Formula Definition and 1000 Threads

So far all I know is that n1 and n2 represent the refractive indices of the two media, and so is theta (I think). Please help

I know the basics of GR, but I'm far from an expert. I'm interested in the general formula for the angle shift experienced by a light ray in presence of a gravitational field. Light bending is topic covered in many books, of course, however the usual treatments would just not do for my purposes...

55. Use the Midpoint Formula three times to find the three points that divide the line segment joining (x_1, y_1) and (x_2, y_2) into four equal parts. 56. Use the result of Exercise 55 to find the points that divide each line segment joining the given points into four equal parts. (a) (x_1...

My book gives this formula for the semidirect product for groups ##Z_p## and ## Z_q## for primes p<q and p divides (q-1). ##(a,b)*(x,y)=(a+_q c^bx,b+_py)## There is also an explanation of what c is but very little else. It doesn't even explain what operation adjacency represents, eq...

Hello, Firstly I am not sure of understanding the problem, I believe that this reduction is related to a high density plasma where the free electrons are very close to the ions and so the ions cannot be considered as separate bodies... I also believe it affects the ground energy state of...

53. A line segment has (x_1, y_1) as one endpoint and (x_m, y_m) as its midpoint. Find the other endpoint (x_2, y_2) of the line segment in terms of x_1, y_1, x_m, and y_m. 54. Use the result of Exercise 53 to find the endpoint (x_2, y_2) of each line segment with the given endpoint (x_1, y_1)...

The problem: Visualising the problem (My question is with regards to this): Why is the above set-up correct? In the above diagram, S would be moving at velocity -v relative to S', instead of v. Is this because the question says "speed v", and so we can set the direction as such? Why would the...

I am interested in the physics of ground penetrating radar. 1) Does anyone know where I can find a derivation of the formula in the attached jpg for the energy reflected? K=the dialectic constant. 2) An intuitive explanation of why the dialectic constant is important in determining the energy...

Hi all, thanks in advance for any constructive feedback. :bow: Definition: If ##x\in R^n\backslash \{0\}## then the map ##\Lambda## takes the point ##x## into ##\bar{x}\in R^n\backslash R^+_3## given by ##\bar{x}=\{x_1,x_2,-x_3\}## We take the reflected point ##\bar{x}## and the fundamental...

My work is attached. I did get the answer right using the formula V=√(G*me/r). Im just confused as to why I can't use V=2pi*r/T to also get the right answer? With this equation I would assume T=86400s. I was able to use both equations to get the correct answer for a problem relating to...

Just as E= hc/λ is anyone aware of a mathematical formula to obtain the mass of a proton from C ?

Hello! I'm sitting with a problem that is causing me some troubles.. First part is using Bayes formula. We have 3 companies that produce some apparatus. Each company has some defective percentage. Company Produced (%) Defective (%) A 45 3 B 25 6 C 30 5 1) Suppose we pick up a...

Hello everybody at the forum I'm from Ukraine, I have Chemistry degree, and last year I began to self studying Quantum Mechanics. I'm reading this article: R. Garcia, A. Zozulya, and J. Stickney, “MATLAB codes for teaching quantum physics: Part 1,” [Online]. Available...

If none of the above is correct, what is a good definition of the symbol t (time)?

The image above is the problem and the image below is the solution I have tried but failed.

Hello, everybody: I am a philologist who is fond of mathematics, but who unfortunately has just an elementary high school knowledge of them. I am translating La leçon de Platon, by Dom Néroman (La Bégude de Mazenc, Arma Artis, 2002), which deals with music theory and mathematics in the works of...

One formula for a person’s maximum heart rate is 220 − x, where x is the person’s age in years for 20 ≤ x ≤ 70. The American Heart Association recommends that when a person exercises, the person should strive for a heart rate that is at least 50% of the maximum and at most 85% of the maximum...

In every book I checked, the energy (per unit mass) of elastic deformation is derived as follows: ## \int \sigma_1 d \epsilon_1 = \frac{\sigma_1 \epsilon_1}{2} ## and then, authors (e.g. Timoshenko & Goodier) sum up such terms and substitute ##\epsilon ## from generalised Hooke's law i.e. ##...

