mingja

6、等比数列题：
1+7^1+7^2+....+7^8=623500(大概是这么一个数），求7^9
A:6*623500+1 (这题并不难注意首项为1，用求和法即可）

实在想不出是如何下手?请指点!

Sn= (S9)=(S8)+ 7^9= ?

S(9)=1+ {7*(1-7^9)/(1-7)}=1+ {(7/6)(1-7^9)=then what?

Please help!

mingja

三个等圆相切，中间夹空部分为阴影部分，其面积为64倍根号3-32派，求半径。不难，仔细算，ans:r=8

我这么算也不对

First find the pizza-shaped area= 1/6 (pi r^2)

and minus the the area of the equilateral triangle= {r^2 (square root 3/4)}

So the sliver's area is {1/6 (pi r^2)-{r^2 (square root 3/4)}

There are 3 of these slivers:  

3*{1/6 (pi r^2)-{r^2 (square root 3/4)}

and it is equal to 64倍根号3-32派

3*{1/6 (pi r^2)-{r^2 (square root 3/4)}=64倍根号3-32派


But r is not equal to 8 ?

rather r^2=-2^7

Please help!

mingja

Thanks!

mingja

Thanks, but I still do not get it:

How do you get

(root3)*r^2-1/2pai*r^2

May be I misunderstand the question.

Is it asking about the bigger 3-leaf-clover-shaped area formed in part by overlappings of 2 circles plus the center 3-cuured-sided smaller curved area?

Or is it asking about the middle 3-curved-sided smaller area?

Or something else?

I appreciate your reply! Thanks!

mingja

我也认为是B和C

75=3*5^2
98=2*7^2
140=2^2*5*7

Common multiple 公倍数m at least =2^2*3*5^2*7^2=14700

故 14700 can be divided by 49 , and also >14000

mingja

Agree

mingja

我同意思路该是两个概率的和

不过cannot understand BE SECRETARY的概率应该是9/10*1/9.

may be 9/10*1/9* (probablility that he is not treasurer)

=9/10*1/9*(7/8) ?

mingja

多谢!

终于知道我想歪到那里

三个圆是tangent to each other, and circumferences touch each other's .  Not Circunference going through each other's center.
怪不得我左看右看上下看就是看不出也找不到等边三角形内那有3个扇形.