The planet is spherical with a radius of 1 unit in length. Suppose that in a coordinate system whose origin is at the center of the planet, the magnetic field strength is given by I(x,y,z)=4xz+4yz+7. What is the strength of the magnetic field where the radio telescope will be positioned? will be positioned in the place where the planet's magnetic field is as weak as possible

Q: A fluid has density 1200 kg/m3 and flows with velocity ī measured in meters, and the components of ū…

A:

Q: What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z = 3 -…

A: To find the equation for the largest ball centered at (0, 0, 1) that can fit in the below equation…

Q: Find a parametrization for the cylinder x2 + y2 = 1.

A:

Q: A fluid has density 1200 kg/m³ and flows with velocity ū = xi + yj + zk, where x, y, and z are…

A: Use the integral formula of flow rate given by stoke's theorem to calculate its value. Determine the…

Q: A hole is drilled through the center of a sphere x² + y² + z² = R,², leaving a ring-shape solid. If…

A: The radius of the sphere is 'Rs' and radius of cylindrical driller is 'Rd'. When the cylindrical…

Q: A point moves along the intersection of the elliptic paraboloid z = 10x + 11y and the plane y = 1.…

A:

Q: D

A:

Q: A fluid has density 1000 kg/m³ and flows with velocity = ci +yj + zk, where x, y, and z are measured…

A: We have to find the rate flow outward through the part of paraboloid . We can to use the methods of…

Q: A point moves along the intersection of the elliptic paraboloid z = 9x? + 3y² and the plane.x…

A:

Q: Find the center of mass and the moment of inertia about the x-axis of a thin rectangular plate…

A:

Q: The axis of symmetry of the cylinder is parallel to the z-axis. х-ахis. O y-axis.

A:

Q: Find a parametrization for the curve y = Vx with terminal point (0, 0) using the angle 0 in the…

A:

Q: Compute the area of the portion of the cone x2 +y = z2 with z z 0 that is inside the sphere x y z…

A: Given the area of the cone is x2+y2 = z2 and the sphere is x2+y2+z2 = 2Rz.

Q: Suppose the temperature at the point (x, y, z) on the sphere x2 + y2 + ?2 = 16 is T= 800xy2z3 .…

A: Solution is given below:

Q: Find the dimensions of the largest rectangular box in the first octant (x, y, z > 0) with one corner…

A:

Q: A fluid has density 1000 kg/m3 and flows with velocity ū = xi + yj + zk, where x, y, and z are…

A: A fluid density 1000 kg/m3 andflows with velocity v→=xi→+yj→+zk→where x,y and z are measured…

Q: sketch the solid whose spherical coordi- nates (p, 4, 0) satisfy the given inequalities. 0<p<2/cos…

A:

Q: Find the extreme values of ƒ(x, y, z) = x( y + z) on the curve of intersection of the right circular…

A:

Q: A point moves along the intersection of the elliptic paraboloid z = a2 + 3y? and the plane y = 1. At…

A:

Q: Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: The line joining P1,0 and Q0,1 is     x-11-0=y-00-1=t(say)⇒x=t+1,y=-t⇒dx=dt,dy=-dt

Q: Solve Sff, 3x² + 3y²dV by using cylindrical coordinates, where G is a solid in the first octant that…

A:

Q: A: Determine the mass and center of mass of the solid that bounded by the paraboloid = 9y? + 9x2 and…

A:

Q: A solid “trough” of constant density is bounded below by the surface z = 4y2, above by the plane z =…

A:

Q: Find all points on the ellipsoid 2x² + 3y² + 4z² = 9at which the plane tangent to the ellipsoid is…

A: Explanation: Given that,  Ellipsoid:2x2+3y2+4z2=9Plane:x-2y+3z=5⇒15x-25y+35z=1   Suppose point of…

Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We need to find points of intersection.

Q: A fluid has density 800 kg/m³ and flows with velocity i = ri + yj+ zk, where x, y, and z are…

A:

Q: Find the volume of a right circular cylinder of radius a = 4.00 with a paraboloid of revolution…

A:

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 +y? + 2? = 1 is T =…

A:

Q: Find a parametrization for the line segment joining points (0, 2) and (4, 0) using the angle 0 in…

A: Modify the given figure as shown in Figure 1.

Q: A body of mass 6 kg moves in a (counterclockwise) circular path of radius 6 meters, making one…

A:

Q: Use cylindrical coordinates to show that the volume of a sphere of radius a from which a central…

A: If a cylinder of radius b is cut from a sphere of radius a, then the volume of sphere depends on the…

Q: The solid in the first octant bounded by the coordinate planes, y+ z = 4, and x = y.

A: The objective is to find the volume for y+z=4,x=y The volume of the integral formula is,…

Q: Find a point on the surface z = 3x^2 − y^2 at which the tangent plane to this surface is parallel to…

A: We need to find the Point on the surface of  z=3x2−y2 given tangent plane to this surface is…

Q: A point moves along the intersection of the elliptic paraboloid z = 10x? + 3y² and the plane y = 1.…

A:

Q: Find the average height of the paraboloid z = x2 + y2 over the square 0&lt;= x &lt;= 2, 0…

A:

Q: The measurements x1 - 10m, x2 - 8m, and x3 - 6m represent the sides of a rectangular parallelepiped…

A:

Q: Calculate the positive value of m so that the x+y+2z=m plane is tangent to the spherical surface…

A:

Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A: Consider M is the mass of the triangular plate bounded by the y-axis and both the lines. To find…

Q: Express [[[vdV in cylindrical coordinates, where 2 is the solid that lies between cylinders x+y = 1…

A: Region is between the cylinders  x2+y2=1x2+y2=4  Thus,  1≤x≤2  1≤x≤2    Thus, changing to…

Q: Let D = 4xyäx + 4yzäy + 2(x² + y²)āz C/m². Find the total charge enclosed in the rectangular…

A: Given, D=4xyax+4yzay+2x2+y2az  C/m2 0&lt;x&lt;2,   0&lt;y&lt;5,   0&lt;z&lt;3

Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

A:

Q: Find the average height of the hemispherical surface z = √(a2 - x2 - y2) above the disk x2 + y2 ≤ a2…

A:

Q: A: Determine the mass and center of mass of the solid that bounded by the paraboloid z = 9y? + 9x?…

A:

Q: A fluid has density 600 kg/m3 and flows with velocity ū = ri + y. measured in meters, and the…

A: Here we have, Velocity v→=xi^+yj^+zk^ where x,y, and z are measured in meters.  the equation of…

Q: A fluid has density 1200 kg/m³ and flows with velocity v = xi + yj + zk, where x, y, and z are…

A:

Q: ~F = z(x2+ y2) ~k through the disk of radius 4 in the plane z = 2, centered on the z-axis, oriented…

A:

Q: Find the area of the surface of the part of the plane 3x + 2y + 4z = 2 that lies inside the cylinder…

A: Here, surface S has an equation of the form z=f(x,y), where (x,y)  D and f has continuous partial…