SS1 Maths Partial variation

Anonymous

2010-05-24 5:15 am

The area of a paper bookmark is A cm^2 and its perimeter is P cm. A is
a function of P. It is known that A is the sum of two parts, one part varies
as P and the other part varies as the square if P. When P = 24, A = 36 and
when P = 18, A = 9.

a) Express A in terms of P.

bi) The best-selling paper bookmark has an area of 54 cm^2. Find the
perimeter of this bookmark.

ii) The manufacturer of the bookmarks wants to produce a gold miniature similar in shape to the best-selling paper bookmark. If the gild miniature has an area of
8 cm^2, find its perimeter.

回答 (1)

用戶2053

2010-05-24 5:34 am

✔ 最佳答案

a)Let A = (k1)P + (k2)P^2 ,
36 = 24(k1) + 576(k2)
3 = 2(k1) + 48(k2)......(1)
9 = 18(k1) + 324(k2)
1 = 2(k1) + 36(k2)......(2)
(1) - (2) :
2 = (48-36)(k2)
k2 = 1/6
sub to (2) , 1 = 2(k1) + 36/6
k1 = -5/2
A = - 5P/2 + (P^2)/6
bi)
54 = - 5P/2 + (P^2)/6
P^2 - 15P - 324 = 0
(P - 27)(P + 12) = 0
P = 27 or P = - 12(rejected)
the perimeter of this bookmark = 27cm
bii)
Let its perimeter = p ,
8 : 54 = (p : 27)^2
√(4/27) = p/27
p = 10.4cm (3 sig.fig)

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