$($can u explain the answer step by step$)$ PROBLEM $2$:

A lake has a surface area of $100k{m}^2.$ One river is bringing water into the lake at the rate of $10,000\frac{m^3}{(s)},$

while another is taking water out at $8,000\frac{m^3}{(s)}.$ Evaporation and seepage are negligible. How fast is the

level of the lake rising or falling?

Solution:

$\frac{1}{}\frac{dm}{dt}=\frac{dV}{dt}=\frac{1}{}(n{Y}_{in}^{}-m{Y}_{\text{o}\text{u}\text{t}}^{})=10,000-8,000=2,000\frac{m^3}{(s)}$

$\frac{dh}{dt}=\frac{1}{A}*\frac{dV}{dt}=\frac{2,000\frac{m^3}{(s)}}{100k{m}^2*{10}^6\frac{m^2}{k{m}^2}}=2{10}^{-5}\frac{m}{s}=72\frac{mm}{hr}=2\mathrm{.}8\frac{in}{hr},$ rising