代入法、公式（１０）

1. Ｃ＝ｐ（１＋ｎｒ／２）　若Ｃ＝５１０　ｐ＝５００　ｎ＝６　ｒ＝？
510 = 500 (1 + 6r/2)
510 / 500 = 1 + 3r
1.02 - 1 = 3r
r = 0.02 / 3
= 1/150 (或0.00667 取3位有效數字)

2. Ｓ＝ａ／１－Ｒ　若　Ｓ＝－１２　ａ＝－８　Ｒ＝？
-12 = -8 / (1-R)
1 - R = -8 / -12
- R = 2/3 - 1
R = 1/3 (或 0.333 取3位有效數字) (注意! R不等於1.)

3. －１／ｆ＝１／ｖ－１／ｕ　若ｆ＝１５　ｖ＝５　ｕ＝？
-1/15 = 1/5 - 1/u
1/u = 1/5 + 1/15 = 4/15
所以 u = 15/4 (或 3.75) (注意! u不等於0.)

4. Ｐ－ｍｇ＝ｍｖ2／ｒ　若Ｐ＝１４５　ｇ＝３２　ｖ＝－９　ｒ＝２　ｍ＝？
問題不清晰 -
(A)
145 - 32m = 2(-9)(-9)m/2
145 - 32m = 81m
113m = 145
m = 145/113 (或 1.283 取至小數後3位)
(B)
145 - 32m = 2(-9)(-9)mXm/2
145 - 32m = 81m2
81m2 + 32m - 145 = 0
m = 1.155 或 -1.550 (取至小數後3位)

5. Ｓ＝ａ（Ｒn－１）／（Ｒ－１）　若ａ＝５０　Ｒ＝２　ｎ＝３　ｎ＝？
問題不清晰 -
(A) 現假設求S, 即 n = 3
S = 50 (2 X 3 - 1) / (2 - 1)
= 50(5)
= 250

(B) 現假設求n, 即 S = 3
3 = 50 (2n - 1) / (2 - 1)
3 = 100n - 50
100n = 53
n = 53/100 (或 0.53)

6. ｎ＝５Ａ（ａ－３ｂ）／３ｋ　請以〔ｂ〕表示
n = 5A (a - 3b) / 3k
3kn = 5A (a - 3b)
3kn / 5A = a - 3b
3b = a - 3kn/5A
b = (5Aa - 3kn)/15A (注意! A及k 不等於0.)

7. Ｑ＝２（ｘ－ｙ）ｋ／７　請以〔ｘ〕表示
Q = 2(x - y) k / 7
7Q = 2kx - 2ky
2kx = -7Q - 2ky
x = (-7Q - 2ky) / 2k (注意! k 不等於0.)

8. １／ｕ＋１／ｖ＝１／ｆ　請以〔ｆ〕表示
1/u + 1/v = 1/f
1/f = (u + v)/uv
f = uv / (u + v) (注意! f, u, v 及 (u + v) 不等於0.)

9. １／ａ－１／ｂ－２＝１／ｃ　請以〔ｂ〕表示
1/a - 1/b - 2 = 1/c
1/b = 1/a - 1/c - 2
1/b = (c - a)/(ac) - 2
1/b = (c - a - 2ac)/ac
b = ac / (c - a - 2ac) (注意! a, b, c 及 (c - a - 2ac) 不等於0.)

10. Ｂ＝３ｅ－８ｆｇ／１２ｆｇ　請以〔ｇ〕表示
B = (3e - 8fg) / 12fg
12Bfg = 3e - 8fg
4fg (3B - 2) = 3e
g = 3e / [4g(3B - 2)] (注意! f, g 及 4g(3B - 2) 不等於0.)

2006-11-05 19:08:05 補充：
11. x ＝ｎｙ／ａ（４ｙ－３）　請以〔ｙ〕表示 x = ny / [a(4y - 3)]ax (4y - 3) = ny4axy - 3ax = ny4axy - ny = 3axy (4ax - n) = 3axy = 3ax / (4ax - n) (注意! a (4y - 3) 及 (4ax - n) 不等於0.)12. Ｆ＝ｇ－１／ｇ　請以〔ｇ〕表示 (A) F = (g - 1)/gFg = g - 1g - Fg = 1g (1 - F) = 1g = 1/(1 - F) (注意! g 及 (1 - F) 不等於0.)

2006-11-05 19:09:18 補充：
Ｐ＝３６ｍ／ｎ　以ｎ表示P = 36m/nn = 36m/P (注意! n 及 P 不等於0.)

1)510=500(1+6r/2)
51/50-50/50=3r
1/150=r
2)-12＝-8／１－Ｒ
-12+12R=-8
R=1/3
3)－１／15＝１／5－１／ｕ
-1/15-3/15=-1/U
-4U=-15
U=15/4

4)145-32M=-9(2M)/2
145=-9M+32M
145/23=M
6)ｎ＝５Ａ（ａ－３ｂ）／３ｋ
3kn=5AA-15ab
3kn-5Aa/-15A=b
7)Ｑ＝２（ｘ－ｙ）ｋ／７
7Q/2K+Y=X
8)１／ｕ＋１／ｖ＝１／ｆ
v+u/uv=1/f
f(v+u)=uv
f=uv/v+u
9)１／ａ－１／ｂ－２＝１／ｃ
-1/b=1+2c/c-1/a
b=-ca/a+2ca-c
11)ｘ＝ｎｙ／ａ（４ｙ－３）
-3ax=ny-4yax
-3ax=y(n-4ax)
-3ax/n-4ax=y
12)Ｆ＝ｇ－１／ｇ
F=g-1/g
gF=g-1
g(F-1)=-1
g=1-F