Consider the circuit below: (a)calculate the voltage vout as a function of the resistance r0. (b)suppose the resistance r0 has an initial value of 16ω, and that r0 is then changed to a value of 32ω. what is the change in power supplied by each of the independent sources in the circuit when r0 is changed from 16 ω to 32 ω? (c)use superposition to determine the contribution of each independent source to the current flowing across the 2ω resistor located between the 4a and 12v sources (in the direction indicated by the arrow).

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

Explain vector addition, triangle method and parallelogram method

Automobile fuel efficiency is often measured in miles that the car can be driven per gallon of fuel (mpg). heavier cars tend to have lower fuel efficiencies (lower mpg ratings). which variable (weight or fuel efficiency) is most naturally considered the explanatory (predictor) variable in this context?