The pressure p (in pounds per square foot), in a pipe varies over time. ten times an hour, the pressure oscillates from a low of 40 to a high of 280 and then back to a low of 40. the pressure at time t = 0 is 40. let the function p = f(t) denote the pressure in pipe at time t minutes. find the formula for the function p=f(t),

Pressure oscillating ten times every hour. So period n = 6 min. So the negative cos is represented in the graph and since it datrt at time 0, P = f(t) = Acos(Bt) + D Amplitude A = (Ph - Pl) / 2 = (280 - 40) / 2 = 240 / 2 = 120 Period B = 2xpi / 6 = pi /3 D = (Ph + Pl) / 2 = (280 + 40) / 2 = 320 / 2 = 160 Subtituting the equation we get f(t) = 120cos (pi x t ) / 3 + 160.

Ican't do any of the other stuff, but i can get you started. the answer, i believe, is $2.50.