Change Definition and 1000 Threads

I rearranged the equation and got $$12x+12y=xy$$ Differentiating this I get $$12\frac{dx}{dt} + 12\frac{dy}{dt} = x\frac{dy}{dt} + y\frac{dx}{dt}$$ Substituting the values I get $$12\frac{dx}{dt} -12= -5+\frac{dx}{dt}$$ SO $$\frac{dx}{dt}=\frac{7}{11}$$ But if I directly differentiate the...

Hi all, I am looking for clarification on what is probably a pretty basic change of variables between a few lines in the following paper: https://journals.aps.org/prd/pdf/10.1103/PhysRevD.34.1326 Equation (9) shows the differential cross section for a Bremsstrahlung process which...

Method 1 is the standard and (probably) the correct answer. I was fiddling around with it and don't understand why I get a different answer using method 2. If the gas is changing pressure, then it is changing volume. So why can't I sum up the entropy changes using method 2? Using method 2 with...

I tried two different methods when solving this question and have no idea why. Method 1: Using the Maxwell relation of $$\left(\frac{\partial S}{\partial V}\right)_T=\left(\frac{\partial P}{\partial T}\right)_V=\frac{R}{V-b}$$ then integrating it, I get $$\Delta S = \int_i^f\frac{R}{V-b}dV$$...

Consider differentiation ##\frac{df(x)}{dx}##. If we change the variable as ##x=-u## how does the differentiation change? Does it change as ##\frac{df(-u)}{-du}##?

Could someone guide me on what change of variable was used to obtain equation 9.138 from equation 9.137? Book : Classical Dynamics of Particles and Systems 5th Edition by Stephen T. Thornton (Author), Jerry B. Marion (Author) They told us to check equation 8.38 and in that page they had...

Hello everyone, If I have an integral ##\int_0^r \sqrt{(r^2 - x^2)}dx## and I'm integrating across the first quadrant to get the area of the first quater of a circle. And I change variables with ##x = r\cos{\theta}## and ##dx = -{r}\sin{\theta}{d\theta}## And I form a new integral that's...

I am sure that the radius of the two spheres changes equally. But in answer of the question it said that their change in volume is the same. Is it correct?! Link of website: https://www.toppr.com/ask/question/two-spheres-of-same-size-are-made-of-the-same-metal-but-one-is-hollow/ I think it is...

Currently when set to 1C, the fridge cools to and maintains 4-5C(As a conversion when set to 34f it cools and maintains approx. 40f. ), all functions like fan/defrost are working correctly. Potentially the main board has an issue but all other zones are working correctly so I would prefer to not...

I want to work out how to calculate the pressure change in a gas cylinder if it is used to fill another cylinder to a lower pressure. For example, if a 50 litre gas cylinder initially at 200 bara is used to fill a 600 litre cylinder from atmospheric pressure to 1.5 Bara. What would the change...

Not a solution. This is the graph provided. I think I start with finding the magnitude of the IF vector but I’m not sure. And I don’t know where to go from there.

Since the system is doing no work, would it be just 4513 J? I don't think there is any other information to use

You've helped me change a couple bulbs so far, hopefully this is the last one. There's a recessed light on a hinge (a gimbal light maybe?) There are three exterior white rings - the outermost is a trim, the middle is a flat piece, the inner is ridged. Both the middle and inner piece move on...

Hello. I was wondering if there have been any further developments on the topic of B-modes in the CMB polarization since this 2015 paper? https://arxiv.org/abs/1502.00612 A Joint Analysis of BICEP2/Keck Array and Planck Data The above paper declares that... 'We find strong evidence for dust...

For this, Why dose they write the change in entropy equation as ##\Delta S = \frac{Q}{T}##? Would it not better to write it as ##\Delta S = \frac{\Delta Q}{T}##, since it clear that we are only concerned about the transfer of heat in our system while it remains at constant temperature as all...

Say I have a magic way to exert lateral forces on a free-rolling ball on a plane, with no slipping. Say I apply a force for a given period from the South, the ball starts rolling to the North and attains a constant speed. Then I suddenly apply the same force for the same period but from the...

