1. Use Newton's method to approximate the given number, correct to eight decimal places: {image} 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. The following algorithm enables a computer to find reciprocals without actually dividing: {image} (You can derive it by apply Newton's method to the equation {image} .) Use this algorithm to compute {image} , correct to seven decimal places. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. A grain silo consists of a cylindrical main section, with height 25 ft, and a hemispherical roof. In order to achieve a total volume of 23,000 {image} (including the part inside the roof section), what would the radius of the silo have to be? Find the result and round to four decimal places.
r = ft
r = ft
r = ft
r = ft 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50