幫多我一次呀!

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) = ¼, 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)

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