When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to CA,V 2gh, where c (0 0. The radius of the hole is 4 in., g = 32 ft/s?, and the friction/contraction factor is c = 0.6. (Assume the removed apex of the cone is of negligible height and volume.) 125 dh ft/s dt 24h

Empirical evidence suggests that the volume V (measured in liters) of a kangaroo's pouch depends on its body weight W (measured in kilograms) according to the formula dV 0.2 dW A'reasonable model for the weight of a kangaroo depending on its height H (measured in m) is W 20 H? Suppose that over the course of 4 years, a kangaroo has grown at a constant rate from 1 m to 2 m. Determine the rate of change of the volume of its pouch with respect to time (measured in liters per year) when its height was 1.3 m. Note: You may round your answer. Please specify at least 3 digits behind the decimal place. So your solution should be accurate up to ±0.001. Answer: liters/year

please show full work and calculations

An ant colony explores an area enclosed by a circle centered at its nest. This area (and the circle containing it) expands as they have time to explore. Due to the need for ants to return to the colony periodically, as the radius expands, the change in the radius of the area explored with respect to time slows down. Specifically, if r is the radius of the area the ants have explored in meters, then = 3 m/day. Find the rate of change of the area explored by the ants 4 in m2/day when the radius of the area explored is 3m. dt