Ella wants to replace old bulbs of her home with new LED bulbs. She buys LED bulb that has inbuilt AC to DC converter of output 5 v and 2.5 A. If the LED is 75% efficient, what would be power dissipated? Also find work done by LED when it is connected to power supply and left for 1 hr 15 minutes?​

Given the position vector of the particle r(t)=(t+1)i+(t^2−1)j+2t k, find the particle's velocity and acceleration vectors at t=1

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)

At an oceanside nuclear power plant, seawater is used as part of the cooling system. this raises the temperature of the water that is discharged back into the ocean. the amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25° c. what is the standard deviation of the temperature increase?