Working with center of mass of a three body system

The center of mass of three objects is located at (1,0). One object with a mass of 5 kg is at (-2,-1) and a second object with a mass of 2 kg is at (0,0). Find the coordinates of the third mass of 3 kg.

A 3.0 kg rod of length 5.0 m has at opposite ends point masses of 4.0 kg and 6.0 kg(a) Will the center of mass of this system be (1) nearer to the 4.0 kg mass, (2) nearer to the 6.0 kg mass, or (3) at the center of the rod? Why?
(b) Where is the center of mass of the system?

Hi. I need some help with a conceptual question.
"A uniform 1-meter stick that is supported by a fulcrum at the 25-cm mark is in equilibrium when a 1-kg rock is suspended at the 0 cm end. Is the mass of the meter stick greater than, equal to, or less than the mass of the rock?"
I thought the answer would be that the mass o

See attached file for full problem description with diagram.
What is the x coordinate of the center of mass of the system described in Part D?
Express your answer in terms of .
=

Prim is primitive!
In genral the moment of inertia around an axis( a line) L is:
Isubl=double prim (dist(.,L)^2*delta*dA)
The collection of lines parallel to the y axis have the form x=a .Let I=Isub(y) be the usual moment of inertia around the y axis
I= double prim of x^2*delta*dA
Let I(bar) be the moment of ine

(See attached file for full problem description with equations)
(Steiner's theorem) If IA is the moment of inertia of a mass distribution of total mass M with respect to an axis A through the center of gravity, show that its moment of inertia IB with respect to an axis B, which is parallel to A and has the distance k from it,

Three point masses are located in an x,y plane as follows:
M1= 7 kg, at (x1, y1)= (5, 6);
M2= 8 kg, at (x2, y2)= (-4, 6); and
M3= 9 kg, at (x3, y3)= (3, -2).
Find the coordinates (xcm, ycm) of the c.m. of the system.

The gravitational force on a body located a distance R from the center of a uniform spherical mass is due solely to the mass lying at distance rcenter of the sphere. This mass exerts a force as if it were a point mass at the origin.
Use the above result to show that if you drill a hole through the