標題:
SS1 Maths Partial variation
發問:
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... 顯示更多 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.
最佳解答:
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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