A particle is moving along the hyperbola 932 3/2 = 1 with the parametric function *y(t) = (cosh(t)7 sinh(t)) for t e ( 1, 1) a) Determine the time t when the density of the particle is maximized. b) Find the tangent vector to the path of the particle at the time t determined in part (a). c) Calculate the rate of change of the density of the particle at the time t obtained in part (a). Problem 5. A runner is following the path of a hyperbola given by 'y = (cosh(0 t), sinh(cxt)) in a field with a temperature distribution represented by T(ac, y) = 3067:5277}? Let's assume that the runner is wearing a wristwatch with markings ranging from T = 0 to T = 30. Find the angular velocity function of the watch's hand in terms of a. Create a plot depicting the angular velocity as a function of time for oz 2 1, 2, within the time interval [2, 2] 12"c .- \ 1:11 PM A . .7 Q Search . . X Cloudy 2023709720 a