關於變分的一個問題

001: 第一條你set的equation是錯誤的
因為這是jointly variation 並不是partly variation

2011-02-12 16:31:20 補充：
1.(a) 設R = kl/d^2, (k是非零常數)
當R = 75, d = 4/1000 , l = 10,
75 = k(10)/(4/1000)^2
k = 3/250
所以R = (3/250)l / d^2

(b) 代入l = 40, d = 1/100
R = (3/250)(40) / (1/100)^2 = 4800

2.(a) A = h + kN^2, (h和k是非零常數)
當N = 30, A = 16000,
16000 = h + k(30)^2
16000 = h + 900k ---(1)
當N = 40, A = 26500,
26500 = h + k(40)^2
26500 = h + 1600k ---(2)
(2) - (1) => 700k = 10500 => k = 15
h = 2500
因此 A = 2500 + 15N^2

(b) 當N = 36, A = 2500 + 15(36)^2 = 21940

1.(a)
Let R = a/d^2 + bl, where a and b are constants.

When d = 4 and l = 10, R = 75.
Then a/16 + 10b = 75.

There is insufficient information to find out the values of a and b.

(b) R cannot be found because we can't find the values of a and b.

2.(a)
Let A = c + k N^2, where c, k are constants.

When N = 30, A = 16,000.
c + 900k = 16000 ... (1)

When N = 40, A = 26,500.
c + 1600k = 26500 ... (2)

(2) - (1): 700k = 10500
k = 15

Putting k = 15 into (1), we have
c + 13500 = 16000
c = 2500

So, A = 2500 + 15N^2

(b)
When N = 36,
A = 2500 + 15(36)^2
= $21940