Value Definition and 1000 Threads

Preceding Problem. Let ##y=f(x)## be a continuous function defined on a closed interval ##[0, b]## with the property that ##0 < f(x) < b## for all ##x## in ##[0, b]##. Show that there exist a point ##c## in ##[0, b]## with the property that ##f(c) = c##. This problem can be solved by letting...

Hello! I am susposed to find the force of q3.The problem is given as in the picture ; Now we are given a hint,and it says the following: "First calculate the forces of the individual charges on q3. The superposition principle says that you can then simply add these forces vectorially to get...

There is an optimum energy which gives the greatest probability of ionisation of a particular element. This is said to align with the wavelength of the electron being close to resonances in the atom. Looking at this in a different way as particles, would it be correct to say that the optimum...

In This wikipedia article is said: "If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator, or more accurately, the ground state of a...

Hi, I was reading this problem and I found a solution on Math Stackexchange which I don't quite understand. Question: Calculate the expected value of the median of rolling a die three times. Attempt: I read the following answer on math stack exchange here "As already noted in a comment, the...

I'm trying to understand from this paper https://pdg.lbl.gov/2020/reviews/rpp2020-rev-bbang-nucleosynthesis.pdf What is the value of the baryon to photon ratio ##\eta=n_b/n_\gamma## as named in figure 24.1, but I can't get from the figure or the paper how ##\eta## is of order ##10^{-10}## Any...

Determine the value $z^*$ that... a. Separates the largest $3\%$ of all z values from the others $=1.88$ b. Separates the largest $1\%$ of all z values from the others $=2.33$ c. Separates the smallest $4\%$ of all z values from the others $=1.75$ d. Separates the smallest...

The picture may be blurry. I couldn't take more less blurry picture hence, giving it. The question is : Find value of ##\theta## when ##V_x## component and ##V_y## component same. I was using a simple equation of vector. $$C=\sqrt{A^2+B^2+2AB\cos\theta}$$...

$\tiny{7.68}$ Normal curve $\quad\mu=12\quad\sigma = 2$ Let z denote a variable that a standard normal distribution. Determintie the value $z*$ to satisfy the following conditions: a. $P(z<z*)=.025$ b. $P(z<z*)=.01$ c. $P(z<z*)=.05$ d. $P(z<z*)=.02$ e. $P(z>z*)=.01$ f. $P(z>z*)\textbf{ or...

Summary:: checking an expected error Given the question: "If a person tosses two coins and gets two heads, the person wins $10. How much should the person pay if the game is to be fair?" The book gives the answer as $2.5 while I calculate $3.333... E(X) = 0 = $10(1/4) - a(3/4) => a =...

hi guys I am trying to implement the a second order differential equation tat contains a time dependent term, the equation looks something like r'' = -\mu/r^3+(g/g^3-m/m^3) the idea is that i want to calculate 'r' the position vector of a point, that is dependent on vectors g and m, I tired to...

I tried to equate the derivative of the two equations: $$\cos x=-ke^{-k}$$ Then how to continue? Is this question can be solved? Thanks

I need to calculate the power and RMS value of some equations. The problem is, I found two methods to do that and don't know which is the right method. I have few equations to find the power and RMS value, but here is one equation. $$x( t) \ =\ 7\cos\left( 20t+\frac{\pi }{2}\right),$$ Method...

Hey everyone, I have been struggling to find the expected value and median of f(x) = 1/2e^-x/2, for x greater than 0. I am just wondering how I do so? Thank you.

Does this mean that initially there will be emf induced on the coil at t = 0 s? Initially, at t = 0 s, the coil has not been rotated yet so based on Faraday's Law, there won't be any change in magnetic flux so why the value of emf is not zero at t = 0 s? Thanks

Write a linear equation. A school district purchases a high-volume printer, copier, and scanner for $24,000. After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $2000. Write a linear equation giving the value V of the equipment during the 10 years it...

You are given the dollar value of a product in 2016 and the rate at which the value of the product is expected to change during the next 5 years. Use this information to write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 16 represent 2016.)1...

While reading in the book of Introduction to Quantum Mechanics by David Griffith in the section of Fine structure of Hydrogen: spin- orbit coupling, he said that the average value of S operator is considered to be the projection of S onto J. I could not understand why he assumed that. please...

