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Question 2 10 marks You should be able to answer this question after studying Unit 9....
Question 4 10 marks You should be able to answer this question after studying Unit 9....
Question 4 10 marks You should be able to answer this question after studying Unit 9. (a) Use proof by contraposition to prove that the following statement is true for all integers n: If n2 + 2n + 7 is odd, then n is even. [6] (b) Hence prove that the following statement is true for all integers n: na + 2n + 7 is odd if and only if n is even. [4]
Question 3 You should be able to answer this question after studying Unit 9. (a) Use...
Question 3 You should be able to answer this question after studying Unit 9. (a) Use mathematical induction to prove that the following statement is 10 marks true: [9 n - n is a multiple of 3 for all n 2 1. (b) Show that the following statement is false: n-n is a multiple of 4 for all n 2 1. Question 4-10 ma You should be able to answer this question after studying Unit 9. (a) Use proof by...
Question 3 10 marks You should be able to answer this question after studying Unit 9....
Question 3 10 marks You should be able to answer this question after studying Unit 9. Use mathematical induction to prove that the following statement is true: 7 + 9 + 11 +. + (2n + 5) = n(n + 6) for all n E N. (10)
QUESTION 9 log8 (16)-1098 (2) = O 14 QUESTION 10 True or False: The domain of...
QUESTION 9 log8 (16)-1098 (2) = O 14 QUESTION 10 True or False: The domain of the log function is all real numbers. O True ︶ False QUESTION 11 What is the domain of the function f(x) -In (x-3) all real numbers
Uestion 6 20 marks You should be able to answer this question after studying Unit 5 A mountain re...
uestion 6 20 marks You should be able to answer this question after studying Unit 5 A mountain rescue team is preparing to move a stretcher (with an injured climber) down a flat slope. The combined mass of the climber and stretcher is 110 kg, and the slope makes an angle of 15° with the horizontal. The stretcher is held at rest by a rope that makes an angle of 20° with the upward slope. The stretcher is on the...
2 6, 9、19/ 1,12 '12,13,16,16, 16,18,3‘ = 12.5 4 IQR=46 Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) Every basic solution in the assignment p...
2 6, 9、19/ 1,12 '12,13,16,16, 16,18,3‘ = 12.5 4 IQR=46 Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) Every basic solution in the assignment problem is necessarily degenerate. 2) The assignment problem cannot be solved using the transportation technique. maximum or minimum. If a single-variable function has two local minima, it must have at least one local 4) maximum. 5) The Golden Section Search method gives better results than the Fibanocci Search...
Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) 2) 3) Every basic solution in the assignment problem is necessarily degenerate. The assignment problem ca...
Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) 2) 3) Every basic solution in the assignment problem is necessarily degenerate. The assignment problem cannot be solved using the transportation technique. If the gradient vector of a function at a given point is zero, the point can only be a maximum or minimum. If a single-variable function has two local minima, it must have at least one local 4) maximum 5) The Golden...
Question 615 marks You should be able to answer this question after studying Unit 10 At a battle re-enactment, a catapult launches a missile with a speed of 38 ms-, at an angle of 40° to the horizont...
Question 615 marks You should be able to answer this question after studying Unit 10 At a battle re-enactment, a catapult launches a missile with a speed of 38 ms-, at an angle of 40° to the horizontal. The height from which the projectile is launched is 10m. Set up coordinate axes at the point where the missile leaves the catapult, as shown below 40° 10 m Let i and j be the Cartesian unit vectors in the positive directions...
Question 4 [35 marks in totalj An n x n matrix A is called a stochastic...
Question 4 [35 marks in totalj An n x n matrix A is called a stochastic matrix if it! satisfies two conditions: (i) all entries of A are non-negative; and (ii) the sum of entries in each column is one. If the (,) entry of A is denoted by any for ij € {1, 2,...,n}, then A is a stochastic matrix when alij 20 for all i and j and I j = 1 for all j. These matrices are...
