be the heat supplied by system to...

Homework Statement [/B] An uncharged parallel-plate capacitor with spacing d is horizontal. A small bead with mass m and positive charge q is shot straight up from the bottom plate with speed v_0. It reaches maximum height y_max before falling back. Then the capacitor is charged with the bottom...

Hello! I have the following expression: $$\delta^2 = \frac{-\mu^2(5a\mu-4\mu^2-b)}{15a\mu-20\mu^2-3b}.$$ where $\mu \in \mathbb{R}$. Since $\delta^2$ is real (in the subject I'm working on) I need to check under which condition(s) the expression is well defined, that is, the RHS is positive...

Homework Statement Loop of wire with the following properties in a magnetic field B. Find an expression for the magnetic flux through the loop and evaluate the magnetic flux at t=25s. The magnetic field is uniform but changes strength at time (t) given by B(t) = B0 exp (kt)Resistance = 20ohms...

The expression to code is: (z complex, m some positive integer) z^m ( ln(z/(z-1)) - sum( 1/(k z^k), {k=1,m} ) ) The way I code is (in fortran) (in case z<2) Z_1=1.0_q/Z ZV1=LOG(Z/(Z-1)) ZK=1.0_q DO K=1,M; ZK=ZK*Z_1 ZV1=ZV1-ZK/K ENDDO ZV1=ZV1/ZK But it gives quite big error...

I'm trying to understand complexity class algorithms off of my professor's lecture notes, but I still can't get a hang of it. void sort(int a[], int N) { //N is the length of the array for (int base=0; base<N; ++base) for (int check=base+1; check<N; ++check) if...

Homework Statement [/B] Simplify: \frac{5\cdot 8\cdot 11 \cdots (3i+2)}{2\cdot 5 \cdot 8 \cdots (3i-1)} Homework EquationsThe Attempt at a Solution I realize the numerator and denominator terms cancel besides the 2, however I'm struggling to write this in a proper form. Only just started...

Homework Statement Given that ##T = \frac{4E(V-E)}{4E(V-E)+V^2\sinh^2 (ka)}## Simplify the expression for T when a is large but not infinite, and again for the case when a tends to zero and the potential tends to infinity, such that ##d = Va## is a real constant. k is a constant, as is E...

Homework Statement Say x is an infinitesimal number on the hyperreal line, is this expression finite, infinite or infinitesimal Homework Equations (sqrt(4+x)-2)/x The Attempt at a Solution [/B] My approach so far has been that sqrt(4+x) is (2+y) where y is another infinitesimal and y<x...

Don't know if this is the correct place to post this, this is not an assignment question, but I am terribly stuck with this. While going through the derivation of contact time for a hertzian contact as given in problem 3 at the following link http://s17.postimg.org/t1kq6mlxr/Capture.png , I am...

This was posted to calculus forum. I suppose it should have been posted here. I am trying to find a closed form expression/or limit as $n\implies\infty$ of ${S}_{n}=\sum_{k=0}^{n}{n \choose k} {a}^{k} \sum_{j=0}^{n}{n \choose j}\frac{{b}^{n-j}{c}^{j}}{(k+j)!}$ where $a$ , $b$ and $c$ are...

Homework Statement To simplify: ##\mid \vec b -\frac{\vec a*\vec b}{\vec a*\vec c} * \vec c \mid## ##\mid \vec b -\frac{(\vec a*\vec c)*(\vec b*\vec b)-(\vec a*\vec b)*(\vec b*\vec c)}{(\vec a*\vec b)*(\vec c*\vec c)-(\vec a*\vec c)*(\vec b*\vec c)} * \vec c \mid## Vectors may be any...

Hello, I hope I am posting this in the correct forum topic. It really is more of a "mathy" type of question, but I am posting it here because it deals with radar, and this type of math is used a lot in radar. To the mods, feel free to move it to a more suitable location if desired. I have...

I tried my best but I wasn't able to solve this can someone please provide me with a detailed solution. Here 's the question : Establish the expression of Vs/Ve (complex) using Thevnin's theorem Here is the circuit : I spent 4 hours trying to solve this but I had no clue how. I'am having...

Homework Statement In a region of space, the magnetic field depends on the co-ordinate ##z## and is given by $$\mathbf{B} = \hat{\jmath} B_0 \cos \left(kz - \omega t \right)$$ where ##k## is the wave number, ##\omega## is the angular frequency, and ##B_0## is a constant. The Electric Field in...

(∃x)[P(x) → Q(x)]∧(∀y)[Q(y) → R(y)]∧(∀x)P(x) → (∃x)R(x)

Hi all! I have a question about representing waves mathematically. I hope it will make sense. The waves I've been learning about are of the form F(x-vt), which represents a wave-form, every point of which is translated spatially with velocity v. I am wondering if there is a way to...

We begin with this definition of a hyperbola. \left(\overline{F_1 P}-\overline{F_2 P}=2 a\right)\land a>0 Perform a few basic algebraic manipulations. \sqrt{(c+x)^2+y^2}-\sqrt{(x-c)^2+y^2}=2 a \sqrt{(c+x)^2+y^2}=2 a+\sqrt{(x-c)^2+y^2} (c+x)^2+y^2=4 a^2+4 a \sqrt{(x-c)^2+y^2}+(x-c)^2+y^2...