Value Definition and 1000 Threads

Homework Statement A flat capacitor formed by two square plates of side 0.3 m which are 2 mm apart. Source keeps voltage 250 V on the plates. What current flows between the plates and the source if the condenser is immersing in kerosene at velocity of 5 mm / s? The relative permittivity of...

Homework Statement i have several example of hardy cross problem involve 2 loops , for the junction that divide 2 loops , is it necessary to use the corrected value for the junction on second loop for the first trial ? or just use the initial assumption will do ...

Homework Statement Prove ##\int_{0}^{b} \frac{e^x}{1+x} dx>b## for every ##b>0##. The Attempt at a Solution Honestly, no idea. I suppose I cannot just calculate the definite integral and estimate. I think it needs to be proven in a more rigorious way.

Homework Statement √[/B] A particle in an infinite square well has the initial wave function: Ψ(x, 0) = A x ( a - x ) a) Normalize Ψ(x, 0) b) Compute <x>, <p>, and <H> at t = 0. (Note: you cannot get <p> by differentiating <x> because you only know <x> at one instance of time)Homework...

Homework Statement An 11 kV motor is fed by cables from a transformer via switchgear, having a phase impedance of 0.3 + j0.3 ohm. The Earth return path to the transformer neutral has a resistance of 0.42 ohm. Determine a suitable value of neutral resistance if the voltage rise at the motor in...

Let ##\mu: \mathbb{R}\to \mathbb{R}##, ##f: \mathbb{R}\to \mathbb{R}##, and ##r: \mathbb{R}\to [1, \infty)## be bounded measurable functions (which may be discontinuous). I'm interested in the function ##v:\mathbb{R}\to\mathbb{R}## given by ##v(x) = \mathbb E \left[ \int_0^\infty e^{-\int_0^t...

Homework Statement Find the SVD of Homework EquationsThe Attempt at a Solution I'm stuck My question is why in the solution it originally finds u_2=[1/5,-2/5]' but then says u_2=[1/sqrt(5),-2/sqrt(5)]'. I don't see what math was done in the solution to change the denominator from 5...

Hello! Can someone please tell me where I'm messing up in this problem? At 4% and 8% elongation, the loads on a tensile test-piece of half-hard aluminium alloy are 1.59 kN and 1.66 kN respectively. The test-piece has an initial width of 10 mm, thickness of 1.4 mm and gauge length of 50 mm...

Homework Statement Calculate the value of the wave at t = (2, 3, 4, 10) ns 0.4 cos(10^8 * t + (1/3) * y) az Homework Equations N/A The Attempt at a Solution This is the last part of a problem. I have already found the phase shift of 1/3 and wavelength of 6 pi. I have already been given the...

Homework Statement Find the ##Q## value for electron capture of ##^{196}Au##. Homework Equations ##Q_\epsilon = [m(^AX)-m(^AX')]c^2-B_n## The Attempt at a Solution How do I know if I have an ##K##- or ##L##-shell for the electron? Assuming I have an ##K## shell taking ##B_n = \; ^{196m1}Au##...

I am interested in the calculation of the mean energy value of CMB (Cosmic Microwave Background) photons from which the recombination is performed. The subject on French Wikipedia says : "Intuitively, one might say that recombination occurs when energy average of photons is of the order of the...

Homework Statement Let p,q,and r be real numbers so that p+q+r = 2 and p2+q2+r2 = 12 Then, the sum of the maximum and minimum value of r is A. 4/3 B. 2 C. 3 D. 10/3 E. 4 Homework Equations basic algebra The Attempt at a Solution [/B] p+q+r = 2 p^2+q^2+r^2 + 2 (pq+qr+pr) = 4 12 + 2...

Homework Statement (a) Suppose we flip a fair coin until two Tails in a row come up. What is the expected number, NTT, of flips we perform? Hint: Let D be the tree diagram for this process. Explain why D = H · D + T · (H · D + T). Use the Law of Total Expectation (b) Suppose we flip a fair...

Homework Statement Prove that the maximum value of the Von Neumann entropy for a completely random ensemble is ##ln(N)## for some population ##N## Homework Equations ##S = -Tr(ρ~lnρ)## ##<A> = Tr(ρA)## The Attempt at a Solution Using Lagrange multipliers and extremizing S Let ##~S =...

