Sketch the situation if necessary and use related rates to solve. A 6 ft tall person walks away from a 10 ft lamppost at a constant rate of 5 ft/s. What is the rate (in ft/s) that the tip of the shadow moves away from the pole when the person is 15 ft away from the pole? 10 ft F ft/s ·15 ft 6 ft What is the rate (in ft/s) at which the tip of the shadow moves away from the person when the person is 15 ft from the pole? O Draw and label a diagram to help solve the related-rates problem. } The side of a cube increases at a rate of m/s. Find the rate (in m³/s) at which the volume of the cube increases when the side of the cube is 8 m. 6 A conical tank has height 3 m and radius 2 m at the top. Water flows in at a rate of 1.9 m³/min. How fast is the water level rising when it is 1.1 m from the bottom of the tank? (Round your answer to three decimal places.)

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Related Rates Problems**

**Problem 1: Shadow Movement**

A 6 ft tall person walks away from a 10 ft lamppost at a constant rate of 5 ft/s. Determine the rate (in ft/s) at which the tip of the shadow moves away from the pole when the person is 15 ft away from the pole.

- **Diagram Explanation**: 
  - A vertical lamppost is shown with a height of 10 ft.
  - A person, 6 ft tall, walks away from the base of the lamppost.
  - The distance from the lamppost to the person is labeled as 15 ft.
  - There is a shadow extending from the person's feet to the ground, outlining a right triangle with the lamppost.

**Question**: What is the rate at which the tip of the shadow moves away from the person when the person is 15 ft from the pole?

**Related Problem**
- **Problem 2: Cube Volume Increase** 
  - The side of a cube increases at a rate of \( \frac{1}{6} \) m/s. Find the rate (in m³/s) at which the volume of the cube increases when the side of the cube is 8 m.

**Problem 3: Conical Tank Water Level**

A conical tank has a height of 3 m and a radius of 2 m at the top. Water flows in at a rate of 1.9 m³/min. Determine how fast the water level is rising when it is 1.1 m from the bottom of the tank. (Round your answer to three decimal places.)
Transcribed Image Text:**Related Rates Problems** **Problem 1: Shadow Movement** A 6 ft tall person walks away from a 10 ft lamppost at a constant rate of 5 ft/s. Determine the rate (in ft/s) at which the tip of the shadow moves away from the pole when the person is 15 ft away from the pole. - **Diagram Explanation**: - A vertical lamppost is shown with a height of 10 ft. - A person, 6 ft tall, walks away from the base of the lamppost. - The distance from the lamppost to the person is labeled as 15 ft. - There is a shadow extending from the person's feet to the ground, outlining a right triangle with the lamppost. **Question**: What is the rate at which the tip of the shadow moves away from the person when the person is 15 ft from the pole? **Related Problem** - **Problem 2: Cube Volume Increase** - The side of a cube increases at a rate of \( \frac{1}{6} \) m/s. Find the rate (in m³/s) at which the volume of the cube increases when the side of the cube is 8 m. **Problem 3: Conical Tank Water Level** A conical tank has a height of 3 m and a radius of 2 m at the top. Water flows in at a rate of 1.9 m³/min. Determine how fast the water level is rising when it is 1.1 m from the bottom of the tank. (Round your answer to three decimal places.)
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