Problem $3.$ For a tank draining problem with a constant feed rate, the governing equation is

$\frac{dh}{dt}=\frac{Q}{A_t}-\frac{A_h}{A_t}\sqrt[\phantom{2}]{2gh}$

Where $Q$ is the flow rate in At is the tank area Ah is the hole area and $h$ is the height in the tank. Lets say the hole diameter in $10$ cm $($watch your units$),$ the tank diameter is $1m,Q$ is $0\mathrm{.}05\frac{m^3}{sec},$ and g is $9\mathrm{.}8066\frac{m}{s^2}.$ We will assume the initial height in the tank is $10$ m and we can assume the tank is very tall $($it wont overflow$).$ Now don't get spooked by the problem. We want to use Euler's method to generate a table of $h$ vs time. You will find this very similar to some examples I provided under "Euler". It should be easy to modify.

a$)$ Write a livescript program which asks the user for the flowrate in and the time duration., but has the other dimensions "built in$"($that is just type $dt=1,$ and $dh=0\mathrm{.}1,$ etc. Your livescript should generate an array of $h$ vst$.$ Have the script plot $h$ vs $t.$ Just use straight Euler for this... not modified.