Variable Definition and 1000 Threads

Hi, I have a question regarding the envelope function in parameter representation. Let an array of curves in cartesian coordinates be given in parameter representation, with curve parameter 𝑡 and array variable 𝑐 𝑥=𝑥(𝑡,𝑐) 𝑦=𝑦(𝑡,𝑐) Condition for envelope is: 𝜕/𝜕𝑡 𝑥(𝑡,𝑐) 𝜕/𝜕𝑐 𝑦(𝑡,𝑐)=𝜕/𝜕𝑐...

If a system is represented by a set of generalized coordinates ##q_i## in which one coordinate say ##\theta## is such that ##d \theta## represents a rotation of the system about a fixed axis( an axis whose orientation remains fixed in space) then the kinetic energy ##T## shouldn't depend on it...

The best I can get is: $$\log_{6} 3=m-n+\log_{6} 2$$ Is it possible to get the final answer in terms of ##m## and ##n## only? If yes, I will try to do it again Thanks

Hi, I was trying to solve the attached problem which shows its solution as well. I cannot understand how and where they are getting the equations 3.69 and 3.69A from. Are they substituting the values of θ₁ and θ₂ into Expression 1 after performing the differentiation to get equations 3.70 and...

Hi, I cannot figure out how they got Table 2.1. For example, how come when x=1, F_X(x)=1/2? Could you please help me with it? Hi-resolution copy of the image: https://imagizer.imageshack.com/img923/2951/w9yTCQ.jpg

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...

#include <iostream> #include <string> #include<iomanip> //prototypes double gettingInfo(double&, double&, double&, bool&, char&); double errorChecking(double&); double calculatingPrice(double&, double&, double&, bool&); double printingReciept(double&, double&, double&,double&); using namespace...

The equations of variable mass systems are usually deduced from some very informal argument. It is so at least for the books I know. So I tried to construct a formal proof based on the continuous media equations. Criticism, remarks etc are welcomed. Let ##D\subset \mathbb{R}^q## be an open...

I have a series of variables X i where ultimately the variables Xi each follow approximately an exponential distribution with a constant rate. In the beginning, there is a certain long-term trend. Is there a probability model in which Xi depends on the outcome of Xi-1 so that in the long run...

It seems the field φ(t, xi) could be integrated over all space to form a single temporal variable (which isn't a field anymore, but is just a function of time) as follows: Φ(t) = ∫φ(t, xi)dxi Suppose we then assume a Lagrangian from this temporal variable to be: L1 = -1/2 Φ'(t)2 + 1/2 b2...

I have tried manipulating this to $$1-\frac{8}{(\pi k_B T)^2}\mu^\frac12(\epsilon^\frac32-\mu^\frac32)=0\Leftrightarrow\left[1+\mu^\frac12(\epsilon^\frac32-\mu^\frac32)\right]^{-\frac{8}{(\pi k_B T)^2}}=0$$ but this doesn't seem to lead anywhere. any hints please? the solution is one of these...

I'm reading "Differential Equations with Applications and Historical Notes" by George F. Simmons and I am confused about something on pages 431-432 He has the second order ordinary differential equation $$\frac {d^2v} {d\phi^2} + \frac {\cos(\phi)} {\sin(\phi)} \frac {dv} {d\phi} + n(n+1)v = 0...

This device, if it or something similar exists at all, needs to be completely mechanical without ANY electricity and be really precise and strong (to last a long time). Press a button in order to trigger the start of the delay time. It must start only when the button is fully pressed down (or...

Summary:: How to keep the same voltage and change the frequency of a A.C. universal motor. Hello there! I need some help regarding my final project for the university. I have a universal motor, supplied by a single phase, 220V source. I need to make this motor work at the same voltage, but to...

Is my solution correct? $$ F(t) = at + b $$$$W=\int_t F(t)dr, ~~~~~~~~~ ~~dr = v(t)dt$$$$W=\int_t F(t)\cdot v(t) dt$$ $$ f = \frac{dp}{dt}$$ therefore $$v(t) = \frac{1}{m}(at^2/2+bt)$$then $$W = \int_t \frac{at+b}{m}\cdot\left(\frac{at^2}{2}+bt\right)dt$$ $$W = \frac{1}{m}\int_t...

