(a) Sketch the set V given in spherical coordinates. Also include a sketch of a vertical cross- section passing through the origin 2θ (b) Calculate the volume of V. (a) Sketch the set V given in...
(a) Sketch the set V given in spherical coordinates. Also include a sketch of a vertical cross- section passing through the origin. 20 (b) Calculate the volume of V. (a) Sketch the set V given in spherical coordinates. Also include a sketch of a vertical cross- section passing through the origin. 20 (b) Calculate the volume of V.
1. Use cylindrical coordinates to SET UP the integral for the volume of the portion of the unit ball, 22 +232 + x2 < 1, above the plane z = 12 2. (a) Write in spherical coordinates the equations of the following surfaces: (i) x2 + y2 + x2 = 4 (ii) z = 3x2 + 3y2 (b) SET UP the integral in spherical coordinates for the volume of the solid inside the surface 22 + y2 + x2 =...
Set up only b. Find the volume of the solid bounded by z x2 y2 and z 3 in spherical coordinates. Set-up only (OJ 7a. Change to spherical coordinates. Set-up only.X 2. f(x, y,z)dzdxdy b. Find fffe'd/where E is the region bounded by z (x2 + y2)2 and z 1, inside x2 + y2 4 in cylindrical coordinates. Set-up only b. Find the volume of the solid bounded by z x2 y2 and z 3 in spherical coordinates. Set-up only...
A) solve this integral in cylindrical coordinates. b) set up the integral in spherical coordinates (without solving) 10 points Compute the following triple integral: 1/ 1.32 + plav JD where D is the region given by V x2 + y2 <2<2. Hint: z= V x2 + y2 is a cone.
3. In spherical coordinates the unit vectors r, and ф are given by (a) Compute the cross products #x f, #x θ, PX φ, θ 0, θ >< φ, and φ >< φ. (b) Express x, y and z in terms of, О and ф. (c) Check the divergence theorern for the function u = r , using for volume the sphere of radius 13] R, centered at the origin, i.e. show that dä -JyV-üö)dr.
b) Sketch the cross-section of a V-belt and label its important parts. (10 marks)
A charged particle is held at the center of two concentric conducting spherical shells. Figure (a) shows a cross section. Figure (b) gives the net flux Φ through a Gaussian sphere centered on the particle, as a function of the radius r of the sphere. The scale of the vertical axis is set by Φs = 5.5 × 105 N·m2/c. what are (a) the charge of the central particle and the net charges of (b) shell A and (c) shell...
pleasee, you can do any solution:( The beam, the cross section of which is given in the figure, consists of 25 mm thick boards. The slip safety stress for nails is given as tem= 100MPa. The diameter of the nails is 5 mm and the gap between the nails along the beam axis is 200 mm · (30P) according to this 50 200 a) Calculate the intensity of the maximum V shear force that can be applied to the cross...
Determine the resultant internal loadings acting onthe cross section through point C. Assume the reactions atthe supports A and B are vertical.
V = 118 KN A beam with the cross-section shown is carrying a vertical shear force of magnitude v. 15mm It has already been calculated that: the neutral plane is 29 mm above the bottom face, and the second moment of area is / = 8.121x107 m (you do not need to re-calculate these values), NP7 29mn 28m mm Isom a) Indicate on the drawing above, where the shear stress () in the beam will be the greatest? b) Calculate...