Newton’s law of cooling states that dx dt = −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 = a0 cos(ωt) for some constants a0 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?

Around faucet handle is part of a(n) a. lever b. screw c. inclined plane d. wheel and axle

Agroup of students is studying convection currents. they fill two identical balloons with the same amount of helium. one balloon is placed in a freezer and the other in an area with warm air. after 10 minutes, the balloons are released from a height of 1 meter. which of the following do the students most likely observe? question 2 options: the balloons rise at the same rate. both balloons are the same size. the ballons both rise. the cold ballon is larger than the warm balloon. the cold balloon expands and rises. the warm balloon shrinks and sinks. the warm balloon expands and rises. the cold balloon shrinks and sinks.

Apair of 10μf capacitors in a high-power laser are charged to 1.7 kv.a. what charge is stored in each capacitor? b. how much energy is stored in each capacitor?