F.4 variations 000

2010-01-29 10:44 pm

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

回答 (1)

用戶2053

2010-01-29 11:23 pm

✔ 最佳答案

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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