Newton's law of cooling states that d x d t = − k ( x − a ) where x is the temperature, t is time, a is the ambient temperature, and k > 0 is a constant. suppose that a = a 0 cos ( ω t ) for some constants a 0 and ω . that is, the ambient temperature oscillates (for example night and day temperatures). a) find the general solution. b) in the long term, will the initial conditions make much of a difference? why or why not?

Which levels of government establish and implement educational requirements for minors

The magnitude of the magnetic field at a certain distance from a long, straight conductor is represented by b. what is the magnitude of the magnetic field at twice the distance from the conductor? a. at twice the distance, the magnitude of the field is 4b. b. at twice the distance, the magnitude of the field is 2b. c. at twice the distance, the magnitude of the field is b/2.d. at twice the distance, the magnitude of the field is b/4.e. at twice the distance, the magnitude of the field remains equal to b.

Use the ratio form of kepler’s third law, = , and the data provided to determine the time it takes mars to orbit the sun. round your answer to the nearest tenth. earth’s orbital period = 1.0 earth year earth’s distance from the sun = 1.0 au mars’s distance from the sun = 1.5 au it takes mars about ⇒ 1.8 earth years to orbit the sun.