Answer:1002
Step-by-step explanation:
and 
and 
as 
Applying this we get
![\Rightarrow \sum_{1}^{1002}\left [ \cos^2\left ( \frac{k\pi }{2\cdot 2005}\right )+\cos^2\left ( \frac{(2005-k)\pi }{2\cdot 2005}\right )\right ]](https://tex.z-dn.net/?f=%5CRightarrow%20%5Csum_%7B1%7D%5E%7B1002%7D%5Cleft%20%5B%20%5Ccos%5E2%5Cleft%20%28%20%5Cfrac%7Bk%5Cpi%20%7D%7B2%5Ccdot%202005%7D%5Cright%20%29%2B%5Ccos%5E2%5Cleft%20%28%20%5Cfrac%7B%282005-k%29%5Cpi%20%7D%7B2%5Ccdot%202005%7D%5Cright%20%29%5Cright%20%5D)
every 
there exist 
such that 
therefore
![\Rightarrow \sum_{1}^{1002}\left [ \cos^2\left ( \frac{k\pi }{2\cdot 2005}\right )+\cos^2\left ( \frac{(2005-k)\pi }{2\cdot 2005}\right )\right ]=1002](https://tex.z-dn.net/?f=%5CRightarrow%20%5Csum_%7B1%7D%5E%7B1002%7D%5Cleft%20%5B%20%5Ccos%5E2%5Cleft%20%28%20%5Cfrac%7Bk%5Cpi%20%7D%7B2%5Ccdot%202005%7D%5Cright%20%29%2B%5Ccos%5E2%5Cleft%20%28%20%5Cfrac%7B%282005-k%29%5Cpi%20%7D%7B2%5Ccdot%202005%7D%5Cright%20%29%5Cright%20%5D%3D1002)
Step-by-step explanation:
since the ratio of children to adult is 2:7,
2+7 = 9
number of children would be
(2 × 2700)/9 = 600 children in the crowd
number of adults would be
(7 × 2700)/9 = 2100 adults in the crowd
So, if a ticket costs £8 per adults, total cash made from adult
= 8 × 2100 = £16800
if a ticket costs £(8 - 3) per children, total cash made from children
= 5 × 600 = £3000
total money made = £(16800 + 3000)
= £19800
Answer: 0.3,I just took that test
The line through (a,b) and (c,d) is
(c-a)(y-b) = (d-b)(x-a)
Picking the last two points,
(-2 - -6)(y - -21) = (-14 - -21)(x - -6)
4(y+21) = 7(x+6)
When x=0
4y + 84 = 42
4y = -42
y = -21/2
Answer: -21/2
We never used the first point, let's check it's on the line
4(y+21) = 7(x+2)
4(-28 + 21) = -28
7(-10 + 6) = -28, good