Question 5 15 marks You should be able to answer this question after studying Unit 10 A crate, initially at rest, is pushed along a straight line up a rough ramp that makes an angle of 18° with the h...
Question 5 15 marks You should be able to answer this question after studying Unit 10 A crate, initially at rest, is pushed along a straight line up a rough ramp that makes an angle of 18° with the horizontal. The magnitude of the pushing force is 33 N, in a direction parallel to and up the ramp, and the acceleration of the crate is 0.16 ms-2. The coefficient of sliding friction between the crate and the ramp is 0.35....
Question 4 10 marks You should be able to answer this question after studying Unit 9. (a) Use proof by contraposition to prove that the following statement is true for all integers n: If n2 + 2n + 7 is odd, then n is even. [6] (b) Hence prove that the following statement is true for all integers n: na + 2n + 7 is odd if and only if n is even. [4]
Question 3 You should be able to answer this question after studying Unit 9. (a) Use mathematical induction to prove that the following statement is 10 marks true: [9 n - n is a multiple of 3 for all n 2 1. (b) Show that the following statement is false: n-n is a multiple of 4 for all n 2 1. Question 4-10 ma You should be able to answer this question after studying Unit 9. (a) Use proof by...
Question 3 10 marks You should be able to answer this question after studying Unit 9. Use mathematical induction to prove that the following statement is true: 7 + 9 + 11 +. + (2n + 5) = n(n + 6) for all n E N. (10)
QUESTION 9 log8 (16)-1098 (2) = O 14 QUESTION 10 True or False: The domain of the log function is all real numbers. O True ︶ False QUESTION 11 What is the domain of the function f(x) -In (x-3) all real numbers
uestion 6 20 marks You should be able to answer this question after studying Unit 5 A mountain rescue team is preparing to move a stretcher (with an injured climber) down a flat slope. The combined mass of the climber and stretcher is 110 kg, and the slope makes an angle of 15° with the horizontal. The stretcher is held at rest by a rope that makes an angle of 20° with the upward slope. The stretcher is on the...
2 6, 9、19/ 1,12 '12,13,16,16, 16,18,3‘ = 12.5 4 IQR=46 Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) Every basic solution in the assignment problem is necessarily degenerate. 2) The assignment problem cannot be solved using the transportation technique. maximum or minimum. If a single-variable function has two local minima, it must have at least one local 4) maximum. 5) The Golden Section Search method gives better results than the Fibanocci Search...
Question #1 (15 Marks) a) (8 Marks) Answer the following questions with True or False. 1) 2) 3) Every basic solution in the assignment problem is necessarily degenerate. The assignment problem cannot be solved using the transportation technique. If the gradient vector of a function at a given point is zero, the point can only be a maximum or minimum. If a single-variable function has two local minima, it must have at least one local 4) maximum 5) The Golden...
Question 615 marks You should be able to answer this question after studying Unit 10 At a battle re-enactment, a catapult launches a missile with a speed of 38 ms-, at an angle of 40° to the horizontal. The height from which the projectile is launched is 10m. Set up coordinate axes at the point where the missile leaves the catapult, as shown below 40° 10 m Let i and j be the Cartesian unit vectors in the positive directions...
Question 4 [35 marks in totalj An n x n matrix A is called a stochastic matrix if it! satisfies two conditions: (i) all entries of A are non-negative; and (ii) the sum of entries in each column is one. If the (,) entry of A is denoted by any for ij € {1, 2,...,n}, then A is a stochastic matrix when alij 20 for all i and j and I j = 1 for all j. These matrices are...
Question 5 15 marks You should be able to answer this question after studying Unit 10 A crate, initially at rest, is pushed along a straight line up a rough ramp that makes an angle of 18° with the horizontal. The magnitude of the pushing force is 33 N, in a direction parallel to and up the ramp, and the acceleration of the crate is 0.16 ms-2. The coefficient of sliding friction between the crate and the ramp is 0.35....
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