The image contains several calculus-related problems involving rates of change. Here's a breakdown and outline of the types of problems present:

1. Problem 1: Rates of Change for a Rectangle

   • A rectangle's length is increasing at a certain rate, while its width is decreasing at a different rate. We need to find how the area, perimeter, and diagonals of the rectangle change over time.
   • Given values:
     • $\frac{dL}{dt} = 4 \, \text{cm/sec}$ (rate of change of length)
     • $\frac{dW}{dt} = -1 \, \text{cm/sec}$ (rate of change of width)
     • $L = 17 \, \text{cm}$
     • $W = 24 \, \text{cm}$

2. Problem 2: Ladder Problem

   • A ladder is sliding down a wall at a constant rate. The question involves determining the rate of change of the height of the ladder as the distance from the wall increases.
   • Given:
     • The ladder is 17 ft long.
     • The ladder is moving away at 5 ft/sec.
     • At some point, the base is 8 ft away from the wall.

3. Problem 3: Kite Problem

   • A kite is flying at a certain height and moving horizontally. We need to find the rate at which the string must be let out as the kite moves away.
   • Given:
     • The kite is at a height of 60 ft.
     • The horizontal velocity of the kite is 3/4 ft/sec.
     • The kite is 170 ft away from the child.

4. Problem 4: Balloon Problem

   • A balloon is inflating at a constant rate, and we need to find the rate at which the radius and surface area are changing.
   • Given:
     • The rate of volume change is 180 ft³/min.
     • The radius is 3 ft at a certain instant.

5. Problem 5: Dinghy Problem

   • A dinghy is being pulled toward a dock, and the question involves calculating the rate at which the distance between the dinghy and the dock is decreasing.
   • Given:
     • The rope is being pulled at 3 ft/sec.
     • The boat is 8 ft away from the dock.

I'll start solving these one by one. Let me know if you'd prefer a specific one first or if I should proceed with all of them in sequence!