Equivalent Definition and 1000 Threads

$$T = m \hspace{0.03 cm}C^2 \left( \dfrac{1}{\sqrt{1-\dfrac{v^2}{C^2}}} -1 \right) $$ $$ T = \dfrac{m \ v^2}{ \left( 1+\sqrt{1-\dfrac{v^2}{C^2}} \right) \sqrt{1-\dfrac{v^2}{C^2}}} $$

my doubt is that let's say we have a ratio 5:10 now the equivalent ratio for this would be 1:2 but what I am not able to understand is - let's say we have a situation in which it is given that the ratio of girls to boys is 5:10 which means for every 5 girls we have 10 boys but if we see the...

Hello, I need help please. I have the following optimization problem defined as \begin{equation} \begin{aligned} & (\mathbf{P1}) \quad \max_{\mathbf{z}} \quad \left| d -\sum_{n=1}^{N} \frac{c_n}{f_n + z_n} \right|^2 \\ & \text{subject to} \quad \sum_{n=1}^{N} \frac{|a_n|^2 \text{Re}(z_n)}{|f_n...

There appear to be at least three concepts of probability. In my words frequencies in a history (theretical and measured) reasonable expectation propensity to outcomes There may be more. I am wondering whether these are actually different meanings, which could affect how probability is used in...

For this, I don't understand how we can apply the change in entropy equation for each solid since the ##\frac{dT}{dt}## for each solid will be non-zero until the solids reach thermal equilibrium. My textbook says that the ##\Delta S## for a system undergoing a reversible process at constant...

Hi, What is the energy dependence of the Equivalent photon approximation? For this approach to be valid, what is the maximum center of mass-energy. As know, this approach is an energy-dependent approach. Can this approach be used to calculate, for example, at a center of mass energy of 100...

I did a few experiments recently of impedance spectroscopy, and I've gathered some data that i'm having some issues to find an equivalent circuit that can fit the data. The equivalent circuit that I've got, it's pretty similar with the data (graph and circuit below) But the problem is, at low...

Why is it that, due to symmetry, ∆V2 = 0 and ∆V1 = ∆V4 = ∆V5 = ∆V3? I don't really understand the reasoning behind the simplification. Thank you.

Rewrite the given equation, attempt 1: ##2\sin(x)\cos(x) + 2\sin(x) + 2\cos(x) = 0## ##\sin(x)\cos(x) + \sin(x) + \cos(x) = 0## ##\sin(x)(\cos(x) + 1) + \cos(x) = 0##, naaah, can't get any relevant out from here. Attempt 2: ##2\sin(x)\cos(x) + 2\sqrt{2}*\sin(x + \pi/4) = 0## ##\sin(x)\cos(x) +...

There are 3 parallel paths: one through 4.0 µF, one through 6.0 µF, and one through 5.0 µF and 7.0 µF. Why wouldn't there be another path through 4.0 µF, 7.0 µF, 5.0 µF, and 6.0 µF? Also, what determines the direction of current flow when there is a diagonal across parallel paths? Thank you.

Hello everyone, Concerning the separation axioms in topology. Our topology professor introduced the equivalent definition for a topological space to be a ##T_{o}-space## as: $$ (X,\tau)\ is\ a\ T_{o}-space\ iff\ \forall\ x\ \in X,\ \{x\}^{\prime}\ is\ a\ union\ of\ closed\ sets. $$ The direction...

We need to find a single wire supporting the load. But, when I think about it there can so many different types of materials we could use for the single wire and each of these single wires would have a different Young's Modulus. So, I don't get what equivalent means here? Anyways, I get the...

I am currently reading about small signal analysis of a MOSFET differential amplifier. The text I am using has the below two figures for a common-mode equivalent circuit for the amplifier. The first makes sense to me except where it calls it a "Norton equivalent circuit", whereas I thought a...

Full problem: I don't normally think about circuits like these in terms of energy (Joules) so I was very much confused. What I did was find where the simplified expressions intercepts with each other to get the voltage. I scanned in my work although this text is a walk through of what I did...

De normal distribution has the following form: $$\displaystyle f \left(x \right) \, = \,\frac{1}{2}~\frac{\sqrt{2}~e^{-\frac{1}{2}~\frac{\left(x -\nu \right)^{2}}{\tau ^{2}}}}{\tau ~\sqrt{\pi }}$$ and it's integral is equal to one: $$\displaystyle \int_{-\infty }^{\infty }\!1/2\,{\frac {...

