(a) Using your knowledge about Permutations/ Combinations, find the answers for the following questions: i. How...

 

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(a) Using your knowledge about Permutations/ Combinations, find the answers for the following questions: i. How many different 3-letter words can be made by using all of the letters in the word "car"? Do not use the same letter more than one time. ii. How many different 4-letter words can be made by using all of the letters of the word "door"? iii. How many 7-letter words can be made by using all of the letters in the word "Mission"? [6] (b) Assume the moon moves in a circular orbit around the Earth with an average radius R of 3.84 x 10 m. If it takes 27.3 days for it to complete one revolution, determine its average orbital speed in m/s. (c) Find the inverse of the following one-to-one function: i. (-3,27), (-2,-8).(-1,-1), (0.0), (1, 1), (2,8), (3,27) ii. State the domain and the range of the function and its inverse. (d) i. Calculate the inverse of the matrix: 1 1 3) A=0 25 301 ii. What is the unknown matrix X for the following matrix equation: 1 2 3 1 1 3 70-1 02-2, - 0 25 X= 30 1 f(x+1) f(x) = 0 2-1 2 2 6 -1 1 2 -2 0, ii. Solve the following exponential equation: 42-181+3 [6] Show your working. (e) i. For an exponential function f(x) = Ca' where a > 0 and a # 1, if z is any real number, then show that [3] [3] [3] [2] [3] (a) Using your knowledge about Permutations/ Combinations, find the answers for the following questions: i. How many different 3-letter words can be made by using all of the letters in the word "car"? Do not use the same letter more than one time. ii. How many different 4-letter words can be made by using all of the letters of the word "door"? iii. How many 7-letter words can be made by using all of the letters in the word "Mission"? [6] (b) Assume the moon moves in a circular orbit around the Earth with an average radius R of 3.84 x 10 m. If it takes 27.3 days for it to complete one revolution, determine its average orbital speed in m/s. (c) Find the inverse of the following one-to-one function: i. (-3,27), (-2,-8).(-1,-1), (0.0), (1, 1), (2,8), (3,27) ii. State the domain and the range of the function and its inverse. (d) i. Calculate the inverse of the matrix: 1 1 3) A=0 25 301 ii. What is the unknown matrix X for the following matrix equation: 1 2 3 1 1 3 70-1 02-2, - 0 25 X= 30 1 f(x+1) f(x) = 0 2-1 2 2 6 -1 1 2 -2 0, ii. Solve the following exponential equation: 42-181+3 [6] Show your working. (e) i. For an exponential function f(x) = Ca' where a > 0 and a # 1, if z is any real number, then show that [3] [3] [3] [2] [3] (a) Using your knowledge about Permutations/ Combinations, find the answers for the following questions: i. How many different 3-letter words can be made by using all of the letters in the word "car"? Do not use the same letter more than one time. ii. How many different 4-letter words can be made by using all of the letters of the word "door"? iii. How many 7-letter words can be made by using all of the letters in the word "Mission"? [6] (b) Assume the moon moves in a circular orbit around the Earth with an average radius R of 3.84 x 10 m. If it takes 27.3 days for it to complete one revolution, determine its average orbital speed in m/s. (c) Find the inverse of the following one-to-one function: i. (-3,27), (-2,-8).(-1,-1), (0.0), (1, 1), (2,8), (3,27) ii. State the domain and the range of the function and its inverse. (d) i. Calculate the inverse of the matrix: 1 1 3) A=0 25 301 ii. What is the unknown matrix X for the following matrix equation: 1 2 3 1 1 3 70-1 02-2, - 0 25 X= 30 1 f(x+1) f(x) = 0 2-1 2 2 6 -1 1 2 -2 0, ii. Solve the following exponential equation: 42-181+3 [6] Show your working. (e) i. For an exponential function f(x) = Ca' where a > 0 and a # 1, if z is any real number, then show that [3] [3] [3] [2] [3] (a) Using your knowledge about Permutations/ Combinations, find the answers for the following questions: i. How many different 3-letter words can be made by using all of the letters in the word "car"? Do not use the same letter more than one time. ii. How many different 4-letter words can be made by using all of the letters of the word "door"? iii. How many 7-letter words can be made by using all of the letters in the word "Mission"? [6] (b) Assume the moon moves in a circular orbit around the Earth with an average radius R of 3.84 x 10 m. If it takes 27.3 days for it to complete one revolution, determine its average orbital speed in m/s. (c) Find the inverse of the following one-to-one function: i. (-3,27), (-2,-8).(-1,-1), (0.0), (1, 1), (2,8), (3,27) ii. State the domain and the range of the function and its inverse. (d) i. Calculate the inverse of the matrix: 1 1 3) A=0 25 301 ii. What is the unknown matrix X for the following matrix equation: 1 2 3 1 1 3 70-1 02-2, - 0 25 X= 30 1 f(x+1) f(x) = 0 2-1 2 2 6 -1 1 2 -2 0, ii. Solve the following exponential equation: 42-181+3 [6] Show your working. (e) i. For an exponential function f(x) = Ca' where a > 0 and a # 1, if z is any real number, then show that [3] [3] [3] [2] [3]

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