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3. the price $P of a litre(L) of wine is partly constant and partly varies directly as the percentage r% of alcohol contained.a) Wine A contains 15% of alcohol and is sold at $50/L. Wine B contains 10% of alcohol and is sold at $45/L. Express Pin terms of r.b)What is the percentage of alcohol contained in wine C... 顯示更多 3. the price $P of a litre(L) of wine is partly constant and partly varies directly as the percentage r% of alcohol contained. a) Wine A contains 15% of alcohol and is sold at $50/L. Wine B contains 10% of alcohol and is sold at $45/L. Express Pin terms of r. b)What is the percentage of alcohol contained in wine C if its price is $43/L? 4. in a geometric sequence, if all the terms are positive, T(3)=16 and T(9)=1/4, find: a)the general term T(n) b)T(11) - T(5)
最佳解答:
Let P = C + r%A, where $P per litre is the selling price, C is the constant, and A is alcohol. (a) Given 50 = C + 15%A……..(i) Given 45 = C + 10%A……..(ii) (i) - (ii), we get 5 = 5%A A = 100 Put A into (i), 50 = C + 15% * 100 C = 35 Put A=100 and C=35 into P = C + r%A. we get P = 35 + r% * 100 P = 35 + r (Ans. A) (b) 43 = 35 + r r = 8 (Ans. b) (a) Given T(3) = 16; that is T(3) = 2^4 Given T(9) = ?, that is T(9) = 2^ (-2) From above, we can deduce that the no. of the sequence are 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, 2^0, 2^(-1), 2^-(2), 2^(-3), 2^(-4), and so on….. Thus, T(n) = 2^ (6 - n), n = 0, 1, 2,…. That is, T(n) = 2^(7 - n), n = 1, 2…. (Ans. a) (b) T(11) = 2^(7 - 11) = 2^(-4) = 1/16 T(5) = 2^ (7 - 5) = 4 Thus, T(11) - T(5) = 1/16 – 4 = -3 15/16 (Ans. b)
其他解答:
3. the price $P of a litre(L) of wine is partly constant and partly varies directly as the percentage r% of alcohol contained. a) Wine A contains 15% of alcohol and is sold at $50/L. Wine B contains 10% of alcohol and is sold at $45/L. Express Pin terms of r. (a)P = 35 + r% * 100 b)What is the percentage of alcohol contained in wine C if its price is $43/L? (b)r = 8 % 4. in a geometric sequence, if all the terms are positive, T(3)=16 and T(9)=1/4, find: a)the general term T(n) (a) T(n) = 2^(7 - n) b)T(11) - T(5) T(11) - T(5) = -3 15/16
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發問:3. the price $P of a litre(L) of wine is partly constant and partly varies directly as the percentage r% of alcohol contained.a) Wine A contains 15% of alcohol and is sold at $50/L. Wine B contains 10% of alcohol and is sold at $45/L. Express Pin terms of r.b)What is the percentage of alcohol contained in wine C... 顯示更多 3. the price $P of a litre(L) of wine is partly constant and partly varies directly as the percentage r% of alcohol contained. a) Wine A contains 15% of alcohol and is sold at $50/L. Wine B contains 10% of alcohol and is sold at $45/L. Express Pin terms of r. b)What is the percentage of alcohol contained in wine C if its price is $43/L? 4. in a geometric sequence, if all the terms are positive, T(3)=16 and T(9)=1/4, find: a)the general term T(n) b)T(11) - T(5)
最佳解答:
Let P = C + r%A, where $P per litre is the selling price, C is the constant, and A is alcohol. (a) Given 50 = C + 15%A……..(i) Given 45 = C + 10%A……..(ii) (i) - (ii), we get 5 = 5%A A = 100 Put A into (i), 50 = C + 15% * 100 C = 35 Put A=100 and C=35 into P = C + r%A. we get P = 35 + r% * 100 P = 35 + r (Ans. A) (b) 43 = 35 + r r = 8 (Ans. b) (a) Given T(3) = 16; that is T(3) = 2^4 Given T(9) = ?, that is T(9) = 2^ (-2) From above, we can deduce that the no. of the sequence are 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, 2^0, 2^(-1), 2^-(2), 2^(-3), 2^(-4), and so on….. Thus, T(n) = 2^ (6 - n), n = 0, 1, 2,…. That is, T(n) = 2^(7 - n), n = 1, 2…. (Ans. a) (b) T(11) = 2^(7 - 11) = 2^(-4) = 1/16 T(5) = 2^ (7 - 5) = 4 Thus, T(11) - T(5) = 1/16 – 4 = -3 15/16 (Ans. b)
其他解答:
3. the price $P of a litre(L) of wine is partly constant and partly varies directly as the percentage r% of alcohol contained. a) Wine A contains 15% of alcohol and is sold at $50/L. Wine B contains 10% of alcohol and is sold at $45/L. Express Pin terms of r. (a)P = 35 + r% * 100 b)What is the percentage of alcohol contained in wine C if its price is $43/L? (b)r = 8 % 4. in a geometric sequence, if all the terms are positive, T(3)=16 and T(9)=1/4, find: a)the general term T(n) (a) T(n) = 2^(7 - n) b)T(11) - T(5) T(11) - T(5) = -3 15/16
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