equation Definition and 125 Threads

The problem is from the book "The Principles of Thermodynamics" by ND Hari dass. It looks trivial problem, but I am not able to form logical arguements for going into next step. For example, It seems like first gas has equation of state ##PV =nRT## and second has ## \left( P_2 +\frac{a}{V_2^2}...

Here is the equation I obtain after simplification, I don't know if it is correct: gmc * V1 + s * C2 * Vout = [{s * (C1 + C2) * ro2 + 1} * Vout - s * C1 * ro2 * V1] * (s * rb * C2 + 1) / {ro2 * rb * (s * C2 - gm2)} I need to eliminate V1 to find the relation between Vin and Vout.

In my approach i have the roots of the equation being ##x=a## and ##x=b##. There are two assumptions, In the first assumption, ##a=\dfrac{1}{2}b## ##2a=b## then, ##4=k(-a)^2(-2a)## ##4=-2ka^3## ##⇒ -2=ka^3## Now since ##2a=b## then ##a=1, b=2⇒k=-2##. our equation becomes...

In the following I ask WA to solve the given equation and it produces a solution using the Lambert W function. I thought : $$W(x*e^x) = x$$ but here it seems $$W_n \left(\frac{-MT}{P}*e^{\frac{-MT}{P}}\right) \neq \frac{-MT}{P}$$ Is there a difference between ##W(x)## and ##W_n(x)## ?

The concentration is the Y axis, and the values are the x axis. What is the equation for finding a target value on a curve between set of points?

$$t_A= 3s$$ $$ s= 100m$$ $$v_A= 5m/s$$ $$v_B=7m/s$$ $$s(t)=7(t-3)+0$$

Wolfram gave the solution and a hint: i want to understand the hands on approach steps... In my approach (following Wolfram's equation) i have, ##(x-3)^2(2+12(x-3)+(x-3)^2=-25## ##(x-3)^2((x+3)^2-33)=-25## ##(x-3)\sqrt{((x+3)^2-33)}=-5i## ...

15 - Tension = 1.53*a T = 15 - 1.53*R*α T*0.33 - 1.10 = Iα Is this approach correct?

Why is this equation (red sign) written in constant volume and not in constant pressure?

I was going through this book called "A Course in Mathematics for Students of Physics Volume 1 by Paul Bamberg and Shlomo Sternberg". There in a part they said something like this: ...if we start with a point P and write ##R=P+u## ##Q=P+v## and ##S=P+(u+v)## then the four points ##P,Q,S,R## lie...

In my working i have, ... ##\cos C = 2\cos^2 \dfrac{1}{2} C -1## ##c^2= a^2+b^2-2ab(2\cos^2 \dfrac{1}{2} C-1)## ##c^2= a^2+b^2+2ab(1-2\cos^2 \dfrac{1}{2} C)## ##c^2= (a+b)^2 (1-2\cos^2 \dfrac{1}{2} C)## Now from here, ##k^2 =2## but text gives different solution. I am still checking...

s1=-u1^2/2a1 s2=-u2^2/2a2 s2>s1+d (If distance the car stops is bigger than the distance the lorry stops plus the initial distance then they will crash) (sub s1 and s2 in) -u2^2/2a2 > -u1^2/2a1+d Switch 2a2 with whole left side of equation. -u2^2/(-u1^2/2a1)+d > 2a2 Make the (d)a fraction by...

I saw this link; is the approach here correct...

I haven't posted for a while and I am still (!) working through some of the things I didn't quite get in MTW Chapter 21. Here is my latest puzzle. I want to work out how to get from Equation (12) in the attachment, to Equation (15). I've tried the "add and subtract" ##\{\frac...

Ok, so i have done many math classes, as i am an engineer, however, a theory class and proof class i h ave not done, except maybe one haha. here is my question, if i draw some sort of curved line by hand, how do i find an equation for that? for example, i draw half of a tear drop but along...

For question 1. I am stuck. I know that the equation involves time and possibly rate, should solve for distance. But not sure how to set it up with information given. 2. Ft= m 🔺️ v F(3)= (100kg)(30m/s) 3 s= 3000 kg m/s Same applied to question 3. 3. F(2)= (100kg)(-30m/s) F(2) = -3000 kg m/s...

m * g * h + (1/2) * m * v² = m * g * y Simplifying the equation: g * h + (1/2) * v² = g * y Substituting the values: g * 0.614 + (1/2) * v² = g * 2.73 * sin(26.7°) Now, let's solve for v: (1/2) * v² = g * 2.73 * sin(26.7°) - g * 0.614 v² = 2 * (g * 2.73 * sin(26.7°) - g * 0.614) v = √(2...

given something like: an = c where c is given and a, n, and c are only allowed to be integers. how would one find the value of say n or a?

Hello everyone, I am reading some book titled: Periodic Structures: Mode-Matching Approach and Applications in Electromagnetic Engineering. In Chapter 2, there is an equation as follows: where . Here the electric field is along the transverse x − y plane like the propagation vector kt. Now it...

I need help solving an equation. I started using Maple, but had no success. Could someone explain to me which command to use? I need to find a very small value of ##x##, that is, ##x \ll 1##. The equation is $$434972871000000000.0+{\frac {\sqrt {6} \left( { 1.488388992\times 10^ {-36}}\,\ln...

What is the difference between these two concepts? An equation is said to be "invariant" under some operation if the form of the equation doesn't change. However, isn't that exactly what "covariance" in physical laws means—that the form of the laws remains unchanged when applying an operation to...

Hi. If I write any random equation in 2D then the graph undoubtedly shows up on that 2D graphing system. Equation example: ##x^2 y^2 + x^2 y + x y =1## My question is: if I take the same equation: ##x^2 y^2 + x^2 y + x y =1## and if I manipulate the equation by including another variable...

Hi. I don´t know if this question should be in the maths forum, but as it´s related with circuit analysis, I will post it here. I just would like to know how you get: v(t) = 1/C ∫tt0 i(τ) dτ + v(t0) From: v(t)=1/C ∫t-∞ i(τ) dτ I just know the basics of calculus and I don´t know how to...

I am confused with the equation to be used for capacitor in electrical analysis The standard equation we have is Q=CV -> 1 the other equation is is V = Z*I ohms law Z is the impedance of the capacitor. Both are giving me voltage, which one to use ?

I encountered a problem in reading Phys.Lett.B Vol.755, 367-370 (2016). I cannot derive Eq.(7), the following snapshot is the paper and my oen derivation, I cannot repeat Eq.(7) in the paper. ##g^{\mu\nu}## is diagonal metric tensor and##g^{\mu\mu}## is the function of ##\mu## only...