1.) In electromagnetics, wavelength in a medium is $$\lambda = \frac{\lambda_{0}}{n}$$, where $$n$$ is the refractive index. What is the equivalent formula for sound wave in a medium? 2.) Is there a reference sound velocity, like electromagetic wave speed in vacuum is $$c_{0} =...

NOTE: THE C1 that is 120 microfarads is meant to be C3. What I did first was find equivalent capacitance of C2 and C3 by doing (40)*(120)/(40+120)=30. Then I found Ceq by doing (20)*(30)/(20+30)=12. For the resistance I did 6*3/(6+3)=2, for R2 and R1. Then to find Req I did (5)*(2)/5+2= 10/7 Am...

First, I calculate the Thevenin resistance by treating the independent current source I0 as an open circuit and noticing that the resistance of the dependent voltage source is α (since V=IR and the voltage across the dependent voltage source is given by αi. In this way, I have: RTH = 1 / (1 /...

For some basic definitions we call connected, metric space a continuum and we say that continuum is aposyndetic if for every pair of points p,q exists a subcontinuum W such that $p \in int(W) \subset W \subset X \setminus \{q\}$ similarly I introduce a notion of "zero set aposyndetic" as: X is...

I have a question about an exercise I don't understand, I don't want the solution, only the first element to begin. I have tried with kirchhoff law, but I failed. thanks

We denote a scalar product of two vectors ##a, b## in Hilbert space ##H## as $(a,b)$. In Bra Ket notation, we denote a vector a in Hilbert space as ##|a\rangle##. Also we say that bras belong to the dual space ##H##∗ . So Bras are linear transformations that map kets to a number. Then it...

Hey, I am having big issues with the following question. I have done node analysis to get the following equations 1-5 and the equation for A i have removed because it was not needed apparently. When solving the equationsystem I get that the voltage in node 1-5 is (using matlab) V =...

Hi guys, I don't really know how to cope with this problem, maybe just because I can't properly understand the data. In the figure we have a beam with its loading(plus a force of 15kN), a pivot O and support at the rightmost point. I would say that in order to find the equivalent system, I...

In MATLAB one can 'hold off' to remove a previously drawn thing on the same graph. How about in python?

i keep getting 45.3 ohms but the answer is 25.6 ohms

There is a bias in the medical community toward getting vaccinated even if you have had Covid with symptoms. Example - https://health.clevelandclinic.org/when-should-you-get-vaccinated-if-youve-had-covid-19/ I am unaware of any hard science - incremental analysis - that would conclude that...

It says that sets that are equal ie having the same types of elements can also be equivalent, having the same number of elements when b has more distinct elements than a. Please explain

We are asked to find the equivalent impedance of the network. Nothing is in series or parallel so I don't know what to do. We cannot use mesh equations or Thevenin's theorem because is no current or voltage source. So I have no clue.

Summary:: So I found Vth=1.19 using Nodal analysis and I'm not sure if that's right, I'm trying to find Rth now but I'm confused as to what to do, any tip that tells me at least from where to start is appreciated. Edit: so I did 12||60 so Rth=10 ohm, is that correct? Is Vth correct too?

How much does the equivalent width of a line change by the introduction of 5% scattered light? We know the equivalent width is defined as We know the equivalent width is defined as $$W = \int_{-\infty}^{\infty} \bigg(\frac{1-F_{\nu}}{F_c}\bigg) \, d\nu$$ where ##F_{\nu}## represents the flux in...

i need a help, this is my first post in this platform, actually few year ago I perform a forging operation in a 6 Ton forging press but now i have 3 Ton hammer press, can i use that press to make that product. is there any calculation to find out equivalent hammer press of a forging press

Conceptually I have never really understood Ohm's law, other than using it in calculations. My brain just cannot understand why this equation works. I was wondering if there is some sort of gravity equivalent to perhaps conceptualise it a bit better. Voltage: would be the acceleration due to...

R1 = 2 ohms ; R2 = 2 ohms; R3 = 1ohm First figure: I need to calculate the resistance between: a) A and C and b) A and B a) R1 and R3 are in series => R13 = R1 + R3 = 3 ohms R13 and R2 are in parallel => 1/Rp = 1/R13 + 1/R2 => Rp = 1.2 ohms b) Here, between A and B there is only R1 so the...

Hi there, In QFT, a free scalar field can be represented by the lagrangian density $$\mathcal{L} = \frac{1}{2}\left(\partial\phi\right)^2 - \frac{1}{2}m^2\phi^2$$ I would like to find a classical system that has the same lagrangian. If we consider the transversal motion of an elastic string...

