use Euler’s identity, e^iθ = cos(θ) + (i)sin(θ), prove that sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
Q: HW11.1 Spherical coordinates (r, 0,0) are defined as: x=rsin cos , y=rsin sind, z=rcos 8. See page…
A:
Q: uonenba x(k + 2) + 3x(k + 1) + 2r(k) = e(k) %3D where k = 0 otherwise 1, e(k) = %3D 0, x(0) = 1 %3!…
A:
Q: Prove [Â, BĈ] = [Â, BJĈ + B[‚, ĈJ-
A: A→,B→C= A→,B→C→+B→A→,C→ Consider L.H.S A→,…
Q: The vector (3, 45°) is equal to (1.83, 2.83) in rectangular coordinate O (1.83, 1.83) in rectangular…
A:
Q: Consider the line element of the sphere of radius a: ds2 = a2(dθ2 + sin2 θ dØ2 ). The only…
A:
Q: d) If [F,G] = 0=[F*,G™] = 0, where m,n integers > 0 e) If [F,H] = 0 & [G,H] = 0= [F G,H] = 0
A: we can use the properties of commutator brackets.
Q: T Consider a PR arm with configuration variables q1,92 the Lagrangian is given by: 1 L= K – P: m, +…
A:
Q: 2(a) – 1 = H²a? Calculate dln |2 – 1|/d In a as a function of 2 and w; by differentiating to show d…
A: This is a very interesting problem in cosmology that can be solved in the FRW universe.
Q: Suppose that you have the functional J (a) = S². ƒ {y(a, x), y' (a, x); x}dx where y (a, x) = 3x – a…
A: Given, Jα=∫-π2π2fyα,x,y'α,x;xdxyα,x=3x-αcos2xTherefore,y'α,x=3+αsin2x
Q: is equivalent to (x, t)= A cos(kx-wt - n/2) (x, t) = A sin(kx - wt).
A: we need to show that ψ(x,t)=Acos(kx-ωt-π/2)is equvalent…
Q: Q.3: Given the two vectors A = i+j and B =j+ k, find the following: (1) ЗА — 2B (2) Ax B (3) |Ãx B |
A:
Q: If A = 2i − j − k, B = 2i − 3j + k, C = j + k, find (A · B)C, A(B · C), (A × B) · C,A · (B × C), (A…
A: (A•B)C = (2i − j − k • 2i − 3j + k)( j + k) (A•B)C = (4 + 3 - 1)( j + k) (A•B)C = 6( j + k)
Q: Find the Gradient (Spheiical) V=(2rsint cos ) ar (rcost cos ) ao - (r sindlap COS COS
A: To find spherical gradient of given function
Q: If  and B are two vectors that commute with Ô, prove the useful identity (Ô· Â)(Ô · B) = · B+ iÔ(Â…
A:
Q: In the following function evaluations f(xA), assume the numbers xA are correctly rounded to the…
A:
Q: Let x(t) = [4 cos(100t) + sin(100t) + e-50t cos(50/19t)]. Then deduce that 2 85 (a) x(t) solves (t)…
A:
Q: find the commutator [Lz,cosφ]
A: The commutator of two operators A and B is given by
Q: (1.30) If ¢ = x²yz³ + 2z²y² find C (a) Vo at the point (1,-1, 1) (b) the magnitude of Vo at (1,-1,…
A: See step 2
Q: In this problem you will use the bisection method to compute the eccentric anomaly E in equation (2)…
A: To solve for the eccentric anomaly E using the bisection method, and subsequently compute the x and…
Q: ), -G. ), a.) Total differentials: U(V,T) dU - C,dT + RydV S(V,T) ds ar + dv H(P,T) S(P,T) dH - C,dT…
A:
Q: Problem 2: Random variable X has the following pmf and Y = eX. Calculate EY] directly (without first…
A:
Q: Consider a sphere of radius R. In the spherical polar coordinate if we choose a particular value for…
A: The small volume element dV and surface element (perpendicular to radius) dS in the spherical polar…
Q: The component form of vector is 7 = (4, 3). v Find 47. 40 =
A: A vector can be represented by its component form. The vector has two components in a…
Q: Find the arc length parameter along the given curve from the point where t= 0 by evaluating the…
A:
Q: 1cm 1cm A P C
A:
Q: Show that (a) [Jz, J+] = J+ = iJ₂
A:
Q: Let X be a random variable whose density is given by the formula f(x) = cx2 if x ∈ (0, 2)…
A: Given: The density is given by, f(x)=cx2 if x∈0,20 if otherwise Introduction: A random variable is…
Q: Prove that the expression e*/(1+ e*)² is an even function of x.
A:
Q: (2) The natural independent variables for U are (S,V), from dU = Tds - pdV. U = U (S,V) gives simple…
A: The first law of thermodynamics is
Q: iven the following information, find the force components of Force A Force A = 200 N Θ = 30o (on x-y…
A: Given: The magnitude of the Force vector is A = 200 N The angle made by the vector is Θ = 30o (on…
Q: Given a function : y(t) = A sin(kx-wt) Prove that: d^2 y / dt^2 = - w^2 y(t) Where A, k, x, w are…
A: Given function is, yt=Asinkx-ωt
Q: For cubic system of [100] reflection, (100), (010), (001), (100), (010), (001), therefore, p100=6.…
A: Below are the planes for cubic system [100] (1,0,0) (0,1,0) (0,0,1)
Q: Using partial derivatives, calculate the propagated uncertainty in the mass in the following case:…
A: Given that, centripetal force Fc = (20.0 ± 0.5) N, angular velocity w = (29.2 ± 0.3) rad/s, radius R…
Q: LzPnem (r.0,0) = mhnem(r, 0, 0)
A: Have a look dear
Q: R(1) = (1, 1,-2), R'(1) = (-2,0, 4) and R(1) = (3,-1,1). (a) Find the vector equation of the tangent…
A:
Q: Show that exp(-i0X/2) where X is the Pauli X-matrix. € (2) 1-isin (1) X = COS
A:
Q: Using partial derivatives, calculate the propagated uncertainty in the mass in the following case:…
A:
use Euler’s identity, e^iθ = cos(θ) + (i)sin(θ), prove that sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
Step by step
Solved in 3 steps with 4 images