Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Problem Statement:**
If \( y \) varies inversely as \( x \), and \( y = 10 \) when \( x = 6 \), find \( y \) when \( x = 9 \).
---
**Solution:**
Since \( y \) varies inversely as \( x \), we have:
\[ y = \frac{k}{x} \]
where \( k \) is a constant.
Given:
\[ y = 10 \quad \text{when} \quad x = 6 \]
Substitute these values into the equation to find \( k \):
\[ 10 = \frac{k}{6} \]
Solve for \( k \):
\[ k = 10 \times 6 \]
\[ k = 60 \]
Now, use the value of \( k \) to find \( y \) when \( x = 9 \):
\[ y = \frac{60}{x} \]
Substitute \( x = 9 \):
\[ y = \frac{60}{9} \]
Simplify the expression:
\[ y = \frac{20}{3} \]
Therefore, when \( x = 9 \), \( y = \frac{20}{3} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12400ac6-d36f-4dfb-a291-490b1b5697d1%2F36652138-dee5-4f5e-ab5d-910160bcfaa8%2F08g45mm_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
If \( y \) varies inversely as \( x \), and \( y = 10 \) when \( x = 6 \), find \( y \) when \( x = 9 \).
---
**Solution:**
Since \( y \) varies inversely as \( x \), we have:
\[ y = \frac{k}{x} \]
where \( k \) is a constant.
Given:
\[ y = 10 \quad \text{when} \quad x = 6 \]
Substitute these values into the equation to find \( k \):
\[ 10 = \frac{k}{6} \]
Solve for \( k \):
\[ k = 10 \times 6 \]
\[ k = 60 \]
Now, use the value of \( k \) to find \( y \) when \( x = 9 \):
\[ y = \frac{60}{x} \]
Substitute \( x = 9 \):
\[ y = \frac{60}{9} \]
Simplify the expression:
\[ y = \frac{20}{3} \]
Therefore, when \( x = 9 \), \( y = \frac{20}{3} \).
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