Maths for computers assignment 2 30% 1. If three solid gold spherical beads of radil 3 cm, 4 cm, and 5 cm respectively are melted into one spherical bead find its radius. (5 marks) 2. Simplify logs 25+ logs 15 - logs 3 Solve for x log10x2 +log 10 2 =log 1050 (5 marks) 4.22x-1 Solve for x (5 marks) 5. Convert the following from decimal to binary: a. 255 (4 marks) 6. Convert the following from binary to decimal a. 11101000 (4 marks) 7. Convert the following to hexadecimal a. lolololo (4 marks) 8. Express the following in scientific notation a. .0000000000001 (4 marks) 9. Complete the following 1 (1.2 x 105 x (1.5 x 10) (4 marks) Differentiate the following. A. Y = X5 + XV2 + 3X +5 (4 marks) B. Y = (7X5 + 4X4 - 7X+5) 12 (6 marks). C. Y= 3x+2 (10 marks) Maths for IT Assignment 1 30% Instructions: All calculations should be shown. To be completed and handed up at last class before easter. Assignment may be hand written or typed. Mark sure that even if hand written to use double line spacing. 1. Solve the following set f equations. X + Y - Z = 4 X-2Y+ 3Z = -6 2x + 3y +z = 7. (10 marks) 2. Solve the following equation a. 5x2 +4x -3 =0 (5 marks) 3. In the following solve for the variable in brackets (y) (5 marks) 4. Formulate the Boolean expression for both circuits and simplify where possible a. (5 marks) (5 marks) 5. If the set is defined by s={1, 2, 3, 4, }. Find p(s) which is the power set of s.(5 marks) If the cartisian product of two sets is given by Axb = {(1,a);(2,b);(3.c);(4,t);(5,y)}. Find the set a and the set b. (5 marks) 6. A bag contains 4 blue discs and 2 red discs. A disc is chosen at random from the bag and not returned. A second disc is then chosen from the bag. Find the probability that a. both discs are blue (2 marks) b. The first disc is red and the second is blue. (2 marks) C. One disc is blue and the other disc red in any order (4 marks) 7. Fifty boxes of matches were taken and a record made of the matches per box. The results are as follow. Number of matches per box 34 35 38 39 40 frequency 14 16 (1) Find the mean number of matches per box and the standard deviation, correct to two decimal places. (8 marks) (2) Hence, estimate the number of matchboxes that are within the range (u -0, H +o) (2 marks) (3) If the number of matches per box was doubled write down (a) the mean (b) the standard deviation. (2 marks)