(1 point) The graph of f(t) is given in the figure. Represent f(t) using a combination of Heaviside step functions. Use h(t - a) for the Heaviside function shifted a units horizontally. f(t) =

The Heaviside function H is defined by H(t) = { 0 1 . It is used in the study of electric circuits to represent the sudden surge of electric current, or voltage, when a switch is instantaneously turned on. (a) Sketch the graph of the Heaviside function. (b) Sketch the graph of the voltage V(t) in a circuit if the switch is turned on at time t = 0 and 120 volts are applied instantaneously to the circuit. Write a formula for V(t) in terms of H(t) . (c) Sketch the graph of the voltage V

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Valve Type Primary Function Common Applications in Petroleum Industry Gate Valve On/Off Isolation Used where straight-line flow and minimum restriction are needed. Common in wellheads, pipelines, and tank farms. Not for flow regulation. Ball Valve Quick On/Off Isolation Excellent shut-off capability. Used in offshore platforms, pipeline scraper traps (launchers/receivers), and fuel handling systems. Fire-safe designs are critical. Globe Valve Flow Regulation / Throttling Precisely controls flow

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