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If the ratio of sum of the first m and n terms of an ap is m2 : n2 , show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1).

The height of a plant, in inches, p years after planting it is given by the polynomial function r(p) = -2p% + 270p. find the height of the plant when p = 90 years.

Zed is making a centerpiece for his dining room table by putting sand in a cube-shaped vase. the vase is 0.25 meters in length, width, and height. he bought 25 kg of sand. assume the density of dry sand is 1,602 kgm3. what is the volume of the sand that zed purchased? the volume of the sand is approximately m3. enter your answer as the number that correctly fills in the blank in the previous sentence. if necessary, round your answer to six decimal places, like so: 42.536475