For any number n, if n2 is even, then n must be even. This means n being even is a condition for n2 being even.

For any number n, if n2 is even, then n must be even. This means n being even is a Necessary condition for n2 being even.

Step-by-step explanation:

Necessary Condition:-A condition that says that the result has to be true but does not guarantee any kind of result.

Suppose we  assume that n is not even (i.e., it is odd)  

and show that n^2 is not even (i.e., it is odd).

n is odd then  you can write

   n = 2*k + 1 for an  integer k.

Then,  

  n^2 = 4*k^2 + 4*k + 1  

      = 2 * (2*k^2 + 2*k) + 1  

which is clearly odd.  

This completes the proof that for any number n, if n2 is even, then n must be even

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204