Expression Definition and 999 Threads

If $x^2+y^2+z^2+xyz=4$ and that $x,\,y,\,x\ge 0$, prove $3!\sqrt{x}+2!y+1!z^2\le 13$.

Homework Statement A bacteria that normally divides every 20 minutes express gene X. The production rate of protein X is 5nM/min. The protein is stable and does not degrade. What is the concentration of X in the steady state?The same bacteria enter into a stress state at t=0 for 3 hours...

Homework Statement A frustum is made by removing a small cone from a large cone. The cones are mathematically similar. (please see picture attached) The large cone has base radius r cm and height hcm. Given that volume of frustum/volume of large cone = 98/125 Find an expression, in terms of...

Why ##d^2 x^\alpha / d\tau^2## is not considered a good expression for the proper acceleration (of a massive particle whose proper time is ##\tau## and coordinates are ##x^\alpha##)?

Homework Statement Hi! I am working on a lab-report where we have measured the time a body use up a inclined plane. i am going to find a expression for the coefficient of friction expressed by the time and acceleration that i have found. This expression do i need for the next task where i am...

Homework Statement Homework Equations v = I + j + k v = d/t The Attempt at a Solution I thought the answer was as simple as: v = 63i + 0j + 0k, since the car only has motion in one direction... ...but I got it wrong, so clearly I'm missing something here.

I've just started using Mathematica and I'm still trying to get used to how things are properly done with it. I tried to do a calculation (this one: https://www.physicsforums.com/threads/lagrangian-of-a-driven-pendulum-landau-problem.965714/) and I had to neglect some terms in an expression. Is...

The other day in a fit of boredom I decided to dust off my old math books (high school and undergrad) and see if I can still crank through the basics. 1. Homework Statement Show the following: $$ \frac { 3 cos^2(x) } { 2 - 2 sin(x) } = \frac { 3 }{ 2 } ( sin(x) + 1 ) $$ Homework Equations $$...

Hi! I have sin^n(x)/(sin^n(x)+cos^n(x)) The expression is the same with 1/(ctg^n(x)+1) and I have no idea how to get to this answer. Can you help me?

Homework Statement The Gibbs-Thompson relation provides a correlation between solubility and radius of curvature. Consider two spherical particles of radius r and R present in a solvent, with R >> r. The rate of dissolution of the smaller particles (the rate of decrease in its radius with time)...

Homework Statement a particle's position is the vector r=(ct^2-2dt^3)i+(4ct^2-dt^3)j where c and d are positive constants. find the expression for the x-component of the velocity (for time t>0) when the particle is moving in the x-direction. you should express your answer in terms of variables...

Hello! So this is my problem here, there's a question I've been studying for an exam in which I really can't understand the answer. Basically it has multiple choices and I'm very undecided. So this is it: Expression: "What does this expression reflect? PV + mgh + 0,5mv^2 = constant " a)...

I'm confused, Is the value of ##(dr)^2## $$dx^2+dy^2+dz^2$$ Or $$\frac{(xdx+ydy+zdz)^2}{x^2+y^2+z^2}$$ ?

I have an equation regarding integration equation. Given: where is found analytically to be: My question is what is the analytical equation for equation 3? I hope that anyone may help me regarding this matter. This is the paper I referred: https://arxiv.org/pdf/1503.05793.pdf Thank you.

I have made an attempt at the question below and just wanted to check if my thinking was correct or totally wrong. Thank you in advance! 1. Homework Statement In a simple model of a star, the density is described as ρ=ρ0(1-r/R), where R is the stellar radius, and ρ0 is the central density...

Hello, I am asked to give the formal expression of the total number density of galaxies and explain why is this expression problematic in practice? From what I saw from my research and into my lectures, I have found the follwing relation which gives the number of galaxies ##N## with mass ##(m...

