I. a. (10) Find the volume of an axisymmetric ‘gum drop, defined by 0< zく1-
Find the moment of inertia I of the rectangular solid of density =1 defined by 0<x<5 , 0<y<10 ,0<z<3 where L is the line through the point 2,1,0 and 2,2,0
Find the volume of the parallelepiped defined by the vectors lessthan 2, 0, 0
Find the volume of the solid generated when the region bounded by y=14 sin x and y = 0, for 0 , is revolved about the x-axis. (Recall that ) Iく元 sin2 cos2.r) 2 Iく元 sin2 cos2.r) 2
Find the volume of the portion of the sphere, /2 and z = 0 using (i) cylindrical coordinates that is contained between the planes z and () spherical coordinates.
I just need a0 and an, please show work!
=4r +3 defined on the interval (0, 4, denote by fe the even extension on-4, 4 of f Given the function f(z) Find fer, the Fourier series expansion of fe fep(z) an COS 1 that is, find the coefficients ag, an, and b, with n 1. Σ 0 do= Σ an= 0 Σ 0
a. Find the center of mass for lamina defined by the interior of
the polar curve r=sin(3) with a density
that varies according to p(r,theta)=1/r
b. Find the volume of the cylinder inside the sphere
For part a I got a mass of 2 but not sure about the x bar and y
bar calculations.
For part b Im stuck on the z bounds for the integral when doing
the problem with the cylindrical coordinate method.
We were unable to...
3. A medium I is defined by x=0, pr=5, while a medium? as defined by oc> O, as a free space (E=&o). Giren the magnetic vector intensity Coc, y, z) = 100 - 20 + 402, A/an] 3.1. Find the magnetic field density, B . 3.2. Determine the angle o, and , find H, and its make reopedinek with the normal to the surface? HINT: B in = B. But tan 6 = 1
a Find Fand Y he as defined in Problem 1. I define a new random variable z-x-2Y. (b) Find P(X = 21Z = 0). 12 ?-
Find the steady-state temperature u(r,z) in a finite cylinder defined by 0< r < 1,0 < z < 1 in a finite cylinder defined by 0 <rs 1,0 < z <1 if the boundary conditions are as given: 0 z< 1 2) u(1, z) = Z, 0, az z 0 0r1
Find the steady-state temperature u(r,z) in a finite cylinder defined by 0
Find the steady-state temperature u(r,z) in a finite cylinder defined by 0< r < 1,0 < z < 1 in a finite cylinder defined by 0 <rs 1,0 < z <1 if the boundary conditions are as given: 0 z< 1 2) u(1, z) = Z, 0, az z 0 0r1
Find the steady-state temperature u(r,z) in a finite cylinder defined by 0