Question 7


a) Express 12 as the product of its prime factors in index notation.
Ans: 12 = 2^2 x 3

b) Find the smallest positive integer,d such as that 120d is a perfect square.
120 = 2^3 x 3 x 5
120d = 2^4 x 3^2 x 5^2
=>d = 2 x 3 x 5
= 30

c) Express 80 as the product of its prime factoring index notation.
80 = 2^4 x 5

d) Hence,find the HCF of 120 and 80.
HCF of 80 and 120 = 2^3 x 3^0 x 5 = 40

e) Two battery operated racing cars start to move around a circular track at the same time.Car X makes 1 lap every 120 seconds while Car Y makes 1 lap every 80 seconds.
i)How long would it take before the cars are at the starting point together again?
LCM 120 and 80 = 2^4 x 3 x 5 = 240

ii)How long would it take the faster car to be ahead by 7 and a 1/2 laps ?Give your answer in hours.
Time taken for faster car to be ahead by 1/2 lap = LCM (60,40)
60 = 2^2 x 3 x 5
40 = 2^3 x 5
LCM (60,40) = 2^3 x 3 x 5 = 120
Time taken to be ahead by 7.5 laps = 15 x 120s =1800s = 30min = 0.5h

HI THERE PLEASE HELP ME SOLVE THIS QUESTION. TIA

Hope this helps!