This assignment consists of only Mathematica problems. Solutions of the problems should be given in a single Mathematica notebook displaying the requested formulas and graphics.
1. Find the exact value of r that creates a perfect 5-pointed star in Example 2.
2. Graph the family of lines connecting the points (a, 0) and (0, b), where a + b = 2, and determine an equation for the envelope of this family of lines2.
3. Graph the family of circles centered at points of the unit circle and all going through the point (1, 0), and determine an equation for the envelope of this family of circles.
4. Determine the envelope of the family of lines of Example 4 of class 6 (March 1): the lines connecting points on the unit circle centered at the origin whose polar angles are in the ratio 3 : 1.
5. Determine the envelope of the family of lines of TikZercise 2 of Homework 5: the lines connecting points on the unit circle centered at the origin whose polar angles are in the ratio 2 : 1.
6. Create an animation of rolling a small disk inside a larger one when the radii are in the ratio 1 : 3.
7. Create an animation of rolling a disk outside a disk of equal radius.
Attachment:- Assignment.rar