Homework Statement I was told that the moody chart can be divided into 4 sections , i don't really understand the 'transition part' . it is said to be a function of R and roughness . what is R ? radius of the pipe ? Homework EquationsThe Attempt at a Solution

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

What is the heat capacity values of diesel in liquid and vapour state?

Homework Statement So I've found a ton of examples that show you how to find cauchy principal values of convergent integrals because it is just equal to the value of that integral and you prove that the semi-circle contribution goes to zero. However, I need to find some Cauchy principal values...

Suppose that a given population is endowed with a pair of characteristics T and K. Let's think of these characteristics as random variables (T,K)∼BiNormal((μT,μS),(σT,σS),ρ) I observe the realisations of T for a sample consisting of those individuals with K<a, where the selection threshold a...

Homework Statement In the very long wire conductor as shown on the picture , flows a current magnitude I. Near the wire there is a square shaped contour , with length a ,which rotates around its axis a constant angular velocity. Axis of square contour and a straight line conductor are...

Homework Statement Prove that there does not exist a continuous function f, defined on R which takes on every value exactly twice. Homework Equations It uses this property: 1... If f is continuous on [a,b], then there exists some y in [a,b], such that f(y)≥f(x), for all x in [a,b]The Attempt...

Homework Statement Let f: ℝ→ℝ be continuous function such that f(x) approaches 0 when x---> -∞ and f(0)=2. In addition, f is decreasing when x≥3. Prove f has a maximum (greatest value) in ℝ. Homework Equations Theorem: If function f is continuous on a closed interval [a, b], then f has maximum...

Homework Statement Show that, quite generally, the Poisson Mass Function has the same value at λ (i.e. the average) and at (λ-1). Homework Equations The Poisson Mass Function is p(x) = [e^(-λ) * λ^(x)]/(x!) The Attempt at a Solution I started out by plugging in λ-1 into the equation to get...

I can't seem to find an explicit or analytical solution to a boundary value problem and thought I might ask those more knowledgeable on the subject than me. If t is an independent variable and m(t) and n(t) are two dependent variables with the following 8 constraints: a) m' =0 @T=0 and...

Homework Statement The average value of the function ##g(x) = 3^{\cos x}## on the closed interval ##[- \pi, 0]## is: Homework Equations3. The attempt at the solution I used the standard method for finding average value over an interval with my calculator using an integral, and got the answer...

The estimated annual maintenance cost associated with the delivery vehicle amounts to R14 000 for the first year that the vehicle will be used (payable at the end of the year). The annual maintenance cost for the subsequent two years will increase by 4% per year as a result of wear and tear...

I have a sine wave produced as an output, which varies. This sine wave has been filtered by a moving average filter. From this output, coming out of a DAC module, I need to obtain the the voltage peak-peak value and store it preferably in an array. How can I do this? More importantly how can I...

I understand that this determines a probability, but of what exactly for a single photon? The probability that the photon will be detected on a surface where the photon is pumped, e.g. where on the surface the laser is aimed?

Hello! (Wave) I want to find the value of $\lim_{\epsilon \to 0}\int_{|x|=\epsilon} \left( \ln{|x|} \frac{\partial{\phi}}{\partial{\eta}}- \frac{\phi}{|x|}\right) dS$, where $\phi$ is a test function and $|x|=\sqrt{x_1^2+ x_2^2}$. Does it hold that $\int_{|x|=\epsilon} \ln{|x|}...

Homework Statement Given ##(\frac{∂H}{∂U})_P = (\frac{C_V+ (π_T + P)*V*a}{C_V + V*a*π_T}) ## Calculate this value of 1 mole of ideal gas at STP that has constant heat capacity of 12.5 ##\frac{J*K}{mol}## n=1 T = 273.15 K P = 1 atm ##C_V = 12.5 \frac{J*K}{mol}## a = ? ##π_T = ?## Homework...

I am trying to make a part of my following code to work but so far I haven't been successful... I have 1 tree file with several branches but the two I care about are named Trigger and Variable. I have calculated in two histograms h(Variable) the weights I want to obtain. My function that I am...

Homework Statement A circuit is arranged like above. To make the energy absorbed by the 6 ohm resistor every second is 1.5 J, voltage X should be ... Volt Homework Equations V = IRThe Attempt at a Solution [/B] I really have no idea. I just know that it's kinda like wheatstone bridge and...

