(中4)polynomial+聯立方程問題急!

2011-01-17 3:18 am

ps.請用最多中4程度知識回答,以免引起我呀sir懷疑thx
另外,請最好用中文解答,當然要有詳細steps

polynomial
1a.What is the remainder when 5+x^999 is divided by x-1?(我搵左係6)
b.Hence or otherwise, find the remainder when 5+9^999 is divided by 8?
c.Find the remainder of 9^999除8

聯立方程(simultaneous equations)
2.A man bought a certain number of books for $360. If each book had been subject to a discount of $4, he should have had three more for the money. Find the cost of each book.

3.Two taps P and Q can fill a tank in 12 minutes. If tap P alone is turned on for 16 minutes to fill the tank, how long does it take for tape Q alone to fill the tank?

唔該哂!

更新1:

to STEVIE-G™: 我唔係好明1b同c,可唔可以講下點解由a就知道b既答案係6? c係咪用左 f(x)=d(x)乘q(x)+r(x)呢題做? thx!

更新2:

b我明明地但c我想知點樣列出黎? 姐係f(x)呀,d(x)呢d應該要代咩? thx!

更新3:

um,其實我係想講根據呢一題應該代邊d數落邊一度咁解.. 例如話,f(x)係咪5+9^999? d(x)係咪(x-1)咁

回答 (1)

STEVIE-G™

2011-01-17 4:12 am

✔ 最佳答案

1a)
設f(x)=5+x^999
餘數=f(1)=5+1=6

b)
由a part,可以知道當5+9^999被(9-1)除時餘數為6

c)
由b part,可知5+9^999=8Q+6, 其中Q為商數
=> 9^999=8Q+1
=> 所以餘數為1

2)
設每本書的價錢為$x及他原來購買了n本書
{nx=360=>n=360/x...(1)
{(x-4)(n+3)=360...(2)

代(1)入(2):
(x-4)(n+3)=360
(x-4)[(360/x)+3]=360
(x-4)(360+3x)=360x
360x+3x^2-1440-12x=360x
3x^2-12x-1440=0
x=24 or x=-20 (rejected)

所以每本書價錢為$24

3)
設管Q需要單獨用t分鐘去裝滿該缸及缸的容量為V
P的速率=V/16及Q的速率=V/t
由於P及Q一齊使用時可以於12分鐘完成工作,即:
V/[(V/16)+(V/t)]=12
(1/16)+(1/t)=1/12
t=48
所以Q需要48分鐘去完成

2011-01-16 21:26:55 補充：
b)
因為由(a)知道5+x^999被(x-1)除,餘數係6,所以考慮當除數大於餘數時,即當x=8,9,10,...餘數都會係6

c)
對...f(x)=d(x)乘q(x)+r(x), 其中q(x)係商數,r(x)係餘數

2011-01-17 18:45:53 補充：
被除數=除數*商數+餘數
例如考慮當9除以7時,
被除數=9, 除數=7, 商數=1, 餘數=2
所以就可以寫成9=7*1+2

2011-01-17 20:04:57 補充：
5+9^999=8乘q(x)+6 -> 咁d(x)=8及r(x)=6

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