Physics, 10.10.2019 06:00 bbyjoker

Atank initially contains 120l of pure water. a mixture continuing a concentration of γγ g/l of salt enters the tank at a rate of 2 l/min, and the well-stirred mixture leaves the tank at the same rate. find an expression in terms of γγ for the amount of salt in the tank at any time tt.

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Answer from: cassidyschmuzler

The amount of salt in the tank at any time t is $A(t)=120\gamma\gamma(1-e^{-t/60} )$

Explanation:

By definition, we have that the change rate of salt in the tank is $\frac{dA}{dt}=R_{i}-R_{o}$ , where $R_{i}$ is the rate of salt entering and $R_{o}$ is the rate of salt going outside.

Then we have, $R_{i}=2\frac{L}{min}*\gamma\gamma\frac{g}{L}=2 \gamma\gamma\frac{g}{min}$ , and

$R_{o}=2\frac{L}{min}*\frac{A}{120} \frac{g}{L}=\frac{A}{60}\frac{g}{min}$

So we obtain. $\frac{dA}{dt}=2 \gamma\gamma-\frac{A}{60}$ , then

$\frac{dA}{dt}+\frac{A}{60}=2 \gamma\gamma$ , and using the integrating factor $e^{\int {\frac{1}{60}} \, dt=e^{\frac{t}{60}$ , therefore

$(\frac{dA }{dt}+\frac{A}{60}}{60}=2 \gamma\gamma)e^{\frac{t}{60}$ , we get $\frac{d}{dt}(A*e^{\frac{t}{60}})= 2 \gamma\gamma e^{\frac{t}{60}$ , after integrating both sides $A*e^{\frac{t}{60}}= 120 \gamma\gamma e^{\frac{t}{60}}+C$ , therefore $A(t)= 120 \gamma\gamma +Ce^{\frac{-t}{60}}$ , to find we know that the tank initially contains 120L of pure water, that means the initial conditions A(0)=0 , so $0= 120 \gamma\gamma +Ce^{\frac{-0}{60}}$

$0= 120 \gamma\gamma +C\\C= -120 \gamma\gamma$

Finally we can write an expression in terms of γγ for the amount of salt in the tank at any time t, it is $A(t)= 120 \gamma\gamma -120 \gamma\gamma e^{\frac{-t}{60}}\\A(t)= 120 \gamma\gamma (1-e^{\frac{-t}{60}})$

Answer from: Quest

relativism, roughly put, is the view that truth and falsity, right and wrong, standards of reasoning, and procedures of justification are products of differing conventions and frameworks of assessment and that their authority is confined to the context giving rise to them. more precisely, “relativism” covers views which maintain that—at a high level of abstraction—at least some class of things have the properties they have (e.g., beautiful, morally good, epistemically justified) not simpliciter, but only relative to a given framework of assessment (e.g., local cultural norms, individual standards), and correspondingly, that the truth of claims attributing these properties holds only once the relevant framework of assessment is specified or supplied. relativists characteristically insist, furthermore, that if something is only relatively so, then there can be no framework-independent vantage point from which the matter of whether the thing in question is so can be established.

relativism has been, in its various guises, both one of the most popular and most reviled philosophical doctrines of our time. defenders see it as a harbinger of tolerance and the only ethical and epistemic stance worthy of the open-minded and tolerant. detractors dismiss it for its alleged incoherence and uncritical intellectual permissiveness. debates about relativism permeate the whole spectrum of philosophical sub-disciplines. from ethics to epistemology, science to religion, political theory to ontology, theories of meaning and even logic, philosophy has felt the need to respond to this heady and seemingly subversive idea. discussions of relativism often also invoke considerations relevant to the very nature and methodology of philosophy and to the division between the so-called “analytic and continental” camps in philosophy. and yet, despite a long history of debate going back to plato and an increasingly large body of writing, it is still difficult to come to an agreed definition of what, at its core, relativism is, and what philosophical import it has. this entry attempts to provide a broad account of the many ways in which “relativism” has been defined, explained, defended and criticized.

explanation:

Answer from: Quest

the higher the current the higher the mag field around it the higher the influence on the compass

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Atank initially contains 120l of pure water. a mixture continuing a concentration of γγ g/l of salt...