數學問題!

2007-08-10 10:20 pm
1)世目公司以原價每件$10購入100件T恤,當中有10件是損壞的。若該公司把完整的T恤以每件$y賣出,而最少可獲50%的盈利,求y的最小值及每件T恤的最低售價。(答案準確至最接近的元)

2)化簡√a√a√a√a

3)化簡x^ -1 -y^ -1/x^ -2 -y ^ -2

4)化簡b^n-b^n+3/b^n

5)化簡3^n+1-2*3^n/3^n-1

6)計算下列各題,並以科学記數法表示答案.
a)√49000000 *√64*10^ -4

b)125*10^ -5+0.4*10^ -4

如有步驟,請列出!10分,pls
更新1:

其他我都明,但第3題就5明...

回答 (1)

2007-08-11 12:40 am
✔ 最佳答案
1)
盈利 / 成本 * 100% = 盈利百分比

90(y - 10) / [ (10)(100) ] * 100% = 50%
90(y - 10) / 1000 = 0.5
y = 140/9 = 15.5555....

每件T恤的最低售價為 16 元

2)
√a√a√a√a
= (√a)^4
= a^2

3)
[ x^ (-1) - y^( -1) ] / [ x^(-2) - y^(-2) ]
= [ (y - x) / (xy) ] / [ (y^2 - x^2) / (x^2 y^2) ]
= [ (y - x)(x^2 y^2) ] / [ (y^2 - x^2)(xy) ]
= [ (y - x)(xy) ] / [ (y - x)(y + x) ]
= (xy) / (y + x)

留意 d 括號點用法,唔加括號個意思相差好大

4)
[ b^n - b^(n+3) ] / b^n
= [ b^n - (b^n)(b^3) ] / b^n
= (b^n)(1 - b^3) / b^n
= 1 - b^3

5)
[ 3^(n+1) - 2 * 3^n ] / 3^(n-1)
= [ 3 * 3^n - 2 * 3^n ] / 3^(n-1)
= 3^n / 3^(n-1)
= 3

6)
√49000000 * √64 * 10^(-4)
= 7000 * 8 / 10000
= 28/5
= 5.6

125 * 10^(-5) + 0.4 * 10^(-4)
= 125/100000 + 0.4/10000
= 125/100000 + 4/100000
= 129/100000
= 1.29 * 10^(-3)

咁多條, 好辛苦啊


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