Expression Definition and 999 Threads

The price of a mandarin is 20 and the price of a guava is 15. Find the number of mandarins and guavas that can be bought for 50. (Thinking) So can an algebraic expression be made and the number of mandarin's and guavas that can be bought for 50. Many Thanks (Happy)

Homework Statement This problem relates to the two body problem of two rotating point masses, where one is much larger than the other. Equate the orbital energy per unit mass ##\epsilon## with the moments of momenta at the apses to get: ##\epsilon = -\mu/2a## Homework Equations The orbital...

[Mentor note: Thread moved from technical forums so no formatting template shown] Unfortunately, I'm completely lost with this question: 1. A particle is moving along the x-axis. Its position as a function of time is given as x=bt-ct^2 Derive an expression for the x- component of velocity...

Hi, I was deriving an expression for the work done by gravitational force of an object in moving another object from infinity to a distance 'r' from it. I think it should be positive valued because since displacement in this case is in the direction of the gravitational force, so work done by...

Homework Statement limit (5/(2+(9+x)^(0.5))^(cosecx) x-->0 attempt: tried applying lim (1+x)^(1/x) = e. x->0 couldn't get anywhere.

Momentum constraint in GR in ADM formalism is written in the form $$\mathcal M_i=\gamma_{ij}D_k\pi^{kj},~~~~~~~~~~(1a)$$ or equivalently $$\mathcal M_i=D_k\pi^{k}_i,~~~~~~~~~~(1b)$$ where ##\pi^{ij}=-\gamma^{1/2}\left(K^{ij}-\gamma^{ij}K\right)~##, ##K=\gamma^{ij}K_{ij}~##, ##\gamma=\det...

$\Large{S6.7.R.19}$ $$\displaystyle I=\int\frac{x+1}{9{x}^{2}+6x+5}\, dx =\frac{1}{18}\ln\left({9{x}^{2}+6x+5}\right) +\frac{1}{9}\arctan\left[{\frac{1}{2}\left(3x+1\right)}\right]+C $$ $\text{from the given I thought completing the square would be the way to solve this} \\$ $\text{but I...

Supposing I have $$(-4x^n)$$ Why does it equal $(-4)^n * x^n$ and not $(-4)^n * (-x) ^ n$? When we have a negative symbol it only applies to the first item in an expression? so $-xbcw$ equals $b * c * w * (-x)$? Which means if we wanted the other items to be negative we would have to do...

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...

If line y=mx+1 intersect the curve y=x^4+2x^2+x at two distinct points Then value of x^2_{1}+x^2_{2}+y^2_{1}+y^2_{2} = My Trail:: Solving these two equation, $x^4+2x^2+x=mx+1\Rightarrow x^4+2x^2+(1-m)x-1=0$ Now how can i calculate m and also find value of that expression, Thanks

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...