show that p(x,t)=psi*(x,t) dot psi(x,t)=(1/a)(sin^2(xnpi/a) +sin^2(n'spi/a)) +2sin(nxpi/a)sin(n'xpi/a)cos((En-En')(t/h))
show that p(x,t)=psi*(x,t) dot psi(x,t)=(1/a)(sin^2(xnpi/a) +sin^2(n'spi/a)) +2sin(nxpi/a)sin(n'xpi/a)cos((En-En')(t/h))
USING MATLAB please show all commands (sin x + cos x)^2 = 1 + 2sin xcos x (b) 1 - 2cos x - 3cos^2 x/sin^2 x = 1 - 3cos x/1 - cos x For each part, verify that the identity is correct by calculating the values of the left and right sides of the equation, substituting x=20 degree.
Show how [sin((x+0.5)theta) - sin((x-0.5)theta)] / [2sin(theta/2)] = cos(x theta) Please show all steps clearly. Please do not overlook the theta in two places in the numerator.
art 1 sin(5t)) z(t) = (cos(50t) + x(t))?, where x(t) = }. z(t) is passed through a filter with impulse response h(t) in order to pass only the product 2x(t) cos(50t). Which filter below is the correct filter to do that? ST sin(5t) sin(15t) / (a) h(t) = {* tt at (b) h(t) sin(5t) sin(100) L 1. Tt at os(1004) 5 it - Tt J (c) h(t) = {i sinft) sin15)} 2cos(50) (a) h(e) = { i sin tuon )*2...
d2y d2y dy +6 da2 (h) +13y 2sin x +9y = 18x -+3 +6 dx da d2y (i) d2y (j d2 18x3 4y = 2 sin x dæ2 d2y ,dy .dy 9y 9x2 +21x - 10 dc (k) (1)2 7 + - 4y = e-4x +6 'da2 da2 d2y dy dy (m) 2 dæ2 (n) 4 7y= e 6 cos x 9y = 4e-3r dr2 dr dx d2y d2y (p*) dy + da2 dy (o* 2a COS I 2y 2...
15. Using that sin' (2) = cos(x), cos' (2) = - sin() show that arccot (0) = 1 +22
4. Let x E C1 (0,T]; R), T > 0 satisfy _ cos(t)x(t)H(t) + sin(t)2(t) = 0 for all t E (0,T). (a) Show that this defines a FODE for at least one T>0. 1 mark 2 mark (c) Find the potential and conclude (briefly) what is the solution space for the FODE for (b) Transform (possibly inverting) the DE into an exact DE. T. 2 mark 4. Let x E C1 (0,T]; R), T > 0 satisfy _ cos(t)x(t)H(t)...
r(t) = 10 sin(300t + 60°) cos(x - 90) sin(x) v(t) 10 cos(300t- 30°) ω = 300, Mag = 10, θ =-30° v 102-30 MLP Mcos(P) +jMsin(P) v = 10 cos(-30) +j10 sin(-30) Step 1: Convert to Cosine Step 2: Identify Frequency, Magnitude, and Phase Step 3: Convert to real/imag form = 8.66-J5 Step 4: Solve Step 5: Convert Back
Solve for 14(b,c) and 18 (b,c) please 16. Find a set of parametrie equations t d) r(t)-(4t,3 cos(t).2sin(t) the line tangent to the graph of r(t) (e.2 cos(t).2sin(t)) at to-0. Use the qu tion to approximate r(0.1). tion function to find the velocity and position vectors at t 2. 17. Find the principal unit normal vector to tih curve at the specified value of the parameter v(0)-0, r(0)-0 (b) a(t)cos(t)i - sin(t)i (a) r(t)-ti+Ij,t 2 (b) rt)-In(t)+(t+1)j.t2 14. Find the...
1. Show that if x(t) is an even function of t, then X(jw)2 (t) cos(wt) dt and if r(t) is an odd function of t, then X(jw)2j (t) sin(wt) dt
The terminal point P(x, y) determined by a real number t is given. Find sin(t), cos(t), and tan(t). 3 sin(t) cos(t) tan(t)