See attachment. I don't understand the solution given by David Cohen. 1. Note: x^2 is nonnegative for any real number x. This is because any value for x when squared is positive. Yes? 2. If x is greater than or equal to 0, then I can say that -2 - x^2 is negative in value, right? 3. What...

Absolute Value (algebraic version) Rule: | x | = x when x ≥ 0 | x | = -x when x > 0 Rewrite each expression without using absolute value notation. Question 1 | x^4 + 1 | I say x^4 + 1 is a positive value. My answer is x^4 + 1. Question 2 |-sqrt{3} - sqrt{5} | The value of -sqrt{3} -...

Absolute Value (algebraic version) Rule: | x | = x when x ≥ 0 | x | = -x when x > 0 Rewrite each expression without using absolute value notation. Question 1 |1 - sqrt{2} | + 1 The value 1 - sqrt{2} = a negative value. So, -(1 - sqrt{2}) = - 1 + sqrt{2}. When I put it all together, I get...

A school district purchases a high-volume printer, copier, and scanner for $24,000. After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $2000. Write a linear equation giving the value V of the equipment during the 10 years it will be in use. Let t =...

The MCNP6.2 manual (page 3-37) says: "There are two nj values that can be used in the lattice array that have special meanings. A zero in the level-zero (real world) lattice means that the lattice element does not exist, making it possible, in effect, to specify a non-rectangular array." How...

I was wondering how you work out what values of s a Laplace transform exists? And what it actually means? The example given in class is an easy one and asks to calculate the Laplace transform of 3, = 3 * Laplace transform of 1 = 3 * 1/s. Showing this via the definition, where does the range of s...

for problem (a), all real numbers of value r will make the system linearly independent, as the system contains more vectors than entry simply by insepection. As for problem (b), no value of r can make the system linearly dependent by insepection. I tried reducing the matrix into reduced echelon...

The line containing point A is rotated $90^o$ anticlockwise about the origin O $\begin{array}{ll} \textit{The y coordinate of point A } & \textit{The y coordinate point A}\\ \textit{before rotation} & \textit{After rotation} \end{array}$ a. The quantity on the left is...

Greetings according to the function we can see that there is a jump at x=e and I know that the value of the function at x=e should be the average between the value of f(x) at this points my problem is the following the limit of f(x) at x=e is -infinity and f(e)=1 how can we deal with such...

I need help with part (a)... I know that the root-mean-square voltage is the dc-equivalent voltage for an AC waveform and what my book labels "##V_{dc}## is actually the average voltage. Hence I am assuming the question is asking me to find ##V_{rms}## ... Is my assumption that the...

If ##f## is a constant function, then choose any point ##x_0##. For any ##x\in K##, ##f(x_0)\geq f(x)## and there is a point ##x_0\in K## s.t. ##f(x_0)=\sup f(K)=\sup\{f(x_0)\}=f(x_0)##. Now assume that ##f## is not a constant function. Construct a sequence of points ##x_n\in K## as follows...

Our class modified an experiment to measure the magnetic field strength in mT between 5cm and 30cm, and I have plotted data and found that the relationship resembles a power relationship (using a log vs log graph). In order to find the percentage uncertainty for the whole experiment I need the...

This proof has three steps and is very similar to (if not the same as) that other proof I posted here.(1) Prove the existence of a ball centered around ##a## with the property that ##f'## evaluated at any point in the ball is positive. (2) Prove that the right end-point of this ball is bounded...

Another member and I, in private conversations, have been discussing the time average tension in a pendulum string. He has done a numerical analysis of the problem, and his calculations indicate that the time average tension is less than mg. I have analyzed the problem analytically by...

Hello. I am reading through a solar farm paper and I am getting a bit confused at looking at this formula: When it says "Value", I am guessing it refers to the cost of electricity per kWh? If that is the case, I wonder how many kWh are 18.4p/kWh?

Hey all. This is about Ohm's Law (and specifically resistance). When you plot the change in current vs the change in voltage you should get a linear trend line (providing it is from an ohmic device). The gradient should be the resistance. My questions is why does the gradient value need to be...

