3. A man 5 feet tall walks at a rate of 4 ft/sec directly away from a street light which is 20 feet above the street. At what rate is the length of his shadow changing? Is the length increasing or decreasing?
3. A man 5 feet tall walks at a rate of 4 ft/sec directly away from a street light which is 20 feet above the street. At what rate is the length of his shadow changing? Is the length increasing or decreasing?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
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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pls help! Also write out the answers. pls do not type
Transcribed Image Text:**3.** A man 5 feet tall walks at a rate of 4 ft/sec directly away from a streetlight which is 20 feet above the street. At what rate is the length of his shadow changing? Is the length increasing or decreasing?
**4.** A train, starting at 11 am, travels east at 45 mph. Another train starts at noon from the same point, traveling south at 60 mph. How fast are the trains separating at 3 pm?
![**Transcription for Educational Website:**
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**1. Find the derivatives of the following functions.**
*Hint: Use logarithmic differentiation (take the natural log of both sides to start), then use implicit differentiation and solve for \( \frac{dy}{dx} \). Substitute in as necessary to reach an answer that only contains the variable \( x \).*
a) \[ y = (x^2 - 1)^{\ln x} \]
b) \[ y = x^{\log_2 x} \]
---
**2. Problem:**
The radius of a right circular cylinder is increasing at a rate of 2 inches/min and the height is decreasing at a rate of 3 inches/min. At what rate is the volume changing when the radius is 8 inches and the height is 12 inches? Is the volume increasing or decreasing?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d5a0c75-4732-4f7d-8b72-1075593f79d9%2F0c7d0a98-ffda-4be0-b8c6-600d6c470c8f%2Fjv09xe_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website:**
---
**1. Find the derivatives of the following functions.**
*Hint: Use logarithmic differentiation (take the natural log of both sides to start), then use implicit differentiation and solve for \( \frac{dy}{dx} \). Substitute in as necessary to reach an answer that only contains the variable \( x \).*
a) \[ y = (x^2 - 1)^{\ln x} \]
b) \[ y = x^{\log_2 x} \]
---
**2. Problem:**
The radius of a right circular cylinder is increasing at a rate of 2 inches/min and the height is decreasing at a rate of 3 inches/min. At what rate is the volume changing when the radius is 8 inches and the height is 12 inches? Is the volume increasing or decreasing?
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