Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of θ (Figure 8). Suppose that Matthew runs with velocity v_a meters per second and Jessica with velocity v_b meters per second. Let ƒ(x, y) be the distance from Matthew to Jessica when Matthew is x meters from P and Jessica is y meters from P.

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(a) Show that f (x, y) = x + y 2xy cos 0. (b) Assume that 0 = 7/3. Use the Chain Rule to determine the rate at which the distance between Matthew and Jessica is changing when x = 30, y = 20, va = 4 m/s, and vb 3 m/s. = A 'a X P A y vb B