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Mathematics And Computing Assignment
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Added on 2021-01-02
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Maths for Computing (L4)
TABLE OF CONTENTSLO 1.................................................................................................................................................1Part 1............................................................................................................................................1Part 2............................................................................................................................................1LO 2.................................................................................................................................................3Part 1............................................................................................................................................3Part 2............................................................................................................................................4LO 3.................................................................................................................................................6Part 1 ...........................................................................................................................................6Part 2 ...........................................................................................................................................7LO 4.................................................................................................................................................8Part 1............................................................................................................................................8Part 2............................................................................................................................................9REFERENCES .............................................................................................................................12
LO 1Part 1Prime numbers: 2, 3, 5, 7, 11Solution: Greatest common divisor (GCD)2 = 2 * 1 3 = 3 * 15 = 3 * 17 = 3 * 111 = 3 * 1 Thus, the GCD of prime numbers is always one. Least common multiple (LCM): The least common multiple of prime numbers is equivalent to their products (Kac, 2018).Thus, for the given pair of numbers LCM is given by: LCM: 2 * 3 * 5 * 7 * 11 = 2310Part 22.1First term (a) = 9Tenth term (a10) = 40.5Last term (L) = 425.5Solution: The expression for the nth term of AP is: a(n) = a + (n-1) *d where d is the common difference The expression for the tenth term can be written as : a10 = a +(10-1)*d40.5 = 9 + 9dOn solving this equation we get : Common difference d = 3.5a. Number of terms Solution: 1
L = a + (n-1)*d425.5 = 9 + (n-1)*3.5 Number of terms (n) = 120B. Sum of all termsSolution: Sum of n terms of A.P. = (n/2)* [2a + (n-1)*d] On substituting values we get: S= (120/2)* [2*9 + (120-1)*3.5] S= 60* [434.5] S= 26070C. 70th term of given series Solution: a(70) = 9 + (70-1)*3.5 70th term = 250.52.2Salary in the first year (a) = £7200 annual increment (d) = £350 Solution: Salary in the 9th year = 7200 + (9-1)*350 = £10000 Sum of salary in the first 12 years = (12/2)* [2*7200 + (12-1)*350] = 6* [14400 + 3850]= £109500Salary in the 9th year = £10000 Sum of salary in the first 12 years = £1095002.3Range of speeds of drilling machine: 50-750 rev/ min Solution: 2