I'm supposed to solve this using nodal analysis. No biggie! I'm just not sure how to handle ia. I've never seen a current indicated in a junction crossing. I searched the web and my textbook and found zilch. I asked a GSI and was informed it is indeed written where is supposed to be. Within the...

I have an integral that depends on two parameters ##a\pm\delta a## and ##b\pm \delta b##. I am doing this integral numerically and no python function can calculate the integral with uncertainties. So I have calculated the integral for each min, max values of a and b. As a result I have obtained...

Hello, I am review some basics. In the case of two variables like ##t## and ##C##, which represent the time in year and the cost in $ of a product respectively, we can graphically represent this pair of variables on a Cartesian plane. The horizonal axis is generally assigned the variable ##t##...

The question is regarding an electrically excited synchronous generator. Consider that this generator is not connected to the grid and thus not locked with the grid frequency. This generator is spinning at variable speed and gets constant and similar excitation current meaning that the...

Hello, In Python and other programming languages, data can be of different types: integer, float, string, Boolean. On the other hand, Data structures are containers of data items which can (or not) have the same data type. A variable, when created, has: a) name (a piece of data stored in...

I have the following function: $$y = s-1 + exp (-ln (-1 / (s-1)) x)$$ with 0 < s < 1. For ##x = 0## you have ##y = s## and for ##x = 1## you have ##y = 0##. The function has a fixed bend, but now I want to make the bend variable, while the two properties, that for ##x = 0## you have ##y = s##...

Let us suppose we have a function such that $$z = e^{1/ab} - 1$$ Where we have two free parameters, a and b. Q1) Can we say that as ##b \rightarrow \infty##, ##z = 0##? Or, since ##a## is a free parameter, there is always some value for ##a## such that ##z \neq 0## for ##b \rightarrow...

I don't understand this header file in the book. In line 4, it declares static int objectCount; I tried to put static int objectCount = 0; it won't compile, I tried putting in the next line objectCount = 0; it doesn't work. I tried putting in line 6, it doesn't work. Being declare in private...

Sometimes I would like to transform an integral ##F(x) = \int_{a}^{x}f(s)ds## into an infinite integral of the form ##F(x) = \int_{0}^{\infty}f(g(u),x)du##. Is there some kind of change of variables that can guarantee this conversion on the boundaries and still give me a function of ##x##, at...

(1) For ##x>a## ##f(x)=x^2+x-a+1 \rightarrow## minimum value obtained when ##x=-\frac{1}{2}## Minimum value of ##f(x)=\frac{3}{4} -a## (2) For ##x<a## ##f(x)=x^2-x+a+1 \rightarrow## minimum value obtained when ##x=\frac{1}{2}## Minimum value of ##f(x)=\frac{3}{4}+a## But the teacher said...

If say we have a scalar function ##T(x,y,z)## (say the temperature in a room). then the rate at which T changes in a particular direction is given by the above equation) say You move in the ##Y##direction then ##T## does not change in the ##x## and ##z## directions hence ##dT = \frac{\partial...

So I found a paper, https://www.sciencedirect.com/science/article/pii/S0022231314006048?via%3Dihub which concerns a property of a compound called "Quantum Yield", which is a result of various factors (independent variables). The authors are trying to figure out what factors affect the quantum...

Using: $$i(t)=\frac{U}{R}.e^{-\frac{t}{RC}} As the power is constant, then the current will be constant, so: t/RC is constant I don't know how to proceed anymore. I think you should use some derivative, but I'm still very new to that part, so how can I proceed?

Bell's superdetermimism seems to imply that there is a hidden variable. Please correct me if I am wrong but that seems like classical physics.

Hi, I have this question: If random variable T is uniformly distributed over [a, b] , what is its failure rate? Please help

Don't really know what they want from me

I am not sure about how to approach this. Since the volume is uniformly distributed, the mean volume is ##(5.7+5.1)/2=5.4##, which is less than ##5.5##. From this, I could say that, on average, the producer won't spend any extra dollars. But then I thought that maybe I should interpret this as...

Hello, I am getting better at using the command line in Windows. I understand that the "set" command at the prompt shows all the various environment variables, PATH variable included, and I see many directories listed in the PATH. However, when I access the environment variables through the...

