Acamera lens used for taking close-up photographs has a focal length f. the farthest the lens can be placed from the film is do. a) write an expression for the shortest distance at which this camera can be positioned from an object and still have it in focus. b) what formula gives the magnification of the closest possible object?

Agraduated cylinder contains 63.0 ml of water. a piece of gold, which has a density of 19.3 g/ cm3, is added to the water and the volume goes up to 64.5 ml. calculate the mass in grams of the gold that was added to the water. explain how you got your answer.

In the circuit, the switch s has been open for a long time and r = 125 kohm. it is then suddenly closed. (a) determine the time constant before the switch is closed. s (b) determine the time constant after the switch is closed. _ s (c) let the switch be closed at t = 0. find the current in the switch as a function of time. (use t for time. express your answer in milliamps and seconds.) i(t) =_

Uranium has two naturally occurring isotopes. 238u has a natural abundance of 99.3% and 235u has an abundance of 0.7%. it is the rarer 235u that is needed for nuclear reactors. the isotopes are separated by forming uranium hexafluoride uf6, which is a gas, then allowing it to diffuse through a series of porous membranes. 235uf6 has a slightly larger rms speed than 238uf6 and diffuses slightly faster. many repetitions of this procedure gradually separate the two isotopes. what is the ratio of the rms speed of 235uf6 to that of 238uf6? express your answer to five significant figures.