Calculate the expected value for the number of Asian Zing wings sold

This is my attempt of the problem Argz = (11π+θ) - 2πn 0 < (11π+θ) - 2πn < π/2 0 < (11π+θ) - 2πn or (11π+θ) - 2πn < π/2 n < (11π+θ)/2π or n > (21π/4 + θ) (21π/4 + θ) < n < (11π+θ)/2π, what i was trying to do was to find the value of n which i thought would help me obtain the value of the...

Solve the following equation [$x^2+1$]=[2x] ,where [x] is the floor value of x

Proof goes like this: (1) Prove the existence of open intervals centered around the end-points of the domain such that the image of the points in these intervals through ##f## has the same sign as the image of the end-point through ##f##. In other words, prove that there is a ##\delta>0## such...

My questions: 1) What about if t = 2? Is there a certain meaning to ##G_X (2)## ? 2) PGF for uniform distribution is ##G_X (t)=\frac{t(1-t^n)}{n(1-t)}## and for t = 1 ##G_X (1)## is undefined so ##G_X (1) =1## is not true for all cases? Thanks

$\tiny{1.8.17}$ \nmh{324] Use direct substitution to verify that y(t) is a solution of the given differential equation in . Then use the initial conditions to determine the constants C or $c_1$ and $c_1$ $y''+4y=0, \quad y(0)=1,\quad y'(0)=0,\quad y(t)=c_1\cos 2t+c_2\sin 2t$

For spherical coordinate, ##dV = r^{2} \sin {\theta} dr d\theta d\phi## Therefore, $$<\frac{1}{r}> = \frac{1}{(\pi)(a_0)^{3}} \int_{0}^{\infty} {r e^{\frac{-2r}{a_0}} dr \int_0^{\pi} \sin {\theta}} d\theta \int_0^{2\pi} d\phi$$ From partial integral, I've found: $$\int_{0}^{\infty} r...

Explain why the Intermediate Value Theorem gives no information about the zeros of the function f(x) = ln(x^2 + 2) on the interval [−2, 2]. Let me see. Let x = -2. f(-2) = ln((-2)^2 + 2) f(-2) = ln(4 + 2) f(-2) = ln (6). This is a positive value. When I let x be 2, I get the same answer...

Figure shows a rectangle OABC in which OA = a and OC = c. F is the midpoint of CB and D is the point on AB such that AD : DB = 2:3 (a) Find _ _ _ _ _ __ (i) CF in terms of a _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (ii) AD in terms of c The lines OD and AF intersect at the point X Given that...

Hi all, I found this notation of expectation values in a NMR text. In class, I learned that expectation values are given by $$<\hat{X}>=\int_{-\infty}^\infty\psi^*x\psi dx$$ why does this textbook divide by the integral of probability density ##\int \psi^*\psi dx##?

A bag contains x beads. 6 of the beads are red and the rest are blue. Ravish is going to take at random 2 beads from the bag. The probability that the 2 beads will be of the same colour is $9 /17$ Using algebra calculate the value of x. ( show sworking if possible)

Is it correct that ##\frac{|x + 1|}{|x + 2|}## equal to ##\left|\frac{x + 1}{x + 2} \right|##? Please explain, I don't understand. Thank you

see attached image, it asks to repesent it in x-graph constant "a" isn't conditioned. Do I need to separate it into a few cases of the constant a and represent each in one x-graph?

Reals $x,\,y$ and $z$ satisfies $3x+2y+z=1$. For relatively prime positive integers $p$ and $q$, let the maximum of $\dfrac{1}{1+|x|}+\dfrac{1}{1+|y|}+\dfrac{1}{1+|z|}$ be $\dfrac{q}{p}$. Find $p+q$.

Maybe a silly question but on the above question using the conservation of momentum: momentum before firing (0) = momentum after firing (55*35)+(M*2.5) If I re-range the above it's M = -(55*35)/2.5 = -770kg. I can I reconcile that minus sign (basically get rid of it)? Thanks

I want to solve this using difference equation. So I set up the general equation to be Pi = 0.5 Pi+1 + 0.5 i-1 I changed it to euler's form pi = z 0.5z2-z+0.5 = 0 z = 1 since z is a repeated real root I set up general formula Pn = A(1)n+B(1)n then P0 = A = 1 PN = A+BN = 0 -> A= -BN...