Homework Statement Determine the R value of the unknown specimen using a conventional hot box. Surface area of the specimen is 0.009 m2. Initial Hot Room Temperature = T Hot Initial = 30 ° C = 303.15 K Initial Cold Room Temperature = T Cold Initial = 20 °C = 293.15 K Time for both rooms reach...

Homework Statement The position vector of a particle is given in the terms of t, by, s = (e-t+3*cos(2t)i+2tj+(e-t+3*sin(2t)k) Find the limiting value of speed when t approaches positive infinity. The answer says "s = ..." The Attempt at a Solution I have evaluated the limits of all the...

$f(x)$ is a real polynominal function with degree 100,and $f(k)=\dfrac {1}{k} , \,\,(k=1,2,3,4,5,------,101),$ please find $f(102)=?$

There is another topic for this but I didn't quite see it and I don't know how I've gone so far through my course not asking this simple question. So what's the difference? My thought process for hydrogen. I know it can have quantised values of energy, the energy values are the Eigen values of...

Homework Statement Given an initial value problem: ##x'(t)=f(t,x)\,,x(t_0)=x_0## Use centered finite differences to approximate the derivative, and deduce a scheme that allows to solve the (ivp) problem. Homework Equations For centered finite differences ##\displaystyle\frac{dx}{dt} \approx...

When does the value of the "Equilibrium Constant (K)" equal one ? and what does that mean ?

Homework Statement The value of g at a point P inside the Earth and at another point Q outside the Earth is g/2. Maximum possible distance in terms of radius of Earth between P and Q is? (g being the acceleration due to gravity on the surface). Homework Equations gh = (1+h/r)-2g...

What is the Largest possible value of n such that there is a multiple of 4 less than n^2 but greater than n^2 + 2016/n^2 ?

Homework Statement Guess the value of the following integral when n is an arbitrary positive integer. Evaluated from 0 to infinity: ∫30xne-x dx Homework EquationsThe Attempt at a Solution I've evaluated the integral for values of n from 0 to 3: n=0: 30 n=1: 30 n=2: 60 n=3: 180 The pattern...

Homework Statement Hello! I am repeating conics, and have stumbled upon this paragraph on purplemath.com " Then a = –1/9. With a being the leading coefficient from the regular quadratic equation y = ax^2 + bx + c, I also know that the value of 1/a is the same as the value of 4p, so 1/(–1/9) =...

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'm having a hard time following the arguments of how the Higgs gives mass in the Standard Model. In particular, the textbook by Srednicki gives the Higgs potential as: $$V(\phi)=\frac{\lambda}{4}(\phi^\dagger \phi-\frac{1}{2}\nu^2)^2 $$ and states that because of this, $$\langle 0 | \phi(x)...

Homework Statement As the captain of the scientific team sent to Planet Physics, one of your tasks is to measure g. You have a long, thin wire labeled 1.80 g/m and a 1.30 kg weight. You have your accurate space cadet chronometer but, unfortunately, you seem to have forgotten a meter stick...

Print either "Fruit", "Drink", or "Unknown" (followed by a newline) depending on the value of userItem. Print "Unknown" (followed by a newline) if the value of userItem does not match any of the defined options. For example, if userItem is GR_APPLES, output should be: Fruit #include <iostream>...

My homework problem is as follows: Consider the Laplace transform shown below. (4s3+15s2+s+30)/(s2+5s+6) a. What is the value of f(t=0) and f(t=∞)? Use the initial and final value theorems. b. Find the inverse transform f(t). Use this expression to find f(t=0) and f(t=∞) and compare with the...

Homework Statement At T1 the root mean square speed (rms) of compound P is 485.2 m s-1 and at T2 the rms speed is 504.1 m s-1. Using this data and the fact that T2 – T1 = 24.0 °C, determine the molar mass of P in g mol-1. Homework Equations From problem statement you have: (3·R·T1/M)1/2 =...

[Note: Thread moved to this forum by a mentor] Hi all, the full question is: A parabola has zeroes at 5/2 and -3/2 and has an optimal value of 4. Determine equation of the parabola in factored form. So I started out with 4 as my y-value on my vertex then took the zeroes(5/2 and -3/2), added...

Let {a}_{n+1} = \frac{4}{7}{a}_{n} + \frac{3}{7}{a}_{n-1} where a0 = 1, and a1 = 2. Find \lim_{{n}\to{\infty}}{a}_{n} Well, seeing as it says that x approaches infinity, the difference between where points an-1, an, and an+1 are plotted on the y-axis is almost insignificant, so we can simply...