b) Find the area of a cylindrical surface described by r = 6,0 following Fig. 1....
Question 8: 10 Marks The area of the surface described by zf(x,y) for (r,)e R is given by Find an approximation to the area of the surface on the hemisphere r2 + y2 + z2-9,2 the region in the plane described by R-((r, yjo-r 1,0 y I) using: 0 that lies above 8.1 Trapezoidal rule in both directions 8.2 Simpson rule in both directions 8.3 Three-term Gaussian quadrature formulas in both directions 131 131 Question 8: 10 Marks The area...
Suppose that we are given the following communication system described in Fig. 1 with the channel corrupted by an additive white Gaussian noise z with zero mean and variance 1 where the channel input.x is used for signal transmission to produce the channel output y,i.e., r- x . Then the channel is further passed through a hard limiter, i.e., sign detector described by Q2(r) in Fig.2 decisions 22(r) Figure 1. A channel with the input x and output r corrupted...
2. Given the vector field F-ki/r+zk22, evaluate the scalar surface integral (1) over the surface of a closed cylinder about the z-axis specified by 2 = +3 and r = 2, as described in Fig. 1, where ki and ky are constants. Fig. 1. A cylindrical surface.
Please show all steps clearly, thank you! (15%) 1 . Two different media are separated by a cylindrical surface or interface as shown below. The radius of the cylindrical surface is r 10 m. D, in medium 1 is given as shown below. Find E, at r- 10+, 30" and z = 5. (15%) 1 . Two different media are separated by a cylindrical surface or interface as shown below. The radius of the cylindrical surface is r 10 m....
The motion of a liquid in a cylindrical container of radius 2 is described by the velocity field F(x, y, z). Find (curl F) N dS, where S is the upper surface of the cylindrical container. УЗі +-X31+ 9k F(x, y, z) The motion of a liquid in a cylindrical container of radius 2 is described by the velocity field F(x, y, z). Find (curl F) N dS, where S is the upper surface of the cylindrical container. УЗі +-X31+...
problem-3 plz 3. (40) In Fig.1, (a) 0 r< a, find B, VxB, and magnetic energy per unit length. (b) a<r< b, find B, VxB, and magnetic energy per unit length. (c) b<r, findB, VxB, and magnetic energy per unit length. (d) Find the inductance per unit length. (3+3+4)x3+ 10) 4. (20) Fig. 2 shows a side view of a cylindrical bar magnet. (a) Find H di for a dashed contour and explain. (b) Describe the direction of H inside...
A) Find the surface area of the paraboloid when by parameterizing the surface using a polar representation. B) Express the surface area of the paraboloid as a triple integral using the Divergence theorem. C) By choosing an appropriate vector field, use the Divergence Theorem to find the surface area of the paraboloid. -yi z 1-r We were unable to transcribe this image -yi z 1-r
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) rectangular coordinates (x,y, z); (ii) cylindrical coordinates (r, 0, 2); (iii) spherical coordinates (p, φ,0). a. Inside the sphere 2 +3+224 and above the conezV b. Inside the sphere x2 + y2 + 22-12 and above the paraboloid z 2 2 + y2. c. Inside the sphere 2,2 + y2 + z2-2 and above the surface z-(z2 + y2)1/4 d. Inside the sphere...
4. A cylindrical silo with a hemisphere top has a surface area, A= 2nrh+37r, where r is the radius of the cylindrical base and the radius of the hemisphere and h is the height of the cylindrical base. The height is measured to be 30 m with a possible error in measurement of 0.2 m and the radius is measured at 5 m with a possible error of 0.1 m. Use differentials to estimate the largest possible relative error when...
3. [4 marks] Using cylindrical polar coordinates, or otherwise, find the value of the surface integral 1 = []6.2? ds, where S is the part of the cone z = z? + y that lies between the planes z = 2 and 2=5.