A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 5 fl from the house, the base is moving away at the rate of 24 it/sec. 13-At ladder a. What is the rate of change of the height of the top of the ladder? b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then? C. At what rate is the angle between the ladder and the ground changing then?The coordinates of a particle in the metric xy-plane are differentiable functions of time t with dx dy dt = - 4 m/sec and = - 3 m/sec. How fast is the particle's distance from the origin changing as it passes through the point (8,6)?On a morning of a day when the sun will pass directly overhead= the shadow of a 7"211 building on level ground is 21 it long. At the moment in question: the angle B the sun makes with the ground is increasing at the rate of 0.2?Oi'min. At what rate is the shadow decreasing? Remember to use radians in your calculations. Express 1.rour answer in inches per minute. A spherical iron ball 12 in. in diameter is coated with a layer of ice of uniform thickness. If the ice melts at a rate of 10 in. /min, how fast is the thickness of the ice decreasing when it is 5 in. thick? How fast is the outer surface area of ice decreasing