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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!

Several calculus-related problems involving rates of change for a rectangle, ladder, kite, balloon, and dinghy.

Explore a series of calculus-related problems involving rates of change for different shapes and situations. This includes finding the rate of change of area, perimeter, and diagonal for a rectangle, the rate at which a kite string is let out, and more. Suitable for students in Grades 11-12 studying calculus.

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