關於10條數學問題 !!help me !

1) 一個長方形面積為256cm,長是闊的4倍.問它的闊是?

設闊是 y cm，則長是 4y cm。

y(4y) = 256
4y2 = 256
y2 = 64
y = 8 (y ≠ -8)

闊 = 8 cm


2)那些是矩形數?41.45.48.53.57.61.67.72.73.89.92.95

矩形數：45, 48, 57, 72, 92, 95

45 = 5 x 9, 48 = 2 x 24, 57 = 3 x 19,
72 = 2 x 36, 92 = 2 x 41, 95 = 5 x 19
41, 53, 61, 67, 73, 89 是質數


3) 那些是正方形數?36.45.54.64.72.81.94.100.117.121.130.144

正方形數：36, 64, 81, 100, 121, 144

36 = 6 x 6, 84 = 9 x 8, 81 = 9 x 9
100 = 10 x 10, 121 = 11 x 11, 144 = 12 x 12


4)循環小數化分數:
a) 0.6
= 6/10
= 3/5

b) 0.74( 4循環)
= 7/10 + 4/90
= 67/90

c) 0.45(45循環)
= 4/10 + 5/90
= 41/90

d) 0.94(4循環)
= 9/10 + 4/90
= 85/90
= 17/18

e) 0.148(148循環)
= 148/999
= 4/27

f ) 0.5678 (678 循環)
= 5/10 + 678/9990
= 5678/9990
= 2839/4995


5) { 4-3} x {4-1} x {8-7} {16-7}

(4-3) x (4-1) x (8-7) (16-7)
= (1/43) x (1/4) x (1/87) (1/167)
= [1/(22)3] x (1/22) x [1/(23)7] x [(24)7]
= (1/26) x (1/22) x (1/221) x (228)
= 228/229
= 1/2


6) An item was sold at a discount of 20% .With this discount .one can save $5 on this item .What is the marked price of this item ??

Let $y be the marked price.
(20%)y = 5
y = 5/(20%)
y = 25

Marked price = $25


7 ) By invest $5000 in a bank at a simple interest rate of 6% per annum . how much interest can he get in 5 months ?

Interest
= $5000 x (6%) x (5/12)
= $125


8) 某長方形的長是闊的3 倍, 周界為24 cm , 求面積? (連式)

設闊為 y cm，則長為 3y cm。

2(y + 3y) = 24
8y = 24
y = 3
3y = 9

面積
= (3 cm) x (9 cm)
= 27 cm2


9)若某數乘以4 加上 10 , 結果等於34 , 求此數? (連式)

設此數為 n。

4n + 10 = 34
4n = 24
n = 6

此數 = 6


10 ) 若某數的五分之二 減去9 , 答案是11. 求某數? (連式)

設某數為 n。

(2/5)n - 9 = 11
(2/5)n = 2
n = 2(5/2)
n = 5

某數 = 5

2009-08-13 00:26:14 補充：
由於閣下的問題太多，我的回答已超出字數限制，所以只好在意見中回答。

4)
0.6 (循環)
= 6/9
= 2/3

7)
Rate per annum
= (240/5000) x (12/3) x 100%
= 19.2%

1 一個長方形面積為256cm,長是闊的4倍.問它的闊是?

設闊是 y cm，則長是 4y cm。

y(4y) = 256
4y2 = 256
y2 = 64
y = 8 (y ≠ -8)

闊 = 8 cm


2那些是矩形數?41.45.48.53.57.61.67.72.73.89.92.95

矩形數：45, 48, 57, 72, 92, 95

45 = 5 x 9, 48 = 2 x 24, 57 = 3 x 19,
72 = 2 x 36, 92 = 2 x 41, 95 = 5 x 19
41, 53, 61, 67, 73, 89 是質數


3 那些是正方形數?36.45.54.64.72.81.94.100.117.121.130.144

正方形數：36, 64, 81, 100, 121, 144

36 = 6 x 6, 84 = 9 x 8, 81 = 9 x 9
100 = 10 x 10, 121 = 11 x 11, 144 = 12 x 12


4循環小數化分數:
a) 0.6
= 6/10
= 3/5

b 0.74( 4循環)
= 7/10 + 4/90
= 67/90

c 0.45(45循環)
= 4/10 + 5/90
= 41/90

d 0.94(4循環)
= 9/10 + 4/90
= 85/90
= 17/18

e 0.148(148循環)
= 148/999
= 4/27

f 0.5678 (678 循環)
= 5/10 + 678/9990
= 5678/9990
= 2839/4995


5 { 4-3} x {4-1} x {8-7} {16-7}

(4-3) x (4-1) x (8-7) (16-7)
= (1/43) x (1/4) x (1/87) (1/167)
= [1/(22)3] x (1/22) x [1/(23)7] x [(24)7]
= (1/26) x (1/22) x (1/221) x (228)
= 228/229
= 1/2


6 An item was sold at a discount of 20% .With this discount .one can save $5 on this item .What is the marked price of this item ??

Let $y be the marked price.
(20%)y = 5
y = 5/(20%)
y = 25

Marked price = $25


7 By invest $5000 in a bank at a simple interest rate of 6% per annum . how much interest can he get in 5 months ?

Interest
= $5000 x (6%) x (5/12)
= $125


8 某長方形的長是闊的3 倍, 周界為24 cm , 求面積? (連式)

設闊為 y cm，則長為 3y cm。

2(y + 3y) = 24
8y = 24
y = 3
3y = 9

面積
= (3 cm) x (9 cm)
= 27 cm2


9若某數乘以4 加上 10 , 結果等於34 , 求此數? (連式)

設此數為 n。

4n + 10 = 34
4n = 24
n = 6

此數 = 6


10 若某數的五分之二 減去9 , 答案是11. 求某數? (連式)


設某數為 n。

(2/5)n - 9 = 11
(2/5)n = 2
n = 2(5/2)
n = 5

某數 = 5