Fencing with the length of 840 m surrounds two identical playing fields with a common side. The fields can be side-by-side and separated by a fence, as shown in the figure. Find the dimensions in the maximum area of each field.

Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. how fast is the height of the pile increasing when the pile is 14 ft high? (round your answer to two decimal places.) ft/min

Abowl contained 270 starbursts of all different colors. if the probability of picking a yellow is 1/9, then how many yellow starbursts are in the bowl ? ?

Since we have computer algebra systems that can solve polynomial division problems for us, why is it necessary to learn how to do these things by hand?