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The system of differential equations dx -0.3x-0.002x²-0.001xy dt dy -0.5y-0.001y2-0.004xy dt is a model for the populations of two species. (a) Does the model describe cooperation, or competition, or a predator-prey relationship? O predator-prey relationship cooperation competition TEACHER (b) Find the equilibrium solutions. (Enter solutions from smallest to largest value of x. If solutions have the same value of x, enter them from smallest to largest y.) (x, y) = 0,0 0,500 (x, y) - 300,0 (*)-(50,150 (x, y) =
The figure below shows a circuit containing an electromotive force, a capacitor with a capacitance of C farads (F), and a resistor with a resistance of R ohms (). The voltage drop across the capacitor is where Q is the charge (in coulombs), so in this case Kirchhoff's law gives RI+2=E(t). But I dQ dt Q(t)= (see this example), so we have dt Suppose the resistance is 5 02, the capacitance is 0.05 F, a battery gives a constant voltage of 40 V, and the initial charge is Q-0.C. 1(t)= + Find the charge Q (in C) at time t. () 2-2e с X Find the current I (in A) at time t. (#)