Nana has a water purifier that filters 1/3 of the contaminants each hour. She used it to purify water that had 1/2 kilogram of contaminants.
Write a function that gives the remaining amount of contaminants in kilograms, t hours after Nana started purifying the water.

Aswimming pool has an input pump for filling the pool and an output pump for emptying the pool. the input pump can fill the pool in 3 hours, and the output pump can drain the pool in 5 hours. as you go to bed, the pool is full, but a neighbor’s kid turns on the output pump. at midnight, you awake to find the pool half empty. immediately, you turn on the input pump, but you are sleepy and forget to turn off the output pump. at what time will the pool become full?

The base of a triangle exceeds the height by 9 inches. if the area is 180 square inches, find the length of the base and the height of the triangle.

Through non-collinear points there is exactly one plane.