Solving trigonometry Equations  sin^2(2x)-cos^2(8x)=0.5cos(10x)

Sum(a^(k/a^k), k= 1..n);

Let A(x , 2 , -1) ,B(0, y , 1) ,C(3 , 4 , -2) , AB=AC and ABC is isosceles right triangle. Find x and y ?

we have number from 1 to 2014. If we underline the number that divide by 3 and 4, how many pattern of two underlines that next to each other as example?(1,2,3,4,5,6,7,8,9,10,...,2014).

From 1 to 1000, how many time we use "5"?