So my professor gave us a study guide for the final but no there is no answer key. Could someone check my answers please? Express cos(2 tan^-1(x/4)) and sin(2tan^-1(x/4) as an algebraic expression in x I got: cos(theta)=8*sqrt(x^2+64)/x^2+64 sin(theta)=x*sqrt(x^2+64)/x^2+64

Homework Statement A charge Q is uniformly distributed throughout a nonconducting sphere of radius R. Write the expression of the charge density in the sphere? Homework Equations Charge density ρ=dQ/dV Gauss's Law ∫EdA = E(4ϖr^2) The Attempt at a Solution If Q is uniform then ρ=Q/dV and the...

I've read in a few places that acetylation of histones creates transcription activation rather than repression (the common example being: H3K9). What I am curious, with the absence of this acetylation (I'm guessing this would the process de-acetylation), do the genes that were previously...

I don't know how to type mathematical symbols and equations and stuff. Like if I want to ask something here in physics forum, I need to type mathematical expressions like everyone here does. How can I do that? Do I need any software?

I am searching sources, which would express purely (without any other expression on how the data was obtained, etc.) elementary origins of the universe. As we would have certain artistic visualisation on how our Mars rover would operate on landing on mars, are there sources which give data on...

Homework Statement Hello, I need to find an expression for the sum of the given power series The Attempt at a Solution I think that one has to use a known Maclaurin series, for example the series of e^x. I know that I can rewrite , which makes the expression even more similar to the...

Find the closed form (or) analytic expression form for the following integral $$ \hspace{0.3cm} \large {\int_{0} ^{\infty} \frac{\frac{1}{x^4} \hspace{0.1cm} e^{- \frac{r}{x^2}}\hspace{0.1cm}e^{- \frac{r}{z^2}} }{ \frac{1}{x^2} \hspace{0.1cm} e^{- \frac{r}{x^2}}+ \frac{1}{y^2}...

Write an expression for normal distribution for the data: Measured values are: 4,393; 4,372; 4,381; 4,373 and 4,401 thanks for help

Homework Statement In the logic circuit shown below , write the Boolean expression for the output function X . Which gate(s) could be removed without affecting the function X ? Homework Equations - The Attempt at a Solution [/B] So , we can get rid of ##A \overline{B} C ## . gate # 4. Right ?

Homework Statement [/B] Homework Equations [/B] The Attempt at a Solution Could someone check my answer please ?

Homework Statement Show that ##\displaystyle \bigcup_{n=2}^\infty \left[ \frac{1}{n} , \frac{n}{n+1} \right] = (0,1)##. Homework EquationsThe Attempt at a Solution I'm not sure how to show this rigorously. It is sufficient to note that ##\lim_{n\to\infty} \frac{1}{n} = 0## and that...

Homework Statement Simplify the Boolean expression : Homework Equations - The Attempt at a Solution [/B] Here is my work : Could someone check my answer please ?

I am using the book 'Fundamentals of thermodynamics' by Moran et al., In the exergy chapter, while deriving the expression for exergy ,a term representing the entropy generation in the combined system is neglected.Then the resulting expression is said to be the expression for exergy.But that...

Hey guys! How do I derive the general expression for delta p times delta x which is the exception value in the harmonic oscillator. I am supposed to establish delta p and delta x as operators and the express those operators by raising and lowering operators.

I'm trying to proof an identity from Munkres' Topology A \ ( A \ B ) = B By definition A \ B = {x : x in A and x not in B} A \( A \ B) = A \ (A ∩ Bc) = A ∩ (A ∩ Bc)c = A ∩ (Ac ∪ B) = (A ∩ Ac) ∪ (A ∩ B) = ∅ ∪ (A ∩ B) = A ∩ B What did I miss?

Homework Statement A voltage of V = V_0 sin(\omega t) is applied to an inductor. Find an expression for the current and hence the power. Homework Equations I have used the equation: V = -L \frac{di}{dt} and for power: P = IV The Attempt at a Solution I tried to find I(t) by integrating...

What is the simplest known first-order expression known to be independent of Peano Arithmetic but decidable in ZFC for some reasonable notion of simplicity (such as number of quantifiers, nesting depth etc.); the precise definition of simplicity does not matter, I just want to see a concrete...

