Assignment:
Q1. A bicycle tire has a diameter of 20 inches and is revolving at a rate of 10 rpm. At t =0, a certain point is at height 0. What is the height of the point above the ground after 20 seconds?
Q2. The sun always illuminates half of the moon's surface, except during a lunar eclipse. The illuminated portion of the moon visible from Earth varies as it revolves around Earth resulting in the phases of the moon. The period from a full moon to a new moon and back to a full moon is called a synodic month and is 29 days, 12 hours, and 44.05 minutes long. Write a sine function that models the fraction of the moon's surface which is seen to be illuminated during a synodic month as a function of the number of days, d, after full moon. [Note: full moon equals illuminated.]
Provide complete and step by step solution for the question and show calculations and use formulas.