What is Change: Definition and 1000 Discussions

"Change" (stylized as "chAngE") is Japanese singer-songwriter miwa's third major label single, released on September 1, 2010.

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1. B Question about the limits of integration in a change of variables

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...
2. Change in volume of sphere with change in temperature

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...

4. Possible to change a thermistor resistance curve?

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...
5. I Calculating Pressure Change Filling Gas Cylinders

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...
6. Calculating Change in Energy: A Graph Analysis

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.
7. Is the Change in Internal Energy Just 4513 J When No Work Is Done?

Since the system is doing no work, would it be just 4513 J? I don't think there is any other information to use
8. Misc. Let's change another light bulb

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...
9. B B-Modes in CMB Polarization - any change since BICEP2 in 2015?

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...
10. The Entropy Change of Melting Ice: Why is the Equation Written as ΔS = Q/T?

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...
11. I Rolling ball, change of direction

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...
12. Change in temperature of air in a closed system

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...
13. B Phase Change in Light: A & B Signal Reflections

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...
14. I Expected coefficient change from simple to multiple linear regression

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...
15. Change in energy stored in a spherical Capacitor

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?
16. Find the magnitude of the momentum change of the ball?

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...
17. I Does Coulomb’s law change at relativistic speeds?

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?

26. I Temperature change due to mixing liquids, heating and heat losses

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...
27. Calculating the change of a Wind Turbine's RPM due to Airflow as f(t)

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...
28. Consequences of global climate change

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...

31. What is the change in internal energy after two processes?

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...
32. How to Determine Over-Amperage on Pulley Size Change?

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...
33. Calculate new RPM after change in g-force in a centrifuge

Supposed answer = 0.482n
34. Viral spillover risk increases with climate change in High Arctic lake

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.
35. F

Jacobian: how to change limits of integration?

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...
36. Sepsis is often misdiagnosed, or just missed. That may change soon.

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...
37. I What is the smallest possible state change in the Universe?

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...
38. BBC - Our eyes can change colour in surprising ways

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...
39. Change of ellipse while accelerating the rocket

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?
40. I Quick Change of Variables Question

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)...
41. Chemistry How can ideal gases be used to determine the change in enthalpy using Hess' law?

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
42. I Integral change of variables formula confusion

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...
43. J

Will Mixture Ratio Change in a Tank?

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...
44. B Gravitational Potential Energy & Mass Change: Andrew's Question

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...
45. Biology Sketch the change of pH in the breakdown of proteins into amino acids

The pH stays the same because the optimum pH of trypsin is around pH 7.5. I think??
46. A Matrix representation of a unitary operator, change of basis

If ##U## is an unitary operator written as the bra ket of two complete basis vectors :##U=\sum_{k}\left|b^{(k)}\right\rangle\left\langle a^{(k)}\right|## ##U^\dagger=\sum_{k}\left|a^{(k)}\right\rangle\left\langle b^{(k)}\right|## And we've a general vector ##|\alpha\rangle## such that...
47. Chemistry Enthelpy Change of Neutralization

Hi, everyone! There's a question I found on website I'm using and the answer key here is given. My question is this, where did the 400g come from? According to the definition of enthalpy of neutralization (chem libretexts), the standard enthalpy change of neutralization is the enthalpy change...
48. I Calculating Relative Change in Travel Time Due to Spacetime Perturbation

Suppose you have the following situation: We have a spacetime that is asymptotically flat. At some position A which is in the region that is approximately flat, an observer sends out a photon (for simplicity, as I presume that any calculations involved here become easier if we consider a...
49. B Why do subatomic particles change what they do when observed?

Why do subatomic particles change what they do when observed? Does it matter who is doing the observing? What happens if a non-sentient robot does the observing? How does that compare with a sentient human doing the observing? Thank you.
50. MCNP6 simulation still running but no change for a while

After previous thread my program finally work and i could get the Keff final. But problem rises when MCNP want to do "predictor" and "corrector". I already wait for 3 hours but there is no update for the corrector (screenshot attached). heres the profof that my program still running: and in...