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.

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explanation:

Answer from: Quest

the answer is the first electromagnet (a). this is because it has more coils around the ferromagnetic material. increasing the number of coils increases the surface area in which the metal interacts with the current in the coil. this enables more atoms in the metal to become aligned hence becoming more magnetized.