Questions from General Calculus

Q: Find the center of mass of a lamina in the shape of

Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length a if the density at any point is proportional to the square of the distance from the vertex o...

Q: A lamina occupies the region inside the circle x2 + y2 =

A lamina occupies the region inside the circle x2 + y2 = 2y but outside the circle x2 + y2 = 1. Find the center of mass if the density at any point is inversely proportional to its distance from the o...

Q: Find the moments of inertia Ix, Iy, I0 for the

Find the moments of inertia Ix, Iy, I0 for the lamina of Exercise 3. Exercise 3: Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D = {...

Q: Find the moments of inertia Ix, Iy, I0 for the

Find the moments of inertia Ix, Iy, I0 for the lamina of Exercise 6. Exercise 6: Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D is...

Q: Use polar coordinates to find the volume of the given solid.

Use polar coordinates to find the volume of the given solid. Under the paraboloid z = x2 + y2 and above the disk x2 + y2 < 25

Q: Electric charge is distributed over the disk x2 + y2 < 1

Electric charge is distributed over the disk x2 + y2 < 1 so that the charge density at (x, y) is (x, y) = √(x^2 + y^2 ) (measured in coulombs per square meter). Find the total charge on the disk.

Q: Use polar coordinates to find the volume of the given solid.

Use polar coordinates to find the volume of the given solid. Below the cone z = √(x^2 + y^2 ) and above the ring 1 < x2 + y2 < 4

Q: Find the maximum and minimum values of f subject to the given

Find the maximum and minimum values of f subject to the given constraints. Use a computer algebra system to solve the system of equations that arises in using Lagrange multipliers. (If your CAS finds...

Q: Find the mass and center of mass of the lamina that occupies

Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D = {(x, y) | 0 < x < a, 0 < y < b}; ρ (x, y) = 1 + x2 + y2

Q: Find the mass and center of mass of the lamina that occupies

Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D is the triangular region enclosed by the lines y = 0, y = 2x, and x + 2y = 1; ρ (x, y)...