The answers are K=73.333 and L=146.67 Ibs, can you explain to me how to get there?

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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The answers are K=73.333 and L=146.67 Ibs, can you explain to me how to get there?

**Problem Statement:**

The maximum load (\(L\)) that a horizontal beam can carry is directly proportional to its width (\(W\)). If a beam 3.0 inches wide can support a maximum load of 220 lbs, find the load that a beam (of the same type of material) can support if its width is 2.0 inches wide. 

**Question:**
What is the constant of variation?

**Solution Approach:**

1. The relationship between the load and the width of the beam is given by:
   \[
   L = k \cdot W
   \]
   where \(k\) is the constant of variation.

2. With the given information for a 3.0-inch wide beam supporting a 220 lbs load, solve for \(k\).

3. Use the value of \(k\) to find the load for a beam that is 2.0 inches wide.
Transcribed Image Text:**Problem Statement:** The maximum load (\(L\)) that a horizontal beam can carry is directly proportional to its width (\(W\)). If a beam 3.0 inches wide can support a maximum load of 220 lbs, find the load that a beam (of the same type of material) can support if its width is 2.0 inches wide. **Question:** What is the constant of variation? **Solution Approach:** 1. The relationship between the load and the width of the beam is given by: \[ L = k \cdot W \] where \(k\) is the constant of variation. 2. With the given information for a 3.0-inch wide beam supporting a 220 lbs load, solve for \(k\). 3. Use the value of \(k\) to find the load for a beam that is 2.0 inches wide.
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