〔數學〕數學4條

2010-02-20 6:53 pm
若a及b均為正整數,則log(a^b b^a)=??




若五個數 15, x+4, x+1, 2x-7, x-3 的平均值為6,則該五個數的眾數為???



設x及y均為非零的數,若2x-3y=0,則(x+3y) : (x+2y)=??:??



偉明售出兩個物業單位,每個單位的售價均為$999,999,其中一個蝕了10%,而另一個則獲利10%,完成該兩項交易後,偉明 獲利/蝕 $xxxxx?

回答 (1)

2010-02-20 9:36 pm
✔ 最佳答案
1)

log(a^b * b^a)
= log(a^b) + log(b^a)
= blog(a) + alog(b)

2)

[15+(x+4)+(x+1)+(2x-7)+(x-3)]/5=6
5x + 10 = 5 * 6
5x + 10 = 30
5x = 30 - 10
5x = 20
x = 4

{15, 4+4, 4+1, 2*4-7, 4-1}
= {15, 8, 5, 1, 3}

3)

2x - 3y = 0
2x = 3y
x/y = 3/2
x:y = 3:2

設x=3a, y=2a; a>0
(x+3y) : (x+2y)
= (3a + 3*2a) : (3a + 2*2a)
= 9a : 7a
= 9:7

4)
淨回報
= [999999*(1-10%) + 999999*(1+10%)] - (999999 + 999999)
= (999999*0.9 + 999999*1.1) - 1999998
= 899999.1 + 1099998.9 - 199998
= 0
無賺蝕
參考: 自己


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