I have two independant experiments have measured ##\tau_{1},\sigma_{1}## and ##\tau_{2},\sigma_{2}## with ##\sigma_{i}## representing errors on measures. From these two measures, assuming errors are gaussian, we want to get the estimation of Ï and its error (i.e with a combination of two...

Let us just lay down some definitions. Both sequences are equivalent iff for each ##\epsilon>0## , there exists an N>0 such that for all n>N, ##|a_n-b_n|<\epsilon##. A sequence is a Cauchy sequence iff ##\forall\epsilon>0:(\exists N>0: (\forall j,k>N:|a_j-a_k|>\epsilon))##. We proceeded by...

I have to apologize if the diagram is awful: I drew it for the sake of asking... I am analyzing the rope that is hanging the pulleys. From the diagram, the pulley at the left (let's call it L), has two objects with mass M at both ends. The pulley at the right (let's call it R), has an object...

I have the solution to the problem, and I mechanically, but not theoretically (basically, why do the C(s) and R(s) disappear?), understand how we go from ##(s^5 + 3s^4 + 2s^3 + 4s^2 + 5s + 2) C(s) = (s^4 + 2s^3 + 5s^2 + s + 1) R(s)## to ##c^{(5)}(t) + 3c^{(4)}(t) + 2c^{(3)}(t) + 4c^{(2)}(t) +...

I've been given this answer: to move from negative to positive angles, ##-\theta'=2\pi-\theta##; and to move from positive to negative angles, ##\theta'=\theta-2\pi##. But my question is if there is any way to calculate it in a sequence of inequalities' steps. If I am being cumbersome, forgive...

Hi, I'm struggling with this question. I feel like I don't even know where to begin. It seems to be a relatively simple calculation, but would the effective capacitance between A and C not just be 1 microFarad? Obviously that can't be the correct answer because such a simple observation wouldn't...

Could anyone please help with the following? Three forces of magnitudes 10, 3 * sqrt(5) and 25 Newtons act along lines whose vector equations are respectively: r1 = i - 2j + k(4i + 3j) , r2 = -2i + 4j + k(2i - j) and r3 = 4i + k(7i - 24j) A fourth force F4 is introduced which reduces the...

I considered that the lengths of pi/4 and 3pi/4 would be in parallel: 1/R = 1/30 + 1/10 R = 7,5 ohm But the answer is 30 ohm. Where am I missing and how do I calculate the potential of the voltmeter.

how come 7271000mm3 is equivalent to 7271cm3) ? from mm to cm you should go back two zeros back right ?

Well, the question is in the title.

I need to brush up on some Chemistry over Summer, and I wondered if anyone knew of some problem books pitched at a similar level to Irodov's problem book for Physics, or things like IChO questions. Preferably it would include all of physical, inorganic and organic, to some degree. I get various...

I asserted C3, C4, and C5 to be in series. **I found the capacitance of "C3-4-5" to be 1.67x10-6 F. This I did by using 1/C = 1/C3 + 1/C4 + 1/C5 Then I noticed that I had another series circuit of "C3-4-5" and C1, and C2. Again, I used a similar formula. I obtained an equivalent capacitance of...

Hey! 😊 Let $\mathbb{K}$ be a field and let $V$ be a $\mathbb{K}$-vector space. Let $1\leq k\in \mathbb{N}$ and let $U_1, \ldots , U_k\leq_{\mathbb{K}}V$ be subspaces of $V$. Let $d_i:=\dim_{\mathbb{K}}U_i$ and $\mathcal{B}_i:=(b_{i,1}, \ldots , b_{i, d_i})$. Show that...

By the use of symmetry, I have found that equal currents will flow through opposite edges like A-C and C'A', but still, the use of kirchhoffs current and voltage laws lead to four equations in four variables which I am not able to solve, neither I am sure that the four equations which I have...

So I'm guessing we need our end unit to be in MPG? a) walking ( 220 kcal/ 1 hr )⋅ ( 1hr / 3 mile ) = 73 .3 kcal/mi⋅⋅ (73 .3 kcal/ 1 mile) ⋅ (4,186 J/1 kcal) = 3,06833.8 J/mi (1.30 x 10^8 J/ 1 gal)(1 mile / 3,06833.8 J) = 423.68 MPG b) bicycling Not sure as it says,"...when riding at 10.0...