A rotating light is located 19 feet from a wall. The light completes one rotation every 3 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 5 degrees from perpendicular to the wall. wall T light Answer is itive luo Q feet per second
A rotating light is located 19 feet from a wall. The light completes one rotation every 3 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 5 degrees from perpendicular to the wall. wall T light Answer is itive luo Q feet per second
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A rotating light is located 19 feet from a wall. The light completes one rotation every 3 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light’s angle is 5 degrees from perpendicular to the wall.
The diagram illustrates a right triangle formed by the wall, the path of the light, and the beam itself. The light is positioned at a point below the wall and emits a beam that strikes the wall. The diagram depicts the following:
- A horizontal line labeled "wall."
- A point labeled "light" below the wall.
- A line connecting the "light" to the "wall," representing the perpendicular distance.
- An angle is formed between the perpendicular line and the light beam when the light is 5 degrees from perpendicular.
___ feet per second
Answer is a positive value.
![**Problem Statement:**
Gravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 21 feet high?
**Mathematical Formulation:**
Recall that the volume of a right circular cone with height \( h \) and radius of the base \( r \) is given by:
\[ V = \frac{1}{3} \pi r^2 h \]
**Objective:**
- Determine the rate at which the height of the pile \( h \) is increasing, expressed in feet per minute, when the pile is 21 feet high.
**Solution Steps:**
- Fill in the calculation or understanding required to solve for the rate of increase in height of the cone-shaped gravel pile.
- Enter the answer in the provided box, expressed in feet per minute (\( \frac{\text{ft}}{\text{min}} \)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6bcd37a4-c8e2-4f55-9647-5bd55a68f1a0%2F21a3c87b-6374-422a-bd65-354d5d8909bd%2Fbnxbypj_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Gravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 21 feet high?
**Mathematical Formulation:**
Recall that the volume of a right circular cone with height \( h \) and radius of the base \( r \) is given by:
\[ V = \frac{1}{3} \pi r^2 h \]
**Objective:**
- Determine the rate at which the height of the pile \( h \) is increasing, expressed in feet per minute, when the pile is 21 feet high.
**Solution Steps:**
- Fill in the calculation or understanding required to solve for the rate of increase in height of the cone-shaped gravel pile.
- Enter the answer in the provided box, expressed in feet per minute (\( \frac{\text{ft}}{\text{min}} \)).
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