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help in math:l
1). If y varies directly as n ^n with a constant of variation k, and z varies directly as y^m with constant of variation c, then z varies directly as some power of x. what power is it, and what is the constant of variation?
2). The moment of inertia of a solid sphere about a diameter varies jointly with the mass of the sphere and the square of its radius. If a sphere of a mass 10 g and a radius of 3 cm has a moment of inertia of 36g-cm^2, what is the moment of inertia of a 6 g sphere of radius 5cm?
3). If x is jointly proportional to v and w, and x=24 when v=15 and w=8 find x when v=10 and w=6.
4).If v varies directly as the square root of x and inversely as y, and v=18 when x=9 and y=45, find v when x=25 and y=3.
5). if the temperature is kept constant, the volume of an ideal gas is inversely proportional to the pressure on it. At 1.8 atmospheres , a given mass of hydrogen occupies 48m^3. what pressure would be necessary to change this volume to be 30m^3.
6). The Kinetic energy of an object varies jointly as its mass and the square of its velocity. If it takes 50 joules of energy to move a 4kg object at 5m/s, how much energy would be required to move an 8kg object at 10m/s?
7).Suppose z varies jointly as x and y and inversely as w, and z=8 when x=6, y=5, and w=10. find z when x=3, y=4 and w=5.
8). Suppose z varies directly as w and inversely as uv, and z=5 when u=9, v=4 and w=13. find w when z=10, u=6, and v=151.
9). The Gravitational force that the earth exerts on an object varies inversely as the square of its distance frm the center of the earth. If the earth exerts a force of 19,000 N on an orbiter module on the earth's surface, 64,00 km frm the center of the earth, what force would it exert on the module when it is 8000 km frm the earth's center.
10). The attractive force between two oppositely charged particles varies jointly with the magnitude of their charges and inversely as the square of the distance between them. the force between two particles with charge of 5 Micro coulombs and 1 micro coulombs, which are 0.3 m apart, is 0.5 N. what is the force between charges of 2 micro coulombs and 6 micro coulombs that are 0.4 m apart.
11). Suppose z varies jointly as x and y and inversely as w, and z=6 when x =4, y= 5 and w= 8. find z when x=2, y=6 and w=4.
12). Suppose z varies directly as w and inversely as uv, and z=10 when u=8, v=6 and w=4. find w when z=16, u=15 and v=3.
13). The electrostatic force of repulsion between two apha particles varies inversely as the square of the distance between them. If this force is 0.384 newtons when the particles are 0.05 picometers apart, what is the force when the particles are 0.2 picometers apart.
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