Please use Jupyter Notebook Coding ONLY. DO NOT use Matlab.

P1. The volume of liquid, V, in a partially filled, horizontal, cylindrical tank of radius r and length L is related to the depth of the liquid, h, at the center line of the cylinder by the formula V=[r2cos1(rrh)(rh)2rhh2]L Develop a Python function to create a plot of liquid volume versus depth. Here are the first few lines: import numpy as np def cyltank (r,L,plot_title): "in" create a plot of the volume of liquid in a horizontal, cylindrical tank from empty to full tank inputs: \[ \begin{array}{l} r=\text { inside radius of tank } \\ L=\text { length } \\ \text { plot_title = string for title of plot } \end{array} \] Test your program with cyltank (3,5, 'Volume vs, Depth for Horizontal Cylindrical Tank') P2. Piecewise functions are sometimes useful when the relationship between a dependent and independent variable cannot be adequately represented by a single equation. For example, the velocity of a rocket might be described by v(t)=10t25t6243t36t+12(t16)22136e0.1(t26)00t8826othenvise Develop a Python function to compute v with an input of t. Then, add a script that uses the function to generate a plot a v versus t for t=5 to 50 . P3. Determination of leap year in the current Western calendar is interesting. Leap year is every year divisible by four, except at the turn of the century, where, if the year is divisible by 400 , there is no leap year. So, 1900 was a leap year, but 2000 was not. Develop a Python function that has an input of the year and returns a result of True if it is a leap year and False if it is not a leap year. Test it with various years to validate the function