Given an LRC-series circuit where the inductance is ½ henry, the resistance is 10ohms, the capacitance is 1/100 farad, and the electromotive force is E(t)=150V. If q(0)=1C and i(0)=0A, find the charge on the capacitor, q(t) and the current, i(t).

Suppose an RL circuit with a 1102 resistor and a 6H inductor is driven by the voltage E(t) = est V. If the initial resistor current is I(0) = 0A, find the current I, the voltages across the inductor E and the resistor ER in terms of time t. A I(t) = = ER(t) EL(t) = = V V

You are told E(X) = 4, V(X) = 10, E(Y) = 6, V(Y) = 20 and cov(X, Y) = −3. Calculate V(8X-5Y) (1 decimal place) Answer:

I. The daily temparature high can be modelled by the formula T(t) = 57.5 22.5 cos(2πt) where T is measured in degrees Farenheit and t measures the fraction of the year that has elapsed since January 1. 1. Find the average annual daily temparature high. 2. Find the value of t for which the average is attained.