t> w
Determine the N-point DFT X[k] of the N-pont sequence x[n]=Cos(w*n),0<=n<=N-1,for w not equals to 2*pi*r/n,0<r<N-1.
Let r be the angle of the ray, and R the angle of reflection.If the wall is flat (i.e., if its angle is 0), then we know that r + R = Pi/2.Now suppose the wall has angle w. Then rotate the diagram by -w,so that the wall is now flat again, and the angles of the ray and itsreflection are now r - w and R - w, respectively.We then have (r - w) + (R - w) = Pi/2, which should give you enoughinformation to find R.
In order to solve this inhomogeneous differential equation you need to start by solving the homogeneous case first (aka when the right hand side is just 0). The characteristic equation for this differential equation is r²+1=0 or r²=-1 which means that r must be equal to ±i. Therefore, the general solution to this homogeneous problem Is y=c1*sin(x)+c2*cos(x) where c1 and c2 are constants determined by the initial conditions. In order to solve the inhomogeneous problem we need to first find the Wronskian of our two solutions. _________|y1(x) y2(x) | __| sin(x) cos(x) | W(y1, y2)= |y1'(x) y2'(x) | = | cos(x) -sin(x) | = -sin(x)²-cos(x)²= -1 Next, we calculate the particular solution Y(x)=-sin(x)* Integral(-1*cos(x)*cot(x)) + cos(x)*Integral(-1*sin(x)*cot(x)) =sin(x)*Integral(cos²(x)/sin(x)) - cos*Integral(cos(x)) =sin(x)*(ln(tan(x/2)) + cos(x)) -cos(x)*sin(x)=sin(x)*ln(tan(x/2)) Finally, to answer the entire equation, we add the particular solution to the homogeneous solution to get y(x)=sin(x)*ln(tan(x/2)) + c1*sin(x)+c2*cos(x)
Reading, (w)righting and (a)rithmetic.
W. R. Holway has written: 'A history of the Grand River Dam Authority, State of Oklahoma, 1935-1968' -- subject(s): Grand River Dam Authority
t> w
The answer is obtained using de Moivre's theorem.Suppose you have a complex number z = x + iyz can also be expressed, in polar coordinates, as r*cos(T) + i*r*sin(T) wherer = sqrt(x^2 + y^2) is the magnitude of zandT = arctan(y/x).Suppose w = sqrt(z)then magnitude of w = sqrt of the magnitude of z = |sqrt(r)| = q, sayand U = T/2so that w = q*cos(U) + i*q*sin(U).Similarly, the cube root of z would be cubert(|z|)*cos(T/3) + i*cubert(|z|)*sin(T/3), and so on.
=w+r
. R is a function of w
Determine the N-point DFT X[k] of the N-pont sequence x[n]=Cos(w*n),0<=n<=N-1,for w not equals to 2*pi*r/n,0<r<N-1.
Gravity is the force that keeps the planets in orbit around the sun. This force is generated by the massive gravity of the sun, which creates a gravitational pull that keeps the planets moving in their elliptical orbits.
W. R. Titterton died in 1963.
W. R. Burnett was born in 1899.
W. R. Berkley was created in 1967.
W. R. Burnett died in 1982.
W. R. Titterton was born in 1876.