I have a problem with this formula: I have two known value series: A1, B1, C1 and A2, B2, C2. That gives me two equations with two unknowns n and k. Mentor note: More readable versions of the two equations: $$A_1 = \sqrt[n]{\frac{B_1} k + C_1^n}$$ and $$A_2 = \sqrt[n]{\frac{B_2} k +...

Today (AUG 1) is RNA Day, an international celebration of one of the most versatile biomolecules in existence. What are some areas of RNA research that excite you most? Some of the most intriguing areas of current research to me (with example links for further reading): The role of RNAs in...

For this task i have to use differentiation to find a general expression for the rocket's velocity as a function of time. Q. A toy rocket has been launched straight upward. Altitude y as a function of time is given as y=bt−ct2, w b = 81 m/s , c = 4.9 m/s2 , t is time in seconds, y is in meters...

Homework Statement I was solving a problem and came to a part where I was dealing with the expression, 1 - e-t -------- 1 - et It turns out that this can be simplified to -e-t but I had no idea from simply looking at the first expression that it could be simplified, and I tried to continue...

Hello. I have an equation which I understand partially but after understanding the purpose of coefficients in the below equation I think my understanding will enhance. * I found it on: https://www.desmos.com/calculator/dnzfajfpym What decides that I need coefficients for x2 in the given...

Homework Statement It's not a problem per se, I'm just trying something, so there's no statement. What I'm trying to do it's to prove the forllowing equation but without using the member of the right. (cos(36º) + 1)²/(cos(36º)) = 5cos(36º) There's the trivial answer, using both members, that...

Hi. I have coefficient of x2 as in an expression that looks like this * calculator shows little yellow triangle because 'x' is not defined. If I can write the coefficient of x2 as - 0.091372213746554 then why did the author write coefficient of x2 like this shown below? Thanks.

Is there an expression similar to the Sackur-Tetrode equation that describes the statistical entropy of fermions or bosons, maybe for the electron gas in a metal or the photon gas in a cavity?

Homework Statement charged particule reaches a uniform magnetic B field with a velocity V , and at angle theta with the magnetic field . What is the expression of the relation , expressed as a ratio, of the radius and helical step of the trajectory of the particule . a- 2pi/tan a b- 2pi...

5+2 root 6 / 7+4root3 = a-b root3 find a and b

Homework Statement Simplify: $$sin^2\left(x\right)+sin^2\left(x\right)tan^2\left(x\right)$$ Homework Equations All trigonometric identities. The Attempt at a Solution (i) ##sin^2\left(x\right)+sin^2\left(x\right)tan^2\left(x\right)## (ii)...

Hi, my question is about the correct means of the expression "computer experiment" in a Monte Carlo simulation. What specifically is an "experiment" in a Monte Carlo simulation? Is the same of "Monte Carlo path" or is the whole process adopted to found a magnetization curve, for example? If the...

Hello there, I am going to implement a numerical method to solve how much Mass of a fluid has gone out of an opened bottle. I am going to get h(t) with some sensors but I am not sure if this expression for Mass gone out "M" is correct. The area of the bottle at the up part. A1 The density of the...

How can we write the below red marker boolean expression to simplify the equation? Which Law is this? B+!BA=B+A Is this correct?

Homework Statement Derive an analytic expression for the distance from the vertex to the focus for a particular ray in terms of (i) the radius of curvature R of the concave mirror (ii) the angle of incidence θ between incident ray and radius of the mirror. Hence show that the focus moves closer...

In a book I'm reading, I'm told to prove that: If m and n are odd, then (m)(n) is odd. The proof goes as such: Let m=(2a+1) and n=(2b+1) Then, mn= (2a+1)(2b+1) = 4ab+2a+2b+1 = 2(2ab+a+b)+1 = 2t+1 ; where t= 2ab+a+b Two questions: When we take an expression, and assign it to a single...

Please help with this algebra II question. It needs to be simplified. Thank you.