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A cake is shaped like a hemisphere of radius 2 with its base on the xy-plane. A wedge of the cake...
QUESTION 9 A cake is shaped like a hemisphere of radius 4 units with its base on the xy plane (a) Find the volume of th...
QUESTION 9 A cake is shaped like a hemisphere of radius 4 units with its base on the xy plane (a) Find the volume of the cake using spherical coordinates (5 marks) (b) Now suppose the cake is sliced by a plane perpendicular to the xy -plane at x = a, a > 0 . Let D be the smaller of two pieces produced. Set up a suitable integral for the volume of D (DO NOT EVALUATE). (7 marks)
QUESTION...
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1 1 point) Find the...
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
Use cylindrical coordinates to work out the volume of a ball of radius 1, and to find the center of mass of the upper half of of the ball. (If you take the hemisphere to have its origin at (0,0,0...
Use cylindrical coordinates to work out the volume of a ball of radius 1, and to find the center of mass of the upper half of of the ball. (If you take the hemisphere to have its origin at (0,0,0) and it's base in the XY-plane the z-coordinate of the center of mass is the "average value of z" over the hemisphere, or the total moment divided by the volume.) Parametrize the upper hemisphere using cylindrical coordinates and find it's...
Let E-xi vi + 2zk be an electrostatic field. Use Gauss's Law to find the total charge enclosed by the closed surface consisting of the hemisphere- V1-x2 - y2 and its circular base in the xy-plane...
Let E-xi vi + 2zk be an electrostatic field. Use Gauss's Law to find the total charge enclosed by the closed surface consisting of the hemisphere- V1-x2 - y2 and its circular base in the xy-plane. Use the Divergence Theorem to evaluate F.N dS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results F(x, y, z) =xyì + 7yj +xzk...
Compute the steady-state temperature distribution in an infinitely long cylindri cal wedge of radius a and...
Compute the steady-state temperature distribution in an infinitely long cylindri cal wedge of radius a and angle B, whose cross-section is illustrated below. The two straight sides of the wedge are held at zero temperature, while the curved edge is at uniform temperature uo uo Here are a few points to consider in r solution to this problem (a) In polar coordinates, the steady-state temperature satisfies You are required to use the usual approach of separation of variables and to...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
QUESTION 9 A cake is shaped like a hemisphere of radius 4 units with its base on the xy plane (a) Find the volume of the cake using spherical coordinates (5 marks) (b) Now suppose the cake is sliced by a plane perpendicular to the xy -plane at x = a, a > 0 . Let D be the smaller of two pieces produced. Set up a suitable integral for the volume of D (DO NOT EVALUATE). (7 marks)
QUESTION...
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
Use cylindrical coordinates to work out the volume of a ball of radius 1, and to find the center of mass of the upper half of of the ball. (If you take the hemisphere to have its origin at (0,0,0) and it's base in the XY-plane the z-coordinate of the center of mass is the "average value of z" over the hemisphere, or the total moment divided by the volume.) Parametrize the upper hemisphere using cylindrical coordinates and find it's...
Let E-xi vi + 2zk be an electrostatic field. Use Gauss's Law to find the total charge enclosed by the closed surface consisting of the hemisphere- V1-x2 - y2 and its circular base in the xy-plane. Use the Divergence Theorem to evaluate F.N dS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results F(x, y, z) =xyì + 7yj +xzk...
Compute the steady-state temperature distribution in an infinitely long cylindri cal wedge of radius a and angle B, whose cross-section is illustrated below. The two straight sides of the wedge are held at zero temperature, while the curved edge is at uniform temperature uo uo Here are a few points to consider in r solution to this problem (a) In polar coordinates, the steady-state temperature satisfies You are required to use the usual approach of separation of variables and to...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
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