Joint and Combined Variations 2

If a variable y varies directly as x and inversely as z, which of the following equations correctly represents this combined variation?

If the pressure of a gas varies directly with its temperature and inversely with its volume, what is the equation for this relationship?

If the frequency f of a vibrating string varies directly as the square root of the tension T and inversely as the length L of the string, which equation represents this relationship?

The volume V of a gas varies jointly with the temperature T and inversely with the pressure P. If V = 40 when T = 300 and P = 50, find the volume V when T = 360 and P = 60.

The electrical resistance R of a wire varies jointly as its length L and the inverse of its cross-sectional area A. If R = 20 ohms when L = 10 meters and A = 5 square millimeters, find R when L = 15 meters and A = 6 square millimeters.

A vehicle travels a distance that varies directly with the speed and inversely with the time of travel. If a vehicle travels 180 miles at a speed of 60 mph in 3 hours, how far will it travel at a speed of 80 mph in 4 hours?

The illumination of a light bulb varies directly with the power of the bulb and inversely with the square of the distance from it. If a 100-watt bulb provides an illumination of 16 units at a distance of 5 meters, what will be the illumination of a 150-watt bulb at a distance of 10 meters?

The gravitational force between two objects varies directly with the product of their masses and inversely with the square of the distance between them. If the force is 36 units when the masses are 4 kg and 9 kg and the distance is 2 meters, what will the force be when the masses are 6 kg and 12 kg at a distance of 3 meters?