math ext help (1 Viewer)

Farhanthestudent005 · Jun 8, 2022

How do I do this? Also I don't understand what the question is trying to ask. Help needed urgently, thanks

jimmysmith560 · Jun 9, 2022

Would the following working help?

$\frac{dm}{dt}=c_{in}\:\frac{dv}{dt}\:_{in}-c_{out}\:\frac{dv}{dt}\:_{out}$

$=15\times 2-\left(\frac{m}{50-3t}\right)\times 5$

$\therefore \frac{dm}{dt}=30-\frac{5m}{50-3t}$

Here, $c_{in}$ denotes the solution being poured into the tank, while $\frac{dv}{dt}\:_{in}$ refers to the rate at which the solution is poured into the tank.

Similarly, $c_{out}$ refers to the element flowing out of the tank. It is determined by dividing mass $m$ by the changing volume, leading to $\frac{m}{50+\left(2-5\right)t}=\frac{m}{50-3t}$ .

$\frac{dv}{dt}\:_{out}$ denotes the rate at which the mixture flows out of the tank.

I hope this helps!

cossine · Jun 9, 2022

Farhanthestudent005 said:
View attachment 35765
How do I do this? Also I don't understand what the question is trying to ask. Help needed urgently, thanks

Also I don't understand what the question is trying to ask?

So the question is telling you to construct a differential equation that can model the amount salt in the tank per time t. A differential equation is equation involving some rate of change or in other words derivative.

Generally for these type of question you need experience or sometimes scientific background to construct a differential equation like in projectile motion.

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math ext help (1 Viewer)

Farhanthestudent005

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jimmysmith560

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cossine

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