# math ext help (1 Viewer)

#### Farhanthestudent005

##### Member

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

#### jimmysmith560

##### Le Phénix Trilingue
Moderator
Would the following working help?

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

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

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

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

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

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

I hope this helps!

#### cossine

##### Active Member
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.