A machine makes 3 items in 5 minutes. Find its rate of production per minute.

Find the rate at which the area of an equilateral triangle is increasing if each side is 12cm long and is increasing at the rate of sqrt3 cm per minute.

A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 minutes, the rate becomes 1250 disintegration per minute. Then its decay constant (per minute) is