數學問題正變聯變

數學問題正變聯變

用戶86933

2009-04-07 2:05 am

工場整一棵聖誕樹的成本$C , 可分為兩部分 , 一部分隨樹的高度 x米而正變 , 另一部分隨樹的高度之平方而正變 , 已知整一棵3米高的聖誕樹成本為$4800 , 整 4米高的聖誕樹成本為$7200

求5米高的聖誕樹成本

回答 (1)

So Much

2009-04-07 2:56 am

✔ 最佳答案

Ans:

Since Cost of Christmas tree (C) is partly proportional to the height ( x ) and partly proportional to the square of height ( x^2) , so we assume that

C = nx+mx^2 , where n and m are constants ,

sub x=3 and C =4800 , we have

4800 = 3n+9n --> 1600 = n+3m -- ( 1 )

sub x=4 and C= 7200 , we have

7200 = 4n+16m --> 1800 = n +4M -- ( 2 )

(2) - (1) : 7200 - 4800 = m --> m=2400 ,

sub m =2400 into (1) , we have n = 5600

so C = 5600 x + 2400 x^2

when x= 5 , C=5600(5)+2400(5)^2= 88000//

2009-04-06 18:57:37 補充：
sub m =2400 into (1) , we have n = -5600

so C = -5600 x + 2400 x^2

when x= 5 , C=-5600(5)+2400(5)^2= 32000//

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