# Need calculus help with Applications of Derivatives

**Question description**

1.) One train travels east at 180 mph towards Christmas Town, while a second train travels south at 130 mph away from Christmas Town. At time t = 0, the first train is 50 miles west and the second train is 30 miles south. Find the rate at which the distance between the trains is changing at time t = 40 minutes.

2.) Water pours into a conical tank of height 7 ft and radius 4 ft at a rate of 1.3 ft^{3}/min. How fast is the water level rising when it is 4 ft high?

3.) Farmer Kenny has a fence of length 22 ft. Kenny wants to create the biggest grazing area possible. What is the maximal area of the grazing area?

4.) A box is constructed out of two different materials. The material for the top and bottom (both square pieces) cost $2/ft^{2} and the material for the sides costs $4/ft^{2}. Find the dimensions that minimize the cost if the box has a volume of 120 ft^{3}

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