I was told this problem could simply be solved with calc-1 techniques, so I'm tempted to say we could do d/dx(x∫(limits: 0,x) sin(t) dt. Then it's a simple product rule: d/dx (x) * ∫(0,x) sint dt + x * d/dx(∫ (0,x) sin (t) dt) = 1 - cos(x) + x*sin(x). However, I wonder if we have to allow that...

If E(X1)>E(X2), does it mean that E(1/X1)<E(1/X2)? Thanks!

The displacement of the particle is; s= ∫v dt s= ∫4-3t^2 dt s=4t-t^3+c When the particle is at the Origin, t=0; 0=4(0)-(0)^3+c c=0 So this becomes; s=4t-t^3 The particle next passes through the origin when; 4t-t^3=0 Factor out the common term -t; -t(t^2-4)=0 Rewrite t^2-4 as t^2-2^2 and factor...

I'm studying the proof of this theorem (Zorich, Mathematical Analysis II, 1st ed., pag.136): which as the main idea uses the fact that a diffeomorphism between two open sets can always be locally decomposed in a composition of elementary ones. As a remark, an elementary diffeomorphism...

This is a very confusing situation for me. If the input voltage were constant, then I would be able to understand that by varying load resistance, I can change the current through it, such that the drop across the load = Vz = 6.8V. But the input voltage is also not constant. So what am I to...

This problem was from the chapter on Work and Energy so, I thought of using the principle of conservation of mechanical energy. Clearly, the potential energy of the block decreases by mgh (assuming the block has mass m). This energy should have been converted to kinetic energy, but it clearly...

Students see my 20+ page calculus bundle on limits, derivatives and integrals and their applications. The summary notes are cleanly written, have background math grid paper, and summarize all major concepts, formulas, and procedures from calculus books. Please tell me what you think and if this...

I have a formula for cost calculation that contain x and y two variable. I have to find the value of (x,y) where that formula will gives minimum value as cost should not be equal to zero, it has some minimum value. I took 1st partial derivative with respect to x and then with y and found the...

Hello! Brand new to the forums, hopefully someone here can help me out. Paths start out at the edge of a circle and "flow" along a polar equation that determines phi based off the initial phi (phi0) and a variable radius (ie. as your radius grows, your phi is changing). Hopefully this image...

Does anyone know any good research on this topic? I'm basically looking for information on what would be solving integral and differential equations in which the unknown you need to solve for is the level of a integral or derivative in the equation. For example F'1/2(u)+F'x(u)=F'1/3(u) where the...

I need to find A_v, I want to relate Vin to Vout. To do this I did KVL on the major loop: $$V_{DD} = I_D*R_D + V_{SD1} - V_{SD2} - I_D*R_D$$ Since M1 = M2 then everything would cancel out and I would just get V_dd = 0 which is probably wrong. This is assuming V_sd1 = V_sd2, is that correct?

Hi, I really struggled to dig valuable things out of internet and books related to high order homogeneous differential equation with variable coefficients but I have nothing. All methods I see involves given solution and try to find others(like reduction of order method), even for second order...

This question stems from one of the recent homework threads. I'm familiar with the derivation given here regarding mass accretion and ejection, where the general idea is to define a system around body and all of the incoming/leaving mass so that we can once again apply NII to the whole thing. I...

Hello, I've got to rationally analice the form of the solutions for the equations of motion of a simple pendulum with a varying mass hanging from its thread of length ##l## (being this length constant). I approached this with lagrangian mechanics, asumming the positive ##y## direction is...

Take the equation for gamma. I know how to get from step 1 to gamma. How would I do that if I have not have seen the instructions? There are many ways to factor step 1 without getting the same values of ## gamma = \frac 1 {\sqrt {1 - \frac {v^2} {c^2}}} ## step 1 = Speaking of factoring and...

Would the following: $$ L = m(\vec{\dot r + \vec v})$$ (constant velocity added to above eq.) lead to equivalent euler-lagrange equations due to the fact that the ratio of T and V is unaffected by an increase in constant velocity? And would this be an example of energy conservation?

Hello, My university offers a couple Complex Analysis courses, among them there is one with the following description: Introduction to complex variables: "substantial attention to applications in science and engineering. Concepts, calculations, and the ability to apply principles to physical...