y varies inversely with x² and inversely with z. When y = 44, x = 3 and z = 16. What is y when x = 4 and z = 9? O y = 44 O y = 11/36 O y = 36/11 O y = 6336
y varies inversely with x² and inversely with z. When y = 44, x = 3 and z = 16. What is y when x = 4 and z = 9? O y = 44 O y = 11/36 O y = 36/11 O y = 6336
Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Mathematics Problem: Inverse Variation**
In this problem, we're examining how the variable \( y \) changes in response to the variables \( x \) and \( z \). Specifically, \( y \) varies inversely with \( x^2 \) and with \( z \).
Given the conditions:
- When \( y = 44 \), \( x = 3 \), and \( z = 16 \)
We need to find the value of \( y \) when:
- \( x = 4 \) and \( z = 9 \)
### Possible Answers:
- \( \circ \) \( y = 44 \)
- \( \circ \) \( y = \frac{11}{36} \)
- \( \circ \) \( y = \frac{36}{11} \)
- \( \circ \) \( y = 6336 \)
### Steps to Solve:
1. **Determine the constant of inverse variation \( k \)**:
The relationship can be described by the equation \( y = \frac{k}{x^2 \cdot z} \).
2. **Using the given values to find \( k \)**:
\( 44 = \frac{k}{3^2 \cdot 16} \)
\[
44 = \frac{k}{144}
\]
\[
k = 44 \cdot 144 = 6336
\]
3. **Apply the constant \( k \) to the new conditions**:
\[
y = \frac{6336}{(4^2) \cdot 9}
\]
\[
y = \frac{6336}{16 \cdot 9}
\]
\[
y = \frac{6336}{144}
\]
\[
y = 44
\]
Therefore, the correct value of \( y \) is \( 44 \).
This explanation and steps can be followed to solve any similar inverse variation problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F253ec4e6-fefa-47c2-a875-f6d418ff65f8%2F49a5f166-f3c4-4144-8d12-94471c7fe0d6%2Fgyjk0k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Mathematics Problem: Inverse Variation**
In this problem, we're examining how the variable \( y \) changes in response to the variables \( x \) and \( z \). Specifically, \( y \) varies inversely with \( x^2 \) and with \( z \).
Given the conditions:
- When \( y = 44 \), \( x = 3 \), and \( z = 16 \)
We need to find the value of \( y \) when:
- \( x = 4 \) and \( z = 9 \)
### Possible Answers:
- \( \circ \) \( y = 44 \)
- \( \circ \) \( y = \frac{11}{36} \)
- \( \circ \) \( y = \frac{36}{11} \)
- \( \circ \) \( y = 6336 \)
### Steps to Solve:
1. **Determine the constant of inverse variation \( k \)**:
The relationship can be described by the equation \( y = \frac{k}{x^2 \cdot z} \).
2. **Using the given values to find \( k \)**:
\( 44 = \frac{k}{3^2 \cdot 16} \)
\[
44 = \frac{k}{144}
\]
\[
k = 44 \cdot 144 = 6336
\]
3. **Apply the constant \( k \) to the new conditions**:
\[
y = \frac{6336}{(4^2) \cdot 9}
\]
\[
y = \frac{6336}{16 \cdot 9}
\]
\[
y = \frac{6336}{144}
\]
\[
y = 44
\]
Therefore, the correct value of \( y \) is \( 44 \).
This explanation and steps can be followed to solve any similar inverse variation problems.
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