Greetings. I'm having a bit of difficulty with getting from the first to the second equation. I know some basic identities, but it all just feels like a mess. My approach was just going to be to write whatever I could, but some of the terms are confusing me...

Hey! :giggle: A woman is walking home with distance $d$ and speed $v$. The dog is happy and runs at speed $\frac{3v }{ 2}$ always between woman and house back and forth. (i) At what distances $(d_n)_{n\geq 1}$ do women and dogs meet? (ii) Determine the total path length of the dog with the...

FIRST TYPE: REVERSIBLE PROCESS At the temperature of 127 ° C, 1 L of CO2 is reversibly compressed from the pressure of 380 mmHg to that of 1 atm. Calculate the heat and labor exchanged assuming the gas is ideal. Q = L = - 34.95 J CONDUCT 380 mmHg = 0.5 atm L = P1 * V1 * ln (P1 / P2) = 0.5 * 1...

I have to do a MATLAB assignment but when it comes to the report (the theory) I am having quite a lot of problems. My tutor used this formula that I am going to attach: However, I don't know if that equation is the Laplace equation, the 2D Heat Diffusion equation, or what exactly that is as I...

Hi, I don't understand how the professor managed to determine the values of alpha, alpha' and omega. What is the formula tha´t is applied to determine alpha = SP / AS and so on... knowing that alpha is a really small angle. Cheers

Moles are proportional to volume. There is 1000 cm3 of gas (carbon dioxide gas plus water vapour) after the reaction, and 200 cm3 of water vapour after the carbon dioxide has been absorbed. Therefore, there is 800 cm3 of carbon dioxide. Since the stoichiometric ratio of carbon dioxide to the...

Hey! :giggle: Let $\displaystyle{I_n(f)=\sum_{i=0}^na_if(x_i)}$ be a quadrature formula for the approximate calculation of the integral $I(f)=\int_a^bf(x)\, dx$. Show that a polynomial $p$ of degree $2n+2$ exists such that $I_n(p)\neq I(p)$. Calculate the approximation of the integral...

Is any way to get Rodrigues' rotation formula from matrix exponential \begin{equation} e^{i\phi (\star\vec{n}) } = e^{i\phi (\vec{n}\cdot\hat{\vec{S}}) } = \hat{I} + (\star\vec{n})\sin\phi + (\star\vec{n})^2( 1 - \cos\phi ). \end{equation} using SO(3) groups comutators properties ONLY...

An amount of water at a temperature of 20 °C is passed through a water boiler in 1.5 min to brought to boiling point. The kettle is broken and does not jump off. The time between the moment when the water reaches boiling point and the moment when all the water is evaporated, is equal to: a) 7,5...

Is in the bottom of a liquid the pressure equal to p 0 + ρ.g.h or only ρ.g.h? please can someone tell me this correctly?

At page 20 of this pdf the two formulas that characterize the behavior of a linear and a circular antenna array are compared. The reason why I write this post is: I don't understand why the second formula is true. Below I show why I am not convinced. In general, given a configuration of sources...

We can determinate if one number is prime with the modulo operation. https://www.researchgate.net/publication/346647223_Primality_Test_Formula

I am trying to prove the following expression below: $$ \int _{0}^{1}p_{l}(x)dx=\frac{p_{l-1}(0)}{l+1} \quad \text{for }l \geq 1 $$ The first thing I did was use the following relation: $$lp_l(x)+p'_{l-1}-xp_l(x)=0$$ Substituting in integral I get: $$\frac{1}{l}\left[ \int_0^1 xp'_l(x)dx...

A while ago I decided to figure out how to prove one of Ramanujan’s formulas. I feel this is the sort of thing every mathematician should try at least once. I picked the easiest one I could find: Hardy called it one of the “least impressive”. Still, it was pretty interesting: it turned out...

I'm looking for a source that fully derives the complete formula for the surface area of a general (triaxial) ellipsoid. I'd prefer a source that has more than just a full derivation, but also has a fair amount of prose discussion on this topic. Some historical context would be nice, as well...

I know he had this ratio: But how did he get this: ?

