標題:
F.4 variations 000
發問:
The production cost of a poster is $A and its perimeter is P cm. It is known that A is the sum of two parts, one part varies as P and the other part varies as the square of P. A =400 when P=200 and A=960 when P=400.(a) Express A in terms of P.(b) (1) Given that the production cost of a poster is $1125, find... 顯示更多 The production cost of a poster is $A and its perimeter is P cm. It is known that A is the sum of two parts, one part varies as P and the other part varies as the square of P. A =400 when P=200 and A=960 when P=400. (a) Express A in terms of P. (b) (1) Given that the production cost of a poster is $1125, find its perimeter. (2) A leaflet similar in shape to the one in b(1) is to be designed for a promotion. If the areas of the poster and the leaflet are 1.26m^2 and 224cm^2 respectively, find the perimeter of the leaflet. *(b)(2) 解得詳細D... thx
最佳解答:
a) A = (k1)P + (k2)P^2 400 = (k1)(200) + (k2)(200^2) 2 = k1 + 200 k2......(1) and 960 = (k1)(400) + (k2)(400^2) 24 = 10k1 + 4000k2.......(2) (2) - (1)*10 : 24 - 20 = (4000 - 2000)k2 k2 = 1/500 , sub it to (2) : 24 = 10k1 + 4000/500 k1 = 8/5 A = (8/5)P + (1/500)P^2 b)1) : A = 1125 : 1125 = (8/5)P + (1/500)P^2 562500 = 800P + P^2 P^2 + 800P - 562500 = 0 (P - 450)(P + 1250) = 0 P = 450 or P = - 1250(rejected) Perimeter = 450 cm b)2) The area of the poster : leaflet = 1.26m^2 : 224cm^2 = 1.26 ((100cm)^2) : 224cm^2 = (1.26 x 100^2) cm^2 : 224 cm^2 = 12600 : 224 = 225 : 4 Hence the perimeter of the (poster : leaflet)^2 = 225 : 4 the perimeter of the poster : leaflet = 15 : 2 450 : leaflet = 15 : 2 the perimeter of the leaflet = 450 / (15/2) = 60cm
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