Find the solution to the wave equation in a cylindrical cavity of radius R and height H. Be sure to give formulas (in terms of integrals) for all coefficients. Utt = c² Au u(t, R, 0, z) = 0 u(t,r,0,0) = 0 u(t,r, 0, H) = 0 u(0,r,0, z) = f(r,0,z) ut(0, r, 0, z) = 0

Find dy/dx and d^2y/dx^2.

Sketch the curve with the vector equation r(t) = cos(t)i − cos(t)j + sin(t)k. Show the direction of increasing t with an arrow drawn on your curve.

WHICH ANSWER IS CORRECT? Given the curve C parametrized by the vector equation r⃗ (t)=3sin(t)i^+[2−sin(t)+cos(t)]j^−3cos(t)k^,t∈[0;2π]   The given curve C has the property that A. Its tangent vector and acceleration vector are always orthogonal. B. The cross product between the tangent vector the acceleration vector always equals −3i^+9j^−3k^. C. The cross product of its acceleration vector and its tangent vector is always parallel to i^+3j^+k^. D. Its vector function is nowhere orthogonal to its tangent vector. E. None of the listed alternatives.

Consider the following problem from Science: A mitochondria with velocity vector r' (t) starts out at (-4, 0, 5) at t = 0 and mitochondrias around for 5 seconds. Where is the mitochondria located at time t = 5 if Ir' (t)| dt = 0? A) (-4, 0, 5) B) (-4, 0,5) C) (3, 0, 7) 6. D) Not enough information

Given f(x,y)=ln(x^2+y^2) a) determine Dv f(2,3) with v =<4, 5> b) what is the angle, in radians, between v and nabla f(2, 3)?