The level of this learning material is high - school level From my note, there are two equations that can be used related to venturimeter: 1. ##P+\rho gh + \frac{1}{2} \rho v^2 = \text{constant}## 2. ##P_1 + \frac{1}{2} \rho {v_1}^2 = P_2 + \frac{1}{2} \rho {v_2}^2## I want to ask about...

In this code, I define a function of x as the sum of the first x integers. In[7]:= fnSum[x_] := Sum[k, {k, 1, x}] In[8]:= fnSum[x] Out[8]= 1/2 x (1 + x) In[9]:= fnSum[3.5] Out[9]= 6 I would like now to take the symbolic formula underlying fnSum, and use it with real arguments. How can I...

Let the empirical formula be ##Na_x S_y O_z## then we can concude $$\frac {29.11}{100} = \frac{xM_{Na}}{xM_{Na} + yM_S + z M_O}$$ $$\frac {40.51}{100} = \frac{yM_S}{xM_{Na} + yM_S + z M_O}$$ $$\frac {30.38}{100} = \frac{zM_O}{xM_{Na} + yM_S + z M_O}$$ where ##M_{Na} = 23, M_S = 32,M_O = 16##...

0.5^x+0.2^x+0.25^x=1.

I've got to do an experiment that essentially involves rolling a ball bearing down a (frictional) ramp and measuring its acceleration. It's quoted in the manual that the linear acceleration of a ball bearing rolling down a ramp at angle ##\theta## is ##a = \frac{5}{9} g \sin{\theta}##. When I...

Hi, If we multiply $En=-\frac{2\pi^2me^4Z^2}{ n^2h^2} $by $\frac{1}{(4\pi\epsilon_0)^2},$ it is the formula of electron energy in nth Bohr’s orbit. Why we should multiply it by $\frac{1}{ (4\pi\epsilon_0)^2}$ a Coulomb's constant in electrostatic force? Where m=mass of electron, e= charge...

My professor gave us a formula for absorption cross section, but he said he did not remember where he found it. The formula is given by $$\sigma_a =\frac {1} {| \mathbf E_i|^2} \int_V k \epsilon^{''}_r | \mathbf {E} |^2 dV = k \epsilon^{''}_r |\frac 3 {\epsilon_r +2}|^2 V.$$ Where does...

Hi, This is my first post, I hope I have done it right. The top mass is represented as m and the weight hanger M.The image below is my attempt with the first formula 2. I have done it in grams because when I did it in kg's it was not anywhere near 9.81ms^-2...I know it is wrong :) g exp. =...

f(x+2h) = f(x) + 2hf’(x) + .5(2h)^2f”(x) f(x+h) = f(x) + hf’(x) + .5h^2f”(x) f(x+2h) - f(x+h)? f(x+2h) - 2f(x+h)?

ive used google https://www.google.com/search?q=n%5E2+%2B+(n-2)%5E2+%2B+..&rlz=1C1SQJL_enUS890US890&oq=n&aqs=chrome.1.69i59l3j69i57j0j69i61j69i60l2.4719j0j7&sourceid=chrome&ie=UTF-8 and I was surprised that there was no relevant formula found How do I get/even begin to get the formula for...

Hello, I am learning how to use calculus to derive the formula for kinetic energy now, I understandthe majority of the steps in how to do this, however, there is one step where I get totally lost, I will post a picture of the steps and I will circle the part where I get lost. If you see the...

I notice that ##pv=t## looks like the ideal gas law but with ##T## in units of energy. I know that ##pV = \text{constant}## means that the pressure of a gas decreases as you expand it (Boyle-Mariotte's law), explaining for instance how we breathe. I guess I could put everything in words even...

The light comes from glass to boundary of glass and soap film, then there will be light which is reflected and transmitted. The reflected light has no phase shift and the transmitted light will hit the boundary of soap film and vacuum and the reflected light from this boundary will also has no...

The pages shown in the pictures are from an engineering book. I am not sure how the thickness of sphere plays a role in the inner surface of the sphere. I know that the surface area of sphere is ##4 \pi r^2 ## . Picture 2 shows how that formula plays a role in understanding the stress...

Question 1. i Suggest a reason why any uncertainty in the values of u can be neglected. I am really rather unsure how to answer this question but I have produced my opinion nonetheless. One could assume that the uncertainty in object distance u, i.e., the distance from the lens to the light...