10. (a) If x- -+xy dy dx dy=1, and y=0 when x = 1, show that the positive value of y when dx x = e² is √5-1. (b) Radioac

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10 A If X Xy Dy Dx Dy 1 And Y 0 When X 1 Show That The Positive Value Of Y When Dx X E Is 5 1 B Radioac 1 (33.17 KiB) Viewed 31 times

10. (a) If x- -+xy dy dx dy=1, and y=0 when x = 1, show that the positive value of y when dx x = e² is √5-1. (b) Radioactive isotopes decay at a rate proportional to the amount of the isotope remaining. If 30% of a certain radioactive isotope has decayed after 10 years, what percentage of the original amount of the isotope remains after 16 years? (c) A particle Q moves along a straight line. The speed of Q at time t seconds is v m s¹¹, where v=at² +bt+c, where a, b and c are constants. The initial speed of Q is 4 m s¹. Q reaches a maximum speed of 10 m s¹ after 2 seconds. Find: (i) the values of a, b and c, (ii) the distance travelled by Q in the fourth second of motion, (iii) the value oft when particle Q first changes direction.