Looking at the given values, I thought the specific heat formula could be used to calculate the final temperature of the air: c = Q/mΔT. Since the final temperature is the sum of the initial temperature and the change in temperature, the formula can be rearranged to ΔT = Q/m*c. Q = 30 W * 10 s...

I would appreciate knowing if there is any error in the mechanics illustrated in this animation with respect to phase change in the signal reflections shown at A and B, or in the description accompanying it. I have embedded the description with the animation and included it in this post for...

Hello forum, I have created some linear regression models based on a simple dataset with 4 variables (columns). The first models simply involve one predictor variable: $$Y=\beta_1 X_1+\beta_0$$ and $$Y=\beta_2 X_2+ \beta_0$$ The 3rd model is multiple linear regression model involving the 3...

I have attached my solution. Unfortunately, after plugging in the values, my answer is 4 times more than the expected one. What am I missing?

I understand that it is a 2D momentum problem with an elastic collision; Looking at the vector diagrams below, I notice that the velocity vectors initial and final in the y direction are in the same direction, indicating that momentum does not change, whereas the velocity vectors initial and...

Would the force (as predicted by Coulomb’s law) exerted on two charged particles q1 and q2, separated by distance r, and at rest relative to frame S change, if q1 and q2, began moving relative to S but we’re still at rest relative to each other?

Hi all, in this question i was asked to find the percentage change in the density, my approach was as following, first i find the change in volume due to putting the gas into the other vessel as: $$ P_{1}V_{1}=P_{2}V_{2}\;\; → \;\;V_{2}=\frac{P_{1}}{P_{2}}V_{1} $$ now i use $$...

Hello, I want to model a thermal battery based on phase change materials (PCM). It is a plate heat exchanger immersed in a PCM bath. The diagram is given in the attached file. I want to determine the temperature at each moment and from everywhere in the battery. The hypotheses are the...

A satellite is orbiting a planet in a circular orbit. The planet's mass doubles instantly. What happens to the orbit of the satellite? I think it would move to an elliptical orbit with major axis equal to the old radius and a minor axis equal to either 1/2 or sqrt(2)/2 times the old radius. I'm...

I came across the following statement from the book Physics for Engineering and Science (Schaum's Outline Series). I cannot seem to find a satisfactory answer to the questions. Is the statement in above screenshot talking about entropy change the statement of Second Law of Thermodynamics or is...

Until now in my studies - matrices were indexed like ##M_{ij}##, where ##i## represents row number and ##j## is the column number. But now I'm studying vectors, dual vectors, contra- and co-variance, change of basis matrices, tensors, etc. - and things are a bit trickier. Let's say I choose to...

The planet is faster when it is closer to the planet because when it is closer to the planet it has less rotational inertia, and rotational momentum is conserved in this system, so less rotational inertia means a greater angular velocity. This explains why it is slower when it is farther away...

The behavior of those two function keys at the top of my Dell Windows 10 laptop recently changed, and I'm trying to figure out how to change it back to normal. At the upper right of my keyboard there are these function keys with 2 functions apiece shown: prtscr/F10 home/F11 end/F12...

In Greiner's Classical Electromagnetism book (page 126) he has a derivation equivalent to the following. $$\int_V d^3r^{'} \nabla \int_V d^3r^{''}\frac {f(\bf r^{''})}{|\bf r + \bf r^{'}- \bf r^{''}|}$$ $$ \bf z = \bf r^{''} - \bf r^{'} $$ $$\int_V d^3r^{'} \nabla \int_V d^3z \frac {f(\bf z +...

Hello, I am stuck how to proceed with the equations below. The problem: A tank containing ##m_0## mass, with a temperature of ##T_0##, is to be filled with a total mass of ##m_1##, with the constant mass flow rate ##G## and temperature ##T_1## during ##t_p## seconds. ##T_0>T_1##. Other than the...

the tldr covers everything I think. I don't expect there will be an analytic solution here lol. but I don't even know where to even begin formulating this problem mathematically. I assume I should find an expression for the initial lift on the blades, multiply by 3 and then model it as a...

It is known, that due to global warming, the average temperature on Earth over the past 100 years has increased by 1.2 degrees. At the same time, I heard that earlier the temperature of the Earth was 7 degrees higher than the current one. I do not deny the danger of global warming, because I...

