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4171950-1905000 A particle starts at point A on the positive x-axis at time t = 0 and travels along the curve from A to B to C to D, as shown tothe right. The coordinates of the position of the particle at timet are given by (x(t), y(t)), where x(t) and y(t) are differentiable functions of time and y't=dydt=-2t2t3-271/3 and x’(t)= dx/dt is not given. Is dx/dt positive at point B? Is dy/dt positive at point B? Give a reason for each answer.Find the value for t at which the particle reaches point C. Justify your answer.What is the y-coordinate of point C? Justify your reasoning.The point (7, 2) lies on the curve, and the line tangent to the curve at that point has the equation y=-23x+203. If, at the point, dx/dt≈1.837, calculate dy/dt. Find the speed at this point.4721444-23648300 The figure to the left shows the initial position of a diver leaping from the edgeof a diving platform into a pool below and her position at a later time. At time t seconds after she leaps, the horizontal distance from the front edge of the platform to the diver’s shoulders is given by x(t), and the vertical distance from the water surface to her shoulders is given by y(t), where x(t) and y(t) are measured in meters. Suppose that the diver’s shoulders are 11.4 metersabove the water when she makes her leap and that dxdt=0.6 anddydt=4.2-9.8t for 0≤t≤A,where A is the time that the diver’s shoulders enter the water. Find A, the time that the diver’s shoulders enter the water.Find the maximum vertical distance from the water surface to the diver’s shoulders.Find the total distance traveled by the diver’s shoulders from the time she leaps from the platform until the time her shoulders enter the water.Find the angle θ, 0<θ<π2, between the path of the diver and the water at the instant the diver’s shoulders enter the water. ................
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