9的999次方 數學高手入

1.Let me tell you one method.While you are doing this type of question.
You can use it. x^(y)=x^(the remainder after y/4) Only when you are finding the 個位數
For example.
9^(999)
=9^(the remainder after 999/4)
=9^(3)
=729
so the 個位數 is 9.

2.The total amount that he borrow
=3x6
=18
As the public library usually ask you return the books after 2weeks (you can also let y be the time he late)
=4weeks-2weeks or = 4weeks-y weeks
=2weeks
So the total money he need to pay
=18x2weeks x$(0.5x7)/weeks or=18x(4-y)weeks x $(0.5x7)/weeks
=$(36x3.5) =$(72x3.5-y x 3.5)
=$126 =$(252-3.5y)

3. I will draw it.
1- - - - - - - - - - - - -1---------------------1
500m 第10位 400m 大文
大文 need to run (500+400)m
So the time he need to finish the competition
=900m / (40km/h)
=(900m/40km)h
=(900m/40000m)h
=0.0225
第10位 need to run 500m
So the time he need to finish the competition
=500m/(35km/h)
=(500m/35km)h
=(500m/35000m)h
=(1/70)h
=0.0142857142857..........
As 0.0142857......h is smaller than 0.0225h
so 大文 need more time than第10位 to finish the competition.
Therefore 大文沒有機會追到第10位衝線.

4. 0+5-4+0.618÷3(0.618)(3)(3)
=(0+5-4)+0.618(0.618)(3)(3)÷3
=1+0.618(0.618)(3)
=1+1.145772
=2.145772

5. 3(3-3+4)/2
=3x4/2
=6

2012-03-02 20:01:46 補充：
sorry that I don't know how to type Chinese words.I'm very sorry for that.

2012-03-02 20:03:50 補充：
sorry that in question 3 ,(0.025)should be 0.025h.

第二條唔理幾多張卡……都係借咗6本，理得佢用6張卡6本書同5張卡借6本書。
問題係按卡收錢定按書收錢？

我見到"9的999次方=999的9次方" =.= 我直接拜服=.=

1.
9^999 = 9 x 9^998 = 9 x (9^2)^499

9^2 = 81 個位數是 1
所以 2^999 的個位數 = 9 x 1^499 = 9 x 1 = 9

第 2 題看不明題目，不再做下去。

樓上的,9既999次方同999既9次方係唔同架= ="(999既9次方都唔係999X9X9X9X9X9X9X9X9X9啦= =")

講番D題目先
1.做呢d題睇下d規律先
9^1=9(個位9)
9^2=9x9=81(個位1)
9^3=81x9=729(個位9)
2次一個循環,個位數字就9,1,9,1,9咁去
所以9^999個位數字係9~

2.小明在圖書館借了六本書,但用3張圖書證借了它的3倍書數量.
4星期假期完結後,小明遲還書. 如果一天罰0.5元,問要罰多少?

題目好唔清楚= =希望我睇岩啦

借左6本書既3倍書數量=18本?
4星期假期完左
=遲左2星期還(通常圖書館都係2星期內要你還書)
=0.5*18*7*2
=$126

(咩人會kai到同一本書用3張圖書證借3次?題目又唔講點先算過期? 4星期假期完結後,小明遲還書姐係小明幾時還書?)

3.上網搵2400米世界盃都係有關跑馬既= ="大明係馬?
無可能,大明係22名,speed又慢過第10名,點追得上?

4. 0+5-4+0618/3(0.618)(3)(3)=?
條式本身就錯 無0.618/3(0.618)(3)(3)呢種數
一係乘一係除,咁樣寫好誤導

5.同上