I proceeded in the usual manner in which we take ##dU = 0## in the case of free expansion because there is no heat transfer in the box, as well as no work is done. We can write, taking ## U ## as the function of ##V## and ##T##, $$ dU(V,T) = \left( \dfrac{\partial U}{\partial V} \right)_T ~...

Hi, Unfortunately, I have problems with the task 4 In task 3 I got the following $$ T_f=T_ie^{\Delta S_i - c_i} $$ Then I proceeded as follows $$ \Delta S = \Delta S_1 + \Delta S_1 $$ $$ \Delta S =c_1ln(\frac{T_ie^{\Delta S_i - c_i}}{T_1})+c_2ln(\frac{T_f}{T_2})$$ $$ \Delta S...

So the question goes like this: find change in internal energy in process 1->2 using diagram. And offered solutions a)-400J b)400J c)600J d)800J. First I found T1 and T2 using (P*V)/T=R and got T1=24K and T2=72K. Then I found n(number of moles) using PV=nRT and got n1=1mol, n2=1mol. Then I...

I have a VPB-808 Fan (rated 4100 RPM) from Viron. I am currently trying to pull 1300 CFM at 7" SP, which needs ~2668 RPM (2.85 HP). I have a pulley drive motor (Baldor, EM3611T, 3HP, rated 1760 RPM, 4.2A). It is drawing about 2.8A with the following configurations. It is currently only blowing...

Supposed answer = 0.482n

https://royalsocietypublishing.org/doi/10.1098/rspb.2022.1073 This raises the specter of pre-human era pathogens being re-released because the permafrost is melting. AFAIK, even the sci-fi authors have not explored that idea.

Hello, I have to compute a double integral of the form ## \int_{0}^{\infty} \int_{0}^{\infty} f(u,v) du dv##, where ##f(u,v)## is not relevant. The following change of variable is advised as a hint: ## u = zt ## and ## v = z(1-t)##. From there, I can reformulate with respect to ##z## and...

Doctors Still Struggle to Diagnose a Condition That Kills More Americans Than Stroke https://www.theatlantic.com/health/archive/2022/10/sepsis-artificial-intelligence-diagnosing-early-detection/671755/ It's important to clean wounds (breaks in the skin or inside surface), even if they appear...

Hello everyone! I was wondering what is the fundamental state change in the universe? I.E the universe is in one state, then it goes into another state, what is the state change? Has science determined what it is? Do we know the dimensional units of the quantity? I'm not sure if this has a...

Our eye colour doesn't always remain constant throughout our lives – in fact, a wide range of external influences can change it, from injury to infection and sun damage. And sometimes the change appears to happen spontaneously...

When the rocket accelerates in space does its trajectory which is an ellipse change in size and not the focal points because the Earth is still in one of two and also the current height doesn't increase, right?

Hey all, I am currently struggling with a change of variables step in my calculations. Suppose the solutions ##f_{1}(x)## and ##f_{2}(x)## of the following system of differential equations is known: Now the system I wish to solve is: Upon first glance, it seems that the association ##f_{2}(-x)...

I feel that the answer is B) because Increasing the pressure increases the intermolecular forces Of the gas molecules but I do not see how this In effect will lead to an increase in the enthalpy

Greetings all. I just got confused by the following. Consider volume integral, for simplicity in 1D. $$ V(A) = \int_{A} dz. $$ If ##z## can be written as an invertible function of ##x##, i.e. ##z=f(x)##, we know the change of variables formula $$ V(A)=\int_{A} dz= \int_{z^{-1}(A)} |z'(x)|dx...

My wife is wanting to place an empty alcohol bottle filled with Dawn in the toilet tank. Have a 1//16 hole drilled 3 inches from the bottom so the fluid will come out when flushed and the water level gets lower than the hole. The Dawn will stop coming out once the water refills above the hole...

If I start with two, otherwise isolated, masses M and m initially together and do work to separate them then the work done, I assume, goes into the gravitational binding energy between them. Will the system of mass M and m have increased in mass due to this in accordance with e=mc^2? I...