# The pressure, P, (inlbs/ft^2) in a pipe varies over time. Five thimes anhour, the pressure oscillates from a low of 90 to a high of230 and then back down to 90. The pressure at t = 0 is 90. a) graph P = f(t) where t is time inminutes. label axes. b) find a possible formulatfor P= f(t) c) by graphing P = f(t) for 0 (isless than or equal to) t ( less than or equal to) 2, estimate whenthe pressure first equals 115 lbs/ft^2

The pressure, $P,\left(inlbs/f{t}^{2}\right)$ in a pipe varies over time. Five thimes anhour, the pressure oscillates from a low of 90 to a high of230 and then back down to 90. The pressure at t = 0 is 90.
a) graph P = f(t) where t is time inminutes. label axes.
b) find a possible formulatfor P= f(t)
c) by graphing P = f(t) for 0 (isless than or equal to) t ( less than or equal to) 2, estimate whenthe pressure first equals $115lbs/f{t}^{2}$
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gardapati5u
Firstly, You should use a sin graph because of the oscillations.The function should be in the form $f\left(t\right)=a\mathrm{cos}\left(\left(2\pi /b\right)t\right)+C$
Since your graph is increasing it must be -a because normally a cosgraph is at its max at 0 and not its min.
a is the amplitude ( this is the difference between the max and themin divided by 2)
b is the frequency( the number of times the graph repeats itselfwithin $2\pi$) $=10\pi$
$2\pi /b$ equals the frequency (that is the cycle in which the graphrepeats itself)(since you said 5 times at t = 1, the period is.2)
c is the vertical shift. (in this case it would be 90 sincenormally it would be 0 but the graph has been shifted 90 up) t is the time
$f\left(t\right)=-70\mathrm{cos}\left(.2t\right)+90$