maths questions

2007-10-24 1:34 am
1.Someone forms an integer by writing the integers 1 to 82 in ascending order.i.e. 1234567891011...808182.Find the sum of the digits of this integer.
某人把1到82之間的整數順次序寫出來,從而得到另一個整數 1234567891011...808182。
求這個數字之和。

求最少的正整數 n ,使得2007n(在十進制中)的最後三位數字是837。

一位貨櫃車穿過隧道時,計算了車子進入隧道直至整輛車離開隧道所需的時間。第二天,車子加上一個貨櫃,使其總長度由6米變成12米。司機把車速調低20%,並再次計算同一時間。他發現需時增加了一半。求隧道的長度(以米為單位)。

設 n = 999.999。以十進制表示n^3,數字共會出現多少次?

2007位
更新1:

數字"9"共會出現多少次?

回答 (1)

2007-10-24 5:03 am
✔ 最佳答案
1) the sum of ascending numbers is easy. Just remember the rule

(1st number + last number) x n / 2
--> n is the number of integers. So for 1 - 82, there are 82 numbers. n = 82.

Therefore, for this question, ANSWER is:
(1 + 82) * 82 / 2 = 3043


2) This is little tricky. I will try to explain.

2007 * n = xxxx837->we don't know how many "x" and we don't need to care

以7的倍數來看, n 的尾數(last digit)一定會是1
So, n = xxx1

2007
* x1
-----
xxx7

跟住,n的第二尾數會是9
因為只有*9先可以有3在尾

2007
* x91
-----
x630
+2007
-----
x637

跟住,n的第三尾數會是6!
因為只有*6先可以有2在尾
咁2+6就有8在answer的第三尾

2007
* 691
-----
4200
+x630
-----
x830
+2007
-----
x837


3) This is a gernal physics question
You just need to know:

velocity = distance / time
(v = d / t)

d = 隧道長度
v = 貨櫃車速
t = 穿過隧道時間

原本
v = (d + 6) / t

第二天,
0.8v = (d + 12) / 1.5t

0.8v -> 車速調低20%
1.5t -> 需時增加了一半

simutaneous equations to solve for d:
d = 24m

4) I do not understand what you are asking for this question, sorry!
數字共會出現多少次 --> not understand..
參考: worked it out myself ! Thanks!


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