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)
,
,
,
,
;; to find the answer, set the expressions equal to each other, since the sum of the numbers should be the same.
Use
and solve for
, which would result in
.
You can also use
to find
– or
.
Plug in the values for
and
, and find
using
or
and results in
.
After plugging in the
value, you can easily find
and
.
– since 66 is the sum of a full row, and the sums of the numbers in each row, column, and diagonal are the same, so therefore,
should also equal 66. This results in
, and, using the same value for the sum of
, or
, we find that
.
The final answer is
,
,
,
,
.
Sorry it took so long;; I hope this helps :)
Explanation: the positive 3y and the negative 3y cancel each other out. Then you combine the x values which equals 13x=13
X=1 then plug the x back into the equation 7x+3y=8. X=1 and Y=1/3
I cant see your work very clearly so I'll work it out below:-
f(x + Δx) = (x + Δx)^2 - 2(x + Δx) - 3
= x^2 + 2x(Δx) + (Δx)^2 - 2x - 2(Δx) - 3
= x^2 - 2x + (Δx)^2 + 2x(Δx) - 2(Δx) - 3
Answer: Maturation
Step-by-step explanation:Internal validity is a type of validity that establishes a cause and effect relationship,this type of validity tries to eliminate alternative explanation for a Discovery.
One of the threats to internal validity is MATURATION.
MATURATION is the type of threat occuring during experiment to prove a particular Discovery as shown by the question where the police officer shot and killed someone against the intention of the experiment.
