I have a very small understanding of this, please help me with these questions. Thank you so so much!
1. As a pendulum swings, air resistance and friction cause the extent of the swings to decrease. Suppose that the tip of the pendulum travels 120 cm on the first swing, 100 cm on its second, 83⅓ on its third and so on.
a) Find and state the appropriate mathematical model that enables the total distance travelled by tip of the pendulum after 10 swings to be found.
b) Calculate this total distance. State your answer to an appropriate accuracy.
c) Find the total distance travelled by the tip of the pendulum as it comes to rest.
2. Use the sum of the first five terms of the series for 1n (1 + x) to find an approximate value for 1n (1.1). Give your answer to 5 significant figures.
3. Use a series to find a value of (1.05)^5 correct to 4 decimal places.