A company advertises that their plastic concrete framework can be used 300 times in casting before it starts to deteriorate

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Q1 Determine the real root of 𝑓(𝑥) = 2 cos(𝑥) − 𝑥 using 20 iterations of the false position method, with initial guesses of xl = 3 and xu = 0 (2.5 marks)

(Final Answer: Root= 1.0355)

Q2 Use Gauss elimination method to solve the following system: 2𝑥 + 𝑦 + 𝑧 = 10 3𝑥 + 2𝑦 + 3𝑧 = 18 𝑥 + 4𝑦 + 9𝑧 = 16 (2.5 marks)

(Final Answer: 𝑥 = 7; 𝑦 = −9; 𝑧 = 5)

Q3 A company advertises that their plastic concrete framework can be used 300 times in casting before it starts to deteriorate. The probability that their product can sustain up to 350 of casting is given in the following formula. Find the probability that the frameworks can last up to 350 times by using the Simpson’s 3/8 rule with n= 300 𝑓(𝑥) = 𝑥 100 + 𝑥 (2.5 marks)

(Final Answer: I= 38.2217)

Q4 Using Heun’s Method, compute the value of y at x= 10 taking h= 0.1, Given 𝑑𝑦 𝑑𝑥 = 𝑥 3 − 2𝑥 2 + 𝑥 − 10 and y(0)= 3 (2.5 marks)

(Final Answer: f(10)= 1783.55)

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