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),

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Mathematics

Joy Greer

Today, 18:14

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),

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Jameson · Answer 1

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.