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F5 maths
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1. Chris throws a ball so that the height (h meters) of the ball above the ground changes with the time (t seconds). It is measured that h is partly varies as t and partly varies as the square of t. When t= 1 or 5, h=25(a) Express h in terms of t.(b) When will the ball hit the ground after the throw?(c)Find the... 顯示更多 1. Chris throws a ball so that the height (h meters) of the ball above the ground changes with the time (t seconds). It is measured that h is partly varies as t and partly varies as the square of t. When t= 1 or 5, h=25 (a) Express h in terms of t. (b) When will the ball hit the ground after the throw? (c)Find the maximum height of the ball above the ground. 2. 5 cards are randomly drawn from a deck of 52 playing cards. What are the probabilities of the following cases? (The ans in fractions) (a) They are all diamond. (b) 3of them are "K" and 2 of them are "8" (c) They form a "fullhouse" i.e. 3 of them are of the same point and the other 2 are of the same point.
最佳解答:
1a) Let h = at2 + bt where a and b are constants. When t = 1, h = 25 and so a + b = 25 ... (1) When t = 5, h = 25 and so 25a + 5b = 25, i.e. 5a + b = 5 ... (2) Solving, we have a = -5 and b = 30 Hence h = -5t2 + 30t b) Sub h = 0, we have -5t2 + 30t = 0, giving t = 0 or 6 So the stone falls back to the ground after 6 secs. c) h = -5t2 + 30t = -5(t2 - 6t) = -5(t - 3)2 + 45 So when t = 3, max. height = 45 m. 2a) 13/52 x 12/51 x 11/50 x 10/49 x 9/48 = 33/66640 b) Out of 52 cards, there are 52C5 = 2598960 poss combinations. So for 3K28, no. of possible combinations = 4C3 x 4C2 = 24 So the required prob. is 24/2598960 = 1/108290 c) According to (b), the prob. of a specific full house is 1/108290 Then to count for no. of possible full house, i.e. from AAA22, AAA33, ..., KKKQQ, there are 13 x 12 = 156 possibilities. Hence the required probability is 156/108290 = 6/4165 Note: Next time do remember to put it in Maths category
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